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6c0c41b9c9df59e13b90df7f3a24ac67668d3258	{ "olmocr-version": "0.1.59", "pdf-total-pages": 24, "total-fallback-pages": 0, "total-input-tokens": 72195, "total-output-tokens": 22212, "fieldofstudy": [ "Engineering" ] }	A New Polyvinylidene Fluoride Membrane Synthesized by Integrating of Powdered Activated Carbon for Treatment of Stabilized Leachate Salahaldin M. A. Abuabdou 1, Zeeshan Haider Jaffari 2, Choon-Aun Ng 1, Yeek-Chia Ho 3,* and Mohammed J. K. Bashir 1,* 1 Department of Environmental Engineering, Engineering and Green Technology Faculty, Universiti Tunku Abdul Rahman, Kampar 31900, Malaysia; [email protected] (S.M.A.A.); [email protected] (C.-A.N.) 2 Department of Environmental Engineering and Management, Chaoyang University of Technology, No. 168, Jifeng E. Rd, Wufeng District, Taichung 413310, Taiwan; [email protected] 3 Centre of Urban Resource Sustainability, Department of Civil and Environmental Engineering, Institute of Self-Sustainable Building, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia * Correspondence: [email protected] (Y.-C.H.); [email protected] (M.J.K.B.); Tel.: +60-5-4688888 (ext. 4559) (M.J.K.B.); Fax: +60-5-466-7449 (M.J.K.B.) Abstract: Stabilized landfill leachate contains a wide variety of highly concentrated non-biodegradable organics, which are extremely toxic to the environment. Though numerous techniques have been developed for leachate treatment, advanced membrane filtration is one of the most environmentally friendly methods to purify wastewater effectively. In the current study, a novel polymeric membrane was produced by integrating powdered activated carbon (PAC) on polyvinylidene fluoride (PVDF) to synthesize a thin membrane using the phase inversion method. The membrane design was optimized using response surface methodology (RSM). The fabricated membrane was effectively applied for the filtration of stabilized leachate using a cross-flow ring (CFR) test. The findings suggested that the filtration properties of fabricated membrane were effectively enhanced through the incorporation of PAC. The optimum removal efficiencies by the fabricated membrane (14.9 wt.% PVDF, 1.0 wt.% PAC) were 35.34, 48.71, and 22.00% for COD, colour and NH$_3$-N, respectively. Water flux and transmembrane pressure were also enhanced by the incorporated PAC and recorded 61.0 L/m$^2$·h and 0.67 bar, respectively, under the conditions of the optimum removal efficiency. Moreover, the performance of fabricated membranes in terms of pollutant removal, pure water permeation, and different morphological characteristics were systematically analyzed. Despite the limited achievement, which might be improved by the addition of a hydrophilic additive, the study offers an efficient way to fabricate PVDF-PAC membrane and to optimize its treatability through the RSM tool. Keywords: stabilized leachate; membrane fabrication; filtration technology; phase inversion technique; powdered activated carbon (PAC) 1. Introduction Sanitary landfills are the widely applied technique to tackle municipal solid waste (MSW). Inappropriately, the majority of these landfills do not fulfill the normal discharged limits [1]. In developing countries such as Malaysia, more than 80% of the MSW produced was received by open duping and landfill sites [2]. This resulted in the generation of highly contaminated leachate, which is the liquid generated due to the precipitation above these solid litters and could be toxic to the surrounding environment. This leachate could contaminate the sources of fresh water if not carefully treated before discharging to the environment [3]. Stabilized leachate, which is more than ten years old, has lower BOD$_5$/COD ratio. Thus, it is almost impossible to treat this kind of leachate using some biological treatment technique [4]. To date, various purification techniques such as adsorption [5], coagulation [6], advanced oxidation [7], electro-Fenton [8], and combinations of these processes [9,10] have been successfully introduced to eliminate the organic contaminants from stabilized leachate. Among these techniques, membrane filtration could be one of the most suitable purification process [11]. The membranes acted as a selective barrier to achieve the objective of separation and purification. Nonetheless, there are still some shortcomings in membrane technology such as membrane fouling upon the higher contaminant concentration [12]. Fouling could affect the separation efficiency as well as permeability of membrane, which are the vital factors in the membrane filtration [13]. Several strategies, including pre-treatment of feed [14], optimization of operating parameters [15], selection and modification of membrane [16], hydraulic flushing [17], and applied field enhancement [18], have been performed to alleviate membrane fouling and water flux rate. Under different circumstances, the workability of membrane can be improved through the membrane characteristics and performance of treatment process. Hence, investigation of membrane characterization can be separated into four groups: membrane activity (permeability, surface wettability, average pore size, and porosity); morphological characterization (surface chemistry and roughness, and external and internal membrane texture); treatment efficiency (separation performance); and antifouling evaluation (pore size decrease and cake formation) [19]. Synthetic polymers such as polypropylene (PP), polyvinylidene fluoride (PVDF), and polysulfone (PS) are commonly applied in the membrane fabrication due to their higher flux, antifouling ability, and separation efficiency [20]. Among all these synthetic polymers, PVDF polymer proved to be an ideal membrane fabrication material due its durability [21], good thermal stability and higher chemical resistance [22]. Additionally, the PVDF polymer can also help to extend the membrane life, as well as reduce the damage caused by the concentrated pollutants [23]. However, the PVDF membranes antifouling capability could be enhanced due to its hydrophobic nature [24]. Many researchers have successfully applied dry–wet phase inversion technique to boost their membrane performance [25]. For instance, Zhou et al. [26] developed an ultrafiltration PVDF membrane using nanoparticles of titanium dioxide (TiO$_2$) and polyvinylpyrrolidone (PVP) as blended additives to increase the fouling resistance and water permeability. The addition of PVP-TiO$_2$ increases the average pore size and porosity of membrane, leading to the higher flux and hydrophilicity of membrane with more than 91.4% removal performance against sulfonamide antibiotics water. Moreover, polyethylene glycol and poly(acrylic acid) were also applied in the fabrication of membrane through chemical reaction with a key focus of enhancing hydrophilicity. Their batch filtration experiments clearly exhibit an increase in critical flux and a declined fouling rate. Similarly, various reports have presented effective ways to boost the antifouling abilities of PVA-based membranes due to their hydrophilic properties [27,28]. Recently, the incorporation of activated carbon (AC) on the surface of the membrane has proven to be an effective way to boost the membrane rejection performance [29]. The utilization of AC in membrane is a relatively new technology for the elimination of organic contaminates for wastewater, which not only enhances the adsorption capacity of AC, but also improves the particle removal capabilities of membrane [30]. To date, there are quite a number of studies which clearly demonstrate that the usage of PAC can significantly improve the filterability of membranes [13]. However, evaluation of PAC addition into PVDF flat sheet membranes with different concentrations, in terms of their treatment efficiency and productivity, has not been investigated. Therefore, the current study was performed to observe the potential of incorporating PAC, for the first time, into the PVDF polymeric membrane for stabilized landfill leachate purification. Furthermore, fabricated membrane was optimized using RSM technique, and the membrane properties and morphologies were systematically characterized. 2. Materials and Methods 2.1. Collection of Leachate Leachate sample was taken from Sahom landfill site located in Perak, Malaysia, which is an operative landfill site with a daily production of 100 tonnes of MSW in average [31]. After collection of leachate sample, it was stored in a refrigerator at 4 °C. Initial leachate characterization was performed using standardized methods of water and wastewater [32]. All measurements, including dissolved oxygen (DO), colour, chemical oxygen demand (COD), 5-day biochemical oxygen demand (BOD₅), and ammoniacal nitrogen (NH₃-N), were undertaken in triplicate. 2.2. Materials The PVDF polymer (Kynar®740) was purchased from Afza Maju trading (Terengganu, Malaysia), and utilized after drying for 24 h at 70 °C. 1-Methyl-2-pyrrolidone (NMP, 99.5%) was purchased from Sigma–Aldrich. Methanol, (99.8%) was supplied by Chem Soln. Ultra-pure distilled water (DI) was utilized throughout the experiments. PAC was purchased from R&M Chemicals. The AC was charcoal-based, and consists of sulfide, chloride, calcium, sulphate, iron, lead, zinc, and copper. This PAC density was 1.8–2.1 kg/m³ with pH (4–7). Particle size analysis (PSA) and field emission scanning electron microscopy (FESEM) tests were used to investigate the distribution and the size of PAC particles, respectively. All these chemical materials were of analytical grade, and used without additional treatment. 2.3. Experiment’s Design and Optimization Process Central Composite Design (CCD) is the design method used in response surface methodology (RSM) for the membrane fabrication’s experimental design [33]. Both CCD and RSM were run by version 8 from the Design Expert. For membrane dope solution design, two factors, the polymer (PVDF) weightage and the additive (PAC) weightage, were set into the CCD. Based on preliminary experiments and the extensive literature [34,35], the total mass of fabricated membrane dope was fixed at 100 g, which represents 100% of the dope weight, thus each 1 g of the dope element is equivalent to 1% weightage. The dosage of the PVDF was set within the range of 10 g to 18 g, and the amount of PAC was set within the range of 0 g to 2 g. Regarding the CCD, the alpha value was selected to be 1.0, and thus the centre points were 14.0 and 1.0 wt.% for the polymer content and additive content, respectively. The rest of the dope weight (to complete 100 g) is the NMP solvent. The total concentration of PVDF/PAC was kept at 20% (as maximum) and 10% (as minimum), as concentration higher than 20% resulted in solutions of extremely high viscosity, and was difficult to be casted on the glass plate, while clumsy, non-thick membrane was the result of using concentration less than 10%. Five responses, which are the removing efficiencies of COD, colour, and NH₃-N, as well as maximum transmembrane pressure (max. TMP), and pure water flux, were also set into the CCD to have the full design of experiments. The influence of various parameters was optimized by RSM using a combination of statistical and numerical techniques. In the current work, nine experiments were reinforced with four replications to assess the pure error [36]. The 13 different membranes were applied in double repetition and have their effluent collected. The quadratic model for every response was investigated by analysis of variances (ANOVA) to identify the results significance, and to find the represented quadratic model after eliminating irrelevant terms. The frontal sign of each model term signifies to either antagonistic or synergistic effect on the response when it is positive or negative, respectively [4]. In RSM, it does mention that Prob > F less than 0.050 indicates model terms are significant, and Prob > F with the values greater than 0.10 indicates model term is not significant. “Not significant”, in the description of lack of fit, is regarded a decent model, as it means the experimental reading is fitting the model [37]. Additionally, a good experimentally fitted data will have a higher coefficient (R²) value. The higher the R² value, the closer the experimental data towards the predicted graph model by the RSM [38,39]. Selection of the best membrane takes into consideration the membrane purification performance. Desirability value closer to 1.0 used to be selected as the ideal design for the data. 2.4. PVDF-PAC Membrane Fabrication 2.4.1. Dope Preparation To produce the polymeric membrane, PVDF and NMP were applied as polymer and solvent, respectively. Figure 1 presents the process used for the dope preparation. Initially, the polymeric PVDF was entirely dissolved in the NMP solvent at a temperature ranging between 60 and 70 °C using a heating mantle (Figure 1a). In order to achieve a better permeate flux of the synthesized membrane, the heating mantle temperature should always be maintained within the above stated range [21]. The dope solution containing dissolved PVDF polymer in the NMP solvent was then infused into a clean Schott bottle. After that, the required amount of PAC was inserted into the dope solution to generate the dope for hybrid membrane. Lastly, the Schott bottle containing the dope solution was placed into a sonicator bath (Cole-Parmer, Vernon Hills, IL, USA) for eight hours to confirm the homogeneous mixing of the additives without any air bubbles raised in the prepared dope [40]. ![Figure 1. PVDF-PAC membrane dope preparation process.](image) 2.4.2. Membrane Casting A semi-automated membrane casting machine (TECH INC, Chennai, India) was applied to synthesize a flat sheet membrane using the dry–wet phase process, as illustrated in Figure 2a. The membrane was produced at temperature 27 °C to 30 °C with an approximate thickness of 60 µm based on literature reports [41,42]. After 60 s of membrane casting above the glass board, it was submerged into a distilled water (DW) basin for 180 s (Figure 2b). As a result, a thin layered polymeric film was generated, which separated from the glass plate. Later, the newly produced membrane was transferred into a DW coagulation bath and remained there for 24 h. Afterwards, a methanol bath was used for 8 h, as shown in Figure 2c, to perform a post-treatment to ensure the excess solvent in the membrane can be removed completely [43]. Finally, the membrane was dried 24 h at the ambient temperature with 60% humidity, as shown in Figure 2d, to be ready to use in the filtration process [13]. 2.5. Membrane Performance and Characterization The produced membranes have been characterized to investigate their treatment efficiencies, fouling, and permeability properties and surface morphologies. To ensure the accuracy of the findings, all of the tests have been duplicated. Each time, a fresh membrane has been utilized to investigate their characteristics and performance. 2.5.1. Treatment Efficiency The membrane filtration performance was investigated using laboratory scale cross-flow filtration setup with a 3.34 cm disc diameter, as exhibited in Figure 3. The membrane rejection capabilities were studied against the treatment of landfill leachate. Before each experiment, initial characterization of leachate was measured to eliminate the small errors which occurred due to the minor changes in organics concentration with time. The steady flux for all individual membranes was acquired by a constant (200 mL/min) flow for 120 min. The volume of permeate, along with the recorded transmembrane pressure, were noted down under the flow of 200 mL/min for different intervals of time (0.5, 1, 2, 5, 10, 20, 40, 90, and 120 min). Final leachate characterizations were evaluated in terms of removing efficiencies for the COD, colour, and NH$_3$-N pollutants using Equation (1): $$\text{Removal efficiency} = \frac{(C_F - C_P)}{C_F} \times 100(\%) \quad (1)$$ where $C_F$ is the contaminant concentration at the feed (mg/L) and $C_P$ is the contaminants concentrations in the permeated solution (mg/L). All contaminants' concentrations were checked using the UV-V spectrophotometer (Hach DR6000, Loveland, CO, USA) in prior and post of filtration practice. 2.5.2. Productivity of Membrane Pure flux plays a dynamic role in the membrane productivity evaluation. Permeability of membrane was investigated through the pure water flux, which was measured via a dead-end filtration apparatus, as illustrated in Figure 4. A metallic ring having 5 mm average pore size and 8.76 cm$^2$ effective permeate area was applied to support the membrane. Initially, the impurities present in the membrane were removed by submerging the membrane in DW for 30 min. Then, a stable flux was achieved by pre-compacting the membrane with N$_2$ gas at a pressure of 30 KPa for 2 min. After 30 min, the permeated water volume was noted at a similar pressure of 30 KPa. The pure water flux can be calculated using the Equation (2): $$J = \frac{V}{A \times t} \quad (L/m^2·h) \quad (2)$$ where $V$ is the permeated pure water volume (L), $A$ is the membrane effective surface area (m$^2$), and $t$ is the time of permeation (h). 2.5.3. Antifouling Valuation Throughout the membrane filtration process, the overall decrease in flux, alongside the improvement of transmembrane pressure, were mainly caused by either membrane fouling, concentration polarization, or a combination of both [44]. Both of these components can be attained from the experimental data using both of the leachate permeate flux and maximum transmembrane pressure (Max. TMP) values which are measured by the cross-flow ring test. Max. TMP was applied to indicate the antifouling ability of fabricated membranes [45]. 2.5.4. Morphological Characteristics It is a well-known fact that the membrane properties and performance are highly dependent on its morphology (pore size, surface texture, and microstructure). Therefore, investigation of membrane morphologies is considered a significant factor in the effectiveness evaluation of the produced membranes. Fourier transform infrared spectroscopy (FTIR, Perkin Elmer Lambda 35, Waltham, MA, USA) was applied to investigate the membrane surfaces chemical compositions. The FTIR spectra ranged between 4000–400 cm$^{-1}$. EDX is a chemical microanalysis method used for quantitative, qualitative, and elemental mapping examination. Octane Silicon Drift Detector (SDD, EADX Inc., Mahwah, NJ, USA) was used at high voltage of 15 kV, using Mn K$_\alpha$ as source of energy. The fabricated PVDF-PAC membranes with different compositions were measured by INCA Energy 400 software (Firmware INCA, Version V1.09R13), along with the image taken by the Quanta FEG 450 instrument. FESEM (Quanta FEG 450, FEI, Hillsboro, OR, USA) was applied to record the cross-sectional and surface morphologies of the fabricated membrane. The cross-sectional morphologies were investigated by fracturing the membranes in liquid nitrogen and immediately cutting them after air drying. FESEM measurement starts by placing the sample on carbon tape, which was attached with the sample stub. The sample was also coated with the platinum nanoparticles in auto fine coater (JFC-1600, SUTD-MIT International Design Centre, Singapore) before performing the analysis. An atomic force microscopy (AFM, Dimension 5000, Bruker AXS, Santa Barbara, CA, USA) was also applied to study the surface morphologies and roughness of the synthesized membranes. Herein, membranes were cut into small square pieces (1 × 1 cm) and pasted on a glass slide. Sample scanning were performed using a probe-optical microscope on tapping mode and images of 10 µm × 10 µm were taken by AFM. The root-mean-square roughness ($R_q$) and average roughness ($R_a$) was applied to measure the surface roughness for each membrane. Porosity of membrane could be easily defined as the pore’s volume divided by the membrane total volume. Wet membranes were weighed after carefully wiping the surface ($W_w$). Afterwards, these membranes were dried in an oven at $50^\circ$C for 24 h and weighed again ($W_d$). The porosity of membrane $\varepsilon$ (%), was measured by gravimetric method using Equation (3) [25] $$\varepsilon = \left( \frac{W_w - W_d}{\rho_w} \right) \times \frac{100}{W_w - W_d \rho_p + W_d \rho_p}$$ where, $W_w$ is the weight of wet membrane (kg), $W_d$ represents the weight of dry membrane (kg), $\rho_w$ is the density of water (1000 kg/m$^3$), and $\rho_p$, the polymer density (1770 kg/m$^3$ for PVDF). Based on the measured distilled water flux, the average pore size ($d$) of the membrane was calculated by the Guerout–Elford–Ferry equation, Equation (4) [46]. $$d = \sqrt{\frac{2.9 - 1.75\varepsilon}{8\delta l V \varepsilon A \Delta P t}}$$ Herein, $\varepsilon$ is membrane porosity (%), $\delta$, the water viscosity ($8.9 \times 10^{-4}$ Pa s), $l$ represents membrane thickness ($60 \times 10^{-6}$ m), $V$ is the volume of the distilled water penetrating through the membrane ($m^3$), $t$ is the experimental time interval (s), $A$, the effective membrane surface area ($m^2$), and $\Delta P$ is the working pressure (30 kPa). 3. Results and Discussion 3.1. Landfill Leachate Characteristics Table 1 displays the key characteristics of the raw leachate sample of more than 10 years in age. The lower BOD$_5$ to COD ratio (0.074) was another strong indication of highly stabilized leachate sample [3]. The other quality parameters of leachate, such as COD, BOD$_5$, NH$_3$-N, colour, and pH values, were around 1188 mg/L, 89 mg/L, 313 mg/L, 1360 PtCo/L, and 8.33, respectively. These obtained values were also compared with the standard discharged limits set by the Malaysian Environmental Quality was conducted (Table 1) [47]. As shown in Table 1, the COD, colour, and NH$_3$-N concentrations were found to be far greater than the standard discharged limits. \| Parameter \| Unit \| Value Range \| Average \| Malaysia Discharge Standards \| \|--------------------\|--------\|--------------\|---------\|------------------------------\| \| DO \| mg/L \| 2.43–5.19 \| 3.81 \| - \| \| COD \| mg/L \| 846–1530 \| 1188 \| 400 \| \| BOD$_5$ \| mg/L \| 55–122 \| 89 \| 20 \| \| BOD$_5$/COD \| \| 0.065–0.080 \| 0.074 \| 0.05 \| \| Colour \| PtCo/L \| 1040–1680 \| 1360 \| 100 \| \| NH$_3$-N \| mg/L \| 164–462 \| 313 \| 5 \| \| Suspended Solids \| mg/L \| 75.0–80.0 \| 77.5 \| 50 \| \| pH \| \| 7.97–8.68 \| 8.33 \| 6.0–9.0 \| \| Turbidity \| NTU \| 15.9–70.2 \| 43.1 \| - \| \| Electrical Conductivity \| mS \| 13.22–22.77 \| 18.00 \| - \| \| Temperature \| °C \| 27–30 \| 28 \| 40 \| 3.2. PAC Characterization Analysis test of the particle size was conducted to investigate the particle size distribution of fine samples in terms of volume. The particle size distribution of PAC sample is shown in Figure 5a. It can be seen from Figure 5 that PAC has small particle sizes which varied between (0.02–50 µm) in diameter. The average particle diameter of the PAC is 25 µm. It is evident from Figure 5a that the distribution curve of PAC particles could be counted a uniform-distribution curve. The percentage of adsorption is higher for those adsorbents have smaller particle size due to the availability of more surface area [48]. The surface morphology of PAC was visualized via FESEM, with a magnification of 10,000×, as shown in Figure 5b. FESEM micrographs of PAC, shows uniform size particles, which confirmed the results obtained from the particle size analysis. To some extent, the PAC surface having small cavities, pores, and more rough surfaces indicates the presence of an interconnected porous network. Increasing the particles’ number of an adsorbent material by decreasing its particles size resulted in increasing the adsorption surface area, and thus the material adsorption characteristics [49]. Figure 5. PAC characterization: (a) Particle size distribution; (b) FESEM image at 10,000× magnification. ### 3.3. Membrane Filtration and Experimental Results Herein, the relationship among the independent factors (PVFD and PAC dosage in membrane) and responses (COD, NH₃-N, colour removal, max. TEM, and pure water flux) were thoroughly investigated. There were 13 different experiments performed on the PVDF and PAC composition based on the central RSM composite design, as shown in Table 2. CFR test was performed to investigate the pollutants removal efficiency together with the max. TEM, while dead-end test was executed to measure the pure water flux. #### Table 2. Experimental results for the PVDF-PAC membranes (RSM design). \| Run Order \| PVDF (wt.%) \| PAC (wt.%) \| COD Removal Efficiency (%) \| Colour Removal Efficiency (%) \| NH₃-N Removal Efficiency (%) \| Pure Water Flux ** (L/m²·h) \| Max. TMP (bar) \| \|-----------\|-------------\|------------\|----------------------------\|------------------------------\|-------------------------------\|-----------------------------\|----------------\| \| 1 \| 10.00 \| 0.00 \| 14.8 \| 15.1 \| 10.9 \| 90.2 \| 0.46 \| \| 2 \| 10.00 \| 2.00 \| 29.1 \| 42.3 \| 7.5 \| 127.7 \| 0.42 \| \| 3 \| 12.00 \| 1.00 \| 32.2 \| 44.6 \| 18.3 \| 89.3 \| 0.48 \| \| 4 \| 14.00 \| 0.50 \| 28.2 \| 39.6 \| 19.6 \| 64.0 \| 0.66 \| \| 5 \| 14.00 \| 1.00 \| 37.2 \| 56.3 \| 23.8 \| 79.9 \| 0.67 \| \| 6 \| 14.00 \| 1.00 \| 35.5 \| 50.3 \| 19.3 \| 72.9 \| 0.63 \| \| 7 \| 14.00 \| 1.00 \| 35.5 \| 56.2 \| 21.3 \| 72.2 \| 0.62 \| \| 8 \| 14.00 \| 1.00 \| 35.7 \| 51.1 \| 21.5 \| 70.3 \| 0.61 \| \| 9 \| 14.00 \| 1.00 \| 32.2 \| 51.5 \| 19.9 \| 69.9 \| 0.60 \| \| 10 \| 14.00 \| 1.50 \| 33.2 \| 52.7 \| 19.2 \| 83.1 \| 0.55 \| \| 11 \| 16.00 \| 1.00 \| 37.1 \| 41.0 \| 22.5 \| 31.8 \| 0.68 \| \| 12 \| 18.00 \| 0.00 \| 29.1 \| 26.7 \| 21.2 \| 26.2 \| 1.00 \| \| 13 \| 18.00 \| 2.00 \| 20.9 \| 15.6 \| 17.3 \| 32.9 \| 0.78 \| * Estimated by Equation (1). ** Estimated by Equation (2). The COD, colour, and NH$_3$-N removal efficiencies were found to be around 14.8–37.2, 14.6–56.3, and 7.5–23.8%, respectively, while the pure flux and max. TMP were ranged between 26.2–127.7 L/m$^2$·h and 0.42–1.00 bar, respectively. ANOVA analysis was performed for the further investigation on the obtained experimental results. It is observed from Table 2 that an increase in both PVDF and PAC concentrations on the membrane leads, to some extent, to an increase in the contaminants removal. When PVDF and PAC concentration are higher than 14 wt.% and 1.0 wt.%, respectively, the removal efficiency starts to decrease with increasing the amount of PVDF and PAC. This behaviour was attributed to the combination effect between polymer and additive in dope. This leads to the creation of large volume voids with increasing polymer dosage, and allows the small particles of contaminants to pass through the membrane [50]. ### 3.3.1. Removal Efficiency of Contaminants Table 3 depicts the empirical model using the data obtained from COD, colour, and NH$_3$-N removals. F-values of the model, together with the low probability values ($P > F > 0.05$), clearly suggest that the models were significant for all responses. \| Source \| COD Removal (%) \| Colour Removal (%) \| NH$_3$-N Removal (%) \| \|-------------------\|-----------------\|---------------------\|----------------------\| \| \| F-Value \| Prob > F \| F-Value \| Prob > F \| F-Value \| Prob > F \| \| Model \| 25.62 \| 0.0002 (S) \| 31.93 \| <0.0001 (S) \| 24.34 \| 0.0003 (S) \| \| A-PVDF (wt.%) \| 4.34 \| 0.0795 \| 3.89 \| 0.0840 \| 0.42 \| 0.0988 \| \| B-PAC (wt.%) \| 32.25 \| 0.0008 \| 21.10 \| 0.0018 \| 4.19 \| 0.0441 \| \| AB \| 0.42 \| 0.5375 \| 9.03 \| <0.0001 \| 0.24 \| 0.6372 \| \| A$^2$ \| 12.18 \| 0.0101 \| - \| - \| - \| - \| \| B$^2$ \| 1.39 \| 0.3665 (NS) \| 3.27 \| 0.1386 (NS) \| 0.17 \| 0.9088 (NS) \| \| Lack of Fit \| \| \| \| \| \| \| \| Std. Dev. \| 1.98 \| \| 4.28 \| \| 1.40 \| \| \| Mean \| 30.85 \| \| 41.69 \| \| 18.64 \| \| \| R$^2$ \| 0.9482 \| \| 0.9411 \| \| 0.9456 \| \| \| Adj R$^2$ \| 0.9112 \| \| 0.9116 \| \| 0.9067 \| \| \| C.V. % \| 6.42 \| \| 10.26 \| \| 7.52 \| \| Significant. b Not significant. The significant model terms for COD removals in the ANOVA analysis were sorted in descending order depending upon the influential terms (AB, B$^2$, A, B, and A$^2$). It was clearly seen that the PVDF and PAC (AB) had the highest impact on the COD removal with an F-value of around 32.25, followed by the quadratic term of PAC concentration (B$^2$), PVDF concentration (A), PAC concentration (B), and finally the quadratic term of PVDF concentration (A$^2$) with an F-value of 12.18, 4.34, 4.19, and 0.42, respectively. The quadratic terms of PVDF concentration together with the linear terms of PAC and PVDF contents caused a positive effect on the COD removal. Nonetheless, interaction and quadratic terms of PAC exhibited negative effects. In fact, an increase in the COD removal was recorded upon the change in the liner terms of PVDF and PAC concentrations, and PVDF concentration with quadratic term from lower to higher level. Hence, this change is complemented by the outstanding COD removal using PVDF-PAC membrane. On the other hand, a decline in COD removal was recorded when the interaction term and quadratic term of PAC was in the higher level. The quadratic term of PVDF contents ($A^2$) has the most significant effect towards the colour removal rate. This is due to the highest F-value (97.03), where other terms had the values of 21.10, 5.69, 3.89, respectively. The PAC content (B) had a progressive influence on the colour removing. However, the quadratic term of PVDF, PVDF concentration, and interaction among the PVDF and PAC displayed a negative effect. Thus, the removal of colour was enhanced with the enhancement of the PVDF contents in membrane fabrication until the optimum amount (>14 wt.% PVDF). Additionally, in case of NH$_3$-N removal, the A, B, $B^2$, $A^2$, and AB were sorted in descending order of their effecting strength. The highest F-value of 55.81 was recorded for the linear term of PVDF concentration (A), and thus it had the huge effect in NH$_3$-N removal. On the other hand, the lowest F-value of 0.032 was recorded for interaction term, which regarded to have a negligible effect on the model. The PVDF linear term only offered a strong influence on removing of NH$_3$-N, while the remaining terms were found to be the negligible influencers. Hence, the NH$_3$-N removal was increased upon enhancing the PVDF contents in membranes. However, for PAC concentration after the point (PAC = 1.0 wt.%); when either the quadratic term of PVDF or PAC, or the interaction term is in the significant level, the NH$_3$-N removal starts to decrease. The lack of fit F-statistic was statistically not significant, as the values of (P) were higher than 0.05. A significant lack of fit suggests that there may be some systematic variation unaccounted for the proposed models. This may be due to the exact replicate values of the independent variables in the models that provide an estimate of pure error [15]. The correlation coefficient value ($R^2$) resulted in the present study for COD removal (0.9482), colour removal (0.9411), and NH$_3$–N removal (0.9436), indicating that only 5.18, 21.09, 5.89, and 5.44% of the total dissimilarity might not be explained by the empirical models. Zielinska et al. [10] stated that the correlation coefficient should be more than 0.80 for a good fit of a model. Moreover, the C.V.% of the obtained models for COD, colour, and NH$_3$-N removals were 6.42%, 10.26%, and 7.52%, respectively, which designates an adequate model [51]. In the current study, all insignificant model terms which have limited effects were eliminated from the study to improve the model. Based on the findings, the response surface models for COD, colour, and NH$_3$-N removal efficiency were constructed to predict responses, which were considered reasonable. The final regression models, in terms of their coded factors, are expressed by the second-order polynomial equations, and are presented in Table 3. Typically, it is vital to study the effect of the operational factors on the different responses. The effect of PVDF and PAC concentration on the responses of COD, colour, and NH$_3$-N removals over PVDF-PAC membranes could be evaluated using perturbation and three-dimensional (3D) response surface plots (Figure 6). Perturbation plots show the comparative effects of independent variables on the responses. For instance, in Figure 6, the different sharp curvatures in PVDF concentration (A) and PAC concentration (B) show that the three responses (COD, colour, and NH$_3$-N removal efficiency) were very sensitive to the fabrication variables, but with different behaviours. In other words, PVDF and PAC contents have a major function in the treatment process under the experimental conditions. This is another confirmation of the important effects of the independent variables (PVDF and PAC concentrations) on the treatment removal efficiency. Therefore, the 3D surface response and contour plots of the quadratic models were utilized to assess the interactive relationships between independent variables and responses. The 3D response surface was introduced as a function of PVDF and PAC concentrations. Figure 6a,c shows a symmetrical 3D surface response for both COD and NH$_3$-N removals. In the meantime, the removal of colour presents a different 3D surface (Figure 6b), which indicates that colour removal was influenced differently by experimental factors than the other responses. Table 4. In a general linear model or a multiple regression model: $Y = \beta_0 + \sum \beta_j X_j + \epsilon$. Figure 6. Perturbation plots (left) and 3D response surface (right) of PVDF-PAC fabricated membrane for the removing efficiency of (a) COD, (b) colour, and (c) NH$_3$-N. Figure 6a,c indicated that the responses for COD and NH$_3$-N removal rate was sufficiently enhanced upon the increase in PVDF contents in applied membranes. On the other hand, the increase in PAC contents in membrane fabrication led, to the removal of COD and NH$_3$-N to some extent. It was seen that, when the PAC contents in membrane were higher than 1.0 wt.%, the removal rate for COD and NH$_3$-N began to decline. According to Figure 6c, for the removal of NH$_3$-N, the effect of interaction between PVDF and PAC concentrations have a noteworthy influence on removal percent. The NH$_3$-N removal were... gradually increased with the increasing of PAC concentration to some extent, which means that the incorporated PAC has enhanced the membrane performance in terms of NH$_3$-N removal, in addition to the main separation action gained by the membrane texture itself. This good result might be ascribed to the high adsorption characteristics of the used PAC, which significantly improved the fabricated membrane efficiency [5,52]. However, PVDF concentration has limited effect on COD removal efficiency compared with the PAC content. Where 35.5 and 38.5% of COD were removed at minimum and maximum PVDF concentration (10.0 and 18.0 wt.%), respectively, 18.5 and 35.5% of COD removal were removed at minimum and medium PAC concentration (0.0 and 1.0 wt.%), respectively. Likewise, the minimum NH$_3$-N removal was found to be 7.5% at membrane concentration of 10.0 wt.% PVDF and 2.0 wt.% PAC, while the maximum NH$_3$-N removal (24.5%) was observed at the PVDF and PAC concentration of 18.0 and 1.0 wt.% respectively. On the other hand, the 3D response surface in Figure 6b displays a different effect of interaction between the experimental factors on the colour removal rates. It was observed that an increase in the concentration of PVDF in the membrane leads to an improvement in the colour removal to some degree. When the concentration of PVDF was higher than (14 wt.%), the colour removal performance starts to decrease. This behaviour was credited to the combined effects of additive and polymer in the dope. This leads to creating large volume voids with increasing polymer dosage, and lets the fine particles from contaminants to permeate through the membrane [50]. Meanwhile, the enhancement of PAC concentration in a membrane drove a steady increase in the colour removal efficiency. As witnessed in Figure 6b, the predicted minimum and maximum efficiencies of colour removal were 15.0 and 56.5% present at fabrication concentrations of (18.0 wt.% PVDF, 0.0 wt.% PAC), and (14.0 wt.% PVDF, 1.0 wt.% PAC), respectively. This also confirms the effectiveness of PAC content in enhancing the removal performance of the filtration process using PVDF fabricated membrane. Despite the incorporation of PAC into membrane enhancing the COD, colour, and NH$_3$-N removal, the filtered leachate still did not meet the Malaysian Discharge Standard (Table 1). This is due to the highly concentrated pollutants of leachate that resulted in a reduction in membrane efficiency owing to the clogging caused by influent SS component. Therefore, a pre-treatment process such as PAC adsorption is suggested to be used before the membrane treatment [33]. 3.3.2. Pure Flux and Transmembrane Pressure Studies By applying the factorial regression analysis on the experimental data related to PVDF-PAC membranes, both max. TMP and pure water flux responses were well agreed to a linear model of the second degree, as shown in the ANOVA analysis presented in Table 4. In a general linear model or a multiple regression model: $Y = \beta_0 + \sum_{i=1}^{k} \beta_i X_i + \epsilon$, where: $Y$ is the response, $X_i$ is the independent factor, $k$ is the number of variables, $\beta_0$ is the constant term, $\beta_i$ represents the coefficient of the linear, and $\epsilon$ is the random error or noise [53]. The final linear models obtained for each response has been expressed by the first order polynomial equation, as presented in the last raw of Table 4. The fitted model for the pure water flux suggests a large F-value (53.56), suggesting that the model is significant. As the value of Prob > F of all terms is less than 0.050, this suggests that all the model terms are significant. Based on their F-values, the PVDF concentration term (A) has the highest influence on the model, followed by PAC concentration term, and lastly the combination term. The term of PAC concentration presents a positive effect on pure flux, while the other two terms have been found to be negative influencers. Hence, the pure water flux was raised only with enhancing PAC contents in the membrane while, in contrast, it is decreased with the increasing of the PVDF content of a membrane. Table 4. ANOVA results and quadratic models of PVDF-PAC membranes for pure flux and max. TMP. \| Source \| Pure Flux (L/m²·h) \| Max. TMP (bar) \| \|-----------------\|--------------------\|----------------\| \| \| F-Value \| Prob > F \| F-Value \| Prob > F \| \| Model \| 53.56 \| <0.0001 (S) a \| 49.62 \| <0.0001 (S) a \| \| A-PVDF (wt.%) \| 144.45 \| <0.0001 \| 131.07 \| <0.0001 \| \| B-PAC (wt.%) \| 11.86 \| 0.0073 \| 13.01 \| 0.0057 \| \| AB \| 4.38 \| 0.0658 \| 4.78 \| 0.0566 \| \| A² \| - \| - \| - \| - \| \| B² \| - \| - \| - \| - \| \| Lack of Fit \| 5.18 \| 0.0681 (NS) b \| 3.38 \| 0.1307 (NS) b \| \| Std. Dev. \| 7.36 \| Std. Dev. \| 0.041 \| \| Mean \| 70.03 \| Mean \| 0.63 \| \| R² \| 0.9470 \| R² \| 0.9430 \| \| Adj R² \| 0.9293 \| Adj R² \| 0.9240 \| \| C.V. % \| 10.50 \| C.V. % \| 6.56 \| Model equation coded, (wt.%) +70.03 -41.68 * A +11.94 * B -7.70 * A * B +0.63 +0.22 * A -0.070 * B -0.045 * A * B a Significant. b Not significant. On the other hand, the suggested model of max. TMP was significant with a high F-value (49.62), as can be seen from Table 4. Based on its effect on the model from the highest to the lowest, the model terms can be arranged as follows: PVDF content, PAC content, and the combination of both, with F-values of 131.07, 13.01, and 4.78, respectively. However, the PVDF concentration is the only factor which showed a positive influence on the max. TMP, due to the positive sign of its term; this indicates a worse impact on the max. TMP, as it could be increased with the increasing of PVDF content on the fabricated membrane. On the other hand, PAC concentration exhibited a better effect on the max. TMP, which showed a reduction in max. TMP occurred due to the increasing of the PAC content. Additionally, both of the models display a non-significant lack of fit F-value, which indicates that well fitted models have been selected to present the experimental results with minor pure errors [15]. The R² values obtained in the present study for pure flux and max. TMP were 0.9470 and 0.9430, respectively. The high value of R² represents good agreement between the observed and the calculated results within the experimental ranges [37]. Moreover, C.V. % for the water flux and TMP were 10.50% and 6.56%, respectively. Where these small values indicate good fitness of the models [51]. Based on these findings, the resulted response surface models in the current work for predicting the two responses (pure flux and max. TMP) were considered reasonable. The influence of integrated PAC and the interaction of content’s concentrations on the max. TMP can be explored by the plots of perturbation and 3D response surface, as shown in Figure 7. From perturbation plots at Figure 7, it is easy to notice that pure flux and max. TMP responses are very sensitive to the experimental factors, and to conclude that both have a different (inversed) behaviour regarding the PVDF and PAC concentration values. As can be seen from Figure 7a, increasing of PVDF concentration (A) resulted in a linear decrease in pure water flux and increase in max. TMP, which attributed to the reduction in membrane porosity due to the increase in polymer concentration, which is well recognized for the system of a single polymer casting solution [50]. However, PAC concentration (B) showed a different effect, as any increase in its value causes a linear increment on the pure water flux, but a decrease in max. TMP. 3.4. Fabricated Membrane Characterization The morphology of produced membrane can explain the effect of dope composition on membrane performance. A collection of membranes composed from different concentrations of PVDF and PAC (wt.%) were chosen from the fabricated membranes to represent the different membrane compositions, and consequently to be investigated by the morphological studies. These membranes were: FM1 with the content of (10.0 wt.% PVDF-0.0 wt.% PAC) to represent minimum PVDF concentration with no PAC; (10.0 wt.% PVDF-2.0 wt.% PAC) to represent minimum PVDF with high PAC, denoted as FM2; (14.0 wt.% PVDF-1.0 wt.% PAC) to represent intermediate composition of both PVDF and PAC. Minimum and maximum predicted pure fluxes (26.0 and 128.5 L/m²·h) were found at the membrane compositions of 18.0 wt.% PVDF with 0.0 wt.% PAC, and 10.0 wt.% PVDF with 2.0 wt.% PAC, respectively. On the other hand, lowest and highest max. TMP according to the suggested model were found to be 0.38 and 0.98 bar at membranes of compositions (10.0 wt.%) PVDF with (2.0 wt.%) PAC, and 18.0 wt.% PVDF with 0.0 wt.% PAC, respectively. From the findings, membranes with lower PVDF concentration and high PAC concentration (10.0 wt.% PVDF and 2.0 wt.% PAC) exhibited the best water permeation and antifouling properties. Nonetheless, this membrane still falls short to produce the highest removing rates of COD, colour, and NH₃-N based on the previous discussion. Figure 7. Perturbation plots (left) and 3D response surface (right) of PVDF-PAC fabricated membrane for (a) pure water flux and (b) max. TMP. Actual Factors A: PVDF (wt.%) = 14.0, B: PAC (wt.%) = 1.0 PAC, named FM3; and finally FM4 with 18.0 wt.% PVDF and 0.0 wt.% PAC to represent maximum concentration of PVDF without PAC. The FTIR spectrum of PVDF-PAC fabricated membranes with the various compositions is illustrated in Figure 8. It is clearly observed from Figure 8 that membranes displayed semi-typical distinctive spectra along the range of 4000 and 400 cm$^{-1}$. Characteristic chemical groups are witnessed in the band of all membranes at waves with lengths 3020, 2990, 2370, 1400, 1070, 875, 590, and 490 cm$^{-1}$ with altered vibrations of strength depends on the different membrane compositions. The spectrum shows bands at 2990 and 3020 cm$^{-1}$ which are attributed to the symmetric and asymmetric stretching vibrations of C-H coming from ketones and carboxylic acids [54], where vibrations at 1070 and 1400 cm$^{-1}$ presented the deformation peaks of C-F related to PVDF. ![Figure 8. FTIR spectra for PVDF-PAC membranes with different concentrations.](image) The notable peaks of the various membranes at 2370, 875, and 590 cm$^{-1}$, assigned to CO$_2$, CO$_3^{-2}$, and C-O- groups, respectively, were the features distinctive of neutralization methanol, used after membrane casting [55]. Moreover, the OH group detected at 490 cm$^{-1}$ is attributed to the DW used for membrane solidification during the casting process [56]. Figure 8 also confirmed that the recorded wave numbers in the spectrum of both membranes without PAC (FM1 and FM4) have higher frequencies in comparison with the spectrums of the other two membranes with PAC content (FM2 and FM3). Furthermore, it could be observed that the peaks of the membrane with higher content of PAC (FM2) have lower vibrations compared with the membranes with lower PAC content (FM3). Evidently, the peaks become narrow with less strength at the increasing of PAC weight, indicating that the hydrogen bonds were constructed well between PVDF polymer chains and the hydroxyl groups from PAC, which reduces the PVDF hydrophobic tendency [57]. These outcomes confirmed that PAC was well integrated to PVDF membranes, and partially relocated on the membrane surface, which leads to membrane treatment efficiency enhancement. To investigate the elemental composition present in the fabricated PVDF-PAC membranes with different compositions, EDX analysis was recorded in the binding energy region from 0 to 15 keV as exhibited in Figure 9. The PVDF characterized elements C and F were clearly observed in the spectra of the pure PVDF membranes (without PAC), while the AL element, which characterizes the presence of PAC, appeared only at the PVDF membranes incorporated with PAC [33]. Figure 9b,d shows the EDX analysis of 2.0 and 1.0 wt.% PAC, respectively. It is clearly witnessed that the presence of PAC was presented well. Table 5 shows the atomic percentages of the different elemental compositions of the selected membranes (FM1–FM4). From the EDX findings, the weight percentages of elemental AL on the FM2 and FM3 were determined as 1.04 and 0.79, respectively, which confirmed the presence PAC with representative weights on the integrated membranes. Table 5. Elemental compositions of selected PVDF-PAC fabricated membranes based on EDX mapping. \| Sample \| Composition (wt.%) \| Elements Weight (%) \| \|--------\|-------------------\|---------------------\| \| \| PVDF \| PAC \| C \| F \| AL \| Total \| \| FM1 \| 10.0 \| 0.0 \| 61.69\| 38.31\| 0.00 \| 100.00\| \| FM2 \| 10.0 \| 2.0 \| 60.85\| 38.11\| 1.04 \| 100.00\| \| FM3 \| 14.0 \| 1.0 \| 61.04\| 38.17\| 0.79 \| 100.00\| \| FM4 \| 18.0 \| 0.0 \| 60.63\| 39.37\| 0.00 \| 100.00\| Figure 10 presents the FESEM images for produced membranes with different compositions, which show the top surface morphology of membranes, along with its cross section. As can be seen from Figure 9a–d, there were many small pores available on the surface of FM1 membrane which contains the lowest PVDF polymer content (10.0 wt.%). Furthermore, the number and size of these pores start to be decreased, first on membrane FM3, with PVDF content 14.0 wt.% and PAC content 1.0 wt.%, followed by FM2 membrane with the highest PAC content (2.0 wt.%), while the membrane FM4 has a semi-impermeable surface due to its high PVDF polymer content (18.0 wt.%) with no PAC content. This was in agreement with the findings earlier discovered by Kunst and Sourirajan [58]. Figure 10. FESEM morphologies of PVDF-PAC membranes with different compositions (FM1 to FM4): (a–d) cross-sections and (A–D) top surfaces. Referring to membrane cross sections on Figure 10a–d, all membranes display the formation of macrovoid with loosely packed structures. Typically, the membrane consists of two layers, which are a spongy porous support layer and a dense top finger-like layer. The establishment of these configurations can be attributed to the instantaneous demixing of polymer and solvent during the process of phase inversion. FM1 membrane, with only PVDF and the weight of 10.0 wt.%, displayed an unimproved finger-like formation and a sponge-like support layer containing large, unconnected pores, delimited by polymer walls (see Figure 10a). The finger-like voids turn become flat, bigger, and even strained to the bottommost of the fabricated membranes with an increase in PAC concentration (i.e., in FM2 and FM3), and the spherical voids of the sponge-like structures connect more closely with themselves (Figure 10b,c). However, the FM4 membrane, containing the highest concentration of PVDF, gives thin, smaller, and non-stretched figure-like pores, with less connection to the little sponge-like pores located on the cross-section’s bottom. This produces low membrane flux due to the greater amount of polymer contributing a higher membrane viscosity, which lead to a decease in the membrane porosity and pore size. The overall FESEM micrographs have proved the significant effect of the PAC presence in improving the fabricated membrane characteristic in terms of membrane rejection, and therefore removal rate of contaminants. Furthermore, an AFM test was carried out to investigate the membrane top surface, along with its roughness, as shown in Figure 11. The FM2 membrane might contain some extra PAC particles which made its top surface rougher compared to others (Figure 11b). Having less depth of facial peaks and valleys, the FM4 membrane surface (Figure 11d) is relatively smooth due to containing only PVDF polymer which received a homogeneous mixing at the preparation phase of dope solution [59]. However, the peaks and valleys of FM1 and FM3 membranes reduced gradually compared to FM2, where FM3 has the smoothest surface compared with other membranes (see Figure 11a–d). To confirm all above observations, the values of membrane surface roughness (R_q and R_a) given in Figure 11 can be considered. ![Figure 11. AFM top surface images with average membrane roughness values (nm) for different compositions of selected PVDF-PAC membranes: (a–d) for (FM1 to FM4).](image-url) For membrane permeability analysis, the impact of PAC addition to membrane permeability, in terms of porosity and average pore size, were evaluated for the produced PVDF membranes. As presented in Table 6, the porosity and average pore size of the fabricated PVDF membranes incorporated with PAC were higher than the other membranes without PAC. Based on Table 6, the resulted fabricated membranes were “micro-filtration”, and the highest mean values of porosity and average pore size were achieved by FM2 membrane at the values 77.48% and 24.43 µm, respectively. On the other hand, the lowest values of the same corresponding permeability parameters were found using membrane FM4 at 48.38% and 12.15 µm, respectively. These findings agreed with the above morphological results. Table 6. Permeability measurements for selected fabricated PVDF-PAC membranes. \| Membrane \| Composition \| Porosity (%) \| Average Pore Size (µm) \| \|----------\|-------------\|--------------\|------------------------\| \| FM1 \| 10.0 \| 57.25 ± 0.18 \| 15.34 ± 0.05 \| \| FM2 \| 10.0 \| 77.48 ± 0.50 \| 24.43 ± 0.15 \| \| FM3 \| 14.0 \| 72.86 ± 0.20 \| 21.27 ± 0.07 \| \| FM4 \| 18.0 \| 48.38 ± 0.62 \| 12.15 ± 0.24 \| Each parameter is expressed as average value ± standard deviation. 3.5. Membrane Treatment Optimization The best synthesized membrane has been selected using the RSM tool, where the membrane efficiencies of COD, colour, and NH$_3$-N removal were optimized during this study. Based on the DoE software, the operational conditions (PVDF weight and PAC weight) were targeted to be within the range. While the dependents of treatment performance (COD, colour, and NH$_3$-N removal) were chosen as “maximum” to achieve the ultimate filtration treatment. The other responses were remained “within the range”. Accordingly, the optimization tool assimilates the singular desirability into a particular number, and then aims to optimize the function. Consequently, the composition of the optimum membrane, together with respective rates of removal efficiency, were obtained. The optimum removals and their corresponding water flux and max. TMP are presented in Table 7. Table 7. Predicted and experimental removal efficiencies of the optimum PVDF-PAC membrane with the corresponding operating condition. \| Operating Conditions \| Desirability \| Optimum Conditions \| \|----------------------\|--------------\|--------------------\| \| PVDF (wt.%) \| PAC (wt.%) \| 0.870 \| Selected \| \| Response \| Predicted Result \| Experimental Result \| Error (%) \| \| Removal of COD (%) * \| 35.34 \| 36.63 \| 3.65 \| \| Removal of colour (%)* \| 48.71 \| 49.50 \| 1.62 \| \| Removal of NH$_3$-N (%) * \| 22.00 \| 23.84 \| 8.36 \| \| Pure water flux (L/m$^2$·h) \| 61.00 \| 61.10 \| 0.16 \| \| Max. TMP (bar) \| 0.67 \| 0.64 \| 4.48 \| Optimum value. The membrane with 14.9 wt.% of PVDF and 1.0 wt.% of PAC was found to be the optimum, and thus selected as the best membrane design, having optimum removal efficiency according to its highest desirability (0.870) [60]. As shown in Table 7, 35.34, 48.71, and 22.00% removal of COD, colour and NH$_3$-N, respectively, was predicted by the software under optimized operational conditions. The corresponding (non-optimized) water flux and max. TMP were found at the val- ues 61.00 L/m²·h and 0.67 bar, respectively. An additional experimentation was then performed to confirm the optimum findings. As illustrated in Table 7, the error column indicates the differences between the predicted and laboratory values, which shows that the lab experiments agree well with the response values estimated by the software. However, less agreement between the predicted and the laboratory result was obtained in case of NH₃-N removal (8.36% error). 3.6. Membrane Performance Comparison with Other Reported Studies The performance of the optimum fabricated membrane with other reported PVDF produced membranes is shown in Table 8. It can be noticed from Table 8 that the current study offered the smoother surface among the existing works based on the average roughness (Rₐ = 36.39 nm), which accordingly improves the removing performance and antifouling properties of the created membrane [61]. There exists few values of pure flux that are higher than the achieved in the current work, such as the flux of 143.24 L/m²·h produced by Penboon et al. [62]. The low value of pure water flux of the current work (61.00 L/m²·h) could be ascribed to the differences in the experimental characteristics such as the type of wastewater or the rates of feed flow. In addition, the rejection efficiency in the current work is lower than previously reported, which could be solved through further enhancement of the produced membranes using hydrophilic additives such as PVA or PVP [25,57]. Based on previous studies, after saturation, membrane corroborated PAC can be washed back and reused [13,63]. Table 8. Comparison of performance with other modified PVDF membranes in wastewater treatment process. \| Modification Agent \| Pure Water Flux (L/m²·h) \| Feed Type & Feeding Rate (L/min) \| Removal Rate Avg. (%) \| Roughness (nm) \| Reference \| \|--------------------\|--------------------------\|-------------------------------\|----------------------\|----------------\|-----------\| \| Titanium dioxide (TiO₂) \| 143.24 \| Wastewater FR = 0.850 \| 86.1 \| - \| [62] \| \| Granular activated carbon (GAC) \| 13.90 \| Berlin tap water (Gravity driven) \| 88.0 \| - \| [64] \| \| Silica nanoparticles (SiO₂) \| - \| Cooking wastewater FR = 48.96 \| 66.7 \| Rₐ = 174 \| [65] \| \| Reduced graphene oxide (rGO) \| - \| NaCl solution FR = 0.385 \| 58.0 \| Rₐ = 84 \| [66] \| \| Powdered activated carbon (PAC) \| 61.00 \| SLF leachate FR = 0.20 \| 35.35 \| Rₐ = 36.39 \| Present study \| 4. Conclusions The adsorbent material PAC was used to fabricate a novel PVDF membrane for the treatment of stabilized landfill leachate. The fabricated PVDF flat sheet membranes integrated with PAC showed better performance when compared with PVDF membrane (without PAC). The addition of PAC effectively enhanced the removal rate and the fouling control parameters of produced membranes. Increasing PAC content to a certain value has a positive influence on the removal efficiency of COD, colour, and NH₃-N, as well as on membrane characteristics. Operational optimization was performed using RSM to select the optimum membrane design in terms of the removal efficiency. The best membrane composition was found at (14.9 wt.%) PVDF and (1.0 wt.%) PAC, which removed 36.63% of COD, 49.50% of colour, and 23.84% of NH₃-N. This was in agreement with the predicted removals. The corresponding experimental values of water flux and max. TMP also agreed with the prediction, with the values of 61.10 L/m²·h and 0.64 bar, respectively. The performance and structure of fabricated membranes were investigated by filtration tests, FTIR, FESEM, and AFM spectroscopy. In general, this work shows the potential of treatment and hydrophilic improvement of hydrophobic PVDF polymer membranes using PAC. For further removal efficiency, membrane properties or practice could be improved by either adding a hydrophilic material, or applying pre-treatment process such as adsorption via PAC. Author Contributions:* S.M.A.A.: experimental work, writing original draft, preparation, and revisions. Z.H.J.: visualization, investigation, and language reviewing. C.-A.N.: supervision. Y.-C.H.: funding and technical support. M.J.K.B.: supervision, conceptualization, methodology, software, and revision. All authors have read and agreed to the published version of the manuscript. 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[CrossRef]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3597, 1 ], [ 3597, 8008, 2 ], [ 8008, 12235, 3 ], [ 12235, 14451, 4 ], [ 14451, 15594, 5 ], [ 15594, 17071, 6 ], [ 17071, 19622, 7 ], [ 19622, 23245, 8 ], [ 23245, 27683, 9 ], [ 27683, 32159, 10 ], [ 32159, 36455, 11 ], [ 36455, 37352, 12 ], [ 37352, 41516, 13 ], [ 41516, 45533, 14 ], [ 45533, 47191, 15 ], [ 47191, 49637, 16 ], [ 49637, 50806, 17 ], [ 50806, 51705, 18 ], [ 51705, 54189, 19 ], [ 54189, 57746, 20 ], [ 57746, 61481, 21 ], [ 61481, 66512, 22 ], [ 66512, 72315, 23 ], [ 72315, 77426, 24 ] ] }
7e2fa3e02fc62da713847d3a86bb15b410a9c624	{ "olmocr-version": "0.1.59", "pdf-total-pages": 15, "total-fallback-pages": 0, "total-input-tokens": 77481, "total-output-tokens": 18038, "fieldofstudy": [ "Mathematics" ] }	Abstract. We say that a submodule $S$ of $H^2(D^n)$ ($n > 1$) is co-doubly commuting if the quotient module $H^2(D^n)/S$ is doubly commuting. We show that a co-doubly commuting submodule of $H^2(D^n)$ is essentially doubly commuting if and only if the corresponding one variable inner functions are finite Blaschke products or that $n = 2$. In particular, a co-doubly commuting submodule $S$ of $H^2(D^n)$ is essentially doubly commuting if and only if $n = 2$ or that $S$ is of finite co-dimension. We obtain an explicit representation of the Beurling-Lax-Halmos inner functions for those submodules of $H^2(D^{n-1})$ which are co-doubly commuting submodules of $H^2(D^n)$. Finally, we prove that a pair of co-doubly commuting submodules of $H^2(D^n)$ are unitarily equivalent if and only if they are equal. 1. Introduction Let $\{T_1, \ldots, T_n\}$ be a set of $n$ commuting bounded linear operators on a separable Hilbert space $\mathcal{H}$. Then we can turn the $n$-tuple $(T_1, \ldots, T_n)$ on $\mathcal{H}$ into a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z] := \mathbb{C}[z_1, \ldots, z_n]$, the ring of polynomials, as follows: $$\mathbb{C}[z] \times \mathcal{H} \to \mathcal{H}, \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$ for all $p \in \mathbb{C}[z]$ and $h \in \mathcal{H}$. The module multiplication operators by the coordinate functions on $\mathcal{H}$ are defined by $M_{z_i}h = z_i(T_1, \ldots, T_n)h = T_i h$, for all $h \in \mathcal{H}$ and $i = 1, \ldots, n$. Therefore, a Hilbert module is uniquely determined by the underlying commuting operators via the module multiplication operators by the coordinate functions and vice versa. Let $S, Q \subseteq \mathcal{H}$ be closed subspaces of $\mathcal{H}$. Then $S$ (or $Q$) is said to be a submodule (quotient module) of $\mathcal{H}$ if $M_{z_i}S \subseteq S$ ($M_{z_i}Q \subseteq Q$) for all $i = 1, \ldots, n$. Note that a closed subspace $Q$ is a quotient module of $\mathcal{H}$ if and only if $Q^\perp \cong \mathcal{H}/Q$ is submodule of $\mathcal{H}$. The Hardy module $H^2(D^n)$ over the polydisc is the Hardy space $H^2(D^n)$ (cf. [17] and [27]), the closure of $\mathbb{C}[z]$ in $L^2(T^n)$, with the standard multiplication operators by the coordinate functions $z_i$ ($1 \leq i \leq n$) on $H^2(D^n)$ as the module maps. The module multiplication operators on a submodule $S$ and a quotient module $Q$ of a Hilbert module $\mathcal{H}$ are given by the restrictions $(R_{z_1}, \ldots, R_{z_n})$ and the compressions $(C_{z_1}, \ldots, C_{z_n})$ of the module multiplications of $\mathcal{H}$, respectively. That is, $$R_{z_i} = M_{z_i}\|_S \quad \text{and} \quad C_{z_i} = P_QM_{z_i}\|_Q.$$ for all $i = 1, \ldots, n$. Here, for a given closed subspace $\mathcal{M}$ of a Hilbert space $\mathcal{K}$, we denote the orthogonal projection of $\mathcal{K}$ onto $\mathcal{M}$ by $P_{R_1}$. A quotient module $Q$ of a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z]$ $(n \geq 2)$ is said to be double commuting quotient module if \[ C_{z_i}C_{z_j}^* = C_{z_j}C_{z_i}^, \] for all $1 \leq i < j \leq n$. Also a submodule $S$ of $\mathcal{H}$ is said to be co-douly commuting submodule* of $\mathcal{H}$ if $\mathcal{H}/S$ is double commuting quotient module of $\mathcal{H}$ (see [28]). Finally, we recall that a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z]$ is said to be essentially doubly commuting if the cross-commutators \[ [M^_i, M_{j}] \in \mathcal{K}(\mathcal{H}), \] for all $1 \leq i < j \leq n$, where $\mathcal{K}(\mathcal{H})$ is the ideal of all compact operators on $\mathcal{H}$. We say that $\mathcal{H}$ is essentially normal* if $[M^_i, M_{j}] \in \mathcal{K}(\mathcal{H})$ for all $1 \leq i, j \leq n$. Natural examples of essentially normal Hilbert modules are the Drury-Arveson module $H^2_n$, the Hardy module $H^2(\mathbb{B}^n)$ and the Bergman module $L^2(\mathbb{B}^n)$ over the unit ball $\mathbb{B}^n$ (cf. [10, 4, 3]). On the other hand, the Hardy module $H^2(\mathbb{D}^n)$ over $\mathbb{D}^n$ with $n \geq 2$ is not essentially normal. However, a simple calculation reveals that $H^2(\mathbb{D}^n)$ is doubly commuting and, in particular, essentially doubly commuting. Therefore, a natural approach to measure a submodule (quotient module) of the Hardy module $H^2(\mathbb{D}^n)$ from being "small" is to consider the cross-commutators $[R^_i, R_{j}]$ $([C^_i, C_{j}]$) for all $1 \leq i < j \leq n$ instead of all possible commutators. Before proceeding further, let us recall the Beurling-Lax-Halmos theorem concerning submodules of vector-valued Hardy modules over $\mathbb{D}$ (cf. [23]). Given a separable Hilbert space $\mathcal{E}$ we shall denote by $H^2_\mathcal{E}(\mathbb{D})$ the $\mathcal{E}$-valued Hardy module (see [23]). Note that by virtue of the unitary module map $\tilde{U} : H^2_\mathcal{E}(\mathbb{D}) \rightarrow H^2(\mathbb{D}) \otimes \mathcal{E}$ defined by \[ z^m \eta \mapsto z^m \otimes \eta, \quad (\eta \in \mathcal{E}, m \in \mathbb{N}) \] we can identify the vector-valued Hardy module $H^2_\mathcal{E}(\mathbb{D})$ with $H^2(\mathbb{D}) \otimes \mathcal{E}$. Theorem 1.1.* (Beurling-Lax-Halmos) Let $\mathcal{E}$ be a Hilbert space and $S$ be a non-trivial closed subspace of the Hardy module $H^2_\mathcal{E}(\mathbb{D})$. Then $S$ is a submodule of $H^2_\mathcal{E}(\mathbb{D})$ if and only if \[ S = \Omega H^2_{\mathcal{F}}(\mathbb{D}), \] where $\Theta \in H^\infty_{L(\mathcal{F}, \mathcal{E})}(\mathbb{D})$ is an inner function and $\mathcal{F}$ is an adequate Hilbert space with dimension less than or equal to the dimension of $\mathcal{E}$. Moreover, $\Theta$ is unique up to a unitary constant right factor, that is, if $S = \tilde{\Omega} H^2_{\mathcal{F}}(\mathbb{D})$ for some Hilbert space $\tilde{\mathcal{F}}$ and inner function $\tilde{\Theta} \in H^\infty_{L(\mathcal{F}, \mathcal{E})}(\mathbb{D})$, then $\Theta = \tilde{\Theta} W$ where $W$ is a unitary operator in $L(\mathcal{F}, \tilde{\mathcal{F}})$. Now we formulate some general problems concerning submodules of the Hardy module $H^2(\mathbb{D}^n)$ $(n \geq 2)$. Question 1. (Essentially doubly commuting submodules) How to characterize essentially doubly commuting submodules of the Hardy modules $H^2(\mathbb{D}^n)$? Let $\mathcal{S} \neq \{0\}$ be a closed subspace of $H^2_{H(D^n-1)}(\mathbb{D})$. By Beurling-Lax-Halmos theorem, Theorem 1.1, that $\mathcal{S}$ is a submodule of $H^2_{H(D^n-1)}(\mathbb{D})$ if and only if $\mathcal{S} = \Theta H^2_{E}(\mathbb{D})$, for some closed subspace $E \subseteq H^2(\mathbb{D}^{n-1})$ and inner function $\Theta \in H^\infty(\mathbb{D}^{n-1})$. Question 2.* (Beurling-Lax-Halmos representations) For which closed subspace $E \subseteq H^2(\mathbb{D}^{n-1})$ and inner function $\Theta \in H^\infty(\mathbb{D}^{n-1})$ the submodule $\Theta H^2_{E}(\mathbb{D})$ of $H^2_{H(D^n-1)}(\mathbb{D})$, realized as a subspace of $H^2(\mathbb{D}^n)$, is a submodule of $H^2(\mathbb{D}^n)$? Let $\mathcal{H}$ be a Hilbert module over $\mathbb{C}[z]$. Denote by $\mathcal{R}(\mathcal{H})$ the set of all non-unitarily equivalent submodules of $\mathcal{H}$, that is, if $S_1, S_2 \in \mathcal{R}(\mathcal{H})$ and that $S_1 \cong S_2$ then $S_1 = S_2$. Question 3. (Rigidity of submodules) Determine $\mathcal{R}(H^2(\mathbb{D}^n))$. The aim of the present paper is to analyze and answer the above questions for the class of co-doubly commuting submodules of $H^2(\mathbb{D}^n)$. We obtain an explicit description of the cross commutators of co-doubly commuting submodules of $H^2(\mathbb{D}^n)$. As an applications, we prove that the cross commutators of a co-doubly commuting submodule $S$ of $H^2(\mathbb{D}^n)$ are compact, that is, $S$ is essentially doubly commuting, if and only if $n = 2$ or that $S$ is of finite co-dimension. We would like to point out that a submodule of finite co-dimension is necessarily essentially doubly commuting. Therefore, the issue of essential doubly commutativity of co-doubly commuting submodules of $H^2(\mathbb{D}^n)$ yields a rigidity type result: if $S$ is of infinite co-dimension co-doubly commuting submodules of $H^2(\mathbb{D}^n)$ and $S$ is essentially doubly commuting, then $n = 2$ (the base case). Our earlier classification results are also used to prove a Beurling-Lax-Halmos type theorem for the class of co-doubly commuting submodules of $H^2(\mathbb{D}^n)$. We also discuss the rigidity phenomenon of such submodules. Note also that most of the results of the present paper, concerning doubly commuting quotient modules and co-doubly commuting submodules, restricted to the base case $n = 2$ are known. However, the proofs are new even in the case $n = 2$. Moreover, as we have pointed out above, the difference between the base case $n = 2$ and the higher variables case $n > 2$ is more curious in the study of essentially doubly commuting submodules of $H^2(\mathbb{D}^n)$ (see Corollaries 2.6, 2.7 and 2.9). We now summarize the contents of this paper. In Section 2 we investigate the essential doubly commutativity problem for the class of co-doubly commuting submodules of $H^2(\mathbb{D}^n)$ and conclude that for $n \geq 3$, except for the finite co-dimension case, none of the co-doubly commuting submodules of $H^2(\mathbb{D}^n)$ are essentially doubly commuting. In Sections 3 and 4 we answer Questions 2 and 3 for the class of co-doubly commuting submodules of $H^2(\mathbb{D}^n)$, respectively. We conclude in Section 5 with some remarks and discussion on the problem of essentially doubly commutativity of Hilbert modules. ## 2. Cross commutators of submodules In a recent paper [28] we completely classify the class of doubly commuting quotient modules and co-doubly commuting submodules of the Hardy module $H^2(\mathbb{D}^n)$, where $n \geq 2$ (see [20] for the case $n = 2$). Theorem 2.1. Let $Q$ be a quotient module of $H^2(D^n)$ and $n \geq 2$. Then $Q$ is doubly commuting quotient module of $H^2(D^n)$ if and only if \[ Q = Q_{\Theta_1} \otimes \cdots \otimes Q_{\Theta_n}, \] where each $Q_{\Theta_i} = H^2(D)/\Theta_iH^2(D)$, a Jordan block of $H^2(D)$ for some inner function $\Theta_i \in H^\infty(D)$, or $Q_{\Theta_i} = H^2(D)$ for all $i = 1, \ldots, n$. Moreover, there exists an integer $m \in \{1, \ldots, n\}$ and inner functions $\Theta_{i_j} \in H^\infty(D)$ such that \[ Q^\perp = \sum_{1 \leq i_1 < \cdots < i_m \leq n} \tilde{\Theta}_{i_j}H^2(D^n), \] where $\tilde{\Theta}_{i_j}(z) = \Theta_{i_j}(z_{i_j})$ for all $z \in D^n$. Finally, \[ P_Q = I_{H^2(D^n)} - \prod_{j=1}^m (I_{H^2(D^n)} - M_{\tilde{\Theta}_{i_j}} M_{\tilde{\Theta}_{i_j}}^), \quad \text{and} \quad P_{Q^\perp} = \prod_{j=1}^m (I_{H^2(D^n)} - M_{\tilde{\Theta}_{i_j}} M_{\tilde{\Theta}_{i_j}}^). \] In what follows, we realize a doubly commuting quotient module $Q$ of $H^2(D^n)$ as $Q_{\Theta_1} \otimes \cdots \otimes Q_{\Theta_n}$ where each $Q_{\Theta_i} (1 \leq i \leq n)$ is either a Jordan block of $H^2(D)$ (see [6], [8], [23]) or the Hardy module $H^2(D)$. Consequently, a co-doubly commuting submodule $S$ of $H^2(D^n)$ will be realized as \[ S = \sum_{1 \leq i \leq n} \tilde{\Theta}_iH^2(D^n), \] where $\tilde{\Theta}_i(z) = \Theta_i(z_i)$ for all $z \in D^n$ and each $\Theta_i \in H^\infty(D)$ is either inner or the zero function. Note that a Jordan block $Q_{\Theta}$ of $H^2(D)$ is of finite dimension if and only if the inner function $\Theta$ is a finite Blaschke products on the unit disk. Moreover, for any Jordan block $Q_{\Theta}$ of $H^2(D)$ we have \[ \text{rank}[C_z^, C_z] \leq 1, \] where $C_z = P_{Q_{\Theta}} M_z\|_{Q_{\Theta}}$. First, we record a simple observation concerning essentially normal doubly commuting quotient modules of the Hardy module $H^2(D^n)$. Proposition 2.2. Let $Q = Q_{\Theta_1} \otimes \cdots \otimes Q_{\Theta_n}$ be a doubly commuting quotient module of $H^2(D^n)$. Then $Q$ is essentially normal if and only if each representing function $\Theta_i$ of $Q$ is a finite Blaschke product for all $i = 1, \ldots, n$, or, equivalently, $\dim Q < \infty$. Proof. Suppose $Q$ is a doubly commuting quotient module of $H^2(D^n)$, that is, \[ [C_{z_i}^, C_{z_j}] = 0, \] and \[ C_{z_i} = I_{Q_{\Theta_1}} \otimes \cdots \otimes P_{Q_{\Theta_i}} M_z\|_{Q_{\Theta_i}} \otimes \cdots \otimes I_{Q_{\Theta_n}}, \] for all $1 \leq i < j \leq n$. Then we obtain readily that \[ [C_{z_i}^, C_{z_j}] = I_{Q_{\Theta_1}} \otimes \cdots \otimes \left( C_{z_i}^ \otimes C_{z_j} \right) \otimes \cdots \otimes I_{Q_{\Theta_n}}, \] and conclude that $[C_{z_i}^, C_{z_j}] \in K(Q)$ for all $1 \leq i \leq n$ if and only if $\dim Q_{\Theta_i} < \infty$, or, equivalently, if and only if $\Theta_i$ is a finite Blaschke product for all $i = 1, \ldots, n$. Hence, $Q$ is essentially normal if and only if $\Theta_i$ is a finite Blaschke product for all $i = 1, \ldots, n$. This concludes the proof. Hence it follows in particular that essential normality of submodules of $H^2(\mathbb{D}^n)$ seems like a rather strong property. Therefore, in the rest of this section we will focus only on essentially doubly commuting submodules of $H^2(\mathbb{D}^n)$. Before proceeding we need to prove the following result concerning the rank of the multiplication operator restricted to a submodule and projected back on to the corresponding quotient module of the Hardy module $H^2(\mathbb{D})$. Proposition 2.3.* Let $Q_\Theta$ be a quotient module of $H^2(\mathbb{D})$ for some inner function $\Theta \in H^\infty(\mathbb{D})$. Then $C_\Theta := P_{Q_\Theta} M^_z\|_{H^2(\mathbb{D})} \in \mathcal{L}(\Theta H^2(\mathbb{D}), Q_\Theta)$ is given by \[ C_\Theta = [M^_z, M_\Theta]M^_\Theta. \] Moreover, $C_\Theta$ is a rank one operator and \[ \\|C_\Theta\\| = (1 - \|\Theta(0)\|^2)^{\frac{1}{2}}. \] Proof.* We begin by calculating \[ (I - M_\Theta M^_\Theta)M^_z M_\Theta = M^_z M_\Theta - M_\Theta M^_\Theta M^_z M_\Theta \] \[ = M^_z M_\Theta - M_\Theta M^_z M_\Theta M^_\Theta \] \[ = M^_z M_\Theta - M_\Theta M^_z \] \[ = [(M^_z M_\Theta - M_\Theta M^_z)M^_\Theta]M_\Theta. \] Therefore, we have \[ C_\Theta = (M^_z M_\Theta - M_\Theta M^_z)M^_\Theta = [M^_z, M_\Theta]M^_\Theta. \] Now for all $l \geq 1$ \[ [M^_z, M_\Theta]z^l = (M^_z M_\Theta - M_\Theta M^_z)M^_z 1 = 0, \] and \[ [M^_z, M_\Theta]1 = (M^_z M_\Theta - M_\Theta M^_z)1 = M^_z \Theta. \] And so, \[ [M^_z, M_\Theta]f = M^_z M_\Theta f(0) = f(0) M^_z \Theta = \langle f, 1 \rangle M^_z \Theta = \langle \Theta f, \Theta \rangle M^_z \Theta, \] for all $f \in H^2(\mathbb{D})$. Hence, we infer that \[ C_\Theta(\Theta f) = [M^_z, M_\Theta]f = \langle \Theta f, \Theta \rangle M^_z \Theta. \] Therefore, $C_\Theta$ is a rank one operator and \[ C_\Theta f = \langle f, \Theta \rangle M^_z \Theta, \] for all $f \in \Theta H^2(\mathbb{D})$. Finally, \[ \\|C_\Theta\\|^2 = \\|\Theta\\|^2 \\|M^_z \Theta\\|^2 = \\|M^_z \Theta\\|^2 \] \[ = \langle M_z M^_z \Theta, \Theta \rangle = \langle (I_{H^2(\mathbb{D})} - P_C) \Theta, \Theta \rangle \] \[ = \\|\Theta\\|^2 - \|\Theta(0)\|^2 \] \[ = 1 - \|\Theta(0)\|^2. \] This completes the proof. In the sequel we will need the following well known fact (cf. Lemma 2.5 in [28]). Lemma 2.4.* Let $\{P_i\}_{i=1}^n$ be a collection of commuting orthogonal projections on a Hilbert space $\mathcal{H}$. Then $$\mathcal{L} := \sum_{i=1}^n \text{ran} P_i,$$ is closed and the orthogonal projection of $\mathcal{H}$ onto $\mathcal{L}$ is given by $$P_\mathcal{L} = P_1(I - P_2) \cdots (I - P_n) + P_2(I - P_3) \cdots (I - P_n) + \cdots + P_{n-1}(I - P_n) + P_n$$ Moreover, $$P_\mathcal{L} = I - \prod_{i=1}^n (I - P_i).$$ We now are ready to compute the cross commutators of a co-doubly commuting submodule of $H^2(\mathbb{D}^n)$. Theorem 2.5. Let $\mathcal{S} = \sum_{i=1}^n \tilde{\Theta}_i H^2(\mathbb{D}^n)$ be a co-doubly commuting submodule of $H^2(\mathbb{D}^n)$, where $\tilde{\Theta}_i(z) = \Theta_i(z_i)$ for all $z \in \mathbb{D}^n$ and each $\Theta_i \in H^\infty(\mathbb{D})$ is either an inner function or the zero function and $1 \leq i \leq n$. Then for all $1 \leq i < j \leq n$, $$[R_{z_i}^, R_{z_j}] = I_{\Theta_{\tilde{z}_i}} \otimes \cdots \otimes P_{\Theta_{\tilde{z}_i}} M_{\tilde{z}_i}^ \|_{\Theta_{\tilde{z}_i} H^2(\mathbb{D})} \otimes \cdots \otimes P_{\Theta_{\tilde{z}_i}} M_{z_j}^* \|_{\Theta_{\tilde{z}_i}} \otimes \cdots \otimes I_{\Theta_{\tilde{z}_n}},$$ and $$\\|[R_{z_i}^, R_{z_j}]\\| = (1 - \|\Theta_i(0)\|^2)^{\frac{1}{2}} (1 - \|\Theta_j(0)\|^2)^{\frac{1}{2}}.$$ and that \[ P_SM^_z M_j^* P_S - P_SM^_z M_j P_S = P_SM^_z M_j^* P_S - P_SM^_z M_j (I - P_Q) M^_z P_S = P_SM^_z P_Q M^_z P_S. \] Furthermore we have for all $ 1 \leq i < j \leq n $, \[ P_SM^_z P_Q M^_z P_S = [\hat{P}_n(I - \hat{P}_{n-1})\cdots(I - \hat{P}_1) + \hat{P}_{n-1}(I - \hat{P}_{n-2})\cdots(I - \hat{P}_1) + \cdots + \hat{P}_2(I - \hat{P}_1) + \hat{P}_1] \] \[ M_z \prod_{l=1}^n (I_{H^2(\mathbb{D}^n)} - \hat{P}_l)] M_{z_j}^* \] \[ [\hat{P}_n(I - \hat{P}_2)\cdots(I - \hat{P}_n) + \hat{P}_n(I - \hat{P}_{n-1})\cdots(I - \hat{P}_1) + \cdots + \hat{P}_2(I - \hat{P}_1) + \hat{P}_1] \] \[ \prod_{l \neq j} (I_{H^2(\mathbb{D}^n)} - \hat{P}_l)] M_{z_j}^[\prod_{l \neq i} (I_{H^2(\mathbb{D}^n)} - \hat{P}_l)] \] \[ [\hat{P}_n(I - \hat{P}_2)\cdots(I - \hat{P}_n) + \hat{P}_n(I - \hat{P}_{n-1})\cdots(I - \hat{P}_1) + \cdots + \hat{P}_2(I - \hat{P}_1) + \hat{P}_1] \] \[ = [\hat{P}_2(I - \hat{P}_{j-1})\cdots(I - \hat{P}_1)] M_{z_j}^ M_{z_j} [\hat{P}_i(I - \hat{P}_{i+1})\cdots(I - \hat{P}_n)] \] \[ = [(I - \hat{P}_1)\cdots(I - \hat{P}_{j-1}) \hat{P}_j M_{z_j} (I - \hat{P}_j) (I - \hat{P}_{j+1})\cdots(I - \hat{P}_n)]. \] These equalities shows that \[ [R_{z_i}^, R_{z_j}] = [(I - \hat{P}_1)\cdots(I - \hat{P}_i)\cdots(I - \hat{P}_{j-1}) \hat{P}_j] M_{z_i}^ M_{z_j} [(I - \hat{P}_1)\cdots(I - \hat{P}_{i-1}) (I - \hat{P}_i) M_{z_i}^* \hat{P}_i] (I - \hat{P}_{i+1})\cdots(I - \hat{P}_{j-1}) (I - \hat{P}_j) (I - \hat{P}_{j+1})\cdots(I - \hat{P}_n).\] Moreover, \[ [R_{z_i}^, R_{z_j}] = [(I - \hat{P}_1)\cdots(I - \hat{P}_{j-1}) \hat{P}_j M_{z_i}^ M_{z_j} [(I - \hat{P}_1)\cdots(I - \hat{P}_{i+1}) \hat{P}_i (I - \hat{P}_{i+1})\cdots(I - \hat{P}_n)], \] and \[ [R_{z_i}^, R_{z_j}] = [(I - \hat{P}_1)\cdots(I - \hat{P}_{j-1}) \hat{P}_j (I - \hat{P}_{j+1})\cdots(I - \hat{P}_n)] M_{z_i}^ M_{z_j} [\hat{P}_i (I - \hat{P}_{i+1})\cdots(I - \hat{P}_n)]. \] We conclude that the cross-commutator $[R_{z_i}^, R_{z_j}]$ is a bounded linear operator from \[ Q_{\Theta_1} \otimes \cdots \otimes Q_{\Theta_{i-1}} \otimes \Theta_j H^2(\mathbb{D}) \otimes Q_{\Theta_{i+1}} \otimes \cdots \otimes Q_{\Theta_j} \otimes \cdots \otimes Q_{\Theta_n} \subseteq S \] to \[ Q_{\Theta_1} \otimes \cdots \otimes Q_{\Theta_i} \otimes \cdots \otimes Q_{\Theta_{j-1}} \otimes \Theta_j H^2(\mathbb{D}) \otimes Q_{\Theta_{j+1}} \otimes \cdots \otimes Q_{\Theta_n} \subseteq S, \] and \[ [R_{z_i}^, R_{z_j}] = I_{Q_{\Theta_1}} \otimes \cdots \otimes P_{Q_{\Theta_i} M_{z_i}^* \Theta_j H^2(\mathbb{D})} \otimes \cdots \otimes P_{Q_{\Theta_j} H^2(\mathbb{D}) M_{z_j}} Q_{\Theta_j} \otimes \cdots \otimes I_{Q_{\Theta_n}}. \] Further, we note that \[ \\|[R_{z_i}^, R_{z_j}]\\| = \\|P_{Q_{\Theta_1}} \otimes \cdots \otimes P_{Q_{\Theta_i} M_{z_i}^ \Theta_j H^2(\mathbb{D})} \otimes \cdots \otimes P_{Q_{\Theta_j} H^2(\mathbb{D}) M_{z_j}} Q_{\Theta_j} \otimes \cdots \otimes I_{Q_{\Theta_n}}\\| \] \[ = \\|P_{Q_{\Theta_i} M_{z_i}^* \Theta_j H^2(\mathbb{D})} \\| \\|P_{Q_{\Theta_j} H^2(\mathbb{D}) M_{z_j}} Q_{\Theta_j} \\|. \] and consequently by Proposition 2.3 we have \[ \\| [R^_z, R_z] \\| = (1 - \|\Theta_i(0)\|^2)^{\frac{1}{2}}(1 - \|\Theta_j(0)\|^2)^{\frac{1}{2}}. \] This completes the proof. In the following corollary we reveal the significance of the identity operators in the cross commutators of the co-doubly commuting submodules of $ H^2(\mathbb{D}^n) $ for $ n \geq 2 $. Corollary 2.6.* Let $ S = \sum_{i=1}^{n} \tilde{\Theta}_i H^2(\mathbb{D}^n) $ be a submodule of $ H^2(\mathbb{D}^n) $ for some one variable inner functions $ \{\tilde{\Theta}_i\}_{i=1}^{n} \subseteq H^\infty(\mathbb{D}^n) $. Then (1) for $ n = 2 $: the rank of the cross commutator of $ S $ is at most one and the Hilbert-Schmidt norm of the cross commutator is given by \[ \\| [R^_z, R_z] \\|_{HS} = (1 - \|\Theta_1(0)\|^2)^{\frac{1}{2}}(1 - \|\Theta_2(0)\|^2)^{\frac{1}{2}}. \] In particular, $ S $ is essentially doubly commuting. (2) for $ n > 2 $: $ S $ is essentially doubly commuting (or of Hilbert-Schmidt cross-commutators) if and only if $ \tilde{\Theta}_i $ is a one variable finite Blaschke product for all $ 1 \leq i \leq n $, if and only if that $ S $ is of finite co-dimension, that is, \[ \dim [H^2(\mathbb{D}^n)/S] < \infty. \] Moreover, in this case, for all $ 1 \leq i < j \leq n $ \[ \\| [R^_z, R_z] \\|_{HS} = (1 - \|\Theta_i(0)\|^2)^{\frac{1}{2}}(1 - \|\Theta_j(0)\|^2)^{\frac{1}{2}}. \] Part (1) of the above corollary was obtained by R. Yang (Corollary 1.1, [30]). We refer the reader to [1] for more details on finite co-dimensional submodules of the Hardy modules over $ \mathbb{D}^n $. As another consequence of the above theorem, we have the following. Corollary 2.7. Let $ n > 2 $ and $ S = \sum_{i=1}^{k} \tilde{\Theta}_i H^2(\mathbb{D}^n) $ be a co-doubly commuting proper submodule of $ H^2(\mathbb{D}^n) $ for some inner functions $ \{\Theta_i\}_{i=1}^{k} $ and $ k < n $. Then $ S $ is not essentially doubly commuting. Combining Corollary 2.6 and Proposition 2.2 we obtain: Corollary 2.8. Let $ S $ be a co-doubly commuting submodule of $ H^2(\mathbb{D}^n) $ and $ Q := H^2(\mathbb{D}^n)/S $ and $ n > 2 $. Then the following are equivalent: (i) $ S $ is essentially doubly commuting. (ii) $ S $ is of finite co-dimension. (iii) $ Q $ is essentially normal. We conclude this section with a “rigidity” result. Corollary 2.9. Let $ n \geq 2 $ and $ S = \sum_{i=1}^{n} \tilde{\Theta}_i H^2(\mathbb{D}^n) $ be an essentially normal co-doubly commuting submodule of $ H^2(\mathbb{D}^n) $ for some one variable inner functions $ \{\Theta_i\}_{i=1}^{n} $. If $ S $ is of infinite co-dimensional, then $ n = 2 $. Proof. The result follows from the implication (i) $ \implies $ (ii) of Corollary 2.8. $ \blacksquare $ 3. Representing Inner functions of Submodules In this section, we will obtain the explicit representations of the Beurling-Lax-Halmos inner functions of a class of submodules of $H^2_2(D)$. Recall that a non-trivial closed subspace $S$ of $H^2_2(D)$ is a submodule of $H^2_2(D)$ if and only if $$S = \Theta H^2_{E_1}(D),$$ for some closed subspace $E_1$ of $E$ and inner function $\Theta \in H^\infty_{E_1}(D)$ (unique up to unitary equivalence). This fact is known as the Beurling-Lax-Halmos theorem and that $\Theta$ as the representing inner function of the submodule $S$. Given a submodule $S$ of $H^2_2(D)$, it is a question of interest to determine the inner function $\Theta$ associated with $S$. Now let $S$ be a co-doubly commuting submodule of $H^2(D^n)$. Then by Theorem 2.1 we have $$S = \sum_{i=1}^n \Theta_i H^2(D^n),$$ where $\Theta_i \in H^\infty(D^n)$ is either the zero function or one variable inner function and $i = 1, \ldots, n$. We realize $S$ as a submodule of $H^2_2(D)$ where $E = H^2(D^{n-1})$. Then by the Beurling-Lax-Halmos theorem, there exists an inner function $\Theta \in H^\infty_{E_1}(D)$, for some closed subspace $E_1$ of $H^2(D^{n-1})$ such that $$S = \sum_{i=1}^n \Theta_i H^2(D^n) = \Theta H^2_{E_1}(D).$$ Since $$R_z R_z^* = M_z P_S M_z^\|_S = M_z P_S M_z^,$$ that $R_z R_z^$ is an orthogonal projection onto $zS$ and hence we have the orthogonal projection $$P_{zS} - R_z R_z^ = P_{zS}.$$ On the other hand $$P_{zS} - R_z R_z^* = M_{\Theta} M_{\Theta}^* - M_{\Theta} M_{\Theta} M_{\Theta}^* M_{\Theta}^* = M_{\Theta}(I_{H^2_{E_1}(D)} - M_z M_z^) M_{\Theta} = M_{\Theta} P_{E_1} M_{\Theta}^$$ and hence $$S \ominus zS = \text{ran}(P_{zS} - R_z R_z^) = \text{ran}(M_{\Theta} P_{E_1} M_{\Theta}^) = \text{ran}(M_{\Theta} P_{E_1})$$ $$= \{ \Theta \Theta : \eta \in E_1 \}.$$ Note also that $S \ominus zS$ is the wandering subspace of $S$, that is, $$S \ominus zS = \text{span}\{ z^l(S \ominus zS) : l \geq 0 \} = \Theta H^2_{E_1}(D).$$ After these preliminaries we can turn to the proof of the main result of this section. Theorem 3.1. Let $S$ be a submodule of $H^2_2(D^{n-1})(D)$ with the Beurling-Lax-Halmos representation $S = \Theta H^2_{E_1}(D)$ for some closed subspace $E$ of $H^2(D^{n-1})$ and inner function $\Theta \in H^\infty_{E_1,H^2(D^{n-1})}(D)$. Then $S \subseteq H^2(D^n)$ is a co-doubly commuting submodule of $H^2(D^n)$ if and only if there exits an integer $m \leq n$ and orthogonal projections $ \{P_2, \ldots, P_m\} $ in $ \mathcal{L}(H^2(\mathbb{D})) $ and an inner function $ \Theta_1 \in H^\infty(\mathbb{D}) $ such that $ \mathcal{E} = H^2(\mathbb{D}^{n-1}) $ and \[ \Theta(z) = \Theta_1(z)(I - \tilde{P}_2) \cdots (I - \tilde{P}_m) + \tilde{P}_2(I - \tilde{P}_3) \cdots (I - \tilde{P}_m) + \cdots + \tilde{P}_{m-1}(I - \tilde{P}_m) + \tilde{P}_m, \] for all $ z \in \mathbb{D} $, where \[ \tilde{P}_i = I_{H^2(\mathbb{D})} \otimes \cdots \otimes P_i \otimes \cdots \otimes I_{H^2(\mathbb{D})} \in \mathcal{L}(H^2(\mathbb{D}^{n-1})). \] Proof. Let $ \mathcal{S} $ be a co-doubly commuting submodule of $ H^2(\mathbb{D}^n) $ so that \[ \mathcal{S} = \sum_{1 \leq i_1 < \cdots < i_m \leq n} \tilde{\Theta}_{i_j} H^2(\mathbb{D}^n), \] for some one variable inner function $ \tilde{\Theta}_{i_j} \in H^\infty(\mathbb{D}^n) $ and $ 1 \leq i_1 < \cdots < i_m \leq n $. Without loss of generality, we assume that $ i_j = j $ for all $ j = 1, \ldots, m $, that is, \[ \mathcal{S} = \sum_{j=1}^m \tilde{\Theta}_j H^2(\mathbb{D}^n). \] Then Theorem 2.1 implies that \[ P_S = I_{H^2(\mathbb{D}^n)} - \prod_{j=1}^m (I_{H^2(\mathbb{D}^n)} - M_{\tilde{\Theta}_j} M_{\tilde{\Theta}_j}^) \] \[ = I_{H^2(\mathbb{D}^n)} - (I_{H^2(\mathbb{D}^n)} - M_{\tilde{\Theta}_1} M_{\tilde{\Theta}_1}^) \prod_{j=2}^m (I_{H^2(\mathbb{D}^n)} - I_{H^2(\mathbb{D})} \otimes \tilde{P}_j), \] where \[ \tilde{P}_j = I_{H^2(\mathbb{D})} \otimes \cdots \otimes M_{\tilde{\Theta}_1} M_{\tilde{\Theta}_1}^* \otimes \cdots \otimes I_{H^2(\mathbb{D})} \in \mathcal{L}(H^2(\mathbb{D}^{n-1})), \] $(n-1)$ times for all $ j = 2, \ldots, m $. Define $ \Theta \in H^\infty_{\mathcal{L}(H^2(\mathbb{D}^{n-1}))}(\mathbb{D}) $ by \[ \Theta(z) = \Theta_1(z)(I - \tilde{P}_2) \cdots (I - \tilde{P}_m) + \tilde{P}_2(I - \tilde{P}_3) \cdots (I - \tilde{P}_m) + \cdots + \tilde{P}_{m-1}(I - \tilde{P}_m) + \tilde{P}_m, \] for all $ z \in \mathbb{D} $. First, note that \[ M_{\Theta} = M_{\Theta_1}(I - \tilde{P}_2) \cdots (I - \tilde{P}_m) + \tilde{P}_2(I - \tilde{P}_3) \cdots (I - \tilde{P}_m) + \cdots + \tilde{P}_{m-1}(I - \tilde{P}_m) + \tilde{P}_m. \] Since the terms in the sum are orthogonal projection with orthogonal ranges, we compute \[ M_{\Theta}^* M_{\Theta} = M_{\Theta_1}^* M_{\Theta_1}(I - \tilde{P}_2) \cdots (I - \tilde{P}_m) + \tilde{P}_2(I - \tilde{P}_3) \cdots (I - \tilde{P}_m) + \cdots + \tilde{P}_{m-1}(I - \tilde{P}_m) + \tilde{P}_m \] \[ = (I - \tilde{P}_2) \cdots (I - \tilde{P}_m) + \tilde{P}_2(I - \tilde{P}_3) \cdots (I - \tilde{P}_m) + \cdots + \tilde{P}_{m-1}(I - \tilde{P}_m) + \tilde{P}_m \] \[ = \prod_{j=2}^m (I_{H^2(\mathbb{D}^n)} - \tilde{P}_j) + \prod_{j=2}^m (I_{H^2(\mathbb{D}^n)} - \tilde{P}_j) \] \[ = I_{H^2(\mathbb{D}^{n-1})}, \] and hence that $\Theta$ is an inner function. To prove that $\Theta$ is the Beurling-Lax-Halmos representing inner function of $\mathcal{S}$, by virtue of (3.1), it is enough to show that $$\overline{\text{span}}\{z^l\Theta H^2(\mathbb{D}^{n-1}) : l \geq 0\} = \sum_{j=1}^{m} \tilde{\Theta}_j H^2(\mathbb{D}^n).$$ Observe that $$\Theta H^2(\mathbb{D}^{n-1}) = \Theta_1 (Q_{\Theta_2} \otimes \cdots \otimes Q_{\Theta_m} \otimes H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D}))$$ $$\oplus (\Theta_2 H^2(\mathbb{D}) \otimes Q_{\Theta_3} \otimes \cdots \otimes Q_{\Theta_m} \otimes H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D}))^{(n-m) \text{ times}}$$ $$\oplus \cdots \oplus (H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D}) \otimes \Theta_m H^2(\mathbb{D}) \otimes H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D})),$$ and hence $$\overline{\text{span}}\{z^l\Theta H^2(\mathbb{D}^{n-1}) : l \geq 0\} = (\Theta_1 H^2(\mathbb{D}) \otimes Q_{\Theta_2} \otimes \cdots \otimes Q_{\Theta_m} \otimes H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D}))^{(n-m) \text{ times}}$$ $$\oplus (H^2(\mathbb{D}) \otimes \Theta_2 H^2(\mathbb{D}) \otimes Q_{\Theta_3} \otimes \cdots \otimes Q_{\Theta_m} \otimes H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D}))^{(n-m) \text{ times}}$$ $$\cdots \oplus (H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D}) \otimes \Theta_m H^2(\mathbb{D}) \otimes H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D}))^{(n-m) \text{ times}}$$ $$= \text{ran} \left[ I_{H^2(\mathbb{D}^n)} - \prod_{j=1}^{m} (I_{H^2(\mathbb{D}^n)} - M_{\Theta_j} M_{\Theta_j}^) \right]$$ $$= \sum_{i=1}^{m} \tilde{\Theta}_i H^2(\mathbb{D}^n).$$ Conversely, if $\Theta$ is given as above, then we realize $\Theta \in H^\infty_c(\mathbb{D}^{n-1}/\mathbb{D}^n) \prod_{j=1}^{m} (I_{H^2(\mathbb{D}^n)} - M_{\Theta_j} M_{\Theta_j}^)$ where $$\tilde{\Theta}(z) = \Theta_1(z_1)(I - \tilde{P}_2) \cdots (I - \tilde{P}_m) + \tilde{P}_2(I - \tilde{P}_3) \cdots (I - \tilde{P}_m) + \cdots + \tilde{P}_{m-1}(I - \tilde{P}_m) + \tilde{P}_m,$$ for all $z \in \mathbb{D}^n$. Thus $$\tilde{\Theta}(z) = \tilde{\Theta}_1(z)(I - \tilde{P}_2) \cdots (I - \tilde{P}_m) + \tilde{P}_2(I - \tilde{P}_3) \cdots (I - \tilde{P}_m) + \cdots + \tilde{P}_{m-1}(I - \tilde{P}_m) + \tilde{P}_m,$$ where $\tilde{\Theta}_1(z) = \Theta_1(z_1)$ for all $z \in \mathbb{D}^n$. We therefore have $$M_{\tilde{\Theta}} M_{\tilde{\Theta}}^* = \tilde{P}_1(I - \tilde{P}_2) \cdots (I - \tilde{P}_m) + \tilde{P}_2(I - \tilde{P}_3) \cdots (I - \tilde{P}_m) + \cdots + \tilde{P}_{m-1}(I - \tilde{P}_m) + \tilde{P}_m,$$ where $\tilde{P}_1 = M_{\tilde{\Theta}_1} M_{\tilde{\Theta}_1}^$. Consequently, $$M_{\tilde{\Theta}} M_{\tilde{\Theta}}^ = I_{H^2(\mathbb{D}^n)} - \prod_{i=1}^{m} (I_{H^2(\mathbb{D}^n)} - \tilde{P}_i),$$ and hence \[ I_{H^2(\mathbb{D}^n)} - M_\Theta^* M_\Phi = \prod_{i=1}^m (I_{H^2(\mathbb{D}^n)} - \tilde{P}_i). \] Therefore, we conclude that \[ (\text{ran} M_\Theta)^\perp = \left( \bigotimes_{i=1}^m (\Theta_1 H^2(\mathbb{D}))^\perp \otimes (P_2 H^2(\mathbb{D}))^\perp \otimes \cdots \otimes (P_m H^2(\mathbb{D}))^\perp \right) \otimes H^2(\mathbb{D}) \otimes \cdots \otimes H^2(\mathbb{D}). \] Combine this with the assumption that $(\text{ran} M_\Theta)^\perp$ is a quotient module of $H^2(\mathbb{D}^n)$ to conclude that $(\text{ran} M_\Theta)^\perp$ is a doubly commuting quotient module. This completes the proof. $\blacksquare$ The above result is a several variables generalization $(n \geq 2)$ of Theorem 3.1 in [25] by Qin and Yang. 4. RIGIDITY OF SUBMODULES Let $\mathcal{M}_i \subseteq H^2(\mathbb{D}^n)$, $i = 1, 2$, be two submodules of $H^2(\mathbb{D}^n)$. We say that $\mathcal{S}_1$ and $\mathcal{S}_2$ are unitarily equivalent if there exists a unitary map $U : \mathcal{S}_1 \to \mathcal{S}_2$ such that \[ U(M_{z_i}\|_{\mathcal{S}_1}) = (M_{z_i}\|_{\mathcal{S}_2})U, \] or equivalently, \[ UM_{z_i} = M_{z_i}U, \] for all $i = 1, \ldots, n$. A consequence of Beurling’s theorem ensures that, any pair of non-zero submodules of $H^2(\mathbb{D})$ are unitarily equivalent. The conclusion also follows directly from the unitary invariance property of the index of the wandering subspaces associated with the shift operators. This phenomenon is subtle, and in general not true for many other Hilbert modules. For instance, a pair of submodules $\mathcal{S}_1$ and $\mathcal{S}_2$ of the Bergman modules $L^2(\mathbb{B}^n)$ are unitarily equivalent if and only if $\mathcal{S}_1 = \mathcal{S}_2$ (see [26], [24]). We refer the reader to [12], [13], [14], [15], [29] and [19] for more results on the rigidity of submodules and quotient modules of Hilbert modules over domains in $\mathbb{C}^n$. The submodules corresponding to the doubly commuting quotient modules also holds the rigidity property. This is essentially a particular case of a rigidity result due to Agrawal, Clark and Douglas (Corollary 4 in [2]). See also [21]. Theorem 4.1. (Agrawal, Clark and Douglas) Let $\mathcal{S}_1$ and $\mathcal{S}_2$ be two submodules of $H^2(\mathbb{D}^n)$, both of which contain functions independent of $z_i$ for $i = 1, \ldots, n$. Then $\mathcal{S}_1$ and $\mathcal{S}_2$ are unitarily equivalent if and only if they are equal. In particular, we obtain a generalization of the rigidity theorem for $n = 2$ (see Corollary 2.3 in [30]). Corollary 4.2. Let $\mathcal{S}_\Theta = \sum_{i=1}^n \tilde{\Theta}_i H^2(\mathbb{D})^n$ and $\mathcal{S}_\Phi = \sum_{i=1}^n \tilde{\Phi}_i H^2(\mathbb{D})^n$ be a pair of submodules of $H^2(\mathbb{D})^n$, where $\tilde{\Theta}_i(z) = \Theta_i(z_i)$ and $\tilde{\Phi}_i(z) = \Phi_i(z_i)$ for inner functions $\Theta_i, \Phi_i \in H^\infty(\mathbb{D})$ and $z \in \mathbb{D}^n$ and $i = 1, \ldots, n$. Then $\mathcal{S}_\Theta$ and $\mathcal{S}_\Phi$ are unitarily equivalent if and only if $\mathcal{S}_\Theta = \mathcal{S}_\Phi$. Proof. Clearly $\tilde{\Theta}_i \in S_\Theta$ and $\tilde{\Phi}_i \in S_\Phi$ are independent of $\{z_1, \cdots, z_{i-1}, z_{i+1}, \ldots, z_n\}$ for all $i = 1, \ldots, n$. Therefore, the submodules $S_\Theta$ and $S_\Phi$ contains functions independent of $z_i$ for all $i = 1, \ldots, n$. Consequently, if $S_\Phi$ and $S_\Theta$ are unitarily equivalent then $S_\Theta = S_\Phi$. ■ The following result is a generalization of Corollary 4.4 in [30] and is a consequence of the rigidity result. Corollary 4.3. Let $S_\Theta = \sum_{i=1}^n \tilde{\Theta}_i H^2(\mathbb{D})^n$ be a submodule of $H^2(\mathbb{D})^n$, where $\tilde{\Theta}_i(z) = \Theta_i(z)$ for inner functions $\Theta_i \in H^\infty(\mathbb{D})$ for all $i = 1, \ldots, n$ and $z \in \mathbb{D}^n$. Then $S_\Theta$ and $H^2(\mathbb{D}^n)$ are not unitarily equivalent. Proof. The result follows from the previous theorem along with the observation that $S_\Theta \neq \{0\}$. ■ We close this section by noting that the results above are not true if we drop the assumption that all $\Theta_i$ are inner. For instance, if $\Theta_i = \Phi_i = 0$ for all $i \neq 1$ then $S_\Theta \cong S_\Phi$ but in general, $S_\Theta \neq S_\Phi$ (see [22]). 5. Concluding remarks One of the central issues in the study of Hilbert modules is the problem of analyzing essentially normal submodules and quotient modules of a given essentially normal Hilbert module over $\mathbb{C}[z]$. There is, however, a crucial difference between the Hilbert modules of functions defined over the unit ball and the polydisc in $\mathbb{C}^n$. For instance, a submodule $S$ of an essentially normal Hilbert module $\mathcal{H}$ is essentially normal if and only if the quotient module $\mathcal{H}/S$ is so (see [1], [10]), that is, the study of essentially normal submodules and quotient modules of essentially normal Hilbert modules amounts to the same. However, this is not the case for the study of essentially doubly commuting Hilbert modules over $\mathbb{D}^n$. In other words, the theory of essentially doubly commuting submodules and quotient modules of an essentially doubly commuting Hilbert modules are two different concepts. One could, however, consider the co-doubly commuting submodules as a special class of submodules of the Hardy module and the results of this paper indicates that the general picture of essentially doubly commuting submodules of the Hardy module will by no means be easy to understand (cf. Corollary 2.6). In particular, the homogenous submodules of $H^2(\mathbb{D}^2)$ are always essentially doubly commuting [9]. Hence Question 1 has an affirmative answer for the class of homogenous submodules of $H^2(\mathbb{D}^2)$. It is not known whether the homogeneous submodules of $H^2(\mathbb{D}^n)$, when $n \geq 3$, are essentially doubly commuting. Corollary 2.6 gives an indication of a possible answer to the case $n \geq 3$. Results related to essentially normal submodules of the Drury-Arveson module over the unit ball of $\mathbb{C}^2$ can be found in [18]. Our result concerning the Beurling-Lax-Halmos inner function, Theorem 3.1, is closely related to the classification theory of multi-isometries (see [7] and [5]) for $n = 2$ case. We hope to discuss the general case in a future paper. We conclude with a result concerning the $C_0$ class. Recall that a completely non-unitary contraction $T$ on some Hilbert space $\mathcal{H}$ is said to be in the class $C_0$ if there is a non-zero function $\Theta \in H^\infty(\mathbb{D})$ such that $\Theta(T) = 0$ [23]. Proposition 5.1. Let $Q$ be a non-trivial doubly commuting quotient module of $H^2(\mathbb{D}^n)$. Then $R_{z_i} \in C_0$ for some $1 \leq i \leq n$. Proof. By virtue of Theorem 2.1, we let $Q = Q_{\Theta_1} \otimes \cdots \otimes Q_{\Theta_n}$ and $Q_{\Theta_i} \neq H^2(\mathbb{D})$ for some $1 \leq i \leq n$. Consequently, $\Theta_i(R_{z_i}) = 0$ and hence $$\tilde{\Theta}_i(R_{z_i}) = I_{Q_{\Theta_1}} \otimes \cdots \otimes I_{Q_{\Theta_i}} \otimes \cdots I_{Q_{\Theta_n}} = 0.$$ This concludes the proof. The above result for the case $n = 2$ is due to Douglas and Yang (see Proposition 4.1 in [11]). However, our proof is more elementary. References [1] P. Ahern and D. Clark, Invariant subspaces and analytic continuation in several variables, J. Math. Mech. 19 (1969/1970) 963-969. [2] O. Agrawal, D. Clark and R. Douglas, Invariant subspaces in the polydisk, Pacific J. Math. 121(1986), 1-11. [3] W. Arveson, Quotients of standard Hilbert modules, Trans. Amer. Math. Soc. 359 (2007), no. 12, 6027-6055. [4] W. Arveson, $p$-summable commutators in dimension $d$, J. Operator Theory 54 (2005), no. 1, 101-117. [5] H. Bercovici, R. Douglas and C. Foias, On the classification of multi-isometries, Acta Sci. Math. (Szeged) 72 (2006), no. 3-4, 639-661. [6] H. Bercovici, Operator theory and arithmetic in $H^\infty$, Mathematical Surveys and Monographs, No. 26, A.M.S., Providence, Rhode Island, 1988. [7] C. Berger, L. Coburn and A. Lebow, Representation and index theory for $C^$-algebras generated by commuting isometries, J. Funct. Anal. 27 (1978), 51-99. [8] A. Beurling, On two problems concerning linear transformations in Hilbert space, Acta Math. 81 (1949), 239-255. [9] R. Curto, P. Muhly and K. Yan, The $C^$-algebra of an homogeneous ideal in two variables is type I, Current topics in operator algebras (Nara, 1990), World Sci. Publ., River Edge, NJ, 1991, 130-136. [10] R. Douglas, Essentially reductive Hilbert modules, J. Operator Theory 55 (2006), no. 1, 117-133. [11] R. Douglas and R. Yang, Operator theory in the Hardy space over the bidisk. I, Integral Equations Operator Theory, 38(2000), 207-221. [12] R. Douglas and R. Yang, Quotient Hardy modules, Houston J. Math. 24 (1998), no. 3, 507-517. [13] R. Douglas, V. Paulsen, C. Sah and K. Yan, Algebraic reduction and rigidity for Hilbert modules, Amer. J. Math. 117 (1995), 75-92. [14] R. Douglas and C. Foias, Uniqueness of multi-variate canonical models, Acta Sci. Math. (Szeged) 57 (1993), no. 1-4, 79-81. [15] R. Douglas and K. Yan, On the rigidity of Hardy submodules, Integral Equations Operator Theory, 13 (1990), 350-363. [16] R. Douglas and V. Paulsen, Hilbert Modules over Function Algebras, Research Notes in Mathematics Series, 47, Longman, Harlow, 1989. [17] C. Fefferman and E. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137-193. [18] K. Guo, Defect operators for submodules of $H^2_3$, J. Reine Angew. Math. 573 (2004), 181-209. [19] K. Guo, Equivalence of Hardy submodules generated by polynomials, J. Funct. Anal. 178 (2000), 343-371. [20] K. Izuchi, T. Nakazi and M. Seto, Backward shift invariant subspaces in the bidisc II, J. Oper. Theory 51 (2004), 361-376. [21] K. Izuchi, Unitary equivalence of invariant subspaces in the polydisk, Pacific J. Math. 130 (1987), no. 2, 351-358. [22] V. Mandrekar, The validity of Beurling theorems in polydiscs, Proc. Amer. Math. Soc. 103 (1988), 145-148. [23] B. Sz.-Nagy and C. Foias, Harmonic Analysis of Operators on Hilbert Space, North Holland, Amsterdam, 1970. [24] M. Putinar, On the rigidity of Bergman submodules, Amer. J. Math. 116 (1994), 1421-1432. [25] Y. Qin and R. Yang, A characterization of submodules via Beurling-Lax-Halmos theorem, To appera in Proc. of AMS. [26] S. Richter, Unitary equivalence of invariant subspaces of Bergman and Dirichlet spaces, Pac. J. Math. 133 (1988), 151-156. [27] W. Rudin, Function Theory in Polydiscs, Benjamin, New York 1969. [28] J. Sarkar, Jordan blocks of $H^2(\mathbb{D}^n)$, [arXiv:1303.1041](http://arxiv.org/abs/1303.1041) to appear in Journal of Operator theory. [29] R. Yang, On two variable Jordan block. II, Integral Equations Operator Theory 56 (2006), no. 3, 431-449. [30] R. Yang, Hilbert-Schmidt submodules and issues of unitary equivalence, J. Operator Theory 53 (2005), no. 1, 169-184. Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, RVCE Post, Bangalore, 560059, India E-mail address: [email protected], [email protected]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2685, 1 ], [ 2685, 6417, 2 ], [ 6417, 10004, 3 ], [ 10004, 12931, 4 ], [ 12931, 15284, 5 ], [ 15284, 16720, 6 ], [ 16720, 19735, 7 ], [ 19735, 22527, 8 ], [ 22527, 24945, 9 ], [ 24945, 27800, 10 ], [ 27800, 30631, 11 ], [ 30631, 33795, 12 ], [ 33795, 37354, 13 ], [ 37354, 40553, 14 ], [ 40553, 41889, 15 ] ] }
2e9e22f9637a8f60cf53944cb591036eeb84850e	{ "olmocr-version": "0.1.59", "pdf-total-pages": 29, "total-fallback-pages": 0, "total-input-tokens": 88698, "total-output-tokens": 27255, "fieldofstudy": [ "Computer Science" ] }	Repair Pipelining for Erasure-coded Storage: Algorithms and Evaluation XIAOLU LI, ZUORU YANG, JINHONG LI, RUNHUI LI, and PATRICK P. C. LEE, The Chinese University of Hong Kong, China QUN HUANG, Peking University, China YUCHONG HU, Huazhong University of Science and Technology, China We propose repair pipelining, a technique that speeds up the repair performance in general erasure-coded storage. By carefully scheduling the repair of failed data in small-size units across storage nodes in a pipelined manner, repair pipelining reduces the single-block repair time to approximately the same as the normal read time for a single block in homogeneous environments. We further design different extensions of repair pipelining algorithms for heterogeneous environments and multi-block repair operations. We implement a repair pipelining prototype, called ECPipe, and integrate it as a middleware system into two versions of Hadoop Distributed File System (HDFS) (namely, HDFS-RAID and HDFS-3) as well as Quanzcast File System. Experiments on a local testbed and Amazon EC2 show that repair pipelining significantly improves the performance of degraded reads and full-node recovery over existing repair techniques. CCS Concepts: • Information systems → Storage recovery strategies; Distributed storage; Additional Key Words and Phrases: Erasure coding, distributed storage systems ACM Reference format: Xiaolu Li, Zuoru Yang, Jinhong Li, Runhui Li, Patrick P. C. Lee, Qun Huang, and Yuchong Hu. 2021. Repair Pipelining for Erasure-coded Storage: Algorithms and Evaluation. ACM Trans. Storage 17, 2, Article 13 (May 2021), 29 pages. https://doi.org/10.1145/3436890 1 INTRODUCTION Distributed storage systems rely on data redundancy to provide fault tolerance, to maintain availability and durability. Replication, which is traditionally used by production systems [11, 18], provides the simplest form of redundancy by keeping identical copies of data in different storage nodes. However, the raw storage cost of replication is overwhelming, especially with the massive scale of data we face today. Erasure coding provides a low-cost redundancy alternative that incurs significantly lower storage overhead than replication at the same fault tolerance level [52]. Today’s distributed storage systems adopt erasure coding to protect data against failures in clustered [17, 23, 41] or geo-distributed environments [6, 12, 32, 44], and reportedly save petabytes of storage [23, 32]. In a nutshell, erasure coding takes two configurable parameters n and k (where k < n) as input. It transforms k fixed-size units (called blocks) of original data into a set of n coded blocks of the same size, such that any k out of n (coded) blocks can reconstruct all original data; in other words, the original data remains available even if any n – k blocks are failed (either lost or unavailable). For example, if n = 14 and k = 10 (the same parameters used in Facebook’s erasure coding deployment [32]), the storage overhead is only 1.4×, while tolerating n – k = 4 failed blocks. In contrast, replication incurs 5× storage overhead to tolerate the same number of failed blocks. We elaborate erasure coding in detail in Section 2.1. Although achieving storage efficiency, erasure coding has a drawback of incurring high repair penalty. Specifically, in erasure-coded storage, the repair of a single failed block needs to read multiple available blocks for reconstruction; in other words, it reads more available data than the size of a failed block. This is in contrast to replication, whose repair can be simply done by reading another replica that is of the same size as the failed block. The excessive data not only increases the read time to failed data as opposed to normal reads but also consumes bandwidth resources that could otherwise be made available for other foreground jobs [41]. Thus, erasure coding in practice is mainly used for storing less frequently read (i.e., warm/cold) data that needs long-term persistence [8, 23, 32], while frequently read (i.e., hot) data remains replicated for efficient access. To mitigate the repair penalty of erasure coding, prior studies propose new constructions of erasure codes that significantly reduce the amount of repair traffic (e.g., References [16, 23, 26, 36, 40, 42, 45, 51]); in particular, the minimum-storage regenerating (MSR) codes [16, 36, 40, 51] provably minimize the amount of repair traffic subject to the minimum storage redundancy. While the repair time is effectively reduced due to the reduction of repair traffic, it remains higher than the normal read time, in general, since the minimum size of repair traffic remains larger than the size of the failed block. In view of this, we pose the following question: Can we further reduce the repair time of erasure coding to almost the same as the normal read time? This creates opportunities for applying erasure coding to hot data for high storage efficiency, while preserving read performance. We present a general technique called repair pipelining to speed up the repair performance in general erasure-coded storage. Its main idea is to decompose the repair of a block in small-size units (called slices) and carefully schedule the repair of multiple slices in a pipelined manner (analogous to wormhole routing [33]), to distribute the repair traffic and fully utilize the bandwidth resources of storage nodes. Contrary to the conventional wisdom that the repair of erasure coding is a slow operation, repair pipelining reduces the single-block repair time to almost the same as the normal read time for a single available block, regardless of coding parameters, in homogeneous environments where network links have identical bandwidth limits. Also, it provides different heuristics to mitigate the single-block repair time in heterogeneous environments where network links have different bandwidth limits. Furthermore, it supports various practical erasure codes that are adopted by today’s production systems, including the classical Reed-Solomon codes [43] and the recent Local Reconstruction Codes [23]. We point out that the notion of repair pipelining has also been studied in several publications by other researchers (e.g., References [9, 24, 53]); note that PUSH [24] was published before the conference version [29] of this article. PUSH [24] addresses full-node recovery by constructing... a linear repair path through $ k $ available blocks and performing block-level repair pipelining. For different block sizes (a.k.a. request unit sizes $[24]$), PUSH achieves $ 1/k $ of the repair time of conventional repair in full-node recovery. Thus, we do not claim that the concept of repair pipelining is the main contribution of this article. Instead, our contributions are to demonstrate the viability of repair pipelining in various deployment environments through in-depth analysis and prototype evaluation. As we show in this article, applying slice-level repair pipelining is non-trivial, since its repair performance gain also depends on how the slice-level repair sub-operations are scheduled. We refer readers to Section 7 for more detailed comparisons of our work with the related approaches. To summarize, we make the following contributions. - We design repair pipelining to address two types of repair operations: degraded reads and full-node recovery. We show that repair pipelining reduces the single-block repair time to almost the same as the normal read time for a single available block in homogeneous environments. - We extend repair pipelining to address heterogeneous environments and present three extensions of repair pipelining algorithms: the first one allows parallel reads of a repaired block when the bandwidth between the storage system and the node that requests for the repaired block is limited; the second one finds an optimal repair path for hierarchical data centers in which the cross-rack link bandwidth is limited; the third one finds an optimal repair path across storage nodes such that the repair time is minimized in a heterogeneous environment where network links have arbitrary bandwidth limits. - We further extend repair pipelining for repairing multiple failed blocks within the set of $ n $ coded blocks. We show that it reduces the multi-block repair time to almost the same as the total normal read time for $ f $ available blocks in homogeneous environments, where $ f $ is the number of failed blocks being repaired. - We implement a repair pipelining prototype called ECPipe, which runs as a middleware system atop an existing storage system and performs repair operations on behalf of the storage system. As a proof of concept, we integrate ECPipe into two versions of Hadoop Distributed File System (HDFS) $[49]$, namely, HDFS-RAID $[1]$ and Hadoop 3.1.1 HDFS (HDFS-3) $[2]$, as well as Quantcast File System (QFS) $[35]$. All the integrations only make minor changes (with no more than 245 lines of code) to the code base of each storage system. The latest source code of our ECPipe prototype is available at: http://adslab.cse.cuhk.edu.hk/software/ecpipe. - We evaluate repair pipelining on a local cluster and two geo-distributed Amazon EC2 clusters (one in North America and one in Asia). We compare it with two existing repair approaches in which the single-block repair time increases with $ k $ (recall that $ k $ is the number of blocks of original data for encoding): (i) conventional repair that is used by classical Reed-Solomon codes $[43]$ and achieves $ O(k) $ single-block repair time, and (ii) the recently proposed partial-parallel-repair (PPR) scheme $[31]$, which achieves $ O(\log_2 k) $ single-block repair time by parallelizing partial repair operations in a hierarchical manner. In contrast, repair pipelining achieves $ O(1) $ single-block repair time if there is a sufficiently large number of slices per block (i.e., independent of $ k $). Our experiments show that repair pipelining reduces the single-block repair time by nearly 90% and 70% compared to conventional repair and PPR, respectively. It also reduces the multi-block repair time by around 60% compared to conventional repair, as well as improves the repair performance in HDFS-RAID, HDFS-3, and QFS deployments. Furthermore, we show that our current repair pipelining implementation in ECPipe, by carefully parallelizing slice-level repair sub-operations, achieves the highest performance for large block sizes compared to several baseline repair pipelining implementations (Section 6.4). The rest of the article proceeds as follows. In Section 2, we describe the basics of erasure coding and motivate the repair problem. In Section 3, we present the design of repair pipelining. In Section 4, we extend repair pipelining for heterogeneous environments and multi-block repair operations. In Section 5, we present implementation details of ECPipe and show how it is integrated into existing open-source distributed storage systems. In Section 6, we present evaluation results. In Section 7, we review related work, and finally, in Section 8, we conclude the article. 2 BACKGROUND AND MOTIVATION We first present the basics of erasure coding and explain the repair problem. We then motivate the need of minimizing the repair time in erasure-coded storage. 2.1 Basics We consider a distributed storage system (e.g., GFS [18], HDFS [49], and Azure [11]) that manages large-scale datasets and stores files as fixed-size blocks, which form the basic read/write units. The block size is often large, ranging from 64 MiB [18] to 256 MiB [42], to mitigate I/O seek overhead. Erasure coding is applied to a collection of blocks. Specifically, an erasure code is typically configured with two integer parameters $(n, k)$, where $k < n$. An $(n, k)$ code divides blocks into groups of $k$. For every $k$ (uncoded) blocks, it encodes them to form $n$ coded blocks, such that any $k$ out of $n$ coded blocks can be decoded to the original $k$ uncoded blocks. The set of $n$ coded blocks is called a stripe. A large-scale storage system stores data of multiple stripes, all of which are independently encoded. The $n$ coded blocks of each stripe are distributed across $n$ distinct nodes to tolerate any $n - k$ node failures. Most practical erasure codes are systematic, such that $k$ of $n$ coded blocks are identical to the original uncoded blocks and hence can be directly accessed without decoding. Nevertheless, our design treats both uncoded and coded blocks the same, so we simply refer to them as “blocks.” Many erasure code constructions have been proposed in the literature (see survey [37] and Section 7). Among all erasure codes, Reed-Solomon (RS) codes [43] are the most popular erasure codes that are widely deployed in production [17, 35, 41]. There are two key properties of RS codes: (i) maximum distance separable (MDS), meaning that RS codes can reconstruct the original $k$ uncoded blocks from any $k$ out of $n$ coded blocks with the minimum storage redundancy (i.e., $n/k$ times the original data size), and (ii) general, meaning that RS codes support any $n$ and $k$ (provided that $k < n$). Practical erasure codes (e.g., RS codes) often satisfy linearity. Specifically, for each stripe of an $(n, k)$ code, let $\{B_1, B_2, \ldots, B_k\}$ denote any $k$ blocks of a stripe. Any block in the same stripe, say $B^$, can be computed from a linear combination of the $k$ blocks as $B^ = \sum_{i=1}^{k} a_i B_i$, where $a_i$'s $(1 \leq i \leq k)$ are decoding coefficients specified by a given erasure code. All additions and multiplications are based on Galois Field arithmetic over $w$-bit units called words; in particular, an addition is equivalent to bitwise XOR. Note that the additions of $a_i B_i$'s are associative (i.e., the additions can be in any order). Some constraints may be applied; for example, RS codes require $n \leq 2^w + 1$ [38]. Each block is partitioned into multiple $w$-bit words, such that the words at the same offset of each block of a stripe are encoded together, as shown in Figure 1. 2.2 Repair In this article, we focus on two types of repair operations in erasure-coded storage: (i) degraded reads to temporarily unavailable blocks (e.g., due to power outages, network disconnection, system maintenance, etc.) or lost blocks that are yet recovered; and (ii) full-node recovery for restoring all lost blocks of a failed node (e.g., due to disk crashes, sector errors, etc.). Each failed block (either lost or unavailable) is reconstructed in a destination termed requestor, which can be a new node. Fig. 1. In erasure coding, blocks are partitioned into words, such that words at the same offset of each block of a stripe are encoded together. Fig. 2. Examples of conventional repair and PPR in a single-block repair. that replaces a failed node, or a client that issues degraded reads. Note that there may be one or multiple requestors when multiple failed blocks are reconstructed. Erasure coding triggers more repair traffic than the size of failed data to be reconstructed. For example, for $(n, k)$ RS codes, repairing a failed block reads $k$ available blocks of the same stripe from other nodes (i.e., $k$ times the block size). Some repair-friendly erasure codes (e.g., References [16, 23, 26, 36, 40, 42, 45, 51]) are designed to reduce the repair traffic (see details in Section 7), but the amount of repair traffic per block remains larger than the size of a block. In distributed storage systems, network bandwidth is often the most dominant factor in the repair performance as extensively shown by previous work [16, 31, 50] (see further justifications in Section 2.3). Thus, the amplification of repair traffic implies the congestion at the downlink of the requestor, thereby increasing the overall repair time. To understand the repair penalty of erasure coding, we use RS codes as an example and call this repair approach conventional repair. Suppose that a requestor $R$ wants to repair a failed block $B^$. It can be done by reading $k$ available blocks from any $k$ working nodes, called helpers. Without loss of generality, let $R$ contact $k$ helper nodes $N_1, N_2, \ldots, N_k$, which store available blocks $B_1, B_2, \ldots, B_k$, respectively. To make our discussion clear, we divide the repair process into timeslots, such that only one block can be transmitted across a network link in each timeslot. Figure 2(a) shows how conventional repair works for $k = 4$. Since $R$ needs to retrieve the $k$ blocks $B_1, B_2, \ldots, B_k$, all $k$ transmissions must traverse the downlink of $R$. Overall, the repair in Figure 2(a) takes four timeslots. In general, conventional repair needs $k$ timeslots to repair a failed block. Conventional repair can address the repair of multiple concurrently failed blocks in the same stripe. Suppose that there are $f \leq n - k$ failed blocks in a stripe (i.e., fault tolerance is still maintained). Our goal is to repair the $f$ failed blocks in $f$ requestors, each of which stores a reconstructed block. The multi-block repair can be done by dedicating one of the $f$ requestors to retrieve $k$ available blocks from $k$ helper nodes. Since the dedicated requestor has sufficient information to reconstruct all original uncoded data, it can also reconstruct all $f$ failed blocks. Thus, it can locally store one of the reconstructed blocks and send the $f - 1$ reconstructed blocks to the other $f - 1$ requestors. The number of timeslots for a multi-block repair is $k + f - 1$ timeslots. A drawback of conventional repair is that the bandwidth usage distribution is highly skewed: the downlink of the requestor is highly congested, while the links among helpers are not fully utilized. PPR [31] builds on the linearity and addition associativity of erasure coding by decomposing a repair operation into multiple partial operations that are distributed across all helpers. This distributes bandwidth usage across the links of helpers. Figure 2(b) shows how PPR repairs $B^$ for $k = 4$. In the first timeslot, $N_2$ and $N_4$ receive blocks $a_1B_1$ and $a_3B_3$ from $N_1$ and $N_3$, respectively. Since the transmissions use different links, they can be done simultaneously in a single timeslot. In the second timeslot, $N_2$ combines the received $a_1B_1$ and its locally stored block $B_2$ to obtain $a_1B_1 + a_2B_2$ and sends it to $N_4$. In the third timeslot, $N_4$ combines all received blocks and its own block $B_4$ to obtain $a_1B_1 + a_2B_2 + a_3B_3 + a_4B_4$, and sends it to $R$. This hierarchical approach reduces the overall single-block repair time to only three timeslots. In general, PPR needs $\lceil \log_2(k + 1) \rceil$ timeslots to repair a failed block. Note that how to generalize PPR for repairing multiple failed blocks in a stripe is still an unexplored issue. 2.3 Motivation Although PPR reduces the single-block repair time, the bandwidth usage distribution remains not fully balanced; for example, the downlink of $N_4$ in Figure 2(b) still carries more repair traffic than other links. Thus, the repair time is still bottlenecked by the link with the most repair traffic. This motivates us to design a new repair scheme that can more efficiently utilize bandwidth resources, with the primary goal of minimizing the repair time. Minimizing the repair time is critical to both availability and durability. In terms of availability, field studies show that transient failures (i.e., no data loss) account for over 90% of failure events [17]. Thus, most repairs are expected to be degraded reads rather than full-node recovery. Since degraded reads are issued when clients request unavailable data, achieving fast degraded reads not only improves availability but is also critical for meeting customer service-level agreements [23]. In terms of durability, minimizing the repair time also minimizes the window of vulnerability. By recovering any failed block in a timely manner, we maintain the redundancy level for fault-tolerant storage. This avoids any unrecoverable data loss if the number of failed blocks exceeds the tolerable limit (i.e., $n - k$ blocks for an $(n,k)$ code). Our work targets distributed storage environments in which network bandwidth is the bottleneck. Although modern data centers now scale to high network speeds, they are typically shared by a mix of application workloads. Thus, the network bandwidth available for repair tasks is often throttled [23, 50]. Also, modern data centers often have hierarchical network topologies by organizing nodes in racks, in which the cross-rack link bandwidth is limited (e.g., due to replica writes [13] or compute job traffic [7, 25]). To tolerate rack failures, data centers distribute each stripe across racks [17, 23, 42, 45]. Thus, the repair of any failed block inevitably retrieves available blocks from other racks and triggers cross-rack transmissions. The repair performance will be bottlenecked by the limited cross-rack link bandwidth. 3 REPAIR PIPELINING We present the design of repair pipelining. We first state our goals and assumptions (Section 3.1). We then explain how repair pipelining addresses degraded reads (Section 3.2) and full-node recovery (Section 3.3). 3.1 Goals and Assumptions Repair pipelining also exploits the linearity and addition associativity of erasure codes as in PPR [31], yet it parallelizes the repair across helpers in an inherently different way. It focuses on (i) eliminating bottlenecked links (i.e., no link transmits more traffic than others) and (ii) effectively utilizing bandwidth resources during a repair (i.e., links should not be idle for most times), to ultimately minimize the single-block repair time to the normal read time for a single block in homogeneous environments where all links have the same bandwidth. Repair pipelining is mainly designed for speeding up the repair of a single failed block per stripe, which is much more common than the repair of multiple failed blocks per stripe in practice [23, 41] (e.g., over 98% of repair cases are single-block repair operations). Optimizing a single-block repair is also the main design goal of most existing repair-friendly erasure codes that aim to minimize the amount of repair traffic [16, 23, 26, 36, 40, 42, 45, 51]. In this section, we focus on studying the single-block repair for one stripe and multiple stripes. The former occurs when a requestor issues a degraded read to an unavailable block; the latter occurs when all lost data of a single failed node is recovered in one or multiple requestors in full-node recovery. If a stripe has multiple failed blocks, then we can also extend repair pipelining to trigger a multi-block repair, which we show incurs less repair time than conventional repair (Section 2.2). See Section 4.4 for details. Repair pipelining does not design new repair-friendly erasure codes that minimize the repair traffic (the same assumption is made in PPR [31]). Instead, each repair of a single failed block still reads $k$ available blocks as in conventional repair, yet it spreads the repair traffic across all $k$ helpers to fully utilize bandwidth resources. The failed block can then be reconstructed as a linear combination of the $k$ available blocks. Some repair-friendly codes, including locally repairable codes [23, 45] and Rotated RS codes [26], work by reconstructing a failed block through a linear combination of fewer than $k$ available blocks. In this case, we can also combine repair pipelining with such repair-friendly codes to reduce the single-block repair time while preserving their repair traffic savings. We evaluate such a combination in Section 6.1. An interesting open question is to augment repair pipelining with the optimal repair of general repair-friendly codes (e.g., regenerating codes [16]), to simultaneously reduce the single-block repair time and minimize the repair traffic. We pose this question as a future work. 3.2 Degraded Reads We first study how repair pipelining reconstructs a single block of a stripe in a requestor in a degraded read. We start with a naïve approach. Specifically, we arrange $k$ helpers and the requestor as a linear path, i.e., $N_1 \rightarrow N_2 \rightarrow \cdots \rightarrow N_k \rightarrow R$. At a high level, to repair a failed block $B^$, $N_1$ sends $a_1 B_1$ to $N_2$. Then $N_2$ combines $a_1 B_1$ with its own block $B_2$ and sends $a_1 B_1 + a_2 B_2$ to $N_3$. The process repeats, and finally, $N_k$ sends $R$ the combined result, which is $B^$. The whole repair incurs $k$ transmissions that span across $k$ different links. Thus, there is no bottlenecked link. However, this naïve approach underutilizes bandwidth resources, since there is only one block-level transmission in each timeslot. The whole repair still takes $k$ timeslots, same as in conventional repair (Section 2.2). Thus, repair pipelining decomposes the repair of a block into the repair of a set of $s$ small fixed-size units called slices $S_1, S_2, \ldots, S_s$. It also partitions each block $B_i$ ($1 \leq i \leq k$) into $s$ slices $B_{i, 1}, B_{i, 2}, \ldots, B_{i, s}$. It pipelines the repair of each slice through the linear path. To repair the first slice $S_1$, $N_1$ sends $a_1 B_{1, 1}$ to $N_2$, $N_2$ sends $a_1 B_{1, 1} + a_2 B_{2, 1}$ to $N_3$, and so on. Note that when $N_2$ sends the slice $a_1 B_{1, 1} + a_2 B_{2, 1}$ to $N_3$, $N_1$ can start the repair of the second slice $S_2$ by sending $a_1 B_{1, 2}$ to $N_2$ without interfering in the transmission from $N_2$ to $N_3$. Thus, we can parallelize the slice-level transmissions. Each slice-level transmission over a link only takes $\frac{1}{s}$ timeslots. Figure 3 shows how repair pipelining works for $k = 4$ and $s = 6$. A slice can have an arbitrarily small size, provided that Galois Field arithmetic can be performed (Section 2.1). For RS codes, the minimum size of a slice is a $w$-bit word; if $w = 8$, a word denotes Fig. 3. Repair pipelining with $k = 4$ and $s = 6$. A byte. However, practical distributed storage systems store data in large-size blocks, typically 64 MiB or even larger (Section 2.1). Since a coding unit (i.e., word) has a much smaller size than a read/write unit (i.e., block), we can parallelize a block-level repair operation into more fine-grained slice-level repair sub-operations. Having smaller-size slices improves parallelism, yet it increases the overhead of issuing many requests for transmitting slices over the network. We study the impact of the slice size in Section 6. We analyze the time complexity of repair pipelining. Here, we neglect the overheads due to computation and disk I/O, which we assume cost less time than network transmission; in fact, both computation and disk I/O operations can also be executed in parallel with network transmission in actual implementation (Section 5). Each slice-level transmission over a link takes $\frac{1}{s}$ timeslots. The repair of each slice takes $\frac{k}{s}$ timeslots to traverse the linear path, and $N_i$ starts to transmit the last slice after $(s-1)$ timeslots. Thus, the whole repair time, which is given by the total number of timeslots to transmit all slices through the linear path, is $\frac{s-1+k}{s} = 1 + \frac{k-1}{s}$ timeslots. In practice, $k$ is of moderate size to avoid large coding overhead [38] (e.g., $k = 12$ in Azure [23] and $k = 10$ in Facebook [41]), while $s$ can be much larger (e.g., $s = 2,048$ for 32 KiB slices in a 64 MiB block). Thus, we have $1 + \frac{k-1}{s} \rightarrow 1$, as $s$ is sufficiently large. Repair pipelining connects multiple helpers as a linear path, so its repair performance is bottlenecked by the presence of poorly performed links/helpers (i.e., stragglers). We emphasize that any repair scheme of erasure coding faces the similar problem, as it retrieves available data from multiple helpers for data reconstruction; for example, conventional repair for $(n, k)$ MDS codes needs to retrieve the available data from $k$ helpers. We address the straggler problem by taking into account heterogeneity and bypassing stragglers via helper selection (Section 4.3). Also, if any helper fails during an ongoing repair, the progress of repair pipelining will be stalled. In this case, we restart the whole repair process with a new set of available helpers and trigger a multi-block repair (Section 4.4). ### 3.3 Full-Node Recovery We now study how repair pipelining addresses a multi-stripe repair (one failed block per stripe) when recovering a full-node failure. As the stripes are independently encoded, we can parallelize the multiple single-stripe repair operations. However, since each repair involves a number of helpers, if one helper is chosen in many repair operations of different stripes, it will become overloaded and slow down the overall repair performance. In practice, each stripe is stored in a different set of storage nodes spanning across the network. Our goal is to distribute the load of a multi-stripe repair across all helpers as evenly as possible. We adopt a simple greedy scheduling approach for the selection of helpers. For each node in the storage system, repair pipelining keeps track of a timestamp indicating when the node was last selected as a helper for a single-stripe repair. To repair a failed block of a stripe, we select $ k $ out of $ n - 1 $ available helpers in the stripe that have the smallest timestamps; in other words, the $ k $ selected helpers are the least recently selected ones in previous requests. Choosing $ k $ out of the $ n - 1 $ helpers can be done in $ O(n) $ time using the quick select algorithm $[19]$ (based on repeated partitioning of quick sort). We use a centralized coordinator to manage the selection process (Section 5). Our greedy scheduling emphasizes simplicity in deployment. We can also adopt a more sophisticated approach by weighting node preferences in real time $[31]$. Unlike the degraded read scenario, the multiple reconstructed blocks can be stored in multiple requestors. Under this condition, the gain of repair pipelining over conventional repair decreases, as the latter can also parallelize the repair across multiple requestors. Nevertheless, our evaluation indicates that repair pipelining still provides repair performance improvements (Section 6). Note that the number of requestors that can be selected and the choices of requestors may depend on various deployment factors $[31]$. In this work, we assume that the requestors are selected offline in advance. 4 EXTENSIONS We now extend the basic design of repair pipelining in Section 3 to address three different heterogeneous settings, in which the links of a distributed storage system no longer have identical bandwidth: (i) a requestor can read slices from multiple helpers in parallel in which the link bandwidth from the storage system to the requestor is limited (Section 4.1); (ii) we arrange the linear path of $ k $ helpers in a hierarchical data center with limited cross-rack link bandwidth (Section 4.2); and (iii) we solve a weighted path selection problem to find an optimal path of $ k $ helpers that maximizes the repair performance in a heterogeneous environment where network links have arbitrary bandwidth (Section 4.3). Finally, we extend repair pipelining to address a multi-block repair (Section 4.4). 4.1 Parallel Reads In the basic design of repair pipelining, a requestor always reads slices from one helper. This may lead to last-mile congestion. For example, a client (requestor) sits at the network edge and accesses a cloud storage system that is far from the client. We propose a cyclic version of repair pipelining that allows a requestor to read slices from multiple helpers. We now describe the cyclic version. Our discussion assumes that all links are homogeneous, and transmitting a block size of data over a link takes one timeslot. The cyclic version again divides a failed block into $ s $ fixed-size slices $ S_1, S_2, \ldots, S_s $, and repairs each slice through some linear path to eliminate any bottlenecked link. However, it now maps the $ k $ helpers $ N_1, N_2, \ldots, N_k $ into different cyclic paths that can be cycled from $ N_k $ through $ N_1 $. Specifically, it partitions the $ s $ slices into $ \lceil \frac{s}{k-1} \rceil $ groups, each of which has $ k - 1 $ slices (the last group has fewer than $ k - 1 $ slices if $ s $ is not divisible by $ k - 1 $). The repair of each group of slices is then performed in two phases. Without loss of generality, we only consider how to repair the first group $ S_1, S_2, \ldots, S_{k-1} $. In the first phase, repairing each slice $ S_i $ ($ 1 \leq i \leq k - 1 $) traverses through the cyclic path $ N_i \rightarrow N_{i+1} \rightarrow \cdots N_k \rightarrow N_1 \rightarrow \cdots N_{i-1} $. We repair all slices through different cyclic paths simultaneously, and each slice-level transmission takes $ \frac{1}{s} $ timeslots. The first phase can be done in $ \frac{k-1}{s} $ timeslots. In the second phase, the last helper of each cyclic path delivers the repaired slice to the requestor. The second phase is also done in $ \frac{k-1}{s} $ timeslots. Figure 4 shows the cyclic version for $ k = 4 $ and $ s = 6 $. Note that we can start repairing the slices of the next group simultaneously while we deliver the repaired slices for the current group. Specifically, while $ k - 1 $ helpers simultaneously transmit slices for the repair in the next group, there is one idle helper that can transmit the repaired slice for the current group to the requestor. They can be done together in $ \frac{k-1}{s} $ timeslots. We analyze the time complexity of the cyclic version under the homogeneous link assumption. We only consider the case where $s$ is divisible by $k - 1$, while the same result can be derived otherwise. Repairing each group of slices takes $\frac{2(k-1)}{s}$ timeslots, and the repair of the last group starts after $(\frac{s}{k-1} - 1) \frac{k-1}{s}$ timeslots. The whole repair time is $(\frac{s}{k-1} - 1) \frac{k-1}{s} + 2\frac{(k-1)}{s} = 1 + \frac{k-1}{s} \rightarrow 1$, as $s$ is sufficiently large. Note that the cyclic version now allows a requestor to read slices from $k - 1$ helpers. If the repair bottleneck lies in the network transfer from the helpers to the requestor, then our evaluation shows that the cyclic version significantly outperforms the basic design of repair pipelining (Section 6). ### 4.2 Hierarchy Awareness We extend repair pipelining to address hierarchical network topologies. Here, we focus on rack-based data centers, which organize storage nodes in racks, such that the available cross-rack link bandwidth is much more limited than the available inner-rack link bandwidth (Section 2.3). Our goal is to not only minimize the single-block repair time but also minimize the amount of cross-rack repair traffic incurred for the single-block repair. Note that our analysis is also applicable for geo-distributed data centers [6, 12, 32, 44], where storage nodes span different geographical regions and the cross-region bandwidth is much more limited than the inner-region bandwidth (Section 6.2). Background: Recent studies (e.g., References [21, 22, 39]) have designed optimal rack-aware erasure codes that provably minimize the amount of cross-rack repair traffic in a single-block repair from an information theoretical perspective. Some studies (e.g., CAR [48] and LAR [53]) focus on RS codes and propose cross-rack-aware repair strategies that minimize the amount of cross-rack repair traffic under RS codes. In all such designs, the idea is to place multiple blocks of a stripe per rack, such that a single-block repair first computes a partially repaired block (which is a linear combination of the available blocks within a rack), followed by aggregating the partially repaired blocks across racks; note that each rack is required to store at most $n - k$ blocks, to provide a single-rack fault tolerance for an $(n,k)$ code. As a rack failure now makes multiple blocks unavailable, such a hierarchical block placement trades rack-level fault tolerance for the reduction of cross-rack repair traffic. We can measure the reliability trade-off based on the commonly used mean-time-to-data-loss (MTTDL) measure via Markov analysis. The MTTDL measure depends on both failure rates (for both independent and correlated node failures) and repair rates. It is shown by Hu et al. [22] that hierarchical block placement can achieve a higher MTTDL than flat block placement through minimizing the cross-rack repair traffic, provided that (i) the rack-based data center has limited cross-rack link bandwidth or (ii) correlated node failures (or rack failures) are less frequent than independent node failures; ALGORITHM 1: Rack-aware Path Selection Input: data center topology Output: path $P$ 1: identify the racks $\{H_i\}$ where the requestor $R$ and $n-1$ available helpers reside 2: let $H_0$ be the rack containing $R$ (and some helpers) 3: let $H_1, H_2, \ldots, H_h$ be the remote racks containing the remaining helpers, sorted by the number of helpers in a rack in descending order 4: $P = R$ 5: $i = 0$ 6: while $P$ has fewer than $k$ helpers do 7: for each helper $N$ in $H_i$ do 8: $P = N \rightarrow P$ 9: if $P$ has $k$ helpers then 10: break the while loop 11: end if 12: end for 13: $i = i + 1$ 14: end while 15: return $P$ Note that condition (ii) is also justified in practical geo-distributed data centers [32]. We refer readers to the study [22] for the detailed reliability analysis. Instead of designing new erasure codes, we extend repair pipelining with rack awareness for general erasure codes under the hierarchical block placement. Since repair pipelining reduces the single-block repair time, we expect that the storage reliability (in MTTDL) further improves. Algorithm: Our idea is that the linear path of $k$ helpers in repair pipelining should limit cross-rack transmissions. Figure 5(a) shows a linear path of $k = 4$ helpers that are randomly ordered without rack awareness. In this example, the middle rack has two simultaneous incoming cross-rack transmissions (i.e., $N_1 \rightarrow N_2$ and $N_3 \rightarrow N_4$), thereby creating congestion at the downlink bandwidth of the middle rack. To make repair pipelining rack-aware, we require that the linear path of $k$ helpers has at most one incoming transmission and at most one outgoing transmission for each rack, while minimizing the total number of cross-rack transmissions. Algorithm 1 shows the pseudo-code of the rack-aware path selection. Specifically, to repair a failed block of a stripe, we identify a requestor $R$ and the remaining $n-1$ available helpers of the stripe. Let $H_i$ ($i \geq 0$) denote a rack where either $R$ or any helper resides, such that $H_0$ denotes the rack that contains $R$ (and possibly other helpers), $H_1, H_2, \ldots, H_h$ denote a total of $h$ remote racks that do not contain $R$ but contain the remaining helpers. Without loss of generality, we sort the number of helpers in the remote racks. $H_i$’s $(1 \leq i \leq h)$ in descending order, where $\|H_1\| \geq \|H_2\| \geq \cdots \geq \|H_h\|$, and $\|H_i\|$ $(1 \leq i \leq h)$ denotes the number of helpers in $H_i$. We first initialize the linear path $P$ with only the requestor $R$ (Line 4). We then iteratively append a helper in $H_i$ to $P$, starting from $i = 0$, until $P$ has $k$ helpers for reconstructing the failed block (Lines 5–14). Figure 5(b) shows a linear path for $k = 4$ with rack-aware path selection. Our rationale is that we prefer to append all helpers that are co-located with $R$ in $H_0$ to $P$, to involve only inner-rack transmissions. Also, when choosing helpers from the remote racks $H_1, H_2, \ldots, H_h$, we prefer to append as many helpers as possible in one rack to $P$, to minimize the number of remote racks to be accessed. Thus, we first choose helpers from $H_1$, followed by $H_2$, and so on. By minimizing the number of remote racks being accessed for a single-block repair, we also minimize the amount of cross-rack repair traffic under RS codes (see CAR [48]). Based on the analysis in Section 3, the single-block repair time still approaches one timeslot, while a timeslot here refers to the time of transmitting one block over a cross-rack link. Remarks: A recent work LAR [53] solves for a minimum spanning tree that takes the network distances among nodes as input and minimizes the cross-rack repair traffic in the network core of a hierarchical topology. For the special case where all nodes share the identical network distance to the network core, LAR can also return a linear path with the minimum cross-rack repair traffic as Algorithm 1. Unlike LAR, which uses network distances as input, Algorithm 1 uses only the block locations in different racks (as in CAR [48]) as input to find the linear path. Repair pipelining takes one step further to reduce the single-block repair time based on the returned linear path. ### 4.3 Weighted Path Selection We now study a more diverse heterogeneous setting in which the link bandwidth can have any arbitrary value. In the following, we extend repair pipelining to solve a weighted path selection problem. Here, we focus on degraded reads, and discuss how we address full-node recovery. Formulation: Recall that for a single-block repair, repair pipelining transmits a number of slices along a linear path of $k$ helpers, say $N_1 \rightarrow N_2 \rightarrow \cdots \rightarrow N_k \rightarrow R$. Suppose that the link bandwidth is different across links. If the number of slices is sufficiently large, then the slices are transmitted in parallel through the path (Figure 3), and the performance of repair pipelining will be bottlenecked by the link with the minimum available bandwidth along the path. To minimize the single-block repair time, we should find a path that maximizes the minimum link bandwidth. To repair a failed block of a stripe, we need to find $k$ out of $n - 1$ available helpers of the same stripe as the failed block, and also find the sequence of link transmissions so that the path along the $k$ selected helpers and the requestor minimizes the single-block repair time. Specifically, there are a total of $n$ nodes, including the $n - 1$ available helpers and the requestor. We associate a weight with each (directed) link from one node to another node, such that a higher weight implies a longer transmission time along the link. For example, the weight can be represented by the inverse of the link bandwidth obtained by periodic measurements on link utilizations [13]. Then our objective is to find a path of $k + 1$ nodes (i.e., $k$ selected helpers and the requestor) that minimizes the maximum link weight of the path. Here, we focus on link weights, and the same idea is applicable if we associate weights with nodes. Any straggler is assumed to be associated with a large weight, so it will be excluded from the selected path. To solve the above problem, a naïve approach is to perform a brute-force search on all possible candidate paths. However, there are a total of $\binom{n-1}{k}$ permutations, and the brute-force search becomes computationally expensive even for moderate sizes of $n$ and $k$. Since the link weights vary over time, the path selection should be done quickly on-the-fly based on the measured link weights. Algorithm: We present a fast yet optimal algorithm that quickly identifies an optimal path. The algorithm builds on brute-force search to ensure that all candidate paths are covered, but eliminates the search of infeasible paths. Our insight is that if a link $L$ has a weight larger than the maximum weight of an optimal path candidate that is currently found, then we no longer need to search for the paths containing link $L$, since the maximum weight of any path containing $L$ must be larger than the maximum weight of the optimal path candidate. Algorithm 2 shows the pseudo-code of the weighted path selection algorithm. Let $P$ be the path that we currently consider, $P^$ be the optimal path candidate that we have found, $w^$ be the maximum link weight of $P^$, and $N$ be the set of $n-1$ available helpers. We first initialize a path $P$ with only the requestor $R$ (Line 2), such that $R$ will be the end node of $P$. We also initialize $P^$, $w^$, and $N$ (Lines 3–5). We call the recursive function EXTENDPATH (Line 6) and finally return the optimal path $P^$ (Line 7). The function EXTENDPATH recursively extends $P$ by one helper in $N$ and appends the helper to $P$ if the link weight from the node to the current beginning node of $P$ is less than $w^$; otherwise, the path containing the link cannot minimize the maximum link weight as argued above. Specifically, the algorithm appends $N \in N$ to $P$ if the current path length is less than $k + 1$ and the weight from $N$ to the beginning node of $P$ is less than $w^$ (Lines 10–13). It calls EXTENDPATH again to consider candidate paths that now include $N \rightarrow P$ (Line 14). It then removes $N$ from $P$ (Line 15), and tries other nodes in $N$. If the length of $P$ is now $k + 1$, then it implies that all of its links have weight less than $w^$, so we update $P$ as the new optimal path $P^$ and $w^$ as the maximum link weight of $P^$ (Lines 19 and 20). Algorithm 2 significantly reduces the search time. We evaluate the search time for $(14,10)$ codes using Monte Carlo simulations over 1,000 runs on a machine with 3.7 GHz Intel Xeon E5-1620 v2. CPU and 16 GiB memory. The brute-force search takes 27 s on average, while Algorithm 2 reduces the search time to only 0.9 ms. Remarks: To address full-node recovery (Section 3.3), we apply Algorithm 2 to each stripe. If we apply greedy scheduling on helper selection, then we simply substitute $\mathcal{N}$ with the set of $k$ selected helpers. Note that the brute-force search for the optimal path on the $k$ selected helpers remains expensive, since it considers $k!$ permutations on the sequence of link transmissions along the path. Thus, Algorithm 2 still significantly saves the search time in this case. We emphasize that Algorithm 2 should not be viewed as a generalization of our rack-aware path selection in Algorithm 1 (Section 4.2) as both algorithms target different problem settings: Algorithm 1 specifically minimizes the number of cross-rack transmissions, while Algorithm 2 minimizes the maximum link weight of the linear path of helpers. Nevertheless, we can still apply Algorithm 2 in a geo-distributed environment (Section 6.2). ### 4.4 Multi-block Repair Finally, we show how repair pipelining simultaneously reconstructs multiple failed blocks of a stripe and reduces the multi-block repair time. Here, we only focus on homogeneous environments, and discuss how we can address the heterogeneous environments. We first define the notation. Let $f$, where $1 \leq f \leq n - k$, be the number of failed blocks of a stripe for an $(n,k)$ code, and $B_1^, B_2^, \ldots, B_f^$ be the failed blocks to be reconstructed. Let $R_1, R_2, \ldots, R_f$ be the $f$ requestors where the failed blocks are reconstructed. Before issuing the repair, we first identify $k$ helpers of the stripe (say, $N_1, N_2, \ldots, N_k$) and their corresponding available blocks (say, $B_1, B_2, \ldots, B_k$, respectively). Each failed block $B_j^$ ($1 \leq j \leq f$) can be reconstructed via the linear combination $B_j^* = \sum_{i=1}^{k} a_{i,j}B_i$, where $a_{i,j}$s ($1 \leq i \leq k$, $1 \leq j \leq f$) are the decoding coefficients specified by a given erasure code. A straightforward multi-block repair approach is to invoke repair pipelining for a single-block repair over a linear path of $k$ helpers as described in Section 3.2 $f$ times, one for each failed block. Thus, the multi-block repair time approaches $f$ timeslots under the homogeneous link assumption, where a timeslot is the time for transmitting one block over a network link. However, each helper needs to read its locally stored block for each single-block repair, so it reads $f$ times its locally stored block in total. In the following, we re-design a multi-block repair approach in which each helper needs to read its locally stored block only once. As in Section 3.2, we start with a naive pipelining approach that realizes a multi-block repair without slicing, and show its limitations. Specifically, we arrange the $k$ helpers in a linear path, i.e., $N_1 \rightarrow N_2 \rightarrow \cdots \rightarrow N_k$, and connect $N_k$ to all $f$ requestors $R_1, R_2, \ldots, R_f$. To repair the $f$ failed blocks $\{B_1^, B_2^, \ldots, B_f^\}$, $N_1$ uses its own block $B_1$ to compute a set of $f$ blocks $\{a_{1,1}B_1, a_{1,2}B_1, \ldots, a_{1,f}B_1\}$, where each $a_{1,j}B_1$ ($1 \leq j \leq f$) is an input term to the linear combination for reconstructing $B_1^$. $N_1$ sends the set of $f$ blocks to $N_2$. Then $N_2$ combines the received blocks with its own block $B_2$ and sends a new set of $f$ blocks $\{a_{2,1}B_1 + a_{2,1}B_2, a_{2,2}B_1 + a_{2,2}B_2, \ldots, a_{2,f}B_1 + a_{2,f}B_2\}$ to $N_3$. The process repeats, and finally $N_k$ reconstructs all $f$ failed blocks $\{B_1^, B_2^, \ldots, B_f^\}$ and sends them to the $f$ requestors. Note that each of the $k$ helpers reads its own block only once. For the total repair time, recall that a block-level transmission over a network link takes one timeslot. Thus, the whole repair incurs $f \times k$ timeslots, including $f(k - 1)$ timeslots from $N_1$ to $N_k$ and $f$ timeslots from $N_k$ to all $f$ requestors. From this example, we observe that this naive pipelining approach is even worse than conventional repair (which takes $k + f - 1$ timeslots as shown in Section 2.2). We now extend the above naive pipelining approach with slicing and show how repair pipelining works for a multi-block repair. Repair pipelining decomposes each failed block $B_j^$ ($1 \leq j \leq f$) into Repair Pipelining for Erasure-coded Storage: Algorithms and Evaluation Fig. 6. Repair pipelining for a multi-block repair with $k = 4, s = 6,$ and $f = 2.$ $s$ slices denoted by $S_{j,1}, S_{j,2}, \ldots, S_{j,s}$. It pipelines the repair of the first set of $f$ slices of the $f$ failed blocks (i.e., $S_{1,1}, S_{2,1}, \ldots, S_{f,1}$) through a linear path, followed by the second set of $f$ slices (i.e., $S_{1,2}, S_{2,2}, \ldots, S_{f,2}$), and so on. In general, each helper pipelines the repair of $f$ slices at the same offset of the $f$ failed blocks along a linear path. Each set of $f$ slices will be reconstructed at $N_k$ (i.e., the last helper of the linear path), which then forwards the reconstructed slices to the $f$ requestors. Figure 6 shows how repair pipelining works for $k = 4, s = 6,$ and $f = 2.$ Again, each of the $k$ helpers reads its locally stored block only once during the repair. We now analyze the time complexity of repair pipelining for repairing $f$ failed blocks under the homogeneous link assumption. Again, we assume that the overheads due to computation and disk I/O are negligible compared to network transmission (Section 3.2). To repair a set of $f$ slices along a linear path, each helper sends $f$ slices to the next helper, or to all $f$ requestors for the last helper $N_k$. Thus, each transmission now takes $\frac{f}{s}$ timeslots. Following the analysis in Section 3.2, the total repair time of repairing $f$ failed blocks is $(s - 1 + k) \times \frac{f}{s} = f \left(1 + \frac{k-1}{s}\right)$ timeslots, which approaches $f$ timeslots if $s$ is sufficiently large. Thus, repair pipelining always incurs less repair time than conventional repair (which takes $k + f - 1$ timeslots). Remarks: For a heterogeneous environment where network links have arbitrary bandwidth (Section 4.3), we discuss two possible solutions to realize a multi-block repair. One solution is to extend our proposed design, in which we aggregate all $f$ requestors as one big requestor, and assign a weight from each of the $n - f$ available helpers to the big requestor. Then, we find an optimal linear path that minimizes the maximum link weight as in Section 4.3. An alternative solution is to call a single-block repair for each of the $f$ failed blocks and find an optimal path for each single-block repair as in Section 4.3. We pose the analysis for the possible solutions as future work. 5 IMPLEMENTATION We have implemented a prototype called ECPipe to realize repair pipelining. ECPipe runs as a middleware atop an existing distributed storage system and performs repair operations on behalf of the storage system. Moving the repair logic to ECPipe greatly reduces changes to the code base of the storage system to realize new repair techniques; in the meantime, we can focus on optimizing ECPipe to maximize the repair performance gain. We have integrated ECPipe with three open-source distributed storage systems, namely, HDFS-RAID [1], HDFS-3 [2], and QFS [35]. Both HDFS-RAID and HDFS-3 are written in Java, while QFS is written in C++. Our ECPipe prototype is mostly written in C++, and the parts for the integration into HDFS-RAID and HDFS-3 are in Java. Our ECPipe prototype has around 6,000 lines of code. The latest source code of ECPipe is available at: http://adslab.cse.cuhk.edu.hk/software/ecpipe. 5.1 Background of HDFS-RAID, HDFS-3, and QFS We first provide the background details of HDFS-RAID, HDFS-3, and QFS. In particular, we describe how they support erasure coding. HDFS-RAID: HDFS-RAID is an erasure coding extension of Hadoop 0.20 HDFS. In this work, we choose Facebook's HDFS-RAID implementation [1]. Specifically, the original HDFS comprises a NameNode for storage management and multiple DataNodes for actual storage. HDFS-RAID deploys a RaidNode atop HDFS for erasure coding management. It performs offline encoding (i.e., asynchronously in the background), in which HDFS initially stores data in DataNodes as fixed-size blocks (64 MiB by default) with replication, and the RaidNode later encodes replicated blocks into coded blocks via MapReduce [15]. The RaidNode also checks for any failed (lost or corrupted) coded block by verifying block checksums. It repairs any failed block being detected, either by itself in local mode or via a MapReduce job in distributed mode. Both modes will issue reads to k available blocks of the same stripe in parallel from HDFS, reconstruct the failed block, and write back to HDFS. HDFS-RAID also provides a RAID file system client to access coded blocks. For a degraded read to a failed block, the RAID file system reads k available blocks of the same stripe in parallel and reconstructs the failed block. HDFS-3: HDFS-3 (Hadoop 3.1.1 HDFS) [2] includes erasure coding in HDFS storage by design. Unlike HDFS-RAID, HDFS-3 performs online encoding (i.e., on the write path), in which an HDFS client performs encoding before writing data to storage. Specifically, the HDFS client first writes data into k data buffers (with the default size of 1 MiB) and encodes them into n – k parity buffers. It then appends the n buffers into n blocks in different DataNodes. Compared to offline encoding in HDFS-RAID, online encoding in HDFS-3 removes the extra I/O costs of reading and encoding the currently stored data blocks. However, it now moves the encoding overhead to the client, which performs encoding and writes the data and parity blocks to HDFS storage. The NameNode monitors any failed blocks via the periodic block reports issued from DataNodes. If a failed block exists, then the NameNode assigns a repair task to a DataNode, which issues parallel reads to k available blocks from other DataNodes, reconstructs the failed block, and writes the reconstructed block back to HDFS-3. QFS: QFS stores all data in erasure-coded format and currently supports (9,6) RS codes [43]. Similar to HDFS-3, QFS performs online encoding. Specifically, a QFS client writes data into six 1 MiB buffers. It then encodes the six 1 MiB buffers into three 1 MiB parity buffers, and appends the nine 1 MiB buffers to nine data and parity blocks (the default block size is 64 MiB) that are stored in different storage nodes (called ChunkServers). To repair any failed block, a ChunkServer retrieves six available blocks from other ChunkServers for reconstruction. 5.2 ECPipe Design Figure 7 shows the ECPipe architecture. It uses a coordinator to manage the repair operation between a requestor and multiple helpers. ECPipe runs atop a distributed storage system. To repair a failed block, the storage system creates a requestor instance, which sends a repair request with the failed block ID to the coordinator (step 1). The coordinator uses the failed block ID to identify the locations of k available blocks of the same stripe. It notifies all helpers with the block locations (step 2). The helpers retrieve the blocks, perform repair pipelining in slices, and deliver the repaired slices to the requestor (step 3). Note that if there are multiple failed blocks in a stripe, the storage system creates multiple requestor instances, each of which issues the failed block ID of one of the failed blocks to the coordinator. Again, the coordinator selects $ k $ helpers to perform a multi-block repair via repair pipelining, so that the failed blocks are reconstructed in multiple requestors. We integrate ECPipe with a storage system in three aspects. First, we implement the requestor as a class (in C++ and Java) that can be instantiated by the storage system to reconstruct failed blocks. For HDFS-RAID, the requestor is created in either the RaidNode or the RAID file system client; for HDFS-3 and QFS, it is created by the storage node that starts a repair operation. Second, we implement each helper as a daemon that is co-located with each storage node to directly read the locally stored blocks. Our insight is that HDFS-RAID, HDFS-3, and QFS all store a block in the underlying native file system as a plain file and use the block ID to form the file name. Thus, each helper can directly read the stored blocks via the native file system. This eliminates the need of helpers to fetch data through the distributed storage system routine. It not only reduces the burden of metadata management of the distributed storage system but also improves the repair performance (Section 6.3). Finally, the coordinator needs to access both the block locations and the mappings of each block to its stripe. For HDFS-RAID, we retrieve the information from the RaidNode; for HDFS-3, we retrieve the information from the NameNode; for QFS, we retrieve the information from a storage node when it starts a repair operation. To simplify our implementation, ECPipe uses Redis [4] to pipeline slices across helpers. Each helper maintains an in-memory key-value store based on Redis, and uses the client interface of Redis to transmit slices among helpers. In addition, each helper performs disk I/O, network transfer, and computation via multiple threads for performance speedup. Adding ECPipe into HDFS-RAID, HDFS-3, and QFS only requires changes of around 110, 245, and 180 lines of code, respectively. To provide fair comparisons (Section 6), we also implement conventional repair (Section 2.2) and PPR [31] under the same ECPipe framework, by only changing the transmission flow of data during a repair. 6 EVALUATION We conduct experiments on both a local cluster and Amazon EC2. We show that repair pipelining outperforms both conventional repair and PPR [31] under various settings. We further show that our repair pipelining implementation in ECPipe outperforms different baseline repair pipelining implementations. 6.1 Evaluation on a Local Cluster Methodology: We first evaluate ECPipe as a standalone system on a local cluster. Our local cluster comprises 17 machines, each of which has a quad-core 3.4 GHz Intel Core i5-3570 CPU, 16 GiB RAM, and a Seagate ST1000DM003-1CH162 1 TiB SATA hard disk. We host the coordinator on one machine and 16 helpers on the remaining ones. By default, all machines are connected via a 1 Gb/s Ethernet switch. The 1 Gb/s bandwidth can be viewed as modeling the cross-rack bandwidth available for repair tasks in a production cluster [45], in which the blocks of a stripe are stored in distinct racks. We also connect the machines via a 10 Gb/s Ethernet switch and evaluate ECPipe in higher network speeds (Figures 8(h) and 8(i)). Initially, we store coded blocks in the local file system of each machine, and load block locations and stripe information into the coordinator. We simulate a “failed” machine by erasing its stored blocks, and repair the failed block of each stripe in a requestor. We host the requestor on a machine that does not store any available block of the repaired stripe, to ensure that the available blocks are always transmitted over the network. By default, we configure 64 MiB block size, 32 KiB slice size, and (14,10) RS codes; note that (14,10) RS codes are also used by Facebook [42, 45]. We vary one of the settings at a time and evaluate its impact. We mainly compare the basic version of repair pipelining described in Section 3 with conventional repair (Section 2) and PPR [31]. We focus on three key repair metrics: --- 1Each machine in our local cluster has a faster CPU and more RAM than the one used in our conference paper [29]. Thus, we have re-run all experiments and the values presented in this article are different from those in Reference [29]. Nevertheless, we still observe the significant performance gain of repair pipelining. --- ACM Transactions on Storage, Vol. 17, No. 2, Article 13. Publication date: May 2021. • Single-block repair time: the latency from issuing a degraded read request to a failed block until the block is reconstructed; • Full-node recovery rate: the ratio of the amount of recovered data in a failed node to the total repair time; and • Multi-block repair time: the latency from issuing a request of repairing multiple failed blocks in a stripe until they are all reconstructed. All results are averaged over 10 runs. We find that the standard deviations are small and hence omit them from the plots. Slice size: Figure 8(a) shows the single-block repair time versus the slice size in repair pipelining; for fair comparisons, we also partition the blocks into 32 KiB slices in both conventional repair and PPR, so that they can also exploit parallelism for better performance. We further plot the transmission time of directly sending a single block over a 1 Gb/s link (labeled as “Direct send”). From the figure, we see that repair pipelining shows high repair time when the slice size is small, even though more slices are pipelined during a repair (i.e., $ s $ is small). The reason is that the overhead of issuing transmission requests for many slices becomes significant. We see that the repair time decreases as the slice size increases up to 32 KiB (where $ s = 2,048 $), and then increases, since there are too few slices in a block being pipelined (i.e., less parallelization). When the slice size is 32 KiB, repair pipelining reduces the single-block repair time by 89.5% and 69.5% compared to conventional repair and PPR, respectively. Also, the direct send time of transferring a 64 MiB block is 0.57s, which is almost network-bound in our 1 Gb/s network. The single-block repair time of repair pipelining is only 8.8% more than the direct send time. This shows the feasibility of reducing the single-block repair time to almost the same as the normal read time for a single available block. Block size: Figure 8(b) shows the single-block repair time versus the block size. Repair pipelining reduces the single-block repair time by 88.8–91.6% and 66.0–91.8% compared to conventional repair and PPR, respectively. Coding parameters: Figure 8(c) shows the single-block repair time versus $(n,k)$. The single-block repair time of conventional repair significantly increases with $k$, while that of PPR also increases with $k$ (albeit less significantly than in conventional repair). However, the single-block repair time of repair pipelining remains almost unchanged. As $k$ increases from 6 to 12, the repair time reduction of repair pipelining increases from 82.5% to 91.2% compared to conventional repair, and from 68.6% to 70.4% compared to PPR. Repair-friendly codes: We demonstrate how repair pipelining is compatible with practical erasure codes. We consider two state-of-the-art repair-friendly codes: Local Reconstruction Codes (LRC) [23] and Rotated RS codes [26]. LRC partitions the data blocks into local groups and associates a local parity block with each local group of data blocks. It improves the performance of a single-block repair, which can now be done within a local group, at the expense of higher storage redundancy. However, Rotated RS codes arrange the layout of parity blocks to improve the performance of a degraded read to a series of data blocks. We configure LRC with $k = 12$ data blocks that are partitioned in two local groups with six blocks each, and Rotated RS codes with $(n,k) = (16,12)$. LRC reads only six available blocks within a local group for repairing a failed block, while Rotated RS codes on average read nine blocks for repairing a failed block. Figure 8(d) shows the normalized single-block repair time with respect to conventional repair of $(16,12)$ RS codes. The normalized single-block repair time of repair pipelining (around 0.1) is much smaller than those of LRC and Rotated RS codes by effectively utilizing the bandwidth resources. of all helpers. We observe the same improvement in PPR, but its repair time reduction is less than that of repair pipelining. Full-node recovery: We now evaluate full-node recovery with multiple requestors and our greedy scheduling in helper selection (Section 3.3). Specifically, we randomly write multiple stripes of blocks across all 16 helpers in the local cluster. We erase 64 blocks from 64 stripes (one block per stripe) in one helper to mimic a single node failure, and recover all the erased blocks simultaneously. We distribute the reconstructed blocks evenly across a number of requestors, varied from one to 16. Each requestor is deployed in a distinct machine. We consider two cases of helper selection in repair pipelining: (i) we index the helpers from 1 to 16, and always select the available blocks from the $k$ helpers that have the smallest indexes in a stripe for repair (labeled as “RP”); and (ii) we use the greedy approach to select $k$ helpers that are least recently accessed for repair (labeled as “RP+scheduling”). We also evaluate conventional repair and PPR, both of which select helpers without greedy scheduling. Figure 8(e) shows the full-node recovery rates. As the number of requestors increases, the recovery rates of all schemes increase. Conventional repair sees the largest gain by distributing the repair load across more requestors. Interestingly, as the number of requestors increases to 16, conventional repair even achieves a slightly higher recovery rate than PPR. However, repair pipelining still outperforms conventional repair by making bandwidth utilization more balanced. Furthermore, our greedy scheduling achieves an observable gain when there are a large number of requestors. For example, when there are eight (respectively, 16) requestors, the recovery rate of repair pipelining without greedy scheduling is 1.89× (respectively, 1.51×) that of conventional repair, and our greedy scheduling further increases the recovery rate of repair pipelining by 13.3% (respectively, 8.9%). Multi-block repair: Figure 8(f) shows the multi-block repair time versus the number of failed blocks in a stripe. Here, we compare repair pipelining and conventional repair only, and omit PPR as its design does not address the multi-block repair of a stripe. Conventional repair has relatively stable repair time (ranging from 5.88 to 6.23 s) regardless of the number of failed blocks being repaired, as it always retrieves $k$ available blocks for repairing the failed blocks of a stripe. However, the repair time of repair pipelining almost increases linearly with the number of failed blocks. Nevertheless, repair pipelining still has 60.9% less repair time than conventional repair for a four-block repair. Limited edge bandwidth: Our previous tests focus on homogeneous environments, and we now move our evaluation to heterogeneous environments. We show the benefits of the cyclic version when a requestor sits at the network edge and the edge bandwidth from the storage system to the requestor is limited (Section 4.1). Specifically, we use the Linux tc command [5] to limit the edge bandwidth from each helper to the requestor. We compare the cyclic version with the basic version in Section 3. Figure 8(g) shows the single-block repair time versus the edge bandwidth. When the edge bandwidth is 1 Gb/s (i.e., the homogeneous case), both the basic and cyclic versions have almost identical repair time. As the edge bandwidth decreases, the repair time of the basic version increases significantly, while that of the cyclic version only increases mildly by allowing the requestors to read the reconstructed data from multiple helpers in parallel. For example, the cyclic version has 82.8% less repair time than the basic version when the edge bandwidth is 100 Mb/s. Rack awareness: We evaluate repair pipelining in a rack-based data center scenario. Specifically, we configure (9,6) RS codes. We divide our cluster into three logical racks, and use the Linux tc command [5] to limit the cross-rack bandwidth. We distribute the $n = 9$ blocks of each stripe Table 1. An iperf Test of Inner- and Cross-region Bandwidth Measurements (in Mb/s) on Amazon EC2 in North America and Asia \| Bandwidth \| California \| Canada \| Ohio \| Oregon \| \|---------------\|------------\|--------\|------\|--------\| \| California \| 501.3 \| 57.2 \| 44.1 \| 299.9 \| \| Canada \| 55.3 \| 732.0 \| 63.3 \| 48.0 \| \| Ohio \| 46.3 \| 65.7 \| 32.3 \| 95.6 \| \| Oregon \| 297.8 \| 50.2 \| 93.6 \| 250.1 \| (a) North America \| Bandwidth \| Mumbai \| Seoul \| Singapore \| Tokyo \| \|---------------\|------------\|---------\|-----------\|-------\| \| Mumbai \| 624.8 \| 62.3 \| 39.5 \| 37.7 \| \| Seoul \| 63.8 \| 265.7 \| 86.1 \| 183.2 \| \| Singapore \| 41.5 \| 88.1 \| 493.0 \| 49.1 \| \| Tokyo \| 39.7 \| 181.0 \| 46.9 \| 489.1 \| (b) Asia Each value is the measured bandwidth from the row region to the column region. Note that the bandwidth values fluctuate across different tests. evenly across the three logical racks (i.e., $n/3 = 3$ blocks per rack), so that the block placement can tolerate any single-rack failure. We compare repair pipelining with and without rack awareness (Section 4.2), as well as conventional repair; we do not consider PPR here as its design does not address rack awareness. Figure 8(h) shows the single-block repair time in two cross-rack bandwidth settings: 400 and 800 Mb/s. Repair pipelining without rack awareness reduces the repair time of conventional repair, yet with rack awareness, we observe a further drop of the single-block repair time. For example, when the cross-rack bandwidth is 800 Mb/s, repair pipelining without rack awareness reduces the single-block repair time of conventional repair by 60.9%; with rack awareness, the reduction further improves to 77.6%, since the cross-rack repair traffic is minimized. Varying network bandwidth: We evaluate repair pipelining when the network bandwidth is above 1 Gb/s, in which the computation and disk I/O overheads become significant. We now connect all machines in our local cluster via a 10 Gb/s Ethernet switch. We use the Linux tc command [5] to vary the available network bandwidth of each node (up to 10 Gb/s). Figure 8(i) shows that single-block repair time versus the network bandwidth. As the available network bandwidth increases, the single-block repair time decreases in all schemes. Also, the repair time reduction of repair pipelining also drops due to the more significant overheads in both computation and disk I/O. Nevertheless, repair pipelining still shows a performance gain. For example, when the network bandwidth is 10 Gb/s, repair pipelining reduces the single-block repair time by 81.4% and 50.0% compared to conventional repair and PPR, respectively (while the reduction reaches around 90% and 70% when the network bandwidth is 1 Gb/s, as shown in Figure 8(a)). 6.2 Evaluation on Amazon EC2 Methodology: We evaluate ECPipe on Amazon EC2. Specifically, we consider geo-distributed clusters that span multiple geographic regions [6, 12, 17], in which erasure-coded blocks are striped across regions to protect against large-scale correlated failures. We evaluate ECPipe on two Amazon EC2 clusters, one in North America and one in Asia. Table 1 shows one of our iperf [3] measurement tests for the inner-region and cross-region bandwidth values on Amazon EC2 across four regions, respectively, in North America and Asia. We observe that the inner-region bandwidth is in general more abundant than the cross-region bandwidth, and the cross-region bandwidth has a high degree of variance. We deploy four EC2 instances per region per cluster to host helpers (i.e., 16 helpers in total), and one EC2 instance in Ohio and Singapore to host the coordinator for the North America and Asia clusters, respectively. Note that the overhead of accessing the coordinator has negligible impact on the overall repair performance. We focus on evaluating the single-block repair time of a degraded read issued by a requestor. We host the requestor on an EC2 instance in each region and study how the performance varies across regions. All EC2 instances are of type t2.micro. We configure 64 MiB block size and 32 KiB slice size for repair pipelining. We use (16,12) RS codes and distribute the 16 blocks of each stripe across the 16 EC2 instances in four regions; this also provides fault tolerance against any single-region failure. We consider two versions of repair pipelining: the basic version in Section 3 (labeled as “RP”), which finds a random path across $k$ randomly selected helpers, and the optimal version in Section 4.3 (labeled as “RP+optimal”), which finds an optimal path via Algorithm 2. Note that the network bandwidth fluctuates over time, although inner-region bandwidth remains higher than cross-region bandwidth, as shown in Table 1. Thus, the optimal version probes the network bandwidth via \texttt{iperf} before each run of experiments. We average our results over 10 runs, and also include the standard deviations as the results have higher variances than in our local cluster. Results: Figure 9 shows the single-block repair time and the standard deviations of PPR and the two versions of repair pipelining in both clusters; we do not show the results of conventional repair, whose repair time goes beyond 200 s. Repair pipelining (without weighted path selection) achieves repair time saving over PPR in all cases when the requestor is in different regions. The repair time reduction is 62.7–78.0% for North America and 66.6–87.1% for Asia. Our weighted path selection further reduces the repair time by 7.3–45.4% for North America and 14.5–45.0% for Asia, compared to repair pipelining without weighted path selection. Note that our weighted path selection can be done in around 1 ms (Section 4.3), which is negligible compared to the repair time in our evaluation. ### 6.3 Evaluation on HDFS-RAID, HDFS-3, and QFS Methodology: We evaluate the integration of ECPipe into HDFS-RAID, HDFS-3, and QFS, all of which are deployed in our local cluster (Section 6.1). We co-locate a helper daemon with each of the 16 storage nodes (i.e., DataNodes in HDFS-RAID and HDFS-3, or ChunkServers in QFS). By default, we set the slice size of repair pipelining as 32 KiB and block size as 64 MiB. For HDFS-RAID and HDFS-3, we vary $(n, k)$, while for QFS, we use its default $(9,6)$ RS codes and vary the slice size and block size. We consider three repair schemes: (i) the original repair implementations of HDFS-RAID, HDFS-3 and QFS, all of which are based on conventional repair, (ii) the conventional repair under ECPipe, and (iii) the basic version of repair pipelining in Section 3 under ECPipe. For HDFS-RAID and QFS, we evaluate degraded reads (in single-block repair time) issued by a requestor that is attached with either an HDFS-RAID client or a QFS ChunkServer. For HDFS-3, we observe similar results of the single-block repair time as in HDFS-RAID. Thus, we focus on evaluating full-node recovery in HDFS-3, in which we evenly distribute 64 stripes of blocks across ![Figure 9. Evaluation on Amazon EC2.](image-url) all DataNodes, followed by erasing all blocks of a DataNode and repairing the lost blocks in a new DataNode. We report the averaged results over 10 runs as in Section 6.1 (the standard deviations are small and omitted). Results: Figure 10 shows the evaluation results. First, repair pipelining under ECPipe significantly improves the repair performance of the original repair implementations of HDFS-RAID, HDFS-3, and QFS. Specifically, for HDFS-RAID, repair pipelining reduces the single-block repair time by 82.7–91.2% for different $(n, k)$ (Figure 10(a)); for HDFS-3, it achieves $5.1-16.0 \times$ full-node recovery rate for different $(n, k)$ (Figure 10(b)); for QFS, it reduces the single-block repair time by up to 86.6% when the slice size is 32 KiB and the block size is 64 MiB (Figures 10(c) and 10(d)). We observe that moving the repair logic to ECPipe improves single-block repair performance. Specifically, conventional repair under ECPipe reduces the single-block repair time by up to 21.8% and 26.3% in HDFS-RAID and QFS, respectively, compared to the original conventional repair implementation. The reason of the performance gain is that the helpers of ECPipe can directly access the stored blocks via the native file system, instead of fetching the blocks through the distributed storage system routine. For full-node recovery, conventional repair under ECPipe outperforms the original conventional repair when $k$ is large (i.e., $k = 10$ or 14). The reason is that when $k$ increases, the overhead of initiating connections to $k$ DataNodes for retrieving available blocks in HDFS-3 also increases. Nevertheless, we emphasize that the repair performance gain mainly comes from repair pipelining, rather than the implementation of ECPipe. Although moving repair to ECPipe reduces the repair time, the reduction is minor compared to the reduction achieved by repair pipelining. 6.4 Evaluation of Different Repair Pipelining Implementations Methodology: We compare different repair pipelining implementations based on ECPipe in our local cluster (Section 6.1). First, we compare the block-level and slice-level repair pipelining approaches, and implement two baseline variants called Pipe-B and Pipe-S. Pipe-B implements block-level repair pipelining (i.e., without slicing) along a linear path of helpers, each of which sends a partially repaired block to the next helper (or the requestor for the last helper); in essence, Pipe-B is the naïve approach as described in Section 3.2. Pipe-S implements slice-level repair pipelining without parallelization. It realizes the sub-operations of repairing a slice inside a helper (i.e., receiving the partially repaired slice from the preceding helper, reading its locally stored slice, computing a new partially repaired slice, and sending the partially repaired slice) in a serial manner. Our current repair pipelining implementation (referred to as RP) also performs slice-level repair pipelining. Compared to Pipe-S, RP carefully parallelizes the sub-operations of slices in each helper to simultaneously utilize all available resources. Note that RP is our default implementation used in the previous experiments (Sections 6.1–6.3). We also compare our repair pipelining implementation with the design in PUSH [24] in full-node recovery as described in Section 6.1 (note that PUSH does not consider single-block repair). As the source code of PUSH is unavailable, we implement the two variants of PUSH, namely, PUSH-Rep and PUSH-Sur, in ECPipe based on the description of the paper [24], which we refer to them as Pipe-Rep and Pipe-Sur, respectively. Both Pipe-Rep and Pipe-Sur implement block-level repair pipelining. Pipe-Rep reconstructs all failed blocks in a single node, while Pipe-Sur distributes the reconstructed blocks across all 16 nodes in our local cluster in a round-robin manner. For comparisons, we consider two variants of our repair pipelining implementation (with greedy scheduling enabled), namely, RP-single and RP-all. RP-single reconstructs all failed blocks in a single node, while RP-all distributes all reconstructed blocks across all 16 nodes in our local cluster. Both RP-single and RP-all are configured with 16 requestors: for RP-single, we deploy all 16 requestors in the node where the failed blocks are reconstructed; for RP-all, we deploy one requestor per node. Compared to PUSH-Rep and PUSH-Sur, both RP-single and RP-all implement slice-level repair pipelining. Results: Figure 11 shows the results, averaged over 10 runs. Figure 11(a) evaluates the single-block repair time versus the block size for Pipe-B, Pipe-S, and RP, where both Pipe-S and RP have the slice size fixed as 32 KiB. Pipe-B has the largest single-block repair time (e.g., 9.0 s for repairing a 64 MiB block), while Pipe-S significantly reduces the single-block repair time (e.g., 1.1 s for repairing a 64 MiB block) through slice-level repair pipelining. This again shows that slice-level repair pipelining can improve the repair performance via more fine-grained parallelization. RP further reduces the single-block repair time (e.g., 0.61 s for repairing a 64 MiB block) by carefully scheduling the slice-level repair sub-operations in a parallel fashion. Overall, RP reduces the single-block repair time of Pipe-S by 41.1-43.0% across all block sizes. Note that we observe similar performance differences between Pipe-S and RP for different slice sizes, so we omit the results here. Figure 11(b) evaluates the full-node recovery rate versus the block size for Pipe-Rep, Pipe-Sur, RP-single, and RP-all. Here, we repair 4 TiB of lost data (i.e., the number of reconstructed blocks is 4 TiB divided by the block size), and fix the slice size for RP-single and RP-all as 32 KiB. We observe that when the block size is 1 MiB, both Pipe-Rep and Pipe-Sur have higher recovery rates than RP-single and RP-all by 9.0% and 9.7%, respectively. The reason is that Pipe-Rep and Pipe-Sur benefit from block-level repair pipelining across a large number of blocks in small block sizes. On the other hand, in RP-single and RP-all, each block is only divided into a limited number of slices (e.g., 32 slices for a 1 MiB block). They do not benefit much from slice-level repair pipelining. Nevertheless, as the block size increases, the recovery rates of both Pipe-Rep and Pipe-Sur drop significantly, as the number of blocks decreases for larger block sizes and the performance gain from pipelining is limited. However, the recovery rates of RP-single and RP-all increase with the block size, as each block can now be divided into more slices. Both RP-single and RP-all can benefit from the slice-level repair pipelining for each block; note that they also allow multiple requestors to reconstruct the lost blocks in parallel. When the block size is 64 MiB, the recovery rates of RP-single and RP-all are 80.2% and 268.1% higher than those of Pipe-Rep and Pipe-Sur, respectively. Also, RP-all has a higher recovery rate than RP-single (e.g., by 58.1% when the block size is 64 MiB) by distributing the repair load across the requestors in different nodes. In summary, our current repair pipelining implementation maintains its high performance gain in large block sizes, which are commonly found in state-of-the-art distributed storage systems (e.g., 64 MiB [18] or 256 MiB [42]). 7 RELATED WORK Many new erasure codes have been proposed in the literature to mitigate repair overhead, especially for a single-node repair. To name a few, regenerating codes [16] minimize the repair traffic by allowing storage nodes to send encoded data during a single-node repair. Rotated RS codes [26] reduce the repair traffic and disk I/O of a degraded read to a sequence of data blocks. Hitchhiker [42] extends RS codes [43] to piggyback parity information of one stripe into another stripe, and is shown to reduce the repair traffic and I/O by up to 45%. PM-RBT codes [40] are special regenerating codes that simultaneously minimize the repair traffic, disk I/O, and storage redundancy. Butterfly codes [36] are systematic regenerating codes that provide double-fault tolerance. Clay codes [51] couple multiple layers of MDS codes and achieve optimality in terms of the repair traffic, disk I/O, storage redundancy, as well as the sub-packetization level (i.e., the number of sub-blocks divided within a block). Locally repairable codes [23, 45] add local parity blocks to mitigate repair I/O with extra storage redundancy. Instead of constructing new erasure codes, we design new repair strategies for general practical erasure codes. Some prior studies are also along this direction. Tree-structured data regeneration [27] specifically targets regenerating codes [16], and constructs a spanning tree that maximizes the bandwidth utilization during repair. Lazy repair [10, 50] defers immediate repair action until a tolerable limit is reached. To speed up full-node recovery, the repair of multiple stripes can be parallelized across available nodes, as also adopted by replicated storage [14, 34] and de-clustered RAID arrays [20]. Degraded-first scheduling [28] targets MapReduce on erasure-coded storage by scheduling map tasks to fully utilize bandwidth in degraded reads. FastPR [46] reconstructs in advance the data stored in soon-to-fail nodes, to speed up the repair operation. A closely related work to ours is PPR [31], which reduces the single-block repair time from $k$ timeslots to $\lceil \log_2 (k + 1) \rceil$. timeslots by parallelizing partial repair operations across different nodes, while repair pipelining reduces the single-block repair time to one timeslot. Several studies improve the repair performance of erasure-coded storage for hierarchical data centers. Some studies [21, 22, 39] propose new regenerating codes that minimize the cross-rack repair traffic for hierarchical topologies, in which storage nodes are organized in racks. CAR [48] minimizes the cross-rack repair traffic for RS-coded storage by first computing partial repaired results in each rack and then sending the partial repaired results across racks. LAR [53], similar to CAR [48], also studies how to minimize the cross-rack repair traffic in the network core of a hierarchical topology by solving for a minimum spanning tree. ClusterSR [47] not only minimizes the cross-cluster repair traffic in geo-distributed storage but also balances the upload and download traffic in full-node recovery. With hierarchy awareness, repair pipelining preserves the minimum cross-rack repair traffic and further reduces the single-block repair time (Section 4.2). Some studies also propose pipelined approaches to improve the repair performance in erasure-coded storage. PUSH [24] forms a reconstruction chain along different helpers and performs block-level repair pipelining for full-node recovery. In contrast, our repair pipelining design schedules a single-block repair at a more fine-grained slice level, and we show that how it substantially reduces the single-block repair time to almost the same as the normal read time for a single block. Compared to PUSH, our contributions include: (i) by slicing a block (a read/write unit of a distributed storage system) into smaller units, we show that repair pipelining can reduce the degraded read time for an unavailable block to almost the same as the normal read time for an available block (in contrast, PUSH only focuses on full-node recovery); (ii) we present extensions of repair pipelining for heterogeneous environments; (iii) we show how repair pipelining can be readily integrated via ECPipe into existing distributed storage systems (i.e., HDFS-RAID, HDFS-3, and QFS); and (iv) we compare different repair pipelining implementations (including our own implementation of PUSH [24]). LAR [53] implements pipelined reconstruction by dividing blocks into packets (i.e., slices in our case). However, it does not formally analyze how the packets are scheduled to minimize single-block repair time. Parallel Pipeline Tree (PPT) [9] constructs an optimized repair tree based on repair pipelining for heterogeneous environments, while we address some special cases of heterogeneous environments, such as the scenario where the link bandwidth between the storage system and the requestor is limited as well as hierarchical data centers. Our recent work, OpenEC [30], provides a framework that simplifies the deployment of repair pipelining through a directed-acyclic-graph abstraction. 8 CONCLUSIONS Repair pipelining is a general technique that reduces the single-block repair time to almost the same as the normal read time for a single available block in erasure-coded storage. It schedules the repair of a failed block across storage nodes in units of slices in a pipelined manner, to evenly distribute the repair traffic and fully utilize bandwidth resources across storage nodes. 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Received July 2019; revised August 2020; accepted November 2020	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 1877, 1 ], [ 1877, 6418, 2 ], [ 6418, 10595, 3 ], [ 10595, 14723, 4 ], [ 14723, 17740, 5 ], [ 17740, 21770, 6 ], [ 21770, 26173, 7 ], [ 26173, 29462, 8 ], [ 29462, 33939, 9 ], [ 33939, 37091, 10 ], [ 37091, 39432, 11 ], [ 39432, 43827, 12 ], [ 43827, 45975, 13 ], [ 45975, 50427, 14 ], [ 50427, 53781, 15 ], [ 53781, 57674, 16 ], [ 57674, 60408, 17 ], [ 60408, 62175, 18 ], [ 62175, 66149, 19 ], [ 66149, 70268, 20 ], [ 70268, 74468, 21 ], [ 74468, 77457, 22 ], [ 77457, 79360, 23 ], [ 79360, 82532, 24 ], [ 82532, 86950, 25 ], [ 86950, 91096, 26 ], [ 91096, 96213, 27 ], [ 96213, 101360, 28 ], [ 101360, 102506, 29 ] ] }
ea38790be4dfe3e5ac202d9af432562f605ded9a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 6, "total-fallback-pages": 0, "total-input-tokens": 22327, "total-output-tokens": 7046, "fieldofstudy": [ "Physics" ] }	NLO Higgs+jet production at large transverse momenta including top quark mass effects Tobias Neumann Department of Physics, Illinois Institute of Technology, Chicago, Illinois 60616, United States of America Fermilab, PO Box 500, Batavia, Illinois 60510, United States of America E-mail: [email protected] Keywords: QCD, Standard Model, Higgs+jet, top quark mass effects Abstract We present a next-to-leading order calculation of $H+\text{jet}$ in gluon fusion including the effect of a finite top quark mass $m_t$ at large transverse momenta. Using the recently published two-loop amplitudes in the high energy expansion and our previous setup that includes finite $m_t$ effects in a low energy expansion, we are able to obtain $m_t$-finite results for transverse momenta below 225 GeV and above 500 GeV with negligible remaining top quark mass uncertainty. The only remaining region that has to rely on the common leading order rescaling approach is the threshold region $\sqrt{s} \simeq 2m_t$. We demonstrate that this rescaling provides an excellent approximation in the high $p_T$ region. Our calculation settles the issue of top quark mass effects at large transverse momenta. It is implemented in the parton level Monte Carlo code MCFM and is publicly available immediately in version 8.2. 1. Introduction With the Higgs boson discovery at the Large Hadron Collider (LHC) [1, 2] setting a milestone for physics research, the hunt for signals beyond those described by the Standard Model (SM) has been more active than ever. Early Higgs studies during Run I, limited by statistics and energy, probed rather inclusive properties, and no significant deviations from the SM have been found [1–7]. Differential Higgs measurements [8–14] testing the SM were limited by statistics rather than theory predictions. Recent experimental analyses consider the Higgs boson in a highly boosted regime with transverse momenta below 250 GeV and above 500 GeV with negligible remaining top quark mass uncertainty. The only remaining region that has to rely on the common leading order rescaling approach is the threshold region $\sqrt{s} \simeq 2m_t$. We demonstrate that this rescaling provides an excellent approximation in the high $p_T$ region. Our calculation settles the issue of top quark mass effects at large transverse momenta. It is implemented in the parton level Monte Carlo code MCFM and is publicly available immediately in version 8.2. Unfortunately the operator used in this EFT description is the same operator of dimension six that appears at large transverse energies was the dependence on the effective field theory (EFT) description. In this EFT approach the top quark is integrated out as a heavy particle to circumvent the calculation of complicated massive two-loop integrals. It is strictly valid only in the region of energies small compared to $m_t$. To constrain physics beyond the Standard Model (BSM) using gluon fusion Higgs production, one of the most promising approaches is to consider large transverse energies [17–30]. A common limitation of all higher order Higgs+jet calculations in the region of large transverse energies was the dependence on the effective field theory (EFT) description. In this EFT approach the top quark is integrated out as a heavy particle to circumvent the calculation of complicated massive two-loop integrals. It is strictly valid only in the region of energies small compared to $m_t$. Unfortunately the operator used in this EFT description is the same operator of dimension six that appears at leading order in the Standard Model EFT to search for new physics in a modified Higgs-gluon coupling. Thus the only reliable way to directly disentangle SM gluon fusion from heavy BSM contributions requires computing the full top quark mass dependence at large energies or at least a sufficient approximation beyond its dependence on the EFT description. It is this region, in which finite top quark mass effects were unconstrained at NLO, which we consider in our study. We give percent level accurate predictions through the use of a high energy expansion of the missing two-loop amplitudes [31]. While finalizing our manuscript we became aware of a study similar to ours in ref. [32]. Additionally, results based on a fully numerical evaluation of the two-loop integrals with full top quark mass dependence have been presented in [33]. We still believe that our study and implementation are useful for large transverse momenta, where the difference to the full calculation should be negligible and the full calculation seems to be numerically challenging for large transverse momenta. © 2018 The Author(s). Published by IOP Publishing Ltd An additional aspect to constrain BSM physics through precision SM predictions comes from the shape of kinematical distributions and not just through their absolute magnitude. Specifically we evaluate in this study whether top quark mass effects distort the shape of the Higgs transverse momentum distribution at high energies compared to previous approximations. Throughout the years various approximations beyond the pure EFT description have been used, which we will briefly summarize here. Gluon fusion induced Higgs production mediated through a massive top quark loop was calculated at LO a long time ago [34], but the difficulty is considerably amplified at NLO and in Higgs production with a jet, where massive two-loop amplitudes have to be calculated. An efficient analytical evaluation of these integrals for Higgs+jet is currently not within reach [35, 36]. Fortunately, at least for the region of transverse momenta below the top-quark threshold $p_T \ll 2m_t$, the EFT approach turned out to provide an excellent approximation of perturbative corrections even for differential Higgs+jet quantities [37, 38]. This was shown using a low energy expansion below the top quark threshold, and as such can not constrain the effects of a finite top quark mass for large energies. Going beyond estimations of top quark mass effects, studies with predictions including partially exact amplitudes were performed [39–42], but were always limited by low energy approximations in other parts. And only the EFT approach, which reduces the needed number of loops to evaluate by one, allowed for an evaluation of Higgs+jet at NNLO [43–47]. Residual perturbative uncertainties estimated by renormalization and factorization scale variation are estimated to be about 10% at NNLO, cutting in half the estimated NLO uncertainty. Studies targeting top quark mass effects specifically in the large transverse momentum region of Higgs production were performed using resummation [49], and by using a factorization of the mass scale from $p_T$ in the high $p_T$ limit [50]. In the latter case the developed formalism was only applied to the subprocess $q\bar{q}$ at leading order in $1/p_T$ and leading order in $\alpha_s$. The former study only improves the NLO calculation through a rescaling $k$-factor and not directly, as their high energy approximation was shown to deviate from the exact result at LO. Their suggested approach is to rescale exact LO results by a $k$-factor obtained in their high energy approximation. A different approach is to match different hard-jet multiplicities and parton showers [26, 41]. It is the goal of this study to extend our previous setup [42], publicly available in MCFM [51–53], which provides finite $m_t$ effects in the region $p_T \ll 2m_t$, to predictions with a finite $m_t$ for $p_T \gg 2m_t$. We also study the validity of the common LO rescaling approach in the region of high $p_T$. To do this we implement the recently published two-loop amplitudes in the high energy expansion [31]. ### 2. Calculation Our calculation is based on the previous NLO Higgs+jet setup in MCFM-8.1 [42]. This previous setup uses an asymptotic expansion in $\Lambda/(2m_t)$ only for the finite part of the virtual two-loop amplitudes, but is exact in the top quark mass otherwise. Here $\Lambda$ is a placeholder for all kinematical scales of the process. For Higgs $p_T$ smaller than $\approx 225$ GeV the asymptotic expansion was shown to be convergent and provides an excellent approximation of the full top quark mass dependence. For energies larger than $\approx 300$ GeV the expansion breaks down and finite top quark mass effects could become larger than 8%, such that either a full calculation is necessary or another approximation is needed for sufficiently large $p_T$. Here, we fill this gap for the latter case. We have implemented the one- and two-loop Higgs plus three parton helicity amplitudes in the high energy expansion from [31]. The expansion is performed in $\kappa \equiv -(m_t^2/3)^4$ to order $k = 1$ while retaining an expansion in $\eta \equiv -(m_H^2/(4m_t^2))^l$ only to first order $l = 0$. Here $m_H$ is the Higgs mass and $\ell$ the partonic center of mass energy. The amplitudes are given as the finite parts after UV renormalization and Catani IR subtraction [54] using $d = 4 - 2\epsilon$ Born one-loop amplitudes. We have performed a conversion to the 'tHooft-Veltman scheme for use in MCFM and additionally restored the renormalization scale dependence. At LO Higgs+jet relies on one-loop amplitudes and is known with the exact top quark mass dependence, which allows us to compare it with the result from the high energy expansion. This gives an estimate on how far we can trust the approximation when using the two-loop amplitudes. Having established trust in the validity of the two-loop amplitudes in the high $p_T$ region we can then compare the results with the Born-rescaling approximation. In this rescaling approximation the finite part of the two-loop virtual amplitude is point-wise rescaled by the Born amplitude in the full theory divided by the Born amplitude in the EFT. For our study we choose a center of mass energy of $\sqrt{s} = 13$ TeV and a common renormalization and factorization scale of $\mu_R = \mu_F = \sqrt{m_H^2 + p_T^2}$, where $m_H = 125.0$ GeV and $p_T$ is the Higgs transverse momentum. Although the region of high $p_T$ motivates using the six-flavor scheme, no matching parton distribution functions (PDFs) are available. So for consistency we work in the five-flavor scheme with an on-shell top quark mass of $m_t = 173.2$ GeV. We use CT14 PDFs [55] at NLO accuracy for the NLO cross section and... --- 2 For a recent overview of Higgs production and decay cross sections we refer to [48]. at LO accuracy for our LO results. The value of $\alpha_s$ is given at the according order by the PDF set. Finally, we require at least one jet clustered with the anti-$k_T$ jet algorithm with $p_{T,\text{jet}} > 30 \text{ GeV}$, $\|\eta_{\text{jet}}\| < 2.4$ and $R = 0.5$. 3. Results The first question one has to ask is in how far one can trust the two-loop high energy amplitudes to describe the exact $m_t$ dependence. In lack of the $m_t$-exact two-loop amplitudes for comparison, one has to resort to a different method to evaluate this trust. For example, one could observe a convergent behavior of the expansion, but this would require some higher expansion order than is available as we will see below. Instead we can study how well the expansion works at LO. This has some limitations though, as will be discussed below. To study the high energy expansion we consider figure 1: shown is the LO Higgs transverse momentum distribution in various approximations normalized to the distribution with exact $m_t$-dependence. The approximations shown are the low energy expansions up to order $m^k_{1/2}$ for $k = 0, 2, 4$, where $k = 0$ describes the EFT, as well as the high energy expansion. The amplitudes in the high energy expansion are given up to order $m^k_{1/2}$ for $k = 0, 2, 4, 6$. Naively using them for the LO cross section includes partial effects of order $\kappa^2$. This is labeled in the plot as 'high, partial $m^k_{1/2}$'. Only including $m^2_t$ terms in the cross section is labeled with 'high $m^2_t$'. By the same argument given above, one would expect the high energy approximation to work better for one-loop diagrams than for two-loop diagrams. For the low energy expansion the convergence is poor and is practically non-existent beyond about $100 \text{ GeV}$. At NLO though, using only the expansion in the two-loop amplitude, the region of convergence increases to about $250 \text{ GeV}$ as shown in [42]. This can also be seen in figure 2. A simple explanation is that for two-loop diagrams the topology does not force all center of mass energy to go through the top quark loop, such that $m^2_t$ threshold effects are further washed out. The amplitudes in the high energy expansion are given up to order $\kappa^2 \equiv (m^2_{1/2}/\kappa)^2$. Naively using them for the LO cross section includes partial effects of order $\kappa^2$. This is labeled in the plot as 'high, partial $m^k_{1/2}$'. Only including $m^2_t$ terms in the cross section is labeled with 'high $m^2_t$'. By the same argument given above, one would expect the high energy approximation to work better for one-loop diagrams than for two-loop diagrams. Nevertheless the difference between using the full $\mathcal{O}(\kappa^2)$ amplitudes and the $m_t$-exact result is less than two percent beyond $500 \text{ GeV}$, which gives motivation to trust that the two-loop high energy amplitudes describe the full top quark mass dependence at a similar level. Considering that the NLO scale uncertainty is about $20\%$ [42] and still about $10\%$ at NNLO [45, 47], any remaining top quark mass uncertainty can then be considered negligible. Ideally a more precise estimate could be established by including full $\mathcal{O}(\kappa^2)$ and $\mathcal{O}(\kappa^3)$ terms, possibly higher order terms in $\eta$ for the one- and two-loop amplitudes. Having shown that the large energy expansion describes the full LO result at percent level accuracy beyond $500 \text{ GeV}$, we expect a similar behavior for the two-loop amplitudes. At NLO the two-loop amplitudes additionally only enter as the virtual corrections and a bulk of the perturbative corrections at large $p_T$ comes from the real emission which we include with full $m_t$ dependence. The error from using the large energy expansion estimated at LO should thus be conservative. At NLO we show the Higgs $p_T$ distribution in figure 2 with a normalization to the distribution using rescaled EFT two-loop amplitudes. Here, to emphasize again, only the finite part of the two-loop virtual corrections is not exact in $m_t$, and is approximated in different ways. It is obtained using either a $1/m_t$ expansion in the region of small $p_T$, or in the high energy expansion up to order $\kappa^2$ for large $p_T$. Additionally, using the rescaling approach as described in section 2 we obtain an approximation that can be used over the whole range of $p_T$ and also serves as the overall normalization. The latter approach was used for example in [41] and shown to agree with the low energy asymptotic expansion at the percent level for $p_T \lesssim 225$ GeV [42]. We present the distributions normalized to the EFT rescaled approximation and not as absolute distributions, since we are strongly interested in possible shape corrections due to using a finite top quark mass. In this way one can easily compare the additional corrections to the previous best approximation at high $p_T$ in percent. The scale variation uncertainty of about 20% changes only little with respect to the EFT result and other approximations, and can be found for example in our previous study [42]. The low energy expansion indeed extends its convergent behavior to about 250 GeV with corrections of less than a percent compared to the rescaling approach. The high energy expansion, which we believe approximates the full result by better than 2%, is consistent with the corrections at low $p_T$ and increases the cross section by about 1%–2% compared to the rescaled result. It is remarkable that these top quark mass corrections are flat within 1% over the whole range of large $p_T$. In this sense one is free to choose either the rescaling approach or the high energy approximation. Nevertheless the high energy approximation is a systematic approach, whereas the rescaling approach was done ad hoc without prior validation. We thus recommend to use the high energy approximation for transverse momenta beyond $\sim 500$ GeV. Finally we would like comment on the case where the whole NLO distribution is evaluated in the EFT and bin-wise rescaled by the ratio of the LO distribution in full theory to the LO distribution in the EFT. This is an approach that is still typically done in many experimental and phenomenological analyses. We find that at low $p_T \lesssim 300$ GeV this approach overestimates the cross-section by about 2%–6%, while at large $p_T \gtrsim 500$ GeV it underestimates the cross-section by about 3%–5% percent. 4. Conclusions We have presented a NLO calculation of Higgs + jet with negligible remaining top quark mass uncertainty in the region of low transverse momenta $p_T \lesssim 225$ GeV [42] and, as shown in this analysis, also in the region of large transverse momenta $p_T \gtrsim 500$ GeV. We have demonstrated that using the high energy expansion in the finite part of the two-loop amplitude, instead of rescaling it by the $m_t$-exact Born amplitude, results in a difference of less than two percent for $p_T \gtrsim 500$ GeV. The high energy expansion is asymptotically correct and at LO shows similarly small single percent level differences to the exact result. Considering additionally that for our NLO result only the finite part of the two-loop virtual amplitudes requires this expansion, we have established considerable trust in the validity of our result to approximate the full NLO result by better than a few percent. The elimination of the top-quark mass uncertainty at high $p_T$ at NLO now allows one to rescale NNLO results obtained in the EFT by a NLO $k$-factor NLO($m_t$)/NLO(EFT). Our implementation is publicly available immediately in MCFM-8.2. 3 We would like to thank the JPhysG referee for this suggestion. Acknowledgments We would like to thank Christopher Wever for providing us with their choice of fixed renormalization scales for the high energy amplitudes [31], which were not given in [31] at that time, as well as some further help. We would like to thank John Campbell for extensive discussion and comments on the manuscript as well as Zack Sullivan for valuable discussion and comments on the manuscript and Stefan Prestel for helpful discussion. Additionally would also like to thank the JPhysG referee for useful suggestions. This work was supported by the US Department of Energy under award No. DE-SC0008347. This document was prepared using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359. 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JHEP08(2016)150 [50] Braaten E, Zhang H and Zhang J-W 2017 J. High Energy Phys. JHEP11(2017)127 [51] Campbell J M and Ellis R K 1999 Phys. Rev. D 60 113006 [52] Campbell J M, Ellis R K and Williams C 2011 J. High Energy Phys. JHEP07(2011)018 [53] Campbell J M, Ellis R K and Giele W T 2015 Eur. Phys. J. C 75 246 [54] Catani S 1998 Phys. Lett. B 427 161 [55] Dulat S, Hou T-J, Gao J, Guzzi M, Huston J, Nadolsky P, Pumplin J, Schmidt C, Stump D and Yuan C P 2016 Phys. Rev. D 93 033006	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4709, 1 ], [ 4709, 10502, 2 ], [ 10502, 14815, 3 ], [ 14815, 18224, 4 ], [ 18224, 22962, 5 ], [ 22962, 23431, 6 ] ] }
efabac66a119d25c20be42191d0053e194a2edf3	{ "olmocr-version": "0.1.59", "pdf-total-pages": 11, "total-fallback-pages": 0, "total-input-tokens": 37674, "total-output-tokens": 13886, "fieldofstudy": [ "Environmental Science" ] }	A framework for selecting and designing policies to reduce marine plastic pollution in developing countries F. Alpizar\textsuperscript{a,b,}, F. Carlsson\textsuperscript{c,k}, G. Lanza\textsuperscript{b}, B. Carney\textsuperscript{d}, R.C. Daniels\textsuperscript{e}, M. Jaime\textsuperscript{f}, T. Ho\textsuperscript{g}, Z. Nie\textsuperscript{e}, C. Salazar\textsuperscript{b}, B. Tibesigwa\textsuperscript{i}, S. Wahdera\textsuperscript{j} \textsuperscript{a} Department of Social Sciences, Wageningen University and Research, The Netherlands \textsuperscript{b} Economics and Environment for Development Research Program, CATIE, Costa Rica \textsuperscript{c} Department of Economics, University of Gothenburg, Sweden \textsuperscript{d} Department of Biology and Environmental Sciences, University of Gothenburg, Sweden \textsuperscript{e} School of Economics, University of Cape Town, South Africa \textsuperscript{f} School of Business and Management, University of Conception, NERRE EFD-Chile and CAPES, Chile \textsuperscript{g} School of Economics, University of Economics Ho Chi Minh City, Viet Nam \textsuperscript{h} Department of Business Management, University of Bio-Bio, EFD Chile and INCAR, Chile \textsuperscript{i} Environment for Development Tanzania (EFDT), Department of Economics, University of Dar es Salaam, Tanzania \textsuperscript{j} Economics and Planning Unit, Indian Statistical Institute, India \textsuperscript{k} Center for Collective Action Research (CeCAR), University of Gothenburg, Sweden \textbf{ARTICLE INFO} \textbf{Keywords:} Plastic pollution policy tools behavioral change developing countries \textbf{ABSTRACT} The polluting of marine ecosystems with plastics is both a global and a local problem with potentially severe consequences for wildlife, economic activity, and human health. It is a problem that originates in countries’ inability to adequately manage the growing flow of waste. We use an impact pathway framework to trace the flow of plastics through the socio-ecological system and identify the role of specific policy instruments in achieving behavioral changes to reduce marine plastic waste. We produce a toolbox for finding a policy that is suitable for different countries. We use the impact pathway and toolbox to make country-specific recommendations that reflect the reality in each of the selected countries. \section{Introduction} Marine plastic pollution is a global transboundary problem that originates at a local level and has captured increased political and scientific attention over the last decade (UNEP, 2016, 2009). Marine plastic pollution has many negative consequences. One is that animals, in particular turtles, mammals, and sea birds, ingest or get trapped in plastic waste (Thompson, 2015). Research also shows the presence of plastics in fish that humans consume (Bonanno and Orlando-Bonaca, 2018; Rockman et al., 2015). However, no research has confirmed or disproved that this poses a risk for humans (Carney Almroth and Eggert, 2019; Rist et al., 2018). There are also aesthetic costs caused by plastic pollution, both near shores and in the oceans, including the Great Pacific garbage patch (Lerotin et al., 2018). Jambeck et al. (2015) predict that with current policies and per capita waste generation, the volume of plastics entering the sea will double by 2025. In this paper, we focus on the design of policies to reduce marine plastic pollution. Our focus is on the local level, although some of the policies can have transboundary effects. We do recognize that local actions will not be sufficient. Thus, the problem should be addressed by a combination of global and local policies (Haward, 2018; Lohr et al., 2017; Jambeck et al., 2015; UNEP, 2017). Various multilateral agreements and United Nations (UN) resolutions have been put in place, in particular from 2007 and onward, yet their impact seems to be very limited so far (see, e.g., (Dauvergne, 2018; UNEP, 2017). Tessa-von Wysocki and Le Billon (2019) propose seven elements to develop and inclusive global treaty that can help overcome the challenges to eliminate marine plastic pollution. We focus on developing countries. A large amount of marine plastic waste originates in such nations (Jambeck et al., 2015). Solid waste management practices in developing countries are highly heterogeneous, with greatly varying levels of treatment, low recycling rates, and a high share of illegal disposals. In Section 2, we present an impact pathway framework that allows for the identification of key policy entry points and for country-specific recommendations that reflect the institutional characteristics at hand. \textsuperscript{} Corresponding author at: Room 1107, Hollandseweg 1, 6706 KN, Wageningen, The Netherlands. E-mail address: [email protected] (F. Alpizar). https://doi.org/10.1016/j.envsci.2020.04.007 Received 31 January 2020; Received in revised form 14 April 2020; Accepted 14 April 2020 1462-9011/ © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/BY/4.0/). In Section 3, we review policy instruments for reducing marine plastic pollution. This includes instruments based on monetary incentives and command-and-control, but also soft interventions based on insights from behavioral economics. In Section 4, we apply the impact pathway framework and policy review in six developing countries with different characteristics and therefore representing different points in the impact pathway: Tanzania, Vietnam, South Africa, India, Costa Rica, China, and Chile. A key contribution of this paper is the provision of country-specific recommendations for improvements. Moreover, we focus on one problem with plastics, namely the pollution of the oceans with long-lived plastic debris. Although we recognize their importance, we do not discuss all the other possible negative aspects of the production, consumption, and disposal of plastics. 2. Impact pathway of marine plastic pollution Fig. 1 shows the pathways of plastics from the first stage of the manufacturing of resin pellets to the loss or disposal of plastics into the marine environment. There are primarily three stages at which plastic waste enters the ocean: production, consumption, and disposal. The first pathway into the ocean is the one originating in the production and transformation of plastic resin pellets, where inputs like oil and natural gas are turned into a plastic resin, which in turn is transformed into plastic products (Mahdi, 2013). In 2014, the global plastics production was estimated to total 300 million metric tons per year (Jambeck et al., 2015; Löhr et al., 2017). The production, transportation, and transformation of pellets into actual plastic products can cause leakages of resin pellets into the oceans. Signs of this are found in environmental samples all over the world (Karlsson et al., 2018; Law, 2017). In the consumption stage, plastic products are purchased, consumed, and ultimately discarded. The consumption stage influences both the upstream and the downstream: By reducing the demand for plastic products, plastic waste from both production and disposal is reduced. There are two pathways through which plastics end up in the oceans, i.e., land-based and marine-based sources, each of which contributes 80% and 20% of the total debris, respectively. However, no studies have quantified the relative contributions of all critical sea-based sources (Geyer et al., 2017). Land-based sources of marine pollution contribute between 4.8 and 12.7 million tons every year (Jambeck et al., 2015), originating from a variety of sectors such as construction, households, packaging, and coastal tourism (UNEP, 2016). For example, plastic consumption in households includes the use of plastic bags, single-use plastics, plastic containers, and plastic furniture, but also microplastics in cosmetics, glitter, microfibers from textiles products, and toothpaste. Given the complexities involved in proper disposal of plastics—e.g., chemical pollution and long-lived components (Galloway et al., 2017)—some authors claim that the main solution is to reduce the actual consumption of plastics, targeting first all areas where suitable substitutes are available or potentially available (Lebreton and Andrady, 2019; Zheng and Suh, 2019). Marine-based sources of plastic pollution include commercial fishing, recreational boaters, and offshore oil and gas platforms (Sheavly and Register, 2007; Thevenon and Sousa, 2017). The pollution is mainly due to lost gear or cargo and the discharge of waste during normal shipboard operations. Although the latter practice is prohibited under Annex V of the International Convention for the Prevention of Pollution from Ships, it only applies to vessels of signatory nations (Raubenheimer and McIlgorm, 2018). To date, no global estimates of plastic pollution from any of the marine-based activities are available, but some argue that their contribution to floating debris is significant (Ryan et al., 2019). The pathway from marine-based sources to marine debris is particularly important for countries with large fishing fleets, especially if those fleets are mostly informal or artisanal and if the country does not have the port facilities for collection of waste. Disposal of plastics can be divided into legal and illegal disposal. Precisely what constitutes legal and illegal varies across national legislations. This fork in the impact pathway is important since illegal disposal is a direct route to the oceans that the government cannot control. There are three forms of legal disposal: beneficiation (i.e. recycling or incineration), landfill/dumpsites, and wastewater treatment. From these forms of proper disposal, there could still be leakages into the marine environment during collection and transportation. An important aspect of waste beneficiation is recycling, which focuses on collecting plastic waste to be reprocessed and reused in some other form. It is essential to understand the complexity inherent to plastics as a material. It consists of many different materials, chemically dissimilar polymers, chemical contaminants, and additives together. Thus, recycling of plastics is not as easy as just grinding and melting plastics into something new, and this is a major obstacle to safe and economically viable recycling. In countries where recycling has been established, plastics are often collected via curbside collection and/or drop-off centers (Guagnano et al., 1995; Sidique et al., 2010). At material recovery facilities, plastics are sorted in order to increase the recycled product quality and value (American Chemistry Council, Inc., 2018). This type of waste beneficiation reduces both the amount of waste deposited into landfills and the need for raw materials to produce plastics. Landfills and dumpsites range from sophisticated technological landfills to open-air dumpsites, so the fact that solid waste is collected and transported to such sites does not by any means guarantee that no particles will leak into the ocean. Torrential rain, landslides, wind, and people might still cause pollution of waterways and, eventually, the oceans. Finally, we include a legal form of wastewater discharge in the impact pathway. Households' wastewater contains plastic microbeads, which are residues from personal care products and fibers from synthetic clothing. Such microbeads require specific wastewater treatments to avoid discharge into the environment (Browne et al., 2011). Recent studies show that new water treatment technologies can effectively decrease microplastics in the effluent by 98% (Mintenig et al., 2017; Murphy et al., 2016). However, developing countries lack this technology (Zhang et al., 2016). Illegal forms of disposal contribute directly to marine plastic pollution and include illegal dumping and littering. In developing countries, waste management facilities are not always available, and solid waste is often dumped in large open areas or directly into rivers. Some waste, like plastic bags, is easily carried by wind and rain into waterways, and from there into the ocean. Lastly, Fig. 1 mentions plastic pollution originating from catastrophic events, including earthquakes, tsunamis, hurricanes, and floods. When these catastrophes occur, large amounts of material from urban and rural areas enter the marine environment. From a policy perspective, not much can be done about these sources of pollution. 3. Problem identification, definition of policy goals, and a menu of instruments We distinguish between four broad types of instruments: 1) price-based instruments, which change the relative price of goods or inputs associated with plastic pollution, either by taxing them or subsidizing alternative, less polluting goods or inputs, 2) rights-based instruments, in which a total allowable quantity of pollution is determined, and trade in pollution rights is allowed to minimize the cost of pollution reductions, 3) regulation, which directly determine allowable pollution levels, and 4) behavioral instruments, which use people's social preferences and/or cognitive limitations to influence behavior in favor of lower plastic pollution. A complex problem like plastic pollution typically requires a mix of policy instruments. From a policy design perspective, waste has three critical complications. The first is the classic “missing market” problem: in order to enable markets to assist with waste management efforts, property rights for waste must be clearly defined in the sense of who owns the waste and is therefore responsible for it. Typically, they are not. The second concern is a moral hazard: putting too much pressure on actors to reduce waste or increasing the price of legal disposal could lead to illegal dumping, which is mostly unobservable. Third, plastic pollution is a problem of the commons, i.e. that each individual action is largely insignificant, while the sum of all of them leads to decreased welfare for everybody. Fig. 2 provides guidelines on how to set policy goals based on the impact pathway of plastics described above. Identifying a problem is the first step in solving it. Policymakers should be able to identify the fundamental problems and hence the desired policy goals by looking at a limited, simplified set of indicators. Fig. 2 suggests a few possible indicators for each step of the impact pathway, such as share of treated wastewater. It includes indicators drawn from the literature and expert opinion. For example, if the balance of trade for plastics is positive, indicating substantial local plastic production, and if the industry predominantly consists of small or informal enterprises, then policies are needed to ensure that pellets are not lost during transport and processing and that plastic products are redesigned to take explicit account of their end-of-life uses and re-uses and/or decomposition. Jambeck et al. (2015) estimate that, on average, 0.2 kg per person per day (ppd) of plastics is consumed worldwide. Sri Lanka is the worst country (5.0 kg/ppd), followed by the U.S. (2.59 kg/ppd) and South Africa (2.0 kg/ppd). China and India have consumption levels of 1.10 kg/ppd and 0.34 kg/ppd, respectively. The top 10 countries in terms of environmental performance have consumption levels of about 0.16 kg/ppd (Wendling et al., 2018). In our analysis, we propose that countries should at least strive to achieve plastic consumption figures below the global average. Littering and illegal dumping of waste require special attention (Willis et al., 2017), as illegal disposal of plastics almost certainly leads to pollution of oceans. There are estimates suggesting that more than 20% of the world's plastic waste is mismanaged (Jambeck et al., 2015). Even if waste is properly collected and managed, the risk of leakage will remain, as long as water treatment plants do not have the proper technology to capture microplastics and landfills do not have mechanisms to prevent it. The challenges in managing plastic waste are enormous, highlighting the importance of waste beneficiation. A recycling/reuse target of no less than 20% of all collected waste should be the aim of policymakers (Geyer et al., 2017). With the problems and policy goals identified, the next step is to choose the combination of policies (see Sterner et al., 2019 and Sterner and Coria, 2012 for full overviews). To date, the most commonly used instruments are price-based instruments aimed at reducing the costs of recycling or increasing the cost of plastics, and regulatory policies. Fig. 3 gives an overview of current and potential policy instruments placed explicitly in the three major parts of the impact pathway. We distinguish between price-based, rights-based, regulation, and behavioral instruments. A key feature of the impact pathway of plastics is that it illustrates how different targets and actions are interconnected, calling for the design of policy packages or policy mixes, rather than isolated efforts. Policies need to be attentive to these interconnections or will run the risk of severe perverse effects. For example, when illicit dumping of waste is an option, any pricing of solid waste collection and/or compulsory recycling targets might result in increased illicit dumping (Fullerton and Kinnaman, 1995). We will revisit this point in Section 3.5. 3.1. Price-based instruments Price-based instruments aim to raise the price of a good or an input, relative to less damaging alternatives, in order to discourage its use. The existence of a market with adequately defined property rights and observable transactions is an absolute requirement for the use of price-based instruments. 3.1.1. Targeting the plastic industry Under ideal conditions, a tax per unit of emissions would be the optimal policy to reduce spills from the production of pellets and the manufacturing of plastics, i.e., firms would have to pay a tax per unit of plastic emitted into the ocean. In practice, however, emissions are challenging to monitor, and it can be difficult to trace them to the right source. Therefore, taxes could instead be linked indirectly to the environmental damage of the products or how recyclable the components of the products are. For example, a government can set higher taxes on polymers with more significant health impacts (like PS or PVC), or can tax certain additives. Subsidies are, to a large extent, the opposite of taxes: firms’ products could get a subsidy if they meet specific criteria such as a certain reduction in plastic pollution. 3.1.2. Targeting plastic consumption Increasing the price of products with high plastic content or putting a price on plastic as an input has at least three indirect effects on plastic pollution: (i) decreased production of plastics and as a result less pollution from the production, (ii) less plastic waste and as a result less pollution from the waste generation, and (iii) reduced illegal disposal because of a higher value of plastics. Various ways to increase the price of plastics have been used in many countries, in particular for single-use plastics. Examples include Botswana, Denmark, Ireland, China, and South Africa (He, 2012; Kish, 2018). The most famous and widespread case is the levy on plastic bags, which was first introduced in Ireland in 2002 (Convery et al., 2007). There is extensive evidence of a significant reducing effect of this measure on plastic bag consumption and a positive effect on the use of reusable bags (Jakovcevic et al., 2014; Luís and Spínola, 2010; Martinho et al., 2017; Wagner, 2017). However, the literature suggests that levies on plastic bags implemented without other reinforcement instruments such as education programs and information campaigns are only effective in the short run (Dikgang et al., 2012; He, 2012; Nahman and Godfrey, 2010; Zen et al., 2013) and may suffer from a rebound effect in the form of an increase in the purchase of plastic garbage bags (Dikgang et al., 2012; Martinho et al., 2017; Wilcox et al., 2016). Policy instruments can also tackle the consumption of marine-based waste-generating products. Taxes and charges for port reception and ship berthing and commercial and recreational fishing fees directly affect the consumption and disposal of plastics (Ten Brink, 2009). 3.1.3. Targeting disposal of plastics There are two main targets for the disposal of plastics. The first is to reduce plastic waste per se. The second is to increase the extent of appropriate disposal. The price-based instrument for reducing waste is to influence the cost associated with waste, for example via weight-based pricing of waste or a “pay-as-you-throw” system (Oosterhuis et al., 2014). The risk with this, in particular with weak institutions and no strong norms associated with doing the right thing, is that it increases illegal disposal. Weight-based pricing of waste collection, for example, could increase illegal dumping (Dahlén et al., 2007; McIlgorm et al., 2011). Price-based payments have also been used to reward the right behavior. Two examples are payments to vessels to incentivize discharge before departure (Matthysen and Spolander, 2007; McIlgorm et al., 2011) and reward payments to fishers for the collection of marine litter (Cho, 2009; Ten Brink, 2009). 3.2. Rights-based instruments 3.2.1. Targeting the plastic industry Extended producer responsibility (EPR) is the main rights-based instrument used. EPR assigns property rights, and hence duties, to the producer of plastic products for the treatment and disposal of these after consumption. The goal is to encourage a reduction in the volume of waste and in the use of virgin materials, and to develop the recycling sector (Brouillat and Oltra, 2012). The EPR approach is being implemented in the European Union, where governments require increased plastic recyclability in product design, e.g., fewer polymers in products, fewer mix-polymer composite products (like chips bags), fewer chemical additives, and increased transparency concerning additives. In the European Union, all plastic products should be recyclable by 2030 (Gilli et al., 2018). 3.2.2. Targeting plastic consumption In our extensive literature review, we could not find a single example of rights-based approaches targeting the consumption of plastics. The one that comes closest, and as discussed below, is a deposit refund scheme. Under a deposit refund scheme (for glass bottles, cans, or plastic bottles/containers), the consumer purchases both the right to the content and the right to the container. As a result, the retail price of the product is relatively higher, discouraging consumption, unless the right to the container can be “sold” to a collection point. But even if there is a right to sell, the fact that there is a time lag and associated transaction costs between the purchase and the sale of the container results in a higher effective price for goods under a deposit refund scheme, and hence lower consumption. 3.2.3. Targeting disposal of plastics A key component explaining the lack of proper waste disposal is that there is a “missing market.” One rights-based instrument that creates a market is a deposit-refund scheme. By assigning a monetary value to waste, a deposit-refund scheme not only promotes recycling but also creates incentives for picking up trash, since the trash now has a value. Bell et al. (2010) and Viscusi et al. (2011) find that deposit-refund schemes for plastic bottles are strong incentives to increase recycling. The success of the deposit-refund system for plastic bottles is to some extent due to the PET bottles being a closed-loop system where there is a high value of recycling. In some countries (e.g., Indonesia and South Africa), private companies offer direct payments for returning empty plastic bottles and bags (McIlgorm et al., 2011; Nahman and Godfrey, 2010). Similar incentives have worked in Australia and the U.S. (Schuyler et al., 2018; Vince and Hardesty, 2017). An extended producer responsibility instrument creates incentives/a responsibility to provide recycling facilities (e.g., curbside collection) and collection centers; there is evidence that recycling rates decrease as the time and transportation costs of accessing recycling locations increase (Bell et al., 2010). Dahlén et al. (2007) find that the provision of curbside collection of recycled materials promotes separation of metal, plastic, and paper packaging for recycling. 3.3. Regulation 3.3.1. Targeting the plastic industry To date there is no existing international framework that explicitly addresses plastic pollution due to industrial spills. Most countries have laws to protect the environment from industrial pollution, and firms are required to have environmental permits to operate. These permits typically include provisions for the management of waste, bans on the production of certain plastic materials and products, and incentives to adopt better recycling practices. Also, there is a push toward a chemical “simplification” of plastics in order to increase the recyclability of materials, for example by using fewer polymers and chemical additives. In developing countries, national legal frameworks generally do not regulate pellet spills from the industry. Developed countries have legislation regulating the production, transport, and usage of pellets. For example, the EU has implemented the Packaging Directive (Directive 2008/98/EC, 2008), REACH (Regulation (EC) No 1907/2006), and the Industrial Emissions Directive (Directive 2008/98/EC) to this end. 3.3.2. Targeting plastic consumption Regulating the consumer market with, e.g., bans is a powerful tool to reduce consumption of certain plastic products, but typically at a non-negligible social cost. One of the most classic examples is the prohibition of the use of plastic bags, with a complete ban on single-use plastic bags being implemented in China, Mauritius, Rwanda, and Kenya (He, 2012; Kish, 2018; Schnurr et al., 2018). Other countries, such as Australia and Senegal, banned light plastic bags thinner than 50 microns (Schnurr et al., 2018). Zhu (2011) indicates that the plastic bag ban reduced the use of plastic bags in China by two thirds, but the effect is heterogeneous, with limited results in wholesale, farmers markets, and the informal sector. Municipal ordinances in the form of both prohibition of single-use plastic bags and changes in their makeup are the most prevalent actions to reduce the use of plastic bags in the U.S. (Wagner, 2017). Although much attention has been placed on regulating plastic bags, efforts are now geared toward reducing plastic straws, plastic cutlery, and polystyrene items such as cups and microbeads (Schnurr et al., 2018). The effectiveness of plastic bans has been questioned in some contexts, e.g. the ban on the use of plastic bags in marketplaces in India has had little impact, possibly due to a widespread lack of enforcement (Gupta, 2011). 3.3.3. Targeting the disposal of plastics A regulation targeting plastic waste should be designed taking into consideration the risk of creating illegal dumping or of turning a dangerous residual into an unobservable one. Regulations should target easily observable agents. Landfill bans have been implemented across EU countries, but this inferior waste disposal method is still ubiquitous in developing countries. Landfill bans are expected to reduce marine plastic litter by reducing the leakage originating from landfills (Scharff, 2014). Recycling laws often target non-hazardous plastic waste. These laws are aimed at establishing institutional mechanisms to facilitate or incentivize waste beneficiation. Recycling laws exhibit a great deal of heterogeneity in terms of type and stringency. Evidence suggests that while the less stringent ones (i.e., announced recycling goals) perform very poorly, the most stringent regimes (i.e., mandatory recycling laws) have almost doubled recycling rates in the U.S. (Bell et al., 2010). 3.4. Behavioral instruments Material payoffs are not the only driver of people’s behavior. Other important factors include social preferences, social norms, social contexts, and people’s cognitive limitations (see e.g. Akerlof and Kranton, 2000; Andreoni, 1996; Thaler and Sunstein, 2009). This suggests several ways for policymakers to influence the production, consumption, and disposal stages of plastics. We distinguish between three broad categories of behavioral interventions: information provision, pure nudges, and moral nudges (Carlsson et al., 2020). Information provision can be used to change people’s behavior when there is imperfect information. For example, individuals might care about the environmental impact of their consumption but have limited information about it. By providing information, individuals change. Pure nudges rest on the assumption that people are bounded rational and inattentive, use decision heuristics, or have limited self-control. Under these circumstances, individual behavior can be affected by changes in the decision environment. Moral nudges rest on the assumption that people have social preference and in particular that they care about their behavior in relation to what others do. By providing information about their own and others’ behavior, individuals might change their ways. Often both descriptive norms (what is commonly done) and injunctive norms (what is commonly approved or disapproved of) are used in combination. All three types of behavioral instruments have been applied in areas focusing on consumers’ environmentally friendly behavior, including information provision (Jessee and Rapson, 2014), design of default options (Ebeling and Lotz, 2015; Egebark and Ekström, 2016), salience of information (Kurz, 2018; Tiefenbeck et al., 2016) and norms in relation to resource use (Allcott, 2011; Ferraro et al., 2011), littering (Cialdini et al., 1990), towel re-use (Goldstein et al., 2008), and food waste (Kallbekken and Sælen, 2013). 3.4.1. Targeting the plastic industry The main behavioral instrument when it comes to firm behavior is the provision of information to both firms and consumers. There could be a direct effect on firms if they have intrinsic motivation to act in an environmentally friendly manner. The literature on corporate social responsibility suggests several motives for why firms behave in this way, including motivation and attraction of employees (Nyborg et al., 2016; Redford et al., 1997). The other effect of information on environmental performance is that the customers could change their behavior as well and put pressure on firms to improve; this rests on the assumption that customers do care about the environmental performance of firms. 3.4.2. Targeting plastic consumption Based on the literature on consumption and behavioral policies, it is relatively straightforward to design policies that could affect plastic consumption. However, very few approaches have been implemented and evaluated. We will, therefore, give some suggestions here. 1) Default: The default effect refers to the tendency of people to stick with an alternative already chosen by someone else, even when the cost of making an active choice is minimal (Johnson and Goldstein, 2003). Today, consumers are often presented with a “plastics” default, with the most prominent examples being plastic bags and single-use plastics. In such settings, providing a default that involves either no plastics or a substitute to plastics could have a substantial effect on behavior. 2) Salience: If people are inattentive to some factors of a decision problem, they will make a different decision than if they were paying attention (see e.g. Allcott, 2011; Chetty et al., 2014). By affecting the salience of certain aspects of the decision, behavior can, therefore, be affected. The best example of this is different types of labeling. A label can have many different roles, including a purely informational role. It is likely that labels also affect the salience of certain characteristics of the product, and they can have moral values and implications (Carlsson et al., 2020). 3) Explicit use of social norms: De Groot et al. (2013) displayed signs with normative messages in a supermarket. These messages varied, but they all aimed to reduce the use of plastic bags and increase the use of reusable bags. One message was “Shoppers in this store believe that re-using shopping bags is a worthwhile way to help the environment. We thank you for helping the environment by continuing to re-use your bags.” The reduction in the number of bags was around 30%. There is also a strand of literature analyzing the combined effects of behavioral and economic policies. As an illustration, there is evidence that the combination of charges for plastic bags and public through information campaigns produced significant and long-lasting reductions in consumption in both Ireland and Argentina (Convery et al., 2007; Jakovcevic et al., 2014), compared with countries such as India and Taiwan, where charges were introduced alone. Provision of environmental education is another possible way to reduce future consumption. Effects have been found on teachers’ and students’ knowledge, perceptions, and self-reported behavior in relation to solid waste in general and marine plastic pollution in particular (Hartley et al., 2018, 2015; Hoang and Kato, 2016). 3.4.3. Targeting the disposal of plastics The literature on behavioral instruments applied to the disposal of waste in general and plastics in particular has mainly focused on the role of behavioral motivations and behavior, and how these are affected by things such as education, information campaigns, and moral nudges. Overall, this literature suggests a stylized fact: while normative behavior is a good predictor of recycling (see, e.g., Barr, 2007; Abbott et al., 2013; Alpízar and Gsottbauer, 2015; Hage et al., 2009; Mahmud and Osman, 2010; Viscusi et al., 2011), personal pro-environmental messages in absence of appeal to norm-based behavior have no effect on recycling (Chong et al., 2013; Xu et al., 2018; Young et al., 2017). Evidence has also shown that while social norms incentivize temporary changes in recycling behavior (Abbott et al., 2013), personal norms generate more persistent changes in behavior (Huber et al., 2018; Viscusi et al., 2011). There are also studies analyzing the effect of economic incentives coupled with behavioral interventions. For instance, direct payments accompanied with door-to-door information provision have been found to be highly effective in promoting residential waste separation (Xu et al., 2018). Similarly, there is evidence that face-to-face information provision facilitates the adoption of recycling facilities compared with information through bills and municipal websites (Willman, 2015). 3.5. The need for comprehensive policies An important aspect of plastic pollution is the complexity of the problem. First, a combination of policy instruments may be required in order to induce behavioral changes at one point in the pathway. For example, when trying to encourage waste sorting and recycling, informational and behavioral instruments are complementary to the use of incentive-based policy instruments (Kirakozian, 2016). Second, the potential link between the different parts of the impact pathway of plastics means that policy changes at one entry point could have implications far beyond the original intention. Hence, a major concern is that policy changes at one point may divert the flow of plastics to a path of higher leakage risk. One particular example is the unit-pricing system of waste. Taxes or fees on household waste can result in increased illegal disposal (Fullerton and Kinnamann, 1995, 1994; Linderhof et al., 2001). Given that the leakage risk of illegal dumping is much higher than that of legal disposal, even a small increase in illegal dumping could be counterproductive. With several policy objectives, such as reducing plastic waste, increasing recycling, and reducing illegal disposal, it is highly unlikely, or even impossible, to expect one policy instrument to be sufficient (Fullerton and Wu, 1998; Walls, 2013). Instead, a combination of instruments will be needed, e.g., a tax on sales. of products with an environmental impact together with subsidies for recyclable designs and a deposit-refund scheme. Finally, while we in this paper focus on policy instruments at the local level, the international trade of plastic products and plastic waste endow local policy changes with global implications. A more restrictive policy enacted in one country could redirect the plastics flow to countries with looser regulations and thus a higher risk of leakage. A landfill ban could reduce local leakage of plastic waste by increasing the incentives to reduce and recycle plastic waste, but it also encourages exporting waste to less regulated regions or countries. Similarly, a ban on single-use plastics may only redirect the plastic consumption to regions without such bans. The transportation process and the final disposal of plastic waste in a less regulated environment could increase the total leakage into the environment. Hence, we need a comprehensive approach that considers global implications when designing national policies. ### 3.6. The role of technological innovation Technological progress plays an essential role in reducing plastic pollution. Innovation can change the amount and types of plastics produced but also the way plastics are disposed of. Although research and development can be supported, investment in it is not a policy instrument in itself, but rather the result of a properly designed mix of policies. For example, a tax on single-use plastics could only redirect the plastic consumption to regions without such bans. The transportation process and the final disposal of plastic waste in a less regulated environment could increase the total leakage into the environment. Hence, we need a comprehensive approach that considers global implications when designing national policies. #### 3.7. The role of voluntary initiatives Our focus has been on instruments that could be implemented by a policymaker. There could also be voluntary actions taken by consumer groups and firms. These voluntary actions could take many forms, and we will discuss a few below. But first, we wish to stress a few things. First, voluntary actions could be implemented in anticipation of upcoming government regulations, in an effort to reduce support for such policies. Second, voluntary actions will in most cases not be enough to address the problem. The fact that they are voluntary means that some actors might be tempted to continue with business-as-usual and still benefit from the voluntary effort of others. In the long term, this free-riding could erode the pro-environmental behavior of all. Organized pressure groups, changing consumer preferences, social and environmental reputation, and preemptive change in anticipation of stringent regulation are all good reasons for firms to act pro-environmentally. Individual firms could also be intrinsically motivated to make organizational, operational, and technological changes to reduce the use of pellets, and motivating their employees to help to improve the companies’ environmental performance (Redford et al., 1997). The results should also increase employees’ commitment to their respective companies. ### 4. Applying the policy toolbox to the reality of individual countries The first step in designing suitable policy tools is identifying the main problems. Table 1 outlines the indicators suggested in Fig. 2 for eight developing countries used as examples. Both the average value of each indicator for the top 10 countries according to the Environmental Performance Index (Wendling et al., 2018) and the world average are also provided. #### 4.1. Chile Chile is the best performing country with outstanding levels of waste collection and waste management. The local production of plastics is small, although the high share of microenterprises could be a concern since they might be less efficient. The per-capita consumption of plastics is low compared with the benchmark. The focus of the --- Table 1 Application of the decision tree to identify policy goals in developing countries. \| Country \| Balance of trade for the plastic industry \| Share of micro-enterprises in the plastic industry (%) \| Plastic consumption per capita (kg/person/day) \| Share of plastic inadequately managed (%) \| Share of wastewater treated (%) \| Share of waste collected legally (%) \| Share of plastic that is recycled (%) \| \|-----------------\|-------------------------------------------\|--------------------------------------------------------\|----------------------------------------------\|----------------------------------------\|----------------------------------\|-------------------------------------\|--------------------------------------\| \| Chile \| Deficit 87° \| 0.12 \| 7 \| 99.8° \| 96.49° \| 1.7° \| \| \| China \| Surplus 98° \| 0.12 \| 74 \| 93.5° \| 62° \| 23° \| \| \| Costa Rica \| Deficit 80° \| 0.26 \| 16 \| 11.7° \| 58.3° \| 1.3° \| \| \| India \| Surplus 75° \| 0.01 \| 85 \| 22° \| 60° \| 47° \| \| \| South Africa \| Deficit 75° \| 0.24 \| 54 \| 57° \| 64° \| 43.7° \| \| \| Tanzania \| Deficit n.a. \| 0.023 \| 84 \| n.a \| 15.6 \| n.a \| \| \| Vietnam \| Deficit 80° \| 0.1 \| 73 \| 11° \| 85° \| 1.1° \| \| \| World average \| \| 0.20 \| 36 \| 26 \| 64° \| 19.5° \| \| \| Top 10 countries\| \| 0.16 \| 0.85 \| 87.5° \| 97.1 \| 46.3 \| \| Sources: 1. Jambeck et al. (2015); UNdata (2018) 2. Plastics South Africa (2017) 3. SUBDERE, 2018; Tello Espinoza et al., 2010 4. MS, 2016 5. BFP (2011) 6. Chalmin and Gaillochet (2009) 7. FICCI (2017) 8. MONRE (2018) 9. Lower-middle income countries average 64% (Kaza et al., 2018) 10. OECD (2019) 11. Kaza et al. (2018) 12. VI (2019) 13. Sii (2016) 14. NBS (2018) 15. NDRC (2014) 16. Guojun (2015) 17. Ministry of Environmental Protection of the People’s Republic of China (2017) 18. CSE (2014) 19. Calderón Cabrera et al. (2011). * Country data for 2018. Trade Balance (TB) = Total Value of Exports – Total Value of Imports; surplus if TB > 0; deficit if TB < 0. Chilean authorities should be on waste beneficiation, given that only 1.7% of the plastics consumed are recycled. Policies to increase recycling and the domestic demand for recycled plastic should be implemented. The plastic industry should be targeted with an EPR policy. A deposit-refund scheme for plastic bottles and containers would increase the value of plastic waste. Behavioral interventions in the form of information and education, and with a focus on people's environmental values and norms should help to incentivize recycling. 4.2. China China is one of the world's largest producers of plastics and one of the most significant contributors to marine plastic pollution (Jambeck et al., 2015; Lebreton and Andrady, 2019). China's plastic production depends mainly on microenterprises. On the other hand, China's per-capita consumption of plastic is low compared with the world average. China's contribution to marine plastic pollution is caused by its high share of mismanaged waste and a low recycling rate (NDRC, 2014). In the short run, the focus should be on improving landfill technology, recycling, and waste beneficiation. The first goal requires government investments to migrate from inefficient dumpsters to modern technologies, backed by regulations. The promotion of recycling, particularly of domestically produced plastics, requires not only behavioral change but also improvements in the regulation of the plastic industry, which now produces plastics with low recycling value due to the high use of surfactant and additives (Velis, 2014). 4.3. Costa Rica Costa Rica has three critical indicators: high levels of plastic consumption per capita, low levels of wastewater treatment, and low levels of plastic beneficiation. In order to reduce the consumption of plastics, the government has already launched an information strategy to replace single-use plastics with renewable and compostable alternatives (MS et al., 2016). A ban on single-use plastics is being considered as a policy option, but Costa Rican authorities could use the policy design framework in this paper to broaden the availability of policy options. Wastewater treatment plants capable of capturing microplastics require direct investments by the government, which already faces serious challenges with the country's standard facilities. Still, even a standard facility is better than none. Finally, policymakers should attempt to increase the demand for locally recyclable plastics by implementing a mix of behavioral, market-based, and regulatory instruments that will increase the recycling of plastics and reduce plastic consumption. A deposit-refund scheme for plastic bottles and containers should be implemented. 4.4. India The share of waste collected legally in India is around 60%, but this does not translate into managed waste, as the waste is disposed of in dumps or open in uncontrolled landfills where it is not fully contained: 85% of the waste is inadequately managed. In addition, 78% of the wastewater goes untreated to the rivers and from there into the ocean. India's policy target is clearly and unequivocally locked on improved management (Plastics South Africa, 2017), and many deposit their litter informally or illegally. In terms of policy design, South Africa should attempt to increase the value of plastic waste, not the least by promoting that actors in the informal sector to become formal. At the industry level, EPR schemes represent an opportunity to assign duties to retail companies for the plastic materials at the end of the product lifecycle. At the consumption stage, deposit-refund schemes for plastic containers should reduce the amount of plastic for recycling that is sourced at the landfill. Finally, the per-capita consumption of plastics in South Africa is much higher than our benchmark, and the largest share of it originates from packaging (Plastics South Africa, 2018). Regulatory changes might go a long way in reducing the amount of discarded plastic packaging material. 4.6. Tanzania Tanzania's plastic originates from land-based activities and is mostly attributable to mismanaged solid waste management, especially in unplanned urban settlements (UNEP, 2009). Only 16% is collected legally, and 84% of all plastics are inadequately managed and disposed of informally in various ways, such as by burning and roadside dumping (NBS, 2017). Urban areas produce most of the waste. For example, in Dar es Salaam, solid waste generation has been steadily increasing. In 1998, less than 2,000 tons per day was produced, and this increased to more than 4,600 tons per day by 2017, 75% of which was produced by households (NBS, 2017). Most of the urban waste is dumped at Pugu Kinyamwezi, the only dumpsite in Dar es Salaam (NBS, 2017). Although initially designed as a proper landfill, Pugu Kinyamwezi has become a basic dumpsite with severe leakages. The case of Tanzania is rather simple from a policy perspective. The focus should be on increasing the legal disposal of solid waste. Although this applies to all solid waste, a proper separation of plastic waste from organic waste would make landfills more viable. The separation of waste at the household level through behavioral instruments could substantially reduce the cost of properly managing both types of waste. 4.7. Vietnam Vietnam is infamous for the amounts of plastic waste in its vast riparian network (Schmidt et al., 2017), especially during the rainy and flood seasons (Lebreton et al., 2018). Agriculture and aquaculture activities generate a large volume of plastic waste (Blanco et al., 2018). As for urban river systems, waste comes from municipalities, causing environmental problems and transportation of waste to the ocean. For instance, a recent study found a high density of both micro- and macro plastics in the Sai Gon River in Ho Chi Minh City (Verma et al., 2016). Unlike some other countries, policies against single-use plastic products are weak (UNEP, 2018). Most waste is not sorted at the source. Only some valued plastics are collected and recycled informally and most waste (e.g., plastic bags and straws) is simply dumped into the environment. About 46% of all solid waste comes from urban municipalities, 17% is discharged from industrial zones, and the rest from rural areas, the medical sectors, and trade villages. The waste collection rate is about 85%. The waste management infrastructure is poor as transportation stations and landfills are insufficient and treatment technologies outdated (Verma et al., 2016). As a result, 73% of all plastic waste is inadequately managed. This should be the target of the decision-maker. 5. Conclusions We present an impact pathway framework that facilitates the identification of critical policy entry points for a decision-maker interested in reducing the flow of plastic waste into the sea. We extend the previous literature on policy instruments to curb marine plastic pollution by providing a comprehensive review of policies, including insights from behavioral economics. Most importantly, we discuss the use of this policy toolbox at different levels or branches of the impact pathway, and suggest critical thresholds for policy-action in each. The result is a decision support tool for policymakers that is both country- and problem-specific. The impact pathway framework also allows for the identification of interactions between policies, interactions that could be either positive or negative. A positive interaction occurs when a policy in one domain, e.g., using extended post-consumption producer responsibility to make companies more responsible for the plastic content of their products, interacts positively with a policy in another domain, e.g., increased recycling. A negative interaction occurs when policies actually conflict with each other, e.g., if improved landfill technologies bring higher prices per kilogram of waste and an increase in illegal dumping of waste. In addition, the fact that waste is created, packaged, and disposed of privately by households means that information is highly asymmetric. Policymakers should attempt to design comprehensive policies that are compatible with this type of information and attentive to the interconnections as described by the impact pathway. Finally, although marine plastic debris is ultimately a global problem, it originates in local decisions in countries that lack proper policies and institutions. Floating plastic debris might be the same irrespective of its origin, but the reason for this differs by location. Policy design needs to be attentive to those differences. In this paper, we propose a decision support tool based on a set of simple indicators that can easily guide the decision-maker to the crux of the problem. Although the selection of indicators can be expanded on and improved, the key rationale is that decision-makers need quick ways to identify the problem and then a menu of potential policy solutions. Too frequently, decision-makers invest time, effort, and political capital promoting good solutions that do not get to the core of the problem. This paper provides a comprehensive review of policy instruments and in doing so reveals some research gaps. First, the literature focuses on understanding the behavior of individuals/households while little attention is devoted to understanding the behavior of a broader group of consumers such as hospitals, schools, and universities. Second, although there is vast evidence regarding the importance of personal norms for individual behavior, most behavioral interventions rely on one-shot information provision while long-run interventions in the form of environmental education are rather scarce. Finally, although marine plastic pollution has both land- and marine-based sources, studies of the effectiveness of policy instruments targeting actors in the latter category (e.g., small fishing and aquaculture companies, fishing communities, and tourists) are absent. Financial support “This paper was produced with the support of grant # 61050043 from Sida, the Swedish International Development Cooperation Agency to the Environment for Development, University of Gothenburg, Sweden. C. Salazar acknowledges financial support from project FONDAP, No. 15110027. M. Jaime acknowledges funding from CAPES through CONICYTPIA/BASAL FB0002. The funders were not involved in any way in the research and/or preparation of the article, nor in the decision to submit the article for publication.” CRediT authorship contribution statement F. Alpizar: Conceptualization, Methodology, Supervision, Investigation, Writing - original draft. F. Carlsson: Conceptualization, Methodology, Supervision, Writing - review & editing. G. Lanza: Writing - original draft, Investigation, Visualization, Project administration. B. Carney: Writing - review & editing. R.C. Daniels: Writing - review & editing, Investigation. M. Jaime: Writing - review & editing. T. Ho: Writing - review & editing. Z. Nie: Writing - review & editing. C. Salazar: Writing - review & editing. B. Tibesigwa: Writing - review & editing. S. Wahdera: Writing - review & editing. 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857ae392a13684c3c27151a84fd6740d7e755515	{ "olmocr-version": "0.1.59", "pdf-total-pages": 16, "total-fallback-pages": 0, "total-input-tokens": 55840, "total-output-tokens": 21464, "fieldofstudy": [] }	Genetics of Interleukin 1 Receptor-Like 1 in Immune and Inflammatory Diseases Loubna Akhabir and Andrew Sandford* Department of Medicine, University of British Columbia, UBC James Hogg Research Centre, Providence Heart + Lung Institute, Room 166, St. Paul’s Hospital, 1081 Burrard Street, Vancouver, BC V6Z 1Y6, Canada Abstract: Interleukin 1 receptor-like 1 (IL1RL1) is gaining in recognition due to its involvement in immune/inflammatory disorders. Well-designed animal studies have shown its critical role in experimental allergic inflammation and human in vitro studies have consistently demonstrated its up-regulation in several conditions such as asthma and rheumatoid arthritis. The ligand for IL1RL1 is IL33 which emerged as playing an important role in initiating eosinophilic inflammation and activating other immune cells resulting in an allergic phenotype. An IL1RL1 single nucleotide polymorphism (SNP) was among the most significant results of a genome-wide scan investigating eosinophil counts; in the same study, this SNP associated with asthma in 10 populations. The IL1RL1 gene resides in a region of high linkage disequilibrium containing interleukin 1 receptor genes as well as interleukin 18 receptor and accessory genes. This poses a challenge to researchers interested in deciphering genetic association signals in the region as all of the genes represent interesting candidates for asthma and allergic disease. The IL1RL1 gene and its resulting soluble and receptor proteins have emerged as key regulators of the inflammatory process implicated in a large variety of human pathologies. We review the function and expression of the IL1RL1 gene. We also describe the role of IL1RL1 in asthma, allergy, cardiovascular disease, infections, liver disease and kidney disease. Received on: June 01, 2010 - Revised on: July 06, 2010 - Accepted on: August 23, 2010 Keywords: Asthma, genetics, IL1RL1, immunity, inflammation, respiratory, SNP. INTRODUCTION Interleukin 1 receptor-like 1 (IL1RL1), also called T1, ST2, DER4 and FIT-1, is a member of the interleukin 1 super-family [1] but does not bind interleukin 1 (IL1) [2]. IL1RL1 was an orphan receptor until the description of its ligand, interleukin-33 (IL33) in 2005 [3]. Since then, IL33 binding to IL1RL1 has been associated with a variety of disease states and in particular to inflammatory processes as outlined in recent reviews [4, 5]. In the present review, we will focus mainly on the genetic associations of IL1RL1 with disease. IL1RL1 GENE AND PROTEINS The IL1RL1 gene is located in chromosome 2q12 and is composed of 11 exons [6]. A number of IL1 family members reside in the immediate vicinity of the IL1RL1 gene namely IL1R2, IL1R1, IL1RL2, IL18 receptor 1 (IL18R1) and IL18 receptor accessory protein (IL18RAP). The region spans about 300 kb and is in high linkage disequilibrium (LD) (Fig. 1). There is evidence for the involvement of the genes surrounding IL1RL1 in human and experimental disease, and therefore the causal locus responsible for genetic association signals from this region is difficult to determine. Address correspondence to this author at the Department of Medicine, University of British Columbia, CBC James Hogg Research Centre, Providence Heart + Lung Institute, Room 166, St. Paul’s Hospital, 1081 Burrard Street, Vancouver, B.C., V6Z 1Y6, Canada; Tel: (604) 806-9008; Fax: (604) 806-8351; E-mail: [email protected] ©2010 Bentham Science Publishers Ltd. corresponds to the extra-cellular domain of IL1RL1 isoform A except for nine amino-acids in the C-terminal region. IL1RL1 isoform A is mainly expressed on cells of hematopoietic provenance, mainly T cells [20]. It has been shown that binding of IL1RL1 isoform A with its ligand on the surface of basophils, eosinophils and mast cells promotes their activation [21], increased adhesion and survival [22] and degranulation [23], respectively. IL33/IL1RL1 isoform A has also been shown to play a role in activating macrophages [24, 25]. The short form, IL1RL1 isoform B, is expressed by various cells including epithelial cells, endothelial cells, fibroblasts and smooth muscle cells. This expression is augmented upon stimulation with IL1α, IL1β, TNFα, LPS and other factors inducing cell stress such as cardiac infarction and hypoxia [26]. The tissue distribution of IL1RL1 isoform B seems to be relatively ubiquitous, with the highest levels of the secreted form found in the lung followed by the heart and the brain [27]. Several studies show that the membrane-bound IL1RL1 protein acts as a specific marker for Th2 cells [20]. In vitro blockade of IL1RL1 signaling with recombinant IL1RL1 protein to compete with the endogenous receptor resulted in the abrogation of differentiation to and activation of Th2, but not Th1, effector cells [28]. Interestingly, IL1RL1 has been found to play a considerable role in a newly discovered immune type2 effector leukocytes, known as nuocytes [29]. An IL13-GFP mouse model was utilized to define these as cells not corresponding to a previously known leukocyte lineage that express ICOS, IL1RL1 and IL25R [29]. The nuocytes’ function included the innate immune response to helminth infection with Nippostrongylus brasiliensis* by secretion of high levels of IL13 in response to IL25 and IL33. The ligand for IL1RL1 is a recently discovered member of the interleukin 1 family: IL33 [3]. The signaling of IL1RL1 isoform A binding to IL33 results in the activation of the Mitogen-Activated Protein kinases ERK1, ERK2 and p38 and the subsequent activation of NFκB [3, 23]. IL1RL1 isoform B corresponds to the extra-cellular domain of isoform A and in vitro studies have shown that it can also bind IL33 and act as a decoy receptor inhibiting the activation of NFκB [30] and the subsequent inflammatory response. This was confirmed in an animal model where introduction of soluble IL1RL1 decreased pro-inflammatory cytokine (IL4, IL5 and IL13) production in a murine asthma model after treatment with IL33. It was shown that this protective effect of the soluble IL1RL1 seems to be IL10 dependent in an animal model of ischemia reperfusion injury [31]. Fig. (1). Linkage disequilibrium in IL1RL1 and surrounding genes on chromosome 2q12 (102280 kb to 102500 kb) in the CEU HapMap population. Asthma and other Respiratory Diseases Increased eosinophil count is a phenotype associated with the majority of asthma cases and correlates with severity of the disease as well as response to glucocorticoid treatment [32]. Using asthma mouse models, it was shown that eosinophilic inflammation is significantly decreased following allergic stimuli in animals subjected to treatments with recombinant IL1RL1 or antibodies directed against the membrane-anchored protein [33, 34]. Soluble IL1RL1 has been shown to be sufficient to reduce experimental allergic airway inflammation using an intravenous IL1RL1 gene transfer mouse model [34], perhaps by acting as a decoy receptor. In addition, a ST2−/− knockdown mouse model of asthma showed decreased airway inflammation [35]. IL1RL1 expression has been shown to increase in murine [35] and human [36] asthmatic lungs; soluble IL1RL1 has been shown to increase in the serum of asthmatic patients during acute attacks, and this increase correlated with lung function decrease as well as an increase in the serum levels of the inflammatory cytokine IL5 [37]. Other in vivo studies of airway allergic inflammation demonstrated a clear involvement of soluble IL1RL1 protein in regulating a Th2 response after allergen challenge [35] as well as in the resolution of allergen-induced inflammation as assessed by airway hyper-responsiveness [38]. Since the late 1990s, genetic studies have shown linkage of chromosome 2 with asthma, lung function (as assessed by FEV1/VC, a common clinically-useful index for airflow limitation), eosinophilia and IgE levels [39-41]. Polymorphisms in IL18R1, a gene in tight LD with IL1RL1, were associated with asthma, atopic asthma and airway hyper-responsiveness using a candidate gene approach in a Danish population and the association consistently replicated in two other European populations [18]. In the same year, another candidate gene association study documented significant genetic association of the gene cluster containing IL1RL1, IL18R1 and IL18RAP with asthma and atopy in a Dutch population [19]. Additional association evidence was reported by the same group using pathway analysis to detect gene-gene interactions in the Toll Like Receptor (TLR)-related pathway. IL1RL1 isoform B has been shown to down-regulate gene expression of TLR4 and TLR1 in vitro after treatment with LPS and in vivo in a LPS-induced shock mouse model [42]. Twenty-nine genes implicated in TLR regulation were selected for a pathway analysis in Dutch populations [43]. IL1RL1 SNPs were associated with allergy and asthma phenotypes as single SNPs although the significance did not survive multiple testing correction. In addition, when gene x gene interactions were tested using the multifactor dimensionality reduction approach, IL1RL1 SNPs were identified as interacting factors in analyses of IgE phenotypes [43]. In a study performed by our group in collaboration with others, we investigated three Canadian and one Australian populations but failed to detect any significant association with IL1RL1 that survived correction for multiple comparisons [44]. The same cohorts, in addition to one American population, were used in an association study of genes in the vitamin D pathway with asthma and atopy phenotypes. IL1RL1 SNPs were selected for this study based on the fact that IL1RL1 was shown to be transcriptionally regulated by vitamin D [45]. The genotyping covered more variants of IL1RL1 than the initial study and the number of candidate genes was substantially less (11 versus 120 genes). Significant associations of these variants were observed with asthma and atopy phenotypes [46]. Given the role of eosinophils in the pathogenesis of asthma, alleles that associate with increased eosinophil count could be detrimental in terms of asthma risk and severity. In a Genome Wide Association Study (GWAS) of eosinophil count in an Icelandic population, a SNP in IL1RL1 (rs1420101) showed the most significant association. The A allele of rs1420101 associated with increased eosinophil count and in further analyses with increased serum IgE as well as with three asthma phenotypes (asthma, atopic asthma, non atopic asthma) in nine European populations and one East Asian population [47], rs1420101 is an intrinsic SNP which is in high LD (r² greater than 80%) with a large number of other variants in IL1RL1, IL18R1 and IL18RAP; this group of SNPs contains mostly intronic SNPs in addition to a coding-synonymous and a few 3’ and 5’ UTR SNPs. No functional studies have been performed thus far to determine the association-causing SNP. It is of note that an association of a SNP in IL33 (rs3939286) with eosinophil count, asthma and atopic asthma was reported in same study, although the IL33 association with eosinophil count did not reach genome-wide significance. The same IL33 SNP was associated with nasal polypsis in a Belgian population in a candidate gene study [48]. Wu et al. used GWAS data of childhood asthma in a Mexican population [49] to perform a candidate gene analysis. In this study, 237 genes were selected from human and animal model published studies of asthma to have at least one SNP associated with an asthma phenotype. They reported IL1RL1 among the most significant associations. Furthermore, their results were subjected to multi-marker analysis, which confirmed IL1RL1 as a significant finding as well as IL18RI. Collectively, there is strong evidence for genetic association of IL1RL1 with asthma and related phenotypes. This association is certainly very well supported by the biology of IL1RL1 and related proteins. IL33 is secreted by the airway epithelium in response to stress such as allergens or viruses, and binds to IL1RL1 isoform A on the surface of immune cells. There are excellent reviews about the central role of the epithelium in initiating and sustaining immune responses [50]. IL33/IL1RL1 isoform A plays a crucial role in that process. The binding of IL1RL1 isoform A and its ligand IL33 triggers the NFκB signaling pathway, which leads to the transcription of cytokines needed for a Th2 immune response. However, the role of IL1RL1 isoform B remains unclear. Several animal models and in vitro studies show that IL1RL1 isoform B prevents the IL33/IL1RL1 isoform A signaling and consequently attenuates inflammation, indicat- ing its role as a negative regulator of the pro-inflammatory IL33/IL1RL1 isoform A axis. Human data on the other hand clearly demonstrate a consistent increase of IL1RL1 isoform B in an array of pathological conditions as well as the correlation of this increase with severity. Additionally, there was a report of an animal study showing that mice deficient in IL1RL1 showed attenuated airway inflammation after challenge with an allergen [51], suggesting that IL1RL1 isoform B might be participating in the excessive inflammation observed in asthma. However, the model used for this study was the transgenic TCR-mouse model; these animals are predisposed to autoimmune disorders because they carry rearranged TCR α and β genes from a diabetogenic T cell clone. The above studies do not seem to be consistent with the antagonist role of IL1RL1 isoform B but rather indicate a possible involvement in the pathology. An alternative explanation would be that the increase of IL1RL1 isoform B is a means of preventing an exaggerated immune response but either occurs too late or is insufficient to remedy to the pathological state. Evidently, soluble IL1RL1 plays a role in the regulation of the immune response, notably in severe disease. Exactly what that role is and the mechanisms underlying it need to be clarified in order to develop efficient strategies for developing therapeutics using the IL1RL1 proteins. Recent human data in Chronic Obstructive Pulmonary Disease (COPD) seem to indicate an involvement of soluble IL1RL1 in the early stages of COPD [52]. This study however involved a small number of patients and needs replication. Allergy and Immune Disorders A SNP in the distal promoter region of IL1RL1, rs6543116 (-26999G/A), was associated with increased risk for atopic dermatitis and up-regulation of gene expression [53]. This study suggested a functional effect of rs6543116 as the A allele correlated with an up-regulation of the gene transcription as well as serum levels. The same group reported the association of serum levels of IL33 and SNPs in the IL33 gene with Japanese cedar pollinosis, the most common form of allergic rhinitis in Japan [54]. In addition, Castano et al. found a protective association of IL1RL1 SNPs with chronic rhinosinusitis using a cohort of surgery-unresponsive chronic rhinitis patients, this association was stronger in more severe disease [55]. IL33 signaling through IL1RL1 was shown to be involved in anaphylactic shock in an animal model study examining the response of IgE-sensitized mice to IL33 treatment [23]. The same authors had shown elevated IL33 levels in the serum of atopic patients undergoing surgery; this effect was demonstrated to derive purely from innate immunity as T or B cells were not required. The pathological effect could be prevented by treatment with anti-IL33 antibody or soluble IL1RL1 and was not observed in ST2+ animals [23]. IL1RL1 and closely linked genes have been implicated in an array of autoimmune diseases. Levels of IL1RL1 isoform B have been shown to be increased in various conditions such as Systemic Lupus Erythematosus (SLE), sclerosis, and rheumatoid arthritis (RA) [56]. Mok et al. found that elevated serum IL1RL1 isoform B levels in SLE patients correlated with disease activity [57]. To date, GWAS performed in Chinese and European populations have not found association of IL1RL1 SNPs with RA [58, 59]. Studies in animal models demonstrated that recombinant IL1RL1 isoform B protein, or anti-IL1RL1 antibody could significantly attenuate the severity of experimental arthritis [60, 61] and IL1RL1 knock-out mice were shown to develop less severe form of disease and had reduced pro-inflammatory cytokine production. Additionally, human studies have shown increased levels of IL33 and IL1RL1 in RA synovium paralleling increased inflammation [62]. Studies in animal models strongly suggest that the involvement of IL33/IL1RL1 in RA is through triggering mast cell degranulation in the RA synovium [63]. Although there is good evidence for a role of IL33/IL1RL1 in human and experimental arthritis, no SNPs in these genes were found associated with susceptibility to RA in GWAS data [64]. The IL1RL1/IL33 signaling axis was implicated in inflammatory bowel disease (IBD) for the first time in two recent studies characterizing IL1RL1 and IL33 protein and mRNA expression in IBD patients [65]. There was an increase in soluble IL1RL1 levels in the gut, which was mainly associated with the active state of ulcerative colitis, indicating a possible negative regulation of the IL1RL1/IL33 pathway in order to dampen the inflammation. Pastorelli et al. confirmed the observation of elevated levels of IL1RL1 and IL33 in the serum and mucosa of IBD patients; they also showed that anti-TNF decreased IL1RL1 isoform A levels and increased the soluble isoform making more decoy receptor available in order to sequester IL33 and reduce the inflammation [66]. A SNP 1.5 kb downstream of IL18RAP (rs917997) was associated with susceptibility to IBD in a Dutch population; the same SNP was associated with celiac disease in three European populations [67]. rs917997 along with another SNP in the intergenic region between IL1RL1 and IL18R1 (rs13015714) were associated with celiac disease in a GWAS of a UK population [68]. The same SNP downstream of IL18RAP (rs917997) was associated with Crohn’s disease in a GWAS [69]. These genetic and mechanistic data suggest that IL1RL1/IL33 plays a role in the gut mucosa similar to the airway epithelium i.e. IL1RL1 isoform A/IL33 eliciting a Th2 immune response and IL1RL1 isoform B serving as a negative regulator. There is evidence that IL1RL1 directly acts on macrophages to suppress their ability to produce pro-inflammatory cytokines [42]. Macrophages are instrumental in diabetes pathogenesis. In an animal model of diabetes (multiple low-dose streptozotocin-induced diabetes), Mensah-Brown et al. [70] showed that specific disruption of the IL1RL1 gene significantly enhanced inflammation in their mouse model as estimated by an increase in cellular infiltration in pancreatic islets and a reduction in cells immuno-positive for insulin. Recently, a genetic linkage study demonstrated linkage of chromosome 2 with type 2 diabetes with a LOD score of 4.5 [71]. Follow-up genetic studies are warranted to narrow down the linkage signal and investigate specific SNP associations. This may lead to the identification of novel pathways in diabetes. In summary, the available data on the involvement of IL1RL1 and its ligand IL33 in immune and autoimmune disorders are reasonably consistent; a clearer understanding of the balance between IL1RL1 isoform A/IL33, IL1RL1 isoform B/IL33 and its regulation is needed in order to make that axis a more attractive target for therapeutic intervention. Cardiovascular Disease In vitro and animal model studies have demonstrated that IL33/IL1RL1 isoform A signaling protects cardiomyocytes from apoptosis by suppressing Caspase 3 activity and promoting the expression of anti-apoptotic proteins in vitro and improves survival in experimental myocardial infarction (MI) animals [72]. Human studies have shown an increase of soluble IL1RL1 after myocardial stress or injury, and MI [26, 73]; the levels correlated with diastolic load [74], cardiac abnormalities on electrocardiogram (ECG) and poor prognosis in dyspneic and MI patients [75-77]. In a study following 150 patients admitted to hospital with acutely destabilized heart failure, multiple serum samples were collected between admission and discharge and soluble IL1RL1 levels were measured. The results showed that IL1RL1 isoform B levels were a powerful predictor of 90-day mortality. Indeed, IL1RL1 isoform B serum levels are considered a reliable biomarker for heart failure [78, 79] as delineated by a recent review by Moore et al. [80]. A more recent study demonstrated for the first time that IL1RL1 isoform B could be used to predict left ventricular and infarct recovery after acute MI [81]. The company Critical Diagnostics in collaboration with the Brigham and Women’s Hospital in Boston has developed a diagnosis kit called Presage that uses soluble IL1RL1 levels for diagnosis and prognosis of cardiovascular disease. However, this kit is not yet approved by the FDA for clinical use. Many U.S. and international patents protect the use of IL1RL1 for the diagnosis and prognosis in cardiovascular disease. The fact that increased level of IL1RL1 is correlated with poor prognosis in different instances of cardiovascular disease points to a role of soluble IL1RL1 as marker for the severity of the immune response. Increased IL1RL1 isoform B is indicative of an overwhelming immune response that is hard to control and thus leads to unfavorable outcome in cardiovascular disease patients, such as after an MI. Infections IL1RL1 isoform B levels correlate with sepsis severity and outcome [82]. A possible mechanism was recently described by Alves-Filho et al. [83]. Using the cecal ligation and puncture model in Balb-c mice [83], a widely used model for experimental sepsis, this group demonstrated that IL33 treatment was protective from peritonitis and enhanced bacterial clearance. Their data also show that the protective effect of IL33 treatment was achieved via the inhibition of a TLR-signaling-induced protein, GRK2. GRK2 plays a prominent role in sepsis as it down-regulates CXCR2 (a receptor for IL8, a chemokine that attracts neutrophils to infection sites) thus leading to inefficient clearance of bacteria. In agreement with the role of IL1RL1 proteins in the promotion of Th2 responses, mRNA levels of both receptor and soluble forms of the IL1RL1 transcript were shown to be up-regulated in an animal model of Toxoplasma gondii parasitic infection and this up-regulation correlated with protection from the infection [84]. In addition, ST2+/− knockout mice demonstrated increased susceptibility and more severe disease compared to wild type mice as assessed by weight loss, increased parasite transcript levels and typical disease pathology [84]. In 2008, a small study of a Somali population reported an association of a SNP in the 3’UTR of IL18R1 (rs3213733) with variability in Rubella vaccine-induced humoral immunity [85]. It is interesting that the same SNP was recently shown to be associated with asthma in two different studies, in Mexican and Japanese populations [47, 86]. As LD patterns differ between populations, this suggests a potential functional role of this SNP in regulating gene expression/function. Additional evidence for a role of the IL33/IL1RL1 axis in host defense comes from an animal study showing the protective role of IL33 in intestinal infection with nematodes [87]. In summary, IL1RL1 confers protection from infection, which is consistent with its involvement in the Th2 immune response. The increase in IL1RL1 signaling skews T cells to Th2 and prevents a parasite-specific Th1 polarized response. Liver and Kidney Disorders In a candidate gene association study of the course of Hepatitis C in a Japanese population, 103 genes including IL1RL1 and IL18R1 were investigated [88]. SNPs in both these genes as well as other genes involved in immune responses were significantly associated with serum levels of alanine aminotransferase (ALT). ALT levels are routinely used as a diagnostic test of liver function and elevated levels are an indicator of infections and other disorders. Nevertheless, this group’s data were not corrected for multiple testing and need to be replicated in other populations. An over-expression of IL1RL1 and IL33 mRNA in fibrotic liver was reported using mouse and human tissue sections [89]. CONCLUDING REMARKS The IL1RL1 gene and its resulting soluble and receptor proteins have emerged as key regulators of the inflammatory process implicated in a large variety of human pathologies (see summary Table 1). IL1RL1 is important for both innate and adaptive immunity as IL1RL1 isoform A binding with its ligand IL33 leads to polarization of T helper cells into Th2 and also activates and promotes the degranulation of mast cells. The resulting inflammation is down-regulated by the soluble form of IL1RL1; levels of the latter are recognized as biomarkers for the severity of various conditions. Except for the functional analysis of the IL1RL1 SNP rs6543116 associated with asthma and atopic dermatitis [36, 53], there has been no functional analysis of the disease-associated variants in Table 1. \| Gene \| SNP \| Chr. Loc. \| SNP Location \| Disease/Phenotype \| pValue \| Study \| Population \| N \| Refs \| \|--------\|----------\|-----------\|--------------\|-----------------------------\|--------\|----------------------------\|------------\|-------\|-------------------------------------------\| \| IL1RL1 \| rs949963 \| 102769786 \| 5' near-gene \| Childhood asthma \| 0.033 \| Candidate gene study follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL1R1 \| rs3917289\| 102781911 \| intronic \| Childhood asthma \| 0.022 \| Candidate gene study follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL1RL1 \| rs11685424\| 102926981 \| 5' near-gene \| Childhood asthma \| 0.04 \| Candidate gene study follow-up to GWAS \| Mexican \| 492 cases + both parents \| Reijmersink - Allergy 2010 \| \| IL1RL1 \| rs11685480\| 102927086 \| 5' near-gene \| Specific IgE egg 1-2 years \| 0.02 \| Candidate gene study gene-gene interaction analysis \| Dutch \| 3062 children (birth cohort) \| Shimizu et al. - Hum Mol Genet 2005 \| \| IL1RL1 \| rs6543116 \| 102927726 \| promoter \| Atopic dermatitis \| 0.000007 \| Candidate SNP study \| Japanese \| 452 cases / 636 controls \| Bossé et al. - Respir Res 2009 \| \| IL1RL1 \| rs1420089 \| 102938389 \| intronic \| Asthma \| 0.033 \| Candidate gene study \| French-Canadian founder population \| 72 families \| Bossé et al. - Respir Res 2009 \| \| IL1RL1 \| rs13431828\| 102954653 \| 5' UTR \| Chronic rhinosinusitis \| 0.008 \| Candidate gene study \| French-Canadian \| 206 cases / 196 controls \| Castano et al. - Am J Rhinol Allergy 2009 \| \| IL1RL1 \| rs13431828\| 102954653 \| 5' UTR \| Childhood asthma \| 0.0002 \| Candidate gene study follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL1RL1 \| rs1041973 \| 102955468 \| Cod.non.syn \| Atopy \| 0.046 \| Candidate gene study \| Canadian birth cohort \| 98 families \| Bossé et al. - Respir Res 2009 \| \| IL1RL1 \| rs1041973 \| 102955468 \| Cod.non.syn \| Course of hepatitis C \| 0.004 \| Candidate gene study \| Japanese \| 238 cases \| Saito et al. - Biochem Biophys Res Commun 2004 \| \| Gene \| SNP \| Chr. Loc. \| SNP Location \| Disease/Phenotype \| pValue \| Study \| Population \| N \| Refs. \| \|--------\|-----------\|-----------\|--------------\|------------------------\|--------------\|----------------------------\|------------\|-----------------\|---------------------------\| \| IL1RL1 \| rs1041973 \| 102955468 \| Cod.non.syn \| Childhood asthma \| 0.00035 \| Candidate gene study_follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL1RL1 \| rs1420101 \| 102957716 \| intronic \| Eosinophil count \| 5.3 x 10^-10 \| GWAS \| Icelandic \| 9392 individuals \| Gudbjartson et al. - Nat Genet 2009 \| \| IL1RL1 \| rs1420101 \| 102957716 \| intronic \| Asthma \| 5.5 x 10^-12 \| Candidate gene study_follow-up to GWAS \| 9 European + 1 East Asian populations \| 7996 cases / 44890 controls \| Gudbjartson et al. - Nat Genet 2009 \| \| IL1RL1 \| rs2160203 \| 102960824 \| 3' UTR \| Chronic rhinosinusitis \| 0.03 \| Candidate gene study \| French-Canadian \| 206 cases / 196 controls \| Castano et al. - Am J Rhinol Allergy 2009 \| \| IL1RL1 \| rs1946131 \| 102961929 \| intronic \| Asthma / Atopy \| 0.015 / 0.050 \| Candidate gene study \| French-Canadian founder population \| 53 / 42 families \| Bossé et al. - Respir Res 2009 \| \| IL1RL1 \| rs1702706 \| 102965332 \| intronic \| Total IgE \| 0.02 \| Candidate gene study_gene-gene interaction analysis \| Dutch 3062 children (birth cohort) \| 3062 children (birth cohort) \| Reijmerink et al. - Allergy 2010 \| \| IL1RL1 \| rs1921622 \| 102966067 \| intronic \| Specific IgE egg 1-2 years \| 0.04 \| Candidate gene study_gene-gene interaction analysis \| Dutch 3062 children (birth cohort) \| 3062 children (birth cohort) \| Reijmerink et al. - Allergy 2010 \| \| IL1RL1 \| rs1921622 \| 102966067 \| intronic \| BHR / asthma / Total IgE \| 0.014 / 0.038 / 0.027 \| Candidate gene study \| Dutch 212 / 193 / 276 families \| 212 / 193 / 276 families \| Reijmerink et al. - J Allergy Clin Immunol 2008 \| \| IL1RL1 \| rs10208293\| 102966310 \| intronic \| Chronic rhinosinusitis \| 0.03 \| Candidate gene study \| French-Canadian \| 206 cases / 196 controls \| Castano et al. - Am J Rhinol Allergy 2009 \| \| IL1RL1 \| rs10208293\| 102966310 \| intronic \| Specific IgE indoor allergens 6-8 years \| 0.03 \| Candidate gene study_gene-gene interaction analysis \| Dutch 3062 children (birth cohort) \| 3062 children (birth cohort) \| Reijmerink et al. - Allergy 2010 \| (Table 1). Contd..... \| Gene \| SNP \| Chr. Loc. \| SNP Location \| Disease/Phenotype \| pValue \| Study \| Population \| N \| Refs. \| \|------------\|--------------\|-----------\|--------------\|---------------------------\|-----------------\|--------------------------------\|------------\|-----------\|-------------------------------\| \| IL1RL1 \| rs1861246 \| 102966783 \| intronic \| BHR / asthma / Total IgE \| 0.021 / 0.05 / 0.02 \| Candidate gene study Dutch \| 175 / 163 / 230 families \| \| Reijmerink et al. - J Allergy Clin Immunol 2008 \| \| IL1RL1 \| rs1861245 \| 102966906 \| intronic \| Asthma \| 0.032 \| Candidate gene study French-Canadian founder population \| 101 families \| \| Bossé et al. - Respir Res 2009 \| \| IL1RL1 \| rs4988957 \| 102968075 \| cod.syn \| Chronic rhinosinusitis \| 0.03 \| Candidate gene study French-Canadian \| 206 cases / 196 controls \| \| Castano et al. - Am J Rhinol Allergy 2009 \| \| IL1RL1 \| rs10204137 \| 102968212 \| Cod.non.syn \| Chronic rhinosinusitis \| 0.04 \| Candidate gene study French-Canadian \| 206 cases / 196 controls \| \| Castano et al. - Am J Rhinol Allergy 2009 \| \| IL1RL1 \| rs10204137 \| 102968212 \| Cod.non.syn \| Childhood asthma \| 0.013 \| Candidate gene study_follow-up to GWAS Mexican \| 492 cases + both parents \| \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL1RL1 \| rs10192157 \| 102968356 \| Cod.non.syn \| Childhood asthma \| 0.013 \| Candidate gene study_follow-up to GWAS Mexican \| 492 cases + both parents \| \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL1RL1 \| rs10206753 \| 102968362 \| Cod.non.syn \| Childhood asthma \| 0.013 \| Candidate gene study_follow-up to GWAS Mexican \| 492 cases + both parents \| \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL1RL1 / IL18R1 \| rs13015714 \| 102971865 \| intergenic \| Coeliac disease \| NS \| Candidate gene study_follow-up to GWAS European (Swedish, Norwegian) \| 325 families \| \| Amundsen et al. - Genes Immun 2010 \| \| IL1RL1 / IL18R1 \| rs12999364 \| 102974129 \| intergenic \| BHR / asthma \| 0.016 / 0.021 \| Candidate gene study Dutch \| 198 / 185 families \| \| Reijmerink et al. - J Allergy Clin Immunol 2008 \| \| IL18R1 \| rs2287037 (C-69T) \| 102979028 \| 5' near-gene \| Coal workers' pneumococnosis \| NS \| Candidate gene study French \| 200 individuals \| \| Nadif et al. - Eur Respir J 2006 \| \| Gene \| SNP \| Chr. Loc. \| SNP Location \| Disease/Phenotype \| pValue \| Study \| Population \| N \| Refs \| \|-------\|----------\|-----------\|--------------\|-------------------------\|--------------\|---------------------------\|---------------------------------\|------\|-----------------------------------------\| \| IL18R1\| rs2287037\| 102979028 \| 5' near-gene \| Asthma \| 0.024 \| Candidate gene study \| European (Danish, British, Norwegian) \| 736 families \| Zhu et al. - Eur J Hum Genet 2008 \| \| IL18R1\| rs1420099\| 102980543 \| intronic \| Asthma / Atopic asthma \| 0.00069 / 0.0008 \| Candidate gene study \| European (Danish, British, Norwegian) \| 736 families \| Zhu et al. - Eur J Hum Genet 2008 \| \| IL18R1\| rs1420098\| 102984279 \| intronic \| Asthma \| 0.037 \| Candidate gene study \| European (Danish, British, Norwegian) \| 736 families \| Zhu et al. - Eur J Hum Genet 2008 \| \| IL18R1\| rs1362348\| 102984624 \| intronic \| Asthma / Atopic asthma / BHR \| 0.0013 / 0.0024 / 0.048 \| Candidate gene study \| European (Danish, British, Norwegian) \| 736 families \| Zhu et al. - Eur J Hum Genet 2008 \| \| IL18R1\| rs1558627\| 102984684 \| intronic \| BHR / Total IgE \| 0.049/0.028 \| Candidate gene study \| Dutch \| 180 / 238 families \| Reijmer-ink et al. - J Allergy Clin Immunol 2008 \| \| IL18R1\| rs2058622\| 102985424 \| intronic \| Atopic asthma \| 0.045 \| Candidate gene study \| European (Danish, British, Norwegian) \| 736 families \| Zhu et al. - Eur J Hum Genet 2008 \| \| IL18R1\| rs3771170\| 102985980 \| intronic \| Humoral immunity to Rubella \| 0.0003 \| Candidate gene study \| Somali \| 89 individuals \| Dhiman et al. - Tissue Antigens 2008 \| \| IL18R1\| rs3771166\| 102986222 \| intronic \| Childhood asthma \| 0.011 \| Candidate gene study, follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL18R1\| rs1974675\| 102986375 \| intronic \| Asthma / Atopic asthma / BHR \| 0.00005 / 0.00001 / 0.036 \| Candidate gene study \| European (Danish, British, Norwegian) \| 736 families \| Zhu et al. - Eur J Hum Genet 2008 \| \| IL18R1\| rs1465321\| 102986618 \| intronic \| Humoral immunity to Rubella \| 0.009 \| Candidate gene study \| Somali \| 89 individuals \| Dhiman et al. - Tissue Antigens 2008 \| (Table 1). Contd….. \| Gene \| SNP \| Chr. Loc. \| SNP Location \| Disease/Phenotype \| pValue \| Study \| Population \| N \| Refs \| \|--------\|------------\|-----------\|--------------\|-----------------------------------\|---------\|---------------------\|------------------\|-----------\|-----------------------\| \| IL18R1 \| rs2270297 \| 102992675 \| intronic \| Humoral immunity to Rubella \| 0.0002 \| Candidate gene study \| Somali \| 89 individuals \| Dhiman et al. - Tissue Antigens 2008 \| \| IL18R1 \| rs2270297 \| 102992675 \| intronic \| BHR \| 0.048 \| Candidate gene study \| Dutch \| 185 families \| Reijmersink et al. - J Allergy Clin Immunol 2008 \| \| IL18R1 \| rs3213733 \| 102997884 \| intronic \| Humoral immunity to Rubella \| 0.009 \| Candidate gene study \| Somali \| 89 individuals \| Dhiman et al. - Tissue Antigens 2008 \| \| IL18R1 \| rs3213733 \| 102997884 \| intronic \| Asthma \| 0.0035 \| Candidate gene study \| Japanese \| 288 cases / 1032 controls \| Imada et al. - BMC Res Notes 2009 \| \| IL18R1 \| rs3213733 \| 102997884 \| intronic \| Childhood asthma \| 0.0054 \| Candidate gene study \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL18R1 \| rs1035130 \| 103001402 \| cod.syn \| BHR / asthma \| 0.048 / 0.046 \| Candidate gene study \| Dutch \| 174 / 159 families \| Reijmersink et al. - J Allergy Clin Immunol 2008 \| \| IL18R1 \| rs3755274 \| 103002395 \| intronic \| Humoral immunity to Rubella \| 0.009 \| Candidate gene study \| Somali \| 89 individuals \| Dhiman et al. - Tissue Antigens 2008 \| \| IL18R1 \| rs2241117 \| 103003043 \| intronic \| Humoral immunity to Rubella \| 0.001 \| Candidate gene study \| Somali \| 89 individuals \| Dhiman et al. - Tissue Antigens 2008 \| \| IL18R1 \| rs3771161 \| 103003961 \| intronic \| Humoral immunity to Rubella \| 0.009 \| Candidate gene study \| Somali \| 89 individuals \| Dhiman et al. - Tissue Antigens 2008 \| \| IL18R1 \| rs4851004 \| 103009537 \| intronic \| Childhood asthma \| 0.0079 \| Candidate gene study \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| Gene \| SNP \| Chr. Loc. \| SNP Location \| Disease/Phenotype \| pValue \| Study \| Population \| N \| Refs. \| \|----------\|----------\|-----------\|--------------\|-----------------------------\|------------\|----------------------------\|-----------------------------\|-----------------------\|--------------------------------\| \| IL18R1 \| rs2287033\| 103011237 \| intronic \| Childhood asthma \| 0.0063 \| Candidate gene study, follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL18R1 \| rs3732127\| 103013750 \| 3' UTR \| Humoral immunity to Rubella \| 0.009 \| Candidate gene study \| Somali \| 89 individuals \| Dhiman et al. - Tissue Antigens 2008 \| \| IL18R1 \| rs1420094\| 103015687 \| 3' UTR \| Childhood asthma \| 0.0063 \| Candidate gene study, follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL18R1 \| rs1420094\| 103015687 \| 3' UTR \| Atopic asthma \| 0.0063 \| Candidate gene study \| European (Danish, British, Norwegian) \| 736 families \| Zhu et al. - Eur J Hum Genet 2008 \| \| IL18R1 / IL18RAP \| rs1035127\| 103019919 \| intergenic \| Crohn's disease \| 1.2 x 10^{-7} \| GWAS \| Caucasian (American, Canadian, Belgian, French, British) \| 2325 cases / 1809 controls + 1339 families \| Barrett et al. - Nat Genet 2008 \| \| IL18RAP \| rs1420106\| 103035044 \| 5' near-gene \| BHR / Total IgE \| 0.023 / 0.012 \| Candidate gene study \| Dutch \| 184 / 234 families \| Videman et al. - Arthritis Rheum 2009 \| \| IL18RAP \| rs1420100\| 103037002 \| intronic \| Lumbar disc signal intensity \| 0.005 \| Candidate gene study \| Finnish \| 588 individuals \| Shirts et al. - Am J Med Genet B Neuro-psychiatr Genet 2008 \| \| IL18RAP \| rs2272127\| 103039873 \| intronic \| Schizophrenia+Herpes seropositivity \| 0.03 \| Candidate gene study \| Caucasian (American) \| 478 cases / 501 controls \| Hunt et al. - Nat Genet 2008 \| \| IL18RAP \| rs917997 \| 103070568 \| intergenic \| Coeliac disease \| 8.49 x 10^{-10} \| Candidate gene study, follow-up to GWAS \| Northern European \| 767 cases / 1422 controls \| Hunt et al. - Nat Genet 2008 \| (Table 1). Contd….. \| Gene \| SNP \| Chr. Loc. \| SNP Location \| Disease/Phenotype \| pValue \| Study \| Population \| N \| Refs. \| \|------------\|-------------\|-----------\|--------------\|-------------------\|------------\|------------------------\|---------------------------------\|--------------------\|-------------------------------\| \| IL18RAP \| rs917997 \| 103070568 \| intergenic \| Type 1 diabetes \| 8.03 x 10^{-5} \| Candidate gene study \| Caucasian (Irish, British, American, Romanian, Danish, Norwegian, Finnish) \| 8064 cases / 9339 controls \| Smyth et al. - N Engl J Med 2008 \| \| IL18RAP \| rs917997 \| 103070568 \| intergenic \| Crohn's disease \| 2.2 x 10^{-6} \| Candidate gene study \| European \| 1689 cases / 1936 controls \| Wang et al. - Hum Genet 2010 \| \| Chr 2 \| \| \| \| Type 2 diabetes \| LOD=4.53 \| Genetic linkage study \| African-American \| 580 families \| Elbein et al. - Diabetes 2009 \| \| IL18RAP \| 6 Tag SNPs \| \| \| Cardiovascular disease \| NS \| Candidate gene study \| European \| 1416 cases / 1772 Controls \| Grisoni et al. - BMC Med Genet 2009 \| \| IL18R1 \| 5 Tag SNPs \| \| \| Cardiovascular disease \| NS \| Candidate gene study \| European \| 1416 cases / 1772 Controls \| Grisoni et al. - BMC Med Genet 2009 \| \| IL1RL1 / IL18R1 \| Haplo: rs1026753/rs12999364/rs1420099 \| - \| \| BHR \| 0.006 \| Candidate gene study \| Dutch \| 179 families \| Reijmer-ink et al. - J Allergy Clin Immunol 2008 \| \| IL18R1 \| Haplo:rs1420099/rs1558627/rs2270297 \| - \| \| Asthma \| 0.002 \| Candidate gene study \| Dutch \| 180 families \| Reijmer-ink et al. - J Allergy Clin Immunol 2008 \| \| IL1RL1 \| Haplo:rs1921622/rs1861246/rs10206753 \| - \| \| BHR / asthma / Total IgE \| 0.0009 / 0.0008 / 0.007 \| Candidate gene study \| Dutch \| 192 / 170 / 245 families \| Reijmer-ink et al. - J Allergy Clin Immunol 2008 \| IL1RL1: functional characterization of genetically-associated variants is necessary to determine the causal pathways leading to expression and/or function changes in the proteins. As shown by numerous animal model studies, targeting the IL1RL1/IL33 axis is potentially a very promising therapeutic avenue for lung, heart and other immune and inflammatory disorders. In order to move the field forward, it will be important to investigate genetic association of the IL1RL1 region (including the surrounding genes) in different populations with different LD patterns; this will permit a better understanding of the biology behind this region’s involvement in immune and inflammatory disorders and thus facilitate and focus future therapeutic targeting efforts. REFERENCES 1. Mitcham, J. L.; Parnet, P.; Bonnett, T. P.; Garka, K. E.; Gerhart, M. J.; Slack, J. L.; Gayle, M. A.; Dower, S. K.; Sims, J. E. T1/ST2 signaling establishes it as a member of an expanding interleukin-1 receptor family. J. Biol. Chem., 1996, 271(10), 5777-5783. 2. Kumar, S.; Minnich, M. D.; Young, P. R. 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Predominant expression of 950delCAG of IL-18Rα chain cDNA is associated with reduced IFN-γ production. --- Table 1. Contd….. \| Gene \| SNP \| Chr. Loc. \| SNP Location \| Disease/Phenotype \| pValue \| Study \| Population \| N \| Refs. \| \|----------\|-----------\|-----------\|--------------\|-------------------\|--------\|------------------------\|------------\|-----------\|---------------\| \| IL18R1 / \| IL18RAP \| 22 candidate SNPs \| - \| - \| - \| Candidate gene study \| German \| 142 cases / 114 controls \| Tret et al. - Circulation 2005 \| \| IL1RL1 \| multimarker (11) \| - \| - \| - \| - \| Candidate gene study_follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| \| IL18R1 \| multimarker (9) \| - \| - \| - \| - \| Candidate gene study_follow-up to GWAS \| Mexican \| 492 cases + both parents \| Wu et al. - J Allergy Clin Immunol 2010 \| Abbreviations - IBID: Inflammatory bowel disease - BHR: Bronchial hyper-responsiveness - GWAS: Genome-wide association study - Chr.Loc: Chromosomal location based on NCBI build 37.1 - Chr 2: Chromosome 2 - Haplo: Haplotype - NS: Non significant - Cod non.syn: Coding non synonymous SNP - Cod.syn: Coding synonymous SNP Same SNPs are hilighted with the same color; different colors are merely for ease of viewing, and are inconsequential. and high serum IgE levels in atopic Japanese children. 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1be2b9fe87061b5d55217601c22b1cc5b2b66487	{ "olmocr-version": "0.1.59", "pdf-total-pages": 6, "total-fallback-pages": 0, "total-input-tokens": 16817, "total-output-tokens": 5911, "fieldofstudy": [ "Medicine" ] }	CASE REPORT Neonatal cardiac tamponade, a life-threatening complication secondary to peripherally inserted central catheter: a case report Mohammad Reza Zarkesh1,2* and Mokaram Haghjoo2 Abstract Background: Although the use of a peripherally inserted central catheter (PICC) has many advantages for the treatment of neonates, catheter malposition may result in serious complications that could be life-threatening. We report the case of a 10-day-old neonate with cardiac tamponade secondary to a PICC line who was successfully treated by pericardiocentesis. Case presentation: An Iranian (Asian) preterm male neonate was born by Cesarean section with a birth weight of 1190 g and a first-minute Apgar score of 7. Based on an increased respiratory distress syndrome (RDS) score from 4 to 7, resuscitation measures and intubation were performed at the neonatal intensive care unit (NICU). On day 3 after birth, a PICC line was inserted for parenteral therapy. A chest X-ray confirmed that the tip of the PICC line was in the appropriate position. Mechanical ventilation was discontinued 72 h post-NICU admission because of the improved respiratory condition. On the day 10 post-NICU admission, he suddenly developed hypotonia, apnea, hypoxia, hypotension, and bradycardia. Resuscitation and ventilation support were immediately started, and inotropic drugs were also given. Emergency echocardiography showed a severe pericardial effusion with tamponade. The PICC line was removed, and urgent pericardiocentesis was carried out. The respiratory situation gradually improved, the O2 saturation increased to 95%, and vital signs remained stable. Conclusions: Dramatic improvement of the neonate's clinical responses after pericardial drainage and PICC removal were suggestive of PICC displacement, pericardial perforation, and cardiac tamponade. Keywords: Neonate, Tamponade, Peripherally inserted central catheter Background A peripherally inserted central catheter (PICC) made of silicone, polyurethane, or polyethylene provides a prolonged route for administration of parenteral fluids, nutrition, and medications. Preterm neonates admitted to hospital usually require a PICC because of their small and fragile vessels [1, 2]. Femoral, subclavian, and internal jugular veins are the most common sites used for PICC catheterization [3]. Although use of a PICC has many advantages for the treatment of neonates, catheter malposition may result in serious complications that could be life-threatening [4]. These potential complications (sepsis, embolism, intravascular thrombosis, pleural effusion, and pericardial effusion with tamponade) indicate that insertion of a PICC line requires special medical qualification and follow-up examination to ensure its Correspondence: [email protected] 1 Maternal, Fetal, and Neonatal Research Center, Family Health Institute, Tehran University of Medical Sciences, Sarv Ave., North Nejatollahi Street, Tehran 1598718311, Iran Full list of author information is available at the end of the article © The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data. proper location (the inferior third of the superior vena cava) [5–8]. Of the above complications, tamponade is a rare but fatal condition that occurs following catheter dislocation and pericardial perforation [8]. Cardiac tamponade is responsible for 47–100% of the mortality rate [9]. We report here the case of a neonate admitted to a neonatal intensive care unit (NICU) with pericardial effusion and cardiac tamponade secondary to a PICC line that was successfully treated with immediate PICC removal and pericardiocentesis. Case presentation An Iranian (Asian) pregnant women aged 32 years old with a primary complaint of preterm uterine contraction and vaginal bleeding presented the obstetric ward of Yas Hospital (Tehran-Iran, January 2021). She was a multipara woman (Gravida: 3, Para: 2, Living: 2, Abortion: 0) with a gestational age of 30 weeks. She did not report any prenatal complications and had received corticosteroid therapy 2 days prior to hospital admission. Upon presentation, magnesium sulfate was immediately administered but she was transferred to the operation room for repeat Cesarean section due to progressive cervical dilation. A preterm male newborn with a first-minute Apgar score of 7 and birth weight of 1190 g was born. Physical examination after birth showed a notable frontal bossing, acrocyanosis, and diffuse head, neck, hand, and leg ecchymosis. Anterior and posterior fontanelles were normal. No congenital anomaly or abdominal organomegaly was observed. Peripheral pulses were palpable and heart sounds were normal without any abnormal sounds. His reflexes were normal, but limb movements were hypotonic. Due to an increase in his respiratory distress syndrome (RDS) score from 4 to 7 and signs of respiratory distress (inter- and subcostal retraction, grunting, and decreased breathing sounds), resuscitation measures were initiated. He was then given nasal continuous positive airway pressure (CPAP) in the operation room that was subsequently switched to mechanical ventilation in the NICU. Intratracheal surfactant and intravenous antibiostic therapy were also initiated in the NICU. Under mechanical ventilation with synchronized intermittent mandatory ventilation (SIMV) setup, his $O_2$ saturation, blood pressure, and heart rate improved to > 94%, 70/35 mmHg, and 160 beats per minute, respectively. On day 3 post-NICU admission, a PICC line (Premicath; 1Fr/28 G; VYGON, Écouen, France; Code 1261.080) was also inserted from the auxiliary vein of the right upper extremity for intravenous therapy, delivery of medications, and parenteral nutrition. A chest X-ray showed that the tip of the PICC line was in the appropriate place in the superior vena cava (SVC) (Fig. 1). Mechanical ventilation was discontinued 72 h post-NICU admission because of improved respiratory condition and normal automatic breathing. After extubation, low-flow oxygen therapy was continued and low-volume feeding was initiated based on his tolerance. His weight gain was acceptable and the clinical situation improved, including a gradual increase in the feeding volume and respiratory support. On day 10 post-NICU admission, he suddenly developed hypotonia, apnea, hypoxia, and bradycardia. He was gasping, had hypotension, and there was an absence of peripheral pulses. In the first minutes after the alarm signs, resuscitation was initiated and ventilation support provided, together with administration of inotropic drugs (1–3 minutes). Despite the high-frequency setup of the mechanical ventilator, the endotracheal tube was checked for displacement or obstruction due to his persistent critical condition (hypotension and shortness of breath). Pneumothorax and equipment failure were also ruled out. Several medical measures were initiated (approximately at minutes 3–4), including nothing by mouth (NPO), high-dose antibiotic therapy, emergency echocardiography, brain ultrasound, arterial and venous blood sampling, blood cell count, and arterial blood gas analysis. Echocardiography was performed over the next 5–7 minutes (Fig. 2), and the results showed SVC perforation caused by the catheter, severe pericardial effusion, right atrial collapse, ventricle dysfunction, and tamponade. The ejection fraction value was 40%, and there was no evidence of atrial septal defect (ASD), pleural effusion, or patent ductus arteriosus (PDA). A peripheral venous catheter was inserted, and the PICC was removed at the same time. Urgent pericardiocentesis was performed through subxiphoid cannulation guided by echocardiography and 10 ml of the pericardial fluid was aspirated (over the next 7–15 minutes) (Electronic Supplementary Material file 1: Video S1). The aspirated fluid was sent to the laboratory for tests, with the results showing severe acidosis (pH 6.80) and hyperglycemia (Table 1). To improve the hyperglycemia and metabolic acidosis, the patient was hydrated with low glucose solution and bicarbonate was initiated. Respiratory support was continued and antibiotics covering Staphylococcus aureus* and Gram-negative bacteria were administered. Brain sonography was also performed, which was normal. The workup sequence is shown in Table 2. Under mechanical ventilation the respiratory parameters improved gradually; pericardial drainage and PICC removal occurred concurrently. O₂ saturation increased to 95%, blood pressure elevated, and vital signs remained stable. Analysis of the aspirated pericardial fluid showed a hyperglycemic fluid (Table 3). A dramatic improvement in the neonate’s clinical responses (after pericardial drainage and PICC removal) was suggestive of PICC displacement, pericardial perforation, and cardiac tamponade. Echocardiography was repeated (×3) every 12 hours to ensure no further pericardial effusion was present. On day 40 after birth, the patient was still in the hospital but showed weight gain; he was in good condition without requiring respiratory support. Discussion and conclusion It is common practice to insert PICC lines for parenteral administration in preterm neonates. Although PICC lines are associated with a number of catheter-related complications, such as infection, catheter block, catheter migration, thromboembolism, and catheter damage, pericardial effusion following PICC insertion is an unusual complication [10]. In the case presented here, we highlight the potential risk of pericardial effusion with tamponade as a fatal complication in a neonate 1 week after PICC insertion. Although this complication is rare and uncommon following PICC insertion (0.5–2%) [11], the diagnosis was suspected immediately in our case and confirmed by echocardiography. The patient recovered gradually after urgent removal of the PICC line followed by pericardiocentesis. Regarding the etiology of tamponade, we believe that the catheter tip eroded the catheterized vessel (SVC) and perforated the pericardium, allowing the infused fluid to move into the pericardial space. This flow of fluid into the pericardia space subsequently increased the pressure on the cardiac chambers, resulting in cardiac tamponade. In accordance with our findings, da Silva Dornaus et al. also reported a preterm neonate (30 weeks) with cardiac tamponade secondary to PICC [8]. The neonate showed episodes of bradycardia, low O₂ saturation, cyanosis, dyspnea, and worsening of clinical condition 5 days after PICC insertion. Radiography and echocardiography examinations revealed that the tip of the catheter was in the cardiac chamber with pericardial effusion and signs of tamponade. These authors also reported improvement in the neonate’s clinical situation after immediate cardiac puncture and extraction of 25 mL of fluid similar to the infused solution [8]. An autopsy study by Warren et al. also showed pericardial effusion with tamponade in five neonates who died unexpectedly and suddenly after receiving parenteral nutrition via PICC. The autopsy findings showed endocardial injury and pericardial filling with permeation of a hyperosmotic parenteral fluid [12]. Iyer et al. reported cardiac tamponade in a 29-week-old preterm neonate with a sudden arrhythmia, ### Table 1 Results of arterial blood gas and laboratory blood tests \| Factors \| Before pericardiocentesis (range) \| After pericardiocentesis (range) \| \|-------------------------------\|-----------------------------------\|----------------------------------\| \| Arterial blood gas results \| \| \| \| pH \| 6.8 \| 7.37 \| \| Partial pressure of carbon dioxide (PmmHg) \| 24 \| 34 \| \| Partial pressure of oxygen (mmHg) \| 55 \| 106 \| \| O₂ saturation (%) \| – \| 98 \| \| HCO₃ (meq/L) \| – \| 19.7 \| \| Base excess (mEq/L) \| – \| – 50 \| \| Blood tests \| \| \| \| Hemoglobin (g/dL) \| 13 \| \| \| Hematocrit (%) \| 42.7 \| \| \| Platelet (cells/mcL) \| 150,000 \| \| \| Mean corpuscular volume (fL) \| 122.3 \| \| \| Mean corpuscular hemoglobin (pg) \| 37.2 \| \| \| Mean corpuscular hemoglobin concentration (g/dL) \| 30.4 \| \| \| White blood cells (cells/mcL) \| 14,200 \| \| \| Neutrophils (cells/mcL) \| 42 \| \| \| Eosinophils (cells/mcL) \| 3 \| \| \| Monocytes (cells/mcL) \| 5 \| \| \| Lymphocytes (cells/mcL) \| 50 \| \| \| Creatinine (mg/mL) \| 0.7 \| \| \| Natrium (mmol/L) \| 139 \| \| \| Calcium (mg/dL) \| 9 \| \| \| Potassium (mmol/L) \| 5.2 \| \| \| Magnesium (mEq/L) \| 2.3 \| \| \| C-reactive protein (mg/L) \| 1 \| \| \| Blood sugar (mg/dl) \| 850 \| 131 \| \| Throxine (pmol/L) \| 9.3 \| \| \| Thyroid-stimulating hormone (mlU/L) \| 0.6 \| \| \| Free thyroxine (pmol/L) \| 0.9 \| \| \| Blood culture \| Negative \| Negative \| ### Table 2 Sequence of performed workups following onset of alarms \| Sequential steps \| Measures \| Time (minutes following first alarm signs) \| \|------------------\|--------------------------------------------------------------------------\|------------------------------------------\| \| 1 \| Resuscitation, ventilation supports, administration of inotropic drugs \| 1–3 \| \| 2 \| Request for medical measures, including nothing by mouth, high-dose antibiotic therapy, emergency echocardiography, brain ultrasound examinations, and blood sampling \| 3–4 \| \| 3 \| Echocardiography examination \| 5–7 \| \| 4 \| Peripheral venous line catheterization, PICC removal, and pericardiocentesis \| 7–15 \| \| 5 \| Hydration and bicarbonate infusion \| 15–20 \| \| 6 \| Initiation of antibiotic therapy \| 20–23 \| \| 7 \| Brain sonography \| 23–25 \| PICC Peripherally inserted central catheter unstable vital signs, and decreased O₂ saturation. The neonate recovered after emergency intubation, administration of inotropic agents, and fluid aspiration from the pericardial space using an echocardiography-guided tap [10]. It should be noted that in cases with cardiac tamponade, the signs and symptoms may be non-specific and misleading (dyspnea, chest pain, tachycardia, hypotension, and non-palpable peripheral pulses). It is important that all infusions through the PICC must be stopped when tamponade is suspected. It has also been reported that in addition to catheter displacement, other factors, such as the material, length, and size of the catheter, duration of parenteral nutrition, osmolarity, and composition of the infused fluids may severely affect and worsen complications and outcomes related to cardiac tamponade. For example, it was reported in one study that pericardial presence of high-potassium infused fluid resulted in electrocardiogram alterations showing a pattern of hyperkalemia instead of a pattern of cardiac tamponade [1, 9, 12]. Another study also showed that tamponade was frequently observed in cases with PICC inserted through a peripheral vein compared to a central vein [4]. In conclusion, the case presented here highlights the potential risk of cardiac tamponade following central line insertion with sudden and unexpected symptoms associated with cardiovascular collapse. In such conditions, it is important to rapidly confirm that the catheter tip had migrated into the pericardial space and urgently initiate pericardiocentesis and catheter removal, all of which are effective measures to prevent death. Based on our and previous cases, we strongly recommend using catheters with soft tips, minimizing the movements of the neonates, and checking the catheter position periodically to reduce the risk of perforation and prevent life-threatening complications. Moreover, pericardial effusion with tamponade should be suspected in every case with PICC, and all neonatologists should be aware of this clinical emergency and the steps to be taken [1, 10]. Further studies are also needed to suggest other preventive strategies. Abbreviations ASD: Atrial septum defect; CPAP: Continuous positive airway pressure; NICU: Neonatal intensive care unit; NPO: Nothing by mouth; PDA: Patent ductus arteriosus; PICC: Peripherally inserted central catheter; RDS: Respiratory distress syndrome; SIMV: Synchronized intermittent mandatory ventilation; SVC: Superior vena cava. Supplementary Information The online version contains supplementary material available at https://doi.org/10.1186/s13256-022-03506-4. Additional file 1. Video S1. Acknowledgements This study was supported by Tehran University of Medical Sciences (TUMS) and the Maternal, Fetal, and Neonatal Research Center. The authors appreciate their kind support. Author contributions The design, experiment, and preparing the manuscript were carried out by MRZ and MH. The authors approved the content of the manuscript. Funding This study was supported by Tehran University of Medical Sciences and the Maternal, Fetal, and Neonatal Research Center. Availability of data and materials The datasets are available from the corresponding author on reasonable request. Declarations Ethics and consent to participate The present investigation was approved by the Institutional Review Board of Tehran University of Medical Sciences based on the Helsinki Declaration of 1964 (IR.TUMS.REC.1400.387). The participant’s parents provided written consent. The information was confidential and no extra expenses were imposed. Consent for publication Written consent was obtained from the patient’s parent for publication of this case report and any accompanying images. A copy of written consent is available for review by the Editor-in-Chief of this journal. Competing interests The authors declare no competing interests. Author details 1 Maternal, Fetal, and Neonatal Research Center, Family Health Institute, Tehran University of Medical Sciences, Sarv Ave., North Nejatolah Street, Tehran 1598718311, Iran. 2 Department of Neonatology, Yas Women Hospital, Tehran University of Medical Sciences, Tehran, Iran. Received: 7 April 2021 Accepted: 26 June 2022 Published online: 28 July 2022 References 1. Orme RLE, McSwiney M, Chamberlain-Webber R. Fatal cardiac tamponade as a result of a peripherally inserted central venous catheter: a case report and review of the literature. Br J Anaesth. 2007;99(3):384–8. --- Table 3 Results of laboratory analysis of aspirated pericardial fluid \| Factors \| Range \| \|-------------------------------\|-------\| \| Glucose (mg/dL) \| 2233 \| \| White blood cell (cells/µL) \| – \| \| Red blood cell (cells/µL) \| 300 \| \| Lactate dehydrogenase (units/L) \| 63 \| \| Protein (g/L) \| 108 \| \| Culture \| Negative \| 2. Chenoweth KB, Guo J-W, Chan B, Dowling D, Thibeau S. The extended dwell peripheral intravenous catheter is an alternative method of NICU intravenous access. Adv Neonatal Care. 2018;18(4):295. 3. Karapinar B, Cura A. Complications of central venous catheterization in critically ill children. Pediatr Int. 2007;49(5):593–9. 4. Colomina MJ, Godet C, Pellisé F, González MÁ, Bago J, Villanueva C. Cardiac tamponade associated with a peripheral vein central venous catheter. Pediatr Anesth. 2005;15(11):988–902. 5. Chiang M-C. Neonatal percutaneous central venous catheters: equations for the inserted length and locations of the insertion sites. Pediatr Neonatal. 2019;60(3):235–6. 6. Chen H, Ou-Yang M-C, Chen F-S, Chung M-Y, Chen C-C, Liu Y-C, et al. The equations of the inserted length of percutaneous central venous catheters on neonates in NICU. Pediatr Neonatal. 2019;60(3):305–10. 7. Bashir RA, Callejas AM, Osovich HC, Ting JY. Percutaneously inserted central catheter-related pleural effusion in a level III neonatal intensive care unit: a 5-year review (2006–2012). J Parenter Enter Nutr. 2017;41(7):1234–9. 8. Dornaus MFPDS, Portella MA, Warth AN, Martins RAL, Magalhães M, Deutsch ADA. Cardiac tamponade due to peripheral inserted central catheter in newborn. Einstein (São Paulo). 2011;9(3):391–3. 9. Ridler S, Nixon C. Peripherally inserted central catheter causing life-threatening cardiac tamponade. Anaesthesia Cases. 2014;2(2):84–7. 10. Iyer VHA, Sharma DM, Charki S, Mohanty PK. Cardiac tamponade in a neonate: a dreadful condition—need for functional echo. Case Rep. 2014;2014:bcr2014207040. 11. Department of Health of England, Donaldson LJ. Review of the deaths of four babies due to cardiac tamponade associated with the presence of a central venous catheter. 2001. https://www.researchgate.net/publication/320020659_Review_of_the_Deaths_of_Four_Babies_due_to_Cardiac_Tamponade_associated_with_the_presence_of_a_Central_Venous_Catheter. 12. Warren M, Thompson KS, Popek EJ, Vogel H, Hicks J. Pericardial effusion and cardiac tamponade in neonates: sudden unexpected death associated with total parenteral nutrition via central venous catheterization. Ann Clin Lab Sci. 2013;43(2):163–71. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4130, 1 ], [ 4130, 7903, 2 ], [ 7903, 12288, 3 ], [ 12288, 17168, 4 ], [ 17168, 22179, 5 ], [ 22179, 24527, 6 ] ] }
c75a63be51000dab29299dcaf11116610d0cfe8d	{ "olmocr-version": "0.1.59", "pdf-total-pages": 18, "total-fallback-pages": 0, "total-input-tokens": 50314, "total-output-tokens": 17972, "fieldofstudy": [ "Chemistry", "Physics" ] }	Distortion dependent intersystem crossing a femtosecond time-resolved photoelectron spectroscopy study of benzene, toluene, and p-xylene Stephansen, Anne Boutrup; Sølling, Theis Ivan Published in: Structural Dynamics DOI: 10.1063/1.4977735 Publication date: 2017 Document version Publisher's PDF, also known as Version of record Document license: CC BY Citation for published version (APA): Stephansen, A. B., & Sølling, T. I. (2017). Distortion dependent intersystem crossing: a femtosecond time-resolved photoelectron spectroscopy study of benzene, toluene, and p-xylene. Structural Dynamics, 4(4), [044008]. https://doi.org/10.1063/1.4977735 Distortion dependent intersystem crossing: A femtosecond time-resolved photoelectron spectroscopy study of benzene, toluene, and p-xylene Anne B. Stephansen and Theis I. Sølling Citation: Structural Dynamics 4, 044008 (2017); doi: 10.1063/1.4977735 View online: http://dx.doi.org/10.1063/1.4977735 View Table of Contents: http://aca.scitation.org/toc/sdy/4/4 Published by the American Institute of Physics Articles you may be interested in Optically induced lattice deformations, electronic structure changes, and enhanced superconductivity in YBa2Cu3O6.48 Structural Dynamics 4, 044007044007 (2017); 10.1063/1.4977672 A comparison of the innate flexibilities of six chains in F1-ATPase with identical secondary and tertiary folds; 3 active enzymes and 3 structural proteins Structural Dynamics 4, 044001044001 (2016); 10.1063/1.4967226 Localized holes and delocalized electrons in photoexcited inorganic perovskites: Watching each atomic actor by picosecond X-ray absorption spectroscopy Structural Dynamics 4, 044002044002 (2016); 10.1063/1.4971999 A general method for baseline-removal in ultrafast electron powder diffraction data using the dual-tree complex wavelet transform Structural Dynamics 4, 044004044004 (2016); 10.1063/1.4972518 Femtosecond dynamics of the 2-methylallyl radical: A computational and experimental study Structural Dynamics 147, 013902013902 (2017); 10.1063/1.4974150 Structural enzymology using X-ray free electron lasers Structural Dynamics 4, 044003044003 (2016); 10.1063/1.4972069 The competition between ultrafast intersystem crossing and internal conversion in benzene, toluene, and p-xylene is investigated with time-resolved photoelectron spectroscopy and quantum chemical calculations. By exciting to $S_2$ out-of-plane symmetry breaking, distortions are activated at early times whereupon spin-forbidden intersystem crossing becomes (partly) allowed. Natural bond orbital analysis suggests that the pinnacle carbon atoms distorting from the aromatic plane change hybridization between the planar Franck-Condon geometry and the deformed (boat-shaped) $S_2$ equilibrium geometry. The effect is observed to increase in the presence of methyl-groups on the pinnacle carbon-atoms, where largest extents of $\sigma$ and $\pi$ orbital-mixing are observed. This is fully consistent with the time-resolved spectroscopy data: Toluene and p-xylene show evidence for ultrafast triplet formation competing with internal conversion, while benzene appears to only decay via internal conversion within the singlet manifold. For toluene and p-xylene, internal conversion to $S_1$ and intersystem crossing to $T_3$ occur within the time-resolution of our instrument. The receiver triplet state ($T_3$) is found to undergo internal conversion in the triplet manifold within $\approx 100–150$ fs (toluene) or $\approx 180–200$ fs (p-xylene) as demonstrated by matching rise and decay components of upper and lower triplet states. Overall, the effect of methylation is found to both increase the intersystem crossing probability and direct the molecular axis of the excited state dynamics. © 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4977735] I. INTRODUCTION Benzene and its singly and doubly methylated derivatives toluene and xylenes (Figure 1) exhibit similar photoinduced properties, but the presence of methyl groups entails subtle differences between the three substances that mark themselves in ultrafast time-resolved investigations. Photoinduced properties of benzene have been extensively studied for decades, yet controversy on certain aspects persists.1–7 One example is the observation of ultrafast intersystem crossing (ISC) competing with internal conversion (IC).1,3,4 ISC, the non-radiative spin-forbidden transition between two electronic states of different spin-multiplicity, is conventionally expected to be slow compared to IC, the equivalent transition between two states of the same multiplicity. Electron spin-flip requires that a magnetic torque, such as spin-orbit coupling, acts on the spin.8 Spin-orbit couplings are frequently evaluated with the Breit-Pauli Hamiltonian to which the associated expectation value scales with the fourth power of the nuclear charge,9 demonstrating the commonly anticipated sensitivity of spin-orbit couplings and ISC efficiencies towards the presence of heavy atoms. In organic chemistry where heavy atoms are sparse, the probability of an ISC process is often estimated from El-Sayed’s rule10 stating that ISC becomes partly spin-allowed if it is paired with a simultaneous change in orbital angular momentum thereby ensuring overall conservation of angular momentum. This propensity rule rationalizes why ISC processes between for instance $^3(n, \pi^)$ and $^1(\pi, \pi^)$ states can be efficient in some hetero-atom containing organic molecules. Benzene exhibits neither heavy atoms to enhance spin-orbit couplings nor heteroatoms to facilitate classic El-Sayed type transitions. The only immediately apparent ISC transition ensuring angular momentum conservation involves $\sigma$-orbitals; however, $\sigma$ and $\pi$ orbitals do not mix in planar geometries like that of ground state benzene. Ultrafast ISC in benzene is therefore not immediately expected. In this contribution, we assess the competition between IC and ISC as $S_2$ deactivation pathways for benzene, toluene, and $p$-xylene (boxed in Figure 1) via femtosecond (fs) time-resolved photoelectron spectroscopy (TRPES) investigations. The inclusion of methylated analogues reveals otherwise elusive information on the unexpected IC vs. ISC competition. The conventional notion that ISC fundamentally is slower than IC has been challenged by several experimental observations presented during the past decade, where ISC processes have been reported to occur on the timescale of molecular vibrations (fs to picoseconds12). The (non-exhaustive) list of organic systems reported to exhibit ultrafast ISC includes a variety of molecules such as nitroaromatic compounds,13–24 some natural nucleobases25–28 but particularly the thionated analogues,26,29–35 molecules known from photovoltaic applications such as perylene diimide,36 poly-methines,37 perylene bisimide,38 and familiar organic solvents such as benzene,3,4 ortho- and meta-xylenes,39–42 and small liquid esters;43 thus, molecules vary in both size and functionality. This diversity suggests that ultrafast ISC could be a general phenomenon. However, in comparison to IC, the importance and behavior of ISC in the ultrafast time regime are much less established. For IC, it has been shown that the ultrafast nature of the process rests on large degrees of non-ergodicity;44,45 in other words, only a few vibrational modes are active during the transition. If the vibrations that are activated upon photon absorption couple different electronic surfaces, the possibility of an ultrafast transition is available and can occur within the timescale of the respective vibrational period. IC and ISC are fundamentally similar,9 and thus, ISC should also be able to occur within a vibrational period. Yet, the requirement of angular momentum conservation persists, and an ultrafast ISC process should preferentially occur along vibrational coordinates that ensure spin-flip compensation. Planar aromatic hydrocarbons like benzene must therefore activate symmetry breaking modes6,11 that allow mixing of $\sigma$ and $\pi$ orbitals at early times for ultrafast ISC to occur. This entails initial activation of out-of-plane modes forming pseudo-radicaloid species. Figure 2 shows an example of such distortion, where the prefulvene-like coordinate is exemplified as the out-of-plane deformation mode. Such mechanism exactly corresponds to the ISC mechanism suggested by the groups of Fielding and Worth for the $S_1 \rightarrow T_2$ ISC in benzene.$^{1,3,4}$ The frequencies of such modes will depend on the presence of methyl-substituents on the pinnacle carbon atom(s) distorting from the molecular plane.$^{46,47}$ The pinnacle carbon atoms are expected to be the ones carrying the methyl-substituents due to the stabilizing effect of methyl-groups on the un-paired electron of the quasi-radicaloid prefulvene-like structure.$^{48}$ This reasoning is fully consistent with the observation that the lowest triplet states of toluene and $p$-xylene exhibit quinoidal structures (Figure 2) with the methyl-groups positioned to support the diradicaloid species as found by EPR measurements$^{49,50}$ and quantum chemical calculations.$^{48}$ Quinoidal triplet structures of benzene derivatives have further been observed by time-resolved electron diffraction experiments by Zewail and coworkers.$^{51}$ Triplet energies and the frequency of the modes that could mediate ISC in benzene and its derivatives are therefore expected to be sensitive towards methylation. The rich photophysics of benzene can briefly be summarized as follows: Resonant excitation to $S_1$ is followed by fluorescence and a slow (nanosecond timescale) ISC pathway$^{52–56}$ and these channels are often referred to as channel 1 and channel 2, respectively. When the excitation energy is increased 3000 cm$^{-1}$ above the $S_1$ onset, the fluorescence yield decreases drastically due to activation of a third channel (the controversial “channel 3” first reported by Callomon in the 1960s$^{57}$), which has been identified as an ultrafast non-radiative process of IC and/or ISC character.$^{58–62}$ The crossing points to both the triplet manifold and the singlet ground state are reached via prefulvene-like out-of-plane distortion positioned just behind an activation barrier of $\approx 3000$ cm$^{-1}$. With 12 permutational isomers of the minimum energy prefulvene conical intersection that can be inter-connected via various conformational routes, prefulvene-like conical intersections are posited to play a significant role for the photoinduced processes of benzene.$^{6,63,64}$ A prefulvene-like conical intersection is also proposed to mediate IC from $S_2$ to $S_1$ in both benzene and toluene, which is found to occur on a 40–60 fs timescale.$^{47,65–67}$ The involvement of a prefulvene-like conical intersection for the $S_2/S_1$ IC is in line with the theoretical finding that the equilibrium structure of $S_2$ is boat-shaped$^{64}$ along with the notion that a boat-shaped geometry constitutes the crossing point between two prefulvenic isomers.$^6$ Importantly, the boat-shaped equilibrium structure of $S_2$ (Ref. 64) differs from the planar Franck-Condon geometry; this indicates that initial relaxation upon excitation to $S_2$ primarily should activate boat-type modes. Newer time-resolved mass spectrometry (TRMS) studies on toluene and $o$, $m$, and $p$-xylene along with$^{46,47}$ TRPES studies on $o$- and $m$-xylene explored non-radiative decays from $S_1$. These studies found that the $S_1 \rightarrow S_2$ transition proceeds via a full-boat distortion, while $S_2 \rightarrow S_1$ proceeds via half-boat distortions.$^{46,47}$ These interpretations were based on correlations between the observed decay rates and the position of methyl groups. Full-boat distortions are slowed down by methyl-groups in $p$-position, which accordingly slows down the IC process for $p$-substituted systems compared to toluene and the $o$-$m$-substituted analogues. The frequency of half-boat (prefulvene-like) distortions on the other hand is more affected by $o$-substitution than $p$-$m$-substitution due to steric congestion, which is in agreement with the observation of slower $S_2 \rightarrow S_1$ rates for $o$-xylene as compared to $p$-xylene and toluene. The TRPES studies on $o$-xylene also invoked ISC from $S_2$ to $T_3$ as a possible competing deactivation channel to explain an observed slightly slower decay component.$^{40–42}$ Qiu et al. also report observation of $S_2 \rightarrow T_3$ ISC in benzene$^{62}$ while other studies assessing the $S_2$ deactivation of benzene do not report observations on the ISC pathway.$^{65,66}$ In this contribution, we explore the $S_2 \rightarrow T_3$ channel further and assess what effect one or two methyl groups have on the dynamics of the benzene-skeleton. Upon excitation to $S_2$ early activation of out-of-plane distortions is expected. IC vs ISC competitions and the role of methylation are considered through comparison of the $S_2$ decay for benzene, toluene, and $p$-xylene measured by fs TRPES. The investigation is supported by quantum chemical calculations primarily assessing (changes in) hybridization of the bonding carbon-orbitals on the $S_2$ surface. The key motivation is to increase the understanding of ultrafast ISC and what effects promote ISC in a non-El-Sayed system. II. EXPERIMENTAL The setup for fs TRPES experiments consists of a fs pulsed laser system and a photoelectron spectrometer employing velocity map imaging (VMI) detection and has been described in detail previously.\textsuperscript{68,70} Briefly, the laser system consists of a Ti:Sapphire oscillator (Tsunami, Spectra Physics) and a regenerative amplifier system (Spitfire, Spectra-Physics) that eventually outputs 798 nm pulses of approximately 140 fs duration with an intensity of ca. 1 W at 1 kHz repetition rate. The pulses were split into two: 50% were used to generate the fourth harmonic of the fundamental (6.2 eV = 200 nm, ca. 1 mW intensity), which was used as pump pulse. The remaining 50% were sent through an optical parametric amplifier (TOPAS-C, Light Conversion), which was set to output pulses at three different energies 4.44 eV (279 nm, intensity of ca. 1.7 mW), 4.35 eV (285 nm, 1.9 mW), and 4.2 eV (295 nm, intensity of ca. 2.5 mW) used as the probe pulses in the experiments on benzene, toluene, and \textit{p}-xylene, respectively. The two beams were collected and focused collinearly into the region of interaction with the molecular beam. The cross-correlation between the two pulses was approximately 150 fs. The molecular beam of either benzene, toluene, or \textit{p}-xylene was generated by bubbling helium at approximately 2 bars over a cartridge containing the sample molecules, and the resulting gaseous solution was expanded into vacuum through a 1 kHz pulsed Even-Lavie valve. The valve temperature was controlled by a copper cooling loop containing a mixture of water and glycol to maintain a temperature of 28–30°C. The expansion was subsequently collimated by a skimmer focusing the molecular beam towards the interaction chamber, where it was intersected at right angles with the laser beams. Upon interaction with the pump pulses (6.2 eV), the molecules were excited slightly above the \textit{S}_2\textit{threshold} (the resonant \textit{S}_2\textit{values} are reported to be benzene: \textit{S}_2\textit{values}: 6.03 eV, toluene: 5.83 eV, and \textit{p}-xylene: 5.68 eV (Refs. 71 and 72)). The \textit{S}_3\textit{onsets} are \textit{S}_3\textit{onsets} >6.7 eV, i.e., well above the pump photon energy.\textsuperscript{71} After a well-defined time-delay, the probe pulses ionized to (mainly) \textit{D}_0\textit{positioned} 9.24 eV, 8.8 eV, and 8.4 eV above the ground state equilibrium.\textsuperscript{71,72} The generated photoelectrons are focused by classic Eppink-Parker VMI ion-optics.\textsuperscript{68} The photoelectrons were detected by a set of 2D position sensitive MCPs on top of a phosphor screen (Photonis) imaged by a monochrome CCD camera. For each data collection acquisition, equivalent pump-only/probe only data were collected and subsequently subtracted to eliminate scattering noise obscuring the data. The photoelectron images were reconstructed using an inverse Abel transformation and calibrated from signals on dimethyl isopropyl amine and butadiene.\textsuperscript{69} The experiments were corroborated by quantum mechanical calculations. State averaged complete active space self-consistent field (SA-CASSCF) with a 6–31G* basis set and an active space of 6 electrons in 6 orbitals for benzene (denoted [6,6]) and [8,8] for toluene and \textit{p}-xylene was used to optimize equilibrium structures of \textit{S}_0\textit{, and frequency calculations on the optimized geometries were used to verify that the geometries represent minimum energy structures. The minimum energy \textit{S}_2\textit{ structure of benzene was optimized on the same level of theory. The \textit{S}_2\textit{ geometry optimization of toluene and \textit{p}-xylene unfortunately did not converge to minimum energy structures, but either converged to planar structures with two imaginary frequencies (as also previously reported for benzene\textsuperscript{64}) or cycled around highly distorted structures in a manner indicating that (cumbersome) full configuration interaction is required in order to optimize the non-planar structures that strongly depend on hyper-conjugation effects, when methyl groups are present. To extract information on the \textit{sp}^n\textit{ hybridization of the carbon atoms, natural bond orbital} (NBO) analyses were made on the SA-CASSCF optimized \textit{S}_0\textit{ and \textit{S}_2\textit{ geometries (when present). Excitation and ionization energies of the optimized \textit{S}_0\textit{ structures of benzene, toluene, and \textit{p}-xylene were evaluated with coupled cluster singles and doubles (CCSD) and the aug-cc-pvdz basis set. All calculations were performed within the Gaussian09 program package.} III. RESULTS AND ANALYSIS A. Computational results The molecular geometries that are key for the current investigation involve the Franck-Condon structures, which correspond to the $S_0$ equilibrium structure, and the $S_2$ equilibrium structure towards which the excited molecules will start to relax. The optimized $S_0$ equilibrium structures of all three molecules were non-surprisingly found to be fully planar, while the $S_2$ minimum of benzene was found to be boat-shaped with the dihedral angle of the pinnacle carbon atoms being $27.1^\circ$ in agreement with the previously reported structure. The coordinates of all structures are given in the supplementary material, while the structures are shown in tube-format in Figure 3 along with the results from the NBO analysis. NBO methods provide a means to gather intuitive chemical insight (in the framework of conceptual models from VB theory and Lewis-like structures) from highly accurate quantum chemical calculations. The current NBO analyses were used to extract information from the SA-CASSCF calculated structures in terms of the orbital-hybridization, which is a somewhat illusory property related to the mixing or symmetry-breaking of pure $s$ and $p$-orbitals. Yet, it provides an intuitive and practical way of interpreting and discussing the consequences of local changes in the structures. The NBO analyses were performed with primary focus on the aromatic carbon atoms that constitute the chromophore and the carbon atoms of the methyl groups. The central results from the NBO analysis are summarized in Figure 3; the ground state optimized structures of all three molecules are shown in the top and the distorted $S_2$ minimum energy structure of benzene is shown in the bottom. The numbers refer to the $s$-character of the $sp^3$ orbitals on carbon engaging in the $\sigma$-bonds, where $36\%$ refers to the amount $s$-character for fully planar, non-perturbed $S_0$ benzene, and the $\pm$ percentages refer to the increase or decrease of $s$-character induced by methylation or geometrical distortion. Note, a decrease in $s$-character yields more $sp^3$-like (i.e., methyl-like) carbon orbitals, which are more prone to form $\sigma$-bonds, which simultaneously implies that less $p$-character is available to form $\pi$-bonds. The amounts of $s$-character were consistently found to be balanced mainly by $p$-character, while the amounts of $d$-character were negligible. As can be seen in Figure 3, going from a fully planar to a boat-shaped structure induced significant amounts of $s$ and $p$ mixing, where all carbon atoms attain $sp^3$-like $sp^2$-character. When the perturbation instead is invoked by methylation, the carbon atoms connected to the methyl groups attain even larger $sp^3$-like character, while the reversed mixing is observed for the remaining carbon atoms albeit to a smaller extent. This mainly reflects that the hybrid-orbitals of a single carbon atom differ depending on whether they engage in bonds with the aromatic ring or the methyl groups and suggest that these orbitals may be more susceptible to ![FIG. 3. Natural bond orbital (NBO) analysis for benzene, toluene, and p-xylene. The numbers indicate the amount of $s$-character in the $sp^3$-hybrid orbitals relative to the $sp^2$-orbitals of planar benzene (corresponding to the $S_0$ equilibrium structure). The changes were found to be balanced by equal changes in $p$-character. See the text for further details.](image-url) rehybridization effects upon distortion. The extent of s-p mixing is found to be similar for toluene and p-xylene, yet with an additional carbon atom exhibiting large mixing in the case of p-xylene. As the S_2 geometry optimizations of toluene and p-xylene did not converge, the extent of orbital scrambling when both perturbations are present could not be assessed directly; regardless, these results indicate that the methylated species are more susceptible to orbital mixing. The lowest singlet and triplet state energies are key to understand the TRPES data. Numerous experimental and calculated energy values have been reported largely agreeing with the SA-CASSCF//CCSD/aug-cc-pvdz values calculated in the current work. The relevant energy values are summarized in Table I. Herein are also included ionization energies, probe photon energies as well as the expected electron kinetic energy (eKE) of the photoelectrons associated with 0–0 transitions (italicized). As apparent from Table I, the number of electronic states that can be probed in the current experiments and the associated eKE values vary between the three molecules. B. Experimental results The photoinduced S_2 dynamics of benzene, toluene, and p-xylene were studied in 1 pump + 1 probe photon photoexcitation and ionization schemes, and the probe energies and intensities were chosen to minimize parallel multiphoton processes. Background subtraction confirmed that the contribution from parallel processes is negligible. Representative contour plots associated with the TRPES experiments on benzene, toluene, and p-xylene are shown in Figures 4(a)–4(c); eKEs are shown on the y-axis while the x-axis indicates the temporal delay between the laser pulses. The TRPES data show significant similarities for the three molecules: (i) all contour plots exhibit large diffuse energy features near time-zero consistent with previously reported photoelectron spectra of these molecules, (ii) rapidly decaying signal intensities are observed in large energy areas, and (iii) to long time-delays signal intensity is primarily observed at low eKEs. The contour plots also exhibit clear differences: (i) p-xylene exhibits a clear signal at 0.95–1.2 eV not immediately visible for benzene and toluene, (ii) progressively (but only slightly) later arrival times and slower dynamics are observed in the low eKE regimes upon increasing methylation (this is most prominent near zero eKE of toluene and p-Xylene), and (iii) more distinct spectral features at early times for benzene and p-xylene as compared to toluene, i.e., the diffuse broad spectra near time-zero show more structure in the data sets of benzene and p-xylene. \| TABLE I. Ionization (D_0) and vertical excitation energies of benzene, toluene, and p-xylene calculated using SA-CASSCF//CCSD/aug-cc-pvdz. The probe energies (hν_{probe}) and the electron kinetic energies (eKE) of the resulting photoelectrons are also summarized. The grey/shaded regions can be white/clear. They were only included to separate the toluene results from those of benzene and p-xylene. \| \|---------------------------------\|---------------------------------\|---------------------------------\| \| Benzene \| Toluene \| p-Xylene \| \| hν_{probe} \| 4.44 \| 4.35 \| 4.2 \| \| D_0 \| 9.24 \| 8.8 \| 8.4 \| \| Vertical excitation (eV) \| eKE (eV) \| Vertical excitation (eV) \| eKE (eV) \| Vertical excitation (eV) \| eKE (eV) \| \| S_2 \| 6.03^a \| 1.2 \| 5.83^a \| 1.38 \| 5.68^a \| 1.48 \| \| S_1 \| 4.72^a \| “0” \| 4.64^a \| 0.19 \| 4.55^a \| 0.35 \| \| T_3 \| 5.6 ± 0.2^b \| 0.4 ± 0.2 \| 5.5 ± 0.2^b \| 1.05 ± 0.2 \| 5.3 ± 0.2^b \| 1.1 ± 0.2 \| \| T_2 \| 4.7 ± 0.2^b \| ... \| 4.5 ± 0.2^a \| 0.05 ± 0.2 \| 4.3 ± 0.2^b \| 0.1 ± 0.2 \| \| T_1 \| 3.7 ± 0.2^d \| ... \| 3.6 ± 0.2^c \| ... \| 3.5 ± 0.2^e \| ... \| ^aReference 71. ^bReference 72. ^cFrom Ref. 72 adjusted slightly to match the current calculations. ^dAverage of Refs. 72 and 75 and in agreement with the current calculations. ^eAverage of Refs. 72 and 76 and in agreement with the current calculations. By comparison with Table I, $S_2$ features are expected in the high eKE range of the spectra, and possible $T_3$ features are expected at intermediate energies just below $S_2$. Only the highly vibrationally excited edge of $S_1$ can be probed for benzene and should appear near zero eKE values, while $S_1$ is expected 0.6–0.7 eV below $T_3$ in toluene and $p$-xylene. For benzene and $p$-xylene, $T_2$ should appear near $eKE = 0–0.2$ eV. The broad and diffuse spectral features observed partly result from a wide envelope of vibrational ionizations but possibly also due to electronic transitions occurring faster than the temporal resolution of the laser ($\approx 150$ fs) yielding broadened and diffuse features. The temporal evolution of the photoelectron spectra was evaluated by fitting the channel integrated and normalized signals. Due to the continuous spectral features, it is not immediately apparent how to integrate the spectra, and thus several different integration regimes were explored to optimize a fair treatment of the data. The final integrations were based on the observed dynamics and further chosen to match the energy areas expected for the respective singlet and triplet states given in Table I. In each case, energy regions representing, respectively, $S_2$, $S_1^/T_3$ (where denotes vibrational excitation), and $S_1$ were evaluated. Additionally, energy regimes corresponding to $T_2$ were evaluated for toluene and $p$-xylene, and for $p$-xylene a highly excited $S_1^$ area was also explored as signal intensity was observed in an area mainly matching highly excited $S_1$ (0.5–0.95 eV). The integrated transients were fit to a sum of exponential functions convoluted with a Gaussian response function. In the cases where relaxed $S_1$ could be probed (toluene and $p$-xylene), the $S_1$ transients exhibit long lifetime components, which here is taken into account by adding a constant offset after time-zero as the signal intensity extends far beyond (100s of nano-second) the picosecond time regime explored here. The number of exponential functions required to fit the data varied across the spectrum; the fitted time-constants along with the integrated energy regions are summarized in Table II, where $\tau_{\text{rise}}$ indicates rise-times, $\tau_{\text{fd}}$ and $\tau_{\text{sd}}$ denote fast and slow decays, respectively, while “- -” indicates that no extra exponential function was needed, i.e., cross correlation limited rise-times or mono-exponential decays. Attempts to fit the (ultrafast) rising behavior observed in the spectral regions of $T_3$ and $S_1$ yielded rise times 5–15 fs in all cases, indicating that the instrumental time-resolution (150 fs) is insufficient to capture the rise of these spectral features. The rise-times are therefore denoted with “- -” in Table II. It should be mentioned that the uncertainties indicated are solely based on the fitted values and included to reflect the variation in data quality. All time-constants shorter than the cross-correlation of $\approx 150$ fs can only be concluded to be faster than or equal to approximately 150 fs, though a reasonable agreement with previous results is observed even for the shortest time-components (in the cases where previous estimates exist). The transients including the associated fits are shown in Figures 5(a)–5(c). The assignments denoted in Table II and Figures 5(a)–5(c) are tentative and based on the calculated and previously reported energy values (Table I). While the spectral manifestation of, for example, the $T_3$ state of benzene is much more ambiguous.... FIG. 4. Contour plots showing the TRPES data recorded for (a) benzene (200 nm + 279 nm), (b) toluene (200 nm + 286 nm), and (c) $p$-xylene (200 nm + 295 nm). TABLE II. Integrated energy regions and the associated rise ($\tau_{\text{rise}}$) and decay ($\tau_{\text{fd}}$ or $\tau_{\text{sd}}$) times of the TRPES data on benzene, toluene, and p-xylene. "- -" denotes that no extra exponential function was needed to fit the data. Tentative assignments are indicated and discussed in the text, e.g., in the case of benzene the assignment of T3 is non-conclusive and the signal intensity should likely be ascribed excited S1$^{}$ instead. The grey/shaded regions can be white/clear. They were only included to separate the toluene results from those of benzene and p-xylene. \| eKE (eV) (state) \| $\tau_{\text{rise}}$ \| $\tau_{\text{fd}}$ (fs) \| $\tau_{\text{sd}}$ (ps) \| eKE (eV) (state) \| $\tau_{\text{rise}}$ \| $\tau_{\text{fd}}$ (fs) \| $\tau_{\text{sd}}$ (ps) \| eKE (eV) (state) \| $\tau_{\text{rise}}$ \| $\tau_{\text{fd}}$ (fs) \| $\tau_{\text{sd}}$ (ps) \| \|------------------\|----------------------\|------------------------\|------------------------\|------------------\|----------------------\|------------------------\|------------------------\|------------------\|----------------------\|------------------------\|------------------------\| \| 0.75–1.7 (S2) \| - - \| 40 ± 10 \| - - \| 0.8–1.75 (S2) \| - - \| 75 ± 5 \| - - \| 1.25–2 (S2) \| - - \| 100 ± 20 \| - - \| \| 0.5–0.7 (S1$^{}$ or T3) \| - - \| 55 ± 10 \| - - \| 0.6–0.8 (S1$^{}$ or T3) \| - - \| 75 ± 5 \| 14 ± 5 \| 0.95–1.2 (T3) \| - - \| 180 ± 20 \| 3.9 ± 0.8 \| \| 0–0.5 (S1$^{}$) \| - - \| 50 ± 10 \| 6.3 ± 0.7 \| 0.1–0.6 (S1$^{}$) \| - - \| 75 ± 5 \| 10 ± 0.5 \| 0.5–0.95 (S1$^{}$) \| - - \| 110 ± 20 \| 3.3 ± 0.4 \| \| 0–0.1 (S1 or T2) \| 150 ± 15 \| 12 ± 0.6 \| Off set \| 0–0.15 (T2) \| 200 ± 50 \| 5000 ± 400 \| - - \| than the equivalent of, e.g., \textit{p}-xylene, integration of the T\textsubscript{3} region of benzene is necessary in order to allow for comparative discussion. For the ease of the discussion, the signals will therefore be referred to accordingly in the remainder, and the validity and rationality of the assignments are discussed in Section IV. IV. DISCUSSION* The general similarity between the contour plots of the TRPES data of benzene, toluene, and \textit{p}-xylene suggests that their S\textsubscript{2} excited state deactivation dynamics are similar. Yet, the three contour plots are more different than what immediately would be expected. The most striking difference is the presence of a distinct signal at 0.95–1.2 eV for \textit{p}-xylene, which is not clearly apparent for benzene and toluene. The observed differences are likely due to subtle changes invoked by methylation that affect the relative prominence of the available S\textsubscript{2} deactivation channels for each of the three molecules. A simplified general Jablonski diagram representative for all three molecules is shown in Figure 6, which only includes the most obvious pathways available, while more complex pathways are omitted, as Figure 6 appears sufficient to discuss the current data. The deactivation pathways drawn are energetically available for all ![Diagram](image.png) FIG. 6. General and simplified Jablonski diagram showing what pathways are available from the Franck-Condon geometry of S\textsubscript{2} based on energetic considerations. three molecules, but the differences in the contour plots suggest that the channels are not equally active. While we acknowledge that the observed differences could be due to varying efficiencies of projection of the dynamics on to the observable (for example, different ionization cross sections), we will in the following discuss which and why certain channels could be more operative in some molecules relative to the other. Subsequently, the generalized Jablonski diagram of Figure 6 is resumed for each of the three species. A. S₂ deactivation: Competing IC and ISC Based on energetic proximity arguments and previous investigations, T₃ and S₁ are the most likely receiver states for S₂ deactivation. The most obvious and conventionally expected S₂ → S₁ relaxation pathway is posited to be a prefulvenic half-boat mode and IC is reported to proceed within 40–60 fs. This is consistent with the current observations of cross-correlation limited decays that can be fitted to 40–100 fs time components (Table II); the slightly longer timescale for p-xylene may be due to slight spectral overlap with the T₃ signal. The rapid cross-correlation limited decay of S₂ concomitant with the observation of signal intensity in the S₁ energy regimes that appear within the cross-correlation of the pump and probe pulses agrees well with a rapid S₂ → S₁ IC process as previously proposed. Close inspection of the early time dynamics in the S₁ regions shows that the S₁ signals reach their maximum intensities at slightly different times for the different molecules; Figure 7 shows a zoom in on the S₁ transients to early times, and as can be seen, the appearance time of the S₁ signal increases in the order (from early to late) benzene < toluene < p-xylene. It should be mentioned that only the upper edge of the S₁ state of benzene could be probed, and thus this observation should be interpreted cautiously. Nonetheless, the trend is consistent with the results from, e.g., Suzuki et al. on benzene and toluene and is interpreted to reflect the higher frequency of the prefulvenic mode for benzene than the methylated analogues yielding a faster S₂ → S₁ IC for benzene. The observation of a ca. 3–10 ps decay of the energy region corresponding to vibrationally excited S₁ is also consistent with earlier work, where it was ascribed IC to S₀. Vibrationally excited S₁ may undergo intramolecular vibrational energy redistribution concurrently with IC to S₀ obscuring the decay times somewhat. Since the IC channel has been the focus of previous studies, we will turn focus towards the possibility and manifestation of S₂ → T₃ transitions in the following. FIG. 7. S₁ transients for benzene (black), toluene (blue), and p-xylene (red) to early times. The zoom in highlights the difference appearance times of the three transients. The observation of an $S_2 \rightarrow S_1$ transition faster than 150 fs implies a highly non-statistical process mainy activating a few reaction coordinates largely determined by Franck-Condon factors and the topology of the potential energy surface near the Franck-Condon region. The current and previous calculations predict the $S_2$ equilibrium structure to be boat-shaped and distorted out-of-plane relative to the Franck-Condon geometry (Figure 3), and thus early activation of prefulvene-like or boat-shaped modes is expected. The highly non-statistical nature of the $S_2 \rightarrow S_1$ IC process suggests that any competing ISC process to form $T_3$ could occur along the same vibrational coordinate. This is similar to what has been proposed for the IC vs. ISC competition for $S_1$ deactivation of benzene (namely, that the transition to $S_0$ and $T_2$ occurs along similar coordinates) and further corroborated by theoretical studies by Cogan et al. showing a tendency for the spin-orbit coupling to increase at triple crossing points, e.g., where a crossing between two singlet surfaces coincides with a crossing to the triplet manifold. Importantly, the prefulvene-like modes break the symmetry of the aromatic ring and enable mixing of $\sigma$-character into the $\pi$-system. The NBO analysis summarized in Figure 3 shows that upon distortion to the boat-shaped $S_2$ minimum of benzene, the carbon orbitals undergo significant rehybridization in that all carbon atoms attain increased $sp^3$-$sp^2$-like characters, implying that the $\pi$-bonds become more $\sigma$-like and vice versa. Distortion and associated rehybridization thereby open the possibility for a partly allowed ISC process involving both $\sigma$ and $\pi$-orbitals. For toluene and $p$-xylene, the methyl carrying carbon atoms already possess notable amounts of $sp^3$-like character in the planar geometries indicating that these carbon-atoms may be even more susceptible to $\sigma$ and $\pi$ mixing. Considering the observation of ultrafast $S_2$ depletion, potential formation of $T_3$ should also likely occur within the cross-correlation of the two laser pulses. The distinct signal observed between 0.95 and 1.2 eV for $p$-xylene matches the expected energy region for $T_3$ and is observed to appear within the cross correlation similar to the $S_1$ signal. The observed signal between 0.95 and 1.2 eV does not match other electronic states of $p$-xylene energetically or dynamically (though the upper edge may overlap slightly with $S_2$). We therefore interpret this feature as an unusually clear manifestation of an upper triplet state of $p$-xylene. As recently discussed, rapid IC of upper triplet states often follow immediately after ISC due to high densities of states in the triplet manifold which in combination with (often) low triplet quantum yields make upper triplet states challenging to observe experimentally. The $T_3$ signal observed for $p$-xylene is thus surprisingly clear. Turning to benzene and toluene similar evidence for $T_3$ states is less prominent. In both cases, the spectra show signal intensity in the energy regions of the respective triplet states, but the features are much less distinct. This might be due to several effects involving smaller triplet yields and/or more rapid decay of $T_3$ as further discussed in Section IV B. At this point, $S_2$ can tentatively be concluded to decay to both $S_1$ and $T_3$ for $p$-xylene at notable (yet, not quantifiable) amounts, and only the $S_2 \rightarrow S_1$ channel is clear for benzene and toluene though some portions of the $S_2$ populations may convert to the triplet manifold; further indications of triplet formation or lack of the same are discussed in Section IV B. B. $T_3$ formation and deactivation efficiencies affecting the $T_3$ manifestation The spectral manifestation of $T_3$ depends on several effects involving quantum yields, photoionization cross-sections, lifetimes, and potentially overlapping features obscuring the signal. Reliable quantum yields are hard to estimate as photoionization cross-sections are not easily predicted. Instead the discussion will first focus on the $T_3$ activation mechanisms thereby invoking the lifetimes and potential overlapping spectral features. The $T_3$ state of $p$-xylene is observed to decay bi-exponentially with time constants of ca. $180 \pm 20$ fs and a small amplitude decay component of $3.9 \pm 0.8$ ps. The spectral regions corresponding to $T_3$ of benzene and toluene in both cases decay cross-correlation limited. The possible deactivation pathways of $T_3$ involve IC in the triplet manifold and back ISC to the singlet manifold (Figure 6). There is no immediate evidence of the latter process; $S_1$ is observed to rise within the cross-correlation for all molecules with no additional slower components. We therefore turn focus to IC in the triplet manifold instead. Signals corresponding to ionization out of $T_2$ should appear in the lowest eKE region of the spectra of p-xylene and toluene (Table I), while the probe photons are not sufficiently energetic to probe the $T_3$ state of benzene. Interestingly, rising features are observed for both toluene and p-xylene in the low eKE ($\leq 0.15$ eV) energy regimes. For p-xylene, the rise-time in this energy region can be fit to $200 \pm 50$ fs thereby mirroring the fast decay of $T_3$ ($180 \pm 20$ fs), while the corresponding rise-time for toluene can be fit to $150 \pm 15$ fs, consistent with the cross-correlation limited decay of $T_3$. The matching rise and decay components indicate that these low eKE features can be ascribed $T_2$. We note that for toluene portions of the $T_2$ spectrum may overlap with the spectrum of $S_1$; however, the rise of the transient is notably slower than the expected (and observed) cross-correlation appearance of the $S_1$ signal. The rising spectral features are visible in both the contour plots (Figure 4) and on the integrated transients (Figure 5). The transient complementarities are more clearly visible in Figures 8(b) and 8(c) where only the $T_3$ and $T_2$ transients are shown for toluene and p-xylene, respectively. Figure 8(a) shows the transients of the $T_3$ region and the 0–0.15 eV regions for benzene to highlight the absence of similar dynamics in the low energy part of the spectrum for benzene (i.e., it appears unlikely that the rising features are due to parallel processes induced by the two laser beams). At this point, we therefore ascribe the approximately 200 fs (for p-xylene) and 150 fs (for toluene) rise and decay components to the $T_3 \rightarrow T_2$ transition. The tendency of the $T_3 \rightarrow T_2$ IC rate in the order toluene > p-xylene matches previous TRMS experiments on $o$, $m$, p-xylene and toluene assessing the $S_3 \rightarrow S_2$ IC. The relative $S_3 \rightarrow S_2$ IC rates were found to be toluene > p-xylene ≈ m-xylene > p-xylene, which (corroborated by knowledge on the equilibrium structures) was taken as an indication that the full-boat out-of-plane distortion mode facilitated the IC process. If the same mechanism transfers to the triplet manifold (considering the equivalent electronic characters of the $S_3 \rightarrow T_3$ and $S_2 \rightarrow T_2$ states, it appears reasonable to compare the rates and mechanisms in the respective multiplicity manifolds), the current observation of relative $T_3 \rightarrow T_2$ IC rates in the order toluene < p-xylene is consistent with the expected. Such an IC mechanism should put benzene in front of toluene as the fastest decaying $T_3$ state, provided that the $T_3$ state of benzene is formed. Rapidly decaying $T_3$ should thus only be observed in the time-zero region. In this respect, it is appropriate to inspect the time-zero spectra more thoroughly. As mentioned in Section III B, the time-zero spectra differ; this is apparent in the contour plots (Figure 4) but more clearly at the time-zero slices shown in Figures 9(a)–9(c). Benzene and p-xylene show more distinct features than toluene, which exhibits one broad diffuse band with very little structure. This could be an indirect indication that the $T_3$ yields increase in the order from benzene < toluene ≤ p-xylene (as further discussed in Section IV C). Assuming this trend is correct the clear features in benzene (corresponding to $S_2$ and $S_1$) result from minimal $S_2$–$T_3$–$S_1$ overlap due to very little (if any) $T_3$ formation. The $T_3$ yield of toluene is possibly FIG. 8. Fitted transients of the energy regions corresponding to the $T_3$ state (red) and the 0–0.15 eV regions (grey/black) of (a) benzene, (b) toluene, and (c) p-xylene. For toluene and p-Xylene, the low energy regions match the $T_2$ energies, and the red and black transients exhibit mirroring dynamics. Similar dynamics is not observed for benzene (a). higher compared to that of benzene, and toluene therefore suffers more from spectral congestion. p-Xylene also undergoes ISC to T\textsubscript{3}, and the T\textsubscript{3} state furthermore lives longer than the T\textsubscript{3} state of toluene, and p-xylene therefore shows an actual discernible spectral feature along with the (slightly overlapping) broad S\textsubscript{2} and S\textsubscript{1} features. C. Unifying picture and the effect of methylation Collecting the observations on the individual TRPES data sets and the differences between them, the combined interpretation can be summarized as illustrated in Figures 10(a)–10(c). The interpretation presented in Figure 10(a) pertaining to the data for benzene illustrates that S\textsubscript{2} primarily deactivates via ultrafast IC to S\textsubscript{1}. The lack of clear T\textsubscript{3} signal (as compared to p-xylene) and the more distinct time-zero spectrum (as compared to toluene) suggests that negligible amounts of T\textsubscript{3} are formed for benzene. Figure 10(b) shows that toluene deactivates S\textsubscript{2} via ultrafast IC to S\textsubscript{1} and likely also via ultrafast ISC to T\textsubscript{3} with lifetimes shorter than 150 fs. The contribution of the triplet manifold is manifested by the ultrafast decaying signal in the T\textsubscript{3} energy regime yielding a diffuse feature overlapping with S\textsubscript{2} and S\textsubscript{1} on the time-zero spectrum, and by the observation of a rising component of about 150 fs in the T\textsubscript{2} energy region. The T\textsubscript{2} signal does not fully match other electronic states of toluene in eKE or in appearance time. This assignment is corroborated by the clearer triplet signals of p-xylene: Figure 10(c) shows that the S\textsubscript{2} state of p-xylene undergoes ultrafast IC and ISC similar to that of toluene. The T\textsubscript{3} signal of p-xylene is more distinct than that of toluene due to the longer T\textsubscript{3} lifetime. Whether the strong T\textsubscript{3} signal also is due to a higher triplet yield of p-xylene compared to toluene can however not be concluded from the present data. T\textsubscript{3} undergoes bi-exponential decay with the majority converting to T\textsubscript{2} on a \textasciitilde\textsubscript{200} fs time-scale which is manifested in the data by matching rise and decay components. Whether the remaining part of T\textsubscript{3} also undergoes IC to T\textsubscript{2} is unclear as a potential bi-exponential T\textsubscript{2} rise would be obscured by simultaneous T\textsubscript{2} decay. The observation of slightly faster T\textsubscript{3} \rightarrow T\textsubscript{2} IC for toluene (\textasciitilde150 fs) compared to p-xylene (\textasciitilde200 fs) is consistent FIG. 10. Unifying interpretation of the S\textsubscript{2} decay dynamics of (a) benzene, (b) toluene, and (c) p-xylene. The black arrows indicate the transitions observed in the data (precursor and successor), the dotted black lines indicate processes that only are indirectly observed as decaying transients of the precursor, and the grey dotted lines indicate inactive processes. with the activation of a full-boat motion as previously suggested for the electronically equivalent $S_3 \rightarrow S_2$ transition.\textsuperscript{46} From this interpretation, methylation is found to increase the ISC yield (possibly but not necessarily progressively upon further methylation). This interpretation agrees well with the results from the NBO analysis based on the degree of $s$ and $p$-mixing (Figure 3). In the framework of the VB theory, the overlap between two orbitals is expected to be better if the orbitals are alike, and orbital hybridizations are expected to adjust accordingly. This is consistent with the current NBO-analysis, where the $sp^n$-orbitals of the carbon atoms which connect the ring with the methyl groups of toluene and $p$-xylene are found to be more $sp^3$-like compared to the remaining $sp^2$ carbon orbitals of the aromatic system and compared to unsubstituted benzene (Figure 3). This indicates that the carbon atoms linking the aromatic and alkyl-moieties are more susceptible to hybridization-effects when the molecules distort on the excited state surface. As mentioned in the introduction and investigated in, for example, Ref. 11, the probability of ISC depends on mixing of $\sigma$ and $\pi$ orbitals when no obvious El-Sayed type transitions are present. For aromatic hydrocarbons this is possible along out-of-plane modes,\textsuperscript{11,78} and as indicated here in both the experimental and theoretical results the effect increases when methyl-substituents are present. Thus, the role of the methyl group is both to guide the axis of the out-of-plane distortion (preferentially along the axis containing methyl groups, due to the stabilization effect of the methyl-groups on the pseudo-radicaloid prefulvenic structure, Figure 2) and to increase the $\sigma$-character mixing into the bonds of the pinnacle carbon atoms thereby enhancing the ISC probability. This is in full agreement with the stronger spectroscopic evidence for triplet formation in toluene and $p$-xylene as compared to benzene. V. CONCLUSION Time-resolved photoelectron spectroscopy (TRPES) has been used to probe the competition between intersystem crossing (ISC) and internal conversion in benzene, toluene, and $p$-xylene upon excitation to $S_2$. All molecules were found to exhibit ultrafast $S_2$ decays. For benzene, the excited state population appears to mainly convert internally in the singlet manifold as deduced from the presence of $S_1$ signal and concomitant absence of clear triplet signal in the TRPES data. It is possible that the triplet yield was too low to be apparent in the data in the case of benzene. This contrasts the case of the methylated benzene derivatives, where ISC to the triplet manifold is indicated by the spectral observations of $T_3$ and $T_2$ signals. For $p$-xylene, the prominence of the triplet signal was unusually clear. In both cases, $T_3$ was observed to appear within the cross-correlation of the experiment ($<150$ fs), which is consistent with the cross-correlation limited decay of $S_2$. The $T_3$ signals decays of $<150$ fs (toluene) and $\approx 200$ fs ($p$-xylene) were observed to mirror the rising components of the $T_2$ signals as clear indicators of population transfer. The key vibrations mediating both IC in the singlet and triplet manifolds as well as the ISC pathway involve prefulvene-like out-of-plane distortions. The TRPES investigations were corroborated by quantum chemical calculations. Natural bond orbital analysis of the SA-CASSCF optimized structures indicated that the carbon atoms distorting out of the aromatic plane during the transition undergo significant amounts of rehybridization along the reaction coordinate. The extent of orbital mixing was found to increase upon methylation, with the most significant rehybridization effects being localized on the methyl-carrying carbon atoms. Methyl-substituents are therefore proposed to both enhance the ISC probability and to direct the excited state dynamics to involve the molecular axis containing the methyl-groups in the case of toluene and $p$-xylene. The consistent results from the TRPES and theoretical investigations imply that ISC can occur even in system where no obvious ISC mechanism appears to be available in the Franck-Condon area. SUPPLEMENTARY MATERIAL See supplementary material for the coordinates of the optimized structures of benzene, toluene, and $p$-xylene. ACKNOWLEDGMENTS The Villum Foundation is gratefully acknowledged for financial support. Dedicated to Professor Ahmed H. Zewail—an eternal source of inspiration. Shukran AZ! We will always honor your memory and think about you often over an espresso—extra hot. 1D. S. N. Parker, R. S. Minns, T. J. Penfold, G. A. Worth, and H. H. Fielding, Chem. Phys. Lett. 469, 43 (2009). 2T. J. Penfold and G. A. Worth, J. Chem. Phys. 131, 064303 (2009). 3R. S. Minns, D. S. N. Parker, T. J. Penfold, G. A. Worth, and H. H. Fielding, Phys. Chem. Chem. Phys. 12, 15607 (2010). 4T. J. Penfold, R. Spesivytev, O. M. Kirkby, R. S. Minns, D. S. N. Parker, H. H. Fielding, and G. A. Worth, J. 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e161a0426444aa82454b1720457904960f605e1f	{ "olmocr-version": "0.1.59", "pdf-total-pages": 13, "total-fallback-pages": 0, "total-input-tokens": 33181, "total-output-tokens": 9511, "fieldofstudy": [ "Psychology" ] }	Impacts of the COVID-19 Pandemic on Children and Families from Marginalized Groups: A Qualitative Study in Kingston, Ontario Hannah Lee 1,, Imaan Bayoumi 1,2,3,4, Autumn Watson 3,5,6, Colleen M. Davison 4, Minnie Fu 1, Dionne Nolan 6, Dan Mitchell 6, Sheldon Traviss 6, Jennifer Kehoe 6 and Eva Purkey 1,2,3,4 Citation: Lee, H.; Bayoumi, I.; Watson, A.; Davison, C.M.; Fu, M.; Nolan, D.; Mitchell, D.; Traviss, S.; Kehoe, J.; Purkey, E. Impacts of the COVID-19 Pandemic on Children and Families from Marginalized Groups: A Qualitative Study in Kingston, Ontario. COVID 2021, 1, 704–716. https://doi.org/10.3390/covid1040056 Abstract: The COVID-19 pandemic has been associated with unprecedented changes to societal structure. School closures, unstable employment, and inaccessible health services have caused enormous disruptions to child and family wellbeing. This study identifies major themes illustrating how child and family wellness were impacted by COVID-19, including unique effects experienced by Indigenous families. In-depth interviews were conducted with key informants (n = 31) recruited from organizations providing healthcare and social services in Kingston, Ontario. Interview transcripts and written survey responses were analyzed using a phenomenological approach to explore themes related to child and family wellbeing. Three major themes identified include school closures, home safety, and outdoor spaces. School closures were generally reported as negatively impacting learning and social development; however, school closures allowed for some Indigenous children to be removed from a colonized education system, contributing to cultural and spiritual growth. Second, respondents reported increased severity and frequency of domestic violence, which negatively impacted child wellbeing. Third, the closure of public outdoor spaces created barriers to maintaining good physical health for children. This study recommends the prioritization of (1) child learning and development by avoiding school closures in pandemic settings and (2) the safety of Indigenous students by decolonizing education. To address the increased exposure to adverse childhood experiences (ACEs) during COVID-19, we recommend improved training for identifying and reporting domestic violence amongst service providers. Our study also reflects the broader need to redefine “essential services”, considering culturally specific services for Indigenous Peoples. Keywords: children; pandemic; Indigenous; pediatrics; COVID-19; wellbeing 1. Introduction Child and family wellness can be broadly described using an ecological framework integrating individual, family, community, and societal factors [1]. The promotion of child and family wellness relies on factors such as education, material needs (e.g., housing, food security), childcare coordination, mental health, cultural health, and psychosocial support [2,3]. These factors are intrinsically linked to one another, and imbalances in one aspect are likely to influence individual as well as family health and function [1]. An individual’s or community’s definition of wellness may also change depending on cultural factors. Since March of 2020, the COVID-19 pandemic has been associated with unprecedented changes to societal structure. School closures, unstable employment, and inaccessible healthcare services, among other changes, have drastically affected people’s ability to work, receive education, access healthcare, and engage in cultural or community supports, resulting in enormous disruptions to the wellbeing of children and families with young children [1,4]. Current research suggests child wellbeing during the COVID-19 pandemic has been adversely affected, especially by financial pressures on families and limited access to school support systems. However, local contexts differ, and qualitative data from a small urban Canadian perspective have yet to be explored [5]. The city of Kingston is located in Southern Ontario and has a population of over 130,000 residents. In Kingston, social distancing and other public health measures began in March of 2020. Safety measures included school closures, non-essential business closures, mandatory face coverings, quarantine between high-risk neighboring regions, and isolation between houses [6]. Although early research suggested children were less vulnerable to COVID-19 infection and illness, it is clear that children are experiencing the effects of the pandemic in different ways [3,7]. In a US-based study, 34.7% of children (0–12) were reported as experiencing behavioural changes since the beginning of the pandemic, including being lonely, sad, or depressed [8]. This study also identified increased rates of major depression and severe anxiety in parents, which were negatively associated with the ability to provide education at home and positively associated with higher child anxiety scores [8]. Another US study found recent social isolation and employment loss to be associated with changes in parent-reported disciplining techniques, including an increase in spanking, physical and emotional neglect, and verbal aggression against the child [9]. These findings reflect how the COVID-19 pandemic has created broader disruptions in family functioning, resulting in negative effects on child wellbeing. Healthy emotional and social development in early childhood is known to reduce the need for mental and physical health services later in life [8,9]. School is an important setting for this socialization and development to happen [10]. Following the closure of Ontario schools in March of 2020 and several periodic school closures since, many teachers have expressed particular concern for the wellbeing of students from marginalized groups [11]. This includes, for example, children from lower socioeconomic status households, children identifying as Black, Indigenous, or persons of colour, children from single-parent families, and children requiring additional educational services (i.e., educational assistants) [12]. Preliminary research suggests that children from these groups may not have the same resources, such as parents who are available to support curriculum during periods of online learning, resulting in learning loss and widening of educational inequities [12]. Indigenous children in Canada may experience pre-existing health inequities as a result of systemic racism, intergenerational trauma due to Canada’s legacy of colonialism, and structural factors such as a high prevalence of poverty, which were heightened during the pandemic [13–16]. The pandemic has made connecting to cultural supports increasingly difficult [17]. Cultural health is important to child development, and it is hypothesized that this lack of community connection has negatively impacted the health of Indigenous children and families [18]. There is clear quantitative evidence to suggest that child and family wellbeing has suffered as a result of COVID-19; however, qualitative data can be used to contextualize these challenges during this socially and culturally complex time. This paper aims to identify major themes illustrating how child and family wellness were impacted by COVID-19, including unique effects experienced by Indigenous children and their families, to inform actionable policy and programming interventions directed towards improving child and family health. 2. Materials and Methods 2.1. Data Source The data for this analysis come from the Cost of COVID study, a mixed methods study exploring the social and emotional impacts of the COVID-19 pandemic in South Eastern Ontario, Canada, specifically in the Kingston, Frontenac, Lennox, and Addington public health region (KFL&A). The in-depth interviews used for this analysis were conducted with key informants recruited from organizations providing healthcare and social services in KFL&A, including child welfare services, school support, mental health services, domestic violence services, and primary care, among others (Table 1). Service providers included in the study reported on changes observed in their clients throughout the COVID-19 pandemic. Service providers and volunteers from organizations providing services to Indigenous Peoples were intentionally recruited. Table 1. Description of the sample of service providers who participated in the in-depth interviews. \| Variable \| Category \| Number n = 31 \| \|------------------------\|-------------------\|----------------\| \| Ethnicity \| Indigenous \| 15 \| \| \| Non-Indigenous \| 16 \| \| Target population \| Urban (exclusively) \| 8 \| \| \| Rural (exclusively) \| 0 \| \| \| Both \| 23 \| \| Service sector \| Healthcare services \| 9 \| \| \| Housing/shelter \| 2 \| \| \| Education \| 3 \| \| \| Social services/other \| 17 \| \| Role in organizations \| Admin/management \| 12 \| \| \| Direct service provision \| 14 \| \| \| Volunteer \| 5 \| \| Length of time in organization \| <2 years \| 4 \| \| \| 2–5 years \| 12 \| \| \| 5–10 years \| 6 \| \| \| >10 years \| 9 \| * Note that there is overlap between sectors; organizations have been categorized based on primary mandate. 2.2. Participants Participants were recruited by email or phone. Trained Research Assistants conducted interviews via Zoom, a video conferencing platform, between October and December 2020 in order to adhere to public health social distancing guidelines. Interviews lasted approximately 60 min. Participant consent was obtained, and the confidentiality of participants was maintained by removing identifiable information from interview transcripts. Ethics approval was obtained through Queen’s University Health Sciences and Affiliated Teaching Hospital’s Research Ethics Board. An Indigenous oversight committee was involved in every step of data collection and analysis, aligning with the First Nations Principles of OCAP® (ownership, control, access, and possession of research data and findings) [19]. The project was led by members of the Cost of COVID Indigenous Health Council (IHC) subcommittee, and monthly meetings were held to ensure all aspects of the study were properly conducted and responsive to community needs. Members of the IHC guided the data analysis so that themes were appropriately interpreted and analyzed. 2.3. Data Analysis A phenomenological approach was used to explore themes related to child and family wellbeing from the perspective of family and child service providers [20]. Phenomenology is the study of people’s experience of a phenomena and allows for an intimate, first-person perspective on otherwise complex topics [20]. In-depth interviews with health and social service providers were audio recorded and transcribed verbatim. Transcripts were read in their entirety twice by two researchers (H.L. and E.P.). Transcripts were analyzed and coded as one dataset using the NVivo software seeking themes related to child and family wellbeing. An Indigenous Research Assistant (AW) also reviewed the data and was consulted to provide validation on themes as they pertained to Indigenous Peoples. A double-coded phenomenological analysis was performed to assess inter-coder agreement and to validate identified themes [21,22]. 3. Results Thirty-one interviews were conducted between 22 October and 14 December 2020. Six themes related to the experiences of children and families with young children during the COVID-19 pandemic were identified from the results. These include routine, school closures, home safety, socialization and development, outdoor spaces, and Indigenous ways of knowing and being. Quotations used to illustrate each theme were intentionally selected to reflect a variety of participant experiences. 3.1. Routine Lack of structure and inconsistent routines during the COVID-19 pandemic due to changes in school attendance, online classes, canceled recreational activities, services, and supports was an important theme affecting child and family wellness. Inaccessible childcare during the pandemic also contributed to disruptions of routine, particularly affecting low-resourced families. “Even though they’re really little, you could see that they were very sad, missing their daily routine and structure of going to Daycare or going to school, playing with their peers, going to that home Daycare, going out to the park, seeing their friends. There was a sadness in them . . . you could kind of see it in their behaviour because their behaviour would escalate . . . when they were frustrated and they couldn’t get out and . . . advocate for themselves that they wanted to [be] with their friends.” (Service Provider, Indigenous, 1A) “A lot of the kids that I saw were struggling with anxiety because they weren’t able to see their friends, their family, having no routine.” (Service Provider, Indigenous, 1A) “Whether that be children, small children or adult children, what we saw was an immediate stripping of peoples’ supports . . . Their social supports . . . their structural supports and all of those things that they depended on to keep them well and regulated.” (Service Administrator, 10B) “Some people struggled immensely with children and family members that require 24 h care and . . . previous to [the] pandemic were shared between systems like health and school and developmental services. So we saw people physically tired very early. We saw the effects of isolation in care giving come on very early. We saw the effects of isolation in care giving come on very early. (Service Administrator, 10B) In general, routine disruptions were reported as negatively affecting child and family wellness. Nevertheless, some respondents indicated that a subset of children and families for whom the rigid structures of school and family life are a source of stress actually seemed to benefit without the pressure of a strict routine. “I have had a handful of children who we support that have done much better without the demands of society telling them they must get up at a certain time. They must brush their teeth. They must go to a school environment that . . . might not work for them. They must participate in the socially acceptable activity in a socially acceptable way. And they must continue with their programs . . . But those are the families that have had the necessary means to maintain an income . . . And they perhaps have some family support that allows for that to happen.” (Service Administrator, 10B) ### 3.2. School Closures The closure of schools had numerous effects on child wellbeing. Children did not receive the same quality of education, which in some cases had harmful effects on learning. The uncertainty around how to return to school safely during the pandemic was a source of anxiety for many young children and families. Additionally, school closures were a significant burden for some families who relied on school for childcare during the day. “I worry deeply about learning loss.” (Service Administrator, 1B) “We’re seeing lots of kids that are really . . . falling behind in school . . . And now the kids are not able to receive the specialized supports that they would have needed. And I’m worried that they’re falling farther and farther behind.” (Service Provider, 5B) “A lot of struggles of--what’s going to happen at school, what is school going to look like now, why do I have to wear a mask, who’s going be in my class, how many times am I going to have to wash my hands. There was just a lot of unknowns for them to go back to school. So I [have] been fielding a lot of questions around children anxiety [and] parent anxiety with school.” (Service Provider, Indigenous, 1A) “When you have families, young families that are where there is a lot of stress, there’s food insecurity, housing insecurity and like inadequate housing like just under housed, it makes it just really hard to create an online learning environment for their children . . . [T]here is continuing to be a profound impact on kids learning.” (Volunteer, Indigenous, 13A) “I think having kids go to school during the day is really important for a lot of reasons. It gives parents a break from kids. It gives kids a break from parents . . . And it’s actually really important . . . for kids that have behavior struggles and parents that struggle to manage them.” (Service Provider, 5B) While, in general, school closures were seen as negative, for Indigenous children, the closure of schools meant removal from an education system built by colonizers, which in some cases allowed for cultural and spiritual growth. For a minority of students, school was an unsafe environment before COVID-19, and school closures allowed children to be extricated from potentially harmful situations. “I feel that it was really humbling to see finally some Indigenous families not having to be in the colonial structure of schools and school boards.” (Volunteer, Indigenous, 9A) “They were including their children in the baking. They were including their children in the measuring. They were going back to our traditional ways of how we teach our young. And it wasn’t the western reading, writing, arithmetic. It was in the most holistic way.” (Service Administrator, Indigenous, 9A) ### 3.3. Home Safety The pandemic forced families to live and work within close quarters of one another, with little access to other means of support. Many service providers reported that this resulted in increased levels of interpersonal stress and conflict among both adults and children. Some providers suggested increased household anxiety was associated with increased anxiety in children. Respondents reported increased severity and frequency of intimate partner violence for their adult clients, putting children in the damaging position of new or increasing exposure to domestic violence. Increased levels of domestic violence contributed to heightened risk of family separation. “Parental stress piece is something that obviously is filtering down into . . . children.” (Service Provider, 3B) “Maybe [children’s own] anxieties were influenced by their parents’ anxieties.” (Service Provider, 8B) “In regard to intimate partner violence or conflict . . . it may not be that we’ve had a huge jump in referrals, but what we see is . . . there [are] more crises. There’s more severity. And heightened risk of separation within the families.” (Service Administrator, 12B) “We’re having more meetings with CAS than ever.” (Service Provider, 5B) “Kids who are witnessing new domestic violence, lateral violence, all kinds of different forms of what is not normal, but is being normalized. And that’s a really hard part to address is how do we now help come out of this as least affected as possible, given what we don’t know . . . And we may not know the adverse childhood experiences of this for a number of years.” (Volunteer, Indigenous, 9A) To contrast, a minority of service providers described improved home environments for their clients as a result of spending more time together. “Some families are happy that they’re spending more time together” (Service Provider, Indigenous, 5A) 3.4. Socialization and Development Interpersonal interaction has been challenging during COVID-19. The lack of play and human interaction for young children at crucial stages in their development was reported as detrimental for social, emotional, and cognitive development. For some children, the drastic changes in their surrounding environments resulted in concerns with meeting developmental milestones, due to an inability to integrate their experiences through normal play. For children who were used to a pre-pandemic world, the sudden changes in socialization, such as mask wearing or required distancing, made previously familiar environments feel strange. “There hasn’t been the kind of play that normally there would be due to . . . the effects of social distancing. And that’s really had a big impact on kids’ . . . socialization. Like the kids that come to [name of social service] tend to be younger and so . . . they really need that play socialization... I think that it’s had a big impact on children in terms of play as being their usual and normal way that they integrate the complexity of their social lives” (Volunteer, Indigenous, 13A) “That was really tough just in terms of just mental health and general wellbeing, not being able to socialize with their peer group the way that they did or were used to doing. And that being such a huge part of their development” (Service Provider, 3B) “Now that the children are integrating back into what normal is, it’s evident that their personalities have changed. The experiences that they’ve experienced have changed them, have maybe perhaps made them a little bit more jaded, has perhaps made them a little bit more grown” (Volunteer, Indigenous, 9A) “One [concern] is the impact on young children and their development in both physical development, their physical wellbeing, their cultural connection, their language.” (Volunteer, Indigenous, 13A) “The kids under [ . . . ] four [ . . . ] there were new behaviours that popped up. So a little bit of depression, a little bit of behaviours regressing. Some of them regressed. Some were potty trained. Some of them regressed . . . and went back and weren’t potty trained. Some of them decided they weren’t eating.” (Service Provider, Indigenous, 1A) “They weren’t understanding why they couldn’t go into the grocery store with mom. Why everybody was wearing a mask. It became scary. Kids that were going to the day care, that went so willingly, were scared because they were getting screened at the door with someone in a full body suit with . . . the temperature thing at their head . . . So a lot of them have said the kids are adjusting.” (Service Provider, 4B) 3.5. Outdoor Spaces The combination of online school and the closure of public outdoor spaces created barriers to maintaining good physical health for some children during the pandemic. This was particularly true for families and children who did not have access to backyards or other private outdoor spaces and for those who perceived public outdoor spaces as potential sources of infection. This limited access to spaces was related to increased stress on family dynamics. “They’re afraid to let them play outside, so the kids are bouncing off the walls and the parents are stressed.” (Service Provider, 5B) “Parents that don’t have a lot of resources, have decided to keep their kids home, they’re sedentary all day. So they’re on the screen or they’re watching TV, they’re gaining weight . . . even if all the restrictions were lifted tomorrow . . . these new pattern of increased . . . sedentariness [has] long-lasting consequences.” (Service Provider, 5B) “They don’t have private back yards so those kids are not going outside because there’s no private space to play. The parks were closed . . . so they’re all cooped up in a small room together. That’s not going to go smoothly for any family.” (Service Provider, 5B) To contrast, for those who were able to take advantage of outdoor spaces, school closures provided some children unique opportunities to connect with the land. For Indigenous children, connection with the land allowed for unlearning of western norms and revitalization of Indigenous ways of life. “I feel that it was really humbling to see finally some Indigenous families . . . connecting to the land.” (Volunteer, Indigenous, 9A) 3.6. Indigenous Ways of Knowing and Being The pandemic has made it increasingly difficult to connect with one’s culture through ceremony or cultural gatherings. This theme was raised primarily by Indigenous respondents, emphasizing togetherness as crucial to a sense of community cohesion. Respondents described togetherness as opportunities to relate and share the same world view through ceremony, language, and song, contributing to a sense of identity, belonging, and overall wellness. Due to social distancing and public health countermeasures, children and families did not have the same opportunities to access community supports. Definitions of “essential services” allowed to remain open during the pandemic did not include culturally important gatherings. Excluding cultural supports from the definition of “essential services”... services” is especially harmful given the history of past and ongoing colonization of Indigenous Peoples in Canada, which has often included restrictions on rights to ceremony and cultural gatherings. “We used to do like traditional teaching workshops with families where we would make let’s say earrings or moccasins or do a teaching or have dinner together... We’re unable to do those things right now and are unable to provide the services for them. We have gone virtual with some of our workshops, but it’s just not quite the same when you’re at home trying to do it on your own.” (Service Provider, Indigenous, 1A) “We love our people. And we like to be together and it’s being together, sharing and loving and giving kindness to one another ... I think it’s hard for Indigenous People because of that. Because we’re missing that.” (Service Provider, Indigenous, 2A) “Multigenerational trauma ... is [exacerbated] by isolation and lack of connection to cultural events, opportunities, relationships, etc. And also [isolation exacerbated] pre-existing barriers to health services and other [...] services that Indigenous [Peoples] struggle accessing.” (Service Administrator, 12B) 4. Discussion These findings reflect the broader narrative of disruptions to child and family well-being during the COVID-19 pandemic [9,12,23]. These disruptions can be categorized into six themes: routine, school closures, home safety, socialization, outdoor spaces, and Indigenous ways of knowing and being. Although the aforementioned themes have been presented discretely, it is important to acknowledge that they are inextricably linked to one another. The six themes reflect the extensive and profound effects the COVID-19 pandemic has had on all aspects of child and family wellbeing. Underlying each of these themes is the issue of disruption of routines, which was shown to affect mood and increase anxiety for many children who relied on structure in their lives. Studies show that flexible routines and proactive adaptations to daily structure to support children during the pandemic and beyond should be encouraged [24,25]. It is important to highlight that COVID-19 has had differential impacts on different groups, depending on their location, perspectives, and ways of living. The themes outlined in this study may not apply to all children and families across all communities. Family and child wellness are complicated, and these findings confirm this. The COVID-19 pandemic has allowed us to pause and rethink societal structures affecting children and families. The results highlight three important priorities for the recovery phase of the pandemic and future public health disasters: (1) education reform, (2) improved education of service providers to the impacts of child and family adverse childhood experiences (ACEs), and (3) re-defining “essential services” to include culturally important supports. School closures have greatly impacted family wellbeing and function, especially families who lack resources to support their children with online learning at home. These findings support current recommendations for schools to provide additional educational supports to families for periods of remote learning [12] and with the transition back to in-person learning. Ontario’s schools have been closed for longer than any other jurisdiction in Canada, and online learning continues to be an option for the 2021–2022 academic year in elementary and high school [26]. Many service providers voiced concerns about perceived learning loss for young children, as a result of prolonged school closures. This reflects the broader discourse about online school in Canada, where many teachers in Ontario have reported being inadequately resourced to teach young children especially in a virtual setting [27]. In Ontario, children start school at the age of 3–4 years old. Young children achieve major physical, social, emotional, and cognitive developmental milestones at this age. through socialization and routine play [28,29]. It is, therefore, unsurprising that participants reported concerns with social, emotional, and cognitive development for young children during the pandemic. Some examples include new fears related to basic tasks (e.g., grocery shopping or attending daycare), depressed mood levels and social withdrawal, and regression in toilet training. These findings stress the importance of addressing barriers to maintaining socialization for young children, including lack of supervision, accessible outdoor spaces, and material resources, during periods of school closure and the closure of early years playgroups. Although current literature suggests school closures were primarily detrimental to the wellbeing of children and families, this study found a subset of children reported improved wellness during periods of school closure [12,30,31]. The results identified that school remains an unsafe environment for a variety of children, including Indigenous children. During the pandemic, Indigenous children were removed from school systems built by colonizers, which may have led to improved cultural and spiritual wellbeing for some children. These results agree with the literature that Eurocentric school systems are unsafe for many Indigenous and marginalized children [32–34]. Overall, findings from this study illustrate two themes to inform policy recommendations: (1) the importance of in-person education for learning and healthy child development or adequate supplemental in-person interactions during pandemic settings, and (2) the need to decolonize western education systems to create safer learning environments for Indigenous children, among others [35]. Prior research suggests the decolonization of schools requires a four-pronged approach: (1) reflecting on the structure of educational institutions and their role within society, (2) confronting power relations within institutions, (3) addressing systemic racism experienced by Indigenous students, and (4) continual reflection of curriculum [36]. Another important finding echoing existing literature was the increased concerns related to home safety during the COVID-19 pandemic. Service providers observed increased reports of family conflict, domestic violence, and Children’s Aid Society (CAS) referrals. Exposure to adverse childhood experiences (ACEs), such as child maltreatment or domestic violence, early in life increases one’s risk for long-term poor health outcomes [37,38]. Children exposed to four or more ACEs are at a significantly increased risk of chronic diseases, including ischemic heart disease, cancer, mental illness, and health risk behaviours [37,38]. Literature supports the need for all health and social service providers to receive training in identifying and responding to child abuse, as well as to children’s exposure to intimate partner violence (IPV) [39,40]. Responses to suspected IPV should prioritize child safety and include emotional support, education about IPV, and signposting to accessible IPV services [40]. The increased number and severity of domestic violence cases reported in this study and in other literature emerging from the pandemic warrants better preparation of health and social service providers, educators, and those who work with children to identify cases of family violence and mitigate the long-term negative effects on children [41]. Although some service providers reported increased levels of stress, conflict, and domestic violence amongst families, others reported increased family bonding and improved family dynamics. We suspect the pandemic has exacerbated current living situations, leading to either stronger family bonds or increased rates of conflict depending on pre-pandemic family situations. We also recognize that the respondents are service providers and, therefore, interact selectively with families that need or choose to seek access to health and social services during the pandemic. While the literature supports increases in both intimate partner violence and child abuse during the pandemic, these findings may reflect a potentially distorted view of the overall experience of home safety [9,41]. Finally, an important discussion during the COVID-19 pandemic has surrounded which services were deemed “essential”. Current literature suggests that failure to consider marginalized populations when classifying “essential services” resulted in negative impacts for these groups [42,43]. For example, the closure of public outdoor spaces such as parks and playgrounds, initially deemed “unessential”, made it increasingly difficult for children to maintain good physical health. This was especially difficult for families without access to private outdoor spaces. Closure of public outdoor spaces has resulted in changes in behaviour including increased screen time, unhealthy weight gain, and increased sedentary behaviour [44]. These data show that children without access to greenspace became increasingly restless during periods of quarantine, contributing to family stress and conflict. To contrast, children who did have access to outdoor spaces reported improved spiritual and emotional wellbeing, especially Indigenous children who were able to connect with the land. These findings support recommendations to create and maintain public spaces for socialization and outdoor play to encourage healthy child development and wellness [13,45]. They also highlight the need for programs and resources to support the unlearning of some of the unhealthy behaviours that developed during the pandemic. Cultural and spiritual health were also not prioritized when identifying which services were deemed “essential”. The results show how challenging this has been for many Indigenous families in particular, where in-person gatherings are important for cultural teachings and language revitalization that have been lost to some degree through past and ongoing colonization. The data show that a lack of cultural connection has been detrimental to overall wellbeing, disproportionately affecting certain groups, and stressing the importance of finding unique ways to safely maintain community connection and support during periods of quarantine. It raises questions around which services are essential to whom, and how the process of reconciliation in Canada can be practically actualized through engaging Indigenous voices when making decisions during times of crisis. 5. Limitations The service providers recruited for this study described the experiences of service users and not necessarily their own experiences. Service providers may have made inaccurate assumptions about how their patients/clients were feeling. Service providers also only have access to those who seek health/service support, which may contribute to a lack of generalizability of these results to the broader population. The data for this study were also collected in semi-structured interviews that explored topics beyond child and family wellness. Questions targeting other topics may have yielded additional information. 6. Conclusions There are three key conclusions from this study: The first is the need for education reform. This study recommends the prioritization of (1) child learning and development by avoiding school closures in the context of pandemics or other disasters and (2) the safety of Indigenous students through efforts to decolonize education. School closures can be avoided with strategies to keep community transmission low through vaccination mandates for education workers and eligible students, smaller class sizes, and mask mandates [46,47]. Second, to address the increased exposure to ACEs during the COVID-19 pandemic and prevent long-term health implications, we recommend improved training for identifying and reporting child maltreatment and intimate partner violence for health and social service providers and educators [40]. We also recommend family services, including support for material, educational, and mental health needs, be better resourced during periods of quarantine to help prevent ACEs and rebuild strong and healthy family relationships. Third, this study reflects the broader need to re-assess the definition of “essential services” as they relate to children and families, considering culturally specific services for Indigenous Peoples. The ongoing connectedness of many Indigenous Peoples throughout periods of isolation reflects the power of language and culture in maintaining a sense of community. We need more fulsome consultation around the designation of “essential services” to ensure child health and safety and engage in meaningful reconciliation practices with Indigenous communities. Author Contributions: Conceptualization, H.L., A.W. and E.P.; data curation, I.B., A.W., C.M.D., M.F. and E.P.; formal analysis, H.L.; funding acquisition, I.B., C.M.D. and E.P.; methodology, H.L. and E.P.; software, H.L.; supervision, E.P.; validation, H.L., A.W., D.N., D.M., S.T., J.K. and E.P.; writing—original draft, H.L.; writing—review and editing, H.L., I.B., A.W., C.M.D., M.F., D.N., D.M., S.T., J.K. and E.P. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the PSI Foundation and the Queen’s University COVID-19 Rapid Response program. Institutional Review Board Statement: The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the Ethics Committee of Queen’s University (protocol code 6029458; date of approval: 17 April 2020). Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Data Availability Statement: Data are available upon request by contacting [email protected]. The full data are not freely available to respect the confidentiality of our participants, ensure data integrity, and avoid scientific overlap between projects. Once initial contact has been made, we request a short research proposal which will be subject to review by the Cost of COVID Committee and approval by institutional IRBs. Conflicts of Interest: The authors declare no conflict of interest. References 1. Prilleltensky, I.; Nelson, G. Promoting child and family wellness: Priorities for psychological and social interventions. J. Community Appl. Soc. 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Population Mental Health Promotion for Children and Youth: A Public Health Primer; National Collaborating Centres for Public Health: Ottawa, ON, Canada, 2017. 11. Doyle, O. COVID-19 Exacerbating Educational Inequalities. Public PolicyIE Evid Policy. 2020. Available online: http://publicpolicy.ie/papers/covid-19-exacerbating-educational-inequalities/ (accessed on 23 June 2021). 12. Macdonald, M.; Hill, C. The educational impact of the COVID-19 rapid response on teachers, students, and families: Insights from British Columbia, Canada. Prospects 2021, 1–15. 13. Kyoon-Achan, G.; Phillips-Beck, W.; Lavoie, J.; Eni, R.; Sinclair, S.; Kinew, K.A.; Ibrahim, N.; Katz, A. Looking back, moving forward: A culture-based framework to promote mental wellbeing in Manitoba First Nations communities. Int. J. Cult. Ment. Health 2018, 11, 679–692. 14. Boyer, Y. Healing racism in Canadian health care. Can. Med. Assoc. J. 2017, 189, E1408–E1409. 15. Baskin, C. Strong Helpers’ Teachings: The Value of Indigenous Knowledges in the Helping Professions; Canadian Scholars Press: Toronto, ON, Canada, 2011. 16. Farmer, R.L.; McGill, R.J.; Dombrowski, S.C.; McClain, M.B.; Harris, B.; Lockwood, A.B.; Powell, S.L.; Pynn, C.; Smith-Kellen, S.; Loethen, E.; et al. Teleassessment with children and adolescents during the coronavirus (COVID-19) pandemic and beyond: Practice and policy implications. Prof. Psychol. Res. Pract. 2020, 51, 477–487. 46. Leng, T.; Hill, E.M.; Thompson, R.N.; Tildesley, M.J.; Keeling, M.J.; Dyson, L. Assessing the impact of secondary school reopening strategies on within-school COVID-19 transmission and absences: A modelling study. medRxiv 2021. [CrossRef] 47. Head, J.R.; Andrejko, K.L.; Cheng, Q.; Collender, P.A.; Phillips, S.; Boser, A.; Heaney, A.K.; Hoover, C.M.; Wu, S.L.; Northrup, G.R.; et al. The effect of school closures and reopening strategies on COVID-19 infection dynamics in the San Francisco Bay Area: A cross-sectional survey and modeling analysis Summary Background. medRxiv 2020. [CrossRef]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3179, 1 ], [ 3179, 7416, 2 ], [ 7416, 11164, 3 ], [ 11164, 14767, 4 ], [ 14767, 18092, 5 ], [ 18092, 21350, 6 ], [ 21350, 24824, 7 ], [ 24824, 28816, 8 ], [ 28816, 33552, 9 ], [ 33552, 37556, 10 ], [ 37556, 42451, 11 ], [ 42451, 42451, 12 ], [ 42451, 43049, 13 ] ] }
352a3da541c818fc68288cd75899c5321059c594	{ "olmocr-version": "0.1.59", "pdf-total-pages": 50, "total-fallback-pages": 0, "total-input-tokens": 266272, "total-output-tokens": 54626, "fieldofstudy": [ "Mathematics" ] }	Abstract. In this manuscript, we investigate the dispersive properties of solutions to the Schrödinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, we obtain a variety of results on the perturbed conic resolvent operator $R_V$ and the nature of the continuous spectrum of $-\Delta + V$. Using these results, we are able to show that the Schrödinger flow on each eigenspace of the link manifold satisfies a weighted $L^1 \to L^\infty$ dispersive estimate. In odd dimensions, the decay rate we compute is consistent with that of the Schrödinger equation in a Euclidean space of the same dimension, but the spatial weights reflect the more complicated regularity issues in frequency that we face in the form of the spectral measure. In even dimensions, we prove a similar estimate, but with a loss of $t^{1/2}$ compared to the sharp Euclidean estimate. 1. Introduction Let $(X, h)$ be a smooth, compact Riemannian manifold of dimension $n - 1$, and consider the cone on $X$, denoted $C(X)$ and defined as $\mathbb{R}^+ \times X$ with metric $g$ given by $g = dr^2 + r^2 h$. The corresponding Laplace operator on $C(X)$ is given by $$\Delta_{C(X)} = \partial_r^2 + \frac{n-1}{r} \partial_r + \frac{1}{r^2} \Delta_h,$$ where $\Delta_h$ is the Laplacian on $X$, taken with the negative semidefinite sign convention. We take $\Delta_{C(X)}$ with the Friedrich’s extension for simplicity. We are interested in dispersive estimates for the Schrödinger flow $$e^{itH} P_c, \quad H = -\Delta_{C(X)} + V; \quad (1.1)$$ where $P_c$ denotes projection onto the continuous spectrum of $H$. Here, we assume that $V$ is a real-valued radial potential satisfying certain decay assumptions at infinity. Besides giving direct insight into the behavior of waves, dispersive bounds also have interesting applications in nonlinear problems. For example, stability questions around static solutions in nonlinear models such as wave maps have been studied using dispersive decay estimates. See the work of Krieger-Schlag [44] and more recently Krieger-Miao-Schlag [43] for instance. See also the many works of Lawrie-Oh-Shahshahani [45, 46, 47, 48, 49, 50] for treatment of geometric wave and Schrödinger equations in hyperbolic space. Pointwise decay estimates also play a role in obtaining enhanced existence times using normal form methods, see for instance recent works of Ifrim-Tataru [40] and Germain-Pusateri-Rousset. It is also an intrinsically interesting question to understand the interaction between a background potential and diffraction in order to better characterize the dynamics of waves on manifolds with conic singularities. Conic manifolds have arisen naturally in the work of Hintz-Vasy and Hafner-Hintz-Vasy on general relativity, see [34, 38, 39] and in particular the recent discussion in the work of Hintz [37]. Dispersive behavior of Schrödinger flows has been studied in a tremendous variety of geometric settings and under many different conditions on the asymptotic decay and regularity properties of the potential $V$. In $\mathbb{R}^n$, some of the first ideas arose in the seminal paper of Journé-Soffer-Sogge [41], who proved dispersive decay for $n \geq 3$ with potentials that had no zero energy eigenvalues or resonances and were somewhat strongly decaying and regular. Since then, decay estimates have been improved in a variety of settings. Early works by Goldberg and collaborators carefully addressed the regularity required of the potential in higher dimensions and decay rates in 3 dimensions in the absence of embedded resonance and eigenvalues, see [4, 24, 25, 29, 30]. Further works for perturbations of the Euclidean Laplacian have extended dispersive decay results to the setting where $-\Delta + V$ has an embedded resonance at zero energy, which results in a weaker decay estimate in time, see for instance especially the works of Erdogan-Schlag in 3 dimensions [16, 18], Erdogan-Green in two dimensions [14, 17], Green in 5 dimensions [31], as well as Goldberg-Green and Erdogan-Goldberg-Green in odd and even dimensions $\geq 4$ [15, 26, 27, 28]. Recent progress by Blair-Sire-Sogge [7] has pushed the construction of the spectral measure for $-\Delta + V$ to cases where the regularity of the potential $V$ is at very critical levels, though the authors have not explored dispersive decay directly. This is by no means an exhaustive list, but these results are representative of the techniques involved, namely careful control of the free resolvent, the use of resolvent expansions, the role of the regularity of the potential $V$, and the spectral structure of the operator $-\Delta + V$. The survey article by Wilhelm Schlag [60] contains an excellent overview of the key ideas involved. Dispersive decay estimates have also been studied in several other geometries. For example, Schrödinger operators with potential were studied on hyperbolic space by David Borthwick and the second author in [8]. See the recent article of Bouclet [9] for a broad overview of results on the asymptotically Euclidean setting, the article by Hassell-Zhang [36] and references therein for results on asymptotically conic manifolds, as well as the articles of Schlag-Soffer-Staubach [61, 62] for manifolds with conical ends. Analysis of the Laplacian on product cones is related to the analysis of Schrödinger operators on $\mathbb{R}^n$ with an inverse square potential which have been studied in various settings, e.g. the works [42, 55, 56, 57, 68] by various authors. The study of the Laplacian on product cones has a rich history. See the classical results of Cheeger-Taylor, [10, 11], where the spectral measure was first described. As a result, there have been several works that studied evolution equations and their decay estimates on product cones, especially wave equations \[3, 5, 6, 19, 20, 51, 71\]. See also \[1\] for information about scattering resonances on hyperbolic cones. Analysis of dispersive estimates for Schrödinger equations using the resolvent and spectral measure on a product cone has been studied in the recent results of Zhang-Zheng \[69, 70\]. These are the most closely related results to ours, but only study specific types of potentials that can be treated more perturbatively, hence they need not fully explore the regularity and decay of the spectral measure in the same fashion undertaken here. See also the very recent work of Chen \[12\] that studies local dispersive behavior on manifolds with non-product conic singularities. On pure product cones, we prove pointwise decay estimates for the mode-by-mode decomposition of the Schrödinger flow (1.1). By this, we mean that if $ \{\varphi_j\}_{j=0}^\infty $ is a basis of $ L^2(X) $ consisting of eigenfunctions of $ \Delta_h $, then the Schrödinger flow on $ C(X) $ can be formally decomposed as \[ e^{itH}P_c = \sum_{j=0}^\infty e^{itH}P_c E_j, \tag{1.2}\] where $ E_j : L^2(X) \to L^2(X) $ denotes projection on to the linear span of $ \varphi_j $. We show that if $ V \in \rho^{-2\sigma}L^\infty(\mathbb{R}^+) $ for $ \sigma $ sufficiently large, where $ \rho(r) = 1 + r $ is a weight function, and if the perturbed resolvent \[ R_V(z^2) := (-\Delta_{C(X)} + V - z^2)^{-1} \] does not have a pole at $ z = 0 $, then each component of (1.2) satisfies a weighted pointwise estimate. In odd dimensions, we prove this with the same $ t^{-\frac{n}{2}} $ decay rate as in the Euclidean case, while in even dimensions, there is a loss of $ t^{\frac{1}{2}} $ which we do not expect to be sharp. The significance of the resolvent can be seen quite directly if we express the Schrödinger flow in terms of the continuous part of spectral measure for $ -\Delta_{C(X)} + V $, which we denote by $ d\Pi_V $. In particular, if we assume for the moment that there are no resonances or eigenvalues embedded in the continuous spectrum, then we have \[ e^{itH}P_c = \int_0^\infty e^{it\mu} d\Pi_V(\mu). \] By Stone’s formula and a change of variables from $ \mu $ to $ \lambda^2 $, we can rewrite the spectral measure in terms of the boundary values of the resolvent via \[ d\Pi_V(\lambda) = \frac{\lambda}{2\pi i} [R_V(\lambda^2 + i0) - R_V(\lambda^2 - i0)] \, d\lambda. \] The behavior of the resolvent is thus of critical importance for understanding the properties of the Schrödinger flow. Hence, a large portion of this manuscript is dedicated to analyzing the structure of $ R_V(z^2) $, or more specifically its projections $ R_{V,j}(z^2) = R_V(z^2)E_j $. Our first main result establishes that each $ R_{V,j} $ admits a meromorphic continuation to the logarithmic cover of $ \mathbb{C} \setminus \{0\} $ and satisfies a version of the limiting absorption principle. Theorem 1. For $ V \in \rho^{-2\sigma} L^\infty(\mathbb{R}^+) $ with $ \sigma > \frac{1}{2} $, $ R_{V,j}(z^2) $ admits a meromorphic continuation to the logarithmic cover of $ \mathbb{C} \setminus \{0\} $. In the region where $ \text{Im}(z^2) > 0 $, we have that \[ R_{V,j}(z^2) : L^{2,\delta}(\mathbb{R}^+, r^{n-1} \, dr) \to L^{2,-\delta}(\mathbb{R}^+, r^{n-1} \, dr) \] is a bounded operator for all $ \frac{1}{2} < \delta < \sigma $. Here, the notation $ L^{2,\delta}(\mathbb{R}^+, r^{n-1} \, dr) $ denotes the weighted $ L^2 $-space given by $ \{ f : \mathbb{R}^+ \to \mathbb{C} : \int \|f(r)\|^2 \rho(r)^{2\delta} r^{n-1} \, dr < \infty \} $. Furthermore, if $ \sigma > \frac{1}{2} + k $, then the derivatives of $ R_{V,j} $ up to order $ k $ satisfy the limiting absorption principle. That is, for $ 0 \leq \ell \leq k $, there exists an $ M_V > 0 $ such that \[ \partial^\ell_\lambda R_{V,j}(\lambda^2 \pm i0) : L^{2,\delta}(\mathbb{R}^+, r^{n-1} \, dr) \to L^{2,-\delta}(\mathbb{R}^+, r^{n-1} \, dr) \] is a bounded operator for all $ \lambda \geq M_V $ and all $ \frac{1}{2} + k < \delta < \sigma $. In particular, we have the operator bound \[ \\| \partial^\ell_\lambda R_{V,j}(\lambda^2 \pm i0) \\|_{L^{2,\delta} \to L^{2,-\delta}} \leq \frac{C_{j,\ell}}{\lambda} \] for each $ 0 \leq \ell \leq k $, for some $ C_{j,\ell} > 0 $ and all $ \lambda \geq M_V $. We note that (1.4) implies that $ -\Delta_{C(X)} + V $ does not have any embedded resonances in the interval $[M_V, \infty)$, but analysis of the Schrödinger flow requires information about the spectrum at low energy as well. The next theorem handles this by showing that indeed there are no embedded eigenvalues or resonances in $(0, \infty)$. In fact, for this theorem, we do not need $ V $ to be a radial potential, since the arguments involved do not rely as heavily on the conic structure. Theorem 2. For $ V \in \rho^{-2\sigma} L^\infty(C(X)) $ with $ \sigma > \frac{1}{2} $, then $ -\Delta_{C(X)} + V $ has continuous spectrum $[0, \infty)$, with no embedded eigenvalues or resonances in the range $(0, \infty)$. This theorem will be used implicitly throughout this manuscript, but we postpone its proof until Appendix A, since the techniques involved in the proof are quite distinct from those used elsewhere in the argument. In order to analyze the Schrödinger flow, we also require estimates on the behavior of the resolvent at low energy. For this we must assume that $ -\Delta_{C(X)} + V $ does not have a resonance at zero. With this assumption, we obtain the following refinements in our operator bounds from Theorem 1. Theorem 3. Suppose $ V \in \rho^{-2\sigma} L^\infty(\mathbb{R}^+) $ with $ \sigma > \frac{1}{2} + k $, and assume that $ -\Delta_{C(X)} + V $ does not have a resonance at zero energy. Then, (1.4) can be improved to \[ \\| \partial^\ell_\lambda R_{V,j}(\lambda^2 \pm i0) \\|_{L^{2,\delta} \to L^{2,-\delta}} \leq \frac{C_{j,\ell}}{\lambda} \text{ for all } \lambda \geq 0 \] for $ \frac{1}{2} + k < \delta < \sigma $ and $ 0 \leq \ell \leq k $. Under the stronger hypothesis that $ \frac{a}{2} + k \leq \delta < \sigma $, we also have that the imaginary part of $ R_{V,j} $ satisfies \[ \\| \partial^\ell_\lambda \text{Im } R_{V,j}(\lambda^2 \pm i0) \\|_{L^{2,\delta} \to L^{2,-\delta}} \leq C_{j,\ell} \lambda^{n-2-k} \text{ for all } \lambda \in [0, 1], \] for some $ C_{j,\ell} > 0 $ and each $ 0 \leq \ell \leq k $. By combining these mapping properties with the behavior of the free resolvent $R_0(z^2) := (-\Delta_{C(X)} - z^2)^{-1}$, we are able to establish weighted pointwise estimates on the Schwartz kernel of $R_{V,j}(\lambda^2 \pm i0)$, from which we can obtain our primary result on the time-decay rate of the Schrödinger flow. Theorem 4. Suppose $C(X)$ is of odd dimension $n \geq 3$. Let $V \in \rho^{-2\sigma}L^\infty(\mathbb{R}^+)$ with $$\sigma > 2n \left\lceil \frac{n}{4} \right\rceil.$$ If $R_V(z^2)$ does not have a pole at $z = 0$, then for any integer $j \geq 0$ and $\alpha \geq 2 \left\lceil \frac{n}{4} \right\rceil (n - 2) - \frac{n-1}{2} + 2$, we have $$\\|\rho^{-\alpha}e^{itH}P_cE_jf\\|_{L^\infty(\mathbb{R}^+)} \leq C_{j,\alpha,\sigma}t^{-\frac{n}{2}}\\|\rho^{\alpha}E_jf\\|_{L^1(\mathbb{R}^+, r^{n-1}dr)},$$ for some $C_{j,\alpha,\sigma} > 0$. We do not claim that the lower bound on the exponent $\alpha$ in the spatial weights is optimal, but these weights are required to obtain Theorem 4 from the techniques used in this article. In particular, the weights are needed to counteract certain regularity issues which arise when differentiating the resolvent with respect to $\lambda$. See Remark 3.7 for additional details. Furthermore, the dependence on $j$ appears as a consequence of the fact that the pointwise bounds we establish on each $R_{V,j}$ are not necessarily summable in $j$. Similar weighted mode-by-mode estimates are obtained in the works of Schlag-Soffer-Staubach [61, 62] in the case of surfaces of revolution and related mode by mode decay rates were established for the wave equation on the Schwarzschild space-time in Donninger-Schlag-Soffer [13]. Remark 1.1. In the case where $n$ is even, the techniques of this article give a slightly weaker estimate of the form $$\\|\rho^{-\alpha}e^{itH}P_cE_jf\\|_{L^\infty(\mathbb{R}^+)} \leq C_{j,\alpha,\sigma}t^{-\frac{n-1}{2}}\\|\rho^{\alpha}E_jf\\|_{L^1(\mathbb{R}^+, r^{n-1}dr)},$$ for analogous conditions on $V$ and $\alpha$, where the loss of the $\frac{1}{2}$ power of decay in $t$ arises as a result of regularity issues encountered in the analysis of the spectral measure near zero energy. We expect that with more sophisticated techniques it may be possible to improve this estimate to give the full $t^{-\frac{n}{2}}$ decay rate exhibited in $\mathbb{R}^n$. 1.1. Outline of the Paper. In Section 2, we summarize known facts regarding the form of the free resolvent $R_0(z^2)$. The results presented are primarily taken from [3], which draws heavily upon the seminal work of [11]. In Section 3, we prove operator bounds on the free resolvent using properties of Bessel and Hankel functions. These bounds include a limiting absorption principle for the projections $R_{0,j} := R_0E_j$. Section 4 combines these bounds on the free resolvent with perturbation theory arguments to prove Theorems 1 and 3. Then, in Section 5, we prove weighted pointwise bounds on the perturbed resolvent kernel using a Birman-Schwinger expansion along with the previous operator estimates. Finally, in Section 6, we use the representation of the spectral measure in terms of the resolvent combined with the pointwise resolvent bounds to establish Theorem 4. We also provide three appendices. at the end of the paper. Appendix A contains the proof of Theorem 2, which demonstrates the absence of embedded eigenvalues and resonances. This fact is of critical importance throughout the paper. For the benefit of the reader, Appendix B provides a full derivation of the free resolvent formula presented in Section 2. This derivation largely follows the work of [3], but we provide some additional clarifying details. Finally, Appendix C uses ideas from [19] to give a modified dispersive estimate for the free Schrödinger flow which is both unweighted and not restricted to individual eigenspaces of the link manifold. Acknowledgements. BK is supported by DMS 1900519 and Sloan Fellowship through his advisor Yaiza Canzani. JLM was supported in part by NSF CAREER Grant DMS-1352353 and NSF Applied Math Grant DMS-1909035. JLM also thanks Duke University and MSRI for hosting him during the outset of this research project. The authors would like to thank Dean Baskin, David Borthwick, Yaiza Canzani, Michael Goldberg, Andrew Hassell and Jason Metcalfe for very helpful discussions about resolvent estimates on conic manifolds and pointwise estimates in general. The authors thank the anonymous referee who reviewed the first version of this manuscript for many valuable comments that led a helpful reorganization of the results and several aspects of the main theorems being clarified. 2. The Free Resolvent In this section, we outline some key facts about the kernel of the free resolvent operator \[ R_0(z^2) = (-\Delta_{C(X)} - z^2)^{-1} : L^2(C(X)) \to L^2(C(X)), \] for complex $ z $. This is equivalent to analyzing solutions of the equation \[ (-\Delta_{C(X)} - z^2)u = f \] for $ f \in L^2(C(X)) $. To proceed, we decompose $ u $ and $ f $ into the basis $ \{\varphi_j\} $ of eigenfunctions on $ X $ as \[ f(r, \theta) = \sum_{j=1}^{\infty} f_j(r)\varphi_j(\theta), \quad u(r, \theta) = \sum_{j=1}^{\infty} u_j(r)\varphi_j(\theta). \] Denote by $ -\mu_j^2 $ the eigenvalues of $ \Delta_h $ associated to each $ \varphi_j $. Then, we obtain that (B.2) is equivalent to the collection of equations \[ \left( \partial_r^2 + \frac{n-1}{r} \partial_r + z^2 - \frac{\mu_j^2}{r^2} \right) u_j(r) = -f_j(r), \quad j = 0, 1, 2, \ldots. \] Therefore, we can express the resolvent $ R_0(z^2) $ as \[ R_0(z^2)f(r, \theta) = \sum_{j=0}^{\infty} u_j(r)\varphi_j(\theta), \] with $ u_j $ as above. If we define the $ j $th radial resolvent $ R_{0,j}(z^2) $ by \[ R_{0,j}(z^2) = \left( \partial_r^2 + \frac{n-1}{r} \partial_r + z^2 - \frac{\mu_j^2}{r^2} \right)^{-1} \] as an operator on $ L^2(\mathbb{R}^+, r^{n-1} dr) $, then the full resolvent is given by \[ R_0(z^2) f(r, \theta) = \sum_{j=0}^{\infty} R_{0,j}(z^2) f_j(r) \varphi_j(\theta). \] The work of Baskin and Yang [3] presents several results about these radial resolvents, which we summarize in the following lemma. Lemma 2.1 (Baskin-Yang [3]). For $ \text{Im } z > 0 $, the action of the $ j $-th radial resolvent is given by \[ R_{0,j}(z^2) f(r) = \int_0^{\infty} R_{0,j}(z^2; r; s) f(s)s^{n-1} ds, \] and the kernel $ R_{0,j}(z^2; r; s) $ takes the form \[ R_{0,j}(z^2; r; s) = \begin{cases} \frac{\pi i}{2} (rs)^{-\frac{n+2}{2}} J_{\nu_j}(zs) H^{(1)}_{\nu_j}(zr), & s < r \\ \frac{\pi i}{2} (rs)^{-\frac{n+2}{2}} J_{\nu_j}(zr) H^{(1)}_{\nu_j}(zs), & s > r, \end{cases} \] where $ J_{\nu_j} $ and $ H^{(1)}_{\nu_j} $ denote the Bessel and Hankel functions of the first kind of order $ \nu_j $, respectively. Moreover, for any fixed $ \chi \in C^\infty_c(\mathbb{R}^+ \times X) $, the cutoff resolvent $ \chi R_0(z^2) \chi $ admits a meromorphic continuation to the logarithmic cover $ \Lambda $ of $ \mathbb{C} \setminus 0 $. Remark 2.2. We note that the above formula for the kernel of $ R_{0,j} $ differs from that presented in [3] by a sign, since we have defined the resolvent as $(-\Delta_{C(X)} - z^2)^{-1}$ rather than $(\Delta_{C(X)} + z^2)^{-1}$, but this is of no consequence for the remainder of the analysis. From Lemma 2.1, we can construct the absolutely continuous part of the spectral measure for the free Laplacian on $ C(X) $, which we denote by $ d\Pi_0 $. By Stone’s formula, we can write the continuous part of the spectral measure in terms of the difference between the boundary values of the resolvent as we approach the continuous spectrum from above and below. That is, for $ \mu \in \mathbb{R}^+ $, \[ d\Pi_0(\mu) = \frac{1}{2\pi i} \lim_{\varepsilon \to 0^+} \left[ (-\Delta_{C(X)} - (\mu + i\varepsilon))^{-1} - (-\Delta_{C(X)} - (\mu - i\varepsilon))^{-1} \right] d\mu \] \[ = \frac{1}{2\pi i} \text{Im}(-\Delta_{C(X)} - (\mu + i0))^{-1} d\mu. \] We can then reparametrize the continuous spectrum by changing variables via $ \mu \mapsto \lambda^2 $ for $ \lambda > 0 $, which allows us to write \[ d\Pi_0(\mu) = \frac{1}{\pi i} \text{Im} R_0(\lambda^2 + i0) \lambda d\lambda. \] Noting that $ H^{(1)}_\nu = J_\nu + iY_\nu $, where $ Y_\nu $ is the Bessel function of the second kind of order $ \nu $, we have by Lemma 2.1 that \[ \text{Im} R_{0,j}(\lambda^2 + i0; r, s) = \frac{\pi}{2} (rs)^{-\frac{n-2}{2}} J_\nu(\lambda r) J_\nu(\lambda s). \] From this, we obtain the following lemma. Lemma 2.3. The continuous part of the spectral measure of $-\Delta_{C(X)}$, with the convention that $ \lambda^2 $ is the spectral parameter, is given by \[ d\Pi_0(\lambda; x, y) = \frac{1}{\pi i} (rs)^{-\frac{n-2}{2}} \sum_{j=0}^{\infty} J_\nu(\lambda r) J_\nu(\lambda s) \varphi_j(\theta) \varphi_j(\zeta) \lambda d\lambda, \quad \lambda > 0, \] where $ x = (r, \theta) $ and $ y = (s, \zeta) $ are points in $ C(X) $. ### 3. Estimates on the Free Resolvent In this section, we prove a variety of weighted estimates on the unperturbed radial resolvents $ R_{0,j} $. These estimates heavily rely on the asymptotic formulae for the Bessel and Hankel functions near zero and infinity. Of particular interest is the behavior of $ R_{0,j} $ measured in the weighted $ L^q $ spaces defined by \[ L^{q,\sigma}(\mathbb{R}^+, r^{n-1} dr) = \{ f : \mathbb{R}^+ \to \mathbb{C} : \int_0^\infty \|f(r)\|^q \rho^\sigma(r) r^{n-1} dr < \infty \}, \] where $ \rho(r) = 1 + r $. For ease of notation, we simply write $ L^{q,\sigma} $ to denote the space $ L^{q,\sigma}(\mathbb{R}^+, r^{n-1} dr) $ where there can be no confusion. The estimates for the free resolvent on these spaces will prove useful in Sections 4 and 5 for establishing the mapping properties of the perturbed resolvent. We begin with a quantitative formulation of the Limiting Absorption Principle for the radial resolvents. See [65] for a recent discussion of this in the more general setting of scattering manifolds. Proposition 3.1. Let $ k \geq 0 $ be an integer. Then for any $ \sigma > \frac{1}{2} + k $, \[ \\| \partial^k_\lambda R_{0,j}(\lambda^2 + i0) \\|_{L^{2,\sigma} \rightarrow L^{2,-\sigma}} \leq C_{j,k,\sigma} \frac{\lambda^k}{\|\lambda\|}\tag{3.1} \] for all $ \|\lambda\| \geq 1 $. Remark 3.2. A noteworthy observation here is that the constant $ C_{j,k,\sigma} $ in Proposition 3.1 is not known \textit{a priori} to be bounded as a function of $ j $. In the special case where $ k = 0 $, the statement of Proposition 3.1 can be shown to hold for the full resolvent $ R_0(\lambda^2 + i0) $ with a uniform constant using extremely precise asymptotics for the Bessel and Hankel functions such as those found in [21]. However, when $ k > 0 $ this method fails due to the fact that differentiating $ J_\nu(\lambda r) H^{(1)}_\nu(\lambda s) $ yields a linear combination of products of Bessel and Hankel functions with mismatched orders, and hence the resulting constants in the estimates for the Hankel functions are not balanced by those of the Bessel functions, in contrast to the k = 0 case. Proof. If $ f \in L^2^\sigma $, we have \[ \\| \partial^k \! R_{0,j}(\lambda^2 + i0) f \\|_{L^2^\lambda - \sigma}^2 = \int_0^\infty \int_0^\infty \partial^k \! R_{0,j}(\lambda^2 + i0; r, s) f(s) s^{n-1} ds \left( 1 + r \right)^{-2\sigma} r^{n-1} dr. \] Inserting a factor of $(1 + s)^{-\sigma}(1 + s)^\sigma$ and applying Cauchy-Schwartz, we see that \[ \\| \partial^k \! R_{0,j}(\lambda^2 + i0) f \\|_{L^2^\lambda - \sigma}^2 \leq \int_0^\infty \\| \partial^k \! R_{0,j}(\lambda^2 + i0; r, \cdot) \\|_{L^2^\lambda - \sigma}^2 \\| f \\|_{L^2^\lambda - \sigma}^2 (1 + r)^{-2\sigma} r^{n-1} dr \] Hence, it suffices to show that the kernel satisfies \[ \\| \partial^k \! R_{0,j}(\lambda^2 + i0; \cdot, \cdot) \\|_{L^2^\lambda - \sigma}^2 \leq \frac{C^2}{\lambda^2}. \] By definition, \[ \\| \partial^k \! R_{0,j}(\lambda^2 + i0; \cdot, \cdot) \\|_{L^2^\lambda - \sigma}^2 = \int_0^\infty \int_0^\infty \partial^k \! R_{0,j}(\lambda^2 + i0; r, s)(1 + s)^{-2\sigma}(1 + r)^{-2\sigma}(rs)^{n-1} ds dr, \] Recalling the piecewise formula $(3.6)$ for the resolvent kernel, we have that \[ \\| \partial^k \! R_{0,j}(\lambda^2 + i0; \cdot, \cdot) \\|_{L^2^\lambda - \sigma}^2 = \frac{\pi^2}{4} \int_0^\infty \int_0^r \left[ \partial^k \! \left( H^{(1)}_{\nu_j}(\lambda r) J_{\nu_j}(\lambda s) \right) \right]^2 (rs)(1 + r)^{-2\sigma}(1 + s)^{-2\sigma} ds dr \] \[ + \frac{\pi^2}{4} \int_0^\infty \int_r^\infty \left[ \partial^k \! \left( H^{(1)}_{\nu_j}(\lambda s) J_{\nu_j}(\lambda r) \right) \right]^2 (rs)(1 + r)^{-2\sigma}(1 + s)^{-2\sigma} ds dr. \] By changing the order of integration, we get that the first term on the right-hand side of $(3.3)$ can be rewritten as \[ \frac{\pi^2}{4} \int_0^\infty \int_0^r \left[ \partial^k \! \left( H^{(1)}_{\nu_j}(\lambda r) J_{\nu_j}(\lambda s) \right) \right]^2 (rs)(1 + r)^{-2\sigma}(1 + s)^{-2\sigma} ds dr. \] We note that up to a relabeling of $ r, s $, this is exactly equal to the second term in (3.3), and hence \[ \\| \partial^k \lambda R_{0,j}(\lambda^2 + i0; \cdot, \cdot) \\|_{L^2_{r,s} L^2_{r,s}} = \frac{\pi^2}{2} \int_0^\infty \int r \left[ \partial^k \lambda \left( H^{(1)}_{\nu_j}(\lambda s) J_{\nu_j}(\lambda r) \right) \right]^2 (rs)(1+r)^{-2\sigma}(1+s)^{-2\sigma} \, ds \, dr. \tag{3.5} \] Note that if $ C_{\nu}(x) $ is either a Bessel or Hankel function of order $ \nu $, we have \[ C'_{\nu}(x) = \frac{1}{2} \left( C_{\nu+1}(x) - C_{\nu-1}(x) \right), \tag{3.6} \] and so the triangle inequality reduces the proof of Proposition 3.1 to showing that the following lemma holds. \[ \text{\textbf{Lemma 3.3.}} \text{ Let } \ell, m, k \text{ be nonnegative integers with } \ell + m = k, \text{ and suppose } \alpha, \beta \in \mathbb{Z} \text{ are such that } \|\alpha\| \leq \ell \text{ and } \|\beta\| \leq m. \text{ Then for any } \nu \geq \frac{n-2}{2}, \text{ there exists a } C > 0 \text{ depending only on } k, \nu \text{ such that } \] \[ \int_0^\infty \int r \|J_{\nu+\alpha}(\lambda r)\|^2 \|H^{(1)}_{\nu+\beta}(\lambda s)\|^2 r^{1+2\ell} s^{1+2m}(1+s)^{-2\sigma}(1+r)^{-2\sigma} \, ds \, dr \leq \frac{C}{\lambda^{2}}, \quad \lambda \geq 1, \tag{3.7} \] provided that $ \sigma > \frac{1}{2} + k $. \textit{Proof.} This proof, and others which follow it, make extensive use of asymptotic estimates for the Bessel and Hankel functions, which we record here for later use. For any $ \nu \in \mathbb{R} $, there exist constants $ C_{\nu}, C'_{\nu} > 0 $ such that when $ 0 < \|\tau\| \leq 1 $, \[ \|J_{\nu}(\tau)\| \leq C_{\nu}\|\tau\|^\nu, \quad \|H^{(1)}_{\nu}(\tau)\| \leq C_{\nu}\|\tau\|^{-\nu} \tag{3.8} \] and when $ \|\tau\| \geq 1 $, \[ \|J_{\nu}(\tau)\| \leq C'_{\nu}\|\tau\|^{-\frac{1}{2}}, \quad \|H^{(1)}_{\nu}(\tau)\| \leq C'_{\nu}\|\tau\|^{-\frac{1}{2}}. \tag{3.9} \] To prove Lemma 3.3, let us first write the left-hand side of (3.7) as $ I(\lambda) + II(\lambda) $, where each term is obtained by restricting the integral in the $ r $ variable to $ 0 < r < \frac{1}{\lambda} $ and $ \frac{1}{\lambda} < r < \infty $, respectively. To estimate $ I(\lambda) $, note that by (3.9), we have \[ \int \frac{s^{1+2m}(1+s)^{-2\sigma}\|H^{(1)}_{\nu+\beta}(\lambda s)\|^2 \, ds}{\lambda} \leq \frac{C'}{\lambda}, \] \[ \int s^{2m}(1+s)^{-2\sigma} \, ds \leq \frac{C'}{\lambda}, \] \[ \int \frac{s^{1+2m}(1+s)^{-2\sigma} \, ds}{\lambda} \leq \frac{C'}{\lambda}, \] as long as $\sigma > m + \frac{1}{2}$. Combining this with (3.8), we have $$\int_0^{\frac{1}{\lambda}} \int_0^{\infty} J_{\nu+\alpha}(\lambda r)^2 \|H^{(1)}_{\nu+\beta}(\lambda s)\|^2 r^{1+2\ell} s^{1+2m}(1+s)^{-2\sigma} (1+r)^{-2\sigma} ds dr \leq \frac{C'}{\lambda} \int_0^{\frac{1}{\lambda}} r^{1+2\ell}(\lambda r)^{2(\nu+\alpha)} dr$$ $$\leq \frac{C''}{\lambda^2}$$ (3.10) for any $\ell \geq 0$, since $\lambda \geq 1$. Furthermore, if $0 < r \leq \frac{1}{\lambda}$, we have $$\int_{\frac{1}{\lambda}}^{\frac{1}{\lambda}} \int_r^{\infty} s^{1+2m}(1+s)^{-2\sigma} \|H^{(1)}_{\nu+\beta}(\lambda s)\|^2 ds \leq \frac{C}{\lambda^{2(\nu+\beta)}} \int_r^{\infty} s^{1+2(m-\nu-\beta)} ds$$ $$\leq \frac{C}{\lambda^{2(\nu+\beta)}} r^{1+2(m-\nu-\beta)} \left( \frac{1}{\lambda} - r \right) \leq \frac{C''}{\lambda^2} (\lambda r)^{2(\nu+\beta)} r^{2m}$$ since $1 + 2(m - \beta - \nu) \leq 0$. Hence, if we recall that $k = \ell + m \geq \|\alpha\| + \|\beta\|$ and apply (3.8), we have $$\int_0^{\frac{1}{\lambda}} \int_0^{\infty} J_{\nu+\alpha}(\lambda r)^2 \|H^{(1)}_{\nu+\beta}(\lambda s)\|^2 r^{1+2\ell} s^{1+2m}(1+s)^{-2\sigma} (1+r)^{-2\sigma} ds dr$$ $$\leq \frac{C'}{\lambda} \int_0^{\frac{1}{\lambda}} r^{1+2k}(\lambda r)^{2(\alpha-\beta)} dr = \frac{C'}{\lambda^{2k+2}} \int_0^{\frac{1}{\lambda}} \lambda r)^{1+2(k+\alpha-\beta)} dr$$ $$\leq \frac{C'}{\lambda^{2k+3}} \leq \frac{C'}{\lambda^2}$$ for all $k \geq 0$ when $\lambda \geq 1$. Combining this with (3.10) proves that $I(\lambda) \leq \frac{C}{\lambda^2}$ for some $C > 0$ and all $\lambda \geq 1$. Since for any fixed $k$ there are only finitely many possibilities for $\ell, m, \alpha, \beta$, we can choose $C$ to depend only on $k$ and $\nu$. Now, to estimate $II(\lambda)$, we apply (3.9) to both the Bessel and Hankel functions to obtain $$II(\lambda) \leq C \int_0^\infty \int_0^\infty r^{1+2\ell} (1+r)^{-2\sigma} (\lambda r)^{-1} s^{1+2m} (1+s)^{-2\sigma} (\lambda s)^{-1} ds \, dr$$ $$= \frac{C}{\lambda^2} \int_0^\infty \int_0^\infty (1+r)^{2(\ell-\sigma)} (1+s)^{2(m-\sigma)} ds \, dr$$ $$\leq \frac{C}{\lambda^2},$$ provided that $\sigma > k + \frac{1}{2}$, which completes the proof of Lemma 3.3. \qed It will also prove useful to have a bound on the $L^{2,\sigma} \to L^{2,-\sigma}$ mapping properties of the imaginary part of each $R_{0,j}$ when $\lambda$ is small. In particular, we are able to show that this operator norm has a precise polynomial rate of vanishing as $\lambda \to 0$. Proposition 3.4. For any integer $k \geq 0$ and any $\sigma > \frac{n}{2} + k$, we have that $$\\| \partial^k \lambda \, \text{Im} \, R_{0,j}(\lambda^2 + i0) \\|_{L^{2,\sigma} \to L^{2,-\sigma}} \leq C_{j,k,\sigma} \lambda^{n-2-k}$$ when $0 < \lambda \leq 1$. Proof. By the discussion at the beginning of the proof of Proposition 3.1, it is sufficient to show that $$\\| \partial^k \lambda \, \text{Im} \, R_{0,j}(\lambda^2 + i0; r, s) \\|_{L^{2,\sigma} \to L^{2,-\sigma}} \leq C_{\ell,m,\alpha,\beta} \lambda^{n-2-k}$$ for $0 < \lambda \leq 1$. By (3.5) we have $$\\| \partial^k \lambda \, \text{Im} \, R_{0,j}(\lambda^2 + i0; r, s) \\|_{L^{2,\sigma} \to L^{2,-\sigma}}^2 \leq C \lambda^{n-2-k}$$ for $0 < \lambda \leq 1$. By (3.5) we have $$\\| \partial^k \lambda \, \text{Im} \, R_{0,j}(\lambda^2 + i0; r, s) \\|_{L^{2,\sigma} \to L^{2,-\sigma}}^2 \leq C \lambda^{n-2-k}$$ for any integers $\ell, m \geq 0$ with $\ell + m = k$ and integers $\alpha, \beta$ with $\|\alpha\| \leq \ell$ and $\|\beta\| \leq m$. Since the above integral is separable, it is in fact enough to show $$\int_0^\infty \int_0^\infty r^{1+2\ell} s^{1+2m} \|J_{\nu_j+\alpha}(\lambda r)\|^2 \|J_{\nu_j+\beta}(\lambda s)\|^2 (1+r)^{-2\sigma} (1+s)^{-2\sigma} dr \, ds \leq C \lambda^{2(n-2-k)}$$ (3.12) for any $ \ell \leq k $ and $ \|\alpha\| \leq \ell $, since analogous estimates will apply to the integral in the $ s $ variable. First, notice that (3.8) implies \[ \int_0^\frac{1}{\lambda} r^{1+2\ell} \|J_{\nu_j+\alpha}(\lambda r)\|^2 (1+r)^{-2\sigma} dr \leq C \int_0^\frac{1}{\lambda} r^{1+2\ell} (\lambda r)^{2(\nu_j+\alpha)} (1+r)^{-2\sigma} dr \] \[ = C\lambda^{2(\nu_j+\alpha)} \int_0^\frac{1}{\lambda} r^{1+2(\ell+\alpha+\nu_j)} (1+r)^{-2\sigma} dr \leq C' \lambda^{2(\nu_j+\alpha)} \int_0^\frac{1}{\lambda} (1+r)^{2(\ell+\alpha+\nu_j-\sigma)} dr \] \[ \leq C'' \lambda^{2(\nu_j+\alpha)} \left( 1 + \frac{1}{\lambda} \right)^{2+2(\ell+\alpha+\nu_j-\sigma)} - 1 \] \[ \leq C_1 \lambda^{2(\sigma-\ell)-2} (\lambda + 1)^{2+2(\ell+\alpha+\nu_j-\sigma)} + C_2 \lambda^{2(\nu_j+\alpha)} \] Recalling that $ \sigma > \frac{n}{2} + k $ and $ \ell \leq k $, we have that $ 2(\sigma - \ell) > n $. Also, we have $ 2(\nu_j + \alpha) \geq n - 2 + 2\alpha $, and since $ \|\alpha\| \leq \ell \leq k $, we have that the above is bounded by a constant times $ \lambda^{n-2-2\alpha} $ for $ 0 < \lambda \leq 1 $ as claimed. Next, we consider the integral over the region where $ \frac{1}{\lambda} \leq r < \infty $. For this, we use (3.9) to obtain \[ \int_\frac{1}{\lambda}^\infty r^{1+2\ell} \|J_{\nu_j+\alpha}(\lambda r)\|^2 (1+r)^{-2\sigma} dr \leq C \int_\frac{1}{\lambda}^\infty r^{1+2\ell} (\lambda r)^{-1} (1+r)^{-2\sigma} dr \] \[ \leq \frac{C'}{\lambda} \int_\frac{1}{\lambda}^\infty (1+r)^{2(\ell-\sigma)} dr \leq \frac{C''}{\lambda} \left( 1 + \frac{1}{\lambda} \right)^{1+2(\ell-\sigma)} \] \[ = C'' \lambda^{2(\sigma-\ell)-2} (\lambda + 1)^{1+2(\ell-\sigma)} \leq C'' \lambda^{2(\sigma-\ell)-2}. \] The restrictions on $ \sigma $ guarantee that the above is bounded by a constant times $ \lambda^{n-2} $ for $ 0 < \lambda \leq 1 $. Therefore, (3.13) holds, and the proof is complete. $ \square $ Next, we aim to prove weighted $ L^q $ estimates on the free radial resolvent kernels $ R_{0,j} $, which enables us to control the terms in the Birman-Schwinger series for $ R_{V,j} $ when applied iteratively. First, we make note of a technical lemma. Lemma 3.5. Let $ \nu \geq \frac{n-2}{2} $, and $ \lambda > 0 $. Suppose that $ \beta, m \in \mathbb{Z} $ are such that $ \|\beta\| \leq m $ and $ \nu + \beta \geq 0 $. Assume also that $ 1 \leq q < \infty $ and that $ \sigma > \frac{n}{q} + m $. Then there exist $ C_1, C_2 > 0 $ such that \[ \int_0^\infty (\lambda s)^{q(m-\frac{n+2}{2})} \|J_{\nu+\beta}(\lambda s)\|^{q(1+s)-q\sigma} s^{n-1} \, ds \leq \begin{cases} C_1 \lambda^{-n} + C_2 \lambda^{q(m-\frac{n+1}{2})}, & 1 \leq \lambda < \infty \\ C \lambda^{q\sigma-n}, & 0 < \lambda \leq 1. \end{cases} \] (3.14) Proof. Let us denote by $ I(\lambda) $ the integral in the statement above, and observe that $ I(\lambda) $ is clearly nonnegative for all $ \lambda > 0 $. If we split the integral into the the regions where $ 0 < s < \frac{1}{\lambda} $ and $ \frac{1}{\lambda} < s < \infty $, we can apply (3.8) and (3.9) to $ J_{\nu+\beta} $ to obtain that \[ I(\lambda) \leq C \int_0^{\frac{1}{\lambda}} (\lambda s)^{q(\nu-\frac{n-2}{2}+\beta+m)} (1+s)^{-q\sigma} s^{n-1} \, ds + C \int_{\frac{1}{\lambda}}^{\infty} (\lambda s)^{q(m-\frac{n+1}{2})} (1+s)^{-q\sigma} s^{n-1} \, ds \] for some constant $ C > 0 $. To estimate these integrals, we treat the cases $ \lambda \geq 1 $ and $ \lambda \leq 1 $ separately. First suppose that $ \lambda \geq 1 $. Then we see that \[ \int_0^{\frac{1}{\lambda}} (\lambda s)^{q(\nu-\frac{n-2}{2}+\beta+m)} (1+s)^{-q\sigma} s^{n-1} \, ds \leq \lambda^{1-n} \int_0^{\frac{1}{\lambda}} (1+s)^{-q\sigma} s^{n-1} \, ds \leq C \lambda^{-n}, \] (3.15) since $ \nu-\frac{n-2}{2}+\beta+m \geq 0 $ and $ q\sigma > 0 $. For the integral over $ \frac{1}{\lambda} < s < \infty $, we have \[ \int_{\frac{1}{\lambda}}^{\infty} (\lambda s)^{q(m-\frac{n+1}{2})} (1+s)^{-q\sigma} s^{n-1} \, ds = \lambda^{q(m-\frac{n+1}{2})} \int_{\frac{1}{\lambda}}^{\infty} s^{n-1+q(m-\frac{n+1}{2})} (1+s)^{-q\sigma} \, ds. \] Under the hypothesis that $ \sigma > \frac{n}{q} + m $, the integral \[ \int_{\frac{1}{\lambda}}^{\infty} s^{n-1+q(m-\frac{n+1}{2})} (1+s)^{-q\sigma} \, ds \] converges and is bounded by constant which is independent of $ \lambda $. For the region where $ \frac{1}{\lambda} < s < 1 $, we have \[ \int_{\frac{1}{\lambda}}^{1} s^{n-1+q(m-\frac{n+1}{2})} (1+s)^{-q\sigma} \, ds \leq C \lambda^{-n-q(m-\frac{n+1}{2})}. \] Thus, \[ \lambda^{q(m-\frac{n+1}{2})} \int_{\frac{1}{\lambda}}^{\infty} s^{q(m-\frac{n+1}{2})} (1+s)^{-q\sigma} s^{n-1} \, ds \leq \max\{\lambda^{-n}, \lambda^{q(m-\frac{n+1}{2})}\} \] when $ \lambda \geq 1 $. Now take the case where $0 < \lambda \leq 1$. Then, since $\|\beta\| \leq m$ and $\nu \geq \frac{n-2}{2}$, we have \[ \int_0^\frac{1}{\lambda} (\lambda s)^d(q^{\frac{\nu}{2} + \beta + m}) (1 + s)^{-q\sigma} s^{n-1} \, ds \leq C \int_0^\frac{1}{\lambda} (1 + s)^{n-1-q\sigma} \, ds \] \[ = C\left(1 + \frac{1}{\lambda}\right)^{n-q\sigma} \leq C'\lambda^{q\sigma-n}. \] For the integral over $\frac{1}{\lambda} \leq s < \infty$, we notice that \[ \int_{\frac{1}{\lambda}}^\infty (\lambda s)^d(q^{\frac{m-n}{2}})(1 + s)^{-q\sigma} s^{n-1} \, ds \leq \lambda^d(q^{\frac{m-n}{2}}) \int_{\frac{1}{\lambda}}^\infty (1 + s)^{n-1+q\left(m-rac{n-1}{2}\right)-\sigma} \, ds \] since $1 \leq \frac{1}{\lambda} \leq s$. Recalling the assumption that $\sigma > \frac{n}{q} + m$, we can see that \[ n - 1 + q \left(m - \frac{n-1}{2} - \sigma\right) < -1, \] and therefore, \[ \lambda^d(q^{\frac{m-n}{2}}) \int_{\frac{1}{\lambda}}^\infty (1 + s)^{n-1+q\left(m-rac{n-1}{2}\right)-\sigma} \, ds \leq C'\lambda^{q\left(m-rac{n-1}{2}\right)} \left(1 + \frac{1}{\lambda}\right)^{n+q\left(m-rac{n-1}{2}\right)-\sigma} \] \[ \leq C''\lambda^{q\sigma-n}. \] Therefore, $I(\lambda) \leq C\lambda^{q\sigma-n}$ for $0 < \lambda \leq 1$. □ Next, we establish some estimates on the $L^{q,\sigma}$ norms of $R_{0,j}(\lambda^2 \pm i0)(r, s)$ when the norm is only taken with respect to one variable. Proposition 3.6. Let $k \geq 0$ be an integer. Also assume that $1 \leq q < \infty$ and \[ \sigma > \frac{n}{q} + k. \] Then for $\lambda \geq 1$, we have \[ \\|\partial^k_\lambda \text{Im} R_{0,j}(\lambda^2 + i0; r, \cdot)\\|_{L^{q,\sigma}} \leq C_{j,q,\sigma,k} \lambda^{n-2-k} \sum_{\ell+m=k} \left[(1 + \lambda r)^{\ell-rac{n-1}{2}} \left(C_1 \lambda^{-\frac{n}{2}} + C_2 \lambda^{m-rac{n-1}{2}}\right)\right] \] for some $C_{j,q,\sigma,k} > 0$. Furthermore, when $\lambda \leq 1$, we have \[ \\|\partial^k_\lambda \text{Im} R_{0,j}(\lambda^2 + i0; r, \cdot)\\|_{L^{q,\sigma}} \leq C_{j,q,\sigma,k} \lambda^{n-2}(1 + \lambda r)^{k-rac{n-1}{2}}. \] By symmetry, we also have the analogous estimates \[ \\| \partial_x^k \text{Im } R_{0,j}(\lambda^2 + i0; \cdot, s) \\|_{L^q,s} \leq C_{j,q,\sigma,k} \lambda^{n-2-k} \sum_{\ell+m=k} \left[ (1 + \lambda s)^{\ell - \frac{\alpha}{2}} \left( C_{1} \lambda^{\frac{n}{2}} + C_{2} \lambda^{m-\frac{\alpha}{2}} \right) \right] \] for $ \lambda \geq 1 $, and \[ \\| \partial_x^k \text{Im } R_{0,j}(\lambda^2 + i0; \cdot, s) \\|_{L^q,s} \leq C_{j,q,\sigma,k} \lambda^{n-2}(1 + \lambda s)^{k-\frac{\alpha}{2}} \] when $ \lambda \leq 1 $. Remark 3.7. Note that in the special case where the order of differentiation is less than or equal to $ \frac{n-1}{2} $, these estimates reduce to simple polynomial behavior in $ \lambda $. However, if the number of derivatives exceeds this threshold value, we begin to see a non-uniformity with respect to the secondary radial variable. This phenomenon is why the spatial weights appear in the statement of Theorem 4. Proof. Recall that the kernel of $ \text{Im } R_{0,j}(\lambda^2 + i0) $ has the explicit expression \[ \text{Im } R_{0,j}(\lambda^2 + i0; r, s) = \frac{\pi}{2} (rs)^{\frac{n-2}{2}} J_{\nu}(\lambda r) J_{\nu}(\lambda s). \] Since Bessel functions satisfy the recursion relation \[ J'_{\nu}(x) = \frac{1}{2} (J_{\nu-1}(x) - J_{\nu+1}(x)), \] we see that $ \partial_x^k \text{Im } R_{0,j}(\lambda^2 + i0) $ can be written as a finite linear combination of terms of the form \[ (rs)^{\frac{n-2}{2}} r^\ell s^m J_{\nu+\alpha}(\lambda r) J_{\nu+\beta}(\lambda s), \] where $ \ell, m, \alpha, \beta $ are integers satisfying $ \ell + m = k $, $ \|\alpha\| \leq \ell $, and $ \|\beta\| \leq m $. Therefore, by the triangle inequality, it suffices to estimate the weighted $ L^q $ norms of such terms. Taking the $ L^{q,\sigma} $ norm with respect to the $ s $ variable in (3.21) yields \[ \chi^{(n-2-k)}(\lambda r)^q(\ell - \frac{n-2}{2}) \|J_{\nu+\alpha}(\lambda r)\| q \int_0^\infty (\lambda s)^q(m-\frac{n-2}{2}) \|J_{\nu+\beta}(\lambda s)\| q(1 + s)^{-q} s^{n-1} ds. \] Note that since $ \|\alpha\| \leq \ell $, we have that the product $ (\lambda r)^{\ell - \frac{n-2}{2}} \|J_{\nu+\alpha}(\lambda r)\| $ is a continuous function of $ \lambda r $, and thus by (3.9) we obtain \[ (\lambda r)^q(\ell - \frac{n-2}{2}) \|J_{\nu+\alpha}(\lambda r)\| q \leq C(1 + \lambda r)^q(\ell - \frac{n-1}{2}). \] Thus, we have that the $ L^{q,\sigma} $ norm of (3.21) is bounded by \[ C\chi^{(n-2-k)}(1 + \lambda r)^q(\ell - \frac{n-1}{2}) \int_0^\infty (\lambda s)^q(m-\frac{n-2}{2}) \|J_{\nu+\beta}(\lambda s)\| q(1 + s)^{-q} s^{n-1} ds. \] Now, observe that the integral above is in exactly the right form for us to apply Lemma 3.5. Hence, we have that (3.22) is bounded by \[ \begin{cases} C\lambda^{q(n-2-k)}(1 + \lambda r)^q(\ell - \frac{n}{n-1}) \max\{\lambda^{-n}, \lambda^{q(\ell - \frac{n}{n-1})}\}, & \lambda \geq 1 \\ C\lambda^{q(n-2-k)}q\sigma - n(1 + \lambda r)^q(\ell - \frac{n}{n-1}), & \lambda \leq 1, \end{cases} \] for some possibly larger constant $C$. In the case where $\lambda \geq 1$, simply taking $q$th roots gives estimate (3.17). When $\lambda \leq 1$, we can use that $\sigma$ satisfies (3.16) to obtain that $q(n-2-k) + q\sigma - n > q(n-2)$. Once again, taking $q$th roots gives (3.18). \[\square\] Next, we estimate the $L^q$ norm of the resolvent when we do not take the imaginary part. Proposition 3.8. Let $k \geq 0$ be an integer and suppose $1 \leq q \leq \frac{n}{n-2}$. Then, if $\sigma$ satisfies (3.16), we have that when $\lambda \geq 1$, \[ \\|\partial^k \lambda R_{0,j}(\lambda^2 + i0; r, \cdot)\\|_{L^q, \sigma} \leq C\lambda^{n-2-k} \sum_{\ell + m = k} \left[ (1 + \lambda r)^{\ell - \frac{n}{n-1}} (C_1 + C_2\lambda^{\ell - \frac{n}{n-1}}) \right] (3.23) \] for some $C, C_1, C_2 > 0$. If $0 < \lambda \leq 1$, then we have \[ \\|\partial^k \lambda R_{0,j}(\lambda^2 + i0; r, \cdot)\\|_{L^q, \sigma} \leq C_1\lambda^{-k} + C_2\lambda^{n-2-k}(1 + \lambda r)^{k - \frac{n}{n-1}}. (3.24) \] Under the same assumptions on $\sigma$, we also have \[ \\|\partial^k \lambda R_{0,j}(\lambda^2 + i0; \cdot, s)\\|_{L^q, \sigma} \leq C\lambda^{n-2-k} \sum_{\ell + m = k} \left[ (1 + \lambda s)^{\ell - \frac{n}{n-1}} (C_1 + C_2\lambda^{\ell - \frac{n}{n-1}}) \right] (3.25) \] when $\lambda \geq 1$, and \[ \\|\partial^k \lambda R_{0,j}(\lambda^2 + i0; \cdot, s)\\|_{L^q, \sigma} \leq C_1\lambda^{-k} + C_2\lambda^{n-2-k}(1 + \lambda s)^{k - \frac{n}{n-1}} (3.26) \] when $0 < \lambda \leq 1$. Proof. Recalling that \[ R_{0,j}(\lambda^2 + i0)(r, s) = \begin{cases} \frac{\pi}{\nu_j} J_{\nu_j}(\lambda s) H^{(1)}_{\nu_j}(\lambda r), & s < r \\ \frac{\pi}{\nu_j} J_{\nu_j}(\lambda r) H^{(1)}_{\nu_j}(\lambda s), & s > r, \end{cases} \] and (3.6), we see that when $s < r$, $\partial^k \lambda R_{0,j}(\lambda^2 + i0; r, s)$ can be written as a finite linear combination of terms of the form \[ (rs)^{-\frac{n-2}{2}} r^\ell s^m J_{\nu_j + \alpha}(\lambda s) H^{(1)}_{\nu_j + \beta}(\lambda r), \] where, as in the proof of Proposition 3.6, $\ell, m$ are nonnegative integers with $\ell + m = k$ and $\alpha, \beta$ are any integers with $\|\alpha\| \leq \ell$ and $\|\beta\| \leq m$. Similarly, when $r < s$, we can write $\partial^k \lambda R_{0,j}(\lambda^2 + i0)(r, s)$ as a combination of terms of the same form, but with the roles of $r$ and $s$ reversed. Therefore, it suffices to estimate \[ I(\lambda, r) := \\|(rs)^{-\frac{n-2}{2}} r^\ell s^m J_{\nu_j + \beta}(\lambda s) H^{(1)}_{\nu_j + \alpha}(\lambda r) \rho^{-\sigma}(s) 1_{\{s < r\}}\\|_{L^q}^2 (3.27) \] and \[ I(\lambda, r) := \\| (rs)^{-\frac{n-2}{2}} r^s m J_{\nu_j+\alpha}(r) H^{(1)}_{\nu_j+\beta}(s) \rho^{-\sigma}(s) 1_{\{s > r\}} \\|^q_{L^q} \] (3.28) for any $ \ell, m, \alpha, \beta $ as above. We first estimate $ I(\lambda, r) $ in the case where $ \lambda r \geq 1 $. Under this hypothesis, we can apply (3.9) to obtain \[ I(\lambda, r) \leq C \lambda^{q(1-\frac{n-2}{2})} (\lambda r)^{q(\frac{\ell}{2}-\frac{n}{2})} \int_0^r (\lambda s)^{q(m-\frac{n-2}{2})} \|J_{\nu_j+\beta}(s)\|^q (1 + s)^{-q\sigma} s^{n-1} ds. \] We now apply Lemma 3.5 to the integral above, which gives \[ I(\lambda, r) \leq \begin{cases} C \lambda^{q(1-\frac{n-2}{2})} (\lambda r)^{q(\frac{\ell}{2}-\frac{n}{2})} \max\{\lambda^{-n}, \lambda^{q(\frac{n-2}{2})}\}, & \lambda r \geq 1, \lambda \geq 1 \\ C \lambda^{q(1-\frac{n-2}{2})} (\lambda r)^{q(\frac{\ell}{2}-\frac{n}{2})}, & \lambda r \geq 1, 0 < \lambda \leq 1. \end{cases} \] (3.29) Now let us consider the case where $ \lambda r \leq 1 $. Here we can apply (3.8), which gives \[ I(\lambda, r) \leq C \lambda^{q(n-2-k)} (\lambda r)^{q(\frac{n}{2}-\nu_j-\alpha)} \int_0^r (\lambda s)^{q(m-\frac{n-2}{2}+\nu_j+\beta)} (1 + s)^{-q\sigma} s^{n-1} ds. \] (3.30) If $ r \leq 1 $, we can bound the right-hand side of (3.30) by \[ C \lambda^{q(n-2-k)} (\lambda r)^{q(k-\alpha+\beta-(n-2))} r^{n-1} \int_0^r (1 + s)^{-q\sigma} ds \leq \widetilde{C} \lambda^{q(n-2-k)} (\lambda r)^{-q(n-2)} r^n \] \[ = \widetilde{C} \lambda^{-qk} r^{n-q(n-2)}, \] since $ k - \alpha + \beta \geq 0 $ and $ \int_0^r (1 + s)^{-q\sigma} ds \leq C' r $ for some $ C' > 0 $. Recalling that $ q \leq \frac{n}{n-2} $, we obtain \[ I(\lambda, r) \leq C \lambda^{-qk}, \quad \lambda r \leq 1, r \leq 1. \] (3.31) Now, if $ r \geq 1 $, we can bound the right-hand side (3.30) by \[ C \lambda^{q(n-2-k)} (\lambda r)^{q(k-\alpha+\beta-(n-2))} \int_0^r (1 + s)^{-q\sigma} s^{n-1} ds \leq C \lambda^{q(n-2-k)} (\lambda r)^{-q(n-2)} (1 + r)^{n-q\sigma} \] (3.32) since $ k - \alpha + \beta \geq 0 $ and $ \lambda r \leq 1 $. Recalling that $ \sigma \geq \frac{n}{q} $, we have that the right-hand side of (3.31) by \[ C \lambda^{-qk} r^{-q(n-2)} \leq C \lambda^{-qk}. \] (3.33) Combining (3.31) and (3.33), we have that \[ I(\lambda, r) \leq C \lambda^{-qk}, \quad \lambda r \leq 1. \] (3.34) Combining (3.34) with (3.29), we have that \[ I(\lambda, r) \leq \begin{cases} C \lambda^{q(n-2-k)}(1 + \lambda r)^{q\left(\ell - \frac{n-1}{2}\right)} \max\{\lambda^{-n}, \lambda^{q(m - \frac{n-1}{2})}\}, & \lambda \geq 1 \\ C_1 \lambda^{-q} + C_2 \lambda^{q(n-2)}(1 + \lambda r)^{q\left(\ell - \frac{n-1}{2}\right)}, & 0 < \lambda \leq 1. \end{cases} \] (3.35) Next, we move on to estimating $\Pi(\lambda, r)$. Again we consider the cases $\lambda r \geq 1$ and $\lambda r \leq 1$ separately. For $\lambda r \geq 1$, we apply (3.8) and (3.9) to obtain \[ \Pi(\lambda, r) \leq C \lambda^{q(n-2-k)}(\lambda r)^{q\left(\ell - \frac{n-1}{2}\right)} \int_{\frac{1}{r}}^{\infty} (\lambda s)^{q\left(m - \frac{n-1}{2}\right)}(1 + s)^{-q\sigma} s^{n-1} ds. \] We can then repeat arguments from the proof of Lemma 3.5 to obtain \[ \Pi(\lambda, r) \leq \begin{cases} C \lambda^{q(n-2-k)}(\lambda r)^{q\left(\ell - \frac{n-1}{2}\right)} \max\{\lambda^{-n}, \lambda^{q(m - \frac{n-1}{2})}\}, & \lambda r \geq 1, \lambda \geq 1 \\ C \lambda^{q(n-2-k)}(\lambda r)^{q\left(\ell - \frac{n-1}{2}\right)}, & \lambda r \geq 1, \lambda \leq 1. \end{cases} \] (3.36) Now consider the case where $\lambda r \leq 1$. Here we rewrite $\Pi(\lambda, r)$ as \[ \lambda^{q(n-2-k)}(\lambda r)^{q\left(\ell - \frac{n-1}{2}\right)} \|J_{\nu_j + \alpha}(\lambda r)\|^{q\frac{1}{q}} \left( \int_{\frac{1}{r}}^{\infty} (\lambda s)^{q\left(m - \frac{n-1}{2}\right)} \|H^{(1)}_{\nu_j + \beta}(\lambda s)\|^{q}(1 + s)^{-q\sigma} s^{n-1} ds \right). \] For the integral over $\frac{1}{r} < s < \infty$, we can apply (3.9) to $H^{(1)}_{\nu_j + \beta}$ and (3.8) to $J_{\nu_j + \alpha}$ and repeat previous calculations to show that \[ \lambda^{q(n-2-k)}(\lambda r)^{q\left(\ell - \frac{n-1}{2}\right)} \|J_{\nu_j + \alpha}(\lambda r)\|^{q\frac{1}{q}} \int_{\frac{1}{r}}^{\infty} (\lambda s)^{q\left(m - \frac{n-1}{2}\right)} \|H^{(1)}_{\nu_j + \beta}(\lambda s)\|^{q}(1 + s)^{-q\sigma} s^{n-1} ds \] \[ \leq \begin{cases} C \lambda^{q(n-2-k)} \max\{\lambda^{-n}, \lambda^{q(m - \frac{n-1}{2})}\}, & \lambda r \leq 1, \lambda \geq 1 \\ C \lambda^{q(n-2-k)} \lambda^{q\sigma - n}, & \lambda r \leq 1, \lambda \leq 1 \end{cases} \] (3.37) \[ \leq \begin{cases} C \lambda^{q(n-2-k)} \max\{\lambda^{-n}, \lambda^{q(m - \frac{n-1}{2})}\}, & \lambda r \leq 1, \lambda \geq 1 \\ C \lambda^{q(n-2-k)}, & \lambda r \leq 1, \lambda \leq 1, \end{cases} \] where the last inequality follows since $\sigma > \frac{n}{q} + k$. Now, in the region where $r < s < \frac{1}{\lambda}$, we must apply (3.8), which yields \[ \int_r^\frac{1}{\lambda} (\lambda s)^q(m-\frac{n-2}{2})\|H_{\nu_j+\beta}(\lambda s)\|q(1 + s)^{-\sigma} s^{n-1} ds \leq C \int_r^\frac{1}{\lambda} (\lambda s)^q(m-\frac{n-2}{2}-\nu_j-\beta)(1 + s)^{-\sigma} s^{n-1} ds \] \[ = C\lambda^{q(m-\frac{n-2}{2}-\nu_j-\beta)} \int_r^{s} s^{n-1+q(m-\frac{n-2}{2}-\nu_j-\beta)}(1 + s)^{-\sigma} ds. \] If $\lambda \geq 1$, then $(1 + s)^{-\sigma}$ is bounded by a uniform constant for all $r < s < \frac{1}{\lambda}$, and so the above is bounded by \[ C \left( \lambda^{-n} r^n(\lambda r)^q(m-\frac{n-2}{2}-\nu_j-\beta) \right) \] after possibly increasing $C$. We note that under our assumptions on $r$ and $\lambda$, this quantity is still nonnegative. Combining this with (3.8) applied to $J_{\nu_j+\alpha}$, we obtain \[ \lambda^{q(n-2-k)}(\lambda r)^q(\ell-\frac{n-2}{2})\|J_{\nu_j+\alpha}(\lambda r)\|q \int_r^\frac{1}{\lambda} (\lambda s)^q(m-\frac{n-2}{2})\|H_{\nu_j+\beta}(\lambda s)\|q(1 + s)^{-\sigma} s^{n-1} ds \] \[ \leq C\lambda^{q(n-2-k)}(\lambda r)^q(\ell-\frac{n-2}{2}+\nu_j+\alpha) \left( \lambda^{-n} r^n(\lambda r)^q(m-\frac{n-2}{2}-\nu_j-\beta) \right) \] \[ \leq \lambda^{q(n-2-k)} \left[ C_1 \lambda^{-n} (\lambda r)^q(\ell-\frac{n-2}{2}+\nu_j+\alpha) + C_2 r^n q(n-2) (\lambda r)^{q(k+\alpha-\beta)} \right], \] for some $C_1, C_2 > 0$. Recalling that $\|\alpha\| \leq \ell$, $\nu_j \geq \frac{n-2}{2}$, and $\|\alpha\| + \|\beta\| \leq k$, we obtain \[ \lambda^{q(n-2-k)}(\lambda r)^q(\ell-\frac{n-2}{2})\|J_{\nu_j+\alpha}(\lambda r)\|q \int_r^\frac{1}{\lambda} (\lambda s)^q(m-\frac{n-2}{2})\|H_{\nu_j+\beta}(\lambda s)\|q(1 + s)^{-\sigma} s^{n-1} ds \] \[ \leq \lambda^{q(n-2-k)} \left[ C_1 \lambda^{-n} + C_2 r^n q(n-2) \right] \] \[ \leq C\lambda^{q(n-2-k)} \] for $\lambda r \leq 1$ and $\lambda \geq 1$, since $q \leq \frac{n}{n-2}$. Finally, we consider the same integral over $r < s < \frac{1}{\lambda}$, once again where $0 < \lambda r \leq 1$ but with $\lambda \leq 1$. For this, we further subdivide into the cases where $r \leq 1$ and $r \geq 1$. If $r \leq 1$, we split the integral into the regions where $r < s < 1$ and $1 < s < \frac{1}{\lambda}$. For the integral over $r < s < 1$, we can repeat the above argument to obtain the same bound as in (3.39). To bound the integral over $1 < s < \frac{1}{\lambda}$, we use (3.8) to obtain $$\lambda^{q(n-2-k)}(\lambda r)^{q\left(\frac{n-2}{2}\right)}\|J_{\nu+\alpha}(\lambda r)\|^q \int_1^\infty (\lambda s)^{q\left(m-\frac{n-2}{2}\right)}\|H_{\nu_j+\beta}(\lambda s)\|^q (1 + s)^{-q\sigma} s^{n-1} ds$$ $$\leq \lambda^{q(n-2-k)}(\lambda r)^{q\left(\frac{n-2}{2}\right)\nu_j+\alpha} \int_1^\infty (\lambda s)^{q\left(m-\frac{n-2}{2}\nu_j-\beta\right)}(1 + s)^{-q\sigma} s^{n-1} ds$$ $$= \lambda^{q(a-\beta)r}q\left(\frac{n-2}{2}+\nu_j+\alpha\right) \int_r^\infty s^{q\left(m-\frac{n-2}{2}\nu_j-\beta\right)+n-1}(1 + s)^{-q\sigma} ds$$ $$\leq \lambda^{-qk} \int_1^\infty s^{qk+n-1}(1 + s)^{-q\sigma} ds$$ $$\leq C\lambda^{-qk},$$ where the last inequality follows from the fact that $\sigma > \frac{n}{q} + k$. Now, if $r \geq 1$, we have $$\lambda^{q(n-2-k)}(\lambda r)^{q\left(\frac{n-2}{2}\right)}\|J_{\nu+\alpha}(\lambda r)\|^q \int_1^\infty (\lambda s)^{q\left(m-\frac{n-2}{2}\right)}\|H_{\nu_j+\beta}(\lambda s)\|^q (1 + s)^{-q\sigma} s^{n-1} ds$$ $$\leq \lambda^{q(n-2-k)}(\lambda r)^{q\left(\frac{n-2}{2}\right)\nu_j+\alpha} \int_r^\infty (\lambda s)^{q\left(m-\frac{n-2}{2}\nu_j-\beta\right)}(1 + s)^{-q\sigma} s^{n-1} ds$$ $$\leq C\lambda^{q(a-\beta)r}q\left(\frac{n-2}{2}+\nu_j+\alpha\right) \int_r^\infty s^{q\left(m-\frac{n-2}{2}\nu_j-\beta\right)+n-1}(1 + s)^{-q\sigma} ds$$ $$\leq C\lambda^{q(a-\beta)r}q(k+a-\beta-(n-2))^{-q\sigma+n}$$ $$\leq C\lambda^{q(a-\beta)r}q(a-\beta-(n-2)),$$ where in the last inequality we once again used that $\sigma > \frac{n}{q} + k$. Now, since $r \leq \frac{1}{\lambda}$, we have that the above is bounded by a constant times $\lambda^{q(n-2)}$ for $\lambda \leq 1$. Combining this with (3.36), (3.37), and (3.39), we obtain $$I(\lambda, r) \leq \begin{cases} C\lambda^{q(n-2-k)}(1 + \lambda r)^{\frac{n-1}{2}} \max\{1, \lambda^{q\left(m-\frac{n-1}{2}\right)}\}, & \lambda \geq 1 \\ C_1\lambda^{-qk} + C_2\lambda^{q(n-2-k)}(1 + \lambda r)^{\frac{n-1}{2}}, & 0 < \lambda \leq 1. \end{cases} \quad (3.40)$$ In light of (3.35) and (3.40), taking $q$th roots completes the proof of Proposition 3.8. \qed In this section we establish some weighted operator norm estimates for the perturbed radial resolvents $R_{V,j}$, defined via the mode-by-mode decomposition of $R_V(z^2)$: $$ R_V(z^2) = \sum_{j=0}^{\infty} R_{V,j}(z^2) E_j. $$ Since $V$ is radial, it follows that we can write $$ R_{V,j}(z^2) = \left( \partial_r^2 + \frac{n-1}{r} \partial_r + z^2 - \frac{\mu_j^2}{r^2} + V(r) \right)^{-1}, \tag{4.1} $$ wherever this inverse is well defined. Here, we prove that the mapping properties established for $R_{0,j}$ in Proposition 3.1 and Proposition 3.4 extend to $R_{V,j}$. Similar weighted estimates for Schrödinger operators on hyperbolic space are given in Section 4 of [8], and the techniques therein follow an analogous structure. For a potential $V \in \rho^{-2\sigma}L^\infty(\mathbb{R}^+)$ with $\sigma > \frac{1}{2}$, the operator norm $\\|VR_0(z^2)\\|_{L^2 \to L^2}$ is small for $\text{Im} \, z$ large by the standard resolvent norm estimate on $R_0(z^2)$, which is computable in a similar fashion to that discussed in Proposition 3.1. Hence, the operator $1 + VR_0(z^2)$ is invertible by Neumann series for large $\text{Im} \, z$. For $z$ in this range, we can write $$ R_{V,j}(z^2) = R_{0,j}(z^2)(1 + VR_{0,j}(z^2))^{-1}. $$ We begin our analysis of these perturbed resolvents by proving Theorem 1, which we recall states that $R_{0,j}$ admits a meromorphic continuation to the logarithmic cover of $\mathbb{C} \setminus \{0\}$ and satisfies the limiting absorption principle. Proof of Theorem 1. As mentioned in Section 2, the meromorphic extension of $$ \chi R_{0,j} \chi $$ with $\chi$ a smooth, compactly supported function, follows from [3]. The meromorphic continuation of $\chi R_{V,j}(\lambda) \chi$ follows from the work of Guillopé–Zworski [33] and the compactness of the resolvent on a compact manifold with a conic singularity, which can be seen for instance in the treatment of domains for conic operators in the work of Melrose-Wunsch [51]. Using the techniques from Section 3, we can easily see that $\rho(r)^{-\eta}R_{0,j}(z)$ is compact as an operator on $L^{2,\delta}$ provided that $\text{Im} \, (z^2) > 0$ and $\eta > \delta$, since the upper bounds (3.8) and (3.9) remain valid for arguments in the upper half plane. Next, we prove the limiting absorption principle for $R_{V,j}$. Following [29], we observe that mapping properties of $R_{V,j}$ can be deduced from the estimates established for $R_{0,j}$. By the resolvent identity $$ R_{0,j}(z^2) = R_{V,j}(z^2) + R_{V,j}(z^2)VR_{0,j}(z^2), $$ we can write $$ R_{0,j}(z^2)\rho^{-\sigma} = R_{V,j}(z^2)\rho^{-\sigma}(1 + \rho^\sigma VR_{0,j}(z^2)\rho^{-\sigma}). $$ for $ \rho(r) = 1 + r $. The factor on the right is meromorphically invertible by the analytic Fredholm theorem, so that \[ R_{V,j}(z^2)\rho^{-\sigma} = R_{0,j}(z^2)\rho^{-\sigma}(1 + \rho^\sigma VR_{0,j}(z^2)\rho^{-\sigma})^{-1}, \] whenever the inverse exists. By Proposition 3.1 and the fact that $ \rho^\sigma V = \rho^{2\sigma} V \rho^{-\sigma} $, we have \[ \\|\rho^\sigma VR_{0,j}(\lambda^2 \pm i0)\rho^{-\sigma}\\|_{L^2 \to L^2} \leq C \\|\rho^{2\sigma} V\\|_{L^\infty} \|\lambda\|^{-1}. \] Hence for $ V \in \rho^{-\sigma} L^\infty $, there exists a constant $ M_V $ such that for $ \|\lambda\| \geq M_V $, \[ \\|\rho^\sigma VR_{0,j}(\lambda^2 \pm i0)\rho^{-\sigma}\\|_{L^2 \to L^2} \leq \frac{1}{2}, \] implying that $ (1 + \rho^\sigma VR_{0,j}(\lambda^2 \pm i0)\rho^{-\sigma})^{-1} $ exists and satisfies \[ \\|(1 + \rho^\sigma VR_{0,j}(\lambda^2 \pm i0)\rho^{-\sigma})^{-1}\\|_{L^2 \to L^2} \leq 2. \] The estimates then follow from (4.2) and Proposition 3.1. $ \square $ As stated in the introduction, we postpone the proof of Theorem 2 until the appendices, and so we take the absence of embedded eigenvalues and resonances in the range $(0, \infty)$ as given for now. With this property in hand, our next goal is to prove the low energy estimates estimates from Theorem 3 under the assumption that $-\Delta_{C(X)} + V$ does not have a resonance at zero energy. Proof of Theorem 3. We prove the desired estimates only for $ R_{V,j}(\lambda^2 + i0) $, since the proof is analogous for $ R_{V,j}(\lambda^2 - i0) $. Using a resolvent expansion motivated by [8], we observe that \[ R_{V,j}(\lambda + i0) = R_{0,j}(\lambda + i0)[I + VR_{0,j}(\lambda + i0)]^{-1}. \] Hence, if we can establish boundedness and regularity of $[I + VR_{0,j}(\lambda^2 + i0)]^{-1}$ through $ \lambda = 0 $, then (1.5) follows immediately from Proposition 3.1. We observe that boundedness and regularity of the operator $(I + R_{0,j}(\lambda^2 + i0)V)^{-1}$ follows from Theorem 2 and the assumption that 0 is not a resonance or an eigenvalue of $-\Delta_{C(X)} + V$ and hence the boundedness of \[ (I + VR_{0,j}(\lambda^2 - i0))^{-1} = [(I + R_{0,j}(\lambda^2 + i0)V)^{-1}]^* \] follows from analytic Fredholm theory. Thus, we may extend (1.4) through $ \lambda = 0 $ to arrive at (1.5). To estimate $ \partial_k^1 \text{Im} R_{V,j} $, we first consider the case where $ k = 0 $ and establish the pointwise bounds in $ \lambda $. For this, we take note of the following resolvent identity \[ R_{V,j}(\lambda^2 + i0) - R_{V,j}(\lambda^2 - i0) = (I + R_{0,j}(\lambda^2 + i0)V)^{-1}[R_{0,j}(\lambda^2 + i0) - R_{0,j}(\lambda^2 - i0)](I + VR_{0,j}(\lambda^2 - i0))^{-1}. \] This shows that the behavior of $\text{Im} \, R_{V,j}(\lambda^2 + i0)$ near $\lambda = 0$ is the same as that of $\text{Im} \, R_{0,j}(\lambda^2 + i0)$, provided that the operators $$(I + R_{0,j}(\lambda^2 + i0)V)^{-1} \text{ and } (I + VR_{0,j}(\lambda^2 - i0))^{-1}$$ are bounded for $\lambda$ in a neighborhood of 0, which we have already observed earlier in the proof. As a result, the $k = 0$ bound in (1.6) clearly follows. The results for $k > 0$ then follow by differentiating term by term and applying Proposition 3.4. □ 5. Full spectral resolution estimates With the mapping properties for both the free and perturbed resolvents established in the previous sections, we are now able to obtain some precise pointwise estimates on the Schwartz kernel of $\text{Im} \, R_{V,j}(\lambda^2 \pm i0; r, s)$. Proposition 5.1. Let $k \geq 0$ be an integer. Suppose $V \in \rho^{-2\sigma} L^\infty(\mathbb{R}^+)$ with $$\sigma > 4 \left\lfloor \frac{n}{4} \right\rfloor - 2 + k,$$ then for any $\alpha \geq \max\{k - \frac{n-1}{2}, 0\}$, $$\sup_{r,s>0} \left\| \rho^{-\alpha}(r) \partial_{\lambda}^k \text{Im} \, R_{V,j}(\lambda^2 \pm i0; r, s) \rho^{-\alpha}(s) \right\| \leq C_{j,k,V} \lambda^{2\left\lfloor \frac{n}{4} \right\rfloor (n-2) - 1}$$ for all $\lambda \geq 1$ and some $C > 0$. Furthermore, if $0 < \lambda \leq 1$, we have that $$\sup_{r,s>0} \left\| \rho^{-\alpha}(r) \partial_{\lambda}^k \text{Im} \, R_{V,j}(\lambda^2 \pm i0; r, s) \rho^{-\alpha}(s) \right\| \leq C_{j,k,V} \lambda^{n-2-k},$$ under the same restrictions on $\alpha$. The proof proceeds similarly to [8, §6], which utilizes the following modified version of Young’s inequality. Lemma 5.2. Suppose that on a measure space $(Y, \mu)$ the integral kernels $K_j(z, w)$, $j = 1, 2$, satisfy $$\\|K_1(z, \cdot)\\|_{L^{q_1}} \leq A, \quad \\|K_1(\cdot, w)\\|_{L^{q_1}} \leq A, \quad \\|K_2(\cdot, w')\\|_{L^{q_2}} \leq B$$ uniformly in $z, w, w'$ for $q_1, q_2 \in [1, \infty]$. Then if $\frac{1}{q_1} + \frac{1}{q_2} = \frac{1}{p} + 1$, we have that $$\left\\| \int K_1(\cdot, w)K_2(w, w') \, d\mu(w) \right\\|_{L^p} \leq AB$$ uniformly in $w'$. The bound on $\\|K_1(\cdot, w)\\|_{L^{q_1}}$ is not required if $p = \infty$. With this lemma in hand, we proceed to the proof of Proposition 5.1. Proof of Proposition 5.1. We begin by expanding $R_{V,j}$ in a Birman-Schwinger series at all frequencies, as in [29], which gives $$R_{V,j}(\tau) = \sum_{\ell=0}^{2M-1} R_{0,j}(\tau)(-V R_{0,j}(\tau))^\ell + \left[ R_{0,j}(\tau)V \right]^M R_{V,j}(\tau)[VR_{0,j}(\tau)]^M. \tag{5.4}$$ As previously discussed, it suffices to consider only the case where we choose $\lambda^2 + i0$ with $\lambda > 0$. For simplicity, we write $R_{0,j}$ for $R_{0,j}(\lambda^2 + i0)$ and $R_{V,j}$ for $R_{V,j}(\lambda^2 + i0)$. We first consider the remainder term $[R_{0,j} V]^M R_{V,j} [VR_{0,j}]^M$. Since $V \in \rho^{-2\sigma}L^\infty$, we may write $V(r) = \rho^{-2\sigma}(r)f(r)$ for some $f \in L^\infty(\mathbb{R}^+)$. Also, note that for any two operators with Schwartz kernels $A(r,s)$, $B(r,s)$, the kernel of their composition is given by $$\langle A(r,\cdot), B(\cdot, s) \rangle_{L^2(\mathbb{R}^+)} = \langle B(\cdot, s), A(r, \cdot) \rangle_{L^2(\mathbb{R}^+)},$$ provided the composition makes sense. Therefore, we can write $$\rho^{-\alpha}[R_{0,j} V]^M R_{V,j} [VR_{0,j}]^M \rho^{-\alpha}(r,s) = \langle (\rho^{-\sigma} R_{V,j} \rho^{-\sigma})A(\cdot,s), A^(r,\cdot) \rangle_{L^2}, \tag{5.5}$$ where $$A(r,s) = (\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})^{M-1}(\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})(r,s),$$ and $A^$ denotes the adjoint with respect to the $L^2$ pairing. However, we know that $A^(r,s) = A(s,r)$, and hence we can express the right-hand side of (5.5) as $$\langle (\rho^{-\sigma} R_{V,j} \rho^{-\sigma})A(\cdot,s), A(\cdot,r) \rangle_{L^2}.$$ By (1.5), we have that $$\left\| \partial^k_\lambda \langle (\rho^{-\sigma} R_{V,j} \rho^{-\sigma})A(\cdot,s), A(\cdot,r) \rangle_{L^2} \right\| \leq \frac{C}{\langle \lambda \rangle} \max_{k_1, k_2 \leq k} \left( \\| \partial^{k_1}_\lambda A(\cdot,s) \\|_{L^2} \\| \partial^{k_2}_\lambda A(\cdot,r) \\|_{L^2} \right). \tag{5.6}$$ To estimate the norms on the right, we wish to iteratively apply Lemma 5.2 to each factor in the definition of $A$. For this we consider the high and low frequency cases separately. First, suppose $\lambda \geq 1$. By Proposition 3.8, we have that for $1 \leq q \leq \frac{n}{n-2}$ and any $0 \leq \tilde{k} \leq k_1$, $$\left\\| \rho^{-\sigma}(r) \partial^k_\lambda R_{0,j} \rho^{-\sigma}(r,\cdot) \right\\|_{L^q} \leq C \rho^{-\sigma}(r) \lambda^{n-2-\tilde{k}} \sum_{\ell+m=\tilde{k}} \left[ (1+\lambda r)^{\ell-\frac{n-1}{2}} \left( C_1 + C_2 \lambda^{m-\frac{n-1}{2}} \right) \right]. \tag{5.7}$$ Note that if $\ell \leq \frac{n-1}{2}$, we can see that the corresponding term in (5.7) is bounded by a constant times $$\lambda^{n-2-\tilde{k}} \max\{1, \lambda^{\tilde{k}-\ell-\frac{n-1}{2}}\} \leq \max\{\lambda^{n-2-\tilde{k}}, \lambda^{\frac{n-3}{2}-\ell}\},$$ uniformly for $r \in [0,\infty)$. On the other hand, if $\ell > \frac{n-1}{2}$ then we have that $$\rho^{-\sigma}(r)(1+\lambda r)^{\ell-\frac{n-1}{2}}\lambda^{n-2-\tilde{k}} \leq (1+\lambda)^{\ell-\frac{n-1}{2}}(1+\tilde{k})^{\ell-\frac{n-1}{2}-\sigma} \lambda^{n-2-\tilde{k}} \leq C(1+\tilde{k})^{-\frac{n-1}{2}} \lambda^{\frac{n-3}{2}-\tilde{k}} (1+\tilde{k})^{\frac{n-3}{2}-\ell}. \tag{5.8}$$ by Cauchy-Schwarz. Recalling our conditions on $ \sigma $, we see that $ \tilde{k} - \sigma - \frac{n-1}{2} < 0 $. Therefore, the corresponding term in (5.7) is bounded by a constant times \[ \lambda^{\frac{n-3}{2}-(\tilde{k}-\ell)} \max\{1, \lambda^{(\tilde{k}-\ell)-\frac{n-1}{2}}\} = \max\{\lambda^{\frac{n-3}{2}-(\tilde{k}-\ell)}, \lambda^{-1}\} \] uniformly in $ r $. Maximizing over the possible combinations of $ \ell, m $ with $ \ell + m = \tilde{k} $, we have that \[ \left\\| \rho^{-\sigma} \partial_j^k R_{0,j} \rho^{-\sigma}(r, \cdot) \right\\|_{L^q} \leq C \max\{\lambda^{n-2-\tilde{k}}, \lambda^{\frac{n-3}{2}}\} \] for some $ C > 0 $, uniformly in $ r $. A similar argument gives \[ \left\\| \rho^{-\sigma} \partial_j^k R_{0,j} \rho^{-\sigma}(\cdot, s) \right\\|_{L^q} \leq C \max\{\lambda^{n-2-\tilde{k}}, \lambda^{\frac{n-3}{2}}\} \] uniformly in $ s $. For the final factor in the definition of $ A $, which has asymmetric weights, we only need an estimate in the left variable in order to apply Lemma 5.2. By Proposition 3.8 we have, for $ 1 \leq q \leq \frac{n}{n-2} $, \[ \left\\| \rho^{-\alpha} g \partial_j^k R_{0,j} \rho^{-\alpha}(\cdot, s) \right\\|_{L^q} \leq C \rho^{-\alpha}(s) \lambda^{n-2-\tilde{k}} \sum_{\ell + m = \tilde{k}} \left[ (1 + \lambda s)^{\max\{\alpha - \frac{n-1}{2}, 0\}} \left( C_1 + C_2 \lambda^{m - \frac{n-1}{2}} \right) \right]. \] We may repeat our previous argument almost exactly in order to bound this quantity. The only difference here is that the analogue of (5.8) has a factor of $ \rho^{-\alpha} $ instead of $ \rho^{-\sigma} $. So in order to obtain an estimate which is uniform in $ s $, we must enforce the condition that $ \alpha \geq \max\{k - \frac{n-1}{2}, 0\} $ and recall that $ \tilde{k} \leq k $. Aside from this, the rest of the argument is identical, and so we have \[ \left\\| \rho^{-\sigma} f \partial_j^k R_{0,j} \rho^{-\alpha}(\cdot, s) \right\\|_{L^q} \leq C \max\{\lambda^{n-2-\tilde{k}}, \lambda^{\frac{n-3}{2}}\} \] uniformly in $ s $, provided that $ \alpha \geq \max\{k - \frac{n-1}{2}, 0\} $. We can now iteratively apply Lemma 5.2 to $ \\| \partial_j^k A(\cdot, s) \\|_{L^2} $. To do this, we must choose $ q = \frac{2M}{2M-1} $ so that $ \frac{M}{q} = \frac{1}{2} + (M - 1) $. We also require $ 1 \leq q \leq \frac{n}{n-2} $, which is equivalent to taking $ M \geq \frac{n}{4} $. This then implies that we must take $ \sigma > \frac{n(2M-1)}{2M} + k_1 $ in order for Proposition 3.6 and Proposition 3.8 to apply. In particular, we can take $ M = \left\lfloor \frac{n}{4} \right\rfloor $, the smallest integer larger than $ \frac{n}{4} $. Using (5.1), we see that \[ \sigma > 4 \left\lfloor \frac{n}{4} \right\rfloor - 2 + k = n \left( \frac{4M - 2}{n} \right) + k \geq n \left( \frac{4M - 2}{4M} \right) + k \geq n \left( \frac{2M - 1}{2M} \right) + k_1, \] and so the following argument holds under this condition on $ \sigma $. Repeatedly applying Lemma 5.2 to $ \\| \partial_j^k A(\cdot, s) \\|_{L^2} $ and using that $ f $ is uniformly bounded, we obtain \[ \\| \partial_j^k A(\cdot, s) \\|_{L^2} \leq C \lambda^{M(n-2)}. \] The analogous estimate for $ \\| \partial_\lambda^k A(\cdot, r) \\| $ combined with (5.6) gives \[ \left\| \partial_\lambda^k (\langle \rho^{-\sigma} R_{V,j} \rho^{-\sigma} \rangle A(\cdot, s), A(\cdot, r)) \right\| \leq C \lambda^{2M(n-2)-1} \] for $ \lambda \geq 1 $, and this estimate holds uniformly in $ r $ and $ s $. Next, we consider the remainder term in (5.4) when $ 0 < \lambda \leq 1 $. In this case, taking the imaginary part in the left-hand side of (5.6) is essential, so we must estimate \[ \partial_\lambda^k \text{Im} \langle \rho^{-\sigma} R_{V,j} \rho^{-\sigma} A(\cdot, s), A(\cdot, r) \rangle_{L^2}. \] First, we note that the above can be written as a finite linear combination of terms where the imaginary part falls on either $ R_{V,j} $ or at least one of the factors of $ A $. Thus, by (1.5) and (1.6), we can write \[ \left\| \partial_\lambda^k \text{Im} \langle \rho^{-\sigma} R_{V,j} \rho^{-\sigma} A(\cdot, s), A(\cdot, r) \rangle_{L^2} \right\| \leq C \max_{k_1+k_2+k_3 \leq k} \lambda^{n-2-k_3} \\| \partial_\lambda^{k_1} A(\cdot, s) \\|_{L^2} \\| \partial_\lambda^{k_2} A(\cdot, r) \\|_{L^2} \] for $ 0 < \lambda \leq 1 $. To estimate the first term on the right-hand side of (5.6), we can argue analogously to the $ \lambda \geq 1 $ case, but now we use the low-frequency estimates from Proposition 3.8, which give \[ \\| \rho^{-\sigma} \partial_\lambda^{\tilde{k}} R_{0,j} \rho^{-\sigma} \\|_{L^q} \leq C_1 \lambda^{\tilde{k}-k} \rho^{-\sigma} + C_2 \lambda^{n-2-\tilde{k}} (1 + \lambda r)^{\tilde{k}-\frac{n-1}{2}} \rho^{-\sigma} \leq C \lambda^{\tilde{k}} \] for any $ \tilde{k} \leq k $ and $ 1 \leq q \leq \frac{n}{n-2} $ as before. Similarly, we have \[ \\| \rho^{-\sigma} \partial_\lambda^{\tilde{k}} R_{0,j} \rho^{-\alpha} \\|_{L^q} \leq C \lambda^{\tilde{k}}, \] for $ \alpha \geq \max\{k - \frac{n-1}{2}, 0\} $. Therefore, using Lemma 5.2, we have that \[ \\| \partial_\lambda^{\tilde{k}} A(\cdot, s) \\|_{L^2} \leq C \lambda^{\tilde{k}} \] uniformly in $ s $, for $ 0 < \lambda \leq 1 $. Therefore, we have \[ \max_{k_1+k_2+k_3 \leq k} \lambda^{n-2-k_3} \\| \partial_\lambda^{k_1} A(\cdot, s) \\|_{L^2} \\| \partial_\lambda^{k_2} A(\cdot, r) \\|_{L^2} \leq C \lambda^{n-2-k} \] Now, to handle the second term on the right-hand side of (5.14), we note that one may expand $ \text{Im} A(\cdot, s) $ into a linear combination of terms in which the imaginary part falls on at least one factor of $ R_{0,j} $. Therefore, we can use Proposition 3.6 to obtain that \[ \\| \rho^{-\sigma} \partial_\lambda^{\tilde{k}} \text{Im} R_{0,j} \rho^{-\sigma} \\|_{L^q} \leq C \lambda^{n-2} (1 + \lambda r)^{k-\frac{n-1}{2}} \rho^{-\sigma} \leq C \lambda^{n-2} \] for any $ \tilde{k} \leq k $. Thus, applying Lemma 5.2 in combination with (5.15) and (5.17) gives \[ \\| \partial_\lambda^{\tilde{k}} \text{Im} A(\cdot, s) \\| \leq C \lambda^{n-2-\tilde{k}} \] for any $ \tilde{k} \leq k $. Hence, we have \[ \max_{k_1+k_2 \leq k} \\| \partial_\lambda^{k_1} A(\cdot, s) \\|_{L^2} \\| \partial_\lambda^{k_2} A(\cdot, r) \\|_{L^2} \leq C \lambda^{n-2-k} \] uniformly in $ r, s $. Combining (5.16) and (5.18) with (5.14) yields \[ \partial^k_{\lambda} \text{Im} \langle \rho^{-\sigma} R_{V,j} \rho^{-\sigma} A(\cdot, s), A(\cdot, r) \rangle_{L^2} \leq C\lambda^{n-2-k}, \] and so the remainder in the Birman-Schwinger expansion of $ R_{V,j} $ satisfies the claimed estimate for $ 0 < \lambda \leq 1 $. Now we consider a generic term in the sum in (5.4) for $ 1 \leq \ell \leq 2M - 1 $. As before, we use the fact that $ V = \rho^{-2\sigma}(r)f(r) $ for some $ f \in L^\infty(\mathbb{R}^+) $ to write \[ \rho^{-\alpha} \partial^k_{\lambda} R_{0,j} (V R_{0,j})^\ell \rho^{-\alpha}(r, s) = \partial^k_{\lambda} (\rho^{-\alpha} R_{0,j} \rho^{-\alpha})(\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})^{\ell-1}(\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})(r, s). \tag{5.20} \] Writing the above as an $ L^2 $-pairing, we have \[ \rho^{-\alpha} \partial^k_{\lambda} R_{0,j} (V R_{0,j})^\ell \rho^{-\alpha}(r, s) = \partial^k_{\lambda} \langle \rho^{-\alpha} R_{0,j} \rho^{-\alpha}(r, \cdot), (\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})^{\ell-1}(\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})(\cdot, s) \rangle_{L^2}. \tag{5.21} \] Upon taking the imaginary part, we obtain a finite linear combination of terms of the form (5.21) where at least one factor of $ R_{0,j} $ has the imaginary part acting on it. We assume without loss of generality that the leftmost factor on the right-hand side of (5.21) has the imaginary part, and thus we can apply Hölder’s inequality to obtain \[ \|\partial^k_{\lambda} \langle \rho^{-\alpha} R_{0,j} \rho^{-\sigma}(r, \cdot), (\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})^{\ell-1}(\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})(\cdot, s) \rangle_{L^2}\| \leq C\\|\rho^{-\alpha} \partial^k_{\lambda} \text{Im} R_{0,j} \rho^{-\alpha}(r, \cdot)\\|_{L^{q'}} \times \\|\rho^{-\alpha} f \partial^k_{\lambda} R_{0,j} \rho^{-\sigma} \cdots (\rho^{-\alpha} f \partial^{k_{\ell-1}}_{\lambda} R_{0,j} \rho^{-\sigma})(\rho^{-\alpha} f \partial^{k_{\ell}}_{\lambda} R_{0,j} \rho^{-\alpha})(\cdot, s)\\|_{L^p} \] for some $ 1 \leq q' < \infty $ to be determined, and $ p $ given by $ \frac{1}{q} + \frac{1}{p} = 1 $, where $ k_1 + k_2 + \cdots + k_\ell = k $. If $ 0 < \lambda \leq 1 $, we recall that by Proposition 3.6, \[ \\|\rho^{-\alpha} \partial^k_{\lambda} \text{Im} R_{0,j} \rho^{-\alpha}(r, \cdot)\\|_{L^{q'}} \leq C\lambda^{n-2} \tag{5.23} \] provided that $ \sigma > \frac{n}{q} + k $ and $ \alpha \geq \max\{k_1 - \frac{n-1}{2}, 0\} $. Similarly, for any $ \tilde{k} \leq k $, we have by Proposition 3.8 that for any $ 1 \leq q \leq \frac{n}{n-2} $, \[ \\|\rho^{-\alpha} \partial^\tilde{k}_{\lambda} R_{0,j} \rho^{-\sigma}(r, \cdot)\\|_{L^q} \leq C\lambda^{-\tilde{k}}, \tag{5.24} \] if $ \sigma > \frac{n}{q} + k $, along with the analogous estimate when the norm is taken with respect to the other variable. Using (5.23), (5.24), and repeated applications of Lemma 5.2 to the right-hand side of (5.22), we obtain \[ \|\partial^k_{\lambda} \langle \rho^{-\alpha} R_{0,j} \rho^{-\sigma}(r, \cdot), (\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})^{\ell-1}(\rho^{-\sigma} f R_{0,j} \rho^{-\sigma})(\cdot, s) \rangle_{L^2}\| \leq C\lambda^{n-2-k} \tag{5.25} \] when $ 0 < \lambda \leq 1 $, as long as we choose $ q, q' $ such that $ \frac{1}{q} + \frac{\ell}{q} = \ell $ and provided that $ \sigma > \max\{\frac{n}{q'}, \frac{n}{q}\} + k $. Since $ \frac{n}{q} \geq n - 2 - k $, we have by (5.1) that \[ \sigma > 4 \left\lceil \frac{n}{4} \right\rceil - 2 + k \geq n - 2 + k, \] DISPERSEIVE ESTIMATES ON PRODUCT CONES and so we can ensure that $ \sigma > \frac{n}{q} + k $ if $ q $ is chosen sufficiently close to, but just below $ \frac{n}{n-2} $. Given this choice of $ q $, we also have that $ q' $ lies just above $ \frac{n}{q'} $, and so \[ \sigma > 4 \left[ \frac{n}{4} \right] - 2 + k = 2(2M - 1) + k, \] and since $ 1 \leq \ell \leq 2M - 1 $, we can ensure that $ \sigma > \frac{n}{q} + k $, since $ \frac{n}{\sigma} + k $ can be made arbitrarily close to $ 2\ell + k $. Therefore, under the claimed conditions on $ \sigma $ and $ \alpha $, we have that \[ \|\partial_k^k R_{0,j} (VR_{0,j})^{\ell}\| \leq C\lambda^{n-2-k} \] for $ 0 < \lambda \leq 1 $ and any $ 1 \leq \ell \leq 2M - 1 $. In the case where $ \lambda \geq 1 $, we have that \[ \\|\rho^{-\alpha} \partial_k^k \text{Im } R_{0,j} \rho^{-\sigma}(r, \cdot)\\|_{L^{q'}} \leq C \max\{\lambda^{n-2-k_1 - \frac{n}{q'}}, \lambda^{\frac{n}{q'} - 3}\} \] uniformly in $ r $ as before, provided that $ \alpha \geq \max\{k - \frac{n + 1}{2}, 0\} $ and $ \sigma > \frac{n}{q'} + k $. Next, choose some $ q $ which lies just below $ \frac{n}{n-2} $ as above. Then, for any $ k \leq k $, \[ \\|\rho^{-\sigma} \partial_k^k R_{0,j} \rho^{-\sigma}(r, \cdot)\\|_{L^q} \leq C \max\{\lambda^{n-2-k}, \lambda^{\frac{n}{q'} - 3}\}, \] uniformly in $ r $, provided that $ \sigma > \frac{n}{q} + k $, along with the analogous estimate when the $ L^q $ norm is taken over the second variable. We also note that for the rightmost factor in $(5.22)$, we have \[ \\|\rho^{-\sigma} \partial_k^k R_{0,j} \rho^{-\alpha} (\cdot, s)\\|_{L^q} \leq C \max\{\lambda^{n-2-k}, \lambda^{\frac{n}{q'} - 3}\}, \] uniformly over $ s $, provided $ \alpha \geq \max\{k - \frac{n - 1}{2}, 0\} $. Given these estimates and Lemma 5.2, we can maximize over the possible combinations of $ k_1, \ldots, k_\ell $ to see from $(5.22)$ that \[ \|\partial_k^k \langle \rho^{-\alpha} \text{Im } R_{0,j} \rho^{-\sigma}(r, \cdot), \rho^{-\sigma} f R_{0,j} \rho^{-\sigma}\rangle^{\ell-1}(\rho^{-\sigma} f R_{0,j} \rho^{-\alpha})(\cdot, s)\\|_{L^2}\| \leq \lambda^{\ell(n-2)-k} \max\{\lambda^{n-2-k_1 - \frac{n}{q'}}, \lambda^{\frac{n}{q'} - 3}\} \] (5.26) provided that $ \frac{1}{q'} + \frac{\ell}{q} = \ell $ and $ \sigma > \max\{\frac{n + 1}{q'}, \frac{n}{q}\} + k $. As shown previously, this condition on $ \sigma $ is satisfied under the hypothesis $(5.1)$ if $ q $ is chosen close enough to $ \frac{n}{n-2} $. Furthermore, for this choice of $ q $, we have that $ q' $ lies just above $ \frac{n}{2q} $. We claim that this implies that the the bound $(5.26)$ is smaller than the estimate $(5.12)$. To see this, note that if $ q' $ is chosen sufficiently close to $ \frac{n}{q'} $, then $ \frac{n}{q'} = 2\ell + \varepsilon $ for some $ \varepsilon > 0 $. Then, we have \[ \ell(n-2) + n - 2 - \frac{n}{q'} = \ell(n-2) + (n-2) - 2\ell - \varepsilon \leq \ell(n-4) + (n-2). \] If $ n \leq 4 $, then the above is smaller than $ n - 2 $ for all $ \ell = 1, \ldots, 2M - 1 $. If $ n \geq 4 $, then we have \[ \ell(n-4) + (n-2) \leq (2M-1)(n-4) + (n-2) = 2M(n-2) - 2(2M-1) \leq 2M(n-2) - 1. \] Furthermore, we note that \[ \ell(n-2) + \frac{n-3}{2} \leq (2M-1)(n-2) - \frac{n-3}{2} \leq 2M(n-2) - \frac{n-1}{2} \leq 2M(n-2) - 1. \] Therefore, the exponent on $\lambda$ in (5.26) is smaller than that of (5.12) for any $\ell$, and hence we have \[ \|\partial^k_{\lambda}\lambda^{-\alpha}\operatornamewithlimits{Im}\int R_{0,j}\rho^{-\sigma}(r,\cdot),(\rho^{-\sigma}fR_{0,j}\rho^{-\sigma})^{\ell-1}(\rho^{-\sigma}fR_{0,j}\rho^{-\alpha})(\cdot,s)\rangle_{L^2}\| \leq \lambda^{2M(n-2)-1} \tag{5.27} \] when $\lambda \geq 1$. Now, if the imaginary part falls on any factor other than the first on the right-hand side of (5.21), we simply repeat the preceding argument, but with the $L^q$ norm on that factor. Finally, we consider the case where $\ell = 0$ in (5.4). For this term, we must simply obtain pointwise bounds on $\rho^{-\alpha}(r)\partial^k_{\lambda}\operatornamewithlimits{Im}\int R_{0,j}(r,s)\rho^{-\alpha}(s)$. Recall that by Lemma B.2, we have \[ \operatornamewithlimits{Im}\int R_{0,j}(r,s) = \frac{\pi}{2}\lambda^{-2}(\lambda r \lambda s)^{-\frac{n+2}{2}} J_{\nu_j}(\lambda r)J_{\nu_j}(\lambda s). \] Therefore, $\partial^k_{\lambda}R_{0,j}(r,s)$ can be written as a finite linear combination of terms of the form \[ \lambda^{n-2-k}(\lambda r)^{\ell-\frac{n-2}{2}}(\lambda s)^{m-\frac{n-2}{2}} J_{\nu_j+\alpha}(\lambda r)J_{\nu_j+\beta}(\lambda s) \tag{5.28} \] for $\ell+m = k$, $\|\alpha\| \leq \ell$, and $\|\beta\| \leq m$. Using the standard asymptotics of the Bessel functions, we have that the above is bounded in absolute value by a constant times \[ \lambda^{n-2-k}(1 + \lambda r)^{\ell-\frac{n-1}{2}}(1 + \lambda s)^{m-\frac{n+1}{2}}. \tag{5.29} \] Next, we note that \[ \rho^{-\alpha}(r)(1 + \lambda r)^{\ell-\frac{n-1}{2}} \leq C(1 + \lambda)^\ell, \] for all $\lambda$, uniformly in $r$, under the assumption that $\alpha \geq \max\{k-\frac{n+1}{2},0\}$. The analogous estimate holds for $\rho^{-\alpha}(s)(1 + \lambda s)^{m-\frac{n-1}{2}}$, and therefore, we have that \[ \|\rho^{-\alpha}(r)\partial^k_{\lambda}R_{0,j}(r,s)\rho^{-\alpha}(s)\| \leq C\lambda^{n-2-k}(1 + \lambda)^k. \tag{5.30} \] Combining (5.30) with (5.19), (5.12), (5.25), and (5.26), the proof of Proposition 5.1 is complete. 6. Dispersive estimates In this section, we prove the main estimate in Theorem 4. To accomplish this, we write the spectral measure for $-\Delta_{C(X)} + V$ as \[ d\Pi_V(\lambda;x,y) = \frac{1}{\pi i}[R_V(\lambda^2 + i0;x,y) - R_V(\lambda^2 - i0;x,y)]\lambda d\lambda = \frac{1}{\pi} \operatornamewithlimits{Im}\int R_V(\lambda^2 + i0;x,y)\lambda d\lambda. \] Then, we can write \[ [e^{i\mu(-\Delta_{C(X)} + V)}P_c](x,y) = \int_0^\infty e^{it\lambda^2}d\Pi_V(\lambda;x,y) = \frac{1}{\pi} \int_0^\infty e^{it\lambda^2} \operatornamewithlimits{Im}\int R_V(\lambda^2 + i0;x,y)\lambda d\lambda, \] where we recall that $P_c$ denotes projection onto the continuous spectrum of $-\Delta_{C(X)} + V$. Projecting further onto the span of $\varphi_j$, we obtain $$\left[ e^{it(-\Delta_{C(X)}+V)} P_c E_j \right](r, s) = \frac{1}{\pi} \int_0^\infty e^{it\lambda^2} \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \lambda \, d\lambda \quad (6.1)$$ since $V$ is radial. Therefore, the estimate in Theorem 4 is equivalent to $$\left\| \frac{1}{\pi} \int_0^\infty e^{it\lambda^2} \rho^{-\alpha}(r) \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s) \lambda \, d\lambda \right\| \leq Ct^{-\frac{n}{4}} \quad (6.2)$$ for $\alpha > 2 \left[ \frac{n}{4} (n-2) - \frac{n-1}{2} + 2 \right]$. Proof of Theorem 4.* Assume that $n$ is odd, and let $\chi \in C_0^\infty(\mathbb{R})$ be a cutoff function which is identically one on $[-1/2, 1/2]$ and zero outside $[-1, 1]$. We then consider the low-frequency component of the left-hand side of (6.2), given by $$\frac{1}{\pi} \int_0^\infty e^{it\lambda^2} \chi(\lambda) \rho^{-\alpha}(r) \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s) \lambda \, d\lambda. \quad (6.3)$$ Noting that the operator $\frac{1}{2it\lambda} \partial_\lambda$ preserves $e^{it\lambda^2}$, we may integrate by parts $N = \frac{n-1}{2}$ times in $\lambda$ to obtain $$\frac{C_N}{t^N} \int_0^\infty e^{it\lambda^2} \partial_\lambda \left( \frac{1}{\lambda} \partial_\lambda \right)^{N-1} \chi(\lambda) \rho^{-\alpha}(r) \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s) \lambda \, d\lambda \quad (6.4)$$ for some $C_N \in \mathbb{C} \setminus 0$. That no boundary terms appear at $\lambda = 0$ follows from the fact that all derivatives of $\chi(\lambda)$ vanish identically near the origin and that $\rho^{-\alpha}(r) \partial_\lambda^k \text{Im} R_{V,j}(\lambda^2 + i0) \rho^{-\alpha}(s)$ vanishes to order $n - 2 - k$. To be more precise, all boundary terms at $\lambda = 0$ must involve factors of the form $$\left( \frac{1}{\lambda} \partial_\lambda \right)^k \chi(\lambda) \rho^{-\alpha}(r) \text{Im} R_{V,j}(\lambda^2 + i0) \rho^{-\alpha}(s)$$ for some $0 \leq k \leq N - 1 = \frac{n-3}{2}$. If any derivatives fall on $\chi$, then the corresponding term obviously vanishes at $\lambda = 0$. If instead, all derivatives fall on $\text{Im} R_{V,j}$, then by Proposition 5.1, the corresponding term is bounded by a constant times $\lambda^{n-2-2k} \leq \lambda^{n-2-(n-3)} = \lambda$, which vanishes at $\lambda = 0$. Therefore, all boundary terms are necessarily zero. Now, observe that when expanding the integrand in (6.4) via the product rule, any terms in which a derivative falls on the factor of $\chi(\lambda)$ can be written as $$C_N t^{-N} \int_0^\infty e^{it\lambda^2} G(\lambda; r, s) \, d\lambda$$ for some $G(\lambda; r; s)$ which is smooth and compactly supported away from 0 in $\lambda$, and bounded uniformly in $r, s$ by Proposition 5.1. Applying the standard dispersive estimate for the Schrödinger equation on $\mathbb{R}$, we have $$t^{-N} \left\| \int_0^\infty e^{i\lambda^2} G(\lambda; r, s) \, d\lambda \right\| \leq Ct^{-N-\frac{1}{2}} \\| \hat{G}(\cdot, r, s) \\|_{L^1},$$ (6.5) where $\hat{G}$ denotes the Fourier transform in $\lambda$ (extend $G$ by zero to a function on $\mathbb{R}$ to compute this Fourier transform). Since $n$ is odd, we may choose $N = \frac{n-1}{2}$, so the right-hand side of (6.5) is bounded by $Ct^{-\frac{n}{2}}$ as claimed, after possibly increasing $C$. Now, any terms obtained from expanding (6.4) where no derivatives fall on the factor of $\chi$ must be of the form $$\lambda^{1-2N+k} \chi(\lambda) \rho^{-\alpha}(r) \partial^k_\lambda \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s)$$ (6.6) for some $k = 1, 2, \ldots, N$ since at least one derivative always falls on the factor of $\text{Im} R_{V,j}$. By Proposition 5.1, we have that each of the above terms is bounded in absolute value by a constant times $$\lambda^{1-2N+k} \chi(\lambda) \lambda^{n-2-k} = \lambda^{n-1-2N} \chi(\lambda)$$ uniformly for $r, s > 0$. For our choice of $N = \frac{n-1}{2}$, we have that $\lambda^{n-1-2N} = 1$, and hence (6.6) is a smooth function of $\lambda$, and so its Fourier transform is bounded in $L^1$. Once again, using the standard $L^1 \to L^\infty$ dispersive estimate for the free one-dimensional Schrödinger equation, we have that $$t^{-N} \left\| \int_0^\infty e^{i\lambda^2} \lambda^{1-2N+k} \chi(\lambda) \rho^{-\alpha}(r) \partial^k_\lambda \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s) \, d\lambda \right\| \leq Ct^{-N-\frac{1}{2}} = Ct^{-\frac{n}{2}},$$ (6.7) uniformly in $r, s$. We remark that it is in this calculation that the choice of $N = \frac{n-1}{2}$, and hence the power of $t^{-\frac{n}{2}}$, cannot be improved, since any additional derivatives which fall on $\text{Im} R_{V,j}(\lambda^2 + i0)$ would yield an integrand which is not bounded smooth near $\lambda = 0$. We also note that for this portion of the argument, we only require that $\alpha \geq 0$, since we did not differentiate $\text{Im} R_{V,j}$ more than $\frac{n-1}{2}$ times. Next, we consider the “high-frequency” component of (6.2), which we define by $$\frac{1}{\pi} \int_0^\infty e^{i\lambda^2} \chi(\lambda/R)(1 - \chi(\lambda)) \rho^{-\alpha}(r) \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s) \lambda \, d\lambda$$ (6.8) for any $R \in [1, \infty)$. To control this term, we integrate by parts as before to obtain \[ \frac{1}{\pi} \int_0^\infty e^{it\Lambda^2} \chi(\lambda/R)(1 - \chi(\lambda)) \rho^{-\alpha}(r) \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s) \lambda \, d\lambda \] \[ = C_N t^{-N} \int_0^\infty e^{it\Lambda^2} \partial_\lambda \left( \frac{1}{\lambda} \right)^{N-1} \left[ \chi(\lambda/R)(1 - \chi(\lambda)) \rho^{-\alpha}(r) \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s) \right] \, d\lambda \] for any $N > 0$ and some corresponding constant $C_N$. We aim to show that the integrand can be bounded uniformly in $L^1(\mathbb{R}, d\lambda)$ as $R \to \infty$. We also claim that it is sufficient to consider the case where all the derivatives in $\lambda$ fall on the factor of $\text{Im} R_{V,j}$. To see this, note that $\partial_\lambda (1 - \chi(\lambda))$ is supported in a fixed compact set which is bounded away from $\lambda = 0$, and that $\partial_\lambda \chi(\lambda/R) = \frac{1}{R} \chi'(\lambda/R)$ is supported away from $\lambda = 0$ in a set of size $\mathcal{O}(R)$. Therefore, we need only show that \[ \frac{1}{\lambda^{N-1}} \chi(\lambda/R)(1 - \chi(\lambda)) \rho^{-\alpha}(r) \partial_\lambda^N \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \rho^{-\alpha}(s) \] has bounded $L^1$ norm, and that the estimate is uniform with respect to $r$, $s$, and $R$. For this, we utilize Proposition 5.1, which implies that if $\alpha \geq \max\{N - \frac{n-1}{2}, 0\}$ and $\sigma > 4 \left\lceil \frac{n}{4} \right\rceil - 2 + N$, then (6.9) is bounded by a constant times $\langle \lambda \rangle^{1-N+L}$, uniformly in $r$, $s$, and $R$, where $L = 2 \left\lceil \frac{n}{4} \right\rceil (n - 2) - 1$. Thus, choosing \[ N = 2 \left\lceil \frac{n}{4} \right\rceil (n - 2) + 2, \] guarantees that (6.9) is uniformly bounded in $L^1$. Noting that $N \geq \frac{n}{2}$ if $N$ is chosen as above, we obtain \[ \lim_{R \to \infty} \left\| \frac{1}{\pi} \int_0^\infty e^{it\Lambda^2} \chi(\lambda/R)(1 - \chi(\lambda)) \text{Im} R_{V,j}(\lambda^2 + i0; r, s) \lambda \, d\lambda \right\| \leq Ct^{-\frac{n}{4}}, \quad (6.10) \] where $C > 0$ is independent of $r$, $s$ and $R$. Our choice of $N$ also determines the maximum number of derivatives of $\text{Im} R_{V,j}(\lambda^2 + i0; r, s)$ that must be taken, which yields \[ \sigma > 4 \left\lceil \frac{n}{4} \right\rceil - 2 + 2 \left\lceil \frac{n}{4} \right\rceil (n - 2) + 2 = 2n \left\lceil \frac{n}{4} \right\rceil \] as the sufficient condition on the decay rate of $V$. Also, the condition on $\alpha$ becomes \[ \alpha > N - \frac{n-1}{2} = 2 \left\lceil \frac{n}{4} \right\rceil (n - 2) + 2 - \frac{n-1}{2}, \] as stated in Theorem 4. Under these conditions on the weights, we can combine (6.7) and (6.10) to obtain (6.2), which completes the proof of Theorem 4. Remark 6.1. In the case where $n$ is even, we find that in repeating the argument just prior to (6.7), the largest $N$ we can choose is $\frac{n-2}{2}$, which leads to a decay rate of $t^{-\frac{n-1}{2}}$ in the $L^1 \to L^\infty$ estimate. The remainder of the argument goes through without modification, yielding (1.8). Appendix A. Absence of Embedded Resonances on Product Cones A.1. Radial potentials and ODE methods. In this appendix, we establish the absence of embedded resonances and eigenvalues result claimed in Theorem 2 using the results from Theorem XIII.56 of [58]. To prove this, we need to use the fact that $V$ is decaying to treat $Vu$ as a perturbative term in the limit and prove that if $u \in L^2$, then hence $Vu$ is perturbative and we can write $$u_\pm(r) = \frac{e^{\pm i \lambda r}}{r^{\frac{n-1}{2}}} + \int_r^\infty \frac{\sin(\lambda(r-s))}{\lambda(rs)^{\frac{n-1}{2}}} V(s)u_\pm(s)ds,$$ where by $u_\pm$ we mean the outgoing/incoming functions converging to the Jost solution asymptotic of the form $$\frac{e^{\pm i \lambda r}}{r^{\frac{n-1}{2}}}.$$ This gives the exact integrability condition in Theorem XIII.56 of [58]. It is also an integral equation that can also be solved using Picard iteration. Using the variation of parameters formula to solve $$(-\Delta_{C(X)} - \lambda^2)u = V(r)u$$ for any $V$ with $\int_a^\infty V(r)dr < \infty$ for some $a > 0$, we can write $$u(r) = c_+u_+(r) + c_-u_-(r)$$ $$+ \int_r^\infty \frac{u_+(r)u_-(s)}{W(s)} V(s)u(s)s^{n-1}ds + \int_r^\infty \frac{u_-(r)u_+(s)}{W(s)} V(s)u(s)s^{n-1}ds,$$ where $W(s) = 2s^{n-1}$. Hence, if we have a resonance $u \in L^{2,\sigma}$ for $\sigma > \frac{1}{2}$, we have that indeed we can see the integral terms on the right converge and hence derive a contradiction to the existence of resonances that are not eigenvalues. For radial potentials, we have observed that there are no embedded eigenvalues using the ODE based tools of Theorem XIII.56 of [58], but the issue of absence of embedded resonances down to $\lambda = 0$ still must be established. We state the result here. Proposition A.1. For $V \in \rho^{-2}L^\infty(\mathbb{R}^+)$ with $\sigma > \frac{1}{2}$, if $R_{V,j}(z^2)$ has a pole at $\tau$ for $\tau \in \mathbb{R}\backslash\{0\}$, then $\tau^2$ is an embedded eigenvalue for $-\Delta_{C(X)} + V$. Proof of Theorem 2. By Proposition A.1, it suffices to prove that $R_V(z^2)$ has no real poles corresponding to eigenvalues of $-\Delta_{C(X)} + V$ embedded in the continuous spectrum. It also suffices to prove this fact for $R_{V,j}(z^2)$, since the fact that $V$ is radial means that $R_V$ respects the decomposition into harmonics on the link. The method of proof from Theorem XIII.56 of [58] proves that for $V$ sufficiently decaying, a radial operator has no positive eigenvalues. This relies on a formal analysis of Jost solutions, proving that no linear combination of them can be an $L^2$ function. In particular, if we assume we have an embedded eigenvalue at energy $\lambda$ with corresponding radial eigenfunction $\phi$ on the $j$th harmonic, it satisfies $$\left(\frac{\partial^2}{\partial r^2} + \frac{n-1}{r} \frac{\partial}{\partial r} + \lambda^2 - \frac{j^2}{r^2}\right) \phi = 0$$ meaning that $\infty$ is a regular singular point. As a result, as $r \to \infty$ the Jost solutions are of the form $$\phi_\pm(r) = e^{\pm i\lambda r} r^{-\frac{n-1}{2}} + O(r^{-\frac{n+1}{2}}).$$ Hence, linear combinations generically take the form $$A \sin(\lambda r + \theta) r^{-\frac{n-1}{2}},$$ which is easily seen to not be in $L^2(C(X))$, which yields a contradiction. Further discussion of the Jost solutions can be computed as in [59], Ch. 5. A.2. Absence of Embedded Resonances for Non-Radial Potentials. For the purposes of ruling out embedded resonances, a geometrically robust approach is to use a boundary pairing formula on radially compactified space, as in [54, §2.3], to prove that an embedded resonance is an embedded eigenvalue and hence has at least $L^2$ decay. The boundary pairing formula for Schrödinger operators on Euclidean space is derived from the observation that a pole of the resolvent corresponds to a solution to $$(-\Delta_{\mathbb{R}^n} + V - \lambda^2)u = f,$$ say for $f \in \mathcal{S}$ a Schwartz class function. The solution to this equation takes the form $$u = e^{i\frac{\lambda}{r} x_{\pm} (n-1)} w_+ + e^{-i\frac{\lambda}{r} x_{\pm} (n-1)} w_-, \quad w_\pm \in C^\infty(S^n_+)$$ where $x = \frac{1}{r}$ and $S^n_+$ is the upper hemisphere of the sphere $S^n$. The boundary pairing formula states that for solutions $$(-\Delta + V - \lambda^2)u^{(\ell)} = f^{(\ell)}$$ with $\ell = 1, 2$, we have $$2i\lambda \int_{S^{n-1}} (v_+^{(1)} v_+^{(2)} - v_-^{(1)} v_-^{(2)}) dz = \int_{\mathbb{R}^n} (f^{(1)} u^{(2)} + u^{(1)} f^{(2)}) dz$$ with $v_+^{(\ell)} = w_{+\ell}\|_{S^n_+}$. For a pole of the outgoing resolvent, we observe that $v_+$ vanishes identically. Hence, any embedded resonance can be seen to be an embedded eigenvalue. To eliminate embedded eigenvalues, we follow the work of Froese et al [22] to prove that $L^2$ eigenfunctions must in fact exhibit super-polynomial decay. The arguments there involve constructing a series of positive commutator arguments to obtain this rapid decay. To begin, take $\varepsilon, \gamma > 0$ and define $\rho(\|x\|) = \langle x \rangle$. Then, the function $$F(x) = \gamma \ln(\rho(1 + \varepsilon \rho)^{-1}).$$ Then, $\nabla F = xg$ for $g = \gamma \rho - 2(1 + \varepsilon \rho)^{-1}$ and $$(x \cdot \nabla)^2 g - (x \cdot \nabla)(\nabla F)^2 \leq 4\gamma(\gamma + 2)\rho^{-2}.$$ Defining $\psi_R = e^{F} \psi$, a conjugated form of the equation can be written as a modified quadratic form. Coupling this form with a Mourre estimate (positive commutator using $r\partial_r$ (the radial version of $x \cdot \nabla$) we can prove that the set of polynomial weights for which $\psi \in L^2$ is open and can be extended to $\infty$. The Mourre estimate serves as a means to construct the weak limit of the resolvent at the real axis. Once super-polynomial behavior is established, a similar open set for exponential decay can be established using the assumption that $e^{a_0 \rho^2 \lambda} \psi \in L^2$ for all $\lambda$ and showing that this implies then that $e^{(a_0 \gamma \lambda)} \psi \in L^2$. To do this, build the function $$F(x) = a_0 \rho + \lambda \ln(1 + \gamma \rho / \lambda)$$ and derive a similar contradiction. Once super-exponential decay is established, the strategy of Vasy-Wunsch [66] can be applied to prove a unique continuation argument by conjugating the operator to $$P_\alpha = e^{ar'} (-\Delta + V - \lambda)e^{-ar'}$$ for $r'$ some smoothed version of $r$ to be determined. Then, $$0 = \\|P_\alpha \phi_\alpha\\|^2 = \\|\text{Re} P_\alpha \psi_\alpha\\|^2 + \\|\text{Im} P_\alpha \psi_\alpha\\|^2 + \langle i[\text{Re} P_\alpha, \text{Im} P_\alpha] \psi_\alpha, \psi_\alpha \rangle.$$ Hence, one uses that $i[\text{Re} P_\alpha, \text{Im} P_\alpha]$ is a positive commutator term. We require that $$[\Delta, 2\partial_r + (\partial_r \log A)] \geq c R^2 \Delta \theta + R$$ for $R$ in the calculus of first order conic vector fields. A.3. The Boundary Pairing Formula. Following a suggestion of Dean Baskin, we can interpret embedded resonances for more general conic Schrödinger operators through the boundary pairing formula of Melrose. A.3.1. Existence of the Boundary Pairing Formula on Cones. We outline the necessary generalizations to the presentation of the Boundary Pairing formula from the book of Melrose [54]. First, we must consider the radial compactification of a cone to a compactified manifold $\hat{C} = X \times [0, 1]$ for $X$ the link of the cone, which is similar to that in [2]. We again consider solutions of the equation $$(-\Delta_{R^2} + V - \lambda^2)u = f$$ for $f \in \mathcal{S}$ for instance say a Schwartz class function. Let \[ u = u_+ + u_-, \] namely a sum of the outgoing and incoming solutions, with \[ u_\pm = e^{\pm i\lambda/x}x^{n+1/2}w_\pm \] for $ w_\pm \in C^\infty(\hat{C}) $. This formula appears in a variety of settings in the literature, starting with the foundational work of Melrose [53] on asymptotically Euclidean manifolds, then Melrose-Zworski [52] on general scattering manifolds with smooth boundary, Hassell-Vasy [35] on scattering manifolds with conic points, and the corresponding discussion of Guillarmou-Hassell-Sikora in [32], Section 5. See also [3, 67] for a recent discussion on product cones that contains formulae from which such a decomposition can be obtained. Then, we claim that \[ 2i\lambda \int_X [v_+^{(1)}v_-^{(2)} - v_-^{(1)}v_+^{(2)}]dv_h = \int_{C(X)} [f^{(1)}u^{(2)} - u^{(1)}f^{(2)}]drdv_h \] with $ v_\pm^{(i)} = w_\pm^{(i)}\|_X $. We will need to consider behaviors both at $ x = 0 $ and 1 whereas on Euclidean space the compactification really only sees $ \infty $. See Ch. 2.3 and Ch. 6 of Melrose [54]. Compactify via the stereographic projection to the quarter circle \[ S^1_{+,+} = \{(z_1, z_2) \in S^1 \subset R^2\|z_1 \geq 0, z_2 \geq 0\} \] with $ r \to (r, 1)/\sqrt{1+r^2} $. This is a manifold with boundaries of the form \[ z_1 = r/\sqrt{1+r^2}, \quad z_2 = 1/\sqrt{1+r^2}. \] Define $ M = S^1_{+,+} \times X $ and we get the compactified structure. The formula (A.2) then follows from integration by parts on the expression \[ \int_{C(X)} [f^{(1)}u^{(2)} - u^{(1)}f^{(2)}]\chi(\varepsilon r)drdv_h \] for $ \chi $ a smooth cut-off function localized near 0. Integrating by parts in $ r $, applying formula (A.1), and taking the limit as $ \varepsilon \to 0 $ the formula follows after an application of the Riemann-Lebesgue lemma. Note, the boundary pairing formula is strongly related to structure of the Jost solutions through the existence of polyhomogeneous expansions (power series solutions near the boundary). A.3.2. Outline of the remaining arguments. To prove the absence of embedded resonances, we use the boundary pairing formula with $ f = 0 $ to prove that any outgoing solution vanishes to leading order on the $ x_1 = 0 $ boundary. This may be iterated to show that in fact the power series vanishes to arbitrary order and hence the solution is indeed Schwarz on the cone. To see this, differentiate the equation with respect to $ x_1 $ and look at the resulting inhomogeneous equation in the boundary pairing. Otherwise, the power series solution depends uniquely on the first terms in the expansion. In most circumstances, eliminating embedded eigenvalues requires unique continuation. In the radial problem, we may apply the Theorem XIII.56 of [58] built around Jost solutions as mentioned above. For conic metrics, we must follow the procedure of Froese-Herbst [22] built around separable metric, which has been extended and formalized by Vasy [63, 64]. Appendix B. Construction of the Free Resolvent In this appendix, we provide a detailed construction integral kernel for the free resolvent operator \[ R_0(z^2) = (-\Delta_{C(X)} - z^2)^{-1} : L^2(C(X)) \to L^2(C(X)), \] for $ \text{Im} \, z \neq 0 $, closely following the exposition of [3]. This is equivalent to analyzing solutions of the equation \[ (-\Delta_{C(X)} - z^2)u = f \] for $ f \in L^2(C(X)) $. To proceed, we decompose $ u $ and $ f $ into the basis $ \{\varphi_j\} $ of eigenfunctions on $ X $ as \[ f(r, \theta) = \sum_{j=1}^{\infty} f_j(r) \varphi_j(\theta), \quad u(r, \theta) = \sum_{j=1}^{\infty} u_j(r) \varphi_j(\theta). \] Denote by $ -\mu_j^2 $ the eigenvalues of $ \Delta_h $ associated to each $ \varphi_j $. Then, we obtain that (B.2) is equivalent to the collection of equations \[ \left( \partial^2_r + \frac{n-1}{r} \partial_r + z^2 - \frac{\mu_j^2}{r^2} \right) u_j(r) = -f_j(r), \quad j = 0, 1, 2, \ldots. \] Therefore, we can express the resolvent $ R_0(z^2) $ as \[ R_0(z^2) f(r, \theta) = \sum_{j=0}^{\infty} u_j(r) \varphi_j(\theta), \] with $ u_j $ as above. If we define the $ j $th radial resolvent $ R_{0,j}(z^2) $ by \[ R_{0,j}(z^2) = \left( \partial^2_r + \frac{n-1}{r} \partial_r + z^2 - \frac{\mu_j^2}{r^2} \right)^{-1} \] as an operator on $ L^2(\mathbb{R}^+, r^{n-1} \, dr) $, then the full resolvent is given by \[ R_0(z^2) f(r, \theta) = \sum_{j=0}^{\infty} R_{0,j}(z^2) f_j(r) \varphi_j(\theta). \] For each $ j $, the defining equation (B.3) for $ R_{0,j}(z^2) f_j $ is an ODE with a regular singular point at zero, and so by applying the Frobenius method we find that the indicial roots of the equation are $ -\frac{n-2}{2} \pm \sqrt{\left( \frac{n-2}{2} \right)^2 + \mu_j^2} $. For this reason, we introduce the notations $ \delta = -\frac{n-2}{2} $. and $\nu_j = \sqrt{(\frac{n}{2})^2 + \mu_j^2}$. The structure of the indicial roots suggests that we rescale by $r^\delta$, and so we define $\omega_j$ by $u_j(r) = r^\delta \omega_j(r)$ so that $\omega_j$ is analytic near $r = 0$. Then, (B.3) becomes $$\partial_r^2 \omega_j + \frac{1}{r} \partial_r \omega_j + \left( z^2 - \frac{\nu_j^2}{r^2} \right) \omega_j = -r^{-\delta} f_j(r), \quad j = 0, 1, 2, \ldots .$$ At this point it is helpful to restrict to particular class of $f_j$, namely those for which the Fourier transform $\hat{f}_j$ is compactly supported (in order to compute the Fourier transform, we simply extend $f_j$ by zero to a function on all of $\mathbb{R}$). For such $f_j$, we know that there exists a holomorphic extension to all of $\mathbb{C}$ by the Paley-Weiner-Schwartz Theorem. We continue to denote this extension by $f_j$. That we can make this restriction without loss of generality follows from the fact that such functions are dense in $L^2$. Given this, if $z \neq 0$, we make the change variables via $\zeta = zr$ to obtain the following inhomogeneous Bessel equation of order $\nu_j$: $$\tilde{\omega}_j'' + \frac{1}{\zeta} \tilde{\omega}_j' + \left( 1 - \frac{\nu_j^2}{\zeta^2} \right) \tilde{\omega}_j = -\frac{\zeta^{-\delta}}{z^2} f_j(\zeta/z), \quad (B.5)$$ where $\tilde{\omega}_j(\zeta) = \omega_j(\zeta/z)$, and the “prime” notation denotes the complex derivative with respect to $\zeta$. Here, we define $\zeta^{-\delta}$ using the principal branch of the square root. For notational convenience, we define $f_{j,z}(\zeta) := -\frac{\zeta^{-\delta}}{z^2} f_j(\zeta/z)$, which is holomorphic for $\zeta \in \mathbb{C} \setminus (-\infty, 0]$. The solutions to the homogeneous Bessel equation of order $\nu$ are the well-known Bessel functions of the first and second kind, denoted $J_\nu$ and $Y_\nu$, respectively. Closely related to these are the Hankel functions $H^{(1)}_\nu$ and $H^{(2)}_\nu$, given by $$H^{(1)} = J_\nu + iY_\nu, \quad H^{(2)} = J_\nu - iY_\nu.$$ Any two of these Bessel and/or Hankel functions can be used to form a fundamental solution set for the homogeneous equation. Given an appropriate choice of fundamental solution set, we use the method of variation of parameters to construct solutions to the inhomogeneous problem. So let $y_1, y_2$ be a fundamental solution set for the homogeneous problem associated to (B.5) for some fixed $j$. We then construct our solution $\tilde{\omega}_j$ as $$\tilde{\omega}_j = v_1 y_1 + v_2 y_2$$ where all objects above are functions of $\zeta$. Straightforward calculations show that if $$v'_1(\zeta) = -\frac{y_2(\zeta) f_{j,z}(\zeta)}{\mathcal{W}(y_1, y_2)(\zeta)}, \quad \text{and} \quad v'_2(\zeta) = \frac{y_1(\zeta) f_{j,z}(\zeta)}{\mathcal{W}(y_1, y_2)(\zeta)},$$ then $\tilde{\omega}_j$ as given above solves the inhomogeneous equation (B.5), where $\mathcal{W}(y_1, y_2)(\zeta)$ denotes the Wronskian determinant of $y_1$ and $y_2$ evaluated at $\zeta$. Therefore, we may compute $v_1$ and $v_2$ by taking path integrals in the complex plane, which yields $$\tilde{\omega}_j(\zeta) = \left( \int_{\mathcal{C}_1(\zeta)} -\frac{y_2(\xi) f_{j,z}(\xi)}{\mathcal{W}(y_1, y_2)(\xi)} d\xi \right) y_1(\zeta) + \left( \int_{\mathcal{C}_2(\zeta)} \frac{y_1(\xi) f_{j,z}(\xi)}{\mathcal{W}(y_1, y_2)(\xi)} d\xi \right) y_2(\zeta)$$ where $ C_1(\zeta), C_2(\zeta) $ are any complex contours connecting fixed points $ c_1, c_2 \in \mathbb{C} \setminus (-\infty, 0] $ to $ \zeta $, respectively. In fact, it suffices to take $ c_1, c_2 \in \mathbb{R}^+ $. We then choose our contours to be the piecewise linear paths defined by \[ C_1(\zeta) = \{(1-t)c_1 + t \Re \zeta : t \in [0, 1]\} \cup \{\Re \zeta + i \Im \zeta : t \in [0, 1]\} \] and \[ C_2(\zeta) = \{(1-t)c_2 + t \Re \zeta : t \in [0, 1]\} \cup \{\Re \zeta + i \Im \zeta : t \in [0, 1]\}. \] Of particular interest are the boundary values of the resolvent near the continuous spectrum of $-\Delta_{C(X)} + V$. Therefore, if we consider $ z^2 = \lambda^2 \pm i \varepsilon $, we have \[ \tilde{\omega}_j(zr) = y_1(zr) \left( \int_{c_1}^{\lambda r} -y_2(t)f_{j,z}(t) dt + i \int_0^{\pm \varepsilon r} -y_2(\lambda r + it)f_{j,z}(\lambda r + it) dt \right) \] \[ + y_2(zr) \left( \int_{c_2}^{\lambda r} y_1(t)f_{j,z}(t) dt + i \int_0^{\pm \varepsilon r} y_1(\lambda r + it)f_{j,z}(\lambda r + it) dt \right) \] All that remains is to determine that appropriate fundamental solution set $ y_1, y_2 $ and constants $ c_1, c_2 $ so that our solution is a well defined element of $ L^2(C(X)) $. If we take $ y_2 = J_{\nu_j} $ and $ c_1 = 0 $, then $ \tilde{\omega}_j $ is bounded as $ r \to 0 $, provided that the coefficient integrals converge. We then choose $ y_1 $ to be either $ H_{\nu_j}^{(1)} $ or $ H_{\nu_j}^{(2)} $, depending on the sign of $ \Im z $. By the asymptotic forms of the Hankel functions, we have \[ H_{\nu_j}^{(1)}(\zeta) \sim \sqrt{\frac{2}{\pi \zeta}} e^{i(\zeta \frac{\nu_j \pi}{2} - \frac{\pi}{4})} \] and \[ H_{\nu_j}^{(2)}(\zeta) \sim \sqrt{\frac{2}{\pi \zeta}} e^{-i(\zeta \frac{\nu_j \pi}{2} - \frac{\pi}{4})} \] for $-\pi < \arg \zeta < \pi$, and the branch of the square root is defined by $ \zeta^{1/2} = e^{i \arg \zeta} $ for such $ \zeta $. We can now see that if $ z^2 = \lambda^2 + i \varepsilon $, then $ \zeta = zr $ also has positive imaginary part, and so $ H_{\nu_j}^{(1)}(zr) $ decays exponentially as $ r \to \infty $, while $ H_{\nu_j}^{(2)} $ exhibits exponential growth. Hence, when $ z^2 = \lambda^2 + i \varepsilon $ we take $ y_1 = H_{\nu_j}^{(1)} $ and $ c_2 = \infty $, which yields \[ \tilde{\omega}_j(zr) = H_{\nu_j}^{(1)}(zr) \left( \int_{c_1}^{\lambda r} \frac{J_{\nu_j}(t)f_{j,z}(t)}{2i/[\pi t]} dt + i \int_0^{\pm \varepsilon r} \frac{J_{\nu_j}(\lambda r + it)f_{j,z}(\lambda r + it)}{2i/[\pi (\lambda r + it)]} dt \right) \] \[ + J_{\nu_j}(zr) \left( \int_{c_2}^{\lambda r} \frac{H_{\nu_j}^{(1)}(t)f_{j,z}(t)}{2i/[\pi t]} dt - i \int_0^{\pm \varepsilon r} \frac{H_{\nu_j}^{(1)}(\lambda r + it)f_{j,z}(\lambda r + it)}{2i/[\pi (\lambda r + it)]} dt \right), \] since $\mathcal{W}(H_{\nu_j}^{(1)}, J_{\nu_j})(\xi) = -\frac{2i}{\pi \xi}$. We can then take the limit as $\varepsilon \to 0$ to obtain $$ \tilde{\omega}_j(\lambda r) = \frac{\pi}{2i} H_{\nu_j}^{(1)}(zr) \int_0^{\lambda r} t J_{\nu_j}(t) f_{j,z}(t) \, dt + \frac{\pi}{2i} J_{\nu_j}(zr) \int_{\lambda r}^{\infty} t H_{\nu_j}^{(1)}(t) f_{j,z}(t) \, dt. $$ Recalling that $u_j(r) = (zr)^{i\nu} \tilde{\omega}_j(zr)$ and $f_{j,z}(t) = -i \frac{\pi i}{2} f_j(t/z)$, we get that the outgoing solution corresponding to the $j$th resolvent is $$ u = \frac{\pi i}{2} (\lambda r)^{-\frac{n-2}{2}} H_{\nu_j}^{(1)}(\lambda r) \int_0^{\lambda r} \frac{t^2 J_{\nu_j}(t) f_j(t/\lambda)}{\lambda^2} \, dt $$ $$+ \frac{\pi i}{2} (\lambda r)^{-\frac{n-2}{2}} J_{\nu_j}(\lambda r) \int_{\lambda r}^{\infty} \frac{t^2 H_{\nu_j}^{(1)}(t) f_j(t/\lambda)}{\lambda^2} \, dt. $$ If we then change variables via $t = \lambda s$, we can rewrite the above as $$ u = \frac{\pi i}{2} \int_0^{\lambda r} s^{\frac{n}{2}} J_{\nu_j}(\lambda s) f_j(s) \, ds + \frac{\pi i}{2} r^{-\frac{n-2}{2}} J_{\nu_j}(\lambda r) \int_{\lambda r}^{\infty} s^{\frac{n}{2}} H_{\nu_j}^{(1)}(\lambda s) f_j(s) \, ds. $$ The integral kernel of $R_{0,j}(\lambda^2 + i0)$ with respect to the measure $s^{n-1} \, ds$ is therefore given by $$ R_{0,j}(\lambda^2 + i0; r, s) = \begin{cases} \frac{\pi i}{2} (rs)^{-\frac{n-2}{2}} J_{\nu_j}(\lambda s) H_{\nu_j}^{(1)}(\lambda r), & s < r, \frac{\pi i}{2} (rs)^{-\frac{n-2}{2}} J_{\nu_j}(\lambda r) H_{\nu_j}^{(1)}(\lambda s), & s > r, \end{cases} $$ since $s^{\frac{n}{2}} = s^{n-1}s^{-\frac{n-2}{2}}$. We can repeat this analysis for $z^2 = \lambda^2 - i\varepsilon$, and we find that we must take use $H_{\nu_j}^{(2)}$ instead of $H_{\nu_j}^{(1)}$ due to the asymptotic behavior at infinity, which also causes the Wronskian to change sign, but otherwise the calculations are identical. We therefore obtain $$ R_{0,j}(\lambda^2 - i0; r, s) = \begin{cases} \frac{\pi i}{2} (rs)^{-\frac{n-2}{2}} J_{\nu_j}(\lambda s) H_{\nu_j}^{(2)}(\lambda r), & s < r, \frac{\pi i}{2} (rs)^{-\frac{n-2}{2}} J_{\nu_j}(\lambda r) H_{\nu_j}^{(2)}(\lambda s), & s > r. \end{cases} $$ \textbf{Remark B.1.} We note that one could also obtain the formula for $R_{0,j}(\lambda^2 - i0)$ from that of $R_{0,j}(\lambda^2 + i0)$ by using the analytic continuation formulae $$ J_{\nu}(z e^{\pi i}) = e^{\pi i} J_{\nu}(z) \quad \text{and} \quad H_{\nu}^{(1)}(z e^{-\pi i}) = -e^{-\pi i} H_{\nu}^{(2)}(z). $$ Given (B.6) and (B.7), we can express the imaginary part of the resolvent kernels $R_{0,j}$ as follows. Lemma B.2. For $\lambda$ real, we have $$\text{Im } R_{0,j}(\lambda^2 + i0; r, s) = \frac{\pi}{2} (rs)^{-\frac{n\nu}{2}} J_{\nu_j}(\lambda r) J_{\nu_j}(\lambda s)$$ as an integral kernel with respect to the measure $s^{n-1} ds$. Proof. This follows immediately from the fact that $$H^{(1)}_{\nu_j} + H^{(2)}_{\nu_j} = (J_{\nu_j} + iY_{\nu_j}) + (J_{\nu_j} - iY_{\nu_j}) = 2J_{\nu_j}.$$ □ We can now write down an expression for the spectral measure of $-\Delta_{C(X)}$ as in [10], which follows from Stone’s formula. Lemma B.3. For $\lambda$ real, $$\text{Im } R_{0}(\lambda^2 + i0; x, y) = \frac{\pi}{2} (rs)^{-\frac{n\nu}{2}} \sum_{j=0}^{\infty} J_{\nu_j}(\lambda r) J_{\nu_j}(\lambda s) \varphi_j(\theta_1) \overline{\varphi_j(\theta_2)}$$ where $x = (r, \theta_1)$ and $y = (s, \theta_2)$ are points in $C(X)$. Moreover, the absolutely continuous part of the spectral measure of $-\Delta_{C(X)}$, with the convention that $\lambda^2$ is the spectral parameter, is given by $$d\Pi_0(\lambda; x, y) = \frac{1}{2\pi i} \left[ R_0(\lambda^2 + i0; x, y) - R_0(\lambda^2 - i0; x, y) \right] 2\lambda d\lambda = \sum_{j=0}^{\infty} (rs)^{-\frac{n\nu}{2}} J_{\nu_j}(\lambda r) J_{\nu_j}(\lambda s) \varphi_j(\theta_1) \overline{\varphi_j(\theta_2)} \lambda d\lambda.$$ APPENDIX C. DISPERSIVE ESTIMATES FOR THE FREE SCHröDINGER EQUATION Here, we discuss bounds on solutions of the unperturbed Schrödinger equation, given by $$\begin{cases} (\frac{1}{i} \partial_t - \Delta_{C(X)}) u = 0, \\ u \|_{t=0} = f. \end{cases} \quad (C.1)$$ We prove that the solution to this equation satisfies a dispersive estimate analogous to Theorem 4, but without the need for projection onto the harmonics of the link, provided that the solution is measured in $L^\infty(\mathbb{R}^+; L^2(X))$, rather than simply $L^\infty(C(X))$. We do this by using a modification of the techniques outlined in [19], which handled flat two-dimensional cones, to obtain an explicit asymptotic formula for the kernel of $e^{it\Delta_{C(X)}}$ as a function of a rescaled variable. Theorem 5. Let $C(X) = \mathbb{R}^+ \times X$ be the product cone on $X$, for $(X,h)$ a compact Riemannian manifold of dimension $n-1$. Then the solution to (C.1) satisfies $$\\|e^{it\Delta_{C(X)}} f\\|_{L^\infty(\mathbb{R}^+; L^2(X))} \leq Ct^{-\frac{n}{2}} \\|f\\|_{L^1(\mathbb{R}^+; L^2(X))}, \quad t > 0,$$ for some $C > 0$. Here, $L^1(\mathbb{R}^+)$ is defined with respect to the measure $r^{n-1} \, dr$. Remark C.1. We note that this result is somewhat weaker than similar estimates obtained in [71], but we include it here because the proof is quite short and requires significantly less machinery. Since $X$ is compact, there exists an orthonormal basis $\{\varphi_j\}_{j=0}^\infty$ of $L^2(X)$, satisfying $$-\Delta_h \varphi_j = \mu_j^2 \varphi_j$$ for $0 = \mu_0^2 < \mu_1^2 \leq \ldots$ repeated according to multiplicity. By the functional calculus of Cheeger [10] discussed in Section 2, we can define the shifted eigenvalues $$\nu_j = \sqrt{\mu_j^2 + \left(\frac{n-2}{2}\right)^2},$$ in order to write the spectral measure of $-\Delta_C(X)$ as $$d\Pi_0(r_1, \theta_1, r_2, \theta_2) = (r_1 r_2)^{-\frac{n-2}{2}} \sum_{j=0}^\infty J_{\nu_j}(\lambda r_1) J_{\nu_j}(\lambda r_2) \varphi_j(\theta_1) \overline{\varphi_j(\theta_2)} \lambda d\lambda,$$ where $J_\nu$ is the Bessel function of the first kind of order $\nu$. Hence, the fundamental solution to (C.1) has the form $$K_{e^{it\Delta_{C(X)}}}(r_1, \theta_1, r_2, \theta_2) = (r_1 r_2)^{-\frac{n-2}{2}} \sum_{j=0}^\infty \left( \int_0^\infty e^{it\lambda^2} J_{\nu_j}(\lambda r_1) J_{\nu_j}(\lambda r_2) \lambda d\lambda \right) \varphi_j(\theta_1) \overline{\varphi_j(\theta_2)},$$ (C.2) with respect to the standard measure on the cone, $r^{n-1} \, dr \, dv_h(\theta)$, where $dv_h$ is the Riemannian volume measure on $X$. As in [19], we let $t = is$ in the above expression to obtain a formula for the heat kernel $e^{-s\Delta_{C(X)}}$. By Weber’s second exponential integral formula, we have that $$\int_0^\infty e^{-s\lambda^2} J_{\nu}(\lambda r_1) J_{\nu}(\lambda r_2) \lambda d\lambda = \frac{1}{2s} e^{\frac{-2\lambda^2 r_1^2 + 2\lambda^2 r_2^2}{4s}} I_{\nu}(\frac{r_1 r_2}{2s}),$$ where $I_\nu$ is the modified Bessel function of order $\nu$, defined by $$I_\nu(x) = \sum_{k=0}^\infty \frac{1}{k! \Gamma(\nu + k + 1)} \left(\frac{x}{2}\right)^{2k+\nu}.$$ Analytic continuation in $s$ and taking $s = -it$ gives us $$K_{e^{it\Delta_{C(X)}}}(r_1, \theta_1, r_2, \theta_2) = \frac{ie^{-\frac{r_1^2 + r_2^2}{4t}}}{2t(r_1 r_2)^{\frac{n-2}{2}}} \sum_{j=0}^\infty i^{\nu_j} J_{\nu_j}(\frac{r_1 r_2}{2t}) \varphi_j(\theta_1) \overline{\varphi_j(\theta_2)},$$ since $I_\nu(ix) = i^\nu J_\nu(x)$. For non-integer values of $\nu$, we choose $z^\nu$ to have its branch cut along the negative real axis. For convenience, we define $x = \frac{\alpha + 1}{2}$ and let $$S(x, \theta_1, \theta_2) = x^{-\frac{n-2}{2}} \sum_{j=0}^{\infty} i^\nu J_{\nu_j}(x) \varphi_j(\theta_1) \overline{\varphi_j(\theta_2)},$$ so that $$K_{e^{i\Delta C(X)}}(r_1, \theta_1, r_2, \theta_2) = \frac{i \exp \left( \frac{r_1^2 + r_2^2}{4it} \right)}{(2t)^{\frac{n}{2}}} S(x, \theta_1, \theta_2). \quad (C.3)$$ Furthermore, we define the family of operators $S(x) : C^\infty(X) \to \mathcal{D}'(X)$ by $$S(x)f(\theta_1) = \int_X S(x, \theta_1, \theta_2)f(\theta_2) \, d\nu(\theta_2) = x^{-\frac{n-2}{2}} \sum_{j=0}^{\infty} i^\nu J_{\nu_j}(x) \langle f, \varphi_j \rangle \varphi_j(\theta).$$ Next, we make note of an asymptotic expansion for $K_{e^{i\Delta C(X)}}$ in the regime where $x \to 0$, which is analogous to [19, Prop 4.1]. Proposition C.2. The free Schrödinger propagator has the asymptotic behavior $$K_{e^{i\Delta C(X)}}(r_1, \theta_1, r_2, \theta_2) = \frac{i \exp \left( \frac{r_1^2 + r_2^2}{4it} \right)}{(2t)^{\frac{n}{2}}} \left[ \frac{(i/2)^\frac{n-2}{2}}{\Gamma(\frac{n}{2}) \text{vol}(X)} + O \left( \left( \frac{r_1 r_2}{2t} \right)^\alpha \right) \right], \quad \text{as } \frac{r_1 r_2}{2t} \to 0,$$ where $\alpha = \min\{2, \nu_1 - \frac{n-2}{2}\}$. Proof. It suffices to show that $$S(x, \theta_1, \theta_2) = \frac{(i/2)^\frac{n-2}{2}}{\Gamma(\frac{n}{2}) \text{vol}(X)} + O(x^\alpha), \quad \text{as } x \to 0, \quad (C.4)$$ uniformly in $\theta_1, \theta_2$. Since the $\varphi_j$ are $L^2$-normalized, we have that $\varphi_0 = \frac{1}{\sqrt{\text{vol}(X)}}$, and so $$S(x, \theta_1, \theta_2) = \frac{(i/2)^{\frac{n-2}{2}}}{\text{vol}(X)} \left( \frac{x}{2} \right)^{-\frac{n-2}{2}} J_{\frac{n-2}{2}}(x) + x^{-\frac{n-2}{2}} \sum_{j=1}^{\infty} i^\nu J_{\nu_j}(x) \varphi_j(\theta_1) \overline{\varphi_j(\theta_2)}.$$ By the standard power series representation for $J_{\frac{n-2}{2}}$, we have $$\left\| S(x, \theta_1, \theta_2) - \frac{(i/2)^{\frac{n-2}{2}}}{\Gamma(\frac{n}{2}) \text{vol}(X)} \right\| = \left\| \frac{(i/2)^{\frac{n-2}{2}}}{\text{vol}(X)} \sum_{k=1}^{\infty} \frac{(-1)^k}{k! \Gamma(\frac{n}{2} + k)} \left( \frac{x}{2} \right)^{2k} + x^{-\frac{n-2}{2}} \sum_{j=1}^{\infty} i^\nu J_{\nu_j}(x) \varphi_j(\theta_1) \overline{\varphi_j(\theta_2)} \right\|. $$ Using the bound $\|J_\nu(x)\| \leq \frac{\gamma}{(\nu+1)\Gamma(\nu+1/2)}$ for $x$ real and $\nu > 0$, along with the standard $L^\infty$ eigenfunction estimate $\\|\varphi_j\\|_{L^\infty} \leq C\nu_j^{\frac{n-2}{2}}$, shows that for $0 \leq x < 2$, we have $$ \left\| S(x, \theta_1, \theta_2) - \left(\frac{i/2}{\Gamma(\nu_1/2)}\right)^{\nu_1} \right\| \leq \frac{1}{\text{vol}(X)} \sum_{k=1}^{\infty} \left(\frac{x^2}{4}\right)^k + \sum_{j=1}^{\infty} \frac{\mu_j^{2(n-1)}}{2^\nu \Gamma(\nu_1 + 1)} \left(\frac{x^2}{2}\right)^{\nu_1 + n - 2} $$ which is uniform in $\alpha = \min\{2, \nu_1 - \frac{n-2}{2}\}$. We observe that by definition, $\nu_1 - \frac{n-2}{2} > 0$. Hence, by (C.3), the proof is complete. \textbf{Corollary C.3.} The family of operators $S(x)$ satisfies $$ \\|S(x)f\\|_{L^2(X)} \leq C\\|f\\|_{L^2(X)} $$ for all $x \geq 0$ and for some $C > 0$ which is uniform in $x$. \textbf{Proof.} For $x < 2 - \varepsilon$ with $\varepsilon > 0$, the estimate follows from the proof of Proposition C.2, which shows that $\|S(x, \theta_1, \theta_2)\| \leq C$ for some $C$ which is uniform in $\theta_1, \theta_2$. Thus, for such $x$, $$ \\|S(x)f\\|_{L^2(X)}^2 = \int_X \left\| \int_X S(x, \theta_1, \theta_2)f(\theta_2) \text{d}v_h(\theta_2) \right\|^2 \text{d}v_h(\theta_1) $$ \leq \int_X \\|S(x, \theta_1, \cdot)\\|_{L^2(X)}^2 \\|f\\|_{L^2(X)}^2 \text{d}v_h(\theta_1) \leq C^2 \text{vol}(X)^2 \\|f\\|_{L^2(X)}^2. For $x \geq 1$, we can simply use the fact that $\|J_\nu(x)\|$ is bounded uniformly in both $x$ and $\nu$ to see that $$ \\|S(x)f\\|_{L^2(X)}^2 = x^{2-n} \sum_{j=0}^{\infty} \|J_\nu(x)(f, \varphi_j)\|^2 \leq C \sum_{j=0}^{\infty} \langle f, \varphi_j \rangle^2 = C\\|f\\|_{L^2(X)}^2, $$ for some $C > 0$, since $n \geq 2$. □ We are now ready to present the proof of the dispersive estimate in Theorem 5. Proof of Theorem 5. Recalling that $K_{\e^{it\Delta_C(X)}}(r_1, \theta_1, r_2, \theta_2)$ is the Schwartz kernel of $\e^{it\Delta_C(X)}$ and applying (C.3), we have that for any $r_1, t > 0$, $$\\|\e^{it\Delta_C(X)} f(r_1, \cdot)\\|_{L^2(X)}^2 = \int_X \left\| \int_0^\infty \int_X K_{\e^{it\Delta_C(X)}}(r_1, \theta_1, r_2, \theta_2) f(r_2, \theta_2) r_2^{n-1} dv_h(\theta_2) dr_2 \right\|^2 dv_h(\theta_1)$$ $$= \int_X \left( \int_0^\infty \frac{ie}{(2t)^{\frac{d}{2}}} \left[ S \left( \frac{r_1 r_2}{2t} \right) f(r_2, \theta_1) \right] r_2^{n-1} dr_2 \right)$$ $$\times \left( \int_0^\infty \frac{ie}{(2t)^{\frac{d}{2}}} \left[ S \left( \frac{r_1 r_3}{2t} \right) f(r_3, \theta_1) \right] r_3^{n-1} dr_3 \right) dv_h(\theta_1)$$ $$= (2t)^{-n} \int_0^\infty \int_0^\infty e^{\frac{(x^2 + y^2)}{2t}} \left( \int_X S \left( \frac{r_1 r_2}{2t} \right) f(r_2, \theta_1) S \left( \frac{r_2 r_3}{2t} \right) f(r_3, \theta_1) dv_h(\theta_1) \right) (r_2 r_3)^{n-1} dr_2 dr_3$$ $$\leq (2t)^{-n} \int_0^\infty \int_0^\infty \left\\| S \left( \frac{r_1 r_2}{2t} \right) f(r_2, \cdot) \right\\|_{L^2(X)} \left\\| S \left( \frac{r_1 r_3}{2t} \right) f(r_3, \cdot) \right\\|_{L^2(X)} (r_2 r_3)^{n-1} dr_2 dr_3.$$ In the last inequality, we are able to omit the complex exponential factor by taking absolute values, since the integral is known to be real-valued and non-negative. 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Email address: [email protected] DEPARTMENT OF MATHEMATICS AND STATISTICS, McGill University, Montreal, QC Email address: [email protected]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2483, 1 ], [ 2483, 5841, 2 ], [ 5841, 8797, 3 ], [ 8797, 12304, 4 ], [ 12304, 15577, 5 ], [ 15577, 17981, 6 ], [ 17981, 20547, 7 ], [ 20547, 23372, 8 ], [ 23372, 25335, 9 ], [ 25335, 27827, 10 ], [ 27827, 29540, 11 ], [ 29540, 31582, 12 ], [ 31582, 34075, 13 ], [ 34075, 36349, 14 ], [ 36349, 38377, 15 ], [ 38377, 40966, 16 ], [ 40966, 43923, 17 ], [ 43923, 46243, 18 ], [ 46243, 48684, 19 ], [ 48684, 51074, 20 ], [ 51074, 53215, 21 ], [ 53215, 55879, 22 ], [ 55879, 58570, 23 ], [ 58570, 60852, 24 ], [ 60852, 64021, 25 ], [ 64021, 67191, 26 ], [ 67191, 70281, 27 ], [ 70281, 73826, 28 ], [ 73826, 77197, 29 ], [ 77197, 79876, 30 ], [ 79876, 82628, 31 ], [ 82628, 85233, 32 ], [ 85233, 88093, 33 ], [ 88093, 90732, 34 ], [ 90732, 93324, 35 ], [ 93324, 96039, 36 ], [ 96039, 98477, 37 ], [ 98477, 100843, 38 ], [ 100843, 104195, 39 ], [ 104195, 107002, 40 ], [ 107002, 109586, 41 ], [ 109586, 111950, 42 ], [ 111950, 114290, 43 ], [ 114290, 116729, 44 ], [ 116729, 118540, 45 ], [ 118540, 120750, 46 ], [ 120750, 124836, 47 ], [ 124836, 128682, 48 ], [ 128682, 132233, 49 ], [ 132233, 132233, 50 ] ] }
8de9938955cb5190430f99d25a3c4b5582fdd372	{ "olmocr-version": "0.1.59", "pdf-total-pages": 7, "total-fallback-pages": 0, "total-input-tokens": 20813, "total-output-tokens": 7804, "fieldofstudy": [ "Medicine" ] }	Qualitative and Quantitative Anatomy of the Humeral Attachment of the Pectoralis Major Muscle and Structures at Risk A Cadaveric Study Phob Ganokroj,† MD, Kaare Midtgaard,‡ MD, Bryant P. Elrick,§ MD, Rony-Orijit Dey Hazra, MD, Brenton W. Douglass,* MD, Philip C. Nolte,* MD, Annalise M. Peebles,* BA, Brad W. Fossum,* BA, Justin R. Brown,* MD, Peter J. Millett,‖ MD, MSc, and CAPT Matthew T. Provencher,*‖§ MD, MBA, CAPT, MC, USNR(Ret) Investigation performed at Steadman Philippon Research Institute, Vail, Colorado, USA Background: Surgical pectoralis major (PM) repair can offer improved functional outcomes over nonoperative treatment. However, there is a lack of literature on consensus of the anatomical site of the humeral attachment. Purpose: To provide qualitative and quantitative anatomic analysis of the PM by focusing on humeral insertion and relevant structures at risk. Study Design: Descriptive laboratory study. Methods: Eight fresh-frozen male cadavers were dissected. The relevant landmarks that were collected and measured included (1) PM footprint length at the humeral insertion (total, sternal head, and clavicular head insertions); (2) PM tendon length from the humeral insertion to the musculotendinous junction; (3) distance from the PM humeral insertion to the lateral (LPN) and medial (MPN) pectoral nerves; and (4) distance from the coracoid process to the musculocutaneous nerve (MCN) in anatomical position. Results: The total PM footprint length was 81.4 mm (95% CI, 71.4-91.3). The sternal and clavicular heads that make up the PM had footprint lengths of 42.1 mm (95% CI, 32.9-51.4) and 56.6 mm (95% CI, 46.5-66.7), respectively. The PM tendon was wider at the clavicular head (74.7 mm; 95% CI, 67.5-81.7) than the sternal head insertions (43.0 mm; 95% CI, 40.1-45.9). The distances from the PM humeral insertion to LPN and MPN were 93.2 mm (95% CI, 83.1-103.3) and 103.8 mm (95% CI, 98.3-109.4), respectively. The coracoid process to MCN distance was 68.5 mm (95% CI, 60.2-76.8). Conclusion: This study successfully quantifies anatomic dimensions of the PM tendon, its sternal and clavicular head insertions, and its location relative to nearby vital structures. Such knowledge can provide surgeons with a better understanding of the PM in relation to nearby neurovascular structures during anatomic PM repair and reconstruction to avoid debilitating complications. Clinical Relevance: Knowledge of the quantitative anatomy of the PM at the humeral footprint along structures at risk may aid surgeons with identifying the injured part of the PM and improve outcomes for anatomic repair and reconstruction. Keywords: shoulder anatomy; pectoralis major tendon; humeral insertion and anatomic footprint Pectoralis major (PM) tendon tears have increased in prevalence because of the growing popularity of sport-related activities and weight training. Young men with an active lifestyle have a higher risk of PM tear with an incidence of 60 per 100,000 person-years. Although PM injuries are frequently reported in younger, active populations, the incidence in the elderly population is likely underreported. This bimodal age distribution exists for diagnosis of PM injury, with indirect trauma being the major mechanism for injury. This occurs when the shoulder is abducted and externally rotated during activities such as performing bench-press exercises. The most common type of PM injury is complete rupture at the humeral attachment, followed by ruptures at the musculotendinous junction and ruptures within the muscle belly. Repair of PM tendon ruptures can improve functional outcomes compared with nonoperative treatment, especially in athletes and those who undergo surgical repair within 6 weeks of injury. The PM tendon and muscle may also be used in reconstructive surgery as a complete or split-thickness tendon transfer.\textsuperscript{14} PM muscle resides on the anterior chest wall and facilitates adduction, internal rotation, and flexion of the humerus. The PM is divided into 2 parts: a clavicular head (CH) and the sternal head (SH). There are extensive differing opinions regarding the number of PM muscle segments and tendon layers. There is also little consensus on the folding or twisting of the PM muscle fibers leading to the insertion at the humerus, the humeral footprint of the PM tendon, and the related neurovascular structures from previous studies.\textsuperscript{4,7,8,12,13,15,16,18} There is also a lack of agreement on the humeral footprint and therefore where anatomic PM repair should occur.\textsuperscript{5,25} Acknowledging and characterizing the complex anatomy of the PM is important at the humeral attachments and nearby neurovascular structures for improving anatomical PM repair (partial and complete repair) and reconstruction. The study aims were to provide a qualitative and quantitative anatomic analysis of the PM by focusing on the humeral footprint and relevant neurovascular structures at risk during surgical repair or when the tendon is harvested as part of a tendon transfer procedure. METHODS Specimen Preparation Eight nonpaired, fresh-frozen male cadaveric chests (mean age, 57.9 years; range, 51-66 years) were utilized in this anatomic study. The exclusion criteria comprised no prior chest injury, no metastasis to bone, no gross deformities, and no history of surgery. The specimens were donated for medical research and subsequently purchased by our institution from corresponding tissue banks. Cadaveric studies do not require institutional review board approval at our facility. Before preparation, all specimens were stored at –20°C and thawed at room temperature for 24 hours. All skin and subcutaneous tissue was removed. Superficial muscle was meticulously dissected to expose and clearly identify the entirety of the PM (SH and CH) and its proximal and distal portions and corresponding tendon insertion points on the proximal humerus (Figure 1). After reflecting the tendonous insertion of the PM, the medial pectoral nerve (MPN) and lateral pectoral nerve (LPN) were traced to where they pierced the PM muscle. The conjoint tendon and musculocutaneous nerve (MCN) were identified and sectioned out (Figure 2). During the course of dissection, specimens were kept hydrated with normal saline. Data Collection The SH and CH of the PM tendon were identified and sharply dissected down to the bony insertion on the humerus (Figure 1). In order to measure the footprint of the PM tendonous insertion on the humerus, the remaining soft tissue was removed, and the bony landmarks were exposed. A joint coordinate frame was established using a coordinate measuring machine (Romer Absolute Arm; Hexagon Manufacturing Intelligence) in accordance with the methodology established by SimVITRO. The robotic arm used in this study has ±0.025 mm of point repeatability and ±0.037 mm of volumetric accuracy, and variability among specimens was minimal. Collected landmarks on the humerus included the proximal and distal points of the SH and CH insertions of the PM, which were used to calculate the total PM footprint length (superior to inferior) as well as SH and CH insertions of PM footprint lengths (Figures 3 and 4). Next, these 2 heads of the PM tendon were identified and measured the tendon length (from the humeral insertion to the musculoskeletal junction) with a caliper. After cutting the humeral insertion of the PM tendon, the distances starting from the center of the humeral insertion of the PM tendon (•) to the closest nerve bundles (MPN and LPN) that entered the PM muscle. Co, coracoid process; LPN, lateral pectoral nerve; MPN, medial pectoral nerve. Figure 2. Anatomy of the related neurovascular structures (left shoulder) after cutting the humeral insertion of the pectoralis major (PM) (•). The distance between points was measured with calipers starting from the humeral insertion of the PM tendon (•) to the closest nerve bundles (MPN and LPN) that entered the PM muscle. Co, coracoid process; LPN, lateral pectoral nerve; MPN, medial pectoral nerve. Figure 3. The posterior surface of the pectoralis major (PM) humeral insertion after reflecting the muscle (right shoulder). After reflecting the PM muscle to the posterior surface, these 2 head insertions could be distinguished by an interposed fat pad (#) and display the 2 directions (arrows) of tendon insertion layers. The falciform ligament or the fibrous expansion of the PM tendon was identified in all specimens. This ligament could be clearly distinguished from the SH of the PM. CH, clavicular head of the PM; F, falciform ligament; H, humerus; L, long head of biceps tendon; SH, sternal head of the PM. Data Analysis The coordinates of the collected points were imported into MATLAB (Version R2021a, The MathWorks Inc., Natick, MA) script for analysis. The distance between landmarks was calculated as a direct linear distance between 2 collected points to determine the PM tendon footprint length (SH, CH, and total PM tendon insertion lengths) (Figure 4). The distance between the proximal point of 2 head insertions and the overlapping distance were also calculated (Figure 4). Descriptive statistical analysis was performed to include means with 95% CIs. Distances were reported in millimeters. The interrater reliability of the measurement was assessed via the ICC using the bootstrapping method. Based on the 95% CI of the ICC, the reliability values were... classified as excellent (ICC, ≥0.9), good (ICC, 0.75-0.89), fair (ICC, 0.5-0.74), or poor (ICC, <0.5). Statistical analyses were performed using the statistical software SPSS for Windows (Version 18.0; SPSS Inc) and R Version 4.1.2 (R Foundation for Statistical Computing). RESULTS Qualitative Anatomy There were 2 heads of the PM muscle (CH and SH) that inserted into the humerus in a bilaminar fashion. The SH of the PM muscle coursed from inferomedial to superolateral and inserted at the lateral lip of the intertubercular sulcus of the humerus (Figure 1). The CH of the PM muscle coursed in a superomedial-to-inferolateral direction (Figure 1). These 2 head insertions of the PM tendon were flat and fused at the level of the musculotendinous junction. However, after reflection of the PM muscle to expose the posterior surface, these 2 head insertions of the PM tendon could be determined by an interposed fat pad and a disparity between 2 directions of tendon insertion layers as mentioned above (Figure 3). In all specimens, there was no clear evidence of folding or twisting of either the SH or CH of the PM tendon under direct visualization. During dissection, the falciform ligament or the fibrous expansion of the PM tendon was identified in all specimens. It formed an oblique fiber orientation from the SH insertion of the PM to the lateral aspect of the bicipital groove. This ligament could be clearly distinguished from the SH of the PM and should be excised to clearly identify the PM footprint on the humerus (Figure 3). Quantitative Anatomy The total footprint length of the PM tendon (from superior to inferior) on the humeral insertion was 81.4 mm (95% CI, 71.4-91.3). The footprint length of the SH was shorter than the CH insertions of the PM, 42.1 mm (95% CI, 32.9-51.4) and 56.6 mm (95% CI, 46.5-66.7), respectively (Table 1). The distance from the proximal border of the SH insertion to the proximal border of the CH insertion of the PM (S1 to I1), and the overlapping distance between these 2 head insertions (I1 to S2). H, humerus; CH, clavicular head of the PM; Co, coracoid process; I1 and I2, the proximal and distal points of clavicular head insertion; S1 and S2, the proximal and distal points of sternal head insertion; SH, sternal head of the PM. Figure 4. The posterior surface of the pectoralis major (PM) humeral insertion after reflecting the muscle (left shoulder). Landmarks on the humerus included the proximal and distal points of the SH (S1, S2) and CH insertions (I1, I2). The total PM footprint length is calculated from S1 to I2, and the SH and CH of PM tendon footprint lengths (S1 to S2 and I1 to I2, respectively). The distance from the proximal border of the SH insertion to the proximal border of the CH insertion of the PM (S1 to I1), and the overlapping distance between these 2 head insertions (I1 to S2). H, humerus; CH, clavicular head of the PM; Co, coracoid process; I1 and I2, the proximal and distal points of clavicular head insertion; S1 and S2, the proximal and distal points of sternal head insertion; SH, sternal head of the PM. Table 1: Distance Measurements Between PM Insertion Points on the Humerus \| Measurement \| Distance, mm \| \|-----------------------------------\|----------------\| \| SH insertion of PM tendon \| 42.1 (32.9-51.4) \| \| CH insertion of PM tendon \| 56.6 (46.5-66.7) \| \| Distance from proximal border of SH-to-CH insertions of PM tendon \| 24.9 (11.9-38.0) \| \| Overlapping tendon (between SH and CH insertions) \| 27.9 (18.4-37.5) \| \| Total PM insertion \| 81.4 (71.4-91.3) \| Data are presented as mean (95% CI). CH, clavicular head of the PM; PM, pectoralis major; SH, sternal head of the PM. TABLE 1 Distance Measurements Between PM Insertion Points on the Humerus \| Measurement \| Distance, mm \| \|-----------------------------------\|----------------\| \| SH insertion of PM tendon \| 42.1 (32.9-51.4) \| \| CH insertion of PM tendon \| 56.6 (46.5-66.7) \| \| Distance from proximal border of SH-to-CH insertions of PM tendon \| 24.9 (11.9-38.0) \| \| Overlapping tendon (between SH and CH insertions) \| 27.9 (18.4-37.5) \| \| Total PM insertion \| 81.4 (71.4-91.3) \| The tendon length (from the humeral insertion to the musculotendinous junction) of the SH insertion of the PM was narrower than the CH insertion of the PM, 43.0 mm (95% CI, 40.1-45.9) and 74.7 mm (95% CI, 67.5-81.7), respectively (Table 2). The closest distances from the humeral insertion to the adjacent neurovascular structures are listed in Table 2. From the PM humeral insertion, the LPN and MPN pierced the PM muscle at means of 93.2 mm (95% CI, 83.1-103.3) and 103.8 mm (95% CI, 98.3-109.4), respectively (Table 2). The ICC values were excellent at 0.963 (95% CI, 0.804-0.982) for interobserver reliability. TABLE 2 PM Tendon Length and Distance Measurements Between the Humeral Footprint and the Adjacent Neurovascular Structures \| Measurement \| Distance, mm \| \|--------------------------------------\|--------------\| \| SH insertion tendon length \| 43.0 (40.1-45.9) \| \| CH insertion tendon length \| 74.7 (67.5-81.7) \| \| PM humeral insertion to LPN \| 93.2 (83.1-103.3) \| \| PM humeral insertion to MPN \| 103.8 (98.3-109.4) \| \| Coracoid process to MCN \| 68.5 (60.2-76.8) \| aData are presented as mean (95% CI). The PM tendon length was measured from the humeral insertion to the musculotendinous junction. CH, clavicular head of the PM; LPN, lateral pectoral nerve; MCN, musculocutaneous nerve; MPN, medial pectoral nerve; PM, pectoralis major; SH, sternal head of the PM. DISCUSSION The principal findings of this study demonstrated that the entirety of the PM footprint length was 81.4 mm (95% CI, 71.4-91.3). Such findings will improve quantitative familiarity for relevant structures that can be applied during anatomical repair or PM reconstruction in a chronic or irreparable PM tear (partial or complete). The reported PM footprint length in the current study is notably greater than that in previous studies, in which the weighted-mean PM tendon length was 62.5 mm.4 In previous literature, there was a large range of PM footprint length spanning from 24 to 97 mm. Variables that may contribute to the wide range of these values include the method of measurement, types of cadaver, and points of measurement. The authors also chose all male cadavers in this study, which may be associated with a higher PM footprint length than other studies. In terms of clinical relevance, the findings from the current study highlight that adequate exposure is essential to facilitate an anatomic repair or reconstruction of the broad footprint length of the PM. This has clinical implications and has been used by some authors in split-thickness PM tendon transfers where the SH principally is transferred for a deficient subscapularis.13 It also has clinical implications in acute PM tendon tears, as the SH tears more commonly and can easily be missed if the surgeon only sees the intact CH layer. There were 2 heads of the PM tendon that were identified in this study. These 2 head insertions were flat and fused at the level of musculotendinous junction. The CH insertion was longer than the SH insertion, with measurements of 56.6 and 42.1 mm, respectively. The footprint length of tendon overlap was measured at 27.9 mm. In a previous study, Jennings et al17 found 2 laminae of the PM at the humeral footprint, which were described as the anterior and posterior laminae. The anterior lamina consisted of the tendon from the clavicular portion of the PM. The anterior lamina was found to be longer than the posterior lamina (sternal portion of the PM), which was measured to be 43.0 mm. The measurement for the overlap of these 2 laminae was 27 mm (range, 1-56 mm).17 Jennings et al17 found an isolated CH of the PM but could not differentiate between each segment of the SH in their study. In previous studies, 1 to 3 layers of PM tendons were found at the humeral footprint.11,13,16,17,26 Huang et al16 completed a PM tendon anatomical study using magnetic resonance imaging (MRI), ultrasound, and histologic investigation. Their team illustrated that the 2 heads of the PM muscle were CH and SH but had a unilaminar presentation on both gross inspection and histologic enthesis.16 We also found that the SH and CH insertions of the PM merged into a single tendon at the humeral insertion in this study. These insertional heads can be differentiated by the interposed fat pad and the tendon’s direction at the posterior surface of the humeral insertion of the PM. Such findings are similar to the 3-dimensional study of the PM muscle and tendon architecture by Fung et al,13 who found that the 2 layers at the humeral PM tendon fused before its insertion at the humeral footprint. From their study, the posterior layer was composed of lower segments of SH and inserted on the humerus superior to the anterior layer.13 The findings from the current study support the bilaminar concept of the PM tendon at the humeral insertion. Previous studies have found that the population with the highest prevalence of chronic PM tendon injuries was male.20 Kowalczyk et al21 found that these chronic tears most commonly occurred between the musculotendinous junction and the humeral tendinous insertion. Partial-thickness and complete-width tears were the most common type of tear pattern.12,21 MRI is the investigation of choice for characterization of tear pattern and preoperative evaluation.5 A combination of the bilaminar characteristics and overlapping of the PM tendon insertion on the humerus makes it difficult to characterize the partial tear using MRI.6,7 The current study also found that it was difficult to differentiate between SH and CH during direct inspection of the humeral insertion at the anterior surface. The authors propose that using the distance from the proximal border of the SH insertion may be useful for determining which portion of the PM was injured. In this study, the proximal part of the CH insertion was 25 mm (1 inch) below the proximal part of the SH insertion. Injury or tear below this point might represent a complete tear of the PM tendon and will guide surgeons to perform an anatomic repair or reconstruction for both portions of the PM tendon (CH and SH). When increasing surgical exposure in a proximal humeral surgery, surgeons should be aware not to release the proximal part of the PM more than 25 mm, as doing so may cause injury to both the CH and the SH of the PM humeral insertion. The current study found that the length (medial to lateral) of the CH insertion was wider than the SH insertion, with measurements being 74.7 mm and 43.0 mm, respectively. Previous literature found that either the posterior lamina (SH) tendon length was wider than the anterior lamina (CH) or there was no difference in tendon length between the 2 laminae.13,17 Variability in these results can be explained by multiple factors. These include the method of measurement (3-dimensional digital model or caliper), types of cadavers (formalin embalmed or fresh-frozen), and points of measurement. The authors of the present study found 2 distinct head insertions (SH and CH) with different lengths and orientations. For total-length PM tears or chronic tears requiring allograft augmentation, a longer graft or 2 distinct graft reconstructions may be possible options for achieving anatomical PM reconstruction. The distances measured in the current study from the PM tendon humeral insertion to LPN and MPN were of similar values when compared with previous studies. The humeral insertion to LPN was 93.2 mm in the current study compared with 125 mm in previous studies, and the humeral insertion to MPN measured 103.8 mm compared with 93 to 119 mm in the literature. There is little to no reporting of cases in the current literature for LPN or MPN injury during PM repair or reconstruction. The safe zone measured in this study was >90 mm from the humeral insertion. For chronic cases, care should be taken to avoid vigorous dissection when mobilizing retracted tendon. For the MCN, this study found that the distance from the coracoid process to the first branch of MCN piercing the coracobrachialis was 68.5 mm. In a similar study, Klepps et al found that the safe distance from the coracoid process to the proximal branch of MCN was 44 mm (range, 14-74 mm). Klepps et al showed that transferring PM superficial to the MCN created less nerve tension when compared with transferring PM deep to the MCN. This team recommended MCN exploration during operation because of the high variability and location of MCN, in order to prevent tension on the nerve. PM repair or reconstruction around this footprint area remains a safe zone for surgery; however, thorough knowledge of the anatomy in this area will help surgeons avoid complications. Limitations This study had several limitations that are commonly observed in cadaveric studies. The limited number of cadavers, monoethnicity, and all specimens being male may influence the generalizability of the results. The nonpaired, fresh-frozen male cadavers analyzed in this study translated to the population with a higher incidence of PM tendon injury. Applying these findings to a female population should be done with caution. Measurement error is also a primary concern because of the nature of the anatomical study. All measurements in this study were done by 2 examiners, and the calculated ICC values were excellent for internal consistency. This study used the coordinate measuring machine to achieve more accuracy and less variability for the anatomy of the humeral attachment of the PM in order to reduce the measurement error. Future studies should focus on the differences in clinical outcome between repair of partial or complete footprint lengths of the PM tendon, along with single- versus double-bundle PM reconstructions. CONCLUSION This study successfully quantifies anatomic dimensions of the PM tendon, its humeral head insertion (SH and CH), and its location relative to nearby vital structures. Such knowledge can provide surgeons with a better understanding of the PM in relation to nearby neurovascular structures during anatomic PM repair and reconstruction to avoid debilitating complications. ACKNOWLEDGMENT The authors gratefully thank Ms. Narumol Sudjai for the statistical analysis and Ms. Waraporn Chalermusuk for graphic materials. REFERENCES 1. Bak K, Cameron EA, Henderson LJ. Rupture of the pectoralis major: a meta-analysis of 112 cases. Knee Surg Sports Traumatol Arthrosc. 2000;8(2):113-119. 2. Balazs GC, Brelin AM, Donohue MA, et al. 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Qualitative and quantitative anatomy of the proximal humerus muscle attachments and the axillary nerve: a cadaveric study. Arthroscopy. 2018;34(3):795-803. 23. Provencher MT, Handfield K, Boniquit NT, et al. Injuries to the pectoralis major muscle: diagnosis and management. Am J Sports Med. 2010;38(8):1693-1705. 24. Rijnberg WJ, van Linge B. Rupture of the pectoralis major muscle in body-builders. Arch Orthop Trauma Surg. 1993;112(2):104-105. 25. Thompson K, Kwon Y, Flatow E, et al. Everything pectoralis major: from repair to transfer. Phys Sportsmed. 2020;48(1):33-45. 26. Wolfe SW, Wickiewicz TL, Cavanaugh JT. Ruptures of the pectoralis major muscle: an anatomic and clinical analysis. Am J Sports Med. 1992;20(5):587-593.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3763, 1 ], [ 3763, 6610, 2 ], [ 6610, 9478, 3 ], [ 9478, 14356, 4 ], [ 14356, 20787, 5 ], [ 20787, 27250, 6 ], [ 27250, 28804, 7 ] ] }
3d65b8b724dede8a5124e9ef01056ac1d8712222	{ "olmocr-version": "0.1.59", "pdf-total-pages": 21, "total-fallback-pages": 0, "total-input-tokens": 46468, "total-output-tokens": 16196, "fieldofstudy": [ "Biology" ] }	MicroRNA profiling of low grade glial and glioneuronal tumors shows an independent role for cluster 14q32.31 member miR-487b Heather Marion Ames, MD, PhD1,, Ming Yuan, PhD1,, Maria Adelita Vizcaíno, MD1,3, Wayne Yu, PhD2, and Fausto J. Rodriguez, MD1,2 1Department of Pathology, Johns Hopkins University School of Medicine, Baltimore, MD 2Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD 3Department of Cellular and Tissue Biology, Universidad Nacional Autónoma de México, Mexico City, DF Abstract Low-grade (WHO I–II) gliomas and glioneuronal tumors represent the most frequent primary tumors of the central nervous system in children. They often have a good prognosis following total resection, however they can create many neurological complications due to mass effect, and may be difficult to resect depending on anatomic location. MicroRNAs have been identified as molecular regulators of protein expression/translation that can repress multiple mRNAs concurrently through base pairing, and play an important role in cancer, including brain tumors. Using the NanoString digital counting system, we analyzed the expression levels of 800 microRNAs in nine low-grade glial and glioneuronal tumor types (n=45). A set of 61 of these microRNAs were differentially expressed in tumors compared to brain and several showed levels varying by tumor type. The expression differences were more accentuated in subependymal giant cell astrocytoma, compared with other groups, and demonstrated the highest degree of microRNA repression validated by RT-PCR, including miR-129-2-3p, miR-219-5p, miR-338-3p, miR-487b, miR-885-5p, and miR-323a-3p. Conversely, miR-4488 and miR-1246 were overexpressed in dysembryoplastic neuroepithelial tumors compared with brain and other tumors. The cluster 14q32.31 member miR-487b was variably under expressed in pediatric glioma lines compared to human neural stem cells. Overexpression of miR-487b in a pediatric glioma cell line (KNS42) using lentiviral vectors led to a decrease in colony formation in soft agar (30%)(p<0.05), and decreased expression of known predicted targets PROM1 and Nestin (but not WNT5A). miR-487b overexpression had no significant effect on cell growth, proliferation, sensitivity to temozolomide, migration or invasion. In summary, microRNA regulation appears to play a role in the biology of glial and glioneuronal tumor subtypes, a finding that deserves further investigation. Keywords microRNA; low grade glioma; pediatric glioma; glioneuronal tumor; miR-487b; subependymal giant cell astrocytoma Introduction The category of low grade gliomas is composed of a diverse group of slow growing tumors that primarily arise in childhood and young adulthood. The related category of glioneuronal tumors demonstrate similar demographics, although they are more heterogeneous with regard to specific subtypes, and can have a variable proportion of glial and neuronal components. Both of these tumor types are initially treated by surgery and are associated with a good prognosis, although they may be associated with seizures and deleterious mass effects. Association with genetic syndromes such as neurofibromatosis and tuberous sclerosis may be present and malignant transformation is very rare. With these characteristics, low-grade gliomas and glioneuronal tumors represent a diverse, yet genetically stable, pool from which to identify potential molecular targets. Our understanding of the biology of pediatric low grade glioma has benefited from major recent advances in molecular genetics. The application of high resolution platforms has discovered alterations not recognizable through traditional cytogenetic analysis. For example, BRAF-KIAA1549 fusions are the most frequent recurrent alteration in pilocytic astrocytoma $^1\text{-}^5$, the predominant subtype of pediatric low grade astrocytoma. BRAF-KIAA1549 fusions, as well as other genetic rearrangements and mutations lead to downstream activation of signaling pathways, particularly the mitogen-activated protein kinase pathway $^2$. More recently, comprehensive sequencing studies have documented genetic hits in mitogen-activated protein kinase pathway components in essentially 100% of pilocytic astrocytomas $^6$. In patients with neurofibromatosis type 1, pilocytic astrocytomas develop homozygous mutations in the NF1 gene, also leading to MAPK pathway activation. Another relevant signaling pathway, involving the mammalian target of rapamycin (mTOR), is frequently activated in pediatric low grade glioma $^7\text{-}^8$, and represents the key molecular property of subependymal giant cell astrocytoma, a tumor frequently developing in the setting of tuberous sclerosis, and characterized by inactivation of TSC1 or TSC2. Other pediatric low grade glioma subsets have different alterations, for example, partial duplication of the transcription factor MYBL1 with truncated transcript, intragenic duplications of the tyrosine kinase domain in the FGFR1 gene, and MYB rearrangements in diffuse pediatric low grade gliomas $^9\text{-}^{10}$. A role for a variety of non-coding ribonucleic acid molecules (RNAs), particularly microRNAs (measuring approximately 22 nucleotides in length), has been increasingly documented in many normal and abnormal physiologic states, including cancer. MicroRNAs have been identified as regulators of RNA transcription and protein translation. Through this mechanism, multiple mRNAs can be concurrently targeted through base pairing. Tumor suppressors may be targeted through microRNA upregulation, while oncogenes may be increased in abundance by downregulation of corresponding microRNAs. Of relevance to this study, several microRNAs have been implicated in gliomagenesis by prior studies (e.g. miR-21, miR-7, miR-181a/b, miR-221 and miR-222)\textsuperscript{11–15}, and also regulate signaling pathways in diffuse gliomas, including glioblastoma\textsuperscript{16,17}. For example, PTEN, a validated tumor suppressor gene, is frequently inactivated in diffuse gliomas, and may be regulated by a number of microRNAs such as miR-21, miR-23a, and miR-26a resulting in increased AKT/mTOR activity\textsuperscript{18,19}. MicroRNAs may have more than one target, and therefore microRNA profiling may uncover molecular subgroups of cancer more robustly than conventional mRNA profiling\textsuperscript{20}. Low grade pediatric gliomas lack the multiple overt genomic alterations typical of higher grade tumors\textsuperscript{21}, and therefore microRNA and other genetic/epigenetic mechanisms are likely to participate in their pathogenesis. Our work and that of others has described differentially expressed microRNAs in pilocytic astrocytomas compared to normal brain, including miR-21, miR-124 and miR-129\textsuperscript{22–25}. Some studies have also reported differential microRNA expression in other pediatric brain tumors, such as medulloblastoma and ependymoma\textsuperscript{26}. Studies of microRNA regulation in other low grade glioma subtypes and glioneuronal tumors are lacking, with some inflammation-associated microRNAs affected in ganglioglioma\textsuperscript{27,28}. In the current study, we investigated global microRNA expression in a series of low grade glioma and glioneuronal subtypes with the aim of identifying biologic and clinically relevant targets. Materials and Methods Tumor Samples Cases of low grade glioma or glioneuronal tumors were queried in the pathology database of Johns Hopkins Hospital. All available slides were reviewed by two of the authors (FJR, MAV). Only sections with greater than 60% neoplastic cellularity were selected for further study. Formalin-fixed paraffin-embedded sample rolls were collected in eppendorf tubes. RNA extractions and quality analysis were performed at the Sidney Kimmel Comprehensive Cancer Center Microarray Core Facility at the Johns Hopkins University (Baltimore, MD) using the miRNeasy formalin-fixed paraffin-embedded tissue Kit (Qiagen). A total of 45 samples were included in the study representing all categories of low grade, primarily pediatric, gliomas and glioneuronal tumors. Mean age was 15 years (range: 17 weeks to 57 years). Diffuse gliomas in adults and NF1-associated tumors were excluded. Demographic features of these tumors per case are outlined in supplementary table 1. Tumor samples included subependymal giant cell astrocytoma (n=6), pilocytic astrocytoma (n=6), pleomorphic xanthoastrocytomas (n=7), gangliogliomas (n=6), dysembryoplastic neuroepithelial tumor (n=5), angiocentric glioma (n=3), pediatric oligodendroglioma (n=3), pediatric diffuse astrocytoma (n=3), rosette forming glioneuronal tumor (n=2) and non-neoplastic brain controls (n=4). All studies were performed using established ethical guidelines and institutional review board approval. MicroRNA Profiling NanoString technology was applied to formalin-fixed paraffin-embedded tissues to quantify the global expression of 800 microRNAs in nine types of low-grade neoplasms of the brain. Raw data was normalized using nSolver software (NanoString), filtered for minimum expression threshold, and log2 transformed prior to analysis. MeV software (version 4.8.0) was used to generate unsupervised hierarchical clusters following significance evaluation via significant analysis of microarray. Results for 10 microRNAs of interest were further validated using standard Taq-man RT-PCR protocols and probes (Life Technologies). The demographics of the samples used for RT-PCR validation are indicated by a star () in supplementary table 1. Cell culture* Pediatric glioma-derived lines Res 186, Res 259, UW479 and SF-188 have been previously described, and were kindly provided by Dr. Chris Jones (Institute of Cancer Research, Sutton, UK). CHLA-200 and SJ-GBM2 were provided by the Children’s Oncology Group Cell Culture and Xenograft Repository banks. The pediatric glioma cell line KNS42 was obtained from the Japan Cancer Research Resources cell bank. Details of the various cell lines is summarized in supplementary table 2. Cells were cultured in Dulbecco modified Eagle medium/ F12 Ham medium (DMEM/F12) supplemented with 10% heat-inactivated fetal bovine serum (FBS). TrypLE express enzyme was used for cell dissociation. Non-neoplastic human neural stem cells (h-NSC) have been previously described and were grown in DMEM/F12 supplemented with 20% B27 supplement, 5ug/mL heparin, 20ng/mL EGF, and 20ng/mL FGF2. All culturing reagents were purchased from ThermoFisher Scientific. miRNA overexpression and inhibition Lentiviral based miRNA plasmids were obtained from Biosetta, including expression plasmids pLV-hsa-mir-487b (mir-487b) and pLV-mir-control (mir-control), inhibition plasmids pLV-hsa-mir-1246 locker (mir-1246 locker) and pLV-mir-locker control (mir-locker). To produce lentiviruses, 293T cells were transfected with miRNA plasmid and VSVG packaging plasmids mixture using Lipofectamine 2000 (ThermoFisher Scientific). Lentiviral supernatants were collected at 72 h post transfection, and concentrated using Polyethylene glycol (PEG) 8000. Virus was resuspended in DMEM and kept frozen at −80oC until needed. KNS42 cells were infected with virus in the presence of polybrene (5μg/ml, Sigma- Aldrich). At 48 hours later, infected cells were selected with 1μg/ml of puromycin (Sigma- Aldrich, for expression plasmids) or 5μg/ml of Blastidin (ThermoFisher Scientific, for inhibition plasmids) for 5 days to generate stable cell lines. Target prediction was performed using TargetScan, version 6.2. Cell cycle analysis Cells were dissociated and fixed with 70% Ethanol at 4_C overnight, then stained with Muse cell cycle reagent for 30 minutes at room temperature and analyzed with Muse flow cytometer (Millipore) according to the manufacturer’s instructions. Cell cycle data were analyzed with FlowJo software. Cell growth and cell survival assay The CellTiter-Blue cell viability assay kit (Promega) was used to count viable cells. Cells were seeded in 96 well plates at a density of 1000 cells per well in growth media. Twenty microliters of CellTiter-Blue reagent was added to 100µl medium and incubated for 1 hour at 37 °C incubator. Fluorescence (560nmEx/590nmEm) was measured using TECAN plate reader. For cell growth assay, relative cell numbers were continuing measured for 5 days. For drug treatment, cells were cultured in the media with different doses of temozolomide (TMZ, Skellchem) for 7 days, DMSO was used as control. Quantitative real-time polymerase chain reaction (qRT-PCR) Primers for miRNA were designed by using miRprimer software. Sequences can be found in Supplementary Table 3, and small RNA RNU48 was used as the endogenous control. Primer sequences for mRNA target genes are listed in Supplementary Table 4, and HPRT1 was used as the endogenous control. Total RNA was isolated from cultured cells using miRNeasy mini kit (QIAGEN), reverse transcription of miRNA was performed per published protocols and cDNA for target genes were produced using QuantiTect reverse transcription kit (QIAGEN). qRT-PCR was performed using SsoAdvanced universal SYBR green supermix (Bio-Rad). The relative fold change was calculated based on the difference of Ct values. In vitro invasion assay Cell invasion assay was analyzed using a 24 well system with growth factor reduced Matrigel coated transwell inserts containing 8μM pore membrane (Corning). KNS42 cells (1x10^5) in 250μl of DMEM/F12 were added on top of each membrane and fill bottom with 750μl of complete growth medium. After 24 hours, migrated cells were dissociated from the membrane by using Accutase (Sigma- Aldrich) and resuspended in growth medium. Relative cell numbers were measured by using Cell-Titer blue reagent (Promega). Wound healing assay Cells were grown in 12-well plates to confluence, then scratched with 1 P1000 pipette tip. The cells were rinsed with PBS, imaged, and allowed to migrate for 48 hours before taking a second image. ImageJ software (National Institutes of Health) was used to quantify cell migration. Soft agar clonogenic assay One thousand cells were resuspended in growth medium with 0.4% soft agar, then seeded in 6-well plate with 0.8% bottom agar layer. After 21 days, cells were fixed and stained with 0.01% Crystal violet in 20% methanol. The number of colonies containing more than 50 cells in each well were counted using a Nikon inverted microscope. Statistical analysis of cell culture assays All data are presented as mean ± SD, and p< 0.05 was considered significant. All experiments were performed in at least 3 biological replicates and data were analyzed with a two-tailed Student’s t-test. Results MicroRNA profiling reveals differentially expressed microRNAs in low grade glioma and glioneuronal tumors compared to brain In an unsupervised hierarchical analysis of microRNA expression data, non-neoplastic brain samples clustered together, while subependymal giant cell astrocytomas and rosette forming glioneuronal tumors segregated furthest from non-neoplastic brain (Figure 1A). A total of 61 microRNAs showed altered expression among the 10 groups of samples as evaluated by significance analysis of microarrays analysis. These microRNAs included a similar list of those that have been previously identified as having altered expression in pilocytic astrocytomas as compared to normal brain. Specifically, miR129-5p, which was previously validated as downregulated in pilocytic astrocytomas was also downregulated to a varying extent in all low grade gliomas and glioneuronal tumors evaluated in this study. Both subependymal giant cell astrocytomas and pilocytic astrocytomas had significant decreases in miR129-5p expression (p<0.05) (Figure 1B), leading us to hypothesize that subependymal giant cell astrocytomas may also have increased staining for the nuclear proteins PBX3 and NFI/B, as previously described in pilocytic astrocytoma. Subependymal giant cell astrocytomas (n=3) were stained for PBX3 and NFI/B according to previously established protocols and were scored for nuclear staining on a 0–3 scale as compared to normal brain. As expected, subependymal giant cell astrocytomas showed strong (3+) nuclear staining for PBX3 (2 of 3) and NFI/B (3 of 3) (Figure 1C). Coordinated repression of cluster 14q32.31 microRNAs in low grade gliomas and subependymal giant cell astrocytomas as compared to low grade glioneuronal tumors When looking at global microRNA expression, subependymal giant cell astrocytomas, pilocytic astrocytomas, and rosette forming glioneuronal tumors clustered together and farthest from non-neoplastic brain, while dysembryoplastic neuroepithelial tumor, ganglioglioma, and pleomorphic xanthoastrocytoma segregated closer to normal brain (Figure 1A). This raised the possibility that since dysembryoplastic neuroepithelial tumor, ganglioglioma, and pleomorphic xanthoastrocytoma have a mixed cellular composition, the heterogeneous elements may lead to relative clustering with brain compared to the homogeneous, well-circumscribed subependymal giant cell astrocytomas and pilocytic astrocytomas. To further identify those microRNAs that are differentially expressed in homogenous glial tumors (subependymal giant cell astrocytomas and pilocytic astrocytomas) and heterogeneous glioneuronal tumors (gangliogliomas and dysembryoplastic neuroepithelial tumors), significance analysis of microarrays was performed to directly compare these two groups. This yielded a list of 35 microRNAs that were differentially expressed between the two groups, of which all but 5 were identified as significant on the initial analysis of all 10 groups (Figure 2A). Additionally, there was a similar directionality for both glial and glioneuronal tumors versus brain for the 30 microRNAs that were both significant among all 10 groups and between the well-circumscribed glial and glioneuronal tumors, with the greatest fold changes seen in subependymal giant cell astrocytomas (Figure 2B). Given the enrichment in subependymal giant cell astrocytomas of significantly altered microRNAs in the low grade gliomas, Significance analysis of microarrays was performed with unsupervised hierarchical clustering of differentially regulated microRNAs compared between subependymal giant cell astrocytomas and brain. This yielded 67 microRNAs with significantly altered expression, with 42 microRNAs upregulated in subependymal giant cell astrocytomas (Figure 3A) and 25 microRNAs downregulated (Figure 3B). It was notable that within the negatively regulated genes there were multiple microRNAs in the neurodevelopmentally regulated 14q32.31 cluster that were significantly downregulated within a single hierarchical cluster (Figure 3B). Looking at the log2(fold change) of every 14q32.31 microRNA that showed sufficient expression for analysis, the majority of these microRNAs were downregulated in each low grade tumor type (Figure 3C), with the exception of miR-494, which was significantly up-regulated in subependymal giant cell astrocytomas and many of the low grade glial and glioneuronal tumors (Figure 3A), and miR-376b, which had a similar upward trend (Figure 3C). To determine whether there were significant differences in expression between the well-circumscribed low grade gliomas evaluated for altered microRNA expression in our Nanostring analysis (subependymal giant cell astrocytoma and pleomorphic astrocytoma), significance analysis of microarrays was performed between these two groups. Interestingly, this yielded only 17 significantly different microRNAs, of which 12 were previously identified as being significantly altered in low grade gliomas as compared to both brain and glioneuronal tumors in our prior analyses (Figure 3D). None of the remaining five microRNAs had a notably large fold change (−1.5<log2[fold change]>1.5) between the two tumors. For further evaluation by RT-PCR, miR-487b along with five other microRNAs (miR-129-2-3p, miR-219-5p, miR-338-3p, miR-487b, miR-885-5p, and miR-323a-3p) that were significantly downregulated in subependymal giant cell astrocytomas and pilocytic astrocytomas as compared to ganglioglioma and dysembryoplastic neuroepithelial tumor, and two microRNAs (miR-21-5p and miR-34a-3p) that were significantly upregulated in subependymal giant cell astrocytomas and pilocytic astrocytomas were selected. Additionally, miR-1246 and miR-4488, which showed global overexpression in the low grade tumors, were evaluated. The log2(fold change) expression of these microRNAs in tumors as compared to normal brain is illustrated in Figure 4A. RT-PCR for these microRNAs was then performed from paraffin derived RNA from subependymal giant cell astrocytoma, pilocytic astrocytoma, dysembryoplastic neuroepithelial tumor, ganglioglioma, and pleomorphic xanthoastrocytoma. Of all the tumors studied, subependymal giant cell astrocytomas demonstrated the highest degree of microRNA repression validated by RT-PCR, including miR-129-2-3p, miR-219-5p, miR-338-3p, miR-487b, miR-885-5p, and miR-323a-3p (Figure 4A). When looking at the differentially overexpressed microRNAs, miR-21 and miR-34a were overexpressed to a greatest extent in subependymal giant cell astrocytoma, followed by pilocytic astrocytoma (Figure 4B). Of interest, miR-4488 and miR-1246 were more highly overexpressed in dysembryoplastic neuroepithelial tumor compared with brain and other... tumors ($p<0.05$), but no repression of miR-219 and miR338, two microRNAs involved in oligodendrocyte differentiation, was identified. mir-487b overexpression affects stem cell markers and colony formation in soft agar Next we selected miR-487b (underexpressed in low grade tumors) and miR-1246 (overexpressed in low grade tumors) for additional functional experiments. miR-1246 is activated by p53, and suppresses the Down syndrome associated protein (DYRK1a). The Targetscan algorithm predicted miR-487 to directly target several proteins involved in stem cell biology including PROM1, Nestin and WNT5A. miR-487b and miR-1246 were similarly expressed in pediatric glioma lines as compared to neural stem cells, although miR-1246 was relatively enriched in tumors versus stem cells (Supplementary Figures 1A and 2A). Next, miR-487b was overexpressed using a lentiviral based miRNA plasmid, while miR-1246 knockdown was attempted with a pLV-hsa-mir-1246 locker in the same pediatric glioma cell lines (data not shown). Effective miR-1246 knockdown was reliably achieved in KNS42 cells, which were subjected to further functional experiments. Infection of lentiviral-based miRNA plasmid miR-487b in the KNS42 cells led to ~6X overexpression of miR-487b compared to control cells (Figure 5A, B). miR-487b overexpression led to a decrease in colony formation in soft agar (30%) ($p<0.05$) (Figure 5C) and decreased expression of the neural stem cell markers, known to be predicted targets of miR-487b, PROM1 and Nestin (but not WNT5A) (Figure 5D). miR-487b overexpression had no significant effect on cell growth, proliferation, sensitivity to temozolomide, migration, or invasion (Supplementary figure 1). Inhibition of miR-1246 with the miR-1246 locker resulted in miR-1246 underexpression (Supplementary figure 2B). There was no downregulation of predicted miR-1246 targets, or effect on cell growth, proliferation, sensitivity to temozolomide, migration, invasion, or colony formation in soft agar (Supplementary figure 2). Discussion Alterations in microRNA levels have emerged as an important mechanism in cancer, including glial tumors $^{19,20,33,34}$. MicroRNA regulation also appears to play an important role in pediatric and low grade glial neoplasms. For example, overexpression of miR-21 and downregulation of miR-124 and miR-129 is common in pilocytic astrocytoma compared with non-neoplastic brain $^{22,23}$. These differences appear to be accentuated in neurofibromatosis type 1-associated pilocytic astrocytomas in particular $^{23}$, and were also present in our current study of a broader spectrum of pathologies. Very little is known about differential microRNA expression in other low grade pediatric and circumscribed gliomas and glioneuronal tumors. In a recent study, a set of microRNAs associated with inflammation (miR-146a, miR-21, and miR-155) were differentially expressed in ganglioglioma and peritumoral cortex $^{28}$. Another study demonstrated increased miR-146a levels in glioneuronal tumors, possibly as a negative feedback loop to an astrocyte-mediated inflammatory response $^{27}$. In our study, the directionality of altered microRNA expression of these low grade gliomas was similar to each other and to microRNAs identified in previously published high grade gliomas studies that were summarized in a recent meta-analysis (Figure 6)\textsuperscript{35} Many of these alterations are consistent in directionality with malignancies from other sites, such as miR-21a-5p, which is upregulated in many tumor types\textsuperscript{23,36}. One notable exception was miR-9, which was downregulated in subependymal giant cell astrocytomas but slightly upregulated in the other low grade tumors, namely in pilocytic astrocytomas. This is one of the most commonly cited upregulated microRNAs in glioblastomas and is often upregulated in other malignant tumor types\textsuperscript{35}. One microRNA that was significantly upregulated in several low grade gliomas and glioneuronal tumors was miR-34a, which is frequently downregulated in other malignant tumors and is thought to act as a tumor suppressor\textsuperscript{37}. In studies of glioblastoma, miR-34a regulation has been inconsistent, with some studies showing down-regulation as compared to brain in the proneural subtype\textsuperscript{38}, but other studies showing upregulation in glioblastoma as compared to anaplastic astrocytoma\textsuperscript{35,39}. In our study, miR-34a was consistently up-regulated in the glial and glioneuronal tumors as shown both in microarray results and in RT-PCR validation studies. Further study is necessary to determine the phenotype conferred by alterations in microRNAs, such as miR-9-5p and miR-34a, that have divergent expression in different glioma types and grades. Regarding microRNA regulation by specific pathologic subtype, it was of interest that subependymal giant cell astrocytomas and rosette forming glioneuronal tumors clustered together, farthest from non-neoplastic brain. These tumors share in common a predominant intraventricular location, and conceivably are less likely to have non-neoplastic brain contamination. However, they also are linked at the biologic level by having frequent alterations in the PI3K/mTOR signaling pathways. Subependymal giant cell astrocytoma is frequently associated with tuberous sclerosis, characterized at the genetic level by germline inactivation of the TSC1 or TSC2 tumor suppressor genes, while rosette forming glioneuronal tumor has frequent mutations in PIK3CA\textsuperscript{40}. Activation of this pathway through TSC1 deletion in mouse and human cell lines has been shown to cause a global inhibition of microRNA biogenesis through the degradation of Drosha\textsuperscript{41}. Conversely, upregulation of the PTEN-inhibitor microRNA miR-21 has been shown to occur as a result of rapamycin inhibition, likely as a mechanism of negative feedback\textsuperscript{42}. This microRNA was frequently upregulated in the low-grade gliomas, including subependymal giant cell astrocytoma, as evaluated by both Nanostring hybridization screening and RT-PCR validation. In our study, we focused on two microRNAs for functional validation, miR-487b and miR-1246, as neither have previously been functionally validated as participating in gliomagenesis, and both have significant alterations in expression in low grade glial and glioneuronal tumors by both Nanostring and RT-PCR assays. While miR487b has been identified as downregulated in gliomas, its functional role in glial neoplasms has not been explored. In the current study miR-487b overexpression led to decreased colony formation in soft agar and decreased levels of the neural stem cell markers nestin and PROM1 in a pediatric glioma cell line. The results of these functional experiments were intriguing, although they were performed on a pediatric high grade glioma cell line (KNS-42), rather than in the pediatric low grade glioma cell lines that we had available (Res186, Res259). This approach was necessary for technical reasons, since KNS-42 cells grow as... neurospheres, therefore being more appropriate for the study of stem cell-like properties. In addition, KNS-42 maintains high levels of miR-487b stem cell targets in culture (e.g. PROM1, Nestin) and miR-1246 knockdown was successful in this cell line in our hands. As more appropriate models of pediatric low grade glioma become available, similar experiments may be performed in the future to more accurately clarify the role of these microRNAs in pediatric low grade glioma at the functional level. miR-487 maps to chromosome 14q32.31, a region that is often deleted in high risk neuroblastoma, and its loss is an indicator of poor prognosis in a manner that is independent of MYC expression. It is part of a parentally imprinted microRNA cluster that contains several other microRNAs that were frequently underexpressed in tumors in this study, including miR-485-3p, miR-410, miR-323a-3p, miR-495, and miR-543. Tested miR-487b targets in this context include components of neurodevelopmental and oncogenic signaling pathways WNT5a, BMI1, MYC, KRAS, and SUZ12. Interestingly, miR-487b may also be regulated by DNA methylation in tumorigenesis, as a response to cigarette smoke, a proposed mechanism for its involvement in lung tumors. The 14q32.31 cluster also appears to be differentially regulated in an epigenetic manner at different stages of stem cell reprogramming. miR-487b specifically appears to be relevant to CNS pathology, being upregulated in the blood of patients with ischemic stroke, and also promotes angiogenesis. Notably, it is downregulated in glioblastomas along with other microRNAs within the 14q32.31 cluster compared to non-neoplastic brain in some studies. As the targets of these genes are enriched in glial-specificity, this cluster may play an important role in glial tumor biology. In contrast to miR-487b, miR-1246 was consistently overexpressed in low grade glioma and glioneuronal tumors in our study by microarray and RT-PCR. miR-1246 maps to chromosome 2q31.1. It is a target of the tumor suppressor p53, but has been found to be upregulated in various cancers. For instance, miR-1246 is upregulated in neuroblastoma cells, and serum exosomes of pancreatic and esophageal cancer patients; it promotes sphere formation and chemoresistance in pancreatic cancer, stemness and invasion in lung cancer, and enhances migration and invasion in hepatocellular carcinoma cell lines. This microRNA is also abundant in the exosomes of neural stem cells. One notable technical difficulty in studying miR-1246, however, is the inclusion of this sequence in the transcript for the small noncoding nuclear RNA RNAU2-1f, which has also been identified as a circulating RNA upregulated in tumorigenesis, that can be alternately spliced to produce miR-1246, and possibly miR-1290. Future sequencing studies may be necessary to determine the extent to which the RNA hybridization assays for miR-1246 are also, or exclusively, recognizing RNAU2-1f. If this is true in this case, RNAU2-1f may be a useful circulating biomarker for glioma growth. Additionally, if miR-1246 does not function independently of RNAU2-1f in glial tumorigenesis, this may explain its lack of a tumorigenic role in cell culture experiments. In summary, differential microRNA expression is a feature of a variety of low grade, primarily pediatric, glioma and glioneuronal tumor types. miR-487b appears to inhibit the expression of stem cell markers and properties in vitro, a finding that should be validated in the future in larger studies. These studies have a potential to increase our basic understanding of glioma biology. Mod Pathol. Author manuscript; available in PMC 2017 April 14. understanding of the genetic and epigenetics mechanisms responsible for gliomagenesis, and lead to the development of rational biomarkers and therapeutic targets. Supplementary Material Refer to Web version on PubMed Central for supplementary material. Acknowledgments This work was supported by the Childhood Brain Tumor Foundation (to F.J.R.), the Pilocytic/Pilomyxoid Astrocytoma Fund including Lauren’s First and Goal (to F.J.R.), Samples quality assessment and microarray analysis were conducted at The Sidney Kimmel Cancer Center Microarray Core Facility at Johns Hopkins University, supported by National Institutes of Health (P30 CA006973) entitled Regional Oncology Research Center. Grant Funding: F.J.R.: Childhood Brain Tumor Foundation, Pilocytic/Pilomyxoid Astrocytoma Fund, including Lauren’s First Goal. MAV: Research to Prevent Blindness W.Y.: The Sidney Kimmel Cancer Center Microarray Core Facility: NIH P30 CA006973 References 1. Bar EE, Lin A, Tihan T, Burger PC, Eberhart CG. Frequent gains at chromosome 7q34 involving BRAF in pilocytic astrocytoma. Journal of neuropathology and experimental neurology. 2008; 67:878–887. [PubMed: 18716556] 2. Forshew T, et al. 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Feng N, et al. miR-487b promotes human umbilical vein endothelial cell proliferation, migration, invasion and tube formation through regulating THBS1. Neurosci Lett. 2015; 591:1–7. [PubMed: 25660232] 50. Laddha SV, et al. Genome-wide analysis reveals downregulation of miR-379/miR-656 cluster in human cancers. Biol Direct. 2013; 8:10. [PubMed: 23618224] 51. Skalsky RL, Cullen BR. Reduced expression of brain-enriched microRNAs in glioblastomas permits targeted regulation of a cell death gene. PLoS One. 2011; 6 52. Liao JM, Zhou X, Zhang Y, Lu H. MiR-1246: a new link of the p53 family with cancer and Down syndrome. Cell Cycle. 2012; 11 53. Zhang Y, Liao JM, Zeng SX, Lu H. p53 downregulates Down syndrome-associated DYRK1A through miR-1246. EMBO Rep. 2011; 12:811–817. [PubMed: 21637297] 54. Zhang Q, et al. p53-induced microRNA-1246 inhibits the cell growth of human hepatocellular carcinoma cells by targeting NFIB. Oncol Rep. 2015; 33:1335–1341. [PubMed: 25591821] 55. Xu LJ, et al. Parallel mRNA and microRNA profiling of HEV71-infected human neuroblastoma cells reveal the up-regulation of miR-1246 in association with DLG3 repression. PLoS One. 2014; 9 56. Madhavan B, et al. Combined evaluation of a panel of protein and miRNA serum-exosome biomarkers for pancreatic cancer diagnosis increases sensitivity and specificity. Int J Cancer. 2015:2616–2627. [PubMed: 25388097] 57. Takeshita N, et al. Serum microRNA expression profile: miR-1246 as a novel diagnostic and prognostic biomarker for oesophageal squamous cell carcinoma. British journal of cancer. 2013; 108:644–652. [PubMed: 23361059] 58. Hasegawa S, et al. MicroRNA-1246 expression associated with CCNG2-mediated chemoresistance and stemness in pancreatic cancer. Br J Cancer. 2014; 111:1572–1580. [PubMed: 25117811] 59. Kim G, et al. Hsa-miR-1246 and hsa-miR-1290 are associated with stemness and invasiveness of non-small cell lung cancer. Lung cancer. 2016; 91:15–22. [PubMed: 26711929] 60. Sun Z, et al. MicroRNA-1246 enhances migration and invasion through CADM1 in hepatocellular carcinoma. BMC cancer. 2014; 14:616. [PubMed: 25159494] 61. Stevanato L, Thanabalasundaram L, Vysokov N, Siniden JD. Investigation of Content, Stoichiometry and Transfer of miRNA from Human Neural Stem Cell Line Derived Exosomes. PLoS One. 2016; 11 62. Mazieres J, et al. Alternative processing of the U2 small nuclear RNA produces a 19-22nt fragment with relevance for the detection of non-small cell lung cancer in human serum. PLoS One. 2013; 8 63. Baraniskin A, et al. Circulating U2 small nuclear RNA fragments as a novel diagnostic biomarker for primary central nervous system lymphoma. Neuro Onc. 2016; 18:361–367. Figure 1. Hierarchical Clustering of MiRNA Expression Levels in Low Grade Gliomas and Glioneuronal Tumors (A) MeV generated heat map of microRNAs with significantly altered expression among the 10 subgroups as evaluated by significance analysis of microarrays. (B) Log2(fold change) of mean normalized expression values for miR129-5p as compared to brain (p<0.05), (C) Immunohistochemical staining for miR-129-5p targets PBX3 and NFIB in normal brain and SEGAs. Figure 2. Differentially Expressed Micrornas in Well-Circumscribed Low Grade Gliomas Compared to Glioneuronal Tumors (A) Heatmap showing a subset of microRNAs that are differentially expressed in well-circumscribed low grade gliomas (subependymal giant cell astrocytomas and pilocytic astrocytomas) as compared to low grade glioneuronal tumors (ganglioglioma and dysembryoplastic neuroepithelial tumor). (B) Mean log2(fold change) from normal brain for the tumor types with n>3 in our data set (subependymal giant cell astrocytoma, pilocytic astrocytoma, pleomorphic xanthoast, ganglioglioma, and dysembryoplastic neuroepithelial tumor) shows similar directionality in expression among all groups. Figure 3. Coordinated repression of cluster 14q32.31 microRNAs in low grade gliomas (A) Heat map showing a hierarchical cluster of microRNAs that are upregulated in subependymal giant cell astrocytoma as compared to normal brain. (B) Heat map showing a hierarchical cluster of microRNAs that are downregulated in subependymal giant cell astrocytoma as compared to normal brain that contains several members of the 14q32.31 cluster of microRNAs (green bar). (C) Mean log2(fold change) from normal brain for the tumor types with n>3 in our data set (subependymal giant cell astrocytoma, pilocytic astrocytoma, pleomorphic xanthoastrocytoma, ganglioglioma, and dysembryoplastic... neuroepithelial tumor) shows similar directionality in expression among all groups for 14q32.31 cluster microRNAs. (D) Heat map showing a hierarchical cluster of microRNAs that have significantly different expression between SEGA and PA. Figure 4. RT-PCR Evaluation of Differentially Expressed MicroRNAs (A) Mean log2(fold change) from normal brain for the tumor types with n>3 in our data set (subependymal giant cell astrocytoma, pilocytic astrocytoma, pleomorphic xanthoastrocytoma, ganglioglioma, and dysembryoplastic neuroepithelial tumor) for miRNAs further evaluated in RT-PCR experiments. (B) RT-PCR results for microRNAs that were upregulated in low grade glial and glioneuronal tumors. (C) RT-PCR results for microRNAs that were downregulated in low grade glial and glioneuronal tumors. p<0.05, p<0.01. Figure 5. mir-487b overexpression in KNS42 cells affects expression of stem cell markers and colony formation in soft agar (A) miRNA expression in virus infected KNS42 cells with mir-control or mir-487b (Red), DAPI for nuclear staining (Blue). (B) mi-487b overexpression in KNS42 cells infected with mir-487b. p<0.01 compared to mir-control cells. (C) Soft agar clonogenic assay. Colony numbers of KNS42 cells infected with mir-control or mir-487b were counted after 21 days culture in 6-well plates. (D) qRT-PCR shows downregulation of Nestin and PROM1 and upregulation of WNT5A after mir-487b overexpression in KNS42 cells. All data were normalized to HPRT1. * p<0.05, ** p<0.01. Figure 6. microRNA expression in lower grade gliomas compared to glioblastoma Mean log2(fold change) from normal brain for the tumor types with n≥3 in our data set (subependymal giant cell astrocytoma, pilocytic astrocytoma, pleomorphic xanthoastrocytoma, ganglioglioma, and dysembryoplastic neuroepithelial tumor) shows similar directionality in expression to previous studies of glioblastoma (GBM) summarized in a recent meta-analysis. \| microRNA \| SEGA \| RFGT \| PA \| PXA \| DNET \| GG \| GBM \| Log2(FC) \| \|----------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|----------\| \| hsa-miR-219-5p \| -6.4 \| -4.7 \| -3.5 \| -2.6 \| -1.0 \| -4.0 \| ↓ \| < -3.0 \| \| hsa-miR-124-3p \| -6.0 \| -7.3 \| -3.4 \| -1.8 \| -1.7 \| -2.3 \| ↓ \| 1.5 to -3.0 \| \| hsa-miR-137 \| -2.0 \| -6.4 \| -2.6 \| -2.8 \| -2.1 \| -1.9 \| ↓ \| 0 +/- 1.5 \| \| hsa-miR-128 \| -4.3 \| -2.9 \| -3.1 \| -2.3 \| -1.6 \| -2.4 \| ↓ \| 1.5 to 3.0 \| \| hsa-miR-485-3p \| -2.7 \| -3.2 \| -2.3 \| -2.9 \| -2.4 \| -1.4 \| ↓ \| > 3.0 \| \| hsa-miR-487b \| -4.3 \| -2.8 \| -2.9 \| -1.7 \| -2.0 \| -1.2 \| ↓ \| \| \| hsa-miR-221-3p \| -1.2 \| -4.0 \| -2.1 \| -1.7 \| -2.4 \| -1.7 \| ↓ \| \| \| hsa-miR-433 \| -2.9 \| -2.9 \| -2.2 \| -2.3 \| -1.8 \| -1.1 \| ↓ \| \| \| hsa-miR-7-5p \| -4.4 \| -4.8 \| -4.2 \| -1.7 \| -1.0 \| -0.9 \| ↓ \| \| \| hsa-miR-132-3p \| -3.5 \| -4.0 \| -2.7 \| -2.4 \| -1.5 \| -0.7 \| ↓ \| \| \| hsa-miR-885-5p \| -4.1 \| -1.9 \| -2.7 \| -1.9 \| -1.7 \| -1.8 \| ↓ \| \| \| hsa-miR-338-3p \| -5.3 \| -1.6 \| -3.2 \| -1.0 \| 0.3 \| -2.7 \| ↓ \| \| \| hsa-miR-129-5p \| -2.6 \| -2.6 \| -2.6 \| -2.0 \| -1.9 \| -0.6 \| ↓ \| \| \| hsa-miR-410 \| -2.3 \| -2.2 \| -2.0 \| -1.8 \| -1.9 \| -0.8 \| ↓ \| \| \| hsa-miR-107 \| -1.9 \| -1.4 \| -1.6 \| -2.0 \| -1.4 \| -1.4 \| ↓ \| \| \| hsa-miR-219-2-3p \| -5.4 \| -2.1 \| -1.6 \| -1.2 \| 0.4 \| -3.2 \| ↓ \| \| \| hsa-miR-95 \| -3.2 \| -1.8 \| -2.5 \| -1.7 \| -1.5 \| -1.5 \| ↓ \| \| \| hsa-miR-149-5p \| -1.8 \| -2.2 \| -2.1 \| -1.7 \| -1.7 \| -1.6 \| ↓ \| \| \| hsa-miR-323a-3p \| -4.0 \| -1.4 \| -1.9 \| -1.2 \| -1.1 \| -0.7 \| ↓ \| \| \| hsa-miR-495 \| -3.2 \| -1.0 \| -1.7 \| -0.9 \| -1.2 \| -0.8 \| ↓ \| \| \| hsa-miR-543 \| -2.7 \| -0.5 \| -1.5 \| -0.5 \| -0.8 \| -0.4 \| ↓ \| \| \| hsa-miR-181a-5p \| -1.1 \| 0.5 \| -0.4 \| 0.1 \| 0.8 \| -0.4 \| ↓ \| \| \| hsa-miR-9-5p \| -1.0 \| 1.9 \| 0.8 \| 0.7 \| 0.9 \| 0.6 \| ↑ \| \| \| hsa-miR-195-5p \| 1.3 \| 2.0 \| 1.0 \| 0.0 \| 0.8 \| 0.9 \| ↑ \| \| \| hsa-miR-135b-5p \| 0.6 \| -1.4 \| 2.0 \| 4.2 \| -0.8 \| 2.6 \| ↑ \| \| \| hsa-miR-302d-3p \| 2.7 \| 1.2 \| 2.2 \| 0.9 \| 0.5 \| 1.2 \| ↑ \| \| \| hsa-miR-223-3p \| 2.5 \| 0.9 \| 1.6 \| 1.8 \| 0.6 \| 1.8 \| ↑ \| \| \| hsa-miR-28-5p \| 2.1 \| 2.1 \| 1.8 \| 2.0 \| 1.3 \| 1.3 \| ↑ \| \| \| hsa-miR-23a-3p \| 2.9 \| 1.6 \| 1.8 \| 2.4 \| 1.1 \| 1.7 \| ↑ \| \| \| hsa-miR-142-3p \| 3.0 \| 1.3 \| 1.9 \| 2.6 \| 1.6 \| 2.1 \| ↑ \| \| \| hsa-miR-450a-5p \| 1.3 \| 2.6 \| 2.4 \| 2.0 \| 2.0 \| 1.6 \| ↑ \| \| \| hsa-miR-424-5p \| 2.1 \| 2.4 \| 2.5 \| 1.9 \| 1.7 \| 1.9 \| ↑ \| \| \| hsa-miR-21-5p \| 4.0 \| 1.2 \| 3.8 \| 4.1 \| 1.7 \| 3.4 \| ↑ \| \|	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2493, 1 ], [ 2493, 5751, 2 ], [ 5751, 9291, 3 ], [ 9291, 12285, 4 ], [ 12285, 14812, 5 ], [ 14812, 18138, 6 ], [ 18138, 21559, 7 ], [ 21559, 24693, 8 ], [ 24693, 28685, 9 ], [ 28685, 32373, 10 ], [ 32373, 35744, 11 ], [ 35744, 39599, 12 ], [ 39599, 43631, 13 ], [ 43631, 44004, 14 ], [ 44004, 44468, 15 ], [ 44468, 45167, 16 ], [ 45167, 45848, 17 ], [ 45848, 46086, 18 ], [ 46086, 46667, 19 ], [ 46667, 47353, 20 ], [ 47353, 50826, 21 ] ] }
bf2fd28a04867cd116f1d33560cbde759b836c3b	{ "olmocr-version": "0.1.59", "pdf-total-pages": 3, "total-fallback-pages": 0, "total-input-tokens": 9971, "total-output-tokens": 4142, "fieldofstudy": [ "Medicine" ] }	Robert M. Zimbroff, MD Department of Internal Medicine, Cleveland Clinic, Cleveland, OH Gina Ayers, PharmD, BCPS, BCGP Center for Geriatric Medicine and Department of Pharmacy, Cleveland Clinic, Cleveland, OH Kenneth Koncilja, MD Center for Geriatric Medicine, Cleveland Clinic, Cleveland, OH Q: Should my older adult patients take aspirin for primary prevention of cardiovascular disease? A: No. Recent evidence shows that the harms of aspirin use for the primary prevention of cardiovascular disease usually outweigh the benefits for patients age 70 and older. An updated draft of the United States Preventive Services Task Force (USPSTF) recommendations for aspirin use was released for public comment on October 12, 2021.1,2 These guidelines have a grade C recommendation for initiating low-dose aspirin for primary prevention of cardiovascular disease in patients ages 40 to 59 with a 10% or greater 10-year risk of cardiovascular disease. (Grade C: Recommends use based on professional judgment and patient preferences. There is at least moderate certainty that the net benefit is small.) These guidelines offer a grade D recommendation for initiating low-dose aspirin for primary prevention of cardiovascular disease in adults age 60 and older. (Grade D: Recommends against. There is at least moderate certainty of no net benefit or that harms outweigh benefit). This guidance is a change from their 2016 recommendation, which was equivocal on adults ages 60 to 69 and avoided a recommendation for adults age 70 and older, citing insufficient evidence.3,4 Trials reviewed in this article were included in these updated draft recommendations, which are still open for comment at the time of this writing. In 2018, results from 3 large double-blind, randomized, placebo-controlled trials offered insight into how to approach aspirin use for primary prevention in older adults. These trials—Aspirin in Reducing Events in the Elderly (ASPREE),5,6 Aspirin to Reduce Risk of Initial Vascular Events (ARRIVE),7 and Aspirin for Primary Prevention in Persons With Diabetes Mellitus (ASCEND)8—provide substantial data to fill knowledge gaps on how to consider prescribing or de-prescribing aspirin for older patients. WHAT DID THE TRIALS FIND? The ASPREE trial This trial enrolled 19,114 community-dwelling older adult patients at least 70 years old, or at least 65 years old for Black and Hispanic patients, without evidence of cardiovascular disease (overall median age was 74).5,6 During a median follow-up of 4.7 years, researchers found that 100 mg/day of aspirin provided no benefit in preventing nonfatal cardiovascular events or death, or in increasing disability-free survival. Aspirin use increased the risk of clinically significant, nonfatal major hemorrhage, defined as a composite measure of intracranial and upper or lower gastrointestinal bleeding that required transfusion, hospitalization, or surgical intervention, or that prolonged hospitalization. Unexpectedly, the aspirin cohort had higher all-cause mortality, attributed to increased cancer-related mortality (including a significant increase in colorectal cancer-related death in aspirin users). Mortality from major bleeding events, including hemorrhage or hemorrhagic stroke, was no different between groups.5,6 The ARRIVE trial This trial enrolled 12,546 patients age 55 and older for men and age 60 and older for women with moderate cardiovascular disease risk assessed by the presence of risk factors including current tobacco use, low levels of high-density lipoprotein cholesterol, elevated systolic blood pressure, and platelet aggregation 1-MINUTE CONSULT Q: Should my older adult patients take aspirin for primary prevention of cardiovascular disease? A: Gina Ayers, PharmD, BCPS, BCGP Center for Geriatric Medicine and Department of Pharmacy, Cleveland Clinic, Cleveland, OH doi:10.3949/ccjm.88a.21024 Kenneth Koncilja, MD Center for Geriatric Medicine, Cleveland Clinic, Cleveland, OH Robert M. Zimbroff, MD Department of Internal Medicine, Cleveland Clinic, Cleveland, OH Gina Ayers, PharmD, BCPS, BCGP Center for Geriatric Medicine and Department of Pharmacy, Cleveland Clinic, Cleveland, OH Kenneth Koncilja, MD Center for Geriatric Medicine, Cleveland Clinic, Cleveland, OH Q: Should my older adult patients take aspirin for primary prevention of cardiovascular disease? A: No. Recent evidence shows that the harms of aspirin use for the primary prevention of cardiovascular disease usually outweigh the benefits for patients age 70 and older. An updated draft of the United States Preventive Services Task Force (USPSTF) recommendations for aspirin use was released for public comment on October 12, 2021.1,2 These guidelines have a grade C recommendation for initiating low-dose aspirin for primary prevention of cardiovascular disease in patients ages 40 to 59 with a 10% or greater 10-year risk of cardiovascular disease. (Grade C: Recommends use based on professional judgment and patient preferences. There is at least moderate certainty that the net benefit is small.) These guidelines offer a grade D recommendation for initiating low-dose aspirin for primary prevention of cardiovascular disease in adults age 60 and older. (Grade D: Recommends against. There is at least moderate certainty of no net benefit or that harms outweigh benefit). This guidance is a change from their 2016 recommendation, which was equivocal on adults ages 60 to 69 and avoided a recommendation for adults age 70 and older, citing insufficient evidence.3,4 Trials reviewed in this article were included in these updated draft recommendations, which are still open for comment at the time of this writing. In 2018, results from 3 large double-blind, randomized, placebo-controlled trials offered insight into how to approach aspirin use for primary prevention in older adults. These trials—Aspirin in Reducing Events in the Elderly (ASPREE),5,6 Aspirin to Reduce Risk of Initial Vascular Events (ARRIVE),7 and Aspirin for Primary Prevention in Persons With Diabetes Mellitus (ASCEND)8—provide substantial data to fill knowledge gaps on how to consider prescribing or de-prescribing aspirin for older patients. WHAT DID THE TRIALS FIND? The ASPREE trial This trial enrolled 19,114 community-dwelling older adult patients at least 70 years old, or at least 65 years old for Black and Hispanic patients, without evidence of cardiovascular disease (overall median age was 74).5,6 During a median follow-up of 4.7 years, researchers found that 100 mg/day of aspirin provided no benefit in preventing nonfatal cardiovascular events or death, or in increasing disability-free survival. Aspirin use increased the risk of clinically significant, nonfatal major hemorrhage, defined as a composite measure of intracranial and upper or lower gastrointestinal bleeding that required transfusion, hospitalization, or surgical intervention, or that prolonged hospitalization. Unexpectedly, the aspirin cohort had higher all-cause mortality, attributed to increased cancer-related mortality (including a significant increase in colorectal cancer-related death in aspirin users). Mortality from major bleeding events, including hemorrhage or hemorrhagic stroke, was no different between groups.5,6 The ARRIVE trial This trial enrolled 12,546 patients age 55 and older for men and age 60 and older for women with moderate cardiovascular disease risk assessed by the presence of risk factors including current tobacco use, low levels of high-density lipoprotein cholesterol, elevated systolic blood pressure, and platelet aggregation. pressure (> 140 mm Hg), prescriptions for antihypertensive medications, or positive family history of cardiovascular disease. The trial was focused on primary prevention, so investigators excluded participants with prior cardiovascular events or interventions (e.g., stenting, angioplasty, bypass surgery). Patients with diabetes were also excluded. The intent-to-treat analysis showed no significant benefit for aspirin use of 100 mg/day during the median 5-year follow-up. A subgroup analysis showed no benefit for patients age 65 and older. As in earlier studies, the aspirin-receiving cohort had an increased risk of gastrointestinal bleeding. The ASCEND trial This trial enrolled 15,480 participants with diabetes but without known cardiovascular disease; nearly one-quarter of participants enrolled were at least 70 years of age. Although 100 mg/day of aspirin provided an overall benefit in reducing first vascular events, a subgroup analysis revealed no benefit for patients age 70 and older. Aspirin use was associated with a higher risk of major bleeding events, defined as bleeding requiring transfusion, hospitalization, surgical intervention, or that prolonged hospitalization, required intensive care unit admittance, or caused death. This risk was significant for patients age 60 and older but was not significant for patients under age 60. ■ HOW DID MEDICAL SOCIETIES REACT? In light of these findings, the American College of Cardiology (ACC) updated its practice guidelines, published in September 2019, to state that low-dose aspirin should not be administered on a routine basis for the primary prevention of atherosclerotic cardiovascular disease in adults over age 70. The American Diabetes Association (ADA), in its practice guidelines published in January 2021, similarly recommended that for patients over age 70 (with or without diabetes), aspirin use appears to have greater risk than benefit and thus is not recommended in these patients. Complementary interventions aimed at reducing the risk of cardiovascular events—statins for hyperlipidemia, improved antihypertensive medications, and aggressive anti-smoking campaigns—may further reduce the utility of aspirin for primary prevention. Nevertheless, data from the National Health and Nutrition Examination Survey (2011-2018) showed that aspirin use for primary prevention significantly increased as patients age, from 24% in those ages 50 to 54 to 45.3% in those age 75 and older. ■ WHAT ABOUT ASPIRIN USE FOR COLORECTAL CANCER? In addition, there is increasingly clear evidence supporting discontinuation of aspirin use in older adults for colorectal cancer prevention. The USPSTF had previously made a grade B recommendation for low-dose aspirin in adults ages 50 to 59 in part because of evidence supporting reduced colorectal cancer incidence after 5 to 10 years of use. A more recent pooled analysis of data on 94,540 participants age 70 and older from both the longitudinal Nurses’ Health Study and the Health Professionals Follow-up Study found that aspirin use was associated with a lower incidence of colorectal cancer after age 70 for patients who initiated aspirin before age 70 with at least 5 years of use. Initiating aspirin after age 70 was not associated with reduced colorectal cancer incidence. The ASPREE investigators reported increased cancer-associated mortality risk in the aspirin-use cohort (including higher colorectal cancer mortality); however, they noted that this result was unexpected in the context of other well-designed aspirin trials and should be interpreted cautiously. ■ THE BOTTOM LINE The proposed updates to its 2016 guidance for aspirin use for primary prevention in adults age 60 and older put the USPSTF recommendations in line with those of the ACC and ADA, which both previously incorporated evidence from the trials discussed above into their recommendations against aspirin use for primary prevention in older adults. Our clinical recommendation is in line with the USPSTF’s proposed update: the risks outweigh the benefits for aspirin in older adults. Providers, in conjunction with patients, should de-prescribe aspirin as able. ■ DISCLOSURES The authors report no relevant financial relationships which, in the context of their contributions, could be perceived as a potential conflict of interest. REFERENCES 1. United States Preventive Services Task Force. Draft recommendation statement: aspirin use to prevent cardiovascular disease. Updated October 12, 2021. https://www.uspreventiveservicestaskforce.org/uspstf/draft-recommendation/aspirin-use-to-prevent-cardiovascular-disease-preventive-medication. Accessed October 18, 2021. 2. Guirguis-Blake JM, Evans CV, Perdue LA, Bean SI, Senger CA. Evidence synthesis number 211. Aspirin use to prevent cardiovascular disease and colorectal cancer: an evidence update for the US Preventive Services Task Force. Kaiser Permanente Evidence-based Practice Center, Kaiser Permanente Center for Health Research. AHRQ Publication No. 21-05283-EF-1. September 2021. https://www.uspreventiveservicestaskforce.org/uspstf/document/draft-evidence-review/aspirin-use-to-prevent-cardiovascular-disease-preventive-medication. Accessed October 18, 2021. 3. Bibbins-Domingo K; US Preventive Services Task Force. Aspirin Use for the Primary Prevention of Cardiovascular Disease and Colorectal Cancer: US Preventive Services Task Force Recommendation Statement. Ann Intern Med 2016; 164(12):836–845. doi:10.7326/M16-0577 4. Dehmer SP, Maciosek MV, Flottemesch TJ, LaFrance AB, Whitlock EP. Aspirin for the primary prevention of cardiovascular disease and colorectal cancer: a decision analysis for the US Preventive Services Task Force. Ann Intern Med 2016; 164(12):836–845. doi:10.7326/M15-2129 5. McNeil JJ, Woods RL, Nelson MR, et al. Effect of aspirin on disability-free survival in the healthy elderly. N Engl J Med 2018; 379(16):1499–1508. doi:10.1056/NEJMoa1800722 6. McNeil JJ, Wolfe R, Woods RL, et al. Effect of aspirin on cardiovascular events and bleeding in the healthy elderly. N Engl J Med 2018; 379(16):1509–1518. doi:10.1056/NEJMoa1805819 7. Gaziano JM, Brotzen C, Coppolecchia R, et al. Use of aspirin to reduce risk of initial vascular events in patients at moderate risk of cardiovascular disease (ARRIVE): a randomised, double-blind, placebo-controlled trial. Lancet 2018; 392(10152):1036–1046. doi:10.1016/S0140-6736(18)31924-X 8. ASCEND Study Collaborative Group, Bowman L, Mafham M, Wallendszus K, et al. Effects of aspirin for primary prevention in persons with diabetes mellitus. N Engl J Med 2018; 379(16):1529–1539. doi:10.1056/NEJMoa1804988 9. Whitlock EP, Burda BU, Williams SB, Guirguis-Blake JM, Evans CV. Bleeding risks with aspirin use for primary prevention in adults: a systematic review for the US Preventive Services Task Force. Ann Intern Med 2016; 164(12):826–835. doi:10.7326/M15-2112 10. Arnett DK, Blumenthal RS, Albert MA, et al. 2019 ACC/AHA guideline on the primary prevention of cardiovascular disease: executive summary: a report of the American College of Cardiology/American Heart Association Task Force on Clinical Practice Guidelines. J Am Coll Cardiol 2019; 74(10):1376–1414. doi:10.1016/j.jacc.2019.03.009 11. American Diabetes Association. 10. Cardiovascular disease and risk management: standards of medical care in diabetes-2021. Diabetes Care 2021; 44(suppl 1):S125–S150. doi:10.2337/dc21-S010 12. Rhee TG, Kumar M, Ross JS, Coll PP. Age-related trajectories of cardiovascular risk and use of aspirin and statin among US adults aged 50 or older, 2011-2018. J Am Geriatr Soc 2021; 69(5):1272–1282. doi:10.1111/jgs.17038 13. Guo CG, Ma W, Drew DA, et al. Aspirin use and risk of colorectal cancer among older adults. JAMA Oncol 2021; 7(3):428–435. doi:10.1001/jamaoncol.2020.7338 14. McNeil JJ, Nelson MR, Woods RL, et al; ASPREE Investigator Group. Effect of aspirin on all-cause mortality in the healthy elderly. N Engl J Med 2018; 379(16):1519–1528. doi:10.1056/NEJMoa1803955 Address: Robert M. Zimbroff, Department of Internal Medicine, G10, Cleveland Clinic, 9500 Euclid Avenue, Cleveland, OH 44195; [email protected]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 7646, 1 ], [ 7646, 11985, 2 ], [ 11985, 15808, 3 ] ] }
17de0a96ab3972d02661810252acf7e8df549931	{ "olmocr-version": "0.1.59", "pdf-total-pages": 12, "total-fallback-pages": 0, "total-input-tokens": 40218, "total-output-tokens": 16451, "fieldofstudy": [ "Biology", "Chemistry" ] }	Research Article The Application of a Three-Step Serum Proteome Analysis for the Discovery and Identification of Novel Biomarkers of Hepatocellular Carcinoma Asako Kimura,1 Kazuyuki Sogawa,2 Mamoru Satoh,1 Yoshio Kodera,2,3 Osamu Yokosuka,4 Takeshi Tomonaga,1,5 and Fumio Nomura1,2 1 Department of Molecular Diagnosis, Graduate School of Medicine, Chiba University, Chiba 260-0856, Japan 2 Clinical Proteomics Research Center, Chiba University Hospital, Chiba, Japan 3 Laboratory of Biomolecular Dynamics, Department of Physics, Kitasato University School of Science, Kanagawa, Japan 4 Department of Medicine and Clinical Oncology, Graduate School of Medicine, Chiba University, Chiba 260-0856, Japan 5 Laboratory of Proteome Research, National Institute of Biomedical Innovation, Osaka, Japan Correspondence should be addressed to Fumio Nomura, [email protected] Received 7 February 2012; Accepted 5 June 2012 Academic Editor: Dayan B. Goodenowe Copyright © 2012 Asako Kimura et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The representative tumor markers for HCC, AFP, and PIVKA-II are not satisfactory in terms of sensitivity and specificity in the early diagnosis of HCC. In search for novel markers for HCC, three-step proteome analyses were carried out in serum samples obtained from 12 patients with HCC and 10 with LC. As a first step, serum samples were subjected to antibody-based immunoaffinity column system that simultaneously removes twelve of abundant serum proteins. The concentrated flow-through was then fractionated using reversed-phase HPLC. Proteins obtained in each fraction were separated by SDS-PAGE. Serum samples obtained from patient with HCC and with LC were analyzed in parallel and their protein expression patterns were compared. A total of 83 protein bands were found to be upregulated in HCC serum. All the protein bands, the intensity of which was different between HCC and LC groups, were identified. Among them, clusterin was most significantly overexpressed ($P = 0.023$). The overexpression of serum clusterin was confirmed by ELISA using another validation set of HCC samples. Furthermore, serum clusterin was elevated in 40% of HCC cases in which both AFP and PIVKA-II were within their cut-off values. These results suggested that clusterin is a potential novel serum marker for HCC. 1. Introduction Hepatocellular carcinoma (HCC) is one of the most common cancers in the world and is a leading cause of death in many countries. Chronic infection by hepatitis B virus (HBV) or hepatitis C virus (HCV) and cirrhosis are major risk factors for HCC development [1, 2]. At present, HCC surveillance with tumor markers and imaging studies such as ultrasonography (US), computed tomography (CT), and magnetic resonance imaging (MRI) have been recommended for patients with cirrhosis [3, 4]. These imaging studies are expensive and the ultrasound is highly dependent on the ability of the operator. Therefore, more sensitive and specific serum biomarkers for early detection of HCC are desirable. Serum tumor markers for detecting HCC could be divided into 4 categories: oncofetal and glycoprotein antigens, enzymes and isoenzymes, genes, and cytokines. Alpha-fetoprotein (AFP) and protein induced by vitamin-K absence or antagonist-II (PIVKA-II) also called des-gamma-carboxyprothrombin (DCP) are representative tumor markers for the diagnosis of HCC. The elevated level of AFP is observed in only 50–70% of patients with HCC and also frequently in patients with cirrhosis or exacerbations of chronic hepatitis [5], and its sensitivity is low in patients with earlier/small tumors [6–8]. Measurement of lectin lens culinaris agglutinin (LCA) bound fraction of AFP (AFP-L3) can improve the specificity of AFP. Elevated DCP activity was only present in 28–47.6%. of HCCs of less than 3 cm in size [9–11]. Therefore, there has been growing interest and need to develop novel HCC serum biomarkers with greater sensitivity and specificity. Recent studies indicate that some other tumor markers, such as glypican 3 [12–17], gamma-glutamyl transferase II [18], alpha-1-fucosidase [19, 20], vascular endothelial growth factor [21–23], and transforming growth factor-beta 1 [24, 25] could serve as a complementary marker for AFP. Furthermore, the circulating genetic markers such as AFP-mRNA [26, 27] and human telomerase reverse transcriptase mRNA [28, 29] have been shown to be diagnostic and prognostic indicators of HCC. Proteomics is the systematic study of proteomes, which describes the complete set or proteins found in a given cell type as well as of body fluids such as serum and urine. Recent advances in sophisticated technologies in proteomics should provide promising ways to discover novel markers in various fields of clinical medicine. Increasing number of recent reports provide evidence that proteomic approach is promising tools to discover and identify novel biomarker for HCC. In particular, surface-enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI-TOF MS) is a representative example of a proteomics technique for the high-throughput fingerprinting of serum proteins and peptides [30]. We used the SELDI technology to generate comparative protein profiles of consecutive serum samples obtained during abstinance from alcoholic patients and found some novel biomarker for excessive alcohol consumption [31, 32]. Using this technique, several protein peaks leading to differentiation of patients with HCC from patients with cirrhosis alone have been discovered [33, 34]. In these studies, crude serum samples were directly analyzed without particular preanalytical preparations. The technical challenge in the analysis of serum proteome is that serum proteins are present at unequal concentrations. Indeed, 22 of the most abundant proteins account for >99% of total serum proteins [35], which hampers the detection of thousands of other low abundance proteins and peptides. To detect the disease-associated proteins present in low abundance using currently available methods, the most abundant proteins have to be removed first by technique such as immunodepletion. We recently developed a three-step serum proteome analysis involving removal of 12 abundant proteins and subsequent reversed-phase high-performance liquid chromatography fractionation and one-dimensional electrophoresis and identified three proteins including YKL-40 as a promising biomarker of sepsis [36]. More recently, using this method, we identified promising biomarkers for alcohol abuse [37], breast cancer [38], and pancreatic cancer [39]. In this study, we applied this three-step proteome analysis to find novel biomarkers of HCC. 2. Material and Methods 2.1. Patients and Serum Samples. As an initial set of samples, blood samples of 12 HCV-related HCC patients and 10 HCV-related LC patients obtained at the Department of Medicine and Clinical Oncology, Chiba University Hospital, were used for comprehensive proteome analysis. All patients were positive for hepatitis C antibodies on the day of sampling and were diagnosed pathologically or clinically. Diagnostic values of marker candidates identified in the initial set of samples were further validated using another set of samples. For this purpose, serum sample sets of 64 HCV-related HCC and 60 HCV-related LC patients were obtained from Chiba University Hospital and 60 healthy individuals for normal control from Kashiwado Clinic in Port-Square of Kashiwado Memorial Foundation, Chiba. These healthy individuals were defined in this study as subjects without medication on a regular basis, obesity, heavy drinking, abnormal liver test results, and hepatitis virus carriage. Written informed consent was obtained from all patients. Serum samples were obtained and processed under the standardized conditions as we reported elsewhere [40] and were stored as aliquots at −80°C until analysis. The clinical characteristics of all the patients are shown in Tables 1 and 2. 2.2. Immunodeficiency Depletion of High-Abundant Proteins from Human Serum. The outline of our experimental procedures is summarized in Figure 1. For removal of the twelve most abundant proteins: albumin, IgG, transferrin, fibrinogen, IgA, alpha2-macroglobulin, IgM, alpha1-antitrypsin, haptoglobin, alpha1-acidglycoprotein, apolipoprotein A-I, and apolipoprotein A-II, Proteome Lab IgY-12HC LC10 column (Beckman coulter Inc., Fullerton, CA, USA) was used. According to the manufacturer’s instructions, 100 μL of each serum was diluted 5-fold with buffer A (dilution buffer) and injected onto the column in 100% buffer A at a flow rate of 0.5 mL/min for 25.0 min and 2.0 mL/min for 5.0 min on a Shimadzu LC10A VP system (Shimadzu Co., Kyoto, Japan). After collection of the flow-through fraction containing unbound proteins, the column was washed and the bound proteins were eluted with 100% buffer B (stripping buffer) at a flow rate of 2.0 mL/min for 18.0 min. The chromatograms were monitored at 280 nm and 8 fractions (flow-through) were collected at 0.5 min intervals from 12.1 to 20.0 min. The fractions were collected into 1.5 mL microcentrifuge tubes. 2.3. Concentrating of Fractions by Centrifugal Ultrafiltration. The flow-through fractions (total 4.0 mL) were applied to Vivasin 2 spin concentrators (MWCO 10 KD, Vivascience, Hannover, Germany) and concentrated to a volume of 80 μL according to the manufacturer’s instructions. The concentrated pool was stored at −80°C until use. 2.4. HPLC Sample Preparation, Separation, and Fraction Collection. HPLC separations were performed on an automated SHISEIDO NANOSPACE SI-2 system (Shiseido Fine Chemicals, Tokyo, Japan). Injection was performed by an autosampler with a completely filled 100 μL injection loop. 75μL of concentrated flow-through samples were directly loaded onto the Intrada WP-RP column (Imtakt, Kyoto, Table 1: Clinical characteristics of the 12 HCC (a) and 10 LC (b) patients. (a) \| Case number \| Sex \| Age \| Stage \| Child-Pugh \| Tumor size (mm) \| Differentiation \| AFP (ng/mL) \| PIVKA-II (mAU/mL) \| \|-------------\|-----\|-----\|-------\|------------\|----------------\|----------------\|-------------\|-------------------\| \| H1 \| M \| 71 \| III \| A \| Multiple, max 30 \| Poorly \| 70.6 \| 18 \| \| H2 \| M \| 73 \| IV \| B \| Multiple, max 50 \| Moderately \| 549.6 \| 44 \| \| H3 \| F \| 69 \| III \| A \| 38 \| Moderately–well\| 11.9 \| 59 \| \| H4 \| M \| 73 \| III \| B \| 32–30 \| Moderately \| 208.1 \| 20 \| \| H5 \| M \| 69 \| III \| B \| 29–25 \| Moderately–well\| 38.3 \| 12 \| \| H6 \| F \| 77 \| III \| A \| Multiple, max 30\| Moderately–well\| 47.3 \| 10 \| \| H7 \| M \| 67 \| III \| A \| 30–10 \| Moderately \| 14.9 \| 35 \| \| H8 \| F \| 71 \| III \| B \| 35–20 \| Well \| 1031.7 \| 466 \| \| H9 \| M \| 58 \| IV \| B \| 20 \| Moderately \| 25.1 \| 75 \| \| H10 \| F \| 71 \| III \| B \| 30 \| Poorly–moderately \| 14640 <10 \| \| H11 \| M \| 81 \| III \| A \| 25 \| Moderately \| 62.3 \| 6854 \| \| H12 \| M \| 70 \| III \| A \| 60 \| — \| 1390 \| 5350 \| (b) \| Case number \| Sex \| Age \| Child-Pugh \| AFP (ng/mL) \| PIVKA-II (mAU/mL) \| \|-------------\|-----\|-----\|------------\|-------------\|-------------------\| \| L1 \| M \| 45 \| B \| 12 \| — \| \| L2 \| F \| 54 \| A \| 36.4 \| <10 \| \| L3 \| M \| 59 \| A \| 24.3 \| 31 \| \| L4 \| M \| 59 \| B \| 12.8 \| 66 \| \| L5 \| F \| 62 \| A \| 4.5 \| — \| \| L6 \| M \| 43 \| A \| 8.5 \| — \| \| L7 \| M \| 48 \| B \| 11.3 \| — \| \| L8 \| M \| 60 \| A \| 37.7 \| — \| \| L9 \| F \| 68 \| A \| 15.3 \| — \| \| L10 \| M \| 45 \| B \| 6 \| — \| Table 2: Clinical characteristics of 64 patients with HCC, 60 with LC and 60 normal control subjects. \| \| HCC \| LC \| Normal control \| \|------------------------\|-----\|----\|----------------\| \| n = 64 \| \| \| n = 60 \| \| Age, mean ± SD \| 66.1 ± 9.9 \| 56.8 ± 12.3 \| 54.5 ± 7.0 \| \| Male/female \| 7.0 \| 6.5 \| 6.5 \| \| AFP level (ng/mL), mean ± SD \| 1926.2 ± 11904.7 \| 14.7 ± 24.2 \| 3.5 ± 1.6 \| \| PIVKA-II level (mAU/mL), mean ± SD \| 11757.2 ± 50071.5 \| 18.1 ± 12.5 \| 19.71 ± 5.4 \| Japan). The RP separations for each flow-through were performed under a set of conditions using a multisegment elution gradient, with eluent A (0.1% TFA in water, v/v) and eluent B (0.08% TFA in 90% acetonitrile, v/v). The gradient conditions consisted of three steps with increasing concentrations of the eluent B: 5% B 5 min, 5–95% B 23 min, 95% B 11 min, and 5% B 21 min for reequilibration of the column, at a flow rate of 0.40 mL/min for a total runtime of 60 min. The chromatograms were monitored at 218 nm and 40 fractions were collected at 0.5 min intervals from 19.1 to 39.1 min. Each fraction was dried in a centrifugal vacuum concentrator and stored at −80°C for subsequent SDS-PAGE analysis. 2.5. Electrophoretic Analysis. Dried fraction samples from HPLC separations were dissolved in 15 μL of sample preparation buffer, vortexed, and then loaded onto the two Perfect NT Gels (10–20% acrylamide, 20 wells, 140 mm × 140 mm × 1 mm; DRC. Co., Ltd.). SDS-PAGE analysis was carried out by an established method [41]. Following electrophoresis, proteins were visualized by silver staining using 2D silver stain II “DAIICHI” (Daiichi Pure Chemicals Co., Ltd., Osaka, Japan). 2.6. In-Gel Digestion. For protein identification, samples were prepared again as described above. To obtain high sensitivity, the same process was repeated three times per sample; finally dried fraction sample of triple amount were obtained. 45 μL of combined dried fraction samples were loaded on to SDS-PAGE gel as described above after these samples were individually dissolved with 15 μL sample buffer. After then, protein spots in Coomassie brilliant blue (CBB) stained SDS-PAGE gels were individually excised in squares of about 1 to 2 mm per side destained in 50% v/v acetonitrile/50 mM NH₄HCO₃ and then washed with Human serum (100 µL) Immunodepletion of 12 high-abundant proteins Reversed-phase HPLC SDS-PAGE In-gel digestion LC-MS/MS Western blotting Figure 1: Schematic diagram of the experimental protocol. deionized water. The gel pieces were dehydrated in 100% acetonitrile for about 15 min and then dried in a SpeedVac evaporator (Wakenyaku, Kyoto, Japan) for 60 min. The pieces were rehydrated in 10–20 µL of 25 mM Tris–Cl (pH 9.0) containing 25 ng/µL trypsin (Trypsin sequence grade, Roche, Mannheim, Germany) for 45 min at 4°C. After removal of excess trypsin, the gel pieces were incubated in a minimal volume (10–20 µL) of 50 mM Tris (pH 9.0) buffer for 24 h at 37°C. The solution containing digested fragments of proteins was transferred to 1.5 mL siliconized plastic test tube and stored at 4°C. Peptide fragments remaining in gel pieces were further recovered after 20 min incubations at room temperature in minimal volumes of 5% v/v formic acid containing 50% v/v acetonitrile. The solutions containing peptides were pooled together in the tube at 4°C. 2.7. LC-MS/MS. Molar quantities of recovered peptide fragments were estimated from the staining intensity of the SDS-PAGE bands that were digested in-gel with trypsin. Digested peptides equivalent to the maximum of 10 pmol. of a protein in an SDS-PAGE band were injected into a Magic C18 column (Michrom Bioresources, Inc., CA, USA), which was attached to the MAGIC 2002 (Michrom Bioresources, Inc., CA, USA) high-performance liquid chromatography (HPLC) system. The flow rate of the mobile phase was 1 µL/min using MAGIC Variable Splitter. The solvent composition of the mobile phase was programmed to change in 50 min cycles with varying mixing ratios of solvent A (2% v/v CH3CN and 0.1% v/v HCOOH) to solvent B (90% v/v CH3CN and 0.1% v/v HCOOH). Next, the peptides were eluted with a linear gradient from 0 to 50% solvent B. Purified peptides were introduced from HPLC to Q-star (Applied Biosystems, Foster City, CA, USA), a hybrid quadrupole time-of-flight mass spectrometer, via an attached FortisTip (AMR, Tokyo, Japan). Mascot search engine (Matrixscience, London, UK) was used to identify proteins from the mass and tandem mass spectra of peptides. Peptide mass data were matched by searching the National Center for Biotechnology Information database using MASCOT engine (http://www.matrixscience.com/). The minimum criterion of the probability-based MASCOT/MOWSE score was set with 5% as the significant threshold level. 2.8. Western Blot Analysis. After the 12 abundant proteins were removed from serum as described above, the depleted samples were separated on SDS-polyacrylamide gel electrophoresis (80 x 40 x 1.0 mm, 10–20% polyacrylamide gradient gel, 240 V) and transferred to a methanol-rinsed polyvinyl-difluoride (PVDF) membrane (0.45 µm pore size in roll form, Millipore, Bedford, MA) (Amersham, Hybond-C Extra Supported) (40 V, 25 min) using the XV Pantera System (DRC Co., Ltd., Tama, Japan). After transferring the proteins to a membrane and blocking with 5% skim milk in phosphate-buffered saline (PBS) for 1 h at room temperature, the membranes were incubated at 4°C overnight with the primary antibody to clusterin (1:3000, mouse monoclonal, upstate (now part of Millipore), CA, USA). The membrane was washed for a total 30 min in 3 changes of PBS-Tween (0.1%) prior to incubation in the appropriate horseradish peroxidase-linked secondary antibody (anti-mouse IgG horseradish peroxidase-linked secondary antisemur, 1:500) for 1 h at room temperature. The membranes were finally washed three times as previously described, and immunoreactive proteins were revealed with an enhanced chemiluminescence substrate reaction using ECL western blotting detection reagents (GE Healthcare UK Ltd., Amersham, England) according to the manufacturer’s instructions. 2.9. Gel Imaging and Analysis. The Silver-stained SDS-gels and CBB-stained gels were scanned with an optical resolution of 400 dpi by EPSON ES-2000 scanner (SEIKO EPSON Corp., Nagano, Japan) using EPSON TWAIN Pro software (SEIKO EPSON Corp., Nagano, Japan). The images were processed using Photoshop 6 (Adobe) software. After scanning, each gel was stored at 4°C. TIFF files of the gel images were transferred for analysis with a TotalLab TL120 (Nonlinear Dynamics Ltd., Newcastle, UK) and were used for band detection and statistical analysis. 2.10. Measurement of Serum Clusterin Concentration by ELISA. Serum clusterin was quantified using a human clusterin ELISA kit (R&D systems, Inc., MN, USA) following manufacturer's instructions. Human clusterin standard as provided in the kit (1,000 ng/mL: stock solution), and the serially diluted standards (200–3.12 ng/mL) were prepared from the stock solution. Calibrator Diluent RD5T (dilution buffer) serves as the blank. Test serum samples were diluted 1:2000 in the dilution buffer. After adding 100 μL of Assay Diluent RD1-19 to each well, 50 μL aliquots of the standards and diluted test samples were added in duplicate to the wells of a microtiter plate coated with antihuman clusterin antibody. After incubation at room temperature for 2 hours on a horizontal orbital shaker, the plate was washed using 400 μL of Wash Buffer and repeated three time processes and a total of four washes. After the last wash, 200 μL of antihuman clusterin monoclonal antibody conjugated to horseradish peroxidase was added to the wells. The plate was incubated for 2 hours at room temperature on the shaker, followed by washes as before and addition of 200 μL of substrate solution containing hydrogen peroxide and tetramethylbenzidine to the wells. The plate was placed at the dark to protect from light and incubated for 30 min at room temperature to allow for color development. The reaction was stopped by the addition of 50 μL of stop solution, and the optical densities were determined by reading absorbance at 450 nm with iMark Microplate Reader (Bio-Rad Laboratories, Inc., CA, USA). 2.11. Other Procedures. Numerical data were presented as mean ± SD. Statistical significance of difference was assessed by Student's t-test; P values less than 0.05 were considered significant. Serum AFP and PIVKA-II levels were determined by commercially available assay kits. 3. Results 3.1. Immunoaffinity Serum Depletion. Schematic diagram of our experimental protocol is summarized in Figure 1. Figure 2 is a representative immunoaffinity chromatogram and shows a substantial removal of high-abundant proteins from a human serum sample. The immunodepletion of the high-abundant serum proteins was conducted in a reproducible manner in samples obtained from seven HCC and five LC patients (data not shown). A total of 4 mL of flow-through fractions were collected, desalted, and concentrated prior to reversed-phase HPLC. 3.2. RP-HPLC. Figure 3 is a representative reversed-phase HPLC chromatogram. Forty fractions were collected every 0.5 minute from 19.1 to 39.1 minutes (Figure 3(a), arrow). Fractions numbers 1–5, numbers 6–8, numbers 26–30, numbers 31–35, and numbers 36–40 were pooled, respectively, since protein concentration of each fraction was apparently very low. Therefore, a total of 22 fractions were processed for SDS-PAGE analysis (Figure 3(b)). Table 3: Upregulated proteins identified by LC-MS/MS in human HCC serum. Details are described in the experimental procedures. \| Protein name \| Theoretical mass \| Experimental mass \| Score \| Coverage \| Queries matched \| \|-------------------------------------------\|------------------\|-------------------\|-------\|----------\|-----------------\| \| Afamin precursor \| 69024 \| 90000 \| 563 \| 23% \| 16 \| \| Alpha-1-antichymotrypsin \| 48606 \| 95000 \| 118 \| 4% \| 2 \| \| Alpha-1-B-glycoprotein \| 51908 \| 95000 \| 88 \| 5% \| 2 \| \| Alpha-1-microglobulin \| 16531 \| 230000 \| 99 \| 15% \| 2 \| \| Alpha-2-macroglobulin \| 163175 \| 170000 \| 2465 \| 34% \| 76 \| \| Angiotensinogen \| 53122 \| 55000 \| 705 \| 29% \| 23 \| \| Antithrombin III \| 49008 \| 62000 \| 389 \| 24% \| 9 \| \| Apolipoprotein A-IV \| 45307 \| 43000 \| 639 \| 30% \| 12 \| \| Apolipoprotein B \| 187126 \| 140000 \| 332 \| 4% \| 7 \| \| Apolipoprotein B-100 \| 515077 \| 140000 \| 267 \| 1% \| 5 \| \| Apolipoprotein E \| 36185 \| 35000 \| 832 \| 44% \| 33 \| \| Beta-actin \| 41710 \| 41000 \| 226 \| 17% \| 4 \| \| C1q \| 26442 \| 33000 \| 113 \| 11% \| 2 \| \| C2 precursor \| 83214 \| 97000 \| 557 \| 15% \| 14 \| \| C3 \| 187046 \| 180000 \| 613 \| 7% \| 11 \| \| C3b \| 103886 \| 120000 \| 2042 \| 26% \| 63 \| \| C3c \| 187046 \| 33000 \| 206 \| 2% \| 4 \| \| C3d \| 120000 \| 187046 \| 153 \| 1% \| 3 \| \| C3, isoform CRA_a \| 70000 \| 143619 \| 1636 \| 28% \| 64 \| \| C4A \| 192741 \| 24000 \| 456 \| 5% \| 21 \| \| C4B \| 40737 \| 41000 \| 138 \| 7% \| 2 \| \| C5 \| 141723 \| 120000 \| 248 \| 4% \| 6 \| \| C6 \| 104776 \| 120000 \| 96 \| 4% \| 2 \| \| C7 \| 93449 \| 95000 \| 874 \| 22% \| 27 \| \| C8-alpha subunit \| 65111 \| 55000 \| 109 \| 3% \| 2 \| \| C8-beta propeptide \| 62008 \| 70000 \| 323 \| 11% \| 7 \| \| C8-gamma polypeptide \| 22206 \| 23000 \| 352 \| 40% \| 15 \| \| C9 \| 60359 \| 70000 \| 496 \| 14% \| 12 \| \| Complement receptor type 2 (Cr2) \| 112900 \| 160000 \| 160 \| 2% \| 2 \| \| Component factor B \| 85450 \| 50000 \| 163 \| 4% \| 3 \| \| Cr2-C3d complex \| 34437 \| 35000 \| 151 \| 10% \| 3 \| \| Complement component (3b/4b) receptor 1 \| 61415 \| 160000 \| 102 \| 4% \| 2 \| \| Carbonic anhydrase I \| 28852 \| 25000 \| 195 \| 18% \| 4 \| \| Carbonic anhydrase II \| 29200 \| 33000 \| 208 \| 18% \| 4 \| \| Carboxypeptidase N Polypeptide 1 precursor\| 52253 \| 45000 \| 147 \| 11% \| 3 \| \| Carboxypeptidase N precursor \| 60578 \| 97000 \| 330 \| 11% \| 6 \| \| Cathepsin D preproprotein \| 44524 \| 49000 \| 103 \| 6% \| 2 \| \| Cationic trypsinogen \| 160000 \| 120901 \| 66 \| — \| 2 \| \| CD14 protein precursor \| 40111 \| 55000 \| 365 \| 21% \| 8 \| \| Ceruloplasmin \| 115398 \| 140000 \| 1520 \| 27% \| 44 \| \| Clusterin \| 48772 \| 39000 \| 95 \| 8% \| 2 \| \| C-type lectin domain family 3, member B \| 22552 \| 25000 \| 243 \| 24% \| 6 \| \| Fibronectin precursor \| 256529 \| 230000 \| 176 \| 2% \| 3 \| \| Galectin 3 binding protein \| 65289 \| 90000 \| 177 \| 3% \| 3 \| \| Gelsolin \| 85644 \| 95000 \| 474 \| 15% \| 11 \| \| Glutathione peroxidase 3 precursor \| 25489 \| 26000 \| 167 \| 16% \| 4 \| \| Hemopexin precursor \| 51512 \| 50000 \| 104 \| 4% \| 2 \| ### Table 3: Continued. \| Protein name \| Theoretical mass \| Experimental mass \| Score \| Coverage \| Queries matched \| \|---------------------------------------------------\|------------------\|-------------------\|-------\|----------\|-----------------\| \| Heparin cofactor II \| 57034 \| 110000 \| 372 \| 21% \| 8 \| \| Insulin-like growth factor binding protein \| 65994 \| 95000 \| 176 \| 6% \| 3 \| \| Interalpha-trypsin inhibitor heavy chain H1 \| 101339 \| 230000 \| 631 \| 14% \| 23 \| \| Interalpha-trypsin inhibitor heavy chain H2 \| 106370 \| 230000 \| 862 \| 15% \| 28 \| \| ITI family heavy chain-related protein \| 103321 \| 120000 \| 348 \| 9% \| 6 \| \| Kininogen 1 \| 47853 \| 120000 \| 355 \| 13% \| 7 \| \| Lactate dehydrogenase B \| 36615 \| 35000 \| 217 \| 13% \| 4 \| \| Leucine-rich alpha-2-glycoprotein 1 \| 38154 \| 50000 \| 301 \| 15% \| 8 \| \| Lumican \| 38375 \| 70000 \| 320 \| 21% \| 7 \| \| M130 antigen \| 160000 \| 120901 \| 66 \| 1% \| 2 \| \| Multimerin 2 \| 104352 \| 20000 \| 88 \| 1% \| 2 \| \| Pancreatic carboxypeptidase A1 precursor \| 47111 \| 41000 \| 92 \| 5% \| 2 \| \| Peptidoglycan recognition protein 2 precursor \| 67927 \| 70000 \| 96 \| 7% \| 2 \| \| Pigment epithelial-differentiating factor (serpin-F1) \| 46313 \| 48000 \| 946 \| 50% \| 22 \| \| Plasma protease (C1) inhibitor precursor \| 55147 \| 90000 \| 829 \| 25% \| 43 \| \| Prepro-plasma carboxypeptidase B \| 48411 \| 62000 \| 100 \| 6% \| 2 \| \| Preserum amyloid P component \| 25381 \| 30000 \| 362 \| 26% \| 13 \| \| Prolidase \| 54348 \| 55000 \| 82 \| 3% \| 2 \| \| Proteasome alpha 4 subunit isoform 1 \| 29465 \| 33000 \| 85 \| 8% \| 2 \| \| Sex-hormone-binding globulin \| 43768 \| 45000 \| 391 \| 28% \| 10 \| \| Thyroxine-binding globulin precursor \| 46295 \| 55000 \| 135 \| 6% \| 3 \| \| Trypsin inhibitor \| 106647 \| 55000 \| 174 \| 5% \| 3 \| \| Vascular cell adhesion molecule 1 isoform \| 81224 \| 97000 \| 133 \| 3% \| 2 \| \| Vitamin D binding protein \| 51183 \| 55000 \| 669 \| 21% \| 17 \| \| Vitamin K-dependent protein S \| 75074 \| 95000 \| 106 \| 3% \| 2 \| \| Vitronectin \| 54308 \| 10000 \| 90 \| 2% \| 2 \| 3.3. SDS-PAGE Analysis. The representative silver-stained SDS-PAGE gel of a fraction (fraction number 13) obtained from seven HCC patients and five LC patients is shown in Figure 4(a). Comparison of SDS-PAGE patterns of a total of 22 fractions revealed that intensities of 83 bands were greater in more than 3 cases of HCC than in those in LC cases. Among these, the intensities of 14 bands were increased in all the seven HCC patients. The representative examples are indicated by arrow heads. 3.4. Identification of Protein. To identify proteins, the expression of which was different between HCC and LC on silver stained gel, four HCC and four LC sera were fractionated and separated using SDS-PAGE again, and then gels were stained by CBB (Figure 4(b)). Because the sensitivity of the CBB stain is lower than of the silver stain, samples for identification were prepared from the beginning by repeating three courses of the procedures, from depletion of the major proteins to RP-HPLC fractionation. As a result, additional 71 bands were found to have altered intensity levels between the two groups on CBB gels. Thus, a total of 154 bands were considered as initial candidate bands. Forty-six out of these 154 bands, derived from more than two adjacent fractions, were not processed further. Finally, 108 bands were subjected to in-gel trypsin digestion: among them 73 proteins were identified by LC-MS/MS (Table 3 and Figure 5). 3.5. Western Blotting. Western blotting analysis could confirm that clusterin was overexpressed in the majority of HCC sera as compared with LC (Figure 6(a)). Semiquantitative analysis of the results by TotaLab TL120 (Shimadzu Co., Ltd., Kyoto) revealed that the difference in serum clusterin levels between HCC and LC was statistically significant (468211.38 ± 103972.69 versus 341686.90 ± 123162.85, $ P = 0.023 $) as indicated in Figure 6(b). 3.6. Clusterin Concentration in Serum from HCC and LC Patients. To evaluate diagnostic values of serum clusterin levels for HCC diagnosis, we examined sera from 64 patients with HCC, 60 with LC, and 60 normal subjects. The concentration of clusterin (mean ± SD) was 210 ± 61.3 μg/mL for HCC, 170.9 ± 50.0 μg/mL for LC, and 139.4 ± 37.4 μg/mL for normal subjects and was significantly higher in HCC than in LC ($ P < 0.01 $, Student’s t-test) and in normal subjects ($ P < 0.001 $) (Figure 7). We set the cut-off value of clusterin at 230 μg/mL by calculating the mean ± 2SD of healthy 60 samples. As a result, clusterin level above the value was found in 23 of 64 HCCs (35.9%) and in 6 of 60 LCs (10.0%). Furthermore, Figure 4: Representative SDS-PAGE pattern of immunodepleted serum sample after RP-HPLC fractionation (fraction number 13). 100 μL of serum samples from seven HCC patients and five LC patients was immunodepleted and injected onto the column. Forty fractions were collected and dried, and among them 22 fractions were separated using 10–20% SDS-PAGE. Each dried fraction was dissolved in 15 μL of sample buffer and loaded onto the gel as described in the experimental procedures. Following electrophoresis, proteins were visualized by silver staining (a). For protein identification, 300 μL of serum samples was prepared again and visualized by CBB staining (b). The intensities of 14 bands were increased in all the seven HCC patients. The representative examples are indicated by arrow heads. Figure 5: Identification of clusterin by LC-MS/MS. The amino acid sequence of clusterin is shown. Matched peptide sequences are printed in bold and underlined. serum clusterin levels were above the cut-off value in 5 of 12 HCCs (41.7%) in whom both serum AFP and PIVKA-II were within their cut-off values, suggesting that clusterin is complementary to the conventional two representative HCC tumor markers. 4. Discussion The sequencing of the human genome has opened the door for comprehensive transcriptome and proteome analysis. Transcriptome analyses have revealed unique patterns for gene expression that are clinically informative. Messenger RNA abundances, however, are not necessarily predictive of corresponding protein abundances [42]. Since the detailed understanding of biological processes, both in healthy and pathological states, requires the direct study of relevant proteins, proteomics bridges the gap between the information coded in the genome sequence and cellular behavior. Therefore, proteomics is among the most promising technologies for the development of novel diagnostic tools. Increasing number of studies has taken advantage of various proteomic technologies to discover and identify novel HCC markers. Clinical tissue samples have been the most extensively studied samples in HCC proteomic studies. Most studies compared protein expression profiles between tumor tissues and adjacent nontumor tissues using two dimensional electrophoresis (2DE) and two dimensional fluorescence difference gel electrophoresis (2D-DIGE). Some studies used laser capture microdissection (LCM) in order to characterize isolated tumor cell populations from heterogeneous tissue sections. By combing LCM and 2D-DIGE, Liang et al [43], found that the protein profiles of well- and poorly differentiated HCC tissues are significantly different. Proteome analyses of tumor tissues should be a basis for HCC marker discovery and a number of proteins have been identified as candidate markers for HCC [44–46]; none of them have been shown to be useful serum marker in a clinical setting. Among thousands of serum proteins and peptides, a few are so dominant that they may hamper the detection of other low abundance proteins or peptides. To overcome this problem, Feng et al. [47] took a strategy to deplete abundant proteins such as albumin and immunoglobulin before analyses, followed by 2DE and MALDI-TOF MS/MS identification. They showed that heat-shock-protein 27 could aid in the diagnosis of HCC. In this study, three-step procedures including the immunodepletion of 12 abundant proteins were carried out to discover novel HCC markers. As a first step, serum samples were subjected to antibody-based immunoaffinity column that simultaneously removes 12 abundant serum proteins. The concentrated flow-through was then fractionated using reversed-phase HPLC. Proteins obtained in each HPLC fraction were further separated by SDS-PAGE. A total of 73 differentially expressed proteins were identified and among them clusterin was of particular interest as potential serum marker for HCC and differences in this expression in serum were confirmed by the western blotting. Further validation using another set of serum sample set showed that clusterin level was significantly higher in HCC than in LC as determined by ELISA. It is notable that serum clusterin levels were elevated in 5 out of 12 HCC cases in which both AFP and PIVKA-II were within their cut-off values. As a result, combination assays of AFP PIVKA-II and clusterin could detect about 90% of HCC cases included in this study. These result suggested that clusterin could be HCC tumor marker complementary to AFP and PIVKA-II. Clusterin, also known as apolipoprotein J (Apo J), sulfated glycoprotein 2, is a heterodimeric glycoprotein present in most animal tissues and body fluids [48]. This glyco-protein plays important roles in a variety of physiological processes including lipid transport [49], reproduction [50], tissue remodeling [51], and senescence [52]. Clusterin overexpression has been shown in various human malignancies including cancer of the breast [53], pancreas [54], and colon [55]. Kang et al. [56] demonstrated the overexpression of clusterin in HCC and suggested that its cytoplasmic overexpression might be a predictor of poor survival. Increased serum levels of clusterin in HCC patients had not been reported before. In conclusion, the results of this study suggest that clusterin can be a supplementary serum biomarker for HCC. Exact mechanisms and pathophysiological significance for the upregulation of clusterin in HCC remain to be investigated. Furthermore, since the majority of HCC cases in Japan are related to HCV, we focused on HCV-related HCC in the present study. It will be necessary to assess diagnostic values of serum clusterin levels in HBV-related cases as well. List of Abbreviations - HCC: Hepatocellular carcinoma - AFP: Alpha-fetoprotein - DCP: Des-gamma-carboxy prothrombin - LC: Liver cirrhosis - SDS-PAGE: Sodium dodecyl sulfate polyacrylamide gel electrophoresis. References [1] J. O. 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bc1affe22f4798639be235f3dd93c516a68e511a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 4, "total-fallback-pages": 0, "total-input-tokens": 10460, "total-output-tokens": 1844, "fieldofstudy": [ "Medicine" ] }	Intramuscular myxoma of the thigh: a rare case report SENHAJI Said ; ABDULRAZAK Saeed; KACIMI ALAOUI Mehdi; EL IDRISSI Mohamed; EL IBRAHIMI Abdelhalim; EL MRINI Abdelmajid Department of osteoarticular surgery B4, HASSAN II teaching hospital, Fès, Morocco ABSTRACT Myxoma is a rare, benign mesenchymal tumor composed of undifferentiated stellate cells within a myxoid stroma resembling that of the umbilical cord. Apart from cardiac locations, skeletal muscle involvement is commonly seen around thigh muscles, although other muscles could be affected with intermuscular, para-articular and even subcutaneous subsets. The authors intend to highlight the diagnostic challenge that could arise in the management of what is a benign tumor through a case report and review of relevant literature. Keywords: myxoma, benign tumor, thigh Correspondence to Author: SENHAJI Said Department of osteoarticular surgery B4, HASSAN II teaching hospital, Fès, Morocco How to cite this article: SENHAJI Said; ABDULRAZAK Saeed; KACIMI ALAOUI Mehdi; EL IDRISSI Mohamed; EL IBRAHIMI Abdelhalim; EL MRINI Abdelmajid Intramuscular myxoma of the thigh: a rare case report. American Journal of Orthopedic Research and Reviews, 2018, 1:6 eSciPub LLC, Houston, TX USA. Website: http://escipub.com/ Introduction Myxoma is a rare, benign mesenchymal tumor composed of undifferentiated stellate cells within a myxoid stromaresembling that of the umbilical cord [1]. Apart from cardiac locations, skeletal muscle involvement is commonly seen around thigh muscles, although other muscles could be affected with intermuscular, para-articular and even subcutaneous subsets. Case report Patient, 70-year-old female with no relevant clinical history, presented with an incipient swelling on the posterior side of the left thigh. Plain x-ray showed a soft tissue thickening of the thigh with no bony lesions. MRI came back for a well-defined cystic tissue mass measuring 64 * 61 * 100mm (figure 1a -b). The solid central component was enhanced on contrast medium injection. It was far from the femoral vessels and was closely linked to the large sciatic nerve anteriorly. The patient underwent a surgical biopsy of the tumor for which histological examination returned for an intramuscular myxoma with no signs of malignancy. Patient subsequently underwent extensive tumor excision (figure 2; 3) and pathology confirmed myxoma. 15 months after treatment no local recurrence has been observed. Discussion Myxoma constitutes a benign tumor of mesenchymal origin composed of undifferentiated stellate cells within a myxoid tissue sometimes resembling that of the umbilical cord [1]. Besides cardiac muscle locations, skeletal muscle involvement is most common in the muscles of the thigh, but may affect other muscles and may be in intermuscular, para-articular or sometimes subcutaneous [1] . Women are commonly affected. The association of intramuscular Fig 1a Fig 1b Fig 1a- b: MRI showing cystic tissue mass measuring 64 * 61 * 100mm. The solid central component was enhanced on contrast medium injection myxoma with fibrous dysplasia is termed Mazabraud syndrome [2]. In imaging, the lesion presents as an intramuscular cystic mass due to its high liquid density due to its predominant mucinous component and low collagen content. It appears hypodense on CT, hypo-intense on T1 and especially hyper-intense on T2 weighted sequences. The solid component of the tumor is often not visible on CT scan. It is best seen on ultrasonography [3], and MRI on T2-weighted sequences (hyposignal septa separating cystic zones) and T1-weighted sequences after gadolinium injection (heterogeneous lesion containing septa with diffuse peripheral enhancement) [4]. It is noteworthy that there is usually no calcifications within the lesion. The contours of the tumor are well limited; a pseudocapsule sometimes seen on ultrasound or MRI, rarely on the CT scan, and blood vessels only located outside the lesion. Myxoma is usually surrounded by a fatty ring often present at the upper and / or lower poles of the lesion thus depicting the bright rim and bright cap sign best seen on MRI. This fatty ring corresponds to an atrophy of the surrounding tumor muscle in direct contact with mucoid stroma, due to the absence of capsule or lack thereof. This phenomenon could also explain peritumoral edema, sometimes found on T2-weighted sequences in MRI [1, 5]. The main differentials include synovial and mucoid cysts, neurogenic tumors, myxoid liposarcoma and myxofibrosarcoma. Synovial and mucoid cysts are usually intermuscular and arise at specific locations with imaging features rather more homogeneous and purely cystic. Neurogenic tumors are also often intermuscular with direct links to adjacent nerve and a typical "target sign" seldom seen on T2 sequences. Myxoid liposarcoma usually contains an intrinsic fat component. Finally, myxofibrosarcoma is often much more heterogeneous on imaging, with tissue component highly enhanced after contrast medium injection and often associated with hemorrhagic modifications [1]. Imaging features are rather less specific and remain insufficient to affirm positive diagnosis. Complete surgical excision is the mainstay as it guarantees no local recurrence and pathology examination allows definitive diagnosis of tumor [6]. Conclusion: Intramuscular myxoma is a well-defined benign tumor whose definitive diagnosis could pose a challenge. MRI remains an essential tool in the preoperative workup. Major differentials include liposarcoma, which could be myxoid in 50% of cases. Wide excision is highly recommended with no recurrences after surgery. References: 1. Murphey M.D., McRae G.A., Fanburg-Smith J.C., Temple H.T., Levine A.M., Aboulafia A.J. Imaging of soft-tissue myxoma with emphasis on CT and MR and comparison of radiologic and pathologic findings Radiology 2002; 225: 215-224 2. Delabrousse E., Couvreur M., Bartholomot B., Lucas X., Kastler B. Syndrome de mazabraud : à propos d’un cas diagnostiqué en IRM J Radiol 2001; 82: 165-167 3. Girish G., Jamadar D.A., Landry D., Finlay K., Jacobson J.A., Friedman L. Sonography of intramuscular myxomas: the bright rim and bright cap signs J Ultrasound Med 2006; 25: 865-871 4. Luna A., Martinez S., Bossen E. Magnetic resonance imaging of intramuscular myxoma with histological comparison and a review of the literature Skeletal Radiol 2005; 34: 19-28 5. Bancroft L.W., Kransdorf M.J., Menke D.M., O’Connor M.I., Foster W.C. Intramuscular myxoma: characteristic MR imaging features AJR Am J Roentgenol 2002; 178: 1255-1259 6. Charron P., Smith J. Intramuscular myxomas: a clinicopathologic study with emphasis on surgical management Am Surg 2004; 70: 1073-1077	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 1282, 1 ], [ 1282, 3086, 2 ], [ 3086, 4164, 3 ], [ 4164, 6731, 4 ] ] }
199a6424ea8343e1fac5e6c4579d29a53b773c8e	{ "olmocr-version": "0.1.59", "pdf-total-pages": 19, "total-fallback-pages": 0, "total-input-tokens": 50122, "total-output-tokens": 16105, "fieldofstudy": [ "Psychology", "Medicine" ] }	Targeting dissociation using cognitive behavioural therapy in voice hearers with psychosis and a history of interpersonal trauma: A case series Filippo Varese1,2, Maggie Douglas3, Robert Dudley3,4, Samantha Bowe5, Thomas Christodoulides3, Stephanie Common6, Tim Grace6, Victoria Lumley6, Laura McCartney3, Sonia Pace3, Thomas Reeves3, Anthony P. Morrison1,5 and Douglas Turkington7 1Division of Psychology and Mental Health, School of Health Sciences, Manchester Academic Health Science Centre, University of Manchester, UK 2Complex Trauma and Resilience Research Unit, Greater Manchester Mental Health NHS Foundation Trust, Manchester Academic Health Science Centre, UK 3Cumbria, Northumberland, Tyne and Wear NHS Foundation Trust, Newcastle upon Tyne, UK 4School of Psychology, Newcastle University, Newcastle upon Tyne, UK 5Psychosis Research Unit, Greater Manchester Mental Health NHS Foundation Trust, Manchester Academic Health Science Centre, UK 6Tees Esk and Wear Valley, NHS Foundation Trust, Darlington, UK 7Institute of Neuroscience, Newcastle University, Newcastle upon Tyne, UK Objectives. Previous studies have suggested that dissociation might represent an important mechanism in the maintenance of auditory verbal hallucinations (i.e., voices) in people who have a history of traumatic life experiences. This study investigated whether a cognitive behavioural therapy (CBT) intervention for psychosis augmented with techniques specifically targeting dissociative symptoms could improve both dissociation and auditory hallucination severity in a sample of voice hearers with psychosis and a history of interpersonal trauma (e.g., exposure to sexual, physical, and/or emotional abuse). Design. Case series. Methods. A total of 19 service users with psychosis were offered up to 24 therapy sessions over a 6-month intervention window. Participants were assessed four times over a 12-month period using measures of dissociation, psychotic symptoms severity, and additional secondary mental-health and recovery measures. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Correspondence should be addressed to Filippo Varese, Division of Psychology and Mental Health, School of Health Sciences, University of Manchester, Zochonis Building, 2nd floor, Brunswick Street, Manchester M13 9PL, UK (email: [email protected]). DOI:10.1111/papt.12304 Results. Sixteen participants engaged in the intervention and were included in last-observation-carried-forward analyses. Dropout rates were in line with those of other CBT for psychosis trials (26.3%). Repeated measures ANOVAs revealed large and significant improvements in dissociation ($d_{rm} = 1.23$) and hallucination severity ($d_{rm} = 1.09$) by the end of treatment; treatment gains were maintained 6 months following the end of therapy. Large and statistically significant gains were also observed on measures of post-traumatic symptoms, delusion severity, emotional distress, and perceived recovery from psychosis. Conclusions. The findings of this case series suggest that the reduction of dissociation represents a valuable and acceptable treatment target for clients with auditory verbal hallucinations and a trauma history. Future clinical trials might benefit from considering targeting dissociative experiences as part of psychological interventions for distressing voices. Practitioner points - Practitioners should consider the role of dissociation when assessing and formulating the difficulties of voice hearers with a history of trauma. - Techniques to reduce dissociation can be feasibly integrated within psychological interventions for voices. - Voice hearers with histories of trauma can benefit from psychological interventions aimed at reducing dissociation. Introduction In recent years, growing evidence has confirmed that trauma (i.e., life events and circumstances that are experienced by the individual as physically or emotionally harmful and life threatening and that may have enduring adverse impacts on the individual’s physical, emotional, or mental well-being; SAMHSA, 2014) represents a crucial risk factor for psychosis. A broad range of complementary research findings, including large-scale epidemiological studies (e.g., Shevlin et al., 2013), prospective studies of trauma survivors (e.g., Cutajar et al., 2010), prognostic research in at-risk groups (Brew, Doris, Shannon, & Mulholland, 2018), and comprehensive meta-analyses of longitudinal and retrospective investigations (Varese, Smeets, et al., 2012) have confirmed that exposure to potentially traumatic life events (e.g., physical and sexual violence, emotional abuse, neglect, or bullying) dramatically increases the risk of developing psychotic symptoms. In parallel, a large body of evidence suggests that people with psychosis who have a history of trauma present with more severe and disabling psychotic symptoms, in particular positive symptoms of psychosis such as delusions and hallucinations (Bailey et al., 2018; Stevens et al., 2019). Given the importance of trauma in psychosis, there has been a growing interest in the application of trauma-focused interventions in psychotic clients who present with comorbid trauma- and stress-related conditions, in particular post-traumatic stress disorder (PTSD). In recent clinical trials with patients with lifetime diagnosis of psychosis and (current) comorbid PTSD, trauma-focused interventions with a robust evidence base for the treatment of PTSD (prolonged exposure and eye movement desensitization and reprocessing) have been linked to reduced severity of post-traumatic symptoms (van den Berg et al., 2015) and symptoms of psychosis (de Bont et al., 2016). The effects of these treatments appeared more robust for delusions than auditory verbal hallucinations. A recent systematic review has largely confirmed these findings; trauma-focused therapies can ameliorate symptoms of psychosis, but their effect on certain symptoms, in particular hallucinations, is negligible in most treatment studies (Brand, McEnery, Rossell, Bendall, & Thomas, 2018). Targeting the psychological processes responsible for the increased vulnerability to specific psychotic experiences in individuals exposed to traumatic experiences represents a promising avenue for the development of more effective interventions for psychotic symptoms that may have a traumatic origin (e.g., Bentall et al., 2014; Brand, Rossell, Bendall, & Thomas, 2017). Whilst the rationale for targeting comorbid PTSD is supported by a growing number of empirical studies indicating that ‘hallmark’ post-traumatic symptoms mediate the observed association between trauma exposure and presence/severity of symptoms of psychosis (Hardy et al., 2016), cognitive-behavioural avoidance, hyperarousal, and re-experiencing symptoms represent only some of the possible post-traumatic sequelae that could influence psychosis vulnerability and maintenance (Williams, Bucci, Berry, & Varese, 2018). Dissociation has been increasingly investigated as a potential mediator of the relationship between trauma and psychotic experiences, and multiple studies suggests that this effect is particularly robust in the context of auditory verbal hallucinations (i.e., hearing voices; Pearce et al., 2017; Varese, Barkus, & Bentall, 2012; Williams et al., 2018). Defined in the DSM-5 as ‘a disruption of and/or discontinuity in the normal integration of consciousness, memory, identity, emotion, perception, body representation, motor control and behaviour (that) can potentially disrupt every area of psychological functioning’ (p. 291; American Psychiatric Association, 2013), dissociation is a term used to describe a range of altered states of consciousness and perception which includes relatively benign forms of psychological and/or attentional disengagement (e.g., experiences of absorption) as well as more pervasive and potentially distressing experiences such as derealization, depersonalization, and identity alteration. These experiences are not only central to specific psychiatric diagnoses (e.g., dissociative identity disorder), but are also observed in the context of numerous other psychiatric presentations, including psychosis (Lyssenko et al., 2017; O’Driscoll, Laing, & Mason, 2014). Proposals that dissociation may represent a response to trauma, or even a ‘defence mechanism’ used by individuals to minimize the distress experienced when faced with overwhelming life circumstances, have received apparent empirical support by a range of cross-sectional and longitudinal studies indicating a robust association between trauma and dissociative experiences (Dalenberg et al., 2012). Furthermore, recent meta-analytic evidence indicates that dissociation is related to having a history of trauma in people with psychosis (Rafiq, Campodonico, & Varese, 2018). In parallel, research studies have suggested that the presence of dissociative experiences is linked to increased vulnerability to hearing voices. Using meta-analytic methods, Pilton, Varese, Berry, and Bucci (2015) found a large and robust association between dissociation and voices, observed not only in samples of patients with psychosis, but also other diagnostic groups. Findings from an experience sampling study indicate that increased levels of state dissociation predict hallucinatory episodes in the daily lives of people with psychosis (Varese, Udachina, Myin-Germeyns, Oorschot, & Bentall, 2011). Furthermore, dissociation predicts the persistence of voices in longitudinal studies of children who hear voices (Escher et al., 2004), and the onset of hallucinatory experiences in prospective studies with adult trauma survivors (Geddes, Ehlers, & Freeman, 2016). Whilst dissociation seems to be a key process in trauma and in voice hearing, the theoretical underpinnings of the relationship between these constructs are poorly delineated in the literature. Some authors have argued that a radical shift is needed in the way hallucinatory experiences are conceptualized by researchers and clinicians, as hallucinations in people with psychosis may be ‘traumatic in origin and dissociative in kind’ (p. 521; Moskowitz, Read, Farrelly, Rudegeair, & Williams, 2009). Other authors have backed more mechanistic perspectives, for example that dissociation, either at the time of the trauma or in response to current cues or reminders of past trauma, could increase confusion between inner and outer experiences, making individuals more vulnerable to voices and other hallucinatory experiences (e.g., Allen, Coyne, & Console, 1997), or that heightened states of dissociation may interact with pre-existing cognitive vulnerabilities for voices (such as source monitoring biases affecting the capacity to correctly identify the source of internally and externally generated cognitive events; Varese, Barkus, et al., 2012). Consequently, dissociation might represent a promising treatment target for psychological therapies aimed at improving voices in individuals with an history of adverse life experiences (Berry, Bucci, & Varese, 2019). Dissociation is often not sufficiently considered in manualized CBT interventions for psychosis (CBTp). Furthermore, the acceptability of cognitive behavioural change strategies for the management of dissociative experiences and the ‘added value’ of considering dissociation in the context of CBTp interventions for distressing voices have not been carefully examined to date. The current study was designed to address this knowledge gap. It examined the impact of a CBT intervention for voices (Morrison, Renton, Dunn, Williams, & Bentall, 2004) specifically modified to include therapeutic techniques suitable for individuals with trauma and dissociative experiences (Kennerley, 1996; Larkin & Morrison, 2005; Newman-Taylor & Sambrook, 2013). More specifically, using a case series design, we examined whether the intervention could ameliorate dissociative symptoms and auditory hallucinations severity as well as a range of secondary outcome measures, including delusions severity, post-traumatic symptoms, emotional distress, and perceived recovery from psychosis. Method Participants Participants were recruited from community mental health teams and early intervention (EI) services in the North East of England. All participants met the following eligibility criteria: (1) received support from community mental health services and had an identified care coordinator; (2) met ICD-10 criteria for schizophrenia, schizoaffective disorder, or delusional disorder or met criteria for first-episode psychosis used within their local EI service; (3) history of voice hearing for a minimum of six months; 4) were 16 years or older; (4) scored ≥ 2 on the frequency item and ≥3 on distress intensity items of the auditory hallucinations subscale of the Psychotic Symptoms Rating Scales (PSYRATS-AH); (5) scored ≥ 1 on any of the items of the expanded version of the Brief Betrayal Trauma Survey (BBTS-14) assessing lifetime exposure to interpersonal trauma (i.e., items 3–11); and (6) presented with potentially clinical significant levels of dissociative symptoms, as indicated by a score≥ 20 on the Dissociative Experiences Scale (DES; Carlson & Putnam, 1993). All participants had capacity to provide informed consent and were judged by their referring clinician to be clinically stable in the preceding 4 weeks. Referring clinicians also provided diagnostic information to confirm trial eligibility. Furthermore, eligible participants had to confirm that they regarded voices, dissociation, or trauma-related symptoms as their main presenting difficulty and that they wished to receive a psychological intervention specifically targeting these problems. Participants were not eligible from this study if their experience of voices/psychosis was attributable to organic causes (e.g., traumatic brain injuries), had insufficient command of English to complete the research interviews and measures, had a primary diagnosis of substance misuse dependency, or were receiving acute inpatient care at the time of referral. Measures The expanded version of the Brief Betrayal Trauma Survey (BBTS-14; Goldberg & Freyd, 2006) is a 14-item scale assessing exposure to potentially traumatic experiences. The scale includes separate items assessing potentially traumatic interpersonal events (e.g., exposure to sexual and physical violence; emotional and psychological mistreatment) as well as non-interpersonal events. For each event, respondents indicate the extent of their exposure both prior to and after the age of 18 using a 3-point scale (0 = never; 1 = one or two times; 2 = more than that). The Dissociative Experiences Scale (DES; Carlson & Putnam, 1993) is a 28-item questionnaire assessing dissociative experiences. Respondents select a percentage ranging from 0 to 100% to indicate how frequently each item is experienced. The overall DES score is obtained by averaging the 28 item scores, yielding a score ranging from 0 to 100. The DES has been shown to have very good validity and reliability, and good overall psychometric properties in many studies (e.g., van Ijzendoorn & Schuengel, 1996; Lyssenko et al., 2017). In this case series, to better capture changes in dissociation over the course of treatment, we assessed the frequency dissociative experiences experienced by participants in the previous month using a ‘time bound’ version of DES (the DES-t; Freyd, Klest, & Allard, 2005). The Psychotic Symptoms Rating Scale (PSYRATS; Haddock, McCarron, Tarrier, & Faragher, 1999) is a clinical interview assessing physical, cognitive, and emotional features of the auditory hallucinations and delusions experienced by the participant in the preceding week. The auditory hallucinations subscale of the PSYRATS (PSYRATS-AH) comprises 11 items assessing several dimensions of auditory verbal hallucinations on a 5-point scale ranging from 0 to 4. The delusions subscale of the PSYRATS (PSYRATS-Del) included six items assessing features of delusional beliefs on a similar 5-point scale. The PSYRATS has demonstrated good psychometric properties in studies with both first-episode (e.g., Drake, Haddock, Tarrier, Bentall, & Lewis, 2007) and ‘chronic’ psychotic patients (e.g., Haddock et al., 1999). In this study, the total PSYRATS-AH and PSYRATS-Del scores were used as aggregate measures of hallucination severity and delusion severity, respectively. The Impact of Events Scale Revised (IES-R; Weiss & Marmar, 1996) is a 22-item questionnaire assessing post-traumatic symptoms, including arousal, hypervigilance, and intrusions. Respondents were asked to anchor their responses to the most difficult life event identified using the BBTS-14 and indicate how much they were affected by each symptom in the previous week using a 5-point scale (0 = ‘not at all’; 4 = ‘extremely’). The IES-R has good psychometric properties and has been used in several studies with psychosis samples (e.g., Bendall, Alvarez-Jimenez, Hulbert, McGorry, & Jackson, 2012). The short Depression, Anxiety and Stress Scales (DASS-21; Lovibond & Lovibond, 1995) is a 21-item questionnaire designed to assess emotional distress, including symptoms of anxiety, depression, and stress. Participants are required to rate the extent to which they experienced symptoms in the past week on a 4-point scale (0 = ‘Did not apply to me at all’; 3 = ‘Applied to me very much or most of the time’). The measure has demonstrated good validity and internal consistency in previous studies with non-clinical hallucination-prone samples (e.g., Badcock, Chhabra, Maybery, & Paulik, 2008) as well as psychiatric patients with psychotic experiences (e.g., Ng et al., 2007). The Questionnaire about the Process of Recovery (QPR; Neil et al., 2009) is a 15-item self-report questionnaire assessing perceived recovery from psychosis-related difficulties. Participants are asked the QPR items using a 5-point Likert scale (0 = ‘disagree strongly’; 4 = ‘agree strongly’). The measure was developed in collaboration with people with lived experience of psychosis; it has good psychometric properties and has been used as an outcome measure in several clinical trials of psychological therapies for psychosis (e.g., Morrison et al., 2018). The short-form of the CHoice of Outcome In Cbt for psychosEs (CHOICE; Greenwood et al., 2009), a service user-led outcome measure, is developed to evaluate outcomes of CBTp interventions. Participants are required to rate a range of domains frequently targeted in psychological interventions for psychosis (e.g., their self-confidence; their ability to deal with everyday stress) in the previous week on an 11-point scale (0 = ‘worst’; 10 = ‘best’). The measure has been employed in previous CBTp trials, demonstrating good psychometric properties and sensitivity to change (e.g., Freeman et al., 2015). Intervention Participants were offered up to 24 sessions of CBT over a 6-month period. The intervention was delivered by a team of nine experienced clinical psychologists and CBT therapists in the context of their routine clinical practice in secondary care community services. All therapists had core CBT training and experience of working with clients with psychosis and trauma-related difficulties before starting the trial. All therapists received one day of training at the onset of the study, to familiarize themselves with the intervention and its rationale. Following the initial training, they had access to monthly trial-specific group supervision. The treatment plan closely followed CBTp approaches with an established evidence base (Morrison, 2017; Morrison et al., 2004), but the intervention was modified to have a preferential focus on dissociative experiences during assessment and formulation of clients’ difficulties and to systematically include therapeutic techniques targeting dissociative symptoms/responses associated with trauma. In this respect, the intervention expanded upon previous case studies that considered dissociation in the context of psychosis (Larkin & Morrison, 2005; Newman-Taylor & Sambrook, 2013). The cognitive framework described by Larkin and Morrison (2005) was used to guide the formulation of clients’ difficulties, and to emphasize the potential role of dissociation as (1) a possible post-traumatic sequela that may be involved in the development of psychotic experiences, and (2) a cognitive behavioural response involved in the maintenance of psychotic experiences (see Figure 1). Although designed to be flexible and adaptable to clients’ needs, the intervention comprised four phases which therapists were encouraged to follow through ongoing supervision and the completion of adherence measures following each therapy session. Sessions 1–4 were focused on engagement, cognitive behavioural assessment of presenting problems, identification of treatment goals and when appropriate normalization/psychoeducation on dissociative responses, trauma and/or psychosis. In sessions 5–14, clients were introduced to and practiced a range of techniques to manage dissociative responses and/or increase perceived controllability of dissociation. These included a range of strategies commonly used in psychological interventions with clients presenting with pervasive dissociative experiences, including identification of triggers, low arousal strategies, distress tolerance, and grounding techniques (e.g., Kennerley, 1996; Linehan, 1993). Although further work on dissociation and/or trauma was encouraged, the targets for intervention in subsequent sessions (15–22) and the strategies selected depended on individual formulation of clients’ difficulties and negotiation with the client (i.e., the acceptability of the proposed work). This could include re-appraisals on negative beliefs about dissociative experiences, cognitive and/or behavioural change strategies targeting core appraisals of voices leading to related distress, trauma-related techniques (e.g., imagery techniques, cognitive restructuring work informed by cognitive therapy for post-traumatic stress), or consolidation of a developmental/longitudinal psychological formulation of the client’s difficulties. The final two sessions were dedicated to the development of plans for relapse prevention and maintenance of gains. An applied example of this treatment approach is described in a previously published case study [reference removed for anonymity purposes]. Procedure The study was approved by an NHS Research Ethics Committee and the Health Research Authority. Participants were referred to the study by a member of their clinical team and were assessed for eligibility by a trained research assistant. After providing informed consent, participants completed a battery of baseline measures comprising the PSYRATS, the DES, and the abovementioned questionnaires. Following the completion of these initial assessments, participants were allocated to a study therapist in their locality. Participants were assessed using the same battery of measures (except for the BBTS-14, which was administered only at baseline) on three subsequent occasions, at mid-treatment (approximately 3 months after the baseline assessment), at the end of treatment (6 months after baseline), and again at 6 months following the end of treatment. All research assessments were conducted by a graduate research assistant during face-to-face meetings with study participants. Statistical analyses In line with the overall rationale for the proposed intervention (i.e., that dissociation may represent a post-traumatic sequela involved in the maintenance of voices), measures of dissociation (DES scores) and auditory hallucinations (PSYRATS-AH) were used as co-primary outcomes in our analyses. A series of repeated measures analyses of variance (ANOVA) were carried out to examine differences between baseline, mid-therapy, and end-of-therapy assessment points on the abovementioned primary outcomes measures and additional secondary outcomes (IES-R, PSYRATS-Del, DASS-21, QPR, and CHOICE). As end of treatment was our primary end point, no inferential tests considered data gathered at the 6-month follow-up assessments; however, these data are presented descriptively to estimate whether any treatment gains were maintained following the end of treatment. Post-estimation tests were conducted to compare mid-therapy and end-of-therapy scores against baseline scores; effect sizes for these comparisons were quantified using the formula for estimating the standardized mean difference for repeated measures design (Cohen’s $ d_{RM} $, see Lakens, 2013). When data violated the assumption of normality for repeated measures ANOVA, Friedman’s test was employed to analyse changes in the outcome of interest over time, and follow-up comparisons were conducted using the Wilcoxon signed-rank test. The above analyses only considered participants who actively engaged in treatment. In line with the structure of our phased protocol, treatment engagement was defined as receiving five or more sessions (as sessions 1-4 focused on treatment engagement and initial psychoeducation on trauma, dissociation, and psychosis). This cut-off is similar to that used to identify treatment non-engagement in past randomized controlled trials of CBTp (Dunn et al., 2012). For those that did engage, the last-observation-carried-forward (LOCF) method was used to impute missing data on relevant mid-therapy and end-of-therapy outcome variables. LOCF-corrected descriptive statistics for the current sample are reported in Table S1 (Supporting Information). All analyses were conducted using SPSS version 23. Results Sample characteristics Nineteen participants were recruited. The demographic and clinical characteristics of the sample are displayed in Table 1, and the flow of participants in the different phases of the study is illustrated in Figure 2. Inspection of the baseline data indicated high level of trauma exposure and trauma-related symptoms in this sample. On the BBTS-14, participants reported having been exposed to an average of nine different traumatic events. Of note, BBTS-14 scores indicated that all participants were exposed to multiple experiences of interpersonal abuse in both childhood and adulthood. All participants reported having been emotionally or psychologically mistreated over a significant period of time; the majority of the sample also reported having survived physical assaults sufficiently severe to cause bodily injuries and episodes of sexual violence, including incidents of childhood sexual abuse. Most participants had IES-R scores suggestive of possible PTSD diagnosis (i.e., 84.2% had scores >33) and DES scores suggestive of levels of dissociation similar to those observed in samples with PTSD or dissociative disorders (Lyssenko et al., 2018). Table 1. Sample characteristics (N = 19) \| Characteristic \| M \| SD \| Range \| \|-------------------------\|-------\|------\|-------------\| \| Age \| 28.1 \| 9.6 \| 16–45 \| \| Illness duration \| 11.5 \| 9.5 \| 0.3–32 \| \| Traumatic events \| 8.9 \| 4.5 \| 2–17 \| \| Emotional/psychological maltreatment exposure \| 19 (100%) \| 13 (68.4%) \| \| Physical violence exposure \| 14 (73.7%) \| 11 (57.9%) \| \| Employment \| Unemployed: 11 (57.9%); Employed: 4 (21.1%); Studying: 4 (21.1%) \| \| Sex \| Male: 8 (42.1%); Female: 11 (57.9%) \| \| Setting \| EI services: 13 (68.4%); Other: 6 (31.6%) \| \| Diagnoses \| Schizophrenia: 5 (26.3%); Unspecified non-organic psychosis: 14 (73.7%) \| Note. EI = Early intervention for psychosis. Study retention and treatment engagement Table 2 displays descriptive statistics for the primary and secondary outcome variables at the four time points of the study. As can be seen, study retention at the end of treatment was acceptable (26.3% drop out rate), but with greater missing data at the 6-month follow-up (36.8%). In terms of treatment engagement, three participants attended less than five therapy sessions. The remaining 16 participants attended an average of 17.6 sessions (range 5–24), with five participants attending all sessions offered as part of this case series. Does the intervention impact dissociation and voices? A repeated measure ANOVA was carried out to examine differences in dissociation scores across baseline, mid-therapy, and end-of-treatment assessment points. The results indicated that DES significantly decreased over the course of treatment; $F(2, 14) = 15.681, p < .001$, partial $\eta^2 = .511$. Post-estimation tests indicated that that there were significant differences between baseline and mid-therapy DES scores ($p = .002; d_{rm} = 0.966$) as well as between baseline and end-of-treatment DES scores ($p < .001; d_{rm} = 1.230$). As the PSYRATS-AH scores at the mid-therapy assessment were negatively skewed ($z_{skewness} = -3.97$), Friedman’s test was used to examine changes in hallucinations severity over time. The results indicated significant reductions in the severity of auditory hallucinations over the course of the study; $\chi^2(2) = 17.93, p < .001$. Post-hoc analyses with Wilcoxon signed-rank tests indicated that PSYRATS-AH scores decreased significantly between baseline and mid-therapy assessments ($Z = -3.02, p = .003; d_{rm} = 0.656$), with a more robust difference being observed between baseline and end of therapy ($Z = -3.30, p = .001; d_{rm} = 1.087$). Inspection of the descriptive statistics of 6-month follow-up DES and PSYRATS-AH scores indicated no deterioration in voices or dissociation, suggesting that treatment benefits were maintained. Does the intervention impact secondary outcomes? The analysis focusing on post-traumatic symptoms indicated that IES-R scores significantly decreased over the course of the study; $F(2, 13) = 16.02, p < .001$, partial $\eta^2 = .534$. Post- estimation test found significant differences between baseline and mid-therapy scores $(p = .005; d_{rm} = 0.947)$ as well as between baseline and end-of-treatment scores $(p < .001; d_{rm} = 1.195)$. As baseline PSYRATS-Del scores were negatively skewed $(z_{skewness} = -2.02)$, Friedman’s test was used to examine changes in delusion severity over time. The analysis found significant reductions in PSYRATS-Del scores over the course of the study; $\chi^2(2) = 18.74, p < .001$. Post-hoc comparisons with Wilcoxon signed-rank tests indicated that there were statistically significant improvements in delusion severity at both the mid-therapy assessment $(Z = -3.06, p = .002, d_{rm} = 1.234)$ and the of end-of-treatment assessment $(Z = -2.94, p = .003; d_{rm} = 1.079)$. Table 2. Descriptive statistics (means and standard deviations; medians and interquartile range) across study assessment points \| Measures \| Baseline (n = 19) \| Mid-Treatment (n = 15) \| End of Treatment (n = 14) \| Post-Treatment (n = 12) \| \|----------------\|-------------------\|------------------------\|---------------------------\|------------------------\| \| \| M (SD) \| Median (IQR) \| M (SD) \| Median (IQR) \| \| DES \| 54.12 (13.93) \| 49.64 (24.64) \| 37.00 (14.43) \| 27.04 (14.66) \| \| PSYRATS-AH \| 33.79 (4.25) \| 33.50 (7.00) \| 29.00 (9.16) \| 23.04 (11.04) \| \| IES-R \| 60.17 (16.96)a \| 68.00 (45.00) \| 51.07 (16.46) \| 38.36 (18.09) \| \| PSYRATS-Del \| 16.44 (7.13)a \| 17.00 (15.00) \| 8.67 (8.33) \| 8.86 (8.43) \| \| DASS-21 \| 42.58 (5.61) \| 41.00 (9.00) \| 28.67 (14.04) \| 25.71 (12.30) \| \| QPR \| 17.41 (11.01)b \| 13.00 (18.50) \| 32.53 (10.53) \| 34.38 (7.79) \| \| CHOICE \| 26.89 (17.40) \| 26.20 (19.25) \| 46.20 (21.40) \| 54.93 (23.46) \| Note. CHOICE = the CHOice of Outcome in Cbt for psychoses; DASS-21 = the short Depression and Anxiety Stress Scale; DES = Dissociative experiences scale, time bound; IES-R = Revised Impact of Events Scale; PSYRATS-AH = Auditory hallucination scale of the PSYRATS; PSYRATS-DEL = delusions subscale of the PSYRATS; QPR = Questionnaire about the Process of Recovery. a n = 18.; b n = 17. There were significant improvements in symptoms of anxiety, depression, and stress assessed through the DASS-21; $F(2, 14) = 17.687, p < .001$, partial $n^2 = .541$. Post-estimation tests indicated that there were significant differences between baseline and mid-therapy DASS-21 scores ($p = .001; d_{rm} = 1.007$) as well as between baseline and end-of-treatment scores ($p < .001; d_{rm} = 1.527$). Finally, analyses focusing on QPR scores indicated that perceived recovery significantly increased over the course of treatment; $F(2, 12) = 22.31, p < .001$, partial $n^2 = .632$, with statistically significant improvements observed at both mid-therapy ($p < .001; d_{rm} = 1.344$) and end-of-treatment assessments ($p < .001; d_{rm} = 1.582$) relatively to baseline scores. Comparable results were observed in our analyses of the CHOICE, which indicated significant overall improvements over the course of treatment, $F(2, 15) = 15.08, p < .001$, partial $n^2 = .485$, with noticeable and statistically significant gains at both mid-therapy ($p = .001; d_{rm} = 1.031$) and end-of-treatment follow-up assessments ($p < .001; d_{rm} = 1.446$). In all cases, inspection of the 6-month follow-up scores found no evidence of deterioration in any of the secondary outcome measures above, suggesting that treatment benefits were maintained beyond the end of treatment. Discussion Our work purposefully and specifically targeted dissociation and voice hearing in people with psychosis with a history of trauma and adversity. The intervention examined in this case series led to a range of promising findings. First, our primary analyses found large and statistically significant improvements on measures of dissociation and auditory hallucination severity. Of note, these improvements were already noticeable at the mid-therapy follow-up assessment, and by the end-of-therapy assessment, they were large in magnitude (i.e., $d_{rm} > 0.80$; Cohen, 1988). Furthermore, treatment gains remained robust at the final follow-up assessment conducted six months after the end of therapy. Second, our secondary analyses found similarly large and statistically significant improvement on a range of other relevant outcome measures, including delusions severity, post-traumatic symptoms, symptoms of anxiety, depression and stress as well as service user-led measures of CBTp outcomes and perceived recovery from psychosis-related difficulties. The signals of efficacy summarized above are particularly striking given the complex clinical characteristics of the participants in this study. All participants had experienced multiple traumatic events in both childhood and adulthood, including prolonged emotional maltreatment, severe physical abuse, and sexual assaults. Over half of the sample were survivors of childhood sexual abuse. At baseline, participants presented not only with distressing psychotic symptoms, but most had post-traumatic symptoms sufficiently severe to warrant a diagnosis of PTSD and levels of dissociation greater than those generally observed in previous studies with participants with psychosis (Lyssenko et al., 2018). Of note, participants’ baseline scores on the QPR were considerably lower than those observed in previous clinical trials with complex psychosis clients, such as patients with diagnoses of schizophrenia who do not respond to clozapine treatment (Morrison et al., 2018). Hence, the sample would seem to be representative of those of clients with psychosis and complex trauma found in EI services and other secondary care mental health services. Furthermore, as the intervention considered in this case series was delivered in the context of practitioners’ routine clinical practice, the findings of this case series may generalize, pending future replication, to the treatment of clients in secondary care mental health settings. The treatment appeared to be acceptable, with only three clients (15% of the sample) dropping out early in the intervention (i.e., before completing less than five therapy sessions); this figure is comparable to those observed in previous CBTp clinical trials (Dunn et al., 2012). Our findings suggest that it is possible to achieve substantial improvements in dissociation-related outcomes in clients with psychosis during relatively brief treatment periods and are consistent with other recent clinical studies, such as ongoing investigations evaluating the use of brief treatment protocols to treat comorbid depersonalization disorder in clients with psychosis (Farrelly, Peters, Azis, David, & Hunter, 2016). The observation of substantial improvements in hallucination severity during treatment phases predominantly focused on the use of strategies to manage dissociative experiences is consistent with proposals that dissociation may represent an important factor in the maintenance of hallucinatory experiences and a valuable treatment target in psychological interventions for distressing voices (Pilton et al., 2015; Berry, Bucci & Varese, 2019). The observation of substantial improvements in hallucination severity during treatment phases predominantly focused on the use of strategies to manage dissociative experiences is consistent with proposals that dissociation may represent an important factor in the maintenance of hallucinatory experiences and a valuable treatment target in psychological interventions for distressing voices (Pilton et al., 2015; Berry, Bucci & Varese, 2019). The observation of substantial improvements in hallucination severity during treatment phases predominantly focused on the use of strategies to manage dissociative experiences is consistent with proposals that dissociation may represent an important factor in the maintenance of hallucinatory experiences and a valuable treatment target in psychological interventions for distressing voices (Pilton et al., 2015; Berry, Bucci & Varese, 2019). Other recently published case series have evaluated other trauma-focused intervention techniques, in particular imagery rescripting, that have been adapted to specifically ameliorate distressing hallucinations in people with psychosis (Brand, Bendall, Hardy, Rossell, & Thomas, 2020; Paulik, Steel, & Arntz, 2019). These case series have also uncovered promising treatment effects, comparable to those reported in our investigation. Future research and intervention development work could focus on evaluating to what extent these interventions could be integrated into a single treatment protocol that could suit the varied needs of individuals with lived experience of voices and a history of trauma. Furthermore, in the light of the multiple ‘routes’ from trauma to psychotic symptoms that have been highlighted in recent studies (Williams et al., 2018), research could be conducted to understand whether specific trauma-focused intervention strategies may be better suited for targeting specific trauma-related mechanisms involved in the maintenance of psychotic symptoms (e.g., whether imagery rescripting might be more indicated when hallucinations are clearly trauma-related in content and linked to trauma intrusions; whether dissociation-focused work might be acceptable and beneficial only to clients with high levels of dissociative experiences). In the present case series, the rationale for embedding dissociation-focused therapeutic work within CBTp was to improve treatment outcomes for voices in clients with histories of trauma. In line with this overarching objective, and to maximize both intervention acceptability and likelihood of benefit, our treatment protocol permitted the use of cognitive behavioural change strategies that could directly impact voices and voice-related distress (e.g., challenging maladaptive appraisals of voices). Therefore, we cannot exclude the possibility that the effects on voices observed in this case series might be attributable to these ‘voice-specific’ strategies rather than the additional dissociation work we aimed to evaluate. Future studies aiming to investigate the value of therapeutic work considering dissociation in clients with distressing voices may benefit from using more specific intervention protocols which solely target dissociation. Alternatively, researchers could employ more sophisticated research designs, such as dismantling studies, to examine more specifically this component of the intervention. Other limitations should be considered when interpreting the findings of this research. First, the lack of a control group is a significant limitation; our design cannot clarify whether the treatment gains we observed are specifically attributable to the intervention rather than to the passage of time. Compounded with the fact that the case series design we employed did not allow for the masking of outcome assessments, it is likely that the effects observed in our study are inflated. Second, we conducted multiple statistical tests on a range of outcome variables, leading to the possibility of inflated type 1 errors (i.e., false positives). We note, however, that the effects observed in our study are highly significant; most would survive the use of very conservative corrections for multiple testing, such as the application of the Bonferroni correction to the entire set of inferential tests conducted in the study (21 tests, leading to a threshold of $p = .0024$). Only three follow-up tests would not survive the application of this conservative correction. These include the follow-up comparison between baseline and mid-treatment PSYRATS-AH scores ($p = .003$), baseline and mid-treatment IES-R scores ($p = .005$), and baseline and mid-treatment PSYRATS-Del scores ($p = .003$). Given the promising findings and acceptable attrition rates observed in this study (which are in line with those of previous definitive efficacy trials of CBTp; e.g., Morrison et al., 2018), a future clinical trial using a randomized controlled design is warranted and needed to evaluate more robustly the approach piloted in this case series. Future studies may also employ more comprehensive and sensitive assessments of the primary and secondary outcomes considered in this investigation. For example, the assessment of dissociation could benefit from the use of recently developed and carefully validated state measures of dissociative symptoms, such as the Dissociative Symptoms Scale (Carlson et al., 2018). Furthermore, as dissociation may be involved in the maintenance of psychotic experiences other than voices, future trials could benefit from assessing hallucinations in other sensory modalities (e.g., Dudley, Aynsworth, Cheetham, McCarthy-Jones, & Collerton., 2018; Longden, House, & Waterman, 2016) as well as other positive symptoms of psychosis such as paranoia (e.g., Pearce et al., 2017). In summary, the findings of this case series suggest that dissociation is a valuable target in psychological interventions for psychosis, but further research is required to corroborate these early findings. Our results can inform future clinical trials of both this specific treatment approach and broader interventionist-causal trials aimed at improving treatment outcomes for distressing psychotic experiences reported by trauma survivors (e.g., Brand et al., 2017). The findings of this case series suggest that when voices are reported during clinical assessments, it is advisable to routinely enquire about the experience of dissociation and trauma. When relevant, clinicians should include information about dissociative experiences and traumatic life events in psychological formulation developed collaboratively with clients and offer interventions that include strategies aimed at improving the management of dissociation. Acknowledgements The authors would like to acknowledge the contribution of Drs Rachel Sellers, Lee Mulligan, Jasper Palmier-Claus, and Alison Brabban for the support provided in the delivery of this case series. Conflicts of interest All authors declare no conflict of interest. Author contribution Filippo Varese, PhD, ClinPsyD (Conceptualization; Formal analysis; Investigation; Methodology; Project administration; Supervision; Writing – original draft) Maggie Douglas (Investigation; Resources; Writing – review & editing) Robert Dudley (Conceptualization; Data curation; Formal analysis; Investigation; Project administration; Supervision; Writing – original draft) Samantha Bowe (Conceptualization; Writing – review & editing) Thomas Christodoulides (Investigation) Stephanie Common (Investigation) Tim Grace (Investigation) Victoria Lumley (Investigation) Laura McCartney (Investigation) Sonia Pace (Investigation) Thomas Reeves (Investigation) Anthony P. Morrison (Conceptualization; Resources; Supervision; Writing – review & editing) Douglas Turkington (Investigation; Project administration; Supervision; Writing – review & editing) Data availability statement The data that support the findings of this study are available on request from the corresponding author, FV. References Allen, J. G., Coyne, L., & Console, D. A. (1997). Dissociative detachment relates to psychotic symptoms and personality decompensation. Comprehensive Psychiatry, 38, 327–334. https://doi.org/10.1016/S0010-440X(97)90928-7 American Psychiatric Association (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC: Author. Badcock, J., Chhabra, S., Maybery, M. T., & Paulik, G. (2008). Context binding and hallucination predisposition. Personality and Individual Differences, 45, 822–827. https://doi.org/10.1016/j.paid.2008.08.016 Bailey, T., Alvarez-Jimenez, M., Garcia-Sanchez, A. M., Hulbert, C., Barlow, E., & Bendall, S. (2018). 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Psychological Medicine, 42, 1025–1036. https://doi.org/10.1017/S0033291711001826 Varese, F., Smeets, F., Drukker, M., Lieverse, R., Lataster, T., Viechtbauer, W., ... Bentall, R. (2012). Childhood adversities increase the risk of psychosis: A meta-analysis of patient-control. Prospective- and Cross-sectional Cohort Studies Schizophrenia Bulletin, 38, 661–671. https://doi.org/10.1093/schbul/sbs050 The following supporting information may be found in the online edition of the article: Table S1. Descriptive statistics (means and standard deviations; medians and interquartile range) for the last observation carried forwards analyses (n = 16)	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2529, 1 ], [ 2529, 6047, 2 ], [ 6047, 10143, 3 ], [ 10143, 13848, 4 ], [ 13848, 17658, 5 ], [ 17658, 21570, 6 ], [ 21570, 23659, 7 ], [ 23659, 27068, 8 ], [ 27068, 30177, 9 ], [ 30177, 30966, 10 ], [ 30966, 32653, 11 ], [ 32653, 36401, 12 ], [ 36401, 40808, 13 ], [ 40808, 44598, 14 ], [ 44598, 47666, 15 ], [ 47666, 52089, 16 ], [ 52089, 55720, 17 ], [ 55720, 59956, 18 ], [ 59956, 60206, 19 ] ] }
6f3254850ced71279e98b4acb9aed776ca00b3bf	{ "olmocr-version": "0.1.59", "pdf-total-pages": 36, "total-fallback-pages": 0, "total-input-tokens": 68687, "total-output-tokens": 13271, "fieldofstudy": [ "Education" ] }	The Students’ Attitudes towards the NESTs versus NNESTs and their Impacts on the Students’ Motivations to Learn English Language at KAU Haneen Saad Al Muabdi Jeddah, Saudi Arabia Author: Haneen Saad Al Muabdi Thesis Title: The Students’ Attitudes towards the NESTs versus NNESTs and their Impacts on the Students’ Motivations to Learn English Language at KAU Institution: English Department, Faculty of Languages and Translation, King Khalid University Degree: MA Major: Applied Linguistics Year of award: 2021 Supervisor: Dr. Mazeegha Al Tale’ ORCid ID: https://orcid.org/0000-0002-8253-2718 Keywords: EFL learners, motivation, NEST, NNEST, Saudi students’ attitudes Abstract: Motivation is one of the crucial aspects of second language acquisition. Students' motivation can be influenced by their teachers. The present study aims to investigate the impact of the two types of teachers on EFL learners' motivations to learn English. These are NESTs (Native English-speaking teachers) and NNESTs (native English-speaking teachers). Hence, it examines learners' attitudes and perceptions towards the two types of teachers. This study employed a mixed method by distributing a questionnaire contains quantitative and qualitative tools. It consists of twenty items of Likert scales and two open-ended questions. The present study subjects are 31 female students at King Abdulaziz University in Jeddah, Saudi Arabia. The results of the study demonstrate that learners have a positive attitude toward NESTs and NNESTs. Despite that, the tendency to learn with NNESTs is higher than NESTs. The findings also show that both types of teachers motivate students to learn English. Moreover, it suggests that the methodology and teachers' personalities are more important than the teachers' nativeness. Cite as: Al Muabdi, H. S. (2021). The Students’ Attitudes towards the NESTs versus NNESTs and their Impacts on the Students’ Motivations to Learn English Language at KAU, King Khalid University, Saudi Arabia (M.A.Thesis). Retrieved from Arab World English Journal (ID Number: 280) November, 2021: 1- 35. DOI: https://dx.doi.org/10.24093/awej/th.280 The Students’ Attitudes towards the NESTs versus NNESTs and their Impacts on the Students’ Motivations to Learn English Language at KAU By Haneen Saad Al Muabdi A project submitted in partial fulfilment of the requirement for the degree of MA in Applied Linguistics 1440-1441 (2020-2021) Supervised by Dr. Mazeegha Al Tale’ Abstract Motivation is one of the crucial aspects of second language acquisition. Students' motivation can be influenced by their teachers. The present study aims to investigate the impact of the two types of teachers on EFL learners' motivations to learn English. These are NESTs (Native English-speaking teachers) and NNESTs (native English-speaking teachers). Hence, it examines learners' attitudes and perceptions towards the two types of teachers. This study employed a mixed method by distributing a questionnaire contains quantitative and qualitative tools. It consists of twenty items of Likert scales and two open-ended questions. The present study subjects are 31 female students at King Abdulaziz University in Jeddah, Saudi Arabia. The results of the study demonstrate that learners have a positive attitude toward NESTs and NNESTs. Despite that, the tendency to learn with NNESTs is higher than NESTs. The findings also show that both types of teachers motivate students to learn English. Moreover, it suggests that the methodology and teachers' personalities are more important than the teachers' nativeness. Keywords: EFL learners, motivation, NEST, NNEST, Saudi students’ attitudes. Acknowledgement: All praises be to Allah who gave me the ability to fulfill this crucial part of my study. I also extend my gratitude towards my supervisor Dr. Mazeegha Al Tale’ for her valuable advice, time, and continuous encouragement and guidance. Her patience and motivation have been vital for my success. I would also like to thank my classmates for their support and reassurance throughout this project’s journey. \| Table of contents: \| Page \| \|---------------------------------------------------------------------------------\|------\| \| Abstract \| I \| \| Acknowledgement \| II \| \| Table of contents \| III \| \| 1. Introduction \| \| \| 1.1. Statement of the Problem \| 1 \| \| 1.2. Significance of the Study \| 3 \| \| 1.3. Study Questions \| 3 \| \| 2. Review of Related Literature \| \| \| 2.1. Native and Non-native English Teachers \| 4 \| \| 2.2. Learners’ Attitudes towards NESTs and NNESTs \| 5 \| \| 3. Methodology \| \| \| 3.1. Participants \| 7 \| \| 3.2. Research Instrument \| 7 \| \| 3.3. Research Procedures \| 8 \| \| 4. Results \| \| \| 4.1. Learners’ Motivation and Attitudes Towards NESTs \| 10 \| \| 4.2. Learners’ Motivation and Attitudes Towards NNESTs \| 11 \| \| 4.3 Students’ preference of the two types of teachers and why \| 13 \| \| 4.4 learners’ perceptions of the most important qualities that motivate them \| 13 \| \| 5. Discussion \| \| \| 5.1. Learners’ motivation and attitudes of NESTs \| \| \| 5.1.1 Learners’ motivation and preference of NESTs and speaking: \| 15 \| \| 5.1.2 Learners motivation and preference of NESTs accent and culture: \| 15 \| \| 5.1.3 Learners’ motivation and preference of NESTs grammar and language skills: \| 17 \| \| 5.2. Learners’ motivation and attitudes of NNESTs \| \| 5.2.1 NNESTs motivate learners because they share the same language 5.2.2 NNESTs motivate learners because they feel more relaxed with them 5.3. The methodology and personality are the most factors that motive learners \| 6. Conclusion and Recommendations \| 21 \| \| References \| 23 \| \| Appendix \| 26 \| CHAPTER ONE: INTRODUCTION 1. Introduction: Motivation is one of the most critical factors in learning a new language. Most researchers and teachers would admit that motivation is a very significant, if not the most significant factor in learning languages (Du, 2009). Motivation is defined as a set of effort, desire, and favorable attitudes to achieve the learning goals (Gardner, 1985). Without this important combination, it is difficult to ensure constant and effective learning. It is the stimulus that keeps learners progressing in their learning journey. First of all, it is important to present the earliest second language acquisition theories to understand the emergence of motivation in second language learning. A popular concept that relates to motivation is the Affective Filter hypothesis. It was initially presented by Dulay and Burt (1977), who explained it as a barrier that prohibits language input from accessing the mental Language Acquisition Device as it prevents the language acquisition process (Nath, et al., 2017). Then, Krashen (1958) incorporated the Affective Filter Hypothesis as one of his five Input Hypotheses. Krashen’s hypotheses are Acquisition-Learning Distinction, Monitor Hypothesis, Natural Order Hypothesis, Input Hypothesis, and Affective Filter Hypothesis (Nath, et al., 2017). The Affective Filter Hypothesis is what matters here, as it describes the role of motivation in learning a new language. Krashen (1982) introduced three major factors that influence the Affective Filter, which are motivation, self-confidence, and anxiety (Nath, et al., 2017). To illustrate, the filter becomes high when the learner is unmotivated, unconfident, and anxious (Du, 2009). Thus, low-motivated learners are not able to benefit from the input they are exposed to because the increased filter prevents them from obtaining the linguistic input. Hence, the evidence suggests that motivation is crucial for enhancing the learning process of EFL (English as a Foreign Language) learners. However, several factors influence motivation. One of them is the learners’ attitudes. Gardner and Lambert (1959) were the first ones who shed light on the strong relationship between motivation and positive attitudes towards a language and its speakers (Todor, Deigi, 2016). Another influential variable that motivates learners are teachers. Yilmaz et al. (2017) pointed out that learners’ motivation is highly affected by their teachers. In this regard, there are two major types of teachers in the EFL context. Native English-speaking teachers and non-native English-speaking teachers. A native speaker (NEST) can be identified as a person with English as her/his first language and has spoken it since childhood. On the other hand, a non-native speaker (NNEST) refers to a person whose mother tongue is not English and has acquired it as a second or foreign language (Al-Nawrasy, 2013). It is considerably argued that NESTs are better teachers than NNESTs because they teach their first language. Some scholars claim that NESTs are the best and ideal teachers because of their superior command of English (Nawrasy, 2013). This assumption formed the concept of employing NESTs in colleges, language institutions, and universities, with no consideration of their qualifications or experience as teachers (Alseweed, 2012). Phillipson (1992) named this as a Native speaker fallacy and defined it as the misconception held by many individuals that the native speaker is a stronger language teacher than a non-native speaker. (as cited in Huys, 2017). The question here is, are the students affected by this concept? EFL learners’ attitudes towards the two types of teachers are still debatable (Al-Nawrasy, 2013; Huys, 2017; Phothongsunan, 2018; Alqahtani, 2019). However, only a few researches were conducted to look at this issue by investigating the impact of the two types of teachers on students’ motivations to learn English, such as (Adara, 2018&2020), especially in the EFL Saudi context. 1.1 Statement of the problem: Unfortunately, in EFL setting, NESTs and NNESTs are seen differently. They are classified according to their linguistic background, not their teaching abilities. According to Moussu (2010), it is widely considered that NESTs are the ideal English teachers (as cited in Alghofaili & Elyas, 2019). Undoubtedly, this concept leads to hiring discrimination and a preference for nativeness over qualifications. As Mahboob (2004) pointed out, program managers consider "nativeness" to be very important when it comes to hiring teachers. This assumption prevailed and spread in the Saudi EFL context without considering the students' attitudes and motivations. Hence, this study tackles the motivation angle and provides an essential investigation about learners' motivation in relation to the different types of teachers in EFL Saudi context. 1.2 Significance of the study: Although extensive research in the Saudi context has been carried out on EFL learners’ attitudes and achievements in relation to NESTs and NNESTs (Al-Nawrasy, 2013; Alghofaili & Elyas, 2019), no study exists which surveyed the EFL learners’ motivations. Thus, the novelty of the current study is to put insight into this matter. It explores EFL learners’ attitudes regarding the two types of teachers and then answers whether English teachers' type impacts the learners’ motivations or not and why. Specifically, it intends to answer the following questions: 1.3 Research questions: 1-What are the attitudes of KAU students towards NESTs and NNESTs? 2-What is the impact of the two types of teachers on the students’ motivation? CHAPTER TWO: REVIEW OF RELATED LITERATURE 2.1 Native and Non-native English teachers: For over 20 years, discussions have been held to decide the best English language teacher (Al-Nawrasy, 2013). The issue has grown in importance in light of the debate regarding the superiority of NESTs over NNESTs. It has been the subject of a large number of published studies (Huys, 2017; Alghofaili & Elyas 2017&2019). Unfortunately, non-native speakers are remarked as those with restricted access to the language or with few native speakers' features (Davies 2004, as cited in Adara, 2019). Due to this claim, NESTs are regarded as the language's ideal teacher (Moussu, 2010, as cited in Alghofaili, Elyas 2017). However, the literature shows contradictory findings of the best English teacher. Alqahtani (2019) conducted a study in Riyadh, Saudi Arabia. The researcher found that NESTs outperform NNESTs as they provide effective teaching styles and methodology that meet the students’ needs. Also, the subjects of the study exhibited explicit preference and satisfaction for NESTs. However, claims that advocate NESTs as better than NNESTs in language teaching are still under intense investigation about their validity. According to Bueno (2006), no research has proven this claim (as cited in Adara, 2019). On the other hand, Alghofaili and Elyas (2017) employed a questionnaire to examine the impact of NESTs and NNESTs on the students' achievement in KAU. The findings indicate that teachers' nativeness has no noticeable influence on the learning process, instead, the teacher’s personality is more important. Thus, students seem to esteem other aspects other than the teachers’ native language. Another study by Alghofaili and Elyas (2019) investigated the impact of NESTs and NNESTs on the Saudi EFL learners’ achievements in listening and speaking skills. The results revealed that the nativeness of teachers does not influence the speaking and listening skills of Saudi EFL students. It is possible to say that even the improvement in students’ performances is not significant enough to favor NESTs over NNESTs. 2.2 Learners’ attitudes towards NESTs and NNESTs: There are arguments regarding learners’ attitudes towards NESTs and NNESTs. Several studies were carried out in various contexts to examine the learners’ attitudes that demonstrated a considerable contradiction in their results. Some of them will be discussed in this section. Urkmez (2015) conducted a study in Turkey to investigate the preference towards NESTs and NNESTs of 120 Turkish students. The finding demonstrated that the learners' views of their NESTs and NNESTs were significantly different. The participants preferred NESTs because they believed NESTs were better at teaching speaking, listening, and cultural knowledge. At the same time, they think that NNESTs were better at teaching grammar and writing. Similarly, Huys (2017) investigated the students’ preference regarding NESTs and NNESTs in Nijmegen. The results showed that there was an overall preference for NESTs. However, the preference regarding the specific subject areas was not only related to NESTs. Most of the students preferred to learn pronunciation with NESTs and grammar with NNESTs. Moreover, Alseweed (2012) conducted a study in Qassim, Saudi Arabia. His research aimed to examine the students’ perception of their NESTs and NNESTs in English classrooms. The findings demonstrated a higher preference for NESTs. Similar to Phothongsunan’s study (2018) in Bangkok. It concludes that most of the participants preferred to study with NESTs, and this positively affected their behavior and motivation to learn. Besides, the participants provided a comparison between the two groups of teachers in their teaching method, marking, language proficiency, personality, etc., but the most preferred qualities of the two types of teachers were related to their personalities. It is interesting to note how these students stated that they preferred NESTs, but when it comes to the detailed investigation, such as the subject preference, it appears that there was a slight preference or no preference at all for a specific type of teacher over the other. This raises a question, are the learners affected by the native speaker fallacy? It seems EFL learners lacked awareness regarding this matter. On the contrary, in Indonesia, Adara (2018) examined students’ motivation in learning English as a second language with NESTs and NNESTs. The findings revealed that most participants preferred NNESTs over NESTs because they had the same mother tongue. Similarly, in Braine and Lings’ (2007) study in Hong Kong, the researchers stated that the students had a positive attitude towards NNESTs, although they shared some weaknesses of NNESTs. Interestingly, the students from the final year showed a greater favorable attitude for NNESTs than the students from the first year. The earliest learners likely had more knowledge and awareness than the new students based on their long-term experience. Mahboob (2004) in Michigan investigated students’ perceptions of NESTs and NNESTs. The researcher asked them to write an essay regarding their preference. The findings demonstrated that students did not have an apparent preference for the two kinds of teachers. Also, they presented strength points for NNESTs more than NESTs. Overall, it is normal to find differences in learners’ attitudes and preferences, but the issue is when the teaching facilities react on a general assumption that says learners prefer NESTs over NNESTs. The learners’ attitudes are important as they wider our understanding of the issue and help to provide an effective learning environment in EFL classrooms. CHAPTER THREE: METHODOLOGY 3.1 The participants: The study samples are 31 female students from different majors at King Abdulaziz University in Jeddah, Saudi Arabia. The subjects’ majors are Statistics, Business Administration, Public Administration, and Law. They were chosen because the two types of teachers have taught them. The age range of the participants is from 19 to 23. The following chart describes the subjects’ English level. ![Figure 3.1. The participants’ English level](image) 3.2 The research instruments: The research design is a mixed method as it carries tools for quantitative and qualitative data. This method was employed to obtain a broader understanding of the collected data. To ensure that the participants understand the key terms NESTs and NNESTs, the researcher added definitions at the beginning of the questionnaire. The questionnaire has three sections: demographic questions, twenty Likert scale items, and open-ended questions. The demographic section contains five questions, age, gender, English level, and a question that asks if they are have been taught by the two types of teachers. The second section was taken from a previous study (Adara, 2020). It comprises twenty Likert scale items with four response options: strongly agree, agree, disagree, and strongly disagree. The first ten statements examine the learners’ motivation and attitudes towards learning English with NESTs. In contrast, the next ten items examine the learners’ motivation and attitudes towards learning English with NNESTs. In the third section, the researcher added two open-ended questions. These questions are set for more clarification and to enrich the data. The first question is “What type of the two types of teachers do you prefer? Why?” this question was used to allow the participants to express themselves because the Likert scale allows only for limited answers. The second question is “What are the most important qualities of English teachers that motivate you to learn?” To identify the fundamental and most crucial English teacher characteristics that motive learners. The open-ended are optional to give more space for participants who want to share their own opinions and experiences. 3.3 The procedures: As mentioned, the Likert scales section was adopted from a previous study (Adara, 2020). The researcher changed the word “Bahasa Indonesia” into “Arabic” because the present study's subjects are native Arabic speakers. Also, the content of the questionnaire was translated into Arabic to make it easier for the participants to answer it correctly. Google Forms was employed to create and design the survey. It took more than two weeks to receive forty-seven responses. Sixteen of them were excluded because they were not the target subjects. The quantitative data were analyzed using the SPSS program and Microsoft Excel. SPSS was used to get the mean and standard deviation, while Excel was used to get the rank. The qualitative data were translated into English and used to support the quantitative data and to get a more comprehensive understanding of the issue. CHAPTER FOUR: RESULTS OF THE STUDY 4.1 Learners’ Motivation and Attitudes Towards NESTs: The results of the study demonstrate that KAU’ learners have positive attitudes towards NESTs. The results also indicate that they are motivated to learn English with NESTs. These results are shown in Table 1 below. Table 1: Mean of Learners’ Motivation and Attitudes Towards NESTs \| statement \| Mean \| Std Deviation \| \|---------------------------------------------------------------------------\|------\|---------------\| \| 1- I want to speak as fluent as my native English-speaking teachers. \| 3.74 \| .445 \| \| 2- Native English-speaking teachers motivate me to speak English more in the classroom. \| 3.16 \| .860 \| \| 3- I feel more excited to study English with native teachers. \| 3.03 \| .875 \| \| 4- I enjoy listening to English spoken by native speakers. \| 3.03 \| .718 \| \| 5- Native English-speaking teachers have better accents than non-native teachers. \| 2.97 \| .752 \| \| 6- If I want to travel abroad, I have to practice speaking with native teachers. \| 2.87 \| .922 \| \| 7- I like learning about American or British cultures from native speakers. \| 2.82 \| .395 \| \| 8 -Learning English with native teachers is more interesting than non-native teachers. \| 2.81 \| .980 \| \| 9 - Native English-speaking teachers motivate me to learn grammar. \| 2.74 \| .999 \| \| 10- My speaking, listening, reading and writing skills of English are improved after being taught by native English-speaking teachers. \| 2.59 \| .682 \| As shown in the above table, the participants wish to speak English fluently like their NESTs (3.74). The participants also believe that native English-speaking teachers motivate them to speak English more in the classroom (3.16). The participants feel more excited to study with NESTs (3.03). The subjects enjoy listening to the language used by NNESTs (3.03). The results indicate that (2.97) believe NESTs have better accents than NESTs. The participants believe that if they plan to travel abroad, they have to practice English with NESTs (2.87). The subjects also like to learn about the American or British cultures from NESTs (2.82). The participants believe that learning English with NESTs is more interesting than learning with NNESTs (2.81). Regarding grammar, participants believe that NESTs motivate them to learn grammar (2.74). The subjects believe that their speaking, listening, reading and, writing skills of English are improved after being taught by native English-speaking teachers (2.59). As shown in the Weighted Mean Table 1, the participants have positive attitudes towards NESTs, and they are motivated to learn English with NESTs (2.970). 4.2 Learners’ Motivation and Attitudes Towards NNESTs: The study's findings indicate that KAU's students have a positive attitude toward NNESTs. They are also motivated to learn English with NNESTs. These findings are presented in Table 2 below. Table 2: Mean of Learners’ Motivation and Attitudes Towards NNESTs \| Statement \| Mean \| Std Deviation \| \|-----------------------------------------------------\|------\|---------------\| \| 11- If I don’t understand something, I can ask in Arabic. \| 3.48 \| .570 \| As shown in table 2, the participants use Arabic in classrooms if they do not understand something (3.48). They also indicate that NNESTs understand what they say in English and Arabic (3.42). The participants believe that NNESTs can explain difficult lessons easily (3.39). According to the subjects, NNESTs use more activities to help them understand English (3.29). The participants believe they study English better with NNESTs (3.19). The respondents feel more relax to study with NNESTs (3.10). Also, they believe that NNESTs know how hard it is to learn English (2.94). The subjects believe that NNESTs provide cultural knowledge like NESTs (2.90). The participants like to listen to the language spoken by NNESTs (2.84). Regarding motivation, the participants believe that NNESTs motivate them to learn English (2.74). In the end, the respondents have positive attitudes towards NNESTs, and they are encouraged to learn English with them, as shown in the Weighted Mean (3.129). 4.3 Students’ preference of the two types of teachers and why: The first question of the open-ended question is “What type of the two types of teachers do you prefer? Why?” All of the participants did not answer this question. Only Twenty-six learners answered it. However, sixteen of them reported that they prefer NNESTs, eight prefer NESTs, and two prefer both types of teachers. Also, few participants answered the second part of the question. Regarding the NNESTs, three of the participants justify their preference for NNESTs because they share the same language. The first participant stated, “I prefer NNEST because they switch to Arabic if I do not understand,” the second students wrote, “I prefer NNESTs because they use English and Arabic to explain difficult lessons” the third respondents stated” I prefer NNESTs because they can explain the lessons well in Arabic. It helps me to understand” one student wrote” I prefer NNESTs because they know how hard it is to learn English. Lastly, one respondent stated, “I prefer NNESTs because their accents are easier to understand”. In regard to NESTs, one learner stated that “I prefer NESTs because they help me learn the correct pronunciation.” Lastly, another student justifies her preference for NESTs by saying, “they are the best.” 4.4 learners’ perceptions of the most important qualities that motivate them: The second question is “What are the most important qualities of English teachers that motivate you to learn?”. The respondents' answers were related to two categories which are methodology and personality. Six students emphasized the methodology aspect. These are some of their suggestions "establish incremental practicing activities," "using English videos," and "preparing classes to practice English with each other." Also, one student state that" the length of the lessons is what makes them boring". Regarding the personality, it was highlighted by five participants. One student wrote, "the teacher and students' relationship should be close to know our difficulties and motivate us". Similarly, another student revealed, "the teacher who respects and considers the student's capabilities." One respondent reported, "the teacher who does not diminish the student who is unfamiliar with the language.". Lastly, two participants stated that the teachers' patience is one of the essential characteristics that motive learners. The overall results indicate that learners have a positive attitude towards both types of teachers, and both motivate them to learn English. Nevertheless, the tendency to learn from NNESTs is higher than the NESTs. This appears in the Weighted Mean of the two sections. In the NESTs' section, the Weighted Mean (2.970), while in the NNESTs' section, it is (3.129). It also occurs in the first open-ended question, when sixteen out of twenty-six replies show a preference for NNESTs over NESTs while only eight responses go with NESTs. CHAPTER FIVE: DISCUSSION 5.1. Learners’ motivation and attitudes of NESTs: The following section previews learners’ attitudes and motivation of NESTs. It will be discussed in relation to the related literature. 5.1.1 Learners’ motivation and preference of NESTs and speaking: The results show that the participants wish to speak English fluently like their NESTs. Similar to the previous study by Mahboob (2004), which investigated the learners' preferences to NESTs and NNESTs regarding the oral skills, its findings indicated that the learners prefer NESTs as being an ideal model in teaching oral skills. Also, Ürkmez (2015) found that 96% of the 120 Turkish students prefer NESTs over NNESTs for teaching speaking skills. However, most English learners regard fluency as the most essential skill (Alghofaili, Elyas, 2019). Considering that, the noticeable preference for NESTs at teaching speaking in many contexts is understandable. Since students consider native speakers are the only teachers who know the true and appropriate English (Amine, 1994, as cited in Photongsunan 2018) It appears that NESTs motivate learners to speak the target language. This can be explained as follows: in addition to NESTs speaking ability which makes them favorable for learners, NESTs force learners to use the target language because it is their only way for communication. Ma (2012) argues that NESTs provide an authentic English-speaking atmosphere by being unable to speak in students' first language to the point that students are required to use English (as cited in Adara, 2020). Unlike NNESTs who use and allow learners to use their first language when needed. 5.1.2 Learners motivation and preference of NESTs accent and culture: As seen in the results, learners enjoy listening to the language of NESTs. This can be explained by their agreement on the fifth statement, which says that NESTs have better accents than NNESTs (2.97). It indicates that learners prefer to be exposed to the target language used by a person who speaks it natively. According to Phothongsunan (2018), students view teachers with non-native accents as less qualified and unfavorably when compared to native teachers. However, this is not the case of all students. For instance, a student of the current study stated that "I prefer NNESTs because I understand their accents". This statement is important because it demonstrates the diversity of learners' preferences. NNESTs aren't necessarily thought to be deficient in comparison to NESTs when it comes to speaking skills. Similarly, in Braine and Lings' (2007) study, the majority of the students stated that they prefer to learn English from NNSETs rather than NESTs with more prestigious accents. Students choose the local and familiar accent because it is easier for them to understand. Huys (2017) also found that learners will not switch classes if they have a teacher with a foreign accent. Overall, despite the significance of learners’ perceptions, they are not enough. It is important to support these findings by examining the real impact of a native's accent on learners' speaking skills. For instance, Al-Nawrasy (2013) conducted a study on the learners' speaking proficiency when they studied with NESTs and NNESTs. The researcher found no significant difference among students' achievement in speaking skills. The current findings suggest that learners like to know about the foreign culture from NESTs. Similar to Urkmez's (2015) study, which reveals that 84% of learners believe that they would learn more about the target culture with NESTs. Moreover, in Alseweed’s (2013) study learners stated that NESTs are a real embodiment of the target culture, and he/she can teach his/her language more effectively than a teacher from another culture. Therefore, students believe that NESTs are the authentic sources of the target culture. It is more appealing for them to learn about the new culture from NESTs. This corresponds to the sixth statement (2.87) which indicates that subjects desire to practice English with NESTs, if they plan to travel abroad, as traveling requires knowledge of the foreign culture. 5.1.3 Learners’ motivation and preference of NESTs grammar and language skills: Although the subjects demonstrate a positive attitude for NESTs. NESTs’ grammar instructions and learners’ development were the two points that received the least agreement from subjects. Likewise, the literature indicates that NNESTs are better at teaching grammar (Mahboob, 2004; Alseweed, 2012; Urkmez, 2015). A possible explanation for this may be that NNESTs studied the grammar and the structure of the language intensively, unlike NESTs who acquired this part of the language. Ma and Ping (2012) stated that when it comes to teaching grammar, NESTs often rely on their grammatical intuition, which is not always reliable (as cited in Alghofaili, Elyas, 2017). The fluency of the NESTs does not automatically fulfill grammar instructions. Grammar is more connected to accuracy. Thus, being a fluent teacher does not necessarily mean that she or he can effectively teach his or her native tongue. However, this argument does not apply to every NEST. It does, nevertheless, clarify why EFL learners prefer NNESTs for grammar instructions. According to the results, it is conceivable to say that there is no significant improvement in learners’ skills after being taught by the NESTs. Similar to the finding of Alghofaili and Elyas’ (2019) study, which resolves that the nativeness of teachers has no remarkable impact on the learners’ achievements. It is important to note that learners strongly promoted NESTs for teaching speaking and listening over NNESTs, but their agreements decreased when they were asked about the NESTs’ impact on their skills. Consequently, a possible explanation for this might be that the concept of nativeness may influence learners because their positive attitudes towards NESTs do not seem to be reflected in their motivations and accomplishments. 5.1. Learners’ motivation and attitudes of NNESTs: The following section previews learners’ attitudes and motivation of NNESTs. It will be addressed in light of previous research. 5.2.1 NNESTs motivate learners because they share the same language: Based on the current results, the participants are motivated to learn with NNESTs because they have the same mother tongue. Sharing one language enables teachers to classify complex ideas via switching to the native language. It also allows learners to use their first language when they cannot find the proper expression. Comparable to Braine& Lings’ (2007) results which indicate that learners show positive attitudes towards NNESTs because in discussing complex issues in English classes, NNESTs might use the students' first language. Adara (2018) also found that students preferred NNESTs over NESTs because they share the same native language. In the Saudi EFL context, nativeness acts as a constraint for developing fresh English students. Students graduate from high school with insufficient English skills, and then they shock by a native English speaker who does not speak their language. It influences the mutual understanding between the teachers and the students. Without a doubt, it ultimately causes the learners to participate less in the class. The former finding is emphasized by the subjects’ statements in the open-ended questions, where at least three students justified their preference for NNESTs by stating, “I prefer NNESTs because they switch to Arabic if I do not understand”. However, using the first language is a double-edged sword. Total dependence on the first language in classrooms is not advantageous in language improvement. The ability to shift to Arabic, if it is needed, raises the learners' chance to understand the lessons. NESTs do not have that privilege. Students' exposure to English is not affected by the limited and careful use of the mother tongue in an English classroom; instead, it can help in the teaching and learning processes (Tang, 2002). The second reason that makes lessons easier with NNESTs occurs in the fourteenth statement (3.29), which shows that learners agree that NNESTs use various activities. Braine and Lings (2007) state that students favor NNETs because they use effective teaching English activities, as they had a similar educational process. Most of NNESTs’ knowledge was obtained through intensive academic courses because the English language is not their mother tongue. Therefore, they had been exposed to plenty of teaching and learning techniques that sharpen their abilities in English language teaching. 5.2.2 NNESTs motivate learners because they feel more relaxed with them: The learners appear to appreciate the common culture and language. The ability to use Arabic in classrooms gives learners a sense of comfort. Learners also feel more relaxed around NNESTs since they had been gone through the same learning experience. As found in the current study, the subjects agree that NNESTs know how challenging it is to learn English. When the students find their teachers aware of their difficulties and needs it reduces their stress and anxiety. Likewise, Alseweed (2012) noted that learners believe that NNESTs are more aware of their difficulties and challenges than NESTs. Overall, a relaxing classroom atmosphere increases learners’ motivation. Based on the results, it is hard to ensure what learners prefer on cultural instructions, but it is possible to state that learners have a natural preference regarding this matter. However, “NNS English teachers can also help students understand the culture of English, even though they are not English native speakers” (Chang, 2016, as cited in Huys 2017). 5.3.1 The methodology and personality are the most factors that motive learners: In this section, most of the learners’ responses are linked to the atmosphere of the classrooms in which they find close, supportive teachers who provide an exciting and motivating environment. It is vital to note that the subjects emphasize certain aspects that are not related to the native language of the teachers. Teachers can offer learners a motivating learning atmosphere regardless of their linguistic background. It matches with the findings of a previous study which suggests that the “teacher’s personality is more involved in the classroom communications and interactions than is the teacher’s nativeness” (Alghofaili, Elyas, 2017, p.8) Therefore, the nativeness concept is a myth that underestimates other more critical factors for good teachers: their teaching methodologies and personality. CHAPTER SIX: CONCLUSION AND RECOMMENDATIONS 6. Conclusion and Recommendations The importance of nativeness in the EFL contexts is an issue that has been under debate in various contexts. This study attempts to provide insight into this issue by targeting an essential aspect of second language acquisition which is motivation. Specifically, it examined the learners’ attitudes towards NESTs and NNESTs. It also looked into the effects of the two types of teachers on the students’ motivation to learn English. The results of the study were obtained via qualitative and quantitative instruments in the form of a survey. The findings demonstrate that the subjects who are female students at KAU have a positive attitude towards the two types of teachers. The results also indicate that both types of teachers motivate them to learn English. Nevertheless, the participants show the tendency to learn from NNESTs is higher than the NESTs. It appears that the learners are more attracted to learn speaking and listening skills from NESTs because they believe they have better accents, while they believe that NNESTs able to explain complicated lessons. They are also motivated to learn English with NNESTs because they share the same commonality of their mother language and learning experience, which increases their comfort level. Additionally, the results suggest that the teachers’ methods and personalities motivate students to learn more than their nativeness. As with many studies, usually, there are limitations. Due to the time constraints, the researcher’s efforts were limited to collecting the data via a survey only. Also, this study was conducted on a small sample of female students at KAU and it is limited to one preceptive. Thus, the findings of this study can’t be generalized due to these limitations. However, it is recommended to expand the sample to include a larger number of female and male students. Both types of teachers can be included as participants to provide information about the learners’ attitudes and motivations in classrooms. It is also suggested to add the interview tool to enrich the understanding of the issue. It is proposed that this research be conducted at multiple settings or locations in Saudi Arabia, such as King Khalid University, King Saud University, etc. Despite these restrictions, the findings have brought attention to the issue and offered insight into this matter. In light of the current results, it is suggested to distribute the tasks between the two teachers. We can keep the balance by assigning NESTs for speaking and listening classes and NNESTs for grammar and complex lessons in order to ensure providing the learners with options that suit them and keep them motivated. Overall, NESTs and NNESTs should have an equal chance in teaching employments opportunities. Teachers should be evaluated equally according to their qualifications regardless of their native languages. References: Adara, R. A. (2018). Students’ motivation and preferences toward native and non-native English speaking teachers. Premise: Journal of English Education, 7(1), 1. https://doi.org/10.24127/pj.v7i1.1288 Adara, R. A. (2019). The differences in students’ attitudes and perceptions of NEST and NNEST. Leksika: Jurnal Bahasa, Sastra dan Pengajarannya, 13(2), 72-81. http://dx.doi.org/10.30595/lks.v13i2.4654 Adara, R. A. (2020). The differences in Indonesian ESL students’ motivation and perceptions of NEST and NNEST. JET ADI BUANA, 5(01), 1-16. https://doi.org/10.36456/jet.v5.n01.2020.2139 Alghofaili, N. M., & Elyas, T. (2017). Decoding the myths of the native and non-native English speakers teachers (NESTs & NNESTs) on Saudi EFL tertiary students. English Language Teaching, 10(6), 1. https://doi.org/10.5539/elt.v10n6p1 Alghofaili, N. M., & Elyas, T. (2019). Native English speakers versus non-native English speakers: The impact of language teachers on efl learner's English proficiency. English Review: Journal of English Education, 7(2), 27. https://doi.org/10.25134/erjee.v7i2.1773 Al-Nawrasy, O. (2013). The effect of native and nonnative English language tachers on secondary students’ achievement in speaking skills. 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Asian Social Science, 5(8). https://doi.org/10.5539/ass.v5n8p162 Gardner, R. C. (1985). Social Psychology and Second Language Learning: The Role of Attitudes and Motivation. London: Edward Arnold. Huys, S. (2017). The Native speaker fallacy and Dutch EFL students-A study into student preference for native or non-native English speaking teachers. https://theses.ubn.ru.nl/bitstream/handle/123456789/4852/Huys,%20Stijn%203026825.pdf?sequence=1 Ling, C. Y., & Braine, G. (2007). The attitudes of university students towards non-native speakers English teachers in Hong Kong. RELC Journal, 38(3), 257-277. https://doi.org/10.1177/0033688207085847 Mahboob, A. (2004). Native or non-native: What do the students think. Learning and teaching from experience, 121-147. Nath, P. R., Mohamad, M., & Yamat, H. (2017). The effects of movies on the affective filter and English acquisition of low-achieving English learners. Creative Education, 08(08), 1357-1378. https://doi.org/10.4236/ce.2017.88096 Phothongsunan, S. (2018). Learners’ attitudes towards native and non-native English speaking teachers in the EFL context. Journal of Yala Rajabhat University, 11(1). https://so04.tci-thaijo.org/index.php/yru_human/article/view/150556/110305 Tang, J. (2002). Using the L1 in the English classroom. In Forum (Vol. 40, No. 1, pp. 36-43). http://exchanges. state. gov/forum/. Todor, E., & Degi, Z. (2016). Language attitudes, language learning experiences and individual strategies what does school offer and what does it lack? Acta Universitatis Sapientiae, Philologica, 8(2), 123-137. https://doi.org/10.1515/ausp-2016-0022 Urkmez, S. (2015). Turkish EFL Learner Perceptions of Native and Non-native English Language Teachers. https://www.21caf.org/uploads/1/3/5/2/13527682/31_urkmez.pdf Yilmaz, E., Sahin, M., & Turgut, M. (2017). Variables Affecting Student Motivation Based on Academic Publications. Journal of Education and Practice, 8(12). https://files.eric.ed.gov/fulltext/EJ1140621.pdf Appendix: English version of the questionnaire: The questionnaire: The purpose of this study is to investigate your personal perceptions and experiences regarding the two types of teachers that have taught you: native English-speaking teachers and non-native English-speaking teachers. There is no correct or wrong answer. Your responses will help accomplish the research objectives as you are the main source. You do not have to write down your names. Your responses will be used only for the purposes of this research. Your cooperation is highly appreciated. - Native English speaker refers to someone who speaks English as her/his first language. Such as people from Canada, United Kingdom, United states of America, Australia etc... - Non-native English speaker is a person who has learned and speaks English as her/his second language (Arab). Such as teachers from Saudi Arabia, Sudan and Egypt. I fully understand the purpose of this survey, and I agree to participate in it: A. Yes B. No Demographic questions: Name: * optional Age: Gender: Major: In which semester: You have been taught by both types of teachers (Native English-speaking teachers and Non-Native English-speaking teachers)? English level: - a. Beginner - b. Intermediate - c. Advanced 1- Choose ONE answer which best reflects your view of the given statement. A. Learners’ Motivation and Attitudes of NEST 1- I want to speak as fluent as my native English-speaking teachers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 2- Native English-speaking teachers have better accents than non-native teachers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 3- I enjoy listening to English spoken by native speakers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 4- Native English-speaking teachers motivate me to learn grammar. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 5- I like learning about American or British cultures from native speakers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 6- Learning English with native teachers is more interesting than non-native teachers. A. Strongly agree B. Agree 7- Native English-speaking teachers motivate me to speak English more in the classroom. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 8- I feel more excited to study English with native teachers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 9- If I want to travel abroad, I have to practice speaking with native teachers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 10- My speaking, listening, reading and writing skills of English are improved after being taught by native English-speaking teachers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree A. Learners’ Motivation and Attitudes of NNEST 11- Non-native English-speaking teachers understand how hard it is to learn English. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 12- Non-native English-speaking teachers motivate me to learn English. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 13- I study English better with non-native English-speaking teachers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 14- Non-native teachers give more activities that make me understand English. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 15- Non-native teachers can explain difficult lessons easily. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 16- If I don’t understand something, I can ask in Arabic. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 17- Non-native teachers understand what I said both in English and Arabic. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 18- I like listening to English spoken by non-native English-speaking teachers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 19- I feel more relaxed to study English with non-native than native teachers. A. Strongly agree B. Agree C. Strongly disagree D. Disagree 20- Non-native English-speaking teachers give me cultural knowledge like native teachers. A. Strongly agree B. Agree 2- Answer the following questions: 1- What type of the two types of teachers do you prefer? Why? 2- What are the most important qualities of English teachers that motivate you to learn? Please mention them in order.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2145, 1 ], [ 2145, 2473, 2 ], [ 2473, 3674, 3 ], [ 3674, 4097, 4 ], [ 4097, 6581, 5 ], [ 6581, 6883, 6 ], [ 6883, 8768, 7 ], [ 8768, 10898, 8 ], [ 10898, 12531, 9 ], [ 12531, 14506, 10 ], [ 14506, 16567, 11 ], [ 16567, 18256, 12 ], [ 18256, 19263, 13 ], [ 19263, 21161, 14 ], [ 21161, 21371, 15 ], [ 21371, 23063, 16 ], [ 23063, 24790, 17 ], [ 24790, 25633, 18 ], [ 25633, 27634, 19 ], [ 27634, 28723, 20 ], [ 28723, 30654, 21 ], [ 30654, 32750, 22 ], [ 32750, 34751, 23 ], [ 34751, 36800, 24 ], [ 36800, 38875, 25 ], [ 38875, 39389, 26 ], [ 39389, 41440, 27 ], [ 41440, 42331, 28 ], [ 42331, 43979, 29 ], [ 43979, 45296, 30 ], [ 45296, 46531, 31 ], [ 46531, 47752, 32 ], [ 47752, 48820, 33 ], [ 48820, 49857, 34 ], [ 49857, 51010, 35 ], [ 51010, 51235, 36 ] ] }
e78258585ec9b97361f5af5dc66c695d9af279ed	{ "olmocr-version": "0.1.59", "pdf-total-pages": 16, "total-fallback-pages": 0, "total-input-tokens": 44001, "total-output-tokens": 13925, "fieldofstudy": [ "Biology" ] }	Coding translational rates: the hidden genetic code Luis Diambra1,2,* 1Universidad Nacional de La Plata, Centro Regional de Estudios Genómicos, La Plata, CP1900, Argentina 2CONICET, Argentina [email protected] ABSTRACT In this paper we propose that translational rate is modulated by pairs of consecutive codons or bicodons. By a statistical analysis of coding sequences, associated with low or with high abundant proteins, we found some bicodons with significant preference usage for either of these sets. These usage preferences cannot be explained by the frequency usage of the single codons. We compute a pause propensity measure of all bicodons in nine organisms, which reveals that in many cases bicodon preference is shared between related organisms. We found that bicodons associated with sequences encoding low abundant proteins are involved in translational attenuation reported in SufI protein in E. coli. Furthermore, we observe that the misfolding in the drug-transport protein, encoded by MDR1 gene, is better explained by a big change in the pause propensity due to the synonymous bicodon variant, rather than by a relatively small change in the codon usage. These findings suggest that bicodon usage can be a more powerful framework to understand translational speed, protein folding efficiency, and to improve protocols to optimize heterologous gene expression. Introduction The central dogma of the molecular biology establishes that the information that specifies which amino acid monomers will be added next during protein synthesis is coded in one or more nucleotide triplets known as codons1. The genetic code establishes a set of rules that associate the 20 amino acids and a stop signal with 64 codons. This code is almost universal with few exceptions2. As there are more codons than encodable signals (amino acids and stop signal) the genetic code is considered degenerated. However, it is well known that synonymous codons are not used with the same frequency. The biased codon usage is a pervasive feature of the information encoded in genomes, but it is not universal because different species have different associated preferences1. The existence of selective pressures to promote the codon usage bias highlights the complex nature of synonymous codon choices3,4. Early reports have pointed out that in prokaryotes the bias is towards codons with high translation rates5,6. In this sense, Guimares et al. established that elongation rate is affected by the specific amino acid composition, as well as by codon bias, in E. coli7. On the other hand, the impact of codon usage on translational rates in eukaryotes, where the mRNA processing can also affect the overall translational rate, is an active topic of research8–13. However, the role of codon usage has gone beyond the translational rates because new experimental findings suggest that codons with slow translation rates temporally separate the synthesis of defined protein portions and can synchronize the synthesis with the concurrently folding process of the proteins domains14–17. It has been proven that translational pauses can schedule the sequential folding schemes and can lead to different protein conformations17, and that the functionality of translated proteins can be affected by replacing rare codons with more frequently used codons18–20. In addition to the use of rare codons associated with scarce tRNA usage, there exist other mechanisms to modulate the speed of translation or to cause pauses. Among them, we can mention the blocking of ribosomal transit due to secondary structure elements in mRNAs21, and interactions of basic residues in the nascent polypeptides with the wall of the ribosomal exit tunnel22. Furthermore, Li et al. showed that translational pauses in E. coli are coded by sequences similar to the Shine–Dalgarno sequence23. However, in the last years emerging evidence has shown that the translational rate could be encoded by a sequence longer than a triplet, in particular by pair of consecutive codons, hereafter, bicodons24. In this sense, a study on over 16 genomes has revealed that bicodons formed by two rare codons are frequently found in prokaryotes but rarely used in eukaryotes25. In addition bicodons such as NNUANN are universally underrepresented, whereas NNGCNN bicodons are mostly preferred26. More recently, it was reported that rare arginine codons, followed by proline codons, were among the slowest translated bicodons27. This evidence could be consequence of the codon co-occurrence bias mechanism28,29 or the kinetics of the mRNA translocation from the A-site to the P-site30. Codon pair bias was also observed in several viral genomes, which matched the codon usage bias of the host31. This fact has been used to produce synthetic viruses with attenuated virulence as a new strategy for vaccine development32. Thus, coding sequences seem to carry further information than the information strictly needed for specifying the linear sequence of amino acids in the protein. This additional information is linked with the overall rate of synthesis of the associated protein and the pauses required for the acquisitions of its correct native structure. Despite the enormous impact that this subliminal coding on biotechnology, there are few systems biology methods to associate nucleotide sequences with the rate of protein synthesis\textsuperscript{13}. Among them, we can mention the sequencing of ribosome-protected mRNA fragment or ribosome profiling. This methodology has been used to correlate mRNA levels with codon decoding times\textsuperscript{33}. In this paper, we present an alternative manner to identify coding sequences that can modulate the ribosomal transit on the mRNA. In this comprehensive survey we did a statistical analysis of bicodon usage frequencies over two sets of proteins, the low abundant and the high abundant proteins, across nine organisms. Our main finding is that there is an important bias of the bicodon usage depending on the protein abundance. In this sense, we determine which bicodons are statistically associated with low or high translational rates, and in which cases such bias can be explained or not by the codon usage bias. Furthermore, we present suggesting evidence for the role of bicodons in the coding translational rate in two well studied cases. In the first case, we show that there exist clusters of bicodons related to low abundant proteins, associated with ribosomal pauses in the surfl synthesis in \textit{E. coli}\textsuperscript{15}. In addition, we also found that the alteration in the structure and function of the MDR1 protein\textsuperscript{16} associated with a synonymous single polymorphism can be better explained by a relatively big change (around 200\%) in pause propensity than by a moderate change in codon usage (around 30\%). Results The preferences of the bicodons The aim of this paper is to associate coding sequences with their relative translational speeds. We expect that this fact to be reflected in differences in the frequency of both codons and codon pairs occurrence in coding sequences associated with proteins with high and low abundance. To check this hypothesis, we select a set of 500 coding sequences associated with proteins with highest abundance, and another 500 coding sequences associated with proteins with lowest abundance, in nine model organisms from different kingdoms. Before showing the whole analysis across several organisms, we begin with an illustrative example. Fig. 1A shows the histogram of the bicodons (red bars) which codifies for the amino acid pair KK, obtained from 500 sequences of \textit{S. cerevisiae} with the lowest protein abundance (PA). We can observe that bicodon usage is not uniform, i.e., it is biased; this fact could be the simple consequence of the known bias observed at the codon level. However, the expected frequency associated with such bicodons (black bars, obtained by the product of each codon frequency) shows that, although some bicodon frequencies can be explained by the bias in the codon usage (for example, the bicodon AAAAAAG), some other bicodons have an associated usage frequency that is underrepresented (such as the bicodon AAAAAA), or overrepresented (as the bicodon AAGAAA). This means that two consecutive codons used for coding a given amino acid pair can be correlated. A similar analysis can be performed with sequences associated with the highest PA, as shown in Fig. 1B, and in all other amino acid pairs. Evidence for nonrandom associations between codon pairs, even once codon bias and bias against specific amino acid pairings were subtracted, was previously reported in \textit{E. coli}\textsuperscript{34}, and across many other genomes\textsuperscript{25}. However, what is a new remarkable fact in Fig. 1 is the strong difference between the histograms computed for the low and high PA samples. Fisher’s exact test allows one to reject, with high significance level, the null hypothesis that bicodons are equally used in sequences from the low and high PA samples. In the particular case of bicodon AAGAAG the \textit{p}-value is $5.3 \times 10^{-93}$. It is important to point out that the two samples of sequences (500 coding sequences for the proteins with the lowest and highest PA) can introduce an additional bias. In this sense, it is known that protein abundance correlates negatively with coding-sequence length in yeast\textsuperscript{35}. To go further in our analysis, we subtracted this bias by constructing two new samples of low and high PA but with similar sequence length distribution, as indicated in the Method section. All subsequent analyses will be made with these unbiased samples (the list of coding-sequence in these samples is given in Supplementary Tables S1 and S2). Fig. 2 shows the histograms corresponding to both low (red bars) and high (orange bars) PA sequences from unbiased samples. It can be seen that bicodon AAAAAAAAA is more frequently used in sequences with low PA than in sequence with high PA, while the frequency usage of bicodon AAGAAG has an inverse relationship. For example, in the last case we have computed the \textit{p}-value from the contingency tables of bicodon AAGAAG which is around $6.5 \times 10^{-48}$, less significant than the one obtained for the biased samples. Figure 2 only illustrates the particular case of KK pair in \textit{S. cerevisiae}. In order to see a broader coverage over amino acid pairs and bicodons we have devised two alternative heat maps: (i) the statistical distance $D_{\text{LH}}$, related to the \textit{p}-value of the Fisher’s exact test, see Method section for its definition. The statistical distance and the pause propensity measures As statistical distance between the frequency distributions associated with low and high PA samples, we computed the Kullback-Leibler divergence $D_{\text{LH}}$ across all amino acid pairs and all studied organisms. Fig. 3 depicts a heat map (21 P-site codons × 20 A-site codons), where each color pixel represents the quotient $D_{\text{LH}}/\log(n)$ for a given amino acid pair, and $n$ denotes the number of synonymous bicodons for such dipeptide. A high value (red color) indicates a large discrepancy between the usage frequencies in both samples for a given amino acid pair. This figure shows that the discrepancy in the bicodon usages between low and high PA samples is not the same across organisms, it is a particular feature like the codon bias. It can be seen that B. subtilis and S. cerevisiae have many dipeptides with relatively large divergences, a feature that is also shared by M. aeruginosa, A. thaliana and both invertebrates, D. melanogaster and C. elegans (see Supplementary Fig. S1). The studied mammalians (H. sapiens and M. musculus) and E. coli are on the other side. Interestingly, it was in E. coli, where bicodon bias was first reported, however, it is clear that bicodon usage bias across the ORFeome does not imply a different usage preference between highly and lowly expressed proteins. Another important feature of the heat maps in Fig. 3 is that they represent a nonsymmetric matrix, i.e., the divergence $D_{LH}$ of dipeptide $X_1X_2$ is not necessarily equal to the divergence associated with $X_2X_1$. This fact cannot be explained solely with codon usage bias, and reveals a complex correlation between two consecutive codons. Fig. 3 offers a general view of the 420 pairs. However, it can be observed that even when $D_{LH}$ can give a relatively small divergence, like the one associated with KK pair in S. cerevisiae, there could exist one or more bicodons with high difference of occurrence in both samples, such as bicodons AAAAAA and AAGAAG in Fig. 2. To appreciate the differences at a bicodon resolution, the second heat is used. In it, the color of each cell is determined by the pause propensity $\pi$ index, which establishes when the bicodon has preference for sequences with low or with high PA, see Method section for this definition. Fig. 4 shows the heat map associated with all organisms. In order to put in evidence some trends or rules across the studied organisms, the colors of the cells were clustered by similarity using an agglomerative method. The pause propensity $\pi$ of all bicodons and organisms is listed in Supplementary Table S3. From the heat maps of Fig. 4 it can be seen that some bicodons, indicated by blue cells on the top side of the grid, have a clear preference for sequences associated with high PA. In some cases this feature is shared by several organisms such as: A. thaliana, C. elegans, D. melanogaster, S. cerevisiae, and M. aeruginosa. On the other hand, there are other bicodons, indicated by red cells at the bottom of the grid, which are more frequently used in sequences associated with low PA. Some bicodons have different sequence preferences depending on the organism. For example, there are blue cells on the bottom side of the yeast heat map, that have preference for sequences with low PA in the M. aeruginosa heat map. The bicodon preferences are less apparent (less intense colors), and also less frequent, in H. sapiens, M. musculus and E. coli. The low preference of bicodon usage observed in E. coli can be a consequence of the fact that there are not a clear distinction between the protein abundance distributions of both samples in this particular case (see Methods). It can also be observed a couple of white rows in all organisms. These cells correspond to bicodons which do not exhibit any preference or they are usually poorly used in both sequence samples and have associated poor statistic. The heat maps shown in Fig. 4 are very useful to see some common features among organisms, however they do not show whether the bicodon preference is explained or not by the preference of the codon in the pair for sequences associated with low or high PA. In order to study this, we have computed residual scores for each bicodon over sequences with low PA, $\chi^2_L$, and over sequences high PA, $\chi^2_H$. When the residual score is high, the bicodon usage cannot be explained by the codon usage in the same sample of sequences, and has been used previously. The value of these residuals, observed frequencies and pause propensity values for all codon pairs and organisms are listed in Supplementary Table S3. In Fig. 5 it can be seen a raster plot of these residual scores for all bicodons in B. subtilis, yeast, humans and E. coli (residual plots associated with the other five organisms are displayed in Supplementary Fig. S2). As we have two sequence samples for each bicodon it is convenient to take the quantity $\chi^2 = \chi^2_L + \chi^2_H$ as a whole residual score. To be conservative, we have considered for all organisms that bicodons with $\chi^2 \geq 5$ are bicodons whose preference is not explained by the preference of the individual codons in the pair. Thus, four types of bicodons on the raster plot of Fig. 5 can be distinguished: (i) codon pairs that are significantly more used in sequences associated with low PA than in sequences associated with high PA ($p$-value $\geq 2$), and whose preferences cannot be explained by the codon usage bias (red dots); (ii) codon pairs which are significantly more used in sequences associated with high PA than in sequences associated with low PA ($p$-value $\geq 2$), and whose preferences cannot be explained by codon usage bias (blue dots); (iii) codon pairs with a significantly different usage frequency in low and high PA samples, but whose preferences can be explained by the codon usage bias, i.e., $\chi^2 < 5$ (green dots), and finally (iv) codon pairs whose usage frequencies in low and high PA samples are not significantly different, i.e., $p$-value $\geq 2$ (black dots). These plots indicate that while there are many bicodons with evident preference for low and high PA sequences in B. subtilis and S. cerevisiae, there are only few in H. sapiens at this significance level. As in humans, mouse and surprisingly also E. coli have few bicodons with evident preference (Supplementary Fig. S2). However, in an example below we will see that synonymous SNP associated with changes in the bicodon preference can explain documented protein misfolding and pathological condition in humans. On the other hand, S. cerevisiae has more codon pairs than B. subtilis, with a significant different usage frequency in low and high PA samples, but such bias is explained by the codon usage bias. The plots for C. elegans and D. melanogaster (Supplementary Fig. S2) are similar to the raster plot obtained for yeast. In particular these organisms share many bicodons with the same preference listed in Table 2. Further evidence for the role of bicodons in translational pauses is provided by a well studied single polymorphism (SNP) in the gene MDRI\cite{15}. This gene encodes the drug-transport pump ABCB1, which transports a variety of drugs from the brain into the blood. Kimchi-Sarfaty et al. observed that as a result of a synonymous SNP (rs1045642) the structure and function of the protein are altered with the consequent change in its substrate specificity\cite{16}. The SNP in exon 26 at position 3435 changes the codon ATC to the synonymous ATT, which reduces the codon usage from 47% to 35%. It was argued that the presence of a rare codon affects the timing of co- translational folding and insertion of P-glycoprotein into the membrane. Although it is difficult to consider the ATT codon as rare, it is clear that the SNP alters the timing of the ribosomal transit. We offer that this hexanucleotide acts together with a small cluster of three bicodons, with high pause propensity, between residues 259 and 276. At this position is also the second highest peak of the folding degree measure (Figure 5A of 1). In addition, around in this position (residue 166) is the highest peak of the degree of folding acquisition, $\Delta Q$, proposed by Tanaka (Figure 5A of 5). A naive sequence analysis in this region reveals three Shine-Dalgarno (SD) sequences indicated with asterisks in Figure 6B. In particular, among nucleotides 486–491 there is the hexanucleotide GGTGGA, which has a predicted affinity with the anti-SD sequence of $-6.5 \text{ kcal mol}^{-1}$ (Figure 4 of 3). In addition to this SD sequence, we have found in this region a cluster of bicodons with high pause propensity, i.e., statistically associated with low PA sequences. These bicodons are listed in Fig. 6C. This speed attenuation is not apparent in rate of translation pattern based on the concentration of the tRNA or codon usage, Fig. 6B (bottom panel). Another translational attenuation experimentally tested is one linked to the intermediate 25-28 kDa (around 214-240 residues)\cite{15}. In this case, we have found the same SD sequence that was mentioned above, located 40 residues downstream (more precisely nucleotides 846-851). Again, this hexanucleotide acts together with a small cluster of three bicodons, with high pause propensity, between residues 259 and 276. At this position is also the second highest peak of the folding degree measure (Figure 5A of 36). These results suggest that bicodons listed in Fig. 6C could be needed for the correct folding of the transient intermediates in E. coli. Further evidence for the role of bicodons in translational pauses is provided by a well studied single polymorphism (SNP) in the gene MDRI\cite{15}. This gene encodes the drug-transport pump ABCB1, which transports a variety of drugs from the brain into the blood. Kimchi-Sarfaty et al. observed that as a result of a synonymous SNP (rs1045642) the structure and function of the protein are altered with the consequent change in its substrate specificity\cite{16}. The SNP in exon 26 at position 3435 changes the codon ATC to the synonymous ATT, which reduces the codon usage from 47% to 35%. It was argued that the presence of a rare codon affects the timing of co- translational folding and insertion of P-glycoprotein into the membrane. Although it is difficult to consider the ATT codon as rare, it is clear that the SNP alters the timing of the ribosomal transit. We offer here an alternative cause of the translational attenuation; in this sense we have observed that this SNP is also associated with a large change in the propensity pause index $\pi$ of the bicodons. Specifically, bicodon ATCGTG has preference for low PA sequence with $\pi = 1.21$, while bicodon ATTGTG has preference for high PA sequence $\pi = -1.55$. This means a change of 178%, almost 8 folds greater than the change in the codon usage. Further, the other synonymous bicodon ATAGTG has a even lower pause propensity, $\pi = -1.73$, in agreement with Kimchi-Sarfaty et al. observation that associates to this haplotype a larger decrease in the inhibitory effect\cite{15}. In addition to the SNP above, there are other synonymous SNPs related to human diseases that could be explained by a large change in the pause propensity. Among them we can mention the SNP rs34533956 in the gene CFHR5 which is associated with age-related macular degeneration\cite{38}. In this case, the mutation changes the bicodon GACGTG to GATGTG and associated change in the pause propensity is 183%, while the change in the relative synonymous codon usage is only 13%. Other example corresponds to the SNP rs11615 in the gene ERCC1 which was associated with \| dipeptide \| bicodon \| $\chi^2 + \chi^2_H$ \| $-\log_{10}(p\text{-value})$ \| \|-----------\|---------\|---------------------\|-----------------------------\| \| NA \| AATGCA \| 8.26623 \| 7.0634 \| \| NA \| AATGCA \| 12.6365 \| 4.2896 \| \| LR \| CTTCGA \| 44.9244 \| 5.3305 \| \| KK \| AAAAAA \| 47.0125 \| 9.4035 \| \| JK \| TATAAA \| 17.1832 \| 4.0035 \| \| FF \| TTITTTT \| 8.103 \| 13.5285 \| \| FQ \| TTTCAG \| 11.1061 \| 7.903 \| \| IT \| ATAACCA \| 11.1095 \| 8.6769 \| \| KI \| AAAATA \| 8.20946 \| 21.1178 \| \| IM \| ATATG \| 14.6726 \| 7.9497 \| Table 1. Shared bicodons in C. elegans, D. melanogaster and S. cerevisiae that have high preference for low PA or high PA sequences ($p\text{-value} \geq 3$), but such preference cannot be explained by the codon usage bias ($\chi^2 > 5$). colorectal cancer\textsuperscript{39}, where the pause propensity change is 192\%, against a small change in the relative synonymous codon usage (again 13\%). These relationship suggest that some pathological synonymous mutations could be understood in terms of the change in the timing needed for co-translational folding programmed by the bicodons. Discussion If we consider an average of three alternative codons for coding each amino acid, there exist more than $1.3 \times 10^{143}$ manners to codify a protein with 300 residues. However, organisms use an insignificant fraction of the number of options offered by the genetic code redundancy. This is due to several constraints operating to optimize many important biological features such as: the expression level\textsuperscript{1}, ribosomal proofreading errors\textsuperscript{40}, protein solubility\textsuperscript{41}, folding accuracy\textsuperscript{19,20,42}, protein stability, etc. In this sense, it has been shown that codon usage in \textit{E. coli} is biased to reduce the cost of translational errors\textsuperscript{43}. In addition, codons that bind to their cognate tRNA most rapidly are preferentially used in highly expressed genes\textsuperscript{44}. It has also been reported a bias in the bicodon usage frequency in several organisms\textsuperscript{25}. More recently, Lian \textit{et al.} have identified codons that regulate translation speed in human cell lines\textsuperscript{45}. Many other studies agree in the key role of ribosomal pause, coded by codon usage or SD-like sequences, in orchestrating the hierarchical co-translational folding of single domains\textsuperscript{15–17,46,47}. In summary, there exist rising evidences that many relevant features, other than the linear sequence of amino acids, are also coded at nucleotide sequence level. These facts should considerably reduce the amount of alternative ways of correctly convey the message from genes to functional proteins, despite the redundancy of the genetic code. Among the above biological constraints determining the codon usage, we have focused our attention on the translational speed, i.e., the sequential process of protein elongation\textsuperscript{4}. Briefly, each proofreading iterative step of this process involves recruitment of the tRNA charged anticodons, tRNA association/dissociation to mRNA, assembly of the residue to the nascent peptide, and translocation of tRNA-mRNA from the A-site to the P-site. Each step has a particular rate and it has been shown that disruption of the interaction between mRNA codon in the A-site from the decoding center is a rate-limiting process\textsuperscript{30}. In fact, there are evidences that such rates are codon dependent in \textit{E. coli}\textsuperscript{48}. Further contributions to the translational rate, not linked to the tRNAs’ abundance, are the non-Watson-Crick (wobble) interactions. These interactions are usually associated with higher dissociation rates between mRNA and decoding center\textsuperscript{49}. In this paper, we assume the hypothesis that ribosomal pauses are encoded by bicodons, and examine the bicodon frequency usage in nine organisms. We found that many codons have an evident preferential usage in sequences that code for highly abundant proteins, while many others have preference for coding proteins scarcely abundant. The latter bicodons can be understood as short sequences linked to translational pauses. The observed bias cannot be explained by the codon usage in many bicodons. However, the small number of such bicodons found in \textit{E. coli}, where most of bicodon preferences, except for 96 bicodons, can be explained by the codon usage, is worth noting. This clearly contrasts with the other prokaryotes studied here; for example, we have report almost 585 bicodons in \textit{B. subtilis} which are preferentially used to encode either low or high abundant proteins without a codon usage correlate. The bicodon preference is also found in a plant, a fungus and two invertebrates. Our results indicate that many bicodon preferences are shared by \textit{S. cerevisiae}, \textit{C. elegans} and \textit{D. melanogaster}, and to a lesser extent they are also shared with \textit{A. thaliana} and \textit{B. subtilis}. In the case of the mammalian species (\textit{H. sapiens} and \textit{M. musculus}), we found a number of bicodons with high preference comparable with \textit{E. coli}. However, we illustrate with an example of synonymous mutations of clinical relevance, that the exchange of two codons with opposite preferences, even when such preferences are moderate, can alter the translation ribosomal traffic. This example suggests that single mutations that changes the bicodon preference can trigger pathological phenotypes by altering the translational attenuation program of the protein. Even though the results provided here suggest that some bicodons should regulate translational attenuation, it is important to remark the limitations of the present approach to assign to each bicodon one value of the pause propensity index. The more evident limitation is that protein abundances are not uniquely dictated by a quick translation, transcription levels have also important roles in prokaryotes\textsuperscript{7}, while RNAi pathway is a common way to regulate expression in mammalians\textsuperscript{50}. These, and other factors, can introduce undesired bias and overshadow some bicodon bias. It is likely that the small number of bicodons with evident preference observed in mammalians is due to the fact that protein abundance is not majorly determined by the bicodon usage, with the consequent poor performance of the method in these organisms. Alternative methods based on the ribosome density profile could overcome these drawbacks. But first it is needed to solve the link between density and ribosomal speed at the nucleotide level, due to the fact that a pause at a given site will stop the transit of many other ribosomes proofreading upstream, increasing artificially the ribosome density of the upstream sequences. Summarizing, we are here reporting that bicodon usage frequency depends on protein abundance. This preference cannot be explained by the traditional codon usage in many bicodons. This empirical evidence supports the hypothesis that bicodons encode translation pauses. Such a scenario allowed us to contrast this hypothesis in various circumstances where translation rates could be altered. Like the naive codon usage, the bicodon usage can empower novel strategies for rational transcript design that minimize misfolding while simultaneously maximizing co-translational folding for foreign proteins in heterologous hosts. Methods Data sources In this work, we have used two kind of data: (i) genome-wide protein abundance across nine model organisms, and (ii) nucleotide sequences associated with proteins indicated above. The absolute protein abundance data from three prokaryotes (M. aeruginosa B. subtilis and E. coli), one unicellular fungus (S. cerevisiae), one plant (A. thaliana), two multicellular eukaryotes (D. melanogaster and C. elegans) and two mammalians (M. musculus and H. sapiens) were downloaded from PaxDb web site (http://pax-db.org/) on May 2015. From these comprehensive data sets we have selected two sample of proteins: the 500 most abundant proteins and the 500 less abundant ones, including into our samples only isoform when more than one are present in the comprehensive data set. As PA distributions are in general biased, i.e., the short proteins should be more abundant than larger ones (see Fig. 7), we have also selected two sets of 500 sequences, but taking into account that the sequence length distribution of both sets were similar (Supplementary Tables S1 and S2). The procedure to sampling sequences with similar length distributions consist in ordering all sequences, corresponding to a given organism, in a PA crescent order. To perform a similar analysis for all possible bicodons (61^2 = 3904), excluding stop:sense bicodons and the stop:stop bicodon. To express the preference degree of a given bicodon for low or high PA sequences we define the pause propensity, $ \pi $, \[ \pi_{ij} = \frac{e_{ij} - \hat{e}_{ij}}{\hat{e}_{ij}}, \] where the * indicates that the sum is only over codon pairs encoding the same amino acid pair encoded for the bicodon $ ij $. From the observed and normalized expected bicodon counts recording in a given sample $ S $, we compute the residual scores for each codon pair as: \[ \chi^2_{Sij} = \frac{(o_{ij} - \hat{e}_{ij})^2}{\hat{e}_{ij}}, \] where $ S $ indicates the sequence samples, i.e., $ S = L $ for low PA sample, or $ S = H $ for high PA sequence sample. Further to use residual scores to test whether the bias in a given codon pair can be explained, or not, by the bias in codons and amino acids, we use the Fisher’s exact test to examine whether a number of occurrences of bicodon $ o_{ij} $, observed in sequences sample associated with low protein abundance are significantly different than the number of occurrences observed in high protein abundance sample $ o_{ij}^H $. Thus, we construct a 2×2 contingency tables for each bicodon as shown, for an illustrative purpose, in Fig. 7 (and also in Supplementary Figs. S3-S10) we have plotted the distributions of whole PA for all organisms used in our study, and the PA and the sequence length distribution of the selected data sets. The nucleotide coding sequences corresponding to the selected proteins were downloaded from Ensembl web sites (four eukaryotes organisms from ftp://ftp.ensembl.org/pub/ and four prokaryotes organisms from http://bacteria.ensembl.org), while Arabidopsis thaliana coding sequences were downloaded from www.arabidopsis.org. We also used ribosome density profiles data of E. coli taken from NCBI GEO accession GSE35641. tRNA levels and codon usage of E. coli from, and http://www.kazusa.or.jp/codon/, respectively. Statistical analyses The bicodon bias was studied in the context of the low and high PA samples. Basically, we count all consecutive pairs of codons on the same reading frame of the coding sequences belonging to a given sample, which allows us to compute the occurrence of each bicodon $ ij $ in all sequences of each sample. The index $ i $ indicates the codon corresponding to P-site, while $ j $ indicates the one corresponding to the A-site. The occurrence of the codon pair $ ij $ will be denoted by $ o_{ij} $. We also compute in the same sample of sequences the number of single codons $ f_i $. Further, we compute expected number of occurrences of each codon pair, as $ e_{ij} = f_i f_j N_p / N_{tot}^2 $, where $ N_{tot} $ is the total number of codons in the set of sequences and $ N_p $ is the number of bicodons. Following, we remove the contribution due to the nonrandomness of amino acid pairs by normalizing the former expected values as: \[ \hat{e}_{ij} = e_{ij} \times \frac{\sum_k \hat{o}_{kl}}{\sum_k e_{kl}}, \] where $ \hat{o}_{kl} $ indicates the sequence samples, i.e., $ S = L $ for low PA sample, or $ S = H $ for high PA sequence sample. Further to use residual scores to test whether the bias in a given codon pair can be explained, or not, by the bias in codons and amino acids, we use the Fisher’s exact test to examine whether a number of occurrences of bicodon $ o_{ij}^H $, observed in sequences sample associated with low protein abundance are significantly different than the number of occurrences observed in high protein abundance sample $ o_{ij}^L $. Thus, we construct a 2×2 contingency tables for each bicodon as shown, for an illustrative purpose, in the Supplementary Fig. S11 for the particular case of the bicodon AAGAAG. Applying the Fisher’s exact test on the right table gives that the observed frequencies of AAGAAG in both samples are significantly different with a p-value of 5.3 × 10^{-93}. In order to compute the binomial coefficients associated with the p-value calculation, we approximate the factorial operator with the Stirling’s formula, $ n! \approx \sqrt{2\pi n}(n/e)^n $ for $ n \geq 25 $. We performed a similar analysis for all possible bicodons (61 × 64 = 3904), excluding stop:sense bicodons and the stop:stop bicodon. To express the preference degree of a given bicodon for low or high PA sequences we define the pause propensity, $ \pi $, as $-S \log_{10}[\rho$-value] where $S$ takes value $+1$, or $-1$, when the bicodon has preference for sequences with low or with high PA, respectively. We also use some measures provided by the information theory (IT). The essential IT idea is that of quantify our ignorance associated to a given probability distribution (PD) in a mathematical fashion and formally deal with it. The ignorance associated to a PD $\{p_i\}$ is measured by the Shannon’s entropy\textsuperscript{53} $H$, defined as: $$H_p = -\sum_{i=1}^{n} p_i \log_b(p_i),$$ (3) where $b$ is the base of the logarithm used; when $b = 2$ the units of entropy are referred to as bits. Hereafter, we work in base 2, and log will be denoted $\log_2$ in order to simplify the notation. A message (concatenation of symbols of an alphabet) whose symbols have associated a non-uniform distribution will have less entropy than if those symbols had an uniform distribution. This measure is between 0 and 1, and allows us to compare the information content of two PD with different alphabet size. Another IT concept used in this manuscript is the statistical distance between two PDs. 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On information and sufficiency. The Annals of Mathematical Statistics 22, 79–86 (1951). Acknowledgements We thank Alejandra Carrea and Christina McCarthy for critical reading of the manuscript. LD is member of CONICET (Argentina). This work was partially supported by CONICET, PIP #: 0020. Author contributions statement L.D. conceived and conducted the study, analysed the results and wrote the manuscript. Additional information Accession codes GEO accession GSE35641; Competing financial interests: The author declare no competing financial interests. Figure 1. Bicodon usage for the KK amino acid pair. Red and orange bars denote the frequency of bicodons observed in a set of 500 coding sequences with the lowest PA (A), and observed in a set of another 500 coding sequences with the highest PA (B), respectively. Black bars represent the expected frequency obtained by the product of each codon frequency. Table 2. Shared bicodons in C. elegans, D. melanogaster and S. cerevisiae that have high preference for low PA or high PA sequences (p-value ≥ 3), but such preference cannot be explained by the codon usage bias ($\chi^2 > 5$). Figure 2. Frequency distributions from unbiased samples of sequences. Frequencies associated with bicodons that encode the amino acid pair KK, computed using sequences from the low PA sample (red bars) and from the high PA sample (orange bars). The frequency usage of bicodon AAGAAA in the sequences of both samples are almost the same, while other bicodons have an evident preference for sequences associated with low or high PA. Figure 3. Divergence measure between histograms obtained from low and high PA samples. Statistical distances between all histograms as in Fig. 2 for B. subtilis, S. cerevisiae, H. sapiens and E. coli. P-site codons occupy the horizontal axis and A-site codons the vertical axis. Divergence measures associated with other organisms are displayed in Supplementary Fig. S1. Figure 4. Pause propensity heat maps for nine organisms. The color of each cell is determined by the pause propensity $\pi$ of the associate bicodons. Red cells indicates bicodons with clear preference for sequence associated to low PA, while blue cells indicates bicodons with high PA preference. Figure 5. Scatter plots indicating the residual scores $\chi_L$ and $\chi_H$ computed over the low PA and high PA samples, respectively, for B. subtilis, S. cerevisiae, H. sapiens, and E. coli. Raster plots of other organisms are displayed in Supplementary Fig. S2. The codon pairs whose preference for sequences with low or high PA cannot be explained by the codon usage bias are out of the grey quadrant (i.e., $\chi^2 \geq 5$). Among them, we distinguish bicodons more frequently used in low PA sequences (red dots), or in high PA sequences (blue dots). Inside the quadrant, there are codon pairs with a significantly different usage frequency in low and high PA samples, but whose bias can be explained by codon usage bias (green dots). Codon pairs whose usage frequencies in low and high PA samples are not significantly different (black dots). Figure 6. Translational attenuations in the sufI protein of E. coli. (A) Schematic representation of two translational pause mechanisms: anti-SD (aSD) sequence in the 16S RNA can link to SD-like sequences in the transcript. In addition, bicodons with high pause propensity (red) can modulate the translocation rate of tRNAs in the decoding center (DC). (B) Top panel: pause propensity profile of sufI, with two clear cluster of bicodons with high pause propensity (red dots) at 160-180 and at 259-276 residues. These clusters co-localized with SD-like sequences (asterisk). These sequences can be responsible for the peaks in the ribosomal density profile (Middle panel), fact that cannot be explained by the translational rate (Bottom panel) based on codon usage (blue line) or tRNA abundance (red line). (C) Positions, nucleotide sequences and pause propensity of the clusters of bicodons denoted by red and green dots in Fig. 6B. Figure 7. Protein abundance and the sequence length distributions. Protein abundance distributions of the whole dataset of S. cerevisiae, lowest and highest PA subsets are indicated in red and blue colors, respectively (A). Sequence length distributions of the subsets of sequences shown in left panel (B). Protein abundance distributions of the whole dataset, the selected low and high PA subsets of sequences used in the study (listed in Supplementary Tables S1 and S2) are indicated in red and blue colors, respectively (C). Sequence length distributions corresponding to the subsets of sequences shown in left panel (D).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5121, 1 ], [ 5121, 11298, 2 ], [ 11298, 17755, 3 ], [ 17755, 23627, 4 ], [ 23627, 30368, 5 ], [ 30368, 36094, 6 ], [ 36094, 40487, 7 ], [ 40487, 44860, 8 ], [ 44860, 47661, 9 ], [ 47661, 48254, 10 ], [ 48254, 48685, 11 ], [ 48685, 49056, 12 ], [ 49056, 49354, 13 ], [ 49354, 50204, 14 ], [ 50204, 51139, 15 ], [ 51139, 51765, 16 ] ] }
e305d3e822832d64a497298089122c006f6ee44f	{ "olmocr-version": "0.1.59", "pdf-total-pages": 6, "total-fallback-pages": 0, "total-input-tokens": 16880, "total-output-tokens": 5218, "fieldofstudy": [ "Medicine" ] }	There is no standard procedure for the treatment of benign bone tumors. The bone defect following the curettage of the bone tumor can be filled with autologous bone marrow, polymethylmethacrylate cement, allograft, tricalcium phosphate, and demineralized bone matrix (DBM). All these procedures have their own advantages and disadvantages. Autografting is the gold standard in tumor surgery; nevertheless, its disadvantages including limited access, cosmetic problems, and donor site morbidity make the alternative treatment modalities as viable options. Resorption of graft material and transmission of disease are associated risks of allograft use. Polymethylmethacrylate cement is non-biological and its Young’s modulus of elasticity is lower than cortical bone, responds to compression-distraction forces differently compared with cortical bone, and has poor tensile and shear strength. Demineralized bone matrix is expensive and osteoinductive without structural support. Our hypothesis was that cement combined DBM treatment stimulates new bone formation, thus improves the functional scores. To the authors’ knowledge, no study has focused on this technique and searched the effect of new bone formation in the cortical window on functional outcomes. Therefore, in this study, we aimed to investigate the effectiveness of cement combined DBM treatment on new bone formation in the cortical window as well as to evaluate the effect of new bone formation on functional outcomes. ABSTRACT Objectives: This study aims to investigate the effectiveness of cement combined demineralized bone matrix (DBM) treatment on new bone formation in the cortical window as well as to evaluate the effect of new bone formation on functional outcomes. Patients and methods: Thirty-two benign bone tumor patients (15 males, 17 females; median age 38 years; range, 12 to 68 years), who were treated with cement combined DBM between February 2010 and December 2014, were evaluated retrospectively. Patient characteristics were recorded as age, gender, tumor localization, histological diagnosis, Enneking stage, tumor size, size of the cortical window, usage of prophylactic fixation, time to return to work, Musculoskeletal Tumor Society (MSTS) functional score, tumor relapse, and new bone formation on the cortical window in the computed tomography scans after one year of surgery. Results: Median tumor volume was 17.2 cm$^3$ (range, 2.8 to 139.6 cm$^3$), median area of the cortical window was 8.3 cm$^2$ (range, 1.6 to 28.4 cm$^2$), and median postoperative one-year MSTS score was 84.5 (range, 66 to 97). MSTS scores were significantly worse with the usage of prophylactic fixation ($p<0.001$). There was a statistically significant difference between the usage of prophylactic fixation and cortical window size ($p=0.013$). There was a low-level negative correlation in terms of age and bone formation on the cortical window ($p=0.046$, $r=-0.356$) and mid-level negative correlation between cortical window size and functional scores ($p=0.001$, $r=-0.577$). Conclusion: Application of cement combined with DBM procedure is an effective, alternative, and biological treatment in bone tumors that provides immediate stability and stimulates new bone formation on the cortical window. Keywords: Benign bone tumor, cement, demineralized bone matrix. PATIENTS AND METHODS Thirty-two benign bone tumor patients (15 males, 17 females; median age 38 years; range, 12 to 68 years), who underwent cement combined DBM procedure at Bezmialem Vakıf University School of Medicine between February 2010 and December 2014 and were followed up for a minimum of one year, were evaluated retrospectively. Patients with axial (n=2), pelvic bone tumors (n=3), metastatic giant cell bone tumor (n=2), or those who underwent adjuvant radiotherapy or chemotherapy (n=1) or were followed up for less than one year (n=11) were excluded. The study protocol was approved by the Bezmialem Vakıf University School of Medicine Ethics Committee. A written informed consent was obtained from each patient. The study was conducted in accordance with the principles of the Declaration of Helsinki. The mean follow-up time was 20.8±7.7 months. There were simple bone cysts (n=6, 19%), enchondromas (n=14, 43%), aneurysmal bone cyst (n=1, 3%), fibrous dysplasia (n=3, 9%), chondroblastomas (n=2, 6%), and giant cell bone tumors (n=6, 19%) according to the pathology results. The lesions were located at the proximal humerus (n=5), proximal femur (n=3), distal femur (n=16), proximal tibia (n=5), distal tibia (n=1), and calcaneus (n=2). There were three (9%) Enneking stage I, 16 (50%) stage II, and 13 (41%) stage III patients. All patients were examined through direct X-ray, computed tomography (CT), and magnetic resonance imaging (MRI) for preoperative surgical planning. All operations were performed by the same experienced tumor surgeon and the operation procedure was similar. A tourniquet was used in all patients if tumor localization allowed. Generally, an adequate longitudinal incision was performed over the lesion to dominate the whole lesion. An oval cortical window was created with a drill and osteotome. The cortical window and affected soft tissue on the cortex were removed. After an extensive curettage was performed, mechanical cleaning was carried out with a high-speed burr. If necessary, the cavity was rinsed with phenol and ethanol solution while preserving the surrounding soft tissue. Then, antibiotic-free bone cement was prepared and the cavity was filled with high viscosity bone cement (Biomet Bone Cement R, Biomet Orthopedics GmbH, Ried, Switzerland). Grooves were created with a scalpel on the surface of cement to increase the cement-graft retention. Thereafter, when the cement was solidified, putty form of DBM (Grafton, Osteotech Inc., Eatontown, NJ, USA) was applied with at least one standard cortical thickness on the cement (Figure 1). Prophylactic osteosynthesis was performed in patients with possible pathological fracture. Tumor volume $\text{volume} = \frac{4}{3}\pi \frac{D_1}{2} \frac{D_2}{2} \frac{D_3}{2}$ was calculated according to the direct preoperative X-rays and CT sections. Patients were routinely controlled with direct radiography every three months for the first year. To assess tumor recurrence and bone regeneration on the cortical window, all patients were evaluated with CT scans in the first postoperative year (Figure 2). As there is no defined classification method in the literature, we used our own methodology to classify the amount of new bone formation on the cortical window regarding CT scans (Table I). Every measurement on radiological ![FIGURE 1. (a) Appearance of tumor after cortical window removal. (b) Bone defect following curettage and burr application. (c) Filled bone defect with cement. (d) View after application of demineralized bone matrix minimally one bone cortex thickness on cement.](image-url) images was performed by a radiologist three times to reduce the dating error. Musculoskeletal Tumor Society (MSTS) functional scores of all patients were performed in the first postoperative year.\[5\] The relationship between new bone formation on the cortical window, age, Enneking tumor stage, functional score, time to return work, size of the cortical window (cm$^2$), tumor size (cm$^3$), and usage of prophylactic fixation were evaluated. Statistical analysis Statistical analysis of the data was performed using the IBM SPSS version 21.0 software (IBM Corp., Armonk, NY, USA). Concordance of the continuous data to normal distribution was tested by Shapiro-Wilk test. Continuous variables were expressed with median (minimum-maximum) and mean $\pm$ standard deviation values and categorical variables were expressed with frequency (percentage) values. Two group comparisons were performed using the Mann-Whitney U test; independent sample t-test and three group comparisons were performed using the Kruskal-Wallis and one-way analysis of variance tests. The relationship between non-normally distributed variables was investigated by Spearman’s correlation coefficient. Results were reported with 95% confidence intervals (CI) and related $p$ values. $P<0.05$ was considered as statistically significant. RESULTS The median size of the cortical window to reach the tumor was 8.3 cm$^2$ (range, 1.6 to 28.4 cm$^2$), while the median tumor volume was 17.2 cm$^3$ (range, 2.8 to 139.6 cm$^3$). The median time to return to work was 60 days (range, 15 to 220 days). The median new bone formation on the cortical window was grade II. Ten patients’ cortical windows were totally healed with the new bone formation (grade IV) and three patients’ cortical windows were healed more than a half (grade III) (Figure 3). The median MSTS score was 84.5 (range, 66 to 97). Nine patients (28%) underwent prophylactic stabilization. There was no statistically significant difference between tumor size and prophylactic fixation \| New bone formation (%) \| Grading \| \|------------------------\|---------\| \| 0 \| 0 \| \| 1-25 \| 1 \| \| 26-50 \| 2 \| \| 51-75 \| 3 \| \| 76-100 \| 4 \| FIGURE 2. (a) Preoperative X-ray image. (b) Postoperative X-ray image. (c) Postoperative axial and coronal computed tomography sections. FIGURE 3. Categorization of patients according to grading system. Demineralized bone matrix is an alternative allograft product for filling bone defects, which provides bone regeneration mainly through osteoconduction and partly osteoinduction.\[^9\] In recent years, the treatment of benign bone tumors with DBM has become popular in orthopedic and maxillofacial surgery due to its high recovery and low complication rates.\[^10,\] Therefore, it has increased its combined use of other graft materials. There are two level 3\[^12,\] and three level 4 studies,\[^14-16\] which show that combined DBM and autologous bone marrow use is effective in the treatment of active bone cysts. Successful results have been also shown with the use of DBM in combination with steroids.\[^17\] Teng et al.\[^18\] reported that the combined use of allograft and cement in giant-cell bone tumors around the knee has led to less mechanical failure and they suggest this method as an optimal reconstruction strategy. In the literature review, we could not find any data about the combined use of DBM and cement as well as the effect of new bone formation in cortical window on functional scores.\[^19\] By the cement combined DBM treatment, we provide initial mechanical strength by taking advantage of the load-bearing effect of the cement which makes early weight bearing possible. Moreover, we optimize the cost effectiveness and reduce the possibility of graft resorption and fracture by using less DBM. In addition, we also increase cortical bone formation that carries the load on removed cortical window. In our study, we found that 3/32 patients had more than 50% new bone formation on the cortical window and the cortical window of 10/32 patients were almost completely healed with new bone in the first year CT scans. Although the efficacy of DBM to produce live bone is best demonstrated only by histological examination, the thin rim layer, which appears in tomography and direct graphs, shows an increased activity in the scintigraphy. The radiological and histological results are parallel to each other in experimental studies.\[^20\] We did not find any correlation between the functional scores and new bone formation. It is known that the effectivity of different brands of DBMs varies from each other.\[^21\] The reasons of different results have been shown such as the sterilization process, washing procedure, varying from donor to donor resulting in differences between products, inherent BMP types, and different amounts of graft.\[^22,\] The fact that the US Food and Drug Administration (FDA) is not performing standard controls for DBMs was shown to be not a surprise in the diversity of DBM results. We think that we have standardized and optimized our treatment, because we used same brand, which has shown superiority, and same form DBM.\[^21\] Traditionally, aging decreases mesenchymal cell differentiation, collagen activity, bone metabolism, and recipient aging declines the effect of allografts.\[^23\] Also, there is an increased risk of non-union with elder population in DBM-treated patients with lumbar fusion.\[^24\] We found a negative correlation between aging and new bone formation on cortical window consistent with the literature. Prophylactic osteosynthesis is indicated to reduce the possibility of pathological fracture for bone tumors greater than 60 cm$^3$ and in the load bearing areas.\[^25,\] We did not find any correlation between... tumor volume and prophylactic fixation. However, no pathological fracture was seen in any patient. In addition, we found a correlation between cortical window size and the use of prophylactic fixation. The literature is unclear and open to research about the relationship between the size of cortical window and the need for prophylactic fixation. We believe that the complication of pathological fracture can be prevented by this surgical technique using the mechanical effect of cement and the biological effect of DBM. We found that functional results were worse in patients undergoing prophylactic fixation. However, it should not be disregarded that the functional outcomes are relatively worse in a possible pathological fracture.[25] This study has some limitations. First, removal of different types of tumors would affect recurrence, time to return to work, and new bone formation on the cortical window. Second, the distribution of the load on the lower and upper extremities could not be the same; therefore, this may have affected the return to work, new bone formation on the cortical window, and functional scores. In conclusion, the cement combined DBM treatment is a cost-effective, alternative method in tumor surgery, that provides immediate stability and stimulates new bone formation on cortical window. Although new bone formation is achieved on cortical window with this method, new bone formation has not been found to create a change in functional results. The transformation of the new bone to the cortical bone and how long it lasts are open to research. We believe that the histological evaluation of this method supported by controlled studies will guide future tumor treatment methods. Declaration of conflicting interests The authors declared no conflicts of interest with respect to the authorship and/or publication of this article. Funding The authors received no financial support for the research and/or authorship of this article. REFERENCES 1. Nogueira Drumond JM. Benign bone tumors and tumor-like bone lesions: Treatment update and new trends. Rev Bras Ortop 2015;44:386-90. 2. Webb JC, Spencer RF. The role of polymethylmethacrylate bone cement in modern orthopaedic surgery. J Bone Joint Surg [Br] 2007;89:851-7. 3. Hass HJ, Krause H, Kroker S, Wagemann W. Implantation of human demineralized bone matrix (DBM) for the treatment of juvenile bone cysts. Oper Orthop Traumatol 2006;18:19-33. 4. Somville J, De Beuckeleer L, De Schepper A, Verstrekken J, Taminiau A. Reliability of measuring volume by different methods for tumors of the musculoskeletal system. Acta Orthop Belg 2001;67:338-43. 5. Enneking WF, Dunham W, Gebhardt MC, Malawar M, Pritchard DJ. A system for the functional evaluation of reconstructive procedures after surgical treatment of tumors of the musculoskeletal system. Clin Orthop Relat Res 1993;286:241-6. 6. Martinez, M, Hwang, J, Beebe KS. Local adjuvants for benign aggressive bone tumors, Current Orthopaedic Practice 2014;25:573-9. 7. Szalay K, Antal I, Kiss J, Szendroi M. Comparison of the degenerative changes in weight-bearing joints following cementing or grafting techniques in giant cell tumor patients: medium-term results. Int Orthop 2006;30:505-9. 8. Özer D, Er T, Aycan OE, Öke R, Coşkun M, Kabukçuoglu YS. May bone cement be used to treat benign aggressive bone tumors of the feet with confidence? Foot (Edinb) 2014;241-5. 9. Urist MR, Strates BS. Bone formation in implants of partially and wholly demineralized bone matrix. Including observations on acetone-fixed intra and extracellular proteins. Clin Orthop Relat Res 1970;71:271-8. 10. Drosos GI, Touzopoulos P, Ververidis A, Tilkeridis K, Kazakos K. Use of demineralized bone matrix in the extremities. World J Orthop 2015;6:269-77. 11. Dinopoulos H, Dimitriou R, Giannoudis PV. Bone graft substitutes: What are the options? Surgeon 2012;10:230-9. 12. Di Bella C, Dozza B, Frisoni T, Cevolani L, Donati D. Injection of demineralized bone matrix with bone marrow concentrate improves healing in unicameral bone cyst. Clin Orthop Relat Res 2010;468:3047-55. 13. Park IH, Micic ID, Jeon IH. A study of 23 unicameral bone cysts of the calcaneus: open chip allogeneic bone graft versus percutaneous injection of bone powder with autogenous bone marrow. Foot Ankle Int 2008;29:164-70. 14. Kanellopoulos AD, Yiannakopoulos CK, Soucacos PN. Percutaneous reaming of simple bone cysts in children followed by injection of demineralized bone matrix and autologous bone marrow. J Pediatr Orthop 2005;25:671-5. 15. Docquier PL, Delloye C. Treatment of aneurysmal bone cysts by introduction of demineralized bone and autogenous bone marrow. J Bone Joint Surg Am 2005;87:2253-8. 16. Rougraff BT, Kling TJ. Treatment of active unicameral bone cysts with percutaneous injection of demineralized bone matrix and autogenous bone marrow. J Bone Joint Surg Am 2002;84:921-9. 17. Sung AD, Anderson ME, Zurakowski D, Hornicek FJ, Gebhardt MC. Unicameral bone cyst: a retrospective study of three surgical treatments. Clin Orthop Relat Res 2008;466:2519-26. 18. Teng W, Lin P, Li Y, Yan X, Li H, Li B, et al. Bone combined cement grafting in giant cell tumor around the knee reduces mechanical failure. Int Orthop 2019;43:475-82. 19. Atik OŞ. Which articles do we prefer to publish?. Eklem Hastalik Cerrahisi 2018;29:91. 20. Enneking WF, Campanacci DA. Retrieved human allografts: a clinicopathological study. J Bone Joint Surg Am 2001;83:971-86. 21. Peterson B, Whang PG, Iglesias R, Wang JC, Lieberman JR. Osteoinductivity of commercially available demineralized bone matrix. Preparations in a spine fusion model. J Bone Joint Surg Am 2004;86:2243-50. 22. Sammarco VJ, Chang L. Modern issues in bone graft substitutes and advances in bone tissue technology. Foot Ankle Clin 2002;7:19-41. 23. Mueller SM, Glowacki J. Age-related decline in the osteogenic potential of human bone marrow cells cultured in three-dimensional collagen sponges. J Cell Biochem 2001;82:583-90. 24. Ajiboye RM, Eckardt MA, Hamamoto JT, Sharma A, Khan AZ, Wang JC. Does Age Influence the Efficacy of Demineralized Bone Matrix Enriched with Concentrated Bone Marrow Aspirate in Lumbar Fusions?. Clin Spine Surg 2018;31:E30-E5. 25. Perisano C, Barone C, Stomeo D, Di Giacomo G, Vasso M, Schiavone Panni A, et al. Indications for prophylactic osteosynthesis associated with curettage in benign and low-grade malignant primitive bone tumors of the distal femur in adult patients: a case series. J Orthop Traumatol 2016;17:377-82. 26. Kornah B, Safwat H, Ghany TA, Aal MA, Saleem N. Prophylactic Fixation of Impending Fractures. MOJ Orthop Rheumatol 2016;6:00206.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3372, 1 ], [ 3372, 6991, 2 ], [ 6991, 9500, 3 ], [ 9500, 12910, 4 ], [ 12910, 18584, 5 ], [ 18584, 19568, 6 ] ] }
b4eb050ab9608e18ac09d9092d3bf8faecc92224	{ "olmocr-version": "0.1.59", "pdf-total-pages": 14, "total-fallback-pages": 0, "total-input-tokens": 51325, "total-output-tokens": 18706, "fieldofstudy": [ "Biology", "Chemistry" ] }	Quantitative Analysis of Prenylated RhoA Interaction with Its Chaperone, RhoGDI§ Received for publication, April 10, 2012 Published, JBC Papers in Press, May 24, 2012, DOI 10.1074/jbc.M112.371294 Zakir Tnimov‡, Zhong Guo‡, Yann Gambin‡, Uyen T. T. Nguyen‡, Yao-Wen Wu‡, Daniel Abankwa§, Anouk Stigter¶, Brett M. Collins‡, Herbert Waldmann†, Roger S. Goody§, and Kirill Alexandrov‡¶ From the ‡Department of Molecular Cell Biology, Institute for Molecular Bioscience, The University of Queensland, 306 Carmody Road, St. Lucia, Queensland 4072, Australia, the Departments of †Physical Biochemistry and §Chemical Biology, Max-Planck-Institute for Molecular Physiology, Otto-Hahn-Str. 11, 44227 Dortmund, Germany, and the ¶Turku Centre for Biotechnology, University of Turku and Abo Akademi University, BioCity, Tykistokatu 6BFIN-20520 Turku, Finland Small GTPases of the Rho family regulate cytoskeleton remodeling, cell polarity, and transcription, as well as the cell cycle, in eukaryotic cells. Membrane delivery and recycling of the Rho GTPases is mediated by Rho GDP dissociation inhibitor (RhoGDI), which forms a stable complex with prenylated Rho GTPases. We analyzed the interaction of RhoGDI with the active and inactive forms of prenylated and unprenylated RhoA. We demonstrate that RhoGDI binds the prenylated form of RhoA-GDP with unexpectedly high affinity (Kd = 5 pm). The very long half-life of the complex is reduced 25-fold on RhoA activation, with a concomitant reduction in affinity (Kd = 3 nm). The 2.8-Å structure of the RhoA-guanosine 5’-[β,γ-imido] triphosphate (GMPPNP)-RhoGDI complex demonstrated that complex formation forces the activated RhoA into a GDP-bound conformation in the absence of nucleotide hydrolysis. We demonstrate that membrane extraction of Rho GTPase by RhoGDI is a thermodynamically favored passive process that operates through a series of progressively tighter intermediates, much like the one that is mediated by RabGDI. The Rho family of GTPases plays important roles in a plethora of cellular functions. The defining members of this family, RhoA, Rac1, and Cdc42, regulate cytoskeleton remodeling, cell polarity (1, 2), and transcription (3), as well as the cell cycle (4). Similar to other Ras family GTPases, the Rho proteins cycle between the inactive GDP-bound and the active GTP-bound effector binding competent states. This cycle is tightly controlled by guanine nucleotide exchange factors (GEFs) that facilitate loading Rho with guanosine triphosphate (5) and GTPase-activating proteins that dramatically accelerate the intrinsic rate of GTP hydrolysis (6). Similar to the majority of other Ras superfamily members, the Rho proteins are posttranslationally prenylated on their C termini. Rho GTPases are predominantly singly geranylgeranylated, although farnesylatation has also been reported (7). These modifications enable small GTPases to reversibly and dynamically associate with intracellular membranes. In a number of cases, membrane delivery was shown to be functionally coupled to GTPase activation. For instance, GTP loading of the Arf GTPases exposes their otherwise buried myristoylated N-terminal helix and promotes association of Arf proteins with the plasma membrane (8). Similarly, GEF-mediated loading of Rab GTPases with GTP reduces its affinity for its chaperone, Rab GDP dissociation inhibitor (RabGDI), by 3 orders of magnitude and promotes association of GTP-bound RabGTPases with their target membrane (9). As in the case of Rab proteins, membrane/cytosol cycling of geranylgeranylated Rho GTPases is regulated by functionally similar but structurally unrelated GDP dissociation inhibitors (RhoGDIs). In contrast to the RabGDI, RhoGDIs were reported to interact with both GDP- and GTP-bound Rho proteins with similar efficiency (10–13). However, the exact affinities of these interactions are still disputed (14–16). The lack of clear evidence for the role of nucleotide exchange in the dissociation of Rho-RhoGDI complexes has led to a search for alternative mechanisms of the membrane recruitment of Rho. A number of putative GDI displacement factors were proposed to promote dissociation of the RhoGDI-Rho This work was supported in part by Australian Research Council DP Grant DP1094080, ARC FF Grant FT0991611, and National Health Research Council project Grant 569652 (to K. A.). ‡ This article contains supplemental Figs. S1–S6. © 2012 by The American Society for Biochemistry and Molecular Biology, Inc. Published in the U.S.A. The atomic coordinates and structure factors (code 4F38) have been deposited in the Protein Data Bank, Research Collaboratory for Structural Bioinformatics, Rutgers University, New Brunswick, NJ (http://www.rcsb.org/). † To whom correspondence should be addressed. E-mail: [email protected]. § The abbreviations used are: GEF, guanine nucleotide exchange factor; GDI, GDP dissociation inhibitor; GMPPNP, guanosine 5’-[β,γ-imido] triphosphate; ITC, isothermal titration calorimetry; FCCS, fluorescence cross-correlation spectroscopy; TRM, tetramethylrhodamine; CCF, cross-correlation function; GGPP, geranylgeranyl pyrophosphate; FPP, farnesyl pyrophosphate. complexes in vivo. These include receptors, such as p75 NTR (17) and integrins (18), and associated proteins, such as ERM (19) and merlin (20). However, no thermodynamically sound model has been proposed that would explain how GDI displacement factors could reduce the high affinity of the RhoGDI/Rho interaction. One alternative explanation is that these molecules act as scaffold proteins that recruit RhoGEFs (21–23) and membrane phosphoinositides (21), which have been proposed to facilitate Rho/RhoGDI complex dissociation (22). Phosphorylation of RhoGDI or Rho proteins was also shown to influence the Rho/RhoGDI interaction, strongly affecting their association in the cell (23–27). Phosphorylation of Rho GTPases is believed to promote their extraction from the membranes by RhoGDI, whereas phosphorylation of RhoGDI diminishes its ability to bind Rho. Despite numerous reports on the possible mechanisms that govern membrane delivery and recycling of Rho GTPases, a kinetic and thermodynamic description of such mechanisms is still outstanding. Therefore, this study reports on the quantitative biophysical analysis of RhoA interaction with RhoGDI with the objective of determining the kinetic and thermodynamic framework of the Rho functional cycle. In contrast to previous findings, we have demonstrated that RhoGDI discriminates strongly between different nucleotide-bound forms of prenylated and unprenylated RhoA. We provide direct evidence for the existence of two populations of the RhoGDI/RhoA complex in the cell, characterized by different lifetimes. We also propose a thermodynamic model of RhoGDI-mediated RhoGTPase recycling. MATERIALS AND METHODS Protein Expression and Purification—All proteins used in this study were expressed in the Escherichia coli BL21(DE3) Codon plus RIL strain (Stratagene). Expression and purification of FTase, GGTase-I, and RhoA F25N were carried out as described previously (28). RhoGDI was cloned in-frame with maltose-binding protein using the pOPINM vector (29), described previously (28). RhoGDI was cloned in-frame with the pOPINM vector using the forward 5'-CATCACAACACTAG-TATGTTGACCAAAGGCAGGAGCTG-3', and reverse primer 5'-ATTCTCATCAGCC-ATGAGTTGTACCTGTCATGCGAG-3', and subcloning the resulting PCR product into the NcoI sites of the pGATEV vector (30). The C-terminal citrine-RhoGDI was cloned using the in-fusion protocol into the pOPINE vector (30). The C-terminal citrine-RhoGDI was expressed in E. coli, and purified by nickel-nitrilotriacetic acid chromatography. The tag was removed by proteolysis with PreScission protease, and the protein was further purified by gel filtration on a Superdex 200 26/60 column (GE Healthcare). The L193A mutant of RhoA F25N was constructed by PCR mutagenesis of the pGATEV-RhoAF25N plasmid using the forward 5'-GATGGGTATCCATGGCTGATG-3', and reverse primer 5'-GGATCCCTCGAGTCATGCGACAAGGCAAGCC-3', and subcloning the resulting PCR product into the NcoI sites of the Xhol sites of the pGATEV vector (30). The C-terminal citrine-RhoGDI was cloned using the in-fusion protocol into the pOPINE vector (29). The Cterminal citrine-RhoGDI was cloned using the in-fusion protocol into the pOPINE vector (29). FTase, GGTase-I, and RhoA F25N were carried out as described previously (31). Expression and purification of FTase, GGTase-I, and RhoA F25N were carried out as described previously (31). Fluorescence Measurements—Fluorescence spectra and long-time base fluorescence measurements were performed at 25 °C in 1-ml quartz cuvettes (Hellma, Germany) with continuous stirring on a Spex Fluoromax-3 or Fluoromax-4 spectrofluorometer (Jobin Yvon Inc., USA). Fluorescence titrations were carried out in buffer containing 25 mm Hepes-NaOH, pH 7.2, 40 mm NaCl, 2 mm MgCl2, 2 mm dithioerythritol, and 20 μM GDP or 20 μM GMPPNP, and 20 μM ZnCl2. A typical reaction contained 60 nmol of the prenyltransferase, mixed with 2-fold excess of RhoA and 260 nmol of GGPP (Sigma) or 550 nmol of NDB-GPP (28). The Rho farnesylation reaction contained 10 nmol of FTase, 100 nmol of RhoA, and 400 nmol of FPP (Sigma). After incubation for 4 h at room temperature, the reaction mixture was chromatographed on a Superdex 200 10/30 gel filtration column (GE Healthcare) equilibrated with prenylation buffer without ZnCl2. The flow rate was 0.35 ml/min, and fractions of 0.3 ml were collected and analyzed by 15% SDS-PAGE. When the fluorescent analog was used as a substrate, the gel was scanned using a Typhoon Trio fluorescent scanner (GE Healthcare) (excitation 488 nm; cutoff filter 520 nm), and the gel was subsequently stained with Coomassie Blue. Isoprenoid conjugation was confirmed by electrospray ionization-mass spectrometry of the selected fractions. The eluted fractions containing the protein complex were combined, concentrated, flash-frozen in liquid nitrogen, and stored at −80 °C. The complex of geranylgeranylated RhoA and GGTase-I was obtained by size exclusion chromatography on a Superdex 200 column of the in vitro prenylation reaction containing equimolar amounts of GGTase-I and RhoA. The fractions containing the protein complex were collected, concentrated to 10 mg/ml, and stored as described above. Labeling of the RhoGDI with Maleimide Dyes—The tetramethylrhodamine-maleimide dye was obtained from Molecular Probes, and RhoGDI labeling was performed according to the manufacturer’s protocol. The degree of labeling, based on spectroscopic observation, was typically 50%. Enzymatic Prenylation of the RhoA—Purified RhoA was enzymatically prenylated in vitro by GGTase-I using geranylgeranyl or NBD-geranyl pyrophosphates as substrates. RhoA F25N was farnesylated by FTase using FPP as a substrate. The prenylation reaction was carried out in 2–4 ml of prenylation buffer containing 25 mm Hepes-NaOH, pH 7.2, 40 mm NaCl, 2 mm MgCl2, 2 mm dithioerythritol, 20 μM GDP or 20 μM GMPPNP, and 20 μM ZnCl2. A typical reaction contained 60 nmol of the prenyltransferase, mixed with 2-fold excess of RhoA and 260 nmol of GGPP (Sigma) or 550 nmol of NDB-GPP (28). The Rho farnesylation reaction contained 10 nmol of FTase, 100 nmol of RhoA, and 400 nmol of FPP (Sigma). Primary data analysis was performed with the programs Grafit 5.0 (Erithacus software) and “fluorescence” implementation (Jobin Yvon Inc., USA) of Origin 7.0 (Originlab Corp., USA). Quantitative Analysis of RhoA Interaction with RhoGDI Fluorescence Cross-correlation Measurements—Measurements were done on an inverted laser scanning confocal microscope Zeiss LSM 710 FCS, equipped with a Confocor 3 module (FCCS detector head and APD detectors). Normally, the excitation laser beams were focused on 20 μl of the sample, placed on the well of an in-house made silicon plate mounted on an optically clear coverslip. Emitted light from the 458-nm and 561-nm lasers passed through an adjustable pinhole and a 458/561 main beam splitter and was separated on a 565-nm dichroic mirror. The 470–540-nm spectra segment was used to quantify fluorescence from CFP, whereas a long pass 580-nm filter was set for measuring the tetramethylrhodamine dye signal. The laser power was set up to achieve a count rate (CPM) that was not giving detectable cross-talk. Typically, CPM was kept at 8 to 12 kHz. The data acquisition time was at least 100 s and included 10 runs of 10 s each. The collected data were analyzed using the ZEN 2011 Zeiss software package. The theoretical basics of autocorrelation and cross-correlation analysis are described everywhere (32). Experimental autocorrelation functions were fitted in a three-dimensional diffusion model (33) for a 2-component model. The Kd for the interaction of geranylgeranylated CFP-RhoA and tetramethylrhodamine-labeled RhoGDI (RhoGDI-TMR) was quantified based on the assumption that the amplitude of the cross-correlation function (CCF) corresponds linearly to the concentration of the CFP-RhoA-GG-RhoGDI-TMR complex. The CCF values obtained by titration of the 50 nM CFP-RhoA-GG-RhoGDI-TMR solution with farnesylated RhoA were fitted to the 3-component competitive model in DynaFit 4.0 (Biokin Ltd.) (34). Analysis of Titrations of NBD-geranylated RhoA Versus Increasing Concentration of RhoGDI or GGTase-1—Titration experiments were done on an inverted laser scanning confocal microscope Zeiss LSM 710 FCS, equipped with a Confocor 3 module (FCCS detector head and APD detectors). Normally, the excitation laser beams were focused on 20 μl of the sample, placed on the well of an in-house made silicon plate mounted on an optically clear coverslip. Emitted light from the 458-nm and 561-nm lasers passed through an adjustable pinhole and a 458/561 main beam splitter and was separated on a 565-nm dichroic mirror. The 470–540-nm spectra segment was used to quantify fluorescence from CFP, whereas a long pass 580-nm filter was set for measuring the tetramethylrhodamine dye signal. The laser power was set up to achieve a count rate (CPM) that was not giving detectable cross-talk. Typically, CPM was kept at 8 to 12 kHz. The data acquisition time was at least 100 s and included 10 runs of 10 s each. The collected data were analyzed using the ZEN 2011 Zeiss software package. The theoretical basics of autocorrelation and cross-correlation analysis are described everywhere (32). Experimental autocorrelation functions were fitted in a three-dimensional diffusion model (33) for a 2-component model. The Kd for the interaction of geranylgeranylated CFP-RhoA and tetramethylrhodamine-labeled RhoGDI (RhoGDI-TMR) was quantified based on the assumption that the amplitude of the cross-correlation function (CCF) corresponds linearly to the concentration of the CFP-RhoA-GG-RhoGDI-TMR complex. The CCF values obtained by titration of the 50 nM CFP-RhoA-GG-RhoGDI-TMR solution with farnesylated RhoA were fitted to the 3-component competitive model in DynaFit 4.0 (Biokin Ltd.) (34). Global Fitting Analysis of Competitive Titrations—Competitive titration was performed by titrating the mixture of fluorescent RhoA-GNBD and prenylated RhoA-GGTase-1 complex with increasing concentrations of RhoGDI. The global fitting procedure of the obtained data were performed in DynaFit 4.0 (Biokin Ltd.) (34). Stopped-Flow Measurements—The kinetics of the prenylated RhoA interaction with RhoGDI was analyzed using an SF-61MX stopped flow apparatus (High Tech Scientific). Isothermal Titration Calorimetry Measurements—Binding affinities of the unprenylated GDP- and GMPPNP-bound forms of RhoA to RhoGDI were determined using ITC200 (MicroCal). All proteins were kept in buffer containing 25 mM Heps-NaOH, pH 7.2, 40 mM NaCl, 2 mM MgCl2, and 1 mM DTT. The concentration of RhoA protein in the syringe was at least 10-fold higher than the concentration of protein in the cell (typically 10 μM). In control experiments, the respective protein was injected from the syringe into the buffer solution, and the recorded background signals were subtracted from the titration experiment data. The titration experiments were carried out at 25 °C in triplicate. The data obtained were fitted using the MicroCal-ITC implementation of the Origin 7 software package. Crystallization of RhoA-GMPPNP-GG-RhoGDI Complex, Data Collection and Structure Determination—Initial crystallization conditions were determined at room temperature using the PEG ion kit from Hampton Research in 200-nl sitting drops, set up against a 50-μl reservoir with a Mosquito nanoliter dispensing robot (TTP LabTech). Promising conditions were optimized with respect to precipitant composition, pH, temperature, and protein concentration and were transferred to hanging drops prepared by mixing 1 μl of protein complex solution with 1 μl of precipitant mixture. Crystals for data collection were obtained at 20 °C with a reservoir consisting of 20% (w/v) PEG 3350, 0.2 M MgCl2, and 0.1 M Heps-NaOH, pH 7.4. The protein complex was used at 13 mg/ml in buffer containing 25 mM Heps-NaOH, pH 7.2, 40 mM NaCl, 2 mM MgCl2, 10 μM GMPPNP, and 1 mM Tris(2-carboxyethyl)phosphate. Prior to flash-cooling in liquid nitrogen, the crystals were washed briefly in 25% (w/v) PEG 3350, 5% (v/v) glycerol, 0.2 M MgCl2, and 0.1 M Heps, pH 7.4. Diffraction data were collected at 100 K at station MX2 of the Australia Synchrotron (Melbourne, Australia). The data were processed with XDS (55). The crystals belonged to the orthorhombic space group P212121 and contained 1 RhoA-GG-RhoGDI complex in the asymmetric unit. Initial phases were determined by molecular replacement with PHASER (56) of the CCP4 suite, using coordinates of Cdc42-GDP-GG-RhoGDI (PDB code 1DOA) from which the nucleotide, Mg2+, and prenylated C terminus of Cdc24 had been deleted. The model was then corrected by alternating rounds of refinement in REFMAC5 (57) and manual adjustment in COOT (58). Restrained libraries were generated with. Quantitative Analysis of RhoA Interaction with RhoGDI FIGURE 1. Interaction analysis of RhoGDI with unprenylated RhoA. A, representative ITC data for titration of 10 μM RhoGDI with either 160 μM RhoA-GDP (filled squares) or buffer (open squares). Solid curve represents a fit of the data to a 1:1 stoichiometry binding model with a calculated K_d value 213 nM; B as in A except that RhoGDI was titrated with 130 μM RhoA-GMPPNP (filled squares) or buffer (open squares). The fit resulted in a K_d value of 5.7 μM. C, kinetic analysis of the RhoGDI interaction with unprenylated RhoA-mGDP. A typical fluorescence change observed upon mixing 0.4 μM RhoAmGDP with 8 μM RhoGDI. The inset represents a plot of the observed rates as function of RhoGDI concentration. D, fluorescence change upon mixing of 0.4 μM RhoAmGDP-RhoGDI complex with 5 μM RhoA-GDP. E, fluorescence change resulting from mixing of 0.4 μM RhoA-mGMPPNP with 12 μM RhoGDI. The inset represents the plot of observed rates as a function of RhoGDI concentration. F, fluorescence change upon mixing of 1.2 μM RhoA-mGMPPNP-RhoGDI with 20 μM RhoA-mGMPPNP. TABLE 1 Summary of thermodynamic and kinetic parameters of the RhoGDI interaction with GDP- and GMPPNP-associated RhoA \| Protein \| K_on [μM⁻¹·s⁻¹] \| K_off [s⁻¹] \| K_d [μM] \| \|---------------------\|----------------\|-------------\|----------\| \| RhoA-GDP \| 2.42 ± 0.15 \| 0.54 ± 0.01 \| 0.17 × 10⁻⁶ \| \| RhoA-GMPPNP \| 3.8 ± 1.9 \| 8.77 ± 0.73 \| 2.5 × 10⁻⁸ \| \| CFP-RhoA-GDP-GG \| 37₉ \| (2.0 ± 0.02) × 10⁻⁴ \| (5.4 ± 2.5) × 10⁻¹² \| \| CFP-RhoA-GMPPNP-GG \| 1.6₉ \| (4.6 ± 0.03) × 10⁻³ \| (2.9 ± 0.65) × 10⁻⁹ \| \| RhoA-GDP-GNBD \| 10.7 ± 0.7 \| (5.8 ± 0.3) × 10⁻² \| (2.0 ± 0.15) × 10⁻⁹ \| \| RhoA-GDP-F \| ND \| ND \| (2.5 ± 1.1) × 10⁻⁹ \| * Calculated from k_on = k_off/K_d. ND, not determined. PRODRG (59). Interface analysis was performed with PISA at the EBI website (35). Structure figures were generated using PyMOL. RESULTS Interaction Analysis of RhoGDI with Unprenylated RhoA—To gain insight into the mechanism of the interaction of RhoGDI with RhoA GTPase and the role of the nucleotide-bound state in this process, we assessed the thermodynamics of this interaction. We measured the affinity of the interaction between RhoGDI and recombinant unprenylated RhoA, loaded with GDP- or the unhydrolyzable GTP analog GMPPNP, using isothermal titration calorimetry (ITC). We found that RhoGDI forms a complex with GDP- and GMPPNP-bound RhoA with K_d values of 0.17 and 2.5 μM, respectively (Fig. 1, A and B). To confirm the obtained affinity values using an independent method, we decided to characterize the kinetics of this interaction. We loaded RhoA molecules with the fluorescent nucleotide mant-GDP or mant-GMPPNP, a nonhydrolyzable fluorescent analog of GTP. Rapid mixing of the mant nucleotide-loaded RhoA with RhoGDI in a stopped-flow apparatus resulted in time-dependent fluorescence signal changes. The plots in Fig. 1, C and E, represent a typical fit to the experimental data. The insets show the dependence of the pseudo-first order rate constants on the concentration of RhoGDI. Although the data give a good estimate of the k_on values, the k_off cannot be extracted from the intercept with y axis reliably, due to its low value in the case of GDP-bound RhoA and low signal amplitudes in the case of the GMPPNP-bound form. Therefore, we determined K_d values experimentally by displacing mant nucleotide-labeled RhoA from RhoA-RhoGDI complexes with an excess of nonlabeled GDP-bound RhoA (Fig. 1, D and F). Analysis of the kinetic parameters of the RhoGDI interaction with both nucleotide-bound forms of RhoA (Table 1) shows that the affinity differences stem from a 15-fold faster off-rate of the RhoGDI complex with the activated RhoA. The affinities that were calculated from the kinetic constants were 0.2 μM for GDP-bound and 2.3 μM for GMPPNP-bound RhoA and are in good agreement with the K_d values obtained in the ITC measurements. To assess the role of the RhoA C terminus in RhoGDI-Rho complex assembly, we prepared C-terminal truncated Δ9 and Δ13 RhoA mutants that lacked the C-terminal stretch lysines or in addition arginine residues, respectively (Fig. 2A). Interaction of the truncation mutants with RhoGDI was assessed by ITC as described for the wild-type protein. The titration experiments showed that deletion of 9 C-terminal residues led to a 15-fold decrease in the affinity of the RhoA/RhoGDI interaction (Fig. 2, B and C). Further deletion of C-terminal residues did not sig- nificantly decrease the affinity (supplemental Fig. S1, A and B). These data suggest that similar to the Rab GTPases, the C terminus of the RhoA significantly contributes to the affinity of the RhoGDI-Rho complex (36). The presence of a lysine- and arginine-rich patch in the C terminus of other Rho GTPases suggests that this is a generic feature that may be important for RhoGDI-mediated membrane recycling of Rho GTPases, because it is also involved in the interaction with negatively charged lipids (22, 37). Fluorescent Prenylated RhoA as a Sensor of RhoGDI/Rho Interaction —To elucidate the mechanism underlying RhoGDI-mediated delivery and extraction of Rho GTPases, it is important to characterize RhoGDI interactions with prenylated Rho proteins. Hence, we sought to develop a fluorescent sensor that would report on the interaction of RhoGDI with prenylated RhoGTPases. This is a challenging task, because prenylated proteins display low water solubility, which largely precludes their direct biophysical analysis. All previous experiments relied on detergent-solubilized prenylated proteins, a situation that is known to strongly change the properties of prenylated proteins (41, 42). To alleviate this problem, we took advantage of synthetic phosphoisoprenoids modified with the fluorescent NBD group. These analogs of FPP and GGPP can transfer fluorescent lipid moieties onto proteins by protein prenyltransferases. These are less hydrophobic than the native lipids due to the shorter isoprenoid chain (28) (Fig. 3A). We enzymatically prenylated the RhoA protein using recombinant GGTase-I and NBD-geranyl pyrophosphate as a lipid donor. The reaction mixture was resolved on a size exclusion column, and the fluorescently prenylated RhoA was eluted at a position corresponding to a 20-kDa monomer. The protein was homogeneous (Fig. 3B) and remained soluble in the absence of detergent, even at concentrations above 10 mg/ml. ESI-MS analysis of the fractions revealed that the majority of protein was modified with geranyl-NBD (Fig. 3C). Purified RhoA-GNBD was also correctly folded, because it was able to form a stoichiometric complex with RhoGDI, as determined by gel filtration analysis (supplemental Fig. S2A). Addition of saturating concentrations of RhoGDI to a solution of RhoA-GNBD resulted in a 1.5-fold decrease in NBD fluorescence that could be used for titration experiments (Fig. 3D). Fitting the data to a quadratic equation led to a $K_d$ value of 2 nM (Fig. 3E). To confirm this affinity estimate by an independent method and gain insight into the kinetics of the interaction, we rapidly mixed both proteins in a stopped-flow apparatus. The observed trace could be fitted using a single exponential function (Fig. 3F). A linear fit of the observed first-order association rate constants at a range of concentrations allowed us to determine a $k_{on}$ value of $10.7 \times 10^6 \text{M}^{-1} \text{s}^{-1}$ for this reaction. To obtain the $k_{off}$ value for this interaction, we mixed 100 nM ![FIGURE 2. Thermodynamic analysis of RhoGDI interaction with C-terminal-truncated RhoA mutants. A, the alignment of human RhoA, Cdc42, and Rac1 protein sequences. The prenylatable cysteine is highlighted in bold, the gray background represents conservative sequence of positively charged amino acid residues, and the C-terminal $\alpha$-helix is underlined. The C-terminal truncation of RhoA are indicated by arrows at corresponding positions. Titration of 10 $\mu$M solution of wild-type RhoA (B) or RhoA with a C-terminal deletion of 13 residues (C) with RhoGDI.](image-url) Quantitative Analysis of RhoA Interaction with RhoGDI RhoGDI-Rho-GNBD complex with 1 μM farnesylated RhoA. This resulted in a time-dependent increase in fluorescence, reflecting dissociation of RhoGDI-RhoA-GNBD and formation of the RhoGDI-Rho-F complex. The fit of the data resulted in a dissociation rate constant of 0.06 s⁻¹ (supplemental Fig. S2B). From the obtained kinetic parameters, we calculated a $K_d$ value of 5.6 nM, which is in good agreement with the equilibrium titration experiments. These data demonstrate that RhoA-GNBD binds to RhoGDI with an affinity higher than that corresponding to $K_d$ of 7, 30, or 180 nM, respectively, estimated for RhoGDI interactions with the native geranylgeranylated Rho protein Cdc42 (15, 16, 38). Taken together, these results suggest that NBD-G mimics the native isoprenoid and that the developed sensor can be used to analyze RhoA/RhoGDI interactions. Interaction of Farnesylated RhoA with RhoGDI—Several Rho proteins can exist in both farnesylated and geranylgeranylated forms in vivo (39–41, 45, 46). Thus, it is expected that RhoGDI will govern the interaction of both prenylated forms with membranes, but the biophysical parameters may differ significantly. To analyze the interaction of farnesylated RhoA with RhoGDI, we generated the RhoAL193A mutant, which is a more efficient FTase substrate than wild-type of RhoA. The protein was farnesylated by recombinant mammalian FTase and purified the resulting complex by size exclusion chromatography. The proteins coeluted as a stoichiometric complex at a position corresponding to a molecular mass of 160 kDa (Fig. 4B). MALDI-MS analysis demonstrated that the majority of RhoA in the complex was geranylgeranylated (Fig. 4C). The availability of solubilized Preparation of Solution-stabilized Geranylgeranylated RhoA and Analysis of Its Interaction with RhoGDI—The data described above demonstrate that prenylation of RhoA significantly increases its affinity for RhoGDI. However, so far, it is unclear to what extent an increase in the length of the isoprenoid chain would influence the strengths of this interaction. This is particularly important because Rho proteins are predominantly geranylgeranylated. In contrast to RhoA-GNBD and farnesylated RhoA, geranylgeranylated RhoA is insoluble in water and rapidly aggregates. To overcome this problem, we took advantage of the observation that prenyltransferases form stable complexes with their reaction products in the absence of excess of lipid donor (43). Hence, we geranylgeranylated RhoA in vitro with recombinant GGTase-I using stoichiometric amounts of both proteins and purified the resulting complex by size exclusion chromatography. The proteins coeluted as a stoichiometric complex at a position corresponding to a molecular mass of 160 kDa (Fig. 4B). MALDI-MS analysis demonstrated that the majority of RhoA in the complex was geranylgeranylated (Fig. 4C). RhoA-GG enabled us to measure the affinity of the RhoGDI interaction with RhoA-GG using RhoA-GNBD as a fluorescent reporter. In this experiment, we titrated RhoGDI to a mixture of 50 nM RhoA-GNBD with 100, 200, or 400 nM of the RhoA-GG/GGTase-I complex. As depicted in Fig. 4D, the titration resulted in an initial increase of fluorescence, followed by its quenching. This can be interpreted as the initial displacement of GGTase-I from the RhoA-GG complex by RhoGDI and the association of GGTase-I with RhoA-GNBD. At higher concentrations, however, all RhoA-GNBD became sequestered by RhoGDI, leading to a signal decrease. We confirmed this by analyzing the interaction of GGTase-I with RhoA-GNBD (supplemental Fig. S4). The availability of the affinity values for the RhoGDI and GGTase-I interactions with RhoA-GNBD and the corresponding fluorescence yields prompted us to attempt to extract the affinity for the RhoA-GG interaction with RhoGDI and GGTase-I from these data. This is a challenging task because it requires a quantitative description of a 4-component system with 2 sets of competitive interactions, i.e., RhoA-GNBD + RhoGDI ⇔ RhoA-GNBD-RhoGDI and RhoA-GNBD + GGTase I ⇔ RhoA-GNBD-GGTase I, and RhoA-GG + RhoGDI ⇔ RhoA-GG-RhoGDI and RhoA-GG + GGTase I ⇔ RhoA-GG-GGTase I, related to each other in a nonlinear fashion. Implementing a recursive least square minimization in Dynafit (Biokin Ltd.) (34) allowed us to calculate the $K_d$ values for the interactions of native prenylated RhoA with RhoGDI and GGTase I. The fit- ting procedure consistently gave us differences of 3 orders of magnitude in the affinities of RhoA-GG/GGTase I and RhoA-GG/RhoGDI interactions, the values of which are 5.4 nM and 5.6 nM, respectively. The affinity for the RhoA-GG/RhoGDI interaction was unexpectedly high, particularly in the view that RabGDI interacts with GDP-bound diprenylated Rab proteins with an affinity nearly 500 times lower (9). Thus, we sought to confirm the RhoA-GG/RhoGDI dissociation constant value by an independent and more direct method. We decided to use fluorescence cross-correlation spectroscopy (FCCS), because it allows direct monitoring of interacting molecules at very low concentrations. To this end, we genetically fused the RhoA N terminus with CFP and produced the proteins in pure recombinant form. We then took advantage of the fact that RhoGDI contains only one solution-exposed cysteine residue (Cys-79) that is located on the loop after β-strand A and that is not involved in interaction with Rho GTPases. Thus modification of this residue does not affect its association with RhoA (38). We chemically labeled RhoGDI with tetramethylrhodamine-maleimide (RhoGDI-TMR). The complex of RhoGDI-TMR with geranylgeranylated GDP-bound CFP-RhoA was formed by mixing both components and purifying the resulting complex by gel filtration (supplemental Fig. S5). As a measure of CFP-RhoA-GG/RhoGDI-TMR complex concentration in the FCCS analysis, we used the cross-correlation function (CCF) (44). We observed a decrease in the CCF value upon addition of farnesylated RhoA, which indicates competitive formation of the RhoGDI-RhoA-F complex. Fitting the competitive titration curve of the CFP-RhoA-GG/RhoGDI-TMR fluorescent complex with RhoA-F using a 3-component competitive model led to a $K_d$ value of 20 pM (Fig. 5B). This provides direct and independent confirmation of the FIGURE 5. Interaction analysis of prenylated RhoA interaction with RhoGDI. A, competitive displacement of the CFP-RhoA-GDP-GG-RhoGDI-TMR complex by farnesylated RhoA observed by FCCS. Open circles correspond to the value of the cross-correlation function at the indicated concentrations of RhoA-F. Solid line is the fit of experimental data to a competitive binding model, leading to a $K_d$ value of 21 pm. Bars represent S.D. from two independent measurements. B, titration of RhoGDI into the 25 nM solution of RhoA-GNBD in the absence (filled circles) or presence of 100 (open circles), 200 (filled triangles), or 400 (open triangles) of the RhoA-GMPPNP-GG/GGtase-l complex. The data were fitted globally by numerical simulation to a competitive binding model in the program Dynafit 4.0. The $K_d$ values obtained for the RhoA-GG/GGtase-I interaction is ~12 nM, and for RhoA-GG/GMPPNP/RhoGDI, the affinity is ~2.9 nM. C, kinetics of dissociation of the CFP-RhoA-GG/RhoGDI-citrine complex, measured by the changes in FRET efficiency ($\lambda_{em, DONOR} = 436$ nm, $\lambda_{em, ACCEPTOR} = 530$ nm). In the experiment, 30 nM CFP-RhoA was displaced from the complex by the addition of 2 μM farnesylated RhoA. Purple curve corresponds to a $E_{FRET}$ change upon dissociation of CFP-RhoA-GDP-GG-RhoGDI-citrine complex, whereas red represents the change in $E_{FRET}$ of dissociating CFP-RhoA-GMPPNP-GG-RhoGDI-citrine. Blue and green curves are $E_{FRET}$ of corresponding complexes alone. Black solid lines are fits to a single exponential function with offset. D, represents titration of CFP-RhoAGDP-GG/RhoGDI-citrine complex with farnesylated RhoA. The fit of experimental data led to a $K_d$ of the CFP-RhoAGDP-GG interaction with RhoGDI of 16 pm. low picomolar affinity of RhoGDI to geranylgeranylated RhoA. Interaction of Activated Geranylgeranylated RhoA with RhoGDI—The current model of GTPase action postulates that GTPases are activated upon membrane delivery and recycled to the cytosol following completion of the functional cycle, marked by GTP hydrolysis. However, several reports suggest that RhoGDI can also efficiently interact with GTP-loaded Rho proteins (10, 11, 15, 16) and promote their release from the intracellular membranes (45, 46). We therefore measured the affinity of RhoGDI for the activated form of prenylated RhoA. We prepared the GMPPNP-bound form of geranylgeranylated RhoA using the approach described for the production of the GDP-bound form of RhoA-GG. We then titrated RhoGDI to a mixture of 25 nM RhoA-GNBD with 100, 200, 400, or 600 nM of the RhoA-GMPPNP-GG-RhoGDI complex (Fig. 5B). Global fit of the titration data resulted in a $K_d$ value of 3 nM for the RhoA/GMPPNP-GG/RhoGDI interaction, whereas the affinity of RhoA-GG interaction with GTTase-I was slightly lower for the GMPPNP-bound form of RhoA, with a $K_d$ value of 12 nM. Thus, RhoGDI displays a 500-fold difference in affinity between the GDP- and GTP-bound forms of geranylgeranylated RhoA. Our data demonstrate that similar to RabGTPases, the nucleotide-bound state of RhoA dramatically affects its affinity for its GDI. Although the discrimination factor is somewhat less than in the Rab/RabGDI interaction (about 2 $\times$ 10$^3$), it is still large and likely to play an important biological role. The fact that affinities for both forms are so high provides an explanation for previous confusion in the field, because most of the biochemical methods of protein interaction analysis cannot distinguish between low nanomolar and picomolar affinities. Analysis of Dissociation Rates of RhoGDI-RhoA-GG Complexes—The postulated biological role of RhoGDI is to sequester the Rho proteins in the cytosol and to transport them to a target membrane. Although the exact time scale of this process is unknown, it is expected to be on the order of minutes (47). This would require Rho-GG/RhoGDI complexes to have a dissociation rate that is slow (2 to 10$^3$ s$^{-1}$). This notion promoted us to determine the dissociation rates of the RhoA-GG-RhoGDI complex experimentally, because the dissociation rate will take about 1 h, which is probably too slow to allow the complex to operate in cellular systems that require responses on a time scale of minutes. Crystal Structure of the RhoA-GMPPNP-GG-RhoGDI Complex—To gain insight into the molecular basis of RhoA-GTP recognition by RhoGDI, we attempted a structural analysis of the activated form of the complex. Using the in vitro prenylation approach described above, we generated preparative amounts of the RhoA-GMPPNP-GG-RhoGDI complex and subjected it to crystallization trials and diffraction testing, as described under "Materials and Methods." The best diffracting crystal was used to collect the dataset to 2.8 Å using a synchrotron beam source. The structure was solved by molecular ### TABLE 2 Data collection statistics for the structure of geranylgeranylated RhoA-GMPPNP-GG/RhoGDI complex \| Parameter \| Value \| \|------------------------------------------\|----------------------------\| \| Wavelength (Å)/beamline \| 0.9537/AS-MXII \| \| Resolution (highest shell, Å) \| 68.0–2.8 (2.9–2.8) \| \| Space group \| P2_1_2_1 \| \| Cell constants (Å$^3$) \| $a = 46.0$, $b = 71.6$, $c = 136.0$; $a = b = y = 90$ \| \| $V_m$ \| 56,189 \| \| Unique reflections \| 20,741 \| \| Average redundancy \| 2.7 (2.7) \| \| Completeness (%) \| 123.3 (3.6) \| \| $R_{ ext{free}}$ \| 97.0 (98.1) \| \| Wilson B-factor (Å$^2$) \| 6.9 (26.2) \| \| Refinement \| 41.7 \| \| Resolution (highest shell, Å) \| 2.8 (2.8–2.8) \| \| $R_e$ \| 20.6 (20.7) \| \| Root mean square deviation bonds (Å$^2$) \| 0.015/1.743 \| \| $B$-factor deviation \| \| \| Bonds/angles (Å$^2$) \| \| \| Main chain \| 0.716/1.415 \| \| Side chain \| 2.095/3.696 \| \| Residues in ramachandran core (%) \| 92.0 \| \| Protein atoms \| 2997 \| \| Solvent atoms \| 80 \| \| Ligand atoms \| 54 \| \| Average B-factor (Å$^2$) \| 32.7 \| $R_{ ext{free}} = \Sigma (I_F - I_{c})/\Sigma (F_i)$, where $I_F$ is the measured diffraction intensity, and the summation includes all observations. $R_e = (\Sigma \|F_o\| - \|F_c\|)/\Sigma \|F_o\|$, where $F_o$ is the observed structure factor. $R_{ ext{free}}$ is the $R$-factor calculated using 5% of the data that were excluded from the refinement. Ramachandran core refers to the most favored regions in the $\psi$-$\psi$-Ramachandran plot, as defined by Laskowski et al. (61). replacement using the Cdc42-GDP-GG-RhoGDI structure as a search model (48). Full data collection and refinement statistics are given in Table 2. The overall structure of the complex is shown in Fig. 6A. The structure is remarkably similar to the structure of the Cdc42-GDP-GG-RhoGDI complex (PDB 1DOA), with an overall root mean square deviation on the α-chain of 0.87 Å. Total interface area in the RhoA-GMPPNP-GG-RhoGDI complex excluding geranylgeranyl-RhoGDI hydrophobic pocket interface is somewhat smaller than in the structure of Cdc42-GDP-GG-RhoGDI complex (1340 versus 1580 Å²) with a significantly lower number of hydrogen bonds and salt bridges forming the RhoA-GMPPNP-GG-RhoGDI complex. These differences predominantly come from extensive interaction of RhoGDI with residues Arg-186 and Arg-187 of Cdc42. The C terminus of RhoA does not have a diarginine patch, instead there are 3 lysine residues that do not form hydrogen bonds with RhoGDI and are solely involved in the electrostatic interaction. The position of geranylgeranyl moiety buried into the hydrophobic pocket on the RhoGDI is nearly identical to what is identified on the structure of Cdc42-GG-GDP-RhoGDI. The minor differences such as involvement of RhoGDI-Leu-170 in interaction with the RhoA geranylgeranyl group are unlikely to be functionally significant. Despite the differences in the interface of RhoGDI complexes with RhoA and Cdc42 the total free binding energy calculated by PISA (35) is similar for both complexes: 25.6 kJ/M for RhoA-RhoGDI and 27.4 kJ/M for Cdc42-RhoGDI. The Rho-specific helix in the RhoA-GDP-GG-RhoGDI structure has different conformations than both in the free form of Cdc42 and in the Cdc42 complex with RhoGDI. In contrast to the Cdc42 the Rho insert in the structures of free RhoA and in complex with RhoGDI has an almost identical position. This might reflect differences in the signaling modes of the RhoA and Cdc42 GTPases in the cell (49). Strikingly, the switch I and II loops of RhoA-GMPPNP adopt a nearly identical conformation to those of Cdc42-GDP in complex with RhoGDI. As can be seen in Fig. 6C, the conformations of both switch I and switch II regions in the complex differ markedly from the conformations observed in unliganded RhoA-GMPPNP. Although switch I adopts a conformation nearly identical to that of GDP-bound RhoA, the switch II region adopts a conformation distinct from both free forms, due to the extensive contacts formed with the N terminus of RhoGDI. The phosphate groups of the bound nucleotide are shifted slightly toward the exterior of the protein, possibly reflecting the fit induced by the complex formation. Overall, the Quantitative Analysis of RhoA Interaction with RhoGDI FIGURE 6. Structure of RhoA-GMPPNP-GG-RhoGDI complex (PDB 4F38). A, overall structure of the complex. RhoGDI is displayed as a gray molecular surface, whereas RhoA is displayed in ribbon representation. The nucleotide and the conjugated geranylgeranyl isoprenoid are displayed in ball-and-stick representation. The Mg²⁺ is displayed as a space-filling magenta ball. B, 2.5 σ (Fo − Fc) difference in electron density of the bound GMPPNP and geranylgeranylated cysteine at the RhoA C terminus before incorporation into the model. C, superimposition of the prenylated CDC42-GDP and RhoA-GPPNHP complexed with RhoGDI. D, as in C but RhoA-GMPPNP complexed with RhoGDI is superimposed with unbound GMPPNP-associated (red) and GDP-associated (blue) forms of RhoA. guanine nucleotide in the structure of RhoA-GMPPNP-GG-RhoGDI has a 15% smaller interaction interface and less number of hydrogen bonds than in the structure of RhoA$^{G14V}$-GTP$\gamma$S alone (50). For instance, there is no interaction between phosphate oxygen atoms and Ala-15 from the P-loop, switch I residues Tyr-34 and Thr-37 are no longer involved in nucleotide-phosphate positioning. Interestingly, important for GTP hydrolysis, the Gln-63 residue in the RhoA-GMPPNP-GG-RhoGDI structure is located closer than in RhoA$^{G14V}$-GTP$\gamma$S, which results in hydrogen bond formation between its amide group and the oxygen of $\gamma$-phosphate with an overall distance of 3.84 Å. The observed structure demonstrates that even in the GTP-bound form, the loop regions of RhoGTPases are sufficiently flexible to adopt an inactive conformation upon binding to RhoGDI. The resulting conformational strain can be compensated by the very high binding energy of the complex formation and results in a complex that is structurally identical to the inactive conformation but displays a faster dissociation rate. DISCUSSION** In the present study, we have performed a comprehensive analysis of the interaction of RhoGDI with prenylated and unprenylated forms of RhoA using kinetic and thermodynamic measurements. We have focused on the role of prenylation and the nucleotide-bound state on complex formation and its implications for recycling RhoGTPases. We constructed a sensor of the RhoGDI/RhoGTPase interaction by \textit{in vitro} prenylation of RhoA with the NBD-derivatized fluorescent isoprenoid. The developed enzymatic route is significantly simpler than the previously described semisynthesis-based approach for construction of fluorescent lipiddiated proteins (51) and can be easily extended to other GTPases. Using the developed sensor, we were able to determine the affinities of geranylgeranylated and farnesylated RhoA for RhoGDI. The affinities for RhoA-GG/RhoGDI interactions were much higher than previously reported (16), with RhoGDI binding to GDP-bound geranylgeranylated RhoA with a $K_d$ value of 5 pM. We demonstrated that the length of the isoprenoid chain has a dramatic impact on the RhoA interaction with RhoGDI. The affinity difference of nearly 3 orders of magnitude between farnesylated and geranylgeranylated complexes indicates that farnesylated and geranylgeranylated Rho proteins will be regulated quite differently by RhoGDI in vivo. Clearly, in the absence of a large pool of free RhoGDI, farnesylated Rhos will be outcompeted by the geranylgeranylated form and therefore are likely to distribute through alternative mechanisms. We also demonstrate that activation of RhoA results in a 500-fold decrease in the affinity of the complex. The high affinity of RhoGDI complexes with both GDP- and GMPPNP-bound prenylated RhoA molecules implies their slow dissociation rates, which we found to be $10^{-6}$ and $10^{-2}$ s$^{-1}$, respectively. These results have revealed that the RhoA-GDP-GG-RhoGDI complex is very tight and has a half-life of ~60 min. In contrast, the half-life of the GMPPNP-loaded RhoA-GG-RhoGDI complex is only 2.5 min, which fits better into the physiological context (47) and suggests the presence of two types of RhoGDI-RhoA complexes. Quantitative Analysis of RhoA Interaction with RhoGDI complexes in vivo with dramatically different half-lives. These findings further support the idea that RhoGDI is actively involved in the recycling and distribution of activated RhoGTPases in the cell (52, 53). To gain insight into the mechanism underlying the ability of RhoGDI to stably associate with the activated form of RhoA, we solved the structure of the activated form of the complex and demonstrated that complex formation induces adoption of the inactive conformation without nucleotide hydrolysis. Formation of an extensive set of contacts between RhoGDI and switch II partially through hydrophobic interaction with Leu-67 and Leu-70 of RhoA stabilizes the loop and, importantly, secures the essential GDP-hydrolysis Gln-63 residue, which results in inhibition of GTPase hydrolytic activity (11). The nucleotide independence of the conformation of switch II, which forms the second largest interface in the RhoA-GMPPNP-GG-RhoGDI complex, most likely promotes association of the proteins, which involves energetically unfavorable changes in the switch I region. Notably, the role of switch II in the recognition of both nucleotide-bound forms of Rho GTPases by RhoGDI was suggested earlier (48). The structural transition of the switch I loop occurs at the cost of interatomic free energy, which is reflected by a difference of almost 3 orders of magnitude in affinities for RhoA-GG action the free energy, which is captured by the lipid-binding pocket of RhoGDI. This eventually triggers release of the complex from the membrane and is captured by the lipid-binding pocket of RhoGDI. This eventually triggers release of the complex from the membrane (Scheme 1). In general, RhoGDI and RabGDI appear to operate in a similar way in extracting the respective GTPases from membranes, using sequential formation of progressively tighter complexes that function as a thermodynamic trap. However, the quantitative data suggest that Rho and RabGDI operate differently in the sense that the former distributes both nucleotide-bound forms between membranes and cytosol, whereas the latter acts only on inactive conformations, albeit with quantitative differences. Given the exceptionally high affinities of RhoGDI complexes with prenylated RhoA of both nucleotide-bound forms, the local concentration of RhoGDI in the cell will govern the extraction process of GDP- and GTP-bound Rho proteins. Low and limiting RhoGDI concentrations will mostly lead to the extraction of GDP-associated Rho proteins that will outcompete short-lived and weak RhoA-GTP-RhoGDI complexes. In contrast, a local abundance of RhoGDI will result in extraction of both inactive and activated RhoGTPases. The transient RhoGDI association with GTP-bound Rho molecules will favor its local distribution. The presence of slow and fast cycling pools of the RhoGTPase cycle in the cell was proposed earlier (27, 53, 54). The mechanism of dissociation of these complexes is unclear at present and, according to our data, cannot be based solely on nucleotide exchange. Therefore, unlike the case of RabGTPases, where GEFs have been suggested to be sufficient to drive targeted membrane insertion of Rabs, it seems likely that dissociation of RhoGDI-RhoGTPase complexes must be further accelerated by other factors. Recently demonstrated Arl-GTP-mediated displacement of farnesylated Rheb from its GDI-like chaperon PDE8 provides an example of a possible mechanism (60). Alternative factors may include some types of lipids and phosphorylation of both Rho and RhoGDI. 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(1993) Main chain bond lengths and bond angles in protein structures. J. Mol. Biol. 231, 1049–1067	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5189, 1 ], [ 5189, 11557, 2 ], [ 11557, 18065, 3 ], [ 18065, 22686, 4 ], [ 22686, 26294, 5 ], [ 26294, 29224, 6 ], [ 29224, 30762, 7 ], [ 30762, 34388, 8 ], [ 34388, 39950, 9 ], [ 39950, 43436, 10 ], [ 43436, 46752, 11 ], [ 46752, 52259, 12 ], [ 52259, 59707, 13 ], [ 59707, 61984, 14 ] ] }
129a0e10a32170d11f902f2ce523d65638e27760	{ "olmocr-version": "0.1.59", "pdf-total-pages": 9, "total-fallback-pages": 0, "total-input-tokens": 29907, "total-output-tokens": 13605, "fieldofstudy": [ "Medicine" ] }	Intraoperative 3D imaging in intraarticular tibial plateau fractures - Does it help to improve the patients’ outcomes? F. Souleiman †, R. Henkelmann †, J. Theopold, J. Fakler, U. Spiegl † and P. Hepp † Abstract Background: In tibial plateau fractures (TPF) the restoration of an anatomical joint surface as well as an exact subchondral screw position for postoperative stability is crucial for the outcome. The aim of this study was to determine whether the additional use of an intraoperative 3D imaging intensifier (3D) might help to improve the outcome of complex TPF. Methods: We performed a retrospective case-control study of a level 1 trauma center. Patients with AO/OTA 41 B3 and C-TPF operated on using a 3D imaging intensifier between November 2015 and December 2018 (3D group) were included. The outcomes of this patients were compared to patients operated without 3D imaging between January 2005 to December 2014 (2D group). The comparison of the groups was performed by matched pair analysis. The functional outcome of both groups was measured by KOOS and Lysholm Score after a follow-up period of at least 12 months. Operation time, infections and postoperative revisions were registered. Results: In total, 18 patients were included in the 3D group (mean age: 51.0± 16.4 years; 12 females) and an equal number of matching partners from the 2D group (mean age: 50.3± 15.2 years; 11 females) were found (p=0.82; p=0.79). We found 9x B3, 2x C1, 1x C2, 6x C3 fractures according to AO/OTA for each group (p=1.00) with comparable ASA score (p=0.27). The mean operation time was 127.9± 45.9 min and 116.1± 45.7 min for the 3D and 2D group (p=0.28). The mean follow-up time was 20.9± 10.7 months for the 3D and 55.5± 34.7 months for the 2D group (p< 0.001). For the 3D group a mean Lysholm overall score of 67.4± 26.8 and KOOS overall score of 72.6± 23.5 could be assessed. In contrast, a mean Lysholm overall score of 62.0± 21.4 and KOOS overall score of 65.8± 21.6 could be measured in the 2D group (p=0.39; p=0.31). Thereby, functional outcome of the 3D group showed a significant higher KOOS Sport/Rec sub score of 54.7± 35.0 in comparison to the 2D group with 26.7± 31.6 (p= 0.01). Postoperative revisions had to be performed in 27.8% of cases in both groups (p=1.00). Due to the 3D imaging an intraoperative revision was performed in 33.3% (6/18). Conclusion: In our study we could show that re-reduction of the fracture or implant re-positioning were performed in relevant numbers based on the 3D imaging. This was associated with a midterm clinical benefit in regard to better KOOS Sport/Rec scores. (Continued on next page) Background Tibial plateau fractures constitute about 1% of all fractures occurring at an incidence of 10.3 per 100,000 annually [1–3]. Arthrosis rates of up to 44% and rates of revision operations of 25.3 to 45.0% have been described [4, 5]. In addition to fracture severity, the reduction quality is crucial for the development of a posttraumatic arthrosis [6, 7]. For dislocated fractures, surgical therapy is the gold standard [8, 9]. For intraoperative analysis of fracture reduction, conventional fluoroscopy is generally applied. Due to the convexity as well as the flat lateral tibial plateau and the concave medial tibial plateau with respective different dorsal slopes, overlaps occur in the lateral fluoroscopy [10, 11]. Complex fracture morphologies are difficult to assess and small joint steps cannot be assessed with sufficient certainty. Postoperative CT imaging is therefore recommended to verify the surgical outcome [12]. If there is a material malposition or an insufficient reduction of the articular surface, a revision operation is necessary. Intraoperative 3D imaging can provide additional information during the operation, which could prevent revision surgeries [13, 14]. There are few studies that support its use in the treatment of intraarticular tibial plateau fractures. Thereby, intraoperative revision rates of up to 26.5% in the treatment of proximal tibial fractures are shown [15–18]. To the authors’ knowledge, there is no study comparing the functional outcome after treatment of tibial plateau fractures using intraoperative 3D imaging versus conventional fluoroscopic evaluation using two planes (2D). The aim of this study was to determine whether the additional use of an intraoperative 3D imaging intensifier might help to improve the clinical outcome after surgical treatment of complex tibial plateau fractures. Secondary it was hypothesized that the rate of postoperative revision surgeries can be reduced. Methods We performed a retrospective case control study at a level 1 trauma center. This study was conducted following approval from the local ethics committee and was performed in accordance with the principles of the Declaration of Helsinki. The consent to participate in the study was given by the patients. All patients who were surgically treated for tibial plateau fractures were identified by querying the hospitals databases using the International Classification of Disease (ICD) code. We have formed two separate groups according to our predefined inclusion and exclusion criteria (Table 1). Study group (3D): Patients who underwent open reduction and internal fixation between December 2015 and December 2018 using 2D and 3D imaging intensifier (Ziehm Vision RFD 3D, Fa. Ziehm Imaging, Nuernberg, Germany). Control group (2D): Patients who were operated between 2005 and 2014 only by 2D fluoroscopy without 3D imaging. We retrospectively evaluated the intraoperative revision rate, reasons for revision and operation time of both groups. Additionally, a minimum 12-month postoperative functional outcome was measured by using the KOOS and Lysholm Score [19–21]. Complications, postoperative revision surgeries and infections were analyzed. Operation procedure: After fracture reduction, including reconstruction of the articular surface and placement of subchondral screws, 2D fluoroscopy was performed in the lateral and anterior-posterior plane. In contrast to the 2D group, an intraoperative 3D scan was now performed in the 3D study group. Whenever possible, as little osteosynthesis material as possible was placed close to the joint surface in order to keep possible artifacts to a minimum for the 3D scan. The decision for repositioning the screws and/or redo the reduction maneuver was made by the attending surgeon. Particularly intraoperative revision reasons were an intra-articular screw position or a joint step of more than 2mm. In order to analyze the effect of intraoperative 3D imaging we compared the outcomes of the study group (3D group) to the historical collective (2D group). We characterized our two groups by means of descriptive statistics: Mean ± standard deviation (SD) for continuous and number (%) for categorical variables. Both groups were compared by a one to one matching of the patients. The matching criteria were age ± 5 years, exact fracture classification by AO/OTA, gender and American Society of Anesthesiologists-Score (ASA). If no matching partner was found, the ASA score was changed by one unit (n=4). If even then no suitable partner was found, gender (n=1) or gender and ASA (n=2) was adapted. During the matching process, attention was also paid to the follow-up time. The matching patient with the next possible follow-up time to the matching partner was selected. Further analyses were performed by using the Mann-Whitney-U test for non-parametric data (two-tailed test, p-value < 0.05). The software SPSS (V.25, Fa. IBM, New York, USA) was used for the calculations and graphical presentations of the results. Results A total of 22 patients with AO/OTA B3 and C tibial plateau fracture were found according to our inclusion criteria. Four patients were excluded due to different circumstances: no follow-up could be determined for two patients, one patient died before the 1-year follow-up and one patient suffered a polytrauma. Finally, 18 patients were included in our 3D study group, of which 12 were women (Table 2). The mean age was 51.0 ± 16.4 years (range 23–85 years). We had 9x B3, 2x C1, 1x C2 and 6x C3 fractures according to AO/OTA. The mean ASA score was 1.44± 0.51. The mean operation time was recorded with 128± 46 min. The mean follow-up time was 20.9± 10.7 months with the outcome scores shown in Table 3. Postoperative revisions had to be performed in 27.8% of cases. In one case a superficial wound revision was necessary due to a wound healing disorder, in one case we observed a deep surgical site infection has been observed in one case. The duration of the operations was 116± 46 min (p=0.28). If postoperative CT control imaging was performed in the 2D control group due to pain, one case showed intra-articular screw position and two cases showed joint steps > 2mm without any operative revision. In the 3D study group no postoperative intraarticular implants or joint steps >2mm were detected. Discussion The hypothesis of the study that the additional use of intraoperative 3D imaging results in a relevant number of intraoperative revisions (33.0%), potentially leading to a significantly improved outcome (KOOS Sport/Rec) could be approved. In the first analysis, this did not lead to a reduction in postoperative revisions. This might be due to the fact that in the 2D control group, relevant joint steps and suboptimal material position were tolerated in the presence of mild clinical symptoms (22.2%). The patients in both groups were about 50 years old and are comparable based on the matching process except for the duration of the follow-up time. Based on previous studies, the duration of follow-up should be evaluated subordinately, as previous studies could show that the outcome of the TPF is stable in the medium-term period of up to ten years after trauma [22, 23]. The outcome between 3D group and 2D group are comparable with respect to Lysholm, KOOS Symptoms, KOOS Pain and KOOS ADL. The sub scores of KOOS Sport/Rec showed significantly better results in 3D group and a trend to higher KOOS Quality of Life scores (p= 0.059). These subscales reflect complaints of the knee joint under higher loads, stress and more demanding movements. It is therefore conceivable that the optimized joint reduction after 3D imaging is not of high relevance for everyday activities and pain, but is particularly evident under physical stress. In the KOOS subscales for everyday movements, symptoms, and pain no significant differences could be shown between the both groups. The majority of fractures in this study were severe joint injuries, B3 and C3 fractures according to AO/OTA. This explains lower scores compared to other studies [22, 24]. However, Jansen et al. who included patients with similar injury severity (C1-3 fractures according to AO/OTA) reported comparable results to our study (Lysholm 66.2; KOOS overall 67.8) [25]. Additionally, better results can be expected in patients with type B1, B2, and C1 fractures compared to B3 and C3 fractures [22, 26, 27]. A major advantage of this study should be not only to record the outcome of patients operated with 3D imaging in a minimum follow-up of 12 months, but also the comparison with patients operated without this technique. We decided to use matching as a method of --- Table 1 Inclusion and exclusion criteria \| Inclusion criteria \| Exclusion criteria \| \|--------------------\|--------------------\| \| Acute complex closed intraarticular proximal tibial fracture Type B3, C1, C2, C3 to AO/OTA [19] \| Open fractures \| \| Age ≥ 18 years \| Polytraumatized patients (Injury Severity Score >16) \| \| Use of intraoperative 3D and 2D imaging intensifier \| Foreign residents \| \| Follow-up ≥ 12 months \| Conservative treatment \| \| Capable of consent \| Pathologic fractures \| Note: Inclusion and exclusion criteria were based on the AO/OTA classification. ### Table 2: Comparison of 3D study group and matched 2D control group: Age, Gender, Trauma mechanism, ASA-Score, AO/OTA, Operation time, intraoperative Revision \| Case \| Age \| Gender \| Trauma mechanism \| AO/OTA \| ASA \| Operation time (min) \| Intraoperative Revision \| Type of Revision \| \|------\|-----\|--------\|------------------\|--------\|-----\|----------------------\|------------------------\|-------------------\| \| 1 \| 65 \| f \| fall \| C3 \| 2 \| 151 \| YES \| Joint step > 2mm, renewed reposition \| \| m1 \| 60 \| f \| fall \| C3 \| 2 \| 121 \| \| \| \| 2 \| 60 \| m \| accident at work (machine) \| C3 \| 2 \| 214 \| NO \| Anterior fragment <2mm, no consequent \| \| m2 \| 63 \| m \| fall \| C3 \| 2 \| 167 \| \| \| \| 3 \| 43 \| m \| motorcycle \| C3 \| 1 \| 151 \| NO \| - \| \| m3 \| 42 \| m \| accident at work \| C3 \| 1 \| 142 \| \| \| \| 4 \| 60 \| m \| fall down stairs \| B3 \| 2 \| 86 \| NO \| - \| \| m4 \| 58 \| m \| skiing \| B3 \| 2 \| 115 \| \| \| \| 5 \| 61 \| f \| biking \| C1 \| 1 \| 191 \| NO \| - \| \| m5 \| 56 \| m \| biking \| C1 \| 1 \| 111 \| \| \| \| 6 \| 52 \| f \| biking \| B3 \| 2 \| 94 \| NO \| - \| \| m6 \| 47 \| f \| biking \| B3 \| 2 \| 71 \| \| \| \| 7 \| 37 \| m \| biking \| C3 \| 1 \| 184 \| YES \| Joint step >2mm, cortical bone chip, reposition \| \| m7 \| 34 \| m \| fall down from ladder \| C3 \| 1 \| 243 \| \| \| \| 8 \| 68 \| f \| fall \| C2 \| 2 \| 131 \| YES \| Anterior joint step 3-4mm, renewed reposition \| \| m8 \| 66 \| f \| fall \| C2 \| 2 \| 77 \| \| \| \| 9 \| 65 \| f \| skiing \| B3 \| 2 \| 64 \| NO \| - \| \| m9 \| 70 \| f \| fall \| B3 \| 2 \| 86 \| \| \| \| 10 \| 51 \| f \| skiing \| B3 \| 1 \| 47 \| NO \| - \| \| m10 \| 54 \| f \| fall \| B3 \| 2 \| 119 \| \| \| \| 11 \| 36 \| f \| skiing \| C3 \| 1 \| 132 \| NO \| - \| \| m11 \| 37 \| m \| biking \| C3 \| 2 \| 135 \| \| \| \| 12 \| 56 \| f \| biking \| B3 \| 1 \| 134 \| YES \| Joint step >2mm lateral, renewed reposition, \| \| m12 \| 54 \| f \| motorcycle \| B3 \| 2 \| 76 \| \| \| \| 13 \| 23 \| m \| motorcycle \| B3 \| 2 \| 155 \| YES \| Negative dorsal slope, joint step >2mm, reposition \| \| m13 \| 27 \| m \| fall \| B3 \| 1 \| 141 \| \| \| \| 14 \| 85 \| f \| fall \| B3 \| 2 \| 81 \| NO \| Anterolateral joint step < 2mm, no consequence \| \| m14 \| 80 \| f \| fall \| B3 \| 2 \| 75 \| \| \| \| 15 \| 38 \| f \| biking \| C3 \| 1 \| 95 \| NO \| - \| \| m15 \| 43 \| f \| biking \| C3 \| 2 \| 104 \| \| \| \| 16 \| 29 \| f \| biking \| B3 \| 1 \| 90 \| NO \| Joint step < 2mm, no consequence \| \| m16 \| 33 \| f \| fall \| B3 \| 1 \| 77 \| \| \| \| 17 \| 30 \| m \| biking \| C1 \| 1 \| 143 \| NO \| Lateral joint step < 2mm, no consequence \| \| m17 \| 26 \| f \| traffic accident \| C1 \| 2 \| 170 \| \| \| \| 18 \| 59 \| F \| skiing \| B3 \| 1 \| 159 \| YES \| Joint step > 2mm, renewed reposition \| \| m18 \| 57 \| f \| biking \| B3 \| 1 \| 63 \| \| \| ASA: American Society of Anesthesiologists- Score; m: Matching partner from 2D control group \| Case \| Follow-up (months) \| Lysholm \| Symptoms \| Pain \| ADL \| Sport/Rec \| QOL \| Postoperative Revision/ time after prim. surgery \| \|------\|-------------------\|---------\|----------\|------\|-----\|-----------\|-----\|-----------------------------------------------\| \| 1 \| 40 \| 99 \| 96.4 \| 97.2 \| 100.0 \| 85.0 \| 100.0 \| - \| \| m1 \| 42 \| 99 \| 85.7 \| 94.4 \| 97.1 \| 55.0 \| 75.0 \| - \| \| 2 \| 36 \| 48 \| 75.0 \| 66.7 \| 64.7 \| 65.0 \| 43.8 \| SSL, 1 month: spacer, 6 months: unicoronal KTEP \| \| m2 \| 38 \| 69 \| 96.4 \| 88.9 \| 88.2 \| 0.0 \| 75.0 \| Screw intraarticular without operative consequence \| \| 3 \| 34 \| 69 \| 46.4 \| 86.1 \| 85.3 \| 60.0 \| 50.0 \| - \| \| m3 \| 35 \| 58 \| 50.0 \| 58.3 \| 72.1 \| 10.0 \| 18.8 \| 14 months: Arthrolysis and material removal / intraop. screw intraarticular \| \| 4 \| 31 \| 87 \| 100.0 \| 80.6 \| 82.4 \| 60.0 \| 31.3 \| - \| \| m4 \| 31 \| 86 \| 100.0 \| 80.6 \| 97.1 \| 90.0 \| 62.5 \| 17 months: Arthrolysis and material removal \| \| 5 \| 36 \| 99 \| 92.9 \| 100.0\| 100.0 \| 85.0 \| 87.5 \| 5 months: superficial wound revision, 19 months: arthrolysis, material removal \| \| m5 \| 32 \| 57 \| 64.3 \| 69.4 \| 55.9 \| 0.0 \| 25.0 \| 17 months: Arthrolysis and material removal \| \| 6 \| 32 \| 37 \| 57.1 \| 52.8 \| 64.7 \| 25.0 \| 31.3 \| 7 months: arthrolysis, material removal due to pain \| \| m6 \| 97 \| 24 \| 14.3 \| 28.0 \| 10.3 \| 0.0 \| 0.0 \| 15 months: Arthrolysis and material removal // intraop. joint step > 2mm \| \| 7 \| 25 \| 34 \| 39.3 \| 33.3 \| 41.2 \| 15.0 \| 18.8 \| - \| \| m7 \| 24 \| 46 \| 46.4 \| 66.7 \| 67.7 \| 0.0 \| 25.0 \| 13 months: Arthrolysis and material removal // intraop. joint step > 2mm \| \| 8 \| 17 \| 79 \| 100.0 \| 100.0\| 100.0 \| 55.0 \| 100.0 \| - \| \| m8 \| 133 \| 33 \| 64.3 \| 58.3 \| 60.3 \| 0.0 \| 18.3 \| Valgus gonarthrosis: after 20 months: Bicondylar KTEP \| \| 9 \| 15 \| 90 \| 96.4 \| 97.2 \| 100.0 \| 100.0 \| 93.8 \| - \| \| m9 \| 25 \| 73 \| 96.4 \| 75.0 \| 86.8 \| 0.0 \| 31.3 \| Postop CT: screw too long without operative consequence \| \| 10 \| 15 \| 71 \| 71.4 \| 97.2 \| 98.5 \| 80.0 \| 43.8 \| Eight times revision: osteomyelitis/ infect; after 20 months hemiprosthes \| \| m10 \| 130 \| 60 \| 53.6 \| 83.3 \| 77.9 \| 90.0 \| 6.3 \| - \| \| 11 \| 12 \| 28 \| 28.1 \| 63.9 \| 63.2 \| 5.0 \| 25.0 \| posttraumatic valgus malalignment, varus osteotomy after 11 months \| \| m11 \| 82 \| 74 \| 92.9 \| 86.1 \| 95.6 \| 45.0 \| 12.5 \| posttraumatic valgus malalignment \| \| 12 \| 12 \| 36 \| 50.0 \| 61.1 \| 77.9 \| 0.0 \| 31.3 \| 9 months: valgus deformity, loss of reduction-> reposition \| \| m12 \| 39 \| 31 \| 28.6 \| 36.1 \| 42.7 \| 20.0 \| 31.3 \| 17 months: Arthrolysis and material removal (valgus deformity) \| \| 13 \| 12 \| 88 \| 67.9 \| 83.3 \| 94.1 \| 95.0 \| 81.3 \| - \| \| m13 \| 42 \| 64 \| 82.1 \| 83.3 \| 92.7 \| 0.0 \| 37.5 \| - \| \| 14 \| 12 \| 95 \| 100.0 \| 100.0\| 95.6 \| 95.0 \| 100.0 \| - \| \| m14 \| 35 \| 100 \| 100.0 \| 100.0\| 100.0 \| 40.0 \| 100.0 \| - \| \| 15 \| 12 \| 62 \| 71.4 \| 63.9 \| 66.2 \| 45.0 \| 62.5 \| - \| comparison, as only the image intensifier was modified throughout the course of time. For this, we had to accept the limitation of the longer follow-up of the control group, with the advantage of no further influencing factors. Main matching criterion was the same fracture morphology (B1, B2, B3, C1, C2, C3) according to AO/OTA, followed by the age ± 5 years. These criteria were always met. In order to show the bone metabolism and the patient’s state of health, the importance of gender and the ASA score followed. The rate of intraoperative revisions due to the used 3D scan is with 33.3% higher than in other studies (17.2±6.1%; range 11.7–26.5% [14–18, 27]). The reasons for this are different revision criteria. Based on the discussed parameters for joint gap with values between 1-4 mm, we decided on a revision, if the joint gap is more than 2 mm [6, 8, 9, 28–31]. An intraarticular or overlong screw certainly causes symptoms. The most common fractures requiring intraoperative revision were B3 and C3 fractures (71.4 %), which can be explained by the severely destroyed, multifragmentary articular surface and the split depression component. For this 2D fluoroscopy has its limitations due to the concave anatomical joint conditions of the proximal tibia, with the result that joint steps < 5 mm cannot be adequately detected with fluoroscopy [11, 32, 33]. Conventional fluoroscopy is highly dependent on the set plane, while 3D imaging provides image information regardless of the position of the device [34, 35]. Due to the high rate of intraoperative revisions, our secondary hypothesis was that the rate of relevant postoperative revisions can be reduced by using 3D scan. Unfortunately, this cannot be confirmed. Both the study group and the control group show a postoperative revision rate of 27.8%. In further analysis of the 2D group, postoperative CT was performed in some patients. In two cases joint steps of more than 2 mm, in one case an intraarticular screw and in one case a too long screw were detected but accepted without revision (22,2%). The estimated number of unreported cases may be higher. The detected 4 patients with revision criteria are the reason why there are no higher revision rates in the 2D group, but could probably be the reason for the poorer functional results of the 2D group in KOOS Sport/Rec and QOL. There were no significant group differences between the 3D and 2D groups except the mentioned longer follow-up time of the control group. Nevertheless, a prolonged surgery time of approximately 12 minutes on average was observed for the study group, which was due to the use of intraoperative 3D imaging and performed intraoperative revisions in 33.3% of cases. Beisemann et al. also describe longer operation time by using intraoperative 3D scan (5 min) [16]. In recent years, numerous studies have been published on the use of intraoperative 3D imaging of joint injuries (proximal humerus, distal radius, proximal and distal tibia fractures). In most cases, acceptable image quality was shown for the assessment of an insufficient joint level or a material defect with high revision rates [15, 16, 36–39]. Overall, the technology of intraoperative 3D imaging remains reserved for the use of large clinics due to high acquisition costs. Limitations Due to the group comparison by matching according to the specific criteria, small differences in the ASA score (five cases), one for gender and one for both criteria together had to be tolerated. In this way a matching in the ratio one to one was possible between the groups. By softening the matching parameters, a matching ratio of 1:2 between the intervention group and the control --- Table 3 Comparison of 3D study group and matched 2D control group: Follow UP time, Outcome parameters by Lysholm and KOOS sub scores, Postoperative revision (Continued) \| Case \| Follow-up (months) \| Lysholm \| Symptoms \| Pain \| ADL \| Sport/Rec \| QOL \| Postoperative Revision/ time after prim. surgery \| \|------\|-------------------\|---------\|----------\|------\|-----\|-----------\|-----\|-----------------------------------------------\| \| m15 \| 37 \| 69 \| 78.6 \| 86.1 \| 98.5\| 25.0 \| 37.5\| 1 month: loss of reposition/renewed reposition; 20 months: Arthrolysis and material removal \| \| 16 \| 12 \| 89 \| 89.3 \| 97.2 \| 97.1\| 95.0 \| 100.0\| - \| \| m16 \| 32 \| 55 \| 50.0 \| 75.0 \| 89.7\| 40.0 \| 40.0\| 21 months: Arthrolysis and material removal \| \| 17 \| 12 \| 74 \| 14.3 \| 30.6 \| 44.1\| 0 \| 18.8\| - \| \| m17 \| 77 \| 74 \| 92.9 \| 83.3 \| 91.2\| 65.0 \| 43.8\| 18 months: Arthrolysis and material removal \| \| 18 \| 12 \| 79 \| 60.7 \| 77.8 \| 85.3\| 50.0 \| 50.0\| - \| \| m18 \| 69 \| 44 \| 60.7 \| 63.9 \| 88.2\| 0.0 \| 50.0\| - \| Symptoms KOOS Symptoms, Pain KOOS Pain, ADL KOOS Function in daily living, Sport/Rec KOOS Function in sport and recreation, QOL KOOS Quality of Life; SSI Surgical site infection, m Matching partner from 2D control group; intraop intraoperative group could certainly have been achieved. However, this was not desired. Also, the follow-up time varied between the 3D group and the 2D group. However, based on existing publications of the medium and longer follow-up time, the time of determination of the functional outcome should not have much influence, since it is below 5 years in both groups [22, 23]. Due to the retrospective study design, we had to rely on the data available in medical records (e.g. operation protocols). Unfortunately, not all intraoperative 3D scans were stored in the database, so that a later evaluation of the image quality of the 3D scan was not possible. It was necessary to rely on the documentation. Additionally, the 3D study group was compared with a historical control group. Nevertheless, the factors to be monitored, such as the implants, the surgical approach, general anesthesia and the postoperative physiotherapeutic regime (with 20 kg of partial weight-bearing for 6 weeks under free range of motion), did not change during this period. Tranexamic acid was not used in any of the groups. However, a certain selection bias that developed over time cannot be excluded with certainty. Due to the retrospective character, the decision for revision was made by the responsible surgeon. A possible learning curve in the supply of a 3D ### Table 4 Parameters of interest for comparison of the 3D and 2D groups \| Parameter \| 3D group \| 2D group \| p-Value \| \|-----------\|----------\|----------\|---------\| \| Age \| 51.0± 16.4 \| 50.3± 15.2 \| 0.82 \| \| Gender \| 12f : 6m \| 11f : 7m \| 0.79 \| \| Fracture AO/OTA \| 9x B3, 2x C1, 1x C2, 6x C3 \| 9x B3, 2x C1, 1x C2, 6x C3 \| 1.00 \| \| ASA \| 1.44± 0.51 \| 1.67± 0.49 \| 0.27 \| \| Operation time (min) \| 127.9± 45.9 \| 116.3± 45.7 \| 0.28 \| \| Follow-up (months) \| 20.9± 10.7 \| 55.5± 34.7 \| P < 0.001 \| \| Lysholm \| 67.4± 26.8 \| 62.0± 21.4 \| 0.39 \| \| KOOS overall \| 72.6± 23.5 \| 65.8± 21.6 \| 0.31 \| \| Symptoms \| 69.8± 26.6 \| 69.8± 25.8 \| 0.94 \| \| Pain \| 77.2± 22.6 \| 71.8± 23.0 \| 0.44 \| \| ADL \| 81.1± 19.5 \| 78.4± 23.7 \| 0.70 \| \| Sport/Rec \| 54.7± 35.0 \| 26.7± 31.6 \| 0.014* \| \| QOL \| 58.0± 31.6 \| 38.2± 26.1 \| 0.059 \| \| Intraoperative revision rate \| 33.3% re-positioning of the screws and/or re-reduction \| Not registered \| - \| \| Postoperative revision rate \| 27.8% revision (n=5): - wound revision - SSL spacer, unicompartmental TEP - varus osteotomy due to valgus alignment - renewed reposition - early material removal \| 27.8% revision (n=5): - 1x screw intraarticular, material removal - 2x loss of reposition/ renewed reposition - bicondylar KTEP - SSI/unicompartmental KTEP \| 1.00 \| \| Postoperative revisions due to intraarticular material position or joint step of ≥ 2mm \| 11.1% (n=2): - varus osteotomy due to valgus malalignment - 1x loss of reposition/ renewed reposition \| 22.2% (n=4): - 1x screw intraarticular, material removal - 2x loss of reposition/ renewed reposition - 1x loss of reposition/ bicondylar KTEP \| 0.58 \| \| Material removal (months) \| 1x arthrolysis and material removal after 19 months \| 10x arthrolysis and material removal after 16.9± 2.6 months \| - \| \| Special details without revision \| - \| 2xPostoperative recognized joint step > 2mm 1xpostoperative recognized intraarticular screw 1xpostoperative recognized too long screw \| - \| SSI: surgical site infection; Symptoms: KOOS Symptoms; Pain: KOOS Pain; ADL: KOOS Function in daily living; Sport/Rec: KOOS Function in sport and recreation; QOL: KOOS Quality of Life; ASA: American Society of Anesthesiologists- Score * significant scan must remain suspected, which might hide additional advantages of the 3D scan. A further deficiency is that the patients of the study group and the control group were treated by different surgeons. Conclusion The intraoperative 3D imaging had in relevant number an immediately intraoperative consequence with revision. An influence of intraoperative 3D imaging on the midterm postoperative outcome could be shown in relation to better KOOS Sport/Rec. Abbreviations ASA: American Society of Anesthesiologists; AO/OTA: Arbeitsgemeinschaft Osteosynthese/Orthopaedic Trauma Association; CT: Computer tomography; KOOS: Knee Injury and Osteoarthritis Outcome Score; TPF: Tibial plateau fractures Acknowledgements None. Authors’ contributions F.S. and R.H. were responsible for data control, study supervision, and writing of the manuscript. J.T., J.F. and P.H. performed the data interpretation. U.S., F.S. and R.H. were responsible for the development of the study design, and project coordination. In addition, J.T. and J.F. undertook the manuscript review. 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637da9d87fad08fa30e3fabfbc818b9fdc9a6c34	{ "olmocr-version": "0.1.59", "pdf-total-pages": 7, "total-fallback-pages": 0, "total-input-tokens": 22933, "total-output-tokens": 7887, "fieldofstudy": [ "Environmental Science", "Biology" ] }	DNA barcode approaches to reveal interspecies genetic variation of Indian ungulates Ranjana Bhaskar, Praveen Kanaparthi and Rengasamy Sakthivel Southern Regional Centre, Zoological Survey of India, Chennai, India ABSTRACT In the past two decades, identification of species from noninvasive sampling has turned out to be an important tool for wildlife conservation. In this study a total 93 specimens representing 22 species of ungulates were analyzed from partial sequences of mtDNA COI and Cytb genes. All the species showed unique clades, and sequences divergence within species was between 0.01–3.9% in COI and 0.01–13.7 in Cytb, whereas divergence between species ranged from 2.2 to 29.5% in COI and 2.3 to 28.8% in Cytb. Highest intraspecific divergence was observed within the Ovis aries in COI and Porcula salvania in Cytb. Bayesian (BA) phylogeny analysis of both genes combined distinguishes all the studied species as monophyletic criteria. The Indian rhinoceros (Rhinoceros unicornis) exhibited closer relation to horse (Equus caballus). No barcode gap was observed between species in COI. This study demonstrates that even short fragments of COI and Cytb generated from fecal pellets can efficiently identify the Indian ungulates, thus demonstrating its high potential for use in wildlife conservation activities. Introduction Ungulates are amongst the most vulnerable group of mammals (Ceballos et al. 2005). These are also known as the hoofed animals’ distinction due to the shape of their toe. Cattle, sheep, goats, deer and pigs belong to family Artiodactyla, horses and rhinos are part of another family Perissodactyla. There are 39 species of ungulates present in India (Sankar and Goyal 2004). Among these, many species are in the extremely endangered category (Schipper et al. 2008), which are declining due to environmental changes, impacts of anthropogenic pressure on wildlife habitats, and poaching (Maisels et al. 2013). Some of the species are completely protected under the schedule of the Wildlife Protection Act of 1972. There are many species which are highly endangered with only single populations in the entire distribution range, for example, the Kashmir stag or hangul (Cervus elaphus hanglu), the Manipur brow-antlered deer or sangai (Cervus eldi eldi), the Central Indian race of the swamp deer or barasingha (Cervus duvaucelii branderi) and the Indian wild ass or khur (Equus hemionus khur) (Daniel 1991). Cervus elaphus wallarchi has disappeared from Sikkim (Sankar and Goyal 2004). The decline of these populations of ungulates to adapt to environmental changes decreases their chances of long-term survival. Terrestrial mammals are threatened to the risk of extinction due to hunting pressure, habitat fragmentation, and habitat modification (Karanth et al. 2010), and around 50% of them are showing a declining trend in the population size from their native range (Channel and Lomolino 2000; Ceballos et al. 2005). Hence, these populations need a higher priority of conservation. As for other wildlife species of India, they are facing severe threats due to alarming increase in the human population (Karanth et al. 2009). Conservation success largely depends upon identifying vulnerable species and understanding the environmental factors that support their persistence in human-dominated landscapes (Kumar et al. 2017). More recently, genetic comparisons with the non-invasive sampling have led to greater understanding of lineages of related species, especially at higher taxonomic levels, where derived morphological characteristics can be difficult to determine owing to ancient divergences, thus leading to often radically different phyletices and species groupings (Waits and Paetkau 2005). The identification of species with non-invasive sampling without disturbing the animals or putting them at health risk still stands as one of the most basic but important issues in a forest. In a recent study, molecular taxonomy has helped in resolving the phylogeny of cervids resulting in clarity on species distribution and relatedness for effective conservation planning (Gilbert et al. 2006). However, the studies indicate further revision in the molecular phylogeny (Groves and Grubb 2011). Successful conservation efforts depend upon the identification of evolutionary significant units (ESU) of vulnerable species. In the present study, we examined COI and Cytb diversity within and among 22 species of Indian ungulates with the goal of testing the utility of DNA barcoding as a tool to identify species. The mitochondrial DNA (mtDNA) cytochrome c oxidase I (COI) and cytchrome b (Cytb) has been widely used as a barcode for biological identification and phylogenetic studies (Hebert et al. 2003). In this study, we determine levels of interspecific variation within COI and Cytb between closely related species and provide an unbiased analysis using the same criteria for each and will make recommendations based on their use in phylogenetic reconstruction and species discrimination in between the 22 ungulates from India from the DNA extracted from non-invasive and highly degraded samples. Materials and methods A total of 83 fresh fecal samples were collected from different protected and local areas of Tamil Nadu and Telangana. The permission was obtained from Chief Wildlife Warden [Ref no of letter WLS(A)/22918 and PCCFWL/E2/CR-17/2018-19]. A total of 14 species of Indian ungulates samples were collected from Arignar Anna Zoological Park in Chennai, Telangana and Nehru Zoological Park in Hyderabad (Table 1). All samples were fixed in 95% ethanol and stored at 20°C until the analysis. A downloaded sequence of eight species from NCBI is also included in this study. A total of 22 species of Indian ungulates were included in the present study (Table 1). Genomic DNA was extracted from fresh fecal samples, by using QIAamp DNA Stool (QIAGEN, Hilden, Germany) with a little modification in temperature. A partial fragment of the COI-1 gene was amplified using the following primers: COI (F2-GTACCGCTAATAATTGGTGCTCC) and COI-1 reverse 5'-GGGTGTATTAAGTGGGTTTG-3' (Faria et al. 2011). PCR amplification of the COI and Cytb gene was performed in a total volume of 25 μL reaction, containing 1X PCR Buffer (5 mM MgCl₂; 10 mM dNTPs; 5 pmol of each primer; 1 U Taq polymerase (CinnaGen)). Negative controls were included in all PCR amplification. PCR reactions were carried out in Eppendorf Thermo Cycler and amplification conditions were 94°C for 5 min followed by 35 cycles at 94°C for 30 s, annealing 50°C (Tₐ) for 30 s and 72°C for 1 min, with the final extension of 72°C for 10 min. PCR products, that yielded a clear band on agarose gel electrophoresis, were used for sequencing bidirectionally, using an automated capillary sequencer (ABI377) following the manufacturer’s instructions. Data analysis All the sequences were individually checked manually using the program BioEdit and ClustalW (http://www.clustal.org/clustal2/). Each sequence was systematically analyzed to find out the identity through Basic Local Alignment Search Tool (BLAST; https://blast.ncbi.nlm.nih.gov). All the sequences obtained were submitted to NCBI to obtain the respective accession numbers. We have retrieved sequences of three species from GenBank from the whole mitochondrial genome. Alignments were then performed using BioEdit (Hall 1999) and ClustalW (http://www.clustal.org/clustal2/) trimmed \| Species \| Antilope cervicapra \| Gazella vanderveldei \| Cervus unicolor \| Muntiacus muntjak \| Axis axis \| Ovis aries \| Capra hircus \| Bos indicus \| Bubalus bubalis \| Bos grunniens \| \|------------------\|---------------------\|----------------------\|----------------\|-------------------\|----------\|-----------\|-------------\|------------\|----------------\|---------------\| \| \| 0.000/0.001 \| 0.173 \| 0.162 \| 0.165 \| 0.192 \| 0.141 \| 0.149 \| 0.158 \| 0.148 \| 0.182 \| \| Gazella vanderveldei \| 0.085/0.019 \| 0.176 \| 0.176 \| 0.193 \| 0.176 \| 0.198 \| 0.186 \| 0.187 \| 0.156 \| 0.161 \| \| Cervus unicolor \| 0.205/0.009 \| 0.023 \| 0.156 \| 0.153 \| 0.099 \| 0.103 \| 0.149 \| 0.181 \| 0.194 \| 0.193 \| \| Muntiacus muntjak \| 0.191/0.022 \| 0.095 \| 0.143 \| 0.141 \| 0.096 \| 0.088 \| 0.140 \| 0.157 \| 0.177 \| 0.189 \| \| Axis axis \| 0.163/0.010 \| 0.089 \| 0.152 \| 0.153 \| 0.119 \| 0.118 \| 0.169 \| 0.176 \| 0.199 \| 0.226 \| \| Ovis aries \| 0.173/0.015 \| 0.115 \| 0.115 \| 0.112 \| 0.000/0.002 \| 0.068 \| 0.134 \| 0.138 \| 0.179 \| 0.145 \| \| Capra hircus \| 0.154/0.121 \| 0.107 \| 0.112 \| 0.052 \| 0.001/0.002 \| 0.143 \| 0.126 \| 0.161 \| 0.163 \| 0.224 \| \| Bos indicus \| 0.187/0.067 \| 0.070 \| 0.095 \| 0.099 \| 0.114 \| 0.088/0.064 \| 0.139 \| 0.139 \| 0.154 \| 0.145 \| \| Bubalus bubalis \| 0.187/0.212 \| 0.201 \| 0.185 \| 0.199 \| 0.163 \| 0.187 \| 0.199 \| 0.111/0.010 \| 0.153 \| 0.154 \| \| Bos grunniens \| 0.194/0.209 \| 0.195 \| 0.190 \| 0.183 \| 0.211 \| 0.238 \| 0.226 \| 0.199 \| 0.199 \| 0.199 \| \| Bos bison \| 0.181/0.170 \| 0.196 \| 0.178 \| 0.169 \| 0.168 \| 0.213 \| 0.212 \| 0.210 \| 0.082 \| 0.062/0.006 \| \| Bubalus bubalis \| 0.150/0.156 \| 0.201 \| 0.199 \| 0.187 \| 0.174 \| 0.175 \| 0.198 \| 0.199 \| 0.216 \| 0.164 \| \| Capra hircus \| 0.190/0.200 \| 0.184 \| 0.188 \| 0.147 \| 0.155 \| 0.186 \| 0.175 \| 0.196 \| 0.189 \| 0.179 \| \| Tetracerus quadricornis \| 0.181/0.150 \| 0.175 \| 0.163 \| 0.171 \| 0.157 \| 0.181 \| 0.175 \| 0.187 \| 0.161 \| 0.206 \| \| Moschiola indica \| 0.188/0.223 \| 0.218 \| 0.194 \| 0.206 \| 0.191 \| 0.206 \| 0.218 \| 0.240 \| 0.243 \| 0.210 \| \| Rhinoceros unicornis \| 0.244/0.224 \| 0.248 \| 0.248 \| 0.206 \| 0.216 \| 0.254 \| 0.248 \| 0.273 \| 0.242 \| 0.235 \| \| Porcine salvini \| 0.245/0.256 \| 0.235 \| 0.258 \| 0.221 \| 0.118 \| 0.229 \| 0.242 \| 0.221 \| 0.252 \| 0.213 \| \| Sus scrofa \| 0.211/0.244 \| 0.237 \| 0.254 \| 0.237 \| 0.247 \| 0.249 \| 0.263 \| 0.217 \| 0.218 \| 0.262 \| \| Equus caballus \| 0.242/0.231 \| 0.268 \| 0.269 \| 0.246 \| 0.269 \| 0.246 \| 0.389 \| 0.295 \| 0.239 \| 0.247 \| \| Bos grunniens \| 0.162/0.195 \| 0.182 \| 0.192 \| 0.188 \| 0.184 \| 0.208 \| 0.206 \| 0.216 \| 0.210 \| 0.065 \| The mean genetic distance within species are represented in bold numbers on diagonal (COI/Cytb). to 408 bp. All statistical parameters, sequence composition and substitution pattern for the entire data set, genetic divergence, variable sites, transition, and transversion rates were calculated using the program MEGA 6 (Tamura et al. 2013). The Bayesian tree was built in Mr. Bayes 3.1.233, the program Modeltest was used to find the suitable model for data test by selecting parameters nst = 6 for GTR + G + I model with four metropolis-coupled Markov Chain Monte Carlo (MCMC) and run for 1,000,000 cycles with 25 burns (Ronquist and Huelsenbeck 2003). The generated BA tree was represented by the FIGTree software. The neighbor-joining (NJ), maximum-parsimony (MP), and maximum-likelihood (ML) were also generated by MEGA 6 (Tamura et al. 2013). The haplotype data were generated using DnaSP5.10 (Librado and Rozas 2009). Automatic barcode gap discovery analysis (ABGD) was implemented online (www.abi.snv.jussieu.fr/public/abgd/abgdweb.html, Puillandre et al. 2012) and was run by selecting Kimura 2-parameter distance (K2P) with transition/transversion ratio (TS/TV) equal to 2 and with a FASTA file input of the alignment, with default values for $P_{\text{min}}, P_{\text{max}}$ and relative gap width. The database sequence of Pteropus giganteus (MG821199) was used as an out-group in the phylogenetic study for making the Bayesian tree. Results and discussion A total number of 83 fecal samples out of these 67 samples obtained good amplification in COI and 65 in Cytb gene, the other samples might have yielded low DNA or were highly degraded samples. Most of the sequences generated 470 bp in COI and 420 bp but trimmed to 408 bp, as few shorter sequences were downloaded from NCBI, in both COI and Cytb. The generated DNA sequences of 14 species of Indian ungulates were submitted to NCBI with accession numbers given in Table 1. COI genes of five species, Axis porcinus, Rucervus duvacellii branderi, Muntiacus putoanesis, Tetracerus quadricornis, and Porcula salvania, that were retrieved from the whole mitochondrial genome, were not obtained from NCBI. A total of 93 sequences of COI and 86 of Cytb of 22 species were included in this study. The partial region of 408 bp of COI gene was analyzed, out of these 212 bp (51.9%) were conserved, 196 (48.0%) variable, 31 (7.6%) singleton, and 165 (40.4%) were parsimony informative. Overall 48 haplotypes were observed from 22 species of ungulates in COI. The overall haplotype diversity was 0.956 and nucleotide diversity was 0.1483. In Cytb, 205 (50.2%) of 408 sites varied among taxa, 183 (44.8%) parsimony-informative, 203(49.7%) conserved and 22 Overall, 45 haplotypes were observed in Cytb. The overall haplotype diversity was 0.974 and nucleotide diversity was 0.1529. The combined sequences of the two gene segments had 816 sites, of which 350 (42.9%) were parsimony informative. With respect to the pairwise distance among the 22 ungulates species, the highest interspecific genetic divergence observed was 0.295 (29.5%) between Equus caballus and Ovis aries in COI and 0.288 (28.8%) between E. caballus and Moschiola indica in Cytb and the lowest genetic divergence was 0.022 (2.2%) in COI and 0.023 (2.3%) in Cytb in R. d. branderi and R. duvaucellii (Table 2). The overall mean divergence was estimated at 17.2% in both COI and Cytb. The highest intraspecific variation was observed in O. aries (3.9%) and lowest (0.01) in Antilope cervicapra, Axis axis, and Muntiacus muntjak (Table 2) in COI. In the Cytb gene, the highest intraspecific sequence divergence was 0.137 (P. salvania) and the lowest 0.001 (O. aries, Bos grunnium, A. cervicapra) (Table 2). The estimated ABGD analysis of COI (Figure 1) revealed a total 22 MOTUs within the studied barcode data in the dataset. One of the species Bos indicus showed similar results in ABGD analysis and BA tree topology showing two MOTUs with two sister’s clades. However, the other two species depicted inconsistent results in ABGD analysis, R. d. branderi Figure 2. The Bayesian analysis tree showing the multiple clades and paraphyletic clustering of Indian ungulates with both generated and database sequences. Species delimitation through ABGD analysis is denoted by black bar beside each clade. Sixteen subclades are represented by different color bars. is the subspecies of R. duvacceli (Groves and Grubb 2011) but in ABDG analysis results, R. duvacceli and R. d. branderi were considered a single species. This could be confirmed by many more markers. The topology patterns are almost alike in all the tree-building methods (NJ, ML, and BA) examined for the studied dataset of 22 species of Indian ungulates with high bootstrap values in COI and combined sequences of both genes COI and Cytb (Figures 1 and 2). The bayesian tree is produced by combined sequences of two genes falling into four major clades. Rhinoceros unicornis and E. caballus are clustered in Clade 1. In Clade 2, P. salvania is close to Sus scrofa. Moschiola indica alone is separated in Clade 3. Clade 4 comprises the family Bovidae and Cervidae (Figure 1). In a separate analysis of COI, there are 16 sub-clades identifying the species in the entire tree with 22 distinct lineages representing all the 22 separate species in COI (Figure 2). Sub clade 1: Moschiola indica; sub clade 14: S. scrofa; Sub clade 15: R. unicornis; and Sub clade 16: E. caballus are separated as paraphylitic group from all the ungulates species (Figure 2). The rhino (R. unicornis) is closer to horse (E. caballus). Pygmy hog (P. salvania) and wild boar (S. scrofa) population are sisters to each other. Recent findings of a genomic analysis on pygmy hog reveal extensive interbreeding of wild boar (Liu et al. 2019). Indian spotted deer (A. axis) and hog deer populations are clustered together as sister species in clade 3 but paraplythic with swamp and Sambar deer. The clade two suggested two subspecies of swamp deer population. A similar finding was reported by (Kumar et al. 2017). Rucervus duvacceli branderi is the subspecies of R. duvacceli (Groves and Grubb 2011) but the genetic distance is low (0.023) (Table 2). We found three nucleotide deletions in R. duvacceli compared to R. d. branderi. Both species are separated by a high bootstrap value (98%) (Figure 2). The Clade 11, four-horned antelope T. quadricornis is the sole member of the genus Tetracerus, and is placed under the family Bovidae is clustered with the nilgai (Boselaphus tragocamelus) in the Boselaphini, (Leslie and Sharma 2009). Tetracerus quadricornis and B. tragocamelus (Nilgai) are clustered together as a monophyletic group and this cluster is again paraphyletic cluster with genus Bos in Bovidae family. Antelope cervicapra and Gazella bennettii form a paraphyletic group closer to (sheep) O. aries and Capra hircus (goat) in Bovidae family. Our study compared barcode data of COI and Cytb in Indian ungulates and may serve as a baseline for future analyses of genetic diversity of ungulates (Ramon-Laca et al. 2014). Therefore, the present study provides significant contributions toward the taxonomic identity confirmation, phylogenetic studies that can be used for better planning of conservation and management of Indian ungulates. In India, very few data are present on many species of ungulates. This study will be helpful to strengthen the global database with barcode sequences of accurately identified other mammalian species from Fecal DNA. Thus, the improvements of both taxonomic studies, generated barcode data are mandatory for more reliable and accurate results. The DNA sequences of COI and Cytb genes revealed that the obtained sequences are very helpful to delineate the Indian ungulates (Bergsten et al. 2012). Acknowledgments We are thankful to our Director, Zoological Survey of India, Kolkata, Ministry of Environment, Forest and Climate Change for providing necessary facilities. Thanks are due to PCCF, (Wildlife) and APCCF and Director of Hyderabad Zoo, Telangana and PCCFWL and APCCF and Director of Chennai Zoo, Tamil Nadu, for permissions to collect samples. Disclosure statement No potential conflict of interest was reported by the authors. 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Waits LP, Paetkau D. 2005. Noninvasive genetic sampling tools for wildlife biologists: a review of applications and recommendations for accurate data collection. J Wildl Manag. 69(4):1419–1433.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4579, 1 ], [ 4579, 7448, 2 ], [ 7448, 11676, 3 ], [ 11676, 14297, 4 ], [ 14297, 15968, 5 ], [ 15968, 22794, 6 ], [ 22794, 23867, 7 ] ] }
3b7499e54726b66506fe0c9d90a07e3d3544b891	{ "olmocr-version": "0.1.59", "pdf-total-pages": 2, "total-fallback-pages": 0, "total-input-tokens": 6740, "total-output-tokens": 4092, "fieldofstudy": [ "Biology" ] }	Stem cell heterogeneity and regenerative competence: the enormous potential of rare cells Emily A.B. Gilbert, Cindi M. Morshead Endogenous stem cells for central nervous system (CNS) repair and regeneration: Endogenous stem and progenitor cells play a fundamental role in the success of repair in regenerative-competent vertebrate species. Considering the cardinal properties of stem cells including their capacity for self-renewal and their ability to generate all of the mature cells within a given organ system (multi-potency) (Reynolds and Weiss, 1992), unlocking and harnessing their potential remains a fundamental target of regenerative medicine approaches. Stem cells are located throughout the body, including within the brain and spinal cord. In mammals, the largest pool of neural stem and progenitor cells (NSPCs) are found in a well-defined region lining the ventricular system within the developing and mature nervous system. In the brain, periventricular NSPCs are neurogenic throughout life, proliferating to give rise to neuroblasts that migrate anteriorly along the rostral migratory stream to the olfactory bulb under homeostatic conditions (Doetsch et al., 1999). In contrast, NSPCs in the spinal cord are aneuregenic in adulthood (Reynolds and Weiss, 1992). Despite these differences in behavior under baseline conditions, both NSPC populations respond following injury by proliferating, migrating to the site of injury, and differentiating primarily into glial cells (astrocytes) that serve to limit the spread of injury, among other roles. Despite this response to injury, NSPC activation within the CNS does not facilitate structural or functional regeneration in mammals, including humans. In stark contrast, NSPCs have been shown to contribute to tissue regeneration following injury to the CNS in regeneration-competent species. One of the most striking examples is in the axolotl (Ambystoma mexicanum), where complete structural and functional repair of the spinal cord occurs just 6 weeks following blunt injury (Thygesen et al., 2019). Despite the fact that NSPCs across regeneration-competent and -incompetent vertebrates are located in homologous anatomical regions, express the same markers (including SRY-box 2, glial fibrillary acidic protein and nestin), and are universally responsive to injury, differences in regenerative capacity across groups remains poorly understood. A key question and area of current research focuses on understanding the cellular and environmental factors that could unlock improved regenerative competence following injury in mammals. Our recent work exploring a novel population of “primitive” neural stem cells suggests that multiple stem cell subpopulations could be harnessed for endogenous repair within the CNS (Sachewsky et al., 2014, 2019). The importance of characterizing and considering stem cell heterogeneity across organ systems and in different species is a refreshed opportunity to explore exciting new questions in the field of regenerative biology. Stem cell heterogeneity: Rapidly advancing scientific approaches, including single-cell sequencing, barcoding technologies, and complex transgenic approaches have allowed us to begin to answer fundamental questions about stem cell heterogeneity and are rapidly revealing the complexities of stem cells with an increasing level of detail (Ayyaz et al., 2019; Sachewsky et al., 2019). Historically, it was believed that all stem cells were created equal, but recent work in mammals has highlighted that this is not the case. For example, some stem cells are elite in terms of their ability to survive and change fate through reprogramming (Shakiba et al., 2019). In a recent study, it was shown that a unique subset of stem cells (derived from the neural crest) have a competitive advantage in identical reprogramming conditions, giving rise to larger, more abundant colonies of cells (Shakiba et al., 2019). This highlights heterogeneity of stem cells, which could have important implications for regenerative medicine when considering which stem cell populations to target for enhanced tissue repair. Here, we further define heterogeneity based on stem cell’s unique cellular signatures, activation responses and kinetics. While heterogeneity within a stem cell population was first recognized in hematopoietic stem cells, this phenomenon has been characterized across other organs including the intestine and brain (Muller-Sieburg et al., 2004; Ayyaz et al., 2019; Sachewsky et al., 2019). It is currently unknown whether homologous stem cell subpopulations exist in regeneration-competent species, however, at least within an invertebrate model, Drosophila, different neural stem cell populations have been observed based on their cell-cycle arrest in either G0 or G2 (Otsuki and Brand, 2020). Moreover, understanding intrinsic and extrinsic factors that regulate stem cell behavior could shed light on dramatic differences in regenerative competence across species. In the CNS, two distinct, lineally related populations of stem cells exist (Sachewsky et al., 2014, 2019; Xu et al., 2016). Definitive neural stem cell populations (dNSCs) represent the largest stem cell population along the neuraxis and are characterized by their expression of glial fibrillary acidic protein and responsiveness to epidermal and fibroblast growth factors in vitro (Reynolds and Weiss, 1992). A second, more rare, and mostly quiescent “primitive” neural stem cell (pNSC) population is upstream of the dNSCs (Sachewsky et al., 2014; Reeve et al., 2017). pNSCs express the pluripotency marker Oct4 and are responsive to leukemia inhibitory factor in vitro. Both populations are injury-responsive, as evidenced by increased clonal dNSC- and pNSC-derived colonies (termed neurospheres) following CNS injury (Sachewsky et al., 2014; Xu et al., 2016). Transplantation and lineage tracking studies reveal that pNSCs not only contribute to neurogenesis, but are the source of dNSC repopulation in models of stem cell ablation (Sachewsky et al., 2014, 2019; Reeve et al., 2017). Establishing the specific role of pNSCs during CNS neuro-regeneration, and determining whether a similar population exists along the neuraxis of regeneration-competent species are compelling questions. Support for the idea that rare stem cell populations have a role to play in tissue regeneration comes from a recent report showing that a strikingly similar stem cell subpopulation can regenerate the intestine. Using single-cell RNA sequencing, intestinal stem cells were profiled and shown to cluster into two main groups (Ayyaz et al., 2019). One cluster identified a well-delineated intestinal stem cell population... stem cell populations across species will not fully address differences in regenerative potential. An additional level of complexity comes from the micro-environment or “niche” where the stem cells reside in species with different regenerative capabilities. To date, it remains unclear how the factors released into the niche via circulation, cerebrospinal fluid, or paracrine factors influence the dynamics of stem cell populations, and how this may differ between species. More detailed information on how the composition of the niche varies between regeneration-competent and -incompetent species could help us to re-model and enhance stem cell niches in mammals to improve regenerative medicine approaches. On a translational level, we predict that stem cell heterogeneity underlies an even more important finding: that different stem cells have different regenerative capacity and play different roles in tissue repair. Understanding heterogeneity serves as a critical component of the pipeline for targeting or enriching for populations of seemingly similar cells, to essentially target those that underlie regeneration. Are different ratios of ‘primitive’ stem cells associated with different regenerative capacities? Or are the stem cells themselves intrinsically different in species with varying degrees of regenerative competence? Does the stem cell niche account for regenerative outcome? How did these differences between species arise? To date, it remains unclear whether regeneration was an ancestral trait (lost during evolution in non-regenerative species), or an adaptive trait (arisen during evolution in regenerative species) (Tanaka and Ferretti, 2009). Exploring the similarities between stem cell populations across species with varying regeneration potential could help to unlock the regenerative switch as well as reveal the evolutionary origins of regeneration within complex organ systems. Clearly there is much to be learned. Species capable of regeneration serve as a unique and important resource for revealing new information about factors that control the precision of injury repair throughout the body. Understanding stem cell heterogeneity could help to enhance regenerative outcomes in mammals, and ultimately have exciting implications for regenerative medicine approaches. Emily A.B. Gilbert, Cindi M. Morshhead* Terrence Donnelly Centre for Cellular and Biomolecular Research; Division of Anatomy, Department of Surgery, University of Toronto, Toronto, ON, Canada (Gilbert EAB, Morshhead CM) Institute of Biomedical and Biochemical Engineering, Institute of Medical Science, University of Toronto; KITE, Toronto Rehabilitation Institute, University Health Network, Toronto, ON, Canada (Morshhead CM) *Correspondence to: Cindi M. Morshhead, PhD, [email protected]. https://orcid.org/0000-0003-4605-4883 (Cindi M. Morshhead) Received: March 16, 2020 Peer review started: March 20, 2020 Accepted: April 16, 2020 Published online: August 24, 2020 https://doi.org/10.4103/1673-5374.290891 How to cite this article: Gilbert EAB, Morshhead CM (2021) Stem cell heterogeneity and regenerative competence: the enormous potential of rare cells. Neural Regen Res 16(2):285-286. Copyright license agreement: The Copyright License Agreement has been signed by both authors before publication. Plagiarism check: Checked twice by iThenticate. Peer review: Externally peer reviewed. Open access statement: This is an open access journal, and articles are distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License, which allows others to remix, tweak, and build upon the work non-commercially, as long as appropriate credit is given and the new creations are licensed under the identical terms. References Ayyaz A, Kumar S, Sangiorgi B, Ghoshal B, Gosio J, Duldan S, Fink M, Barutso S, Trcka D, Kooy D, Chan K, Wrana JL, Gregorieff A (2019) Single-cell transcriptions of the regenerating intestine reveal a revival stem cell. Nature 569:121-125. Doetsch F, Caille I, Lim DA, Garcia-Verdugo JM, Alvarez-Buylla A (1999) Subventricular zone astrocytes are neural stem cells in the adult mammalian brain. Cell 97:703-716. Muller-Sieburg CE, Cho RH, Karlsson L, Huang JF, Sieburg HB (2004) Myeloid-biased hematopoietic stem cells have extensive self-renewal capacity but generate diminished lymphoid progeny with impaired IL-7 responsiveness. Blood 103:4111-4118. Otsuki L, Brand AH (2020) Quiescent neural stem cells for brain repair and regeneration: lessons from model systems. Trends Neurosci 43:213-226. Reeve RL, Yammine SZ, Morshhead CM, van der Kooy D (2017) Quiescent Oct4+ neural stem cells (NSCs) repopulate ablative gliotic and acidic injuries in the adult mouse brain. Stem Cells 35:2071-2082. Reynolds B, Weiss S (1992) Generation of neurons and primitive and definitive neural stem cell proliferation in the adult mammalian brain. Cell 824. Sachnevsky N, Leeder R, Xu W, Rose KL, Xu Y, van der Kooy D, Morshhead CM (2014) Primitive neural stem cells in the adult mammalian brain give rise to GFAP-expressing neural stem cells. Stem Cell Reports 2:810-824. Sachnevsky N, Xu W, Fuehrmann T, van der Kooy D, Morshhead CM (2019) Lineage tracing reveals the hierarchical relationship between neural stem cell populations in the mouse forebrain. Sci Rep 9:17730. Shakiba N, Fahmy A, Jayakumaran G, McGibbon S, David L, Trcka D, Eibaz J, Pur I, Nagy A, van der Kooy D, Goyal S, Wrana JL, Zandstra PW (2019) Cell competition during reprogramming gives rise to dominant clones. Science doi: 10.1126/science.aau6005. Tanaka EM, Ferretti P (2009) Considering the evolution of regeneration in the central nervous system. Nat Rev Neurosci 10:713-723. Thygesen MM, Lauridsen H, Pedersen M, Orlovski D, Mikkelsen TW, Rasmussen MM (2015) A clinically relevant blunt spinal cord injury model in the regeneration competent axolotl (Ambystoma mexicanum) tail. Exp Ther Med 17:2322-2328. Xu W, Sachnevsky N, Azimi A, Hung M, Goppasov A, Morshhead CM (2016) Myeloid-biased progenitor regulates primitive and definitive neural stem cell proliferation from the adult spinal cord. Stem Cells 35:485-496. Perspective stem cell heterogeneity and comparative regenerative potential: Characterizing the presence and relative abundance of these rare subpopulations of stem cells across species of varying regenerative ability could reveal the breadth of their reparative potential. When considering stem cell heterogeneity, one of the most striking phenomena is the enormous potential of exceeding rare cells. One can imagine that stem cells with extraordinary potential are only needed in small numbers as it only takes a few of them to produce all of the cells needed for regenerating lost tissue. Equally plausible, is that the rarity of the stem cells with extraordinary potential is what dictates the poor regenerative capacity of mammals. How can we best delineate these possibilities? A first place to start would be the explore stem cell heterogeneity and the relative frequency of pNSCs and revSCs (for example) in regenerative competent species. Future studies should include an analysis of stem cell population dynamics; lineage tracking to explore their respective contributions to regeneration, and utilize knock-out models to inhibit their role following injury in regeneration competent species. These experiments would elucidate whether rare stem cell populations could be expanded in mammals and exploited to improve endogenous repair. Additionally, single cell-RNA-sequencing now permits the evaluation of how similar CNS-derived pNSCs and intestine-derived revSCs are to their developmental counterparts, and would enable comparison of these cell populations across species of varying regenerative abilities. An investigation of these novel stem cell populations including their frequency, gene profile, cell cycle kinetics and differentiation potential across species would inform a prediction about which stem cells have the most “regenerative potential”. This knowledge would help to inform future efforts to target distinct stem cell populations for neurorepair. Even with powerful techniques that enable single cell analysis, a direct comparison of expressing a leucine-rich repeat containing G-protein coupled receptor 5 (LGR5) known as crypt-base columnar cells, which are responsible for homeostatic turnover of the intestinal epithelium. A second, quiescent population expressed clustatin, and were termed “revival” stem cells (revSC) based on their response to injury (Ayyaz et al., 2019). revSCs are rare, quiescent, and linearly related to crypt-base columnar cells and have the capacity to generate LGR5+ stem cells following intestinal ablation (Ayyaz et al., 2019). pNSCs and revSCs share several key attributes: they are a largely quiescent, extraordinary population expressed clusterin, and were notably responsive to injury where they serve to repopulate downstream stem cell populations that generate all of the major cell types within the respective tissues. Stem cell heterogeneity and comparative regenerative potential: Characterizing the presence and relative abundance of these rare subpopulations of stem cells across species of varying regenerative ability could reveal the breadth of their reparative potential. When considering stem cell heterogeneity, one of the most striking phenomena is the enormous potential of exceeding rare cells. One can imagine that stem cells with extraordinary potential are only needed in small numbers as it only takes a few of them to produce all of the cells needed for regenerating lost tissue. Equally plausible, is that the rarity of the stem cells with extraordinary potential is what dictates the poor regenerative capacity of mammals. How can we best delineate these possibilities? A first place to start would be the explore stem cell heterogeneity and the relative frequency of pNSCs and revSCs (for example) in regenerative competent species. Future studies should include an analysis of stem cell population dynamics; lineage tracking to explore their respective contributions to regeneration, and utilize knock-out models to inhibit their role following injury in regeneration competent species. These experiments would elucidate whether rare stem cell populations could be expanded in mammals and exploited to improve endogenous repair. Additionally, single cell-RNA-sequencing now permits the evaluation of how similar CNS-derived pNSCs and intestine-derived revSCs are to their developmental counterparts, and would enable comparison of these cell populations across species of varying regenerative abilities. An investigation of these novel stem cell populations including their frequency, gene profile, cell cycle kinetics and differentiation potential across species would inform a prediction about which stem cells have the most “regenerative potential”. This knowledge would help to inform future efforts to target distinct stem cell populations for neurorepair. Even with powerful techniques that enable single cell analysis, a direct comparison of	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 6717, 1 ], [ 6717, 17837, 2 ] ] }
525352053a44e55ec52fbfce180d3a17d2ee719a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 11, "total-fallback-pages": 0, "total-input-tokens": 30255, "total-output-tokens": 11343, "fieldofstudy": [ "Biology" ] }	miR-448 targets Rab2B and is pivotal in the suppression of pancreatic cancer JING JIN, YINGSHENG WU, DONGKAI ZHOU, QIANG SUN and WEILIN WANG Key Laboratory of Precision Diagnosis and Treatment for Hepatobiliary and Pancreatic Tumor of Zhejiang Province, Division of Hepatobiliary and Pancreatic Surgery, The First Affiliated Hospital, School of Medicine, Zhejiang University, Hangzhou, Zhejiang 310003, P.R. China Received March 7, 2018; Accepted July 3, 2018 DOI: 10.3892/or.2018.6562 Abstract. Improvements in survival rates for pancreatic cancer have been slow and the morality rate continues to increase in patients. MicroRNA (miR)-448 is reported to be significantly downregulated in several types of cancer. In this study, Rab2B is target of miR-448 was confirmed by bioinformatics analysis and validated using a luciferase reporter assay. A total of 72 cases of pancreatic cancer in patients diagnosed at The First Affiliated Hospital, School of Medicine, Zhejiang University (Hangzhou, China) were enrolled, and cancer specimens and their adjacent normal tissues were collected for analysis. The expression levels of miR-448 and Rab2B in these tissues and in pancreatic cancer cell lines were quantified using reverse transcription-polymerase chain reaction analysis. miR-448 overexpression was achieved by cell transfection. Protein expression was assessed using western blot analysis. Cell viability, cell cycle and apoptosis were analyzed using CCK-8 assay and flow cytometry, respectively. The results revealed a negative correlation between miR-448 and Rab2B in the pancreatic tissues and cell lines. The results of bioinformatics analysis indicated that miR-448 directly targeted Rab2B. Aberrant miR-448 levels in PANC-1 cells downregulated the expression of Rab2B, and significantly decreased cell proliferation and promoted apoptosis of cancer cells. It was also found that miR-448 mimics resulted in G0/G1 cell cycle arrest and affected the expression of cell cycle regulators, including cyclin D1, p21 and p27. In addition, the miR-448 mimics led to inactivation of the Akt/Mammalian target of rapamycin signaling pathway. The miR-448 mimics induced apoptosis and activated the expression of caspase-3, caspase-9 and poly(ADP-ribose) polymerase. The results suggested that miR-448 was a negative regulator of Rab2B and promoted cell cycle arrest and apoptosis in pancreatic cancer. Introduction According to the cellular direction of the differentiation of tumor cells, malignant neoplasms of the pancreas can be classified into three categories: Ductal, acinar, and neuroendocrine (1). Pancreatic ductal adenocarcinoma, which accounts for ~90% of malignant pancreatic tumors, has become the fourth leading cause of cancer-associated mortality in the USA and has an annual mortality rate of 227,000 worldwide (2). Based on a previous report, despite decades of research, advances in terms of survival rates have been slow for pancreatic cancer. The 5-year survival rate for patients diagnosed with pancreatic cancer is 8%, and the morality rate continues to rise by 0.3% per year among men (3). The poor prognosis is primarily attributable to late stage disease at diagnosis and inherent cancer cell resistance to standard chemotherapy (4-6). Due to the lack of a more sensitive and precise biomarkers under imaging detection, molecular technology has been applied to identify biomarkers that have the potential to detect disease at the early stage and assist in predicting disease progression (4). The significance of microRNA (miRNA) profiling has been highlighted in a variety of human diseases, for example, malignant tumors (7-9). miRNAs, a group of non-coding RNA molecules of 18-22 nucleotides in length, are key in cellular functions, including apoptosis, metabolism, cell proliferation and differentiation. Aberrant miRNAs levels can lead to gene mutations, epigenetic modifications or defects in the miRNA processing pathway (10). The Rab family, known alternatively as small GTP-binding proteins, are members of the Ras-like small GTPase superfamily. It has been demonstrated that the family contributes to the control of intracellular membrane trafficking in eukaryotic cells (11). The majority of Rab proteins have been shown to be expressed in numerous tissues, although the expression levels vary among diverse tissues and cells. Tissue specificity and cell specificity have been identified in several Rab proteins (12,13). Rab2 contains a conservative GTP binding domain and a variable N-terminus domain and C-terminus. To the best of our knowledge, the association between pancreatic cancer and the dysregulation of miRNA-448 (miR-448) has not been investigated previously. In addition, the regulation of the expression of Rab2B by miRNAs remains to be fully elucidated. The present study aimed to examine the role of miR-448 in pancreatic cancer in vitro. In addition, the study intended to determine whether the experimental manipulation of miR-448 in pancreatic cancer cells can regulate the expression of Rab2B and inhibit the growth of pancreatic cancer at a molecular level. Materials and methods Tumor samples and cells. A total of 72 patients with pancreatic cancer admitted to the First Affiliated Hospital, School of Medicine, Zhejiang University (Hangzhou, China) were accepted into the present study. Cancer tissue specimens and adjacent normal pancreatic tissue samples were collected from surgical tumor resections from the patients. The basic clinical and pathological data of these patients were collected with their signed written informed consent. All experimental protocols were approved by the Ethics Committee of The First Affiliated Hospital, School of Medicine, Zhejiang University. The HPDE6-C7 normal pancreatic cell line, and the AsPC-1, BxPC-3, Capan-1, CFPAC-1, HPAC, Hs 766T and Panc-1 pancreatic cancer cell lines were purchased from Nanjing Cobioer Biotechnology Co., Ltd. (Nanjing, China). The cells were cultured in Dulbecco's modified Eagle's medium (DMEM) containing 10% fetal calf serum (FCS; Thermo Fisher Scientific, Inc., Waltham, MA, USA) with 5% medium (DMEM) containing 10% fetal calf serum (FCS; Thermo Fisher Scientific, Inc., Rockville, MD, USA) was co-transfected with either miR-448 mimic or miR-448 negative control using Lipofectamine 3000 (Thermo Fisher Scientific, Inc.). At 48 h post-transfection, the luciferase activity was determined with the Secrete-Pair™ Dual-Luciferase Reporter assay (GeneCopoeia). The miR-448 mimics (mature sequence: UUGCAUAUGGAAGUCCCAU) (miR10001532-1-5) and miR-448 inhibitors (miR20001532-1-5) are obtained from Guangzhou Ribobio Technology Co., Ltd. (Guangzhou, China). CCK-8 assay. Cell proliferation in the control, mock and mimics group were determined using a CCK-8 assay (Shanghai Haling Biotechnology, Co., Ltd., Shanghai, China). The cells were seeded into a 96-well plate (100 µl/well) and cultured in an incubator with 5% CO2 at 37°C for 1-4 h. The control using Lipofectamine 3000 (Thermo Fisher Scientific, Inc.). At 48 h post-transfection, the luciferase activity was determined with the Secrete-Pair™ Dual-Luciferase Reporter assay (GeneCopoeia). The miR-448 mimics (mature sequence: UUGCAUAUGGAAGUCCCAU) (miR10001532-1-5) and miR-448 inhibitors (miR20001532-1-5) are obtained from Guangzhou Ribobio Technology Co., Ltd. (Guangzhou, China). Flow cytometry (FCM). The cells were digested by 0.25% trypsin-EDTA (Beyotime Institute of Biotechnology, Haimen, China) and collected by centrifugation at 500 x g at 4°C for 5 min and washed three times with phosphate-buffered saline (PBS). The precipitated cells were resuspended and fixed in 70% absolute alcohol. Subsequently, for the purpose of analyzing cell cycle, the cells were washed with PBS and centrifuged at 500 x g at 4°C for 5 min to collect the precipitate. Propidium iodide (PI) was added for staining. The cell cycle status was determined using an EPICS XL-MCL FCM system (Beckman Coulter, Inc., Brea, CA, USA). Cells in the logarithmic phase were collected and seeded into 6-well plates (3x10^4/well). The cells were then digested in EDTA-free trypsin (Shanghai Lanpai Biotechnology Co., Ltd., Shanghai, China), and stained with Annexin V-FITC and PI (Shanghai Lanpai Biotechnology Co., Ltd.). The cells were then incubated in the dark for 15 min at room temperature. The apoptotic rate of the cells in each group was detected using an EPICS XL-MCL FCM system (Beckman Coulter, Inc., Brea, CA, USA). Bioinformatic analysis. Bioinformatic analysis was performed using prediction software. The target genes of miR-448 were predicted via miRanda (http://www.microrna.org/microrna/home.do), miRDB (http://www.mirdb.org/), PicTar (http://pictar.mdc-berlin.de/) and TargetScan (http://www.targetscan.org/vert_71/). The probable functions of the miRNA were predicted via the Database for Annotation, Visualization and Integrated Discovery (https://david.ncifcrf.gov/). Luciferase reporter assay. The 3’-untranslated region (UTR) fragment of Rab2B with a binding site for miR-448 was cloned into luciferase vectors (Promega Corp., Madison, WI, USA). The PANC-1 cells were seeded into 96-well plates at a density of 1x10^4 cells/well 1 day prior to transfection. The control luciferase reporter plasmid, Rab2B 3’-UTR or mutated Rab2B 3’-UTR (GeneCopoeia, Inc., Rockville, MD, USA) was co-transfected with either miR-448 mimic or miR-448 negative control using Lipofectamine 3000 (Thermo Fisher Scientific, Inc.). At 48 h post-transfection, the luciferase activity was determined with the Secrete-Pair™ Dual-Luciferase Reporter assay (GeneCopoeia). The miR-448 mimics (mature sequence: UUGCAUAUGGAAGUCCCAU) (miR10001532-1-5) and miR-448 inhibitors (miR20001532-1-5) are obtained from Guangzhou Ribobio Technology Co., Ltd. (Guangzhou, China). CCK-8 assay. Cell proliferation in the control, mock and mimics group were determined using a CCK-8 assay (Shanghai Haling Biotechnology, Co., Ltd., Shanghai, China). The cells were seeded into a 96-well plate (100 µl/well) and cultured in an incubator with 5% CO2 at 37°C for 4 h. Subsequently, 10 µl of CCK-8 reagent was added to the cells, which were placed into a CO2 incubator again for 1-4 h. The optical density (OD) values were read by an iMark microplate absorbance reader (Bio-Rad Laboratories, Inc., Hercules, CA, USA) at the wavelength of 450 nm. Flow cytometry (FCM). The cells were digested by 0.25% trypsin-EDTA (Beyotime Institute of Biotechnology, Haimen, China) and collected by centrifugation at 500 x g at 4°C for 5 min and washed three times with phosphate-buffered saline (PBS). The precipitated cells were resuspended and fixed in 70% absolute alcohol. Subsequently, for the purpose of analyzing cell cycle, the cells were washed with PBS and centrifuged at 500 x g at 4°C for 5 min to collect the precipitate. Propidium iodide (PI) was added for staining. The cell cycle status was determined using an EPICS XL-MCL FCM system (Beckman Coulter, Inc., Brea, CA, USA). Cells in the logarithmic phase were collected and seeded into 6-well plates (3x10^4/well). The cells were then digested in EDTA-free trypsin (Shanghai Lanpai Biotechnology Co., Ltd., Shanghai, China), and stained with Annexin V-FITC and PI (Shanghai Lanpai Biotechnology Co., Ltd.). The cells were then incubated in the dark for 15 min at room temperature. The apoptotic rate of the cells in each group was detected using the EPICS XL-MCL FCM system (Beckman Coulter, Inc.) with an excitation wavelength of 488 nm and emission wavelength of 530 nm. Determination of caspase activities. The activities of caspase-3/-9 were evaluated using caspase-3 and caspase-9 colorimetric assay kits, according to the manufacturer's protocol. The cells were lysed in lysis buffer. Substrates for caspase-3 and caspase-9 (Ac-DEVD-pNA and Ac-LEHD-pNA) were added to the cell lysates (50 µg proteins). The protein concentration was determined by BCA assay kit (Thermo Fisher Scientific, Inc.). The samples were then incubated at membranes were subsequently incubated with a horseradish peroxidase-conjugated secondary antibody (dilution 1:2,000; cat. no. ab205718; Abcam) at room temperature for 1 h. The primary antibodies were as follows: Anti-Rab2B (dilution 1:1,000; cat. no. ab95952; Abcam); anti-cyclin D1 (dilution 1:10,000; cat. no. ab134175; Abcam); anti-cyclin-dependent kinase inhibitor 1B (p27; dilution 1:5,000; cat. no. ab32034; Abcam); anti-procaspase-9 (dilution 1:500; cat. no. ab135544; Abcam); anti-procaspase-3 (dilution 1:1,000; cat. no. ab32150; Abcam); anti-p-Akt (dilution 1:500; cat. no. ab38449; Abcam); anti-p21 (dilution 1:1,000; cat. no. ab109520; Abcam); anti-Akt (dilution 1:6,000; cat. no. ab81283; Abcam); anti-poly(ADP-ribose) polymerase (PARP; dilution 1:5,000; cat. no. ab32138; Abcam); anti-GAPDH (dilution 1:2,500; cat. no. ab9485; Abcam). Blots were developed with enhanced chemiluminescence detection kit (GE Healthcare, Chicago, IL, USA). The density of the blots was read with Quantity One software version 4.6.2 (Bio-Rad Laboratories). Reverse transcription-quantitative polymerase chain reaction (RT-qPCR) analysis. Quantification of the expression of miR-448 was determined using a TaqMan miRNA assay (Thermo Fisher Scientific, Inc.). Reverse transcription of 10 ng of template RNA was performed using the TaqMan MicroRNA Reverse Transcription kit and miRNA-specific stem-loop primers. The expression was normalized by U6. The primers used were as follows: miR-448, forward, 5'-TTG CATATGTTAGGTGCCCAT-3' and reverse, 5'-CTCAAAC TGTGTGTGTGGAGTCCGGCAATTTCGTTGAGATGGGA CA-3'; and U6, forward, 5'-ACGAATTTGCGTGCATCCT-3' and reverse, 5'-ACGAATTTGCGTGCATCCT-3'. To determine the mRNA levels of other genes, including Rab2B, total RNA (2 µg) was first reverse transcribed using the Takara PrimeScript RT reagent kit (Takara Bio, Inc., Otsu, Japan) (containing PrimeScript buffer and PrimeScript™ RT Enzyme). Quantification of mRNA was performed with the TaqMan Gene Expression Assay (Thermo Fisher Scientific, Inc.). The thermocycling conditions were as follows: 5 min pretreatment at 94°C; 94°C for 10 sec, 60°C for 30 sec (30 cycles); final extension at 72°C for 10 min. Target gene expression was normalized on the basis of glyceraldehyde‑3‑phosphate dehydrogenase (GAPDH). The quantification was determined by the 2-ΔΔCq method. The primer sequences for the gene were as follows: Rab2B, forward, 5'-GGT CCG GGA AGT CCA TAC TC-3' and reverse, 5'-GGC TGG AAC CCG TTT ATC TCT GT-3'; and GAPDH, forward, 5'-AACCTCTGCGTGACTAAC-3' and reverse, 5'-GCA TCACCGAGGAAAT-3'. Western blot analysis. The total protein of the cells in each group was extracted using a ProteoPrep® Total Extraction Sample kit (Sigma-Aldrich; EMD Millipore, Billerica, MA, USA). The cell lysates were prepared in cell lysis buffer, and the supernatant was collected following centrifugation at 500 x g at 4°C for 10 min. The concentration of the protein was determined using a Bradford assay (Bio-Rad Laboratories) and 30 µg of each protein sample was separated via 10-15% SDS-PAGE (Merck Millipore, Darmstadt, Germany). The membranes were blocked with 5% skimmed milk for 2 h at room temperature. Then, the membranes were incubated with primary antibodies at 4°C overnight. The membranes were subsequently incubated with a horseradish peroxidase-conjugated secondary antibody (dilution 1:2,000; cat. no. ab205718; Abcam) at room temperature for 1 h. The primary antibodies were as follows: Anti-Rab2B (dilution 1:1,000; cat. no. ab95952; Abcam); anti-cyclin D1 (dilution 1:10,000; cat. no. ab134175; Abcam); anti-cyclin-dependent kinase inhibitor 1B (p27; dilution 1:5,000; cat. no. ab32034; Abcam); anti-procaspase-9 (dilution 1:500; cat. no. ab135544; Abcam); anti-procaspase-3 (dilution 1:1,000; cat. no. ab32150; Abcam); anti-p-Akt (dilution 1:500; cat. no. ab38449; Abcam); anti-p21 (dilution 1:1,000; cat. no. ab109520; Abcam); anti-Akt (dilution 1:6,000; cat. no. ab81283; Abcam); anti-poly(ADP-ribose) polymerase (PARP; dilution 1:5,000; cat. no. ab32138; Abcam); anti-GAPDH (dilution 1:2,500; cat. no. ab9485; Abcam). Blots were developed with enhanced chemiluminescence detection kit (GE Healthcare, Chicago, IL, USA). The density of the blots was read with Quantity One software version 4.6.2 (Bio-Rad Laboratories). Statistical analysis. Statistical analyses were performed using SPSS software, version 22.0 (IBM SPSS, Armonk, NY USA) and GraphPad Prism software 6.0 (GraphPad Software, Inc., La Jolla, CA, USA). Each experiment was repeated three times. Data are presented as the mean ± standard deviation. Student's t-test and one-way analysis of variance (ANOVA) with Turkey's test were performed to calculate statistical significance. Spearman's rank order was used to analyze the correlations between variables. Kaplan-Meier survival curve analysis was used to show the survival rates. P<0.05 was considered to indicate a statistically significant difference. Results Levels of Rab2B are negatively correlated with the expression of miR-448 in pancreatic cancer tissues and cell lines. A total of 72 patients with pancreatic cancer with an average age of 55.28±4.08 years were accepted into the present study (Table I). The mRNA levels of miR-448 and Rab2B in pancreatic cancer samples and their adjacent normal tissues were examined using RT-qPCR analysis. In the cancer tissues, the expression of miR-448 was inhibited, whereas the level of Rab2B was significantly enhanced (P<0.05; Fig. 1A and B). In addition, a significant negative correlation between the expression of miR-448 and Rab2B was detected (P<0.01; Fig. 1C). The patients were then divided either into a higher Rab2B group and lower Rab2B group based on the median value of the expression of Rab2B. Survival analysis revealed that... patients with a weaker expression of Rab2B were likely to survive longer than those who had a high expression level of Rab2B (P<0.01; Fig. 1D). Through the analysis of normal and cancer cell lines of the pancreas (HPDE6-C7, AsPC-1, BxPC-3, Capan-1, CFPAC-1, HPAC, Hs 776T and PANC-1), lower levels of miR-448 and higher levels of Rab2B were detected in the cancer cell lines (P<0.05; Fig. 1E and F). Identification of Rab2B as the direct target of miR-448. The in silico analysis of human miR-448 started with surveys of its target-prediction. The four prediction software packages, miRanda, miRDB, PicTar and TargetScan, respectively identified 3,488, 483, 1,127 and 684 target genes of human miR-448. On the basis of these predicted target genes, a total of 104 target genes of intersection of miR-448 were isolated by the means of a Venn diagram (Fig. 2A). Subsequently, 20 annotations of biological processes in association with miR-448 were predicted using Gene Ontology analysis (P<0.01; Fig. 2B). The results revealed that the genes targeted by miR-448 were primarily abundant in the cytoplasm and plasma membrane, and mainly functioned in protein binding. Subsequent analysis of the alignment of miR-448/Rab2B was performed to confirm the target association between miR-448 and Rab2B. miR-448 interacts with the Rab2B-3' UTR reporter. A luciferase reporter containing the human Rab2B-3' UTR was used to identify whether miR-448 specifically interacted with the Rab2B-3' UTR or not (Fig. 3A and B). The luciferase activity in... Figure 4. Overexpression of miR-448 affects cell proliferation, migration and invasion. (A) Ectopic expression of miR-448 was confirmed, which (B) decreased the mRNA level of Rab2B. (C) Protein expression of Rab2B was inhibited by miR-448 mimics. (D) Overexpression of miR-448 decreased the proliferative ability of PANC-1 cells. (E) miR-448 induced G0/G1 cell cycle arrest in PANC-1 cells. (F) miR-448 promoted the apoptotic rate of PANC-1 cells. Data are shown as the mean ± standard deviation of three independent experiments. P<0.05, *P<0.01, vs. control; ^P<0.05, ^^P<0.01, vs. mock. miR, microRNA; glyceraldehyde-3-phosphate dehydrogenase. each group was determined 24 h following transfection with the luciferase reporter, and the miR-448 overexpression and inhibiting constructs. In the assay system, a reduction in luciferase expression indicated a specific miR-448-3'-UTR interaction. It was found that the luciferase activity was markedly reduced in the high miR-448 cells, particularly in the miR-448 mimics + Rab2B-WT group (P<0.01). By contrast, mutation of the predicted binding sites in the Rab2B-3'-UTR eliminated the reduction of luciferase reporter activity (Fig. 3C). When combined with the results of the bioinformatics analysis, it was confirmed that miR-448 contributed to the control of the expression of Rab2B. Overexpression of miR-448 downregulates Rab2B levels in PANC-1 cells. In PANC-1 cells transfected with miR-448 mimics, the level of miR-448 was distinctly enhanced, compared with that in the control group (P<0.01; Fig. 4A). The results of the RT-qPCR and western blot analyses also showed that the aberrant expression of miR-448 led to the significant downregulation of Rab2B at the mRNA and protein levels (P<0.05; Fig. 4B and C). The protein expression of Rab2B was reduced by >50% in the miR-448 mimics group (P<0.01). Overexpression of miR-448 inhibits cell proliferation and promotes apoptosis. Subsequently, the effects of the Overexpression of miR-448 on the biological processes of PANC-1 cells, including cell viability, cell cycle and apoptosis, were observed (Fig. 4D-F). In the miR-448 mimics group, it was found that the aberrant expression of miR-448 significantly inhibited PANC-1 cell growth and proliferation in vitro, however, it induced G0/G1 cell cycle arrest in comparison with the control group. A marked increase in apoptotic rate was identified under the condition of a high level of miR-448 (P<0.01). The above results revealed the importance of miR-448 in the development of pancreatic cancer. Overexpression of miR-448 decreases the expression of cyclin D1 but upregulates the expression of p21 and p27. The effects of aberrant miR-448 levels on the expression of cell cycle proteins cyclin D1, p21 and p27 were detected by western blot analysis (Fig. 5A). In the miR-448 overexpressing cells, the protein level of cyclin D1 was reduced by >50%, compared with that in the control (P<0.01). By contrast, the expression of p21 and p27 were significantly upregulated by miR-448 at the protein level (P<0.01). Overexpression of miR-448 suppresses the activation of Akt, Mammalian target of rapamycin (mTOR) and S6K1. The phosphorylation levels of Akt, mTOR and S6K1 were determined using western blot analysis (Fig. 5B-D). The results showed an apparent negative correlation between a high level of miR-448 and the Akt/mTOR signaling pathway. In the presence of miR-448, the protein levels of phosphorylated Akt, mTOR and S6K1 were observed to be reduced by >50%, compared with those in the control. These results indicated inactivation of the Akt/mTOR pathway by miR-448 (P<0.01). Overexpression of miR-448 increases the activities of caspase-3 and caspase-9 and upregulates the expression of poly(ADP-ribose) polymerase (PARP). The results of spectrophotometric methods showed significant increases in the activities of caspase-3 and caspase-9 in the miR-448 mimics group (P<0.01; Fig. 6A and B). The protein levels of pro-caspase-3 and pro-caspase-9 were found to be significantly decreased in the presence of a high level of miR-448 (P<0.01; Fig. 6D). miR-448 overexpression also increased the expression of PARP at the mRNA and protein levels (P<0.01; Fig. 6C and D). A model summarizing the results of the present study is shown in Fig. 7. Discussion As a key regulator of gene expression, miRNAs are reported to control numerous physiological and pathophysiological events in malignant tumors. A number of miRNAs have been identified to contribute to the regulation of cancer cell proliferation, apoptosis, immune evasion and metastasis (16-18). Multiple molecular target genes of miRNAs have been identified. Advances in specific inhibitors and mimics, which can be locally or systemically transferred to the organs, enable the development of miRNAs to be treated as novel therapeutic targets (19). Generally, a single miRNA is able to regulate a number of protein-coding genes. As miRNAs can identify certain ‘seed sequences’ in sections of genes, any gene containing a sequence complementary to the seed region is potentially regulated by the respective miRNAs (20). The results of the present study revealed a significant role of miR-448 in inhibiting the development of pancreatic cancer by regulating the expression of Rab2B in vitro. Silencing of the expression of miR-448 and a negative correlation between miR-448 and Rab2B were identified in pancreatic cancer tissues and cell lines. Interacting through its specific effector molecules, Rab is generally accepted as a key regulator of intracellular membrane trafficking. However, to date, due to the large number of Rab isoforms in mammals, specific effector molecules for the majority of mammalian Rab proteins have not been elucidated, and the Rab binding specificity of the previously characterized Rab effectors remains unclear (11). In silico analysis confirmed that Rab2B was one of 90 reliable target proteins of miR-448. At the cellular level, miR-448 mimics resulted in the apparent inhibition of cell growth and proliferation, leading to a significant increase in apoptotic rate and downregulated the expression of Rab2B. These results extend those of previous reports on the role of miR-448 in pancreatic cancer and provide novel insight into how the expression of Rab2B can be regulated at the post-transcriptional level. As aberrant protein levels of Rab have been shown to be involved in certain malignant tumors, the present study provides scope for a wide range of cancer investigations (21,22). The cell cycle is divided into the G1 phase (DNA-synthetic phase), S phase (synthesis phase), G2 phase (post-synthesis phase) and M phase (mitotic phase). The irreversibility of these events determines the uni-polarity of the cell cycle. The cell cycle is regulated by multiple factors, including the cyclin, maturation promoting factor, growth factor, colyone and cell division cycle genes. Once the process lacks the support of the internal or external signals, cells are unable to transfer into the next phase, which may result in cycle arrest (23,24). The present study applied FCM to investigate the effect of miR-448 mimics on cell cycle in PANC-1 cells. Based on the results, no significant difference in cell cycle distribution was observed between the control and mock groups. In the miR-448 mimic group, the aberrant expression of miR-448 increased the cell rate in the G0/G1 phase, but decreased the rates in the S phase and G2/M phase, suggesting that miR-448 was likely to inhibit the G0/G1, cell cycle phase, and inhibit the proliferation of PANC-1 cells. Akt is a kinase of diverse cell signaling pathways. p-Akt, the activated form of Akt, is important in enhancing cell growth and proliferation, promoting cell cycle development and suppressing apoptosis. The activation of Akt is involved in tumorigenesis and cancer metastasis (25-27). mTOR is a untypical serine/threonine protein kinase, and has attracted much attention due to its close association with tumorigenesis and the development of numerous types of cancer. S6K1, one of the downstream target proteins of mTOR, is a multifunctional kinase. When the extracellular environment changes, mTOR is involved in the regulation of cell growth, differentiation, proliferation and protein synthesis through phosphorylating S6K1. Previous studies on S6K1 have mainly focused on its role in tumorigenesis. It is hypothesized that activated S6K1 can phosphorylate substrates, inhibit apoptosis, and promote development of the cell cycle, and is also involved in vascularization (23,28,39). In the present study, a significant negative correlation between a high level of miR-448 and the Akt/mTOR signal pathway was observed by western blot analysis. Upregulating the expression of miR-448 substantially suppressed the phosphorylation of Ak, which inhibited the activation of its downstream targets, including mTOR and S6K1. Suppression of the Akt/mTOR/S6K1 pathway is likely to be closely associated with the promotion of apoptosis in pancreatic cancer through mediating associated gene expression. The results of the present study suggested that the overexpression of miR-448 affected the expression of a series of apoptosis-related genes. Caspase-3 belongs to the CED-3 subfamily. Caspase-3 is an inactive zymogen in the cytoplasm under a normal state, but it can be activated by caspase-9 in apoptosis. As a key enzyme in the apoptotic process, caspase-3, which was alternatively named as apoptotic effector, is pivotal to the mitochondrial apoptosis pathway, and is also one of the important molecular mechanisms underlying tumor cell apoptosis. The activation of caspase-3 can split corresponding substrates in the cell nucleus and cytoplasm, promote the fragmentation of DNA and finally kill cells (30). PARP, a type of modification enzyme existing in the majority of eukaryocytes, is one of the substrates of caspase-3 and is primarily located in the cell nucleus (31). It is involved in the post-translational modification of numerous proteins and enzymes in the cell nucleus and is important in DNA damage repair, DNA duplication, regulation of cell proliferation and differentiation, apoptosis and tumorigenesis (32,33). Evidence shows that the aberrant activation of PARP can trigger apoptotic signals, and induce mitochondria to release apoptosis-inducing factor, resulting in DNA cleavage and apoptosis (34-36). In pancreatic cancer cells, significantly elevated activities of caspase-3 and miR-448 mimics resulted in G0/G1 cell cycle arrest and cell proliferation and promoted the apoptosis of cancer cells. The expression of Rab2B, however, it significantly decreased the expression of miR-448. The results of western blot analysis also indicated substantial reductions in the levels of pro-caspase-3, caspase-9 and increased expression of PARP in miR-448 induced the apoptosis of pancreatic cancer cells. 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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) License.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4563, 1 ], [ 4563, 12067, 2 ], [ 12067, 17886, 3 ], [ 17886, 19181, 4 ], [ 19181, 19424, 5 ], [ 19424, 20072, 6 ], [ 20072, 21397, 7 ], [ 21397, 24753, 8 ], [ 24753, 29944, 9 ], [ 29944, 34281, 10 ], [ 34281, 37594, 11 ] ] }
4b9d27124c4f7563f0e3a61dfe75284cf27d59b8	{ "olmocr-version": "0.1.59", "pdf-total-pages": 7, "total-fallback-pages": 0, "total-input-tokens": 23432, "total-output-tokens": 9201, "fieldofstudy": [ "Materials Science", "Medicine" ] }	Evaluation of the cytocompatibility of methacrylate resin-based root canal sealers with osteoblast-like cells Yadanar Su PHYO, Kentaro HASHIMOTO, Nobuyuki KAWASHIMA, Masashi KURAMOTO and Takashi OKIJI Department of Pulp Biology and Endodontics, Division of Oral Health Sciences, Graduate School of Medical and Dental Sciences, Tokyo Medical and Dental University (TMDU), Tokyo, Japan Corresponding author, Nobuyuki KAWASHIMA; E-mail: [email protected] This study compared the cytocompatibilities of three methacrylate resin-based root canal sealers [MetaSEAL Soft (MSS), Hybrid Root SEAL (HRS), and Superbond Sealer (SBS)] in either freshly mixed or set conditions using the Kusa A1 osteoblastic cell line. The three sealers and an epoxy resin-based sealer (AH Plus; AHP) were extracted in culture medium; cell growth and osteogenic properties were analyzed. Cell adhesion on set sealers was analyzed with scanning electron microscopy. The respective extents of cell growth were as follows in freshly mixed and set sealers extracts: SBS>MSS>AHP>HRS and SBS>AHP>MSS>HRS. Light irradiation of MSS and HRS increased the cell growth of set sealer extracts. Set SBS, MSS, and AHP did not alter expression of osteogenic genes or formation of mineralized nodules. Attached cells were observed only on SBS. In conclusion, the four sealers exhibited varying degrees of compatibility to osteoblasts; SBS and HRS were the most and least compatible, respectively. Keywords: Cytocompatibility, Methacrylate resin-based root canal sealers, Osteoblasts, Scanning electron microscopy INTRODUCTION The primary objective of endodontic treatment is to eradicate intracanal pathogens and pathogenic substances. This is followed by hermetic sealing of the cleaned and shaped root canal space to prevent reinfection and entomb residual microorganisms$^1$. Regardless of the root-filling technique, sealers are necessary to establish hermetic sealing by filling the space between the dentinal wall and the obturating core material$^2$. Available root canal sealers are currently composed of various formulations, including zinc oxide–eugenol, calcium hydroxide, silicone, calcium silicates, and several classes of resinous materials$^3$. However, none of the products are considered ideal; in particular, “traditional” sealers (e.g., zinc oxide–eugenol-based materials) show no or low adhesiveness to dentinal walls$^4$. Because of advancements in dentin bonding technology, several methacrylate resin-based sealers have been developed in attempts to establish simultaneous bonding of root canal sealers to root-filling materials and dentin$^5$. Among these, Hybrid Root SEAL (HRS, also known as MetaSeal; Sun Medical, Moriyama, Japan) is a self-adhesive dual-curable sealer that contains 4-methacryloxyethyl trimellitate anhydride (4-META) as an adhesive monomer. MetaSEAL Soft (MSS; Sun Medical) is the next generation of Hybrid Root SEAL; it contains organic fillers to reduce the hardness of the set material, thereby improving removability if retreatment is necessary$^6$. Superbond Sealer (SBS; Sun Medical) is a 4-META/methyl methacrylate-tri-n-butyl borane resin-based sealer developed by modification of the SuperBond resin cement. Root canal sealers extruded from apices during root canal filling procedures may exert harmful effects on periapical tissue. In particular, freshly mixed sealers may induce periapical inflammation$^7$; if they are in contact with osteoblasts on the alveolar bone surface, freshly mixed sealers may demonstrate cytotoxicity that negatively influences the repair and healing process. Furthermore, some harmful components released from set sealers may prolong periapical inflammation$^8$. However, research has been inconclusive regarding the cytocompatibilities of methacrylate resin-based root canal sealers; notably, the methacrylate polymer is considered to exhibit negligible cytotoxicity in the set condition, but causes moderate cytotoxicity early in the setting process$^9$. HRS exhibits less cytotoxicity$^10$ and milder connective tissue reaction compared with a zinc oxide–eugenol sealer$^11$, but is more cytotoxic than AH Plus (AHP; Dentsply Sirona, Ballaigues, Switzerland), an epoxy resin-based sealer$^12$. Compared with other methacrylate resin-based sealers (e.g., EndoREZ and RealSeal/Epiphany), HRS is reportedly either less cytotoxic$^13$ or induces more severe cytotoxicity$^12$. SBS shows better cytocompatibility than methacrylate resin-based sealers$^14-16$ and AHP$^16$. Evidence concerning the biocompatibility of MSS is limited and conflicting; MSS has been reported to cause milder connective tissue reactions than AHP and a zinc oxide–eugenol sealer$^17$, whereas it exhibits greater cytotoxicity than several other types of sealers$^17$. This study aimed to compare the cytocompatibility of MSS, HRS, and SBS in either freshly mixed or set conditions using the Kusa-A1 osteoblastic cell line. The These authors contributed equally to this work. Color figures can be viewed in the online issue, which is available at J-STAGE. Received Sep 9, 2020: Accepted Nov 9, 2020 doi:10.4012/dmj.2020-335 JOI JST.JSTAGE/dmj/2020-335 null hypothesis was that there would be no difference in cytocompatibility among the three methacrylate resin-based sealers. MATERIALS AND METHODS Cell culture and sample preparations Kusa-A1 cells (an osteoblastic cell line derived from mouse osteogenic mesenchymal progenitor cells; Cell No: RCB2081; Cell Engineering Division, RIKEN BioResource Research Center, Ibaraki, Japan) were cultured in alpha-modified minimum essential medium (α-MEM, Wako Pure Chemical Industries, Osaka, Japan) containing 10% fetal bovine serum (Thermo Fisher Scientific, Waltham, MA, USA) at 37°C in 5% CO₂. Culture medium was changed at 3-day intervals. Preparation of sealer extracts Three methacrylate resin-based sealers (i.e., MSS, HRS, and SBS) and an epoxy resin-based sealer (AHP) were used in this study (Table 1). The sealers were mixed aseptically in accordance with the manufacturers’ instructions and placed in sterile cylindrical plastic rings (Ø 7 mm and height 3 mm; 250 mg per ring). They were immersed in 3 mL of α-MEM immediately after filling in the rings (i.e., fresh samples) or following storage in a CO₂ incubator (5% CO₂ and 95% air) at 37°C for 24 h to allow complete setting. The prepared samples were then shaken in 3 mL of α-MEM at room temperature for 24 h (i.e., set groups without irradiation). Light irradiation was performed immediately after the injection of MSS and HRS into sterile cylindrical plastic rings (i.e., set samples). Light-irradiated samples of MSS and HRS [referred to as MSS(+) and HRS(+)] were prepared by irradiating the sealers filled in the ring with an LED light curing unit (Blue Lex, Yoshida, Tokyo, Japan; 1,400 mW/cm², 20 s); they were then immersed in α-MEM as described above. The media with sealers were shaken for 24 h at room temperature, sterilized with a syringe filter (pore size 0.45 µm, Sartorius, Göttingen, Germany), and used as sealer extracts for further experiments. Cell viability assay Kusa-A1 cells (3×10⁴ cells/well) seeded in 96-well plates were cultured with 100 µL α-MEM for 24 h, then cultured with sealer extracts for an additional 48 h. Cells cultured with α-MEM were used as control samples. Vital cell numbers were measured using the Cell Counting Kit-8 (CCK8; Dijindo Molecular Technologies, Kumamoto, Japan). Briefly, 10 µL of CCK8 solution was added to the culture medium and the absorbance at 450 nm was measured with a spectrophotometer (TECAN Sunrise, Mannedorf, Switzerland), following 1 h of incubation at 37°C. Osteoblastic marker expression Kusa-A1 cells (5×10⁴ cells/well) were seeded in 24-well dishes and cultured with eightfold diluted set samples (MSS without light irradiation, HRS without light irradiation, SBS, and AHP) or α-MEM (control) for 72 h. Total RNA was extracted using an ultra-thin polymer membrane (QuickGene, Kurabo, Osaka, Japan), and cDNA was synthesized (PrimeScript RT reagent Kit: Perfect Real Time, Takara Bio, Shiga, Japan) from extracted RNA (150 ng). Real-time polymerase chain reaction was performed with Taq polymerase mixture including SYBR Green (GoTaq qPCR Master Mix, Promega, Madison, WI, USA), synthesized cDNA, and specific primers for osteoblasts using a real-time thermal cycler (CFX96, Bio-Rad, Hercules, CA, USA). PCR reactions were performed using 2-step cycling profiles (40 cycles) with 15 s denaturation (95°C) and 60 s annealing (60°C) per cycle following 2 min denaturation (95°C). Beta-actin was used as an internal control. The primer sequences were as follows: alkaline phosphatase (Alp; accession number NM_007431), anti-sense: 5'-GGAATGTAGTTCTGCTCATGGAC-3' and sense: 5'-GGAAATGAGTCTCGTCATGGA-3'; integrin Table 1 Root canal sealers used in this study \| Material \| Manufacturer \| Lot No. \| Composition \| \|-----------------\|--------------------------------\|---------------\|-----------------------------------------------------------------------------\| \| MetaSEAL Soft \| Sun Medical, Moriyama, Japan \| Liquid: TW1 \| Liquid: 4-META, HEMA, di-methacrylates, photoinitiator, water \| \| \| \| Powder: VF 1 \| Powder: bismuth carbonate oxide, organic filler, aromatic amine \| \| Hybrid Root SEAL \| Sun Medical \| Liquid: VG 11 \| Liquid: 4-META, HEMA, di-methacrylates, photoinitiator \| \| \| \| Powder: TX 12\| Powder: zirconium oxide, amorphous silica, aromatic amine \| \| Superbond Sealer\| Sun Medical \| Liquid: TE 2 \| Liquid: 4-META, MMA \| \| \| \| Powder: TM 1 \| Powder: zirconium oxide (80%/w), PMMA (20%/w) \| \| \| \| Catalyst: SW 33\| Catalyst: TBB-O \| \| AH Plus \| Dentsply Sirona, Ballaigues, Switzerland \| 1911001017 \| Paste A: bisphenol A epoxy resin, bisphenol F epoxy resin, calcium tungstate, zirconium oxide, silica, iron oxide pigments \| \| \| \| \| Paste B: dibenzylidamine, aminoadamantane, tricyclodecane-diamine, calcium tungstate, zirconium oxide, silicone oil, silica \| 4-META: 4-methacryloxyethyl trimellitate anhydride, HEMA: 2-hydroxyethyl methacrylate, MMA: methyl methacrylate, PMMA: polymethyl methacrylate, TBB-O: partially oxidized tri-n-butylborane binding sialoprotein (Ibsp; accession number NM_008318), aNT: 5'-AGTAATAATTCTGACCCCTGAGCC-3' and sense: 5'-TATGAAGTCTATGACAACGAGAACG-3'; β-actin (accession number NM_007393), anti-sense: 5'- GTAAGACCTCTATGCAACAGT-3' and sense: 5'- AATGATCTTTGATCTTCATGGTCTA-3'. Mineralized nodule formation Kusa-A1 cells (2×10^4 cells/well) were seeded in 48-well plates and cultured in α-MEM containing 10% fetal bovine serum. After 24 h of culture, the medium was changed to an osteoinduction medium containing L-ascorbic acid (0.2 mM; Wako Pure Chemical Industries) and β-glycerophosphate (5.0 mM; Sigma Aldrich, St. Louis, MO, USA), with or without eightfold diluted sealer extracts. Mineralized nodules were stained with alizarin red S (Wako Pure Chemical Industries) after 10 days of culture. The mineralized nodule area was measured with ImageJ2 software (https://imagej.net/ImageJ2). Scanning electron microscopy Set sealers filled in the ring were rinsed with phosphate-buffered saline and placed in 48-well plates; Kusa-A1 cells (2×10^4 cells/well) were then seeded and cultured on the samples for 3 days. Following fixation with 2.5% glutaraldehyde (Wako Pure Chemical Industries), the specimens were dehydrated using a graded ethanol series, dried in a critical-point dryer (HCP 2, Hitachi, Tokyo, Japan), sputter-coated with platinum using an ion-coater (E102, Hitachi), and examined with a scanning electron microscope (Hitachi S-4500) at an accelerating voltage of 5 kV. Statistical analysis Data regarding cell viability and osteoblastic marker expression were compared among groups using one-way analysis of variance and Tukey post hoc test. Data regarding mineralized nodule formation were compared among groups using one-way analysis of variance and Dunnett’s post hoc test. All statistical analyses were performed using statistical software (GraphPad Prism v8.1, GraphPad, San Diego, CA, USA), and p-values <0.05 were considered to be statistically significant. RESULTS Cell viability Figure 1 shows the viabilities of Kusa-A1 cells after exposure to fresh samples. Cells exposed to MSS and MSS(+) exhibited significant reductions in viability, compared with the control, at dilutions up to 1/8 and 1/2, respectively (p<0.05); they exhibited viabilities comparable with the control at dilutions of 1/32 and 1/8, respectively. Cells exposed to SBS, the viable cell count was comparable with the control at 1/2 dilution, whereas it was significantly higher than the control at dilutions of 1/8 and 1/32 (p<0.05). Cells exposed to AHP exhibited significant reduction in viability, compared with the control, at dilutions up to 1/32 (p<0.05). Figure 2 shows the viabilities of Kusa-A1 cells after exposure to set samples. Cells exposed to MSS and MSS(+) exhibited significant reductions in viability, compared with the control, at dilutions up to 1/8 (p<0.05); cells exposed to MSS(+) exhibited significantly greater ![Fig. 1 Viability of Kusa-A1 cells cultured with diluted extracts of freshly-mixed sealers.](image1) ![Fig. 2 Viability of Kusa-A1 cells cultured with diluted extracts of set sealers.](image2) viabilities than MSS in comparisons of extracts with the same dilution (p<0.05). Cells exposed to HRS and HRS(+) also showed significant reductions in viability, compared with the control (p<0.05); cells exposed to MSS showed a significant reduction in viability, compared with MSS(+), in extracts with the same dilution (p<0.05). Cells exposed to SBS and AHP did not show significant differences in viability, compared with the control (p>0.05). Osteogenic marker expression* As shown in Fig. 3, exposure to eightfold diluted set MSS, SBS, and AHP extracts induced the expression of Alp and Ibsp in Kusa-A1 cells at levels similar to the control, with no significant differences among test extracts (p>0.05). No expression of Alp or Ibsp mRNA was detected in Kusa-A1 cells cultured with eightfold diluted set HRS extracts. Mineralized nodule formation As shown in Fig. 4, exposure to all eightfold diluted set sealer extracts induced mineralized nodule formation in Kusa-A1 cells. Cells exposed to HRS exhibited Fig. 3 Osteogenic marker expression in Kusa-A1 cells cultured with diluted extracts of set sealers. Cells were cultured with 8-fold diluted extracts of set samples, and Alp and Ibsp mRNA expression was measured at 72 h by real-time PCR using specific primers. There were no significant differences among groups (n=4, p>0.05). MSS, MetaSEAL Soft; HRS, Hybrid Root SEAL; SBS, Superbond Sealer; and AHP, AH Plus. Hybrid Root SEAL is not indicated in this graph because RNA extraction was not possible because of the limited number of vital cells. Fig. 4 Mineralized nodule formation in Kusa-A1 cells cultured with diluted extracts of set sealers. Cells were cultured in the osteoinducing medium with 8-fold diluted extracts of set samples for 10 days and mineralized nodules were stained with alizarin-red staining solution. Stained nodules were quantified by ImageJ2 software. An asterisk mark indicates significant difference compared with control (n=4, p<0.05). Images above each bar in the graph show two representative alizarin-red-stained cultures of the corresponding group. MSS, MetaSEAL Soft; HRS, Hybrid Root SEAL; SBS, Superbond Sealer; and AHP, AH Plus. Fig. 5 Scanning electron microscopic observation of Kusa-A1 cells attached on the surface of set sealers. Kusa-A1 cells were cultured on set MetaSEAL Soft (A), Hybrid Root SEAL (B), AH Plus (C), and Superbond Sealer (D, E) for 3 days. (E) Higher magnification view of the boxed area in D. significant less mineralized nodule formation than the control (p<0.05). Cell attachment Survival and attachment to sealers was not observed among cells exposed to MSS, HRS, or AHP (Figs. 5A–C). In contrast, substantial populations of well-spread, attached cells with numerous filopodia or pseudopodia were observed upon exposure to SBS (Figs. 5D, E). DISCUSSION This study demonstrated that exposure to MSS or HRS significantly reduced the viability of Kusa-A1 cells. The toxic effects of MSS and HRS were also clearly observed in scanning electron microscopy analysis where Kusa-A1 cells did not remain adhered during exposure to MSS or HRS. Notably, cells exposed to SBS showed significantly greater viability than cells exposed to MSS and HRS; cells cultured on SBS exhibited a well-spread shape with numerous cytoplasmic processes that may be associated with cell adhesion. Thus, the null hypothesis that cytocompatibility would not differ among the three methacrylate resin-based sealers was rejected. The cytotoxicities of resin-based materials are primarily attributable to residual monomers released from these sealers[20,21]. Among the constituents of the presently examined sealers, 2-hydroxyethyl methacrylate (HEMA) contained in MSS and HRS may be associated with the lower cytocompatibilities of these sealers, because HEMA is able to penetrate into the cell wall and cause cellular damage at low concentrations[22,23]. A high concentration of HEMA (4 mg/mL medium) inhibits intracellular tyrosine phosphorylation, which is an important signal transduction messenger, in L929 fibroblasts[24]. Cell growth inhibition and cell cycle perturbation are also induced by HEMA in human gingival epithelial cells and dental pulp cells[25]. Furthermore, depletion of glutathione (an index of oxidative stress) and production of reactive oxygen species are both induced by HEMA[26]. Notably, dimethacrylates, such as bisphenol A glycolate dimethacrylate, urethane-dimethacrylate, and triethylene glycol dimethacrylate, have been reported to show higher cytotoxicity to human gingival fibroblasts, compared with HEMA[27], suggesting that dimethacrylates are also associated with the lower cytocompatibilities of HRS and MSS. Triacrylate, which is contained only in HRS, may also be associated with the inferior cytocompatibility of HRS compared with MSS, because triacrylate-derived acrylic acid exhibits greater toxicity than methyl methacrylate[28]. Light irradiation improved the cytocompatibilities of MSS and HRS, supporting the notion that the cytotoxicities of light-cured resin-based materials are inversely proportional to the light-curing time, which enhances the rate of monomer conversion[29]. Thus, the severe cytotoxicity of HRS suggests a lower monomer conversion rate in this material, even when it has been light-cured. From a clinical perspective, light curing of dual-curable resin sealers primarily tends to polymerize the coronal portion for early establishment of a tight coronal seal[30]; it presumably shows limited effects in the apical portion because of restricted access for the curing light. In this study, SBS exhibited the most prominent cytocompatibility. 4-META, the main functional monomer of the three sealers examined, has been reported to show mid-range cytotoxicity among monomethacrylates with functional groups[27]. However, 4-META appears to be well tolerated, because SBS did not interfere with Kusa-A1 cell viability. This finding is consistent with the results of an earlier report, in which 4-META showed lower cytotoxicity to human dental pulp cells[31]. Methyl methacrylate, the major component of SBS, reportedly less cytotoxic than many other resin monomers[27,32]. Tributyl borane, a polymerization initiator, may reduce the amounts of residual monomers and free radical synthesis after polymerization[33]. The present findings are also consistent with the results of an earlier study, in which a 4-META/methyl methacrylate-n-butyl borane resin was found to be minimally cytotoxic to osteoblastic cells except during the early curing stage[34]. This study also revealed that fresh and diluted SBS promoted the cell growth. SBS is reported to release boron[35], which stimulates cell growth in low concentrations (0.1–0.5 mM) via activation of mitogen-activated protein kinase pathways[36]. Moreover, boron at physiological concentration induces lymphocyte proliferation[37] probably through its antioxidant potential[38]. Accordingly, boron released from SBS may be involved in the promoted cell growth induced by fresh and diluted SBS samples. In this study, the cytotoxicities of three methacrylate resin-based sealers were compared with the cytotoxicity of AHP, which is one of the most widely evaluated sealers[28,29]. Fresh AHP showed substantial cytotoxicity, which is consistent with the results of previous investigations; this might be due to the release of unpolymerized epoxy resin monomers[39,40]. AHP is reportedly formaldehyde-free, which represents an improvement from its predecessor, AH26; however, AHP has been found to release a small amount of formaldehyde during the setting process[39], which might be responsible for the observed cytotoxicity of fresh AHP extracts. In contrast, set AHP showed minimal cytotoxicity to Kusa-A1 cells. Similarly, several earlier studies showed that set AHP was minimally cytotoxic[14,39,40], although one study showed that set AHP severely interfered with cell viability[10]. mRNA expression levels of Alp and Ibsp in Kusa-A1 cells were not disturbed by exposure to eightfold diluted set sealer samples, with the exception of HRS. This agreed with the results of our cell growth experiments and with prior findings that HRS diluent induces downregulation of Alp and Ibsp mRNA expression in cementoblasts[33,41]. Mineralized nodule formation was also significantly disturbed in cells exposed to eightfold diluted set HRS, although the formation was confirmed. To induce mineralized nodule formation, standard culture medium was changed to osteoinduction medium containing sealer samples after detection of confluency. Thus, mineralized nodule formation was induced in the remaining viable cells, although further cell growth may have inhibited in the presence of HRS samples. Cells exposed to eightfold diluted set MSS showed slight inhibition of growth, but did not exhibit disturbed osteogenic gene expression or mineralized nodule formation, suggesting minimal harmful effects of MSS on the osteogenic potential of osteoblasts. Scanning electron microscopy images of cell culture experiments revealed that attached cells were only observed upon exposure to SBS; Kusa-A1 cells cultured in the presence of SBS appeared to be elongated and possess multiple cytoplasmic extensions that projected from the cells to the surrounding surface (Fig. 5D, E). These results may be attributed to various factors such as chemical composition, particle size, surface topography, and sample bioactivity. No attached cells were found upon exposure to MSS, HRS, or AHP, although cells exposed to set AHP extract did not demonstrate significant reductions of viability (Fig. 2). Cells placed on the samples may have been directly affected by non-diluted toxic components released from the samples. Moreover, AHP diluents have been reported to disturb mRNA expression of collagen type I$^4$, a major component of extracellular matrix that is essential for cell attachment$^42$). Therefore, disturbance of extracellular matrix synthesis (e.g., through disruption of collagen type I mRNA expression) may have occurred in Kusa-A1 cells cultured on set sealers except SBS, which may have led to the absence of cell attachment upon exposure to MSS, HRS, or AHP. CONCLUSION Our findings indicate that MSS, HRS, SBS, and AHP exhibited varying degrees of cytocompatibility with Kusa-A1 osteoblasts, such that SBS and HRS were the most and least compatible, respectively. ACKNOWLEDGMENTS The authors have no conflicts of interest related to this study. 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9670440b3041bd8dcb5b392347f954c97bd1c1a0	{ "olmocr-version": "0.1.59", "pdf-total-pages": 5, "total-fallback-pages": 0, "total-input-tokens": 19215, "total-output-tokens": 6890, "fieldofstudy": [ "Computer Science" ] }	Abstract—In video coding, in-loop filters are applied on reconstructed video frames to enhance their perceptual quality, before storing the frames for output. Conventional in-loop filters are obtained by hand-crafted methods. Recently, learned filters based on convolutional neural networks that utilize attention mechanisms have been shown to improve upon traditional techniques. However, these solutions are typically significantly more computationally expensive, limiting their potential for practical applications. The proposed method uses a novel combination of sparsity and structured pruning for complexity reduction of learned in-loop filters. This is done through a three-step training process of magnitude-guided weight pruning, insignificant neuron identification and removal, and fine-tuning. Through initial tests we find that network parameters can be significantly reduced with a minimal impact on network performance. Keywords — neural networks, video coding, in-loop filtering, quality enhancement, pruning, sparsity I. INTRODUCTION Recent research efforts show that learned tools, such as deep Neural Networks (NNs), can be successfully applied to improve the performance of video compression algorithms. For example, the upcoming Versatile Video Coding (VVC) standard already includes a tool derived from learning-based techniques [1]. Furthermore, methods based on deep learning have been used as intra/inter-prediction [2-5], quantisation, entropy coding [6] and loop filtering tools [7]. When compressing a video at higher quantization rates, artifacts can occur due to poor frame reconstruction. In-loop filtering is a well-known video compression method applied at the end of the coding process that aims to reduce or remove artifacts. VVC implements three filters, namely the Deblocking Filter (DBLF), the Sample Adaptive Offset filter (SAO), and the Adaptive Loop Filter (ALF). The loop filtering process can be expanded with new filters that apply deep learning techniques, as demonstrated with Attention-Based Dual-Scale CNN (ADCNN) [7]. ADCNN utilises Coding Unit (CU) maps as an attention mechanism that guides the neural network, to remove artifacts such as blocking. ADCNN has exhibited improved compression performance over the baseline VVC. However, the encoder processing time is increased by 66% on a Central Processing Unit (CPU). The decoder processing time is increased by more than 130 times when processed by a Graphics Processing Unit (GPU), and by more than 450 times with a CPU. The substantial increase in coding running time makes this method unfeasible for practical solutions. This paper proposes to reduce the coding complexity of learning-based methods within video coding applications by developing an automated NN pruning methodology. Pruning identifies redundant parameters from trained NNs and removes them to reduce the NN size with minimal impact on network accuracy. The presented approach inspired by ADCNN, is an initial attempt to test the feasibility of pruning NN in-loop filters. This work focuses on pruning three single-branch networks at the decoder stage, each processing separate Y, U, V components. The rest of the paper is organised as follows. Section II introduces related work in the areas of deep learning, in-loop filtering and neural network pruning. Section III describes the proposed pruning methodology, while Section IV analyses the experimental results of the trained network applied within VVC. Section V presents conclusions. II. RELATED WORK A. In-loop Filtering In-loop filtering is an essential operation for lossy video coding standards, as compression removes information from raw video data to reduce its bitrate. Modern video coding standards such as High-Efficiency Video Coding (HEVC) [8] and VVC [1] divide regions of an input frame into Coding Tree Units (CTUs), which further separate regions into rectangular blocks or CUs. During the encoding step, each CU is predicted with different methods, such as inter/intra-prediction, merge mode or skip mode. The final choice is selected according to the approach that minimizes the Rate-Distortion (RD) cost in the presence of quantisation. The level of quantisation is defined by a Quantisation Parameter (QP), high QP values can cause artifacts within the reconstructed frame. Video coding artifacts are present in many forms. For example, blockiness can occur within frames on the borders of adjacent CUs. Additionally, ringing artifacts can appear in large CUs. VVC applies several filters to reduce artifacts. DBLF is used to apply deblocking and softens the borders between CUs, while SAO reduces ringing distortions [9]. A third filter, ALF/ALF-CC, is used to restore the objective quality, expressed in PSNR, lost by the application of the previous filters [9]. B. Deep Learning Approaches for In-loop Filtering When applied to video coding, deep learning methods for in-loop filtering often utilise residual models [7,10,11]. Residual models learn the difference, or the residual, between the output and the input of the network [12]. Learning the residual means that the network weights are sparser than if required to learn the entire frame reconstruction, and it is therefore an easier task to approximate. Additionally, by stacking multiple repeated residual layers, weights in each subsequent layer become more specialised [13], improving model performance. Challenging deep learning tasks such as image restoration, denoising and super-resolution share similar properties with loop filtering problems, as they also aim to restore and enhance frame quality. Therefore, Convolutional Neural Networks (CNNs) used for these tasks have also been successfully applied to in-loop filtering. The seminal Super-Resolution Convolutional Neural Network (SRCNN) [14] extracts features from the input and maps them to high resolution patch representations to improve the resolution of JPEG encoded images. SRCNN was extended in size [15] and applied to picture compression artifacts, spatial temporal information further improved model performance in [2]. Inspired by the SRCNN structure, an In-loop Filtering CNN (IFCNN) was proposed in [16] and used as a replacement for the DBLF and SAO filters in HEVC, achieving -4.8 % Bjontegaard-Delta rate (BD-rate) [17] savings under the All-Intra (AI) configuration. A residual network called Enhanced Deep Convolutional Neural Network (EDCNN) achieved a -6.45 % BD-rate reduction on average for all HEVC configurations [10]. A CNN architecture for post-processing and in-loop filtering called MFRNet was introduced in [11] and achieved up to -5.1 % coding gains when integrated within VVC. However, it increased the decoder running time more than 80 times. Combining wide activated models [18] and squeeze-excitation models [19] resulted in an Attention-Based Dual-Scale CNN (ADCNN) [7] that, when implemented in VVC, achieved -6.54 %, -13.27 % and -15.72 % BD-rate savings over traditional filters for the Y, U and V channels, respectively. This model is attention based, with the attention input being the CU map extracted from the decoder, selected filtered blocks are signalled with flags in the bit stream. C. Neural network pruning Neural network pruning identifies redundant components within a trained neural network. Learned parameters are zeroed out [20] or removed from the model entirely [21]. Sparsity pruning is applied on pre-trained networks and aims to reduce the number of active neuron connections. The network is sparsified by setting weight values in network layers to zero. When applied to large-scale deep NNs, sparsity pruning can remove up to 80 % of learned network connections with a minimal impact on network performance [20]. While sparsity pruning does not reduce model parameters, structured pruning physically removes neurons from neural networks [21]. Structured pruning is highly dependent on its application and the type of NN used. For visual data applications that utilise CNNs, structured pruning can remove entire trained convolutional channels from layers of the network [22,23], significantly reducing the trained network size. The approach in [22] structurally prunes image recognition networks ConvNet, AlexNet, VGG-16 and ResNet-50 by removing channels, achieving speed ups in computation up to 4 times. Several algorithms for identifying redundant neurons in structured NN pruning have been proposed. A data-driven approach in [24] uses validation data to calculate the Average Percentage of Zeros (APoZ) for a given layer. A high APoZ indicates many redundant neurons. Filter clustering identifies similar filter groups and retains one filter per group [25]. Filters can also be removed based on the L1 norm of their weights [26] or their overall contribution to the output feature maps [27]. Fig. 1. a) General structure of the ADCNN model. b) Network structure for a channel after separating the Y, U, V network into three UCLF networks. III. METHODOLOGY The ADCNN architecture, illustrated in Fig. 1a, provides significant improvements when compared to traditional filters. The basic structural blocks used in ADCNN are used for constructing the separate models of our approach. Spatial attention was removed from the blocks of ADCNN, as the proposed pruning method is only applicable on single-branch networks. The resulting model was named Uni-Component Loop Filter (UCLF), shown in Fig. 1b, for the Y channel. Two models for the U and V channels also have the same architecture as the one for Y. The architectures are separated into three stages, each stage consists of generalised residual and non-residual blocks. The residual block structure is displayed in Fig. 2a, with two convolutional layers (2DConv) of 3-by-3 kernel sizes followed by two dense layers. Non-residual blocks follow the same structure as residual ones, without the input being added to the output. Each model was individually pruned using a novel combination of sparsity and structured pruning. The NN-based filter in ADCNN is integrated within VVC as a switchable filter, meaning that the encoder can select either conventional filters (DBLF, SAO, ALF) or the learned filter to obtain a reconstructed rectangular block within the currently coded frame. The filter choice is decided according to the RD cost calculation. However, our approach applies learned in-loop filters directly on each blocky video frame, rather than through a switchable implementation. A. Pruning Algorithm The proposed pruning method is detailed in Algorithm 1 (Subsection III-A). For a pretrained neural network T sparsity pruning (Subsection III-B) is applied to each prunable layer. The validation set is passed through the intermediary model, and its activation maps are then used to identify redundant channels (Subsection III-C). A pruned network P is obtained from T by iteratively analysing the activation maps and removing channels from each layer that have values lower than a set pruning threshold (Subsection III-D). P is then re-trained for a defined number of optimization epochs to retain performance. layers (Sec. III.B), number of optimization. The pruning algorithm stops if any of the constraints are satisfied, once a constraint is satisfied. Algorithm 1. PROPOSED PRUNING ALGORITHM Input: Pretrained neural network $T$, number of parameters $\text{num}_{\text{par}}$, list of prunable layers pl, training samples $x$, validation samples $v$, sparsity threshold $st$ (Sec. III.B), channel threshold $ct$ (Sec. III.C), number of optimization epochs $\text{train}_{\text{epochs}}$ (Sec. III.A), accuracy_threshold $at$ and pruning_threshold $pt$ (Sec. III.D) Output: Pruned neural network $P$ while True: for layer in $T$: if layer in pl: model = apply_sparsity_pruning(layer, $T$, st) chan_to_remove = identify_redundant_channels($v$, model, $ct$ $P$ = apply_structured_pruning(model, chan_to_remove) $P$.train($v$, $\text{train}_{\text{epochs}}$) if $P$.accuracy < at or $P$.num_par / $T$.num_par < 1 - pt: $P$ = $T$ break else $T$ = $P$ B. Sparsity Pruning Sparsity pruning sets weight values within a layer to zero according to a specified sparsity threshold. For the pretrained UCLF network from Fig. 1b, it is applied on both residual and non-residual blocks in all three stages. To retain network performance, sparsity was only applied to specific layers within the model. Additionally, the first and last layer of the network are not pruned. The total number of prunable convolutional channels and dense units is presented in Table I. The values listed in Table I indicate the initial numbers of filters and dense units in a UCLF network; these numbers will reduce as pruning progresses. C. Insignificant Channel Identification Sparsity pruning does not guarantee that all weights associated with a channel will be zero. When applied to a certain layer, magnitude-based weight pruning sparsifies the entire layer across channels, rather than within each channel individually. In convolutional layers, filters are considered as channels. In dense layers, neurons are also considered as channels. To identify which channels in a layer can be removed from the UCLF network, a data-driven approach is adopted. The validation set is used as an input to the network. Neuron activation and filter activation maps are stored at each prunable layer. The stored values are then averaged over the entire validation set. If the average channel value is below the channel threshold, then that channel is marked for removal. D. Structured Pruning Structured pruning removes channels that were identified as insignificant for a specific UCLF network. For channels within convolutional and dense layers, this means removing all associated weight and bias information. An example of a pruned residual block from a UCLF network is presented in Fig. 2b. As each stage of the network consists of stacked generalised blocks from Fig. 2a, the dimensionality at the input and the output must be retained. In this example, the input is set to 64 channels. The first convolutional layer, marked in blue, and the first dense layer, marked in green, can be pruned without restrictions. The second convolutional layer and the second dense layer need to have an equal number of channels, as they are multiplied together. Therefore, when a channel is removed from the second convolution, it must also be removed from the second dense layer. The pruned channels are then added to the corresponding channels from the input to the block. Finally, these are concatenated to the rest of the input channels and constitute the output of the residual block. \| Stage \| Block type \| No. of blocks \| Prunable channels per block \| \|-------\|------------\|---------------\|----------------------------\| \| 1 \| Non-res. \| 2 \| 48 \| \| 2 \| Residual \| 1 \| 48 \| \| 3 \| Non-res. \| 2 \| 48 \| \| 4 \| Residual \| 1 \| 48 \| TABLE I NUMBER OF PRUNABLE CHANNELS AT EACH NETWORK STAGE TABLE II: CODING PERFORMANCE OF PROPOSED APPROACH IN VTM 7.0 FOR THE AI CONFIGURATION, TESTED ON CTC SEQUENCES \| Class \| UCLF before pruning \| UCLF after pruning \| Time Reduction (%) \| \|-------\|---------------------\|--------------------\|--------------------\| \| \| BD-rate [%] \| BD-PSNR [dB] \| BD-rate [%] \| BD-PSNR [dB] \| \| \| \| Y \| U \| V \| Y \| U \| V \| Y \| U \| V \| Y \| U \| V \| \| \| B \| -5.53 \| -3.82 \| -2.58 \| 0.13 \| 0.07 \| 0.06 \| -3.07 \| -4.75 \| -3.90 \| 0.12 \| 0.09 \| 0.09 \| 31% \| \| C \| -4.68 \| -5.16 \| -2.37 \| 0.29 \| 0.19 \| 0.21 \| -4.52 \| -5.91 \| -5.30 \| 0.28 \| 0.22 \| 0.21 \| 36% \| \| D \| -6.57 \| -7.58 \| -8.68 \| 0.47 \| 0.30 \| 0.35 \| -6.43 \| -7.93 \| -9.03 \| 0.46 \| 0.32 \| 0.37 \| 44% \| \| E \| -5.13 \| -2.35 \| -2.12 \| 0.25 \| 0.08 \| 0.06 \| -5.09 \| -3.89 \| -3.49 \| 0.25 \| 0.14 \| 0.11 \| 59% \| \| Average \| -4.98 \| -4.71 \| -3.94 \| 0.29 \| 0.16 \| 0.17 \| -4.78 \| -5.62 \| -5.43 \| 0.28 \| 0.19 \| 0.20 \| 42% \| \| #Par \| Y: 879,681; U: 879,681; V: 879,681 \| Y: 667,265; U: 293,811; V: 116,972 \| \| \| Time [s] \| Y: 285; U: 120; V: 120 \| Y: 243; U: 84; V: 76 \| \| IV. RESULTS In this section, a description of the dataset, training and testing configuration for UCLF networks is presented, followed by experiments that validate the proposed model pruning approach. A. Dataset, model training and testing configuration UCLF networks for Y, U and V channels are trained on the DIV2K dataset [28], which contains 800 high definition high resolution images for training and 100 images for validation purposes. Images are separately encoded by VVC Test Model (VTM) 7.0 [29] under the All-Intra (AI) configuration at 4 QPs levels, 22, 27, 32, 37. Common Test Conditions (CTC) as defined by JVET [30] are modified to disable the three in-loop filters within VVC, to obtain blocky images as network inputs. Additionally, CU map information was extracted for each encoded image. Image patches of size 48 × 48 are used for training the Y network, while 24 × 24 patches are used for the U and V networks. The individual Y, U and V models are trained with the Mean Absolute Error (MAE) loss function, Adam optimizer and a learning rate set to 0.001. The trained, individual models are then pruned according to Algorithm 1. Sparsity pruning is configured to achieve 80% sparsity for the intermediary model. A channel value threshold of 0.001 is used. The models are trained and tested on an NVIDIA Quadro RTX 5000 GPU. After the pruning process is finished, the learned in-loop filters are tested on CTC video sequences, where each class represents a set of sequences of same spatial resolution. All sequences were processed in the same manner as the training dataset. The obtained blocky videos are filtered by the pruned networks and then compared to videos encoded by the baseline VTM 7.0 anchor. B. Network performance during pruning The performance of a pre-pruned UCLF network during the pruning process is reported in Fig. 3. Two metrics, PSNR and inference time, are measured during each pruning loop. The pre-trained network for the Y channel reports an average PSNR of 36.77 dB on the validation dataset and requires 285 seconds to process the dataset on a GPU. With each iteration, inference time decreases, while the PSNR remains stable. Compared to the original pre-trained network, the final pruned network produces a PSNR value lower by 0.04 dB and a reduction of 15% in processing time. The coding performance of unpruned and pruned UCLF networks for in-loop filtering is compared in Table II. A significant reduction in the number of parameters for each network is observed, with a slight decrease in BD-rate for the Y channel. However, the pruned networks for the U and V channels exhibit higher BD-rates and increase the overall BD-PSNR more than the unpruned baselines. It must be noted that the reduction in parameters only provides a general measure of network complexity, whilst the inference time shows the real benefits of pruning a network with the proposed approach. The pruned network for the V channel has nearly 87% less parameters than its unpruned counterpart but displays 37% lower inference time. On average, the pruned networks increase the BD-PSNR by 0.05 dB more than unpruned ones, while processing the video sequences 23% faster. The results suggest that the original models may be over-parameterized and contain redundant information that can be removed through pruning. V. CONCLUSIONS An initial approach for reducing complexity of learned in-loop filters has been presented. The approach combines sparsity pruning and structured pruning to remove redundant parts of a neural network without heavily impacting its performance. Experimental results show that this method can reduce the number of parameters of in-loop filtering networks by as much as 87% and improve inference time by up to 59%. Our results show this method has minimal impact on PSNR, and, in some cases, PSNR performance can improve. The presented method has the potential to reduce the size of neural networks used in video compression, making them applicable for practical applications. Future work will focus on improvements to redundant neuron identification, pruning of multi-branch networks, and application of the method to other neural networks used as video compression tools. These improvements will allow for direct a comparison with other similar methods. REFERENCES [1] B. Bross, J. Chen and S. Liu, “Versatile video coding (VVC) draft 10,” Document JVET-S2001 Teleconference Meeting, 2020. [2] J. Pfäffli, P. Helle, D. Maniry, S. Kolenstadler, W. Samek, H. Schwarz-D. Marpe, and T. 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Chandler, “A perceptual quantization strategy for HEVC based on a convolutional neural network trained on natural images,” in Applications of Digital Image Processing XXXVIII, vol. 9599. International Society for Optics and Photonics, 2015. [7] M. Wang, S. Wan, H. Gong and M. Ma, “Attention-Based Dual-Scale CNN In-Loop Filter for Versatile Video Coding,” in IEEE Access, vol. 7, 2019. [8] S. Kim J. Chen, Y. Ye, “Algorithm description for versatile video coding and test model 7 (VTM 7),” Document JVET-P2002, Geneva, October 2019. [9] M. Karczewicz et al., “VVC In-Loop Filters,” in IEEE Transactions on Circuits and Systems for Video Technology, vol. 31, no. 10, pp. 3907-3925, Oct. 2021. [10] Z. Pan, X. Yi, Y. Zhang, B. Jeon and S. Kwong, “Efficient In-Loop Filtering Based on Enhanced Deep Convolutional Neural Networks for HEVC,” in IEEE Transactions on Image Processing, vol. 29, 2020. [11] D. Ma, F. Zhang and D. R. Bull, “MFRNet: A New CNN Architecture for Post-Processing and In-loop Filtering,” in IEEE Journal of Selected Topics in Signal Processing, vol. 15, no. 2, Feb. 2021. [12] S. Xie, R. Girshick, P. Dollár, Z. Tu, and K. He, “Aggregated residual transformations for deep neural networks,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition 2017. [13] Olah, et al., “Feature Visualization,” Distill, 2017. [14] C. Dong, C.C. Loy, K. He, and X. Tang, “Learning a deep convolutional network for image super-resolution,” in European Conference on Computer Vision, 2014. [15] C. Dong, Y. Deng, C. C. Loy, and X. Tang, “Compression artifacts reduction by a deep convolutional network,” in Proc. IEEE Int. Conf. Comput. Vis. (ICCV), Santiago, Chile, Dec. 2015. [16] W.S. Park, and M. Kim, “CNN-based in-loop filtering for coding efficiency improvement,” in IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop (IVMSP) 2016. [17] G. Bjontegaard, “Calculation of average PSNR differences between 822 RD-curves,” VCEG-M33, 2001. [18] J. Yu, Y. Fan, J. Yang, N. Xu, Z. Wang, X. Wang, and T. Huang, “Wide activation for efficient and accurate image super-resolution,” CoRR, vol. abs/1808.08718, Dec. 2018. [19] J. Hu, L. Shen, and G. Sun, “Squeeze-and-excitation networks,” in Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit., Salt Lake City, UT, USA, Jun. 2018. [20] W. Wen, C. Wu, Y. Wang, Y. Chen, and H. Li, “Learning structured sparsity in deep neural networks,” Advances in Neural Information Processing Systems, 2016. [21] S. Anwar, K. Huang, and W. Sung, “Structured pruning of deep convolutional neural networks,” ACM Journal on Emerging Technologies in Computing Systems (JETC), 13(3), 2017. [22] H. Wang Q. Zhang, Y. Wang and H. Hu. “Structured probabilistic pruning for convolutional neural network acceleration,” arXiv preprint arXiv:1709.06994, 2017. [23] Z. Hou, and S.Y Kung, “Efficient image super resolution via channel discriminative deep neural network pruning,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2021. [24] H. Hu, R. Peng, W.Y. Tai, and C.K. Tang, “Network trimming: A data-driven neuron pruning approach towards efficient deep architectures,” arXiv preprint arXiv:1607.03250, 2016. [25] L. Li, Y. Xu, J. Zhu, “Filter Level Pruning Based on Similar Feature Extraction for Convolutional Neural Networks,” EICE Transactions on Information and Systems, 2018. [26] L. Hao, K. Asim, D. Igor, S. Han, and P.G. Hans. “Pruning filters for efficient convnets,” arXiv preprint arXiv:1608.08710, 2016. [27] H. Yi, Z. Xiao, S. Jia, “Channel pruning for accelerating very deep neural networks,” in International Conference on Computer Vision (ICCV), volume 2, 2017. [28] E. Agustsson and R. Timofte, “Ntire 2017 challenge on single imagesuper-resolution: Dataset and study,” in Proc. IEEE Conf. Comput. Vis. Pattern Recognit. Workshops, vol. 3, Jul. 2017. [29] S. Kim J. Chen, Y. Ye, “Algorithm description for versatile video coding and test model 7 (VTM 7),” Document JVET-P2002, Geneva, October 2019. [30] J. Boyce, K. Suedhring, X. Li, and V. Seregin, “JVET common test conditions and software reference configurations,” Document JVET-J1010, Ljubljana, Slovenia, Jul. 2018.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5426, 1 ], [ 5426, 11131, 2 ], [ 11131, 15239, 3 ], [ 15239, 20828, 4 ], [ 20828, 26189, 5 ] ] }
196b5324ad48971564659791cb78b556d3fa5adc	{ "olmocr-version": "0.1.59", "pdf-total-pages": 10, "total-fallback-pages": 0, "total-input-tokens": 35185, "total-output-tokens": 10599, "fieldofstudy": [ "Biology" ] }	Drug Delivery via Cell Membrane Fusion Using Lipopeptide Modified Liposomes Jian Yang, Azadeh Bahreman, Geert Dauduy, Jeroen Bussmann, René C. L. Olsthoorn,* and Alexander Kros* Department of Supramolecular Chemistry & Biomaterials, Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, Leiden, 2300 RA, The Netherlands Supporting Information ABSTRACT: Efficient delivery of drugs to living cells is still a major challenge. Currently, most methods rely on the endocytotic pathway resulting in low delivery efficiency due to limited endosomal escape and/or degradation in lysosomes. Here, we report a new method for direct drug delivery into the cytosol of live cells in vitro and in vivo utilizing targeted membrane fusion between liposomes and live cells. A pair of complementary coiled-coil lipopeptides was embedded in the lipid bilayer of liposomes and cell membranes respectively, resulting in targeted membrane fusion with concomitant release of liposome encapsulated cargo including fluorescent dyes and the cytotoxic drug doxorubicin. Using a wide spectrum of endocytosis inhibitors and endosome trackers, we demonstrate that the major site of cargo release is at the plasma membrane. This method thus allows for the quick and efficient delivery of drugs and is expected to have many in vitro, ex vivo, and in vivo applications. INTRODUCTION The plasma membrane is the protecting interface between cells and their surrounding environment. Uptake of nutrients occurs through this interface using specialized mechanisms such as endocytosis. Nutrients, or drugs for that matter, are frequently internalized into small transport vesicles called endosomes, which are derived from the cell membrane. For many medicines to become an active drug, they have to enter the cell’s cytosol. However, the detrimental environment inside these endosomes can result in degradation of the drug. To date, intracellular delivery of macromolecules is still a major challenge in research and therapeutic applications. It is therefore highly desirable to develop new alternative delivery methods that circumvent the endocytosis pathway. So far, all attempts in drug delivery using particles as carriers have been unsuccessful in avoiding this pathway, hence current efforts to develop ways of enhancing endosomal escape. Cell penetrating peptides (CPPs) have been studied extensively to achieve efficient uptake into the cytosol. However, the current view is that CPPs conjugated to large molecular weight cargo (e.g., liposomes) are predominantly internalized via endocytosis. Moreover, the positive charge of CPPs such as the Tat peptide leads to unfavorable interaction with blood components. Other transfection techniques have been devised, such as viral vectors and physical methods. These methods have their own limitations, including safety issues or their reliance to electrical fields or high pressure. Fusion of lipid membranes is a vital process in biological systems, facilitating the efficient transport of molecules across membranes. Fusion of lipid membranes is a vital process in biological systems, facilitating the efficient transport of molecules across membranes. In vivo membrane fusion shows a broad variety, from synaptic to viral and extracellular fusion, and was found to be a highly regulated process, specific in time and place, which is achieved by a complex interplay of different functional proteins. For example, in the process of neuronal exocytosis, docking of transport vesicles to the target plasma membrane is mediated by the coiled-coil formation of complementary SNARE protein subunits on the opposing membranes. This forces the opposing membranes into close proximity, resulting ultimately in lipid mixing followed by pore formation and concomitant content transfer. As a bottom-up approach, several synthetic models systems have been developed to mimic membrane fusion events, but in general these simple systems do not always recapitulate the basic characteristics of native membrane fusion. Furthermore, all these approaches were limited to liposome–liposome fusion studies and have not shown to induce fusion events in live cells, thereby limiting their use for future drug delivery purposes. Inspired by the SNARE protein complex, our laboratory has developed a fully artificial membrane fusion system composed of a complementary pair of lipiddated coiled-coil peptides enabling targeted liposome-liposome fusion. This model system possesses all the key characteristics of targeted membrane fusion similar to SNARE mediated fusion including lipid and content mixing in the absence of leakage (Figure 1A–B). In our membrane fusion system, coiled-coil forming peptides “E,” [(EIAALEK)₃] and “K,” [(KIAALKE)₃] were conjugated to a cholesterol moiety via a polyethylene glycol. (PEG) spacer, yielding lipopeptides CPE3 and CPK3. The cholesterol moiety allows for the immediate insertion of the lipidated peptides into any phospholipid membrane. We demonstrated that plain membranes could become fusogenic by the spontaneous insertion of CPE3 and CPK3 in the bilayer. A follow-up study showed that CPK3 modified cells and zebrafish embryos could be specifically labeled with the complementary fluorescently labeled E3 peptide, revealing that E3/K3 coiled-coil formation is also functional in an in vivo environment, thereby paving the way for targeted delivery using peptide modified liposomes. Here, we report a new drug delivery method based on targeted membrane fusion between liposomes and live cells. We demonstrate that a wide range of cell lines could become fusogenic by the spontaneous insertion of CPE4 and CPK4 in the bilayer. A follow-up study showed that CPK3 modified cells and zebrafish embryos could be specifically labeled with the complementary fluorescently labeled E3 peptide, revealing that E3/K3 coiled-coil formation is also functional in an in vivo environment, thereby paving the way for targeted delivery using peptide modified liposomes. RESULTS AND DISCUSSION Coiled-Coil Formation between CPE4 and CPK4 Previously, we reported docking of liposomes at cell membranes using peptides CPE3 and CPK3, but membrane fusion was not observed. In the present study we increased the number of heptad repeats in CPE and CPK to four thereby enhancing coiled-coil stability, expecting that this would favor liposome-cell fusion. Figure 1C shows that the cholesterol- and PEG-modified E4 and K4—hereafter called lipopeptides CPE4 and CPK4—when attached to liposomes, are capable of coiled-coil formation as evident from circular dichroism (CD) spectroscopy, in agreement with previous experiments using CPE3 and CPK3. Next, lipid mixing experiments were performed to investigate the fusogenicity of the CPE4/CPK4 pair in a liposome–liposome assay. In these experiments a fluorescence resonance energy transfer (FRET)-pair consisting of NBD fluorescence which indicates lipid mixing between E and K decorated liposomes, as measured through an increase in NBD fluorescence. Total lipid concentrations were 0.5 mM with 1 mol % of lipidated peptide in PBS. (D) Lipid mixing and content mixing between CPE4-liposomes and CPK4-liposomes. Fluorescence traces showing lipid mixing between E and K decorated liposomes, as measured through an increase in NBD fluorescence. Total lipid concentrations were 0.5 mM with 1 mol % of lipidated peptide in PBS. (E) Scheme of fusion between cell and liposomes. Figure 1. Schematic representation of (A) coiled-coil structure between peptides E and K (adapted from PDB 1UOI), (B) targeted liposome fusion mediated by coiled-coil formation between CPE4 modified liposomes and CPK4 modified liposomes, (C) CD spectra of CPE4 modified liposomes, and CPK4 modified liposomes and a equimolar mixture thereof. The total lipid concentrations were 0.5 mM with 1 mol % of lipidated peptide in PBS. (D) Lipid mixing and content mixing between CPE4-liposomes and CPK4-liposomes. Fluorescence traces showing lipid mixing between E and K decorated liposomes, as measured through an increase in NBD fluorescence. Total lipid concentrations were 0.5 mM with 1 mol % of lipidated peptide in PBS. (E) Scheme of fusion between cell and liposomes. of nitrobenzoxadiazole (NBD) and lissamine rhodamine (LR) fluorophore labeled lipids was incorporated into the membrane of CPK-decorated liposomes. Upon lipid mixing of the latter liposomes with CPE4-liposomes the distance between NBD and LR increased, resulting in increased NBD-fluorescence as shown in Figure 1D. Content mixing was quantified by incorporating a sulforhodamine B at a self-quenching concentration of 20 mM into CPE-decorated liposomes and mixing these with CPK-liposomes as described. The increase in sulforhodamine B fluorescence over time indicated that full fusion took place between CPE4 and CPK4-liposomes (Figure 1D). Control experiments verified that the increase in sulforhodamine B fluorescence was not caused by leakage during fusion (Supplementary Figure 1). Coiled-Coil Formation Triggers Liposome-Cell Fusion. Next we investigated whether CPE4 and CPK4 could also mediate membrane fusion between liposomes and living cells. To this end, HeLa cells were preincubated with a micellar solution of CPK4 for 0.5−2 h before CPE4-decorated liposomes (lipid composition DOPC/DOPE/CH, 50:25:25 mol %) containing the nucleic acid stain propidium iodide (PI) or TOPRO3 in their aqueous interior were added as schematically shown in Figure 1E. In order to localize the lipid bilayer, these liposomes also contained 1 mol % of green-fluorescent NBD-DOPE lipids. As expected, confocal microscopy showed that cell membranes became labeled with the green NBD-dye on their outside in line with previous studies. Strikingly, the red dye was observed in the cytosol and nucleus, indicating that membrane fusion and content release had occurred (Figure 2A and Supplementary Figure 2A for TOPRO). Control experiments in which one of the two lipopeptides was omitted showed neither uptake of PI or TOPRO nor NBD-labeling of the cell plasma membrane (Figure 2B,C,E and Supplementary Figure 2C). This control experiment rules out the possibility that residual non-encapsulated dye in our liposome preparation entered the cell by transient membrane destabilization during fusion events. Finally cell incubation with free dyes also did not show any signal of the dye inside the cells (Figure 2F and Supplementary Figure 2F). Similar to CPE4 decorated liposomes, we also used CPK4 decorated liposomes containing PI and incubated these with CPE4 pretreated HeLa cells. However, the delivery of PI was less efficient. A reason might be the asymmetric nature of the fusion system. It was recently shown that peptide E does not interact with a membrane. In contrast, peptide K does interact with the membrane in a so-called snorkeling mode, and this peptide−membrane interaction is in equilibrium with either peptide K homocoiling or E/K coiled-coil formation. These studies suggest that peptide K-membrane interactions result in increased membrane curvature supporting membrane fusion. A cell membrane is more complex in composition and therefore less susceptible to undergo fusion as compared to the fusogenic liposomes (DOPC/DOPE/CH 2:1:1) used in this study. Our current thought is that peptide K needs to be on the cell membrane prior to a fusion event in order to activate the complex cell membrane by inducing membrane curvature. However, more studies are required to support this hypothesis. To exclude the possibility that peptide-mediated liposomal dye delivery was a peculiarity of HeLa cells, the membrane fusion experiments were repeated with Chinese hamster ovary (CHO) and mouse fibroblast (NIH/3T3) cell lines. Again the appearance of TOPRO3 and PI was observed inside cells suggesting that the peptide-mediated delivery of the dye is cell Importantly, we found that uveal melanoma cells (Mel270), which are generally hard to transfect,\textsuperscript{30,31} could also be modified with TOPRO3 using this method (Supplementary Figure 3D). To address the potential toxicity of CPK\textsubscript{4} and CPE\textsubscript{4} liposomes toward CHO, NIH/3T3, and HeLa cells, cell viability assays were carried out. These assays indicated that lipopeptides CPE\textsubscript{4} and CPK\textsubscript{4} liposomes, with or without CPE\textsubscript{4}, at the concentrations used throughout this study are well tolerated by all cell lines (Supplementary Figure 5A). Higher concentrations of these lipopeptides, even up to 100 μM, did not significantly reduce cell viability when exposed for 2 h but only did so after 24 h of exposure (Supplementary Figure 5B,C). Altogether, these results show that coiled-coil formation between CPK\textsubscript{4} and CPE\textsubscript{4} is critical for fusion and release of the dyes and that these compounds are not toxic for living cells at the concentrations used allowing to investigate potential applications and their uptake mechanism. Delivery of Doxorubicin. Doxorubicin (DOX) is one of the mostly used drugs for cancer treatments in the clinic today but as a free drug has serious cardiotoxicity. DOX is a cell-permeable drug whose fluorescence is strongly enhanced upon binding to nucleic acids. Intercalation into DNA ultimately results in apoptosis.\textsuperscript{32} To test delivery of liposomal DOX, HeLa cells were preincubated with CPK\textsubscript{4} and subsequently exposed to CPE\textsubscript{4}-decorated liposomes containing 5 μM DOX for 15 min. As can be seen in Figure 3a,b this resulted in strong nuclear (and cytosolic) fluorescence. Control experiments... Figure 5. Investigation into the uptake mechanism. (A) Effect of low temperature incubation of HeLa cells on liposomal delivery of TOPRO3 and endosomal uptake of pHrodo. Cells were preincubated on ice with 5 μM CPK (2 h), followed by 15 min incubation with 0.25 mM CPE-decorated liposomes containing TOPRO3. After three washes confocal images were taken immediately (0 min) and after 60, 120, and 180 min. Top row: TOPRO3 (red), bottom row: pHrodo (blue). (B) Graphical representation of the percentage of TOPRO dye uptake by HeLa cells on ice. Fluorescence intensities were calculated by Imagej and plotted as a percentage relative to the fluorescence of TOPRO3 delivery at 37 °C (100%). Scale bar is 25 μm. (C) Effect of endocytosis and macropinocytosis inhibitors on delivery of PI by liposomes to HeLa cells. Cells were incubated with medium (Ctrl+), or medium containing 0.25 μM wortmannin (Wor), 40 μM chlorpromazine (Chl), 200 μM genistein (Gen), 40 μM nocodazole (Noc) for 1 h, 0.01% w/v sodium azide (NaN3), followed by 2 h incubation with 5 μM CPK in the presence of inhibitors, and then treated for 15 min with CPE-liposomes containing PI. Final concentration of lipids (liposomes) was 0.25 mM. Cellular uptake was measured by flow cytometry. Positive control (100%): fluorescence of PI dye in the absence of inhibitors. showed that DOX delivery is highly dependent on the presence of CPE4 and CPK4 (Supplementary Figure 6). To investigate cytotoxicity of liposomal delivered DOX, HeLa cells preincubated with CPK were exposed with increasing concentrations of DOX-loaded liposomes for 12 h. Cell viability was measured 24 h later. Figure 3c shows cell viability as a function of liposomal and free DOX. As expected, very low concentrations of free DOX (<1 μM) did not affect the viability of HeLa cells as passive crossing into cells is not efficient at this concentration. Importantly, in current treatments in the clinic the DOX concentration is up to 9 μM in the serum of patients. In contrast, liposomes loaded with 1 μM Dox did show a significant effect as the DOX uptake is significantly enhanced. Liposomally delivered DOX reduced cell viability at DOX concentrations as low as 0.1 nM with an IC50 of ~0.01 μM, while free DOX did not affect cell viability at concentrations up to 1 μM (IC50 ~ 5 μM). Control experiments in which either CPK4 or CPE4 was omitted showed 100-fold or higher IC50 values (Supplementary Figure 7). Thus, our peptide-mediated delivery of DOX can potentially reduce the dose of DOX needed for anticancer treatments thereby lowering the cardiotoxicity of DOX. The presented fusion mediated delivery approach is also promising for the delivery of other drugs or biomolecules like DNA or siRNA. Liposomes and Content Only Partially Co localize with Endosomes. Endocytosis is the most common pathway for the uptake of small particles including liposomes by cells. To investigate whether endocytosis played a role in the liposomal delivery, the endosome tracker pHrodo, a fluorescently labeled dextran, was used in combination with TOPRO3 loaded liposomes. TOPRO3 was chosen as encapsulated dye for this experiment instead of PI because its emission (Ex/Em 642/661 nm) is expected not to interfere with emission of pHrodo (Ex/Em 560/585 nm) making investigation of colocalization of dyes easier. pHrodo and CPE-decorated liposomes containing 1 mol % NBD-DOPE and TOPRO3 were simultaneously added to CPK-modified HeLa cells. Confocal microscopy showed the presence of TOPRO3 in the cytosol and to a lesser extent in the nucleus (Figure 4B), while pHrodo was mainly observed as individual dots in the cytosol in agreement with its endosomal uptake (Figure 4C). Overlaying the fluorescent images of TOPRO3 and pHrodo revealed some overlap between TOPRO3 and endosomes (Figure 4E, pink dots), but the majority of TOPRO3 signal remains unmixxed. Again, the signal from NBD-DOPE (Figure 4A, white dots) remained at the plasma membrane, although some overlap with pHrodo was observed at the plasma membrane (Figure 4F). This could be the result of both liposomes and endosome tracker binding at a common spot at the plasma membrane or could mean that some liposomes are initially taken up by endocytosis but then rapidly fuse with the endosomal membrane. These results suggest that the endosomal uptake pathway only plays a minor role in CPE4−CPK4 mediated liposomal uptake and that liposome-cell membrane fusion is the main route for cargo delivery. This is also illustrated by performing the same experiment at 4 °C, conditions under which active uptake by endocytosis is inhibited. Imaging of cells over a period of 3 h showed the increasing uptake of TOPRO3 (Figure 5A, upper panels). In contrast only a faint signal of endosome tracker pHrodo was observed after 3 h, indicating that endocytosis was severely limited at 4 °C (Figure 5A, lower panels). Quantification of the fluorescence intensity using software (Imagej) showed that after 3 h the uptake of TOPRO3 reached ~80% of the level obtained after 30 min at 37 °C (Figure 5B). The slower uptake is presumably caused by the reduced rate of liposome-cell fusion events at 4 °C. This is supported by the observation that liposome-lipid mixture induced by CPE4/CPK4 is also significantly slower at 4 °C than at room temperature (Supplementary Figure 8). Endocytosis and Macropinocytosis Inhibitors Marginally Affect Delivery. As independent support for our conclusion that fusion at the plasma membrane is the major pathway for our liposome-based delivery system, several well-characterized inhibitors of endocytotic pathways were tested using flow cytometry measurements and confocal microscopy imaging. Wortmannin blocks PI3-kinase and inhibits macropinocytosis, chlorpromazine interferes with clathrin-dependent endocytosis, genistein inhibits tyrosine-phosphorylation of Cav 1 and caveola-dependent endocytosis. In addition, nocodazole, an inhibitor of microtubule formation, Importantly, we observed widespread liposome docking after 30 min of indicated site of the embryo in (A, B) displaying membrane associated DOPE-NBD labeling (NBD) and predominantly nuclear DOX labeling. DOX delivery in living zebrafish decorated liposomes (0.25 mM total lipid concentration and 1 mol % CPE) loaded with DOX. (A, B) Whole-embryo imaging showing widespread needs for endocytosis and restrict metabolic activity. Sodium azide was therefore used to deplete the energy endocytosis of nanoparticles is an energy-dependent mechanism. Sodium azide PI uptake was reduced less than 20%. These results argue against a major role of endocytosis or pinocytosis whereas in the presence of wortmannin, chlorpromazine and sodium azide PI uptake was reduced less than 20%. These results argue against a major role of endocytosis or pinocytosis in uptake of liposomal cargo and support that the dominant pathway for delivery is indeed targeted membrane fusion between liposomes with the plasma membrane of live cells. Intracellular Delivery in Vivo. As a first step toward clinical application, we used zebrafish embryos to evaluate direct cytoplasmic delivery in vivo. We previously established coiled-coil mediated docking of liposomes onto the zebrafish embryonic skin. During embryonic stages, the zebrafish skin is composed of a layer of ridged, mucus-covered enveloping layer (EVL) cells. Through interspersed gaps in the EVL layer, cells within the underlying epidermal basal layer (EBL), including mucus-secreting cells and ionocytes, are exposed to the external environment. To test for in vivo delivery to skin epithelial cells, we exposed 48-h-old zebrafish embryos to CPK in embryo medium for 30 min. After washing, embryos were exposed to NBD-labeled, CPE-decorated liposomes containing DOX for 30 min. Consistent with previous results, 21 we observed widespread liposome docking after 30 min of incubation, as evidenced by NBD and DOX colabeling. Importantly, we identified nuclear DOX labeling within a subset of skin epithelial cells (Figure 6) consistent with delivery into EBL-layer, but not EVL layer cells, which appeared to be inaccessible due to mucus covering or membrane ridging. Control experiments established that cytoplasmic delivery was specific to coiled-coil interaction (Supplementary Figure 9). We further confirmed intracellular delivery using liposomes loaded with PI, which becomes highly fluorescent only after interaction with cellular DNA or RNA (Supplementary Figures 10 and 11). Together, these results indicate the potential application of coiled-coil induced membrane fusion for direct cellular drug delivery in vivo. CONCLUSIONS Numerous methods exist to deliver drugs and (bio)-macromolecules to living cells. Depending on the nature of these molecules they can be delivered into cells via electroporation, microinjection, calcium phosphate coprecipitation, nanoparticles, or viral particles. However, many of these methods are either not suitable for in vitro use or cannot be safely applied in in vivo applications, or are inefficient due to endosomal entrapment and degradation. The membrane fusion system described here involves the targeted fusion of liposomes with the plasma membrane of live cells. As a result, endosomal pathways are almost completely circumvented, and therefore this efficient drug delivery method is suited for labile (bio)molecules. In addition, the lipopeptides and modified liposomes have a low toxicity at the used concentration—in contrast to CPP-based delivery approaches or PEG-induced liposome fusion. 58 We anticipate that this membrane fusion strategy will spark new in vitro, ex vivo research in the field of chemical biology and possibly in long term in vivo applications, enabling new basic and applied research studies for gene therapy. Moreover any compound that can be encapsulated in liposomes like hydrophilic low molecular weight drugs or DNA/siRNA could be considered as well as many hydrophilic drugs are unable to enter cells effectively and are known to be degraded in a lysosomal environment thereby lowering their therapeutic efficacy. 52 Here, fusion mediated delivery could result in less degradation of sensitive molecules and might therefore find use as a new transfection agent in in vitro cell studies. Also lipid bilayer-coated nanoparticles might be delivered more efficiently when coiled-coil mediated membrane fusion is applied thereby increasing the scope of molecules and nanoparticles/nanomedicines that can be delivered into cells. Future in vivo application of this technique requires cells to be premodified with one of the two peptides and is currently not cell-type specific due to the cholesterol-anchor; several applications are still conceivable. These include topical administration of drugs to treat, e.g., pulmonary disease or combat respiratory infections like influenza. On the other hand, delivery of liposomally encapsulated mRNA or DNA coding for the tumor suppressor p53 will only affect tumor cells and leave healthy cells unharmed. 58 Similarly, liposomal delivery of miRNA or siRNA to upregulate tumor suppressors or downregulate oncogenes could selectively kill only tumor cells. MATERIALS AND METHODS Fmoc-protected amino acids were purchased from Novabiochem, and Biosolve Sieber Amide resin was purchased from Chem-Impex International and Agilent Technologies. DOPE, DOPC, DOPE-NBD, and DOPE-LR were purchased from Avanti Polar Lipids. Cholesterol, propidium iodide (#BCBM1455V), and sulphorhodamine were obtained from Sigma-Aldrich. Topro3-Iodide (#1301286) and pHrodo Red dextran 10,000MW were purchased from Life Technologies. Eight wells slide Lab-tek was purchased from Thermo Scientific, USA. DMEM medium was obtained from Gibco, life technologies. N3-PEG4-COOH61 and 3-azido-5-choleste-tene62 were synthesized following literature procedures. Lipopeptide Synthesis and Purification. The peptide components of CPK₄ and CPE₄, i.e., E₄ (EIAALEK)₄ and K₄ (KIAALEKE)₄, were synthesized on an automatic CEM peptide synthesizer on a 250 μmol scale using Fmoc chemistry and standard solid-phase peptide synthesis protocols as previously described. After Fmoc deprotection N₃-(ethylene glycol)₄-COOH was coupled to the peptide on the resin. After azide reduction cholesterol-4-amino-4-oxobutanoic acid was coupled to the PEG₄ linker to yield the CPE₄ and CPK₄ peptides as described. The final products were purified by HPLC using a C₄ column, and their identity was confirmed by LC-MS. Liposome Preparation and Characterization. Lipids were dissolved in CHCl₃ in the molar ratio DOPC, DOPE, cholesterol, and DOPE-NBD of 49.5:24.75:24.75:1 [total lipid concentration] = 1 mM. Peptide stock solutions of 50 μM were prepared in CHCl₃/CH₃OH (1:1 v/v). Liposomes were prepared by mixing the appropriate amount of lipids and CPE₄ in a 20 mL glass vial and evaporating the solvents over air pressure to form lipid films. Traces of solvent were removed under high vacuum for 3–4 h at 25 °C. Each sample was then hydrated with 15 mM PI (Sigma Aldrich #BCBM1455V) or 0.25 mM Topro3 (Life Technologies, #1301286, after removing DMSO by freeze-drying) or FITC-dextran (35 mg/mL) in PBS buffer and sonicated for 2–3 min in a sonication bath at 55 °C. Nonencapsulated dyes or FITC-dextran were removed via Sephadex G25 or G50 size-exclusion PD-10 Columns (GE-Healthcare, USA). Liposomes were characterized by dynamic light scattering (DLS) at 25 °C to determine the average diameter (80–100 nm in general). The final concentration of lipids and CPE₄ in each sample before cell treatments was 250 μM and 2.5 μM, respectively. Doxorubicin (DOX) was entrapped as follows. The lipid film was hydrated with citrate buffer (pH 3.5) and sonicated in a sonication bath at 50 °C for 30 min. The citrate buffer was replaced by PBS (pH 7.4) through Sephadex G-25 filtration, leaving the inside of liposomes acidic. Doxorubicin powder (Sigma Aldrich #44538) was added into liposomal dispersion at a drug-to-lipid molar ratio of 1:3 and subsequently rotated at 4 °C overnight. Untrapped free DOX was separated from liposomes by size exclusion chromatography using a Sephadex G-25 column. The entrapment efficiency was determined using UV–vis spectrophotometry (see Supporting Information). Finally, a certain degree of selectivity can be achieved using a light-induced membrane fusion system that was recently developed in our laboratory. This system makes use of photoinduced deshielding of a PEGylated CPE and thus allows potentially for spatiotemporal control of liposomal drug delivery in vivo.²⁵ Cell Viability Assay. Cells were seeded in a 96 well-plate at a concentration of 1 × 10⁴ cells per well and incubated for 24 h prior to the WST-1 assay. The medium was removed, and cells were incubated with 100 μL of CPK₄ stock solution (5 μM) in DMEM containing NBD, PI, TOPRO3. After 15 min incubation, cells were washed three times with medium, and fluorescent images were acquired on Leica TCS SP8 confocal laser scanning microscope. Leica application suite advanced fluorescence software (LAS AF, Leica Microsystems B.V., Rijswijk, The Netherlands) and ImageJ (developed by the National Institutes of Health) were used for image analysis and liposome colocalization studies. Wavelength settings for pHrodo Red dextran were Ex/Em: 560/585 nm (Ex laser: 488 nm), for Topro3 Ex/Em: 641/662 nm (Ex laser: 633 nm), for propidium iodide Ex/Em: 535/567 nm (Ex laser: 543 nm), for NBD-DOPE Ex/Em: 455/530 nm (Ex laser: 488 nm) and for DOX Ex/Em: 490/590 nm (Ex laser: 543 nm). When performing cellular uptake assays on ice, an 8-well slide was placed on ice for 1 h, before adding CPK₄. After 2 h on ice, CPK₄ was removed and after washing CPE₄-decorated liposomes loaded with TOPRO3 and endosome tracker were added simultaneously. After 15 min incubation on ice, cells were washed three times with ice-cold medium and imaged immediately (time point 0 h). After 1, 2, and 3 h the slide was transferred to the microscope and images were recorded. In between measurements the cells were kept on ice. tation was 1 mM, containing 1 mol % of CPE; DOX concentration was 0.25 mM), final concentration of DOX in liposomes were from 100 μM to 0.1 nM (100 μM, 50 μM, 25 μM, 10 μM, 5 μM, 2.5 μM, 1 μM, 0.1 μM, 0.05 μM, 0.01 μM, 1 nM, 0.5 nM, 0.1 nM). In parallel cells were incubated with liposomes in the absence of lipopetides. After 12 h, all the medium was removed from the wells, and cells were incubated in fresh medium for 24 h prior to the WST assay. Flow Cytometry Measurements. HeLa cells and NIH/3T3 cells were seeded in a 24-well plate at a density of 1 × 10⁴ cells per well and incubated at 37 °C. After 24 h medium was removed and cells were incubated with 500 μL of nocardazole (40 μM), wortmannin (0.25 μM), chlorpromazine (40 μM), genistein (200 μM), or sodium azide 0.01% w/v in medium. After 1 h preincubation, inhibitors were removed, and the cells were treated with 500 μL of CPK₅, 5 (μM) for 2 h followed by addition of 500 μL of CPE₄-liposomes containing PI (250 μM) in the presence of fresh inhibitors. After 15 min liposomes and inhibitors were removed and washing steps were performed. The cells were incubated at 37 °C for 1 h. Finally the cells were detached using PBS/EDTA for 15 min, centrifuged, and resuspended in fresh medium at a concentration of 200,000 cells/mL medium. The mean fluorescence intensity of the cells was measured by flow cytometry using a Beckman Coulter Quanta SC machine. Zebrafish Embryo Assay. Zebrafish (Danio rerio) were handled in compliance with the local animal welfare regulations and maintained according to standard protocols (http://ZFIN.org). Embryos were treated with 0.16 mM 1-phenyl-2-thiourea (15 for 30 min with liposomes containing CPE, NBD-PE and DOX. At 48 hpf, embryos were exposed in groups of 10 in 12-well plates from 24 h post fertilization (hpf) to prevent pigment formation. Embryos were treated with 0.16 mM 1-phenyl-2-thiourea (15 for 30 min with liposomes containing CPE, NBD-PE and DOX. At 48 hpf, embryos were exposed in groups of 10 in 12-well plates from 24 h post fertilization (hpf) to prevent pigment formation. Embryos were treated with 0.16 mM 1-phenyl-2-thiourea (15 for 30 min with liposomes containing CPE, NBD-PE and DOX. At 48 hpf, embryos were exposed in groups of 10 in 12-well plates from 24 h post fertilization (hpf) to prevent pigment formation. Embryos were treated with 0.16 mM 1-phenyl-2-thiourea (15 for 30 min with liposomes containing CPE, NBD-PE and DOX. At 48 hpf, embryos were exposed in groups of 10 in 12-well plates from 24 h post fertilization (hpf) to prevent pigment formation. Embryos were treated with 0.16 mM 1-phenyl-2-thiourea (15 for 30 min with liposomes containing CPE, NBD-PE and DOX. At 48 hpf, embryos were exposed in groups of 10 in 12-well plates from 24 h post fertilization (hpf) to prevent pigment formation. Embryos were treated with 0.16 mM 1-phenyl-2-thiourea (15 for 30 min with liposomes containing CPE, NBD-PE and DOX. At 48 hpf, embryos were exposed in groups of 10 in 12-well plates from 24 h post fertilization (hpf) to prevent pigment formation. ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscentsci.6b00172. Full details of the methods (PDF) AUTHOR INFORMATION Corresponding Authors (A.K.) E-mail: [email protected]. (R.C.L.O.) E-mail: [email protected]. Author Contributions J.Y. and A.B. contributed equally to this manuscript. Author Contributions A.K. designed the study and supervised the work. J.Y., A.B., and J.B. performed biological studies and synthesized compounds. G.D. aided in peptide synthesis. J.Y., A.B., J.B., R.C.L.O., and A.K. wrote the manuscript. Notes The authors declare no competing financial interest. in successful gene expression depends on both cell line and polyethyleneimine polyplex type. Mol. Ther. 2006, 14, 745−753. (40) Huth, U. S.; Schubert, R.; Peschka-Suss, R. Investigating the uptake and intracellular fate of pH-sensitive liposomes by flow cytometry and spectral bio-imaging. J. Controlled Release 2006, 110, 490−504. (41) Gabrielsson, N. P.; Pack, D. W. Efficient polyethyleneimine-mediated gene delivery proceeds via a caveolar pathway in HeLa cells. J. Controlled Release 2009, 136, 54−61. (42) Akiyama, T.; Ishida, J.; Nakagawa, S.; Ogawara, H.; Watanabe, S.; Itoh, N.; Shibuya, M.; Fukami, Y. Genistein, a specific inhibitor of tyrosine-specific protein kinases. J. Biol. Chem. 1987, 262, 5592−5595. (43) Orlandi, P. A.; Fishman, P. H. 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(57) Lipid Coating of microparticles increases cell uptake, alters endocytosis and elevates glioma distribution and internalization. Sci. Rep. 2013, 3, 2534. (58) Lipid Coating of microparticles increases cell uptake, alters endocytosis and elevates glioma distribution and internalization. Sci. Rep. 2013, 3, 2534. (58) Wang, K.; Huang, Q.; Qiu, F.; Sui, M. Non-viral delivery systems for the application in p53 cancer gene therapy. Curr. Med. Chem. 2015, 22, 4118–4136. (59) Saito, Y.; Nakaoka, T.; Saito, H. MicroRNA-34a as a therapeutic agent against human cancer. J. Clin. Med. 2015, 4, 1951–1959. (60) Kong, L.; Askes, S. H.; Bonnet, S.; Kros, A.; Campbell, F. Temporal control of membrane fusion through photolabile PEGylation of liposome membranes. Angew. Chem., Int. Ed. 2016, 55, 1396–1400. (61) Voskuhl, J.; Wendeln, C.; Versluis, F.; Fritz, E. C.; Roling, O.; Zope, H.; Schulz, C.; Rinnen, S.; Arlinghaus, H. F.; Ravoo, B. J.; Kros, A. Immobilization of liposomes and vesicles on patterned surfaces by a peptide coiled-coil binding motif. Angew. Chem., Int. Ed. 2012, 51, 12616–12620. (62) Sun, Q.; Cai, S.; Peterson, B. R. Practical synthesis of 3beta-amino-5-cholestene and related 3beta-halides involving i-steroid and retro-i-steroid rearrangements. Org. Lett. 2009, 11, 567–570.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4825, 1 ], [ 4825, 8225, 2 ], [ 8225, 11884, 3 ], [ 11884, 13670, 4 ], [ 13670, 19651, 5 ], [ 19651, 24864, 6 ], [ 24864, 29777, 7 ], [ 29777, 33572, 8 ], [ 33572, 37474, 9 ], [ 37474, 38457, 10 ] ] }
eea3f534109456b9270600928f6d7dc0770bd35e	{ "olmocr-version": "0.1.59", "pdf-total-pages": 24, "total-fallback-pages": 0, "total-input-tokens": 122314, "total-output-tokens": 29686, "fieldofstudy": [ "Mathematics" ] }	The average number of elements in the 4-Selmer groups of elliptic curves is 7 Manjul Bhargava and Arul Shankar December 30, 2013 1 Introduction Any elliptic curve $E$ over $\mathbb{Q}$ is isomorphic to a unique curve of the form $E_{A,B} : y^2 = x^3 + Ax + B$, where $A, B \in \mathbb{Z}$ and for all primes $p$: $ p^6 \mid B $ whenever $p^4 \mid A$. Let $H(E_{A,B})$ denote the (naive) height of $E_{A,B}$, defined by $H(E_{A,B}) := \max\{4\|A^3\|, 27B^2\}$. In previous papers ([6] and [7]), we showed that the average size of the 2-Selmer group of all elliptic curves over $\mathbb{Q}$, when ordered by height, is 3; meanwhile the average size of the 3-Selmer group is 4. The purpose of this article is to prove an analogous result for the average size of the 4-Selmer group of all elliptic curves over $\mathbb{Q}$. Specifically, we prove the following theorem: Theorem 1 When all elliptic curves $E/\mathbb{Q}$ are ordered by height, the average size of the 4-Selmer group $S_4(E)$ is equal to 7. We will in fact prove a stronger version of Theorem 1 where we compute the average size of the 4-Selmer group of elliptic curves satisfying any finite set of congruence conditions: Theorem 2 When elliptic curves $E : y^2 = x^3 + Ax + B$ over $\mathbb{Q}$, in any family defined by finitely many congruence conditions on the coefficients $A$ and $B$, are ordered by height, the average size of the 4-Selmer group $S_4(E)$ is 7. We will also prove an analogue of Theorem 2 for certain families of elliptic curves defined by infinitely many congruence conditions (e.g., the family of all semistable elliptic curves). Since we have shown in [6] that the average number of elements in the 2-Selmer groups of elliptic curves over $\mathbb{Q}$ is 3, we may use Theorem 1 to prove that a positive proportion of 2-Selmer elements of elliptic curves do not lift to 4-Selmer elements: Theorem 3 For an elliptic curve $E$ over $\mathbb{Q}$, let $\times 2 : S_4(E) \to S_2(E)$ denote the multiplication-by-2 map. Then, when elliptic curves $E$ over $\mathbb{Q}$ are ordered by height, the average number elements in the 2-Selmer group of $E$ that have no preimage under $\times 2$ is at least $3/5 > 0$. It follows, in particular, that a positive proportion (in fact, at least one fifth) of all 2-Selmer elements of elliptic curves $E$ over $\mathbb{Q}$, when such $E$ are ordered by height, correspond to nontrivial 2-torsion elements of the Tate–Shafarevich group $\text{III}_E$ of $E$. Another consequence is that there exist infinitely many elliptic curves $E$ over $\mathbb{Q}$ with trivial rational 2-torsion for which the 2-primary part of the group $\text{III}_E$ contains $\mathbb{Z}/2\mathbb{Z}$ as a factor. As we will explain, Theorems 1 and 2 and the methods of their proofs, lead naturally to the following conjecture on the average size of the $n$-Selmer group of elliptic curves for general $n$: Conjecture 4 Let $n$ be any positive integer. Then, when all elliptic curves $E$ are ordered by height, the average size of the $n$-Selmer group $S_n(E)$ is $\sigma(n)$, the sum of the divisors of $n$. Thus the conjecture is proven for $n = 2$, $n = 3$, and $n = 4$ (and also for $n = 1$!). We will prove Conjecture 4 for $n = 5$ in [8]. This paper represents the first time that the average size of the $n$-Selmer group has been determined for a composite value of $n$. Conjecture 4 also has consequences for the distribution of ranks of elliptic curves. Since $\epsilon n^2$ grows faster than $\sigma(n)$, as a function of $n$, for any $\epsilon > 0$, we obtain: Proposition 5 Suppose that Conjecture 4 is true for all $n$, or indeed, any infinite sequence of positive integers $n$. Then when all elliptic curves over $\mathbb{Q}$ are ordered by height, a density of 100% have rank $\leq 1$. The parity conjecture states that an elliptic curve has even rank if and only if its root number is 1. Hence the above proposition has the following consequence: Corollary 6 Suppose that Conjecture 4 is true for all $n$, or any infinite sequence of positive integers $n$. Further assume that the root numbers of elliptic curves are equidistributed and that the parity conjecture holds. Then when elliptic curves are ordered by height, 50% have rank 0 and 50% have rank 1. Thus our results on Selmer groups above give independent theoretical evidence for the elliptic curve rank distribution conjecture, due to Goldfeld [22] and Katz–Sarnak [24] (see also [2] for a nice survey), which states that 50% of all elliptic curves have rank 0 and 50% rank 1. Our method for proving Theorem 1 is as follows. We view $n$-Selmer elements of an elliptic curve $E$ as locally soluble $n$-coverings of $E$. Here, an $n$-covering of $E$ is a genus one curve $C/\mathbb{Q}$ together with maps $\phi : C \to E$ and $\theta : C \to E$, where $\phi$ is an isomorphism defined over $\mathbb{C}$, and $\theta$ is a degree $n^2$ map defined over $\mathbb{Q}$, such that the following diagram commutes: $$ \begin{array}{ccc} \mathbb{P}^n & \overset{[n]}{\longrightarrow} & \mathbb{P}^n \\ \phi \downarrow & & \downarrow \theta \\ C & \rightarrow & E \end{array} $$ An $n$-covering $C$ is said to be locally soluble if $C$ has points defined over $\mathbb{R}$ and over $\mathbb{Q}_p$ for all primes $p$. Cassels [14] proved that any locally soluble $n$-covering has a degree $n$ divisor defined over $\mathbb{Q}$, yielding an embedding of $C$ into $\mathbb{P}^{n-1}$ defined over $\mathbb{Q}$. We may thus represent $n$-Selmer elements of elliptic curves as genus one normal curves in $\mathbb{P}^{n-1}$. When $n = 4$, as is well known, any such genus one curve in $\mathbb{P}^{n-1} = \mathbb{P}^3$ arises naturally as the complete intersection of a pair of quadrics in $\mathbb{P}^3$, where the two quadrics are well-defined up to appropriate changes-of-basis. Indeed, it turns out that 4-Selmer elements of an elliptic curve $E_{A,B}$ over $\mathbb{Q}$ may naturally be viewed in terms of the “locally soluble” orbits of $G_\mathbb{Q}$ on $V_\mathbb{Q}$, where $G$ is the algebraic group such that $$ G_R := \{(g_2, g_4) \in \text{GL}_2(R) \times \text{GL}_4(R) : \det(g_2) \det(g_4) = 1\}/\{(\lambda^{-2}I_2, \lambda I_4) : \lambda \in R^\times\} $$ for all rings $R$, and $V$ is the representation $2 \otimes \text{Sym}^2(4)$ of pairs of quadrics (see [5, §4.3] for the reasons behind this choice of group $G_R$). The invariant ring for the representation of $G_\mathbb{C}$ on $V_\mathbb{C}$ turns out to be freely generated by two invariants, which naturally correspond to the invariants $A$ and $B$ of the Jacobian elliptic curve $ E_{A,B} $ of the associated genus one curve in $ \mathbb{P}^3 $. These classical connections among orbits on pairs of quadrics, genus one normal curves in $ \mathbb{P}^3 $, and explicit 4-descent on elliptic curves over global fields were fully developed in recent years in a series of beautiful works by An, Kim, Marshall, Marshall, McCallum, and Perlis \[1\], Siksek \[30\], Merriman, Siksek, and Smart \[24\], Womack \[32\], and Fisher \[20\] \[21\]. Furthermore, it is a theorem of Cremona, Fisher, and Stoll \[15\] that the orbit of $ G_\mathbb{Q} $ on $ V_\mathbb{Q} $ corresponding to any 4-Selmer element of $ E_{A,B} $ always contains an element of $ V_\mathbb{Z} $ having invariants exactly $ A $ and $ B $ (up to bounded powers of 2 and 3). To prove Theorem 1 we are thus reduced to counting suitable orbits of $ G_\mathbb{Z} $ on $ V_\mathbb{Z} $, where a counting method involving the geometry-of-numbers, developed in \[3\], \[4\], and \[6\], may be applied. The method involves counting lattice points, in fundamental domains for the action of $ G_\mathbb{Z} $ on $ V_\mathbb{R} $, corresponding to elliptic curves of bounded height. The difficulty, as in \[6\], lies in dealing with the cusps of these fundamental domains. In the case at hand, a number of suitable adaptations to the method of \[6\] are required. For example, the geometry of the cusps of the fundamental domains is considerably more complicated than that in \[6\]. In addition, the method requires a count of elements having squarefree discriminant, which again necessitates a technique that is quite different than that used in \[6\] (but is closer to that used in \[7\]); this is perhaps the most technical ingredient of the paper. The end result of the method, however, is quite simple to state. Namely, we show that the average occurring in Theorem 1 arises naturally as the sum of two contributions. One comes from the main body of the fundamental domains, which corresponds to the average number of elements in the 4-Selmer group having exact order 4; we show that this average is given by the Tamagawa number $ \tau(G_\mathbb{Q}) = \tau(\text{PGL}_4(\mathbb{Q})) = 4 $. The other comes from the cusps of the fundamental domains, which corresponds to the average number of elements in the 4-Selmer group having order strictly less than 4. This latter contribution is equal to the average size of the 2-Selmer group, which is 3 by the work of \[6\]. The sum $ 4 + 3 = 7 $ then yields the average size of the 4-Selmer group, as stated in Theorem 1. (This also explains why, in general, we expect the average size of the $ n $-Selmer group to be $ \sigma(n) $. Namely, by the analogous reasoning, we expect the average number of order $ n $ elements in the $ n $-Selmer group to equal $ n $, the Tamagawa number of $ \text{PGL}_n $; summing over the divisors of $ n $ yields Conjecture \[4\].) In Section 2, we recall the parametrization of elements of the 4-Selmer groups of elliptic curves by orbits of $ G_\mathbb{Z} $ on $ V_\mathbb{Z} = \mathbb{Z}^2 \otimes \text{Sym}^2(\mathbb{Z}^4) $, collecting the necessary results from \[1\], \[5\], and especially \[15\]. In Section 3, we then adapt the methods of \[4\] and \[6\] to count the number of $ G_\mathbb{Z} $-orbits on $ V_\mathbb{Z} $ of bounded height. In Section 4, by developing a suitable sieve, we then count just those elements that correspond to 4-Selmer elements of exact order 4 in appropriate congruence families of elliptic curves having bounded height. Combined with the average size of the 2-Selmer group in such congruence families as determined in \[6\], this is then used to deduce Theorems 1, 2, and 3. 2 Pairs of quaternary quadratic forms and 4-coverings of elliptic curves Let $ E : y^2 = x^3 + Ax + B $ be an elliptic curve over $ \mathbb{Q} $, where $ A $ and $ B $ are integers such that, for all primes $ p $, we have $ p^6 \nmid B $ if $ p^4 \mid A $. We define the quantities $ I(E) $ and $ J(E) $ by \[ I(E) := -3A, \quad J(E) := -27B. \] In this section, we collect results relating 4-coverings of elliptic curves to certain orbits on pairs of quaternary quadratic forms. For our applications, we need to consider not just elliptic curves over $ \mathbb{Q} $, but also elliptic curves over other fields such as $ \mathbb{R} $ and $ \mathbb{Q}_p $. For any ring $ R $ of characteristic 0 (or prime to 6), let $ V_R $ denote the space of pairs of quaternary quadratic forms with coefficients in $ R $. We always identify quadratic forms with their Gram-matrices, and write elements $(A, B) \in V_R$ as pairs of $4 \times 4$ symmetric matrices with \[ 2 \cdot (A, B) = \begin{pmatrix} 2a_{11} & a_{12} & a_{13} & a_{14} \\ a_{12} & 2a_{22} & a_{23} & a_{24} \\ a_{13} & a_{23} & 2a_{33} & a_{34} \\ a_{14} & a_{24} & a_{34} & 2a_{44} \end{pmatrix}, \quad \begin{pmatrix} b_{11} & b_{12} & b_{13} & b_{14} \\ b_{12} & 2b_{22} & b_{23} & b_{24} \\ b_{13} & b_{23} & 2b_{33} & b_{34} \\ b_{14} & b_{24} & b_{34} & 2b_{44} \end{pmatrix} \] (2) where $a_{ij}$ and $b_{ij}$ are elements of $ R $. The group $ \text{GL}_2(R) \times \text{GL}_4(R) $ acts naturally on $ V_R $: an element $ g_2 = \begin{pmatrix} r & s \\ t & u \end{pmatrix} \in \text{GL}_2(R) $ acts via $ g_2 \cdot (A, B) = (rA + sB, tA + uB) $ while an element $ g_4 \in \text{GL}_4(R) $ acts via $ g_4 \cdot (A, B) = (g_4A_1g_4^t, g_4B_1g_4^t) $. It is clear that the actions of $ g_2 $ and $ g_4 $ commute. Also note that the element $(\lambda^{-2}I_2, \lambda I_4)$ acts trivially on $ V_R $, where $ \lambda \in R^\times $ and $ I_n $ denotes the identity element in $ \text{GL}_n(R) $. We thus obtain a faithful action of $ G_R $ on $ V_R $, where $ G_R $ is the group \[ G_R := \{(g_2, g_4) \in \text{GL}_2(R) \times \text{GL}_4(R) : \det(g_2) \det(g_4) = 1\}/\{\lambda^{-2}I_2, \lambda I_4 : \lambda \in R^\times\}. \tag{3} \] We now describe the ring of invariants for the action of $ G_C $ on $ V_C $. If $(A, B) \in V_C$, we define the binary quartic resolvent form $ f_{A,B} $ of $(A, B)$ by \[ f_{A,B}(x, y) := 2^4 \det(Ax + By). \tag{4} \] If $(A', B') = (g_2, g_4) \cdot (A, B)$ for $(g_2, g_4) \in G_C$, then one checks the identity \[ f_{A',B'}(x, y) = \det(g_4)^2 f_{A,B}((x, y) \cdot g_2) = \frac{f_{A,B}((x, y) \cdot g_2)}{\det(g_2)^2}. \tag{5} \] The action of $ \text{PGL}_2(\mathbb{C}) $ on the space of binary quartic forms over $ \mathbb{C} $, defined by [5], has a free ring of invariants, generated by two elements traditionally denoted by $ I $ and $ J $. (See, e.g., [6] Equation (4) for the definitions of $ I $ and $ J $.) Thus the quantities $ I $ and $ J $ defined by \[ I(A, B) := I(f_{A,B}), \quad J(A, B) := J(f_{A,B}) \tag{6} \] are also invariant, under the action of $ G_C $ on $ V_C $, and in fact they freely generate the full ring of invariants for this action. We may use the above definitions of $ f_{A,B}, I(A, B), $ and $ J(A, B) $ for elements $(A, B) \in V_R$, where $ R $ is any ring. Note that since $ I(f) $ and $ J(f) $ are polynomials having degrees 2 and 3, respectively, in the coefficients of $ f $, the polynomials $ I(A, B) $ and $ J(A, B) $ have degrees 8 and 12, respectively, in the coefficients of $(A, B)$. The significance of the action of $ G_R $ on $ V_R $ may be seen from the following three propositions. For a field $ K $, we say that $(A, B) \in V_K$ is $ K $-soluble if the quadrics defined by $ A $ and $ B $ have a $ K $-rational point of intersection in $ \mathbb{P}^3 $. Then we have: Proposition 7 Let $ K $ be a field having characteristic not 2 or 3. Let $ E : y^2 = x^3 - \frac{t}{44}x - \frac{t}{17} $ be an elliptic curve over $ K $. Then there exists a bijection between elements in $ E(K)/4E(K) $ and $ G_K $-orbits of $ K $-soluble elements in $ V_K $ having invariants equal to $ I $ and $ J $. Under this bijection, a $G_K$-orbit $G_K \cdot (A, B)$ corresponds to an element in $E(K)/4E(K)$ having order less than 4 if and only if the binary quartic resolvent form of $(A, B)$ has a linear factor over $K$. Furthermore, the stabilizer in $G_K$ of any (not necessarily $K$-soluble) element in $V_K$, having nonzero discriminant and invariants $I$ and $J$, is isomorphic to $E(K)[4]$, where $E$ is the elliptic curve defined by $y^2 = x^3 - \frac{1}{3}x - \frac{1}{27}$. Proof: The first and third assertions of the proposition, concerning the bijection and the stabilizer, follow immediately from [1] and [5, §4.3]. For the second assertion, regarding the elements of $E(K)/4E(K)$ having order less than 4, [1, §3.3] states that if $C_4 \rightarrow E$ is the 4-covering of $E$ corresponding to $(A, B)$, then it factors through a 2-covering $C_2$ of $E$, i.e., we have maps $C_4 \rightarrow C_2 \rightarrow E$, where $C_2 \rightarrow E$ is the 2-covering corresponding to the binary quartic resolvent form of $(A, B)$ via [1, §3.1]. Hence $(A, B)$ corresponds to an element having order less than 4 if and only if its binary quartic resolvent form corresponds to a trivial element in $E(K)/2E(K)$, i.e., it has a linear factor over $\mathbb{Q}$ [16, Proposition 2.2]. An element $(A, B) \in V_\mathbb{Q}$ is said to be locally soluble if it is $\mathbb{R}$-soluble and $\mathbb{Q}_p$-soluble for all primes $p$. We similarly then obtain the following proposition: Proposition 8 Let $E : y^2 = x^3 - \frac{1}{3}x - \frac{1}{27}$ be an elliptic curve over $\mathbb{Q}$. Then there exists a bijection between elements in the 4-Selmer group of $E$ and $G_\mathbb{Q}$-orbits on locally soluble elements in $V_\mathbb{Q}$ having invariants equal to $I$ and $J$. Furthermore, if $(A, B)$ has invariants $I$ and $J$, then the $G_\mathbb{Q}$-orbit $G_\mathbb{Q} \cdot (A, B)$ corresponds to an element in $S_4(E)$ having order less than 4 if and only if the binary quartic resolvent form of $(A, B)$ has a rational linear factor. By the work of Cremona, Fisher, and Stoll [15, Theorem 1.1], any locally soluble element $(A, B) \in V_\mathbb{Q}$ having integral invariants $I$ and $J$ is $\text{GL}_2(\mathbb{Q}) \times \text{GL}_4(\mathbb{Q})$-equivalent to an integral element $(A', B') \in V_\mathbb{Z}$ having the same invariants $I$ and $J$. In particular, it follows that such an $(A, B)$ is $G_\mathbb{Q}$-equivalent to either $(A', B')$ or $(A', -B')$. Since $(A', B')$ and $(A', -B')$ have the same invariants, we obtain the following proposition: Proposition 9 Let $E/\mathbb{Q}$ be an elliptic curve. Then the elements in the 4-Selmer group of $E$ are in bijective correspondence with $G_\mathbb{Q}$-equivalence classes on the set of locally soluble elements in $V_\mathbb{Z}$ having invariants equal to $I(E)$ and $J(E)$. Furthermore, under this correspondence, elements of exact order 4 correspond to the $G_\mathbb{Q}$-equivalence classes whose binary quartic resolvent forms have no rational linear factor. Motivated by Propositions 7–9, we say that an element of $V_\mathbb{Z}$ (or $V_\mathbb{Q}$) is strongly irreducible if its binary quartic resolvent form does not possess a rational linear factor. Thus to count the number of 4-Selmer elements of elliptic curves having bounded invariants, we wish to count the number of $G_\mathbb{Q}$-equivalence classes of strongly irreducible elements in $V_\mathbb{Z}$ having bounded invariants. In the next section, we begin by first determining the asymptotic number of $G_\mathbb{Z}$-equivalence classes. ### 3 The number of $G_\mathbb{Z}$-classes of strongly irreducible pairs of integral quaternary quadratic forms having bounded invariants For $i \in \{0, 1, 2\}$, let $V_\mathbb{R}^{(i)}$ denote the set of elements $(A, B) \in V_\mathbb{R}$ such that the binary quartic resolvent form $f_{A,B}(x,y) := 2^4 \det(Ax + By)$ has nonzero discriminant, $i$ pairs of complex conjugate roots in $ \mathbb{P}^1 \mathbb{C} $, and thus $ 4 - 2i $ roots in $ \mathbb{P}^1 \mathbb{R} $. It follows from [30] Lemma 6.2.2 that every element in $ V^{(1)}_\mathbb{Z} $ and $ V^{(2)}_\mathbb{Z} $ is $ \mathbb{R} $-soluble. However, this is not the case for all elements in $ V^{(0)}_\mathbb{Z} $; we denote the set of $ \mathbb{R} $-soluble elements in $ V^{(0)}_\mathbb{R} $ by $ V^{(0#)}_\mathbb{R} $. Let $ V^{(i)}_\mathbb{Z} := V^{(0)}_\mathbb{Z} \cap V^{(i)}_\mathbb{R} $ for $ i \in \{0, 1, 2, 0#\} $. Then the action of $ G^\mathbb{Z} $ on $ V^\mathbb{Z} $ preserves also the sets $ V^{(i)}_\mathbb{Z} $. The invariants $ I(A, B) $ and $ J(A, B) $ of $ (A, B) \in V^\mathbb{Z} $ are as defined in [3]. We then define the discriminant and the height of $ (A, B) $ having invariants $ I $ and $ J $ as follows: \[ \Delta(A, B) := \Delta(f_{A,B}) = \Delta(I, J) := (4I^3 - J^2)/27; \\ H(A, B) := H(f_{A,B}) := H(I, J) := \max\{\|I^3\|, J^2/4\}. \] Equation (7) yields an expression for the discriminant $ \Delta(A, B) $ that is an integer polynomial of degree 24 in the entries of $ A $ and $ B $. We use (7) as the definition of the discriminant of elements in $ V^\mathbb{R} $ for any ring $ R $, and as the definition of the height of elements in $ V^\mathbb{R} $. Our purpose in this section is to count the number of strongly irreducible $ G^\mathbb{Z} $-orbits on $ V^{(i)} $ having bounded height for $ i \in \{0#, 1, 2\} $. To state the precise result we need some further notation. For any $ G^\mathbb{Z} $-invariant set $ S \subseteq V^\mathbb{Z} $, let $ N(S; X) $ denote the number of $ G^\mathbb{Z} $-equivalence classes on $ S^{irr} $ having height less than $ X $, where $ S^{irr} $ is used to denote the set of strongly irreducible elements of $ S $. Let $ N^+(X) $ (resp. $ N^-(X) $) denote the number of integer pairs $(I, J)$ satisfying $ \Delta(I, J) > 0 $ (resp. $ \Delta(I, J) < 0 $) and $ H(I, J) < X $. By [3] Proposition 2.10], we have \[ N^\pm(X) = \frac{8}{5} X^{5/6} + O(X^{1/2}); \\ N^{\pm}(X) = \frac{32}{5} X^{5/6} + O(X^{1/2}). \] Let $ \omega $ be a fixed algebraic nonzero top-degree left-invariant differential form on $ G $ such that, for every prime $ p $, the measure of $ G^\mathbb{Z}_p $ computed with respect to $ \omega $ is $ \#G^\mathbb{Z}_p/p^{\dim G} = \#G^\mathbb{F}_p/p^{18} $. There is a natural map $ G^\mathbb{R} \times R^{(i)} \to V^{(i)}_\mathbb{R} $ given by $(\gamma, x) \mapsto \gamma \cdot x $, where the sets $ R^{(i)} \subseteq V^\mathbb{R} $ are defined just after (10). We will see in Section 3.3 that the Jacobian change of variables of this map (computed with respect to the measure on $ G^\mathbb{R} $ obtained from $ \omega $, the measure $ dIdJ $ on $ R^{(i)} $, and the Euclidean measure on $ V^\mathbb{R} $ normalized so that $ V^\mathbb{Z} $ has covolume 1) is a nonzero rational constant independent of $ i $. Henceforth, we will denote this constant by $ J $. The aim of this section is to prove the following theorem: Theorem 10 We have: (a) $ N(V^{(1)}_\mathbb{Z}; X) = \frac{1}{4} \|J\| \cdot \Vol(G^\mathbb{Z}\setminus G^\mathbb{R})N^-(X) + o(X^{5/6}) $; (b) $ N(V^{(i)}_\mathbb{Z}; X) = \frac{1}{8} \|J\| \cdot \Vol(G^\mathbb{Z}\setminus G^\mathbb{R})N^+(X) + o(X^{5/6}) $ for $ i = 0# $ and 2, where the volume of $ G^\mathbb{Z}\setminus G^\mathbb{R} $ is computed with respect to the measure obtained from $ \omega $. The value of $ J $ is not difficult to compute, but is irrelevant for the proofs of Theorems 1 and 2 because of its cancellation in (31). 3.1 Reduction theory In this subsection, we construct certain finite covers of fundamental domains for the action of $G_Z$ on $V_R^{(i)}$ for $i \in \{0\# , 1, 2\}$. We start by constructing fundamental sets for the action of $G_R$ on $V_R^{(i)}$, for $i \in \{0\# , 1, 2\}$. The following result is a consequence of Proposition 7 along with the fact that every element in $V_R^{(0\#)}$, $V_R^{(1)}$ and $V_R^{(2)}$ is $R$-soluble. Proposition 11 Let $(I, J)$ be an element of $\mathbb{R} \times \mathbb{R}$ such that $\Delta(I, J) \neq 0$. Then 1. If $\Delta(I, J) < 0$, then the set of elements in $V_R$ having fixed invariants $I$ and $J$ consists of one $R$-soluble $G_R$-orbit. The size of the stabilizer in $G_R$ of any element in this orbit is 4. 2. If $\Delta(I, J) > 0$, then the set of $R$-soluble elements in $V_R$ having fixed invariants $I$ and $J$ consists of two $G_R$-orbits. There is one such orbit from each of $V_R^{(0\#)}$ and $V_R^{(2)}$. The size of the stabilizer in $G_R$ of any element in either of these orbits is 8. For $i = 0\# , 1, 2$, we choose fundamental sets $R^{(i)} \subset V_R^{(i)}$ for the action of $G_R$ on $V_R^{(i)}$ as follows. Let $f^{(i)}_{I, J}$ be the forms constructed in [6, Table 1], for $i = 0, 1, 2$. Then for each $(I, J) \in \mathbb{R} \times \mathbb{R}$ with $\Delta(I, J) > 0$ (resp. $\Delta(I, J) < 0$) and $H(I, J) = 1$, we obtain two binary quartic forms $f^{(0)}_{I, J}$ and $f^{(2)}_{I, J}$ (resp. one binary quartic form $f^{(1)}_{I, J}$) having invariants $I$ and $J$. The coefficients of all these forms $f^{(i)}_{I, J}$ are bounded independently of $I$ and $J$. We write $$f^{(0)}_{I, J} = \kappa y(x + \lambda_1 y)(x + \lambda_2 y)(x + \lambda_3 y),$$ $$f^{(1)}_{I, J} = \kappa y(x + \lambda y)(x^2 + r y^2),$$ $$f^{(2)}_{I, J} = \kappa(x^2 + r_1 y^2)(x^2 + r_2 y^2),$$ with $\kappa > 0$, $\lambda_1 > \lambda_2 > \lambda_3$, $r > 0$ and $r_1 > r_2 > 0$. Consider the sets $$L^{(0\#)} = \left\{ \kappa^{1/4} \begin{pmatrix} 0 & -1 \\ -1 & \frac{\lambda_1}{\lambda_2} \\ \frac{1}{\lambda_3} & \frac{1}{\lambda_4} \end{pmatrix} \right\},$$ $$L^{(1)} = \left\{ \kappa^{1/4} \begin{pmatrix} 0 & -1 \\ -1 & 1 \end{pmatrix} \right\},$$ $$L^{(2)} = \left\{ \kappa^{1/4} \begin{pmatrix} 1 & \frac{1}{r_1} \\ \frac{1}{r_2} & \frac{1}{r_3} \end{pmatrix} \right\}.$$ Since the coefficients of the forms $f^{(i)}_{I, J}$ are bounded independently of $I$ and $J$, the coefficients of the elements in $L^{(0\#)}$, $L^{(1)}$, and $L^{(2)}$ are also bounded independently of $I$ and $J$. Let $R^{(i)}$ be defined to be $\mathbb{R}_{>0} \cdot L^{(i)}$. The sets $R^{(i)}$ then satisfy the following two properties that we use throughout this section: 1. The sets $R^{(i)}$ are subsets of $V_{\mathbb{R}}^{(i)}$ for $i = 0\#, 1,$ and 2. Furthermore, $R^{(0\#)}$ and $R^{(2)}$ (resp. $R^{(1)}$) contain exactly one point having invariants $I$ and $J$ for each pair $(I, J) \in \mathbb{R} \times \mathbb{R}$ with $\Delta(I, J) > 0$ (resp. $\Delta(I, J) < 0$). 2. For $i \in \{0\#, 1, 2\}$, the coefficients of all the elements of height $X$ in $R^{(i)}$ are bounded by $O(X^{1/24})$. To verify that $R^{(i)} \subseteq V_{\mathbb{R}}^{(i)}$, it suffices to show that the elements in $L^{(i)}$ are soluble over $\mathbb{R}$. For $(A, B) \in L^{(0\#)}$, this follows by applying [30] Theorem 6.3.1 on $(A + \epsilon B, B)$ for sufficiently small $\epsilon$, and for $(A, B) \in L^{(i)}$ with $i = 1, 2$ this follows from [30] Lemma 6.2.2. The second part of the first assertion is immediate from our choices of the $f_{I, J}$’s. The second assertion follows from the fact that the height of $(A, B)$ is a homogeneous function of degree 24 in the coefficients of $A$ and $B$. Let $F$ denote a fundamental domain in $G_{\mathbb{R}}$ for the left action of $G_{\mathbb{Z}}$ on $G_{\mathbb{R}}$ that is contained in a standard Siegel set [11, §2]. We may assume that $F = \{nak : n \in N'(a), a \in A', k \in K\}$, where $$ K = \{\text{subgroup of orthogonal transformations } \text{SO}_2(\mathbb{R}) \times \text{SO}_4(\mathbb{R}) \subset G_{\mathbb{R}}\}; A' = \{a(s_1, s_2, s_3, s_4) : s_1 > c_1; s_2, s_3, s_4 > c_2\}, $$ where $$ a(s_1, s_2, s_3, s_4) = \begin{bmatrix} s_1^{-1} & 0 \\ 0 & s_1 \end{bmatrix}, \begin{bmatrix} s_2^2 s_3^2 & s_3^{-1} s_4^{-1} \\ s_3 s_4 & s_2^{-2} s_3^2 \end{bmatrix}, \begin{bmatrix} s_2 s_3 s_4 & 0 \\ 0 & s_2 s_3 s_4 \end{bmatrix}; $$ $$ N' = \{n(u_1, \ldots, u_7) : (u_i) \in \nu(a)\}, $$ where $$ n(u) = \begin{bmatrix} 1 & 0 \\ u_1 & 1 \end{bmatrix}, \begin{bmatrix} 1 & u_2 & 1 \\ u_3 & u_4 & 1 \end{bmatrix}, \begin{bmatrix} 1 & u_5 & u_6 & u_7 & 1 \end{bmatrix}; $$ here $\nu(a)$ is a bounded and measurable subset of $[-1/2, 1/2]^7$ depending only on $a \in A'$, and $c_1, c_2 > 0$ are absolute constants. Fix $i \in \{0\#, 1, 2\}$. For $h \in G_{\mathbb{R}}$, we regard $Fh \cdot R^{(i)}$ as a multiset, where the multiplicity of an element $v \in V_{\mathbb{R}}$ is equal to $\#\{g \in F : v \in gh \cdot R^{(i)}\}$. As in [6, §2.1], it follows that for any $h \in G_{\mathbb{R}}$ and any $v \in V_{\mathbb{R}}^{(i)}$, the $G_{\mathbb{Z}}$-orbit of $v$ is represented $m(v)$ times in $Fh \cdot R^{(i)}$, where $$ m(v) := \#\text{Stab}_{G_{\mathbb{Z}}}(v)/\#\text{Stab}_{G_{\mathbb{Z}}}(v). $$ That is, the sum of the multiplicity in $Fh \cdot R^{(i)}$ of $v'$, over all $v'$ that are $G_{\mathbb{Z}}$-equivalent to $v$, is equal to $m(v)$. The set of elements in $V_{\mathbb{R}}^{(i)}$ that have a nontrivial stabilizer in $G_{\mathbb{Z}}$ has measure 0 in $V_{\mathbb{R}}^{(i)}$. Thus, by Proposition [11] for any $h \in G_{\mathbb{R}}$ the multiset $Fh \cdot R^{(i)}$ is an $n_1$-fold cover of a fundamental domain for the action of $G_{\mathbb{Z}}$ on $V_{\mathbb{R}}^{(i)}$, where $n_1 = 4$ and $n_{0\#} = n_2 = 8$. It follows that if we let $R^{(i)}(X)$ denote the set of elements in $R^{(i)}$ having height bounded by $X$, then for any $G_{\mathbb{Z}}$-invariant set $S \subset V_{\mathbb{Z}}$, the product $n_1 N(S^{\text{irr}}; X)$ is equal to the number of elements in $Fg \cdot R^{(i)}(X) \cap S^{\text{irr}}$, with the slight caveat that the (relatively rare—see Proposition [21]) elements with $G_{\mathbb{Z}}$-stabilizers of size $r$ ($r > 1$) are counted with weight $1/r$. Counting strongly irreducible integer points in a single such region $Fg \cdot R^{(i)}(X)$ is difficult because it is an unbounded region. As in [6], we simplify the counting by suitably averaging over a continuous range of elements $g$ lying in a compact subset of $G_{\mathbb{R}}$. 3.2 Averaging and cutting off the cusp Throughout this section, we let $dg$ denote the Haar measure on $G_{\mathbb{R}}$ obtained from its Iwasawa decomposition $G_{\mathbb{R}} = NAK$ normalized in the following way: for $g = n a k$ with $n = n(u_1, \ldots, u_7) \in N$, $a = a(s_1, \ldots, s_4) \in A$, and $k \in K$, we set $$dg = s_1^{-2} s_2^{-12} s_3^{-8} s_4^{-12} \prod_i du_i d^x s_1 d^x s_2 d^x s_3 d^x s_4 dk,$$ where $d^x s$ denotes $s^{-1} ds$ and $dk$ is Haar measure on $K$ normalized so that $\int_K dk = 1$. Let $G_0 \subset G_{\mathbb{R}}$ be a compact, semialgebraic, left $K$-invariant subset that is the closure of some nonempty open set in $G_{\mathbb{R}}$. Fix $i$ to be equal to $0\#$, $1$, or $2$. Then, by the arguments of \[3.1\] we may write $$N(S; X) = \frac{\int_{g \in G_0} \#(Fg \cdot R^{(i)}(X) \cap S^{\text{irr}}) dg}{C_{G_0}}, \tag{11}$$ where $C_{G_0} = n_i \int_{g \in G_0} dg$. We use the right hand side of (11) to define $N(S; X)$ also for sets $S \subset V_Z$ that are not necessarily $G_{\mathbb{Z}}$-invariant. Identically as in [6, Theorem 2.5], the right hand side of (11) is equal to $$\frac{1}{C_{G_0}} \int_{g \in N(a)A'} \#(S^{\text{irr}} \cap B(n, a; X)) s_1^{-2} s_2^{-12} s_3^{-8} s_4^{-12} du d^x s \tag{12}$$ where $B(n, a; X) := n a G_0 \cdot R^{(i)}(X)$ and $d^x s := d^x s_1 d^x s_2 d^x s_3 d^x s_4$. To estimate the number of integer points in the bounded multiset $B(n, a; X)$, we use the following proposition due to Davenport. Proposition 12 ([17]) Let $R$ be a bounded, semi-algebraic multiset in $\mathbb{R}^n$ having maximum multiplicity $m$, and that is defined by at most $k$ polynomial inequalities each having degree at most $\ell$. Then the number of integer lattice points (counted with multiplicity) contained in the region $R$ is $$\text{Vol}(R) + O(\max\{\text{Vol}(\bar{R}), 1\}),$$ where $\text{Vol}(\bar{R})$ denotes the greatest $d$-dimensional volume of any projection of $R$ onto a coordinate subspace obtained by equating $n - d$ coordinates to zero, where $d$ takes all values from $1$ to $n - 1$. The implied constant in the second summand depends only on $n$, $m$, $k$, and $\ell$. Proposition 1[2] yields a good estimate on the number of integer points in $B(n, a; X)$ when the $s_i$’s ($a = a(s_1, s_2, s_3, s_4)$) are bounded by a small power of $X$ (we shall make this more precise in what follows). Our next aim is to show that when one of the $s_i$’s is large relative to $X$, the set $B(n, a; X)$ has very few strongly irreducible integer points. To this end, we first give conditions that guarantee that an element in $V_Z$ is not strongly irreducible. Lemma 13 Let $(A, B)$ be a point in $V_Z$ expressed in the form (2), and suppose that one of the following four conditions is satisfied: 1. $a_{11} = a_{12} = a_{13} = a_{14} = 0$; 2. $a_{11} = a_{12} = a_{13} = a_{22} = a_{23} = 0$; (3) $ a_{11} = a_{12} = a_{13} = b_{11} = b_{12} = b_{13} = 0; $ (4) $ a_{11} = a_{12} = a_{22} = b_{11} = b_{12} = b_{22} = 0. $ Then $(A, B)$ is not strongly irreducible. Proof: In the first two cases, we see that $\det(A) = 0$. This implies that the $x^4$-coefficient of $f(x, y)$ is equal to zero; hence $f(x, y)$ is reducible over $\mathbb{Q}$ and $(A, B)$ is not strongly irreducible. In the last two cases, the binary quartic resolvent form $f(x, y)$ of $(A, B)$ has a multiple root over $\mathbb{Q}$. Thus, the discriminant $\Delta(A, B) = \Delta(f)$ of $(A, B)$ is equal to zero and so again $(A, B)$ is not strongly irreducible. $\square$ Next, note that the action of $a(s_1, s_2, s_3, s_4)$ on $(A, B) \in V_{\mathbb{R}}$ scales each coordinate $t = a_{ij}$ or $b_{ij}$ of $V_{\mathbb{R}}$ by a rational function $w(t)$ in the $s_i$’s. We define the weight of a product of such coordinates to be the product of the weights of these coordinates. Then evidently the size of the coordinate $t$ of an element in $B(n, a; X)$ is $O(X^{1/24}w(t))$. For example, we have $w(a_{11}) = s_1^{-1}s_2^{-6}s_3^{-2}s_4^{-2}$, and so if $(A, B) = ((a_{ij}), (b_{ij})) \in B(n, a; X)$, then $a_{11} = O(X^{1/24}w(a_{11}))$. We now have the following lemma: Lemma 14 Let $na(s_1, s_2, s_3, s_4) \in N'(a)A'$ be such that $V_{Z}^{\text{irr}} \cap B(n, a; X)$ is nonempty. Then $s_i = O(X^{1/24})$ for $i \in \{1, \ldots, 4\}$. Proof: Let $na$ be an element satisfying the hypothesis of the lemma. Since $B(n, a; X)$ contains an integral point $(A, B)$ not satisfying any of the four conditions of Lemma 13, we see that $X^{1/24}w(t) \gg 1$ for $t = a_{14}, a_{23}, b_{13}, $ and $b_{22}$. Thus, we obtain the following four estimates: \[ (1) \frac{s_1s_2^2}{s_4^3} = O(X^{1/24}), \quad (2) \frac{s_1s_4^2}{s_2} = O(X^{1/24}), \quad (3) \frac{s_2s_3^2}{s_1} = O(X^{1/24}), \quad (4) \frac{s_2s_4^2}{s_1s_2} = O(X^{1/24}). \] Multiplying the first two estimates immediately yields $s_1 = O(X^{1/24})$. Using this bound on $s_1$ and the third estimate then gives $s_2 = O(X^{1/24})$ and $s_4 = O(X^{1/24})$. Finally, multiplying the first and fourth estimates gives $s_3 = O(X^{1/24})$, completing the proof of the lemma. $\square$ We now prove the following estimate which bounds the number of strongly irreducible points in $\mathcal{F}g \cdot R^{(4)}(X) \cap V_Z$ that have $a_{11} = 0$, as we average over $g \in G_0$. More precisely: Lemma 15 We have \[ \int_{g \in N'(a)A'} \# \{(A, B) \in \mathcal{V}^{\text{irr}}_Z \cap B(n, a; X) : a_{11} = 0\} s_1^{-2}s_2^{-12}s_3^{-8}s_4^{-12}du \, d^sX = O(X^{19/24}). \] Proof: The proof of this lemma is very similar to that of [1] Lemma 11]. We partition the set $\{(A, B) \in \mathcal{V}^{\text{irr}}_Z : a_{11} = 0\}$ into fourteen subsets defined by setting certain coordinates of $(A, B) \in \mathcal{V}^{\text{irr}}_Z$ equal to zero and certain other coordinates to be nonzero. These sets are listed in the second column of Table 1 and it follows from Lemma 13 that they do indeed form a partition. For any subset $T \subset V_Z$, let us define $N^(T, X)$ by \[ N^(T, X) := \int_{g \in N'(a)A'} \# \{T \cap B(n, a; X)\} dg. \] 10 Then Lemma 14, together with the bound $N^(T, X) = O(X^{19/24})$ for the fourteen sets $T$ listed in Table 1, imply Lemma 15. We now describe how the required bound on $N^(T, X)$ may be obtained for Cases 1, 2a, and 3a of Table 1. In Case 1, we have $$N^(T, X) = O\left(\int_{g \in N'(a)A'} \frac{X^{20/24}}{X^{1/24}w(a_{11})} s_1^{-2} s_2^{-12} s_3^{-8} s_4^{-12} du \, d^x s \right)$$ $$= O\left(X^{19/24} \int_{g \in N'(a)A'} s_1^{-1} s_2^{-6} s_3^{-6} s_4^{-10} du \, d^x s \right).$$ Since the $s_i$'s are bounded from below, we obtain the required bound. \| Case \| The set $T \subset V_{2\pi}^$ defined by \| $N^(T, X) \ll$ \| Use factor \| \|------\|-----------------------------------------------\|------------------\|-----------\| \| 1 \| $a_{11} = 0$ \hspace{1cm} \hspace{1cm} $a_{12}, b_{11} \neq 0$ \| $X^{19/24}$ \| - \| \| 2a \| $a_{11}, a_{12} = 0$ \hspace{1cm} \hspace{1cm} $a_{13}, a_{22}, b_{11} \neq 0$ \| $X^{18/24+\varepsilon}$ \| - \| \| 2b \| $a_{11}, b_{11} = 0$ \hspace{1cm} \hspace{1cm} $a_{12} \neq 0$ \| $X^{18/24+\varepsilon}$ \| - \| \| 3a \| $a_{11}, a_{12}, a_{13} = 0$ \hspace{1cm} \hspace{1cm} $a_{14}, a_{22}, b_{11} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{14}$ \| \| 3b \| $a_{11}, a_{12}, a_{22} = 0$ \hspace{1cm} \hspace{1cm} $a_{13}, b_{11} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{13}$ \| \| 3c \| $a_{11}, a_{12}, b_{11} = 0$ \hspace{1cm} \hspace{1cm} $a_{13}, a_{22}, b_{12} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{13}^2$ \| \| 4a \| $a_{11}, a_{12}, a_{13}, a_{22} = 0$ \hspace{1cm} \hspace{1cm} $a_{14}, a_{23}, b_{11} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{14}^3$ \| \| 4b \| $a_{11}, a_{12}, a_{13}, b_{11} = 0$ \hspace{1cm} \hspace{1cm} $a_{14}, a_{22}, b_{12} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{14}^2 b_{12}$ \| \| 4c \| $a_{11}, a_{12}, a_{22}, b_{11} = 0$ \hspace{1cm} \hspace{1cm} $a_{13}, b_{12} \neq 0$ \| $X^{18/24+\varepsilon}$ \| - \| \| 4d \| $a_{11}, a_{12}, b_{11}, b_{12} = 0$ \hspace{1cm} \hspace{1cm} $a_{13}, a_{22} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{13}^2$ \| \| 5a \| $a_{11}, a_{12}, a_{13}, a_{22}, b_{11} = 0$ \hspace{1cm} \hspace{1cm} $a_{14}, a_{23}, b_{12} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{14}$ \| \| 5b \| $a_{11}, a_{12}, a_{13}, b_{11}, b_{12} = 0$ \hspace{1cm} \hspace{1cm} $a_{14}, a_{22}, b_{13} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{14}^2 b_{13}$ \| \| 5c \| $a_{11}, a_{12}, a_{22}, b_{11}, b_{12} = 0$ \hspace{1cm} \hspace{1cm} $a_{13}, b_{22} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{13}^2 b_{22}$ \| \| 6 \| $a_{11}, a_{12}, a_{13}, a_{22}, b_{11}, b_{12} = 0$ \hspace{1cm} \hspace{1cm} $a_{14}, a_{23}, b_{13}, b_{22} \neq 0$ \| $X^{18/24+\varepsilon}$ \| $a_{14}^2 b_{13} b_{22}$ \| Table 1: Estimates on the number of strongly irreducible points in cuspidal regions Similarly, in Case 2a, we have \[ N^(T, X) = O\left( \int_{g \in \mathcal{N}'(a)A'} \frac{X^{20/24} \cdot X^{1/24} w(a_{14})}{X^{3/24} w(a_{11}) w(a_{12}) w(a_{13})} s_1^{-2}s_2^{-12}s_3^{-8}s_4^{-12} du d^x s \right) \] \[ = O\left( X^{18/24} \int_{g \in \mathcal{N}'(a)A'} s_2^{-4}s_3^{-4}s_4^{-4} du d^x s \right). \] Again, since the $ s_i $ are bounded by $ O(X^{1/24}) $, we obtain the required bound $ N^(T, X) = O(X^{18/24+\epsilon}) $. Finally, in Case 3a, we have \[ N^(T, X) = O\left( \int_{g \in \mathcal{N}'(a)A'} \frac{X^{20/24}}{X^{3/24} w(a_{11}) w(a_{12}) w(a_{13})} s_1^{-2}s_2^{-12}s_3^{-8}s_4^{-12} du d^x s \right) \] \[ = O\left( X^{18/24} \int_{g \in \mathcal{N}'(a)A'} s_2^{-4}s_3^{-4}s_4^{-4} du d^x s \right), \] where the second equality follows by multiplying the integrand by $ X^{1/24} $ times the weight of the “factor” listed in the fourth column of Table 1. This yields an upper bound for the desired integral since the factor (which is an integer) was assumed to be nonzero, and therefore is at least 1 in absolute value; hence the corresponding weight must also be bounded from below by an absolute positive constant. As in Case 2a, we obtain the required bound $ N^(T, X) = O(X^{18/24+\epsilon}) $. The proof of the bound for the other eleven cases are identical. This concludes the proof of Lemma 15. $ \square $ We have proven that the number of irreducible elements in the “cuspidal regions” of the fundamental domain is negligible. The next lemma states that the number of reducible elements in the “main body” of the fundamental domain is negligible: Lemma 16* With notation as above, we have \[ \int_{g \in \mathcal{N}'(a)A'} \#\{(A, B) \in V^\text{red}_Z \cap B(n, a; X) : a_{11} \neq 0\} dg = o(X^{5/6}), \] where $ V^\text{red}_Z $ denotes the set of elements in $ V_Z $ that are not strongly reducible. Therefore, in order to estimate $ N(V_Z; X) $, it suffices to count the total number of (not necessarily strongly irreducible) integral points in the main body of the fundamental domain. We do this in the following proposition: Proposition 17 With notation as above, we have \[ \frac{1}{C_{G_0}} \int_{g \in \mathcal{N}'(a)A'} \#\{(A, B) \in V_Z \cap B(n, a; X) : a_{11} \neq 0\} dg = \frac{1}{n_i} \text{Vol}(\mathcal{F} \cdot R^{(i)}(X)) + o(X^{5/6}), \] where the volume of sets in $ V_Z $ is computed with respect to Euclidean measure normalized so that $ V_Z $ has covolume 1. Proof: The proof of Proposition 17 is similar to that of [4, Proposition 12]. If $ v \in B(n, a; X) $, then we know that $ a_{12}(v) = O(X^{1/60} w(a_{12})) $. Thus, from Propositions 15 and 16 we obtain \[ \frac{1}{C_{G_0}} \int_{n a \in F} \# \{ B(n, a; X) \cap V_{Z}^{irr} \} dI dJ = \frac{1}{C_{G_0}} \int_{n a \in F} \# \{ B(n, a; X) \cap V_{Z} \} dI dJ + o(X^{5/6}). \] Since $ a_{11} $ has minimal weight, and the projection of $ B(n, a; X) $ onto the $ a_{11} $-axis has length greater than an absolute positive constant when $ X^{1/24} w(a_{11}) \gg 1 $, Proposition 12 implies that the main term on the right hand side of (13) is equal to \[ \frac{1}{C_{G_0}} \int_{X^{1/24} w(a_{11}) \gg 1} \text{Vol}(B(n, a; X)) dI dJ. \tag{14} \] Since the region $ \{ n a \in F : w(a_{11}) \ll X^{\epsilon} \} $ has volume $ o(1) $ for any fixed $ \epsilon $, (14) is equal to \[ \frac{1}{C_{G_0}} \int_{n a \in F} \text{Vol}(B(n, a; X)) dI dJ + o(X^{5/6}). \] The proposition follows since \[ \frac{1}{C_{G_0}} \int_{n a \in F} \text{Vol}(B(n, a; X)) dI dJ = \frac{1}{C_{G_0}} \int_{h \in G_0} \text{Vol}(F h \cdot R^{\pm}(X)) dh, \] and the volume of $ F h \cdot R^{\pm}(X) $ is independent of $ h $. ∎ Lemmas 15 and 16 and Proposition 17 imply that, up to an error of $ o(X^{5/6}) $, the quantity $ n_i \cdot N(V_{Z}^{irr}; X) $ is equal to the volume of $ F \cdot R^{(i)}(X) $ for $ i = 0\#, 1, $ and 2. In the next section, we obtain a useful expression for this volume. ### 3.3 Computing the volume Recall that at the beginning of Section 3, we fixed an algebraic nonzero top-degree left invariant differential form $ \omega $ on $ G $ such that for all primes $ p $, the measure of $ G_{Z_{p}} $ with respect to $ \omega $ is \#$ G_{Z_{p}} / P_{18} $. Let $ dv $ denote Euclidean measure on $ V_{R} $ normalized so that $ V_{Z} $ has covolume 1. Finally, note that for $ i = 0\#, 1, $ and 2, the sets $ R^{(i)} $ contain at most one point $ p_{I, J} $ having invariants $ I $ and $ J $ for any pair $ (I, J) \in R \times R $. We choose $ dIdJ $ to be the measure on $ R^{(i)} $. With these measure normalizations, we have the following proposition whose proof is identical to that of [6, Proposition 2.8]: Proposition 18 For any measurable function $ \phi $ on $ V_{R} $, we have \[ \|J\| \cdot \int_{p_{I, J} \in R^{(i)}} \int_{h \in G_{R}} \phi(h \cdot p_{I, J}) \omega(h) dIdJ = \int_{G_{R} \cdot R^{(i)}} \phi(v) dv = n_i \int_{V_{R}^{(i)}} \phi(v) dv, \tag{15} \] where $ J $ is a nonzero constant in $ Q $ independent of $ i $. Using Proposition 18, it is easy to compute the volume of the multiset $ F \cdot R^{(i)}(X) $: \[ \int_{F \cdot R^{(i)}(X)} dv = \|J\| \cdot \int_{p_{I, J} \in R^{(i)}(X)} \int_{F} \omega(h) dI dJ = \|J\| \cdot \text{Vol}(F) \int_{R^{(i)}(X)} dI dJ. \tag{16} \] Up to an error of $O(X^{1/2})$, the quantity $\int_{R^{(i)}} (X)\ dI\ dJ$ is equal to $N^+(X)$ when $i = 0# \text{ or } 2$, and $N^-(X)$ when $i = 1$ (see the proof of [6, Proposition 2.10] for details). We conclude that $$N(V^{(i)}_Z; X) = \frac{1}{4} \|J\| \cdot \text{Vol}(G_Z \backslash G_{\mathbb{A}}) N^-(X) + o(X^{5/6}),$$ $$N(V^{(i)}_Z; X) = \frac{1}{8} \|J\| \cdot \text{Vol}(G_Z \backslash G_{\mathbb{A}}) N^+(X) + o(X^{5/6}),$$ (17) for $i = 0# \text{ and } 2$. We thus obtain Theorem 10. ### 3.4 Congruence conditions In this subsection, we present a version of Theorem 10 in which we count pairs of integral quaternary quadratic forms satisfying any finite set of congruence conditions. For any set $S$ in $V_Z$ that is definable by congruence conditions, let us denote by $\mu_p(S)$ the $p$-adic density of the $p$-adic closure of $S$ in $V_{Z_p}$, where we normalize the additive measure $\mu_p$ on $V_{Z_p}$ so that $\mu_p(V_{Z_p}) = 1$. We then have the following theorem whose proof is identical to that of [6, Theorem 2.11]. Theorem 19 Suppose $S$ is a subset of $V^{(i)}_Z$ defined by congruence conditions modulo finitely many prime powers. Then we have $$N(S \cap V^{(i)}_Z; X) = N(V^{(i)}_Z; X) \prod_p \mu_p(S) + o(X^{5/6}),$$ (18) where $\mu_p(S)$ denotes the $p$-adic density of $S$ in $V_Z$, and where the implied constant in $o(X^{5/6})$ depends only on $S$. We furthermore have the following weighted version of Theorem 19 whose proof is identical to that of [6, Theorem 2.12]. Theorem 20 Let $p_1, \ldots, p_k$ be distinct prime numbers. For $j = 1, \ldots, k$, let $\phi_{P_j} : V_Z \to \mathbb{R}$ be bounded $G_Z$-invariant functions on $V_Z$ such that $\phi_{P_j}(v)$ depends only on the congruence class of $v$ modulo some power $p_j^{\alpha_j}$ of $p_j$. Let $N_{\phi}(V^{(i)}_Z; X)$ denote the number of strongly irreducible $G_Z$-orbits in $V^{(i)}_Z$ having height bounded by $X$, where each orbit $G_Z \cdot v$ is counted with weight $\phi(v) := \prod_{j=1}^k \phi_{P_j}(v)$. Then we have $$N_{\phi}(V^{(i)}_Z; X) = N(V^{(i)}_Z; X) \prod_{j=1}^k \int_{v \in V_{Z_{p_j}}} \tilde{\phi}_{P_j}(v) \, dx + o(X^{5/6}),$$ (19) where $\tilde{\phi}_{P_j}$ is the natural extension of $\phi_{P_j}$ to $V_{Z_{p_j}}$ by continuity, $dv$ denotes the additive measure on $V_{Z_{p_j}}$ normalized so that $\int_{v \in V_{Z_{p_j}}} dv = 1$, and where the implied constant in the error term depends only on the local weight functions $\phi_{P_j}$. ### 3.5 The number of reducible points and points with large stabilizers in the main bodies of the fundamental domains is negligible In this section we prove Lemma 16, which states that the number of integral elements that are not strongly irreducible in the main body of the fundamental domain is negligible. We then prove that the number of strongly irreducible $G_\mathbb{Z}$-orbits on elements with a nontrivial stabilizer in $G_\mathbb{Q}$ having bounded height is negligible. Proof of Lemma 16: An element $(A, B) \in V_\mathbb{Z}$ with $\Delta(A, B) \neq 0$ fails to be strongly irreducible if and only if the binary quartic resolvent form $f_{A,B}(x, y) = 16 \det(Ax + By)$ has a root in $\mathbb{P}^1_\mathbb{Q}$. Let $p > 3$ be prime. If $f(x, y)$ has a root in $\mathbb{P}^1_\mathbb{Q}$, then the reduction of $f(x, y)$ modulo $p$ has a root in $\mathbb{P}^1_\mathbb{F}_p$. We construct elements $(A, B) \in V_\mathbb{F}_p$, for a positive density family of primes $p$, such that $f_{A,B}(x, y)$ has no root in $\mathbb{F}^1(\mathbb{F}_p)$. Let $p$ be a prime congruent to 3 modulo 4 such that there exists an element $s \in \mathbb{F}_p$ satisfying $s^2 = -2$. Consider the pair $$\begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix}, \begin{pmatrix} 1 & s \\ s & 1 \end{pmatrix}. \tag{20}$$ We have $\det(Ax + By) = x^4 + y^4$, implying that $f_{A,B}(x, y)$ has no root defined over $\mathbb{F}_p$. Therefore, if the reduction modulo $p$ of $(A, B) \in V_\mathbb{Z}$ is $G_\mathbb{F}_p$-equivalent to any $\mathbb{F}_p^\times$-multiple of the right hand side of (20), then $(A, B)$ is not strongly irreducible. Since $\# \{ g \cdot \lambda \cdot (A, B) : g \in G_\mathbb{F}_p, \lambda \in \mathbb{F}_p^\times \} \gg V_\mathbb{F}_p/p$, we obtain $$\int_{g \in N' \lambda(a) A'} \# \{ (A, B) \in V_\mathbb{F}_p^{\text{red}} \cap B(n, a; X) : a_{11} \neq 0 \} dg = O \left( X^{5/6} \prod_{p \equiv 3 \pmod{4}} (1 - p^{-1}) \right)$$ for any $Y > 0$. Letting $Y \to \infty$ yields Lemma 16. \qed Proposition 21 The number of $G_\mathbb{Z}$-orbits on elements on $V_\mathbb{Z}$ that are strongly irreducible, have height bounded by $X$, and have a nontrivial stabilizer in $G_\mathbb{Q}$ is $o(X^{5/6})$. Proof: Proposition 17 implies that an element $(A, B) \in V_\mathbb{Z}$ having invariants $I$ and $J$ has a nontrivial stabilizer in $G_\mathbb{Q}$ if and only if the elliptic curve $E : y^2 = g_{A,B}(x) = x^3 - \frac{I}{3} - \frac{J}{27}$ contains a nontrivial 4-torsion point over $\mathbb{Q}$, which happens exactly when $g(x)$ has a rational root. Let $p$ be a prime congruent to 1 modulo 3. Let $t \in \mathbb{F}_p$ be an element having no solution $a^3 = t$ for $a \in \mathbb{F}_p$. Consider the pair $(A, B)$ given by $$2(A, B) = \begin{pmatrix} 0 & 1 \\ 1 & 1 \end{pmatrix}, \begin{pmatrix} -1 & 1 \\ 1 & -t \end{pmatrix}. \tag{21}$$ We have $16 \det(Ax + By) = x^3y - ty^4$, implying that $g_{A,B}(x, y) = x^3 - ty^3$ is irreducible over $\mathbb{F}_p$. Therefore, if the reduction modulo $p$ of $(A, B) \in V_\mathbb{Z}$ is $G_\mathbb{F}_p$-equivalent to the right hand side of (21) for any prime $p$, then $(A, B)$ has a trivial stabilizer in $G_\mathbb{Q}$. Proposition 21 now follows from Lemma 15 and an argument identical to the proof of Lemma 16. \qed 3.6 Tail estimates and a squarefree sieve In order to prove Theorems 1 and 2, we require a stronger version of Theorem 20: one which counts weighted $G_2$-orbits where the weights are defined by congruence conditions modulo infinitely many prime powers. In this subsection, we use the methods and results of [9] to prove the necessary result. We start with the following two definitions. A function $\phi : V \to [0, 1] \subset \mathbb{R}$ is said to be defined by congruence conditions if, for all primes $p$, there exist functions $\phi_p : V_{zp} \to [0, 1]$ satisfying the following conditions: (1) For all $(A, B) \in V$, the product $\prod_p \phi_p(A, B)$ converges to $\phi(A, B)$. (2) For each prime $p$, the function $\phi_p$ is locally constant outside some closed set $S_p \subset V_{zp}$ of measure zero. Such a function $\phi$ is called acceptable if, for sufficiently large primes $p$, we have $\phi_p(A, B) = 1$ whenever $p^2 \nmid \Delta(A, B)$. Then we will prove the following theorem: Theorem 22 Let $\phi : V \to [0, 1]$ be an acceptable function that is defined by congruence conditions via the local functions $\phi_p : V_{zp} \to [0, 1]$. Then, with notation as in Theorem 20, we have: $$N_{\phi}(V(i)_p; X) = N(V(i)_p; X) \prod_p \int_{v \in V_{zp}} \phi_p(v) \, dv + o(X^{5/6}). \quad (22)$$ For a prime $p$, let $W_p$ denote the set of elements in $V$ whose discriminants are divisible by $p^2$. The key ingredient needed to prove Theorem 22 is the following tail estimate: Theorem 23 Let $\epsilon > 0$ be fixed. Then for any $i \in \{0#, 1, 2\}$ we have: $$N(\cup_{p > M} W_p, X) = O(\epsilon X^{5/6}/(M \log M) + X^{19/24}) + O(\epsilon X^{5/6}). \quad (23)$$ Proof: Let $W_p^{(1)}$ denote the set of elements in $(A, B) \in V$ whose discriminants are divisible by $p^2$ for (mod $p$) reasons; i.e., $p^2$ divides the discriminant of $(A, B) + p(A', B')$ for every $(A', B') \in V$. For $\epsilon > 0$, let $\mathcal{F}^{(\epsilon)} \subset \mathcal{F}$ denote the subset of elements $na(s_1, s_2, s_3, s_4)k \in \mathcal{F}$ such that the $s_i$ are bounded above by an appropriate constant to ensure that $\text{Vol}(\mathcal{F}^{(\epsilon)}) = (1 - \epsilon)\text{Vol}(\mathcal{F})$. Then $\mathcal{F}^{(\epsilon)} \cdot R^{(i)}(X)$ is a bounded domain in $V_\mathbb{R}$ that expands homogeneously with $X$. By [9, Theorem 3.3], we obtain $$\#\{\mathcal{F}^{(\epsilon)} \cdot R^{(i)}(X) \cap (\cup_{p > M} W_p^{(1)})\} = O(X^{5/6}/(M \log M) + X^{19/24}). \quad (24)$$ Also, the results of (3.1) and (3.2) imply that $$\#\{(\mathcal{F} \setminus \mathcal{F}^{(\epsilon)}) \cdot R^{(i)}(X) \cap V_{\mathbb{Z}}^{\text{irr}}\} = O(\epsilon X^{5/6}). \quad (25)$$ Combining the estimates (24) and (25) yields (23) with $W_p$ replaced with $W_p^{(1)}$. Next, let $(A, B)$ be an element of $W_p^{(2)} := W_p \setminus W_p^{(1)}$ for some prime $p > 2$. By definition, $v_p(\Delta(A, B)) = v_p(\Delta(f))$, where $f = f_{A,B}$ is the binary quartic resolvent form of $(A, B)$. Thus $p^2$ divides the discriminant of $f$, and since $(A, B) \notin W_p^{(1)}$ we may assume that the reduction of $f$ modulo $p$ contains the square of a linear factor. By replacing $(A, B)$ with a $G_2$-translate, if necessary, we may further assume that $p^2$ divides the $x^2$-coefficient of $f(x, y)$ and $p$ divides the $x^3 y$-coefficient of $f(x, y)$. This condition (along with the fact that $(A, B) \notin W_p^{(1)}$) implies that we may assume $(A, B) = ((a_{ij}), (b_{ij}))$ satisfies the following conditions: Lemma 24 The map $\phi$ from $G_Z$-orbits on $W_p^{(2)}$ to $G_Z$-orbits on $W_p^{(1)}$ is at most 2 to 1. Proof: Let $(A, B) \in W_p^{(1)}$ be any element in the image of $\phi$ and let $(\overline{A}, \overline{B})$ denote its reduction modulo $p$. It is easy to see that $\overline{\phi^{-1}}(A, B)$ is integral if and only if $b_{22} \equiv b_{23} \equiv b_{24} \equiv b_{33} \equiv b_{34} \equiv b_{44} \equiv 0 \pmod{p}$. Therefore, the $G_Z$-orbits on $\phi^{-1}(A, B)$ give rise to elements $[r : s] \in \mathbb{P}_p^1$ along with a linear factor of the quadratic form corresponding to $r \overline{A} + s \overline{B}$. If there are two elements in $\mathbb{P}_p^1$ such that the corresponding quadratic forms factor, then $(A, B)$ is $G_Z$-equivalent to $(A_1, B_1)$, where the reductions of $A_1$ and $B_1$ modulo $p$ both factor over $\mathbb{F}_p$. We may thus assume that the bottom $3 \times 3$ submatrix of $B_1$ is congruent to zero modulo $p$. If $(A_2, B_2)$ is $\gamma_p^{-1}(A_1, B_1)$, then we see that the reduction of $A_2$ modulo $p$ also factors over $\mathbb{F}_p$, implying that $(A_2, B_2) \in W_p^{(1)}$. Thus, $(A, B)$ cannot lie in the image of $\phi$ contradicting our hypothesis. Therefore, if $(A, B)$ is in the image of $\phi$, then there is exactly one element $[r : s] \in \mathbb{P}_p^1$ such that the quadratic form corresponding to $r \overline{A} + s \overline{B}$ factors. We assume without loss of generality that $[r : s] = [0 : 1]$. If $\overline{B}$ has more than two linear factors, then $\overline{B} \equiv 0 \pmod{p}$. Then it is easy to see that $\gamma_p^{-1}(A, B) \in W_p^{(1)}$ because its binary quartic resolvent form is congruent to zero modulo $p$, again contradicting the hypothesis that $(A, B)$ is in the image of $\phi$. This concludes the proof of the lemma. □ Therefore, we obtain $$N(\cup_{p \geq M} W_p^{(2)}(V), X) \leq 2N(\cup_{p \geq M} W_p^{(1)}(V), X) = O_e(X^{5/6}/(M \log M) + X^{19/24}) + O(eX^{5/6}), \quad (26)$$ and Theorem 23 follows. □ Theorem 22 follows from Theorem 23 just as [6] Theorem 2.21] followed from [6] Theorem 2.13]. 4 The average number of elements in the 4-Selmer group of elliptic curves In this section, we prove Theorems 1 and 2 by computing the average size of the 4-Selmer group of elliptic curves over $\mathbb{Q}$, when these curves are ordered by height. In fact, we prove a generalization of these theorems that allows us to average the size of the 4-Selmer group of elliptic curves whose defining equations satisfy certain acceptable sets of local conditions. To state the theorem, we need the following definitions. For any elliptic curve $ E $ over $ \mathbb{Q} $, we defined the invariants $ I(E) $ and $ J(E) $ as in (1). Let us denote the elliptic curve having invariants $ I $ and $ J $ by $ E^{I,J} $. Throughout his section we work with the slightly different height $ H' $ on elliptic curves $ E $, defined by \[ H'(E) := H(I(E), J(E)) = \max\{\|I(E)^3\|, J(E)^2/4\}, \] so that the height on elliptic curves agrees with the height on $ V_Z $ defined in (7). Note that since $ H $ and $ H' $ differ by a constant factor of 4/27, they induce the same ordering on the set of (isomorphism classes of) elliptic curves. For each prime $ p $, let $ \Sigma_p $ be a closed subset of $ Z_p^2 \backslash \{ \Delta = 0 \} $ whose boundary has measure 0. To this collection $ \Sigma = (\Sigma_p)_p $, we associate the family $ F_\Sigma $ of elliptic curves, where $ E^{I,J} \in F_\Sigma $ if and only if $ (I, J) \in \Sigma_p $ for all $ p $. Such a family of elliptic curves over $ \mathbb{Q} $ is said to be defined by congruence conditions. We may also impose “congruence conditions at infinity” on $ F_\Sigma $ by insisting that an elliptic curve $ E^{I,J} $ belongs to $ F_\Sigma $ if and only if $ (I, J) $ belongs to $ \Sigma_\infty $, where $ \Sigma_\infty $ is equal to $ \{(I, J) \in \mathbb{R}^2 : \Delta(I, J) > 0\}, \{(I, J) \in \mathbb{R}^2 : \Delta(I, J) < 0\}, $ or $ \{(I, J) \in \mathbb{R}^2 : \Delta(I, J) \neq 0\} $. For such a family $ F $ of elliptic curves defined by congruence conditions, let $ \text{Inv}(F) $ denote the set $ \{(I, J) \in \mathbb{Z} \times \mathbb{Z} : E^{I,J} \in F\} $, and let $ \text{Inv}_p(F) $ be the $ p $-adic closure of $ \text{Inv}(F) $ in $ Z_p^2 \backslash \{ \Delta = 0 \} $. Similarly, we define $ \text{Inv}_\infty(F) $ to be $ \{(I, J) \in \mathbb{R}^2 : \Delta(I, J) > 0\}, \{(I, J) \in \mathbb{R}^2 : \Delta(I, J) < 0\}, $ or $ \{(I, J) \in \mathbb{R}^2 : \Delta(I, J) \neq 0\} $ in accordance with whether $ F $ contains only curves of positive discriminant, negative discriminant, or both, respectively. Such a family $ F $ of elliptic curves is said to be large if, for all but finitely many primes $ p $, the set $ \text{Inv}_p(F) $ contains at least those pairs $ (I, J) \in \mathbb{Z}_p \times \mathbb{Z}_p $ such that $ p^2 \nmid \Delta(I, J) $. Our purpose in this section is to prove the following theorem which generalizes Theorems 1 and 2. Theorem 25 Let $ F $ be a large family of elliptic curves. When elliptic curves $ E $ in $ F $ are ordered by height, the average size of the 4-Selmer group $ S_4(E) $ is 7. ### 4.1 Computation of $ p $-adic densities Throughout the rest of this section, we fix $ F $ to be a large family of elliptic curves. Proposition 9 asserts that elements in the 4-Selmer group of the elliptic curve $ E^{I,J} $ over $ \mathbb{Q} $ are in bijection with $ G_{\mathbb{Q}} $-equivalence classes on the set of locally soluble elements in $ V_Z $ having invariants $ I $ and $ J $. Furthermore, elements of exact order 4 in the 4-Selmer group of $ E^{I,J} $ are in bijection with strongly irreducible $ G_{\mathbb{Q}} $-equivalence classes in the set of locally soluble elements in $ V_Z $ having invariants $ I $ and $ J $. In Section 2, we computed the asymptotic number of $ G_{\mathbb{Z}} $-equivalence classes of strongly irreducible elements in $ V_Z $ having bounded height. In order to use this to compute the number of $ G_{\mathbb{Q}} $-equivalence classes of strongly irreducible locally soluble elements of $ V_Z $ having bounded height and invariants in $ \text{Inv}(F) $, we count each strongly irreducible $ G_{\mathbb{Z}} $-orbit $ G_{\mathbb{Z}} \cdot x $ weighted by $ \phi(x) $, where $ \phi : V_Z \rightarrow \mathbb{R} $ is a $ G_{\mathbb{Z}} $-invariant function that we now define. For $ x \in V_Z $, let $ B(x) $ denote a set of representatives for the action of $ G_{\mathbb{Z}} $ on the $ G_{\mathbb{Q}} $-equivalence class of $ x $ in $ V_Z $. We define our weight function $ \phi $ to be: \[ \phi(x) := \begin{cases} \left( \sum_{x' \in B(x)} \frac{\# \text{Aut}_\mathbb{Q}(x')} {\# \text{Aut}_\mathbb{Z}(x')} \right)^{-1} & \text{if } x \text{ is locally soluble and } (I(x), J(x)) \in \text{Inv}_p(F) \text{ for all } p; \\ 0 & \text{otherwise}, \end{cases} \] (27) where $\text{Aut}_Q(x)$ and $\text{Aut}_G(x)$ denote the stabilizers of $x \in V_Z$ in $G_Q$ and $G_Z$, respectively. Note that if $x \in V_Z$ has a trivial stabilizer in $G_Q$, it is locally soluble, and satisfies $(I(x), J(x)) \in \text{Inv}(F)$, then $\phi(x) = \#B(x)^{-1}$. Thus, Proposition 21 implies the following result: Proposition 26 Let $F$ be a large family of elliptic curves. Following the notation of Theorem 20 and 22, we have $$\sum_{E \in F, H'(E) < X} \#\{\sigma \in S_4(E) : \sigma^2 \neq 1\} = N_\phi(V_Z; X) + o(X^{5/6}).$$ To evaluate the right hand side of the above equation using Theorem 22, we need to show that the weight function $\phi$ is acceptable in the sense of Section 3.6. To this end, we define local functions $\phi_p : V_{Z_p} \to \mathbb{R}$ as follows. For $x \in V_{Z_p}$, let $B_p(x)$ denote a set of representatives for the action of $G_{Z_p}$ on the $G_{Q_p}$-equivalence class of $x$ in $V_{Z_p}$. Then we define $$\phi_p(x) := \begin{cases} \left( \sum_{x' \in B_p(x)} \frac{\#\text{Aut}_{Q_p}(x')}{\#\text{Aut}_{Z_p}(x')} \right)^{-1} & \text{if } x \text{ is soluble over } \mathbb{Q}_p \text{ and } (I(x), J(x)) \in \text{Inv}_p(F); \\ 0 & \text{otherwise}, \end{cases} \quad (28)$$ where $\text{Aut}_{Q_p}(x)$ and $\text{Aut}_{Z_p}(x)$ denote the stabilizer of $x \in V_{Z_p}$ in $G_{Q_p}$ and $G_{Z_p}$, respectively. Before we prove that $\phi$ is acceptable, we need the following lemma: Lemma 27 For sufficiently large primes $p$, if $(A, B) \in V_{Z_p}$ satisfies $\phi_p(A, B) \neq 1$, then the discriminant of $(A, B)$ is divisible by $p^2$. Proof: Since $F$ is a large family of elliptic curves, we know that for large enough primes $p$, if $(I, J) := (I(A, B), J(A, B)) \notin \text{Inv}_p(F)$, then $p^2 \| \Delta(A, B)$. Now suppose that $(I, J) \in \text{Inv}_p(F)$ but $\phi_p(A, B) \neq 1$. Then either $(A, B)$ is not soluble over $\mathbb{Q}_p$, $\text{Aut}_{Q_p}(A, B)$ is not trivial, or $B_p(A, B)$ has size at least two. Let $C \in \mathbb{P}_F^3$ be the curve cut out by the intersection of the quadrics defined by the reductions of $A$ and $B$ modulo $p$. The Lang-Weil estimates [25] imply that, for sufficiently large primes $p$, either $C$ is geometrically reducible or $C$ has a smooth $\mathbb{F}_p$-point. Thus either $p^2$ divides the discriminant of $(A, B)$ or $(A, B)$ is locally soluble. Finally, [28, Corollary 2.2] implies that if $(A, B)$ is soluble and either $\text{Aut}_{Q_p}(A, B)$ is nontrivial or $\#B_p(A, B) > 1$, then the reduction type of the elliptic curve $E^I,J$ over $\mathbb{Q}_p$ is not $I_0$ or $I_1$. This implies that $p^2 \| \Delta(E^I,J) = \Delta(A, B)$, as desired. $\square$ This leads us to the following proposition: Proposition 28 The function $\phi : V_Z^{\text{HT}} \to \mathbb{R}$ is acceptable. Proof: The local weight functions $\phi_p$ are supported and locally constant outside the set of elements in $V_{Z_p}$ having discriminant zero. That $\phi(A, B) = \prod_p \phi_p(A, B)$, for $(A, B) \in V_Z$, follows from an argument identical to the proof of [6, Proposition 3.6] and the fact that the class number of $G_Q$ is 1. Lemma 27 then implies that $\phi$ is acceptable. $\square$ We end the section with a proposition that evaluates $\int_{V_{Z_p}} \phi_p(x)dx.$ Proposition 29 We have \[ \int_{x \in \mathbb{Z}_p} \phi_p(x) dx = \|J_p\| \cdot \text{Vol}(G_{\mathbb{Z}_p}) \cdot \int_{(I,J) \in \text{Inv}_p(F)} \frac{\#(E_{I,J}^{p}(\mathbb{Q}_p))/4E_{I,J}^{p}(\mathbb{Q}_p)}{\#(E_{I,J}^{p}(\mathbb{Q}_p)[4])} \] \[ = \begin{cases} \|J_p\| \cdot \text{Vol}(G_{\mathbb{Z}_p}) \cdot \text{Vol}(\text{Inv}_p(F)) & \text{if } p \neq 2; \\ 4 \cdot \|J_p\| \cdot \text{Vol}(G_{\mathbb{Z}_p}) \cdot \text{Vol}(\text{Inv}_p(F)) & \text{if } p = 2, \end{cases} \] where the volume of $ \text{Inv}_p(F) \subset \mathbb{Z}_p \times \mathbb{Z}_p $ is taken with respect to the additive Haar measure on $ \mathbb{Z}_p \times \mathbb{Z}_p $ normalized so that $ \text{Vol}(\mathbb{Z}_p \times \mathbb{Z}_p) = 1 $. The first equality in Proposition 29 follows from an argument identical to [6, Proposition 3.9]. The second follows from an argument identical to the proof of [13, Lemma 3.1], yielding that $ \#(E_{I,J}^{p}(\mathbb{Q}_p))/4E_{I,J}^{p}(\mathbb{Q}_p)) $ is equal to $ \#(E_{I,J}^{p}(\mathbb{Q}_p)[4]) $ when $ p \neq 2 $ and equal to $ 4 \#(E_{I,J}^{p}(\mathbb{Q}_p)[4]) $ when $ p = 2 $. ### 4.2 The proof of the main theorem (Theorem 25) We first state a theorem, proved in [6, Theorem 3.17], that counts the number of elliptic curves having bounded height in a large family $ F $. Theorem 30 Let $ F $ be a large family of elliptic curves and let $ N(F; X) $ denote the number of elliptic curves in $ F $ that have height bounded by $ X $. Then \[ N(F; X) = \text{Vol}(\text{Inv}_\infty(F; X)) \prod_p \text{Vol}(\text{Inv}_p(F)) + o(X^{5/6}), \tag{29} \] where $ \text{Inv}_\infty(F; X) $ denotes the set of elements in $ \text{Inv}_\infty(F) $ that have height bounded by $ X $. For any large family $ F $ of elliptic curves over $ \mathbb{Q} $, it follows from Proposition 28 that \[ \lim_{X \to \infty} \frac{\sum_{E \in F \text{ s.t. } H'(E) < X} \#\{\sigma \in S_4(E) : \sigma^2 \neq 1\}}{\sum_{E \in F \text{ s.t. } H'(E) < X} 1} = \lim_{X \to \infty} \frac{N_\phi(V; X)}{N(F; X)}. \tag{30} \] Proposition 28 states that $ \phi $ is acceptable. Thus, the right hand side of (30) can be evaluated using Theorems 22 and 30 \[ \lim_{X \to \infty} \frac{N_\phi(V; X)}{N(F; X)} = \lim_{X \to \infty} \frac{\frac{1}{4} \|J\| \cdot \text{Vol}(G_{\mathbb{Z}} \setminus G_{\mathbb{R}}) \text{Vol}(\text{Inv}_\infty(F; X)) \prod_p \int_{\mathbb{Z}_p} \phi_p(x) dx}{\text{Vol}(\text{Inv}_\infty(F; X)) \prod_p \text{Vol}(\text{Inv}_p(F))} \] \[ = \frac{\|J\| \cdot \text{Vol}(G_{\mathbb{Z}} \setminus G_{\mathbb{R}}) \prod_p (\|J_p\| \cdot \text{Vol}(G_{\mathbb{Z}_p}) \cdot \text{Vol}(\text{Inv}_p(F)))}{\prod_p \text{Vol}(\text{Inv}_p(F))}, \tag{31} \] where the second equality follows from Proposition 29. Since $ \text{Vol}(G_{\mathbb{Z}_p}) \prod_p \text{Vol}(G_{\mathbb{Z}_p}) $ is equal to the Tamagawa number of $ G_{\mathbb{Q}} $ which is 4 (see $[26]$), we obtain that \[ \lim_{X \to \infty} \frac{\sum_{E \in F} \# \{ \sigma \in S_4(E) : \sigma^2 \neq 1 \}}{\sum_{E \in F} 1} = 4. \] (32) Now, for any elliptic curve $ E $ over $ \mathbb{Q} $, the short exact sequence \[ 0 \to E[2] \to E[4] \to E[2] \to 0 \] yields the long exact sequence \[ 0 \to E[2](\mathbb{Q}) \to E[4](\mathbb{Q}) \to E[2](\mathbb{Q}) \to H^1(\mathbb{Q}, E[2]) \to H^1(\mathbb{Q}, E[4]). \] Therefore, if $ E $ has no nontrivial rational 2-torsion points, then the group $ H^1(\mathbb{Q}, E[2]) $ injects into $ H^1(\mathbb{Q}, E[4]) $. This implies that $ S_2(E) $ injects into $ S_4(E) $, and thus \[ \#S_4(E) = \# \{ \sigma \in S_4(E) : \sigma^2 \neq 1 \} + \#S_2(E). \] The number of elliptic curves over $ \mathbb{Q} $ having nontrivial rational 2-torsion and height less than $ X $ is negligible, i.e., is $ o(X^{5/6}) $. That the sum of the sizes of the 4-Selmer groups of such elliptic curves is negligible follows from Proposition 21. Since we have shown in [6, Theorem 3.1] that the average size of the 2-Selmer group of elliptic curves in any large family $ F $ is equal to 3, we obtain from (32) that \[ \lim_{X \to \infty} \frac{\sum_{E \in F} \#S_4(E)}{\sum_{E \in F} 1} = 4 + 3 = 7. \] This concludes the proof of Theorem 25 (and hence also of Theorems 1 and 2). Finally, to obtain Theorem 3 we note that for an elliptic curve $ E $ over $ \mathbb{Q} $ with no rational 2-torsion, if the 4-Selmer group $ S_4(E) $ is isomorphic to $(\mathbb{Z}/4\mathbb{Z})^a \times (\mathbb{Z}/2\mathbb{Z})^b $, then the 2-Selmer group $ S_2(E) $ is isomorphic to $(\mathbb{Z}/2\mathbb{Z})^{a+b}; $ the number of 2-Selmer elements that are not in the image of the $ \times 2 $ map from $ S_4(E) $ to $ S_2(E) $ is thus $ 2^{a+b} - 2^a $ in this case. To prove Theorem 3 we wish to determine a lower bound on the liminf of the average of $ 2^{a+b} - 2^a $ over all elliptic curves $ E $ over $ \mathbb{Q} $ (having trivial rational 2-torsion), when these elliptic curves are ordered by height. Equivalently, we wish to determine an upper bound on the limsup of the average size of $ 2^a $. We have proven that the average number of order 4 elements in the 4-Selmer groups of these elliptic curves is 4, i.e., the average size of $(4^a - 2^a)2^b $ is 4. It follows that the limsup of the average size of $ 4^a - 2^a $ is at most 4. Since $ 5 \cdot 2^a - 8 \leq 4^a - 2^a $ for all integers $ a > 0 $, we conclude that the limsup of the average size of $ 2^a $ is at most $ 12/5 $. Hence the liminf of the average size of $ 2^{a+b} - 2^a $ is at least $ 3 - 12/5 = 3/5 $; this completes the proof of Theorem 3. (We note that the proof also naturally yields a distribution of 2- and 4-Selmer groups—for which the average sizes of these groups are given by 3 and 7, respectively—that achieves the bound of 3/5; hence the bound of 3/5 in Theorem 3 is in fact the best possible given these two constraints.) As a consequence, we see that a proportion of at least $(3/5)/3 = 1/5$ of 2-Selmer elements of elliptic curves $E$ over $\mathbb{Q}$, when ordered by height, do not lift to 4-Selmer elements; i.e., we have proven that at least a fifth of all 2-Selmer elements yield nontrivial 2-torsion elements in the corresponding Tate–Shafarevich groups. 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Womack, Explicit Descent on Elliptic Curves, Ph.D. Thesis, University of Nottingham, 2003.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2926, 1 ], [ 2926, 6616, 2 ], [ 6616, 10838, 3 ], [ 10838, 14721, 4 ], [ 14721, 18663, 5 ], [ 18663, 22350, 6 ], [ 22350, 25063, 7 ], [ 25063, 28938, 8 ], [ 28938, 31839, 9 ], [ 31839, 35156, 10 ], [ 35156, 37951, 11 ], [ 37951, 40431, 12 ], [ 40431, 43327, 13 ], [ 43327, 46150, 14 ], [ 46150, 49120, 15 ], [ 49120, 52675, 16 ], [ 52675, 55249, 17 ], [ 55249, 59753, 18 ], [ 59753, 63071, 19 ], [ 63071, 65801, 20 ], [ 65801, 68842, 21 ], [ 68842, 71367, 22 ], [ 71367, 74072, 23 ], [ 74072, 74356, 24 ] ] }
2fc654128033667519c42568b1d2ec5e661c0d45	{ "olmocr-version": "0.1.59", "pdf-total-pages": 7, "total-fallback-pages": 0, "total-input-tokens": 22064, "total-output-tokens": 7242, "fieldofstudy": [ "Medicine" ] }	Comparative Analysis of the Pain Provocation Test and the HABER Test to Diagnose Nonspecific Low-Back Pain Associated with the Sacroiliac Joint Background: This study aimed to investigate the correlation between the pain provocation test and the hip abduction-external rotation (HABER) test for diagnosing low-back pain (LBP)-related sacroiliac joint (SIJ) syndrome, and to determine the efficacy of the HABER test as a potential diagnostic tool for SIJ syndrome. Material/Methods: One hundred patients with LBP participated. The first and second examiner examined the patients using the pain provocation test and the HABER test, respectively. Positive and negative findings were analyzed to determine the correlation and reliability. Results: The HABER test showed similar pain reproduction in groups that were positive or negative for SIJ syndrome (P<0.05). Based on the analysis of the receiver-operating characteristic curve, the cutoff values from the HABER test were found to be 29° and 32° of external rotation in the left and right hip joints, respectively. Conclusions: The HABER test can reproduce similar level of pain in patients with chronic LBP associated with SIJ syndrome, and it can be used as a diagnostic tool in patients presenting with chronic LBP. Keywords: Clinical Trial • Low Back Pain • Sacroiliac Joint Full-text PDF: https://www.medscimonit.com/abstract/index/idArt/929307 Authors' Contribution: - Study Design A - Data Collection B - Statistical Analysis C - Data Interpretation D - Manuscript Preparation E - Literature Search F - Funds Collection G Corresponding Author: Seung-Chul Chon, e-mail: [email protected] Source of support: This paper was supported by the Konyang University Research Fund in 2019 Background Low-back pain (LBP) is one of the most common musculoskeletal disorders in modern society. Ehrlich [1] reported that more than 70% to 80% people experience LBP in their lives, and other studies reported that LBP was associated with sacroiliac joint (SIJ) syndrome in 10% to 38% of patients [2-4]. SIJ syndrome causes pain in various areas of the body including the buttocks, groin, and back [5]. Most cases of LBP resolve rapidly, but 10% of patients report progression to chronic LBP [6]. One of the major causes of LBP is SIJ syndrome. However, because of the difficulty in the diagnosis of SIJ, the treatments for LBP vary and have a range of results [7]. There are 3 clinical methods used to identify SIJ syndrome. The first is the motion palpation test. In this method, the examiner places their hands on the SIJ landmark to determine if both sides of the patient’s SIJ move symmetrically. The second test is the location symmetry palpation test. This method is used to determine the symmetry of the SIJ landmark in the patient. The third is the pain provocation test. In this method, pressure is applied to the SIJ structure with the intent of causing pain. The motion palpation test shows moderate interexaminer reliability (prevalence-adjusted and bias-adjusted kappa [PABAK]= 0.52), while the pain provocation test shows high interexaminer reliability (PABAK=0.92) [8]. The pain provocation test was used as the standard in the current study because of its high interexaminer reliability in comparison with the other test methods (ie, location symmetry palpation test and motion palpation test). When evaluating LBP with SIJ syndrome, it is difficult to determine if a positive result of a pain provocation test is LBP associated with SIJ; an accurate diagnosis requires the use of more than one of the aforementioned tests. Additionally, the pain provocation test is composed of the following 5 components: the Gaenslen test, compression test, distraction test, thigh thrust test, and sacral thrust test [9,10]. When 3 or more of the 5 pain provocation test components are positive, the overall test result is positive (validity [sensitivity=85%, specificity=76%] [11], interrater reliability [k=0.51-0.75] in SIJ syndrome) [10]. The pain provocation test can diagnose the presence or absence of SIJ syndrome in patients with nonspecific LBP, but it does not indicate changes in its biomechanics [12,13]. Researchers have found that the motion palpation test can provide biomechanical information related to SIJ syndrome and can discriminate among its various causes [4,8,14]. This test has revealed that the most commonly reported cause of SIJ syndrome-related nonspecific LBP is abnormal movement of the innominate bone (ilium+pubis+ischium) [15-17]. Due to the complex anatomical structure of the SIJ, accurate and reliable physical examination methods for evaluating the movement pattern of the innominate bone are currently lacking [5,18-20]. A more efficient and clinical test method is needed to address the diagnostic deficiencies of the motion palpation test and pain provocation test when each is administered alone. The hip abduction-external rotation (HABER) test combines the abduction and external rotation of the hip joint in the prone position, making it possible to control the load of the SIJ through gradual hip joint movement [21]. In previous studies, the HABER test successfully identified the exact movement pattern of the innominate bone using electromagnetic palpation digitization technique on the pelvic landmarks in the HABER test positions [21-24]. Adhia et al [23] showed that the innominate movement pattern measured through the HABER test demonstrated a high level of interrater reliability (intraclass correlation coefficient=0.97). In a recent study, the HABER test revealed a relationship of LBP with SIJ syndrome and the kinematics (movement pattern and rotation trends) of the innominate bone [25]. As reported, the HABER test appears to have the advantage of distinguishing between the kinematic characteristics of the SIJ and LBP. Additionally, the HABER test does not reproduce the specific angle of the hip joint in patients with nonspecific LBP associated with SIJ syndrome. The purpose of the current study was to examine the correlation between the HABER test and the pain provocation test in identifying patients with nonspecific LBP associated with SIJ syndrome. The diagnostic accuracy of the HABER test in relation to the pain provocation test was examined. The reference values and diagnostic accuracy of the HABER test were assessed using SIJ syndrome-positive predictions based on the pain provocation test results. Material and Methods Subjects This study included 100 adult patients (56 men and 44 women) who visited a local metropolitan university hospital in the Republic of Korea for the treatment of nonspecific chronic LBP. With regard to the study sample size, the median effect size was 0.15, the significance level was 0.05, and the power was 0.9. The appropriate sample size was determined to be a minimum of 88. To account for the potential dropout rate during the research process, 100 people were recruited in total. The mean age, height, weight, body mass index, and visual analog scale (VAS) score of participants were 35.5 years, 164.6 cm, 64.3 kg, 23.4 kg/m², and 4.6, respectively (Table 1). The inclusion criteria were as follows: (1) LBP for more than 3 months, (2) current LBP rated as 4 or higher on a VAS for pain, and (3) no lower extremity pain during the straight leg raise test. The exclusion criteria were as follows: (1) fracture of the Table 1. General characteristics of the participants. \| Variable \| Nonspecific chronic low-back pain patients \| \|----------------------\|-------------------------------------------\| \| Sex, Male/Female \| 56/44 \| \| Age, years \| 35.5 (11.70)* \| \| Height, cm \| 164.6 (10.94) \| \| Weight, kg \| 64.3 (14.80) \| \| BMI, kg/m² \| 23.4 (3.52) \| \| VAS, score \| 4.6 (0.81) \| BMI – body mass index; VAS – visual analog scale. * Mean (standard deviation). vertebral joint, (2) spinal joint surgery, and (3) hip joint surgery or fracture. Explanations about the procedure and stability were provided to all patients before the experiment, and written informed consent was obtained from all participants. This study was approved by the Bioethics Committee of Konyang University (approval number: 2019-195-02) in the Republic of Korea, and it is registered with the World Health Organization International Clinical Trials Registry Platform (KCT0005663). Procedure First, the pain provocation test was performed to distinguish SIJ syndrome. If 3 or more of the 5 component tests were positive, the case was judged as SIJ-positive. A second examiner performed the HABER test and diagnosed positive and negative SIJ syndrome on the left and right sides (Figure 1). Pain Provocation Test The pain provocation test result was classified as positive if it reproduced pain similar to the patient’s pain during the test. Test results were classified as SIJ-positive if 3 or more tests were positive and SIJ-negative if fewer than 3 tests were positive. The experiment was conducted in a random order to avoid examiner’s bias. The pain provocation tests were conducted as follows. First, in the distraction test, the subject lay in the supine position with the experimenter’s hand placed on both sides of the anterior superior iliac spine in turn. Then, checks were performed to find whether the pain occurred by applying pressure in the posterior and lateral directions. The second test, the thrust test, was performed with the subject in the prone position. The experimenter’s hand was on the sacrum, and pressure was applied from the back to the front. In the third test, the compression test, the subject was in the side-lying position. The experimenter’s hand was on the iliac crest, and pressure was applied. In the fourth test, the thigh thrust test, the subject was looking up at the ceiling while lying down with the hip and knee joints bent at 90° and in a slightly adducted position. The experimenter checked whether the pain was caused by applying a shearing stress to the back of the thigh, by vertically pressing the femur. In the fifth test, the Gaenslen test, the subject looked up at the ceiling and dropped one hip off the table while the other leg was bent at the knee and hip, as much as possible. After that, the experimenter checked whether the pain caused was due to the overpressure on both hip joints. Hip Abduction and External Rotation Test A second examiner administered the HABER test after the patient rested for 10 min following the pain provocation test. The results of the pain provocation tests were unknown to the second examiner. The HABER test was performed using the hip joint rotating frame used by Bussey et al [26]. The angle of the hip joint was measured on the left and right sides of the motion combined with abduction and external rotation. The HABER test was conducted as follows. The subject lay in the prone position, and the knee joint was bent 90° and then immobilized. The subject moved the hip joint in an external rotation, and when the pain typically felt by the subject was reproduced or when the VAS for the pain increased by 1 point or more, the result was recorded as positive and the angle at which the pain was reproduced was measured. To measure the external rotation angle of the hip joint, a mobile phone was fixed with a band under the tibial tuberosity. The Goniometer Pro application (5fu5, Bloomfield, NJ, USA) was then used to measure the angle at which the pain appeared. Three HABER tests were performed on each subject, and the results were averaged. Statistical Analysis The data were analyzed with SPSS Statistics for Windows, version 18.0 (SPSS Inc., Chicago, IL, USA). The necessary sample size was calculated using the G Power 3.1.9.2 program (Franz Faul, Christian-Albrechts-Universität Kiel, Kiel, Germany). The correlation between the pain provocation test and the HABER test was analyzed using binary logistic mixed model regression analysis. To determine the overall diagnostic accuracy of the HABER test; sensitivity, specificity, positive predictive value (PPV), odds ratio (OR), and negative likelihood ratio (NLR) were calculated using a 2×2 table (95% confidence interval [CI]). MedCalc Version 16.8.4 (MedCalc Software, Mariakerke, Belgium) was used to examine the cutoff value and diagnostic accuracy of the HABER test. The receiver-operating characteristic (ROC) curve was analyzed to determine the 95% CI and the area under the curve (AUC). The AUC was classified as follows: 0.5 ≤ AUC ≤ 0.7 is less accurate; 0.7 < AUC ≤ 0.9 is moderately accurate; 0.9 < AUC < 1 is very accurate; and AUC = 1 is a complete test. Results Binary logistic mixed model regression analysis of the HABER test and pain provocation test demonstrated a correlation between the results generated by the 2 tests (Table 2). Binary logistic regression analysis showed a significant correlation with pain reproduction between the pain provocation test group and the HABER test group (P < 0.002). The Nagelkerke R² value showed that approximately 14% of the dependent variables were explained by the logistic regression model. The sensitivity, specificity, predictive value, OR, PLR, and NLR of the HABER test compared with those of the provocation test are shown in Table 3. The HABER test showed 80% sensitivity and 53% specificity for diagnosing LBP associated with SIJ syndrome. The PPV was 0.48 and the negative predictive value (NPV) was 0.83. The PLR was 1.73 and the NLR was 0.37. The OR was 4.67. Based on the HABER test value, the calculated cutoff value accurately predicted a positive result in the pain provocation test (Table 4, Figure 2). A cutoff value of 32° was shown in the ROC analysis in the left (L)-SIJ with 73% sensitivity, 91% specificity, 0.288 AUC, 8.53 PLR, and 0.29 NLR (P<0.001). ROC analysis of the right (R)-SIJ revealed a cutoff value of 29° with --- Table 2. Results of the binary logistic mixed model regression analyses for the interactions of the HABER test side and the clinical group. \| \| R² \| B \| Standard error \| Sig Exp(B) \| 95% CI Exp(B) \| \|--------\|-----\|------\|----------------\|------------\|---------------\| \| HABER Test \| 14.4 \| 1.54 \| 0.002 \| 4.668 \| 1.785 - 12.202 \| CI – confidence interval; HABER – hip abduction and external rotation. Table 3. Measures of the cutoff criterion of the HABER test for identifying SIJ-positive LBP individuals. \| PPT group \| HABER side \| Cutoff value \| Sen* \| Spec* \| AUC* \| PLR* \| NLR* \| SE \| P \| \|-----------\|------------\|--------------\|------\|-------\|------\|------\|------\|------\|-------\| \| L-SIJ \| Left \| >32 \| 0.79 \| 0.91 \| 0.828\| 8.25 \| 0.29 \| 0.062\| 0.001\| \| R-SIJ \| Right \| >29 \| 0.68 \| 0.92 \| 0.804\| 0.24 \| 0.34 \| 0.063\| 0.001\| AUC – area under curve; HABER – hip abduction and external rotation; LBP – low-back pain; NLR – negative likelihood ratio; PLR – positive likelihood ratio; PPT – pain provocation test; SE – standard error; SIJ – sacroiliac joint; Sen – sensitivity; Spec – specificity. * 95% confidence interval; # significant difference between groups. Table 4. Overall measures of the HABER test for identifying SIJ syndrome-positive LBP individuals. \| Test \| Sen* \| Spec* \| PPV* \| NPV* \| PLR* \| NLR* \| OR* \| \|------------\|------\|-------\|------\|------\|------\|------\|-----\| \| SIJ test \| 0.8 \| 0.53 \| 0.48 \| 0.83 \| 1.73 \| 0.37 \| 4.67\| HABER – hip abduction and external rotation; LBP – low-back pain; NLR – negative likelihood ratio; PPV – positive predictive value; PLR – positive likelihood ratio; PPT – pain provocation test; PPV – positive predictive value; OR – odds ratio; SIJ – sacroiliac joint; Sen – sensitivity; Spec – specificity. * 95% confidence interval. 68% sensitivity, 92% specificity, 0.804 AUC, 9.24 PLR, and 0.34 NLR (P<0.001). Discussion This study yielded multiple significant findings. First, the pain provocation test is both time consuming and complicated for diagnosing SIJ syndrome because it involves the results of 5 tests. Second, as the pain provocation test causes pain and is performed repeatedly, the sensitivity of the test may be reduced by increasing the patient’s sensitivity to pain. As such, the HABER test may be superior for diagnosing SIJ syndrome in clinical practice because it is simpler and can be safely repeated. In addition, movement of the innominate bone, which is highly correlated with back pain, can be evaluated. We assessed, in detail, the correlation between the pain provocation test and the HABER test, and tested the reliability of the HABER test as a stand-alone test to diagnose LBP associated with SIJ syndrome. Correlation was shown to exist between the 2 tests (R²=0.14, P<0.002). The reliability of the HABER test as a stand-alone test to diagnose LBP associated with SIJ syndrome by measuring the cutoff value was also strengthened by this study. As a result of the study, the pain provocation test and HABER test were correlated with the diagnosis of LBP-related SIJ syndrome. The HABER test, a single test, can identify whether SIJ is associated with LBP. The high level of sensitivity (80%) of the HABER test shown in this study differs from previous study findings [27]. The test has also previously been proven to be effective in evaluating the innominate bone in patients with LBP associated with SIJ syndrome [23,26,27]. Most pain-causing tests of the SIJ structures focus on the compression of the structures through multiple tests. The HABER test, however, was hypothesized to effectively reflect the complex anatomical structures of the SIJ and to help diagnose SIJ syndrome with only 1 test. The single-test design of the pain provocation test can also be viewed as a test constraint that could affect the accuracy of the diagnosis, and it requires further examination [4,9,27]. Bussey et al [21] predicted that the movement pattern of the innominate bone could be altered by a small range of hip abduction and external rotation. Moreover, Adhia et al [25] reported that a change occurred in the movement pattern of innominate bone in people with LBP associated with SIJ syndrome. Together, these studies strengthen the likelihood that the HABER test could be an effective single diagnostic tool for SIJ syndrome, and the results led us to explore its accuracy. Additionally, the current study revealed that the probability of the HABER test being positive when the pain provocation test was also positive was about 5 times higher than when the pain provocation test was negative. The moderate level of specificity (53%) of the HABER test shown in this study is consistent with previous study findings [27]. The moderate specificity of the HABER test may have been influenced by the complex anatomical structure of the SIJ. This could be due to the test delivering a weight load to a joint other than the SIJ [21,26]. The test is intended to transmit the force applied to the hip joint to the SIJ through the abduction and... external rotation of the hip joint. The applied force is, howev- er, not limited to the SIJ and can be distributed to the lumbar spine through the lumbosacral junction [27]. This can influence the outcome of the test. For example, the dispersed force can stimulate inflammation in inflammatory spinal diseases, to cause pain. In this situation, the HABER test could be result positive for LBP that is not associated with SIJ syndrome. The misdiagnosis rate from false positives could explain the moderate rate of specificity. To address this problem, providing stability to the lumbar-sacral junction could be helpful in future study and possibly result in a higher rate of specificity for a modified HABER test. This study showed that the external rotation of the hip joint during the HABER test in the SIJ syndrome-positive group had AUC values of 29° in the left hip joint and 32° in the right hip joint. Previous studies have suggested that patients diagnosed with SIJ syndrome have limitations of the axial rotation and abduction of the hip joint [21,28]. Adhia et al [27] previously determined that a 30° widening of the hip joint distinguishes LBP associated with SIJ syndrome from LBP syndrome in the HABER test. Our similar findings further strengthen our conclusion. It is important to note that additional objective variables are also useful when differentiating LBP associated with SIJ syndrome from LBP unrelated to the SIJ. Based on the results of our study, the advantages of the HABER test are as follows. First, the HABER test can facilitate obtaining information usually gained from the pain provocation test and the motion palpation test in a single test. Second, patient discomfort is minimized and the patient undergoes a simplified process with the HABER test. Third, the HABER test can be used as an objective evaluation tool to discriminate LBP associated with SIJ syndrome from LBP not associated with SIJ syndrome by utilizing the test’s cutoff value. Our study differs from previous similar studies in multiple ways. First, in terms of research methods, unlike previous studies, we used an automatic smartphone protractor to enhance ease of use and digitalization of data. Second, in previous studies, outer hip joint rotation during the HABER test was classified in increments of 10°, whereas in this study, we used the total angle of the outer hip joint rotation to obtain more accurate results. Nevertheless, there were some limitations to this study, including the following. First, recruiting patients with LBP occurred over a short period. Second, the HABER test cannot be used to determine the amount of force distributed to the lumbar vertebrae through the lumbosacral junction. Third, the standard test for the differentiation of SIJ syndrome is based on the SIJ block. In this study, the pain provocation test was used as the standard. Many studies have shown the power of both the SIJ block and the pain provocation test; however, it is expected that future HABER test studies will require the use of the SIJ block as the standard test. Conclusions The HABER test can reproduce a similar level of pain in patients with chronic LBP associated with SIJ syndrome, and it can be used as a diagnostic tool when examining patients presenting with chronic LBP. References: 1. Ehrlich GE. Back pain. J Rheumatol Suppl, 2003;67:26-31 2. Manchikanti L, Singh V, Pampati V, et al. Evaluation of the relative contributions of various structures in chronic low back pain. Pain Physician, 2001;4:308-16 3. Irvin RW, Watson T, Minick RP. Ambrosius WT. Age, body mass index, and gender differences in sacroiliac joint pathology. Am J Phys Med Rehabil, 2007;86:37-44 4. van der Wurff P, Buijs EI, Groen DJ. A multistest regimen of pain provocation tests as an aid to reduce unnecessary minimally invasive sacroiliac joint procedures. Arch Phys Med Rehabil, 2006;87:10-14 5. Cattley P, Winyard J, Trevaskis J, Eaton S. Validity and reliability of clinical tests for the sacroiliac joint: A review of literature. Australas Chiropr Osteopathy, 2002;10:73-80 6. Briggs A, Buchbinder R. Back pain: Aa National health priority area in Australia? Med J Aust, 2009;190:499-502 7. O’Sullivan P. Diagnosis and classification of chronic low back pain disorders: Maladaptive movement and motor control impairments as underlying mechanism. Manual Ther, 2005;10:242-55 8. Arab AM, Abdollahi J, Joghataei MT, et al. Inter-and intra-examiner reliability of single and composites of selected motion palpation and pain provocation tests for sacroiliac joint. Manual Ther, 2009;14:213-21 9. Laslett M, April CN, McDonald B, Young SB. Diagnosis of sacroiliac joint pain: Validity of individual provocation tests and composites of tests. Manual Ther, 2005;10:207-18 10. Robinson HS, Brox JI, Robinson R, et al. The reliability of selected motion- and pain provocation tests for the sacroiliac joint. Manual Ther, 2007;12:72-79 11. Szaké K, van der Wurff P, van Tulder MW, et al. Diagnostic validity of criteria for sacroiliac joint pain: A systematic review. J Pain, 2009;10:354-68 12. Dreyfuss P, Michelsen M, Pauza K, et al. The value of medical history and physical examination in diagnosing sacroiliac joint pain. Spine (Phila Pa 1976), 1996;21:2594-602 13. McGrath MC. Composite sacroiliac joint pain provocation tests: A question of clinical significance. Int J Osteopath Med, 2010;13:24-30 14. Fryer G, Morse CM, Johnson JC. Spinal and sacroiliac assessment and treatment techniques used by osteopathic physicians in the United States. Osteopath Med Prim Care, 2009;3:4 15. Hansen HC, Helm S. Sacroiliac joint pain and dysfunction. Pain Physician, 2003;6:179-90 16. Zeile BA, Gruen GS, Brown S, George S. Sacroiliac joint dysfunction: Evaluation and management. Clin J Pain, 2005;21:446-55 17. Al-Khayer A, Greivillt MP. The sacroiliac joint: An underestimated cause for low back pain. J Back Musculoskelet Rehabil, 2007;20:135-41 18. van der Wurff P, Hagmeijer RH, Meyne W. Clinical tests of the sacroiliac joint: A systematic methodological review. Part 1: Reliability. Manual Ther, 2000;5:30-36 19. van der Wurff P, Meyne W, Hagmeijer RH. Clinical tests of the sacroiliac joint: A systematic methodological review: Part 2: Validity. Manual Ther, 2000;5:89-96 20. Stuber KJ. Specificity, sensitivity, and predictive values of clinical tests of the sacroiliac joint: A systematic review of the literature. J Can Chiropr Assoc, 2007;51:30-41 21. Bussey MD, Bell ML, Milosavljevic S. The influence of hip abduction and external rotation on sacroiliac motion. Manual Ther, 2009;14:520-25 22. Bussey MD, Milosavljevic S, Bell ML. Sex differences in the pattern of innominate motion during passive hip abduction and external rotation. Manual Ther, 2009;14:514-19 23. Adhia DB, Bussey MD, Mani R, et al. Inter-tester reliability of non-invasive technique for measurement of innominate motion. Manual Ther, 2012;17:71-76 24. Bussey MD, Milosavljevic S. Can innominate motion be used to identify persons with ankylosing spondylitis? A pilot study. Manual Ther, 2013;18:118-23 25. Adhia DB, Milosavljevic S, Tumilty S, Bussey MD. Innominate movement patterns, rotation trends and range of motion in individuals with low back pain of sacroiliac joint origin. Manual Ther, 2016;21:100-8 26. Bussey MD, Yanai T, Milburn P. A non-invasive technique for assessing innominate bone motion. Clin Biomech, 2004;19:85-90 27. Adhia D, Tumilty S, Mani R, et al. Can hip abduction and external rotation discriminate sacroiliac joint pain? Manual Ther, 2016;21:191-97 28. Cibulka MT, Sinacore DR, Cromer GS, Delitto A. Unilateral hip rotation range of motion asymmetry in patients with sacroiliac joint regional pain. Spine (Phila Pa 1976), 1998;23:1009-15	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 1752, 1 ], [ 1752, 7400, 2 ], [ 7400, 11619, 3 ], [ 11619, 15962, 4 ], [ 15962, 19208, 5 ], [ 19208, 25484, 6 ], [ 25484, 26956, 7 ] ] }
9f4a21c189791e0c443ac0266173c741cc8e4215	{ "olmocr-version": "0.1.59", "pdf-total-pages": 28, "total-fallback-pages": 0, "total-input-tokens": 85541, "total-output-tokens": 15676, "fieldofstudy": [ "Mathematics" ] }	Phase transitions in an exactly soluble one-dimensional exclusion process G. Schütz\textsuperscript{1} AND E. Domany\textsuperscript{2} \textsuperscript{1} Department of Physics, Weizmann Institute, Rehovot 76100, Israel \textsuperscript{2} Department of Electronics, Weizmann Institute, Rehovot 76100, Israel We consider an exclusion process, with particles injected with rate $\alpha$ at the origin and removed with rate $\beta$ at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to the right only. For the special case of $\alpha = \beta = 1$ the model was solved previously by Derrida et al. Here we extend the solution to general $\alpha, \beta$. The phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation. Key words: asymmetric exclusion process, steady state, boundary induced phase transitions 1 Introduction One-dimensional asymmetric exclusion models \cite{1} are of interest for various reasons. They are closely related to vertex models \cite{2}, growth models \cite{3} and, in the continuum limit, the KPZ equation \cite{4} and the noisy Burgers’s equation. Various types of phase transitions occur as a consequence of the interplay of particle transport with a localized defect or inhomogeneity. Suitably chosen boundary conditions can represent the effect of such a defect in an otherwise homogenous system. Such transitions have been the focus of many recent studies \cite{1,5-9}. Some of these models could be solved exactly and allow for a detailed study of their steady state properties such as the density profile or density correlations \cite{1,7,8,9}. Totally asymmetric simple-exclusion models with nearest neighbour hopping can be divided into four classes according to the dynamics (sequential or parallel) and the choice of boundary conditions (open or periodic). In all these models each lattice site $i$ in a chain of $N$ sites is either occupied by a single particle ($\tau_i = 1$) or empty ($\tau_i = 0$) and a particle can hop to the neighbouring site in one direction if this site is empty.\footnote{A model with two different kinds of particles and nearest neighbour hopping has been studied in \cite{10}, a simple-exclusion model where particles can hop over several lattice sites in each time step is discussed in \cite{11}.} By convention, we choose the direction of hopping as to the right. The dynamics can be chosen either sequential as in refs. \cite{1,5,6,8} or parallel \cite{2,7,9}. In the case of sequential dynamics which we study in this paper particles jump independently and randomly in each time step according to the following rules: At each time step $t \to t + 1$ one chooses at random one pair of sites $(i, i + 1)$ with $1 \leq i \leq N - 1$. If there is a particle on site $i$ and site $i + 1$ is empty, then the particle will jump from $i$ to $i + 1$. All other configurations do not change, i.e., \[ \tau_i(t + 1) = \tau_i(t)\tau_{i+1}(t) \] \[ \tau_{i+1}(t + 1) = \tau_{i+1}(t) + (1 - \tau_{i+1}(t))\tau_i(t) . \] (1.1) In the case of parallel updating the lattice is divided into neighbouring pairs of sites and some stochastic hopping rules are applied in parallel to each pair in a first half time step. In the second half time step the pairs are shifted by one lattice unit and the same rules are applied again [2, 7, 9]. Both models can be defined with either periodic or open boundary conditions. When periodic boundary conditions are used, a non-trivial phase diagram can be observed by introducing, for example, a single defect [6, 7]. With open boundary conditions particles are injected with rate $ \alpha $ at the left boundary (which we shall call the origin), and absorbed with rate $ \beta $ at the right boundary [1, 5, 8, 9]. Injection and absorption are implemented in the following way: when one considers the pair $(0,1)$ where site 0 represents the origin, then the occupation number $ \tau_1(t + 1) $ of site 1 at time $ t + 1 $ is given by \[ \tau_1(t + 1) = 1 \text{ with probability } \tau_1(t) + \alpha(1 - \tau_1(t)) \] \[ \tau_1(t + 1) = 0 \text{ with probability } (1 - \alpha)(1 - \tau_1(t)) . \] (1.2) On the other hand, considering the pair $(N, N+1)$ where site $N+1$ represents the (right) boundary, the occupation number $ \tau_N(t + 1) $ at site $N$ after one time step is \[ \tau_N(t + 1) = 1 \text{ with probability } (1 - \beta)\tau_N(t) \] \[ \tau_N(t + 1) = 0 \text{ with probability } 1 - (1 - \beta)\tau_N(t) . \] (1.3) The model defined by eqs. (1.1) - (1.3) can be viewed as a homogeneous system connected to a reservoir of fixed particle density $ \alpha $ at the origin and fixed density $ 1 - \beta $ at the boundary. The model with parallel dynamics and periodic boundary conditions with a defect [7] was solved by the Bethe ansatz. Recently some steady state properties of the model with parallel dynamics and open boundary conditions were also found [9]. The Bethe ansatz was used also to solve the model with sequential updating [11] and translationally invariant periodic boundary conditions without defect [12]. The case of sequential dynamics with open boundary conditions was studied by Krug [5] and by Derrida et al [1]. Krug studied numerically the steady state behavior of this model on the line $\beta = 1$ (Fig. 1). He found, at $\alpha = 1/2$, a phase transition and an associated diverging length scale [5]. For $\alpha < 1/2$ he found an exponential decay of the profile to its bulk value with increasing distance $r$ from the boundary, while for $\alpha > 1/2$ the profile decayed as $r^{-1/2}$. Derrida et al [1] expressed the exact steady state and the steady state density distribution for arbitrary $\alpha$ and $\beta$ in terms of recursion relations (eqs. (2.9) - (2.11) below). These recursions were solved explicitly only for $\alpha = \beta = 1$. For this case they showed that the density profile approaches algebraically its bulk value $\rho_{\text{bulk}} = 1/2$ with increasing distance $x$ from the origin, $\rho - 1/2 \sim x^{-1/2}$. The same behavior characterizes the approach of $\rho_{\text{bulk}}$ from below as $r^{-1/2}$, with increasing distance $r$ from the boundary, confirming the numerical result of Krug. The phase diagram in the whole $\alpha - \beta$ plane was obtained in [1] by a mean field calculation. Three phases were identified (Fig. 1). In a low density phase $A$, found for $\alpha < \beta$ and $\alpha < 1/2$, the density profile approaches $\rho_{\text{bulk}} = \alpha$ exponentially with $r$. This supports Krug’s observation of an exponential behaviour for $\beta = 1$, $\alpha < 1/2$. A high density phase $B$ was found for $\alpha > \beta$, $\beta < 1/2$, which is related to the low density phase by a particle-hole symmetry. Here the profile approaches $\rho_{\text{bulk}} = 1 - \beta$ exponentially with $x$, the distance from the origin. Finally, for $\alpha, \beta > 1/2$ the system is in the maximal current phase $C$. In this phase mean field predicts a power law for Figure 1: Mean field phase diagram of the model in the $\alpha - \beta$ plane as obtained in [1]. Region A is the low density phase, region B the high density phase and region C is the maximal current phase. The phases are separated by the curves $\alpha = \beta < 1/2$ and $\alpha = 1/2, \beta > 1/2$ and $\beta = 1/2, \alpha > 1/2$ respectively. The sign of the slope of the density profile (as shown in the insets) changes when the line $\alpha = 1 - \beta$ is crossed. Note that this is not a phase transition line. the profile, with exponent $\kappa = 1$, whereas the exact result \cite{1} yields $\kappa = 1/2$. Here we present the exact solution to the recursion relations giving the steady state and the density profile for arbitrary values for $\alpha$ and $\beta$. We show that the phase diagram has a richer structure than that predicted by mean field. In particular, we show that there is a phase transition with an associated diverging length scale along the two lines, $\alpha = 1/2$ and $\beta = 1/2$, dividing both the low density phase and the high density phase found in the mean field calculation into two different phases. In the low density phase $A_1$ defined by $\alpha < \beta < 1/2$ the profile is exponential, as predicted by the mean field calculation. The situation is different, however, in the low density phase $A_H$, defined by $\alpha < 1/2$ and $\beta > 1/2$; there the profile approaches $\rho_{\text{bulk}} = \alpha$ as $r^{-3/2} \exp(-r/\xi)$ for $r \gg 1$. This was expected neither from the mean field approach nor from the numerical results of Krug. The paper is organized as follows. In sec. 2 we present the recursion relations obtained in \cite{1} and give an exact solution for arbitrary $\alpha$ and $\beta$. In sec. 3 we draw some conclusions from these results and derive the exact phase diagram. Then we study the density profile in the various phases for large systems (sec. 4) and in sec. 5 discuss in detail the various phase transitions that were identified. 2 Exact solution of the recursion relations The steady state of the model defined in eqs. (1) - (3) is given in terms of the quantities $P_N(\tau_1, \tau_2, \ldots, \tau_N)$ which are the probabilities of finding the specific configuration of particles represented by the occupation numbers $(\tau_1, \tau_2, \ldots, \tau_N)$ on the chain with $N$ sites. It turns out to be more convenient to work with unnormalized probabilities $f_N(\tau_1, \tau_2, \ldots, \tau_N)$ related to \[ P_N(\tau_1, \tau_2, \ldots, \tau_N) \text{ by} \] \[ P_N(\tau_1, \tau_2, \ldots, \tau_N) = f_N(\tau_1, \tau_2, \ldots, \tau_N)/Z_N \tag{2.1} \] where \[ Z_N = \sum_{\tau_1=0,1} \cdots \sum_{\tau_N=0,1} f_N(\tau_1, \tau_2, \ldots, \tau_N). \tag{2.2} \] As shown in [1] all the $ f_N(\tau_1, \tau_2, \ldots, \tau_N) $ can be obtained recursively from the corresponding quantities in a system with $ N - 1 $ sites (eqs. (8) and (9) of ref. [1]). Here we are interested only in the average occupation number $ \langle \tau_i \rangle_N $ of site $ i $ in a system of length $ N $, given by \[ \langle \tau_i \rangle = T_{N,i}/Z_N \tag{2.3} \] with \[ T_{N,i} = \sum_{\tau_1=0,1} \cdots \sum_{\tau_N=0,1} \tau_i f_N(\tau_1, \tau_2, \ldots, \tau_N). \tag{2.4} \] The normalization $ Z_N $ and the unnormalized particle density $ T_{N,i} $ can be computed from the quantities \[ Y_{N,K} = \sum_{\tau_1=0,1} \cdots \sum_{\tau_N=0,1} (1 - \tau_N)(1 - \tau_{N-1}) \cdots (1 - \tau_K) f_N(\tau_1, \tau_2, \ldots, \tau_N) \tag{2.5} \] and \[ X_{N,K}^p = \sum_{\tau_1=0,1} \cdots \sum_{\tau_N=0,1} (1 - \tau_N) \cdots (1 - \tau_K) \tau_p f_N(\tau_1, \tau_2, \ldots, \tau_N) \tag{2.6} \] by defining \[ Y_{N,N+1} = Z_N \tag{2.7} \] and \[ X_{N,N+1}^p = T_{N,p}. \tag{2.8} \] (Note that we made a slight change in notation as compared to ref. [1].) There the quantities$ Y_{N,K} $ were denoted $ Y_N(K) $ and the quantities $ X_{N,K}^p $ were denoted $ X_N(K,p) $. The reason for the introduction of $ Y_{N,K} $ for $ 1 \leq K \leq N+1 $ and $ X_{N,K}^p $ for $ p+1 \leq K \leq N+1 $ is that they can be obtained from the following closed recursions [1] \[ \begin{align} Y_{N,1} &= \beta Y_{N-1,1} \\ Y_{N,K} &= Y_{N,K-1} + \alpha \beta Y_{N-1,K} \quad \text{for } 2 \leq K \leq N \\ Y_{N,N+1} &= Y_{N,N} + \alpha Y_{N-1,N} \end{align} \] with the initial condition \[ \begin{align} Y_{1,1} &= \beta \\ Y_{1,2} &= \alpha + \beta . \end{align} \] These recursions can be simplified somewhat by extending the range of definition of $ K $ to $ 1 \leq K \leq N+2 $. If we set $ K = N+1 $ in the second of eq. (2.9), the resulting equation is precisely the third of (2.9), provided we use the extended definition $ Y_{N-1,N+1} = \beta^{-1} Y_{N-1,N} $ for $ \beta \neq 0 $. Similarly, eqs. (2.10) become a consequence of (2.9) by redefining the initial condition as $ Y_{0,1} = 1 $. These extensions of the definitions of the quantities $ Y_{N,K} $ are useful in some of the calculations presented below. Once the $ Y_{N,K} $ are determined, the $ X_{N,K}^p $ can be obtained from the recursion relations [1] \[ \begin{align} X_{N,K}^p &= X_{N,K-1}^p + \alpha \beta X_{N-1,K}^p \quad \text{for } p+2 \leq K \leq N \\ X_{N,N+1}^p &= X_{N,N}^p + \alpha X_{N-1,N}^p \quad \text{for } 1 \leq p \leq N-1 \end{align} \] with the initial condition \[ X^p_{N,p+1} = \alpha \beta Y_{N-1,p+1} \quad \text{for } 1 \leq p \leq N \tag{2.12} \] where we used the extended definitions $ Y_{0,1} $ and $ Y_{N,N+2} $ of the $ Y_{N,K} $. Solving these recursion relations gives the exact average occupation numbers $ \langle \tau_i \rangle $ through eqs. (2.3), (2.7) and (2.8). This was done in ref. [1] for $ \alpha = \beta = 1 $. Here we present the solution for arbitrary $ \alpha $ and $ \beta $. For a solution of these recursion relations and initial conditions define the functions $ G_{N,K}^M(x) $ by \[ G_{N,K}^M(x) = \sum_{r=0}^{M-1} b_{N,K}(r)x^r \quad (N \geq 1) \tag{2.13} \] with \[ b_{N,K}(r) = \binom{K-2+r}{K-2} - \binom{K-2+r}{N}. \tag{2.14} \] For later convenience also define $ b_{0,1}(0) = G_{0,0}^1 = G_{0,1}^1 = 1 $. As a result of the symmetries of the coefficients $ b_{N,K}(r) $ these functions satisfy various relations given in the appendix. In particular, from the recursion relations (A.3) and the special values (A.4) one can show that the quantity \[ Y_{N,K}(\alpha, \beta) = \beta^N G_{N,K}^N(\alpha) + \sum_{s=0}^{K-2} \alpha^{N-s} \beta^{N-K+1+s} G_{N,N}^{s+1}(\alpha) \tag{2.15} \] solves the recursion relations eq. (2.9) with the initial conditions (2.10). Relations (2.11) with initial condition (2.12) are satisfied by \[ X^p_{N,K}(\alpha, \beta) = \sum_{r=0}^{N-p} b_{N-p,K-r}(r)\alpha^{r+1} \beta^{r+1} Y_{N-r-1,p+1}(\alpha, \beta) + \] \[ \beta^{N-K+2} \sum_{r=0}^{K-p-2} \alpha^{N+1-p-r} G_{N-p,N-p}^{K-p-1-r}(\beta) Y_{p-1+r,p+1}(\alpha, \beta). \tag{2.16} \] Using the first of equations (A.4), one obtains from this \[ Z_N = Y_{N,N+1} = \sum_{s=0}^{N} \beta^s \alpha^{N-s} G_{s,N}^{s+1}(\alpha) \] and after some computation, involving relabeling of indices, we get \[ T_{N,p} = X_{N,N+1}^p = \alpha \beta \sum_{s=0}^{N-p} \alpha^s G_{N-p,N-p}^{s+1}(\beta) Y_{N-s-1,p+1}(\alpha, \beta). \] This expression is exact for any $N \geq 1, 1 \leq p \leq N$. Substitution in (2.3) gives the exact density profile for arbitrary $\alpha$ and $\beta$. Eqs. (2.17) and (2.18) provide also an exact expression for the conserved current $j = \langle \tau_i \rangle - \langle \tau_i\tau_{i+1} \rangle = \text{const.}$, and consequently, for the correlation function $\langle \tau_i\tau_{i+1} \rangle$. To see this, note that taking $i = N$ one obtains $\langle \tau_N\tau_{N+1} \rangle = (1 - \beta)\langle \tau_N \rangle$ since site $N+1$ represents the reservoir of constant density $1 - \beta$. Therefore one has \[1\] \[ j = \beta \langle \tau_N \rangle. \] On the other hand, taking $i = 0$ one gets $\langle \tau_0\tau_1 \rangle = \alpha \langle \tau_1 \rangle$ since site 0 is the reservoir of constant density $\alpha$. Thus we also have \[1\] \[ j = \alpha (1 - \langle \tau_1 \rangle). \] Since, however, our exact result yields $\langle \tau_i \rangle$ for any $i$, we can calculate the exact current $j$, and hence $\langle \tau_i\tau_{i+1} \rangle$. 3 Discussion of the density profile In order to analyse the density, it is convenient to study the quantity \[ t_N(p) = (T_{N,p+1} - T_{N,p})/Z_N \] which becomes the spatial derivative of the density profile in the continuum limit. It turns out to be given by $(p \neq N)$ \[ t_N(p) = (1 - \alpha - \beta)\beta^p G_{N-p,N-p}^N(\beta)^{\alpha^{-p}} G_{p,p}^p(\alpha) / Z_N. \] which for $\alpha \neq 1 - \beta$ can be more conveniently written in the form \[ t_N(p) = F_p(\alpha) F_{N-p}(\beta) / \tilde{Z}_N \] with \[ F_N(x) = x^{-N-1} G_{N,N}^N(x) \] and \[ \tilde{Z}_N = \frac{Z_N}{(1 - \alpha - \beta)\alpha^{N+1} \beta^{N+1}} = \left\{ \begin{array}{ll} \frac{F_N(\beta) - F_N(\alpha)}{\alpha(1 - \alpha) - \beta(1 - \beta)} & \alpha \neq \beta, 1 - \beta \\ - \frac{F'_N(\beta)}{1 - 2\beta} & \alpha = \beta \neq \frac{1}{2} \end{array} \right. \] where the prime denotes the derivative w.r.t. $\beta$. The last of the two eq. (3.5) can be obtained by changing the order of summation in (2.17). For $\alpha = 1 - \beta$ one obtains directly from (3.2) that $t_N(p) = 0$, i.e., the profile is constant on this curve. This result was already obtained in [1]. From (3.3) we learn that up to the amplitude $\tilde{Z}$, the derivative $t_N(p)$ of the density profile can be written as a product of two functions; one of $\alpha$ and the other of $\beta$: $t_N(p) \propto F_p(\alpha) F_{N-p}(\beta)$. This fact has important and surprising consequences. It clearly implies that phase transitions (i.e. non-analytic changes in the $p$-dependence of the density profile) can occur on two kinds of lines: $\alpha = \alpha_c$ and $any \ \beta$, or $\beta = \beta_c$ and $any \ \alpha$. Hence if a phase transition is predicted to occur on the $\beta > 1/2$ segment of the line $\alpha = 1/2$ (the mean field transition to the maximal current phase), then the transition must extend to the $\beta < 1/2$ regime as well! This means that instead of a single high density phase $B$, predicted by mean field, there are, in fact, two such phases. Indeed, analysis of the function $F_p(x)$, presented below, reveals that its dependence on $p$ changes at $x = 1/2$. Similar considerations hold for the line $\beta = 1/2$ and $\alpha < 1/2$, which separates the low density phase $A$ into two distinct phases (Fig. 2). These new transitions were not found by the mean field calculation. Another unexpected consequence of the separability into a product is the existence of two independent length scales in the model, one determined by the injection rate $\alpha$, the other one by the absorption rate $\beta$. This is surprising, as one might believe that only the larger of these two quantities determines the behaviour of the system. In fact, as long as the system is not in the maximal current phase, this indeed is the case as far as the current $j = \langle \tau_i \rangle - \langle \tau_i \tau_{i+1} \rangle$ is concerned: In the continuum limit one has $j = \beta (1 - \beta)$ for $\alpha > \beta$, $\beta < 1/2$, and $j = \alpha (1 - \alpha)$ for $\beta > \alpha$, $\alpha < 1/2$, (whereas $j = 1/4$ if both $\alpha$ and $\beta$ are larger than $1/2$). Since in the mean field calculation the shape of the density profile is determined by only the current, phase transitions are seen neither at $\alpha = 1/2$, $\beta < 1/2$, nor at $\beta = 1/2$, $\alpha < 1/2$. Prior to presenting an explanation for the unexpected existence of the additional phases and phase transitions, we study the density profile in the thermodynamic limit $N \to \infty$. 4 Density profile in the large $N$ limit We want to discuss the density profile of a large system ($N \gg 1$) as a function of the space coordinate $p$, at large distances from both ends, i.e., we consider $p \gg 1$ and $r = N - p \gg 1$. So we need an asymptotic expression for $F_L(x)$ for large $L$. Splitting $F_L(x)$ into two pieces $F_L^{(1)}(x)$ and $F_L^{(2)}(x)$ as in eq. (A.11) allows for an expansion in $1/L$. For $x < 1/2$ the dominating contribution is Figure 2: Exact phase diagram of the model in the $\alpha - \beta$ plane. The low (high) density phase shown in Fig. 1 is divided into two phases $A_I$ and $A_{II}$ ($B_I$ and $B_{II}$) along the curve $\beta = 1/2$ ($\alpha = 1/2$). since $F_L^{(2)} / F_L^{(1)} \propto \exp(-aL)$ with some constant $a$: $$F_L(x) = \frac{1 - 2x}{(x(1-x))^{L+1}} \left( 1 + O(e^{-aL}) \right) \quad x < \frac{1}{2} \quad (4.1)$$ If $x > 1/2$ then $F_L^{(1)} = 0$ and up to order $1/L$ $$F_L(x) = \frac{c_L}{(1 - 2x)^2} \left( 1 + O(L^{-1}) \right)$$ $$= \frac{4^L}{(1 - 2x)^2 \sqrt{\pi} L^{3/2}} \left( 1 + O(L^{-1}) \right) \quad x > \frac{1}{2} \quad (4.2)$$ This expression diverges for $x \to 1/2$. For $x = 1/2$ one obtains (see (A.14)) $$F_L(x) = 2 \frac{4^L}{\sqrt{\pi} L} \left( 1 + O(L^{-1}) \right) \quad (4.3)$$ Using the expansions eqs. (4.1) - (4.3) and the expression (3.5) for the normalization $\tilde{Z}_N$ one can compute the shape of the density profile given by $t_N(p)$. We define a length scale $\xi_\sigma$ by $$\xi_\sigma^{-1} = -\log(4\sigma(1-\sigma)). \quad (4.4)$$ As $\sigma$ reaches 1/2, $\xi_\sigma$ diverges. For the various phases $A_1$ - $C$ (Fig. 2) one finds in the large $N$ limit (such that $1 \ll p$, $1 \ll N - p$, i.e., $p$ is far from both ends of the system) the following results: High density phase $B_1$: This phase is defined by the region $\beta < \alpha < 1/2$. From the expansion (4.1) one finds an exponential decay of the density profile with a exponential decay with length scale $\xi^{-1} = \xi_\alpha^{-1} - \xi_\beta^{-1}$, $$ t_N(p) = (1 - 2\alpha) \left(1 - \frac{4\beta(1 - \beta)}{4\alpha(1 - \alpha)}\right) \left(\frac{4\beta(1 - \beta)}{4\alpha(1 - \alpha)}\right)^p = (1 - 2\alpha) \left(1 - \frac{4\beta(1 - \beta)}{4\alpha(1 - \alpha)}\right) e^{-p/\xi}. $$ The density approaches its bulk value $\rho_{\text{bulk}} = 1 - \beta$ from below. One has $j = \beta(1 - \beta)$ and from (2.20) $\langle \tau_1 \rangle = 1 - \beta(1 - \beta)/\alpha < 1 - \beta = \langle \tau_N \rangle$. Transition line from high density phase B_I to high density phase B_{II}: On approaching $\alpha = 1/2$ from below in the region $\beta < 1/2$, we find that $\xi_\alpha$ diverges but $\xi_\beta$ remains finite. For $\alpha = 1/2$ the slope of the profile is of the form $$ t_N(p) \sim p^{-z_\alpha} e^{-p/\xi_\beta}. $$ The values of the length scale $\xi_\beta$ and the exponent $z_\alpha$ can be read off the exact expression (4.3) which for large $N$ becomes $$ t_N(p) = \frac{(1 - 2\beta)^2 (4\beta(1 - \beta))^p}{2\sqrt{\pi} p^{1/2}} = \frac{(1 - 2\beta)^2}{2\sqrt{\pi}} p^{-1/2} e^{-p/\xi_\beta}. $$ The current and the boundary values are given by the same expressions as in the high density phase I. High density phase $B_{II}$: On crossing the phase transition line into the high density phase $B_{II}$ defined by $\alpha > 1/2$ and $\beta < 1/2$, the decay exponent changes to $z_\alpha = 3/2$ (see eq. (4.2)) and one obtains $$t_N(p) = \frac{(1 - \alpha - \beta)(\alpha - \beta)(4\beta(1 - \beta))p}{(1 - 2\alpha)^2 \sqrt{\pi} p^{3/2}}$$ $$= \frac{(1 - \alpha - \beta)(\alpha - \beta)}{(1 - 2\alpha)^2 \sqrt{\pi}} p^{-3/2} e^{-p/\xi_\beta} .$$ (4.8) The current and the boundary values are given by the same expressions as in the high density phase I, but note that the slope of the profile changes sign on the curve $\alpha = 1 - \beta$. Along this curve the density is constant, $\langle \tau_i \rangle = \rho_{bulk} = 1 - \beta$ for $1 \leq i \leq N$. For $\alpha > 1 - \beta$ the slope is negative. Transition from high density phase $B_{II}$ to the maximal current phase $C$: When $\beta$ reaches the critical value $1/2$ in the region $\alpha > 1/2$, $\beta \leq 1/2$, then also $\xi_\beta$ diverges and the slope of the profile is given by $$t_N(p) = -\frac{1}{4\sqrt{\pi}}(1 - \frac{p}{N})^{-1/2} p^{-3/2} .$$ (4.9) Near the origin ($1 \ll p \ll N$) we can neglect the piece with $p/N$ in (4.3), so the slope is dominated by $p^{-z_\alpha}$ with $z_\alpha = 3/2$. In the boundary region ($p = N - r$, $1 \ll r \ll N$) the shape of the profile is determined by $r^{-z_\beta}$ with $z_\beta = 1/2$, but the amplitude of $t_N(r)$ is only of order $1/N$. Therefore, up to corrections of order $1/N$, the profile near the boundary is flat, whereas it decays as $p^{-1/2}$ with the distance $p$ from the origin to its bulk value $\rho_{\text{bulk}} = 1/2$. The current reaches its maximal value $j = 1/4$ and one finds $\langle \tau_N \rangle = \rho_{\text{bulk}} = 1/2$ and $\langle \tau_1 \rangle = 1 - 1/(4\alpha)$. Maximal current phase: If $\beta > 1/2$ and $\alpha > 1/2$, the derivative $t_N(p)$ depends neither on $\alpha$ nor on $\beta$. Near the origin and near $N$ the slope of the profile is determined by $z_\alpha = z_\beta = 3/2$: $$t_N(p) = -\frac{1}{4\sqrt{\pi}}(1 - p/N)^{-3/2}p^{-3/2}$$ \hspace{1cm} (4.10) Therefore the density approaches its bulk value $\rho_{\text{bulk}} = 1/2$ as $p^{-1/2}$ with the distance $p$ from the origin from above and as $r^{-1/2}$ with the distance $r = N - p$ from the boundary from below. The current takes its maximal value $j_{\text{max}} = 1/4$ throughout the phase and one obtains $\langle \tau_N \rangle = 1/(4\beta)$ and $\langle \tau_1 \rangle = 1 - 1/(4\alpha)$. Low density phase $A_1$: This phase is defined by $\alpha < \beta < 1/2$ and is related to the high density phase $B_1$ by a particle-hole symmetry and therefore the decay is exponential. One finds $$t_N(p) = (1 - 2\beta) \left(1 - \frac{4\alpha(1 - \alpha)}{4\beta(1 - \beta)}\right) \left(\frac{4\alpha(1 - \alpha)}{4\beta(1 - \beta)}\right)^{N-p}$$ $$= (1 - 2\beta) \left(1 - \frac{4\alpha(1 - \alpha)}{4\beta(1 - \beta)}\right) e^{-r/\xi}$$ \hspace{1cm} (4.11) with a length scale $\xi^{-1} = \xi_\alpha^{-1} - \xi_\beta^{-1}$ and $r = N - p \gg 1$. The density approaches its bulk value $\rho_{\text{bulk}} = \alpha$ from above. The current is given by $j = \alpha(1 - \alpha)$ and therefore according to (2.19) $\langle \tau_N \rangle = \alpha(1 - \alpha)/\beta > \alpha = \langle \tau_1 \rangle$. Low density phase $A_{\text{II}}$: The profile in this regime ($\beta > 1/2, \alpha < 1/2$) is obtained from (4.8) by exchanging $\alpha$ and $\beta$ and substituting $p$ by $r = N - p$. This is a result of the particle-hole symmetry of the model. In the same way one obtains the profile on the phase transition lines from $A_I$ to $A_{\text{II}}$ and from $A_{\text{II}}$ to $C$ out of the profiles on the phase transition lines from $B_I$ to $B_{\text{II}}$ and $B_{\text{II}}$ to $C$ respectively. Coexistence line: If $\alpha = \beta < 1/2$ both $\xi_\alpha$ and $\xi_\beta$ are finite, but since $\xi_\alpha = \xi_\beta$, one gets $\xi^{-1} = 0$. As a result one finds a linear profile with a positive slope $$t_N(p) = (1 - 2\alpha)/N.$$ \hfill{(4.12)} The current is given by $j = \alpha(1 - \alpha)$ and one has $\langle \tau_1 \rangle = \alpha$ and $\langle \tau_N \rangle = 1 - \alpha$. 5 Discussion of the phase diagram We turn now to discuss the various phases and the transitions between them on a more physical, intuitive basis. First we consider the case $\beta = 1$. This situation corresponds to connecting the system to a reservoir of fixed density. $ \rho_0 = \alpha $ at the origin, and another "reservoir" with $ \rho_{N+1} = 1 - \beta = 0 $ at the boundary. We will consider the limit $ N \to \infty $, and ask what are the possible steady state density profiles that the system can have, and which interpolate between the two limiting values $ \rho_0 $ and $ \rho_{N+1} $. Let us start with $ \alpha < 1/2 $, and try a density profile $(a)$ that approaches (for $ 1 \ll x \ll N $) a constant bulk value $ \rho < \alpha $, before it decays to $ \rho_{N+1} = 0 $. We now show that such a profile cannot be a steady state. To see this, note that in a bulk region with constant density there are no correlations (the steady state factorizes into a product measure) and therefore the current in the bulk is given by $ j = \rho(1 - \rho) $; whereas at the origin it is $ j_0 = \alpha(1 - \rho_1) $, where $ \rho_1 $, the density at $ x = 1 $, satisfies $ 1/2 > \alpha \geq \rho_1 \geq \rho $. If we can show that $ j_0 > j $, particles accumulate between the origin and the bulk, and hence the density is not stationary. Clearly, for $ \rho_1 = \rho $ we have $ j_0 = \alpha(1 - \rho) > \rho(1 - \rho) = j $ since $ \alpha > \rho $. On the other hand, for $ \rho_1 = \alpha $ we have $ j_0 = \alpha(1 - \alpha) > \rho(1 - \rho) = j $ for $ 1/2 > \alpha > \rho $. Hence $ j_0 > j $ at the two endpoints of the interval $[\rho, \alpha]$ to which $ \rho_1 $ is limited; and since $ j_0 $ is a linear function of $ \rho_1 $, we must have $ j_0 > j $ for the entire interval. A different possible steady state profile $(b)$ is one with $ \alpha < \rho < 1/2 $. Here we can show that $ j_0 = \alpha(1 - \alpha) < \rho(1 - \rho) = j $: Under the present assumptions the density first interpolates between $ \alpha $ and $ \rho $, and hence $ \alpha < \rho_1 < \rho $, and as before, the relationship we wish to prove holds at both endpoints of this interval. If this holds, however, more particles leave the bulk than enter it, and $ \rho $ must decrease. Thus also $(b)$ cannot be a steady state. The last possibility of the kind considered, $(c)$, has $ \rho > 1/2 > \alpha $; we will return to this case later and show that for the presently used values of $ \alpha $ and $ \beta $ it cannot be a steady state profile either. The only remaining situation is the one in which $ \rho = \alpha $. Then, obviously, $ j_0 = \alpha(1 - \alpha) = j $. Hence the bulk steady state density must equal that of the reservoir. The assumption $\alpha < 1/2$ was crucial for our proof of this fact, which is no longer true if $\alpha > 1/2$. In that case the bulk density is, independently of $\alpha$, given by $\rho = 1/2$. To see this, we again assume all other possible values for the bulk steady statedensity, and rule out every other scenario. Let us start by assuming a decay to a bulk value $\rho < 1/2$; since, supposedly, we are in a steady state, we can choose some point $i$ at which $1/2 > \rho_i > \rho$ as a new initial point of fixed density $\alpha' = \rho_i$; $\alpha'$ plays now the role of $\alpha < 1/2$ of the previously discussed situation $(a')$, which, as we have shown, cannot be a steady state. Another possibility $(b')$ has $\alpha > \rho > 1/2$. In this case we recall that near $N$ the density profile must go from $\rho$ to $\rho_{N+1} = 0$. To rule this out, we view the site $N + 1$ as a reservoir of holes of fixed density $1$. The bulk with $\rho > 1/2$ corresponds to hole density $\rho_h = 1 - \rho < 1/2$; holes move to the left, and if we exchange the roles of holes and particles, this situation becomes precisely the case $(a')$ discussed above. Hence $(b')$ is not possible either.\footnote{Note that the situation (c) of the $\alpha < 1/2$ case, to which we promised to return, also requires that $\rho$ goes from $\rho > 1/2$ to $\rho_{N+1} = 0$, and therefore is ruled out in the same way as $(b')$.} We have just shown that for $\alpha > 1/2$ no steady state is possible with either bulk density $\rho < 1/2$ or $\rho > 1/2$; hence the only possibility left is $\rho_{\text{bulk}} = 1/2$. That is, for $\alpha > 1/2$ the bulk density is that one which supports the maximal current, irrespective of $\alpha$, the density of the reservoir. This explains the transition observed at $\alpha = 1/2$, from a low density phase with $\rho_{\text{bulk}} = \alpha$ to the maximal current phase, in which $\rho_{\text{bulk}} = 1/2$. For the sake of convenience we limited the previous discussion to the $\beta = 1$ line. We now show that the transition survives when we move off this line. Of the cases discussed above, $(a),(b)$ and $(a')$ were ruled out with no mention of the fact that $\beta = 1$. In case $(b')$ (and its equivalent, case $(c)$), we used a particle-hole symmetry to map the situation onto case $(a')$. Since there we had $\alpha > 1/2$, the same argument goes through for holes if $\beta > 1/2$; hence the same considerations give rise to the same phases as were obtained on the $\beta = 1$ line. This completes the picture for the regions $1/2 < \beta \leq 1$, and by particle-hole symmetry, for $1/2 < \alpha \leq 1$ as well. Note that in the low density phase $A_{II}$ with $\rho_{bulk} = \alpha$ the slope of the density profile changes sign on the curve $\alpha = 1 - \beta$. This can be understood as follows. The probability that a particle moves in the bulk (its average velocity) is $v = 1 - \alpha$, while the probability that it moves at the boundary is $v_N = \beta$. If $\beta > 1 - \alpha$ then $v_N > v$ and the system becomes depleted near the boundary because the current $j = \rho v$ is conserved. This corresponds the negative slope of the profile in this regime. On the other hand, if $\beta < 1 - \alpha$ one has $v_N < v$ and particles pile up. This leads to a positive slope. In the high density phase $B_{II}$ one finds the same result when comparing the velocity $v_0 = 1 - \alpha$ at the origin with the bulk velocity $v = \beta$. Next, we discuss the low density phase $A_{I}$, the high density phase $B_{I}$ in the region $0 < \alpha, \beta < 1/2$ and the transition between them. The bulk values in both phases and the slope of the profile can be derived in the same way as for the phases $A_{II}$ and $B_{II}$ . Note that in both phases one has $v_0 = 1 - \alpha > \beta = v_N$ and therefore the slope is always positive (particles pile up). The current is given by $$j = \min (\alpha(1 - \alpha), \beta(1 - \beta)) . \tag{5.1}$$ In order to understand the shape of the profile in phases $A_{I}$ and $B_{I}$ we assume that it is built up by a superposition of profiles with a constant density $\alpha$ up to some point $x_0$, followed by constant density $1 - \beta$. We call this sudden increase of the average density a domain wall since it separates a region of high density $1 - \beta$ from a region of low density $\alpha$. The picture we have 3We assume the width of this domain wall to be very small compared to the size of the system. in mind for this scenario is that particles injected with rate $\alpha$ at the origin move with constant average velocity $1 - \alpha > 1/2$ until they hit the domain wall where they get stuck and continue to move only with velocity $\beta < 1/2$. This region of high density is caused by the blockage introduced through the connection to the reservoir of density $1 - \beta$ at the boundary. Such a scenario is plausible, since constant densities $\alpha < 1/2$ starting from the origin and $1 - \beta > 1/2$ connected to the boundary are both stable situations of the system as discussed above. The probability $p(x) \propto \exp(-x/\xi)$ of finding this domain wall at position $x$ is determined by the length scale $\xi$ given by $\xi^{-1} = \xi_{\alpha}^{-1} - \xi_{\beta}^{-1}$ (see (4.5) and (4.11)). If $\alpha < \beta$ (low density phase) then particles are absorbed with a higher probability than they are injected and the probability of finding the domain wall decreases exponentially with increasing distance $r = N - x$ from the boundary. On the other hand, in the case where $\alpha > \beta$ (high density phase) the situation is reversed and $p(x)$ decreases with increasing distance from the origin. Averaging over all such profiles with the weight $p(x)$ leads to the observed exponential decay to the respective bulk value. This picture provides also a natural explanation of the linear profile on the transition line $\alpha = \beta$ where the absorption and injection probabilities are equal. Here $\xi$ diverges and the probability of finding the domain wall at $x$ is independent of $x$. Averaging over step functions with an equal weight for every position of the step clearly gives a linear profile. It is worth noting that the mean field calculation done in [1] gives a correct description of the phases $A_1$ and $B_1$, but it singles out the constituent step function with the domain wall located in the center as the profile on the phase transition line. We should mention that this analysis, in particular the use of the domain wall picture for a description the two phases and the phase transition line, is based on our studies of a similar exclusion process with open boundary conditions but parallel dynamics [2]. For this model we found phases of type $A_1$ and $B_1$ and a phase transition separating them. as in the system with sequential dynamics studied here. A careful study of the equal time correlation functions leads to our interpretation in terms of domain walls. As the transition lines to the the phases $A_{II}$ or $B_{II}$ are approached, this picture becomes invalid. Finally we briefly discuss the phase transition from the high density phase $B_I$ to the high density phase $B_{II}$. On approaching $\alpha = 1/2$ (but $\beta < 1/2$) the length scale $\xi_\alpha$ diverges while $\xi_\beta$ remains finite. As a result neither the bulk density nor the way how the bulk density is approached depends on $\alpha$ (except for the trivial fact that the density at the origin and consequently the amplitude of the profile depend on $\alpha$). The decay to the bulk density $\rho_{bulk} = 1 - \beta$ is determined by $\xi_\beta$ alone. Similarly the current does not depend on $\alpha$, being $j = \beta(1 - \beta)$. A description of phase $B_{II}$ also in terms of constituent profiles is appealing at first sight, but it is less convincing since a constant profile of density $\alpha > 1/2$ at the origin is not a stable situation. In order to get a more intuitive insight regarding this phase transition, we consider again the transition from the low density phase $A_{II}$ to the maximal current phase on the line $\alpha = 1/2$ but $\beta > 1/2$. In the maximal current phase $C$ the bulk density and the way how it is approached does not depend on $\alpha$ whereas in the low density phase $A_{II}$ $\alpha$ does determine the bulk density and how the profile decays to it. This is obviously due to the fact that if $\alpha > 1/2$ the particles close to the origin block each other rather than flowing away. As a result, the information corresponding to a change in the injection rate does not penetrate into the system. Clearly this description of the effect of $\alpha$ increasing beyond $1/2$ on the transition from the low density phase $A_I$ to the maximal current phase does not depend on the absorption at the boundary and is therefore also applicable to the transition from phase $B_I$ to phase $B_{II}$. \[^4\] As a result of the particle-hole symmetry of the problem, the discussion of the transition from the low density phase $A_I$ to the low density phase $A_{II}$ proceeds along analogous lines. We conclude that the phase transitions to the maximal current phase from the phase $A_{II}$ (or $B_{II}$) is of the same nature as the phase transition from $B_I$ to $B_{II}$ (or from $A_I$ to $A_{II}$). These transitions are caused by reaching the maximal transport capacity of the system at the origin (or boundary) and result in the divergence of the corresponding length scale determining the shape of the profile. Note that in our explanation it was necessary to take into account local correlations rather than only the current. This is the reason why these phase transitions are not found in the mean field calculation. As opposed to these transitions, the one at $\alpha = \beta$ that takes the system from the low density phase $A_I$ to the high density phase $B_I$ is caused by the building up of domain walls. Such a wall is generated by the inhomogeneity forced on the system by being connected to two reservoirs of different densities. At the transition line the wall can be anywhere with equal probability. The “coexistence” of low and high density regions is known to occur also in other systems with such an inhomogeneity [6, 7, 9, 10]. Note added: After completion of this work we received a preprint by B. Derrida, M.R. Evans, V. Hakim and V. Pasquier, who solved the same problem by a different method. Acknowledgments We thank B. Derrida and D. Mukamel for useful discussions. This research was partially supported by the Deutsche Forschungsgemeinschaft and the US-Israel Binational Science Foundation. Appendix Some useful identities for the $G$-function The function $G_{N,K}^M(x)$ was defined in eq. (2.13) as $$G_{N,K}^M(x) = \sum_{r=0}^{M-1} b_{N,K}(r)x^r \quad (N \geq 1) \quad (A.1)$$ with $$b_{N,K}(r) = \binom{K - 2 + r}{K - 2} - \binom{K - 2 + r}{N} \quad (A.2)$$ Furthermore we defined $b_{0,1}(0) = G_{0,0}^1 = G_{0,1}^1 = 1$. Using the symmetries of the coefficients $b_{N,K}(r)$ it is easy to prove the following recursion relations: $$G_{N,K}^M(x) = G_{N,K}^{M-1}(x) - xG_{N,K}^{M-1}(x) \quad (2 \leq K \leq N + 1) \quad (A.3)$$ One also finds $$G_{N,N}^M(x) = G_{N,N+1}^N(x) = G_{N,N+1}^{N+1}(x) = G_{N,N+1}^{N+1}(x) \quad (N \geq 1) \quad (A.4)$$ Eqs. (A.3) and (A.4) are necessary to prove that the function $Y_{N,K}(\alpha, \beta)$ and $X_{N,K}^p(\alpha, \beta)$ satisfy the recursion relations and initial conditions (2.9) - (2.12). $G_{N,K}^M(x)$ can be expressed in terms of incomplete $\beta$-functions: $$(1-x)^{K-1}G_{N,K}^M(x) = I_{1-x}(K-1, M) - \left(\frac{x}{1-x}\right)^{N-K+2} I_{1-x}(N+1, M-N+K-2) \quad (A.5)$$ (This is a direct consequence of the definition of $I_x(P, Q)$.) From this expres- (1 - x)^{N+1} G_{N,K}^M(x) - x^M G_{M-1,M-N+K-1}^{N+1}(1 - x) = (1 - x)^{N-K+2} - x^{N-K+2} \tag{A.6} and by setting $ M = N $ and $ M = N + 1 $ \[ G_{N,K}^{N+2}(x) = (1 - x)G_{N+1,K+1}^{N+1}(x) \quad (2 \leq K \leq N + 1) . \tag{A.7} \] From this relation one can see that relations (A.3) are consistent for $ M = N = K $. In the expression (3.3) for the density profile only the function $ G_{L,L}^L(x) $ appears. From eq. (A.7) one finds \[ G_{L,L}^L(x) = (1 - x)G_{L+1,L+1}^{L+1}(x) + c_L x^{L+1} \tag{A.8} \] with \[ c_L = -b_{L,L}(L + 1) = \frac{(2L)!}{L!(L + 1)!} . \tag{A.9} \] Defining $ F_L(x) = x^{-(L-1)} G_{L,L}^L(x) $ one gets \[ F_L(x) = \frac{1 - x}{(x(1 - x))^{L+1}} - \sum_{k=0}^{L-1} c_k (x(1 - x))^{k-L} . \tag{A.10} \] Now we can reexpress $ F_L(x) $ for $ x \neq 1/2 $ in terms of a hypergeometric function: \[ F_L(x) = (1 - 2x)\Theta(1 - 2x) \] \[ \frac{1}{(x(1 - x))^{L+1}} + \frac{c_L}{(1 - 2x)^2} F(1; \frac{3}{2}; L + 2; \frac{4x(1-x)}{(1-2x)^2}) \tag{A.11} \] \[ = F_L^{(1)}(x) + F_L^{(2)}(x) \] Here $\Theta(z)$ is the step function $$\Theta(z) = \begin{cases} 1 & z > 0 \\ 0 & z < 0 \end{cases} . \tag{A.12}$$ For large $L$ the hypergeometric function $F(1, \frac{3}{2}; L + 2; z)$ reduces to $$F(1, \frac{3}{2}; L + 2; z) = 1 + O(L^{-1}) . \tag{A.13}$$ Special exact values of $F_L(x)$ are $$F_L\left(\frac{1}{2}\right) = 2\binom{2L}{L} = \frac{4^L}{\sqrt{\pi} L^{3/2}} \left(1 + O(L^{-1})\right) \tag{A.14}$$ and $$F_L(1) = c_L = \frac{4^L}{\sqrt{2\pi} L^{3/2}} \left(1 + O(L^{-1})\right) . \tag{A.15}$$ References [1] B. Derrida, E. Domany and D. Mukamel, J. Stat. Phys., 69, 667 (1992). [2] D. Kandel, E. Domany and B. Nienhuis, J. Phys. A, 23, L755 (1990). [3] J. Krug and H. Spohn in Solids far from Equilibrium: Growth, Morphology and Defects. Ed. C. Godreche, Cambridge University Press, 1991. [4] M. Kardar, G. Parisi and Y. Zhang, Phys. Rev. Lett., 56, 889 (1986). [5] J. Krug, Phys. Rev. Lett., 61, 1882 (1991). [6] S.A. Janowsky and J.L. Lebowitz, Phys. Rev. A45, 618 (1992). [7] G. Schütz, J. Stat. Phys. (to appear) [8] B. Derrida and M.R. Evans, J. Physique (to appear) [9] G. Schütz, Weizmann preprint. [10] D. Kandel and D. Mukamel, Europhys. Lett. 20, 325 (1992). [11] K. Nagel and M. Schreckenberg, J. Physique I 2, 2221 (1992). [12] L.-H. Gwa and H. Spohn, Phys. Rev. Lett., 68, 725 (1992). L.-H. Gwa and H. Spohn, Phys. Rev. A, 46, 844 (1992).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 928, 1 ], [ 928, 2969, 2 ], [ 2969, 4789, 3 ], [ 4789, 7109, 4 ], [ 7109, 7629, 5 ], [ 7629, 9603, 6 ], [ 9603, 10895, 7 ], [ 10895, 12475, 8 ], [ 12475, 14082, 9 ], [ 14082, 15667, 10 ], [ 15667, 17402, 11 ], [ 17402, 19578, 12 ], [ 19578, 19812, 13 ], [ 19812, 21092, 14 ], [ 21092, 22315, 15 ], [ 22315, 23754, 16 ], [ 23754, 25375, 17 ], [ 25375, 26913, 18 ], [ 26913, 29460, 19 ], [ 29460, 31886, 20 ], [ 31886, 33968, 21 ], [ 33968, 36310, 22 ], [ 36310, 38631, 23 ], [ 38631, 40164, 24 ], [ 40164, 41301, 25 ], [ 41301, 42352, 26 ], [ 42352, 42872, 27 ], [ 42872, 43743, 28 ] ] }
d3ba65cf14601f52695143e3ec9f6da80bbb4616	{ "olmocr-version": "0.1.59", "pdf-total-pages": 6, "total-fallback-pages": 0, "total-input-tokens": 20105, "total-output-tokens": 7127, "fieldofstudy": [ "Chemistry" ] }	Abstract Uroporphyrinogen III, the universal progenitor of macrocyclic, modified tetrapyrroles, is produced from aminolaevulinic acid (ALA) by a conserved pathway involving three enzymes: porphobilinogen synthase (PBGS), hydroxymethylbilane synthase (HmbS) and uroporphyrinogen III synthase (UroS). The gene encoding uroporphyrinogen III synthase has not yet been identified in Plasmodium falciparum, but it has been suggested that this activity is housed inside a bifunctional hydroxymethylbilane synthase (HmbS). Additionally, an unknown protein encoded by PF3D7_1247600 has also been predicted to possess UroS activity. In this study it is demonstrated that neither of these proteins possess UroS activity and the real UroS remains to be identified. This was demonstrated by the failure of codon-optimized genes to complement a defined Escherichia coli hemD mutant (SASZ31) deficient in UroS activity. Furthermore, HPLC analysis of the oxidized reaction product from recombinant, purified P. falciparum HmbS showed that only uroporphyrin I could be detected (corresponding to hydroxymethylbilane production). No uroporphyrin III was detected, showing that P. falciparum HmbS does not have UroS activity and can only catalyze the formation of hydroxymethylbilane from porphobilinogen. INTRODUCTION Haem, as an iron-containing porphyrin, is a modified tetrapyrrole that is derived from the starting material 5-aminolevulinic acid (5-ALA) [1]. The construction of the macrocyclic framework of haem is mediated in just three steps [1]. Firstly, two molecules of 5-ALA are condensed to give a pyrrole, porphobilinogen (PBG), in a reaction catalyzed by PBG synthase [2, 3]. The next step involves the polymerization of four pyrrole units (termed A–D) into a linear bilane called hydroxymethylbilane (HMB) and is mediated by an enzyme called HMB synthase (HmbS) that deaminates and links together four molecules of PBG [4–7]. Finally, the bilane undergoes cyclization, but only after inversion of the terminal D ring, to give uroporphyrinogen III [6, 7]. These three steps are found in all organisms that make modified tetrapyrroles [1]. These reactions are shown in Fig. 1. A pathway for haem biosynthesis is found in Plasmodium falciparum, the protozoan parasite and causative agent of malaria [8]. As a haematophagous organism (blood-feeding parasite), it exists for part of its life cycle in a haem-rich environment and releases large quantities of haem as an insoluble crystalline material called haemozoin [9]. Nonetheless, it requires a functional haem synthesis pathway for survival in the liver and mosquito growth stages [10, 11]. Recent studies have biochemically characterized the complete set of haem synthesis enzymes from P. falciparum with the notable exception of uroporphyrinogen III synthase (UroS, formerly HemD) [12–18]. This enzyme is sometimes called uroporphyrinogen III cosynthase, as it often co-purifies with hydroxymethylbilane synthase (HmbS, formerly porphobilinogen deaminase or HemC), and both of these enzymes are required to make uroporphyrinogen III from PBG [5, 19]. HmbS catalyzes the synthesis of an unstable linear tetrapyrrole, HMB [4, 6, 7]. This rapidly cyclizes into uroporphyrinogen I unless the cosynthase is present to invert the terminal ring and cyclize HMB into uroporphyrinogen III [6, 7, 20]. This is the only isomer that can proceed through the haem synthesis pathway. A candidate gene encoding UroS in P. falciparum (PF3D7_1247600) has been identified by bioinformatics, but there have been no biochemical studies to validate the finding [21]. Another report in the literature has suggested that the parasite does not need a separate cosynthase because UroS activity can be found within a bi-functional HmbS that houses both HMB synthase and uroporphyrinogen III cosynthase activities [18]. The evidence presented for this was HPLC identification of the (oxidized) reaction product as uroporphyrin III from both native and recombinant HmbS when incubated with PBG. Although such dual activity has previously been reported for HmbS from Leptospira interrogans, this is a very different protein from P. falciparum HmbS, being a fusion of HmbS and UroS enzymes [22]. Conversely, the P. falciparum HmbS is clearly not a fusion protein because it has similarity to other HmbS enzymes throughout its entire sequence length (with the exception of the N-terminal apicoplast localization sequence, but dual activity was claimed for a truncated HmbS without this signal sequence) [18]. There are some short inserts in the P. falciparum sequence, but it is unlikely that UroS activity is contained within these inserts because they are not very long – the longest is 31 amino acids. The sequence does not align to known UroS sequences. A multiple sequence alignment is shown in Figs S1 and S2 (available in the online version of this article). It is, therefore, hard to understand how this enzyme could house two very different activities. Consequently, this report investigates more closely the evidence for dual activity using genetic complementation studies and analytical chemistry. The possibility that UroS activity is encoded by PF3D7_1247600 is also investigated. EXPERIMENTAL PROCEDURES Gene cloning Synthetic, codon-adapted genes, based on PF3D7_1209600 (hemC) and PF3D7_1247600 (putative hemD), were purchased from GeneArt for optimal expression in Escherichia coli (Fig. S3) and subcloned into a pET-3a vector (Novagen) using NdeI and SpeI restriction sites (the pET-3a had been modified to include a SpeI site 5′ of the BamHI site). Two further constructs were made containing a truncated version of the hemC gene to remove a potential signal sequence from the protein product [18]. The truncated gene was obtained by PCR using the following primers: 5′ primer containing NdeI site and start codon: CAC CATATG GGCA TCAA AGAT GAAA TTAT TATCGG; 3′ primer containing SpeI site and stop codon: ctc actagt tatttattgttcagcagg. The PCR product was ligated into pET-3a and pET-14b (Novagen) using Ndel and SpeI restriction sites (both vectors had been previously modified to include a SpeI site 5′ of the BamHI site). --- Fig. 1. Reactions of HmbS and UroS. HmbS polymerizes porphobilinogen into hydroxymethylbilane, which auto-cyclizes to uroporphyrinogen I. If UroS is present, then hydroxymethylbilane is cyclized into uroporphyrinogen III, a reaction that involves the inversion of ring D. A, acetic acid; P, propionic acid. The constructs were sequenced by GATC Biotech to check for the correct insert and reading frame and the absence of mutations. Complementation studies A defined hemD$^{-}$ mutant SASZ31 (CGSC# 7153 Coli Genetic Stock Center, Yale University) [23] was transformed with the following plasmids: pET-3a empty vector; pET-14b empty vector; pET-3a hemD $P.$ falciparum 3D7_1247600; pET-3a hemC $P.$ falciparum hemC; pET-3a hemC$_{\text{truncated}}$ $P.$ falciparum; pET-14b hemD $(E.$ coli\); pET-14b hemD $(B.$ megaterium\) (a kind gift from Professor Peter Shoolingin-Jordan, Southampton). The transformations were plated onto LB (lysogeny broth) agar plates with 100 µg ml$^{-1}$ ampicillin and 2% glucose and incubated at 37 °C for 48 h. The size of any resultant colonies was recorded after 24 and 48 h. To test for viability, the colonies were restreaked onto a fresh plate and grown for a further 24 h and examined for evidence of growth. The growth is indicated in the table by the number of plus signs from + (poor growth) to ++++ (normal growth). A indicates that no growth was observed. Protein overproduction and purification BL21$^{\text{DE3}}$ pLysS (Invitrogen) was transformed with the appropriate construct and a 1 l culture of the resulting strain was grown in LB at 37 °C with shaking to an OD$_{600}$ of 0.6. Gene expression was induced for 20 h at 19°C by adding 0.4 mM IPTG. Cells were harvested by centrifugation at 4000 r.p.m. for 15 min at 4 °C. The pellet was resuspended in 15 ml resuspension buffer containing 20 mM Tris/HCl pH 8.0, 500 mM NaCl, 5 mM imidazole. Cells were lysed on an ice-water slurry by sonication at 60% amplitude for 3 min at 30 s intervals. The lysate was spun for 15 min at 19 000 r.p.m. and the supernatant loaded onto a Ni$^{2+}$–Sepharose column (GE Healthcare) preequilibrated with resuspension buffer. The column was washed with resuspension buffer containing 50 mM imidazole and eluted with resuspension buffer containing 400 mM imidazole. The protein was buffer exchanged with a PD-10 column (GE Healthcare) into 50 mM Tris/HCl pH 8.0, 100 mM NaCl. Identification of the reaction product Purified recombinant HmbS was heated to 60 °C for 10 min on a heat block prior to the assay to deactivate any contaminating UroS. HmbS (25 µg) was incubated with 200 µM porphobilinogen at 37 °C in 0.1 M Tris/HCl pH 8.0. After 1 h, the reaction was stopped by diluting 10× into 1 M HCl. The reaction product was oxidized by adding 10 µl of a 1 mg ml$^{-1}$ benzoquinone in methanol and incubating for 60 min. The mixture was run on an HPLC to identify which uroporphyrin isomer was present. Commercial standards of uroporphyrin I and III (Frontier Scientific) were also run to aid identification. The uroporphyrin I and III isomers were separated on an ACE 5 AQ column, dimensions 250×4.6 mm, using an Agilent 1100 HPLC system with a flow rate of 1.0 ml min$^{-1}$. The mobile phase was 1 M ammonium acetate pH 5.16 and the organic phase was acetonitrile. A 100µl sample was injected onto the column (temperature 25 °C) and the porphyrins were detected by their absorbance at 405 nm. A gradient elution was used rising from 13 to 30% acetonitrile in 25 min and held there for a further 5 min. This was adapted from the protocol used elsewhere [18]. Enzyme activity assay Enzyme at various concentrations was incubated with 100 µM porphobilinogen at 37 °C in 0.1 M Tris/HCl pH 8.0. After 25 min, the reaction was stopped by diluting 10× into 1 M HCl. The reaction product was oxidized by adding 10 µl of a 1 mg ml$^{-1}$ benzoquinone in methanol and incubating for 60 min. Absorbance was read at 405 nm and the amount of uroporphyrin calculated using the extinction coefficient of 54.8×105 M$^{-1}$l.$^{-1}$. \| Construct \| 24 h growth \| 48h growth \| Restreaked 24h growth \| \|-----------\|-------------\|------------\|-----------------------\| \| pET-3a \| + \| ++ \| − \| \| pET-14b \| + \| ++ \| + \| \| pET-3a hemC $(P.$ falciparum\) \| + \| ++ \| − \| \| pET-3a hemC$_{\text{truncated}}$ $(P.$ falciparum\) \| + \| ++ \| − \| \| pET-14b hemD $(E.$ coli\) \| ++++ \| ++++ \| ++++ \| \| pET-14b hemD $(B.$ megaterium\) \| ++++ \| ++++ \| ++++ \| RESULTS Complementation studies To test if either $P.$ falciparum hemC (encoding HmbS) or $P.$ falciparum 3D7_1247600 (putative coding sequence for UroS) harbour UroS activity, complementation studies were performed to see if either gene could restore growth to a defined hemD$^{-}$ mutant (SASZ31) lacking UroS activity [23]. Two $P.$ falciparum hemC constructs were used, both of which were codon-optimized for expression in $E.$ coli. One contained the full-length hemC gene in a pET-3a vector and the other a truncated hemC gene, also in a pET-3a vector. The Fig. 2. HPLC analysis of HmbS reaction product. HPLC traces showing (a) commercial standards of uroporphyrin I (left) and III (right) and (b) the oxidized reaction product of HmbS alone and (c) spiked with uroporphyrin I and (d) uroporphyrin III. truncation removed a signal sequence known to hinder gene expression in E. coli and has been shown not to be essential for activity [18]. The hemD mutant SASZ31 was transformed with these constructs and with control plasmids. The controls included an empty pET-3a as a negative control and plasmids harbouring known hemD genes from Bacillus megaterium and E. coli as positive controls. As these control genes were in a pET-14b plasmid, an empty pET-14b was also used as a further control. The resulting strains were grown on LB agar at 37°C and the size of colonies was noted at 24 and 48 h. To test for the viability of the colonies after 48 h they were restreaked onto a fresh LB agar plate and incubated at 37°C for 24 h. The plates were examined for colonies. The control plasmids harbouring known hemD genes were able to restore normal growth to the hemD mutant. However, the empty vectors and both the P. falciparum hemC constructs and the P. falciparum 3D7_1247600 construct were unable to restore normal growth. This demonstrates that neither the P. falciparum hemC gene nor P. falciparum 3D7_1247600 can complement an E. coli hemD mutant, showing that neither encodes for UroS activity. The results are shown in Table 1. *Protein overproduction in E. coli* and identification of the reaction product** A pET-14b construct harbouring the P. falciparum hemC gene in frame with an N-terminal hexa-His tag coding sequence was used for protein production in E. coli. The hemC gene was codon-optimized for E. coli and lacked the apicoplast localization sequence. The overproduced protein was mostly insoluble but a small quantity of soluble protein was successfully purified to homogeneity from the cell lysate using Ni²⁺ affinity chromatography. The purity was assessed by SDS-PAGE (Fig. S4). The purified protein was subjected to a 60°C heat treatment for 10 min to deactivate any contaminating UroS. P. falciparum HmbS was demonstrated to be resistant to heat treatment in the original study [18]. The protein was incubated with substrate for 60 min at 37°C and the resulting product was oxidized with HCl and benzoquinone. This sample was analysed by HPLC to see if the product was uroporphyrin I (corresponding to hydroxymethylbilane) or uroporphyrin III (corresponding to uroporphyrinogen III). Identification was by comparison with commercial standards of uroporphyrin I and III. The reaction product matched the retention time of uroporphyrin I. The results are shown in Fig. 2. As a positive control, analysis of known HmbS and UroS enzymes was also performed (Fig. S5). To confirm that the observed reaction product was enzymatically generated by HmbS, the assay was repeated with different concentrations of enzyme and the reaction product was quantified by absorbance spectrometry. A linear correlation was observed between enzyme concentration and the amount of product formed, which is indicative of enzymatic reactions. The results are presented in Fig. S6. DISCUSSION The claim that P. falciparum HmbS has UroS activity [18] has been challenged through complementation studies with a hemD mutant and HPLC analysis of the reaction product from recombinant enzyme. SASZ31 is a defined hemD mutant that grows very poorly [23]. Complementation with control hemD genes from B. megaterium and E. coli was able to restore normal growth to the mutant, but P. falciparum hemC could not restore normal growth. Because HmbS has an apicoplast localization sequence that hinders expression but is not required for alleged dual activity [18], a truncated gene lacking this sequence was also made. This also failed to complement the mutant. Furthermore, the truncated HmbS was overproduced in E. coli with an N-terminal hexa-His tag and purified. After incubation with substrate for an hour at 37°C, the sample was oxidized and run on HPLC along with commercial standards of uroporphyrin I and uroporphyrin III. The HPLC result clearly identified the enzyme’s oxidized product as uroporphyrin I. No uroporphyrin III could be detected. These results contradict those previously published [18] where HPLC analysis of the reaction product from native and recombinant HmbS identified the (oxidized) reaction product as uroporphyrin III. This conflict could be explained by the presence of a contaminating UroS in the earlier study. Although the researchers used heat treatment to denature any UroS (HmbS is heat stable but UroS is not), it is possible that any UroS could have refolded and reactivated itself during the 12 h incubation of heat-treated HmbS with substrate [25–27]. Further, the assay buffer contained additives known to increase the stability of UroS [27]. Our results clearly demonstrate that the previous claim that P. falciparum HmbS contains uroporphyrinogen III synthase (UroS) activity is mistaken [18]. Another report [21] has postulated that UroS activity could reside in the protein encoded by PF3D7_1247600. Our complementation studies have shown that this is also incorrect. It should now be a matter of importance to find the gene that encodes for the real uroporphyrinogen III synthase. Funding information This work was supported by Pfizer Global Research and Development. Acknowledgements H. Gwawr Davies is thanked for proofreading the manuscript. Conflicts of interest The authors declare that there are no conflicts of interest. References 1. Heinemann IU, Jahn M, Jahn D. The biochemistry of heme biosynthesis. Arch Biochem Biophys 2008;474:238–251. 2. Semin D, Russell CS. δ-aminolevulinic acid, its role in the biosynthesis of porphyrins and purines 1. J Am Chem Soc 2002;75:4873–4874. 3. Jaffe EK. The remarkable character of porphobilinogen synthase. Acc Chem Res 2016;49:2509–2517. 4. Battersby AR, Fookes CJR, Gustafson-Potter KE, Matcham GWJ, McDonald E. Proof by synthesis that unrearranged hydroxymethylbilane is the product from deaminase and the substrate for cosynthetase in the biosynthesis of Uro’gen-III. J Chem Soc Chem Commun;0:1155. 5. Bogorad L. The enzymatic synthesis of porphyrins from porphobilinogen. J Bio Chem 1958;233:501–509. 6. Battersby AR, Fookes CJR, Gustafson-Potter KE, McDonald E, Matcham GWJ. Biosynthesis of porphyrins and related macrocycles. Part 18. Proof by spectroscopy and synthesis that unarranged hydroxymethylbilane is the product from deaminase and the substrate for cosynthetase in the biosynthesis of uroporphyrinogen-III. J Chem Soc Perkin Trans 1;0:2427. 7. Battersby AR, Fookes CJR, Gustafson-Potter KE, McDonald E, Matcham GWJ. Biosynthesis of porphyrins and related macrocycles. Part 17. Chemical and enzymatic transformation of isomeric aminomethylbilanes into uroporphyrinogens: Proof that unarranged bilane is the preferred enzymic substrate and detection of a transient intermediate. J Chem Soc Perkin Trans 1;0:2413. 8. Surolia N, Padmanaban G. De novo biosynthesis of heme offers a new chemotherapeutic target in the human malarial parasite. Biochem Biophys Res Commun 2002;367:321–327. 9. Egan TJ. Haemoglobin formation. Mol Biochem Parasitol 2008;157:127–136. 10. Ke H, Sigala PA, Miura K, Morrissey JM, Mather MW, et al. The heme biosynthesis pathway is essential for Plasmodium falciparum development in mosquito stage but not in blood stages. J Biol Chem 2014;289:34827–34837. 11. Goldberg DE, Sigala PA. Plasmodium heme biosynthesis: To be or not to be essential? PLoS Pathog 2017;13:e1006511. 12. Varadhajaran S, Dhanasekaran S, Bonday ZQ, Rangarajan PN, Padmanaban G. Involvement of delta-aminolevulinic acid synthase encoded by the parasite gene in de novo haem synthesis by Plasmodium falciparum. Biochem J 2002;367:321–327. 13. Dhanasekaran S, Chandra NR, Chandrasekhar Sagar BK, Rangarajan PN, Padmanaban G. Delta-aminolevulinic acid dehydratase from Plasmodium falciparum: Indigenous versus imported. J Biol Chem 2004;279:6934–6942. 14. Nagaraj VA, Prasad D, Rangarajan PN, Padmanaban G. Mitochondrial localization of functional ferrochelatase from Plasmodium falciparum. Mol Biochem Parasitol 2009;168:109–112. 15. Nagaraj VA, Arumugam R, Prasad D, Rangarajan PN, Padmanaban G. Protoporphyrinogen IX oxidase from Plasmodium falciparum is anaerobic and is localized to the mitochondrion. Mol Biochem Parasitol 2010;174:44–52. 16. Nagaraj VA, Prasad D, Arumugam R, Rangarajan PN, Padmanaban G. Characterization of coproporphyrinogen III oxidase in Plasmodium falciparum cytosol. Parasitol Int 2010;59:121–127. 17. Nagaraj VA, Arumugam R, Chandra NR, Prasad D, Rangarajan PN, et al. Localisation of Plasmodium falciparum uroporphyrinogen III decarboxylase of the heme-biosynthetic pathway in the apicoplast and characterisation of its catalytic properties. Int J Parasitol 2009;39:559–568. 18. Nagaraj VA, Arumugam R, Gopalakrishnan B, Jyothsna YS, Rangarajan PN, et al. Unique properties of Plasmodium falciparum porphobilinogen deaminase. J Biol Chem 2008;283:437–444. 19. Shoolingin-Jordan PM. Porphobilinogen deaminase and uroporphyrinogen III synthase: structure, molecular biology, and mechanism. J Bioenerg Biomembr 1995;27:181–195. 20. Battersby AR, Fookes CJR, McDonald E, Meegan MJ. Biosynthesis of type-III porphyrins: Proof of intact enzymic conversion of the head-to-tail bilane into uro’gen-III by intramolecular rearrangement. J Chem Soc Chem Commun;0:185. 21. Mohanty S, Srinivasan N. Identification of “missing” metabolic proteins of Plasmodium falciparum: a bioinformatics approach. Protein Pept Lett 2009;16:961–968. 22. Guégan R, Camadro J-M, Saint Girons I, Picardeau M. Leptospira spp. Possess a complete haem biosynthetic pathway and are able to use exogenous haem sources. Mol Microbiol 2003;49:745–754. 23. Chartrand P, Tardif D, Sásármán A. Uroporphyrin- and coproporphyrin I-accumulating mutant of Escherichia coli K12. J Gen Microbiol 1979;110:61–66. 24. Raux E, Leech HK, Beck R, Schubert HL, Santander PJ, et al. Identification and functional analysis of enzymes required for precorrin-2 dehydrogenation and metal ion insertion in the biosynthesis of sirohaem and cobalamin in Bacillus megaterium. Biochem J 2003;370:505–516. 25. Jordan PM, Thomas SD, Warren MJ. Purification, crystallization and properties of porphobilinogen deaminase from a recombinant strain of Escherichia coli K12. Biochem J 1988;254:427–435. 26. Alwan AF, Mgbeje BI, Jordan PM. Purification and properties of Uroporphyrinogen III synthase (co-synthase) from an overproducing recombinant strain of Escherichia coli k-12. Biochem J 1989;264:397–402. 27. Omata Y, Sakamoto H, Hitahimoto Y, Hayashi S, Noguchi M. Purification and characterization of human Uroporphyrinogen III synthase expressed in Escherichia coli. J Biochem 2004;136:211–220. Edited by: M. Welch and N. Scott	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3372, 1 ], [ 3372, 6541, 2 ], [ 6541, 11561, 3 ], [ 11561, 11808, 4 ], [ 11808, 17750, 5 ], [ 17750, 22623, 6 ] ] }
972f0e9bfde0253dda03afe52722739a7fe07b6b	{ "olmocr-version": "0.1.59", "pdf-total-pages": 11, "total-fallback-pages": 0, "total-input-tokens": 47098, "total-output-tokens": 16057, "fieldofstudy": [ "Physics" ] }	Direct Measurement of Astrophysically Important Resonances in $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ G. Christian,1,2,∗ G. Lotay,3,‡ C. Ruiz,2 C. Akers,2,4,‡ D. S. Burke,5 W. N. Catford,3 A. A. Chen,3 D. Connolly,6,§ B. Davids,2 J. Fallis,2,¶ U. Hager,6 D. Hutcheon,2 A. Mahl,6 A. Rojas,2 and X. Sun2,7,∗∗ 1Department of Physics & Astronomy, Cyclotron Institute, and Nuclear Solutions Institute, Texas A&M University, College Station, TX 77843, USA 2TRIUMF, Vancouver, BC V6T 2A3, Canada 3Department of Physics, University of Surrey, Guildford, GU2 7XH, UK 4Department of Physics, University of York, Heslington, York YO10 5DD, UK 5Department of Physics & Astronomy, McMaster University, Hamilton, ON L8S 4M1, Canada 6Department of Physics, Colorado School of Mines, Golden, CO 80401, USA 7Department of Physics, McGill University, Montréal, QC H3A 2T8, Canada (Dated: January 4, 2018) Background: Classical novae are cataclysmic nuclear explosions occurring when a white dwarf in a binary system accretes hydrogen-rich material from its companion star. Novae are partially responsible for the galactic synthesis of a variety of nuclides up to the calcium ($A \sim 40$) region of the nuclear chart. Although the structure and dynamics of novae are thought to be relatively well understood, the predicted abundances of elements near the nucleosynthesis endpoint, in particular Ar and Ca, appear to sometimes be in disagreement with astronomical observations of the spectra of nova ejecta. Purpose: One possible source of the discrepancies between model predictions and astronomical observations is nuclear reaction data. Most reaction rates near the nova endpoint are estimated only from statistical model calculations, which carry large uncertainties. For certain key reactions, these rate uncertainties translate into large uncertainties in nucleosynthesis predictions. In particular, the $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ reaction has been identified as having a significant influence on Ar, K, and Ca production. In order to constrain the rate of this reaction, we have performed a direct measurement of the strengths of three candidate $\ell = 0$ resonances within the Gamow window for nova burning, at 386 ± 10 keV, 515 ± 10 keV, and 689 ± 10 keV. Method: The experiment was performed in inverse kinematics using a beam of unstable $^{38}\text{K}$ impinging on a windowless hydrogen gas target. The $^{39}\text{Ca}$ recoils and prompt $\gamma$ rays from $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ reactions were detected in coincidence using a recoil mass separator and a bismuth-germanate scintillator array, respectively. Results: For the 689 keV resonance, we observed a clear recoil-$\gamma$ coincidence signal and extracted resonance strength and energy values of $120^{+20}_{-10}$ (stat.)$^{+30}_{-20}$ (sys.) meV and $679^{+15}_{-15}$ (stat.) ± 1 (sys.) keV, respectively. We also performed a singles analysis of the recoil data alone, extracting a resonance strength of $120 \pm 20$ (stat.) ± 15 (sys.) meV, consistent with the coincidence result. For the 386 keV and 515 keV resonances, we extract 90% confidence level upper limits of 2.54 meV and 18.4 meV, respectively. Conclusions: We have established a new recommended $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ rate based on experimental information, which reduces overall uncertainties near the peak temperatures of nova burning by a factor of ~250. Using the rate obtained in this work in model calculations of the hottest oxygen-neon novae reduces overall uncertainties on Ar, K, and Ca synthesis to factors of 15 or less in all cases. I. INTRODUCTION Classical novae are some of the most common explosive stellar events to occur in our galaxy, with an estimated frequency of $35 \pm 11$ per year [1]. Novae happen when a white dwarf in a binary system accretes hydrogen-rich material from its main-sequence companion, igniting thermonuclear runaway. Observations of the spectra of ejected material indicate that two main classes of nova exist, depending on the initial composition of the underlying white dwarf: carbon-oxygen (CO) and oxygen-neon (ONe). Model calculations indicate that ONe novae, which occur on more massive white dwarves, can reach peak temperatures around 0.4 GK and synthesize nuclei up to the calcium region ($A \sim 40$). At present, there are a number of outstanding discrepancies between astronomical observations of the spectra of nova ejecta [2–5] and nova model predictions [6, 7]. In particular, the model predictions of Ref. [7] indicate Ar and Ca abundances at roughly the solar level, while in contrast the observations of Ref. [3] point towards nova ejecta with Ar and Ca abundances around an order of magnitude greater than solar. Resolution of such discrepancies requires that nova models be capable of making detailed predictions regarding the synthesis of nucleides in the Ar–Ca region. In turn, this requires improved constraints on the rates of key nuclear reactions involved in nova nucleosynthesis, in particular for reactions near the nucleosynthesis endpoint. In 2002, Iliadis et al. published a seminal paper investigating the influence of nuclear reaction rate variations on nucleosynthesis in classical novae [8]. In this study, the authors varied the rates of 64 nuclear reactions within their recommended uncertainties and examined the effect of these variations on the nucleosynthesis predictions of seven different... within the Gamow window for ONe novae ($T_\text{peak} \approx 0.2-0.4$ GK). The first results of this study were published in a review article [10] and a recent Letter, which recommends a new, experimentally-based rate with uncertainties over two orders of magnitude smaller than before [11]. In the present Article, we expand upon Ref. [11], providing significantly more detail concerning the experiment and data analysis. We also report the results of a new sensitivity study investigating the effect of the accepted rate, prompted an attempt by the present authors to measure the strengths of the three $\ell = 0$ resonances lying within the Gamow window for ONe novae. The results presented here supersede those published previously. II. EXPERIMENT The experiment was performed in the ISAC-I [12] hall at TRIUMF, Canada’s national laboratory for particle and nuclear physics. A beam of radioactive $^{38}$K was produced by impinging 500 MeV protons from the TRIUMF cyclotron onto a high-power TiC production target. The $^{38}$K$^{(+1)}$ ions produced by spallation reactions in the target were extracted and sent through a high-resolution mass separator. They were then charge bred to the $7^+$ charge state in an electron cyclotron resonance (ECR) charge state booster before post-acceleration. The charge breeding is necessary because the ISAC-I radio frequency quadrupole (RFQ) is restricted to a mass-to-charge ratio of 30 or less [13]. The $^{38}$K$^{(+1)}$ beam was delivered to the Detector of Recoils and Gammas of Nuclear Reactions (DRAGON) where it impinged on a windowless extended gas target [14], filled with H$_2$ at an average pressure and temperature of 10.6 mbar and 298 Kelvin, respectively. The H$_2$ was cleaned by continuous recirculation through a LN$_2$ cooled zeolite trap. The prompt $\gamma$ rays from $^{38}$K$(p, \gamma)^{39}$Ca reactions were detected in array of 30 bismuth germanate (BGO) scintillators surrounding the target, while the $^{38}$K recoils were transmitted to the focal plane of DRAGON, separating them from unreacted and elastically scattered $^{38}$K. A timing signature for recoils was established as the time difference between signals from a pair of microchannel plates (MCPs) separated by 59 cm, which detected secondary electrons produced by the interaction of the recoil ions with a diamond-like carbon foil intersecting the beam line. The total kinetic energy and stopping power of the recoil ions was measured in a multi-anode ionization chamber (IC) [15]. Coincidences between recoils and prompt $\gamma$ rays were identified using a timestamp-based algorithm [16]. The $^{39}$Ca recoils were separated from a background of scattered and charge-changed $^{38}$K ("leaky beam") based primarily on the local time of flight (TOF) between the two MCPs ("MCP TOF") and the time difference between the $\gamma$ ray and the upstream MCP ("separator TOF"). Laboratory beam energies of 15.58 MeV, 20.56 MeV, and 27.17 MeV were employed for measurements of the ${38}$K$^{+}$ resonances at $10$ keV, $515 \pm 10$ keV, and $689 \pm 10$ keV, respectively. The beam energies were measured using the procedure given in Ref. [17]. The beam was centered on 2 mm slits downstream of DRAGON’s first magnetic dipole, and the measured field value was converted to energy by solving the relativistically-correct equation, \[ E/A = c_{\text{mag}} (qB/A)^2 - \frac{1}{2uc^2} (E/A)^2, \] where $E, A, q$ are the beam kinetic energy, mass number, and charge state, respectively, and $u$ is the atomic mass unit. The quantity $c_{\text{mag}}$ is related to the effective bending radius of the dipole. The recommended value from Ref. [17], $c_{\text{mag}} = 48.15 \pm 0.07$ MeV·T$^2$, was employed for this experiment. The estimated uncertainty on this procedure is 0.17%. The chosen beam energies cover respective center-of-mass energies in the DRAGON gas target of $386 \pm 13, 515 \pm 13,$ and $689 \pm 13$ keV. The resonances in question were previously identified as $5/2^+$ $^{39}$Ca states through $^{40}$Ca($^{3}$He, $\alpha$)$^{39}$Ca [18], $^ {40}$Ca(d,$d$)$^{39}$Ca [19], and $^{40}$Ca(p,$d$)$^{39}$Ca [20] transfer reaction studies. Their recommended excitation energies are $6157 \pm 10, 6286 \pm 10,$ and $6460 \pm 10$ keV, corresponding to $38$K$+p$ resonances at $386 \pm 10, 515 \pm 10,$ and $689 \pm 10$ keV, respectively [21]. The respective $(p, \gamma)$ cone angles for measurements at the 15.58 MeV, 20.56 MeV, and 27.17 MeV beam energies were 5.98 mrad, 5.29 mrad, and 4.73 mrad. Each of these is well within the $\pm 2$ mrad angular acceptance of DRAGON [22]. For each beam energy, only a single charge state was transmitted to the end of DRAGON. The respective charge states were $7^+, 9^+,$ and $10^+$ for the 15.58 MeV, 20.56 MeV, and 27.17 MeV beam energies. The charge state fractions and stopping powers for K and Ca ions passing through the gas target were measured separately using stable beams of $^{39}$K and $^{44}$Ca. Charge state fractions were determined by measuring the ratio $(I_2/I_0)^g/(I_2/I_0)^ng$, where $I_0, I_1,$ and $I_2$ represent the current on Faraday cups upstream of the gas target, downstream of the gas target, and downstream of the first magnetic dipole, respectively; and the superscripts $g$ and $ng$ represent currents measured with and without gas in the target, respectively. Current measurements were taken with the magnetic dipole set to accept each of the charge states that resulted in a measurable $I_2$. The resulting distributions were then fit with a Gaussian function (normalized to unity). The value of the Gaussian at each charge state was taken to represent the corresponding charge state fraction. Measurements were taken at three different beam energies spanning the range of beam \[^{38}\text{K}(p, \gamma)^{39}\text{Ca}\] reaction as having a significant influence on the production of Ar, K, and Ca. Qualitatively, the predicted abundances of these elements were found to vary by respective factors of 24, 58, and 57 when the $^{38}$K$\gamma$$^{39}$Ca rate was varied within its existing uncertainties. When Ref. [8] was published, the $^{38}$K$\gamma$$^{39}$Ca rate was estimated entirely from statistical model predictions with no experimental nuclear physics input [9]. This rate estimate was assigned an overall uncertainty of $10^3$, i.e. the upper and lower limits were established at 100 and 0.01 times the central value, respectively. The importance of this reaction for nova nucleosynthesis, along with the paucity of experimental input regarding the accepted rate, prompted an attempt by the present authors to measure the strengths of the three $\ell = 0$ resonances lying within the Gamow window for ONe novae. The results presented here supersede those published previously. energies employed in the experiment, and the resulting charge fractions were fit with a quadratic function. The value of this quadratic function at the various beam energies employed in the experiment was then taken as the charge state fraction to use in the recoil yield analysis. All fits were performed using MINUIT and errors on the fit parameters were calculated using MINOS [23]. The errors on the Gaussian fit were propagated along with the errors on the quadratic interpolation to arrive at the final error on the charge state fractions used in the analysis. The number of incoming $^{38}\text{K}^{(7+)}$ ions was determined by counting delayed ($t_{1/2} = 7.6$ minutes) 2.2 MeV $\gamma$ rays emitted by the daughters of beam ions implanted into the mass slits just downstream of DRAGON’s first electric dipole. These $\gamma$ rays were detected in a NaI scintillator with an efficiency of $(8.46 \pm 0.95) \times 10^{-6}$. This efficiency was determined from a GEANT4 [24] simulation, which included the entire geometry of the mass slit box and NaI detector. The 11% relative uncertainty on the NaI efficiency was determined by comparing simulation results to known $^{22}\text{Na}$ and $^{137}\text{Cs}$ source measurements. This analysis includes an uncertainty on the source position of ±0.5 cm. The average beam rate for each ~1 hour run was determined by fitting the decay rate vs. time curves with the expected response function, $$A(t) = I \left(1 - e^{-\lambda t}\right) + N_0 \lambda e^{-\lambda t},$$ where $A(t)$ is the decay rate, $I$ is the average beam intensity, $N_0$ is the initial number of particles implanted in the slit, and $\lambda = 1.5 \times 10^{-3}$ s$^{-1}$ is the $^{38}\text{K}$ decay constant. In the fit, both $I$ and $N_0$ were allowed to vary as free parameters. Cases where the average beam rate fluctuated significantly over the course of a run were identified by a noticeable deviation from the expected response. These fluctuations in the beam rate (or the complete loss of beam delivery) arose from a number of sources upstream of the DRAGON target, for example loss of a run were identified by a noticeable deviation from the average beam rate fluctuated significantly over the course of the experiment. The overall rate was approximately $2 \times 10^7$ particles per second. ### A. $386(10)$ keV and $515(10)$ keV Resonances At beam energies of 15.58 MeV and 20.56 MeV (corresponding to the $386 \pm 10$ keV and $515 \pm 10$ keV resonances, respectively), we observed zero events in the expected recoil region. This is demonstrated in Figure 2(a), which shows MCP vs. separator TOF spectra for each of the 15.58 MeV and 20.56 MeV beam energies. The dashed and dotted ellipses included on the plots indicate the expected location of $^{50}\text{Ca}$ recoils, based on GEANT3 simulations of the reaction and transmission through the DRAGON separator. As can be seen, in both cases no recoil events fall within this expected window. As a result, we extracted upper limits on the resonance strengths using a modification of the Rolke profile likelihood method for calculating confidence intervals in the presence of uncertain background rates and detection efficiencies [25]. In the standard Rolke treatment, the likelihood is the product of the individual likelihoods describing the signal rate $\mu$, background rate $b$ (both treated as Poisson), and the detection efficiency $\eta$ (treated as Gaussian with uncertainty $\sigma_\eta$). Mathematically, this is expressed as $$L(\mu, b, \eta \| x, y, z) = \frac{\left(\eta \mu + b\right)^x}{x!} e^{\eta \mu + b} \cdot \frac{\left(b \nu\right)^y}{y!} e^{b \nu} \cdot \frac{e^{(z - \eta^2)/(2\sigma_\eta^2)}}{\sqrt{2\pi\sigma_\eta}},$$ where $x$ is the number of events observed in the signal region, $y$ is the number of events observed in a background region that is $ \tau $ times as large as the signal region, and $ z $ is the observed signal rate. Equation (3) is then maximized with respect to $ b $ and $ \eta $ to construct a one-dimensional likelihood curve that is a function of only the signal strength $ \mu $ and can be analyzed to extract upper limits. In the present analysis, we extend the Rolke method to also account for uncertainties in the resonance energy $ E_r $, the number of incoming beam particles $ N $, and the $^{38}\text{K}+\text{H}_2$ stopping power $ \epsilon $. Each of these quantities factors into the calculation of the resonance strength, and hence their uncertainties should be included for a complete treatment of the problem. For each of these quantities, we treat the uncertainty as Gaussian (with widths $ \sigma_{E_r}, \sigma_N, $ and $ \sigma_\epsilon $, respectively). The complete likelihood function is then given by \[ \mathcal{L} \left( \omega \gamma, b, \eta, E_r, N, \epsilon \right\| x, y, z, E_{0}, N_0, \epsilon_0) = \\ \left( \frac{(\eta \mu + b)}{x!} \right)^{x} x^x e^{-x(b \tau + \eta \mu + b)} y! y^y e^{-y(b \tau + \eta \mu + b)} \times \\ \frac{e^{(x-\eta)^2/(2\sigma_\eta)}}{\sqrt{2\pi}\sigma_\eta} \times \\ \frac{e^{(y-\epsilon)^2/(2\sigma_\epsilon)}}{\sqrt{2\pi}\sigma_\epsilon} \times \\ \frac{e^{(z-\epsilon-M)^2/(2\sigma_M^2)}}{\sqrt{2\pi}\sigma_M} \times \\ \frac{e^{(z-\epsilon-I)^2/(2\sigma_I^2)}}{\sqrt{2\pi}\sigma_I} \times \\ \frac{e^{(z-\epsilon-N)^2/(2\sigma_N^2)}}{\sqrt{2\pi}\sigma_N}, \] where $ E_{0}, N_0, $ and $ \epsilon_0 $ are the observed central values of the resonance energy, beam ions on target, and stopping power, respectively. In Eq. (4), the signal rate $ \mu $ is no longer a constant parameter but rather a function of the resonance strength $ \omega \gamma $, resonance energy $ E_r $, number of incoming beam particles $ N $, center-of-mass stopping power $ \epsilon $, beam mass $ M $, and target mass $ m $, \[ \mu(\omega \gamma, E_r, N, \epsilon) = \frac{N(\omega \gamma)(hc)^2}{2\epsilon \left( E_r^2 + 2E_r mM / (m + M) \right)}. \] Following the Rolke prescription, we maximize Eq. (4) with respect to the “nuisance” parameters $ \{b, \eta, E_r, N, \epsilon\} $ to arrive at a profile likelihood that is a function of only the resonance strength $ \omega \gamma $. In practice, we first take the negative logarithm of Eq. (4) and then calculate the minimum numerically using the MINUIT package [23]. The resulting profile likelihoods for the 15.58 MeV and 20.56 MeV beam energies are shown in Figures 2(b) and 2(c), respectively (plotted as negative log-likelihoods). To extract single-sided 68\%, 90\%, and 95\% upper limits from the profile likelihood curves, we follow exactly the prescriptions of Ref. [25]. The resulting upper limits, along with all of the measured parameters going into the upper limit calculation are summarized in Tables I and II. It should be noted that when we refer to “68\%” or “95\%” confidence intervals, we mean the area under a normalized gaussian distribution between the $ \pm 1\sigma $ or $ \pm 2\sigma $ limits. These are more precisely equal to 68.27\% and 95.45\%, respectively. ### B. 689(10) keV Resonance In contrast to the two lower-energy resonances, we observed a clear recoil signal when running with a beam en- FIG. 3. Summary of the coincidence analysis for the data taken with a beam energy of 27.17 MeV. The individual descriptions of panels (a) through (f) are as follows: (a) Separator vs. MCP TOF particle identification spectrum. The blue filled circles represent data collected with the radioactive $^{38}\text{K}$ beam, while the single filled yellow triangle represents data collected with a $^{38}\text{Ar}$ beam, for background characterization. The open ellipse outlines the expected recoil region. Projections onto the horizontal and vertical axes are also included (as the unshaded orange and green histograms). (b) Target density as a function of center-of-mass beam energy. The filled circles with error bars represent the data points and the solid line shows the fit to Eq. (7). (c) NLL contour plot, calculated by comparing simulated and measured BGO $z$-positions as explained in the text. The solid blue point shows the location of the global minimum. (d) Measured BGO $z$-position distribution for recoil events (filled circles), compared with the best-fit simulation result at $E_r = 679$ keV and $\omega\gamma = 120$ eV (solid orange lines). (e) Same as panel (d), but showing the measured energy of the most energetic $\gamma$-ray hit in the BGO array. (f) Total energy deposited in the IC vs. energy loss in the third (most downstream) anode. The filled (blue) circles show the location of the $^{39}\text{Ca}$ coincidence recoils observed with the $^{38}\text{K}$ beam. The filled yellow triangle denotes the location of the event observed with a beam of pure $^{38}\text{Ar}$. The greyscale color map shows the location of all heavy-ion singles events observed with the 27.17 MeV $^{38}\text{K}$ beam. This distribution is dominated by leaky beam. Energy of 27.17 MeV. This is demonstrated in the separator TOF vs. MCP TOF distribution shown by the filled circles in Figure 3(a). This spectrum exhibits a clear clustering of 27 recoil events in the region indicated by the open ellipse. The BGO $z$-position distribution of the identified recoil events is clustered downstream of the target center, indicating a resonance energy less than the central value of 689 keV [17]. Hence to extract a resonance strength, $\omega\gamma$, and a resonance energy, $E_r$, we use a technique similar to that employed in Ref. [26]. For a fixed beam energy of 27.17 MeV, we generate a simulated BGO $z$-position spectrum over the range of resonance energies contained within the gas target. For the simulations, we use the standard DRAGON GEANT3 package [27] and convolute the resulting BGO energies with a realistic hardware threshold. The hardware threshold was determined experimentally by taking long background runs with the threshold set to the value employed in the experiment, and to a reduced value of 50 mV. The resulting spectra were normalized, divided into each other, and fit with a Fermi function to arrive at the functional form used in the analysis. Following the threshold convolution, we scale the simulated spectra by the factor $$\eta Y_{\omega\gamma} N_b / N_{\text{sim}},$$ where $\eta = 0.121 \pm 0.003$ is the heavy-ion detection efficiency, $Y_{\omega\gamma}$ is the reaction yield at a given resonance strength $\omega\gamma$, $N_b = (2.53 \pm 0.30) \times 10^{12}$ is the number of incoming beam ions, and $N_{\text{sim}} = 50,000$ is the number of simulated events. Scaled in this manner, the simulated spectrum represents both the magnitude and the shape of the BGO $z$-position distribution for a given $\omega\gamma$ and $E_r$. The $\gamma$-ray efficiency is implicitly included in the generation of the simulated spectra since the number of counts appearing in the spectra prior to scaling is determined by the detection efficiency, as modeled in the GEANT3 simulation. This modeling is sensitive to the branching ratios for $\gamma$-ray decay from the 6460 keV state in $^{39}$Ca. These branching ratios have not been measured, and hence we have assumed dominant decays either directly to the ground state or through the first excited $\frac{5}{2}^-$ state, as observed for the decay of known $\frac{5}{2}^+$ excited states in the well-studied mirror nucleus $^{39}$K [21]. The location of the $\frac{5}{2}^-$ state in $^{39}$Ca has not been conclusively assigned, but there are a number of candidates in the $\sim 3-4$ MeV excitation energy region [21]. Hence for the present analysis, we have assumed decay through a state at 3.5 MeV to represent the feeding through the $\frac{5}{2}^-$. To quantitatively account for the uncertainty related to the $\gamma$-ray decay scheme, we have utilized a profile likelihood technique to marginalize over the unknown branching ratios. Specifically, we performed separate simulations for a range of different fractional feedings directly to the ground state or through a state at 3.5 MeV. In the simulations, the ground state/excited state ratios ranged from 0%–100% in steps of 10%. For each set of simulations, we took the branching with the highest likelihood value and incorporated it into the eventual likelihood surface used to extract confidence intervals on the resonance strength and energy (the calculation of likelihoods and construction of the likelihood surface is detailed later in this section). This technique of using profile likelihoods to marginalize over relevant, but uninteresting “nuisance” parameters is well established in the statistical literature; see, for example Refs. [25, 28]. It should be noted that the uncertainty on the $\gamma$-ray detection efficiency is dominated by geometrical and Monte-Carlo uncertainties and not the unknown branching ratios. The yield parameter in Eq. (6), $Y_{\gamma\gamma}$, is given by the convolution of the standard Breit-Wigner narrow-resonance cross section [29] with the gas target density profile. The density profile was measured in a previous experiment by recording the $\gamma$-ray yield from the $^3$He($^{12}$C, $p$)$^{14}$N reaction in a shielded BGO detector moved along the length of the target [30]. These data (scaled to the 27.17 MeV beam energy employed in the present experiment) are shown in Figure 3(b). The density profile was determined by fitting the data with the following function: $$f(E) = 1 \left[ 1 + e^{(E - E_0 - \Delta E/2)/a} \right], \quad (7)$$ where $E_0$ is the beam energy at the center of the gas target, $\Delta E$ is the energy loss across the full length of the gas target, and $a$ is a free parameter. The resulting best-fit is shown as the orange solid line in Figure 3(b). The fitting procedure implicitly includes the stopping power, $\varepsilon = (3.95 \pm 0.14) \times 10^{-15}$ eV cm$^2$ (in the center-of-mass frame). To extract a resonance strength and energy, we calculate the negative log-likelihood (NLL) by comparing our model (the scaled BGO z-position simulations) with experimental data, over a grid of resonance strengths and energies. We assume the counts per bin in the BGO z-position spectra are Poisson distributed, meaning the NLL is given by $$-\ln \mathcal{L} = \sum_i \left\{ \ln(n_i!) - n_i \ln(f_i) \right\} + S. \quad (8)$$ Here $n_i$ is the number of measured counts in bin $i$, $f_i$ is the number of simulation counts in bin $i$, and $S$ is the integral of the simulated distribution. The result of this likelihood analysis is shown in Figure 3(c). This figure shows a contour plot of the NLL as a function of the resonance energy and resonance strength, which contains two local minima. The first (global) minimum is in the constant-pressure region of the target with $E_r = 679$ keV, $\omega \gamma = 120$ meV, and $-\ln \mathcal{L}_0 = 16.2$. The second (local) minimum is far upstream in the target, where the density has not yet reached equilibrium, at $E_r = 677$ keV, $\omega \gamma = 650$ meV, and $-\ln \mathcal{L}_1 = 16.9$. Based on the NLL values, we exclude the $E_r = 677$ keV solution at a 76% significance level. This significance level was calculated using the likelihood ratio test, wherein $2 \ln (\mathcal{L}_0 / \mathcal{L}_1)$ (here equal to 1.4) is taken to be $\chi^2$ distributed [28]. The significance level is thus the value of $X^2(1.4)$, where $X^2(n)$ is the $\chi^2$ cumulative distribution function with one degree of freedom. The resulting best fits to both the BGO z-position and the $\gamma$-ray energy spectra are shown in Figures 3(d) and 3(e), respectively. Analyzing the region of the contour plot surrounding the global minimum, we extract 68% confidence intervals for the resonance energy and resonance strength of $E_r = 679^{+2}_{-1}$ keV and $\omega \gamma = 120^{+50}_{-30}$ meV. These quantities represent statistical uncertainties only. A number of sources of systematic uncertainty are also present, and are summarized in Table III. Note that the 0.17% systematic uncertainty on the beam energy (c.f. Section II) is implicitly included since it is already folded into the quoted uncertainty on the stopping power. The resonance energy measurement is subject to systematic uncertainties related to each of the quantities in Table III, while the resonance energy measurement is affected only by the stopping power. Adding all of the relative uncertainties in quadrature, we arrive at the following resonance energy and strength values: $$E_r = 679^{+2}_{-1} \text{(stat.)} \pm 1 \text{(sys.) keV}$$ $$\omega \gamma = 120^{+50}_{-30} \text{(stat.)}^{+20}_{-60} \text{(sys.) meV}.$$ The uncertainty due to potential background from reactions occurring on isobaric $^{38}$Ar contamination in the beam was determined through a background measurement using a stable beam of pure $^{38}$Ar, with a total ion on target of $(6.9 \pm 0.6) \times 10^{11}$. This measurement observed a single count near the edge of the expected recoil region, shown as the filled triangle in Figure 3(a). This count is likely a random leaky \| Quantity \| Measured Value \| Relative Uncertainty \| \|---------------------------------------\|----------------\|----------------------\| \| $^{38}$Ar background \| (see text) \| +0% \| \| Beam ions on target \| $(2.53 \pm 0.30) \times 10^{12}$ \| 12% \| \| BGO efficiency \| 0.541 \pm 0.054 \| 10% \| \| Stopping power [eV cm$^2$] \| $(3.95 \pm 0.14) \times 10^{-15}$ \| 3.5% \| \| MCP transmission \| 0.789 \pm 0.021 \| 2.7% \| \| Charge state fraction \| 0.192 \pm 0.002 \| 1.0% \| \| MCP efficiency \| 0.997 \pm 0.003 \| 0.3% \| \| Live time \| 0.79806 \pm 0.00002 \| 0.002% \| beam event based on its location in the IC total energy vs. energy loss spectrum. This is demonstrated in Figure 3(f), which clearly shows that the suspected background event is well separated from the locus of $^{38}\text{Ar}$ recoils and is consistent with the locus of leaky beam events. Furthermore, the known properties of $^{38}\text{Ar} + p$ radiative capture imply that background from $^{38}\text{Ar}$ contamination is highly unlikely. There are no known $^{38}\text{Ar} + p$ resonances within 10 keV of the energies covered in the DRAGON gas target [21]. As a result, resonant capture is only possible through heretofore unknown proton-unbound states in the well-studied $^{39}\text{K}$ nucleus. Concerning direct capture, we calculate an estimated cross section of 0.38 mb. We can then calculate the energy loss spectrum. This is demonstrated in Figure 3. Given the small likelihood that the single event observed in the measurement with pure $^{38}\text{Ar}$ beam is a genuine $^{38}\text{Ar}(p,\gamma)^{39}\text{K}$ recoil, we do not alter the $\omega\gamma = 120$ meV central value extracted from our likelihood analysis. However, for a conservative estimate of the associated uncertainties, we recommend that the lower-bound systematic uncertainty include the possibility of unforeseen contamination arising from $^{38}\text{Ar}(p,\gamma)^{39}\text{K}$ reactions. To calculate this uncertainty, we first determine an upper limit of 2.4 events, or a yield of $3.4\times10^{-12}$, in the pure $^{38}\text{Ar}$ beam measurement. We do this by applying the standard Rolke method [25] to the single count observed in the recoil region. In the production runs with the $^{38}\text{K}$ radioactive beam (mixed with $^{38}\text{Ar}$ contamination), this translates into an upper limit of 13 events. This upper limit is calculated assuming an Ar/K ratio of 1.54 in the production beam, determined by sending attenuated beam to the end of DRAGON and fitting the individual Ar and K components in the IC energy loss spectrum. Dividing by the 27 observed recoil events, we arrive at a relative uncertainty of 50%. This uncertainty applies only to the lower limit on the resonance strength since the presence of background due to beam contamination can only reduce, never increase, the measured resonance strength. We emphasize that this procedure for determining a systematic uncertainty due to potential $^{38}\text{Ar}$ background is an ad hoc adjustment, not one formulated from rigorous statistical methods. Overall, it provides a conservative estimate on the total systematic uncertainty applied to the resonance strength measurement. The beam delivered to DRAGON was also contaminated by isomeric $^{38m}\text{K}$ ($E_{c} = 130$ keV, $t_{1/2} = 924$ ms). The ratio of $^{38m}\text{K}$ to $^{38}\text{K}$ was measured to be $7.1\times10^{-2}$ at the ISAC yield station. The yield measurements bypass the charge state booster, and hence some additional fraction of the isomers will decay before reaching DRAGON. The delay between production and arrival at the DRAGON target is dominated by the charge breeding time, which has been measured to be on the order of a few hundred milliseconds [32]. Taking a nominal delay time of 400 ms, the $^{38m}\text{K}/^{38}\text{K}$ ratio would decrease to $5.3\times10^{-2}$ by the time the beam reaches the DRAGON target. Given the small fraction of $^{38m}\text{K}$ in the beam, no background from isomeric capture is expected. C. Singles Analysis In addition to the coincidence analysis of the 689 keV resonance presented in Section II B, we have also performed a separate extraction of the resonance strength using heavy-ion singles data alone. This analysis was guided by the results of the prior coincidence analysis, i.e. regions of interest in various parameter spaces were identified by the location of coincidence recoils. However, the final quantitative cuts applied to the singles data were determined from the distributions of the singles parameters alone. This singles analysis made use of the time difference between the incoming beam bunch (measured from the ISAC-1 RFQ signal) and the upstream MCP to construct a separator TOF parameter without requiring prompt $\gamma$ rays. This analysis is summarized in the plots shown in Figure 4. Panel (a) shows the standard MCP TOF signal plotted vs. the RF–MCP TOF, where the 27 events already identified as recoils in the coincidence analysis (represented by the blue filled circles) are tightly clustered in a narrow region of the plot. Continuing the analysis, we first set a gate on the entire upper-left region of the plot, which contains all of the coincidence recoils (the actual gate is included in the Figure 4(a) as the blue dashed line). We then project these events onto the solid black diagonal axis shown in the figure. The new projected parameter ("RF-MCP projection") is shown in the panel (b) of Figure 4, plotted vs. two separate parameters: 1) the $y$ position in the upstream MCP, deduced from a resistive-anode readout scheme; and 2) the energy loss in the third (most downstream) anode of the IC. In both cases, the confirmed recoil events are tightly clustered in a single region of the plot. To further separate recoil events from background, we place a one-dimensional cut on the "RF-MCP projection" parameter, including all events to the left of the black dotted line in the figure. For these events only, we then plot the IC energy loss vs. the MCP $y$ position, shown in Figure 4(c). Here, the singles events cluster into two distinct loci, with the confirmed recoil events falling entirely within the upper-right cluster. From this, we conclude that the singles events in the upper-right locus correspond to recoils, while the events in the lower-left locus correspond to background leaky beam events. To quantify the overlap between the recoil and leaky beam regions in Figure 4(c), we project onto the diagonal axis indicated by the solid black line in the figure. This projection is shown in the Figure 4(d). The measured data (shown as open circles with error bars) are well-described by a double-Gaussian distribution (shown as dashed, dot-dashed, and solid lines, as indicated in the legend). The smaller Gaussian on the left of the figure corresponds to the estimated background distribution, and the larger Gaussian on the right of the figure corresponds to the recoil distribution. We take the true number of recoil events to be equal to the integral of the signal distribution, 52.0 ± 8.2. The uncertainty on this quantity comes from propagating the $1\sigma$ uncertainties on the individual fit parameters, which were calculated with MINUIT. To calculate the singles resonance strength, we use the standard thick-target formula [29], $$\omega\gamma = 2N_{e}/(\eta N_{p}A^{2}),$$ (9) FIG. 4. Summary of the singles resonance strength analysis for the 27.17 MeV beam energy. In panels (a) – (c), the blue filled circles represent events already identified as recoils in the coincidence analysis, and the greyscale intensity maps represent all singles data. In panel (d), the open circles represent all singles data, and the various curves represent fits as indicated in the legend. The solid black lines in panels (a) and (c) represent diagonal axes onto which the two-dimensional data are projected for subsequent analysis. The dashed black lines in panel (b) represent the cut placed on the “RF-MCP Projection” parameter. The full significance of each plot is explained in the main text. where $N_r = 52.0 \pm 8.2$ is the number of recoil events, $\varepsilon = (3.95 \pm 0.14) \times 10^{-15}$ eV cm$^2$ is the center-of-mass stopping power, $\eta = 0.110 \pm 0.003$ is the heavy-ion detection efficiency, $N_b = (2.53 \pm 0.30) \times 10^{12}$ is the number of beam ions, and $\Lambda = (3.513 \pm 0.005) \times 10^{-12}$ cm is the center-of-mass deBroglie wavelength. Note that the heavy-ion detection efficiency includes the IC efficiency of 0.913 $\pm$ 0.003. This was not included in the heavy-ion efficiency used in the coincidence analysis since the IC was not used to select coincidence events. The deBroglie wavelength assumes a resonance energy of $E_r = 679 \pm 2$ keV, as extracted from our previous maximum likelihood analysis. The influence of this assumption is minor; calculating the resonance strength using the previous resonance energy of $689 \pm 10$ keV increases the result by less than 1 meV. The resulting resonance strength is $\omega \gamma = 120 \pm 20$ meV (statistical uncertainty only), which is in good agreement with our coincidence result of $120 \pm 30$ meV (the exact agreement of the central values should be considered fortuitous). The estimated singles systematic uncertainty is $\pm 15$ meV, calculated by propagating the uncertainties for the stopping power, number of beam particles, and detection efficiency. In practice, the singles technique frequently results in a lower systematic uncertainty than the coincidence method since there is no need to estimate the $\gamma$-ray detection efficiency. This efficiency typically comes with a relative uncertainty of 10% or greater, resulting from uncertainties in the \textsc{Geant3} simulation of the BGO array [27], as well as from unknown $\gamma$-ray decay schemes. However, for reliable application of the singles technique, it is crucial that the full width of the resonance be contained within the gas target, to ensure that the thick-target approximation of the resonance strength formula is valid. In the future, technical advances will likely improve the ability to discern resonance positions based on only a handful of recoil events. With this capability, an off-center resonance would be spotted early on during a running period, and the beam energy could be adjusted accordingly. One example presently under development is the use of a fast-timing LaBr array for $\gamma$-ray detection. The fast timing properties of LaBr allow the resonance position to be deduced from the time difference between the detected $\gamma$-rays and the arrival of the corresponding beam bunch. Preliminary calculations and simulation work suggest that this method is more precise than the presently-employed $z$-position technique and may be applied to data sets with as few as $\sim 5$ confirmed recoils [33]. As discussed in Ref. [11], the present measurements place significant constraints on the overall $^{38}$K$(p,\gamma)^{39}$Ca reaction rate at nova temperatures. This is demonstrated in Figure 5, which shows the calculated rate vs. temperature curves for the three presently reported resonances, along with their sum. Assuming the astrophysical rate is dominated by these three resonances, the lower curve (the nominal 689 keV resonance) sets a lower limit on the astrophysical rate, while the sum sets an upper limit. For comparison, the recommended rate from Iliadis et al., along with the factor 100 up/down uncertainty band, is also included in the figure. At peak temperatures for ONe nova burning, $T \sim 0.4$ GK, the total uncertainty has been reduced from a factor of $10^4$ to a factor of $\sim 40$. Applying these new, experimentally based, limits to the model predictions of the Iliadis et al. sensitivity study [8] results in a reduction of overall uncertainties on $^{38}$Ar, $^{39}$K, and $^{40}$Ca production. in ONe novae from respective factors of ~25, 136, and 57 to factors of ~2, 18, and 9. Note for these calculations, the nucleosynthesis models which maximized the sensitivity to the $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ rate were used. For $^{38}\text{Ar}$ and $^{40}\text{Ca}$ this corresponds to the “S1” model ($T_{\text{peak}} = 418$ MK), while for $^{39}\text{K}$ the “P2” model ($T_{\text{peak}} = 356$ MK) was used. In order to investigate the dependence of these sensitivity results to specific nova models, we have performed a separate $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ sensitivity study based on an independent calculation performed with the NuGrid package, using the single-zone “post processing network” (ppn) code [34]. The initial conditions of the calculation are a 1.3 solar mass white dwarf with a temperature of 7.0 MK. The white dwarf composition is given by the “Denisenkov” model, evolved using the Modules for Experiments in Stellar Astrophysics (MESA) code [35]. The accretion rate is $10^{-11} M_\odot/\text{yr}$, and the composition of the accreted material is assumed to be solar. The peak temperature of the model outburst is 408 MK, similar to the 418 MK peak temperature of the S1 model from Ref. [8]. A complete description of the parameters going into the NuGrid calculation can be found in Ref. [34]. The results of the NuGrid sensitivity study are summarized in Table IV, with results from the Iliadis et al. study included for comparison. The recommended rate utilized for this analysis is identical to the one presented in Ref. [9]. Overall, the predictions of the NuGrid and the S1 models are rather consistent, with agreement to within a factor of two in all cases. Our measurements and sensitivity analyses indicate that the $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ rate is not a likely source of significant over- or under-production of $^{38}\text{Ar}$, $^{39}\text{K}$ or $^{40}\text{Ca}$ in novae (relative to solar abundances). Hence the over-production of Ar and Ca observed in the spectra of nova ejecta [2–5] remains unexplained. We encourage more extensive sensitivity studies and multi-zone model calculations to investigate the source of this anomaly. It should be noted that the present results intrinsically depend on the veracity of previous transfer reaction studies, which have established the $^{39}\text{Ca}$ level scheme in the $E_r = 6–7$ MeV region. If the spins or level energies established from these studies are incorrect or incomplete, the present experiment may have neglected to cover the most important resonance energy windows for astrophysics. For this reason, we encourage future high-resolution transfer reaction studies that are targeted specifically at measuring the properties of potential astrophysical proton capture resonances in $^{39}\text{Ca}$. Although the present measurements are not directly sensitive to the spins of the measured resonances, we can still infer properties of the resonances in question based on the measured strengths. For this, we use the standard formula for the resonance strength [29], $$\omega \gamma = \frac{2J_\gamma + 1}{(2J_p + 1)(2J_{39}\text{K} + 1)} \frac{\Gamma_\gamma \Gamma_p}{\Gamma_\gamma + \Gamma_p},$$ where $J_\gamma = 5/2$, $J_p = 1/2$, and $J_{39}\text{K} = 3$ are the respective spins of the resonance, proton, and $^{38}\text{K}$; and $\Gamma_\gamma$ and $\Gamma_p$ are the respective $\gamma$-ray and proton partial widths of the resonance. Assuming a “hard” upper limit on the proton spectroscopic factor for unbound states of $C_2S \leq 0.1$ and the measured strength value of $\omega \gamma = 120$ meV for the $679 \pm 2$ keV resonance, we calculate an upper limit on the mean $\gamma$-decay lifetime for this state of $\tau \leq 2.2$ fs. For shorter lifetimes, as $\tau \rightarrow 0$, $\Gamma_\gamma/(\Gamma_\gamma + \Gamma_p) \rightarrow 1$, and we calculate a lower limit on the spectroscopic factor of $C_2S \geq 0.0055$. For the $515 \pm 10$ keV resonance, the $90\%$ confidence level (CL) upper limit on the strength of $18.4$ MeV sets an upper limit on the lifetime of $\tau \leq 12$ fs (again taking the “hard” upper limit on the spectroscopic factor at $C_2S = 0.1$). For short lifetimes, $\Gamma_\gamma/(\Gamma_\gamma + \Gamma_p) \simeq 1$, we calculate an upper limit on the spectroscopic factor of $C_2S \leq 0.022$. For the $386 \pm 10$ keV resonance, the calculated upper limit on the lifetime is $\tau \leq 38$ fs (again taking the measured $90\%$ upper limit on the strength of $\omega \gamma < 2.54$ MeV and the “hard” spectroscopic factor limit of 0.1). For short lifetimes satisfying $\Gamma_\gamma/(\Gamma_\gamma + \Gamma_p) \simeq 1$, we calculate an upper limit on the spectroscopic factor of $C_2S \leq 0.066$. We emphasize that these limits are simply “back of the envelope” calculations and not intended to set any rigid limits on the single-particle properties of the resonances in question. To summarize, we have performed the first ever direct measurement of the $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ reaction, focusing on the three potential $\ell = 0$ resonances within the Gamow Window for classical novae, whose energies have been determined previously to be $386 \pm 10$ keV, $515 \pm 10$ keV, and $689 \pm 10$ keV. For the highest-energy resonance, we observed a clear $^{39}\text{Ca}$–$\gamma$ coincidence signal consisting of 27 events. We performed a two-dimensional likelihood analysis on the position distribution of the measured $\gamma$-rays to extract a resonance strength and energy of $\omega \gamma = 120^{+90}_{-50}(\text{stat.})^{+20}_{-60}(\text{sys.})$ meV and $E_\gamma = 679^{+34}_{-32}(\text{stat.}) \pm 1(\text{sys.})$ keV, respectively. The quoted systematic uncertainties are conservative and include the possibility of background events arising from stable $^{38}\text{Ar}$ beam contamination. We also performed a separate analysis of $^{39}\text{Ca}$ singles data and extracted a resonance strength of $\omega \gamma = 120 \pm 20(\text{stat.}) \pm 15(\text{sys.})$ meV, consistent with the coincidence result. For the lower two resonances, we observed no events consistent with recoils and used a profile likelihood technique to extract $90\%$ CL upper limits on the resonance strengths of $2.54$ MeV and $18.4$ MeV for the lower and middle resonances, respectively. Based on these measurements we have established new recommended upper and lower limits for the $^{38}\text{K}(p, \gamma)^{39}\text{Ca}$ reaction rate which reduce uncertainties at peak nova temperatures ($T_\text{e} \sim 0.4$) from a factor of $10^4$ to a factor $\sim 40$. Incorporating these new limits into two separate nova model calculations we find that the uncertainties on the predicted abundances of $^{38}\text{Ar}$, $^{39}\text{K}$, and $^{40}\text{Ca}$ are reduced to a factor of 15 or below in all cases. ACKNOWLEDGMENTS The authors are grateful to the ISAC operations team and the technical staff at TRIUMF for their support during the experiment, in particular F. Ames for dedicated operation of the ECR charge state booster. We also thank R. Wilkinson for calculations of proton single-particle widths for the three resonances measured in this work. TRIUMF’s core operations are supported via a contribution from the federal government through the National Research Council of Canada, and the Government of British Columbia provides building capital funds. DRAGON is supported by funds from the National Sciences and Engineering Research Council of Canada. Authors from the Colorado School of Mines acknowledge support from the Department of Energy, grant DE-FG02-93ER40789. The U.K. authors acknowledge support by STFC. The authors acknowledge P. Denisenko for assistance in running the NuGrid code and for fruitful discussions. Support for NuGrid is provided by the National Science Foundation through grants PHY 02-16783/PHY 08-22648 and PHY-1430152, which fund the Joint Institute for Nuclear Astrophysics (JINA) and the JINA Center for the Evolution of the Elements, respectively. NuGrid support is also provided by the European Union through grant MIRG-CT-2006-046520. The NuGrid collaboration uses services of the Canadian Advanced Network for Astronomy Research (CANFAR) which in turn is supported by CANARIE, Compute Canada, University of Victoria, the National Research Council of Canada, and the Canadian Space Agency. [1] A. W. Shafter, Astrophys. J 487, 226 (1997). [2] S. Pottasch, Ann. Astrophys. 22, 412 (1959). [3] J. Andrea, H. Drechsel, and S. Starrfield, Astron. Astrophys. 291, 869 (1994). [4] V. P. Arkhipova, M. A. Burlak, and V. F. Esipov, Astron. Lett. 26, 372 (2000). [5] A. Evans, R. D. Gehrz, T. R. Geballe, C. E. Woodward, A. Salama, R. A. Sanchez, S. G. Starrfield, J. Krautter, M. Barlow, J. E. 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Giguetti, Efficiency calibration measurement and GEANT simulation of the DRAGON BGO gamma ray array at TRIUMF, Master’s thesis, University of Northern British Columbia, Prince George, Canada (2004), unpublished. [28] F. James, Statistical methods in experimental physics (2006). [29] C. Iliadis, Nuclear Physics of Stars (Wiley-VCH, 2007) pp. 335, 341. [30] M. Carmona, Experimental Studies of the Astrophysical Nuclear Reaction $^3$He$(a,\gamma)^7$Be, Ph.D. thesis, Universidad Complutense de Madrid, Madrid, Spain (2014), unpublished. [31] R. Longland, C. Iliadis, A. Champagne, J. Newton, C. Ugalde, A. Coc, and R. Fitzgerald, Nucl. Phys. A 841, 1 (2010), the $S$-factor is parametrized as $S(E) = 741.0$ keVb $- E \cdot 0.2598 b + E^2 \cdot 1.208 \times 10^{-4}$ b/keV, with parameters obtained from http://starlib.physics.unc.edu/. [32] F. Ames, R. Baartman, P. Bricault, K. Jayamanna, M. McDonald, M. Olivo, P. Schmor, D. H. Liu, Yuan, and T. Lamy, Rev. Sci. Instrum. 77, 03B103 (2006). [33] C. Ruiz, “La$\beta_3$ array for DRAGON et al.” Presented at the Workshop on Recoil Separators for Nuclear Astrophysics, Vancouver, BC (October 2016). [34] P. A. Denissenkov, J. W. Truran, M. Pignatari, R. Trappitsch, C. Ritter, F. Herwig, U. Battino, K. Sestoedehnia, and B. Paxton, Mon. Not. R. Astron. Soc. 442, 2058 (2014). [35] B. Paxton, L. Bildsten, A. Dotter, F. Herwig, P. Lesaffre, and F. Timmes, Astrophys. J. Suppl. Ser. 192, 3 (2011).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5457, 1 ], [ 5457, 12407, 2 ], [ 12407, 16276, 3 ], [ 16276, 19627, 4 ], [ 19627, 23520, 5 ], [ 23520, 30395, 6 ], [ 30395, 37232, 7 ], [ 37232, 40745, 8 ], [ 40745, 41770, 9 ], [ 41770, 48981, 10 ], [ 48981, 54928, 11 ] ] }
98d8a20c4329519c58da1843b5689eb22a26bfc0	{ "olmocr-version": "0.1.59", "pdf-total-pages": 9, "total-fallback-pages": 0, "total-input-tokens": 28642, "total-output-tokens": 9223, "fieldofstudy": [ "Medicine" ] }	Observational Review and Analysis of Concussion: a Method for Conducting a Standardized Video Analysis of Concussion in Rugby League Andrew J. Gardner1,2, Christopher R. Levi1,2 and Grant L. Iverson3,4,5 Abstract Background: Several professional contact and collision sports have recently introduced the use of sideline video review for club medical staff to help identify and manage concussions. As such, reviewing video footage on the sideline has become increasingly relied upon to assist with improving the identification of possible injury. However, as yet, a standardized method for reviewing such video footage in rugby league has not been published. The aim of this study is to evaluate whether independent raters reliably agreed on the injury characterization when using a standardized observational instrument to record video footage of National Rugby League (NRL) concussions. Methods: Video footage of 25 concussions were randomly selected from a pool of 80 medically diagnosed concussions from the 2013–2014 NRL seasons. Four raters (two naïve and two expert) independently viewed video footage of 25 NRL concussions and completed the Observational Review and Analysis of Concussion form for the purpose of this inter-rater reliability study. The inter-rater reliability was calculated using Cohen’s kappa (κ) and intra-class correlation (ICC) statistics. The two naïve raters and the two expert raters were compared with one another separately. Results: A considerable number of components for the naïve and expert raters had almost perfect agreement (κ or ICC value ≥ 0.9), 9 of 22 (41%) components for naïve raters and 21 of 22 (95%) components for expert raters. For the concussion signs, however, the majority of the rating agreement was moderate (κ value 0.6–0.79); both the naïve and expert raters had 4 of 6 (67%) concussion signs with moderate agreement. The most difficult concussion sign to achieve agreement on was blank or vacant stare, which had weak (κ value 0.4–0.59) agreement for both naïve and expert raters. Conclusions: There appears to be value in expert raters, but less value for naive raters, in using the new Observational Review and Analysis of Concussion (ORAC) Form. The ORAC Form has high inter-rater agreement for most data elements, and it can be used by expert raters evaluating video footage of possible concussion in the NRL. Keywords: Concussion, Video analysis, Injury management Key Points - Identifying concussion from the sideline during a match is challenging, but with the use of video out-of-view or fleeting signs may be captured and a player can be removed from play. - Having a reliable form for coding and analysing concussion can be a useful adjunct to the sideline clinical management strategy of the athletic trainer and team physician. We present the first objective and reliable coding form for rugby league to capture the game situation, the mechanism of injury, and possible signs of concussion. Background Rugby league is a high-intensity collision sport [23]. The game is played continuously in two 40-min halves, and game-play involves two teams of 13 on-field players and four interchange players who may be switched in and out of the game. The published incidence rates of concussion in rugby league vary [12]; at the National Rugby League (NRL) level, medically diagnosed concussions in three clubs from the 2013 season revealed an incidence rate of 14.8 concussions per 1000 player match hours [15], while a rate of 28.3 concussion per 1000 player match hours were reported from one NRL club over a 15-year (1998–2012) period [41]. The incidence of use of the concussion interchange rule (CIR) was 24.0 (95% CI 20.7–27.9) uses of the CIR per 1000 NRL player match hours [14] and 44.9 (95% CI 38.5–52.3) uses of the CIR per 1000 National Youth Competition player match hours [15]. One method that has becoming increasingly relied upon to assist with improving the identification of possible concussion has been the review of video footage on the sideline. The use of video for reviewing a concussion may identify signs of injury that may have been blocked from view or otherwise missed by medical staff. A number of professional contact and collision sports have recently introduced the use of sideline video review for club medical staff to help identify and manage concussions [29]. A number of studies of video footage have been conducted in a variety of sports, for example, rugby league [13–15], rugby union [25], and Australian Rules Football [9, 29, 30]. Other sports, such as boxing [37], soccer [1], taekwondo [24], ice hockey [6, 10, 18, 19], and lacrosse [28], have also reported on the use of video footage for understanding the circumstances and mechanisms of injury unique to their sports. A risk prediction model among National Hockey League (NHL) players reported that both visual signs of concussion and information pertaining to mechanisms of injury improved a clinician’s ability to identify athletes who should be removed from play and evaluated [6]. Specifically, the study indicated that suspected loss of consciousness, motor incoordination or balance problems, being in a fight, having an initial hit from another player’s shoulder, and having a secondary hit on the ice were all associated with increased risk of subsequent concussion diagnosis. Sport-specific coding criteria of concussion for game situational factors and injury mechanisms have been developed for hockey (e.g., the ‘Heads-Up Checklist’ [20]), but these criteria do not generalize to other sports like rugby union or rugby league. Video criteria and coding forms require validation in each individual sport [29, 30]. In a more recent NHL study examining the predictive ability of visual signs of concussion, loss of consciousness, motor incoordination, and blank/vacant look had a positive association with concussion diagnosis, whereas slow to get up and clutching of the head, despite occurring frequently, had low positive predictive values [10]. Several video studies have examined signs of concussion, together with player characteristics, injury characteristics, and match situational factors, in professional rugby league [13–15]. In 2014, video reviews of injury have been implemented in the NRL to help medical staff and promote player health and safety. The aim of this study was to present a standardized observational recording form and to determine whether independent raters agreed on the antecedent events, mechanisms of injury, and concussion signs when using the form to code digital video records of concussions in the NRL. Methods Participants This study was conducted in the national professional rugby league competition in Australia during the 2013 and 2014 seasons. All medically diagnosed concussion events during 2013 and 2014 NRL seasons were available to be included in this study. Procedure For this study, 25 medically diagnosed concussions were randomly selected from the 2013 to 2014 NRL seasons’ video library (n = 80). The video library included only excerpts of the incidents for each case, not the entire game. The duration of the game footage recorded for each of the 25 cases selected from the library and used in this study ranged from 138 to 473 s. Four raters (two ‘expert’ and two ‘naïve’) independently reviewed the video footage of the 25 NRL concussion events. The naïve raters were novices of the sport. They had limited to no knowledge or experience with rugby league match play and no experience identifying and managing concussion. The expert raters were defined as individuals with experience in rugby league match play and expertise in concussion management at the professional (NRL) level. Both expert raters had at least one NRL season of experience working on the sideline for an NRL club with the responsibility of identifying and assessing athletes suspected of having sustained a concussion. The medically diagnosed NRL concussion library was gathered from three teams during the 2013 season (n = 20 concussions) [13], and all teams during the 2014 NRL season (n = 60 concussions). The Concussion in Sport Group consensus definition of concussion was used by all clubs involved in this study [32]. Raters viewed the match digital records of 25 concussions using the Quicktime Multimedia Player V.7.7.5. Each rater completed all components of the form for each... of the 25 concussion events. The raters were permitted to view the incident as many times as required and in any playback speed as deemed necessary to complete all categories of the form. All participants provided informed consent. This study was conducted in accordance with the standards of the ethics outlined in the Declaration of Helsinki. Approval of this study was provided by the University of Newcastle Human Ethics Committee. Instruments* A rating form was created to provide a simple but standardized framework for coding and analysing video footage of the situations and consequences of concussion events in rugby league. The form was developed by a neuropsychologist with extensive experience in the sport and concussion management and was based on work conducted previously in ice hockey in North America, and a similar, but not identical, approach to validating the form was used for the validation of the ‘Heads-Up Checklist’ [20]. The form was adapted to include specific information to rugby league. Concussion signs that have been previously examined in video review studies in rugby league were included [13–15]. The form consists of various sections related to the player and game characteristics (e.g., ball carrier versus tackler, tackle height, type of play, etc.), the anatomical region of contact, the injury location on the field of play, the injured player’s on-field management, and six possible concussion signs (see Fig. 1). Statistical Analysis The results from the two naïve raters and the expert raters were considered separately. The intra-class correlation (ICC) was used to determine the level of agreement between the two naïve raters and the two expert raters for interval and ratio variables (i.e., ‘number of players in tackle’ and ‘time taken to leave’). Inter-rater reliability analyses using Cohen’s kappa (κ) statistics [17] were used to determine the level of agreement between the two naïve raters and the two expert raters for all other (nominal) variables. Unlike the total percent agreement, Cohen’s kappa considers the proportional agreement that could occur simply by chance. The κ coefficients are calculated by considering the proportion of rater agreement and the expected proportion [17]. Using the interpretations of κ described by McHugh [34], κ agreement was categorized as almost perfect (>90), strong (.80–.90), moderate (.60–.79), weak (.40–.59), minimal (.21–.39) and none (0–.20). All analyses were performed using IBM SPSS Statistics V.23.0 [21] and used two-sided tests for significance at the 0.05 level, with 95% confidence intervals (CIs). Results The inter-rater reliabilities for the various components of the rating form for both the naïve and expert raters are presented in Table 1. For the naïve raters, 6 of 20 (30%) components of the form, and 5 of 6 (83%) concussions signs, had ω values between .60 and .79 (‘moderate’ agreement), while 2 of 2 (100%) interval/ratio variables of the form had very good ICC. According to the interpretations of ω described by McHugh [34], 8 of 22 components were categorized as ‘almost perfect’; 3 components were classified as ‘strong’; 2 components were classified as ‘weak’; 2 components were classified as ‘minimal’; and one of the components (playing position) was not classified. For the concussion signs, the naïve raters had no signs that had ‘almost perfect’ or ‘strong’ agreement; 5 (83%) signs were classified as ‘moderate’ and 1 (17%) sign was classified as ‘weak’. For the expert raters, 19 of 20 (95%) components of the form had ω values of between .90–1.00 (‘almost perfect’ agreement) and one (5%) had moderate agreement. The expert raters had perfect ICC for 2 of 2 (100%) interval/ratio variables. For the concussion signs, the expert raters had 1 of 6 (17%) of concussions signs with ω values between .80–.90 (‘strong’ agreement); 4 (67%) of were classified as ‘moderate’; and 1 (17%) was classified as ‘weak’ agreement. No signs classified by either the naïve or expert raters had a ‘minimal’ or ‘none’ level of agreement. There were nine components that were all rated with ‘almost perfect’ agreement by both the naïve and the expert raters (game time, score, whether the concussed player was a ball carrier or a tackler, the number of players involved in the tackle, whether the offending player was placed on report by a match official, the initial contact, the region of contact, whether the player was removed from play, and how the player left the field). The level of agreement between the expert raters and between the naïve raters was also very consistent for the tackle height and whether the injury occurred as a result of foul play (i.e., the offending player was penalized). The naïve raters had a ‘strong’ level of agreement for these components. The naïve raters had a moderate level of agreement on whether the game was played during the night or day, the tackle number in the set, the anatomical location of the impact, and the location of the field where the concussion took place, whereas all of these components had an ‘almost perfect’ level of agreement between the two expert raters. The expert raters also achieved an ‘almost perfect’ level of agreement on the secondary contact, whether the concussed player had anticipated the impact that caused the injury, and the time taken to leave the field of play. However, the naïve raters only had a ‘minimal’ level of agreement on these components. For type of play, and whether or not the player returned to play, the naïve raters had a ‘weak’ agreement on these components compared to the ‘almost perfect’ agreement by the expert raters. Whether or not there was secondary contact was the most difficult component to agree upon; the expert raters’ level of agreement was ‘moderate’ for this component, and the naïve raters’ level of agreement was ‘minimal’ (see Table 1). Regarding concussion signs, slow to get up had the best level of agreement between expert and naïve raters of all possible concussion signs (strong and moderate agreement, respectively), whereas a blank or vacant stare had the worst agreement (both rater groups had a ‘weak’ level of agreement). Clutch or shake head, gait ataxia (or having wobbly legs), unresponsiveness, and post-impact seizure-like features had moderate agreement for both expert and naïve raters. Discussion Rugby League is a full contact collision sport that has high concussion incidence rates [13–15]. The in-game management and decision-making process surrounding concussion is a challenge. Video review is increasingly being used as one method for improving this in-game decision-making process for medical staff, although a standardized approach to the use of such information had not been published. Although there is a large body of research examining on-field markers of concussion and their association with outcome [2–5, 7, 8, 11, 16, 22, 26, 27, 31, 33, 35, 36, 38–40, 42–46], very few of these studies have been focused on possible signs of concussion at the time of injury (versus collected later as part of a questionnaire or interview with the athlete). This study presents a standardized observational form and examines intra-rater and inter-rater agreement on the antecedent events, mechanisms of injury, and concussion signs. Overall, the results of this study suggest that a certain level of knowledge about the game is required to complete the form components accurately. Expert rates achieved an ‘almost perfect’ level of agreement on 21/22 (95%) of components compared to only 9/22 (41%) components for the naïve raters. In a similar study conducted with the ‘Heads-Up Checklist’ for National Hockey League (NHL) concussions, the naïve raters also had worse agreement across components pertaining to the antecedent events and mechanism of injury compared to the expert raters. Of the 15 components in version 1 of the Heads-Up Checklist, naïve raters 7 (47%) had weak or minimal agreement, compared to only 1 of the 15 (7%) components for the expert raters [20]. For the Heads-Up Checklist, the acceleration of the head (which was not considered a component or review item in our form) was the single component with the worst agreement across naïve and expert raters. Rating secondary contact was also challenging in the hockey study as it was in the current study. The location of the playing surface where the concussion... occurred and the time in the game when the concussion occurred were the two components with the strongest agreement by naïve and expert raters for the hockey study [20]. For the current study, the time in the game was rated well. However, the location on the field did not have a high agreement for the naïve raters. The discrepancy between naïve raters for the hockey study compared to this rugby league study may have occurred for at least three reasons. First, we divided the playing surface in our study into 12 different components and the hockey study used fewer zones. Second, the hockey study designated \| Component \| Expert raters (κ) \| McHugh [34] κ Agreement Classification \| Naïve raters (κ) \| McHugh [34] κ Agreement Classification \| \|----------------------------------\|------------------\|----------------------------------------\|------------------\|----------------------------------------\| \| Game time \| 1.00 \| Perfect \| 1.00 \| Perfect \| \| Score \| 1.00 \| Perfect \| 0.95 \| Perfect \| \| Day/night game \| 1.00 \| Perfect \| 0.70 \| Moderate \| \| Tackle number \| 1.00 \| Perfect \| 0.75 \| Moderate \| \| Ball carrier vs. tackler \| 1.00 \| Perfect \| 0.92 \| Perfect \| \| Playing position \| 1.00 \| Perfect \| NR \| N/A \| \| Tackle height \| 1.00 \| Perfect \| 0.86 \| Strong \| \| Foul play \| 0.90 \| Perfect \| 0.89 \| Strong \| \| Offending player on report \| 0.90 \| Perfect \| 1.00 \| Perfect \| \| Type of play \| 1.00 \| Perfect \| 0.56 \| Weak \| \| Initial contact \| 0.90 \| Perfect \| 0.90 \| Perfect \| \| Secondary contact \| 0.71 \| Moderate \| 0.27 \| Minimal \| \| Region of contact \| 1.00 \| Perfect \| 1.00 \| Perfect \| \| Location of impact \| 1.00 \| Perfect \| 0.70 \| Moderate \| \| Anticipation of impact \| 0.70 \| Perfect \| 0.37 \| Minimal \| \| On-field medical attention \| 1.00 \| Perfect \| 0.65 \| Moderate \| \| Removal from play \| 1.00 \| Perfect \| 1.00 \| Perfect \| \| How did the player leave \| 1.00 \| Perfect \| 1.00 \| Perfect \| \| Location of the field \| 1.00 \| Perfect \| 0.79 \| Moderate \| \| Did they return to play \| 1.00 \| Perfect \| 0.43 \| Weak \| Table 1 Inter-rater reliability (κ, ICC) for naïve and expert raters for each component of the form \| Component \| Expert raters (ICC) \| Naïve raters (ICC (95% CIs)) \| \|----------------------------------\|---------------------\|------------------------------\| \| Number of players in tackle \| 1.00 \| 0.87 (0.68–0.95) \| \| Time taken to leave \| 1.00 \| 0.99 (0.97–1.00) \| Concussion signs \| Component \| Expert raters (κ) (95% CIs) \| McHugh [34] κ Agreement Classification \| Naïve raters (κ) (95% CIs) \| McHugh [34] κ Agreement Classification \| \|----------------------------------\|-----------------------------\|----------------------------------------\|-----------------------------\|----------------------------------------\| \| Clutch or shake head \| 0.73 (0.46–0.93) \| Moderate \| 0.63 (0.36–0.87) \| Moderate \| \| Slow to get up \| 0.83 (0.15–1.00) \| Moderate \| 0.52 (0.09–1.00) \| Strong \| \| Gait ataxia \| 0.73 (0.47–0.94) \| Moderate \| 0.60 (0.58–0.61) \| Moderate \| \| Blank/vacant stare \| 0.50 (0.23–0.76) \| Weak \| 0.44 (0.15–0.71) \| Weak \| \| Unresponsiveness \| 0.78 (0.56–1.00) \| Moderate \| 0.70 (0.45–0.93) \| Moderate \| \| Post-impact seizure \| 0.65 (N/A) \| Moderate \| 0.53 (0.04–0.90) \| Moderate \| McHugh κ Agreement Classification: almost perfect (>0.90), strong (0.80–0.90), moderate (0.60–0.79), weak (0.40–0.59), minimal (0.21–0.39), and none (0–0.20) CIs confidence intervals, ICC intra-class correlation, κ kappa, N/A not applicable, NR not recorded offensive ends and defensive ends, whereas the rugby league study required the raters to record the direction of the play, and some of the disagreement between the naïve raters for the location on the field was due to the indication of the direction of the play. Finally, the hockey study used naïve raters who where more familiar with their sport (i.e., individuals with limited experience who might have played or coached [ice] hockey at a competitive level), whereas our naïve raters were complete novices, who had limited to no experience even watching the sport as fans and certainly no experience identifying concussions. In the current study, there were a number of variables that appear to rely on knowledge, understanding, and experience with rugby league match play (i.e., the expert raters outperformed the naïve raters). For example, there were large differences between the coding by expert and naïve raters of variables such as secondary contact and anticipation of impact. There was also a large difference between the coding by expert and naïve raters of variables such as secondary contact and anticipation of impact. It appears that the naïve raters were not as savvy in identifying the return to play of an interchanged athlete and/or did not identify the athlete as being re-involved in match play following their return to the field of play. As with our previous video reviews of concussion signs [14, 15], we once again found that determining whether a concussed player had a blank or vacant stare was difficult to agree upon. We had weak agreement between naïve (0.44, 95% CI = 0.15–0.71) and expert (0.50, 95% CI = 0.23–0.76) raters in this study, and our previous work has also revealed difficulty with agreement between raters (i.e., 0.36 (95% CI = 0.29 to 0.43) [14] and 0.62 (95% CI = 0.37 to 0.88) [15]). In a recent Australian Football League (AFL) video review, inter-rater reliability for the blank/vacant stare on first review was reported to be 0.24 (95% CI = 0.04 to 0.41) and minimal improvements were observed on second review [0.26 (95% CI = 0.07 to 0.43)]. The intra-rater reliability in the AFL study was somewhat better for the two raters over the two rating sessions [i.e. 0.63 (95% CI = 0.50 to 0.74) and 0.36 (95% CI = 0.18 to 0.51)]. The concussion sign ‘blank/vacant stare’ was reported to have 9% sensitivity, 100% specificity, 100% positive predictive value and 58% negative predictive value in the sample of AFL concussions [29]. When the quality of the video (including the zoom capacity to see the players face) is limited, attempting to code the presence or absence of a blank or vacant stare from video is challenging [15]. This supports the notion that good-quality video from multiple camera angles are crucial for effective video surveillance of injuries [30]. In the current study, however, this was not a limitation, suggesting that it is also important to have clear definitions, including the inclusion and exclusion criteria for coding concussion signs [30]. In a recent series of video reviews of concussions from the AFL [9, 29, 30], Makdissi and Davis indicated that video review may be an avenue that facilitates the assessment of the mechanism and impact of injury and allows for the identification of brief early signs of concussion [29]. The authors suggest that video analysis may be a useful adjunct to the sideline assessment of possible concussion [29] and that the implementation of a flowchart may improve the timely assessment of concussion [9]. We recently completed a study on the frequency (or base rates) of concussion signs in NRL match play (Gardner et al., under review). That study reviewed every game (n = 201) from the 2014 NRL season, which included 127,062 tackles, and found unresponsiveness occurred 52 times [24 (46%) were diagnosed with a concussion], slow to get up occurred 2240 times [60 (3%) were diagnosed with a concussion], clutching or shaking the head occurred 361 times [38 (11%) were diagnosed with a concussion], gait ataxia occurred 102 times [35 (34%) were diagnosed with a concussion], blank or vacant stare occurred 98 times [45 (46%) were diagnosed with a concussion], and a post-impact posturing or seizure occurred 4 times [3 (75%) were diagnosed with a concussion]. The unresponsiveness sign had 40% sensitivity, 91% specificity, 46% positive predictive value, and 89% negative predictive value. The slow to get up sign had 100% sensitivity, 50% specificity, 27% positive predictive value, and 100% negative predictive value. Clutching or shaking the head had 63% sensitivity, 46% specificity, 18% positive predictive value, and 87% negative predictive value. Gait ataxia had 58% sensitivity, 79% specificity, 34% positive predictive value, and 91% negative predictive value. Blank or vacant stare had 75% sensitivity, 84% specificity, 46% positive predictive value, and 95% negative predictive value. Post-impact seizure had 5% sensitivity, 100% specificity, 75% positive predictive value, and 85% negative predictive value in the 2014 NRL season (Gardner et al., under review). One of the unusual and unexpected findings of this study was the discrepancy observed between the naïve raters in coding variables that were conceivably thought to be obvious (e.g., game time, score, day/night game). The naïve raters did not always have 100% agreement. Because rugby league is a continuous sport, it is common for the game to continue Despite an injury, and therefore, the game clock also does not stop. As such, an injury can occur well before the game and the game clock is stopped. The discrepancies in the ‘time in game’ variable are explained by this issue; one of the naïve reviewers recorded the time correctly (i.e., when the injury occurred), whereas the other naïve rater often recorded the time when the game clock was stopped. In terms of the ‘game score’ variable, it is possible that the naïve raters were unfamiliar with teams, and therefore, errors were made in coding the score of each team. For the ‘day/night game’ variable, there were a number of games that were played during twilight, as well as the footage of some of those cases being zoomed in, and the wide view did not make the day/night difference obvious to the naïve raters who do not watch NRL games. Video review appears to be a useful adjunct to traditional methods for making in-game decisions pertaining to the identification of potential concussion (and an athlete subsequently being removed from play). However, to better understand and quantify the value of this process, future research should be conducted under time limits and/or during a game to replicate the real-world/practical pressure, neither of which was replicated in this study. Future studies might focus on whether agreement between experts improves under ‘ideal circumstances’ (i.e. as many reviews as required without time limitations) versus ‘real-world circumstances’ (i.e. a quick decision required to identify a possible injury and immediately remove the athlete from play). The current study has several limitations. Firstly, clubs used their own personnel and methods for identifying possible injuries on the field and diagnosing concussions on the sideline, which presumably makes the final specific criteria for a ‘medically diagnosed concussion’ variable across clubs. The current study does not generalize to the real-world use of in-game video analysis because the study was not conducted under the time pressure associated with in-game decision-making. Further, the sample size is small, and only two naïve and two expert reviewers were used. Whether the current results hold true for more cases and a greater number of raters is unknown. Conclusions The present study suggests that determining the presence or absence of a blank or vacant stare is challenging for both naïve and expert raters to rate reliably, but that showing unresponsiveness (i.e. possible LOC), clutching or shaking of the head, a post-impact seizure, or being slow to get up are more reliably rated signs. However, in this study, there was no variability in the clinical outcome measure, as our sample came from a pool of individuals who were all medically diagnosed with a concussion. Therefore, the predictive value of any one component or concussion sign, or a combination of these items, is unknown and may be the focus of future research. Given the variability of in-game decision-making in professional rugby league [13–15], we sought to provide validation of a standardized approach for collecting information surrounding possible concussions to help inform the in-game decision-making process. Although the form was created for all levels of competition, it only had a good level of agreement among experienced raters. Therefore, it might only be useful for those teams or clubs that have experts available to them (i.e., the professional level). For lower levels of competition, the form may have less of a benefit, because the naïve raters had a low level of agreement on many components of the form. It is important to note, however, that the management of suspected concussion at these lower levels should always be conservative. If a concussion is suspected, then the athlete should be removed from play and not returned to play the same day [32]. At the professional level, data collected from this form may allow for a thorough understanding of the situational and contextual factors related to concussion, which may be used to strategize future interventions to reduce the risk of concussion at this level. Acknowledgements The authors would like to thank Mrs. Kathryn Gurr and Ms. Vanessa Case (University of Newcastle, School of Medicine and Public Health) for completing the video review as the nominated naïve raters and Dr. Jinho Lee (School of Human Movement and Nutrition Sciences, University of Queensland) for completing the review as an expert rater. Funding The funding was provided by Hunter Medical Research Institute (HMRI) supported by Anne Greaves. Financial Disclosure None. Authors’ Contributions AG conceived the design of the study, designed the data collection tool, collected the video footage, liaised with the other raters to complete the data collection and monitored the data collection, managed the study database, conducted the statistical analysis, and drafted, revised, and finalized the manuscript. He had the final veto on the submission. CL assisted with the design of the study and provided the editorial comment to the drafts of the manuscript prepared for the submission. GI assisted with the design of the study, assisted with the statistical analysis of the data, provided expert editorial comment for all the drafts of the manuscript, and had the final veto on the submission. All authors read and approved the final manuscript. Competing Interests Andrew Gardner is an early career fellow with the National Health and Medical Research Council (NHMRC) and is supported by the School of Medicine and Public Health, University of Newcastle, and the Priority Research Centre for Stroke and Brain Injury, School of Medicine and Public Health, University of Newcastle. He has a clinical practice in neuropsychology involving individuals who have sustained sport-related concussion (including current and former athletes). He has operated as a contracted concussion consultant to the Australian Rugby Union (ARU) from July 2016. He has received travel funding... from the Australian Football League (AFL) to present at the Concussion in Football Conference in 2013 and 2017. The previous grant funding includes the NSW Sporting Injuries Committee, the Brain Foundation (Australia), and the Hunter Medical Research Institute (HMRI), supported by Jenine Thomas. He is currently funded through the HMRI, supported by Anne Greaves, and the University of Newcastle’s Priority Research Centre for Stroke and Brain Injury. Christopher Levi declares that he has no conflict of interest. Grant Iversen has been reimbursed by the government, professional scientific bodies, and commercial organizations for discussing or presenting research relating to mild TBI and sport-related concussion at meetings, scientific conferences, and symposiums. He has a clinical and consulting practice in forensic neuropsychology involving individuals who have sustained mild TBIs (including athletes). He has received research funding from several test publishing companies, including ImPACT Applications, Inc., CNS Vital Signs, and Psychological Assessment Resources (PAR, Inc.). He received past salary support from the Harvard Integrated Program to Protect and Improve the Health of athletes. He has received research funding from several test publishing companies, including ImPACT Applications, Inc., CNS Vital Signs, and Psychological Assessment Resources (PAR, Inc.). He received past salary support from the Harvard Integrated Program to Protect and Improve the Health of athletes. He has received research funding from several test publishing companies, including ImPACT Applications, Inc., CNS Vital Signs, and Psychological Assessment Resources (PAR, Inc.). He received past salary support from the Harvard Integrated Program to Protect and Improve the Health of athletes. He has received research funding from several test publishing companies, including ImPACT Applications, Inc., CNS Vital Signs, and Psychological Assessment Resources (PAR, Inc.). He received past salary support from the Harvard Integrated Program to Protect and Improve the Health of athletes. He has received research funding from several test publishing companies, including ImPACT Applications, Inc., CNS Vital Signs, and Psychological Assessment Resources (PAR, Inc.). He received past salary support from the Harvard Integrated Program to Protect and Improve the Health of athletes. He has received research funding from several test publishing companies, including ImPACT Applications, Inc., CNS Vital Signs, and Psychological Assessment Resources (PAR, Inc.). He received past salary support from the Harvard Integrated Program to Protect and Improve the Health of athletes. He has received research funding from several test publishing companies, including ImPACT Applications, Inc., CNS Vital Signs, and Psychological Assessment Resources (PAR, Inc.). 36. Meehan WP, Monuteaux MC. Early symptom burden predicts recovery after sport-related concussion. Neurology. 2014;83:2204–10. 37. Mele VJ, Bailes JE. Objectifying when to halt a boxing match: a video analysis of fatalities. Neurosurgery. 2007; 60: 307-15-6. 38. Moor HM, Eisenhauer RC, Killian KD, Proudfoot N, Henriques AA, Congeni JA, Reneker JC. The relationship between adherence behaviors and recovery time in adolescents after a sports-related concussion: an observational study. Int J Sports Phys Ther. 2015;10:225–33. 39. Morgan CD, Zuckerman SL, Lee YM, King L, Beaird S, Sills AK, Solomon GS. Predictors of postconcussion syndrome after sports-related concussion in young athletes: a matched case-control study. J Neurosurgery Pediatr. 2015;15:589–98. 40. Nelson LD, Guskiewicz KM, Marshall SW, Hammeke T, Barr W, Randolph C, McCrea MA. Multiple self-reported concussions are more prevalent in athletes with ADHD and learning disability. Clin J Sport Med. 2016;26:120–7. 41. Savage J, Hooke C, Orchard J, Parkinson R. The incidence of concussion in a professional Australian rugby league team, 1998–2012. J Sports Med. 2013; online first. 42. Terwilliger VK, Pratson L, Vaughan CG, Gioia GA. Additional post-concussion impact exposure may affect recovery in adolescent athletes. J Neurotrauma. 2016;33:761–5. 43. Vargas G, Rabinowitz A, Meyer J, Arnett PA. Predictors and prevalence of postconcussion depression symptoms in collegiate athletes. J Athl Train. 2015;50:250–5. 44. Zuckerman SL, Apple RP, Odom MJ, Lee YM, Solomon GS, Sills AK. Effect of sex on symptoms and return to baseline in sport-related concussion. J Neurosurg Pediatr. 2014;13:72–81. 45. Zuckerman SL, Solomon GS, Forbes JA, Haase RF, Sills AK, Lovell MR. Response to acute concussive injury in soccer players: is gender a modifying factor? J Neurosurg Pediatr. 2012;10:504–10. 46. Zuckerman SL, Yengo-Kahn AM, Buckkey TA, Solomon GS, Sills AK, Kerr ZY. Predictors of postconcussion syndrome in collegiate student-athletes. Neurosurg Focus. 2016;40:E13.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2974, 1 ], [ 2974, 8402, 2 ], [ 8402, 11153, 3 ], [ 11153, 16817, 4 ], [ 16817, 23064, 5 ], [ 23064, 28511, 6 ], [ 28511, 34566, 7 ], [ 34566, 37423, 8 ], [ 37423, 39459, 9 ] ] }
1daee42947f26a18351f29927cc7bde03879f9e8	{ "olmocr-version": "0.1.59", "pdf-total-pages": 9, "total-fallback-pages": 0, "total-input-tokens": 27678, "total-output-tokens": 11388, "fieldofstudy": [ "Environmental Science" ] }	Effects of prey density, temperature and predator diversity on nonconsumptive predator-driven mortality in a freshwater food web Lukáš Veselý 1, David S. Boukal 2,3, Miloš Buňič 1, Pavel Kozák 1, Antonín Kouba 1 & Arnaud Sentis 2,3,4 Nonconsumptive predator-driven mortality (NCM), defined as prey mortality due to predation that does not result in prey consumption, is an underestimated component of predator-prey interactions with possible implications for population dynamics and ecosystem functioning. However, the biotic and abiotic factors influencing this mortality component remain largely unexplored, leaving a gap in our understanding of the impacts of environmental change on ecological communities. We investigated the effects of temperature, prey density, and predator diversity and density on NCM in an aquatic food web module composed of dragonfly larvae (Aeshna cyanea) and marbled crayfish (Procambarus fallax f. virginalis) preying on common carp (Cyprinus carpio) fry. We found that NCM increased with prey density and depended on the functional diversity and density of the predator community. Warming significantly reduced NCM only in the dragonfly larvae but the magnitude depended on dragonfly larvae density. Our results indicate that energy transfer across trophic levels is more efficient due to lower NCM in functionally diverse predator communities, at lower resource densities and at higher temperatures. This suggests that environmental changes such as climate warming and reduced resource availability could increase the efficiency of energy transfer in food webs only if functionally diverse predator communities are conserved. Investigating the effects of environmental drivers on food webs is crucial to better understand global change impacts on energy and nutrient fluxes across trophic levels. A growing number of studies have thus investigated the effects of global change drivers such as temperature, enrichment, pollutants, and habitat fragmentation on trophic interactions1–4. For example, previous studies have shown that predation rate often increases with temperature but decreases with prey density5–8. Thermal effects on predation rate are mainly driven by the acceleration of physiological processes (metabolism and digestion) leading to higher energetic demands of the predators, and by more frequent predator-prey encounters due to faster movement of predators or prey with warming. The effects of prey density are caused by the non-linearity of the predator feeding rate that increases with prey density and reaches a plateau at high prey densities (i.e., saturating Holling type II or III functional responses). Altogether, these temperature- and density-dependent effects on predation rates can alter population dynamics and species persistence by modifying trophic interaction strengths9. 1University of South Bohemia in České Budějovice, Faculty of Fishery and Protection of Waters, South Bohemian Research Centre of Aquaculture and Biodiversity of Hydrocenoses, Zátiší 728/II, 389 25, Vodňany, Czech Republic. 2University of South Bohemia, Faculty of Science, Department of Ecosystem Biology, Branišovská 1760, 370 05, České Budějovice, Czech Republic. 3Czech Academy of Sciences, Biology Centre, Institute of Entomology, Laboratory of Aquatic Insects and Relict Ecosystems, Branišovská 1160/31, 370 05, České Budějovice, Czech Republic. 4Unité Mixte de Recherche 5174 ‘Évolution et Diversité Biologique’, Université de Toulouse III - Institut de Recherche pour le Développement-Centre National de la Recherche Scientifique-École Nationale Supérieure de Formation de l’Enseignement Agricole. 118 route de Narbonne, F-31062, Toulouse, France. Correspondence and requests for materials should be addressed to L.V. (email: [email protected]) However, prey also face predation-induced types of death other than direct consumption by predators. Predator attacks are not always successful and injured prey sometimes escape and die later away from the predator14,41. Predators can also abandon or only partially consume some of the killed prey, a widespread behaviour in many invertivorous and vertebrate predators referred to as surplus killing13–14. This feeding behaviour is an important component of consumer-resource interactions that can influence population dynamics and predator-prey co-evolution15–18. Finally, the “ecology of fear” framework posits that the presence of predators can mobilize stress hormone secretion and consequently decrease prey energetic reserves9,20. Persistent stress reaction may thus “scare prey to death” and further increase prey mortality rates21–24. While surplus killing is well documented and relatively common, cases of prey mortality linked to high stress levels and unsuccessful predator attacks remain largely unexplored. All these phenomena contribute to nonconsumptive predator-driven mortality (hereafter NCM) in food webs. Overall, the proportion of dead prey not eaten by predators can be substantial11,25. These prey individuals do not contribute to the flux of energy and nutrients to higher trophic levels, which can alter ecosystem functioning through lowered trophic transfer efficiency. Altogether, this suggests that NCM is relevant to the understanding and predictions of global change impacts on energy flux and ecosystem functioning. Factors modulating NCM strength are insufficiently understood. Previous studies reported that prey availability strongly influences surplus killing13,26–33, which typically increases with prey density. Nevertheless, the dependence of surplus killing on prey density varies strongly among taxa and can be linear or unimodal15–18. Moreover, we are not aware of any study about prey density effects on prey mortality linked to high stress levels caused by predation risk. The role of global change drivers in NCM is essentially unknown. Human activities lead to rapid environmental changes including pollution, habitat alteration, nutrient enrichment, and global warming. Understanding how these drivers impact organisms and their interactions, including surplus killing and other processes affecting energy transfer across trophic levels, is important to better predict global change consequences on Earth’s biota4,37–40. To our knowledge, the effects of temperature (or any other of the above drivers) on the “prey scared to death” phenomenon and unsuccessful predator attacks remain unexplored. Only one study reported a decrease in surplus killing with warming14, possibly due to higher metabolic demands of predators at warmer temperatures and hence higher ingestion rates required to fulfill these demands21. Most food webs consist of multiple predators that share similar prey14,41 and provide important ecosystem services42,43. There is mounting evidence that the effects of multiple predators on prey populations can rarely be predicted from single-predator effects. Interactions among multiple predators and their prey often result in emergent effects such as predation risk reduction or enhancement6,44–46. Does this disconnect between observations based on single and multiple predators also apply to NCM? Benke47 suggested that interactions among conspecific predators increase surplus killing, which could in turn exacerbate the effects of exploitative competition among conspecific predators48. However, no study has compared prey surplus killing in intraspecific and interspecific predator assemblages, which limits our knowledge about the relative importance of the effects of predator density versus diversity on surplus killing. The impact of multiple predators and functionally diverse predator communities on the amount of prey “scared to death” has not been thoroughly explored either. More generally, knowledge of the impact of multiple predators and predator functional diversity on NCM are limited. Previous studies reported that predator diet breadth and functional diversity of predator assemblages can strongly affect the relationship between predator diversity and ecosystem functioning (e.g. primary production and prey suppression via trophic cascades)9,29. For instance, Finke and Snyder49 suggested that communities composed of generalist consumers exploit resources better than those including only specialists. Similarly, communities including diverse consumer types such as predators, omnivores and scavengers should exhibit reduced NCM values compared to communities composed only of predators44, e.g., when scavengers and omnivores eat prey killed by other predators. These observations provide qualitative insights but do not sufficiently advance our ability to quantify NCM strengths in predator-rich communities. In this study, we experimentally investigated the effects of temperature, resource availability (i.e., prey density), and predator density and diversity on NCM strengths (i.e., the proportion of dead prey not eaten by predators). Changes in temperature and resource availability are two of the most important global change drivers1. It is thus crucial to investigate their impacts on energy fluxes to better understand the consequences of global change on ecological communities6,57. Our study provides an initial step in the exploration of the effects of abiotic and biotic factors on NCM strengths in food webs. It helps better understand and predict global change consequences on energy fluxes in ecological communities. Results While prey mortality was negligible in controls without predators (0–2% of the initial prey died during the experiment, mean ± SD = 0.84 ± 1.06%), the proportion of dead uneaten prey per predator (see Methods for details; hereafter only NCM strength) was significantly positive in treatments with predators. The overall average value of NCM in treatments with predators was 4% with a maximum of 20%. Moreover, we found dead uneaten prey at all prey densities as well as in each predator assemblage. In addition, dead uneaten prey were found in 64% of the replicates with predators. NCM strength varied significantly with temperature, prey density and predator assemblage (Table 1). Furthermore, temperature effect depended on predator assemblage (significant temperature × predator assemblage interaction, Table 1 and Fig. 1). Warming decreased the strength of NCM caused by dragonfly pairs, but had the opposite effect in the single dragonfly treatment and did not affect NCM strength in the other predator treatments (Fig. 1A). NCM strength increased significantly with prey density (Fig. 1B) and this effect was independent of temperature or predator treatments (Table 1). In addition, we found a temperature-dependent effect of predator density on NCM strength that was independent of prey density and predator species and size (Table 2). NCM strength tended to decrease with predator density, but this effect was more pronounced and significant only at 20 °C (Table 2 and Fig. 2). When grouping the treatments by predator functional groups (predators, scavengers and their mix), we found that NCM strength varied significantly among functional groups and with prey density but did not depend on temperature or any statistical interactions of these three variables (Table 3). NCM was lowest in mixed treatments involving one scavenger and one predator and highest in treatments involving only predators (Table 3 and Fig. 3). The estimated dependence of NCM strength on prey density was nearly the same as when we grouped the data by predator assemblages (compare Figs 1B and 3B). Table 1. F and p values of the most parsimonious GLM for the effects of temperature, prey density and predator assemblage on NCM strength. Data were corrected for predator density by dividing the proportion of dead prey not eaten by predator density. df = degrees of freedom, resid. df = residual degrees of freedom. Bold values represent significant explanatory variables (P < 0.05). \| \| df \| resid. df \| F \| p \| \|--------------------------\|----\|-----------\|------\|------\| \| temperature \| 1 \| 446 \| 3.23 \| 0.07 \| \| prey density \| 1 \| 445 \| 21.4 \| <0.001\| \| predator assemblage \| 8 \| 437 \| 16.6 \| <0.001\| \| temperature × predator assemblage \| 8 \| 429 \| 3.82 \| <0.001\| Table 2. F and p values of the most parsimonious GLM for the effects of temperature, prey density, and predator identity and density on per capita NCM strength. Only single predator treatments and treatments with predator pairs of the same size and species were used in this analysis. Variables not retained in the final model are omitted. Symbols as in Table 1. \| \| df \| resid. df \| F \| p \| \|--------------------------\|----\|-----------\|------\|------\| \| temperature \| 1 \| 343 \| 2.02 \| 0.24 \| \| prey density \| 1 \| 342 \| 10.81\| <0.001\| \| predator density \| 1 \| 341 \| 21.31\| <0.001\| \| temperature × predator density \| 1 \| 340 \| 9.03 \| <0.005\| Figure 1. Dependence of per capita NCM strengths (number of dead uneaten prey per predator; mean ± 95% CI) on temperature, prey density and predator assemblage. (A) NCM strengths for all predator treatments and prey densities at 16 °C (blue) and 20 °C (red). Predator assemblages: D = dragonfly larva, SC = small crayfish, LC = large crayfish; predator pairs with underscore. Significant differences (P < 0.05) between temperatures within each predator assemblage marked by asterisk; ‘ns’ = differences not significant. Significant differences (P < 0.05) between predator assemblages at given temperature marked with different letters (16 °C = capital letters, 20 °C = small letters). (B) Effect of prey density on NCM strength across all predator assemblages and both temperatures. Predictions from the multiplicative risk model mostly overestimated the observed NCM strengths except for the treatment with two dragonflies at 16 °C, in which the observation exceeded the prediction (Fig. 4). That is, NCM strengths in predator assemblages were almost always weaker than expected from single-predator treatments. Temperature, prey density and predator assemblages and density affected the per capita proportions of dead prey with and without visible attack marks in very similar but not identical ways to how they affected the overall NCM strength. Both per capita proportions were significantly affected by temperature, prey density and predator assemblage, and the statistical interaction between temperature and predator assemblage (Table S1). Figure 2. Dependence of per capita NCM strength (mean ± 95% CI) on predator density at two temperatures. Black bars = single predator treatments (D, SC and LC), grey bars = predator pair treatments (D_D, SC_SC and LC_LC). Dependence on prey identity (not shown) qualitatively identical to those shown in Figs 1B and 3B. Figure 3. Dependence of per capita NCM strength (mean ± 95% CI) on prey density and predator functional groups. (A) NCM strength for each functional group. Mixed treatments (i.e., scavenger and predator) = D_SC and D_LC; scavengers = SC, LC, SC_SC, LC_LC and SC_LC; predators = D_D and D. (B) Effect of prey density on NCM strength. Different letters mark significant differences (P < 0.05) between predator functional groups or prey density. \| \| df \| resid. df \| F \| p \| \|----------------\|----\|-----------\|------\|---------\| \| prey density \| 1 \| 445 \| 20.2 \| < 0.001 \| \| functional group\| 2 \| 444 \| 37.7 \| < 0.001 \| Table 3. F and p values of the most parsimonious GLM for the effects of temperature, prey density and predator functional group on per capita NCM strength. Variables not retained in the final model are omitted. Symbols as in Table 1. significantly reduced the per capita proportion of dead prey with visible attack marks in two intraspecific predator assemblages (D_D and LC_LC) but had no effect in the other assemblages (Table S1 and Fig. S1). Warming also reduced the per capita proportion of dead prey without visible attack marks in the D_D assemblage but had the opposite effects in the single dragonfly treatment (Table S2 and Fig. S2). Finally, the per capita proportions of both types of dead prey increased with initial prey density (Figs S1B and S2B). Discussion Nonconsumptive predator-driven mortality (NCM) is a common but underestimated component of predator-prey interactions. Previous studies mainly focused on consumptive mortality and often neglected NCM linked to unsuccessful predator attacks, surplus killing or predator-induced high stress levels. These three different sources of mortality are widespread across many invertebrate and vertebrate taxa12,23,24,34,35,53,54 and can influence population dynamics, food web structure, and the co-evolution of predators and prey16,17,34. However, the magnitude and dependence of NCM on external factors remains largely unexplored, which limits our understanding of when and how biotic and abiotic factors influence the strength of consumer-resource interactions and thus the dynamics and structure of ecological communities. Here, we investigated the effects of temperature, prey density, and predator density and functional diversity on NCM strengths in an aquatic food web module. Like all laboratory studies, our experiments have limitations that prevent strong quantitative inference from the results. They were conducted in an artificial environment at a small spatio-temporal scale that cannot be directly extrapolated to long-term community and ecosystem dynamics. The environment and arena size could have influenced prey mortality, but we found it to be negligible in control trials without predators and much lower than the observed magnitude of NCM in predation trials. This suggests that the qualitative patterns found in our experiment are sufficiently robust. Moreover, the habitat volume and duration of our experimental trials fall within the range commonly used in predation experiments with aquatic invertebrate predators. We therefore think that our study helps identify factors influencing NCM strengths and provides an additional step towards a better understanding of the effects of biotic and abiotic factors on predator-prey interaction strengths in aquatic systems. Effect of temperature on NCM. We found that NCM strength was not influenced by temperature except in treatments involving only dragonflies. This indicates that the effect of temperature on NCM is species specific and potentially related to consumer functional type (pure predator vs. scavenger). Moreover, the effects of temperature depended on dragonfly density: warming increased NCM in treatments with a single dragonfly whereas it decreased NCM in treatments with two dragonflies. Our more detailed analyses revealed that the effect of temperature in the single dragonfly treatment was caused by a magnified “scared to death” phenomenon rather than a change in surplus killing. Although the mechanisms and physiological processes underlying these effects remain to be investigated in more detail, our results suggest that the additional stressor (i.e., warming) led to increased mortality of fish fry in the presence of a single dragonfly predator. As the per capita prey density was reduced in treatments with two dragonfly predators, it is plausible that they fed on the prey more efficiently to compensate for the joint effect of higher metabolic demands and lower prey availability at the higher temperature. Additional aspects of predator and prey behaviour that would alter NCM strength with temperature may also change with predator density. For instance, predators can become more careful when catching and handling prey and hence feed more efficiently in the presence of other predators16,43,44, and their awareness of other predators may increase with temperature due to more frequent mutual encounters. Overall, our results indicate that warming effects on NCM strengths depend on predator identity and density, which we discuss... Effect of prey density on NCM. NCM strength significantly increased with prey density and this effect was independent of temperature and predator identity or density. Prey density effect on overall NCM strength was driven by a combined increase of surplus killing and “scared-to-death” mortality with prey density. Previous studies have also shown that surplus killing is more frequent at higher prey densities12,34,35,57, but the shape of this relationship varies among taxa from linear to unimodal. We found a nearly linear relationship between prey density and surplus killing, which corroborates the results of previous studies on predatory aquatic insects including larvae of the damselfly Anomalagrion hastatum58, aquatic bug Diplonychus rusticus59 and the backswimmer Notonecta hoffmanni60. To our knowledge, the effect of prey density on nonconsumptive predator-induced mortality has never been explored. We found that, while prey mortality in the absence of predators was negligible and did not increase with prey density, the proportion of dead prey without visible attack marks increased strongly with prey density, suggesting that prey are more “scared to death” by predators in denser prey populations. Higher stress levels in the prey may result from oxygen depletion or more frequent physical contacts with conspecifics. These stressors alone may be sublethal but can become lethal when magnified by or combined with an additional stressor such as predator presence57,58. For instance, predators can increase prey respiration rate (e.g., if predator avoidance requires faster or more frequent swimming), which would accelerate oxygen depletion and increase prey mortality. This effect is likely to be stronger at high prey densities when prey are more likely to deplete oxygen. Although we cannot resolve the mechanism underlying the “scared to death” phenomenon in our experiment, our results indicate that predator presence can modify this type of prey mortality. Interestingly, the effects of prey density on “scared-to-death” mortality and surplus killing were independent of predator species and assemblage, suggesting a general effect of prey density on NCM strengths. We thus predict that declines in trophic transfer efficiency due to NCM will become more pronounced at higher prey densities. This would act as a stabilizing factor in communities with fluctuating predator and prey population densities59. Effects of predator density and functional diversity on NCM. The observed decline in per capita NCM with predator density, especially at the higher temperature, can be explained by a combination of two behavioural responses: increased individual feeding rates and the ability of predators to recognize conspecifics. The former response would help cover higher metabolic demands of predators at warmer temperatures23, while the latter would enable them to adjust to the perceived scarcity of resources. Further investigations are needed to determine which of these two behavioural responses contributes most to the observed pattern. Interactions among predators and predator functional types can strongly influence consumer-resource interactions in species-rich communities5,24,60,61. We found that NCM strength varied substantially among predator assemblages, being higher in pure predators (i.e., dragonflies) than in scavengers (i.e., crayfish). Interestingly, NCM strength was lowest when a predator and a scavenger were paired together. The underlying mechanisms remain to be investigated in more detail. We assume that scavengers either feed on the dead prey abandoned by dragonfly larvae that cannot locate immobile prey62 or that scavengers and predators modify their behaviour when together. Whatever the exact mechanism, our results suggest that increased predator functional diversity in food webs can lower NCM strengths. Moreover, multi-predator NCM strengths in our experiment could not be predicted from single-predator NCM strengths alone. Both predator density and predator diversity, including the functional differences between pure predators (dragonfly larvae) and scavengers (crayfish), thus affected NCM strength. Overall, our results suggest that trophic transfer efficiency is higher in functionally diverse ecosystems, which may have important implications for population dynamics and community structure. Conclusions Nonconsumptive mortality is an important but under-appreciated component of consumer-resource interactions. Here we showed that abiotic and biotic factors such as temperature, prey density, predator functional diversity and density influence NCM strength. The effect of temperature on NCM strength varied among predator assemblages and was often not significant. On the other hand, NCM strength increased with prey density independently of temperature and predator assemblage, suggesting a general effect of prey density on NCM strength. Moreover, NCM strength declined in functionally diverse predator assemblages. Our results indicate that energy transfer across trophic levels is more efficient in functionally diverse predator communities, at lower resource densities and at higher temperatures, which has important implications for community dynamics, ecosystem services, and biological conservation. Material and Methods Experiments were conducted at the Research Institute of Fish Culture and Hydrobiology in Vodňany (RIFCH), Czech Republic during summer 2015. No specific permissions were required for capturing and manipulating the organisms used in the experiments. The study did not involve endangered or protected species. All experimental manipulations (capture, rearing and measurements) followed principles of animal welfare and their protection against abuse. We used two size classes of marbled crayfish Procambarus fallax f. virginalis (Decapoda; Cambaridae) and one size class of the dragonfly Aeshna cyanea (Odonata; Aeshnidae) as predators preying on common carp Cyprinus carpio (Cypriniformes; Cyprinidae) fry in the protopterygiolarval ontogenetic phase55. Marbled crayfish is an actively searching, benthic omnivore that is currently invading most freshwater ecosystems in Europe63. Larvae of the dragonfly Aeshna cyanea are widespread native predators that can alternate between a ‘sit-and-wait’ and active foraging strategy targeting moving prey, and are often top predators in small fishless water bodies64. Dragonfly larvae were collected in small sandpit pools in southern Bohemia and released back to the source locality after the experiments. Fish fry were obtained from a hatchery belonging to RIFCH. Crayfish were obtained from laboratory cultures maintained at RIFCH. Before the experiment, predators and prey were maintained at 16 °C and respectively fed in excess with sludge worm (Tubifex tubifex) and brine shrimp (Artemia salina) nauplii. Dragonfly larvae were maintained individually in 0.5-litre plastic boxes (125 × 45 × 80 mm) with 0.4 litres of aged tap water containing a willow twig as a perching site. Crayfish were kept in groups at low densities (0.8 ind. L−1) in 50-litre aquaria with access to shelters (>1 per animal) to avoid excessive competition and cannibalism. Experimental design. We standardized prey size (mean total length ± SD: 6.42 ± 0.20 mm) and used F-1 instar dragonfly larvae (further abbreviated as D) (total length: 30.1 ± 2.3 mm, wet weight: 0.53 ± 0.12 g) and two sizes of crayfish: small (abbreviated as SC; mean carapace length: 11.3 ± 0.9 mm, measured from the tip of the rostrum to the posterior edge of cephalothorax; wet weight: 0.45 ± 0.13 g) and large (LC; mean carapace length: 15.5 ± 1.0 mm; wet weight: 1.12 ± 0.18 g). One day before the experiment, predators were placed individually without food in 0.5-litre plastic boxes (125 × 45 × 80 mm) filled with 0.4 litres of aged tap water. Four hours before the experiment, predators were acclimated to the experimental temperature (16 or 20 °C). Similarly, prey were acclimated to the experimental temperature four hours before the experiment and were kept in 20-litre buckets. Experimental arenas consisted of plastic boxes (163 × 118 × 62 mm) filled with 1 litre of aged tap water and lined with a 1 cm layer of fine crystalline sand. We performed a full factorial experiment with two temperature regimes (16 and 20 °C), three prey densities (70, 110, 220 ind. L−1, representing low, medium, and high prey densities based on pilot experiments), and nine predator treatments with the three predator types: single predators (3 treatments), pairs with two predators of the same size and species (3 treatments), and pairs with two predators differing in size or species (3 treatments). Each combination of temperature, prey density and predator treatment was replicated seven times. In addition, five controls without predators were deployed to assess background mortality of prey for each combination of temperature and prey density. Prey were introduced into the experimental arenas for acclimation one hour before the start of the experiment. All predators were simultaneously introduced into the experimental arenas at the start of the experiment. After 24 hours, predators were removed and the number of living, killed (with visible attack marks), and dead prey (without visible attack marks) were recorded. During a pilot experiment, we observed that prey killed by the predators used in this study always had visible attack marks and all predator attacks were successful. Moreover, we did not observe partially eaten prey in this experiment. Although we did not directly measure stress levels of the fish fry, we attribute dead prey without visible attack marks to mortality due to high stress levels associated with predator presence. Statistical analyses. Prey mortality in controls without predators was negligible (range 0–2% of initial prey) and prey mortality in controls without predators did not increase with prey density (GLM, F1,68 = 2.07, p = 0.15). The data were thus not corrected for background mortality. We calculated per capita NCM strength as the ratio of dead uneaten prey density over initial prey density, divided by the number of predators. In addition, we also calculated an alternative measure of per capita NCM strength as the ratio of the density of dead uneaten prey over the density of eaten prey, divided by the number of predators. As the results were qualitatively similar, we do not present results for the latter NCM metric. We also tested the goodness of fit of our models using the Hosmer-Lemeshow test and verified that all models fitted the data well (P > 0.05). All model results are shown as mean ± 95% Wald confidence interval (CI). We tested whether the per capita NCM strength (hereafter only NCM strength) is influenced by temperature, prey density, predator assemblage and their interactions using a GLM with a quasibinomial distribution to account for overdispersion. The most parsimonious model was determined by sequential deletion of the least significant explanatory parameters or interaction terms from the full model. Parameter significance was evaluated using F-tests from the analysis of deviance. The final model included only parameters with significant p-values, significant explanatory parameters or interaction terms from the full model and parameter significance was evaluated using F-tests from the analysis of deviance. NCab = Npab(Pa + Pb − Pab) (1) where NCab is the predicted NCM strength measured as the density of dead uneaten prey, Np is the initial prey density, and Pp and Pb are NCM strengths measured as the respective proportions of dead uneaten prey in single predator a and b treatments. To better understand the mechanisms underlying our results, we further tested the influence of temperature, prey density, predator assemblage and their interactions on the per capita (i.e., per predator) proportion of dead prey with and without visible attack marks using two GLMs (one for each dependent variable) with quasibinomial distribution. The most parsimonious model was determined by sequential deletion of the least significant explanatory parameters or interaction terms from the full model and parameter significance was evaluated using F-tests from the analysis of deviance. Finally, we tested whether per capita NCM strength depended on predator density along with predator identity, temperature, prey density and their interactions. Only single predator treatments and treatments with predator pairs of the same size and species were used in this analysis. 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R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/. (2016). Acknowledgements This study was supported by the Ministry of Education, Youth, and Sports of the Czech Republic (projects CENAKVA – CZ.1.05/2.1.00/01.0024 and CENAKVA II – LO1205 under the NPU I program) and the Grant Agency of the University of South Bohemia (012/2016/Z). Work of D.S. Boukal and A. Sentis was supported by the Grant Agency of the Czech Republic (14–29857S). A. Sentis was also supported by the “Development of postdoc positions of the University of South Bohemia” project no. CZ.1.07/2.3.00/30.0049, co-founded by the European Social Fund and the state budget of the Czech Republic, by the French Laboratory of Excellence project ‘TULIP’ (ANR-10-LABX-41; ANR-11-IDEX-0002–02), and by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007–2013) under REA grant agreement n. PCOFUND-GA-2013-609102 through the PRESTIGE program coordinated by Campus France. We thank Irina Kuklina, Martin Prchal for technical assistance and three anonymous reviewers for helpful comments. Author Contributions L.V., D.S.B. and A.S. conceived the experiment and conducted data analyses. L.V., A.K., M.B., and P.K. conducted the experiment. L.V. wrote the first draft of the manuscript. D.S.B., A.K. and A.S. provided comments and additional revisions of the text. Additional Information Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-017-17998-4. Competing Interests: The authors declare that they have no competing interests. Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. © The Author(s) 2017	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3800, 1 ], [ 3800, 10675, 2 ], [ 10675, 13805, 3 ], [ 13805, 15796, 4 ], [ 15796, 20072, 5 ], [ 20072, 26486, 6 ], [ 26486, 32353, 7 ], [ 32353, 39384, 8 ], [ 39384, 44264, 9 ] ] }
6ec0064eddb2860cf44a54d61ddc13977f4fc191	{ "olmocr-version": "0.1.59", "pdf-total-pages": 12, "total-fallback-pages": 0, "total-input-tokens": 35723, "total-output-tokens": 15388, "fieldofstudy": [ "Environmental Science" ] }	Factors Influencing Bank Geomorphology and Erosion of the Haw River, a High Order River in North Carolina, since European Settlement Janet Macfall, Paul Robinette, David Welch Center for Environmental Studies, Elon University, Elon, North Carolina, United States of America Abstract The Haw River, a high order river in the southeastern United States, is characterized by severe bank erosion and geomorphic change from historical conditions of clear waters and connected floodplains. In 2014 it was named one of the 10 most threatened rivers in the United States by American Rivers. Like many developed areas, the region has a history of disturbance including extensive upland soil loss from agriculture, dams, and upstream urbanization. The primary objective of this study was to identify the mechanisms controlling channel form and erosion of the Haw River. Field measurements including bank height, bankfull height, bank angle, root depth and density, riparian land cover and slope, surface protection, river width, and bank retreat were collected at 87 sites along 43.5 km of river. A Bank Erosion Hazard Index (BEHI) was calculated for each study site. Mean bank height was 11.8 m, mean width was 84.3 m, and bank retreat for 2005/2007-2011/2013 was 2.3 m. The greatest bank heights, BEHI values, and bank retreat were adjacent to riparian areas with low slope (<2). This is in contrast to previous studies which identify high slope as a risk factor for erosion. Most of the soils in low slope riparian areas were alluvial, suggesting sediment deposition from upland row crop agriculture and/or flooding. Bank retreat was not correlated to bank heights or BEHI values. Historical dams (1.2–3 m height) were not a significant factor. Erosion of the Haw River in the study section of the river (25% of the river length) contributed 205,320 m³ of sediment and 3759 kg of P annually. Concentration of suspended solids in the river increased with discharge. In conclusion, the Haw River is an unstable system, with river bank erosion and geomodification potential influenced by riparian slope and varied flows. Introduction Streams and rivers are considered to be in a state of dynamic equilibrium when the sediment delivered to the channel is in balance with the capacity of the stream to transport and discharge that sediment [1]. Stream channels alternatively experience periods of alluvial deposition, followed by erosional downcutting of the alluvium, followed by periods of additional deposition. These cycles have created a landscape of terraces and floodplains, sculpted by the streams and rivers flowing through them [2]. Globally, changes in land use, climate and other factors have altered the historic patterns of transport and discharge, with significant changes to river shape, processes, sediment dynamics and water quality [2]. With these changes, soil erosion has been identified as a significant challenge in both developing and developed countries. A landscape perspective of rivers and their watersheds demonstrates the influence of land use and disturbance on river structure and ecology at multiple scales [5]. European settlement in the southeastern United States began a period of forest clearing in the 1700’s, followed by row crop agriculture [3]. These practices had deleterious ecological consequences to surface waters in the form of increased sediment loads and habitat degradation [3,4,6-9]. Before urbanization and agricultural clearing, streams in the Piedmont region of the southeastern United States, had low levels of suspended solids and high connectivity between the stream and surrounding floodplains [3,4]. It has been estimated that 25 km² of soil have eroded from agricultural lands in the Piedmont region between the coastal plain and the Appalachian Mountains, with an average of 14 cm of topsoil lost from North Carolina since the early 1700’s [3]. This erosion from agriculture has left a legacy of upland gullies and sediment deposition near and in streams and rivers [3]. Another anthropogenic disturbance to streams and rivers is the proliferation of dams and artificial water bodies. There are over 2 million artificial surface water impoundments including 82,000 dams in the continental United States, with some dating from the 17th century [10,11]. Both natural and man-made dams can have profound impacts on the ecology and geomorphology of rivers, altering patterns of sediment transport and deposition, water and energy flow, and aquatic habitat [10,12,13]. Downstream channel degradation due to dams has been documented for more than 85 years and in many cases has been extreme [14–17]. Downstream changes often include channel incision, channel pattern change (braided to single-thread or vice-versa), loss or encroachment of vegetation, and bank collapse [13,18,19]. Upstream of the dam there may be sediment deposition within the impoundment, leading to incision when the dam is removed [20]. Upstream urbanization, with the increase in impervious surface, has been shown to alter the flow of streams, increasing the frequency of “flashiness” and bank incision [2]. Susceptibility to erosion and hydromodification from urbanization varies with stream bed composition, armorng, bank height, bed and bank materials, precipitation patterns, and other factors [21,22]. Sediment loading from bank erosion is a land management problem of global importance [23,24]. Sediment is one of the most common pollutants from non-point sources, with over 6,000 water bodies across the United States showing significant suspended sediments [25–27]. Different bank materials, aerial and subaerial weathering, variations in grain size, shear strength of the bank materials, bank angle, and water potential can influence river bank mass wasting, failure and fluvial entrainment [23–25]. The ability to predict bank failure and erosion, however, is often uncertain, especially for stream banks with a varied depositional history such as from anthropogenic disturbance [26]. Processes that determine channel geomorphology differ between first and second order streams and larger rivers with larger watersheds [27–29]. Few high order rivers have been studied [27,30]. In large rivers, conditions leading to river widening often are nonlinear, with energy adjustment resulting in different and sometimes opposite adjustment processes. This was seen in the North Fork Toutle River system in Washington State in the NW United States, where following the eruption of Mount St. Helens, one river was dominated by aggradation and widening, while another similar river was dominated by degradation [31]. Unstable channels continue to adjust following major disturbances, both anthropogenic and natural, until a stable floodplain is established with a progressive arming of the channel bed [32,33]. Sediment and nutrient loading are a global water quality concern, and are significant issues in the Haw River, a high order river in the North Carolina Piedmont, Jordan Reservoir, a major drinking water supply, is formed by a dam on the Haw [34]. However, water in the reservoir is considered impaired due to algal blooms from excess nutrients. To improve water quality, nutrient reduction goals have been established. Understanding the patterns of geomorphic change of the river and contributions of the river bank to sediment and nutrient load may provide a model for water quality improvement in this and similar systems. Similarly to other developing areas, the Haw River watershed has a history of profound disturbance through forest conversion to row crop agriculture, the construction of dams, and upstream urbanization. In 2014, it was identified as the 9th most threatened river in the United States by the organization American Rivers. The river today has little resemblance to the clear water and low banks from historical descriptions [35]. The primary objective of this study was to identify factors influencing bank geomorphic change and erosion of the Haw River using field measurements. Few reports on erosion of high order rivers have been published, with most based on model estimations. River traits included river slope, riparian soil type and slope, land cover, bank angle, surface protection, bank height, bankfull height and root density and depth. The Haw River has highly incised, unstable banks exhibiting extensive mass wasting, undercutting with bank collapse and fluvial entrainment. Understanding alluvial channel behavior and the channel response to disturbance will provide insight into understanding the factors controlling erosion patterns, shape and balance of the Haw and other high order rivers. Materials and Methods For study sites that were located on public lands, the field sites were located in local parks (town parks). Local government agencies were project partners and did not require permits for access. For sites that were located on private land, we obtained landowner permission for access. However, most landowners in our region are reluctant to allow access to their lands by strangers and requests for access may result in alienation of landowners. This research is being used as the foundation for development of the Haw River Trail - a project which uses recreation to achieve regional conservation goals. Because of the trust and contacts established with the research project described in the submitted paper, landowners have been willing to work with us and with local governments on this conservation/recreation project. Alienation of landowners would compromise progress on the conservation work we are developing on the Haw. When we made contact for this study, some of the landowners requested that their identities not be made public. Landowners highly value the personal connections that were established with this project, which is contributing to the success of the conservation work. However, landowners in this region also highly value their privacy and private property rights. We will share an excel spreadsheet with the GPS coordinates through requests to the senior author. The authors will assist landowner contacts if requested. The Haw River is located in the north central Piedmont region of North Carolina (Figure 1). This area is located between the coastal plain to the east, and the Appalachian Mountains to the west. North Carolina borders the Atlantic Ocean in the southeastern United States. The river is approximately 177 km long with a watershed of about 3952 km², including agricultural, forested, urban and suburban land cover. Nearly one million people live within the Haw River watershed, including the urbanized areas of Greensboro, Graham, Elon, and Burlington, North Carolina which are all upstream of the study reach. The Haw River ends at the confluence with the Deep River near Moncure, North Carolina, forming the headwaters of the Cape Fear River. For most of its length, including the section studied, the river is relatively straight with few meanders. The watershed is characterized by low, gently rolling hills. Low naturally formed levees (typically ≤1.5 m in height) are frequently found on the river bank. Behind the river bank is a backswamp of varied width. Behind the backswamp is the toe slope, extending to the upland areas. The river channel bottom ranges from bedrock to mixed sand/silt/cobbles with large woody debris. The river is a riffle – pool system [36]. Mean discharge at the United States Geological Survey monitoring station near Bynum, North Carolina (1973–2012) immediately downstream of the study area was 34 m³/s, with discharge ranging from 1642 m³/s (1996) to 0.005 m³/s (1983) [37]. Elevation ranged from 97 m at the lower end of the study area to about 304 m at the top of the watershed upriver of the study section. The study area extended 43.5 km, from the intersection of the Haw River and Interstate 40/85 in Burlington, North Carolina to the intersection of the river and US 15-501 in Bynum, North Carolina, flowing through the counties of Alamance, Orange, and Chatham. The upriver location beginning the study area was approximately 112 km downstream from the headwaters and 65 km upstream from the confluence of the Haw River and the Deep River. The studied portion of the river is a fourth order river and higher [38]. Data were collected from 87 bank sites within the study area. Sites were accessed by kayak and land. (Figure 1). An opportunistic sampling strategy for study site selection which was contingent upon landowner permission was used. Most study sites were on privately owned land. Study sites that were on public land were located in local parks where the local governments were project partners and no permits were required. Eighty-seven river sections that had more than 6 m in length of relatively homogenous slope, bank angle, bank height, and vegetation cover were selected for study. There were no endangered or protected species present at any of the study sites. Measurements were collected during 2006–2007, primarily during spring, summer and fall. The geographic locations of the bank sites were documented using a Magellan handheld GPS. The lengths of the banks with homogenous characteristics were measured using a Leica Laser Distometer and heights were determined using a telescoping measuring rod and the distometer. The sites were also photographed and sketched to record the appearance of toppled trees and bare soil. Bank Erosion Hazard Index Methods* A Bank Erosion Hazard Index (BEHI) was used to assess the potential stability of the Haw River’s banks [39,40]. This method estimates and predicts erosion potential of rivers and streams, providing documentation of geomorphic field parameters and channel adjustment predictions. While the BEHI methodology is often a small component of more extensive river geomorphic assessments, it is a convenient and useful tool to rapidly create an inventory of river bank characteristics and to assess river bank and river adjustments. Rosgen’s BEHI method is normally used to assess lower order rivers and is not often used on large rivers, such as the Haw River [39]. The BEHI is based on five measurements related to bank erosion potential (Table 1). Measurements were conducted according to methods outlined in Rosgen [39,40]. The bank height was measured at the top of the vertical or sloped area rising from the channel bed. Rooting depth was measured across the bank surface. Root density was determined from a visual estimation of the surface coverage across the bank surface. Surface protection was determined from the percentage of the bank with root, vegetation or hardened structure coverage. From these field measures, bank height ratio (bank height/bankfull height) and root depth ratio (root depth/bank height) were calculated [39]. \| Criteria \| Value \| \|----------\|-------\| \| Bank Height Ratio \| 1–2 \| \| Rooting Depth \| 80–100% of the bank \| \| Root Density \| High \| \| Bank Angle \| Low \| \| Bank Protection \| Extensive \| \|bankfull height, bank depth, root depth, root density, bank angle, and surface protection. Summing the BEHI index values for the physical and biological traits gives a total of 5–10, indicating a low potential for erosion. In contrast, attributes that would suggest extreme risk of erosion (the bottom row) include high banks, few roots extending down the bank with low root density, an undercut riverbank with high angle, and little surface protection. \| A BEHI value was calculated at each studied site on the river based on Rosgen’s BEHI method [40]. A value of 1 (very low) to 10 (extreme) was assigned to each of the bank metrics, as indicated in Table 1. Numbers for all traits were summed for each site. A total value of <10 was considered a very low bank erosion hazard index. A value > 45 was considered an extreme bank erosion hazard index. Identification of the bankfull stage can be difficult to determine for rivers with an unstable channel. Rather than presenting a stable state, rivers are open systems which respond to variations in energy and materials, making bankfull assessment sometimes uncertain [31]. In cases where the bank height exceeded the bankfull height, the bankfull height was measured at the place on the river bank with visible vegetation changes indicating plants experienced flooding, such as a change in root morphology or root washout [26,27,41]. Where roots were not present, the bankfull height was measured from the point on the bank where bank... materials showed evidence of saturation or shear force stress from flowing water. Soils were sampled for nutrient analysis by bulk density sampler from the top 20 cm of the river bank at 31 locations throughout the study area. Duff was removed and soils were air dried and analyzed for bulk density and nutrient content by the NC Department of Agriculture and Consumer Services. River Width and Slope Calculation Methods The river width was measured using a geographic information system (ArcGIS, ESRI, Inc.) to analyze aerial photographs of the study area. Aerial photographs for Alamance, Orange (2005) and Chatham counties (2007) were obtained from the county GIS offices. Aerial photographs for Alamance and Orange (2011) were from DigitalGlobe (supplied through ESRI, Inc., Redlands, CA) and for Chatham Co. (2013) through NCOOneMap. Widths were determined from the aerial photographs by measuring a line placed perpendicular to the center line of the river. The river width measurements were taken of the visible water surface, representing the river width at base flow. The river was at base flow at all dates of image acquisition. Digital resolution was 0.27 m. Locations of dams which are still present in the river were recorded from these aerial photographs. To confirm consistency of measurements, lengths of 10 hardened structures (dams, bridges, buildings) were measured in 2005/2007 and 2011/2013 images. There were no differences in measurements between the two image sets for hardened structures. The slope of the river was estimated from Digital Elevation Models obtained from the NC Floodplain Mapping Program, 2013. Digital vertical resolution was 0.25 m and horizontal resolution was 6 m. A center line was established on the river image and points were placed every 500 meters. The river slope was measured for the entire length of the study section of the river. Historical Dam Locations The locations of historical dams, which are no longer present on the river, were determined by comparing the GIS data layers with photographs and topographic maps. Locations of historical dams were estimated from U.S. Geological Survey topographic quadrangles (scale 1:24,000) and historical records [42–44](Figure 1). Soil and Land Cover Methods Aerial photographs from 2005/2007 were used to digitize different types of land cover within 153 meters (500 ft.) of both of the river banks for evaluation of the riparian corridor over the entire river length studied. Within the GIS, polygons were drawn around each type of designated land cover. The areas for these polygons were then calculated and summed for each land cover category. The land cover classes were: - Forest – areas with evident canopy coverage of mature trees - Open - areas lacking trees or shrubs - Shrubland – areas dominated with small-canopied vegetation - Impervious – areas such as roads and buildings - Water – streams, ponds and other water features Soil type and traits at each study site were determined from the Alamance, Orange and Chatham Co. Soil Survey. Soil maps (SSURGO) were obtained from the Natural Resource Conservation Service Web Soil Survey [45]. Locations for each study site were identified in the Soil Surveys using GIS. Soil types were determined for soils immediately adjacent to each study location, using the GIS shapefiles for soils in each county. Slopes which are characteristic for each soil type adjacent to the study sites were recorded based on the SSURGO soil type descriptions. Statistical Analysis Statistical analyses were conducted with SAS Enterprise Guide 4.3 (SAS Institute, Cary, NC). A Pearson product moment correlation analysis was calculated to determine independence of the river attributes and erosion potential. Analysis of variance or a Whitney Mann Rank Sum Test was calculated to determine effect of riparian slope and historical dams. Data used in these analyses is freely available at http://www.elon.edu/e-web/academics/elon_college/environmental_studies/macfall-plos-one.xhtml. Results Bank Erosion Hazard Index A majority, 84% percent, of the studied banks had a BEHI value of moderate to high erosion potential (Table 2). The mean bank height was 11.8±0.5 m and the mean bankfull height was 52±0.1 m. The mean bank angle was 53°, with a maximum of 90°. The river had widened (bank retreat) by 2.3 m over the six year period from 2005/2007 to 2011/2013, suggesting rapid change to the river bank and ongoing erosion (Table 2). A number of significant correlations between the river bank geomorphology and erosion potential with attributes of the studied sites were noted (Table 3). There was a significant negative correlation between river width with bank height and BEHI, suggesting that as the river widens, the bank height and BEHI decrease. One of the most significant results was that the slope of the riparian soils adjacent to the river bank was negatively correlated with bank height, BEHI and bank retreat. The BEHI, bank retreat and the bank heights were significantly higher at study sites with low riparian slope (<2%) compared to riparian areas with greater slopes (Table 4), suggesting greater erosion and erosion potential in areas with low riparian slope. The flatter the land adjacent to the river banks, the more the river had widened, the greater the height of the river banks, the greater the erosion potential (BEHI) and the more erosion had occurred through river widening. Rooting patterns were negatively correlated with bank heights. There are likely two reasons for this observation. First is the protective effect from erosion which has been described from vegetation. A second reason, however, is if bank collapse or slumping had occurred, trees on the river bank would have also moved downward with the soil, increasing both the root depth ratio and root density lower in the river bank face. In contrast to the correlation with bank height, root density and root depth ratio were not correlated with bank retreat. Areas with measureable erosion and river widening were also independent of river physical attributes including bank height, bank angle and the BEHI (Table 3). Based on river bank height and bank retreat measurements, the amount of soil lost through erosion can be estimated for the six year period between 2005/2007 and 2011/2013. The mean value for annual soil loss from the 43.5 km section of the river which was studied was 205,320±23,000 m³ per year. The bulk density measurement of the riparian soil adjacent to the river was 1.01. Based on this bulk density measure, 2.3 × 10⁸ kg of soil are lost annually from the studied river segment. The P concentration from soil nutrient analyses was measured to be 17.6±1.0 mg/L. Since P generally does not leach through the soil profile and is primarily retained in the surface, if P loading to the river with erosion is only from the top 20 cm of soil, approximately 3759 kg (8286 lb.) of P enters the river annually with sediment [46]. Historical Dams Historically, there have been ten dams along the river reach studied, three of which still exist. The only two dams still providing hydroelectric power are the Saxapahaw Dam and the Bynum Dam (Table 5). There were low BEHI values and bank heights upriver of and closest to the Bynum and Saxapahaw Dams, as the sites were adjacent to upper reaches of the pools formed behind the dams. BEHI values and bank heights indicating severe erosion were measured downstream of the Saxapahaw dam. No measurements were made downstream of the Bynum dam, the downstream limit of this study. Dams which are no longer present on the Haw River had little effect on river bank height, BEHI estimates of erosion potential or bank retreat. While it is generally accepted that sediment is deposited upstream of dams in the impoundments, the presence of historical dams on the Haw River does not appear to be a strong factor influencing current conditions (Table 6). In addition, the heights of the dams (with the exception of Saxapahaw Dam) were all lower than the mean values for bank heights measured in the current study. Impacts will likely be much greater with the remaining dams in Saxapahaw and Bynum, however, which are larger. Riparian Land Cover and Soil Types Most of the riparian areas adjacent to the study sites were forested with mature trees, primarily hardwoods, at the time of this study (Table 7). There was no relationship between BEHI values or bank heights with land cover in 2005/2007, as most of the riparian lands were forested. However, much of the land had been in agriculture for the past two centuries, so current geomorphic patterns may be a legacy from past land use. Agriculture was a major land use for the first half of the past century in the 3 study area counties within the watershed (Table 8). Both farm number and percentage of agricultural land decreased, with the greatest loss in the last half of the twentieth century. Counties in the Haw River watershed had 80–85% of the land area in agriculture at the beginning of the twentieth century. The 2007 agricultural census indicates this area had shrunk to 24–32% of each county [47–49]. There were twenty one different soil types at the 87 BEHI study sites (Table 9). The most common soil type was Riverview Silt Loam, followed by Buncomb loamy fine sand. Discussion The banks of the Haw River, located in the central Piedmont of North Carolina, are deeply incised (11.8 m mean bank height), with steep banks in the straight reaches, inside bends, and outside bends of the river channel. There is overhanging vegetation at the top of banks, with mass wasting, bank failures, and collapse of trees into the river. The high banks, BEHI indices and bank retreat indicate active erosion is occurring and the potential for future erosion is high. Over half of the study sites had a BEHI of moderate to high erosion potential, supporting observations that the banks along the Haw River in the study area are unstable. The average difference between bank height and bankfull height was 6.6 meters. The slopes of the riparian areas were significantly correlated with the BEHI, bank height and bank retreat, primarily through an increase in bank height, BEHI and bank retreat as the slope of the riparian areas decreased (Tables 3 and 4). This suggests that river banks adjacent to riparian areas with low slope are more eroded and erodible than river reaches with more steeply sloped riparian areas. The riparian areas with low slope are mostly alluvial (Table 9), likely including migrating soils from the surrounding agricultural uplands and deposited sediment from past floods. Gross floodplain sediment trapping potential has been shown to be a function of floodplain area, with larger floodplains having greater trapping potential [50]. If sediment migrating from the uplands was deposited in riparian areas with low slope, the deposited sediment would likely be more erodible than the original base. Riparian areas with high slope adjacent to the river would be less likely to have extensive sediment deposition as the waters carrying the sediment have comparatively more energy than areas which were more flattened. \| Table 2. Summary statistics for bank characteristics of the Haw River. \| \|-------------------------\|-----\|-----\|-----\|-----\|-----\| \| Attribute \| Mean\| SE \| Min \| Max \| Median \| \| River Width 2005/2007 (m)\| 84.3\| 5.7 \| 27.4\| 300.5\| 64.8 \| \| River Width 2011/2013 (m)\| 86.7\| 5.6 \| 27.4\| 300.2\| 68.6 \| \| Bank retreat (m) \| 2.3 \| 0.3 \| -1.4\| 9.5 \| 1.5 \| \| Riparian slope (%) \| 6.6 \| 0.9 \| 1 \| 30 \| 1 \| \| Bank angle \| 53.2\| 2.5 \| 3 \| 90 \| 55 \| \| Elevation (m) \| 122.7\| 1.4 \| 97 \| 145.7\| 120.4 \| \| River bed slope (%) \| 0.08\| 0.01\| 0 \| 0.37 \| 0 \| \| Bank height (m) \| 11.8\| 0.5 \| 1.8 \| 29.8 \| 12.1 \| \| Bankfull height (m) \| 5.0 \| 0.1 \| 1.8 \| 9.2 \| 5 \| \| Bank height ratio \| 2.4 \| 0.09\| 1 \| 4.2 \| 2.4 \| \| Root depth ratio \| 0.59\| 0.04\| 0 \| 1.0 \| 0.6 \| \| Surface protection (%) \| 35 \| 2.4 \| 4.3 \| 83.4 \| 30 \| \| Root density (%) \| 43 \| 2 \| 0 \| 100 \| 45 \| \| BEHI \| 24.3\| 0.7 \| 9.1 \| 39.6 \| 24.1 \| \| BEHI Category \| \| Very low \| Low \| Moderate \| High \| Very High \| \| Number of Sites \| 1 \| 13 \| 58 \| 15 \| 0 \| \| Percent of Sites \| 1.2 \| 14.9 \| 66.7\| 17.2 \| 0 \| \| Total sites \| 87 \| doi:10.1371/journal.pone.0110170.t002 Figure 2. Longitudinal profile of the Haw River study site. doi:10.1371/journal.pone.0110170.g002 Riparian sediment deposition from agriculture on the Haw River is consistent with descriptions of sediment deposition layers between 1 and 6 m in depth which have been found adjacent to other streams of the eastern United States. A history of row crop agriculture has caused a loss of 14 cm of topsoil from the North Carolina Piedmont, with sediments migrating from the upland fields to riparian areas and associated rivers and streams [3,4]. These sediment deposit layers are likely an outcome of land clearing for development, agriculture within the watershed, deposition behind dams, and deposits from past flood events, showing the potential for substantial sediment migration to storage areas along riparian river borders [17]. Recent and continued sediment deposition from current agriculture into riparian areas has been documented in the upper Midwest of the United States [51], similarly to patterns on the Haw River. The riparian areas were mostly forested at the time of the study, with root density and root depth ratios negatively correlated with bank height, but not with bank retreat. Although mature trees were present in the riparian zone throughout the length of the study site, roots rarely extended to the base of the bank. Root \| Table 3. Pearson Product-Moment Correlation Analysis of Erosion Factors on the Haw River. \| \|------------------------------------------\|---------------------------------\|-----------------\|-----------------\| \| Attribute \| Bank height (m) \| Bankfull height (m) \| BEHI \| Bank Retreat (m) \| \|------------------------------------------\|-----------------\|---------------------\|----------\|------------------\| \| Bank angle \| r \| −0.04 \| −0.04 \| 0.11 \| \| \| p \| 0.7 \| 0.7 \| 0.29 \| \| Bank height (m) \| r \| 0.55 \| −0.04 \| 0.7 \| \| \| p \| <0.001 \| −0.07 \| \| \| Bank height ratio \| r \| 0.76 \| 0.76 \| \| \| \| p \| <0.001 \| 0.49 \| \| \| Bank retreat (m) \| r \| −0.04 \| 0.10 \| 0.11 \| \| \| p \| 0.7 \| 0.38 \| 0.34 \| \| River width 2005/2007 (m) \| r \| −0.68 \| −0.48 \| −0.40 \| \| \| p \| <0.001 \| <0.001 \| −0.09 \| \| Riparian slope (%) \| r \| −0.341 \| −0.15 \| −0.50 \| \| \| p \| <0.001 \| 0.16 \| \| \| River bed slope (%) \| r \| 0.02 \| 0.21 \| −0.04 \| \| \| p \| 0.9 \| 0.05 \| 0.73 \| \| Surface protection (%) \| r \| −0.19 \| −0.10 \| −0.002 \| \| \| p \| 0.08 \| 0.35 \| 0.98 \| \| Root density (%) \| r \| −0.36 \| −0.17 \| 0.004 \| \| \| p \| <0.001 \| 0.12 \| 0.96 \| \| Root depth ratio \| r \| −0.29 \| −0.26 \| −0.16 \| \| \| p \| 0.006 \| 0.02 \| 0.14 \| doi:10.1371/journal.pone.0110170.t003 \| Table 4. Analysis of Variance comparing bank characteristics between areas with low (<2%) and high (≥ 2%) riparian slopes. \| \|----------------------------------------------------------------------------------------------------------------------------------\| \| Traits/Location \| n \| Median values (m) \| Mean values (m) \| SE \| P* \| \|------------------------------------------\|-------\|------------------\|----------------\|-----\|----\| \| Bank retreat \| \| \| \| \| \| \| Low slope \| 61 \| 2.1 \| 2.7 \| 0.31\| 0.03\| \| High slope \| 26 \| 0.8 \| 1.5 \| 0.45\| \| \| Bank height \| \| \| \| \| \| \| Low slope \| 61 \| 12.7 \| 12.8 \| 0.42\| 0.002\| \| High slope \| 26 \| 10.4 \| 9.6 \| 1.23\| \| \| Bank angle \| \| \| \| \| \| \| Low slope \| 61 \| 60.0 \| 56.1 \| 2.60\| 0.06\| \| High slope \| 26 \| 40.0 \| 46.1 \| 5.35\| \| \| BEHI \| \| \| \| \| \| \| Low slope \| 61 \| 26.5 \| 26.3 \| 0.70\| <0.001\| \| High slope \| 26 \| 20.6 \| 19.5 \| 1.08\| \| Mann Whitney Rank Sum Test was used for Bank retreat and Bank height analyses. ANOVA was used for BEHI and Bank Angle analyses. doi:10.1371/journal.pone.0110170.t004 density in river banks has been shown to reduce scour through both mechanical root reinforcement and matric suction [52]. However, on the Haw, the bank height frequently exceeded rooting depth (Table 2). The absence of roots at the base of the river bank would mean that roots are not present to provide reinforcement and protection from shear. In contrast to the protective effect of roots on bank height, the lack of correlation with bank retreat suggests vegetation provided no protection from erosion of the bank toe slope at the river’s edge, a significant concern in river management [53]. The influence of dams on river geomorphology has been well documented [10,12,13]. In the present study, dams were lower than the heights of banks measured in the study area and the eroded bank areas extended well upriver beyond dam impoundments. The highest dam currently on the Haw is the Saxapahaw Dam, with a height of 9.1 m. The mean height for all dams in the studied segment was 2.9 m, including both historical and present dams. Yet the mean bankfull measurement was 5 m, and the mean bank height was 11.8 m, higher than all the dams. If bank erosion was primarily through legacy sediments from dam impoundments, it would be expected that the bankfull and bank heights would not exceed the heights of the dams. The Haw River bed is rocky, lined with rocks from 0.2 m diameter to large boulders and bedrock, so the contribution to bank heights from erosion of the river bed is likely to be minimal. Comparison of the bank heights, BEHI values and bank retreat upstream of the legacy dam sites with other study sites showed no difference between locations (Table 6). Although low dams can have significant ecological effects in many cases, the impact to higher order rivers such as the Haw appears to be small. The lack of a correlation between bank height and the BEHI with bank retreat suggests that different but related processes are occurring. Bank retreat often occurs following bank failure and collapse, with the river bank collapsing downward towards the water’s edge then eroding away as the river flows past. River bank stability can be highly variable, with many factors contributing to the structural integrity. The negative correlation between bank height and BEHI with river width suggests that many of the tall banks are stable, reflective of the wide range of conditions present in the river corridor. However, both high banks and bank retreat were correlated with low riparian slope, suggesting this condition increases risk from both patterns of erosion [54]. Geomorphic patterns of the Haw River are consistent with conceptual models describing changes in river geomorphology following disturbance such as the removal of a small dam. Following dam removal, the sequence would be: a) lowered water surface, b) degradation, c) degradation and widening d) aggradation and widening, ending with e) quasi-equilibrium [32,55,56]. This process usually happens quickly after removal of small dams, reaching quasi-equilibrium within a few years. A similar sequence of geomorphological changes following disturbance seems to be \| Table 5. Historical and current dams on the Haw River listed in order on the river. \| \| --- \| \| Dam Name* \| Dam Height (m) \| Years \| \| Virginia Falls Dam \| 3.0 \| 1874- present, removed 2013 \| \| Puryear Dam \| 2.4 \| 1763 - present \| \| Cedar Cliffs Dam \| 1.5 \| 1860–1910 \| \| Saxapahaw Dam \| 9.1 \| 1938 - present \| \| Dark’s Dam \| - \| 1790–1875 \| \| Elliot’s Falls \| 1.2 \| 1778–1810 \| \| Love’s Dam \| - \| 1790–1920 \| \| Pace’s Dam \| 2.4 \| 1789–1924 \| \| Burnett-Powell Dam \| - \| 1776–1880 \| \| Bynum Dam \| 3.0 \| 1874 - Present \| \| doi:10.1371/journal.pone.0110170.t005 \| \| Table 6. Effect of historical dams on river bank geomorphology. \| \| --- \| \| Traits/location \| n \| Median values (m) \| Mean values (m) \| SE \| p \| \| Bank retreat \| Behind dam \| 8 \| 1.8 \| 2.3 \| 0.87 \| 0.94 \| \| Not behind dam \| 79 \| 1.5 \| 2.2 \| 0.28 \| \| Bank height \| Behind dam \| 8 \| 11.7 \| 11.4 \| 1.5 \| 0.83 \| \| Not behind dam \| 79 \| 12.1 \| 11.9 \| 0.52 \| \| BEHI \| Behind dam \| 8 \| 23.2 \| 24.1 \| 2.5 \| 0.65 \| \| Not behind dam \| 79 \| 24.4 \| 27.2 \| 0.69 \| Mann Whitney Rank Sum Test was used for Bank retreat and Bank height analyses. ANOVA was used for BEHI analysis. \| doi:10.1371/journal.pone.0110170.t006 Changes in Bank Geomorphology and Erosion of the Haw River increasing erosion, a significant management concern. Impervious surface, high flow events are likely to also increase with upstream of the study area continues to urbanize with increasing concentration of suspended solids also increased exponentially, averaging 15 mg/L. As the energy in the river increased with flow, suspended solids in the river ranged from 1 mg/L to 187 mg/L, ranging from 2 m³/sec to 659 m³/sec, averaging 31 m³/sec. The study area were examined from 2005–2010, with flow and changes in flow can affect soil loss from erosion and sediment load. Data from a U.S.G.S. monitoring station just downstream of the study sites. Reaching dynamic equilibrium does not always occur quickly. Following an eruption of Mount St. Helens in 1857, stable floodplains and re-vegetation of riparian zones had not yet been re-established at the time of the 1980 eruption [33]. In this case, dynamic equilibrium had not been reached over a century after the earlier disturbance. Similar patterns have been observed in other regions [5,58,59]. For the Haw River, re-connection with flood plains and equilibrium will likely take centuries or longer, if it all, compared with the decadal time scale described with dam removal. In addition to the effects from dams and past agriculture, changes in flow can affect soil loss from erosion and sediment load. Data from a U.S.G.S. monitoring station just downstream of the study area were examined from 2005–2010, with flow and sediment measures collected on the same day [37,60]. As flow increased, so did sediment loading to the river, as reflected in the concentration of suspended solids (Figure 3). River discharge ranged from 2 m³/sec to 659 m³/sec, averaging 31 m³/sec. The suspended solids in the river ranged from 1 mg/L to 187 mg/L, averaging 15 mg/L. As the energy in the river increased with flow, the concentration of suspended solids also increased exponentially, a relationship well documented in the literature [2]. As the region upstream of the study area continues to urbanize with increasing impervious surface, high flow events are likely to also increase with increasing erosion, a significant management concern. Sediment loading from bank erosion to the Haw River will also contribute P. The analyses of riparian soil indicated approximately 3759 kg (8286 lb.) of P enters the river annually from sediment. This is about 1.5% of the total target P load from non-point sources in the Haw River flowing to Jordan Reservoir (of a targeted 106,884 kg), and potentially 6% of the total P load to the Haw River from river bank erosion (the study area was about 25% of the river length). Currently this is an unaccounted non-point source of P, with no Best Management Practices or nutrient loading targets assigned to this P source [34]. Like many other high order rivers globally, the geomorphology of the Haw River in North Carolina is changing following agricultural and other disturbances, with significant sediment and P loading to the river. The river is undergoing a process of reshaping with river widening and the formation of very high river banks. Occasional high flow events further contribute to erosion with the concentration of suspended solids in the water column increasing with discharge (Figure 3). Future study of the Haw River and similar systems could be directed at understanding the patterns of erosion seen on this river. One major area of investigation would be to determine the origin and age of sediments deposited along the river, especially those in low slope areas which are experiencing the most erosion. Another study would be to evaluate the impacts of past land use and land cover on contemporary geomorphology, flow and erosion. Comparison with commonly used models for erosion estimates would also be valuable. Conclusion Few studies on the patterns of bank erosion and hydrogeomorphic change following disturbance have been published for high order rivers such as the Haw River. However, differences in geomorphology have been described between high and low order segments of rivers, with factors impacting the river attributes changing throughout the river’s length. These studies show processes and attributes of low order rivers may not be applicable to larger river systems [32]. For most studies estimating erosion and erosion potential of larger rivers, a modeling approach has been used. Common methods are the Universal Soil Loss Equation and the Soil and Water Assessment Tool [61,62]. In contrast, field measurements of large systems are seldom the major approach used to identify factors influencing erosion and geomorphic change. For the Haw River, regions of high erosion potential (as indicated by the BEHI and bank height) are negatively correlated with river width, suggesting regions high BEHI values and bank heights are have narrow river width and are relatively stable. On this river, erosion as measured by bank retreat is independent of most physical features such as bank height, BEHI, bank angle and \| Land Use \| Percentage \| \|--------------\|------------\| \| Forest \| 78.4 \| \| Open \| 15.3 \| \| Shrubland \| 5.5 \| \| Impervious \| 0.8 \| doi:10.1371/journal.pone.0110170.t007 Table 7. Land cover within the 153 m zone adjacent to BEHI study sites. \| Year \| Number of farms \| Alamance \| Chatham \| Orange \| \|------\|-----------------\|----------\|---------\|--------\| \| 1910 \| 2508 \| 3640 \| 1957 \| \| \| % of county in agriculture \| 80 \| 85 \| 84 \| \| 1950 \| 2940 \| 2977 \| 2038 \| \| \| % of county in agriculture \| 79 \| 66 \| 70 \| \| 2007 \| 753 \| 1089 \| 604 \| \| \| % of county in agriculture \| 32 \| 24 \| 24 \| doi:10.1371/journal.pone.0110170.t008 Table 8. History of farming within the studied counties of the Haw River watershed. bankfull height, suggesting different erosional processes are occurring. Although these physical features are often used to predict erosion potential, such as through use of the BEHI, that does not appear to be the case in this study. Independence of bank physical features with bank retreat has been observed in a few other systems [65]. Areas with low riparian slope (≤2%) appear to have the highest erosion risk, experiencing high bank heights, BEHI values and bank retreat. This relationship is in contrast to some common models used for erosion estimation, which rank high slope as an erosion risk factor [61,62]. In the Haw River system, a history of extensive soil loss from upland agriculture suggests erosion of agricultural legacy sediments deposited on areas with low slope beside the river has occurred, with high erodibility. Increasing sediment concentration with flow suggests the river is still changing, reshaping as an outcome of past and present distur- \| Soil ID \| Soil Type \| % slope \| # sites \| \|---------\|-----------------------------------------------\|---------\|---------\| \| AdE \| Appling, sandy loam, steep phase \| 20 \| 2 \| \| Ba \| Buncombe loamy fine sand, frequently flooded \| 1 \| 14 \| \| BaE \| Badin Nanford Complex \| 23 \| 6 \| \| CbE \| Cecil fine sandy loam, moderately steep phase \| 17 \| 2 \| \| Cg \| Congaree fine sandy loam, frequently flooded \| 1 \| 2 \| \| ChA \| Chewacla and Wehadkee soils, frequently flooded \| 1 \| 1 \| \| Cp \| Congaree fine sandy loam, frequently flooded \| 1 \| 4 \| \| GaE \| Georgievle silt loam, moderately steep phase \| 17 \| 1 \| \| GbE3 \| Georgievle silt loam, severely eroded, moderately steep phase \| 20 \| 1 \| \| Ge \| Goldston silt loam, moderately steep phase \| 17 \| 5 \| \| GkE \| Georgievle Badin complex \| 23 \| 2 \| \| LbE \| Lloyd loam, moderately steep phase \| 17 \| 1 \| \| Mc \| Mixed alluvial land, poorly drained \| 1 \| 6 \| \| Md \| Mixed alluvial land, well drained \| 1 \| 6 \| \| NaD \| Nanford Badin complex \| 5 \| 1 \| \| RvA \| Riverview silt loam, frequently flooded \| 1 \| 28 \| \| TaD \| Tirza silt loam, strongly sloping phase \| 30 \| 1 \| \| WcE \| Wilkes stony soils, moderately steep phase \| 17 \| 4 \| Figure 3. Relationship between log of river discharge and log of total suspended solids in the Haw River. doi:10.1371/journal.pone.0110170.g003 Table 9. Soil types at BEHI study sites. bance. The potential for further impairment as upstream urban development increases should be a management concern for the river health and water quality. Rate of bank retreat and river widening is similar to the rate reported for other high order rivers. In rivers of southern Minnesota, in the Midwest of the United States, LIDAR studies have indicated widening rate of 0.57–5 m/yr since European settlement [63]. In our study, the Haw has widened 0.38 m/yr, slightly less than in Minnesota. But both studies indicate the rivers are not at equilibrium. The Haw River is an unstable system, with river bank erosion and geomodification potential influenced by disturbance, riparian slope and episodes of high flow. The greatest erosion, measured by bank height and bank retreat occurred in regions with low riparian slope, usually with alluvial soils, suggesting erosion of deposited sediments. Historical dams were not a significant factor in influencing current conditions on the Haw River. This study provides a model for high order rivers, identifying factors driving erosion and changes to channel morphology which will help in management of these and other high order river systems. Acknowledgments* We would like to thank Dr. Greg Jennings for his assistance and guidance throughout development of this project. We would also like to sincerely thank the reviewers of this manuscript for their thoughtful and insightful comments. Author Contributions Concepted and designed the experiments: JM PR DW. Performed the experiments: JM PR DW. Analyzed the data: JM PR DW. Contributed reagents/materials/analysis tools: JM PR DW. Wrote the paper: JM PR DW. Obtained landowner permission for access: JM PR DW. 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Geomorphology 201: 312–322.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4411, 1 ], [ 4411, 12045, 2 ], [ 12045, 16498, 3 ], [ 16498, 20005, 4 ], [ 20005, 26574, 5 ], [ 26574, 29164, 6 ], [ 29164, 34804, 7 ], [ 34804, 39208, 8 ], [ 39208, 45117, 9 ], [ 45117, 47884, 10 ], [ 47884, 56218, 11 ], [ 56218, 59156, 12 ] ] }
bea11c816d8c1f7c7fe3a27f4905031bfed98f3c	{ "olmocr-version": "0.1.59", "pdf-total-pages": 18, "total-fallback-pages": 0, "total-input-tokens": 50994, "total-output-tokens": 12915, "fieldofstudy": [ "Computer Science", "Medicine" ] }	Noise-residue learning convolutional network model for magnetic resonance image enhancement Ram Singh¹ and Lakhwinder Kaur² Department of Computer Science & Engineering, Punjabi University Patiala - 147002 (Punjab), INDIA E-mail: [email protected], [email protected] Abstract. Magnetic Resonance Image (MRI) is an important medical image acquisition technique used to acquire high contrast images of human body anatomical structures and soft tissue organs. MRI system does not use any harmful radioactive ionized material like x-rays and computerized tomography (CT) imaging techniques. High-resolution MRI is desirable in many clinical applications such as tumor segmentation, image registration, edges & boundary detection, and image classification. During MRI acquisition, many practical constraints limit the MRI quality by introducing random Gaussian noise and some other artifacts by the thermal energy of the patient body, random scanner voltage fluctuations, body motion artifacts, electronics circuits impulse noise, etc. High-resolution MRI can be acquired by increasing scan time, but considering patient comfort, it is not preferred in practice. Hence, post-acquisition image processing techniques are used to filter noise contents and enhance the MRI quality to make it fit for further image analysis tasks. The main motive of MRI enhancement is to reconstruct a high-quality MRI while improving and retaining its important features. The new deep learning image denoising and artifacts removal methods have shown tremendous potential for high-quality image reconstruction from noise degraded MRI while preserving useful image information. This paper presents a noise-residue learning convolution neural network (CNN) model to denoise and enhance the quality of noise-corrupted low-resolution MR images. The proposed technique shows better performance in comparison with other conventional MRI enhancement methods. The reconstructed image quality is evaluated by the peak-signal-to-noise ratio (PSNR) and structural similarity index (SSIM) metrics by optimizing information loss in reconstructed MRI measured in mean squared error (MSE) metric. Keywords: MRI reconstruction, Convolution Neural Network, deep learning, Rician noise, MRI denoising, image enhancement. 1. Introduction MRI is an important and widely used non-invasive medical imaging technique in patient care which can provide high quality three-dimensional (3D) images of internal anatomical and physiological structures of human body. MRI is used in a number of clinical and research applications to provide complete structural information for disease diagnosis and prognosis of the affected human body organs. In practice, it is not always possible to acquire higher resolution high contrast MRI due to... many real-time constraints. Sometimes a contrast medium is injected into the desired area of human body to detect and acquire high contrast images such as blood flow streaming, tumors, bone fractures and tissue cell inflammations [1]. As MRI utilizes non-ionized radiation and strong magnetic field to generate accurate image. It is safer imaging modality than other techniques such as computerized tomography and x-rays. MRI provides detailed information images of internal bone structures, soft-tissue regions and blood-flow streaming in cardiac region for diagnosis and accurate image analysis. The MRI scanners used to acquire images applying a strong magnetic field created with the scanner hardware gradient-coils generating radio waves. MRI scanners can scan the desired human body parts provide 3-D volumetric images by scanning multiple 2-D sequential slices. However, it is possible that the outer-plane resolution may lower than the in-plane direction which permits faster image acquisition and also minimize the noise levels in each 2-D slice. MR image scan takes a longer scan time to acquire high resolution and high signal-to-noise ratio (SNR). Considering patient condition and comfort, it is not preferred to scan again and again the same data. Hence, low resolution images with non-uniform intensity region gets acquired. To enhance these low resolution and non-uniform intensity region images, post-acquisition image enhancement techniques are used. This is one of the most important steps in MRI quality enhancement and reconstruction of high-resolution images. This operation aims to identify and detect the pixels groups in the image to improve their spatial contrast in the low-contrast regions. MRI signal is acquired in the image scanner in complex frequency domain by forward Fourier transform and inverse transformation. This process provides frequency spectrum of the acquired complex MR signal, called $ k $-space which is degraded by various environmental factors such as random additive white Gaussian noise, body motion artifacts, scanner electric voltage fluctuations etc. When the spatial 2-D computer readable digital image is constructed taking squared magnitude of real-part and imaginary-part of the complex data, the resulted image is created with low intensity regions and degraded quality with noise artifacts [2]. The MR image enhancement process is the transform of image data into improved perceptual quality of the given image which enable the observers to see the image information which is not be immediately available in the original acquired image. This can happen when the dynamic intensity range in the image of that not commensurate with display device when image contains high noise contents or having low contrast. Main motive of the image enhancement technique is to provide high perceptual quality MRI with maximum structural details for visually analysis and for automated quantitative processing by computer algorithms. Rest of the paper has been organized as: Section 2 gives background of basic MRI filters used in noise removal and enhancement of spatial low intensity image regions. Section 3 elaborates the traditional frequency domain filtering techniques exploits the conditional probability of 2-D and 3-D MRI and self-similarity property of image regions. Section 4 contains proposed deep convolutional neural network filtering details for MRI. Section 5 gives experimental and analysis details and in section 6, conclusion and future scope has been given. 2. Background Image enhancement techniques are mathematical procedures designed to manipulate and enhance the MRI contrast in the low-contrast image regions. A set of operations is performed on low contrast images to enhance its perceptual quality to make it suitable for automated clinical analysis. Conventionally, various image quality enhancement methods have been applied to low-resolution images as a post-processing operation [3]. Conventionally, histogram equalization (HE), adaptive histogram equalization (AHE) and contrast limited adaptive histogram equalization (CLAHE), image enhancement methods have been used to scale up the pixel intensities in the low-resolution MRI [4][5]. Despite the tremendous advancement in the digital signal sensing technologies, the problem of acquiring good quality MRI with high resolution is still facing many challenges. Over the last many years, medical MRI denoising reconstruction research area witnessed a commendable growth and the process is continuously flourishing with new research in this domain. The reason behind this is that no single technique is capable in handling the issues and challenges occurred in medical MRI. A fundamental reason in MRI enhancement and reconstruction is to provide perceptually good quality images with visible fine details to the human observer for analysis. Also, MRI with high signal-to-noise ratio (SNR) found suitable for automated image analysis and for further image processing tasks like, tumor segmentation, classification, registration and edge detection. The major issues in MRI acquisition is how to balance efficiently and optimally between the MRI spatial resolution, SNR and scan-time. These three factors are highly inter-dependent. Spatial high-resolution MRI enable the observers to perceive finer image details, but it comes on the cost of low-SNR or longer scan-time. During image acquisition, it is desirable to scan image with adequate SNR level for perceptual analysis of region-of-interest in the image. Availability of MRI scanning resources is limited and costly. Long scan-times are not preferred to acquire high SNR MRI due to patient condition and comfort. Moreover, in long scan-time, patient’s body movement also induce motion artifacts in the acquired MRI. Due to these three parameters, post-acquisition image processing and enhancement techniques are preferred to reconstruct high resolution MR images [3] from the low quality as shown below: ![Figure 1](image) Figure 1: Starting from left, (a) is the normal acquired image, (b) is the low intensity image and (c) is the enhanced MRI slice. Historically, image quality enhancement started from calculating and equally distributing the intensity levels of all image pixels by histogram equalization in all pixel locations. The low contrast image regions contain pixel vectors with each intensity level count at each pixel position. The histogram $hist(i)$ for image intensity levels can be defined from total number of pixels of each intensity level as: $$h(i) = \sum_{x=0}^{M-1} \sum_{y=0}^{N-1} H(f(x,y) - i)$$ \hspace{1cm} (1) where as operator $H$ is defined is: $$H(i) = \begin{cases} 1, & \text{if } i = 0 \\ 0, & \text{otherwise} \end{cases}$$ \hspace{1cm} (2) A normal image intensity distribution and redistribution after equalization of intensity histogram is shown in figure-2 below. A local convolution filter mask or window $ W(k, l) $ of odd size dimensions is used to scale the pixel intensity by convolving the filter weights with image pixels. A kernel window can be of size $(2K + 1 \times 2L + 1)$ coefficients, where each pixel location $(x,y) = (0)$ is the center of filter window and the convolution operation can be defined as: \[ g(x, y) = W * f(y) = \sum_{x=0}^{M-1} \sum_{y=0}^{N-1} W(k,l) * f(x-k, y-l) \] where $ g(x,y) $ is the output image of the convolution operation of $ W(k,l) * f(y) $ filter and input image. Figure 2: First, left-side figure is a normal histogram and second, right-side is of intensity equalized histogram of the image shown in figure 1 above. The convolution filter weight parameters are convolved with the input image in order to upscale the pixel intensity levels by a specific enhancement operation. This will modify the desired pixel values by amplifying their intensity while suppressing unwanted pixel intensities penalizing them with specified kernel weights. The specific values of the kernel weights can be set depending on the different types of enhancements operations. In frequency domain, the image enhancement operation is performed by Fourier transform. The Fourier transformation $ F(u,v) $ on an image $ f(x,y) $ can be performed as: \[ F(u,v) = \frac{1}{MN} \sum_{x=0}^{M-1} \sum_{y=0}^{N-1} f(x,y)e^{-2\pi ij \left( \frac{u}{M} \right) \left( \frac{v}{N} \right)} \] where $ u = 0,1,2,..., M-1 $ and $ v = 0,1,2,..., N-1 $ are transformed image coefficients of the two-dimensional input image. A spatial domain 2-D image can be reconstructed from the inverse of transform domain coefficient which is given here as: where $ f(x, y) $ is the reconstructed output image. $ x = 0, 1, 2, \ldots, M - 1 $ and $ y = 0, 1, 2, \ldots, N - 1 $ are spatial pixel locations of $ M \times N $ MRI [6]. 2.1. Pixel Intensity Scaling Image pixel intensity levels is scaled to enhance the intensity levels in the range of the desired regions of the acquired MRI which can be in a very narrow range of intensity band. The limited band intensity can be scaled focusing on specific intensity bands. For example, if two images, $ f_1(x, y) $ and $ f_2(x, y) $ are known to be defined for the pixel intensity band of interest, an intensity scaling transformation can be applied by defining the same as: \[ \begin{align} \text{eim} &= \begin{cases} f, & f_1 \leq f \leq f_2 \\ 0, & \text{otherwise} \end{cases} \\ \text{and} \\ g &= \begin{cases} \text{eim} - f_1, \\ f_2 - f_1, \quad (f_{\text{max}}) \end{cases} \end{align} \] where parameter $ \text{eim} $ is an intermediate image and $ g $ is the output image with maximum pixel intensity as $ \text{asf}(\text{max}) $. 2.2. Intensity Equalization The low-resolution image regions enhanced by stretching specific pixel intensity levels. For this purpose, the probability distribution of pixel intensities is normalized to map with a maximum flat histogram intensity levels which ranges from 0 to $ L - 1 $ gray-levels for the total pixels of $ M \times N $ size image. For equal distribution of the intensity levels over all image regions, each level of histogram represents with pixel counts of $ M \times N $ image. A very simple approach to redistribute the image pixels is the normalized cumulative histogram which is defined as: \[ H(j) = \frac{1}{MN} \sum_{i=0}^{j} \text{hist}(i) \] where $ j = 0 $ to $ L - 1 $ is the maximum gray-scale intensity levels i.e. 0-255, and $ H(j) $ is the normalized cumulative histogram. Now, $ H(j) $ is used to map pixel intensity levels between the original input image and the scaled intensity gray-levels required for image quality enhancement. The enhanced image $ \hat{f}(x, y) $ will have a maximal equal intensity distribution in all its regions, and is defined as: \[ \hat{f}(x, y) = (L - 1) * H(f(x, y)) \] 2.3. Enhancement by noise suppression When MRI quality is degraded with any amount of the random noise contents, traditionally local filtering method is applied to assign a new pixel value for each pixel in the image by calculating it from the neighborhood pixels values around that pixel. These operators can be different sizes and weight values. The linear transform-based spatial domain filters are designed to convolve in a sliding-window fashion and some are non-linear. These filters are applied to update the center value under the operator by a mathematical or statistical operation such as calculating mean or median, to replace the original value of the pixel. The convolution operation is performed by convolving the filter window of $(2K+1\times2L+1)$ $(K = \text{horizontal Rows}) \times (L = \text{vertical Columns})$ size. ### 2.4. Edge Enhancement MRI is also enhanced highlighting the edges and boundary pixels of a region within the image. Edges can be selectively identified in different orientation of image details and enhanced by a key factor on horizontal and vertical edge directions. Following edge masks can be applied for horizontal edge or line enhancement as: \[ W_{Hz1}(k, l) = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 0 & 0 \\ -1 & -1 & -1 \\ \end{bmatrix} \quad \text{or} \quad W_{Hz2}(k, l) = \begin{bmatrix} -1 & -1 & -1 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \\ \end{bmatrix} \] (10) and for vertical edge or line enhancements these filters can be defined as: \[ W_{Vz1}(k, l) = \begin{bmatrix} 1 & 0 & -1 \\ 1 & 0 & -1 \\ 1 & 0 & -1 \\ \end{bmatrix} \quad \text{or} \quad W_{Vz2}(k, l) = \begin{bmatrix} -1 & 0 & 1 \\ -1 & 0 & 1 \\ -1 & 0 & 1 \\ \end{bmatrix} \] (11) A single all-directional mask, named as un-sharp mask can be applied to enhance all directional edges in an image which is defined as: \[ W_{HP}(k, l) = \begin{bmatrix} -1/8 & -1/8 & -1/8 \\ -1/8 & 1 & -1/8 \\ -1/8 & -1/8 & -1/8 \\ \end{bmatrix} \] (12) These filters with positive filter weights produce an output image with positive and negative pixel values. A high contrast image with only positive pixel values can be reconstructed by setting an threshold criteria for selecting the desired intensity levels of image pixels. ### 2.5. Local Area Histogram Equalization The local-region based image enhancement operation can be applied to equalize the all pixel’s intensity levels in an image by overlapping the local-region intensity levels $[7, 8]$. This nonlinear operation will significantly improve the perceptual image quality of low intensity image details. The local-area histogram of an image region intensity levels for its each low-intensity pixel location $(x, y)$ can be defined as: \[ h_{LA}(x, y)(i) = \sum_{k=-1}^{K} \sum_{l=-1}^{L} \delta(f(x+k, y+l) - i) \] (13) where $i = 0 \text{ to } L - 1$ is the gray-scale intensity levels are representing the $h_{LA}(x, y)(i)$hist which is called local area cumulative histogram. Finally, the output image $ g(x,y) $, with histogram equalized intensity level distribution is reconstructed setting filter mask of size $ K = L = 15 $ i.e. the mask window size of $ 31 \times 31 $ as: \[ H_{LA}(x,y)(j) = \frac{1}{(2K+1) \times (2L+1)} \sum_{i=0}^{l} h_{LA}(x,y)(i) \] (14) and the equalized histogram image $ g(x,y) $ is recovered from the localized histogram as: \[ g(x,y) = (L - 1).H_{LA}(x,y)(i) \] (15) 2.6. Image enhancement and denoising by averaging A high-quality image can be restored from the original noisy image by suppressing noise contents by averaging operation based on following three prior conditions: (i) When relatively large number of images are available of same object. (ii) Each image is contaminated with same nature and type of noise (iii) Noise is independently and identically distributed with zero mean and equal variance in the image. Based on these three priors, multiple images of the same scene or object are used to calculate average and assigned to each pixel location in the output image. This method can effectively restore and significantly enhance even severely noise corrupted images. Each $ i^{th} $ noisy input image $ f_{Noisy(i)}(x,y) $ is represented as: \[ f_{Noisy(i)}(x,y) = f(x,y) + \eta(x,y) \] (16) Here $ f(x,y) $ is the clean image and $ \eta(x,y) $ is the random additive type noise component. If a total number of available images is $ Q $, then an averaged output image $ g(x,y) $ is computed as: \[ g(x,y) = \frac{1}{Q} \sum_{i=1}^{Q} f_{Noisy(i)} \] (17) The expected image $ E\{g(x,y)\} $ obtained by the expectation operator $ E\{\cdot\} $ from the $ g(x,y) $ such that the expected image value $ g(x,y) $ is very close to the original input image $ f $ and standard deviation of the output image $ g(x,y) $ is taken as: \[ \sigma_g = \frac{\sigma_d}{\sqrt{Q}} \] (18) whereas $ \sigma_d $ is the noise standard deviation in the image. When large the averaging image data-set $ Q $ will be, higher the quality of averaged noise free image. 2.7. Enhancement by Image Subtraction MRI is also enhanced by subtraction operation between two or more images. By this method, the estimated difference equal to the noise components is subtracted from the noisy image. Images acquired under different conditions are not required to be registered. When two images $ f_1(x, y) $ and $ f_2(x, y) $ are given, then the difference between two images $ b(x, y) = f_2(x, y) - f_2(x, y) $ is used to obtain the re-scaled output $ g(x, y) $ as: \[ g(x, y) = f_{\text{max}} \left( \frac{b(x, y) - \min \{b(x, y)\}}{\max \{b(x, y) - \min \{b(x, y)\}\}} \right) \] (19) Whereas $ f_{\text{max}} $ represent the maximum intensity levels available in the obtained image $ g $. The $ b(x, y) $ is a un-scaled input image. The component $ \min \{b(x, y)\} $ and $ \max \{b(x, y)\} $ are the minimum and maximal intensity values respectively in the $ b(x, y) $ image. 2.8. Frequency Domain MRI Enhancement Techniques The linear transform image enhancement methods can also be applied in frequency transform by the forward Fourier transform and inverse Fourier transform pair to the noise corrupted input image. The output image $ g(x, y) $ is obtained by convolving an input image with a sliding window intensity modifier filter mask $ W(k, l) $ which can be defined as: \[ g(x, y) = W(k, l) * f(x, y) \] (20) The frequency transformed complex coefficients are obtained in $ G(u, v) $ from the spatial Fourier transform frequency spectrum of the input image $ g(x, y) $ as: \[ G(u, v) = W(k, l) * F(u, v) \] (21) where $ W(k, l) $ is the filter mask and $ F(u, v) $ is the Fourier transform of basis function and is computed as defined in Eq. (4 and 5) above. A hard or soft threshold criterion is followed to modify the noise coefficients while preserving the high edge details in the image. The threshold pixel values $ D(u, v) $ is computed from the square root of the squared sum $ \sqrt{u^2 + v^2} $ from a threshold criteria $ T $ of $ D_T $ used to determine the $ (u, v) $ pixel value. For constructing a smoothing region output image, the simplest approach is to use the ideal low-pass filter $ W_L(u, v) $ which modify the pixel value as 1 when $ D(u, v) \leq D_T $ and 0 otherwise. Similarly, ideal high-pass filter $ W_H(u, v) $ is used to update a pixel assigning 1 when $ D(u, v) \geq D_T $ and 0 otherwise. But due to inception of ringing effects in images by these filters while noise removing and smoothing, these filters are not preferred. 3. Related Work The enhanced MRI reconstruction from the noise corrupted signal is a well-studied ill-posed research problem where no unique solution exists or many solutions exists. In computer vision and image processing tasks, various ill-posed problems exist such as image denoising, deblurring, inpainting, motion correction etc. Various MRI denoising and enhancement techniques have been presented over the years from which some of the techniques outperformed others and achieved the state-of-the-art image denoising and enhancement performance. A new wavelet-based MRI denoising and reconstruction methods has been presented in [9] by shrinking Laplacian distributed wavelet coefficients based on conditional probability of each coefficient considering it as noise or image pixels. In [10], Chang et al, proposed two-stage block-wise 3D non-local means (3DNLM) method to restore the noisy MRI slices from neighborhood-slices and then applying multi-dimensional PCA as a post processing step to denoising MRI while preserving the important image information. In [11], the higher-order singular-value decomposition (HOSVD) algorithm presented for volumetric 3D MRI denoising which achieved comparable performance that of famous block-matching BM4D for 3D medical images. Manjon et al presented 2D nonlocal means noise filtering based new methods for Rician distributed noise filtering in [12] for 3D MRI denoising and reconstruction exploiting self-similar image regions in noise corrupted 3D MRI [13], further an extension of the self-similar patch-based sub-bank wavelet mixing for 3D MRI denoising is presented and in [14], and an optimized block-wise non-local means filter is presented for 3D MRI denoising, which outperformed other existing denoising methods at that time. Similarly, in [15] presented a two-stage noise estimation and removal method exploiting sparsity and self-similarity property of image regions for denoising MRI. First, the non-local PCA based threshold is applied to image coefficient to automatically estimate the noise contents and then rotationally invariant non-local means noise filtering applied which automatically estimate the noise in spatially varying noise levels and correct the bias effect induced by Rician probability distribution modeled image. A non-local means (NLM) along with Laplacian of Gaussian (LoG) filter has been applied in [16] on squared magnitude MRI simultaneously to filter out noise contents and compensating bias effect efficiently while preserving the structural details in the image. An artificial neural network (ANN) presented in [17] to predict the noise parameter in MRI with texture feature analysis for automatic denoising. The proposed method effectively restores the MRI and process the results very fast. A linear minimum mean square error estimation-based 3D-MRI restoration technique is presented in [18] which exploits self-similar property of MRI regions to restore the images while preserving the important structural details. The noise parameter is estimated with Bayesian mean square error to address the denoising problem. A supervised feature learning methodology has been extended developing the unsupervised discriminative-learning models for processing large imaging databases. A multi-layer network model is used to extract the multiple features in image convolving a set of different weight filters to memorize the image details to preserve the important structural information. In [19], a feedforward denoising convolutional neural network model has been presented for natural images. This model consists many hidden layers, conforming a deep neural network architecture which can learn every important image feature from each orientation. This model exploits the random Gaussian noise affected image pixels with unknown noise levels. The difference between the input noisy image and target image is estimated by learning the difference between the input and estimated output image. The model can learn to improve from the training images and removes the noise in intermediate hidden-layers. In [19], it has been proved that deep CNN model can restore the maximum useful image information while performing denoising operations. CNN methods are more efficient to reconstruct the original image from the heavily noise corrupted images. Next in [20] a fast and flexible image denoising method has been presented which is more robust to handle the varying white Gaussian noise levels in degraded images. A robust multi-channel (MCDnCNN) deep learning CNN model has been presented in [21] with noise residual-learning for denoising Rician distributed 3-D MRI. This technique significantly denoised MRI with varying noise levels and outperformed other state-of-the-art denoising schemes. In [22] a noise residual based discriminative learning scheme is proposed with fully connected CNN model for multi-dimensional feature map extraction from noisy MRI focusing attention on data loss during each layer with varying noise levels. This scheme extracts the feature maps by normal and dilated convolution operation in parallel manner. A Bayesian shrinkage method is applied to wavelet transform image coefficients combining block-based auto-encoder network to denoise Rician distributed brain MRI in [23] which shows significant performance. Similar approach has been proposed in [24] to reconstruct a denoised MRI from its under-sampled \textit{k-space} data to speed-up the data acquisition. An un-decimated wavelet transform coefficients are utilized as a prior to train the denoising auto-encoder network which are obtained from transformed highly redundant feature maps at multiple levels which enable robust network driven prior to learn. In [25], a deep learning based regularized scheme is presented to reduce the MRI scan-time. This method utilizes the compressive sensed acquisition of $ k $-space MR signal from which MRI is reconstructed. A calibration-less compressed sensing regularizer is used to control the over-flow and under-flow. A stacked convolutional auto-encoder is used for noise reduction based on noise estimation map from coil-wise data sensitivity-map. 4. Methods The deep noise-residue learning convolutional neural network (CNN) model learns the noise levels in the noisy input image blocks and subtract the residue noise from the final output image to produce a denoised and enhanced MR image. A CNN model requires a prior input image in order to learn the useful feature maps. The primary aim of the MRI restoration is to provide a high-quality MRI with enhanced feature maps and preserving the important structural details in the clean image. Let $ g \in \mathbb{R}^{x \times y} $ be denoted as a input noisy MRI and $ \hat{f} \in \mathbb{R}^{x \times y} $denoted as the corresponding restored clean image. The input and output correspondence between noise corrupted and denoised image is represented as: \[ \hat{f} = \delta(g) \] (22) where $ \delta(.) $ is a noise content mapping function. In deep CNN models, the noise characteristics are independent of statistical mapping. Therefore, the denoising optimally approximated by the inverse of $ \delta^{-1} $ and noise is measured from the residue difference of input noise and output denoised clean image which can be defined as: \[ \text{arg min}_\hat{f} \\| g - \hat{f} \\|_2^2 \] (23) and where $ \hat{f} = \delta(g) $is used to estimate the $ g $ and $ f $ is the optimal approximation of $ \delta^{-1} $[26]. 4.1. Network Architecture As shown in the next Figure, the first layer of the denoising network takes input image which convoluted with the randomly initialized filter weights adding bias term followed by a rectification function ReLU is applied. The network’s output layer generates same sized denoised image as is the input image. A padding scheme is used with processing patch to have a same output size. No max-pooling or min-pooling layer is applied because it eliminates the useful features. The convolution and deconvolution layers work in a symmetric way to predict the pixel-wise denoising and the input size can be arbitrary. The first convolution layer includes 128 of $ 3 \times 3 $ size weighted filter kernels to extract and learn the feature map from single channel gray-scale images. Patch-similarity measure is performed considering the neighboring slice patches of size $ 32 \times 32 $. Further, the residual learning and batch normalization is used to generalize intermediate data and speed-up the network training process and for improving the denoising performance. At the last outer layer, a deconvolution is performed to reconstruct the noise free image. Following figure shows the proposed residue learning denoising convolution neural network architecture. This is a fully convolution-deconvolution network model without pooling layer to learn the all feature details in the image. The network has been trained with Adam optimizer to control and avoid the over-fitting and under-fitting problem. The learning rate is fixed at $ 10^{-6} $ and standard deviation of the noise is used maximum up to 70 percentage. 4.2. MRI Dataset A 3D simulated BrainWeb [27] MRI phantom database has been used to evaluate the denoising performance of the proposed model. This is a freely available MRI phantom database called BrainWeb [27], which comprises of (a) T1-W, (b) T2-W and (c) Proton Density (PD) each having resolution of 181 × 217 × 181 pixels. ![Figure 3: CNN based residual MRI denoising.](image) 4.3. Network Training A major constraint in deep learning CNN models is the non-availability of huge amount medical MRI data for training purposes. A single subject huge amount of MRI data is normally not available for training of medical MRI denoising tasks. The proposed model trained on 100 MRI slices each from T1-W, T2-W and PD volumes from BrainWeb database. The MRI database partitioned into three subsets i.e. training set, testing and validation sets. 70 slices used for training purpose and 15 from each modality. In these three types of 70 slices, synthetic noise is added in the range of 1 to 25. Further these noise corrupted data are fed to the proposed network model to perform denoising task. Now suppose $g$ is the input image, the convolution and deconvolution of the input image can be represented as: $$ \text{Conv} \times \text{ReLU} \times \text{Deconv}$$ \[ R(l) = \max (0, W_i \ast l + B_i) \] (24) where $ W_i $ and $ B_i $ are denoising filter weights and bias terms respectively. Operator $ \ast $ indicating the convolution and deconvolution operations. The pixel-wise convolutional sum of the two input images after applying the ReLU is represented as: \[ R(g_1, g_2) = \max (0; g_1 + g_2) \] (25) For end-to-end feature mapping between input noisy and output filtered image, convolutional and deconvolution network filter weights are continuously updated for each convolution and deconvolution pair $ \{g^i, f^i\} $ which are noise corrupted $ g^i(x, y) $ and $ f(x, y) $ is the original ground-truth noise free images respectively. ### 4.4. Loss Function The information loss in image restoration and reconstruction process usually calculated by aggregating the squared difference of mean values between the noisy image and corresponding reconstructed denoised image [19, 28]. The mean square error (MSE) metric is used to compute information loss $ L $ for each image patch-pair to tune the network weights computing the loss after each convolution-deconvolution process as: \[ L = \frac{1}{MN} \sum_{i,j=0}^{M-1,N-1} \\| R(g^i, \theta) - f^i \\|_F^2 \] (26) where $ R $ is the noise residue difference between the denoised recovered noise free image $ f^i $ and ground-truth real noise free image $ f^i $ of $ M \times N $ pixel square size. The network learns feature maps from the input noisy image $ g(x, y) $. It has been observed that optimization for the noisy image better converges than denoised image. Empirically, optimizer Adam [29] with base learning rate $ 10^{-4} $ has been found fast converging than SGD [30]. The learning rate is set same for all layers. The gradients $ \nabla $ with respect to network filter weights of $ l^{th} $ layer is computed as: \[ G = \nabla \theta_i L(\theta_i) \] (27) ### 4.5. Back-propagation to gradients update Back propagation is used to feed backward the gradients information from the connected layers. After two convolution $ C_1 $ and $ C_2 $ of first layer input $ f_1 $, the output is $ g_1 $. The filter weight parameters $ \theta_2 $ is update by deriving the information loss from these convolution and deconvolution as: \[ \nabla \theta_2 L(\theta_2) = \frac{\partial L}{\partial f_1} \frac{\partial f_1}{\partial \theta_2} + \frac{\partial L}{\partial f_2} \frac{\partial f_2}{\partial \theta_2} \] (28) where $ f_1 $ and $ f_2 $ are input image blocks and these are similar for further layered inputs. After obtaining noise residue for every MRI slice, the entire noise free MRI volume can be restored. Conventionally, first the pixelwise noise variance is estimated statistically from the image noise characteristics. This approach affects the denoising performance according to estimation. accuracy. The deep learning-based CNN models demonstrate the robustness in general image denoising. This CNN model is first trained with a specific noise value to evaluate its performance with other existing denoising algorithms. Further, this model extended to single channel gray-scale Rician probability distributed MRI with unknown noise variance. 5. Experimental Evaluation and Analysis The proposed method has been tested using freely available MRI phantom database BrainWeb [27] comprising T1-W (weighted), T2-W and Proton Density (PD) 3D MRI volumes, each having resolution of 181×217×181. The performance and results are analyzed comparing with other existing methods such classical non-local means MRI denoising [12], [14], [13] by adding new features such as fully automated smoothing parameter tuning, selection of relevant blockwise image voxels and parallel processing into denoising filters. This method shows improved performance than non-local means. Similarly, 3D wavelet sub-band mixing noise removal used while keeping the computation time low. 3D oracle-based DCT (ODCT3D) which is rotationally invariant denoising filter and an extension of non-local means for 3D MRI. A pre-filtered MRI with DCT based on threshold noise suppression is filtered by this method. One another denoising filter which is call NLMPCA [15]. The model is evaluated with known and unknown Rician probability distribution noise in MRI with varying level from 3% to 15% with patch-size 32×32 using sliding window scheme to extract the MRI patches to train the corresponding noise filter kernels. The denoising performance of the CNN model is evaluated measuring its quantitative and qualitative scores based on two well-known performance indicators metrics, peak-signal-to-noise ratio (PSNR) and structural similarity index (SSIM) [31-35]. These metrics are defined as: $$PSNR = 10 \log_{10} \left( \frac{255^2}{MSE} \right)$$ \hspace{1cm} (29) where $MSE$ is computed as information loss as sum of the mean squared error between ground-truth noise free image and restored denoised image as given in Eq. (26) above. The following Table-1 shows the practical simulation results of the proposed MRI denoising method and comparison with other existing state-of-the-art denoising methods. \| Noise Levels \| 3% \| 5% \| 7% \| 9% \| 11% \| 13% \| 15% \| 17% \| 19% \| 21% \| \|--------------\|----\|----\|----\|----\|-----\|-----\|-----\|-----\|-----\|-----\| \| Methods \| \| \| \| \| \| \| \| \| \| \| \| PRINLM \| 37.8 \| 34.8 \| 32.8 \| 31.3 \| 30.1 \| 29.0 \| 28.0 \| 27.1 \| 26.3 \| 25.5 \| \| B3DNLM \| 38.0 \| 35.1 \| 33.1 \| 32.5 \| 30.1 \| 29.0 \| 27.9 \| 27.0 \| 26.2 \| 25.3 \| \| FFDNet \| 37.6 \| 34.8 \| 32.9 \| 31.6 \| 30.5 \| 29.6 \| 28.8 \| 28.0 \| 27.4 \| 26.7 \| \| MCDnCN \| 38.6 \| 35.5 \| 33.5 \| 32.1 \| 30.9 \| 30.0 \| 29.0 \| 28.2 \| 27.5 \| 26.8 \| \| CNNDMR \| 39.6 \| 36.5 \| 34.3 \| 32.7 \| 31.5 \| 30.5 \| 29.6 \| 28.9 \| 28.2 \| 27.6 \| Table 1: Comparison of the PSNR (dB) values of the existing vs proposed MRI denoising method. Figure 5: Starting from left-top of first row (a) is the reference noise T1-W, (b) is noisy with 9% Rician noise and (c) is denoising recovered MRI. Similarly, in second and third rows (d) to (e) are reference, 9% noisy and denoised T2-W and (g) to (i) are reference, 9% noisy and denoised PD MRI slices. The structural information restoration in the recovered image is measured by structural-similarity score between the real noise-free image and denoised recovered image which is defined as: $$SSIM(f, f') = \frac{(2\mu_f \mu'_f + C_1) \times (\sigma_f \sigma'_f + C_2)}{\mu^2_f + \mu^2'_f + C_1} \times \frac{(\sigma_f \sigma'_f + C_2)}{\sigma^2_f + \sigma^2'_f + C_2}$$ \hspace{1cm} (30)$$ where $\mu_f$ and $\mu'_f$ are means of reference noise-free image and recovered denoised images; $C_1$ and $C_2$ are constant variables; $\sigma_f$ and $\sigma'_f$ are variances and $\sigma_f$ and $\sigma'_f$ are the covariance of both the images. ![Noise Levels vs PSNR (db) Score in 3D MRI Denoising](image) Figure 6: Noise levels present in the noisy MRI vs PSNR (db) values. Comparison of the existing and proposed MRI denoising methods. Figure 7: Structural Similarity Index score calculated with existing MRI denoising and proposed methods. Table-2 next shows the image reconstruction Structural Similarity Index (SSIM) performance results between the reference image and denoised images and their comparison with other existing MRI denoising enhancement methods. \| Noise Levels \| 3% \| 5% \| 7% \| 9% \| 11% \| 13% \| 15% \| 17% \| 19% \| 21% \| \|--------------\|-----\|-----\|-----\|-----\|-----\|-----\|-----\|-----\|-----\|-----\| \| Methods \| \| \| \| \| \| \| \| \| \| \| \| PRINLM \| 0.97 \| 0.95 \| 0.92 \| 0.89 \| 0.86 \| 0.83 \| 0.79 \| 0.76 \| 0.72 \| 0.69 \| \| B3DNLM \| 0.97 \| 0.95 \| 0.93 \| 0.90 \| 0.87 \| 0.83 \| 0.79 \| 0.76 \| 0.72 \| 0.68 \| \| FFDNET \| 0.97 \| 0.95 \| 0.33 \| 0.91 \| 0.89 \| 0.88 \| 0.86 \| 0.84 \| 0.83 \| 0.81 \| \| MCDnCNN \| .098 \| 0.96 \| 0.94 \| 0.92 \| 0.90 \| 0.89 \| 0.87 \| 0.85 \| 0.84 \| 0.82 \| \| RLCNNMR I \| 0.987 \| 0.974 \| 0.959 \| 0.941 \| 0.923 \| 0.905 \| 0.890 \| 0.873 \| 0.863 \| 0.846 \| Table 2: Structural Similarity (SSIM) index of the existing and proposed MRI denoising method 6. Conclusion In this paper, a deep learning data-dependent medical image denoising technique is presented to denoise MRI using convolutional neural network. This model learns the image features from the residual noise maps extracted by subtracted each residue patch from the noisy image patch. The The proposed method is based on specific noise feed-forward model which outperform some existing denoising methods to provide a high-quality MRI with respect to PSNR and SSIM quality metrics. We have used only single BrainWeb MRI database and further required to evaluate with other real clinical and other medical imaging data sets. An MRI denoising and enhancement method has been presented based on convolution, rectification, batch-normalization and deconvolution processing to generalize the weighted filtered images. The CNN-based image processing and enhancement methods shown significant performance over the traditional techniques. With the advancement in powerful computing resources and availability of large volume cheaper storage device, it becomes possible to mine the voluminous imaging databases. Therefore, the emerging deep learning-based CNN model learn the important feature details from the large imaging data sets and trained to enhance the image quality by down-sampling and up-sampling through the encoding-decoding process. The network trained on the BrainWeb MRI phantom to memorize the detailed feature maps from varying noise corrupted volumes. Testing and validation is performed on the noise degraded and noise free MRI and demonstrated promising quantitative and perceptual improvement in the results. In the conclusion, the proposed deep convolution network-based MRI denoising method has provided better denoising results in 2D and 3D MRI corrupted with Rician distributed noise. 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b89c77e4392f67321aa3d2c316bd6b9014d34803	{ "olmocr-version": "0.1.59", "pdf-total-pages": 7, "total-fallback-pages": 0, "total-input-tokens": 20576, "total-output-tokens": 5347, "fieldofstudy": [ "Medicine" ] }	Sonographic assessment of the prevalence and evolution of fluid collections as a complication of kidney transplantation Maryla Kuczyńska¹, Ewa Piasek¹, Łukasz Światłowski¹, Ewa Kuklik¹, Jan Sobstyl¹, Anna Drelitch-Zbroja¹, Tomasz Słomka², Krzysztof Pyra¹, Olga Furmaga³, Małgorzata Szczerbo-Trojanowska¹ ¹ Department of Interventional Radiology and Neuroradiology, Medical University of Lublin, Lublin, Poland ² Department of Information Technology and Medical Statistics, Medical University of Lublin, Lublin, Poland ³ Department of Radiology, 424 General Military Hospital, Thessaloniki, Greece Correspondence: Maryla Kuczyńska, Department of Interventional Radiology and Neuroradiology, Medical University of Lublin, Jaczewskiego 8, 20-954 Lublin, Poland, tel. +48 81 72 44 154, e-mail: [email protected], [email protected] DOI: 10.15557/JoU.2018.0018 Abstract Aim of the study: The aim of this study is to assess the prevalence and evolution of perirenal fluid collections in a group of 488 patients who have undergone kidney transplantation. Material and methods: Sonographic documentation of 488 deceased-donor kidney recipients was evaluated for the prevalence of perirenal fluid collections and their evolution in time, depending on selected demographic features of the patients, time of detection, initial dimensions and precise position of the collection relative to the kidney and the location of the transplanted organ in the right or left iliac fossa. The collected data were used for statistical analysis to determine the strength of the potential relationships. Results: In 146 out of 488 subjects perirenal fluid collections were found. In 1/3 of the patients more than one fluid collection was diagnosed. Over 40% of fluid collections were detected within 10 days from the date of the first scan and 24.11% were detected within 10–20 days from the date of the first scan. The majority of fluid collections were located near the lower pole of the kidney. Perihilar collections were the least common. Collections encapsulating the kidney and subcutaneous collections were the largest in size on average. A statistically significant difference between the size of collections located on the surface and the size of those located near the upper pole of the transplanted kidney was demonstrated. However, no correlation was proven to exist between the persistence of the fluid collection and its position relative to the transplanted kidney and its initial size. Conclusions: The correct evaluation of a fluid collection’s dynamics of development and nature requires periodic follow-up of the recipient, preferably in a single clinical center. Ultrasonography is an inexpensive, non-invasive and repeatable method for the determination of the presence of fluid collections. However, the decision whether treatment is necessary requires the sonographic image to be compared with the laboratory signs of inflammation and biochemical analysis of the contents of fluid collections. Introduction The current data of the Poltransplant register indicate that approximately 1000 deceased-donor kidney transplantsations are performed in Poland every year(1). These procedures have a significant risk of postoperative complications, including the formation of perirenal fluid collections. According to the literature on the subject the prevalence of fluid collections in kidney recipients is estimated to be approximately 20–50%, which makes them the most common transplantation-related complication(2,3). Furthermore, a significant proportion of fluid collections are considered to form as a result of imperfect surgical techniques, both in terms of the dissection of perihilar structures of the transplanted kidney and damage to the lymphatic pathways accompanying the iliac vessels of the recipient(4–6). The clinical significance of perirenal fluid collections is associated partly with their nature as well as with their location, original size and growth dynamics. This is because large, expansive collections can exert mechanical pressure on the key structures around the transplanted organ, causing significant impairment of its vasculature or function(3,4,7). Considering these facts it should be noted that a kidney transplant patient requires comprehensive and long-term diagnostic imaging follow-up in order to detect and monitor potentially dangerous complications. Therefore, a method which is non-invasive, relatively inexpensive and safe for the transplanted organ is necessary. As a method meeting all these criteria, ultrasonography has become a method of choice for the postoperative assessment of a graft. It is also worth emphasizing the fact that the superficial location of the transplant in one of the iliac fossae allows for easy visualization of the kidney and vascular anastomoses in the essential projections in the majority of cases (due to the lack of deflections from intestinal gas), which is invaluable particularly in the early post-transplant period(3,4,7). The standard sonographic examination of a transplanted kidney involves morphological evaluation of the kidney and perirenal structures, including fluid collections in B-mode imaging and detailed analysis of renal vasculature using color and spectral Doppler imaging. The analysis takes into account the peak systolic flow in the main vessels of the anastomosis as well as intrarenal pulsation index (PI) and resistance index (RI)7). Considering the typical time of occurrence following transplantation and the nature of their contents, fluid collections have been divided into early ones which include haematomas, seromas and urine leaks and late collections which include lymphoceles and abscesses(4,7,8). The ultrasound image of a fluid collection depends on its nature and location. The fluid surrounding an extraperitoneal graft is well-delimited and has a fairly regular shape, while in the case of a kidney transplanted intraperitoneally unstructured, free fluid is usually found(4). In the immediate postoperative period perirenal haematoma and serous leaks can assume the form of a narrow rim encapsulating the kidney. An acute haematoma is usually characterised by high echogenicity (Fig. 1), which becomes significantly lower with time and evolution of the haematoma. Haemorrhage-related collections are characterised by a tendency to form internal compartments (Fig. 2). The sonographic image of a urine leak is equally non-specific. A weakly to well-delimited hypoechoic or anechoic area may be visualised near the kidney, and, more commonly, the distal segment of the ureter or urinary bladder. This location of a urinoma is associated with the significantly higher susceptibility of the distal part of the ureter to ischaemic necrosis and the resultant perforation and with imperfect ureterovesical anastomoses. Urine collections can contain deposits visible as internal deflections and septation is less com- mon in them than in haematomas$^{(3,4,7,8)}$. Lymphocele is the most common type of fluid collection (22\%) complicating the post-transplantation period. It usually occurs in the form of a small, round pocket, which may be associated with the pelvicalyceal system dilatation. As in the case of urine leaks the lymphocele image can be characterized by echo reduction or absence (Fig. 3, Fig. 4)$^{(5,7,8)}$. Careful, systematic ultrasound follow-up primarily aims to identify those fluid collections which may threaten or are already threatening the normal function of the graft. Research shows that it is mainly fluid collections which exceed 50–100 ml, grow rapidly, are symptomatic and are associated with acute graft rejection episodes that should be the cause for clinical concern and need intervention$^{(2)}$. The treatment strategy also depends on the type of a fluid collection. In the majority of cases a draining catheter is recommended, while simple needle aspiration procedures are associated with a high rate of recurrence$^{(8,9)}$. In the case of a lymphocele after the fluid has been drained an obliterating agent may be additionally applied (ethanol, povidone, doxycycline or fibrin glue), which increases the efficacy of the procedure. In rare cases requiring surgical treatment classic or laparoscopic marsupialization of the fluid pocket into the peritoneal cavity is applied$^{(2,4,7,8,10)}$. Abscess evacuation should be combined with an antibiotic therapy$^{(8,9)}$. The treatment of perirenal haematomas requires a somewhat different approach. In the case of uninfected fluid collections drainage is not recommended since the catheter can become blocked with blood clots$^{(7,10)}$. However, some authors argue for the efficacy of percutaneous drainage with large lumen catheters, i.e. 12–14 Fr. Haematomas which do not spontaneously resolve with time should be evacuated with surgical methods$^{(8,9)}$. In contrast, the majority of cases of postoperative urine leak require primary surgical repair; minimally invasive radiological procedures such as percutaneous temporary nephrostomy or double J catheter can represent additional bridging methods or methods supporting the healing process$^{(2,7,9)}$. \textbf{Material and methods} The available documentation (descriptive and imaging records) of ultrasound scans of 488 consecutive patients who had undergone deceased-donor kidney transplantation between January 2001 and May 2017 were included in a retrospective analysis. Ultrasound scans were routinely conducted in the immediate postoperative period (up to 3 days from the procedure), before the patient’s discharge (usually between day 10 and 14 after the operation) and subsequently at approximately 6–12 month intervals as well as in every case of developing clinical signs of graft function deterioration. Doppler linear 6–12 MHz and convex 3.5–5 MHz transducers were used for the scans depending on the conditions of the examination. This study is an attempt to perform a statistical evaluation of the prevalence of perirenal fluid collections and their evolution in time depending on selected demographic features of the patients, time of detection, initial size and precise position of the fluid pocket relative to the kidney. the kidney and the location of the transplanted organ in the right or left iliac fossa. The collected data were used for statistical analysis to determine the strength of potential relationships. The STATISTICA, version 12 (StatSoft, Inc., 2014) software was used to conduct the statistical analysis. Patients with data deviating to an extreme extent from the statistical distribution of data from other patients, regardless of the cause, were excluded from the assessment of fluid collection evolution. Statistical significance level of $p < 0.05$ was assumed. Categorical data were analyzed using the Pearson chi-square test. The normality of quantitative data distribution was verified using the Shapiro-Wilk test. The homogeneity of variance was evaluated using the Brown–Forsythe test. The comparison of two groups of quantitative data was made using the Student’s t-test (for normal distribution and homogeneous variances). For cases which did not meet these conditions the Mann–Whitney U test was applied. The correlation of quantitative data with a different distribution than normal was evaluated using the Spearman’s rank correlation coefficient. The relationships between more than two groups of quantitative data were evaluated using the non-parametric Kruskal–Wallis ANOVA test (after non-normality of the data distribution was determined). In certain cases post hoc tests (for multiple comparisons) were applied. Results The study included 488 individuals with a mean age of 45 years (±13.69). Half of the subjects were below 47 years of age, 25% were up to 34 years old, and 75% were up to 56 years old. The youngest person was 14 and the oldest one was 73 years old (Tab. 1). Among 488 patients who had undergone allogeneic kidney transplantation perirenal fluid collections were diagnosed in 146 individuals. In 43 patients (29.45%) the presence of more than one fluid collection was found. In total, 224 perirenal fluid collections were identified. In the sample of 146 patients fluid collections were most commonly diagnosed in the age range of 40–50 years (nearly 1/3 of the patients – 30.82%). However, there was no evidence to conclude that there was a statistically significant relationship between age and the fluid collection diagnosis. Despite the fact that fluid collections seemed to be more common in the male population (n = 97; 66.44%), no statistically significant relationship between gender and the presence of a fluid collection was found either. The ultrasound follow-up period lasted between 1 (single assessment) and 5536 days. Despite that, in more than half of the cases the number of days did not exceed 62 (Mdn = 62.5). Patients with a diagnosed fluid collection were most commonly followed up for 20 to 30 days from the date of the first scan (13.70%). Nearly half of the identified fluid collections appeared up to 10 days from the first scan (n = 95; 42.41%). One fourth of all fluid collections were detected between day 10 and 20 (n = 54; 24.11%) (Fig. 5). Out of 146 transplanted kidneys with the associated fluid collections 67 (45.89%) were transplanted to the right and 79 (54.11%) were transplanted to the left iliac fossa. The choice of the target location for the transplant did not correlate significantly with the gender or age of the patient. In terms of the position of the fluid collection relative to the transplanted organ it was concluded that the majority of fluid collections were found near the lower pole of the kidney (n = 72; 52.14%), and the lowest number of fluid collections were found near the renal hilum (n = 10; 4.46%) (Fig. 6). The present authors have also compared the sizes of the fluid collections in relation to their position relative to the kidney. The largest dimension of the fluid pocket upon its detection in ultrasound was used for calculations. Fluid collections encapsulating the kidney seemed to grow larger than fluid pockets located elsewhere (mean = 57 mm, median [Mdn] = 48 mm). It was demonstrated in the tested sample that there is a relationship between the original size of the collection and its position relative to the kidney $ (p = 0.03) $. A multiple comparisons test demonstrated a statistically significant difference between the size of collections located on the surface and the size of those located near the upper pole of the transplanted kidney $ (p = 0.02) $. Larger collections (Mdn = 49 mm) were located subcutaneously (Fig. 7). An attempt has also been made to determine whether there is a relationship between the duration of the presence of a fluid pocket (the period from the date of detection to the date when the fluid collection was reported for the last time) and its position relative to the transplanted kidney (Fig. 8) and its initial size (Tab. 2, Tab. 3). However, based on statistical analysis no correlations of this type have been demonstrated. ### Discussion In a long-term evaluation of 488 patients who underwent allogeneic kidney transplantation fluid collections have been found in nearly 30% of subjects. These results correlate well with reports in medical literature according to which perirenal fluid collections should be expected in 20–50% of cases$^2$. Based on the research material collected in the study it has been demonstrated that fluid collections formed most commonly within 20 days of the date of the first scan (66.52%) with the largest number of fluid pockets developing before day 10 of follow-up (42.41%). This means that the majority of cases involved a fluid collection as an acute complication of the organ transplantation procedure or a sign of acute graft rejection. Ac- Sonographic assessment of the prevalence and evolution of fluid collections as a complication of kidney transplantation According to the literature the immediate postoperative period is usually complicated by small encapsulating haematomas and plasma effusion$^{(4,7,9)}$. Statistical data from numerous scientific reports regarding lymphocele occurrence indicate that this type of fluid collection usually occurs within the first year after the transplantation, with a peak between week 4 and 8. Lymphocele accounts for approximately 10–22% of all diagnosed fluid collections, 0.04–14.6% of which require intervention$^{(2,4–6)}$. Our observations revealed that between day 20 and 40 from the first scan (the peak of lymphocele occurrence) 19.20% of fluid collections were diagnosed. However, one should bear in mind that the present authors did not have access to the results of biochemical analysis of the diagnosed fluid collections’ contents; therefore, it is not possible to determine their clinical nature. It seems, therefore, that an important step in clinical investigation would be to conduct a prospective study to ascertain the nature of fluid collections, which would allow for the determination of the causes of their development as well as the methods of their prevention and elimination of the predisposing factors. Moreover, according to the medical literature some of the types of fluid collections can be the sign of pathologies which threaten the graft function and the patient’s health$^{(2,5)}$. It is also worth adding that the length of follow-up for half of the patients did not exceed 62 days (Mdn = 62.5) – due to their remote place of residence some patients underwent ultrasound evaluation in our center only up to the time of discharge from hospital. This situation could have affected the percentage distribution obtained in this study. This indicates the huge significance of following transplant patients up in the transplant center; otherwise, the evaluation of the dynamics and nature of the fluid collection and the decision whether to drain the fluid pocket can be inadequate or even impossible. The authors of the present study have not managed to demonstrate the existence of any statistically significant correlations between the prevalence of perirenal fluid collections and demographic characteristics of the recipients or the location of the graft in the right or left iliac fossa and between the persistence of the fluid pockets and their initial dimensions and position relative to the kidney. However, a statistically significant relationship between the largest initial dimension of the fluid pocket and its position relative to the kidney has been demonstrated. It is not surprising that the loose texture of the subcutaneous tissue creates the most favorable conditions for the development of large fluid collections. Similar fluid collections spreading around the renal capsule and considered to be encapsulating the organ tended to grow larger; however, it should be emphasized that unidimensional assessment of the fluid collection’s size may not fully correspond with the actual volume of the fluid collection. This is because fluid collections encapsulating the kidney, unlike other, more rounded types of fluid pockets, tend to assume a shape similar to a thin crescent. Interestingly enough, however, fluid collections are least common in the parahilar area and their mean size is relatively small. Therefore, a fluid collection rarely causes compression of the vessels or ureter of the graft, producing severe clinical signs. As mentioned above, only a small proportion of fluid pockets require draining and possibly sclerotisation. Conclusions Perirenal fluid collections are a common finding in patients who have undergone allogeneic kidney transplantation. The majority of fluid collections do not give any distinct clinical signs and thus do not require treatment. Despite growing large subcutaneous fluid pockets and those encapsulating the kidney tend to be spontaneously absorbed. In contrast, fluid collections which can compress key structures of the graft are a rare finding and they are often small in size. The correct evaluation of a fluid collection’s dynamics of development and nature requires periodic follow-up of the recipient, preferably in a single clinical center. Sonography is an inexpensive, non-invasive, non-damaging, repeatable method of assessment of fluid collections, particularly in such a superficial and easily accessible location as the iliac fossa. This method, however, is insufficient to evaluate the clinical nature of this abnormality. The decision whether a fluid collection requires treatment must also take into account the observation of laboratory signs of inflammation and the biochemical analysis of the collection’s contents. Conflict of interest The authors do not report any financial or personal affiliations to persons or organisations that could negatively affect the content of or claim to have rights to this publication. References 1. Centrum Organizacyjno-Koordynacyjne ds. Transplantacji: http://www.poltransplant.pl/ 2. Pollak R, Veremis SA, Maddux MS, Mozes MF: The natural history of and therapy for perirenal fluid collections following renal transplantation. J Urol 1988; 140: 716–720. 3. Friedewald SM, Molmenti EP, Friedewald JJ, DeJong MR, Hamper UM: Vascular and nonvascular complications of renal transplants: sonographic evaluation and correlation with other imaging modalities, surgery, and pathology. J Clin Ultrasound 2005; 33: 127–139. 4. Brown ED, Chen MY, Wolfman NT, Ott DJ, Watson NE Jr: Complications of renal transplantation: Evaluation with US and radionuclide imaging. Radiographics 2000; 20: 607–622. 5. Dubaux VT, Oliveira RM, Moura VJ, Pereira JM, Henriques FP: Assessment of lymphocele incidence following 450 renal transplantations. Int Braz J Urol 2004; 30: 18–21. 6. Ranghino A, Segoloni GP, Lasaponara F, Biancone L: Lymphatic disorders after renal transplantation: New insights for an old complication. Clin Kidney J 2015; 8: 615–622. 7. Moreno CC, Mittal PK, Ghonge NP, Bhargava P, Heller MT: Imaging complications of renal transplantation. Radiol Clin North Am 2016; 54: 235–249. 8. Richard HM: Perirenal transplant fluid collections. Semin Intervent Radiol 2004; 21: 235–237. 9. Iezzi R, la Torre MF, Santoro M, Dattesi R, Nestola M, Posa A et al.: Interventional radiological treatment of renal transplant complications: A pictorial review. Korean J Radiol 2015; 16: 593–603. 10. Presser N, Kerr H, Gao T, Begala S, Paschal S, Shoskes DA et al.: Fibrin glue injections: A minimally invasive and cost-effective treatment for post-renal transplant lymphoceles and lymph fistulas. Am J Transplant 2016; 16: 694–699.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3021, 1 ], [ 3021, 6958, 2 ], [ 6958, 10247, 3 ], [ 10247, 14241, 4 ], [ 14241, 15901, 5 ], [ 15901, 20960, 6 ], [ 20960, 22690, 7 ] ] }
327e55eac05413f6b1b962534c932c6a5684f4af	{ "olmocr-version": "0.1.59", "pdf-total-pages": 3, "total-fallback-pages": 0, "total-input-tokens": 10502, "total-output-tokens": 5232, "fieldofstudy": [ "Medicine" ] }	SYMPTOMATIC INTRADISCAL VACUUM PHENOMENON FENÔMENO DE VÁCUO INTRADISCAL SINTOMÁTICO FENÔMENO DE VACÍO INTRADISCAL SINTOMÁTICO PEDRO LUIS BAZÁN, RICHARD ALEJANDRO ÁVIERO GONZÁLEZ, NICOLÁS MAXIMILIANO CECOLI, ÁLVARO ENRIQUE BORRI, MARTÍN MEDINA 1. HIGA San Martín La Plata, La Plata, Buenos Aires, Argentina. 2. Hospital Italiano La Plata, La Plata, Buenos Aires, Argentina. Study conducted at: HIGA San Martín La Plata and Hospital Italiano La Plata, La Plata, Buenos Aires, Argentina. Descriptores: Degeneración del disco intervertebral; Disco intervertebral; Dolor lumbar. ABSTRACT Objective: Intradiscal vacuum phenomenon (IVP) is a common finding in the study of degenerative disc disease. Discogenic low back pain can be manifested in different ways, including irradiation to the lower limbs. This study aims to acknowledge the complementary studies used to diagnose IVP, determine their sensitivity, and assess the correlation between clinical and imaging findings. Methods: This is a descriptive, observational and prospective study involving clinical and imaging evaluation of 100 patients with IVP, using dynamic and plain radiographs, computed tomography and magnetic resonance imaging. The factors of analysis include sex, age, reason for consultation, visual analogue scale, irradiation and topography of the pain, the existence of sciatica and claudication, smoking status, and body mass index. Results: The overall average age of the patients was 64.6 years, who particularly evidence degenerative pathology. IVP was observed in 99 CT, 85 dynamic radiographs, 80 plain radiographs and 65 nuclear magnetic resonance images (MRI). Conclusion: The most useful studies for diagnosing the vacuum disc phenomenon are plain and dynamic radiographs, tomography, and magnetic resonance. The CT is the most sensitive imaging study for IVP detection, followed by dynamic radiographs obtained during extension. A correlation was observed between older age, overweight, and IVP. Level of evidence IV; Case-series. Keywords: Intervertebral disc degeneration; Intervertebral disc; Low back pain. RESUMO Objetivo: O fenômeno do vácuo intervertebral (FVI) é um achado comum no estudo da doença degenerativa do disco. A dor lombar discogênica pode se manifestar de diferentes formas, incluindo a irradiação para os membros inferiores. O presente estudo pretende reconhecer os estudos complementares utilizados para diagnosticar o FVI, determinar sua sensibilidade e avaliar a correlação entre os achados clínicos e de imagem. Métodos: Estudo descritivo, observacional e prospectivo envolvendo a avaliação clínica e por imagem de 100 pacientes com FVI, utilizando radiografias simples e dinâmicas, tomografia computadorizada e ressonância magnética. Os fatores da análise incluem sexo, idade, motivo da consulta, escala visual analógica, irradiação e topografia da dor, existência de ciatalgia e claudicação, tabagismo e índice de massa corporal. Resultados: A idade média geral dos pacientes foi de 64,6 anos, evidenciando particularmente a patologia degenerativa. O FVI foi observado em 99 tomografias computadorizadas, 85 radiografias dinâmicas, 80 radiografias simples e 65 ressonâncias magnéticas nucleares (RM). Conclusão: Os estudos mais úteis para detectar FVI são as radiografias simples e dinâmicas, a tomografia e a ressonância magnética. A tomografia computadorizada é o exame de imagem mais sensível para a detecção do FVI, seguido pelas radiografias dinâmicas obtidas durante a extensão. Observou-se uma correlação entre a idade avançada, obesidade e o fenômeno do vácuo intervertebral. Nível de evidência IV; Série de casos. Descritores: Degeneração do disco intervertebral; Disco intervertebral; Dor lombar. RESUMEN Objetivo: El fenómeno del vacío intervertebral (FVI) es un hallazgo común en el estudio de la enfermedad degenerativa del disco. El dolor lumbar discogénico puede manifestarse de diferentes maneras, incluyendo la irradiación para los miembros inferiores. El presente estudio pretende reconocer los estudios complementarios utilizados para diagnosticar el FVI, determinar su sensibilidad y evaluar la correlación entre los hallazgos clínicos y de imagen. Métodos: Estudio descritivo, observacional y prospectivo involucrando la evaluación clínica y por imagen de 100 pacientes con FVI, utilizando radiografías simples y dinámicas, tomografía computarizada y resonancia magnética. Los factores de análisis incluyen sexo, edad, motivo de consulta, escala visual analógica, irradiación y topografía del dolor, existencia de cialgie y claudicación, tabaquismo e índice de masa corporal. Resultados: La edad promedio general de los pacientes fue de 64,6 años, evidenciando particularmente la patología degenerativa. El FVI fue observado en 99 tomografías computarizadas, 85 radiografías dinámicas, 80 radiografías simples y 65 resonancias magnéticas nucleares (RM). Conclusión: Los estudios más útiles para diagnosticar FVI son las radiografías simples y dinámicas, la tomografía y la resonancia magnética. La tomografía computarizada es el estudio de imagen más sensible para la detección de FVI, seguido por las radiografías dinámicas obtenidas durante la extensión. Se observó una correlación entre la edad avanzada, sobrepeso y el fenómeno del vacío intervertebral. Nivel de evidencia IV; Serie de casos. Descritores: Degeneración del disco intervertebral; Disco intervertebral; Dolor de la región lumbar. Study conducted at: HIGA San Martín La Plata and Hospital Italiano La Plata, La Plata, Buenos Aires, Argentina. Correspondence: Pedro Luis Bazán. Address 51 Nro 1725 (1900) La Plata, Buenos Aires - Argentina. Email [email protected] http://dx.doi.org/10.1590/S1808-185120191804222787 Coluna/Columnar 2019;18(4):280-2 INTRODUCTION Intervertebral vacuum phenomenon is a common finding in the study of degenerative disc disease.1 Considered the last stage of disc degeneration,2 it is often the cause of low back pain.3 Low back pain associated with disc degeneration can present with a wide variety of symptoms ranging from benign to unbearable low back pain, and may include radicular pain in the lower limbs.4 A classic study by Gershon-Cohen5 found the vacuum phenomenon in radiographs of 21% of 130 asymptomatic elderly patients (Figure 1). Larde et al.6 report that at least one disc-level degenerative disease is observed in 12% of plain radiographs and 40% of computed tomography (Figure 2) scans of the lumbar spine in patients aged over 40 years. In a study of patients with degenerative spinal disease, intervertebral vacuum phenomenon (IVP) remains grossly underreported.7 The aims of the present study are to acknowledge the complementary studies used to diagnose IVP, determine their sensitivity, and assess the correlation between clinical and imaging findings. METHODS A descriptive, observational and prospective study was designed for all patients who attended consultations at the two hospitals where this study was conducted due to degenerative lumbar pathology. Among 100 patients studied, vacuum disc phenomenon was observed in at least one study. The exclusion criteria comprised sacralization of the fifth lumbar vertebra, traumatic and infectious pathology, and previous lumbar surgery. The data were collected considering sex, age, reason for consultation, visual analogue scale, irradiation and topography of the pain, the existence of sciatica and claudication, smoking status, and body mass index. The imaging studies requested for the patients with IVP were AP view radiographs and maximum extension-flexion radiographs of the lumbosacral spine, MRI and CT. A digital imaging record was kept for subsequent analyses. The analysis of 500 lumbar disc segments found multi- and mono-segmental degenerative disc disease in 100 patients. The analysis also helped to determine the presence of Modic type changes in the studied segments.8 All patient data were gathered in a table specially designed for this purpose, and analyzed using statistical data collection software (Microsoft Excel®). RESULTS Of the total patients, 64 were women and 36 were men. The average age was 64.6 years (ranging from 33 to 92 years). In 99 out of the 100 patients, IVP was observed in the CT (221 disc spaces). The IVP was mono-segmental in 42 patients and multi-segmental in 57 patients. Consequently, CT is the most sensitive study for diagnosing vacuum disc phenomenon. Among the other studies, IVP was observed in plain radiographs (131 disc spaces), 85 dynamic radiographs (158 disc spaces in extension) and 65 MRI scans (Figure 3) of 80 patients. Considering the reasons for consultation, 49 patients presented lumbosciatic pain (36 with unilateral pain), 43 presented low back pain without irradiation to the lower limbs, and 5 presented lumbo-crural pain. Claudication pain was present in 40 patients, and the number of patients who were current or former smokers was also 40. The average body mass index was 29.15. Scoliosis was diagnosed in 35 patients. Of the 64 patients with pain of 6 points or higher on the visual analogue scale (VAS), 39 presented multiple IVP (60.91%). In the present study, it was determined that T2 in MRI provides better information compared to the T1 relaxation parameter, as it shows the IVP with greater precision (Hypointensity marked). DISCUSSION Fick8 first observed the presence of gas within the intervertebral disc space while he was studying joints under traction. It was first named “vacuum phenomenon” by Magnusson9 in 1937, without attributing any clinical significance. In 1942, Knutsson10 correlated vacuum phenomenon with disc degeneration for the first time. In 1946, Gershon-Cohen11 referred to the phenomenon as “the phantom nucleus pulposus” when observing radiolucent areas within the interbody space found in lumbar plain radiographs. The vacuum phenomenon is a gas collection that may originate in the intervertebral disc (Figure 3). It is relatively frequent in radiographs of patients with lumbar degenerative disease.12,13 This phenomenon is considered the last stage of disc degeneration, and is often the cause of low back pain.3 The vacuum is composed of approximately 90% nitrogen and small amounts of oxygen or carbon dioxide.14 Since the introduction of CT scans, this method has become Figure 1. X-rays in flexion and extension, in the areas where the vacuum phenomenon is evidenced in the fifth disc space by increasing the space, with the difference of the annulus fibrosis. Figure 2. Sagittal section of the Multi Slice Tomography showing vacuum phenomenon in the first 4 lumbar discs. Figure 3. Diagnosis of Vacuum Disc Phenomenon. popular due to its sensitivity.6 It is the most sensitive study for detecting IVP followed by dynamic radiographs obtained during extension.10 The least sensitive study is the radiograph in flexion, due to the reduced disc space height and the lesser fiber strain on the annulus fibrosus. MRI provides better information on disc pathology by showing a more precise delineation of the anatomy.1,16,17 The intervertebral disc undergoes age-related changes, resulting in disc degeneration over the course of lifetime.4,18 Degenerative disc disease is usually considered a sign of intervertebral instability, and requires treatment.19 Hence the importance of a precise diagnosis. Many authors mention the endplates as one of the components of the intervertebral disc, due to the important role they play in disc disease.2,4 The pathogenesis of IVP is debatable and is most likely multifactorial. The prevailing hypothesis for gas formation in a degenerative disc is based on the endplate-degeneration theory. The endplates provide nutrition for the disc through a porous surface, while preventing disc protrusion into the vertebral bodies. As the vertebral endplates degenerate, the hyaline cartilage becomes calcified, and inflammatory cytokines are produced. This combination blocks the nutritional pathways, which results in metabolic imbalance and decreased synthesis of structural matrix proteins. As a result, the structural integrity of the disc becomes unstable, and the continuous compression-and-distraction motion creates a cleft that is gradually filled with gas.3 Some publications present a relationship between IVD and weather changes, e.g., that of Morishita et al., who associate IVP with low back pain in the mornings and when standing up. Low back pain may also be influenced by changes in the weather.20,21 Kasai et al. report that patients with IVP in the lumbar intervertebral disc experienced a worsening of low back pain when the atmospheric pressure was decreased.13 Many publications associate the presence of IVP with compression radiculopathy, as the gas occupies the space created by the clefts in the nucleus pulposus within the intervertebral disc, causing disc protrusion.22,27 CONCLUSION The most useful studies for the diagnosis of vacuum disc phenomenon in patients with lumbar degenerative disc disease are plain and dynamic radiographs, computed tomography, and magnetic resonance. Computed tomography with sagittal reconstruction is the most sensitive imaging study for IVP detection, followed by dynamic radiographs during extension. A correlation was observed between advanced age, overweight, and IVP. All authors declare no potential conflict of interest related to this article. CONTRIBUTION OF THE AUTHORS: Each author made significant individual contributions to this manuscript. BPL (0000-0003-0060-6558): work planning, bibliographic support control, results control, discussion of conclusions and final edition. AGR (0000-0001-9489-5615): bibliographic review, data management, discussion of conclusions and final draft. BAE (0000-0002-5568-867X)* and MM (0000-0002-5281-5645): discussion of conclusions and primary edition. ORCID (Open Researcher and Contributor ID). REFERENCES 1. D’Anastasi M, Birkenmaier C, Schmidt GP, Wegener B, Reiser M, Baur-Melnik A. Correlation Between Vacuum Phenomenon on CT and Fluid on MRI in Degenerative Disks. AJR Am J Roentgenol. 2011;197(5):1182-9. 2. Fardon DF, Mikette PC. (2001) Nomenclature and Classification of Lumbal Disc Pathology: Recommendations of the Combined Task Forces of the North American Spine Society, American Society of Spine Radiology, and American Society of Neuroradiology. Spine (Phila Pa 1976). 2001;26(5):E93-113. 3. Li FC, Zhang N, Chen WS, Chen QX. Endplate degeneration may be the origination of the vacuum phenomenon in intervertebral discs. Med Hypotheses. 2010;75(2):169-71. 4. Madigan L, Vaccoar AR, Spector LR, Milam RA. Management of Symptomatic Lumbal Degenerative Disk Disease. J Am Acad Orthop Surg. 2005;13(172):102-11. 5. Gershanon-Cohen J. The phantom nucleus pulposus. Am J Roentgenol Radium Ther. 1946;55:43-8. 6. Larde D, Mathieu D, Frig J, Gaston A, Vasile N. Spinal vacuum phenomenon: CT diagnosis and significance. J Comput Assist Tomogr. 1982;6(4):671-6. 7. Yen CP, Beckman JM, Vivas AC, Bach K, Uribe JS. Effects of intradiscal vacuum phenomenon on surgical outcome of lateral interbody fusion for degenerative lumbar disease. J Neurosurg Spine. 2017;26(4):1419-25. 8. Miod M, Steinberg PM, Ross JS, Masaryk TJ, Carter JR. (1988). Degenerative disk disease: Assessment of changes in vertebral body marrow with MR imaging. 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Gas-containing lumbar disc herniation. Spine (Phila Pa 1976). 1993;18(16):2553-6.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5772, 1 ], [ 5772, 10688, 2 ], [ 10688, 18368, 3 ] ] }
ddb2b6e0145a344ec7466f1a3d02da4c61cb0db5	{ "olmocr-version": "0.1.59", "pdf-total-pages": 16, "total-fallback-pages": 0, "total-input-tokens": 67614, "total-output-tokens": 15363, "fieldofstudy": [ "Biology" ] }	Interaction of Cytochrome C Oxidase with Steroid Hormones Ilya P. Oleynikov, Natalia V. Azarkina , Tatiana V. Vygodina and Alexander A. Konstantinov A.N. Belozersky Institute of Physico-Chemical Biology, M.V. Lomonosov Moscow State University, Leninskie gory 1, Bld. 40, 119 992 Moscow, Russia; [email protected] (I.P.O.); [email protected] (T.V.V.); [email protected] (A.A.K.) Correspondence: [email protected] Received: 22 August 2020; Accepted: 23 September 2020; Published: 29 September 2020 Abstract: Estradiol, testosterone and other steroid hormones inhibit cytochrome c oxidase (CcO) purified from bovine heart. The inhibition is strongly dependent on concentration of dodecyl-maltoside (DM) in the assay. The plots of $K_i$ vs [DM] are linear for both estradiol and testosterone which may indicate an 1:1 stoichiometry competition between the hormones and the detergent. Binding of estradiol, but not of testosterone, brings about spectral shift of the oxidized CcO consistent with an effect on heme $a^3$. We presume that the hormones bind to CcO at the bile acid binding site described by Ferguson-Miller and collaborators. Estradiol is shown to inhibit intraprotein electron transfer between hemes $a$ and $a^3$. Notably, neither estradiol nor testosterone suppresses the peroxidase activity of CcO. Such a specific mode of action indicates that inhibition of CcO activity by the hormones is associated with impairing proton transfer via the K-proton channel. Keywords: cytochrome oxidase; steroid hormones; regulation 1. Introduction Cytochrome c oxidase (CcO) is a key enzyme of aerobic metabolism and of oxidative phosphorylation, in particular, providing living organisms with access to the usage of oxygen reduction energy (reviewed, [1–3]). It is conceivable that an enzyme of such high importance should be subject to thorough control at all levels of cell metabolism—biosynthesis, assembly and regulation of the assembled enzyme turnover in response to various intracellular stimuli, for example by signal molecules emerging in the cells. The latter type of regulation is particularly suitable for in vitro biochemical studies. Regulation of CcO activity by nucleotides (see numerous works of B. Kadenbach and his laboratory, for instance [4]) and gaseous ligands of the oxygen-reducing center (see the review by Cooper & Brown [5]) has been amply studied. Recently, direct modulation of the mitochondrial CcO activity by Ca$^{2+}$ and Na$^+$ ions binding to a special cation-binding center was described (see the series of works from our laboratory, for example [6–11]). A promising new venue for research of CcO regulation has been provided by recent works of Ferguson-Miller and collaborators. In a series of papers [12–16], the Michigan group described a conserved bile acid binding site (BABS) in the crystal structure of cytochrome c oxidase (CcO) from Rhodobacter sphaeroides or bovine heart mitochondria. The site is located near the inner side of the membrane close to the entrance of the so-called K-proton channel and binds a variety of amphiphilic ligands of diverse nature sharing structural similarity, such as bile acids, thyroid hormones, retinoic acid and many other compounds; see Buhrow et al. [15]. Binding of the ligands was found to bring about inhibition or sometimes stimulation of the enzyme activity. Structural considerations allowed to rank steroid hormones, such as testosterone or estradiol, high in the list of potential ligands of the... BABS [15]. Surprisingly, no effect of steroid hormones on the activity of CcO from R. sphaeroides was found, whereas many other ligands of the site, e.g., thyroid hormone T3, inhibited the enzyme. We surmised that CcO from animal mitochondria may be a more appropriate object for the studies of hormone action than the bacterial enzyme. In this work we show that sex hormones, testosterone and estradiol, as well as several other steroid hormones can markedly inhibit activity of CcO purified from bovine heart mitochondria. The inhibition is accompanied by deceleration of electron transfer between hemes a and a3. Interestingly, peroxidase activity of the enzyme is not affected by the steroid hormones, supporting the proposal by Hiser et al. [14] that the inhibition of the oxidase reaction by the ligands of BABS is caused by their action on proton delivery to the oxygen-reducing site via the K-proton channel. 2. Materials and Methods Chemicals Testosterone, estradiol-3-benzoate, sodium dithionite, cytochrome c (type III from equine heart), TMPD (N,N,N',N'-tetræmethyl-p-phenylenediamine), L-ascorbic acid, potassium ferricyanide, catalase and hydrogen peroxide were from Sigma-Aldrich (Saint Louis, MO, USA), hexaammineruthenium (III) was from Alfa Division (Ward Will, MA, USA). Hydrogen peroxide solution (about 30%) was kept at 4 °C and its concentration was checked spectrophotometrically using molar extinction coefficient $\varepsilon_{240} = 40 \text{ M}^{-1} \text{cm}^{-1}$ [17]. Dodecyl-maltoside of “Sol-Grade” type was purchased from Anatrace (Maumee, OH, USA). pH-buffers and EDTA (ethylenediaminetetraacetic acid) were from ICN Biomedicals Inc (Irvine, CA, USA). Testosterone was dissolved in ethanol and estradiol-3-benzoate in dimethyl sulfoxide for stock solutions. Cytochrome oxidase was isolated from bovine heart mitochondria using the modified method of Fowler et al. [18] as described previously by Vygodina et al. [8]. Concentration of the enzyme was determined from the difference absorption spectra (dithionite reduced minus air oxidized) using molar extinction coefficient $\varepsilon_{605-630} = 27 \text{ mM}^{-1} \text{cm}^{-1}$. Cytochrome oxidase activity assay. Oxygen uptake rates were measured with a covered Clark-type electrode by an Oxytherm instrument (Hansatech, UK) in a thermostatted cell at 25 °C with permanent stirring. The assays were performed in a basic medium containing 50 mM Hepes, 50 mM Tris, pH 7.5 and 0.1 mM EDTA. The medium was also supplemented with indicated concentrations of DM which are given throughout the text in mM (0.05% = 1.0 mM DM). 5 mM ascorbate, 0.1 mM potassium ferricyanide, sodium dithionite, cytochrome c were used as the oxidation substrate. Other details are indicated in the legends to figures. Peroxidase activity of CcO was assayed as described by Vygodina and Konstantinov [19] by following spectrophotometrically peroxidation of 0.2 mM o-dianisidine at 432 nm minus 580 nm in a dual-wavelength SLM Aminco DW-2000 spectrophotometer (USA). The reaction mixture contained 0.6 μM CcO in the aerobic basic medium supplemented with different concentrations of DM. No o-dianisidine oxidase activity was observed and the peroxidase reaction was initiated by addition of 4 mM H$_2$O$_2$. Absorption spectra of CcO were recorded with a Cary 300 Bio spectrophotometer (Varian, USA) in semi-micro cuvettes with blackened walls and 10 mm light pathway (Hellma, Germany), in the basic medium at pH 8.0 supplemented with indicated different additions. The kinetics of spectral changes was monitored in a dual-wavelength mode in a SLM Aminco DW-2000 spectrophotometer. The kinetics of CcO reduction by dithionite in the presence of ruthenium hexamine (RuAm) was studied in an Applied Photophysics SX-20 stopped-flow spectrophotometer (UK) operated in a diode array mode, using a 20 μL cell with 1 cm optical pathway. The spectra in the 280–720 nm range were collected with a minimal interval of 1 ms. The assay medium contained 100 mM Hepes, 100 mM Tris, 50 mM KCI, 100 μM EGTA, catalase (2 μL/5 mL of the solution, indicated activity 23,000 units/mg protein), 0.05% DM, pH 8.0. Aerobic buffer with 6 μM CcO and 0.4 mM or 1 mM estradiol was rapidly mixed with the equal volume of the same buffer containing 40 mM sodium dithionite and 10 mM RuAm. Procession of the stopped-flow data was performed with ProKineticist software provided with the Applied Photophysics SX-20 instrument, as well as by using Origin 7 and Origin 9 Microcal software. 3. Results 3.1. Inhibition of CcO Oxidase Activity by Steroid Hormones At variance with Buhrow et al. [15], we found that several steroid hormones bind to the isolated CcO bringing about considerable inhibition of the enzyme activity. 3.1.1. Inhibition of CcO Oxidase Activity by Estradiol Figure 1 shows the inhibitory effect of estradiol on oxygen consumption by isolated bovine CcO oxidizing ascorbate + TMPD in the presence of cytochrome c. The effect of estradiol depends significantly on the concentration of DM in the assay. Panel A gives representative oxygraph recordings. At 1 mM DM, 2 mM estradiol brings about near 4-fold inhibition of the activity (trace 1). Notably, the inhibition is not instantaneous but takes a couple of minutes to develop. In the presence of 20 mM DM (trace 2), the same addition of estradiol results in only a slight inhibition. Moreover, the inhibition induced by 1 mM estradiol at 1 mM of DM can be partially released by subsequent addition of high concentration of the detergent (trace 3). ![Figure 1](image-url) Figure 1. Inhibition of cytochrome c oxidase activity by estradiol. (A) Oxygen consumption was registered in the presence of 1 mM (traces 1, black and 3, blue), or 20 mM (trace 2, red) dodecyl-maltoside (DM). The reaction was triggered by addition of 24 nM CcO. Trace 3—the medium contained initially 1 mM estradiol. Other additions are indicated by the arrows. The traces have been corrected for ascorbate autoxidation. Dashed line overlapping trace 2 shows the kinetics in the absence of estradiol. (B) Titration of CcO activity by estradiol at different concentrations of DM. The experimental conditions, essentially as above. DM concentration: 1 (black circles)—1 mM; 2 (red... cells 2020, 9, 2211 2 (green triangles) — 10 mM; 5 (magenta squares) — 20 mM. The reaction was initiated by addition of CcO, and estradiol was added in 5 min after the onset of respiration. The ordinate axis represents the respiration rate after estradiol addition normalized to the initial rate. Theoretical curves are drawn through the experimental points starting from the end of the lag-phase (see the text). Inset shows dependence of the lag-phase length on DM concentration (filled circles). (C) Dependence of an apparent K_i for estradiol on DM concentration. The segment being cut off on the Y axis indicates the true K_i value in the absence of DM, the segment being cut off on the X axis in its negative area indicates the value of dissociation constant for DM in the absence of estradiol (Estr.), K_c (both segments are pointed out by arrows). Concentration dependence of the estradiol-induced inhibition was measured at different concentrations of DM in the assay (Figure 1B). The titrations fit to hyperbolic curves tending to 100% inhibition at infinite concentration of the inhibitor. It can be seen that the higher the concentration of DM, the more estradiol is required to inhibit the enzyme. Notably, a distinct lag phase is observed at high concentrations of DM (see traces 3–5). The normalized activity, v, in the presence of estradiol, I, can be described by hyperbolic equation shifted on the abscissa scale by a value of lag phase, L: \[ v = \frac{1}{1 + \frac{I}{K_{i(app)}}} \] where K_{i(app)} is the apparent value of inhibition constant in the presence of a given DM concentration. We propose that the lag phase may reflect binding of estradiol with the empty DM micelles. As one can see from the Inset in Figure 1B, the lag-phase value depends on DM concentration almost linearly in the range of 2–10 mM and then levels off. The plot of K_{i(app)} vs [DM] is shown in Figure 1C. The dependence is close to linear in the entire range of DM concentrations studied. This points out a 1:1 competition between estradiol and DM for binding with the enzyme, with the slope tangent equal to 0.25 which is the ratio of the respective affinities. Extrapolation of the plot to zero concentration of DM yields true K_i value of 0.37 mM. The estimated dissociation constant for the competitor, DM, in the absence of estradiol is K_c = 1.47 mM. 3.1.2. Testosterone Induced Inhibition of CcO Oxidase Inhibition of cytochrome oxidase activity by testosterone is shown in Figure 2. Under certain conditions (high concentrations of both testosterone and DM, e.g., Figure 2A, trace 1) the inhibition directly observed can be as high as 3-fold and occurs instantaneously. As with estradiol, the inhibitory effect of testosterone depends on DM concentration, but in a more complex way. Addition of excess testosterone (4 mM) at low concentration of DM (1 mM) inhibits the activity but weakly, whereas strong inhibition is induced by this concentration of the hormone in the presence of 20 mM DM (traces 2 and 1, respectively). Accordingly, when DM concentration is raised in the course of respiration (trace 3), the inhibition by the initially present excess testosterone (3 mM) is not released as it was observed with estradiol but rather is slightly augmented. Figure 2. Inhibition of cytochrome c oxidase activity by testosterone. (A) Oxygraph traces. Basic conditions as in Figure 1A. The initial DM concentrations are: trace 1 (black)—20 mM, traces 2 (red) and 3 (blue)—1 mM. Trace 3—the medium was also supplemented with 3 mM testosterone. Other additions are indicated by the arrows. The dashed straight line is drawn to visualize the effect of testosterone at 1 mM DM. (B) Titrations of CcO activity by testosterone at different concentrations of DM. The DM concentrations were: 1 (black squares)—1 mM; 2 (red circles)—5 mM; 3 (blue triangles)—10 mM; 4 (green triangles)—20 mM; 5 (magenta diamonds)—40 mM. Other conditions are mostly as in Figure 1B. Theoretical curves described by hyperbolic function (see the text) are drawn through the experimental points in the range of testosterone concentrations above the lag-phase value. For the lower concentrations of the inhibitor, the experimental points are connected by empirical lines simply to guide the eye. Dependences of the lag-phase length (filled circles, the left-hand Y axis) and of maximal inhibition level (filled triangles, the right-hand Y axis) on DM concentration are shown in the Inset. (C) Dependence of an apparent Ki for testosterone on DM concentration. The true value of Kc for testosterone (Tst.) in the absence of DM and Kc (dissociation constant) for DM in the absence of testosterone can be graphically determined as in the case of estradiol (see Figure 1C). The complex pattern of CcO inhibition by testosterone can be better understood from the titrations made at different concentrations of DM (Figure 2B). At low [DM], the activity does not tend to zero with increased concentrations of testosterone as in the case of estradiol, but rather the titration curves level off at some saturation levels attained at relatively low concentrations of the hormone (cf. the dashed lines). The maximal level of inhibition by excess testosterone grows with increased concentration of DM in the assay from ca. 25% at 1 mM of the detergent to 70–85% at 20–40 mM of DM. At high concentrations of DM, the testosterone titration curves reveal a clear lag phase (see the initial parts of the titration curves 2–5) and as with estradiol, we assign this lag phase to hormone binding with the empty DM micelles. In order to determine $K_{i\text{(app)}}$, the titration curves in Figure 2B were approximated by Equation (2) that connects normalized activity, $v$, with testosterone concentration, $I$. It is similar to Equation (1) but has an additional parameter $R$ which denotes the fraction of the activity resistant to inhibition: $$v = \frac{1-R}{1+\frac{[I]}{K_{i\text{(app)}}}} + R$$ Equation (2) fits well the experimental data after the end of the lag-phase (see other details in the legend). All the parameters ($K_{i\text{(app)}}, L$ and $R$) were found to depend on DM concentration. In particular, the dependence of the lag phase on [DM] is linear throughout the entire concentration range explored, i.e., 1–40 mM (see the Inset in Figure 2B, circles, left Y axis). Dependence of the extent of maximal inhibition (which is 1-R) on [DM] is also shown in the Inset (triangles, right Y axis). As seen, the maximal inhibition grows from ~25% to ~90%. The dependence of $K_{i\text{(app)}}$ on [DM] is shown in Figure 2C. It points to a competition between testosterone and DM with the 1:1 stoichiometry. Although the scatter of the experimental points is quite large here (due to low solubility of testosterone), we assume a linear dependence, as in all other cases; see below Table 1 in Section 4. The slope tangent gives the ratio $K_{i}/K_{c} = 0.05$. Extrapolation to zero DM concentration yields the true $K_{i}$ value for testosterone as low as 80 μM, whereas the $K_{c}$ value is now determined as 1.3 mM (compare to 1.47 mM as estimated in Figure 1C). Table 1. Steroid regulatory molecules affecting CcO. \| Steroid Regulatory Molecule \| Inhibition of CcO Oxidase Activity \| Inhibition of CcO Peroxidase Activity \| Spectral Response Induced in Oxidized CcO \| \|----------------------------\|------------------------------------\|---------------------------------------\|------------------------------------------\| \| DM Influence \| $K_{i}$, mM (DM→0) \| \| \| \| Estradiol \| competes 1:1 \| 0.37 \| no \| red shift of $a_{333}^{3+}$; $\varepsilon = 10$ mM$^{-1}$-cm$^{-1}$ \| \| Testosterone \| competes 1:1; increases maximal level of inhibition \| 0.08 \| no \| no \| \| Dehydroepiandrosterone (DHEA) \| competes 1:1 \| 0.11 \| no \| no data \| \| Progesterone \| competes 1:1 \| 0.12 \| no \| no data \| \| Cholecalciferol (vitamine D3) \| competes 1:1 \| 0.009 \| yes ($K_{c}$~0.2 mM) \| red shift of $a_{333}^{3+}$; $\varepsilon = 25$ mM$^{-1}$-cm$^{-1}$ \| \| Ergocalciferol \| competes 1:1 \| 0.02 \| no data \| no data \| 3.2. Effect of Estradiol on CcO Spectral Properties 3.2.1. Estradiol Shifts Absorption Band of Heme $a^3$+ We found that binding of estradiol not only inhibits the enzyme but also perturbs the absorption spectrum of the oxidized CcO. No effect of estradiol on the absorption spectrum of the reduced CcO was observed. Some typical data are shown in Figure 3. Small but distinct changes are observed at estradiol concentrations as low as 0.5 mM (Figure 3A, spectra 1–4) but much better spectra are obtained at 1 mM of the hormone (spectra 5–7 in Figure 3A). Note that at 13 mM of DM as used in this experiment, the indicated concentrations of estradiol correspond to ca. 0.14 and 0.29 of the $K_{i(app)}$ value obtained in the activity inhibition studies (see Figure 1C). The symmetric S-shaped difference spectrum induced by estradiol (Figure 3A, 5–7, Figure 3B, 1) with a maximum at 437 nm and a trough at 415 nm is typical of a red shift of ferric heme $a^3$ Soret band induced by strong ligands such as cyanide. The magnitude of 10 mM$^{-1}$·cm$^{-1}$ obtained at 1 mM of the hormone corresponds to ca. 1/5 of the effect induced by cyanide, see van Buuren et al. [20]. In this case the spectral shift develops rapidly enough, reaching completion in 3–5 min after the hormone addition (Figure 3A,C, trace 2) in reasonable agreement with the time course of the inhibitory action of estradiol that takes a few minutes to develop (Figure 1A). Figure 3. Estradiol-induced spectral changes of CcO. (A) Difference spectra induced by addition of 0.5 mM (1–4) or 1 mM (5–7) estradiol benzoate to the air oxidized CcO (1.22 μM). Spectra were recorded at the indicated time intervals after the hormone addition. The basic medium (pH 8.0) was supplemented with 13 mM DM. (B) Effect of cyanide on the estradiol-induced spectral shift of heme $a^3^+$. Spectrum 1 (black)—control (difference spectrum recorded 3 min after addition of 1 mM estradiol to the air oxidized CcO). Spectrum 2 (red) was obtained as 1 but with the cyanide-complexed CcO (produced by 1 hr incubation of CcO in the assay medium supplemented with 5 mM KCN and 25 μM potassium ferricyanide which prevented oxidized cyanide adduct from slow reduction). Spectrum 3 (blue)—as 2 but recorded 3 hrs after estradiol addition. Other conditions are as in panel A. (C) Time dependence of the estradiol-induced spectral changes. Traces 1 (black circles) and 2 (red triangles) represent time evolution of absorption difference at (437–415 nm) caused in the ligand-free oxidized CcO by incubation with 0.5 mM and 1 mM estradiol, respectively (see panel A). Trace 3 (blue triangles)—development of absorption difference at (428–450 nm) induced in the cyanide-complexed CcO by incubation with 1 mM estradiol (see panel B). 3.2.2. Cyanide Interferes with Estradiol-Induced Spectral Effect in CcO The spectral perturbation of CcO induced by estradiol is strongly modified by cyanide (Figure 3B). The S-shaped difference spectrum typical of heme $a^3^+$ red shift is no longer observed and is replaced by a trough at 428 nm corresponding to the maximum of $a^3^+\cdot$CN complex, which develops very slowly (for at least 3 h, Figure 3B, spectra 2, 3, Figure 3C, trace 3). These data allow to suggest that the spectral perturbation of the oxidized ligand-free CcO induced by estradiol is associated with heme $a_1$. Perturbation of the heme $a_1$ spectrum would be consistent with the proposal by Hiser et al. [14] that the steroid hormones and other ligands of the BABS affect the K-proton channel interacting with the oxygen-reducing binuclear site of CcO. 3.3. Mechanism of CcO Inhibition by Steroid Hormones To the best of our knowledge, mechanism of the inhibitory action of the BABS ligands on CcO activity has not been studied experimentally so far. 3.3.1. Inhibition of Electron Transfer between Hemes $a$ and $a_1$ by Estradiol We investigated effect of estradiol on the kinetics of electron transfer from heme $a$ to heme $a_1$. To this end, the kinetics of the hemes’ reduction by dithionite in the presence of RuAm was studied. In the experiment shown in Figure 4, 3 μM CcO was mixed rapidly with 20 mM dithionite and 5 mM RuAm and the reaction time course was followed by taking the spectra each ms in the 280–720 nm range in a rapid mixing diode array spectrophotometer. Under these conditions, heme $a$ is almost fully reduced within the mixing time as evidenced by the spectra in the α-band region (panel A, visible), which is followed by time-resolved electron transfer to heme $a_1$ observed in the Soret region (panel A, Soret) [6,21]. Figure 4. Estradiol inhibits reduction of heme a. (A) Series of absolute spectra obtained upon rapid mixing of CcO with strong reductant using diode array spectrophotometer SX-20. Final concentrations: 3 μM CcO, 20 mM sodium dithionite, 5 mM RuAm. The left and right panels represent the Soret and the visible regions of the spectra, respectively. (B) Kinetics of absorption difference at (445 nm–407 nm) upon rapid reduction of the air-oxidized CcO is shown (see panel A for experimental conditions). Trace 1 (black)—control, trace 2 (red)—CcO was treated with 0.4 mM estradiol before mixing with the reductant, 3 (blue)—CcO was treated with 1 mM estradiol before the mixing. The experimental data are superimposed on the theoretical curves (dashed traces) described by the function: $ f(x) = A_1 \exp(-x/\tau_1) + A_2 \exp(-x/\tau_2) $, where $ A_1, A_2 $ are normalized amplitudes and $ \tau_1, \tau_2 $ are characteristic times of the rapid and slow phases, respectively (see the text). As shown in Figure 4B, the kinetics of heme $ a_1 $ reduction monitored at 445 nm vs the 407 nm reference is noticeably decelerated in the presence of 200 μM and, especially, 500 μM estradiol (compare control trace 1 with traces 2 and 3, respectively). The effect was reproduced with several samples. Kinetic analysis of the traces shown in Figure 4B revealed two phases which upon the conditions used (see above) reflect reduction of heme $ a_1 $. In the control (trace 1), the rate constants are 105.3 s$^{-1}$ and 6.15 s$^{-1}$, which is in agreement with our earlier data at these concentrations of dithionite and RuAm [6]. In the presence of 0.2 mM estradiol (trace 2) the rate constants change to 67.75 s$^{-1}$ and 5.3 s$^{-1}$. An increase in the estradiol concentration to 0.5 mM (trace 3) yields a further decrease of the values to 39.6 s$^{-1}$ and 2.5 s$^{-1}$, respectively. The contributions of the rapid and slow phases make up about 70% vs 30% in all three cases. These estimates are consistent with the data obtained in the experiments with an oxygen electrode. For example, according to the rapid mixing data, 0.5 mM estradiol decreases by ca. 60% the rate constants of the both phases (without a notable effect on their contributions), and the same concentration of estradiol inhibits oxygen consumption approximately by half (Figure 1B, curve 1; Figure 1C). Unfortunately, higher concentration of estradiol could not be used in the optical experiments because of increased sample turbidity. 3.3.2. Effect of the Hormones on Peroxidase Activity of CcO Taking into consideration close proximity of the BABS to the entry point of the K-proton channel, it was speculated that binding of the ligands to the amphipathic site could result in impairment of proton transfer to the binuclear site via the K-pathway, see Hiser et al. [14]. Reduction of dioxygen to two water molecules by cytochrome oxidase occurs in two sequential phases. In the first phase denoted as eu-oxidase (see Konstantinov [22]), O₂ bound to the reduced binuclear site withdraws 4 electrons from CcO, the O–O bond is cleaved, and the first H₂O molecule is formed, which requires uptake of 2 “chemical” protons delivered via the K-channel. Reduction of dioxygen to two water molecules by cytochrome oxidase occurs in two sequential phases. In the first phase denoted as eu-oxidase (see Konstantinov [22]), O₂ bound to the reduced binuclear site withdraws 4 electrons from CcO, the O–O bond is cleaved, and the first H₂O molecule is formed, which requires uptake of 2 “chemical” protons delivered via the K-channel. The second oxygen atom of the dioxygen remains as the oxene ligand bound to iron of ferryl heme at a Fe⁴⁺=O²⁻/Tyr• compound. This intermediate denoted as FI-607 (or Pₐ in the outdated terminology) is two oxidizing equivalents deficient relative to the resting oxidized state of CcO and is homologous to Compound I of peroxidases. The second oxygen atom is subsequently reduced to H₂O by two sequential electron transfers from exogenous substrate, a process fully analogous to reduction of Compound I to the resting state in peroxidases. Formation of this second water molecule by CcO was denoted therefore as the peroxidase phase of the CcO catalytic cycle. The protons consumed in H₂O formation in the peroxidase phase are delivered exclusively via the D-proton channel and the K-channel is not involved in this part of the CcO catalytic cycle. The binuclear site of CcO can use H₂O₂ instead of O₂ as the electron acceptor [19,22]. In this case, the eu-oxidase phase of the catalytic cycle can be bypassed and the enzyme cycles exclusively through the peroxidase phase. Accordingly, the peroxidase activity of CcO is blocked by mutations in the D-channel whereas mutations in the K-channel such as K362M replacement in CcO from R. sphaeroides do not affect the peroxidase activity of CcO while fully inhibiting the oxidase activity of the enzyme, see Vygodina et al. [23]. Therefore, we were excited to see that testosterone and estradiol, while suppressing the oxidase reaction, do not inhibit peroxidase activity of CcO (Figure 5). This observation suggests that the inhibitory effect of the steroid hormones on the activity of CcO may be indeed associated with impairment of proton transfer via the K-channel. Figure 5. Effect of steroid hormones on the peroxidase activity of CcO. (A) Effect of estradiol. Peroxidation of o-dianisidine was monitored by increase of absorption at 432 nm vs. 580 nm as a reference. The basic reaction medium (pH 7.6) with 1 mM DM contained 0.2 mM o-dianisidine and... 0.6 μM CcO. The reaction was initiated by addition of 4 mM H₂O₂. Trace 1 (red)—recording in the presence of 0.5 mM estradiol benzoate, trace 2 (black)—the control. The initial jump upon H₂O₂ addition corresponds to spectral response of heme a₁ in CcO. Inset: 0.5 mM estradiol in the presence of 1 mM DM does inhibit cytochrome oxidase activity of CcO (see Figure 1A for more details). (B) Effect of testosterone (Tst). The conditions are as in panel A except that concentration of DM in the buffer was 20 mM. Trace 1 (red)—recording in the presence of 4 mM testosterone, trace 2 (black)—the control, trace 3 (blue)—testosterone (4 mM) was added during the reaction time course (indicated by the arrow), which was followed by temporary increase of turbidity (the supposed trajectory until spectral registration became possible is shown by the dashed line). Inset: 4 mM testosterone in the presence of 20 mM DM does inhibit oxidase activity of CcO (see Figure 2A for other conditions). 4. Discussion Our work shows that testosterone and estradiol can inhibit significantly isolated cytochrome oxidase from bovine heart mitochondria. The inhibition of the isolated bovine CcO has been observed also with a number of other steroid hormones including progesterone and DHEA, as well as with vitamin D which is classified as secosteroid (Table 1). All the tested steroid compounds induced inhibition of CcO activity at 10⁻⁵–10⁻⁴ M concentration. All of them revealed competition with dodecyl-maltoside. None of the assayed compounds inhibited peroxidase activity of CcO, with the exception for cholecalciferol which, however, affects peroxidase reaction in concentrations an order of magnitude higher than oxidase activity (Table 1). These findings corroborate the proposal of Ferguson-Miller and collaborators based on structure considerations that steroid hormones are to be highly ranked in the list of potential ligands of the bile acid binding site of CcO. At the same time, experiments of the East Lancing group did not reveal inhibition of CcO by testosterone, estradiol or other steroid hormones (cf. Supplemental Figure 2 to Buhrow et al. [15]), while many other amphipathic ligands of the BABS, e.g., retinoic acid, or thyroid hormone T3, strongly inhibited the enzyme [15]. The discrepancy between the results of the present work and that of Buhrow et al. [15] could be explained by different experimental conditions. Firstly, the CcO species used in the two studies are different. Ferguson-Miller and collaborators worked with CcO from R. sphaeroides whereas bovine heart oxidase was studied in our experiments. It would be tempting to speculate that the animal CcO can be more susceptible to inhibition by animal hormones than the bacterial enzyme, emphasizing physiological relevance of the effect. However, discrepancy between the data here and in [15] may probably be explained by some other significant differences in the experimental conditions. For instance, the activity assay conditions in [15] ([DM] = 0.2 mM) were not optimal for the inhibitory effect of testosterone to be revealed. With the concentrations of testosterone (100 μM) and DM (1 mM) close to those used in [15], we observed inhibition of bovine oxidase by only 13% (see Figure 2B, curve 1). In order to clarify the issue, it would be best to carry out side-by-side experiments with the bovine and bacterial oxidases under identical conditions. Our preliminary experiments reveal inhibition of R. sphaeroides CcO by estradiol. While Ferguson-Miller and collaborators described inhibition of CcO by a number of amphipathic ligands of the BABS, the mechanism of the inhibition was not investigated earlier. Ferguson-Miller and collaborators [14] pointed out close proximity of the BABS to the entry of the K-proton channel and proposed that the amphipathic ligands may impair proton delivery to the oxygen-reducing site via the K-pathway. This proposal was supported by strong modulation of the BABS ligand effects on the activity of CcO by mutations in residue E101 in Subunit II that is thought to be the entry point for protons in the K-pathway, see Hiser et al. [16]. The inhibition of intramolecular electron transfer from heme a to heme a₁ by estradiol observed in our work is consistent with inhibition of the K-channel. A distinctive feature of CcO inhibition induced by blocking the K-channel consists in that the peroxidase activity of the enzyme is not affected (see Vygodina et al. [23]) because the K-channel is not involved in proton delivery to the binuclear site in the so-called peroxidase phase of the catalytic cycle [22,23]. As shown in this work, testosterone, estradiol and other steroids, while suppressing the oxidase reaction, actually do not inhibit peroxidase activity of CcO (Figure 5, Table 1). This observation strongly supports the proposal that the inhibitory effect of the steroid hormones on the activity of CcO may indeed be associated with impairment of proton transfer via the K-channel. Effect of estradiol on the proton conducting relay of the K-channel is also in agreement with the spectral shift of heme $a_i$ induced by the hormone (Figure 3). Indeed, the K-channel delivers protons right to the binuclear site and perturbation of the proton relay could affect $\text{H}_2\text{O}/\text{OH}^+$ equilibration at the 6-th axial position of heme $a$, leading to partial high-to-low-spin transition of the ferric heme. An obvious important question is whether the inhibition of the isolated CcO by steroid hormones may be relevant to physiology. The first point to be concerned is the hormone concentration range. Physiological concentration of the steroid hormones in the blood serum is around $10^{-7}$–$10^{-6}$M for the total [24], ca. $1 \times 10^{-10}$–$1.2 \times 10^{-8}$M for free testosterone and ca. $2 \times 10^{-8}$–$5 \times 10^{-7}$M for free estradiol [25,26] that seems to be incompatible with the $K_c$ values of $10^{-5}$–$10^{-4}$M determined for the hormone action on CcO in our experiments. However, it is noted that steroid hormones are very lipophilic and partition from water to octanol with a coefficient of $10^3$–$10^4$ [27], so that their concentration in the mitochondrial membranes may be very much higher than in blood serum. It is widely accepted that accumulation of hormones in membranes can be an important step of their action mechanism in the cell, see Mayne et al. [28]. Thus, the highest partition coefficient of $10^4$ brings the values of the order of $10^{-8}$ M (the free hormones in the blood serum) to the hormone concentrations in the mitochondrial membranes close to the estimated $K_c$ (ca. $10^{-4}$M). Therefore, quite noticeable inhibition of cytochrome oxidase by physiological concentrations of the steroid hormones looks possible. At the same time, our data may be relevant to the experimental studies of steroid hormones action in vivo, studies with whole animals or (and particularly so) with cell cultures. Concentration of the hormones employed in such studies often reach a submillimolar or even millimolar range [29–33]. For example, in the paper of D’Ascenzo et al. [29], the following IC$_{50\%}$ values are cited for inhibition of cell growth by anabolic steroids: testosterone, 100 μM; androstenedione, 375 μM; nandrolone, 9 μM; norandrostenedione, 500 μM; norandrostenediol, 6 mM. Effective concentrations of tens to hundreds of micromoles are also given in the rest of the works mentioned above. The second point as to the physiological relevance of our data is that inhibition of the isolated CcO by steroid hormones has been observed under conditions rather far from physiological. For instance, all the data have been obtained in the presence of a detergent dodecyl-maltoside and it remains to be established whether the inhibition by the hormones can take place in case of the membrane-bound enzyme. Experiments with intact mitochondria and liposome-reconstituted CcO are required in order to resolve this question. Finally, we would like to discuss the role of DM in the inhibition of CcO by steroids. Experiments with both testosterone and estradiol suggest that DM competes with the steroid hormones for binding with the enzyme. Notably, the close values of affinity between DM and CcO are determined independently in the two cases of inhibition ($K_c = 1.47$ mM and 1.3 mM, see Figures 1C and 2C, respectively). Moreover, we obtained nearly the same value (1.2 mM) in our study on the inhibition of CcO by Triton X-100, the detergent which structurally resembles steroids in some respects (the paper is submitted for publication). One can assume from these data that DM specifically interacts with the enzyme at the site with high affinity to some native ligand. This conclusion is in agreement with the structure analyses in [12,14], that visualize decyl-maltoside molecule binding very close to the BABS with a hydrophobic tail binding to a groove near the amphipathic region to which the steroid group of the bile acids adheres, and with the maltoside head being able to reach the steroid group binding motif of the amphiphilic site competing with the typical BABS-ligand for binding with CcO. How can it be that DM at the same time increases the maximal inhibition obtained with excess testosterone? At this time we can only speculate on this issue. One possible explanation is that there are two DM binding sites involved. Binding at one site confers CcO ability to bind testosterone, presumably stabilizing a putative testosterone-reactive conformational state of the enzyme, and so increases the maximal level of inhibition that can be attained with saturating concentrations of the hormone. DM bound at the other site competes with testosterone for binding with the BABS which explains the growth of Ki with increase in [DM]. These two putative binding sites may bind two different molecules of DM, however, binding of a single molecule of DM can fit to this purpose as well. Namely, binding of the hydrophobic tail to the groove could be responsible for stabilizing the testosterone-reactive state of CcO, whereas overlapping of the maltose head group with the steroid-binding motif could hamper testosterone binding to the BABS. In any case, the different character of the influence of DM on the inhibition imposed by estradiol and testosterone points to the probable difference in mutual arrangement of the hormone and detergent molecule in these two cases. It is possible that the absence of spectral changes in CcO incubated with testosterone (as opposed to estradiol, see Table 1) reflects the shifted disposition of BABS ligands which causes a difference in their sum effect on the K-channel structure and, ultimately, on the binuclear center. It is worth noting that DM can be viewed as a structural analog of phospholipids, see Qin et al. [34]. So, the effects of DM on the hormone binding with CcO may in fact mimic the effects imposed in vivo by endogenous phospholipids binding to a site adjacent to the BABS and controlling reactivity of the BABS to amphipathic ligands. In conclusion, we presume in agreement with Ferguson-Miller and collaborators [12] that CcO is endowed with a specific regulatory site, capable of binding various amphiphilic ligands, including steroid hormones. Binding of the ligands to the site in mitochondria may be controlled by endogenous phospholipids. Let us discuss some of the implications and future prospects. One of the promising directions of our work would be to study the relationship between the effect of inhibition of CcO by steroid hormones and the tissue specificity of the enzyme. The first stage of steroidogenesis proceeds in mitochondria of adrenal glands, gonads, and some other organs. This is the conversion of cholesterol into pregnenolone which is catalyzed by the cytochrome P450 side chain cleavage enzyme system located in the inner mitochondrial membrane, see Stocco [35]. Apparently, CcO in steroidogenic tissues must function in the presence of at least these two steroid compounds, and their inhibitory action in this case looks unlikely. According to our unpublished data, cholesterol actually does not inhibit the oxidase activity of the bovine heart enzyme. It is of interest to test pregnenolone from this point of view. Additionally, it would be useful to test the sensitivity of CcO from steroidogenic tissue to estradiol and testosterone. On the other hand, the presented study was performed on enzyme from the heart, which is one of the target organs for steroid hormones. Cytoplasmic and nuclear receptors for sex hormones and some other steroids including vitamin D were found in cardiomyocytes long ago, see Stumpf et al. [36]. The physiological effect of “cardiac glycosides” is probably based just on their structural similarity with steroids. The effects of steroid hormones on the tissue of heart and blood vessels are diverse and very complex—this is the subject of studies by physiologists and of active discussion in the special medical literature. Without being clinicians, we only venture to suggest that the inhibition of the respiratory chain at the CcO level by steroid hormones may play a prominent role in the whole picture which should be clarified. Mitochondrion, in its turn, is a target organelle for steroid hormones. All currently known cases of steroid interaction with mitochondria are receptor-dependent. They include transcriptional regulation of nuclear- as well as mitochondrial-encoded mitochondrial proteins, and the effects on mitochondria due to interactions with cytoplasmic signaling peptides and non-genomic control of cation fluxes (reviewed by Gavrilova-Jordan and Price [37]). From a global point of view, it seems very remarkable that the same regulatory molecule (steroid hormone) implements its influence on metabolism in two parallel ways: indirectly, through complex cascades of reactions, and directly, by selective interaction with the key respiratory enzyme resulting in modulation of its activity. Presumably, such double regulation makes the system more flexible: for example, it could accelerate the response to a stimulus, increase the control over responses, etc. We hope that our work will stimulate further research on this problem. Author Contributions: Conceptualization, A.A.K.; methodology, A.A.K., T.V.V. and N.V.A.; software, T.V.V., N.V.A. and I.P.O.; validation, T.V.V., N.V.A. and I.P.O.; formal analysis, A.A.K., T.V.V., N.V.A. and I.P.O.; investigation, T.V.V., N.V.A. and I.P.O.; resources, A.A.K.; data curation, A.A.K., T.V.V., N.V.A. and I.P.O.; writing—original draft preparation, A.A.K. and N.V.A.; writing—review and editing, N.V.A. and T.V.V.; visualization, T.V.V., N.V.A. and I.P.O.; supervision, A.A.K.; project administration, A.A.K.; funding acquisition, A.A.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded in part by RFBR (Russian Foundation for Basic Research), grant number 17-04-00160a (to A.A.K.). Conflicts of Interest: The authors declare no conflict of interest. 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3522, 1 ], [ 3522, 7762, 2 ], [ 7762, 9803, 3 ], [ 9803, 13083, 4 ], [ 13083, 14439, 5 ], [ 14439, 17898, 6 ], [ 17898, 19341, 7 ], [ 19341, 22502, 8 ], [ 22502, 25032, 9 ], [ 25032, 28131, 10 ], [ 28131, 32913, 11 ], [ 32913, 37825, 12 ], [ 37825, 42415, 13 ], [ 42415, 47186, 14 ], [ 47186, 51536, 15 ], [ 51536, 52177, 16 ] ] }
84378dab7f197fa15fefd98c8ac7024bb1d8963a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 29, "total-fallback-pages": 0, "total-input-tokens": 154341, "total-output-tokens": 29916, "fieldofstudy": [ "Mathematics" ] }	Qualitative properties of a nonlinear system involving the $p$-Laplacian operator. F. Demengel Abstract In this article we consider the nonlinear system involving the $p$-Laplacian \[ \begin{align} \|u'\|^{p-2}u'' &= u^{p-1}v^p \\ \|v'\|^{p-2}v'' &= v^{p-1}u^p \\ u &\geq 0, v \geq 0 \end{align} \] for which we prove symmetry, asymptotic behavior and non degeneracy properties. This can help to a better understanding to what happens in the $N$ dimensional case, for which several authors prove a De Giorgi Type result under some additional growth and monotonicity assumptions. 1 Introduction In this article we extend some of the results obtained in [5] in the case of the Laplacian, to the $p$-Laplacian case. More precisely we consider the system in $\mathbb{R}^N$: \[ \begin{align} \text{div}(\|\nabla u\|^{p-2}\nabla u) &= u^{p-1}v^p \\ \text{div}(\|\nabla v\|^{p-2}\nabla v) &= v^{p-1}u^p, \end{align} \] where $u$ and $v$ are supposed to be positive. In the case $p = 2$ this problem comes from a phase separation model. As an example the Gross Pitaevskii, [9] model can be described by the non linear elliptic system \[ \begin{align} -\Delta u + \alpha u^3 + \Lambda u^2 v &= \lambda_{1,\Lambda} u & \text{in } \Omega \\ -\Delta v + \alpha v^3 + \Lambda u^2 v &= \lambda_{2,\Lambda} v & \text{in } \Omega \\ u > 0, v > 0, & \text{in } \Omega, u = v = 0 & \text{on } \partial\Omega \\ \int_{\Omega} u^2 &= \int_{\Omega} v^2 = 1 \end{align} \] (1.1) where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$ and $\alpha, \beta$ are positive parameters, $\Lambda$ will become large. Assuming that $\sup(\lambda_{1,\Lambda}, \lambda_{2,\Lambda}) \leq C$ for some constant independent of $\Lambda$, formally and up to subsequences $(u_{\Lambda}, v_{\Lambda})$ converges to some pair $(u, v)$ which satisfies $uv = 0$ and the equations \[ \begin{cases} -\Delta u + \alpha u^3 = \lambda_{1,\Lambda} u & \text{in } \Omega_u = \{x, u(x) > 0\} \\ -\Delta v + \beta v^3 = \lambda_{2,\Lambda} v & \text{in } \Omega_v = \{x, v(x) > 0\} \end{cases} \] (1.2) Several papers treat the convergence of $(u_{\Lambda}, v_{\Lambda})$ away the interface $\gamma = \{x, u(x) = 0 = v(x)\}$, see for example [29] and [10], [24] for the uniform equicontinuity of $(u_{\Lambda}, v_{\Lambda})$. Near the interface, the profile of bounded solutions of (1.1) of the blow up equation is a system, which is completely classified in the one dimensional case, [5], [6]. This system is the following \[ \begin{cases} U'' = UV^2 \\ V'' = VU^2 \\ U > 0, V > 0 \end{cases} \] In [6], the authors expect that the same system occurs in the $N$ dimensional case, say \[ \begin{cases} \Delta U = UV^2 \\ \Delta V = VU^2 \\ U > 0, V > 0 \end{cases} \] in $\mathbb{R}^N$. Furthermore they conjecture that for any dimension $N \leq 8$, the system is in fact one dimensional. They obtain this result under some additional assumption on the growth of the solution, in dimension 2. The assumption $N \leq 8$ is motivated by the case of scalar equations for which it is known that the scalar equation is not necessary one dimensional for $N \geq 9$, [13]. The condition on the growth in the two dimensional case is satisfied in particular if the solution of the system is at most linear at infinity, as it is proved in the case $N = 1$. When $N > 2$, this is not sufficient, and up to now, even in the case $N = 2$, this increasing behaviour is not proved. In [18] the author improved the result by establishing that for $N = 2$, as soon as $u$ and $v$ have at most algebraic increasing behavior and satisfy for some component $\partial_N u > 0$, $\partial_N v < 0$, then the solution is one dimensional. This result is recently improved by Farina and Soave by replacing the condition $\partial_N u > 0$, $\partial_N v < 0$ by the weaker condition $\lim_{x_N \to \pm \infty} u(x', x_N) - v(x', x_N) = \pm \infty$, $2$ uniformly with respect to $x'$, conserving the assumption of algebraic growth. Let us cite also the recent result of K. Wang \[28\] which replaces the monotonicity condition by the fact that $(u, v)$ is a local minimizer. The present paper is motivated by the asymptotic study of (1.1), say $$ \begin{align} \begin{cases} -d\text{div}(\abs{\nabla u}^{p-2}\nabla u) + \alpha u^{p+1} + \Lambda u^{p}u^{p-1} = \lambda_{1,\Lambda}u^{p-1} & \text{in } \Omega \\ -d\text{div}(\abs{\nabla v}^{p-2}\nabla v) + \beta v^{p+1} + \Lambda u^{p}v^{p-1} = \lambda_{2,\Lambda}v^{p-1} & \text{in } \Omega \\ u > 0, \ v > 0 \text{ in } \Omega, \ u = v = 0 \text{ on } \partial\Omega \end{cases} \end{align} $$ (1.3) where $\Omega$ is a smooth bounded domain in $\mathbb{R}^{N}$ and $\alpha, \beta$ are positive parameters, $\Lambda$ will become large. Such a pair of solutions is a critical point for the functional $E_{\Lambda}(u, v) = \frac{1}{p}\int_{\Omega}((\abs{\nabla u}^{p} + \abs{\nabla v}^{p}) + \frac{\alpha}{p+2}\int_{\Omega}u^{p+2} + \frac{\beta}{p+2}\int_{\Omega}v^{p+2} + \frac{\Lambda}{p}\int_{\Omega}u^{p}v^{p})$ under the constraint $\int_{\Omega}u^{p} = \int_{\Omega}v^{p} = 1$. Assume that there exists some constant $C$ independent on $\Lambda$ with $$ \sup_{\Lambda}(\lambda_{1,\Lambda}, \lambda_{2,\Lambda}) \leq C, \text{ for } \Lambda \text{ large }. $$ As $\Lambda$ goes to infinity, and up to subsequence $(u_{\Lambda}, v_{\Lambda})$ tends formally to some pair $(u, v)$ which satisfies $$ \begin{align} \begin{cases} -d\text{div}(\abs{\nabla u}^{p-2}\nabla u) + \alpha u^{p+1} = \lambda_{1,\Lambda}u^{p-1} & \text{in } \Omega_{u} \\ -d\text{div}(\abs{\nabla v}^{p-2}\nabla v) + \beta v^{p+1} = \lambda_{2,\Lambda}v^{p-1} & \text{in } \Omega_{v} \end{cases} \end{align} $$ (1.4) where $\Omega_{u} = \{x, u(x) > 0\}$, $\Omega_{v} = \{x, v(x) > 0\}$. It is not our purpose here to follow this way. We are interested in the one dimensional case and especialy in the behavior of the limit pair of solutions $(u, v)$ near the interface $\gamma = \{x \in \Omega, u(x) = v(x) = 0\}$. When $N = 1$ and $\Omega = ]a, b[\text{ one has the result} Theorem 1.1. Assume that $\Omega = ]a, b[$, that $(u_{\Lambda}, v_{\Lambda})$ solves (1.3). There exists $x_{\Lambda} \in \Omega$ such that $u_{\Lambda}(x_{\Lambda}) = m_{\Lambda} = v(x_{\Lambda})$ goes to zero, and $x_{\Lambda}$ tends to some point in $\gamma$. Furthermore if $\bar{u}_{\Lambda} = \frac{1}{m_{\Lambda}}u_{\Lambda}(m_{\Lambda}y + x_{\Lambda})$, $\bar{v}_{\Lambda} = \frac{1}{m_{\Lambda}}v_{\Lambda}(m_{\Lambda}y + x_{\Lambda})$ and $y \in ]\frac{a-x_{\Lambda}}{m_{\Lambda}}, \frac{b-x_{\Lambda}}{m_{\Lambda}}[$, $(\bar{u}_{\Lambda}, \bar{v}_{\Lambda})$ converges locally uniformly to some pair $U, V$ which satisfies $$ \begin{align} \begin{cases} (U''\|^{p-2}U')' = V^{p}U^{p-1} & \text{on } \mathbb{R} \\ (V''\|^{p-2}V')' = U^{p}V^{p-1} \\ U(0) = V(0) = 1. \end{cases} \end{align} $$ (1.5) Furthermore there exists some positive constant $T_{\infty}$ such that $$ \|U'\|^{p} + \|V'\|^{p} - U^{p}V^{p} = T_{\infty}. $$ 3 Next we are interested in the existence and in the properties of the solutions of (1.5). The existence of a non trivial solution is given in Theorem 3.1. In a second time we prove the following Theorem 1.2. Let $N = 1$ and $(U, V)$ be a non negative solution of $$ \begin{align} \frac{(\|U'\|^p - 2U')'}{p} &= V^pU^{p-1}, \\ \frac{(\|V'\|^p - 2V')'}{p} &= U^pV^{p-1} \end{align} $$ on $\mathbb{R}$. Then up to exchanging $U$ and $V$, 1) Up to translation $V(y) = U(-y)$. 2) $U' > 0$ everywhere, $U'(+\infty) = (T_\infty)^{\frac{1}{p}}$, and there exist some positive constants, $m, M, k, K, c, C$ such that near $-\infty$, $me^{-Kx^2} \leq U(x) \leq Me^{-kx^2}$, $c\|x\|U \leq U' \leq C\|x\|U$. Symmetric estimates hold for $V$ exchanging $-\infty$ and $+\infty$. 3) Suppose that $\phi, \psi$ is a bounded solution of the linearized system $$ \begin{align} \frac{(\|U'\|^p - 2\phi')'}{p} &= (p-1)U^{p-2}V^p\phi + pV^{p-1}U^{p-1}\psi, \\ \frac{(\|V'\|^p - 2\psi')'}{p} &= (p-1)V^{p-2}U^p\psi + pU^{p-1}V^{p-1}\phi \end{align} $$ in $\mathbb{R}$, then there exists some constant $c$ such that $(\phi, \psi) = c(U', V')$. We end this introduction by some reflexions about the De Giorgi’s conjecture, which, even if we do not treat it here, is after all, at the origin of the present paper. As we said in the abstract, the previous classification is a first step if one want to prove a De Giorgi type result on the system $$ \begin{align} \text{div}(\|\nabla u\|^{p-2}\nabla u) &= u^{p-1}v^p, \\ \text{div}(\|\nabla v\|^{p-2}\nabla v) &= u^pv^{p-1} \end{align} $$ in $\mathbb{R}^N$. In [15], [16] the authors consider a more general system than the present one, the quasilinear operator she studies includes the $p$-Laplacian operator, and the right hand side included the case studied here. She proves that under some condition of growth on the solution, together with some stability assumption on the couple of solutions, then the solution is in fact one dimensional. The stability is in particular implied when the solution is ”half monotone ”, i.e. if there exists one direction say $e_1$ such that $\partial_1 u > 0$ and $\partial_1 v < 0$. It is an exercise to prove that the growth condition (1.14) in [15] is satisfied when the solution has at most linear growth at infinity, in dimension 2, hence we recover a generalization of the results in [6] in the case $p \neq 2$. Several questions are of interest: As we said above, in [18], and [19] the authors suppose that the solution has at most algebraic growth. Can we have the same result in the $p$-Laplacian case? The answer is not immediate, since the proof of Farina and Soave relies on some properties of the Almgren frequency function which do not extend to the $p$-Laplacian case. Another interesting question is the following: Suppose that one replaces the Laplacian system by a Fully Nonlinear system. Of course for Pucci’s operators the one dimensional system is reduced, up to constant, to the Laplacian case. But due to the non differentiability of the Pucci’s operators, the definition of stable solutions must be precised. In the same order of ideas, one can imagine to treat the case of Fully Nonlinear degenerate or singular systems, based on the model of the $p$-Laplacian type treated here, but not under divergence form, as the following \[ \begin{cases} \|\nabla u\|^{\alpha} F(D^2 u) = u^{\alpha+1} v^{\alpha+2} \\ \|\nabla v\|^{\alpha} F(D^2 v) = v^{\alpha+1} u^{\alpha+2} \end{cases} \text{in } \mathbb{R}^N \] where $\alpha$ is some number $> -1$ and $F$ is fully nonlinear elliptic. The reader may consult [7] for properties of such operators and a convenient definition of viscosity solutions. It would be far too long to cite all the papers written about the De Giorgi type result in the case of one equation in place of a system. Let us cite for the $p$-Laplacian case the recent paper of A. Farina and Valdinoci [21], and the very complete paper of Savin et al. [26]. For variations on the subject on De Giorgi’s conjecture in the case of a single equation the reader may consult [12], [17], [22], [20], [2], [3], [23], [1], [25], [8]. The paper is organized as follows: In Section 2, we consider the one dimensional system defining $(u_\Lambda, v_\Lambda)$ and prove Theorem 1.1. Section 3 is devoted to the proof of Theorem 1.2. Most of the technical details of this section are postponed to the appendix in section 4. Acknowledgment The author wishes to thank Alberno Farina and Enrico Valdinoci for having pointed out several papers on the question. 2 The original problem: Proof of theorem 1.1 In all that section we will frequently use in place of sequences, subsequences, without mentioning it. Let us consider for $\alpha, \beta$ and $\Lambda, \lambda_1, \lambda_2$ some given positive constants $$\begin{aligned} \begin{cases} -u_A'' + \alpha u_A^{p+1} + \Lambda u_A^{p-1} = \lambda_1 u_A^{-1} \\ v_A'' + \beta v_A^{p+1} + \Lambda v_A^{p-1} = \lambda_2 v_A^{-1} \end{cases} \end{aligned} \quad \text{in } [a, b]. $$ (2.1) $$u, v > 0, u(a) = u(b) = v(a) = v(b) = 0, \quad \int_a^b \|u\|^p = \int_a^b \|v\|^p = 1.$$ (2.2) $(u_A, v_A)$ is then a solution of the minimizing eigenvalue problem $$\inf_{\|u\|_p = \|v\|_p = 1, (u, v) \in W^{1, p}([a, b])} E_\Lambda(u, v),$$ where $$E_\Lambda(u, v) = \frac{1}{p} \int_a^b \|u'\|^p + \frac{1}{p} \int_a^b \|v'\|^p + \alpha \int_a^b \frac{\|u\|^{p+2}}{p+2} + \beta \int_a^b \frac{\|v\|^{p+2}}{p+2} + \Lambda \int_a^b \|u\|^p \|v\|^p.$$ (2.3) Assume that $$\max_{\lambda} (\lambda_1, \lambda_2) \leq C,$$ Due to the first equation in (2.1) multiplied by $u_A$, and integrated over $[a, b]$, one gets $$\int_a^b \|u'_A\|^p + \alpha \int_a^b u_A^{p+2} + \Lambda \int_a^b u_A v_A^p = \lambda_1.$$ (2.2) Doing the same for $v_A$, one gets that $(u_A, v_A)$ is bounded in $W^{1, p}([a, b])^2$. Furthermore Lemma 2.1. There exist $T_\Lambda$, $C_1$ and $C_2$ independent on $\Lambda$ such that $$\frac{\|u'_A\|^p}{p} + \frac{\|v'_A\|^p}{p} - \Lambda \frac{u_A^p v_A^p}{p} - \alpha \frac{u_A^{p+2}}{p+2} - \beta \frac{v_A^{p+2}}{p+2} + \lambda_1 \frac{u_A^p}{p} + \lambda_2 \frac{v_A^p}{p} = T_\Lambda$$ (2.3) and $$0 < C_1 \leq T_\Lambda \leq C_2 < \infty$$ 6 Proof Multiply the first equation in (2.1) by $ u'_\Lambda $, the second one by $ v'_\Lambda $, and add the two equations, we obtain that \[ -\left( \frac{\|u'_\Lambda\|^p}{p} \right)' - \left( \frac{\|v'_\Lambda\|^p}{p} \right)' + \alpha \left( \frac{\|u''_\Lambda\|^p}{p + 2} \right)' + \beta \left( \frac{\|v''_\Lambda\|^p}{p + 2} \right)' + \Lambda \left( \frac{\|u''_\Lambda\|^p}{p} \right)' = \lambda_{1,\Lambda} \left( \frac{\|u'_\Lambda\|^p}{p} \right)' + \lambda_{2,\Lambda} \left( \frac{\|v'_\Lambda\|^p}{p} \right)' \] Hence there exists some constant $ T_\Lambda $ such that (2.3) is satisfied. Integrating on $[a, b]$ the equation defining $ T_\Lambda $, one gets \[ \int_a^b \frac{\|u'_\Lambda\|^p}{p} + \int_a^b \frac{\|v'_\Lambda\|^p}{p} - \Lambda \int_a^b \frac{\|u''_\Lambda\|^p}{p + 2} - \alpha \int_a^b \frac{\|u''_\Lambda\|^p}{p + 2} - \beta \int_a^b \frac{\|v''_\Lambda\|^p}{p + 2} + \lambda_{1,\Lambda} + \lambda_{2,\Lambda} = \frac{T_\Lambda (b - a)}{p}. \] On the other hand, using (2.2) for $ u_\Lambda $ and its analogous for $ v_\Lambda $, one has \[ \int_a^b \|u'_\Lambda\|^p + \int_a^b \|v'_\Lambda\|^p + \alpha \int_a^b \|u''_\Lambda\|^p + \beta \int_a^b \|v''_\Lambda\|^p + 2\Lambda \int_a^b u''_\Lambda v''_\Lambda = \lambda_{1,\Lambda} + \lambda_{2,\Lambda}. \] Combining the two equations one gets \[ T_\Lambda (b - a) = 2 \int_a^b \|u'_\Lambda\|^p + 2 \int_a^b \|v'_\Lambda\|^p + \frac{2\alpha}{p} \int_a^b \|u''_\Lambda\|^p + \frac{2\beta}{p + 2} \int_a^b \|v''_\Lambda\|^p + \lambda_{1,\Lambda} \int_a^b u''_\Lambda v''_\Lambda \] and using Poincaré’s inequality $ \int_a^b \|u'_\Lambda\|^p \geq C \int_a^b \|u_\Lambda\|^p \geq C $, one obtains that $ T_\Lambda \geq C > 0 $. On the other hand since $(u_\Lambda)$ and $(v_\Lambda)$ are bounded in $ W^{1, p}([a, b]) $ and since $ \lambda_{1,\Lambda} $ and $ \lambda_{2,\Lambda} $ are bounded, one gets that $ T_\Lambda $ is bounded from above. Furthermore using the equation defining $ T_\Lambda $, and the fact that $ u_\Lambda $ and $ v_\Lambda $ vanish on the end points, one gets that $ u'_\Lambda (a) $, $ u'_\Lambda (b) $, $ v'_\Lambda (a) $, $ v'_\Lambda (b) $ are bounded independently on $ \Lambda $. Integrating the first equation in (2.1) between $ a $ and $ x $ one gets \[ \|u'_\Lambda\|^{p-2} u'_\Lambda (x) - \|u'_\Lambda\|^{p-2} u'_\Lambda (a) = \alpha \int_a^x u''_\Lambda + \Lambda \int_a^x u''\Lambda u''_\Lambda + \lambda_{1,\Lambda} \int_a^x u''_\Lambda \] using this on $ \{ x = b \} $ one gets $ \Lambda \int_a^b u''_\Lambda v''_\Lambda \leq C $, and by the positivity that $ \|u'_\Lambda\|^{p-2} u'_\Lambda (x) - \|u'_\Lambda\|^{p-2} u'_\Lambda (a) \leq C $. Doing the same between $ x $ and $ b $ one obtains that $ \|u'_\Lambda\| \leq C $ for some constant independent on $ \Lambda $. In the same manner, $ \|v'_\Lambda\| \leq C $. Theorem 2.2. Assume that $(u_\Lambda, v_\Lambda)$ solves the system (2.1) in $[a, b]$. There exists $x_\Lambda$ such that $m_\Lambda = u(x_\Lambda) = v(x_\Lambda) \rightarrow 0$ as $\Lambda$ goes to infinity, and $x_\Lambda \rightarrow x_\infty \in ]a, b[$. Furthermore $m_\Lambda^{2p} \rightarrow C_0 > 0$ and $\Lambda^{\frac{1}{2p}} \min(x_\Lambda - a, b - x_\Lambda) \rightarrow +\infty$. Proof of Theorem 2.2 By the previous estimates $(u_\Lambda)$ and $(v_\Lambda)$ are relatively compact in $C([a, b])$. In particular up to subsequence, $u_\Lambda$ and $v_\Lambda$ are uniformly convergent. Let $(u_\infty, v_\infty)$ be the limit of such subsequence. By the identity $\int_a^b \|u_\infty\|^p = \int_a^b \|v_\infty\|^p$, and by the uniform convergence, there exists $x_\infty$ and $x_\Lambda$ which tends to $x_\infty$, such that $m_\Lambda = u_\Lambda(x_\Lambda) = v_\Lambda(x_\Lambda)$ and $x_\infty \in \{u_\infty(x) = v_\infty(x)\}$ = $\gamma$. To prove that \[ \lim \sup \Lambda m_\Lambda^{2p} < \infty, \] we argue by contradiction and define $\tilde{u}_\Lambda = \frac{1}{m_\Lambda} u\left(\frac{y}{m_\Lambda^{\frac{1}{p}}} + x_\Lambda\right)$, $\tilde{v}_\Lambda = \frac{1}{m_\Lambda} v\left(\frac{y}{m_\Lambda^{\frac{1}{p}}} + x_\Lambda\right)$ where $y \in ]-x_\Lambda + am_\Lambda^{\frac{1}{p}}, -x_\Lambda + bm_\Lambda^{\frac{1}{p}}[$, interval which tends to $\mathbb{R}$. Then $(\tilde{u}_\Lambda, \tilde{v}_\Lambda)$ satisfy the equation \[ \frac{\tilde{u}'_{\Lambda}}{p} + \frac{\tilde{v}'_{\Lambda}}{p} - \frac{\tilde{u}^p_{\Lambda} \tilde{v}^p_{\Lambda}}{p} - \alpha \frac{\tilde{u}^{p+2}_{\Lambda}}{(p+2)m^{p-2}_{\Lambda}} - \beta \frac{\tilde{v}^{p+2}_{\Lambda}}{(p+2)m^{p-2}_{\Lambda}} - \frac{T_\Lambda}{pm^{2p}_{\Lambda}} = 0, \] where \[ \frac{\tilde{u}^p_{\Lambda}}{p m^{p}_{\Lambda}} + \frac{\tilde{v}^p_{\Lambda}}{p m^{p}_{\Lambda}} = \frac{T_\Lambda}{pm^{2p}_{\Lambda}}. \] Using the fact that $(u'_\Lambda)$ is bounded independently on $\Lambda$, by the mean value’s theorem \[ \|\tilde{u}_\Lambda(y) - \frac{1}{m_\Lambda} u(x_\Lambda)\| \leq \frac{1}{m_\Lambda^{\frac{1}{p}}} \|u'_\Lambda\|_\infty \] and we have analogous estimates for $\tilde{v}_\Lambda$, so using $u_\Lambda(x_\Lambda) = m_\Lambda = v(x_\Lambda)$ one obtains that $\tilde{u}_\Lambda$ goes to 1 uniformly, $\tilde{v}_\Lambda$ goes to 1, finally passing to the limit in the equation (2.3) one gets that \[ -\frac{1}{p} = 0, \] a contradiction. We have obtained that $\Lambda m_\Lambda^{2p}$ is bounded. To end the proof, suppose by contradiction that $\Lambda m_\Lambda^{2p} \rightarrow 0$ for a subsequence and let $\tilde{u}_\Lambda(y) = \frac{1}{m_\Lambda} u_\Lambda(m_\Lambda y + x_\Lambda)$, then $\tilde{u}_\Lambda$ and $\tilde{v}_\Lambda$ satisfy the identity constant before. We have obtained that $ \tilde{m} $ these constant are zero, which yields a contradiction with the identity (the sense, and so, also does its derivative. By passing to the limit one obtains that $ \|\tilde{u}\| $ converges strongly in $ L^p $, in particular $ \|u'\|^{p-2}u'' $ converges in the distributional sense, and so, also does its derivative. By passing to the limit one obtains that $(\tilde{u}'', \tilde{v}')$ tends locally uniformly to $(u, v)$ which satisfies $ \|u'\|^{p-2}u'' = 0 $ and $ \|v'\|^{p-2}v'' = 0 $, hence $ u = cte $, $ v' = cte $. Since $ u$ and $ v$ are bounded, these constant are zero, which yields a contradiction with the identity \[ \frac{\|u\|}{p} + \frac{\|v\|}{p} = T_{\infty}, \] where we have used the fact that $ T_{\infty} := \lim_{\Lambda \to \infty} T_{\Lambda}, $ by the estimates on $ T_{\Lambda} $ proved before. We have obtained that $ m^2p\Lambda $ is bounded from above by some constant $ > 0 $. We finally prove that $ \Lambda \frac{2}{p} \min(x_{\Lambda} - a, b - x_{\Lambda}) \to +\infty $. Suppose for example and by contradiction that up to a subsequence $ \Lambda \frac{1}{p} (x_{\Lambda} - a) \to C_1. $ Define $ \tilde{u}_{\Lambda} = \Lambda \frac{1}{p} u(x_{\Lambda} - a) $. Then $ \tilde{u}_{\Lambda}, \tilde{v}_{\Lambda} $ satisfy \[ \|\tilde{u}\|^{p-2}u' - \frac{\alpha}{\Lambda^{p+2}} \tilde{u}^{p-1}_{\Lambda} + \lambda_{1, \Lambda} \tilde{u}^{p-1}_{\Lambda} = 0, \] \[ \|\tilde{v}\|^{p-2}v' - \frac{\beta}{\Lambda^{p+2}} \tilde{v}^{p-1}_{\Lambda} + \lambda_{2, \Lambda} \tilde{v}^{p-1}_{\Lambda} = 0. \] We also get from the energy estimate \[ \frac{\|\tilde{u}'\|}{p} + \frac{\|\tilde{v}'\|}{p} = \frac{\tilde{u}^{p+2}}{(p + 2)\Lambda^{p+2}} - \frac{\beta \tilde{v}^{p+2}}{(p + 2)\Lambda^{p+2}} + \lambda_{1, \Lambda} \tilde{u}^{p}_{\Lambda} + \lambda_{2, \Lambda} \tilde{v}^{p}_{\Lambda} = T_{\Lambda}. \] Remark as before that when $ \Lambda $ goes to infinity, $(\tilde{u}, \tilde{v})$ tends locally uniformly to some $(U, V)$, which satisfies \[ \|U'\|^{p-2}U'' = V^p U^{p-1} \] \[ \|V'\|^{p-2}V'' = U^p V^{p-1} \] and $ U(-C_1) = V(-C_1) = 0 $. Note that if $(b - x_A) \Lambda \frac{1}{x} \rightarrow C_2 < \infty$ one has $ U(C_2) = 0 $ and then $ U'' = 0 $ and $ U \geq 0 $ implies $ U \equiv 0 $. We then assume that $ C_2 = +\infty $. Furthermore using Fatou’s lemma one gets \[ \int_{-C_1}^{\infty} V^p U^{p-1} \leq \liminf \int_{(a-x_A) \Lambda \frac{1}{x}}^{(b-x_A) \Lambda \frac{1}{x}} \tilde{v}^p \tilde{u}^{p-1} = \Lambda \int_{a}^{b} v^p u^{p-1} \leq C \] as stated in the proof of Lemma 2.1. Since $ U' $ is increasing and $ U \geq 0 $, if $ U $ is not identically zero, there exists $ C'_1 \geq C_1 $, such that $ U'(C'_1) > 0 $, and $ U = 0 $ on $[-C_1, -C'_1]$ then $ U(x) \geq U(-C'_1) + U'(-C'_1)(x - C'_1) = U'(-C'_1) + (x - C'_1) $. In the same manner there exists $ C''_1 \geq C_1 $, such that $ V(x) \geq V(-C''_1) + V'(-C''_1)(x - C''_1) $. We have obtained that near $+\infty$, $ U^{p-1}V^p \geq C x^{2p-1} $, which contradicts the fact that $ U^{p-1}V^p $ is integrable on $[-C_1, +\infty[$. Finally $ U = V = 0 $, a contradiction with the identity defining $ T_{\infty} $, when passing to the limit. We have obtained that $ \Lambda \min(x_A - a, b - x_A) \rightarrow +\infty $. This ends the proof of Theorem 1.1. 3 Qualitative properties of the $ p $-system in the one dimensional case : Proof of Theorem 1.2 In this section we want to prove the existence of non trivial solutions to the limit system (1.6). Note that the previous existence’s result is obtained under the assumption $(\lambda_{1, A}, \lambda_{2, A}) \leq C$. Theorem 1.2 is a consequence of several Theorems and propositions: Theorem 3.1. There exists an entire solution for (1.6) such that $ U(x) = V(-x) $. Proof We argue as in [5], up to technical arguments due to the non linearity of the $ p $-Laplacian, and due to the singularity ($ p < 2 $) or the degeneracy ($ p > 2 $). Let us consider for $ R $ large the variational problem \[ \inf_{\{(U,V) \in H^1([-R,R],[U(x)=V(-x),U(-R)=0, U(R)=R]\}} \frac{1}{p} \int_{-R}^{R} \|U'\|^p + \frac{1}{p} \int_{-R}^{R} \|V'\|^p + \frac{1}{p} \int \|U\|^p \|V\|^p. \] This problem admits a unique solution $(U_R, V_R)$. We prove that $ U_R $ is non negative. Indeed one has \[ \|U'_R\|^{p-2}U''_R = \|U_R\|^{p-2}U_R V_R\|^p, \] and a symmetric equation for $ V_R $. Multiplying by $ U_R^- $ and integrating by parts, using the fact that $ U_R(-R) $ and $ U_R(R) $ are nonnegative, one gets that $ U_R^- = 0 $ and then $ U_R \geq 0 $. The same is valid for $ V_R $. By the strong maximum principle of Vasquez [27], $ U_R > 0 $, on $[0, R], U'_R (-R) > 0 $ and $ \|U'_R\|^{p-2}U''_R $ is increasing implies that $ U'_R > 0 $ everywhere, finally $ U''_R \geq 0 $. Analogously $ V'_R < 0 $, then $ U_R - V_R $ vanishes only on zero. $ U_R - V_R > 0 $ on $[0, R] $ implies that $ \|U'_R\|^{p-2}U''_R - \|V'_R\|^{p-2}V''_R = U''_R - V''_R \leq 0 $ on $[0, R] $. First case $ p \geq 2 $. Using $ V'_R(x) = -U'_R(-x) $ one has for $ x > 0 $ $ \|V'_R\|(x) = U'_R(-x) < U'_R(x) $ and then $ \|U'_R\|^{p-2}U''_R \leq \|V'_R\|^{p-2}V''_R $ which implies since $ U'_R > 0 $, that $ U''_R - V''_R \leq 0 $. From this one gets that $ U_R \geq V_R + x $ for $ x > 0 $. Indeed on 0, $ U_R(0) = V_R(0) \geq V_R(0) + x $ and on $ R, U_R(R) = R \geq V_R(0) + R = R $, in particular $ U_R(x) > x $ for $ x > 0 $. We have obtained that \[ \|V'_R\|^{p-2}V''_R \geq (x^+)^{p-1} \quad \text{since } V''_R \geq 0 \text{ anywhere else, in particular on } \mathbb{R}^-. \] Let $ \tilde{V} $ be the solution, (given by Lemma (4.3)), of \[ \|\tilde{V}'\|^{p-2}\tilde{V}'' = x^p \|\tilde{V}\|^{p-2} \tilde{V}, \] on $ \mathbb{R}^+ $, which is positive and satisfies $ \tilde{V}'(0) = -2 $. Let us extend $ \tilde{V} $ on $ \mathbb{R}^- $ by the linear function $-2x + \tilde{V}(0)$. Since $ \tilde{V} $ hence defined is $ C^2 $ and is a solution of \[ \|\tilde{V}'\|^{p-2}\tilde{V}'' = (x^+)^{p} \|\tilde{V}\|^{p-2} \tilde{V} \] on both $ \mathbb{R}^+ $ and $ \mathbb{R}^- $, one gets that it is a solution on $[0, R] $. For $ R $ large enough, $ V_R(-R) = R \leq -2(-R) + \tilde{V}(0) = \tilde{V}(-R) $, while $ V_R(R) = 0 \leq \tilde{V}(R) $ since $ \tilde{V} $ is positive. Using the comparison principle, since $ \tilde{V} $ and $ V_R $ are respectively solution and sub-solution of the same equation, one gets that $V_R \leq \tilde{V}$ on $[-R, R]$. Using Harnack’s inequality, one gets that $(U_R, V_R)$ tends to a non trivial solution (since $U_R \geq x^+$), $(U, V)$ which satisfies $V(x) = U(-x)$. Second case $p < 2$: We begin to prove that $U_R'(x) \geq \frac{1}{1+2^{\frac{1}{p-1}}}$ for $x > 0$. Note that for $x > 0$ $$(U_R')^{p-1} \leq \|V_R'\|^{p-2}V_R'(x) + 2(U_R'(0))^{p-1}$$ which implies that $U_R'(x) \leq 2^{\frac{1}{p-1}}U_R'(0)$. Hence $U_R(R) = R \leq U_R(0) + 2^{\frac{1}{p-1}}RU_R'(0)$ On the other hand when $x \in \mathbb{R}^-$ $$U_R'(x) \leq U_R'(0)$$ which implies by the mean value’s theorem that $U_R(0) \leq U_R(-R) + U_R'(0)R$. We have obtained that $$U_R'(0) \geq \frac{1}{1+2^{\frac{1}{p-1}}}$$ as soon as $R$ is large enough. We derive from this that on $\mathbb{R}^+$ $\|V_R'\|^{p-2}V_R'' \geq \left(\frac{1}{1+2^{\frac{1}{p-1}}}\right)^p (x^+)pV_R^{p-1}$. We now consider the solution $\tilde{V}$ of $\|\tilde{V}'\|^{p-2}\tilde{V}'' = \left(\frac{1}{1+2^{\frac{1}{p-1}}}\right)^p x^p \tilde{V}^{p-1}$ on $\mathbb{R}^+$, $\tilde{V} > 0$ given by Proposition 4.1 which satisfies $\tilde{V}'(0) = -2$, extended by $-2x + \tilde{V}(0)$ on $\mathbb{R}^-$. One obtains as in the case $p \geq 2$ that $V_R \leq \tilde{V}$ and by Harnack’s inequality, one gets that $(U_R, V_R)$ tends locally uniformly to $(U, V)$ which is not identically zero. Lemma 3.2. Suppose that $(U, V)$ satisfies (1.6). Then either $U' > 0$ and $V' < 0$ or $U' < 0$ and $V' > 0$. Furthermore there exists some constant $C$ such that $\|U'\|^p + \|V'\|^p \leq C$. Proof Clearly the identity $$\|U'\|^p + \|V'\|^p - U^pV^p = T_\infty$$ holds for some finite constant $T_\infty$. Since $U'' \geq 0$, either $U' > 0$ or $U' < 0$ or there exists $x_1$ such that $U''(x) > 0$ for $x > x_1$ and conversely for $x < x_1$, and the same for $V'$. 12 Suppose that $ U' $ and $ V' $ have the same sign somewhere, then if this sign is positif, by the increasing behavior of $ U' $ and $ V' $, it is true also for $ x $ large. In particular $ U(+\infty) = V(+\infty) = +\infty $. The case $ p \geq 2 $ Let $ \varphi = U + V $. For $ x $ large enough, $\|\varphi'\|^{p-2} = (\|U'\| + \|V'\|)^{p-2} \geq c(\|U'\|^{p-2} + \|V'\|^{p-2})$ and then $\|\varphi'\|^{p-2}\varphi'' \geq c(\|U'\|^{p-2} + \|V'\|^{p-2})(U'' + V'') \geq c(\|U'\|^{p-2}U'' + \|V'\|^{p-2}V'') \geq 2^{p-1}(V^p + U^p) \geq (U + V)^p$ as soon as $ x $ is large enough since $ U $ and $ V $ go to infinity. Then $\|\varphi'\|^{p-2}\varphi'' \geq \varphi^p$, for $ x $ large enough. Multiplying by $ \varphi' \geq 0 $, one gets that $ \frac{d^2}{dx^2}(\|\varphi'\|^p) \geq c\frac{d^1}{dx}(\|\varphi'\|^{p+1}) $. Then $(\varphi')^p \geq c(\varphi^{p+1} + 1)$, and since $ \varphi $ tends to infinity, for $ x $ large enough, $(\varphi')^p(x) \geq \frac{p(p+1)}{2} $. This implies $ \varphi' \geq c\varphi^{\frac{p+1}{p}} $, and then for $ x $ large enough, $ \frac{d}{dx}(-\varphi^-\frac{1}{p}) \geq c_p $, which would imply that $ \varphi $ becomes negative for $ x $ large enough. The case $ p < 2 $ Let $ \varphi = ((U')^{p-1} + (V')^{p-1})^{\frac{1}{p-1}} $, note that $ \varphi^{p-1} = (U')^{p-1} + (V')^{p-1} $, that $ \varphi \geq U' + V' $ and $ \varphi \leq 2^{\frac{1}{p-1}}(U' + V')^p $. One has \[ (\varphi^{p-1})' = \frac{d}{dx}((U')^{p-1} + (V')^{p-1}) \\ = (p-1)(U'^{p-1}V + V'^{p-1}U) \\ \geq (V + U)^p, \] for $ x $ large by the behavior at infinity of $ U $ and $ V $. Multiplying by $ U' + V' > 0 $ one obtains that \[ \left( \frac{d}{dx}(\varphi^{p-1}) \right)(U' + V') \geq \frac{1}{p + 1} \frac{d}{dx}((V + U)^{p+1}). \] On the other hand, by the positivity of $ \frac{d}{dx}(\varphi^{p-1}) $, and $ U' + V' $ one has \[ \frac{d}{dx}(\varphi^{p-1})(U' + V') \leq \frac{p-1}{p} \frac{d}{dx}(\varphi^p) \] hence integrating and using the fact that $ U + V $ goes to infinity when $ x $ goes to $ +\infty $, one gets that there exists some constant $ c_p $ such that for $ x $ large enough \[ (U' + V')^p \geq c_p \varphi^p \geq c_p(U + V)^{p+1} \] We end as in the case $ p \geq 2 $ and get an absurdity. If the sign of $U'$ and $V'$ are both negative somewhere they are both negative for $x < -x_1$. By considering the invariance of the equation by changing $x$ in $-x$, and reasoning as above one gets a contradiction. We have obtained that up to exchanging $U$ and $V$, $U' > 0$ and $V' < 0$. Suppose that $U' \to +\infty$ somewhere, then it occurs at $+\infty$ since $U'$ is increasing, in particular $U$ goes to $+\infty$ at $+\infty$, and using \[3.1\] so does $UV$. Then $(V'\|V'\|^{-2})' = (p-1)(UV)^{p-1}U \to +\infty$, which implies that $V'$ goes to $+\infty$ at $+\infty$, a contradiction with $V' < 0$. We have obtained that $U'$ is bounded. If $V' \to -\infty$ somewhere, it occurs at $-\infty$, then $V$ goes to $+\infty$ at $-\infty$, by \[3.1\] $UV$ goes to $+\infty$ at $-\infty$ and $\|U'\|^{-2}U' = (UV)^{p-1}V \to +\infty$ at $-\infty$, hence $U'$ becomes $< 0$ for $x$ large negative, a contradiction. We have obtained that $\|U'\| + \|V'\| \leq C$. Proposition 3.3. let $(U, V)$ be a solution such that $U' > 0$ and $V' < 0$. Then $V^pU^{p-1} \to 0$, $U^pV^{p-1} \to 0$ at $\pm\infty$. Furthermore the following assertions hold: $$ U(-\infty) = 0, U'(-\infty) = 0, U'(+\infty) = (T_\infty)^{1\over p}, \quad (3.2) $$ $$ V(+\infty) = 0, V'(+\infty) = 0, V'(-\infty) = -(T_\infty)^{1\over p} \quad (3.3) $$ Proof Since $d\over dx(\|U'\|^{-2}U') \geq 0$, and $d\over dx(\|V'\|^{-2}V') \geq 0$, $U'$ and $V'$ have a limit at infinity. Furthermore $V' \leq 0$ and is increasing so it converges at $+\infty$. Its limit must be zero since if not for $x$ large enough, $V' \leq -m < 0$ and $V$ would become negative for $x$ large. By Lemma 1.2, $U'$ is bounded. Furthermore it has a positive finite limit at infinity, and by \[3.1\] it-s so does $U^pV^p$. Then $U$ goes to infinity, more precisely $U$ behaves like an increasing linear function. Then $U^{p-1}V^p = {1\over b}(U^pV^p) \to 0$. Furthermore for $x > x_o$ and $x_o$ large, $\|V'\|^{-2}V'' - V^{p-1} \geq 0$. Let us consider $W = V(x_o)e^{-x+x_o}$ which satisfies $\|W'\|^{-2}W'' - W^{p-1} \leq 0$. Using lemma 4.1 in the appendix one gets that $V \leq W$ on $[x_o, \infty]$ and then $\lim_{x \to +\infty} UV = 0$ as well as $\lim_{x \to +\infty} U^pV^{p-1} = 0$. Since $V' \to 0$ at infinity, \[3.1\] implies that $\|U'\|p(+\infty) = T_\infty$. In particular $T_\infty > 0$. A symmetric result holds near $-\infty$ exchanging $U$ and $V$. Lemma 3.4. Let $U$ and $V$ be as in Proposition 3.3. There exist some positive constants $m, M, k, K$ which depend on $T_\infty$, such that $$ me^{-Kx^2} \leq U(x) \leq Me^{-kx^2} $$ 14 and some positive constants $c$, $C$ such that $c\|x\|U(x) \leq U'(x) \leq C\|x\|U(x)$, for $x$ large negative, and analogous inequalities for $v$ near $+\infty$. Furthermore $U$ has two asymptotic lines $y = 0$ at $-\infty$ and $y = (T_\infty)^{\frac{1}{p}}x + b_1$ for some $b_1 \in \mathbb{R}$, at $+\infty$. Similarly $V$ has asymptotic lines $0$ at $+\infty$ and $y = -(T_\infty)^{\frac{1}{p}}x + b_2$ for some $b_2$ at $-\infty$. Remark 3.5. The constant $k$ and $K$ can be explicitly determined in function of $T_\infty$. Proof: Let $k$ be such that $V(x) \geq 2k\|x\|$ near $-\infty$, define $W(x) = C e^{-k\|x\|^2}$ which satisfies $\|W'\|^{p-2}W'' \leq V^pW^{-1}$ for $x$ large enough negative, where the constant has been chosen in order that $W(-M) = U(-M)$, and $M$ is large enough $> 0$. By Lemma 3.1, using the fact that $W'$ and $U'$ are bounded, one gets that $U \leq W$. The lower bound can be obtained by considering some $K$ such that near $-\infty V(x) \leq K\|x\|$. Consider $W(x) = C e^{-K\|x\|^2}$ where $C$ is chosen so that $W(-M) = U(-M)$ and $M$ is large. $\|W'\|^{p-2}W'' \geq V^pW^{-1}$ as soon as $x$ is large enough negative. From this one derives that $W \leq U$. We prove the assertions concerning $U$ and $U'$. We begin to prove that $U' \geq U$ for $x$ large negative. Indeed let us observe that for $\|x\|$ large negative $\|U'\|^{p-2}U'' \geq U^{-1}$ and then multiplying by $U'$ and integrating, using $U(-\infty) = U'(-\infty) = 0$, one obtains $(U')^p \geq U^p$. To prove a better estimate, observe that by the behavior of $V$ at $-\infty \|U'\|^{p-2}U'' \geq C\|x\|^pU^p$. We multiply by $U'$ and prove that $\int_{-\infty}^{-x} \|t\|^p U^{-1}(t)U'(t)dt \geq C\|x\|^pU^p$ Indeed $\int_{-\infty}^{-x} \|t\|^p U^{-1}(t)U'(t)dt = \int \|t\|^p \frac{U(t)}{p} \frac{-x}{p} dt + \int_{-\infty}^{-x} \|t\|^{p-1} U(t)dt = \|x\|^{\frac{p}{p}(-x)} + \int_{-\infty}^{-x} \|t\|^{p-1} U(t)dt \geq \|x\|^{\frac{p}{p}(-x)}$, from this one yields $$\int_{-\infty}^{-x} \|t\|^p U^{-1}(t)U'(t)dt \geq \|x\|^{\frac{p}{p}(-x)},$$ and then using the fact that near $-\infty$, $U'$ and $\|x\|^pU^p$ tend to zero, one gets that $(U')^p - C\|x\|^pU^p \geq 0$. In the same manner by the behaviour of $V$ at $-\infty$ there exists $C$ such that $\|U'\|^{p-2}U'' \leq C\|x\|^pU^{p-1}$, here we use $\int_{-\infty}^{-x} \|t\|^p U^{p-1}(t)U'(t)dt = \int \|t\|^p \frac{U(t)}{p} \frac{-x}{p} dt + \int_{-\infty}^{-x} \|t\|^{p-1} U(t)dt \leq \|x\|^{\frac{p}{p}(-x)} + \frac{1}{\|x\|} \int_{-\infty}^{-x} \|t\|^p U^{p-1}(t)U'(t)dt$. From this as soon as $\|x\| > 2$, \[ \int_{-\infty}^{-x} \|t\|^p U^{p-1}(t) U'(t) dt \leq 2\|x\|^p \frac{U^p}{p}(-x). \] We have obtained the estimate on the right $U' \leq CU\|x\|$. To deduce from this the asymptotic of $U$ and $V$, we use the previous estimates on $U$ for $V$ near $+\infty$. So we have $\|V'\| \geq C\|x\| e^{-kx^2}$ and then by (3.1) one derives that $(U')^p - T_\infty \geq -C\|x\| e^{-p k x^2}$, hence $U'(x) - T_\infty \geq -C\|x\| e^{-kx^2}$ which implies by integrating that $U(x) - T_\infty x \geq -C$ for $x$ large positive. Since $U$ is convex, $(U' - T_\infty \frac{1}{p})$ is increasing and since it tends to $0$ at infinity, it is negative, hence $U - T_\infty \frac{1}{p} x$ is decreasing. Finally $U - (T_\infty \frac{1}{p}) x$ is decreasing and minorated, hence defining $b_1 = \lim_{x \to +\infty} (U - T_\infty \frac{1}{p} x)$, one has $(U - T_\infty \frac{1}{p} x) \geq b_1$. Of course a symmetric result holds for $V$. Proposition 3.6. Let $(U, V)$ be a solution of (1.1), with $U(0) = V(0) = 1$. Then $V(y) = U(-y)$. We assume that $U' > 0$, hence we are in the hypothesis of the previous propositions. We can assume that $b_1 \geq b_2$, since if not one can replace $(U(x), V(x))$ by $(V(-x), U(-x))$ which exchanges $b_1$ and $b_2$. We use the sliding method of Berestycki and Nirenberg, [2]. Let $I_\lambda = \{ x, x > \lambda \}$ and $U_\lambda(x) = U(2\lambda - x)$, $V_\lambda(x) = V(2\lambda - x)$ Let $w_1 = U - V_\lambda$, $w_2 = U_\lambda - V$. We prove in what follows that for $\lambda$ large enough and $x \in I_\lambda$, $w_1(x) > 0$ as well as $w_2 > 0$. From the asymptotic behaviour of $U$ and $V$, and since $U$ is convex, $U(x) \geq T_\infty \frac{1}{p} x + b_1$, and by the asymptotic behavior of $V$ there exists $K$ such that $V(x) \leq -T_\infty \frac{1}{p} x + K$, this implies that $w_1(x) \geq T_\infty \frac{1}{p} (x + (2\lambda - x)) + b_1 - K$ for $x \in I_\lambda$. So by taking $\lambda$ such that $\lambda T_\infty \frac{1}{p} > K - b_1$ one gets that if $x \in \lambda, 2\lambda$, $w_1(x) \geq T_\infty \frac{1}{p} (\lambda + 0) + b_1 - K > 0$ and for $x > 2\lambda$, $w_1(x) \geq T_\infty \frac{1}{p} (x + x - 2\lambda) + b_1 - K \geq 2\lambda T_\infty \frac{1}{p} + b_1 - K > 0$. We now derive from this that $w_2$ is also $> 0$ in the same $I_\lambda$ for large values of $\lambda$. Indeed, we have \[ \|U_\lambda'\|^{p-2} U_\lambda'' - \|V'\|^{p-2} V'' = U^p(U_\lambda^{p-1} - V^{p-1}) + U_\lambda^{p-1}(V^p - U_p). \] Multiplying this by $w_2^\gamma$, integrating between $\lambda$ and $x$ and using $(U_\lambda - V)(\lambda) = (U - V)(\lambda) = w_1(\lambda) > 0$ one gets implies that $ \lambda $ behaviour, there exists $ w $ strong maximum principle $ \lambda < $ has if \[ - \int_\lambda^x (\|U'_\lambda\|^{p-2}U'_\lambda - \|V'\|^{p-2}V')(w_2^-)' + \left[ \frac{1}{p-1}(\|U'_\lambda\|^{p-2}U'_\lambda - \|V'\|^{p-2}V')(w_2^-) \right]_\lambda^x \\ = \int_\lambda^x U^p(U_{-1}^p - V^{p-1})w_2^- \\ + \int_\lambda^x U_{-1}^p(V - U)p)w_2^- \\ \leq 0 \] Using $- \int_\lambda^x (\|U'_\lambda\|^{p-2}U'_\lambda - \|V'\|^{p-2}V')(w_2^-) \geq 0, w_2^- (\lambda) = 0 $ and $ w_2(\infty) = 0 $, as well as the fact that $ U' $ and $ V' $ are bounded, letting $ x $ go to infinity, one gets that $ w_2^- = 0 $ and then $ w_2 > 0 $ for $ x \in I_\lambda $ and $ \lambda $ large enough. We now define $ \lambda^* = \inf\{\lambda > 0, w^\mu_1(x) > 0 \text{ in } I_\mu, \text{ for all } \mu > \lambda\} $. By the previous observations $ w^\mu_2 > 0 $ in $ I_\mu $ for all $ \mu > \lambda^* $. Since $ U(0) = V(0) = 1 $, one has if $ \lambda < 0 $, by the increasing behaviour of $ U - V $, $ (U - V)(\lambda) < 0 $, which implies that $ \lambda^* \geq 0 $. We want to prove that $ \lambda^* = 0 $. Let us observe that by continuity $ w^\lambda_1^* \geq 0 $ and $ w^\lambda_2^* \geq 0 $ on $ I_\lambda^* $. By the strong maximum principle $ w^\lambda_1^* > 0 $ and $ w^\lambda_2^* > 0 $ in $ I_\lambda^* $. By the asymptotic behaviour, there exists $ B_1 $ such that for $ x < B_1 < 0, V(x) + \frac{1}{\lambda_1^}x - b_2 < \frac{b_1 - b_2}{2} $. Take $ A = \sup(2\lambda^ - B_1, \lambda^) $ then for $ x > A $, and for $ 0 < \lambda < \lambda^ $, \[ V(2\lambda - x) + \frac{1}{\lambda_1^}(2\lambda - x) - b_2 < \frac{b_1 - b_2}{2}, \] hence for $ x > A $ and $ \lambda \in [0, \lambda^], w^\lambda_1^(x) - \frac{1}{\lambda_1^}2\lambda \geq \frac{b_1 - b_2}{2}. \] We now observe that \( \inf_{[\lambda^, A]} w^\lambda_1^ = m > 0 $, indeed $ w^\lambda_1^(\lambda^) = U(\lambda^) - V(\lambda^) > U(0) - V(0) $ since $ U' > 0, V' < 0, U(0) = V(0) $ and $ \lambda^* > 0 $. By the uniform continuity of $ V $ in a compact set, there exists $ \eta < \lambda^* $ such that for $ \|\lambda - \lambda^\| < \eta, $ for all $ x \in [\lambda^ - \eta, A], $ one has $ \|V(2\lambda^* - x) - V(2\lambda - x)\| \leq \frac{m}{2} $ and then for $ x > \lambda > \lambda^* - \eta $ and $ x < A, U(x) - V(2\lambda - x) \geq \frac{m}{2} $. Finally $ \inf_{[\lambda, \lambda^]} w^\lambda_1^ > 0 $ for $ \lambda^* - \eta < \lambda < \lambda^* $, and then $ w^\lambda_1^* > 0 $ on a neighborhood on the left of $ \lambda^* $. This contradicts the definition of $ \lambda^* $. We have obtained $ \lambda^* = 0 $ and then $ U(x) \geq V(-x) $ for $ x \geq 0 $. Since we have seen before that $ w^0_1 \geq 0 $ implies $ w^0_2 \geq 0 $, $ U(-x) \geq V(x) $ for $ x > 0 $. We have obtained that $ U(x) \geq V(-x) $ for $ x \in \mathbb{R} $. Since $ U(0) = V(0), U(x) - V(-x) $ reaches its minimum at zero. This implies that $ (w^0_1)''(0) = U'(0) + V'(0) = 0 $. By the strong comparison principle one gets that $ U(x) = V(-x) $. We have obtained in the same time that $ b_1 = b_2 $. Part 3) in Theorem 12 is contained in the Proposition 3.7. Suppose that $ \phi, \psi $ are bounded solutions of \[ \begin{align} \{ & (\|U'\|^{p-2} \phi')' = (p-1)U^{p-2}V'\phi + pU^{p-1}V'\psi \\ & (\|V'\|^{p-2} \psi')' = (p-1)V^{p-2}U'\phi + pU^{p-1}V'\phi. \end{align} \] Then there exists some constant $ c $ such that $ (\phi, \psi) = c(U', V') $. Proof For personal convenience we use minuscule letters $ (u, v) $ in place of $ (U, V) $. We do not distinguish the case $ p > 2 $ or $ p < 2 $ for the moment. Let $ \bar{\phi}, \bar{\psi} $ be defined as $ \phi = u'\bar{\phi}, \psi = v'\bar{\psi} $. One has \[ \begin{align} (\|u'\|^{p-2} \phi')' &= (\|u'\|^{p-2} u'') \bar{\phi} + p\|u'\|^{p-2} u'' \bar{\phi}' \\ & \quad + \|u'\|^{p-2} u'' \bar{\phi} \\ & = pu^{p-1} v' \bar{\phi} + pu^{p-1} v' \bar{\phi} + (p-1)u^{p-2} v' u' \bar{\phi} \\ & \quad + \|u'\|^{p-2} u'' \bar{\phi}. \end{align} \] On the other hand using the equation satisfied by $ \phi $ one gets \[ p\|u'\|^{p-2} u'' \bar{\phi}' + \|u'\|^{p-2} u' \bar{\phi}'' = pu^{p-1} v^{p-1} v' (\bar{\psi} - \bar{\phi}). \] In the same manner for $ v $ \[ p\|v'\|^{p-2} v'' \bar{\psi}' + \|v'\|^{p-2} v' \bar{\psi}'' = pu^{p-1} v^{p-1} v' (\bar{\phi} - \bar{\psi}). \] Multiplying the first equation by $ u' \bar{\phi} $ and the second one by $ v' \bar{\psi} $, one gets \[ p\|u'\|^{p-2} u' u' \bar{\phi} \bar{\phi}' + \|u'\|^{p} \bar{\phi} \bar{\phi}'' + p\|v'\|^{p-2} v' v' \bar{\psi} \bar{\psi}' + \|v'\|^{p} \bar{\psi} \bar{\psi}'' = -p(uv)^{p-1} u' v'(\bar{\psi} - \bar{\phi})^2. \] Let us now observe that \[ p\|u'\|^{p-2} u' u'' \bar{\phi} \bar{\phi}' + \|u'\|^{p} \bar{\phi} \bar{\phi}'' = (\|u'\|^{p} \bar{\phi} \bar{\phi}')' - \|u'\|^{p} (\bar{\phi}')^2. \] Claim: $ \|u'\|^{p} \bar{\phi} \bar{\phi}' $ and $ \|v'\|^{p} \bar{\psi} \bar{\psi}' $ go to zero at $ +\infty $ and $ -\infty $ This claim will end the proof since then we will have \[ 0 = \lim_{\infty} [(\|u'\|^{p} \bar{\phi} \bar{\phi}') + (\|v'\|^{p} \bar{\psi} \bar{\psi}')] = \int_{\mathbb{R}} \|u'\|^{p}(\bar{\phi}')^2 + \|v'\|^{p}(\bar{\psi}')^2 \\ - p \int_{\mathbb{R}} (uv)^{p-1} u' v' (\bar{\psi} - \bar{\phi})^2 \geq 0. \] and since $u'v' < 0$ this will imply $\bar{\phi}' = \bar{\psi}' = 0$ and $\bar{\phi} = \bar{\psi}$. In the sequel we prove the claim for $u$ and $\phi$. The result for $v$ and $\psi$ can be done by obvious symmetric arguments. Proof of the claim for $u$ and $\bar{\phi}$ \[ \|u'\|^p \bar{\phi} \bar{\phi}' = \|u'\|^{p-2}(u' \bar{\phi})(u' \bar{\phi}') \] \[ = \|u'\|^{p-2} \phi u' \left( \frac{\phi'}{u'} - \frac{\phi u''}{u'^2} \right) \] \[ = \|u'\|^{p-2} \phi \phi' - \|\phi\|^2 \frac{\|u'\|^{p-2} u''}{u'} \] \[ = \|u'\|^{p-2} \phi \phi' - \phi^2 \frac{u^{p-1}v^p}{u'} \] We consider separately the cases $+\infty$ and $-\infty$. The case $+\infty$. Since $u$ increases like a linear function, $u'$ is minorated by some positive constant and $v$ goes exponentially towards zero, the term $\phi^2 \frac{u^{p-1}v^p}{u'}$ on the right goes to zero. On the other hand $\|u'\|^{p-2} \phi'$ tends to zero. Indeed, its derivative is integrable for $x$ large by the asymptotic behavior of $u$ and $v$, and the fact that $\phi$ and $\psi$ are bounded. So it has a limit. Suppose that the limit is $l \neq 0$, then $\phi' \sim \frac{l}{T_\infty^p}$, this contradicts $\phi$ bounded. Finally $\lim_{x \to +\infty} \|u'\|^p \bar{\phi} \bar{\phi}'(x) = 0$. The case $-\infty$. We now distinguish the case $p \geq 2$ and $p < 2$ The case $p \geq 2$. Let us recall that there exist some positive constants $M, k, c$ such that near $-\infty$, $u \leq Me^{-kx^2}$, and $u' \geq c\|x\|u$ for $x$ large enough negative. In particular since $v$ is linear at infinity $\frac{\|u^{p-1}v^p\|}{u'} \leq c\|x\|^{p-1}e^{-(p-2)kx^2}$. Using $\phi$ bounded, one gets that $\phi^2 \frac{u^{p-1}v^p}{u'}$ goes to zero at $-\infty$. Furthermore $\|u'\|^{p-2} \phi'$ has a limit at $-\infty$ by the equation, if this limit was $\neq 0$, this would imply that $\phi'$ goes to $\pm \infty$ and would contradict $\phi$ bounded. All this implies that $\|u'\|^p \bar{\phi} \bar{\phi}'$ tends to zero at $-\infty$. The case $p < 2$ This case is much more involved and requires several steps. Step 1: There exists $t_p$ which goes to $-\infty$ such that $(\|u'\|^{p-2} \phi')(t_p) \to 0$. 19 Suppose for a while that there does not exist $ t_p $ which goes to $-\infty$ such that \[ \|u'\|^{p-2} \phi'(t_p) \to 0. \] Then there exists $ C > 0 $ such that for all $ t $ large negative either \[ (\|u'\|^{p-2} \phi')(t) \geq C \] or \[ (\|u'\|^{p-2} \phi')(t) \leq -C. \] One assumes that we are in the first case and will give at the end the arguments in the other case. Then $ \phi' > 0 $ near $-\infty$, hence $ \phi $ has a finite limit since $ \phi $ is bounded. We begin to prove that $ \phi $ tends to zero at $-\infty$. Suppose $ \phi $ does not tend to zero, then there exists $ m > 0 $ such that either $ \phi > m $ or $ \phi \leq -m $ for $ x $ large negative. In the first case for some constant $ c > 0 $ which can vary from one line to another, $ (\|u'\|^{p-2} \phi') \geq cu^{p-2} \geq cu^{p-2} \|x\|^p $ since the last term $ pu^{p-1}v^{p-1} \psi $ tends to zero. Integrating between $-x $ and $-x_o $ large negative, one gets for $ x > x_o $, \[ \|u'\|^{p-2} \phi'(-x_o) - \|u'\|^{p-2} \phi'(-x) \geq c \int_{-x_o}^{-x} u^{p-3}(t)u'(t)\|t\|^{p-1}dt \geq c\|x\|^{p-1}u^{-2}(-x). \] Indeed \[ \int_{-x}^{-x_o} u^{p-3}(t)u'(t)\|t\|^{p-1}dt = \frac{u^{p-2}\|t\|^{p-1}}{p-2} \|_{-x}^{-x_o} + \frac{p-1}{p-2} \int_{-x}^{-x_o} u^{p-2}(t)\|t\|^{p-2}dt \] \[ \geq \frac{u^{p-2}(-x)\|x\|^{p-1}}{p-2} - \frac{p-1}{(2-p)\|x\|^2} \int_{-x}^{-x_o} u^{p-3}u'\|t\|^{p-1}dt \] which implies that \[ \|u'\|^{p-2} \phi'(-x) \leq C_1 - C_2 \|x\|^{p-1}u^{p-2} \] and then in particular \[ \phi' \leq -C_3x^{2-p}x^{p-1} = -C_3x. \] This contradicts $ \phi $ bounded. In the same manner if $ \phi \leq -m < 0 $ one gets \[ \|u'\|^{p-2} \phi'(-x_o) - \|u'\|^{p-2} \phi'(-x) \leq -c\|x\|^{p-1}u^{p-2} \] which implies $ \phi' \geq C_3x $, this still contradicts $ \phi $ bounded. So we are in the hypothesis that $ \phi $ tends to zero and \[ \|u'\|^{p-2} \phi' \geq C > 0. \] Then $ \phi(x) \geq \int_{-\infty}^{-x} C(u')^{2-p}(t)dt \geq \int_{-\infty}^{-x} \|t\|^{1-p}u^{1-p}(t)u'(t)dt. \] Observe that \[ \int_{-\infty}^{-x} \|t\|^{1-p}u^{1-p}(t)u'(t)dt \geq c\|x\|^{1-p}u^{2-p}. \] Indeed \[ \int_{-\infty}^{-x} \|t\|^{1-p}u^{1-p}u'(t)dt = \frac{1}{2-p} \int_{-\infty}^{-x} \|t\|^{1-p} \frac{d}{dt}(u^{2-p})dt \] \[ = \frac{1}{2-p} \left[ \|t\|^{1-p}u^{2-p} \right]^{-x}_{-\infty} - \frac{p-1}{(2-p)\|x\|^2} \int_{-\infty}^{-x} \|t\|^{1-p}u^{1-p}u'(t)dt. \] This ends the proof by taking \( \|x\| $ large enough. We have obtained that \[ \phi(x) \geq C\|x\|^{1-p}u^{2-p} \] and replacing in the equation satisfied by $ \phi $ one gets \[ \|u'\|^{p-2} \phi'(-x_o) - \|u'\|^{p-2} \phi'(-x) \geq C \int_{-x_o}^{-x} \|t\|^{1-p}\|t\|^{p}dt = C\|x\|^2. \] From this one derives that $\|u'\|^{p-2}\phi'(-x) \leq -Cx^2$, a contradiction with the assumption. The case where $\|u'\|^{p-2}\phi(-x) \leq -C < 0$ for $x$ large enough can be recovered by changing $\phi$ in $-\phi$, noting the fact that the previous computations do not use the sign of $\psi$. We have obtained that there exists $t_p$ which goes to $-\infty$, such that $(\|u'\|^{p-2}\phi')(t_p) \to 0$. Step 2: $(u')^{p-2}\phi\phi'$ and $u^{p-1}\phi' v$ both tend to zero at $-\infty$. We multiply the equation satisfied by $\phi$, by $\phi$ and integrate between $t_p$ and $t_{p+1}$, where $t_p$ is some subsequence decreasing to $-\infty$, given by step 1. One obtains \[ [u'\|^{p-2}\phi\phi']_{t_{p+1}}^{t_p} = \int_{t_{p+1}}^{t_p} ((p-1)u^{p-2}v^p\phi^2 + \|u'\|^{p-2}(\phi')^2) + \int_{t_{p+1}}^{t_p} pu^{p-1}v^{p-1}\phi\psi, \] and since $u^{p-1}v^{p-1}\phi\psi$ is absolutely integrable by the estimates on $u$ and $v$ one gets with the positivity of $(p-1)u^{p-2}v^p\phi^2 + \|u'\|^{p-2}(\phi')^2$ and summing on $p$ that $u^{p-2}v^p\phi^2$ and $\|u'\|^{p-2}(\phi')^2$ are integrable. Finally for all $s$ and $t$ going to $-\infty$ $[u'\|^{p-2}\phi\phi']_{t}^{s}$ tends to zero, hence $\|u'\|^{p-2}\phi\phi'$ has a limit, and since it possesses a subsequence which tends to zero, this limit is zero. We now prove that $\phi^2 u^{p-1}v^p$ has a finite limit. For this it is enough to prove that its derivative is integrable at $-\infty$. \[ (\phi^2 u^{p-1}v^p)' = (\phi^2) \left( \frac{u^{p-1}v^p}{u'} \right)' + 2\phi\phi' u^{p-1}v^p \] \+ \[ (p-1)u^{p-2}v^p + \frac{u^{p-1}v^p - (u')^2}{u'} \phi^2 + 2\phi\phi' u^{p-1}v^p \] \=\n \[ (p-1)u^{p-2}v^p + \frac{u^{p-1}v^p - (u')^2}{u'} - u''(u')^{p-2} \left( \frac{u}{u'} \right) v^p \phi^2 + 2\phi\phi' u^{p-1}v^p \] \=\n \[ (p-1)u^{p-2}v^p + \frac{u^{p-1}v^p - (u')^2}{u'} - u^{p-2}v^p \left( \frac{u}{u'} \right)^{p-2} \phi^2 + 2\phi\phi' u^{p-1}v^p. \] Each of the first three terms above can be majorized near $-\infty$ by $Cu^{p-2}v^p\phi^2$ and then are integrable near $-\infty$. Lemma 4.1. We begin with the comparison principle used in section 3. For $(\phi^2)' \frac{u^{p-2}}{\partial u} $ we use Cauchy Schwarz’s inequality as follows \[ \left\| \phi' \frac{u^{p-1}}{u'} \right\| = \|\phi'\| u' \left\| \frac{u^{p-2}}{\partial u} u^{p-1} \phi \right\| \\ \leq C \|\phi'\| (u')^{\frac{p-2}{2}} \|xu\|^{\frac{p}{2}} u^{p-1} \phi \| \\ \leq C \|\phi'\| (u')^{\frac{p-2}{2}} \|x\|^{\frac{p}{2}} \|\phi\| \\ \leq C (\phi')^2 (u')^{p-2} + C v^p u^{p-2} \phi^2 \] We deduce that since $\phi^2 u^{p-2} v^p$ is integrable near $-\infty$, so is $\phi^2 u^{p-1} v^p$ and then it tends to zero. Of course we would obtain symmetric properties for $\psi$ and $v$ near $+\infty$. This ends the proof. 4 Appendix : Global existence uniqueness and qualitative results for solutions of $ \|y'\|^{p-2} y'' = x^p \|y\|^{p-2} $ on $ \mathbb{R}^+ $ We begin with the comparison principle used in section 3. Lemma 4.1. Suppose that $a$ is some continuous and bounded function such that $a(x) > 0$ for $x > x_o$. Suppose that $W'$ and $V'$ are bounded at infinity, that $W(x_o) = V(x_o)$, or $W'(x_o) = V'(x_o)$, $\lim_{x \to +\infty} W(x) = \lim_{x \to +\infty} V(x) = 0$, and $\|W'\|^{p-2} W'' - a(x)\|W\|^{p-2} W \leq 0$ for $x > x_o$, $ \|V'\|^{p-2} V'' - a(x)\|V\|^{p-2} V \geq 0 $. Then $V \leq W$ for $x > x_o$. Proof : Let us multiply the difference of the equations satisfied by $V$ and $W$, by $(V-W)^+$ and integrate by parts, one gets $\int_{x_o}^x (\|V'\|^{p-2} V'' - \|W'\|^{p-2} W'')((V-W)^+) + \int_{x_o}^x a(t)(\|V\|^{p-2} V - \|W\|^{p-2} W)(V-W)^+ (t) dt \leq 0$. Passing to the limit when $x$ goes to infinity and using $(\|V'\|^{p-2} V'' - \|W'\|^{p-2} W'')((V-W)^+) > 0$ one gets in particular that $\int_{x_o}^x a(t)(\|V\|^{p-2} V - \|W\|^{p-2} W)(V-W)^+ (t) dt = 0$ and then $V \leq W$ on $[x_o, +\infty]$. Proposition 4.2. For $(y_o, y_1)$ given there exists a unique global solution on $\mathbb{R}^+$ of \[ \|y'\|^{p-2} y'' = x^p \|y\|^{p-2} y, \ y(0) = y_o, \ y'(0) = y_1. \] Proof of Proposition 4.2 We begin to prove local existence and uniqueness of solutions. Suppose that $ x_0 \geq 0 $. Let $ y_0 = y(x_0) $, $ y_1 = y'(x_0) $. If $ y'(x_0) \neq 0 $, Cauchy Lipschitz theorem can be applied and provides local existence and uniqueness of the solution. Suppose that $ y_0 = y_1 = 0 $. Then we use some strict maximum principle to get that $ y \equiv 0 $ on the right and the left of $ x_0 $. Suppose indeed that $ y $ is not identically zero. We begin to prove that if $ y(x_0 + h) > 0 $ for some $ h > 0 $, then $ y \geq 0 $ on $ [x_0, x_0 + h] $. We multiply the equation by $ y^- $ and integrate between $ x_0 $ and $ x_0 + h $, we get \[ \int_{x_0}^{x_0 + h} \gamma \|y'\|^{p-2}y'(-y') - p \int_{x_0}^{x_0 + h} x^p \|y\|^{p-2}yy^- + \|\|y'\|^{p-2}y'(-y')\|_{x_0}^{x_0 + h} = 0 \] and since $ y^- = 0 $ on $ x_0 $ and $ x_0 + h $ one obtains \[ \int_{x_0}^{x_0 + h} \|(y^-)'\|^{p-2} + p \int_{x_0}^{x_0 + h} x^p \|y\|^{p-2} \|y^-\| = 0 \quad \text{and} \quad y^- = 0 \quad \text{on} \quad [x_0, x_0 + h]. \] So we are in the situation where $ y \geq 0 $ on $ [x_0, x_0 + h] $. We prove that if $ y $ is not identically zero on the right, there is a contradiction with $ y'(x_0) = 0 $. Let $ \gamma $ be such that $ \gamma > x $ on $ [x_0, x_0 + \delta] $, $ \beta $ such that $ \beta(e^{\gamma \delta} - 1) < y(x_0 + \delta) $, and consider $ w = \beta(e^{\gamma (x-x_0)} - 1) $. Then $ w \leq y $ on $ \{x_0\} $ and on $ \{x = x_0 + \delta\} $, and \[ \|w'\|^{p-2}w'' > x^p \|w\|^{p-2}w. \] By the classical comparison principle one gets that $ u \geq w $ on $ [x_0, x_0 + \delta] $, which implies that \[ \liminf \frac{y(x_0 + h) - y(x_0)}{h} \geq \liminf \frac{w(x_0 + h) - w(x_0)}{h} = \gamma \beta > 0 \] and contradicts $ y'(x_0) = 0 $. Doing the same on the left, one gets that $ y \equiv 0 $. We now suppose that $ y_1 = 0 $ and $ y_0 \neq 0 $. We use the fixed point theorem to obtain existence and uniqueness of solution. One can suppose without loss of generality that $ y_0 = 1 $. In the following we suppose first that $ x_0 \neq 0 $, and will give at the end the changes to bring when $ x_0 = 0 $, considering only the right hand side. Define for $ y \in B_{x_0,\delta}(1, \frac{1}{2}) := \{y \in C([x_0-\delta, x_0+\delta]), \|y-1\|_{C([x_0-\delta, x_0+\delta])} \leq \frac{1}{2}\} $. Let us define the function $ \phi $ as $ \phi(Z) = \|Z\|^{p-1} $, and the operator $ T $ as \[ T(y)(x) = 1 + \int_{x_0}^{x} \phi(\int_{x_0}^{t} (p-1) s^p \|y\|^{p-2} y(s) ds) dt. \] We prove in what follows that one can choose $ \delta $ small enough in order that $ T $ sends $ B_{x_0,\delta}(1, \frac{1}{2}) $, into itself and is contracting in that ball. Indeed we use for $ y $ in $ B_{x_0,\delta}(1, \frac{1}{2}) $ \[ (p-1)(\|x_0-\delta\|)^p \|t-x_0\| \left( \frac{1}{2} \right)^{p-1} \leq \int_{x_0}^{t} (p-1) s^p \|y\|^{p-2} y(s) ds \leq (p-1)(\|x_0+\delta\|)^p \|t-x_0\| \left( \frac{3}{2} \right)^{p-1}. \] Using the mean value’s theorem, denoting $ Y_i(t) = \left( \int_{x_0}^{t} (p-1) s^p \|y_i\|^{p-2} y_i(s) ds \right) $ for $ i = 1, 2 $, one gets that for some $C$ independent on $\delta$ $$\|\phi(Y_1(t)) - \phi(Y_2(t))\| \leq \|Y_1(t) - Y_2(t)\|\|t - x_o\|\frac{1}{p^{-1}}.$$ We now observe that $\|Y_1(t) - Y_2(t)\| \leq (p-1)(\|x_o\| + \delta)^p \left(\frac{3}{2}\right)^{p-2} \|\|y_1 - y_2\|\|_{\infty}\|t - x_o\|$, from this one derives that $$\|\phi(Y_1(t)) - \phi(Y_2(t))\| \leq C\|\|y_1 - y_2\|\|_{\infty}\|t - x_o\|\frac{1}{p^{-1}},$$ and then for $x > x_o$ $$\int_{x_o}^{x} \|\phi(Y_1(t)) - \phi(Y_2(t))\|dt \leq C\|\|y_1 - y_2\|\|_{\infty}\|x - x_o\|\frac{1}{p^{-1}}.$$ In particular choosing $\delta$ such that $C\delta\frac{1}{p^{-1}} < \frac{1}{2}$, the map $T$ is contracting. Under the same condition $T$ maps $B_{x_o,\delta}(1, \frac{1}{2})$ into itself. Then it possesses a unique fixed point. Since any solution is around $x_o$ a fixed point of $T$ we have obtained the local existence and uniqueness. We now give the changes to bring when $x_o = 0$. Define for $y \in B_{0,\delta}(1, \frac{1}{2}) := \{y \in C([0, \delta]), \ \|y - 1\|_{C[0, \delta]} \leq \frac{1}{2}\}$, $T(y) = 1 + \int_0^t \phi(\int_0^t (p-1)s^p\|y\|^{p-2}y(s)ds)dt$. We prove in what follows that one can choose $\delta$ small enough in order that $T$ send $B_{0,\delta}(1, \frac{1}{2})$, into itself and is contracting in this ball. Indeed we use for $y$ in that ball $\frac{p-1}{p+1}\left(\frac{1}{2}\right)^{p-1} t^{p+1} \leq \|\int_0^t (p-1)s^p\|y\|^{p-2}y(s)ds\| \leq \frac{p-1}{p+1}\left(\frac{3}{2}\right)^{p-1}$ and by the mean value’s theorem, denoting $(\int_0^t (p-1)s^p\|y\|^{p-2}y(s)ds) = Y_i(t)$, one gets $$\|\phi(\int_0^t (p-1)s^p\|y\|^{p-2}y_1(s)ds) - \phi(\int_0^t (p-1)s^p\|y\|^{p-2}y_2(s)ds)\| $$ $$\leq \|Y_1(t) - Y_2(t)\|Ct^{\frac{p+1}{p+1}-(p+1)}$$ We now observe that $\|Y_1(t) - Y_2(t)\| \leq (p-1)(\|x_o\| + \delta)^p \left(\frac{3}{2}\right)^{p-1} \|\|y_1 - y_2\|\|_{\infty}\|t\|^{p+1}$, from this one derives that $$\|\phi(Y_1(t)) - \phi(Y_2(t))\| \leq C\|\|y_1 - y_2\|\|_{\infty}\|t\|^{\frac{p+1}{p+1}}$$ and then for $x > 0$ $$\int_0^x \|\phi(Y_1(t)) - \phi(Y_2(t))\|dt \leq C\|\|y_1 - y_2\|\|_{\infty}\|x\|^{\frac{2p}{p+1}}.$$ 24 In particular choosing δ such that $C\delta^{\frac{2p}{p-1}} < \frac{1}{2}$, the map $T$ is contracting. Under the same condition $T$ maps $B_{0, \delta}(1, \frac{1}{2})$ into itself. We want to prove global existence. For that aim, suppose that there exists $\bar{x}$ such that either $y'(\bar{x}) = +\infty$ or $y(\bar{x}) = +\infty$. If $y(\bar{x}) < \infty$, $\|y'\|^{p-2}y' = \|y'\|^{p-2}y'(\bar{x} - h) + \int_{\bar{x} - h}^{\bar{x}} pt^{p-1}\|y'\|^{p-2}y(t)\,dt$ then $\lim_{x \to \bar{x}} y'(x)$ is finite and we get local existence after $\bar{x}$, so we can assume that $y(\bar{x}) = +\infty$. We begin to observe that by continuity $y > 0$ in a neighborhood on the left of $\bar{x}$, and then by the equation $\|y'\|^{p-2}y'$ is increasing on the left of $\bar{x}$, hence has a limit for $x \to \bar{x}$, $x < \bar{x}$. Suppose for a while that this limit is $L \leq 0$. Then one would have for $x < \bar{x}$ $$\|y'\|^{p-2}y'(x) = L + (p - 1) \int_{\bar{x}}^{x} t^{p-1}\|y'\|^{p-1}\,dt < 0.$$ Then $y(x) > y(\bar{x}) = +\infty$ a contradiction. We have obtained that $\lim_{x \to \bar{x}} y'(x) = L > 0$. We now write using the equation and the increasing behaviour of $y$ on $[x_o, \bar{x}]$, $(y')^{p-1}(x) \leq (y')^{p-1}(x_o) + (p - 1) \int_{x_o}^{x} t^{p-1}\|y'\|^{p-1}\,dt \leq (y')^{p-1}(x_o) + (p - 1)y^{p-1}(x)(\bar{x})^{p+1}$. This implies that $y'(x) \leq \sup(2^{\frac{2-p}{p-1}}, 1)(y'(x_o)+(p-1)(\bar{x})^{\frac{p+1}{p-1}}y(x))$, and by integrating between $x_o$ and any $x < \bar{x}$, $\int_{x_o}^{x} \frac{y'(t)\,dt}{y'(x_o)+(p-1)(\bar{x})^{\frac{p+1}{p-1}}y(t)} \leq \sup(2^{\frac{2-p}{p-1}}, 1)(x-x_o)$, which implies that $\log(y'(x_o)+(\bar{x})^{\frac{p+1}{p-1}}y(x)) \leq C(x-x_o)$ and this contradicts the fact that $y(\bar{x}) = +\infty$. We have obtained that $y$ is defined on $\mathbb{R}^+$. We now consider the equation $$V''\|V'\|^{p-2} = x^p\|V'\|^{p-2}V$$ and suppose that $V(0) < 0$. Then either $V \leq 0$, or there exists $\bar{x}$ such that for $x > \bar{x}$, $V > 0$. Indeed, if we contradict this fact, there exists $\bar{x}_1$ which is such that $V(\bar{x}_1) > 0$ and it is a local maximum for $V$. Then $V'(\bar{x}_1) = 0$. Since $V'$ is increasing around $\bar{x}_1$ by the equation, $V'(x) < 0$ for $x < x_1$, $V'(x) > 0$ for $x > x_1$, which contradicts the fact that $x_1$ is a local maximum. So we are in the hypothesis that $V(x) \geq 0$ for $x$ large and by the strict maximum principle $V > 0$, hence $V'$ is increasing in particular either it is negative and in that case necessarily tends to zero, or $V' > 0$ somewhere and then it remains $> 0$, which implies that $V$ goes to infinity at $+\infty$. We want to prove that it is possible to choose $V(0) > 0$ in order that for $V'(0) = -2$, the solution satisfy $V > 0$ on $[0, \infty]$, and $V$ and $V'$, tend to zero at infinity). Lemma 4.3. There exists a solution which satisfies on $\mathbb{R}^+$ $$\|y'\|^{p-2}y'' = t^p y^{p-1},$$ which is positive and satisfies $y'(\infty) = y(\infty) = 0$. Furthermore, for $y_1 < 0$ given, there exists a unique positive solution as above with the initial condition $y'(0) = y_1$. We use the existence of a sub- and a supersolution on $[0, \infty]$ which satisfies $y'(\infty) = y(\infty) = 0$. Note that any positive constant is a supersolution. Let us exhibit a sub-solution. Let $w_2(t) = e^{-(x^2+2x)}$. Then $w_2'(t) = -(2x + 2) w_2$, $w_2''(t) = ((2x + 2)^2 - 2)w_2 \geq 4x^2w$, then $\|w_2'\|^{p-2}w_2'' \geq 2^p x^pw_2^{p-1} \geq x^pw_2^{p-1}$. Now we use Perron's method on every compact set $[0, R]$, ie we define $y_R = \sup\{y, w_2(t) \leq y(t) \leq 1, \text{ on } [0, R]\}$, $y$ is a sub - solution on $[0, R]$. $y_R$ is classically a solution on $[0, R]$. The sequence $y_R$ is locally uniformly bounded and then by Harnack’s inequality, it converges locally uniformly to a solution $y$ which satisfies $w_2 \leq y \leq 1$. Since $y > 0$ and is bounded we know by the analysis made previously that $y$ goes to zero at infinity, as well as $y'$. Let us observe that for $V'(0) < 0$ given, there exists some $V(0) > 0$ such that $V$ is a solution for such initial conditions, which satisfies $V(+\infty) = V'(+\infty) = 0$. Indeed, let $y$ be the positive solution obtained above, let $V = \frac{V'(0)}{y'(0)} y$, then $V$ is a positive solution which satisfies the required condition. Let us prove the uniqueness of solutions $V$ such that $\lim V = 0$, $V'$ is bounded and $V'(0)$ given. Suppose for that aim that $V_i, i = 1, 2$ are two such solutions. Then substracting the equations satisfied by $V_1$ and $V_2$, multiplying by $(V_1 - V_2)$ and integrating on $[0, R]$ with $R$ large, one gets using $(V_1 - V_2)'(0) = 0$ and $(\|V_1'\|^{p-2}V_1' - \|V_2'\|^{p-2}V_2')(V_1 - V_2)(R) \to 0$ that $\int_0^R (\|V_1'\|^{p-2}V_1' - \|V_2'\|^{p-2}V_2')(V_1 - V_2) \to 0$ and then $V_1 = V_2$. Proposition 4.4. Let $\beta, \gamma > 0$ be given. There exists a unique solution $W$ which satisfies $$\begin{cases} \|W'\|^{p-2}W'' = \beta^p x^p W^{p-1} \text{ on } \mathbb{R}^+ \\ W'(0) = -\gamma, \lim_{x \to +\infty} W(x) = 0 \end{cases}$$ Furthermore $W$ and $W'$ are bounded. Proof Let $W$ be a solution of the previous equation with $W'(0) = -1$, and consider $\bar{W}(x) = \frac{2}{\beta} W(\beta x)$, then $\bar{W}$ satisfies $$\|\bar{W}\|^{p-2}\bar{W}'' = \left(\frac{2}{\beta}\right)^{p-1} \beta^p \|W'\|^{p-2}W''(\beta x)$$ $$= \beta^p x^p \bar{W}^{p-1}(x)$$ $W$ is convenient. References [1] L. Ambrosio, X. Cabré, Entire solutions of semilinear elliptic equations in $\mathbb{R}^3$ and a conjecture of De Giorgi, J. American Math. Soc. 13 (2000), 725-739. [2] M.T. Barlow, R. F. Bass, C. Gui, The Liouville property and a conjecture of De Giorgi, Comm. Pure Appl. Math. 53 (2000), no. 8, 1007-1038. [3] H. Berestycki, F. Hamel, R. Monneau, One dimensional symmetry of bounded entire solutions of some elliptic equations Duke Math. J. 103 (2000), 375-396. [4] H. Berestycki, L. Nirenberg, On the method of moving planes and the sliding method Bol. Soc. Brasil. Mat. 22 (1991), 1-37. [5] H. Berestycki, T. C. Lin, J. Wei, C. Zhao, On phase-separation models: asymptotics and qualitative properties. Arch. Ration. Mech. Anal. 208 (2013), no. 1, 163-200. [6] H. Berestycki, S. Terracini, K. Wang, J. Wei, On entire solutions of an elliptic system modeling phase separations. Adv. Math. 243 (2013), 102-126. [7] I. Birindelli, F. Demengel, Eigenvalue, maximum Principle and Regularity for Fully non linear operators. Communications on pure and applied Analysis, Vol 6, 2007, p. 355-366. [8] Birindelli, I, Demengel, F. One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations. Symmetry for elliptic PDEs, 115, Contemp. Math., 528, Amer. Math. Soc., Providence, RI, 2010. [9] S.M. Chang, C.S. Lin, T.C. Lin and W.W. Lin, Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates, Phys. D 196 (2004), no. 3-4, 341 -361. [10] M. Conti, S. Terracini and G. Verzini. Asymptotic estimates for the spacial segregation of competitive systems, Adv. Math. 195 (2005) , 524-560. [11] L. Damacelli, B. Sciunzi Harnack inequalities, maximum and comparison principles, and regularity of positive solutions of m-Laplace equations, Calculus of Variations and pde, 25, (2), 2006, p. 139-159. [12] E. De Giorgi, Convergence problems for functionals and operators Proc. int. Meeting on recent methods in Nonlinear Analysis, Rome , 1978, Pitagora, 1979; 131-188. [13] M. Del Pino, M. Kowalczyk, J. Wei On De Giorgi’s conjecture in dimension N ≥ 9. Ann. of Math. (2) 174 (2011), no. 3, 1485- 1569. [14] De Silva, O. Savin, Symmetry of global solutions to a class of fully non-linear elliptic equations in 2D, Indiana Univ. Math. J. 58 (2009), 301–315. [15] S. Di Pierro Geometric inequalities and symmetry results for elliptic systems discrete and continuous Discrete and continuous dynamical systems, Volume 33, Number 8, 2013 pp. 3473- 3496 [16] S. Di Pierro , A. Pinamonti Symmetry results for stable and monotone solutions to fibered systems of PDEs arxiv 1212. 0408 v1. [17] A. Farina, Symmetry for solutions of semilinear elliptic equations in RN and related conjectures, Ricerche di Matematica XLVIII, (1999), 129-154. [18] A. Farina Some Symmetry results for entire solutions of an elliptic system arising in phase transition. To appear in Discrete and Continuous Dynamical Systems - Series A : Special Volume ”Qualitative properties of solutions of nonlinear elliptic equations and systems”. [19] A. Farina, N. Soave Monotonicity and 1-dimensional symmetry for solutions of an elliptic system arising in Bose-Einstein condensation arxiv 1303.1265v1 [20] A. Farina, B. Sciunzi and E. Valdinoci Bernstein and De Giorgi type problems: new results via a geometric approach Ann. Scuola Norm. Sup. Pisa Cl Sci (5), Vol VII (2008), 741-79. [21] A. Farina, E. Valdinoci 1D Symetry for solutions of semi linear and quasi-linear elliptic equations Transaction Of the Am. Math. Society, Vol. 363, Number 2, 2011, p. 579-609. [22] A. Farina and E. Valdinoci, The state of the art of a conjecture of De Giorgi and related problems Recent progress in reaction-diffusion systems and viscosity solutions, World Scientific Publishers, Hackensack, NJ, 2009, 74-96. [23] N. Ghoussoub and C. Gui, On a conjecture of De Giorgi and some related problems. Math. Ann. 311(3) (1998) 481-491. [24] B. Noris, H. Tavares, S. Terracini, G. Verzini, Uniform Holder bounds for nonlinear Schrödinger systems with strong competition. Comm. Pure Appl. Math. 63 (2010), no. 3, 267-302. [25] O. Savin Regularity of flat level sets in phase transitions, Annals of Math, 169, (2009), 41-78. [26] V. O. Savin, B. Sciunzi, E. Valdinoci, Flat level set regularity of p Laplace phase transitions. Mem. Amer.Math. Soc., 182, 2006. [27] J. L. Vasquez, A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12 (1984), no. 3, 191–202. [28] K. Wang On the De Giorgi type conjecture for an elliptic system modeling phase separation arxiv 1207 528v1. [29] J. Wei and T. Weth, Asymptotic behavior of solutions of planar elliptic systems with strong competition, Nonlinearity 21 (2008), 405-317.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 1466, 1 ], [ 1466, 3898, 2 ], [ 3898, 7005, 3 ], [ 7005, 9245, 4 ], [ 9245, 11554, 5 ], [ 11554, 13200, 6 ], [ 13200, 16069, 7 ], [ 16069, 18921, 8 ], [ 18921, 20983, 9 ], [ 20983, 22817, 10 ], [ 22817, 25453, 11 ], [ 25453, 27374, 12 ], [ 27374, 29696, 13 ], [ 29696, 32297, 14 ], [ 32297, 34809, 15 ], [ 34809, 37436, 16 ], [ 37436, 40685, 17 ], [ 40685, 42800, 18 ], [ 42800, 44968, 19 ], [ 44968, 47642, 20 ], [ 47642, 49760, 21 ], [ 49760, 51790, 22 ], [ 51790, 54971, 23 ], [ 54971, 57018, 24 ], [ 57018, 59854, 25 ], [ 59854, 62152, 26 ], [ 62152, 63796, 27 ], [ 63796, 65719, 28 ], [ 65719, 67274, 29 ] ] }
e47adc11aa1ec370b08038d1d9882bb4f89a1410	{ "olmocr-version": "0.1.59", "pdf-total-pages": 8, "total-fallback-pages": 0, "total-input-tokens": 30851, "total-output-tokens": 11096, "fieldofstudy": [ "Biology", "Chemistry" ] }	Effect of Liposome Characteristics and Dose on the Pharmacokinetics of Liposomes Coated with Poly(amino acid)s Birgit Romberg, Christien Oussoren, Cor J. Snel, Wim E. Hennink, and Gert Storm Received April 29, 2007; accepted June 25, 2007; published online August 3, 2007 Abstract. Long-circulating liposomes, such as PEG-liposomes, are frequently studied for drug delivery and diagnostic purposes. In our group, poly(amino acid) (PAA)-based coatings for long-circulating liposomes have been developed. These coatings provide liposomes with similar circulation times as compared to PEG-liposomes, but have the advantage of being enzymatically degradable. For PEG-liposomes it has been reported that circulation times are relatively independent of their physicochemical characteristics. In this study, the influence of factors such as PAA grafting density, cholesterol inclusion, surface charge, particle size, and lipid dose on the circulation kinetics of PAA-liposomes was evaluated after intravenous administration in rats. Prolonged circulation kinetics of PAA-liposomes can be maintained upon variation of liposome characteristics and the lipid dose given. However, the use of relatively high amounts of strongly charge-inducing lipids and a too large mean size is to be avoided. In conclusion, PAA-liposomes represent a versatile drug carrier system for a wide variety of applications. KEY WORDS: biodistribution; liposome clearance; long-circulating liposomes; pharmacokinetics; poly(amino acid)s. INTRODUCTION Liposomes have repeatedly shown to be able to improve the therapeutic index of a variety of drugs. Intravenously administered liposomes generally undergo extensive opsonization and are therefore rapidly cleared by macrophages of the mononuclear phagocyte system (MPS), particularly Kupffer cells in the liver and spleen macrophages. As a result, liposome targeting to pathological tissues is impeded. This drawback could be amended by coating liposomes with hydrophilic, neutral polymers such as polyethylene glycol (PEG) (1). PEG increases the hydrophilicity of the liposome surface and provides a steric barrier against opsonization (1, 2). The resulting long-circulating liposomes, also referred to as ‘stealth’ or ‘sterically stabilized’ liposomes, are still removed from the blood circulation, however, removal occurs at a much lower rate and with less involvement of the hepatosplenic macrophages. Consequently, they circulate in the bloodstream for a prolonged period of time, enabling their extravasation into solid tumors and sites of inflammation by virtue of the presence of capillary discontinuities. This so-called enhanced permeability and retention (EPR) effect allows for increased local drug concentrations in the target region (3). Besides PEG, several other hydrophilic polymers have been successfully applied as coatings for long-circulating liposomes, among them conjugates based on poly(oxazoline) (4), polyglycerol (5), poly[(N-(2-hydroxypropyl)methacryl-amide)] (6), poly-N-vinylpyrrolidone (7, 8) and polyvinyl alcohol (9). Our group proposed liposome coatings based on poly(amino acid)s (PAA): poly[hydroxyethyl l-glutamine]-N-succinyldioctadecylamine (PHEG-DODASuc) and poly[hydroxyethyl l-asparagine]-DODASuc (PHEA-DODA-Suc) (Fig. 1) (10, 11). PAs have the advantage of being degradable by lysosomal proteases, allowing for a complete elimination from the body, and reducing the risk of side effects associated with polymer accumulation, as described to occur in case of some non-degradable polymers (12–15). Their degradability can also be exploited for enzyme-induced drug release and/or target cell interaction, as the coating may be shed by proteolytic cleavage in the extracellular space of tumors and sites of inflammation. It has been demonstrated that PAA coatings can prolong circulation times of liposomes to an equal extent as a PEG coating (10). An understanding of the effect of physicochemical characteristics of long-circulating liposomes on their pharmacokinetics and biodistribution is crucial for the rational development of therapeutic applications. Liposome clearance is a very complex mechanism and is mediated by a diversity of protein molecules such as immunoglobulins, complement factors and nonimmune opsonins, and the opsonization process can be very different for different types of liposomes (16–18). For long-circulating liposomes with PEG as a Liposome Characteristics and Dose on Liposomes Fig. 1. Structures of PHEA-DODASuc (average degree of polymerization (n=15) and PHEG-DODASuc (n=18). ‘stealth’ coating, it has been reported that circulation times are relatively independent of factors such as lipid dose, lipid composition, surface charge and liposome size, which makes them versatile drug carriers (19). In the present study, we investigated if this also holds true for PAA-liposomes. Therefore, the influence of PAA grafting density, cholesterol inclusion, surface charge, particle size and lipid dose on the circulation kinetics and biodistribution of PAA-liposomes was evaluated. MATERIALS AND METHODS Materials PHEA-DODASuc (average MW=3,000 Da, determined by NMR and MALDI-ToF MS, corresponding with an average degree of polymerization of 15) and PHEG-DODASuc (average MW=4,000 Da, determined by NMR and MALDI-ToF MS, corresponding with an average degree of polymerization of 18) were synthesized as described previously (10). Dipalmitoyl phosphatidylcholine (DPPC), egg phosphatidylcholine (EPC) and egg phosphatidylglycerol (EPG) were kindly provided by Avanti Polar Lipids, Inc., Alabaster, AL, USA. Cholesterol and egg phosphatidylglycerol (EPG) were kindly provided by Lipoid GmbH, Ludwigshafen, Germany. 1,2-Dioleoyl-3-trimethylammonium-propane (DOTAP) and 1-α-phosphatidylserine (PS, porcine brain, sodium salt) were purchased from Avanti Polar Lipids, Inc., Alabaster, AL, USA. Cholesterol was purchased from Sigma-Aldrich Chemie BV, Zwijndrecht, The Netherlands. [3H]-Cholesteryl oleylether was a product of Amersham, Roosendaal, The Netherlands. Ultima Gold liquid scintillation cocktail and Solvable tissue solubilizer were purchased from Perkin Elmer BioScience B.V., Groningen, The Netherlands. All other reagents were of analytical grade. Animals Male outbred Wistar rats (body weight approximately 250 g) were obtained from Harlan Nederland, Horst, The Netherlands. Rats were housed in groups of four under standard laboratory conditions and had free access to rat chow and water. All animal experiments were performed according to national regulations and approved by the local animal experiments ethical committee. Liposome Preparation Liposomes were prepared as described previously by a lipid film hydration method (20). Appropriate amounts of DPPC, EPC, EPG, cholesterol, PS, or DOTAP were dissolved in ethanol in 50 ml round-bottom flasks (for lipid compositions see Table 1). To each formulation 20 μl of the lipid phase marker [3H]-cholesteryl oleylether (approximately 740 kBq) were added. This label has been shown to be non-metabolizable and non-exchangeable (21, 22). The solvent was evaporated under a stream of nitrogen. The obtained lipid film was hydrated by gentle shaking in 2.5 ml HBS (5 mM HEPES, 0.9% NaCl, pH 7.4) resulting in a final concentration of 20 μmol total lipid/ml, except for two formulations to study the effect of the lipid dose: besides the formulation of 20 μmol total lipid/ml, a second formulation was prepared at a concentration of 0.2 μmol/ml and divided into two equal parts. One part was diluted 1:10 in HBS, yielding a lipid concentration of 0.02 μmol total lipid/ml. Liposomes of the different sizes were obtained by multiple extrusion through two stacked polycarbonate filters (Poretics, Livermore, CA, USA, 400, 200, and 100 nm pore size) with a high-pressure extruder. Formulations were stored at 4°C and used within 1 week after preparation. Liposome Characterization The mean particle size and polydispersity index (PD) of the liposome dispersions (diluted 1:100 with HBS) were measured by dynamic light scattering on a Malvern ALV/CGS-3 Goniometer, detected at an angle of 90° to the laser beam. The polydispersity index gives information on the particle size distribution, it ranges from 0 for an entirely monodisperse up to 1 for a polydisperse system. The phospholipid content of the liposomal dispersions was determined colorimetrically according to Rouser et al. (23). Radioactivity of the liposomal dispersions was analyzed in an Ultima Gold liquid scintillation cocktail (dilution of 1:1,000) and counted in a Packard Tricarb 2200 CA liquid scintillation counter. Pharmacokinetics Rats were put under light isoflurane anesthesia and liposomes were injected via the tail vein. To study the effect of lipid dose, injections of 25, 0.25, and 0.025 μmol total lipid/kg were given. For all other studies the injected dose was 20 μmol total lipid/kg. Blood samples (approximately 150 μl) were drawn under isoflurane anesthesia from the tail vein of each rat immediately after injection (from the opposite vein) and at 1, 4, 8, 24 and 48 h after injection. Hundred microliters of each blood sample were mixed with 100 μl Solvable tissue solubilizer and 100–200 μl 35% hydrogen peroxide to decolorize the samples and incubated overnight. Samples were diluted in 10 ml Ultima Gold scintillation cocktail and radioactivity was subsequently assessed in a Packard Tricarb 2200CA liquid scintillation counter. Forty-eight hours after injection, the rats were sacrificed by cervical dislocation and for the studies involving variations in surface charge, liposome size and lipid dose, liver and spleen were dissected and homogenized in 25 and 5 ml water, respectively. To 0.5 ml of the liver homogenate and 1 ml of the spleen homogenate, 200 μl of Solvable tissue solubilizer and 200 μl 35% hydrogen peroxide were added and mixtures were incubated until samples were dissolved and colorless. Radioactivity of the samples was assessed in 10 ml Ultima Gold scintillation cocktail as described above. Besides tissue and blood samples, also liposome samples were analyzed to... \| Liposome Characteristic Studied \| Liposome Type \| Formulation \| Composition (Molar Ratio) \| Mean size (nm) \| PD \| \|-------------------------------\|--------------\|-------------\|--------------------------\|----------------\|----\| \| Size \| PHEA-liposomes \| Desired size: 360 nm \| EPC/EPG/PHEA-DODASuc 1.425:1.425:0.15 \| 355 \| 0.26 \| \| \| \| Desired size: 230 nm \| EPC/EPG/PHEA-DODASuc 1.425:1.425:0.15 \| 230 \| 0.13 \| \| \| \| Desired size: 120 nm \| EPC/EPG/PHEA-DODASuc 1.425:1.425:0.15 \| 120 \| 0.07 \| \| \| PHEG-liposomes \| Desired size: 360 nm \| EPC/EPG/PHEG-DODASuc 1.425:1.425:0.15 \| 370 \| 0.21 \| \| \| \| Desired size: 230 nm \| EPC/EPG/PHEG-DODASuc 1.425:1.425:0.15 \| 225 \| 0.13 \| \| \| \| Desired size: 120 nm \| EPC/EPG/PHEG-DODASuc 1.425:1.425:0.15 \| 125 \| 0.02 \| \| Grafting density \| PHEA-liposomes \| Grafting density: 2.5% \| DPPC/cholesterol/PHEA-DODASuc 1.95:1:0.05 \| 145 \| 0.08 \| \| \| \| Grafting density: 7.5% \| DPPC/cholesterol/PHEA-DODASuc 1.85:1:0.15 \| 145 \| 0.04 \| \| \| \| Grafting density: 15% \| DPPC/cholesterol/PHEA-DODASuc 1.7:1:0.3 \| 135 \| 0.05 \| \| Cholesterol content \| PHEA-liposomes \| Without cholesterol \| EPC/PHEA-DODASuc 2.85:0.15 \| 135 \| 0.14 \| \| \| \| With cholesterol \| EPC/cholesterol/PHEA-DODASuc 1.85:1:0.15 \| 140 \| 0.08 \| \| \| PHEG-liposomes \| Without cholesterol \| EPC/PHEG-DODASuc 2.85:0.15 \| 150 \| 0.10 \| \| \| \| With cholesterol \| EPC/cholesterol/PHEG-DODASuc 1.85:1:0.15 \| 145 \| 0.06 \| \| Negative charge \| PHEA-liposomes \| EPC \| EPC/PHEA-DODASuc 2.85:0.15 \| 135 \| 0.14 \| \| \| \| EPC/EPG 4:1 \| EPC/EPG/PHEA-DODA-Suc 2.250:0.6:0.15 \| 125 \| 0.06 \| \| \| \| EPC/EPG 1:1 \| EPC/EPG/PHEA-DODA-Suc 1.425:1.425:0.15 \| 125 \| 0.01 \| \| \| \| EPC/PS \| EPC/PS/PHEA-DODA-Suc 2.55:0.3:0.15 \| 105 \| 0.09 \| \| \| PHEG-liposomes \| EPC \| EPC/PHEG-DODASuc 2.85:0.15 \| 150 \| 0.10 \| \| \| \| EPC/EPG 4:1 \| EPC/EPG/PHEG-DODA-Suc 2.250:0.6:0.15 \| 160 \| 0.13 \| \| \| \| EPC/EPG 1:1 \| EPC/EPG/PHEG-DODA-Suc 1.425:1.425:0.15 \| 135 \| 0.03 \| \| \| \| EPC/PS \| EPC/PS/PHEG-DODA-Suc 2.55:0.3:0.15 \| 120 \| 0.05 \| \| Positive charge \| PHEA-liposomes \| EPC/DOTAP/PHEA-DODASuc 1.425:1.425:0.15 \| 125 \| 0.05 \| \| Lipid dose \| PHEG-liposomes \| Lipid dose: 25 μmol/kg \| EPC/EPG/PHEG-DODASuc 1.425:1.425:0.15 \| 135 \| 0.05 \| \| \| \| Lipid dose: 0.25 and 0.025 μmol/kg \| EPC/EPG/PHEG-DODASuc 1.425:1.425:0.15 \| 120 \| 0.10 \| Table II. Percentage of Injected Dose of PHEA-Coated DPCC/Cholesterol Liposomes in the Circulation at 4 and 24 h Post-Injection \| PHEA-DODASuc Grafting Density (%) \| Blood Concentration (% ID) \| 4 h \| 24 h \| \|----------------------------------\|---------------------------\|-----\|-----\| \| 2.5 \| 50±23 \| 16±11 \| \| \| 7.5 \| 55±8 \| 21±2 \| \| \| 15 \| 60±5 \| 20±2 \| \| Results are expressed as mean±SD (n=3–4). * Differences not significant Determine the radioactivity of the injected amount of liposomes. Data Analysis Blood concentrations of liposomes at the different time points were calculated from the radioactivity of the blood samples as the percentage of the radioactivity measured immediately after injection (% injected dose). For the blood samples, a Q-test for identification of outliers was applied. From the blood concentration-time curves, area under the curve values were calculated for the analyzed time interval from zero to 48 hours using the trapezoidal rule [AUC_0-48 h (% injected dose×h)]. The percentage of the injected dose (% ID) in the organs was calculated by division of the radioactivity of the organs by the radioactivity of the injected liposome amount. Differences in AUCs and liver and spleen values were compared by a one-way analysis of variance. The Bonferroni method was used to correct for multiple comparison. Differences were considered significant when the p-value was <0.05. All analyses were performed using Graph Pad Prism 4 software. RESULTS AND DISCUSSION To study the effect of liposome characteristics on the pharmacokinetics and biodistribution, different liposome types were prepared. Liposome compositions, sizes and polydispersity indices are presented in Table I. Different grafting densities of PAAs on the liposome surface were studied. The bilayer fluidity of liposomes was varied by inclusion of cholesterol. The effect of charge was examined by inclusion of the negatively charged lipids egg phosphatidylglycerol (EPG) and phosphatidylserine (PS) and the positively charged lipid dioleoyl phosphatidyltrimethylammonium propane (DOTAP). The effect of particle size was assessed with liposomes of sizes between 120 and 360 nm. The lipid doses needed in therapeutic settings can differ substantially. PEG-liposomes show dose-independent pharmacokinetics over a broad dose range, however at low doses (<1 μmol/kg) rapid clearance has been reported. To investigate if this also holds true for PAA-liposomes, the effect of lipid dose on the pharmacokinetics of PAA-liposomes was examined. Except for liposome formulations prepared to study the effect of liposome size, the hydrodynamic diameter of liposomes varied between 105 and 160 nm and the polydispersity index was ≤0.14, indicating a relatively narrow size distribution. Effect of Grafting Density In Table II the effect of three different grafting levels of PHEA-DODASuc (i.e. 2.5, 7.5 and 15 mol%) on the circulation kinetics of liposomes is shown. For this study the composition of DPCC and cholesterol (2:1) was chosen to be able to compare the data to earlier published results on the effect of grafting density of PHEG-DODASuc (1, 2.5, 7.5 and 15 mol%) on liposome circulation times (10). The blood concentrations at 4 and 24 h post-injection show no significant differences between the formulations. This is in line with the findings on the effect of grafting density of PHEG-DODASuc on liposome circulation times (10). The density of stealth polymers on the liposome surface has been shown to be of importance in the design of long-circulating liposomes. For example, for PEG-liposomes with a PEG_2000-conjugate a grafting density of 5 to 7.5 mol% is often used in preclinical studies (24, 25). At PEG levels >4 mol%, a transition from the mushroom state, where PEG chains do not interact laterally, to the denser and thicker brush state of PEG occurs, the latter being the condition for optimal steric stabilization of the liposomes (26). It has been shown that a further increase of the density of PEG up to 20 mol% did not change circulation kinetics and biodistribution. However, considerable foaming made liposome preparation difficult; the foaming was likely related to the presence of PEG-DSPES micelles (24). Our studies show that at grafting densities between 2.5 and 15%, PAAs are able to prolong liposome circulation times similar to PEG. In previous studies a PAA grafting density of 7.5% was used, however, the present study indicates that a lower grafting density of 2.5% is also sufficient to prolong liposome circulation times. Fig. 2. Pharmacokinetic behavior of EPC-liposomes coated with PHEA (top left) and PHEG (top right) without (empty squares) or with (filled squares) 33% cholesterol (% injected dose). Area under the curve (AUC_0-48 h) values (bottom) calculated from blood concentration time curves. All results are expressed as mean±SD (n=3–4). p<0.05; n.s. Not significant. Fig. 3. Pharmacokinetic behavior of EPC liposomes with a negative charge. EPC-liposomes (filled diamonds), EPC/EPG-liposomes in a molar ratio of 4:1 (filled circles) or 1:1 (filled squares) and EPC/PS-liposomes (9:1) (filled triangles) coated with PHEA (top left) and PHEG (top right) (% injected dose). Area under the curve (AUC$_{0-48h}$) values (bottom) calculated from blood concentration time curves. All results are expressed as mean±SD (n=3–4). p<0.01; p<0.05; n.s. Not significant. Effect of Cholesterol Inclusion The circulation kinetics of EPC-based liposomes without or with 33 mol% cholesterol and coated with PHEA or PHEG were determined (Fig. 2). For both PHEA- and PHEG-liposomes, only small differences in circulation profiles and AUC values of liposomes with or without cholesterol were observed. Cholesterol is known to influence the bilayer fluidity, resulting in increased rigidity and lateral packing and an increased phase transition temperature (27). For conventional PC-based liposomes interaction with proteins was reduced and circulation times were extended upon inclusion of cholesterol (28, 29). For PEGylated liposomes controversial observations have been made. Addition of 20–50 mol% cholesterol resulted in improved circulation kinetics (25). In other studies, however, no differences in circulation times and biodistribution have been observed when 33 mol% cholesterol were added, indicating that differences in bilayer rigidity have only little influence on the circulation kinetics of liposomes that are shielded by a ‘stealth’ coating (30, 31). Our findings are in agreement with this observation made with PEG-liposomes: shielding of liposomes by PAAs diminished the influence of bilayer fluidity on circulation times. Effect of Charged Lipids Charged lipids are often added to liposome formulations to improve drug loading and/or stability of the formulation against aggregation during storage (30, 31). Changing the surface charge of conventional liposomes has been shown to greatly influence their pharmacokinetic behavior (32, 33). For PEG-liposomes it has been reported that the polymer is able to shield liposome charge. For example, PEG-liposomes containing up to 30 mol% of the negatively charged phospholipid EPG showed no altered pharmacokinetic behavior (30, 31). This is in line with our findings that inclusion of 20 mol% of EPG in PAA-coated liposomes did not result in significant changes in circulation kinetics and biodistribution (Fig. 3 and Table III). When 47.5 mol% of this lipid were included, only a slight decrease in circulation times was observed. When the negatively charged phospholipid PS was included in PHEA- and PHEG-liposomes at a level of 10 mol%, a very rapid removal from the circulation was observed. Apparently, at the grafting density level of 5 mol%, PAAs are not able to sufficiently shield PS-containing liposomes from opsonization. This is in line with the findings that 5 mol% of PEG was not effective in protecting PS-containing liposomes from rapid clearance (24). PS-containing PAA-liposomes showed an enhanced liver distribution when compared to PAA-liposomes containing EPG. The results indicate that PAA-coatings are able to shield the surface of EPG-containing liposomes more effectively than that of PS-containing liposomes. It has been suggested that the position of the negative charge within the molecule might play a role in the differences in shielding capacity (33). The negatively charged carboxyl group of PS is located at the terminal position of the hydrophilic part of the molecule, directed to the outer fluid, whereas the negatively charged phosphate group of EPG is located closer to the hydrophobic anchor and therefore shielded more effectively by the coating. In addition, the observed differences in pharmacokinetics of both types of liposomes may be related to the involvement of a receptor recognition mechanism in case of the PS-containing PAA-liposomes (33). PS has important physiological functions, it serves as signal for recognition and removal of aged erythrocytes and apoptotic cells by macrophages, which display a PS-specific receptor (34). In addition, it binds to clotting factors and initiates coagulation (35, 36). \| Table III. Percentage of Injected Dose of PHEA- and PHEG-Coated EPC-Liposomes with or without a Negative Charge in Liver and Spleen 48 h Post-Injection \| \|-----------------\|-----------------\|-----------------\| \| Liposomes \| Liver [% ID]$^a$ \| Spleen [% ID]$^b$ \| \| PHEA-liposomes \| EPC \| 15±2 \| 7±1 \| \| \| EPC/EPG 4:1 \| 10±3 \| 11±1 \| \| \| EPC/EPG 1:1 \| 8±1 \| 7±2 \| \| \| EPCPS \| 27±2 \| 12±1 \| \| PHEG-liposomes \| EPC \| 19±3 \| 9±1 \| \| \| EPC/EPG 4:1 \| 12±3 \| 15±1 \| \| \| EPC/EPG 1:1 \| 12±1 \| 7±3 \| \| \| EPCPS \| 19±3 \| 9±2 \| Results are expressed as mean±SD (n=3–4). $^a$p<0.05 for PHEA/EPC vs PHEA/EPC/EPG 4:1 and vs PHEA/EPC/EPG 1:1 and vs PHEA/EPC/PS, PHEA/EPC/EPG 4:1 and vs PHEA/EPC/PS, PHEA/EPC/PS, PHEG/EPC vs PHEG/EPG 1:1, PHEG/EPC/PS vs PHEG/EPC/EPG 4:1 and vs PHEG/EPC/EPG 1:1 $^b$p<0.05 for PHEA/EPC vs PHEA/EPC/EPG 4:1 and vs PHEA/EPC/PS, PHEA/EPC/EPG 1:1 vs PHEA/EPC/PS, PHEG/EPC/EPG 4:1 and vs PHEG/EPC/EPG 1:1 and vs PHEA/EPC/PS, PHEG/EPC/EPG 4:1 vs PHEG/EPC and vs PHEG/EPC/EPG 1:1 and vs PHEG/EPC/PS Liposome Characteristics and Dose on Liposomes Table IV. Percentage of Injected Dose of PHEA- and PHEG-Coated EPC/EPG Liposomes in Liver and Spleen 48 h Post-Injection \| Liposomes \| Size (nm) \| Liver (% ID) \| Spleen (% ID) \| \|---------------\|-----------\|--------------\|---------------\| \| PHEA-liposomes\| 350 \| 16±3 \| 26±2 \| \| \| 230 \| 14±4 \| 26±7 \| \| \| 120 \| 10±3 \| 16±2 \| \| PHEG-liposomes\| 350 \| 22±8 \| 15±2 \| \| \| 230 \| 18±4 \| 23±6 \| \| \| 120 \| 11±3 \| 18±3 \| Results are expressed as mean±SD (n=4). Table V. Percentage of Injected Dose of PHEG-Coated EPC/EPG Liposomes in Liver and Spleen 48 h Post-Injection \| Dose (μmol/kg) \| Liver [% ID]a \| Spleen [% ID]b \| \|----------------\|--------------\|----------------\| \| 25 \| 18±1 \| 18±2 \| \| 0.25 \| 19±4 \| 5±1 \| \| 0.025 \| 22±2 \| 6±1 \| Results are expressed as mean±SD (n=4). Effect of Particle Size The circulation kinetics and AUC values of PHEA- and PHEG-liposomes of approximately 360, 230 and 120 nm are shown in Fig. 4. Table IV summarizes their distribution to liver and spleen. Liposomes with a mean size of 120 nm were removed from the bloodstream at a lower rate than liposomes of 230 and 360 nm, respectively, for both PHEA- and PHEG-coated liposomes. This observation has also been reported in independent studies for conventional and PEGylated liposomes (25, 30, 32, 41–43). PEG-liposomes with a diameter of more than 200 nm are more rapidly cleared than liposomes with a diameter between 100 and 200 nm. A decrease in size has been shown to also reduce recognition by the complement system (44–46). At 48 hours after administration, the liposome formulation tested showed only small differences regarding the degree of uptake by liver and spleen. As mentioned above, differences may have been obscured as at this late time point redistribution of the label may already have occurred. Our results indicate that, as observed for PEG-liposomes, also for PHEA- and PHEG-liposomes a particle size below 150 nm is the most optimal to achieve long-circulation properties. Effect of Lipid Dose The effect of the administered lipid dose of PHEG-liposomes on the circulation kinetics and AUC values is shown in Fig. 5. No differences in clearance were observed when liposomes were administered at doses of 25, 0.25, and 0.025 μmol/kg. At 48 hours after administration, liver uptake was also independent of the lipid dose but spleen uptake was lower at both lower lipid doses (Table V). For PEG-liposomes dose-independent kinetics have been observed over a dose range between 4 and 400 μmol/kg (47). However, at doses <1 μmol/kg, which are used in case of for instance diagnostic imaging of tumors and sites of inflammation, PEG-liposomes are much more rapidly cleared from the circulation (48, 49). The mechanism behind this ‘enhanced clearance effect’ at low lipid dose is not yet fully understood. It has been suggested that rapid clearance is mediated by a limited pool of circulating opsonic factors that interact with PEG-liposomes and induce phagocytosis. At higher lipid doses, the influence of this relatively low amount of opsonic factors becomes more restricted and the majority of the administered liposomes will be long-circulating (49, 50). For PHEA-liposomes, a recent study showed dose-independent pharmacokinetics for doses as low as 0.025 μmol/kg (51). The present study demonstrates that this is also the case for PHEG-liposomes. This benefit of PAA-liposomes over PEG-liposomes can be advantageous in situations in which only low lipid doses of liposomes are required for the desired application. CONCLUSION This study demonstrates that the prolonged circulation kinetics of PAA-liposomes can be maintained upon variation of liposome characteristics and the lipid dose given. 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Stealth liposomes and long circulating nanoparticulates: critical issues in pharmacokinetics, opsonization and protein-binding properties. Prog Lipid Res. 42:463–478 (2003). 51. B. Romberg, C. Oussoren, C. J. Snel, M. G. Carstens, W. E. Henriksen, and G. Storm. Pharmacokinetic profile of (hydroxethylasparagine)-coated liposomes is superior over that of PEG-coated liposomes at low lipid dose and upon repeated administration. Biochimica et Biophysica Acta (BBA)-Biomembranes. 1768:737–743 (2007).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4427, 1 ], [ 4427, 10143, 2 ], [ 10143, 13229, 3 ], [ 13229, 18302, 4 ], [ 18302, 23905, 5 ], [ 23905, 26218, 6 ], [ 26218, 33084, 7 ], [ 33084, 36329, 8 ] ] }
78faedeff99b605f9f46c17b5e9f72d9219fc1cb	{ "olmocr-version": "0.1.59", "pdf-total-pages": 13, "total-fallback-pages": 0, "total-input-tokens": 23783, "total-output-tokens": 6075, "fieldofstudy": [ "Medicine", "Psychology" ] }	Children’s competence to consent to medical treatment or research Hein, Irma Citation for published version (APA): Hein, I. M. (2015). Children’s competence to consent to medical treatment or research Amsterdam: Amsterdam University Press General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Informed consent instead of assent is appropriate in children from the age of twelve Policy implications of new findings on children's decision-making competence in the clinical context Irma M. Hein, Martine C. de Vries, Pieter W. Troost, Gerben Meynen, Johannes B. van Goudoever, Ramón J.L. Lindauer Submitted Abstract Background For many decades, the debate on children's competence to give informed consent in medical settings concentrated on ethical and legal aspects, with little empirical underpinnings. Recently, data from empirical research became available to advance the discussion. It was shown that children's competence to consent to clinical research could be accurately assessed by the modified MacArthur Competence Assessment Tool for Clinical Research. Age limits for children to be deemed competent to decide on research participation have been studied: generally children of 11.2 years and above were competent, while children of 9.6 years and younger were not. Age was pointed out to be the key determining factor in children's competence. In this article we reflect on policy implications of these findings, considering legal, ethical, developmental and clinical perspectives. Discussion Although assessment of children's competence has a normative character, ethics, law and clinical practice can benefit from research data. The findings may help to do justice to the capacities and challenges children may face when deciding about treatment and research options. We discuss advantages and drawbacks of standardized competence assessment in children on a case-by-case basis compared to application of a fixed age limit, and conclude that a selective implementation of case-by-case competence assessment in specific populations is preferable. We recommend the implementation of age limits based on empirical evidence. Furthermore, we elaborate on a suitable model for informed consent involving children and parents that would do justice to developmental aspects of children and the specific characteristics of the parent-child dyad. Background In clinical practice an accurate assessment of children's decision-making competence is needed to avoid two pitfalls: to impose complex medical decisions on children who are unable to make them, and to inadvertently exclude capable children who want to take part in decision-making.(106) For many decades, the debate on children's competence to give informed consent or assent in medical settings concentrated around ethical and legal aspects, with little empirical underpinnings.(150) In clinical practice many questions remained unanswered, for example which age span to evaluate, how to study the full range of abilities relevant to children's decision-making described in the literature, how to assess decision-making capacities regarding different types of medical decisions, and how to objectively assess children's competence. Progress was hard to achieve in debates on the subject and the lack of consensus on children's competence to consent was reflected by the restricted clinical implementation of the concept. There was a gap between recommendations regarding policies for children's involvement in the consent procedure and what had been documented in scientific research about children's competence assessment. The empirical approach emerged as a designated way to examine the dilemmas. Recently, objective data stemming from empirical research on children's competence to consent became available, offering an opportunity to further the discussion. Research demonstrated in a sample of 161 pediatric patients that children's competence to consent to clinical research could be assessed in a valid and reliable way by means of an instrument, the modified MacArthur Competence Assessment Tool for Clinical Research (MacCAT-CR).(150) In the same study, the four domains representing competence in most jurisdictions (understanding, appreciation, reasoning and expressing a choice) appeared to constitute a single trait or continuum of competence in children, which allowed for estimating a cutoff score on MacCAT-CR above which competence was likely. This is in contrast with adult literature, stating that scores on subscales need to be weighted independently, and that failure in one domain could translate into an incompetent assessment. In adults, because of this presumption, dimensionality was never tested. Age limits for children to be deemed competent to decide on research participation were estimated: children of 11.2 years and above generally appeared to be competent, while children of 9.6 years and younger were not. Between 9.6 and 11.2 years, there was a change-over. For treatment decisions, a preliminary study using MacArthur Competence Assessment Tool for Treatment (MacCAT-T) on decisions about predictive genetic testing, revealed that most children above the age of 11.8 were competent to consent. The results from these studies in the research and in the treatment context show that MacCAT-scales modified for children are practicable in both settings and suggest that age-limits for competence align. Furthermore age turned out to be the key determining factor in children’s competence, with a small additional contribution of intelligence. Theoretical assumptions that risk and complexity of the decision would be related to a competence classification could not be confirmed with empirical data. This demonstrated that more radical decisions, requiring a higher level of competence, could possibly be made by children as young as the group of children who were able to make lower impact decisions. An explanation might be that children at a certain age have the required capacities, and competent decision-making is possible when information provision is of good quality. For other potential determining factors for competence, like gender, systemic influences, disease experience, ethnicity and socio-economic status, no clear relationship with competence could be demonstrated either. Interestingly, parents appeared to judge their child more readily competent than experts would. These recent empirical findings do not stand alone however, and need to be considered in view of their context. Since the age limits for asking children’s consent stated in many jurisdictions do not coincide with those demonstrated in our research, we need to evaluate whether it would be advisable to reset local statutory age-limits. Having the possibility to assess children’s competence individually in a standardized way, an alternative option (namely to let go of rigid age limits for alleged competence and switch to a case-by-case assessment) might be considered. For example, now that it is possible to establish a very intelligent eight-year old boy’s competence, we need to consider if it would be judicious to do so and to allow him an independent consent. Although our assessment instrument proved to be accurate, there might be possible drawbacks of the normative classification of children into groups of competent and incompetent ones. Overall, we should evaluate whether the clinical assessment of children's competence by an instrument is comprehensive, or that we miss out on important non-measurable factors. Finally, we need to consider if we are fully aware of the influence of developmental aspects affecting children's competence, and if this makes children's competence different from adults.' In this article we will reflect on possible implications of the recent empirical findings on children's competence to consent considering normative, developmental, and clinical perspectives. Subsequently, we will derive recommendations for policies. Discussion Normative aspects Considering children either competent or incompetent is a normative judgment. However, the fact that competence is a normative judgment does not mean that it cannot be informed by research data. Research shows that a competence assessment can be reliably performed using a structured tool like the MacCAT-CR. The MacCAT-CR's total and sub-scores showed a good reproducibility and the overall accuracy of MacCAT-CR scores in correctly classifying children as competent against the reference standard was high as well. In addition, it was shown that using such a tool, three age groups could be distinguished: one in which children are most probably incompetent, one in which children are most probably competent, and a group in which probability of (in)competence is less clear (between 9.6 and 11.2 years). Such findings do not prescribe how ethics and law should deal with (in)competence and children. But, as we will discuss below, the findings may help to do justice to the capacities and challenges children may face when deciding about treatment and research options. For instance, for health care professionals, as well as parents, it is important to know that a structured and reliable tool for assessing competence in children is available. Performing such a structured competence assessment may clarify the capacities of an individual child in case professionals have doubt about the child's competence. In addition, the findings concerning the age groups may support the development of guidelines dealing with informed consent in children. Still, clearly, the ethical and legal norm for competence in children cannot be directly derived from these research findings. For instance, establishment of cutoff scores for competence is after all based on normative judgments. Ethical Aspects _Rational Reasons versus Emotions and Values_ Some authors have raised doubts about the validity of competence assessment by MacCAT-scales, and argued that the MacCAT-assessment puts the main emphasis on rational reasoning. Ethicists and other commentators bring into the discussion the role of values and emotions in competence. In the case of patients with anorexia nervosa, Hope and colleagues$^\text{164}$ suggest that to develop a better understanding of competence, research needs to be expanded by factors of competences not covered by the four criteria that are commonly applied (understanding, appreciation, reasoning, expressing a choice). Charland argues that MacCAT-scales seldom sufficiently recognize emotive components and values in decision-making competence.$^\text{165}$ He states that “pathological values” may be present in patients with anorexia nervosa or substance abuse disorders, which are both mental disorders that effect competence. He proposes to incorporate a measure of emotional competence into a competence assessment instrument before considering it a valid measure. Appelbaum, author of MacCAT-T, agrees that emotions aid humans in processing information but suggests that the feasibility of adding emotional capacity to the list of capacities essential for decisional competence should be demonstrated first.$^\text{166}$ No consensus in this debate has been reached yet. It is conceivable that in children “immature values” might be present that are not covered by competence assessment using MacCAT-scales. The study on accuracy of MacCAT-CR in children was performed using a reference standard established by experts. In cases of anorexia nervosa and substances abuse disorders the pathological values might be recognized by clinical experts, in children we might expect the clinical experts to have recognized immature values when present in children. If not, the study might have missed out on an unmeasured component of children’s competence. This would then have resulted in considering more children competent using the MacCAT-CR than actually justified. Legal Aspects _Age-Limits versus Case-by-Case Assessment_ It is widely recognized that the evolving capacities of children and adolescents are reflected by a gradual development of decision-making competence.$^\text{133}$ The use of a fixed age-limit as cutoff for competence is defensible, since age is an efficient proxy for competence with considerable practical advantages as an administrative and normative gauge. It can be measured easily and offers a clear framework. However, the disadvantage of fixed age-limits is the all or nothing character, meaning that relevant differences between individuals are not taken into account. With a set age-limit, some incompetent individuals above the limit will unjustly be deemed competent and some competent individuals below the limit unjustly deemed incompetent. An alternative for the fixed age-limit is a case-by-case assessment of decision-making competence. A recent study has shown that doctors and researchers tend to judge a child to be competent if the child's decision conforms to their own ideas of the child's best interest. This means that competence is gauged by the outcome of the decision rather than by the process of reasoning in deciding about participation. Data suggest that unstructured performance of competence assessments is often sub-optimal and hence the reliability of unstructured judgments has been poor. To avoid this bias, a case-by-case assessment would require an objective assessment instead of the currently used intuitive one. The MacCAT-CR would be an appropriate instrument for this purpose in the research context and there are indications that MacCAT-T is feasible for use in the pediatric treatment setting. Reset Age-Limits Age-limits for asking children's consent vary widely over nations and states. In Europe, domestic law determines whether or not people are competent to consent to healthcare interventions. In some countries autonomous decision-making is lawful only from 18 years onwards and in other countries minors are allowed to take healthcare decisions from a fixed age below legal majority, e.g., 12 years in the Netherlands and 15 years in Denmark. Another variant applied in most Canadian provinces and Switzerland is a flexible system stating that anyone who is capable can give informed consent, whereby competence is evaluated on a case-by-case basis. In the United States, generally speaking, it often falls to parents or legal guardians to provide informed permission for medical decisions and children under 18 are to give assent. Ideally, age-limits accomplish the goal of striking a proper balance in order to both protect children's interests when they are not fully able to do so themselves and to respect their autonomy when they can exercise it. So if a fixed age-limit is used, it must be generally in accordance with the developmental stages. Our research outcomes now offer scientific input for setting a reasonable and just age-limit; as far as we currently know the age-limit that presents closest accordance with children's competence is eleven or twelve years. Children's Decision-Making Competence in Civil Law and Criminal Law The development of decision-making capacities in children is not solely of importance in health law, but also considered in other juvenile laws e.g., civil law and criminal law. In many jurisdictions the age of twelve constitutes a cardinal point, for example regarding adjudicative competence. The age of twelve is not very different from the ages for competence resulting from the studies with MacCAT-CR and MacCAT-T. However, there are arguments mentioned in literature to reconsider these age-limits for juveniles’ pre-adjudicative and adjudicative competence, and criminal responsibility, as adolescents in the criminal setting might show typical deficiencies in their decision-making due to additional risk-factors: for instance, lower intelligence, higher rates of psychiatric disorders and brain trauma’s, higher prevalence of prenatal exposure to alcohol and drugs, exposure to violence and abuse, dysfunctional family backgrounds and substance abuse. In addition, we should note that although there are certain similarities between competence and criminal responsibility, there are differences as well. Developmental Aspects Difference between Competence Assessment in Adults and Children In adults, patients are deemed competent unless the clinician has reasons to believe otherwise. In children, it is generally the other way around, they are presumed not to be competent in most jurisdictions. Whereas in adults MacCAT-scales are merely used to ascertain incompetence in mentally compromised patients out of an overall competent population, in children it might be more important to discover competence in a mainly incompetent population. The application of MacCAT-scales in children puts higher demands on the specificity of the instrument; it serves to weed out the proportion of children that are correctly identified as competent from those (possibly incorrectly) identified as incompetent. In the MacCAT-CR study, specificity in children of 11.2 years and older was good: 90%. Parent versus Professional Research showed that judgments of incompetence by parents frequently coincided with the MacCAT-CR incompetent classification, however parents’ assessments of competence showed only moderate agreement with the MacCAT-CR standard. This might imply that parents express a higher expectation regarding their children’s competence, assigning them more voice and responsibility, than professionals do. In literature the opposite was described: in a sample of 120 young people undergoing orthopedic surgery in 1993, health professionals recommended a much lower mean age for competence than parents did (10.3 vs. 13.9).(137) The recent finding that parents judged their children more readily competent than clinicians, might be related to the specific dynamics of parent-child relationships.(14) Parents are expected to inhibit their child's impulsive, risky, and sometimes harmful behavior and to substitute the child's ineptitude and inability to judge situations, appropriate behavior and actions with their superior judgment. Parents tailor their parenting behavior to the specific abilities of the child. Children who are raised in a warm and understanding atmosphere are often able to present their part in a joint decision-making process at an early stage of their development.(16) An authoritative parenting style, which includes direction-giving and limit-setting, is positively related with an adolescent’s capacity for autonomous decision-making.(20) In the medical context children might be capable of autonomous decision-making, albeit, within the guiding environment set by their parents. Possibly parents assign their children more decision-making competence than professionals do, because parents shape the family context and professionals regard the child more independently. Assessment Must Cover Developmental Aspects Differences between children and adults regarding decision-making competence have been found in the ability to restrain impulsivity and in the ability to place a given decision in a larger temporal context.(19) The inadequate capacity of children in risk assessment could be connected to the late full maturation of the frontal lobes that are essential for effective executive functions.(20) Adolescents generally do not fully possess the capacity to appreciate the long-term consequences of their choices until the age of 21.(20) Research demonstrated a difference between decision-making under low levels of arousal or in situations with low emotional upheaval (cold cognition), and thought processes under high levels of arousal and emotional valance (hot cognition).(167) Hot cognition may result in intuitive responses rather than carefully considered, rational responses.(167) Decisions on medical research participation involving information provision, rehearsal of information, time to consider, and reflection with parents, generally result in cold cognition decisions. Treatment decisions are more prone to hot cognition when involving time pressure or weighty risks. With the research results showing that children of 11.2 years and above have comparable decision-making capacities to adults concerning research participation, we need to consider their possible immaturity in decisions of a supervisory or managerial nature normally made by their parents, for example overseeing the family agenda, or arranging transport to the hospital. Possibly, children are able to decide with cold cognition on research participation, but are less able to responsibly respond to, for example, unforeseen traffic situations and therefore need the dyadic relationship with parents who provide the necessary direction-giving and limit-setting. Practical Aspects From a practical point of view, assessment of all pediatric patients’ competence on a case-by-case basis with an instrument would impose a heavy burden on patients, professionals, and the medical system. A selective implementation of a standardized competence assessment in exceptional cases would be preferable over a broad implementation (Table 8). Table 8. Recommendations for Structured Assessment of Decision-Making Competence in Children in the Clinical Context \| Context \| Proposal \| Comments \| \|---------\|----------\|----------\| \| Treatment \| – Individual cases: strike proper balance between protecting and respecting the child’s interests \| – General population: burden on medical system, not much better than age limits \| \| \| – Children < 12 years: if competent in exceptional case with weighty decision \| \| \| \| – Children > 12 years: in case doubts exist on competence \| \| \| Research \| – Individual cases: children between 10 and 12 years \| – General population: burden on medical system, not much better than age limits \| \| \| – Children > 12 years: in case doubts exist on competence \| \| \| \| – Feasible for research purposes at group level \| \| \| \| – Feasible in special research populations (intellectual disabled, psychiatrically ill) \| \| For the research context, under the age of 9.6 years children were generally incompetent to decide on research participation, so an individual assessment does not seem profitable. Children between 9.6 and 11.2 years were in the change-over period, an individual assessment of competence might be applicable in this age group. Children of 11.2 years and above can generally be considered decision-making competent, no individual assessment is needed unless there are reasons to doubt a child’s competence. In special research populations like intellectual disabled children or pediatric patients with a psychiatric disorder that diminishes competence, a research protocol could include a standardized competence assessment of participants in order to warrant the interests of incompetent patients. In the treatment context, there are no conclusive age-limits for competence established empirically, yet preliminary findings indicate agreements with the research context. An age-limit that is generally in accordance with the age that children reach decision-making competence could be applied; derived from the studies on MacCAT-CR and MacCAT-T a preliminary appropriate age may be 11 or 12 years. In case of doubt, competence will have to be assessed in children older than 12 years as well. Individual competence assessment of all pediatric patients in the change-over period might possibly overburden clinicians. However, it may be valuable to create the possibility for clinicians to take into account exceptional cases, such as the assessment of a child under the age of 12, seemingly competent, who has to make a weighty decision. In these cases an individual standardized competence assessment contributes to substantiate the exception. Parents are generally provided with the legal authority to raise their children, assigning them rights and responsibilities. To achieve an equitable consideration between the legal position of the child and that of the parents, a double consent procedure (child and parent) is recommended for minors from the age of 12 until majority. Even if we establish a child's decision-making competence regarding the medical decision at hand, a double consent procedure will do justice to developmental aspects of children and the specific characteristics of the parent-child dyad. The parental role is needed to offer extra protection by creating the context for the child's competent decision-making and by facilitating the child's long term autonomy. Besides the advantages of a double consent procedure, there may be a disadvantage concerning possible disagreement between child and parent, which may require elaborated policies. In the Dutch situation experience has been gained with a double consent procedure and evaluation shows that disagreement between parent and child was not a concern.(168;169) A double consent procedure is fundamentally different from a procedure of parental permission and child assent, and would imply a considerable shift regarding some current legislations. For instance, in the current Code for Federal regulations of the United States (13) by definition children are “persons who have not attained the legal age for consent to treatments or procedures involved in the research” (45CRF46.402(a)). The legal age of adulthood is a matter of local law, but is in a large majority of states 18 years. Regulations state that some children might be able to give their assent, meaning an affirmative agreement. However, in research the institutional review board may still waive the assent requirement under certain circumstances (45CFR46.116). Some authors have proposed that children's assent should only be required from a fixed age of 14 years, based on theories of subject autonomy and child development. The empirical evidence that children are generally competent not only to assent, but even to consent from the age of 12 offers a force opposing to these regulations and theories. There is no indication of a considerable difference in children's development between regions with widely varying policies regarding children's consent. These local variations in regulations may have evolved under the influence of historical, cultural, or emotional preferences, representing a local normative view. Empirical data now provide underpinnings for more evidence-based age limits in policies. Limitations and Directions for Future Research Although our recent empirical research provides substantial data to consider in debate and practice, many aspects of children's decision-making competence are still to be studied, of which we will name just a few. For instance, regarding medical decision-making, the age limits for reaching legal majority vary between countries and states from 16 to 21 years. Research does not show at what age a double consent procedure will no longer prove effective. In addition, more research is needed to demonstrate the validity of a cutoff score on a standardized assessment instrument for competence and the desirability of such a cutoff must be considered. In the treatment setting, more extended research on reliability and validity of the MacCAT-T in children is recommended. The importance of children's decision-making competence is not confined to the medical context alone but may be of significance to adjacent fields, for instance children's competence to proceed to criminal adjudication or to be consulted in civil procedures, which requires further research. Furthermore, new developments in neuropsychiatry may contribute to the understanding of the functioning of specific brain regions or connections that promote competent decision-making. Summary Research outcomes show that the legal concept of medical decision-making competence could be operationalized into a standardized assessment instrument for children in the clinical context. The MacCAT-CR proved accurate for children's competence assessment in clinical research, preliminary findings show feasibility of MacCAT-T in the treatment setting. Developmental aspects, especially the fine-tuning of decision-making within the parent-child dyad, including the broader family context, are of importance in addition to a standardized competence assessment. Policy recommendations include a selective implementation of individual assessment of children's competence in medical decision-making by a standardized tool in combination with practicable, generally appropriate age-limits. In the research context children can be deemed competent from the age of 12 and above, preliminary findings suggest the same age-limit for the treatment context. In the research context, case-by-case assessment of competence might be valuable in children in the change-over period between 10 and 12, in special research populations of mentally comprised patients, and in case of children older than 12 years when there are reasons to doubt their competence. In the treatment context, individual competence assessment might create an opportunity in exceptional cases to allow a competent child under the age of 12 to co-decide over significant medical interventions. A double consent procedure, including both child as well as parents, is recommended for children from the age of 12 until legal majority.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 1056, 1 ], [ 1056, 2777, 2 ], [ 2777, 5362, 3 ], [ 5362, 8111, 4 ], [ 8111, 10549, 5 ], [ 10549, 13106, 6 ], [ 13106, 15767, 7 ], [ 15767, 18286, 8 ], [ 18286, 21111, 9 ], [ 21111, 23325, 10 ], [ 23325, 26180, 11 ], [ 26180, 28696, 12 ], [ 28696, 30077, 13 ] ] }
737a97c1bb3191916a0229433aebe2044fcd6e11	{ "olmocr-version": "0.1.59", "pdf-total-pages": 15, "total-fallback-pages": 0, "total-input-tokens": 32709, "total-output-tokens": 8907, "fieldofstudy": [ "Medicine", "Biology" ] }	Evaluation of trabecular bone microstructure of mandibular condyle in edentulous, unilateral edentulous and fully dentate patients using cone beam computed tomography Authors: Alaettin Koç, İdris Kavut, Mehmet Uğur DOI: 10.5603/FM.a2019.0133 Article type: ORIGINAL ARTICLES Submitted: 2019-10-10 Accepted: 2019-11-22 Published online: 2019-12-04 This article has been peer reviewed and published immediately upon acceptance. It is an open access article, which means that it can be downloaded, printed, and distributed freely, provided the work is properly cited. Articles in "Folia Morphologica" are listed in PubMed. Evaluation of trabecular bone microstructure of mandibular condyle in edentulous, unilateral edentulous and fully dentate patients using cone beam computed tomography Running Title: Evaluation of microstructure of mandibular condyle in patients using tomography Alaettin Koç¹, Idris Kavut², Mehmet Uğur² ¹Van Yüzüncü Yıl University Faculty of Dentistry, Department of Oral and Maxillofacial Radiology, Van, Turkey ²Van Yüzüncü Yıl University Faculty of Dentistry, Department of Prosthetic Dentistry, Van, Turkey Address for correspondence: Alaettin Koç, Van Yüzüncü Yıl University, Faculty of Dentistry, Department of Oral and Maxillofacial Radiology, 65080, Van, Turkey, tel: +904322251744, fax: +904322251747, e-mail: [email protected] Abstract Background: The aim of this study was to compare the trabecular bone microstructure of the mandibular condyle in edentulous, unilateral edentulous (Kennedy Class II), and fully dentate patients. Materials and methods: The study used the cone-beam computed tomography (CBCT) images of 17 fully dentate (34 condyles), 16 edentulous (32 condyles), and 17 unilateral edentulous patients (34 condyles) aged 19 to 80 years. The trabecular bone microstructure of the mandibular condyle was evaluated on eight consecutive cross-sectional images of these patients. In the microstructure analysis, structural model index (SMI), ellipsoid factor (EF), bone volume fraction (BV/TV), trabecular thickness (Tb.Th) and trabecular separation (Tb.Sp) were measured. Results: There was no significant difference between the mean SMI, BV/TV, EF and Tb.Th microstructure values of each group (p = 0.243, p = 0.095, p = 0.962, p = 0.095, respectively). However, there was significant difference in terms of mean Tb.Sp between the groups (p =0.021). The trabecular structure in all three groups was more rod-shaped. No correlation was found between age factor and microstructure values. Conclusions: Considering the in vivo microstructure analysis of CBCT images, it can be said that teeth loss does not have a significant effect on the microstructure parameters excluding Tb.sp of mandible condyles and does not affect mandibular condyle trabecular endurance. Key words: mandibular condyle, cone beam computed tomography, quantitative evaluation, bone tissue --- Introduction The facial profile, as well as environmental and genetic factors, may affect the masticatory system of individuals and subsequently affect bone morphology in the mandible [1, 2]. The temporomandibular joint (TMJ) may be exposed to degenerative changes when there are changes in masticatory functions or when force is applied powerful enough to disrupt the joint structure [3]. Furthermore, sudden changes in masticatory functions may deteriorate the ongoing delicate balance between dental occlusion, masticatory muscles and TMJ structure, and the deteriorated balance may concentrate on a different system [4, 5]. Loss of occlusal support deteriorating the balance in the masticatory system may be one of the factors that accelerate TMJ deterioration. Premature contacts have been found to be present in patients with TMJ disorder and this abnormal relationship has been observed to be more frequent in these patients than people with normal joints. This imbalance can lead to degenerative changes due to increased stress on the masticatory muscles and excessive pressure on the joint surface [6]. In the literature, techniques such as electromyography and kinesiography have been used to analyze the relationship between dental malocclusion and TMJ disorder. However, no significant correlation has been found between dental malocclusion and TMJ disorder with the above-mentioned techniques [7]. Edentation, teeth movements, and parafunctional habits such as bruxism are effective in the formation of occlusal force. Parameters such as dentition status, occlusal force, internal structure and morphology of TMJ are known to be correlated with each other. Considering the correlation between these parameters, it is possible that the trabecular structures of the mandibular condyle of the edentulous and fully dentate patients are of different types [8]. In other words, properties such as density, thickness, and separation of the trabecular structure may change due to the above-mentioned external factors [9]. For instance, it has been reported that the density and bone volume fraction (BV/TV) of mandibular condyle trabeculae are lower in edentulous patients than in fully dentate patients [10]. Similarly, in a different study [11], patients with high bone densities were found to have a plate-like trabecular structure whereas patients with low bone densities had a rod-like trabecular structure considering the relationship between mandibular condyle trabecular structure and density of related bone of the fully dentate patients. Different imaging techniques such as plain radiographs, computed tomography (CT), magnetic resonance imaging (MRI) and cone-beam CT (CBCT) have been used to examine the TMJ [5-7]. A three-dimensional image of the mandibular condyle can be obtained, analysis of surrounding tissues and morphological changes in bones can be examined, and the cavity and dynamic functioning of the TMJ can be analyzed using CT, MRI and CBCT techniques. There is an increasing demand for CBCT devices because it has voxel dimensions of up to 0.075 mm, has exact measurement capability, and required low dose and cost compared to multi-slice CT (MSCT) devices [12-14]. Although Hounsfield unit values could not be determined exactly with CBCT, bone microstructure values were measured using CBCT in some studies [15, 16]. Microstructure evaluation values close to micro CT devices, which are accepted as the gold standard for the evaluation of bone microstructure, have been reported to be obtained with CBCT with the help of images taken at low voxel dimensions [16]. To the best of our knowledge, there is no study in the literature that compares the mandibular condyle trabecular structure parameters of edentulous, unilateral edentulous, and fully dentate patients. The aim of this study was to compare the bone volume fraction (BV/TV), structural model index (SMI), ellipsoid factor (EF), trabecular thickness (Tb.Th) and trabecular separation (Tb.Sp) parameters of the groups and to determine the effect of loss of occlusion on the trabecular bone structure of the mandibular condyle. Material and Methods A total of 50 patients (25 female and 25 male) aged 19-80 years were classified according to their edentation status. Of these patients, 17 were fully dentate with 34 condyles (mean age 40.7), 16 were edentulous with 32 condyles (mean age 52.3), and 17 were unilateral edentulous with 34 condyles (mean age 56.9). Trabecular bone microstructures of mandible condyle were analyzed on their cross-sectional images. Patients with systemic diseases that can affect the bone metabolism and microstructure, deformity, fracture, or tumoral lesion in the mandibular condyle region and those having cross-sectional images with poor quality were excluded from the study. KaVo 3D eXam (Biberach, Germany) tomography device was used to obtain the images. Scanning parameters were selected as follows: 20.27 mA, 14.7 seconds, 120 kVp, 16 × 6 cm FOV, and 0.2 mm isotropic voxel. The gonion of the patients was fixed with a plastic holder to prevent movement artifact during screening. This study was conducted following the receipt of approval from University Ethical Committee (Approval no: Van YYU-2018/04/04-05). CBCT scanning data was converted to Digital Imaging and Communications in Medicine (DICOM) format. Cross-sectional images of the patients' mandibular condyle region were imported into ImageJ software (U.S. National Institutes of Health, Bethesda, Maryland, USA). Eight consecutive sections without intersection gaps between each other were stacked into ImageJ software. In microstructure analysis, 2 mm apical of the cortical bone at the head of the condyle and trabecular bone area within 2 mm of the cortical bone of the condyle in the each axial sectional image were included while selecting the region of interest (ROI). The ROI region was duplicated to be measured and then the images were converted to binary image form to make them suitable for microstructure evaluation (Figure 1). Then, SMI, BV/TV, EF, Tb.Th and Tb.Sp values were measured by BoneJ plugin in the software. Measurements were made by an oral and maxillofacial radiologist who have been analyzing CBCT images for three years and performing microstructure analysis with related software for two years. Statistical analysis of the data obtained was performed using SPSS version 20.0 software (IBM SPSS Statistics 20.0; IBM Co., Armonk, NY, USA). The relationship between loss of occlusion and SMI, BV/TV, EF, Tb.Th and Tb.Sp values was analyzed by one-way ANOVA test. Mann-Whitney U test was used to compare the trabecular microstructure parameters of condyles belonging to edentulous and dentate sides in unilateral edentulous patients. Intra-class correlation coefficient (ICC) was calculated to measure intra-rater reliability. Randomly selected trabecular bone microstructures of 34 condyle heads were analyzed by an observer twice in one-month intervals. Results Descriptive statistics of the parameters are presented in Table 1. Mean SMI value was found to be 2.80 in the fully dentate group, 2.99 in the edentulous group, and 2.69 in the unilateral edentulous group. In other words, the trabecular microstructure of the condyle was more rod-shaped in each group. The highest BV/TV value was measured in the fully dentate group whereas the highest EF and Tb.Th values were in the fully dentate group and unilateral edentulous group, respectively, and the highest Tb.Sp value was in the edentulous group. In the microstructure analysis of mandibular condyle of each group, no statistically significant difference was observed between the groups in terms of mean SMI, BV/TV, EF, and Tb.Th values (p = 0.243, p = 0.095, p = 0.962, p = 0.095, respectively). However, there was significant difference in terms of mean Tb.Sp between the groups; the mean Tb.Sp of edentulous group was significantly higher than the mean of fully dentate group’s (p = 0.021) (Table 2). When the correlation between age and microstructure values were examined, no correlation was observed between age and SMI (r = -0.062, p = 0.540), BV/TV (r = 0.037, p = 0.715), Tb.Th (r = -0.014, p = 0.889), Tb.Sp (r = 0.008, p = 0.935) and EF (r = -0.038, p = 0.707) values. In the comparison of SMI, BV/TV, EF, Tb.Th and Tb.Sp parameters of two sides in the unilateral edentulous group, there was no significant difference between two sides in terms of relevant parameters (p = 0.708, p = 0.518, p = 0.760, p = 0.454, p = 0.160, respectively). Good intra-rater reliability was observed in repeated measurements of SMI (ICC = 0.706), BV/TV (ICC = 0.774), EF (ICC = 0.747) and Tb.Sp (ICC = 0.859) in terms of intra-rater reliability values, whereas excellent intra-rater reliability was observed in Tb.Th (ICC = 0.986). Discussion The results of our study have shown that there was no significant difference between the groups in terms of condyle microstructures excluding Tb.Sp. Magnetic resonance imaging is the gold standard for demonstrating cartilage structures in TMJ, position of the joint disc, and pathologies such as effusion. However, it is inadequate in the analysis of changes in condyle trabecula due to its relatively low resolution [17]. Methods such as micro CT, histomorphometric measurements and high-resolution peripheral quantitative CT have been used to evaluate the trabecular structure of the condyle. However, sacrificed dead animal tissues are generally used for these methods [18, 19]. In a study by Parsa et al. [16], mandibular images of 20 dry edentulous patients were obtained through CT, micro CT, and CBCT and a strong correlation was observed between CBCT and CT ($r = 0.89$) and between CBCT and micro CT ($r = 0.82$) when the trabecular microstructure correlations were examined. Therefore, we preferred to use CBCT to obtain images in vivo, it has relatively lower radiation dose, is cost-effective, and has lower acquisition time. In orthodontic patients with various malocclusion, malocclusion has been shown to increase the prevalence of TMJ disorder. For instance, more than 60% of the MRI images of the patients with anterior open bite showed pathological changes in the bone [20]. In patients with malocclusion, canine guidance and posterior occlusion are not ideal. It has been reported that condyles can make unusual deviations to compensate for these imbalances and these unusual movements may cause damage to the joint structures [21]. Furthermore, in a study including about 300 patients, the proportion of open bite patients with and without TMJ disorder complaints was reported to be the same with the abovementioned ratio (about 6%) and malocclusion was reported to be not associated with TMJ disorder [22]. Similarly, Sousa et al. reported in their study of 100 patients that there was no significant difference in joint disorder between patients with and without an anterior open bite, posterior crossbite and more than five posterior teeth lost [23]. Furthermore, in unilateral edentulous cases, the masticatory muscles on both the dentulous and edentulous sides must work harmonically and there is a decrease in the force load on the muscles on both sides. This explains why the resorption process... on both sides continues in parallel with each other [24]. Similarly, the condyle trabecular structures on both sides of our patients in the unilateral edentulous group were similarly affected by teeth loss and no significant difference was observed in terms of the microstructure parameters. Structural model index refers to the average shape of the trabecular structure of the bone. An SMI of 0 is referred to as plate-shaped trabeculae, SMI of 3 is referred to as rod-shaped trabeculae, and SMI of 4 is referred to as sphere-shaped trabeculae [25]. Doube [26] reported that there were concave curvatures to a large extent in the real bone, it was not possible to accurately measure this bone trabecular structure with SMI, and using EF, instead of SMI, in the analysis of trabecular structure can provide more accurate results. They have further reported that EF gets values between -1 and +1. It gets -1 when discus-shaped ellipsoids are the majority, it gets 0 when there are discus- and javelin-shaped ellipsoids, and it gets +1 when javelin-shaped ellipsoids are the majority. Although there was no significant difference between the three groups in terms of SMI in the present study, the highest mean SMI value was found to be 3 in the edentulous patient group and the lowest mean SMI value was 2.70 in the unilateral edentulous patient group, meaning that the trabecular structure in all three groups was more rod-shaped. When the mean values in all three groups were analyzed according to the EF, the trabecular structure was found to be more javelin-shaped. In other words, we can state that SMI and EF parameters reflect trabecular structure similarly. In a study by Giesen et al. [27] comparing the condyles of the fully dentate and edentulous patients, the edentulous patient group was found to have lower BV/TV values and their bone trabecula was seen to be not as stiff and strong as in fully dentate patients. This reduction in BV/TV was reported to be associated with the conversion of the trabecula to a more rod-like structure, but not associated with the reduction in Tb.Th. In their study, it was not known when edentulous patients lost their teeth or whether they were using dentures. Similarly, in the present study, it was not known how long the edentulous patients had no teeth or whether they were using dentures. No difference was observed between bone microstructure values due to teeth loss in our study. As the BV/TV, i.e. the strength of the bone structure decreased, the trabecula was observed to turn into a more rod-like structure. For instance, the mean BV/TV values of the fully dentate and edentulous group were 0.32 and 0.23, respectively, whereas the mean SMI values were 2.80 and 3, and Tb.Th values were 0.93 and 1.16, respectively. As can be seen, the bone trabecular volume in the edentulous group was lower, and its structure turned into a more rod-like pattern. However, the decrease in BV/TV was seen to be not parallel to the decrease in Tb.Th. Findings obtained in our study are compatible with the findings reported by Giesen et al. [27] in their study. Ding et al. [28] analyzed the age-related changes in the tibial bone trabecular microstructure values of 40 patients aged 16-85. They reported that the trabecular structure became more rod-like with the increasing age, however, it was further reported that there was no significant change in Tb.Th in patients in the age group of 20-80 and no difference was observed in microstructural values due to the low time-dependent remodeling activity of the tibial bone. In the present study, the duration of teeth loss may not have been long enough to cause remodeling in the trabecular structure of the condyles of the edentulous patients and to affect microstructural values. This study has some limitations. Firstly, it was not known how long the patients have been edentulous and whether they were using dentures. Secondly, we only used the images of patients participating from the Eastern Anatolia Region of Turkey and the results of our study are, therefore, shaped according to the characteristics of the ethnic structure in this region. In our study, CBCT images with a high resolution of 200 μm were used. Since the value range of Tb.Th and Tb.Sp dimensions vary between 0.46-5.16 and 0.62-5.76 mm, it can be said that the voxel size used in our study is sufficient to evaluate the related structures. Furthermore, bone microstructure measurements were seen to be performed in vitro in most of the studies [8-11, 16, 25, 27, 28] in the literature whereas our study was carried out in vivo thanks to lower acquisition time and radiation dose provided by CBCT than micro CT. Conclusions Although there was no significant difference between the fully dentate, edentulous, and unilateral edentulous patient groups in terms of the trabecular microstructure excluding Tb.Sp of condyle, the trabecular structure of the edentulous group was more rod-like and the mean Tb.Sp of edentulous group was significantly higher than the mean of fully dentate group’s. As the trabecular structures of the condyle turned into more rod-like structures, BV/TV value reflecting the strength of the trabecular bone was found to decrease. Moreover, no significant change was observed in trabecular bone microstructure parameters with increasing age. 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Changed morphology and mechanical properties of cancellous bone in the mandibular condyles of edentate people. J Dent Res. 2004; 83: 255–9, doi: 10.1177/154405910408300314, indexed in Pubmed: 14981130. 28. Ding M, Hvid I. Quantification of age-related changes in the structure model type and trabecular thickness of human tibial cancellous bone. Bone. 2000; 26: 291–5, doi: 10.1016/s8756-3282(99)00281-1, indexed in Pubmed: 10710004. Table 1. Descriptive statistics of bone trabeculae parameters \| Parameters \| N \| Min \| Max \| Mean ± SD \| \|------------\|----\|-----\|------\|-----------\| \| SMI \| 100\| 0.80\| 4.73 \| 2.83 ± 0.72 \| \| BV/TV \| 100\| 0 \| 0.96 \| 0.29 ± 0.20 \| \| EF \| 100\| -0.51\| 0.72 \| 0.4 ± 0.18 \| \| Tb.Th \| 100\| 0.46\| 5.16 \| 1.11 ± 0.61 \| \| Tb.Sp \| 100\| 0.62\| 5.76 \| 1.99 ± 1.15 \| SMI, structure model index; BV/TV, bone volume fraction; EF, ellipsoid factor; Tb.Th, trabecular thickness; Tb.Sp, trabecular separation; N, number; Min, minimum; Max, maximum; SD, standard deviation. Table 2. Comparison of trabecular microstructure parameters of edentulous, unilateral edentulous and fully dentate patients using One-Way ANOVA \| Group \| SMI \| BV/TV \| EF \| Tb.Th \| Tb.Sp \| \|--------------------\|---------\|--------\|--------\|--------\|--------\| \| \| Mean ± SD\| \| \| \| \| \| Fully dentate \| 2.80 ± 0.67 \| 0.32 ± 0.16 \| 0.05 ± 0.17 \| 0.93 ± 0.25 \| 1.56 ± 1.14 \| \| Edentulous \| 3 ± 0.70 \| 0.23 ± 0.20 \| 0.04 ± 0.16 \| 1.16 ± 0.53 \| 2.31 ± 1.05 \| \| Unilateral Edentulous \| 2.70 ± 0.79 \| 0.31 ± 0.22 \| 0.04 ± 0.20 \| 1.24 ± 0.85 \| 2.11 ± 1.16 \| \| p value \| 0.243 \| 0.095 \| 0.962 \| 0.095 \| 0.021 \| SMI, structure model index; BV/TV, bone volume fraction; EF, ellipsoid factor; Tb.Th, trabecular thickness; Tb.Sp, trabecular separation; SD, standard deviation. Figure 1. Selection of region of interest in axial sectional image (a), and conversion of sectional image into binary image format to make suitable for microstructure analysis (b).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 622, 1 ], [ 622, 2374, 2 ], [ 2374, 4600, 3 ], [ 4600, 7062, 4 ], [ 7062, 9422, 5 ], [ 9422, 11748, 6 ], [ 11748, 14191, 7 ], [ 14191, 16798, 8 ], [ 16798, 19126, 9 ], [ 19126, 21060, 10 ], [ 21060, 23149, 11 ], [ 23149, 25277, 12 ], [ 25277, 27078, 13 ], [ 27078, 28128, 14 ], [ 28128, 28128, 15 ] ] }
0027c2d0d6800fe51926624f824cc2ed4354dfca	{ "olmocr-version": "0.1.59", "pdf-total-pages": 19, "total-fallback-pages": 0, "total-input-tokens": 40851, "total-output-tokens": 12239, "fieldofstudy": [ "Materials Science", "Engineering" ] }	Improved Dispersion of Carbon Nanotubes in Polymers at High Concentrations Chao-Xuan Liu 1 and Jin-Woo Choi 1,2,* 1 Department of Electrical and Computer Engineering, Louisiana State University, Baton Rouge, LA 70803, USA; E-Mail: [email protected] 2 Center for Advanced Microstructures and Devices, Louisiana State University, Baton Rouge, LA 70803, USA * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +1-225-578-8764; Fax: +1-225-578-5200. Received: 3 September 2012; in revised form: 24 September 2012 / Accepted: 6 October 2012 / Published: 26 October 2012 Abstract: The polymer nanocomposite used in this work comprises elastomer poly(dimethylsiloxane) (PDMS) as a polymer matrix and multi-walled carbon nanotubes (MWCNTs) as a conductive nanofiller. To achieve uniform distribution of carbon nanotubes within the polymer, an optimized dispersion process was developed, featuring a strong organic solvent—chloroform, which dissolved PDMS base polymer easily and allowed high quality dispersion of MWCNTs. At concentrations as high as 9 wt.%, MWCNTs were dispersed uniformly through the polymer matrix, which presented a major improvement over prior techniques. The dispersion procedure was optimized via extended experimentation, which is discussed in detail. Keywords: polymer, carbon nanotubes, nanocomposite, high concentration, dispersion 1. Introduction Polymers possess a great variety of material characteristics (e.g., mechanical flexibility, optical transparency, biocompatibility, chemical stability, etc.) enabling them to be used in diverse applications such as microfluidic systems and bio-implantable systems. A polymer can be produced in huge volumes thanks to the development in its manufacturing industry. For example, microelectromechanical systems (MEMS) can be readily made from polymer by processes such as cast molding, injection molding, hot embossing and photolithography. However, due to lack of electrical conductivity in most polymers, the role of this material has been limited to a structural component in most applications. Often, polymer-based MEMS devices require conductive elements to electrically control or collect signals from systems. While metal suffers coherent incompatibility issues with polymers, a mixture of polymer and nanoscaled fillers—termed nanocomposite provides an alternative of incorporating conductivity into polymer systems. This class of material is unique in the sense that it retains many desirable features of polymers (flexibility, biocompatibility, processability) yet adds electrical conductivity and/or piezoresistivity from the nanofiller which is not an intrinsic property of most polymers. By utilizing polymer nanocomposite, components such as conductive electrodes and sensor elements could be incorporated into conformal all-polymer systems. Polymer nanocomposite is composed of a thorough mixture of polymer matrix and nanoscale filling materials. To use as the matrix of nanocomposite, there are numerous polymers of diverse properties to choose from, including both plastics and elastomers which are the main two types of polymers. For the purpose of sensing specifically, a good deal of research effort has been committed to select an appropriate hosting matrix for the nanocomposite. Various polymers such as poly(methyl methacrylate) (PMMA) [1,2], polycarbonate (PC) [3], poly(ethylene) (PE) [4], poly(L-lactide) (PLLA) [5], etc. have been incorporated with nanofillers to construct strain sensors, which are capable of holding larger tensile strain than conventional metallic strain gauges [6]. Compared with above polymers, silicone-based elastomer poly(dimethylsiloxane) PDMS owns superior mechanical elasticity as it easily holds over 100% of tensile strain without any structural failure [7], making it an ideal choice for large-range strain sensing applications. Its flexibility allows it to be readily attached to curved surfaces, which is often necessary in biomedical sensors. Moreover, PDMS being a chemically inert and biocompatible material is widely used in microfluidics and biomedical areas [8]. Since MEMS-based sensors require feature sizes on the microscale, conductive fillers of polymer nanocomposite typically have feature size on the nanometer scale, so that the conformity of microstructures could be ensured. Common nanofillers include carbon nanotubes, carbon black (nanoscaled carbon particles), metal particles and flakes [9]. Amongst these, carbon nanotubes are particularly interesting candidate for sensing applications. Ever since the discovery of carbon nanotubes by Iijima in 1991 [10], numerous research has been conducted to explore the potentials of this “magic” material [11]. With a high aspect ratio because of its long tubular structure, carbon nanotubes demonstrate relatively high electrical conductivity. For example, compared with other conductive nanofillers (e.g., metal flakes or particles with lower aspect ratios), carbon nanotubes composites of various polymers reach percolation threshold at a lower weight percentage [9,12]. Probably, tubular structures allow the formation of a more efficient electron-conducting network in CNT-based composite. Also, the piezoresistivity of CNTs make them a suitable candidate for sensors: when a CNT-based composite is exposed to mechanical deformation, the geometry and interconnections of nanotubes within the polymer matrix vary accordingly, which leads to a change in its electrical resistance. Further, CNTs are one of strongest materials known to man, with tensile strength up to 63 GPa using multi-walled carbon nanotubes (MWCNTs) [13], giving them another edge over other materials for fabricating robust sensors. In this work, multi-walled carbon nanotubes were chosen over single-walled carbon nanotubes (SWCNTs) because MWCNTs generally offer better conductivity [32]. Plus, economic wise MWCNTs generally cost less to purchase. Thus, MWCNTs were picked as the preferred material over SWCNTs [14]. 2. Results and Discussion In itself, dispersion is a spatial property whereby the individual carbon nanotubes are spread with the roughly uniform number density throughout the continuous polymer matrix. The first challenge is to separate the tubes from their initial aggregated assemblies, which is usually achieved by local shear forces. Direct manual mixing of CNTs with polymer resin, though the simplest approach, does not create sufficient local shear force and therefore leads to poor dispersion of CNTs inside polymer matrix. More effective separation of CNT bundles requires the overcoming of the inter-tube van der Waals attraction [15]. Depending on the tube shape/size and the orientation of nanotubes with respect to each other, such an attraction can act within a spacing of a few nanometers [16]. For closely packed tubes within a medium, the surface adsorption of a dispersant, or the wetting of the polymer/solvents, both require a temporary exfoliation state. Physical approaches such as shear mixing [17], mechanical stirring, sonication [18], ball milling [19] and micro-bead milling [20] processes have been employed for this purpose. Although these techniques may appear very different, they are all governed by the transfer of physical shear stress onto nanotubes which breaks down bundles. In shear mixing, for example, the separation of individual CNTs from bundles is achieved in shear flow induced by the rotation of an extrusion in a polymer solution or melt. Usually, dispersion via shear mixing is only achievable for specific types of MWCNTs, with a high shear rate in a rather viscous medium. Terentjev et al. demonstrated that nanocomposite containing high loading concentrations of CNTs (up to 7 wt.%) could be dispersed via this technique [21]. However, the processing time significantly goes up as loading concentration rises. More importantly, shear mixing tends to section carbon nanotubes into shorter length scale, thereby reducing their conductivity significantly—an undesired attribute for nanocomposite intended for use as a sensor material. The dispersion of carbon nanotubes could be assisted by the introduction of a common solvent—an organic solution which dissolves polymer resin easily and at the same time allows monodispersion of carbon nanotubes. In this case, two dispensed solutions sharing common solvent but containing carbon nanotubes and polymer resin respectively, undergoes mechanical stirring or the increasingly popular sonication process. Following that, two solutions are mixed together to further go through stirring or sonication. Finally with the complete evaporation of solvent, CNTs would leave dispersed in polymer. Here the choice of organic solvent is critical for determining the final dispersion quality and depends on the polymer matrix. For PDMS alone, various organic solvents have been reported to assist dispersion of CNTs, such as toluene [22], tetrahydrofuran (THF) [23], chloroform [24,25], dimethylformamide (DMF) [26], etc. While each report claims high dispersion quality of CNTs, there is lack of standard characterization protocol for dispersion of CNTs within polymers [15], leaving room for subjective judgment. Comparative experimental tests are still needed to verify optimal solvent choice for the dispersion of carbon nanotubes. It should be noted that even with optimal common solvent to help dispersion, the optimization of process conditions is still critical to ensure final dispersion quality. In the stage of solvent evaporation, for instance, as CNTs concentration continuously increases so does the re-aggregation effect of CNT bundles. Thus, this step needs to be best shortened to minimize the compromise of dispersion. 2.1. Materials and Reagents Pristine multi-walled carbon nanotubes (MWCNTs) used in this work were purchased from Cheaptubes, Inc., (Brattleboro, VT, USA) with a relative purity >95 wt.%. The dimension of the MWCNTs was 20–30 nm in outer diameter, 5–10 nm in inner diameter and 10–30 µm in length. To comparatively study the effect of surface functionalization on its dispersion state, MWCNTs treated with carboxylic acid groups (MWCNTs-COOH) were also obtained from the same company (MWCNTs-COOH contains 1.23 wt.%-COOH groups. The other properties remained the same, with relative purity >95 wt.%, 20–30 nm in outer diameter, 5–10 nm in inner diameter and 10–30 µm in length, to affirm the validity of the comparative study. The polymer matrix used in this work—poly(dimethylsiloxane) (PDMS)—is a silicone elastomer. Specifically, Sylgard 184 silicone elastomer kit was purchased from Dow Corning Inc. (Midland, MI, USA), which had two parts: polymer base resin and curing agent. The two parts are recommended to be mixed at the ratio of 10:1 and exposed to thermal curing in order to realize solidified PDMS. In fact, the mixing ratio could be varied in order to tune mechanical properties of PDMS (Young’s modulus), making it a versatile material to utilize. 2.2. Selection of Optimal Solvent for the Dispersion of CNTs within PDMS The dispersion assisting solvent depends on the type of polymer and CNTs, as it needs to dissolve both well to be effective. Also, even when a solvent disperses both polymer and filler well separately, the combination of the two could have an adverse effect on the dispersion state. Therefore, the conclusion of an optimal common solvent could only be drawn after careful comparative experimental studies. 2.2.1. CNTs Dispersion in Different Organic Solvents As noted earlier, a variety of organic solvents have been used to assist dispersion of CNTs in polymers. Solvents including toluene [22], tetrahydrofuran (THF) [23], chloroform [24,25], dimethylformamide (DMF) [26], etc., in particular, have been reported to reach great dispersion. Nevertheless, due to the lack of sufficient dispersion characterization data from these reports, experimental studies are still required to compare their actual performances and verify optimal choice for the dispersion of carbon nanotubes. An advantage of comparative study is that only relative dispersion quality is required to be evaluated, based on which a best solvent could be chosen from the solutions tested. To compare the dispersion of MWCNTs in different solvents, four organic solutions including toluene, chloroform, DMF, and THF, as shown in Table 1, were used for experimental test in the following manner. Table 1. Important properties of experimentally tested organic solvents. \| Organic solvent \| Chemical formula \| Density (g/mL @ 20 °C) \| Boiling point (°C) \| Vapor pressure (kPa @ 20 °C) \| \|-----------------------\|------------------\|------------------------\|--------------------\|------------------------------\| \| Toluene \| C₆H₅CH₃ \| 0.86 \| 110.6 \| 2.93 \| \| Chloroform \| CHCl₃ \| 1.48 \| 61.2 \| 21.1 \| \| Tetrahydrofuran \| C₄H₈O \| 0.89 \| 66 \| 19.3 \| \| Dimethylformamide \| C₃H₇NO \| 0.94 \| 153 \| 0.3 \| \| PDMS base resin \| (C₂H₆OSi) \| 1.11 \| N/A \| N/A \| First, quantities of pristine MWCNTs weighing about 3 mg were added into four vials containing 10 mL of respective solutions, yielding a concentration of 0.3 mg/mL, as shown in Figure 1 (chloroform). Figure 1. Images showing 3 mg of multi-walled carbon nanotubes (MWCNTs) being added into 10 mL of chloroform. In the magnified view black bundles settled on vial bottom were from as-is MWCNTs. Here, a low concentration was desired to offer partial optical transparency in dispersed solutions. Through trial and error, it was found that solution with concentrations higher than about 1 mg/mL, after dispersion, would become completely nontransparent, which was not desirable for direct visual observation. On the other hand, it was found in experiments that a concentration of 0.3 mg/mL or lower was possible for direct visual observation of dispersion qualities. Although the 0.3 mg/mL threshold was somewhat empirical, MWCNTs dispersed around this concentration were able to be observed clearly and consistently. With this small amount of MWCNTs the inaccuracy of the weight equipment was relatively significant (±1 mg) which might cause variations in the concentration of MWCNTs in different solvents. However, later optical observation would prove, though, this variation was not significant in affecting the dispersion quality of solutions. After introducing MWCNTs into four solutions, each mixture was then sonicated using a mild sonication bath (FS20D Fisher Scientific, frequency 42 kHz, output power 70 W) for 30 min at nominal power. This process yielded semi-transparent dispersed MWCNT suspensions, as shown in Figure 2a, composed of individual nanotubes and micro-sized bundles which were invisible to the bare eye. The stability of CNT dispersion state is a valuable indication of its dispersion quality, as CNTs tend to reaggregate into bundles with time in an unstable environment. The longer dispersion lasts and the fewer/smaller CNT bundles occur, the higher its dispersion quality. Here a simple approach of optical observation of CNT bundles was applied to evaluate dispersion quality. Although this approach could not determine the absolute quality of dispersion, it was well suited for comparative studies, where only relative information was extracted and compared from samples tested under identical conditions. All four vials were held still after their sonication. Seventy hours later, unstable dispersions showed signs of reaggregation to different extents, as indicated in Figure 2b. Visible MWCNT bundles were observed to settle at the bottom of vials, as shown in Figure 2c (chloroform) as an example. In the worst case of toluene, suspension showed apparent phase separation, with MWCNTs almost completely settled at the bottom and upper solution void of dispersed MWCNTs. Based on visual observation of the amount of reaggregated MWCNTs in various comparative experiment settings, it was likely that the reaggregation effect had an order of: toluene > chloroform > THF > DMF. One week after sonication, as shown in Figure 2d, solutions largely remained their dispersion state, other than the now transparent toluene solution. Figure 2e shows that, even after an extended holding period of 8 months, MWCNTs dispersion in the other three solutions maintained its stability, regardless of the fact that part of solutions evaporated causing CNT concentration to rise. In the case of chloroform, especially, the amount of its CNT bundles, as shown in Figure 2f, did not increase notably from the 70 h mark, which proved it to be also a stable dispersion. Overall, despite minor variations in dispersibility of MWCNTs, all three solvents including chloroform, THF and DMF could be considered candidates to help the dispersion of CNTs inside polymer nanocomposite. 2.2.2. Solubility of PDMS Base Polymer in Different Organic Solvents As a common solvent to assist dispersion of polymer nanocomposite, another important requirement is its ability to dissolve the polymer matrix. Therefore, the choice of solvent varies significantly depending on the type of polymer matrix. For PDMS specifically, the four organic solvents (toluene, chloroform, DMF, THF) which have been used in previous reports were used here for testing. It should be noted that since PDMS is a two-part thermal curable polymer, only one part should be used in the dispersion process of CNTs. As dispersion usually takes more than a few hours, the presence of two parts mixed together could render PDMS partially polymerized, which then would not be usable anymore for microfabrication. With a manufacturer-recommended mixing ratio of 10:1, PDMS base polymer resin occupies more than 90% weight of the polymer matrix, thus the base polymer is generally the part used for dispersion with CNTs. Curing agent, on the other hand, would be added after the evaporation of the common solvent, which will be further discussed later. Figure 2. MWCNTs dispersed in different organic solvents via 30 min of sonication. Solutions from left to right: toluene (0.3 mg/mL MWCNTs), chloroform (0.3 mg/mL), dimethylformamide (DMF) (0.3 mg/mL), tetrahydrofuran (THF) (0.4 mg/mL). (a) Dispersion state directly after sonication, showing no visible MWCNT bundles; (b) Solutions at 70 h after sonication showing reaggregation effect of MWCNTs in order of toluene >> chloroform > THF > DMF; (c) Magnified view of visible MWCNTs bundles in chloroform solution; (d) one week after sonication. Volume of THF solution was slightly adjusted to match the others after 4 days with no further sonication; (e) eight months after sonication. Solutions have evaporated to different extents but three out of four dispersions remained stable; (f) Magnified view of visible MWCNTs bundles in chloroform dispersion, indicating that amount of bundles remained about the same with (c). Out of the four organic solutions tested, toluene was found to have great solubility for PDMS base polymer. Nonetheless, it could not be an ideal candidate as common solvent because of its relatively poor dispersion of MWCNTs. DMF, although had the best dispersibility for MWCNTs, was found to react with PDMS base resin. Upon mixing of these two solutions, a white colored gel-like substance was formed due to chemical reaction. Thus, while it may be useful to be used for dispersion of other polymer matrices, in the case of PDMS, due to chemical incompatibility, it would not be useful for the fabrication of nanocomposite. Interestingly, chloroform and THF were both found to own high solubility of PDMS base resin, able to dissolve PDMS at concentration higher than 0.3 g/mL. Because of their relatively high dispersion of MWCNTs, both of these could potentially work as common solvents for the preparation of polymer nanocomposite. Further tests were conducted (as follows) as visual observation alone may not be sufficient to distinguish which of the two solutions would work better for PDMS. 2.2.3. The Effect of PDMS on Dispersed Carbon Nanotubes in Different Organic Solvents Supposedly, as long as the common solvent can dissolve MWCNTs and PDMS well separately, it should work for the combination of the two. The two suspended solutions could simply be poured together to go through further sonication in order to achieve high quality dispersion. Surprisingly, that was found to be not the case with certain organic solvents. From the above section, both THF and chloroform were promising candidates to work as common solvent due to their exceptional ability to disperse MWCNTs and PDMS separately. However, when MWCNTs and PDMS were both present in the solvent, THF and chloroform had dramatically different performances. In the case of THF, firstly MWCNTs were dispersed at 0.4 mg/mL (±0.2 mg/mL) via sonication for 10 min. Then, PDMS base resin at 0.15 g/mL concentration was added into the already-dispersed CNTs, as shown in Figure 3a. From Table 1, as the density of PDMS base resin (1.1 g/mL) was higher than THF (0.89 g/mL), PDMS settled at the vial bottom and could be clearly told from the dispersed CNTs. Afterwards, the mixture was sonicated for an additional 30 min, resulting in a fully dispersed solution, as in Figure 3b. However, this dispersion state was not stable with time. MWCNTs almost started reaggregating immediately, forming visible bundles just 30 min after sonication was finished, as seen in Figure 3c. Moreover, after a period of 21 h, originally dispersed MWCNTs had now completely settled at the vial bottom, as shown in Figure 3d, leaving the upper portion of solution fully transparent. Figure 3. Vial images showing effect of poly(dimethylsiloxane) (PDMS) on dispersion state of MWCNTs in THF solution: (a) PDMS added into dispersed MWCNTs-THF solution; (b) THF solution containing PDMS and MWCNTs directly after 30 min of sonication; (c) solution at 30 min after completion of sonication, showing visible CNTs bundles, and (d) solution at 21 h after sonication, showing complete phase separation which indicated the instability of dispersion. In fabrication of polymer nanocomposite, PDMS base was normally first dissolved in an organic solvent before being added into a CNT dispersion solution, instead of directly being added like in the above process. With the pre-dissolution of PDMS, similar effects also occurred when MWCNT dispersion significantly deteriorated after the introduction of PDMS content. The reason for the adverse effect of PDMS on THF-CNT dispersion has yet to be understood, however, although THF did not alter properties of PDMS base resin when mixed with it, some functional groups on PDMS base molecules could have affected the affinity between THF and MWCNTs. In the case of chloroform, similar experimental procedures were carried out to test the effect of PDMS on the dispersion state of MWCNTs. Briefly, MWCNTs were first dispersed at 0.4 mg/mL (±0.2 mg/mL) via sonication for 10 min. Then, PDMS base at around 0.12 g/mL concentration was added into solution, as shown in Figure 4a. Since the density of PDMS base (1.1 g/mL) was lower than chloroform (1.48 g/mL), PDMS stayed at the solution top separated from CNT. Then, solution was mechanically stirred for 14 min (to help expedite dissolution of PDMS) and consequently sonicated for 1 min, leading to a fully dispersed solution. Unlike THF-CNT dispersion, the chloroform suspension remained much more stable, as shown in Figure 4b, showing no visible deterioration of dispersion state even at 42 h after sonication. Figure 4. Vial images showing effect of PDMS on dispersion state of MWCNTs in chloroform solution: (a) PDMS added into dispersed MWCNTs-chloroform solution, staying on top portion and (b) Chloroform solution containing PDMS and MWCNTs 42 h after sonication. Based on the above visual comparison in Figure 4 of THF and chloroform in which PDMS and MWCNTs were dispersed, it can be concluded that, with similar circumstances, chloroform yielded a much more stable—thus higher quality dispersion of PDMS base and MWCNTs. Therefore, the best choice of common solvent among tested solutions should be chloroform. ### 2.3. Effect of CNT Functionalization on Dispersion It has been reported that carbon nanotubes with functionalized surfaces by carboxyl (–COOH) groups, compared to their pristine counterpart, could have better dispersion in polymer matrices [22,27]. To verify the effect of surface functionalization, comparative experiment was carried out, in which pristine and –COOH carbon nanotubes were dispersed with PDMS base in chloroform solutions in a parallel fashion under similar conditions. Briefly, both pristine MWCNTs (0.14 mg/mL) and COOH-MWCNTs (0.16 mg/mL) were first sonicated inside two vials for 5 min. Then, PDMS base at around 0.13 g/mL concentration was added into both solutions, which went through additional sonication for 1 h and mechanical stirring (magnetic stirrer at 1150 rpm) for 10 min. This process resulted in well dispersed solutions, as indicated in Figure 5a. However, due to the adverse effect of mechanical stirring on an established dispersion state which will be discussed in next section, dispersed solutions became unstable 4 h after stirring, as revealed in Figure 5b, leading to visible phase separation in the pristine MWCNTs solutions. Relatively speaking, it was clear that the COOH-MWCNT dispersion, after going through the same processing steps, was much more stable than the pristine MWCNT dispersion. Therefore, it could be verified that carboxyl functionalized carbon nanotubes had better dispersion in polymers than pristine carbon nanotubes. Figure 5. Comparative studies of functionalized and pristine MWCNTs in their dispersion with polymer matrix in common solvent: (a) initial dispersion of MWCNTs directly after sonication and stirring showing nontransparent solutions and (b) dispersion at 4 h after the stoppage of stirring, with pristine MWCNT case showing clear phase separation. A potential reason for that was the covalent bond between CNTs and the polymer matrix due to surface functionalization could help prevent nanotubes from agglomerating and forming bundles. Moreover, it was thought that, aside from dispersion, the production of robust nanocomposite materials may prefer strong covalent chemical bonding between the nanofillers and the polymer matrix rather than the much weaker van der Waals physical bonds which occur if the fillers were not functionalized [27]. 2.4. Comparison of Dispersion Approaches Amongst the main forms of physical dispersion methods three are particularly interesting: shear mixing, mechanical stirring, and sonication. In effort to optimize the dispersion process in the preparation of polymer nanocomposite, in this work these three approaches were experimentally tested and compared in terms of their performance, and a combinatory approach was proposed for the fabrication process. 2.4.1. Shear Mixing Shear mixing separates individual CNTs from bundles via the shear flow induced by the rotation of an extrusion in a polymer solution or melt. Usually, dispersion via shear mixing is only achievable for specific types of MWCNTs, with high shear rate in a rather viscous medium. Therefore, it does not necessarily require any common solvent to assist dispersion, which simplifies the process. Nanocomposite containing high loadings of CNTs (up to 7 wt.%) have been realized via this technique [21]. However, a major downside is that the processing time significantly goes up as loading concentration rises. More importantly, shear mixing tends to section carbon nanotubes into shorter length scale, thereby reducing their conductivity significantly—an undesired attribute for nanocomposite intended for use as a sensor material. In our experiments, various loading percentages of MWCNTs (~2–8 wt.%) were shear mixed with PDMS base polymer using a drilling machine (GMC 10-inch drill press stage, rpm 1000–1500 rpm). It was found that, although CNTs could be well dispersed within PDMS directly, the conductivity of the final nanocomposite was simply compromised too much for it to work effectively as a sensing material. The shortening of nanotubes due to shearing caused conductivity to decrease by more than 10 times compared to other approaches, which was undesirable for conductive nanocomposite. Therefore, this method was eventually not incorporated into the process of nanocomposite fabrication. 2.4.2. Sonication Being the most popular dispersion technique today, ultrasonic agitation exposes CNTs to ultrasonic waves and transfers shear forces to individual nanotubes which break them from agglomerates. There are two frequencies of ultrasonic waves that are used: (1) low frequency (~20–24 kHz); and (2) high frequency (~42–50 kHz). The sonication bath used in this work has high frequency but relatively low power (FS20D Fisher Scientific, frequency 42 kHz, output power 70 W). Although higher power of the sonication bath (>500 W) is desired as it provides higher shearing force to break down CNT bundles, nevertheless, prolonged exposure could also cause damaging of CNTs (especially shortening) which could significantly decrease the conductivity of CNTs [28]. Considering all factors, a mild sonication bath would be an ideal option as it allowed high quality of dispersion yet avoided severe damaging of CNTs during sonication. Sonication was an essential process to control because it covered most of the nanocomposite preparation steps. Temperature was an important factor to control and normally needed to be low in the initial dispersion stage. Due to lack of cooling sinks on sonication bath, temperature was maintained relatively constant by changing bath water about every 30 min. 2.4.3 Mechanical Stirring Mechanical stirring facilitates dispersion as it creates shearing force through the high speed rotary motion of the stirrer. In this work, a magnetic stirrer was used which could rotate at maximal of 1150 rpm. Experiments found that, for the dissolution of PDMS in organic solvents, magnetic stirring worked more efficiently time wise than sonication. To dissolve 2 g of PDMS base in 15 mL of chloroform, for example, magnetic stirring (1150 rpm) could shorten dissolution time (could be estimated by disappearance of phase separation) from 1 h (sonication time) to around 8 min which was a significant improvement. In our experiments, however, mechanical stirring was found to be not beneficial for the improvement of CNT dispersion quality. As a matter of fact, it was shown to have an adverse effect on the dispersion state of PDMS-MWCNTs in common solvents. For the pristine MWCNT solution shown in Figure 5 above, the PDMS-MWCNTs dispersion in chloroform was, with 1 h of sonication, stable when observed 3 days afterwards. But when solution went through 10 additional minutes of mechanical stirring (1150 rpm), the dispersion almost immediately became less stable, showing visible CNT agglomerates in the vial. After comparing the three common dispersion approaches, it seemed that a combinatory approach would provide the optimal process. Mechanical stirring could be used for the initial dissolution of PDMS base in common solvent, as it was more time efficient. Sonication, on the other hand, could be used in the other aspects/steps of material preparation. 2.5. Experimental Procedure for Preparation of Polymer Nanocomposite After numerous experimental trials and improvements, the so-far optimized procedure to obtain homogenous polymer nanocomposite is as follows. In the stage of initial dispersion, first COOH-MWCNTs (e.g., 0.2 g) are added into a solution of chloroform (e.g., 50 mL) inside a metric cylinder (e.g., 100 mL). Note that the CNT concentration here (4 mg/mL) is much higher than that used in the testing section, perhaps even higher than the solubility of CNTs in chloroform, but it was necessary to have a relatively high concentration because the weight of final nanocomposite needs to be at least a few grams to be useable. Plus, the small diameter of cylinder is usually preferred over a wide mouse beaker, because as little as the final polymer nanocomposite is (e.g., for 5 wt.% PDMS-CNTs, 0.2 g MWCNTs could produce only 4 g final nanocomposite), a wide beaker would cause majority of nanocomposite to stick onto the wall and bottom areas, leaving little for later usage. After initial mixing of COOH-MWCNTs and chloroform, the mixture is sonicated for around 1 h. Meanwhile, PDMS base resin (e.g., 3.5 g) is added into a separate solution of chloroform (e.g., 10 mL), and stirred with a magnetic stirrer (1150 rpm) for 15 min. Then, the two solutions are mixed together to go through 1–2 h of additional sonication to ensure sufficiently uniform dispersion of MWCNTs and PDMS. Experiments suggest that, on top of this time, further extended time of sonication does not significantly improve dispersion quality anymore. Next in the state of solvent evaporation, it is highly desirable to minimize the required time to fully dry up the organic solution. As the concentration of CNTs continuously rise (for more than 2 orders) during the solvent drying process, some reaggregation of nanotubes is bound to happen. To minimize the size and amount of CNT agglomerates, solution should be dried as soon as possible. In this work, two techniques have been introduced to help expedite the solution evaporation process. Firstly, the temperature of the nanocomposite-containing chloroform solution could be raised close to its boiling point (61.2 °C). At this temperature, the properties of the nanocomposite stay virtually intact while the drying process dramatically speeds up. Simply, the fastest way to elevate solution temperature is to pour in pre-boiled water into the sonication bath, and carefully mix it to adjust the temperature to be at or slightly over the boiling point. Secondly, the introduction of a vacuum pump into the cylinder could speed up the evaporation process as well. One problem with the narrow-mouthed cylinder is that it usually takes days for solution (e.g., 50 mL) to fully evaporate even at elevated temperature, since vapor molecules get saturated inside cylinder and could not quickly escape. A Teflon tube connected to a vacuum pump could quickly remove the chloroform vapors from the upper portion of the cylinder, thus reducing evaporation time significantly from several days to a couple of hours (actual time depends on solution volume, CNTs percentage, temperature and vacuum level). Finally, after the complete evaporation of the common solvent and before the microfabrication of polymer nanocomposite, curing agent—another part of PDMS polymer should be introduced into the mixture. Since the mixing of curing agent and base polymer would cause PDMS to gradually solidify, usually in 24 h at room temperature, it is desired to minimize the mixing time for curing agent. Simple manual mixing for 10–20 min is normally carried at here. At the mixing ratio of 10:1 (base to curing agent ratio), experiments suggest that the relatively short manual mixing time does not alter the dispersion quality obviously. 2.6. Dispersion Characterization of Final Nanocomposite While the dispersion and clustering of spherical particles has been studied well, for both spherical and highly asymmetrical (platelets, rods and fibers) [29–32], it has remained a technical challenge to directly and reliably observe carbon nanotubes in the bulk of a nanocomposite suspension. All optical methods (e.g., optical microscopy) cut off below a length scale of 0.2–0.5 $ \mu \text{m} $; all electron microscopy methods, though prominent in observations of individual nanotubes, could only provide information about the sample surface, \textit{i.e.}, only representative for the selected fields of view. This leaves reciprocal space techniques and, more importantly, global indirect techniques of characterizing the dispersed nanocomposites; each of these techniques suffers from the unavoidable difficulty in interpretation of results. Although attempts have been made to quantitatively assess the dispersion characteristics of CNTs inside polymer matrices (e.g., using Minkowski connectivity, radial power spectral density) [33], most reports still have to rely on optical and electron micrographs, despite their shortcomings, to evaluate relative quality of CNT dispersion [22,24,25,34]. In an effort to compare relative quality of various CNT dispersions within polymer matrices, this work has also adopted optical microscopy and electron microscopy for observation of CNT dispersion within polymer matrix. For instance, during the dispersion process, a drop of chloroform solution containing dispersed functionalized MWCNTs and PDMS base (CNT~4 mg/mL) was observed under a stereomicroscope. The optical micrographs shown in Figure 6 suggest that CNT cluster sizes generally did not exceed 10 μm. Compared to cluster sizes reported in existing literatures [22,34], this was indicative of relatively high dispersion quality. Figure 6. Optical micrographs of CNT dispersion inside a solution which contains chloroform, PDMS and functionalized MWCNTs. In the final polymer nanocomposite, it is difficult to use optical microscopy to directly observe the bulk dispersion of CNTs within polymer matrix, especially for those nanocomposite having a high loading percentage (>1%) of CNTs, since the samples normally become optically non-transparent. Scanning electron microscopy (SEM), on the other hand, provides a tool for observing the inside of a bulk sample. For example, a PDMS-MWCNTs nanocomposite sample containing functionalized MWCNTs was fractured in liquid nitrogen to obtain a cross section, and viewed under SEM, as in Figure 7. After optimization of our dispersion procedure, SEM images demonstrated relatively uniform distribution of nanotubes throughout the fractured surface. Cluster size throughout the nanocomposite remained consistently under about 3 μm. Compared with previously reported SEM images, this indicates an excellent dispersion quality, especially for nanocomposite containing high percentage of carbon nanotubes (>5 wt.%). Figure 7. SEM images showing dispersed MWCNTs on a cross section of polymer nanocomposite that was fractured in liquid nitrogen. Nanocomposite contains around 7 wt.% of functionalized carbon nanotubes throughout its matrix. Observation was made on same area of surface with following increasing magnification: (a) 160×; (b) 1000×; (c) 3000×; and (d) 10,000×. 3. Conclusions In this work, to assist the dispersion of MWCNTs inside PDMS matrix and realize a uniform distribution, a common solvent was selected amongst various tested organic solutions. Based on its high solubility for PDMS and MWCNTs respectively, and its ability to retain dispersed state of MWCNTs in presence of PDMS, chloroform was found to be an optimal choice as a common solvent. Also, the surface functionalization of CNTs by carboxyl groups was found to be beneficial for further improvement of dispersion quality. Through extensive testing of a variety of widely used physical dispersion techniques such as shear mixing, mechanical stirring and sonication, a combinatory approach was developed in which mechanical stirring was used to facilitate the initial dissolution of PDMS inside common solvent, and mild sonication used to as a main tool to disperse MWCNTs within PDMS. Following the dispersion stage of MWCNTs and PDMS within the common solvent, the evaporation process was facilitated and expedited by use of vacuum pump and accurate control of elevated temperatures. Solution drying time was significantly shortened, and thereby initial dispersion quality was largely retained throughout solvent evaporation. Even at high loading concentrations of CNTs within polymer, high quality dispersion of nanocomposite was achieved, which showed significant improvement over prior approaches. Dispersion quality was studied using various characterization tools such as optical microscopy and electron microscopy. 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 1782, 1 ], [ 1782, 5568, 2 ], [ 5568, 9200, 3 ], [ 9200, 12255, 4 ], [ 12255, 15019, 5 ], [ 15019, 18321, 6 ], [ 18321, 19243, 7 ], [ 19243, 20059, 8 ], [ 20059, 22442, 9 ], [ 22442, 24769, 10 ], [ 24769, 26351, 11 ], [ 26351, 29529, 12 ], [ 29529, 32767, 13 ], [ 32767, 36447, 14 ], [ 36447, 38571, 15 ], [ 38571, 40167, 16 ], [ 40167, 43242, 17 ], [ 43242, 46377, 18 ], [ 46377, 46848, 19 ] ] }
8acdcc2ba94e0e15e6085aff6cc06d6f7be6b8a6	{ "olmocr-version": "0.1.59", "pdf-total-pages": 4, "total-fallback-pages": 0, "total-input-tokens": 12320, "total-output-tokens": 3776, "fieldofstudy": [ "Medicine", "Biology" ] }	Decrease and Recovery of Olfactory and Gustatory Function in a Case of SARS-CoV-2 Infection David Tianxiang Liu¹ Bernhard Prem¹ Gerold Besser¹ Christian Albert Mueller¹ Bertold Renner² ¹Department of Otorhinolaryngology, Head and Neck Surgery, Medical University of Vienna, Vienna, Austria; ²Institute of Clinical Pharmacology, Medical Faculty Carl Gustav Carus, Technische Universität Dresden, Dresden, Germany Keywords Smell · Taste · COVID-19 · Recovery Abstract Self-reported chemosensory dysfunction in severe acute respiratory syndrome coronavirus 2 patients is common. We present a case of reversible smell loss in a young patient with mild coronavirus disease 2019 infection assessed with established testing methods over a period of 8 weeks. Introduction The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for the coronavirus disease 2019 (COVID-19) pandemic, keeping the world in suspense since its first outbreak in December 2019. A recent summary of the clinical characteristics of infected individuals suggested that the spectrum of presenting symptoms can vary greatly among different groups of disease severity [1]. One emerging symptom in young patients that has been reported by numerous professional societies is “smell loss” or anosmia. Various sources have suggested that young patients may experience smell and taste loss alone as a major, or even prodromal, symptom without difficulties in nasal breathing or general symptoms, such as fever or cough [2]. The interpretation of these symptoms is critical as young, asymptomatic, and unaware individuals represent a major source of viral transmission that can delicately interfere with worldwide efforts in combating this pandemic [3]. Reports of anosmia in COVID-19 rely on verbal patient complaints. Although patients with olfactory dysfunction (OD) generally report smell loss accurately, unnoticed anosmia or subjective complaints with normal test scores are found occasionally. Therefore, data on chemosensory function in COVID-19 patients are needed, as this disease spreads rapidly and symptoms require objectification. Here, we report the clinical and self-perceived course of OD combined with nasal airflow measurements in a young patient with mild COVID-19 infection who was monitored by established testing methods for smell and taste function. Case Presentation A 35-year-old male healthcare professional without any preexisting medical conditions, who had direct patient care responsibilities with COVID-19 patients (ear, nose, and throat examinations), reported a mild cough and sore throat starting on March 14. On March 17, he reported a sudden loss of smell after waking up in the morning, but no nasal congestion was noticed (Table 1). As he was a healthcare professional and represented a high-risk group, he voluntarily isolated at home and testing via nasopharyngeal swab was performed. The result obtained via real-time reverse transcription polymerase chain reaction was positive for SARS-CoV-2. Seven days after symptom onset, on March 21, olfactory and gustatory testing were performed by means of validated test procedures using the 16-item Sniffin’ Sticks Identification test (Burghart GmbH, Wedel, Germany), the Candy Smell Test (for testing retro-nasal olfaction), and the Taste Strips Test (Burghart GmbH) for bilateral (whole-mouth) taste function according to the manufacturer’s instructions [4–6]. Uni- and bilateral nasal airflow was also measured based on a validated procedure using a peak nasal inspiratory flowmeter (Clement Clarke International Ltd., Essex, UK). All tests were sent by post to the patient and performed in a self-administered testing procedure based on video-assisted guidance. From March 21 through March 28, self-rated olfactory and gustatory function were recorded on a daily basis using a visual analog scale ranging from 0 (“no smell/taste”) to 10 (“excellent smell/taste”). Similarly, uni- and bilateral nasal airflow were quantified daily using a visual analog scale ranging from 0 (“no airflow”) to 100 (“excellent airflow”). Every second day olfactory, gustatory, and retro-nasal olfactory testing were performed. Long-term chemosensory outcome was measured 8 weeks after symptom onset and 6 weeks after subjective recovery on May 12. Ortho- and retro-nasal olfactory function objectively decreased, but no subjective complaints of nasal congestion were noted during the initial onset of anosmia. Follow-up testing revealed an increase in subjective and objective test scores during the next 7 days (Table 1). Long-term testing revealed full recovery of olfactory, gustatory, and retro-nasal olfactory function within the normative range. Discussion Our results suggest that otherwise asymptomatic patients infected with SARS-CoV-2 report their olfactory (dys-)function correctly; thus, self-perceived olfactory impairments may be a concomitant symptom of COVID-19 infection. We also found that these impairments are reversible, as both subjective and objective results improved during the first 2 weeks after symptom onset and fully recovered within the long-term follow-up period of 2 months. These findings support previous reports that OD is common in mild to moderate COVID-19 cases and may serve as a potential marker in otherwise asymptomatic and healthy young patients [7–9]. The pathophysiology can only be speculated on, however, previous studies suggested that SARS-CoV-2 might impair olfactory function through targeting of olfactory epithelium (OE)-supporting cells (such as sustentacular or microvillar cells). These cells express both the angiotensin-converting enzyme 2 and the transmembrane protease, serine 2, which are both believed to be crucial for SARS-CoV-2 cell entry [10]. Therefore, the observed chemosensory dysfunction might be related primarily to the local peripheral inflammation. The suspected local inflammation within the OE might also explain OD without nasal congestion as the main symptom in SARS-CoV-2 patients. By way of contrast, the common (long-lasting) postinfectious smell loss is believed to be the result of a direct damage to olfactory receptor neurons within the OE. Regarding recovery rates, COVID-19-associated smell loss seems to resolve spontaneously within a short timeframe of a few weeks in the majority of cases [11]. Noteworthy, although recovery rates for patients with common postinfectious smell loss have been reported previously, these data refer only to those with long-lasting smell loss (i.e., months) [12, 13]. The percentage of patients in whom an acute non-COVID-associated postinfectious OD only persists for a short period of time is currently still unknown. Furthermore, radiological studies of SARS-CoV-2 patients with OD also revealed alterations to the olfactory bulb, hence a central involvement cannot be ruled out at this point [14, 15]. Indeed, a recent study comparing olfactory function of patients with COVID-19-associated smell loss and common postinfectious OD revealed that results from odor identification and discrimination testing were significantly lower in those with COVID-19-associated smell loss compared to those with common postinfectious OD. Moreover, the authors found that odor identification test results (compared to discrimination and threshold test results) were most sensitive to discriminate between the above-mentioned entities. The authors hypothesized that this difference might be explained by an involvement of central structures related to the sense of smell [16]. The epidemiological characteristics of patients with COVID-19 and postinfectious OD have also been summarized previously [17]. The authors found a female predominance in both COVID-19 and postinfectious OD patients. Similarly, older age was also associated with both entities. Based on these findings, the authors hypothesized that the pathomechanisms might be similar. Nonetheless, they also mentioned that histological studies of the OE are necessary to further elucidate the role of SARS-CoV-2 in smell loss. Regarding gustatory function, a validated test for sweet, salty, sour, and bitter taste in a self-administered testing procedure based on video-assisted guidance revealed an impaired sense of taste, which recovered within the same period compared to olfactory function. This finding was not surprising, since gustatory dysfunction has also been reported previously in patients with OD [16, 18, 19]. Interestingly, self-reported gustatory function was initially not impaired and showed no relevant changes within the follow-up period. This finding might be explained by the difficulty of patients to self-evaluate gustatory function, since true taste problems are often mistaken for flavor-related deficits [20]. Therefore, validated smell and taste tests are indispensable and should always be incorporated into routine clinical practice. Conclusion Care should be taken not to overlook the symptom of smell loss in otherwise asymptomatic COVID-19 patients, and awareness needs to be raised within the general population and among healthcare personnel worldwide about these potential markers of SARS-CoV-2 infection. Further studies are needed to evaluate chemosensory function and incidence of recovery in patients with SARS-CoV-2. Statement of Ethics This case report was conducted in accordance with the World Medical Association Declaration of Helsinki. Written informed consent to publish this case report was given by the patient. Conflict of Interest Statement The authors have no conflicts of interest to declare. Funding Sources No funding was obtained for this case report. Author Contributions D.T. Liu, B. Prem: data collection. D.T. Liu, G. Besser, B. Renner, C.A. Mueller: analysis of results. D.T. Liu, B. Prem, G. Besser, B. Renner, C.A. Mueller: writing of the manuscript. D.T. Liu, B. Prem, G. Besser, B. Renner, C.A. Mueller: critical review of all contents. Olfaction and Taste in SARS-CoV-2 References 1 Guan WJ, Ni ZY, Hu Y, Liang WH, Ou CQ, He JX, et al.; China Medical Treatment Expert Group for Covid-19. Clinical Characteristics of Coronavirus Disease 2019 in China. N Engl J Med. 2020 Jul;382(18):1708–20. 2 Giacomelli A, Pezzati L, Conti F, Bernacchia D, Siano M, Oreni L, et al. Self-reported olfactory and taste disorders in patients with severe acute respiratory coronavirus 2 infection: a cross-sectional study. Clin Infect Dis. 2020 Jul;71(15):889–90. 3 Bai Y, Yao L, Wei T, Tian F, Jin DY, Chen L, et al. Presumed Asymptomatic Carrier Transmission of COVID-19. JAMA. 2020 Apr;323(14):1406–7. 4 Hummel T, Sekinger B, Wolf SR, Pauli E, Kobal G. “Sniffin’ sticks”: olfactory performance assessed by the combined testing of odor identification, odor discrimination and olfactory threshold. Chem Senses. 1997 Feb;22(1):39–52. 5 Mueller C, Kallert S, Renner B, Staissny K, Temmel AF, Hummel T, et al. Quantitative assessment of gustatory function in a clinical context using impregnated “taste strips.” Rhinology. 2003 Mar;41(1):2–6. 6 Renner B, Mueller CA, Dreier J, Faulhaber S, Rascher W, Kobal G. The candy smell test: a new test for retronasal olfactory performance. Laryngoscope. 2009 Mar;119(3):487–95. 7 Spinato G, Fabbris C, Polesel J, Cazzador D, Borsetto D, Hopkins C, et al. Alterations in Smell or Taste in Mildly Symptomatic Outpatients With SARS-CoV-2 Infection. JAMA. 2020 May;323(20):2089–90. 8 Lechien JR, Chiesa-Estomba CM, De Siati DR, Horoi M, Le Bon SD, Rodriguez A, et al. Olfactory and gustatory dysfunctions as a clinical presentation of mild-to-moderate forms of the coronavirus disease (COVID-19): a multicenter European study. Eur Arch Otorhinolaryngol. 2020 Aug;277(8):2251–61. 9 Haehner A, Draf J, Dräger S, de With K, Hummel T. Predictive Value of Sudden Olfactory Loss in the Diagnosis of COVID-19. ORL J Otorhinolaryngol Relat Spec. 2020;82(4):175–80. 10 Cooper KW, Brann DH, Farruggia MC, Bhatnari S, Pellegrino R, Tsukahara T, et al. COVID-19 and the Chemical Senses: Supporting Players Take Center Stage. Neuron. 2020 Jul;107(2):219–35. 11 Hopkins C, Surda P, Whitehead E, Kumar BN. Early recovery following new onset anosmia during the COVID-19 pandemic – an observational cohort study. J Otolaryngol Head Neck Surg. 2020 May;49(1):26. 12 Reden J, Mueller A, Mueller C, Konstantinidis I, Frasnelli J, Landis BN, et al. Recovery of olfactory function following closed head injury or infections of the upper respiratory tract. Arch Otolaryngol Head Neck Surg. 2006 Mar;132(3):265–9. 13 Duncan HJ, Seiden AM. Long-term follow-up of olfactory loss secondary to head trauma and upper respiratory tract infection. Arch Otolaryngol Head Neck Surg. 1995 Oct;121(10):1183–7. 14 Politi LS, Salsano E, Grimaldi M. Magnetic Resonance Imaging Alteration of the Brain in a Patient With Coronavirus Disease 2019 (COVID-19) and Anosmia. JAMA Neurol. 2020 Aug;77(8):1028–9. 15 Laurendon T, Radulesco T, Mugnier J, Géraud M, Chagnaud C, El Ahmadi AA, et al. Bilateral transient olfactory bulb edema during COVID-19-related anosmia. Neurology. 2020 Aug;95(5):224–5. 16 Huart C, Philpott C, Konstantinidis I, Altundag A, Whitcroft KL, Trecca EM, et al. Comparison of COVID-19 and common cold chemosensory dysfunction. Rhinology. 2020 doi: 10.4193/Rhin20.251 [Epub ahead of print]. 17 Imam SA, Lao WP, Reddy P, Nguyen SA, Schlosser RJ. Is SARS-CoV-2 (COVID-19) postviral olfactory dysfunction (PVOD) different from other PVOD? World J Otorhinolaryngol Head Neck Surg. 2020 doi: 10.1016/j.wjol.2020.05.004 [Epub ahead of print]. 18 Landis BN, Scheibe M, Weber C, Berger R, Brämmerson A, Bende M, et al. Chemosensory interaction: acquired olfactory impairment is associated with decreased taste function. J Neurol. 2010 Aug;257(8):1303–8. 19 Gudziol H, Rahneberg K, Burkert S. Anosmics are more poorly able to taste than normal persons. Laryngorhinootologie. 2007 Sep;86(9):640–3. German. 20 Liu DT, Besser G, Renner B, Seyferth S, Hummel T, Mueller CA. Retronasal olfactory function in patients with smell loss but subjectively normal flavor perception. Laryngoscope. 2020 Jul;130(7):1629–33.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2366, 1 ], [ 2366, 5221, 2 ], [ 5221, 9977, 3 ], [ 9977, 14155, 4 ] ] }
f55e13c91accc5059df8e846dcf09b3e49ed0470	{ "olmocr-version": "0.1.59", "pdf-total-pages": 18, "total-fallback-pages": 0, "total-input-tokens": 50249, "total-output-tokens": 16919, "fieldofstudy": [ "Psychology", "Medicine" ] }	“Euphoria”: Trans children and experiences of prepubertal social transition Cal Horton Department of Education, Goldsmiths, University of London, UK Correspondence Cal Horton, Department of Education, Goldsmiths, University of London, UK. Email: [email protected] Abstract Objective: This research explored experiences of prepubertal social transition, listening to trans children who were affirmed in childhood, as well as hearing from their parents. Background: Despite being a topic of significant importance, there is limited qualitative literature on parents’ or indeed children’s experiences of prepubertal social transition and little qualitative research on how childhood rejection or affirmation influences well-being. Method: This study examines qualitative data from 30 parents with experience supporting a trans child to socially transition at average age 7 years (range 3–10 years), alongside data from 10 of the trans children. Data were analyzed through inductive reflexive thematic analysis. Results: The first major theme explored experiences pre-transition, with subthemes on children correcting assumptions, becoming distressed, struggling alone, reaching crisis, or growing withdrawn and frustrated. The second major theme examined experiences posttransition, with subthemes on a weight being lifted, validation at school, and well-being. Conclusion: This qualitative research complements existing quantitative evidence on the importance of social transition, with childhood affirmation critical to the happiness and well-being of trans children. Implications: The research has significant relevance for parents of trans children, professionals working with families, and policymakers and legislators influencing policy and practice toward trans children and their families. KEYWORDS affirmation, children, families, social transition, transgender Received: 19 October 2021 Revised: 5 April 2022 Accepted: 12 July 2022 DOI: 10.1111/fare.12764 This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. © 2022 The Author. Family Relations published by Wiley Periodicals LLC on behalf of National Council on Family Relations. Across the globe, increasing numbers of trans children are being supported in childhood (Ehrensaft et al., 2018; Olson & Gülgöz, 2018; Roche, 2020), including support for a social transition (Ehrensaft et al., 2018). The term social transition may denote a child’s shift in name, pronouns, or presentation, as well as signifying a point of external recognition of a child’s gender identity, when others in their family, school, or community respect and validate their gender identity through use of an appropriate pronoun, name, or both (Ehrensaft, 2020). It is distinct from diverse gender expression, with Ashley (2019a) noting that “social transition involves something beyond gender non-conformity and speaks to a shift in lived gender identity” (p. 679). Existing literature has noted the benefits of childhood social transition in terms of mental health and well-being (Turban, 2017). A study with 73 socially transitioned trans children aged 3 to 12 years found they had high levels of mental health, with levels of depression similar to cis children (Olson et al., 2016). A follow-up study on 116 socially transitioned trans children aged 6 to 14 years found high levels of mental health and self-worth in socially transitioned trans children, concluding “these findings are in striking contrast to previous work with gender-nonconforming children who had not socially transitioned, which found very high rates of depression and anxiety” (Durwood et al., 2017, p. 1). In the past decade, clinical guidance for supporting trans children has moved away from an earlier approach of delayed social transition to affirmative approaches (Ashley, 2019b; Turban, 2017). Affirmative approaches emphasize supporting trans children in their identity without trying to predict their future identity or needs and without putting up age-based barriers to children living authentically (Temple Newhook et al., 2018). Medical guidelines published over the past 5 years from a wide range of prominent health care bodies endorse gender affirmative support. This includes guidance from the American Academy of Pediatrics (Rafferty et al., 2018), the Paediatric Endocrine Society Special Interest Group of Transgender Health (Lopez et al., 2017), and from national health care standards in Australia (Telfer et al., 2018) and New Zealand (Oliphant et al., 2018). Clinical authors of such consensus-based affirmative health care guidelines have written about how much they have learned and how much their approach has been influenced by the accounts of families of trans children, by listening to trans children themselves, and by learning from trans adults’ reflections on their childhood (Ehrensaft et al., 2018; Telfer, 2020). In the past decade, growing numbers of parents of trans children are accessing community support groups, whether in person or virtual, enabling families to learn from each other’s experiences, exchanging stories and providing peer support (Kuvalanka et al., 2014; Pullen Sansfaçon et al., 2015; Pyne, 2016). These community networks are reported as pivotal for parents finding the knowledge, trans-positivity and confidence to affirm and advocate for a preadolescent trans child (Galman, 2020; Horton, 2021). Parents and carers are known to be resistant to trans possibilities, needing to overcome their own fears or lack of knowledge in related areas to support a trans child’s social transition (Horton, 2022). The stories and lived experience of families of trans children shared within parent networks are influential in shaping parent community consensus on appropriate support for trans children; yet these parental accounts are little captured in the academic literature (Chen et al., 2017; Kuvalanka et al., 2014; Kuvalanka & Munroe, 2021; Olson et al., 2019). Existing research provides limited qualitative perspectives on parents of trans children’s experiences, with trans children’s own experiences and perspectives on prepubertal social transition even rarer in the literature (Ehrensaft et al., 2018; Gill-Peterson, 2018). Some insights into the impacts of childhood affirmation or rejection can be gained from retrospective research with trans adults (Kennedy, 2022; Turban et al., 2020), but there is limited research on the experiences of parents and children who have experience-based insight into prepubertal social transition. THEORETICAL FRAMEWORK The research is underpinned by a trans-emancipatory theoretical framework, building on wider work on emancipatory research (Noel, 2016). Here a trans-emancipatory framework is one that recognizes and takes account of the role of cisnormativity and pathologization of gender diversity in upholding structural injustice. Cisnormativity is the assumption that everyone is cisgender (not trans) or should be (Keo-Meier & Ehrensaft, 2018). Newbury (2013) discussed the ways in which structural or institutional cisnormativity permeates societies and institutions, invisible to most cis people, yet exacting harm on trans people in structures and systems that were not designed to include trans lives. The research recognizes the negative impacts of cisnormativity on trans children, in research as in society (Ansara & Hegarty, 2012). Herein the word trans is used to include those who are binary-oriented as well as nonbinary (Vincent, 2020). The research recognizes the continued legacy of past pathologization of gender diversity, from decades where gender diversity was deemed a disorder to be prevented or reformed (Bryant, 2006). The research maintains commitment to trans-emancipatory research, influencing the selection of research questions, the research ethics and research methodology, recognizing that gender diversity is neither pathological nor problematic, acknowledging that trans lives are equal to cis lives, and being attentive to cisnormativity or pathologization of gender diversity within and across the research. RESEARCH QUESTIONS The existing literature on social transition provides limited insights from parents who have supported a child’s prepubertal social transition and even less insight from trans children who themselves socially transitioned preadolescence. This research aimed to address this gap in the literature, guided by the following research questions: 1. What are parents’ and trans children’s experiences of prepubertal social transition? 2. What can we learn from parent and child accounts of their experiences before and after a prepubertal social transition? METHODS Sample Thirty parents were interviewed from across England, Scotland, and Wales. Individualized demographic information is not presented, responding to participant requests for additional privacy in a small, vulnerable, and potentially identifiable cohort. One hundred percent of interviewees were cis; 90% were White; 93% were women, and 23% were disabled. Seventy percent were aged 40 to 50 years, and 10% were immigrants to the United Kingdom. Interviewees had a wide range of levels of household income and a range of levels of education, with 20% reporting secondary education as their highest qualification, 37% reporting a graduate degree, and 43% a postgraduate degree as their highest qualification. In terms of sexual orientation, the cohort was diverse; 60% of parental interviewees were heterosexual, 23% pansexual, 10% bisexual, and 7% gay or lesbian. The parents interviewed shared experiences of 30 socially transitioned trans children, including 15 girls, 12 boys, and three nonbinary children. These children socially transitioned at an average age of 7 years (range 3–10 years). At time of parental interview, their children were age 11 years on average (range 6–16 years). Ten trans children, who were children of 10 of the interviewed parents, were also interviewed. These children were on average 12 years old at time of interview (range 9–16 years) and had socially transitioned an average of 4.5 years before the interview. Study design The research presented here is a portion of a wider PhD on cisnormativity, rights and well-being of trans children who socially transition preadolescence in the United Kingdom. The inclusion criteria for parent interviewees were (a) being a parent or carer of a socially transitioned trans child in the United Kingdom, (b) their child having socially transitioned while under age 11 years, (c) their child currently being under age 16 years (one child in the sample had just turned 16 by the time the interview took place). The inclusion criteria prioritized interviewees with recent experience of prepubertal social transition. To recruit parental participants, details about the study were shared on closed online spaces in six UK support groups for parents of trans children. None of these support groups are actively trans-hostile, with group moderators ensuring the groups are a safe space away from transphobic discourse. Avoidance of advertisement on trans-hostile parenting fora was judged as unlikely to affect the sample, as trans-hostile parents would not support a trans child’s social transition under age 11 years and, therefore, would not fall into the cohort prioritized in this research. Additional parental interviewees were brought in via snowball sampling, through introduction from other members of these parent support groups. Access to hard-to-reach families and children was enabled by the author’s positionality as a nonbinary parent of a trans child, helping overcome trust-related barriers to hearing from this cohort. The author is themselves a member of four of these closed online spaces and posted there directly, with other parents sharing details on two other groups. The sample of interviewed parents were also asked to consider inviting their trans child to participate, with just under a third of their trans children opting to participate. Research participants received a project information sheet in advance, outlining the purpose of the research, their rights, and how their data would be used, with one version tailored for child participants. Parents and adolescents provided written informed consent, and for younger interviewees, parents provided written consent on behalf of their child, with children of all ages additionally providing either written consent or verbal informed assent (Lundy et al., 2011; World Medical Association, 2013). After interview each parental interviewee completed a short demographic survey. Data collection Interviews were conducted remotely via Microsoft Teams during the period December 2020 to September 2021. Semistructured interviews, covering broad topics including health care, education, and families, lasted approximately 1 to 3 hours (median approximately 2 hours) for parents, and 20 to 50 minutes for children (average 25 minutes). This article considers a subset of the wider data corpus, focusing on portions of the interviews discussing social transition, and specifically portions of interviews discussing experiences before and after social transition. Interviews used broad, open-ended questions, allowing interviewees to talk openly and at length around each topic. Interviews were scheduled to fit with interviewee availability (many being conducted during periods of COVID-related lockdown), remaining flexible to adapt to times when interviewees could be interviewed in privacy without family members overhearing. Key parental questions relating to their experiences of their child’s social transition included the following: “Has your child socially transitioned? Can you tell me about your experience?” After each initial answer prompts were used flexibly to elicit further responses: “Can you tell me about the time before the point of social transition?” “What do you remember about the time when the social transition occurred?” “How were things in the months/years after that?” The interview methodology with trans children was flexible and bespoke, adapting to individual child preference with some interviews conducted one-on-one, some conducted with a parent present, some with their parent asking questions and recording the interview, and one child providing written input. Questions for trans children were tailored to their age, including broad questions such as “Do you remember before your parents understood your identity?” and “Can you tell me about that time?” with prompts such as “And what happened next” and “Do you remember how you felt at that time?” Interviews were recorded, stored securely on an encrypted platform, and transcribed by the author. Transcripts were checked against the recording, with anonymized transcripts uploaded into NVivo. The research received ethical approval from the author’s university. The research built in ethical best practices for trans-related research (Adams et al., 2017; International Transgender Health Forum, 2019; Vincent, 2018), combined with ethical practices in research with children (Lundy et al., 2011; Moore et al., 2018). Participant anonymity was a high priority, with interviewees further emphasizing the importance of individual quotes not being identifiable, given the vulnerable and small population that this research cohort is taken from. For this reason, it was agreed jointly with research participants to go a step beyond the usual criteria for anonymity and to avoid linking individual quotes to specific pseudonyms, as well as omitting child ages from specific parental quotes, thereby preventing patchwork identification. This particular cohort places a high level of importance on privacy and safety, and a strong duty of care was upheld to respecting interviewee preferences in how their data were shared. Data analysis Data were analyzed through inductive reflexive thematic analysis (Braun & Clarke, 2006) to understand interviewee experiences and perspectives related to the timing of social transition, with data-driven development of codes and themes. The analysis comprised rereading each transcript to become familiar with the data, coding diversely without predefined coding categories. The initial codes were then reviewed to identify themes and subthemes, with all extracts for each subtheme collated and reread. The initial subthemes were then reviewed, and revised to ensure they were internally coherent, consistent, and distinctive and accurately captured the dataset. Each subtheme was analyzed and interpreted, including with reference to existing literature. Indicative quotations from a range of interviewees were selected to illustrate each subtheme accurately. Efforts were made to include multiple quotations in this article, with this decision informed by the underpinning emancipatory approach. Several interviewees expressed a hope that their voices would be shared directly, noting a lack of voice of parents of socially transitioned trans children in the literature or wider discourse, and emphasizing the privacy and safety concerns that limit their ability to share their experiences safely in other forums. The analysis accompanying the quotations is recognized as the author’s interpretation, acknowledging the role of any researcher in actively interpreting data (Braun & Clarke, 2006). RESULTS The research examined parent and child experiences before and after a prepubertal social transition. The first major theme presents a range of challenging experiences pretransition, with subthemes on children correcting assumptions, becoming distressed, struggling alone, reaching... crisis, or growing withdrawn and frustrated. The second major theme presents experiences post-transition, with subthemes on a weight being lifted, validation at school, and well-being. The results section comes with a trigger warning, including references to distress, self-harm, and child suicidal ideation, particularly in section “Reaching Crisis.” Each subtheme is illustrated with quotations from parents [P] and children [C]. Challenging experiences pretransition The first major theme explores parent and child experiences pre-social transition. Children correcting assumptions This subtheme captures the ways in which trans children challenge assigned labels, including examples of children asserting their identity to their parents, siblings and peers. Children correcting their parents’ assumptions around gender identity was a common theme in many parental accounts, with some trans children correcting their parents from age 2 to 3, insisting on being correctly gendered. One parent described how their young child challenged their assumptions: “He kept correcting us” [P]. Another parent recalled how their child would assert her identity every time she was misgendered: “She was saying say ‘sister not brother’ every time I said, ‘Oh pass your brother the bla bla bla,’ she would say ‘sister, not brother,’ say ‘she not he’” [P]. Some children asserted their gender more vocally as they joined primary school (age 4). A parent recalled a conversation with their child on the first day of starting school: “[I said] ‘I’ve got two big school boys now.’ And she just looked at me, and she just went ‘school girl mummy’” [P]. Some children were able to challenge misclassification with self-confidence, with parents describing how their children asserted themselves: “She said to me, mum, you do know I’m a girl, don’t you?” [P]. Several interviewed children remembered trying to correct their parent regularly from a young age: “At about 4, I kept telling my mum that I felt like a boy” [C]. Other children prioritized getting their peers to gender them correctly; one parent found out that their child had been asserting her identity in front of other children, without parental knowledge: Our older child said to us that whenever they’d gone to parks, soft plays or that kind of thing where children meet each other…. for as long as he could remember, whenever they’d gone to places where they met other children, she had introduced herself as [new name], she had introduced herself as his sister. [P] These accounts of children correcting misassumptions align with wider research on young trans children’s identities, with a body of psychological research demonstrating that preschool and primary school–age trans children have a strongly felt gender identity and know who they are (Fast & Olson, 2018; Olson et al., 2015; Rae et al., 2019). Becoming distressed The second subtheme highlights examples of children growing increasingly distressed at being misgendered, with their parents noticing their child’s distress, and children recalling their own frustration and sadness. One trans child reflected on how it felt before their parents understood and affirmed them: Interviewer: Was it hard to show your feelings when you were younger? Child: I did like [cross facial expression]. I think they knew that I was angry. Interviewer: How did it make you feel? Were you bothered? Child: I was kind of bothered. Interviewer: Can you tell me any emotions that you might have felt? Child: Anger, sadness. Many parents recalled noticing how misgendering affected their child’s happiness and well-being: “She was kind of happy before, but every time she was called a boy’s name, she wasn’t happy. Every time I used the wrong pronouns. She wasn’t happy. … these things would upset her” [P]. Another child recalled how it had felt when they were being misgendered: “When people got it wrong, when I corrected them, they said sorry, so it was alright. It didn’t feel that good (visibly upset here) before I corrected them” [C]. A majority of parents and children were operating in a world without trans possibilities, and described how a lack of access to trans narratives impeded understanding: He used to cry himself to sleep a lot. And we used to have what we used to call sort of meltdowns, where you’d be hugging him. And you know, and he couldn’t be consoled, because, and this is when he was about, I suppose it started when he was about 6 or 7, these meltdowns. And because he wanted a beard, and you know, as a cis person, it just sounded ridiculous to me, you know, that a 6-year-old would be crying about wanting a beard. [P] Another trans child described how it felt when they were incorrectly gendered: Interviewer: What did it feel like when people got it wrong? Child: Like crying. These examples highlight the strain, stress, and distress trans children can experience while they are not being understood, supported, or affirmed in their identity. Struggling alone The third subtheme captures experiences in which parents were not aware of their child’s distress or did not know that depression or anger were related to identity. This theme highlights examples of children struggling on their own and parents only later understanding their child’s experiences. Some children were aware of their identity at very young ages but did not assert it, hiding their gender identity from their family, often for several years, and dealing with their feelings and emotions alone. Parents only became aware of their child’s lonely struggle when their child came out to them. There was one night when [child] was absolutely bereft, and I was just, we were just lying in his bed, and I was just like hugging him and I was like, you know, you can tell me anything. Like, it doesn’t matter. But if there’s something and we can do something to help, then, you know, it is, so much better if we talk about it. And that’s when he was like, “Mummy, I’m a boy, like everybody thinks I’m a girl and I’m—I’m just not—like—I am a boy.” [P] Children had tried to suppress their identity and were in need of parental acceptance: “And we were laid in bed one night reading a story. And she turned around to me, and she just said, ‘My, my heart keeps making me feel like a girl and I can’t make it stop’” [P]. Within this subtheme, some parents were aware of their child’s depression or anger but had not understood the connection to gender identity. Several parents who had noticed their child’s depression and felt relief once they understood what was happening and were able to help their child. But she’d been so low and so depressed for such a long time. And it was like, the lightbulb moment for us as a family. It was like, oh, so that’s what’s been wrong all this time. We can help with that, you know, and so, because we could look back and say, yes, that was obviously why you were struggling so much. We knew she’d been thinking about it for a lot longer than, you know, that moment. [P] For a few parents, understanding that their child had struggled with disclosing their identity helped them understand past difficulties they had observed: “She was a very angry child, and looking back, it’s kind of clear where that came from” [P]. Within this subtheme, parents only later understood what their child had been through before coming out. A parent recounted how their child has described the time before disclosing their identity: She has sort of said little things to me, like how she felt she was climbing a really, really, really, really tall ladder. And she felt like she finally got to the top and was able to see, which I quite liked as an analogy from like, a 7-year-old, when she said that, and that it was a really hard climb, and a really long and lonely climb. but she did it, you know, so she feels quite proud of it. [P] These accounts echo literature on trans adults’ childhood memories, with research emphasizing there often being a significant gap between a person understanding their identity, and them disclosing their identity to anyone else (Kennedy, 2022). Reaching crisis [Please be aware the information in this subtheme may be triggering.] Within this subtheme we hear examples of children experiencing extreme distress, pain, frustration, and suicidal ideation, before disclosing their identity. Several parents described their children being in acute despair before disclosing their identity, and some parents were only fully aware of this later. She was so depressed and it later came out that she had been coming downstairs, and it wasn’t just once, she said she used to come downstairs and hold the kitchen knives, and will herself to die. Like she wanted to kill herself. She would have only been 6 years old at that time. And finding out that your child was in so much distress like that, and not able to tell me, I mean, she sort of said to me, “I decided that I couldn’t do it and I just had to tell you I’m a girl instead.” [P] Another parent only found out about the depth of their child’s suffering when their child confided in a friend: I was picking up my child from a birthday party and another parent came over. And said that my child had confided to their child, that they wanted to die by suicide, because they were so miserable. … My child is literally 9 years old, and they want to die by suicide. [P] One parent shared their child’s description of why she benefits from attending counseling sessions with a trans-positive counselor: She said, even the other day, that she enjoys having those meetings, because it helps her get some of her demons out. I think that was the language she uses. She’s like, I’ve still got all this pain and frustration from before mummy, from before I came out, and it helps to talk to them, because it helps to get it out. [P] These accounts provide insights into the acute distress trans children may feel when they are not understood, or fear being rejected, by those closest to them. Growing withdrawn and frustrated Within this subtheme parents describe recognizing their trans child’s growing frustration and depression as they waited for parental acceptance. Several parents noticed their children’s well-being declining while they were waiting for the world and waiting for their families to understand them and support them. I saw that she was becoming more withdrawn. I saw that she was struggling with school. … The best way I can describe it is there was just this air of sadness around her. And I don’t really know how else to articulate it. [P] Parents noted how living inauthentically caused their child pain: Well, just how unhappy [child] was when she was having to live as [assigned name]. Because effectively she was being forced to live like that. She didn’t want to be a boy—having to present as a boy was, you could see, it was painfully uncomfortable for her. [P] Parents noted how living inauthentically had negative impacts across all areas of their child’s life: “I think that before he, before he transitioned socially, yes, absolutely, he was completely struggling in the world” [P]. Parents also reported slowly understanding how much being correctly gendered mattered to their child. One parent described their child’s reaction, after a stranger referred to the child as a boy and the parent did not “correct” them: When we left the store and he was like “thank you for letting me be a boy, mummy.” And I … That, that is straight from his heart, you’re letting me be a boy. And I am like, the power that you have, as a parent, to utterly destroy your child in that one second. [P] A number of children grew increasingly frustrated at delays in parental support. One parent emphasized their child’s exasperation at waiting for parents to understand. The parent recalled the conversation when they discussed affirming their child: Like her face was saying “Oh for fucks sake like someone gets it.” Like you stupid people. I’m 6 and I’m spelling this all out for you. So we were like OK, “you’d like us to say [new name],” “Yeah.” “And you’d like us? Well does that mean, you’d like us to say she and her?” Sigh. “Yes” [exasperated, obvious yes]. [P] One parent reported how their child remembers that period before receiving support: She often refers to it as, you know, like, “when everyone was idiots” and “when none of the rest of you had a clue about anything.” I get the sense from conversations I’ve had with her, that she was literally just waiting for the rest of us to catch up. And I, you know, I think she knew who she was from before she could even speak. And so, for her, the transition was us catching up. [P] These accounts highlight how parents grew to recognize the negative impacts on trans children of rejection or being denied recognition. Experiences posttransition The second major theme explores parent and child experiences post social transition. A weight lifted Within this subtheme parents and children describe significant positive impacts of parental affirmation and social transition. A majority of parental interviewees described a weight being lifted from their child once parents understood and embraced their child’s identity. “But she, you know, as soon as she told us, she was like, the weight had been lifted” [P]. Several parents described significant emotional shifts once children were affirmed. She was a really, really angry toddler and young child. And, and almost all of that dissipated with transition. [P] It was brilliant for him. It was brilliant for him, the meltdowns stopped. [P] She just, she just changed overnight, you know, back to this bubbly, vivacious child that I hadn’t seen for a couple of years. And, and she continued, you know, she’s dancing down the street, singing all the time, she’s just sunshine. [P] Once using affirming language, parents understood how important it was for their child. “And the benefits were immediate, her—at every stage, every time we had a conversation that validated her, there would be this shift, there would be this light in her eyes, that we were seeing her” [P]. Another parent stated: “It was really, it was just so amazing to see how such a small action could make such an impact. And conversely how misgendering can do the reverse” [P]. A child interviewee was asked how they felt when their parents used affirming language: “It felt right, and it gave me the biggest feeling of euphoria” [C]. These accounts align with findings from a growing body of research that demonstrates the importance of family support for trans children (Hill et al., 2010; Pollitt et al., 2019; Riggs et al., 2020; Russell et al., 2018). Validation at school Within this subtheme, interviewees reflected on the critical importance of social transition at school, with positive impacts on their child’s happiness, stress levels, and willingness to attend school. One parent recalled the strain placed on a child who was affirmed at home but was not socially transitioned at school. And I think, it was from that point, she was so happy, fully living as a girl. And then it was like, right, off you go to school in your boys’ school uniform. And pretty much weekly from that point. It always seemed to be in the bath. She’d say, “When can I go to school as a girl? When can I go to school as a girl?”” [P] Some families had a longer period of affirmation at home, without affirmation in other spheres including at school, noting the stress and strain this placed on their child: Things deteriorated quite rapidly because she was [new name] full time at home, and with a couple of select friends, and then had to go and be in boy mode at school, and see her dead name written down everywhere, and answer to her dead name on the register, and [we noticed] very rapidly deteriorating behavior at home because of that. [P] Several parents emphasized a dramatic improvement in their child’s willingness to attend school once affirmed there. In the sense that it made her happier—yes. It was a huge deal for her. She was miserable going to school in a boy’s uniform. Honestly, it was a fight every day, the day that she was allowed to go in a dress, she was up and ready for school. You know, before I’d even got out of bed. Yeah, completely changed her life. [P] Before he transitioned, he was actually coming home from school, really, really angry. And he’s, you know, he is a very well-behaved child. He likes to do the right thing. But he was coming home angry. And literally overnight, when we agreed that date [for social transition at school], he changed. He was happier, the anger had gone. [P] Another parent described a conversation with teachers, and the significance of teacher support to their child: So, we were sat there at the end of the normal parents evening, and there was the teacher and the student teacher there. And I said, oh, [child] wants me to tell you something. She would like to wear the girl’s uniform to school. And he said, straightaway, not a blink, that’s absolutely fine. And [child]’s reaction was to burst out crying, she just burst, burst out crying, leaning into me, that first bit of acceptance from outside of the family. [P] One parent reflected on the stresses of a school initially offering acceptance of a name change without acceptance of affirmed pronoun: She [teacher] went, “No problem, … after we’ve finished, do you want to go and change the label on your school peg, the label on your books and all that sort of stuff.” And he [child] literally grew like a couple of inches in his seat when all this was going on. Then she said, “Is there anything else you want to say?” And he said, “I want to be a boy. I want you to call me ‘him.’” And at this she baulked, and she went, … “Why don’t we try that in September?” And he shrunk down, his grip got hard, you know, when he was holding my hand. And I just looked at him. And I just said, “No, we change everything now. We cannot—we do not have the right to say you can change your name, but you can’t change your pronoun. He knows what he wants, he is absolutely certain. We are changing his pronoun.”” [P] Once children were affirmed at school, their happiness and willingness to attend school increased: “They changed all his books to have his new name on and new pronoun … and he came home sort of high as a kite” [P]. Another parent described their child being happier after socially transitioning at school despite experiencing increased harassment and bullying: The social transition bit at school, I guess, in that period, from September to January, was hard in terms of managing it, and then it got easier, because then I wasn’t worried about, like, are we doing the right thing. It was clear we were doing the right thing. It was crystal clear that she was happier. And she was happier, even though she was dealing with a lot more, you know, difficult stuff from her peers. [P] These accounts of the importance of school affirmation are in line with research on the importance of trans-positive supportive educational environments for allowing trans children to thrive (Horton, 2020; McBride, 2021). Well-being Within this subtheme, interviewees noted the positive impacts of social transition across diverse areas of trans children’s lives. Parents reflected on what difference social transition meant to their child. Happiness was a key word used to describe the difference affirmation made to their children. Through that period, [child] just got happier and happier and happier. [P] Seeing how happy she was. It was like there was a huge weight off her shoulders. [P] Definitely, it improved things. She was a lot happier. Definitely improved. [P] We’re seeing a happier child for—since the social transition. [P] A parent, interviewed jointly with their child, asked how affirmation made their child feel: Parent: Can you remember when we started calling you he and him? What that felt like? Child: It. Made. It made me feel joyful. And happy. Several parents described how much difference affirmation, both at home and at school, made to their child’s well-being: And just the benefits, were so clear, to her, you know—to see who she was. And her behavior and her attitude, and, you know, little things, like she’d been really slow to pick up reading. But I don’t think there’s a coincidence that, literally within a couple of months of her transitioning, she was reading, and by the end of year three, so a year after social transition, she had caught up and began to overtake peers, you know, there’s that kind of—how much of her brain power had been given over to existing in a world that didn’t see her as who she was. And when she was allowed to be herself, all other aspects of her life kind of began to, to catch up and fall into place, as they should have been. [P] Parents noted significant improvement in their child’s well-being across diverse domains: She was happy, content. She started to go into loads of different social clubs, she joined brownies, she went to youth group, she joined a netball club, she went to drama club, and she had a network of close friends that—she was just a really happy, settled child. [P] Several parents were surprised that children’s educational performance improved after social transition. One parent noted, “Academically he went through the roof. Which was the most astonishing thing” [P]. Another described this change as follows: They [the school] did notice this massive change in her … you know, she had no interest in school whatsoever, she wasn’t doing very well, but now she’s just a sponge. Now she’s not worrying about gender stuff as much. And she’s able to concentrate and give her opinions freely in class … she’s actually doing really well in all of the areas at school … It’s like, it’s freed her. [P] These findings highlight the different ways in which social transition can protect trans children’s well-being, with interviewees noting improvements in educational achievement, social connections, and childhood happiness. DISCUSSION Parental accounts pretransition reveal common examples of children correcting assumptions, asserting their identity at home and amongst their peers. When trans children were not understood or promptly affirmed, parents noted growing distress, with misgendering and miscategorization affecting trans children’s happiness. Some children tried to adhere to cisnormative expectations, only disclosing their identity at a point of distress or despair. For some young children, their despair was acute, and some carry longer term impacts linked to the fear and pain of rejection or not being understood. Many parents reported noticing increasing levels of sadness and frustration as their child waited for family, school, and peers to accept and affirm them. These accounts highlight a range of levels of distress and despair, but a common theme of unsupported children who were not able to thrive or enjoy their childhoods while continually dealing with instances of nonaffirmation and rejection. The accounts also highlight a striking theme of improvements in well-being after social transition, with children referencing the happiness or “euphoria” of being affirmed and living authentically. Parents describe a weight off their child’s shoulders, with affirmation reducing stress, anger and frustration, and with children able to succeed in other aspects of their lives once their gender identity was affirmed. Parental accounts emphasized the importance of in-school affirmation, with noticeable improvements in child willingness to go to school, enjoyment of school, and enthusiasm for social and extracurricular activities. Parents, interviewed at an average of 4 years since their child’s social transition, noted that affirmation at home and at school was associated with both an immediate and a sustained improvement in happiness. Parents also reported improvements in educational attainment that they perceived as direct outcomes of affirmation. Several described trans children as unable to thrive before social transition, with affirmation “setting them free.” Accounts of distress and unhappiness before affirmation align with what is known about the negative mental health consequences of family rejection. A body of predominantly quantitative research has shown the negative effects of childhood rejection, with evidence that nonaffirmation leads to insecure attachment (Wallace & Russell, 2013), shame (Turban, 2017), psychological harm (Priest, 2019), lack of belonging, posttraumatic stress disorder, and low self-worth (Ehrensaft et al., 2018). Trans children and adolescents are known to be at risk of poor mental health, with a wide variety of studies noting high levels of depression, anxiety or suicidal ideation (Srivastava et al., 2020; Strauss et al., 2020; Veale et al., 2017). A growing body of research has also shown that poor mental health is not intrinsic to being trans, with evidence demonstrating a wide range of external factors that correlate with good mental health, including family support (Katz-Wise et al., 2018; Klein & Golub, 2016; Pullen Sansfaçon et al., 2019; Simons et al., 2013; Travers et al., 2012), social affirmation (Durwood et al., 2017; Olson et al., 2016; Whyatt-Sames, 2017), and safe and welcoming trans-inclusive primary and secondary education (Horton, 2020; McGuire et al., 2010). This study also aligns with the reflections of clinicians with decades of experience working with trans children and their families. Clinician Dr. Diane Ehrensaft (2018) noted that supportive families “are discovering an increase in happiness and well-being in their child once that child is allowed to live in their authentic gender” (p. 5). She further stated that “through a social transition, children often express great relief that people understand who they are, while parents describe a deep joy and comfort previously unseen in their young child” (p. 7). Parental interviewees acknowledged that they started out with low understanding of the harms and stresses of rejection or denied social transition, as well as having limited understanding of the potential benefits of affirmation. A number expressed surprise at the positive impacts they observed accompanying social transition. It is also important to note that a majority of both parents and children were initially (before social transition) navigating through a world without visible trans “possibility models” (Pearce, 2021). With no visible reference point of socially transitioned trans children, a majority of both parents and children in this sample stumbled through periods of turmoil and distress, without access to other possibility models of how life could be. Strengths and limitations Several potential limitations are noted, linked to the inclusion of parental perspectives, linked to the sample, and linked to the length of time for outcomes to be observed. First, the findings include a significant emphasis on parental perspectives. Drawing from (cisgender) parental accounts brings with it a risk of parental oversimplification, miscommunication, and misunderstanding of trans children’s experiences, with recent examples where trans-antagonistic parental accounts have been used to discredit and discourage support for trans adolescents (Ashley, 2020; WPATH, 2018). This risk is mitigated by asking parents to speak about things that are within their knowledge—what they did, what they saw, what impacts on their child they observed. It is also critical to acknowledge the context in which parental observations occur. These observations were drawn from families in which at least one parent was affirming and where children were affirmed in their primary residence. Parental observations from transphobic and rejecting parents of trans children have noted less positive accounts of trans children’s well-being, and critics have pointed out that living in trans-hostile homes is likely relevant to the well-being outcomes that trans-hostile parents observe, with extensive literature drawing a connection between safe and affirming homes and trans youth well-being (Hill et al., 2010; Pollitt et al., 2019; Riggs et al., 2020; Russell et al., 2018). There is also a potential limitation in the selected sample—that is, perhaps those with more positive experiences would be more willing to volunteer for interviews. Further insights could be drawn from a different sampling strategy, although this would still be faced with challenges of differential willingness to consent to participation. Researcher positionality could also influence participation, with prospective interviewees being aware of the researcher’s situation as a nonbinary parent of a socially transitioned trans child. This positionality was both critical in gaining trust, access, and engagement from a hard-to-reach group, and at the same time could potentially deter engagement from parents who were less positive about social transition. A final potential limitation is on the length of the follow-up of these children, with the children in this sample having socially transitioned for an average of 4 years at the time of parental interview. Parents in this sample describe the critical importance of children having been able to enjoy their childhoods for this period, irrespective of future and long-term outcomes. Follow-up research could potentially revisit the same cohort, understanding well-being outcomes over a longer period. Implications The research has significant relevance for families with preadolescent trans children, who can draw from this research encouragement to listen to and support their trans children. The research has significant relevance for professionals working with trans children and their carers across diverse fields, including social workers, family courts, health care professionals, and teachers. Professionals need to understand the importance of prepubertal social transition for many trans children, taking an evidence-led approach that recognizes the harms of childhood rejection, and the benefits of family and community affirmation. Professionals interested in mental health and well-being need to recognize the potentially protective impact of prepubertal social transition on trans children and need to help create supportive and affirmative environments, including through education and support to parents and carers. The research also has significant relevance for policymakers and legislators, demonstrating the need for evidence-based policy and practice that recognizes the importance of social transition in safeguarding trans children’s mental health and well-being. Conclusion This research highlights common experiences of child distress, sadness, frustration, and despair in the time before social transition. In contrast, trans children described feelings of “joy” or “euphoria” once they were supported by their parents. Parents, in turn, observed profound and sustained improvements in mental health, well-being, educational attainment, and happiness once their children had socially transitioned. These qualitative insights complement existing quantitative data on the protective mental health benefits of family and school affirmation. The research also highlights the importance of positive “possibility models.” Trans children, parents, and carers, and those around them, need to be aware of positive possibilities: Trans children do not need to endure rejection, distress, and despair; preadolescent social transition and affirmation present opportunities for trans children to enjoy a positive and happy childhood. ORCID Cal Horton © https://orcid.org/0000-0003-1944-4122 REFERENCES Adams, N., Pearce, R., Veale, J., Radix, A., Castro, D., Sarkar, A., & Thom, K. C. (2017). Guidance and ethical considerations for undertaking transgender health research and institutional review boards adjudicating this research. Transgender Health, 2(1), 165–175. https://doi.org/10.1089/trgh.2017.0012. Ansara, Y. G., & Hegarty, P. (2012). Cisgenderism in psychology: Pathologising and misgendering children from 1999 to 2008. Psychology & Sexuality, 3(2), 137–160. https://doi.org/10.1080/19419899.2011.576696. Ashley, F. (2019a). 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World Medical Association Declaration of Helsinki: Ethical principles for medical research involving human subjects. JAMA, 310(20), 2191. https://doi.org/10.1001/jama.2013.281053. WPATH. (2018). WPATH position on rapid-onset gender dysphoria. https://www.wpath.org/media/cms/Documents/Public%20Policies/2018/9_Sept/WPATH%20Position%20on%20Rapid-Onset%20Gender%20Dysphoria_9-4-2018.pdf How to cite this article: Horton, C. (2022). “Euphoria”: Trans children and experiences of prepubertal social transition. Family Relations, 1–18. https://doi.org/10.1111/fare.12764	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2357, 1 ], [ 2357, 6723, 2 ], [ 6723, 10172, 3 ], [ 10172, 13940, 4 ], [ 13940, 17848, 5 ], [ 17848, 21054, 6 ], [ 21054, 24100, 7 ], [ 24100, 27243, 8 ], [ 27243, 30146, 9 ], [ 30146, 32897, 10 ], [ 32897, 36024, 11 ], [ 36024, 39080, 12 ], [ 39080, 43144, 13 ], [ 43144, 47390, 14 ], [ 47390, 51573, 15 ], [ 51573, 57377, 16 ], [ 57377, 63247, 17 ], [ 63247, 65031, 18 ] ] }
33ae7e7a119af58dfe90d65be75e8151129338a0	{ "olmocr-version": "0.1.59", "pdf-total-pages": 4, "total-fallback-pages": 0, "total-input-tokens": 12496, "total-output-tokens": 3583, "fieldofstudy": [ "Physics" ] }	Pressure Dependence of BaNi$_2$As$_2$ T. Park$^1$, H. Lee$^2$, E.D. Bauer$^2$, J.D. Thompson$^2$, F. Ronning$^2$ $^1$Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea $^2$Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA E-mail: [email protected] Abstract. We report resistivity measurements of BaNi$_2$As$_2$ up to pressures of 27.4 kbar. We find the structural transition at 130 K is broadened slightly with increasing pressure. There is also minimal influence on the superconducting transition, where the resistive onset increases from 2 to 3 K, but the temperature at which zero resistance is obtained is unchanged up to 27.4 kbar. This behavior is in contrast to that observed in the Fe-based systems as well as in LaNiPO and LaNiAsO. 1. Introduction Following the discovery of superconductivity at 26 K in LaFeAs(O,F)$^1$ many new superconductors were discovered which possessed the same fundamental building block of puckered T$_2$Pn$_2$ planes (T=Transition metal, Pn=Pnictide element). Most attention has focused on compounds with Fe$_2$As$_2$ planes which not only have the highest transition temperatures, but also are in close proximity to magnetism, therefore suggesting some similarity to the high T$_c$ cuprates. However, many Ni-based $^{[2-14]}$ and several other non-Fe-based$^{[15; 16]}$ superconductors have also been discovered. The transition temperature of these compounds has yet to exceed 5 K, and to date there is no evidence for proximity to an antiferromagnetic ground state$^{[17]}$. Thermal conductivity measurements of BaNi$_2$As$_2$ reveal that the system is a fully gapped superconductor$^{[18]}$; consequently, the more complex Fermi surfaces of the Ni-compounds$^{[19]}$ relative to the Fe-analogs suggest that BaNi$_2$As$_2$ is a conventional BCS superconductor. This is supported by phonon calculations which can account for the magnitude of T$_c$ within a conventional electron-phonon coupling framework$^{[19]}$. As this is not possible for the FeAs compounds it further suggests that there is no relation, other than structural similarity, between the Fe-based and non-Fe-based T$_2$Pn$_2$ superconductors. However, the trend of the superconducting transition temperature in doped LaTAsO is similar$^{[17]}$ for T=Fe$^{[1; 20]}$ and T=Ni$^{[8; 9]}$. In addition, the trend in T$_c$ across several families of compounds is similar for both Fe and Ni compounds$^{[11]}$. The origin for these two similarities is unknown and thus leaves open the possibility that the mechanism of the Fe-based and Ni- (and other non-Fe-) based compounds are related. Thus, one is motivated to continue studying the non-Fe-based superconductors either because they are simply good non-magnetic reference compounds for comparing to the Fe-based systems or because they may provide an alternative route for unraveling the mechanism of superconductivity due to the fact that their pairing is not as well optimized as it is in the Fe-based systems. © 2010 IOP Publishing Ltd In this work we report on the pressure dependence of the structural and superconducting transition temperatures of BaNi$_2$As$_2$ up to 27.4 kbar. At ambient pressure BaNi$_2$As$_2$ possesses a structural transition at 130 K and becomes superconducting at a transition temperature of 0.7 K\cite{6}. Theoretical work has argued that the structural transition is an electronically driven structural transition\cite{21}. We find that with increasing pressure the structural transition is slightly broadened, while there is negligible influence on the superconducting transition. 2. Experimental Single crystals of BaNi$_2$As$_2$ were synthesized as reported in ref. \cite{6}. A crystal was mounted inside a Teflon cup within a hybrid BeCu/NiCrAl clamp-type pressure cell. Silicon oil was used as the pressure transmitting medium, and a small piece of Pb whose known pressure-dependent superconducting transition enabled a determination of the pressure within the cell\cite{22}. A standard 4 point setup with spot welded contacts was used to measure resistivity. 3. Results With applied pressure the sharp first order structural transition is progressively broadened with increasing pressure, as shown in figure 1. Similar behavior occurs in CaFe$_2$As$_2$ [23; 24] and is believed to result from the fact that the pressure transmitting medium while liquid at room temperature, freezes before the structural transition of the material being studied. Consequently, there is a slight nonhydrostatic environment (< 0.01 GPa) nucleating structural inhomogeneity which induces further strain on the crystal allowing for a broadened transition and possibly even a structurally composite phase at low temperature. The pressure dependence of the transition and its width for BaNi$_2$As$_2$ is presented in figure 2. Figure 1. Resistivity versus temperature of BaNi$_2$As$_2$. With increasing applied pressure the transition broadens. The inset shows the low temperature resistivity at ambient pressure and 27.4 kbar, with a superconducting onset temperature of 2 K and 3 K respectively. The temperature at which zero resistance occurs does not change. Figure 2. Pressure dependence of the structural and superconducting transitions from resistivity data. Squares indicate the lowest temperature to which measurements were made. At ambient pressure the onset of superconductivity is observed by resistivity at 1.94 K, despite a bulk superconducting transition as observed by heat capacity occurring at 0.68 K\cite{6}. The origin of this onset transition is unknown, and is observed in crystals grown both in Pb flux and NiAs flux [25]. By applying pressure we observe this onset to monotonically increase with increasing pressure up to 3.06 K at 27.4 kbar, the maximum pressure studied. On the other hand, the zero resistance state correlates much better with the heat capacity anomaly at ambient pressure. Data were measured below 1.8 K only at ambient pressure and at 27.4 kbar, for which the temperature at which zero resistance occurred was unchanged as can be seen in figure 1. While we can not rule out a pressure dependence to the bulk transition, it seems unlikely that significant variation occurs given the fixed endpoints at 1 bar and 27.4 kbar and the slow monotonic increase to the resistive onset. This is in contrast to the behavior in LaNiXO (X=As, P), which demonstrates a dome of superconductivity with applied pressure[26] similar to the Fe-analog LaFeAs(O,F)[27]. Perhaps larger pressures are required to observe similar behavior as is the case for BaFe$_2$AS$_2$[28; 29]. In SrNi$_2$P$_2$ $T_c$, which is 1.4 K at ambient pressure, is monotonically suppressed with increasing pressure[11]. 4. Conclusions In conclusion, we have measured the pressure dependence of the structural as well as superconducting transition in BaNi$_2$As$_2$ up to 27.4 kbar. In contrast to LaFeAsO, LaNiAsO, and LaNiPO, we find very little pressure dependence on either the structural or superconducting phase transitions. Acknowledgments TP acknowledges a support by KOSEF grant (R2009-0058687) funded by the Korean government (MEST). Work at Los Alamos was performed under the auspices of the United States Department of Energy. References [1] Kamihara Y, Watanabe T, Hirano M and Hosono H 2008 Journal of the American Chemical Society 130 3296–3297 [2] Watanabe T, Yanagi H, Kamiya T, Kamihara Y, Hiramatsu H, Hirano M and Hosono H 2007 Inorganic Chemistry 46 7719–7721 [3] Tegel M, Bichler D and Johrendt D 2008 Solid State Sciences 10 193 – 197 ISSN 1293-2558 [4] Klimczuk T, McQueen T M, Williams A J, Huang Q, Ronning F, Bauer E D, Thompson J D, Green M A and Cava R J 2009 Physical Review B (Condensed Matter and Materials Physics) 79 012505 (pages 4) [5] Mine T, Yanagi H, Kamiya T, Kamihara Y, Hirano M and Hosono H 2008 Solid State Communications 147 111 – 113 ISSN 0038-1098 [6] Ronning F, Kurita N, Bauer E D, Scott B L, Park T, Klimczuk T, Movshovich R and Thompson J D 2008 Journal of Physics: Condensed Matter 20 342203 (4pp) [7] Watanabe T, Yanagi H, Kamihara Y, Kamiya T, Hirano M and Hosono H 2008 Journal of Solid State Chemistry 181 2117 – 2120 ISSN 0022-4596 [8] Li Z, Chen G, Dong J, Li G, Hu W, Wu D, Su S, Zheng P, Xiang T, Wang N and Luo J 2008 Physical Review B (Condensed Matter and Materials Physics) 78 060504 (pages 4) [9] Fang L, Yang H, Cheng P, Zhu X, Mu G and Wen H H 2008 Physical Review B (Condensed Matter and Materials Physics) 78 104528 [10] Bauer E D, Ronning F, Scott B L and Thompson J D 2008 Physical Review B (Condensed Matter and Materials Physics) 78 172504 (pages 3) [11] Ronning F, Bauer E D, Park T, Baek S H, Sakai H and Thompson J D 2009 Physical Review B (Condensed Matter and Materials Physics) 79 134507 (pages 7) [12] Kozhevnikov V L, Leonidova O N, Ivanovskii A L, Shein I R, Goshchitskii B N and Karkin A E 2008 JETP letters) 87 649 [13] Fujii H and Kasahara S 2008 Journal of Physics: Condensed Matter 20 075202 (5pp) [14] Matsumura Y, Ogino H, Horii S, Katsura Y, Kishio K and ichi Shimoyama J 2009 Applied Physics Express 2 063007 [15] Jeitschko W, Glaum R and Boon L 1987 Journal of Solid State Chemistry 69 93 – 100 [16] Hirai D, Takayama T, Higashinaka R, Aruga-Katori H and Takagi H 2009 Journal of the Physical Society of Japan 78 023706 [17] Ronning F, Bauer E, Park T, Kurita N, Klimeczuk T, Movshovich R, Sefat A, Mandrus D and Thompson J 2009 Physica C: Superconductivity 469 396 – 403 ISSN 0921-4534 [18] Kurita N, Ronning F, Tokiwa Y, Bauer E D, Subedi A, Singh D J, Thompson J D and Movshovich R 2009 Physical Review Letters 102 147004 (pages 4) [19] Subedi A and Singh D J 2008 Physical Review B (Condensed Matter and Materials Physics) 78 132511 (pages 4) [20] Wen H H, Mu G, Fang L, Yang H and Zhu X 2008 EPL (Europhysics Letters) 82 17009 (5pp) [21] Chen Z G, Xu G, Hu W Z, Zhang X D, Zheng P, Chen G F, Luo J L, Fang Z and Wang N L 2009 URL http://arXiv.org:0905.0841 [22] Eiling A and Schilling J S 1981 Journal of Physics F: Metal Physics 11 623–639 [23] Park T, Park E, Lee H, Klimeczuk T, Bauer E D, Ronning F and Thompson J D 2008 Journal of Physics: Condensed Matter 20 322204 (3pp) [24] Torikachvili M S, Bud’ko S L, Ni N and Canfield P C 2008 Physical Review Letters 101 057006 (pages 4) [25] Sefat A S, McGuire M A, Jin R, Sales B C, Mandrus D, Ronning F, Bauer E D and Mozharivskyj Y 2009 Physical Review B (Condensed Matter and Materials Physics) 79 094508 (pages 8) [26] Okada H, Takahashi Y, Igawa K, Ariii K, Takahashi H, Watanabe T, Yanagi H, Kamihara Y, Kamiya T, Hirano M, Hosono H, Nakano S and Kikegawa T 2008 Journal of the Physical Society of Japan 77SC 119–120 [27] Takahashi H, Igawa K, Ariii K, Kamihara Y, Hirano M and Hosono H 2008 Journal of the American Chemical Society 453 376–378 [28] Alireza P L, Ko Y T C, Gillett J, Petrone C M, Cole J M, Longarich G G and Sebastian S E 2009 Journal of Physics: Condensed Matter 21 012208 (4pp) [29] Fukazawa H, Takeshita N, Yamazaki T, Kondo K, Hirayama K, Kohori Y, Miyazawa K, Kito H, Eisaki H and Iyo A 2008 Journal of the Physical Society of Japan 77 105004	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3033, 1 ], [ 3033, 5551, 2 ], [ 5551, 8803, 3 ], [ 8803, 11142, 4 ] ] }
3de1a45f74a40063ec7a65ce2d47b2044941f0b3	{ "olmocr-version": "0.1.59", "pdf-total-pages": 15, "total-fallback-pages": 0, "total-input-tokens": 56586, "total-output-tokens": 19607, "fieldofstudy": [ "Biology", "Medicine", "Psychology" ] }	Possible Effect of the use of Mesenchymal Stromal Cells in the Treatment of Autism Spectrum Disorders: A Review Ryad Tamouza1, Fernanda Volt2†, Jean-Romain Richard3, Ching-Lien Wu3, Jihène Bouassida3, Wahid Boukouaci3, Pauline Lansiaux4, Barbara Cappelli2,5, Graziana Maria Scigliuolo2,5, Hanadi Rafii2, Chantal Kenzey2, Esma Mezouad1, Soumia Naamoune1, Leila Chami1, Florian Lejuste1, Dominique Farge4 and Eliane Gluckman2,5 1Translational Neuropsychiatry, INSERM, IMRB, DMU, AP-HP, Univ Paris Est Créteil, Créteil, France, 2Institut de Recherche Saint Louis (IRSL), Eurocord, Hôpital Saint Louis, Assistance Publique-Hôpitaux de Paris (AP-HP), Université Paris Cité, Paris, France, 3Translational Neuropsychiatry, INSERM, IMRB, Univ Paris Est Créteil, Créteil, France, 4Unité de Médecine Interne (UF 04), CRM MATHEC, Maladies Auto-immunes et Thérapie Cellulaire, Centre de Référence des Maladies Auto-immunes Systémiques Rares D’Île-de-France MATHEC, AP-HP, Hôpital St-Louis, Paris, France, 5Monacord, Centre Scientifique de Monaco, Monaco Autism spectrum disorder (ASD) represents a set of heterogeneous neurodevelopmental conditions defined by impaired social interactions and repetitive behaviors. The number of reported cases has increased over the past decades, and ASD is now a major public health burden. So far, only treatments to alleviate symptoms are available, with still unmet need for an effective disease treatment to reduce ASD core symptoms. Genetic predisposition alone can only explain a small fraction of the ASD cases. It has been reported that environmental factors interacting with specific inter-individual genetic background may induce immune dysfunctions and contribute to the incidence of ASD. Such dysfunctions can be observed at the central level, with increased microglial cells and activation in ASD brains or in the peripheral blood, as reflected by high circulating levels of pro-inflammatory cytokines, abnormal activation of T-cell subsets, presence of auto-antibodies and of dysregulated microbiota profiles. Altogether, the dysfunction of immune processes may result from immunogenetically-determined inefficient immune responses against a given challenge followed by chronic inflammation and autoimmunity. In this context, immunomodulatory therapies might offer a valid therapeutic option. Mesenchymal stromal cells (MSC) immunoregulatory and immunosuppressive properties constitute a strong rationale for their use to improve ASD clinical symptoms. In vitro studies and preclinical models have shown that MSC can induce synapse formation and enhance synaptic function with consequent improvement of ASD-like symptoms in mice. In addition, two preliminary human trials based on the infusion of cord blood-derived MSC showed the safety and tolerability of the procedure in children with ASD and reported promising clinical improvement of core symptoms. We review herein the immune dysfunctions associated with ASD provided, the rationale for using MSC to treat patients with ASD and summarize the current available studies addressing this subject. Keywords: autism, mesenchymal stromal cells, cellular therapy, inflammation, immuno-modulation 1 INTRODUCTION Autism spectrum disorder (ASD) is a set of heterogeneous neurodevelopmental conditions with onset of symptoms within the first 3 years of life. It is characterized by repetitive behaviors, restricted range of activities, and impairments in social communication (King et al., 2014). As per the DSM-5 ( Diagnostic and Statistical Manual of Mental Disorders) definition, ASD combines the formerly separated disorders of autism, Asperger’s syndrome, pervasive developmental disorders not otherwise specified, and childhood disintegrative disorder (American Psychiatric Association, 2013). The number of ASD reported cases has increased over the past decades. The World Health Organization estimates that 1 in 270 people has ASD, with a prevalence 4 times higher in men compared to women (World Health Organization, 2021). The ASD incidence in Europe is, approximately, 1% with a total of 3 million patients at the present time. In the United States, a 30% increase of the pediatric prevalence of ASD was observed from 2012 to 2014 alone (Corcoran et al., 2015). It is, currently, estimated that ASD affects over 2 million individuals with approximately 1 in 68 American children identified as having ASD (World Health Organization, 2021). In the most severe form, ASD is considered a chronic, disabling disorder that compromises the full potential of the affected individual. In the United States, the lifetime cost of supporting an individual with ASD is estimated between $1.4 and $2.4 million, depending on the degree and severity of involvement (Buescher et al., 2014). Beyond the financial aspect, ASD remains a condition that severely debilitates social integration and creates a major emotional burden for the patients’ families. There is no currently accessible effective medical treatment to address ASD core symptoms such as communication impairment, social inadaptability or lack of empathy (Thompson Foundation for Autism, 2012). Therapeutic options include non-specific medications, as well as behavioral, occupational and speech therapies, and specialized educational and vocational support. Currently available treatments, such as psychotropic medications, are prescribed to improve irritability, seizures, mood disorders or hyperactive syndrome, but they are not disease-modifying compounds per se (Lai et al., 2014). Although the exact etiology of ASD is unknown, recent studies have indicated that genetic and environmental factors contribute to the disease development (Chaste and Leboyer, 2012; Bennabi et al., 2015; Meltzer and Van de Water, 2017; Bennabi et al., 2018; Brown et al., 2018). In recent years, through genetic analysis and sequencing, de novo mutations, several genes copy number variants (CNV) and single-nucleotide polymorphisms (SNP) have been identified and were shown to increase the risk for ASD. Many of the affected genes, such as those encoding neuroligin-3, neurexin-1,2,3 (Vaags et al., 2012) multiple ankyrin repeat domains 3 (SHANK3) (Guilmatre et al., 2014) and contactin-associated protein-2 (CNTNAP2) (Scott-Van Zeeland et al., 2010) are known to regulate the synaptic function. Moreover, several ASD associated CNVs are enriched in genes required for normal synaptic transmission (Abrahams and Geschwind, 2010). A specific genetic cause for ASD can be identified in less than 20% of cases; in the remaining individuals, ASD development is likely attributed to complex interactions between multiple genetic and environmental factors. Among the environmental factors associated with an increased risk of ASD are prematurity, birth complications, maternal teratogen exposure, environmental toxins, and advanced parental age (Rylaarsdam and Guemez-Gamboa, 2019). In addition, inflammation and immune dysfunctions have been amply demonstrated to be implicated in ASD (Chaste and Leboyer, 2012; Bennabi et al., 2015; Meltzer and Van de Water, 2017; Bennabi et al., 2018; Brown et al., 2018). In this context, immunoregulatory treatment approaches for ASD patients are appealing. Several studies have emphasized and demonstrated that the immunoregulatory and immunosuppressive properties of the mesenchymal stromal cells (MSCs) constitute an experimental rationale for the use of these cells to treat immune-mediated diseases. While their immunoregulatory properties have been primarily focused on their ability to inhibit the proliferation of T-lymphocytes, studies have shown that MSCs affect the function and the differentiation of several other types of immunocompetent cells (Di Nicola et al., 2002; Jiang et al., 2005; Corcione et al., 2006; Sotiropoulou et al., 2006). This review aims to describe ASD, present an overview of the immune dysfunctions that may be associated with the disorder, provide a rational on the use of MSC for the treatment of affected patients, as well as to briefly present and discuss pertinent research done in this context. 2 MAIN TEXT 2.1 Immune Dysregulation in ASD It can be hypothesized that the development of subgroups of patients with ASD may follow a sequence of successive events, which include: 1) multiple stressful events during the critical neuro-developmental process, such as early infections or maternal autoantibodies interactions with specific immunogenetic background, 2) generation of immune dysfunction leading to further pro-inflammatory processes, gut- and blood-brain barriers alterations and autoimmune processes and 3) consequent brain alterations in otherwise genetically determined individuals. 2.1.1 Susceptibility to Infections Epidemiology has repeatedly shown an increased rate of ASD in children born from mothers who had an infection during pregnancy. These associations have been consistent across countries and time periods, and has been reported as early as the 1970s after the rubella pandemic in the United States (Chess, 1971) and throughout the decades in Denmark, Sweden and other countries (Atladóttir et al., 2010a). For instance, maternal viral infection requiring hospitalization during the first trimester or bacterial infections during the second trimester have been associated with a diagnosis of ASD in a large Danish cohort of 1,418,152 children of whom 7,379 had a diagnosis of ASD. Infections with intracellular pathogens were more prevalent in patients with ASD; for example, Nicolson and colleagues reported a prevalence of 8.3% of infections with Chlamydia species in ASD subjects as compared to only 2.1% in healthy controls (Nicolson et al., 2007). A putative mechanism for a link with the neuronal activity was proposed by Vojdani who found an increased level of cross-reactive antibodies to Chlamydia determinants in patients with ASD (Vojdani et al., 2002). Infections with other intracellular pathogens such as Mycoplasma fermentans, Mycoplasma species (poly-infection), Borrelia burgdorferi (mono-infection or in combination with Rickettsia or Mycoplasma) have also been reported to be associated with ASD (Bransfield et al., 2008). The potential association of congenital rubella, herpes, cytomegalovirus, varicella, mumps, polyomavirus and enterovirus with ASD have also been cited in other reports (Stubbs, 1976; Stubbs, 1978; Libbey et al., 2005; Lintas et al., 2010). The occurrence of these infectious events might be mediated by genetic backgrounds that predispose an individual to inappropriate response to environmental stressors. Some genes associated with autism may reduce the capacity to respond to bacterial toxins, while other genetic factors may cause inappropriate/overwhelmed immune responses (Heuer et al., 2011; Onore et al., 2012). Associations with genes implicated in the immune response against pathogens, namely immunogenetics, may thus be related to the risk of developing ASD. For instance, a gene-gene expression analysis of brain samples of patients with ASD has identified two distinct gene expression modules associated with autism that might act in concert to disrupt normal brain development (Voineagu et al., 2011). Such observations indicate that the brain of patients with autism show altered expression of genes relating to normal synapses development and increased expression of genes that mediate inflammation. The genetic diversity of Dectin-1, which encodes a key molecule involved in fungal-mediated signaling in the gastro-intestinal tract, has been associated with ASD, suggesting a genetically determined inability to mount efficient innate immune responses against danger signals (Bennabi et al., 2015); similarly the MHC cluster through HLA alleles/haplotypes or complement C4 alleles either in patients (Odell et al., 2005; Lee et al., 2006; Johnson et al., 2009) or in their mothers (Heuer et al., 2011) has been reported to modify ASD risk. ### 2.1.2 Pro-Inflammatory Processes As a consequence of the above-mentioned triggering events along with inability to mount efficient anti-infectious responses, marked immune response in the brain and microglial cell activation is one of the most prominent ASD characteristics (Vargas et al., 2005; Li et al., 2009). In children diagnosed with ASD, brain tissue demonstrates excessive white matter growth regions along with inflammation (Vargas et al., 2005). In the peripheral blood, elevated circulating levels of pro-inflammatory cytokines such as interleukin (IL) IL-1beta, IL-6, IL-8, IL-12p40 (Jüttler et al., 2002; Ashwood et al., 2011) together with diminished anti-inflammatory cytokines (TGF-beta, IL10) (Enstrom et al., 2010; Ashwood et al., 2011) have been reported. The underlying mechanisms linking immune dysregulation and neuronal dysfunction are not clear, but there is evidence indicating that certain cytokines can impair neurodevelopment. IL-6, for example, has been described as a possible neuromodulator induced by neuronal activity regulating brain function, neurodevelopment (Jüttler et al., 2002). Elevated levels of IL-6 in the brain decrease the number of primary dendrites and have a negative impact in neuron survival and neuronal plasticity and, thereby, potentially impacting behavior (Wei et al., 2013). Of interest, increased expression of IL-6 gene transcripts and IL-1 pathways, as well as increased circulating levels of IL-6 and IL-1 beta (Vargas et al., 2005; Li et al., 2009) have been noted in post mortem brains of patients with ASD. ### 2.1.3 Immune Cells Abnormalities Circulating monocytes from children with ASD display enhanced production of pro-inflammatory cytokines upon Toll-like receptor (TLR)-2 and TLR-4 dependent stimulation, while TLR-9 stimulation resulted in decreased cytokines production (Enstrom et al., 2010). Plasma levels of macrophage inhibitor factor (MIF), a pro-inflammatory immune regulator of both neural and endocrine systems, have been shown to be higher in ASD patients compared to healthy controls (Grigorenko et al., 2008). Further, several abnormal adaptive cellular responses have been reported such as altered T-cell activation (Ashwood et al., 2004), increased of basal levels of NK cells with diminished potential of response to stimulation (Enstrom et al., 2009), reduced number of CD4+ T cells, decreased of peripheral blood lymphocytes (Ashwood et al., 2003), inefficient response of T cell to mitogens (Molloy et al., 2006), and B cell dysfunction as evidenced by imbalance of serum immunoglobulin (Ig) levels (Enstrom et al., 2009). Bias towards T-helper2 (Th2) phenotype and reduced response of Th1 cells have also been documented (Noriega and Savelkoul, 2014). Plioplys et al. (1994) and Warren et al. (1992) demonstrated that a substantial number of subjects with autism have an increased number of HLA DR + activated T cells. Ashwood et al. (2004) found a higher number of B cells and NK cells in children with autism compared to controls as well as increased markers of cellular activation such as CD38 on B Cells, HLA-DR and CD26 on T cells subsets. Altogether, ASD patients display an increased activation of the innate and adaptive immune response. ### 2.1.4 Autoimmune Processes The association between auto-immunity and autism was first described in 1971 with the report of a child with autism and a family history of autoimmune diseases (Money et al., 1971) and further extended when families of children with autism were shown to have higher prevalence of autoimmune disorders (Comi et al., 1999; Atladóttir et al., 2010a). Croen et al. (2005), found that mothers who had developed autoimmune diseases during the second trimester of pregnancy carried a high risk of having a child with autism. It was reported that mothers of autistic patients had increased rates of rheumatoid arthritis (Atladóttir et al., 2010a). The presence of anti-fetal brain antibodies in the serum of mothers supports the hypothesis of an association between the maternal immune system and the diagnosis of ASD. (Braunschweig et al., 2007; Braunschweig and Van de Water, 2012; Fox et al., 2012). In a different study, serum from a mother of an autistic child was found to bind to Purkinje cells and other neurons, and behavioral changes were induced in mice injected with these antibodies (Dalton et al., 2003). Though not yet tested in animal models, it is hypothesized that autoreactive antibodies in the maternal bloodstream can cross the placenta, enter the fetal circulation, and access the brain via a premature blood-brain barrier. The production of such auto-antibodies might be linked to a deregulated anti-inflammatory response, where molecular mimicry of antigenic components of the pathogen leads to cross-reactivity of antibodies. Another possibility is that unresolved infectious processes with repeated antigen stimulation may lead to chronic inflammation and autoimmune rupture of tolerance. Finally, we cannot exclude deregulated tolerogenic processes, which are mandatory for tolerance by the maternal immune system of the semi-allogeneic foetus at the fetal-placental interface (Ferreira et al., 2017). In this context, several studies have reported associations between molecular and genetic aspects of the potent immuno-regulatory HLA-G locus and ASD risk (Guerini et al., 2015; Guerini et al., 2018a; Guerini et al., 2018b; Guerini et al., 2019). Various other auto-antibodies have been found in patients with autism: antibodies directed against 5HT receptors, myelin basic protein, neuron axon filament protein, cerebellar neurofilaments, nerve growth factor, alpha 2 adrenergic binding sites, and brain endothelial cell proteins (Ashwood et al., 2006). However, the pathogenic roles of such auto-antibodies are still unknown, and it is unclear whether they are a consequence or a cause of the disorder. In summary, dysfunctions affecting the vast majority of immune processes are present from the early developmental stages through childhood and adulthood in subgroups of patients with ASD. Potential pathophysilogic mechanisms include alterations in maternal-fetal immune tolerance (via maternal antibodies and/or cellular immunity) and fetal brain inflammation, which may lead to changes in brain cytokines profile and microglial activation that may be detrimental for neurodevelopment. Evidence of increased numbers of microglia and increased microglial activation in ASD has been obtained via brain post-mortem studies, positron emission tomography (PET) brain imaging and animal models yielding offspring with ASD phenotypes by inducing immune activation in the pregnant women (Harvey and Boksa, 2012; Malkova et al., 2012). The above-described immune dysfunctions, for example, genetically-determined non-resolved infectious events, even if resulting from a triggering event/process in the very early developmental stages, are still observed in adults with core ASD symptoms and reflected by elevated pro-inflammatory cytokines levels, highly activated T cells with consequent production of endogenous autoantibodies (Gusencheck et al., 2013; Gesundheit and Rosenzweig, 2017; Meltzer and Van de Water, 2017), suggesting a potential role of immune alterations and the associated chronic inflammation in the development or manifestation of ASD symptoms. ### 2.2 Microbiota Alteration and Intestinal Permeability An increasing body of literature has reported that patients with ASD often have a combination of intestinal microbes that is distinct from healthy controls (Cao et al., 2013; De Angelis et al., 2013), and gastrointestinal symptoms are widely reported in patients with ASD (Luna et al., 2017). Differences have been reported for the population of phyla Bacteroidetes, Firmicutes and genus Clostridiales among others (Finegold et al., 2010; Williams et al., 2011; Luna et al., 2017; Coretti et al., 2018). Convergent with these findings, one study found that Vancomycin, a powerful antibiotic targeting gram positive germs such as Clostridium, improved the symptoms in 8 out of 10 children with ASD and diarrhea (Sandler et al., 2000), but, a relapse of the symptoms relapsed shortly after antibiotic discontinuation. Also, increased intestinal permeability (“leaky gut”) in patients with ASD, potentially related to abnormal microbiome, were observed in a study showing that 43% of children with ASD compared to 0% of the controls presented an abnormal mannitol: lactulose test (D’Eufemia et al., 1992). Disrupted gut–blood–brain barriers may allow bacteria metabolites and other substances to get into the bloodstream and, subsequently, alter the brain (Al-Ayadhi et al., 2021). The modified microbiota and the metabolites produced by the adapted intestinal microorganisms are likely to play an import role in the pathophysiology of ASD, particularly by having an effect in the production of neurotransmitters and interacting with the host nervous system, but also by impacting host immunity and inflammation (Xu et al., 2019). All together, sustained abnormal microbiota and abnormal immune-inflammatory processes, increased oxidative stress induced by microbial, inflammatory and metabolic pathways could also explain the link between alterations in mitochondrial function and autism (Lombard, 1998; Pons et al., 2004). In the context of ASD the potential role of cell therapy would be in attempting to address the immune dysfunction and inflammation that might develop in consequence of an altered microbiota. ### 2.3 Synaptic Dysfunction and Neuro-Structural Changes in ASD Synapses are points of communication between neurons that the organized passage of information via electrical and chemical signaling. While there is a period of intensified synaptogenesis early in development, synapses retain plasticity throughout life, allowing the processes for learning and memory. Normal synaptic development and maintenance are essential to proper neuronal function, and abnormalities in either process have been associated with multiple neurodevelopmental conditions, including ASD. Additionally, human and animal studies have demonstrated a reduction in the size, number, and morphology of dendritic spines and an increase in immature spine morphology in ASD (Phillips and Pozzo-Miller, 2015). It is also likely that environmental factors influence synaptic changes. These alterations may lead to altered neuronal connectivity, such as large-range under-connectivity and short-range over-connectivity (Geschwind and Levitt, 2007; Maximo et al., 2014). Individuals with ASD show structural and histological changes such as increased brain size, decreased number of Purkinje cells in the cerebellum and increased packing density with small body neurons in the hippocampus, the amygdala and the entorhinal cortex (Fatemi et al., 2012). These changes could indicate abnormal developmental processes involving neurogenesis, pruning and apoptosis. Connolly et al. (2006), unveiled the possibility that affected neurogenesis could be linked to immune processes in children with ASD by showing that abnormal neurogenesis could be mediated by increased levels of brain-derived neurotrophic factor (BDNF) and IgM/IgG anti-BDNF antibodies in sera of children with ASD when compared to neutotypical controls, even if the exact mechanism remains to be elucidated. Similar findings involving neurotrophic factors, such as nerve growth factor (NGF), were observed in a preliminary study in a Turkish population (Dinçel et al., 2013). Changes in the apoptotic process also seem important in ASD. Fatemi et al. (2001) describe decreased levels of anti-apoptotic Bcl-2 protein in ASD. A different study showed decreased anti-apoptotic signaling Bcl2 pathway paralleled by an increased expression of the pro-apoptotic p53 in the cerebellum of nine autistic patients (Sheikh et al., 2010). There is scarce neuroimaging study support to correlate the mitochondrial dysfunctions at the cerebral levels which, consequently, could explain changes in oxidative stress and energy production abnormalities. Yet, an older study using neuroimaging methods found that N-acetyl aspartate is decreased in the cerebellum of autistic children probably due to impaired mitochondrial functions (Chugani et al., 1999). 2.4 Mesenchymal Stromal Cells MSCs, first identified by Friedenstein 45 years ago (Friedenstein et al., 1976), have since been extensively characterized. They can be isolated and various other sources and can be relatively easily isolated and cultured in vitro. MSCs were defined in 2006 by the International Society of Cellular Therapy (ISCT) MSC committee as: 1) a plastic-adherent polyclonal population with the capacity to give rise to adipocytes, and chondroblasts (Dominici et al., 2006). MSCs primary mechanism of action is thought to result from immunomodulatory effects (Le Blanc and Davies, 2015; de Castro et al., 2019), mostly through their paracrine activities induced by inflammatory stimuli in the local milieu (Spees et al., 2016) (MSC priming), but also by cell-cell contact. MSCs interact with the innate and adaptive immune system on both the T cell proliferation in a mixed lymphocyte reaction (MLR) (97). The inhibition has no immunological restriction as it was observed regardless of the MSCs origin: autologous or from a third party (Bartholomew et al., 2002; Tse et al., 2003). MSCs inhibit the proliferation of both naïve and memory CD4+ and CD8+ T cells through arrest in the G0/G1 phase of the cell cycle, and abrogate T cell activation (Glennie et al., 2005). In an inflammatory setting, MSCs appear to increase the number and activity of Treg cells and IL-10 expression, while suppressing Th1, Th2, and Th17 cells. MSC can also reduce the release of pro-inflammatory cytokines from different T cell populations, including interferon IFN-γ, TNF, IL-6, and IL-7, and increase the anti-inflammatory cytokines, such as IL-4 and IL-10 (Aggarwal and Pittenger, 2005; Prevosto et al., 2007). Typically, the mechanism of action of MSCs first involves the release of chemokines, allowing the attraction of activated T cells (Ren et al., 2008) that in turn prime MSCs towards an immunosuppressive phenotype, which then secrete several growth factors, cytokines, enzymes and hormones (e.g., VEGF, PDGF, ANG-1, IL-11, PGE2, TSG-6, SDF-1, HGF, IFG-1, and IDO) (Kramer et al., 2006; Polchert et al., 2008; Ren et al., 2008; Spees et al., 2016). MSCs secretion of the IFN-γ-inducible-indoleamine 2,3-dioxygenase (IDO) enzyme in human play a major role in inhibiting T lymphocytes proliferation via the degradation of tryptophan in metabolites (Ren et al., 2008; Menard et al., 2013). Other MSCs-secreted-soluble factors have also been proposed to contribute to the inhibition of T cell proliferation, including galectin-1 and 3, or IL-10 (Gieseke et al., 2007; Yang et al., 2009; Patel et al., 2010; Sioud et al., 2011). The capacity of MSCs to induce Treg is mediated by TGF-β and soluble HLA-G5, with IL-10, IL1Ra, and PGE2 release, which in turn interact with the Th17/Treg balance (Selmani et al., 2008; Terraza-Aguirre et al., 2020). MSCs also act through the release of MSC-derived exosomes, which content have immunosuppressive and immunomodulatory activity, and can favor Treg expansion (Zhang et al., 2018). Direct cell to cell contact mechanisms are also part of the MSC immune effect on T cells, in particular throughout CD106/ VCAM-1 and CD54/ICAM-1, that are both upregulated on MSC by TNFα, which play a critical role in MSC immunosuppressive capacities by favoring adhesion of MSC to T cells (Ren et al., 19502010). MSCs were also shown to directly promote apoptosis of activated T cells via the Fas/Fas ligand pathway (Akiyama et al., 2012) and to suppress T cell proliferation via engagement of the inhibitory molecule programmed death 1 (PD-1) by its ligands PD-L1 and PD-L2 (Augello et al., 2005). ### 2.5.2 MSCs and B Cells The interaction between MSCs and B cells is complex and depends on the culture environments and the type of cells (Ribeiro et al., 2013; Fan et al., 2016). MSCs were shown to inhibit B-cell proliferation, differentiation, antibody production, and chemotaxis under inflammatory conditions (Ribeiro et al., 2013; Fan et al., 2016). This inhibition involves MSC secretion of IFN-γ inducible IDO (Maby-El Hajjami et al., 2009) and appears to be indirect, since it requires the presence of CD4+ and CD8+ T cells (Rosado et al., 2015). Importantly, non-inflammatory resting MSCs do not inhibit B-cell proliferation but induce B-reg expansion. ### 2.5.3 MSCs and NK Cells MSCs and NK cells have been shown to interact in vitro and the outcome of this interaction may depend on the state of NK-cell activation and/or on the cytokines present in the milieu. MSCs are capable of inhibiting IL-2-induced proliferation of resting NK cells and partially inhibit the proliferation of activated NK cells and thereby the NK mediated cytotoxicity (Spaggiari et al., 2008). The effect of MSCs on NK cells depends both on cell contacts and on soluble factors synthesis. The secretion of PGE2 and HLA-G5 by MSCs are involved in the suppression of NK function (Spaggiari et al., 2008). Treatment of MSC with IFN-γ leads to the upregulation of MHC class I expression and the downregulation of NK cell receptor ULBP3 expression (Götherström et al., 2011), and thereby MSCs become more resistant to NK cell cytotoxicity (Krampera et al., 2006; Spaggiari et al., 2008; Götherström et al., 2011). ### 2.5.4 MSCs and Myeloid Cells MSCs immunomodulatory effect can also be explained by their ability to interfere with the differentiation, the maturation and the function of dendritic cells (DC) (Jiang et al., 2005; Ramasamy et al., 2007). Indeed, MSCs can inhibit antigen presentation by DC via negative regulation of the CD11c, CD83 and MHC Class II DC-cell surface molecules expression (Beyth et al., 2005). MSCs can halt the monocyte differentiation into DC, through secretion of PGE2 and IL-6 soluble factors (Nauta et al., 2006; Remes Lenicov et al., 2018). MSCs also interact with macrophages with reciprocal immunosuppressive effects on both cell types. Direct cell contact between MSCs and pro-inflammatory M1-macrophages increases the MSCs immunosuppressive capacities by: 1) upregulating and enriching CD54/ICAM-1 at the contact area on MSCs, which in turn favor the adhesion to T cells, and 2) increasing IDO expression (Espagnolle et al., 2017). MSCs effect on macrophages are mostly paracrine. IDO and PGE2 are involved in the polarization of monocytes into IL-10 secreting anti-inflammatory M2 macrophages (Németh et al., 2009; Maggini et al., 2010; François et al., 2012). Other immunosuppressive activities of MSC on myeloid cells are driven by soluble factors. These include CCL2 and CXCL12, which cooperate as a heterodimer to upregulate IL-10 in CCR2pos macrophages (Giri et al., 2020) and tumor necrosis factor-stimulated gene 6 (TSG-6), which promotes the early inhibition of neutrophil and macrophage activity at sites of inflammation and inhibits CXCL8-dependent neutrophil transendothelial migration and chemotaxis (Dyer et al., 19502014; Lee et al., 2009; Choi et al., 2011). ### 2.6 Relevant MSCs Pre-clinical and Clinical Trials #### 2.6.1 MSCs in Neurologic Conditions Numerous preclinical studies using MSCs infusion for diseases of the central nervous system suggest that MSCs can act through release of different neurotrophic, anti-inflammatory, and anti-apoptotic factors to promote recovery of the injured area and prevent further damage. Most studies were performed on adults with stroke, with a few additional reports on patients with neurodegenerative conditions or multiple sclerosis. Several small studies using systemically administered autologous bone marrow-derived MSCs have been conducted in adults with acute or chronic stroke, with no significant side effects (Dulamea, 2015). A phase II study of an allogeneic MSC product (MultiStem) was recently conducted in 126 adults with stroke (65 treated, 61 placebo) (Mays and Deans, 2016). MSC therapy was well-tolerated. While there was no difference between placebo and treated patients in measures of stroke recovery, the treatment group had a lower rate of mortality and infections, associated with down regulation of inflammatory biomarkers including IL-6. In addition, patients who received MSCs earlier (24–36 h post-stroke vs. 36–48 h post-stroke) demonstrated more favorable recovery than patients who received later treatment or placebo. A few clinical trials of autologous MSC therapy have been conducted in patients with multiple sclerosis. In a study including 25 patients with progressive multiple sclerosis treated with a single intrathecal autologous bone marrow-derived MSCs, the disease stabilized in half of the patients over a one-year period (Mohyeddin Bonab et al., 2012). Side effects, all transient and self-limited, included low-grade fever, nausea/vomiting, lower limb weakness, and headache, and were likely related to the intrathecal route of administration of MSCs. Another study that treated 10 patients, with progressive visual deficits due to multiple sclerosis, with a single intravenous dose of autologous bone marrow- derived MSC demonstrated improvements in visual acuity, visual evoked response latency, and optic nerve area (Karussis et al., 2010; Yamout et al., 2010). A clinical trial has been conducted in seven patients with Parkinson’s disease who received a single dose of autologous bone marrow-derived MSCs injected into the sub-ventricular zone using stereotactic surgery. Three patients demonstrated an improvement in disease symptoms with a follow-up of 10–36 months. Two additional patients reported subjective improvement of symptoms and reduction in drug dosage (Mendes Filho et al., 2018). 2.7 Cell Therapies in ASD 2.7.1 Potential Mechanism of MSCs in Treating ASD The exact mechanism of action of MSCs in ASD is the subject of ongoing investigations, but there are several potential means through which MSCs may exert therapeutic effects, including cell-mediated immunomodulation, molecular-mediated neuroprotection, and restoration of functional neurologic circuitry (Siniscalco et al., 2014). As ongoing immune dysregulation may contribute to the pathophysiology of subgroups of patients with ASD, suppressing the cell-mediated immune response with MSCs could have potential therapeutic benefit. MSCs may also provide neuroprotection through anti-inflammatory mechanisms by inhibiting neural apoptosis, microglial activation, astrocyte proliferation, and oxidative stress molecules (Gesundheit et al., 2015). Koh et al. (2015) demonstrated that UCB-derived MSCs promote neuron survival via secretion of neurotrophic factors. In several other models, MSCs were shown to have the ability to decrease both the number and the activation of microglial cells, which play a critical role in the development of ASD (Ooi et al., 2015; Jaimes et al., 2017). It is unclear if this phenomenon is caused by a direct effect of the MSCs or if it is mediated through activation of cytokines (i.e., TCP, IL-6). Finally, MSCs may also aid in synaptogenesis and restoration/regeneration of functional neurological pathways by supplying bioactive agents that stimulate the action of intrinsic neural progenitor cells. Various molecular targets have been implicated, including tissue plasminogen activator (tPA), synaptophysin, brain-derived neurotrophic factor (BDNF), and neurotransmitter receptors. Through a series of in vitro experiments via coculture, patch-clamp, inhibitory, and biochemical techniques, Koh et al. (2015) demonstrated that UCB-derived MSCs can induce synapse formation and enhance synaptic function and that thrombospondin proteins are both produced by UC-derived MSC and necessary for their synaptic effects. The main dysregulations and other dysfunctions in ASD as well as the related potential mechanisms by which MSCs might aid in correcting or improving them are described in Table 1. 2.7.2 Pre-Clinical Studies Mouse models of single gene disorders that are associated with the ASD phenotype, such as Fragile X syndrome, Rett syndrome, and tuberous sclerosis complex syndrome, have been used to study the effects of cellular therapy on both brain and behavior. Reported data from such animal studies may reflect differences related to the specific genetic subtype of ASD and may not be generalized to all cases (e.g., idiopathic ASD). Derecki et al. (2012) report recovery of function in a mouse model of Rett syndrome, an X-linked condition associated with ASD typically caused by a mutation of the MECP2 gene. This gene encodes a methyl-CpG-binding protein, and the mutation leads to deficient phagocytic function in glial cells. Transplantation of cells from wild type bone marrow via intravenous infusion arrested disease development in the mouse model of Rett syndrome (Mecp2-null C57BL/6 mice). Following engraftment, survival was improved, breathing patterns normalized, apneas were reduced, body weight increased, and locomotor activity was improved. The BTBR T + 1tpr3tf (BTBR) mouse strain, derived from the inbred Black and Tan Brachyury strain, is another mouse model of ASD. In addition to impaired social behavior, aberrant communication, increased repetitive behaviors, and increased cognitive rigidity, BTBR mice also exhibit increased levels of peripheral CD4+ T-cells, peripheral B-cells, and serum and brain immunoglobulin levels, among other immune abnormalities was hence an interesting model for MSC-based treatment. Accordingly, Segal-Gavish et al. (2016) deliver human MSCs to BTBR mice via intraventricular injection into the central nervous system. Mice were immunosuppressed with cyclosporine before and after treatment. In this model, improvements in all three domains—social behavior, stereotyped behaviors, and cognitive rigidity—were observed in MSC-treated mice compared to controls. However, differences in anxiety-related behaviors and locomotion were not observed. In two separate studies, Perets et al. (2018) showed that intranasal administration of purified exosomes derived from mesenchymal stem cell improved autistic like behaviors such as social interactions and vocalization, and decreased repetitive behavior in BTBR and Shank3B mice, respectively (Perets et al., 2020). These murine models were all favorable arguments to test the potential benefit of cellular therapies, in subtypes of ASD. 2.7.3 Clinical Trials of Cell Therapies in ASD-Clinical Trial Registries Several clinical trials of cell therapies for ASD have been conducted or proposed. A search performed on ClinicalTrials.gov (May 2021) using the terms “(Autism Spectrum Disorder OR Autism OR Autistic Spectrum Disorder \| Cell Therapy OR Cellular Therapy.”) yielded 43 studies, of which only 18 actually turned out to have cell therapies interventions for ASD. Two of the studies had a “withdrawn” status. Form the remaining 16 studies, only 3 involved MSC infusions. No trials involving MSCs and autism were identified in the European Clinical Trial Registry. In a review of cell therapies for ASD recently published, Price et al. present the results of 13 studies (2 on MSCs) that they identified with a similar search in December of 2019. In their review, the authors discuss the published results and conclude that the data available on cell therapy for ASD is still very limited and does not allow for comparison among the different studies. Nevertheless, the authors firmly state that the studies reviewed consistently demonstrated the safety of cell therapy interventions. and that from this point forward only placebo controlled studies are justifiable (Price, 2020). 2.7.4 Clinical Trials of Cell Therapies in ASD-From UCB to Umbilical Cord-Derived MSCs The collection of MSCs from UC blood or tissue is non-invasive, easier, and less expensive than the collection from other tissue types. Moreover, UC-derived cells are potentially less immunogenic due to their immaturity (Divya et al., 2012). Although MSCs retain their inducible immunoregulatory properties regardless of the tissue type they derive from (Amati et al., 2017), it is now recognized that some of their biological properties vary, with consequent potential repercussion in their clinical applications (Marquez-Curtis et al., 2015; Liu et al., 2016). In addition, a previous study suggested that the expanded UC-derived MSCs include a small unique population of cells that express both MSC and pluripotent stem cell markers resulting in an innate neurogenic potential (Divya et al., 2012). Also, it has been demonstrated that effector cells present in umbilical cord blood are able to alter brain connectivity through paracrine signaling and also to control inflammation (Bachstetter et al., 2008; Shahaduzzaman et al., 2013; Dawson et al., 2017). Investigators from Duke University in the United States completed an open-label phase 1, safety and tolerability, study in 25 children diagnosed with ASD who were treated with autologous UCB and followed for a year (NCT02176317). UCB was administered as a single infusion (median infused dose of 2.6 x 10^7/kg) with no prior immunosuppression. The safety and tolerability profile of autologous UCB infusion in ASD was excellent. Improvement in social communication abilities were noted on the caregiver-completed Vineland Adaptive Behavior Scales-Second Edition (VABS-II) and on the Pervasive Developmental Disorder Behavior Inventory (PDDBI). The Clinical Global Impression- Improvement scale, completed by clinicians, reflected beneficial changes during the 6-month period post-infusion in core ASD symptoms in approximately 60% of the participants, as manifested by the participants increased social communication skills, receptive/prosody language, decreased repetitive behavior, and decreased sensory sensitivities (Dawson et al., 2017). In a secondary analysis, researchers showed that electrophysiological biomarkers could predict improvement in autistic symptoms (Murias et al., 2018) and that behavioral and social communication improvements were associated with specific changes in the brain (Carpenter et al., 2019; Simhal et al., 2020). The same group proceeded with a phase 2 double-blind randomized study (NCT02847182) to evaluate the safety and efficacy of UCB, compared to placebo, in improving social communication abilities in 180 children with ASD. The children enrolled in the trial received a single intravenous autologous ($n = 56$) or allogeneic ($n = 63$) UCB infusion, or a placebo ($n = 61$). The infusions were well tolerated and patients were evaluated 6 months after the procedure. The results showed no evidence of improvement in social communication or other autism symptoms. However, in a subgroup of children without intellectual deficit, significant improvement in communication skills, exploratory measures \| TABLE 1 \| Observed immune and other dysregulations (peripheral, neurological and enteric) along with the MSC potential alleviating mechanisms. \| \|---------------------------------------------------------------\| \| Dysregulation* \| Potential mechanism of MSC \| \| Immuno-genetically determined inability to mount efficient anti-inflammatory responses with consequent chronic inflammation \| Overall restoration/improvement of the dysimmune pathways through; \| \| Diminished anti-inflammatory cytokine levels \| - Synthesis and releasing of anti-inflammatory cytokines and growth factors; \| \| Altered cytokine production by monocyte after TLR-based stimulation \| - Suppression of cell-mediated immune response through inhibition of proliferation of several cell subsets including T-lymphocytes and NK cells \| \| Altered CD8+ and CD4+ T-cell profiles \| \| \| Altered NK cell activity \| \| \| Imbalance of serum immunoglobulin due to B cell dysfunction \| \| \| Peripheral and central autoimmune processes due to deregulated anti-inflammatory responses leading to inflammation and autoimmunity after rupture of tolerance and autoantibodies production \| \| \| \| Altered composition of intestinal microbiota leading to increased intestinal permeability (leaking of unwanted bacteria metabolites that might harm the brain) and chronic inflammation \| \| \| \| Altered immune-related transcriptome profiles \| \| \| Altered genome-wide expression profiles in lymphoblastoid cells \| \| \| Elevated activation of astrocytes and microglia \| Provide neuroprotection through anti-inflammatory mechanisms by inhibiting microglial activation and astrocyte proliferation \| \| Synaptic dysfunction and neuro-structural changes \| Act in the existing neural and synaptic network to restore plasticity; \| \| \| Local secretion of substances that could reduce inflammation and promote tissue repair; \| \| \| Promote neuron survival via secretion of neurotrophic factors; \| \| \| Aid in synaptogenesis and regeneration of functional neurological pathways by supplying bioactive agents that stimulate the action of intrinsic neural progenitor cells \| ... \| Study number* \| Title \| Study characteristics/Cell type \| Population \| Main findings \| Authorship \| Journal \| \|---------------\|-------\|---------------------------------\|------------\|---------------\|------------\|---------\| \| NCT01343511 \| Transplantation of human cord blood mononuclear cells and umbilical cord-derived mesenchymal stem cells in autism \| Phase I/II, open-label clinical trial \| CBMNC and UC-derived MSCs \| 37 children with ASD (CBMNC n = 14, CBMNCs and MSCs combined n = 9, control n = 14); median age of 7.08 years (range 6.51–5.02) \| Treatment was deemed safe and well tolerated; Infusion of CBMNCs and MSCs combined showed more effects than the CBMNC transplantation alone and control \| LV et al. (2013) \| J Transl Med \| \| NCT02176317 \| Autologous cord blood infusions are safe and feasible in young children with autism spectrum disorder: Results of a single-center phase I open-label trial \| Phase I, open-label clinical trial \| Autologous UCB \| 25 children with ASD; 72% with moderately severe or severe symptoms; median age of 4.62 years (range 2.26–5.97) \| Treatment was deemed safe and well tolerated; only mild and moderate AE reported. Improvements of ASD symptoms were observed within the 6 months after infusion. Behavioral improvements after UCB infusion were associated with increased white matter connectivity. \| Dawson et al. (2017) \| Transl Med \| \| \| White matter tract changes associated with clinical improvement in an open-label trial assessing autologous umbilical cord blood for treatment of young children with autism \| Study conducted as part of NCT02176317 \| \| \| Carpenter et al. (2019) \| Stem Cells Transl Med \| \| \| Measuring robustness of brain networks in autism spectrum disorder with Ricci curvature \| Study conducted as part of NCT02176317; secondary analysis using diffusion tensor imaging (DTI) data. \| \| \| Simhai et al. (2020) \| Sci Rep \| \| \| Electrophysiological biomarkers predict clinical improvement in an open-label trial assessing efficacy of autologous umbilical cord blood for treatment of autism \| Study conducted as part of NCT02176317 \| \| \| Murias et al. (2018) \| Stem Cells Transl Med \| \| NCT01638819 \| Safety and observations from a placebo-controlled, crossover study to assess use of autologous umbilical cord blood stem cells to improve symptoms in children with autism \| Phase II, randomized, blinded, placebo-controlled, crossover trial \| Autologous UCB \| 29 children with ASD; mean age of 4.53 years (range 2.42–6.80) \| Treatment was safe no serious adverse events reported; trend towards improvement in socialization (not statistically significant) \| Chez et al. (2018) \| Stem Cells Transl Med \| \| NCT03099239 \| Infusion of human umbilical cord tissue mesenchymal stromal cells in children with autism spectrum disorder. \| Phase I, open-label. \| Allogeneic UC-derived MSC \| 12 children with ASD; median age of 6.4 years (range 4–9) \| Treatment was deemed safe, feasible, and well tolerated, except for agitation during procedure; 5 patients developed anti-HLA antibodies, but with no clinical manifestations; -Half of the participants showed improvement in at least 2 ASD measures (Continued on following page) \| Sun et al. (2020) \| Stem Cells Transl Med \| (attention to toys and sustained attention), and increased alpha and beta electroencephalographic power were observed in those treated with UCB (Dawson et al., 2020). A similar phase II clinical trial (NCT01638819) including 29 children with ASD who received autologous UCB infusion performed by a different group of researchers also in the United States although a trend for socialization improvement was observed, the results were not statistically significant (Chez et al., 2018). After the clinical trials with UCB therapy in patients with ASD, the Duke University group completed an open-label, phase I study (NCT03099239) on 12 children treated with umbilical cord (UC) derived MSCs from an unrelated donor. The enrolled children received 1, 2 or 3 doses of $2 \times 10^6$/Kg in intervals of 1 week. The clinical trial confirmed the safety of the use of MSCs for treating children with autism, but the efficacy of the treatment still warrants further evaluation (Sun et al., 2020). In addition, the same research group has two ongoing clinical trials to investigate the use of UC- derived MSCs in pediatric patients with ASD: 1) the TACT, an open label phase I trial (NCT04294290) to evaluate the safety and feasibility of the treatment in toddlers aged 18–48 months; 2) the IMPACT (NCT04089579) which is a randomized, double blinded, phase II study to determine the efficacy UC -derived MSCs in children with ASD aged 4–11 years. Results for the trials are expected by the end of 2022 and mid-2023, respectively. They have also proposed an open label, phase I trial to evaluate the safety and feasibility of the use of UC derived MSCs in adults with ASD, but at the time this review was written, patient recruitment had not yet started. A summary of the publications associated with the clinical trials on ASD using UCB or MSCs in patients with ASD (Lv et al., 2013; Dawson et al., 2017; Chez et al., 2018; Murias et al., 2018; Carpenter et al., 2019; Simhal et al., 2020; Sun et al., 2020), including those detailed above, are provided in Table 2. ### Table 2 \| (Continued) Summary of Publications Issued from Clinical Trials on ASD Using MSC or UCB. \| Study number* \| Title \| Study characteristics/ \| Cell type \| Population \| Main findings \| Authorship \| Journal \| \|---------------\|-------\|------------------------\|-----------\|------------\|---------------\|------------\|---------\| \| NCT02847182 \| A phase II randomized clinical trial of the safety and efficacy of intravenous umbilical cord blood infusion for treatment of children with autism spectrum disorder \| Phase II, prospective randomized, placebo-controlled, double-blind UCB \| Autologous or allogeneic UCB \| 180 children with ASD, aged 2–7 years (mean 5.47); autologous UCB (n = 56); allogeneic UCB (n = 63), placebo (n = 61) \| UCB infusion was, in general, not associated with decrease in ASD symptoms or improvements in socialization; in a subgroup of children without intellectual disability improvements in communication skills was observed \| Dawson et al. (2020) \| The Journal of Pediatrics \| ### 3 CONCLUSION AND FURTHER PERSPECTIVE The immune-brain axis is now well known to play a primordial key role in the development of ASD as evidenced by the existence of inefficient anti-infectious responses, low grade inflammation, immune-cell subset alterations and autoimmunity. All of these immune dysfunctions are similar to those observed in common inflammatory/autoimmune chronic disorders, known to be improved by stem cell-based therapies, including those using MSCs. Correcting or improving the immune dysfunctions in patients with ASD, via direct or indirect mechanisms, might induce changes that would potentially result in improvement in core domains of autistic symptomatology in these patients and contribute to increasing their quality of life. Thus, continuing research in this field is encouraged, in particular future studies considering cohorts selected on the basis of immune dysfunction parameters that seem essential to determine the efficacy of MSC in this context. The mechanistic rationale and overarching theory of this line of investigation is that MSCs can act through paracrine and allocrine mechanisms to modulate ongoing inflammation and/or immune pathology in the brain and possibly protect neurons from further damage. In many contexts, MSCs dampen, rather than augment/overwhelm, immunological and inflammatory responses. Documented mechanisms include shifts in effector T cells such as generation of regulatory T cell populations and changes in monocyte/dendritic cell cytokine generation leading to anti-inflammatory cytokines. Therefore, it is plausible to consider a population of MSCs as an immunological and/or anti-inflammatory agent. Both post-mortem brain tissue studies and PET imaging data from living individuals with ASD have revealed evidence of increased microglial activation, suggesting that immune and/or inflammatory mediated brain damage plays a role in the etiology of ASD as discussed above. The combination of ASD symptoms and the related co-morbidities places a very high burden on the affected individual, their families and society. Because of the lack of effective treatments, non-evidence-based interventions, often costly, are usually sought by concerned families, making ASD, an area in crucial need for therapeutic innovation. Developing drugs for ASD has been challenging because of a limited understanding of its underlying pathophysiology. In this frustrating context, emerging evidences shed light towards a primordial key role of immune dysfunction in ASD characterized by inflammation, T-lymphocyte abnormalities, autoantibodies resulting in structural brain changes and abnormal immune mediation of synaptic functions, which serve as the rationale for immune-related interventions such as MSC-based treatment. Successful treatments will reduce care costs, increase productivity and family income and increase family quality of life. AUTHOR CONTRIBUTIONS RT and FV take the primary responsibility of the review. J-RR, C-LW, JB, WB, BC, GS, HR, CK, DF, PL, EM, SN, LC, and FL were involved in discussions about the review, participate to the manuscript design and writing and carefully read the manuscript. RT, FV, and EG designed and supervised the whole review and wrote the manuscript. All authors read ad approved the final version of the manuscript. 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Neurol. 83, 2071–2084. doi:10.1002/ana.24744 Copyright © 2022 Tamouza, Volt, Richard, Wu, Bouassida, Boukouaci, Lamsaia, Cappelli, Scigliuolo, Ra	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3187, 1 ], [ 3187, 9426, 2 ], [ 9426, 16037, 3 ], [ 16037, 22414, 4 ], [ 22414, 26879, 5 ], [ 26879, 33251, 6 ], [ 33251, 39664, 7 ], [ 39664, 45811, 8 ], [ 45811, 49156, 9 ], [ 49156, 54627, 10 ], [ 54627, 60584, 11 ], [ 60584, 60584, 12 ], [ 60584, 60584, 13 ], [ 60584, 65932, 14 ], [ 65932, 70094, 15 ] ] }
c55c6f6deacd9c93d273c9ec35ad890235b9f5f3	{ "olmocr-version": "0.1.59", "pdf-total-pages": 16, "total-fallback-pages": 0, "total-input-tokens": 43836, "total-output-tokens": 12905, "fieldofstudy": [ "Materials Science", "Engineering" ] }	Effect of Shrinkage Reducing Admixture on Drying Shrinkage of Concrete with Different w/c Ratios Mahdi Kioumarsi 1,, Fazel Azarhomayun 2, Mohammad Haji 3 and Mohammad Shekarchi 2 1 Department of Civil Engineering and Energy Technology, OsloMet—Oslo Metropolitan University, 0166 Oslo, Norway 2 School of Civil Engineering, College of Engineering, University of Tehran, Tehran 141793840, Iran; [email protected] (F.A.); [email protected] (M.S.) 3 Faculty of Civil Engineering, Semnan University, Semnan 351319111, Iran; [email protected] Correspondence: [email protected]; Tel.: +47-67-23-87-45 Received: 22 November 2020; Accepted: 8 December 2020; Published: 15 December 2020 Abstract: The reduction of the moisture content of concrete during the drying process reduces the concrete’s volume and causes it to shrink. In general, concrete shrinkage is a phenomenon that causes concrete volume to dwindle and can lead to durability problems. There are different types of this phenomenon, among them chemical shrinkage, autogenous shrinkage, drying shrinkage including free shrinkage and restrained shrinkage, and thermal contraction. Shrinkage-reducing admixtures are commercially available in different forms. The present study investigates the effect of liquid propylene glycol ether on mechanical properties and free shrinkage induced by drying at different water-cement (w/c) ratios. Furthermore, the effect of shrinkage-reducing admixtures on the properties of hardened concrete such as compressive and tensile strength, electrical resistivity, modulus of elasticity, free drying shrinkage, water absorption, and depth of water penetration was investigated. The results indicated that shrinkage reducing agents performed better in a low w/c ratio and resulted in up to 50% shrinkage reduction, which was due to the surface reduction of capillary pores. The prediction of free shrinkage due to drying was also performed using an artificial neural network. Keywords: concrete; mechanical properties; shrinkage reducing admixture; water-cement ratios; artificial neural network 1. Introduction Concrete is the most widely used building material in the world, such that in some countries, the use of reinforced concrete is more common than steel structures [1–3]. The scope of concrete consumption encompasses everything from small concrete blocks to the spillways of dams and bridge decks. One of the biggest concerns about concrete is cracking and the factors contributing to this. One of the factors that cause cracking in concrete is drying shrinkage. The evaporation rate is high for curing concrete in environments with insufficient moisture, when water temperature is high, and in windy conditions. Drying shrinkage is also more likely to occur in structures with a high surface-to-volume ratio. It has long been the concern of researchers in the field of concrete technology to find ways to reduce this type of shrinkage [4]. In this regard, one of the most effective methods is to use shrinkage reducing admixtures (SRA). The use of SRA increases the time it takes to reach the maximum hydration temperature in concrete and mortar, and by increasing the amount of SRA, the time it takes to reach maximum temperature increases; the application of SRA in mixtures with superplasticizers will further delay hydration reactions. Mora et al. [4] showed that SRA, even in high strength concrete (HSC), not only reduces shrinkage and cracking due to a reduction in evaporation rate, but also results in... delayed maximum capillary pressure because of crescent cavity growth. The rate of evaporation and pore pressure in concrete containing SRA is lower than that of conventional concrete, and this difference results in reduced concrete discharge. Adding 1% SRA by cement weight, will reduce short-term and long-term shrinkage, and will be more effective when the internal moisture content and porosity of concrete are higher. Increasing the dosage of SRA in self-compacting concrete does not decrease workability [5]. In addition to reducing the pore solution, SRA with a highly retained moisture content leads to better internal curing [6]. The application of SRA has been found to increase the retention time of concrete and extend the initial and final setting time of concrete compared to a control specimen [7–9]. In addition to shrinkage reducing agents, the use of poly vinyl alcohol (PVA) fiber and volcanic ash are also effective in reducing shrinkage. These additives can increase the compressive strength of concrete, while reducing the surface stresses and strains associated with shrinkage. It should be noted that SRA reduces the tensile strength of concrete, its versatility and its compressive strength, which can be compensated for by using fiber [10,11]. Typically, SRA delays the hydration reaction at the start of concrete setting due to the presence of organic molecules. SRA molecules decrease the polarity of concrete mortar and increase specific surfaces, which result in an increase in the amount of water needed for hydration. This in turn leads to an improvement of hydration at higher ages [10,11]. SRA generally reduces the large pores of the cement matrix, delays crack initiation time, significantly reduces crack width, and is more effective than geopolymer materials [11,12]. Today, the use of soft computing in civil engineering to predict experimental results has been extended due to its high accuracy. Many researchers in the field of concrete technology have used soft computing and artificial neural networks (ANN) in particular to predict concrete properties based on experimental results. Mechanical properties of different types of concrete such as compressive strength, tensile strength, elastic modulus, and flexural strength can be predicted using soft computing methods. The most important studies using artificial neural networks predict compressive strength in different concretes such as self-compacting concrete [13–17]; high-performance concrete [13,18]; recycled aggregate concrete [19–22]; cement mortars [23]; cement mortars containing nano and micro silica [24]; concrete containing rice husk ash as a partial replacement for cement and reclaimed asphalt pavement as a replacement for aggregates [25]; concrete under different temperatures [15,26,27] and relative humidity [15]; heavy weight concrete [28]; laterized concrete [29]; polymer concrete with various percentages of fly ash [30]; silica fume concrete [31]; high-strength concrete [32]; rubberized concrete [33]; clinker mortars [34]; lightweight concrete [27]; and self-consolidating high-strength concrete containing palm oil fuel ash [35]. In a study conducted by Bui et al. [18], the tensile strength of high-performance concrete (HPC) was predicted using a combination of ANN and firefly algorithm. The firefly algorithm was used to optimize biases and weights of ANN. The input parameters were curing age and cubic compressive strength, while the compressive strength of HPC was the output. The accuracy of the model was compared to other models and showed faster and better prediction [18]. The flexural strength of cement mortars containing nano and micro silica was predicted using ANN and genetic expression programming (GEP) [24]. The prediction of elastic modulus of concrete [36] and recycled aggregate concrete [37,38] was conducted by elephant herding optimization and ANN, respectively. An estimation of the compressive strength of concrete obtained by mechanical wave velocities was conducted using the ANN method [39,40]. The results of the ASTM C1012-95 testing method on sulfate attack of concretes, which were made with different cement types and pozzolanic additives, were predicted by ANN [40]. ANN was also applied to investigate the impermeability of concrete made with lightweight aggregate [41]. Hybrid artificial intelligence was used to predict foamed cellular lightweight concrete compressive strength using 418 experimental datasets. An equation was proposed based on a water cycle algorithm and its predictions were compared to other methods such as support vector regression, multiple linear regression, and artificial neural network [42]. An ANN model was also presented to estimate the autogenous shrinkage of concrete. The model was developed on the basis of 77 datasets, including specimens of traditional concrete as well as modern concrete [43]. Given that the effect of SRA on concrete shrinkage has not been extensively investigated in low, medium, and high water-cement (w/c) ratios, this study was conducted to investigate the effect of different w/c ratios on concrete containing SRA. For this purpose, six mix designs were considered and the effect of SRA on parameters such as free shrinkage, tensile compressive strength, Young’s modulus, electrical resistance, water absorption, and depth of penetration were investigated. Furthermore, an artificial neural network was applied to predict dry shrinkage of concrete based on the experimental results conducted in the study. 2. Experimental Program 2.1. Materials The cement used in this study was Portland Cement Type II—in accordance with the ASTM C150 [44]—with a specific gravity of 3.15 N/m³. The chemical composition of the constitutive elements of the cement used in the study is presented in Table 1 below. Propylene glycol ether is a colorless liquid whose etheric property means that it is counted as an SRA material. Table 2 shows the properties of fine and coarse aggregates in accordance with the ASTM C33 [45], which were used to make the concrete. The superplasticizer used in this study was based on polycarboxylate ether and has a specific gravity of 1.1 N/m³. The size distribution of coarse and fine aggregate sand was in accordance with the standards ASTM C136 and ASTM C33 [45]. \| Composition \| CaO \| SiO₂ \| Al₂O₃ \| Fe₂O₃ \| MgO \| K₂O \| Na₂O \| C₂S \| C₃S \| C₃A \| C₄AF \| \|-------------\|-----\|------\|-------\|-------\|-----\|-----\|------\|-----\|-----\|-----\|------\| \| % \| 64.3\| 21.8 \| 4.5 \| 3.9 \| 1.5 \| 0.54\| 0.17 \| 56 \| 20 \| 5 \| 12 \| Table 2. Physical properties of the fine and coarse aggregate. \| Properties \| Coarse Aggregate \| Fine Aggregate \| \|-------------------------------------------\|------------------\|----------------\| \| Specific gravity (saturated surface dry) (N/m³) \| 2.56 \| 2.55 \| \| Water absorption (%) \| 1.7 \| 2.7 \| \| Physical shape \| Crushed \| Well-rounded \| 2.2. Specimen Preparation In order to achieve the objectives of this study and obtain the mechanical properties of the intended mix designs, the concrete was manufactured with the desired mixing design. There are various tests to determine the properties of fresh and hardened concrete, some of which have been used in this study. For fresh concrete slump and air content and for hardened concrete compressive and tensile strengths, electrical resistance, modulus of elasticity, restrained drying, and water absorption, were obtained on the basis of different standards. Table 3 displays the types of experimental tests, geometry, and dimensions of the specimens based on the related standards. Table 3. Type and number of specimens prepared, and standards used. \| Test \| Specimen \| Dimensions (mm) \| Number Samples for Each Test \| Standard \| \|-----------------------\|----------\|-----------------\|-----------------------------\|-------------------\| \| Air content \| - \| - \| 1 \| ASTM C231 \| \| Slump \| - \| - \| 1 \| ASTM C143 \| \| Compressive strength \| Cubic \| 150 × 150 × 150 \| 3 \| EN 12390-3 \| \| Tensile strength \| Cylinder \| 150 × 300 \| 2 \| ASTM C496 \| \| Unrestrained drying shrinkage \| Prism \| 75 × 75 × 285 \| 3 \| ASTM C157 \| \| Electrical resistance \| Cubic \| 100 × 100 × 100 \| 3 \| ASSHTO T358 \| \| Modulus of elasticity \| Cylinder \| 100 × 200 \| 3 \| ASTM C469 \| \| Water absorption \| Cubic \| 750 × 750 × 750 \| 3 \| BS 1881: Part 122 \| As mentioned, the aim of this study is to investigate the effect of SRA on the drying-induced shrinkage of concrete in different w/c ratios. For this purpose, specimens in three low, medium, and high w/c ratios as well as control specimens were made. The concrete manufacturing process was as follows: Pouring sand into the mixer, adding gravel to the sand, adding cement to the aggregate, adding water to the mixture, adding SRA together with mix water which was kept from the previous steps, and, finally, adding superplasticizer with mix design water to the mixture. The concrete poured into the mold was kept for 24 h and then immersed in lime-saturated water at 23 ± 2 °C. 2.3. Mixture Proportion The impact of SRA on the properties of fresh and hardened concrete was investigated in six mix designs classified in three groups. Table 4 illustrates the concrete’s composition in various mix designs. The dosage of superplasticizer was designed to achieve a slump of 15 ± 5 cm for mix designs with w/c ratios of 0.4 and 0.5. Since the slumps of the specimens with w/c ratio of 0.6 were in acceptable range, these specimens were designed without superplasticizer. Table 4. Concrete components in various mix designs. \| Group \| Specimen Name \| Cement (kg/m³) \| Water (kg/m³) \| w/c \| Fine Aggregate (kg/m³) \| Coarse Aggregate (kg/m³) \| SRA % (Weight of Cement) \| Superplasticizer % (Weight of Cement) \| \|-------\|----------------\|----------------\|--------------\|-----\|-----------------------\|-------------------------\|--------------------------\|----------------------------------------\| \| 1 \| Plain-0.6 \| 350 \| 210 \| 0.6 \| 1151 \| 619 \| - \| - \| \| \| SRA-0.6 \| 350 \| 210 \| 0.6 \| 1151 \| 619 \| 1.5 \| - \| \| 2 \| Plain-0.5 \| 350 \| 175 \| 0.5 \| 1173 \| 632 \| - \| 0.5 \| \| \| SRA-0.5 \| 350 \| 175 \| 0.5 \| 1173 \| 632 \| 1.5 \| 0.5 \| \| 3 \| Plain-0.4 \| 350 \| 140 \| 0.4 \| 1196 \| 644 \| - \| 0.9 \| \| \| SRA-0.4 \| 350 \| 140 \| 0.4 \| 1196 \| 644 \| 1.5 \| 0.9 \| 3. Results and Discussion After fabricating the concrete with the intended mix design, the tests for fresh and hardened concrete were carried out. The results of the specimens and comparisons between them are presented in this section. 3.1. Fresh Concrete In this study, two slump and air content tests were conducted based on the ASTM C143 and ASTM C231 standards in order to determine the effect of different percentages of SRA on the workability and air content of the manufactured concretes. As shown in Table 5 below, the air content is about 2%–3% for fresh concrete when shrinkage-reducing admixtures are added to the concrete paste. Based on the results of previous studies, the impact of different types of commercial SRA materials on concrete workability is slightly different, but, overall, the impact of the SRA material on fresh concrete workability is negligible [46,47]. Table 5 shows that the SRA material increased the percentage of air and decreased the workability of fresh concrete. The same results are reported by Hamedanimojarrad [46]. \| Group \| w/c \| Specimen Name \| Slump (cm) \| Air Content (%) \| \|-------\|-----\|---------------\|------------\|-----------------\| \| 1 \| 0.6 \| Plain-0.6 \| 21 \| 1.6 \| \| \| 0.6 \| SRA-0.6 \| 18 \| 2.1 \| \| 2 \| 0.5 \| Plain-0.5 \| 15 \| 2 \| \| \| 0.5 \| SRA-0.5 \| 12 \| 2.4 \| \| 3 \| 0.4 \| Plain-0.4 \| 15 \| 2.6 \| \| \| 0.4 \| SRA-0.4 \| 11 \| 3 \| 3.2. Hardened Concrete 3.2.1. Compressive Strength A compressive strength test was performed on cubic specimens of 150 by 150 mm in accordance with EN 12390-3 [47] at the age of 28 days. Figure 1 shows the effect of SRA on compressive strength. The average of the three compressive strengths was recorded for each mix design. SRA reduces the rate of cement hydration reactions, which consequently influences compressive strength. The mix design containing SRA reduced the compressive strength of concrete and this reduction was less with the reduction of the w/c ratio [48]. As shown in Figure 1, the SRA material in higher w/c ratios further reduces the compressive strength, which in the w/c ratio of 0.6, caused around a 14% decrease in compressive strength. ![Figure 1](image) Figure 1. Compressive strength in specimens with three different water-cement (w/c) ratios with and without shrinkage reducing admixtures (SRA) after 28 days. 3.2.2. Tensile Strength The tensile strength test was performed on cylindrical specimens measuring 300 by 150 mm in accordance with the ASTM C496 [49] standard at 28 days, and was reported as the mean tensile strength for each specimen. Figure 2 shows the effect of SRA on tensile strength. In general, the specimen containing SRA has less tensile strength, which changes with compressive strength. The average reductions in tensile strength by adding SRA to concrete were 10.33% and 7.18% for 7 and 28 days, respectively, in which the amount of reduction decreased by increasing the w/c ratio and the number of days. In other words, SRA has a greater effect on reducing tensile strength at early ages. 3.2.3. Electrical Resistivity The electrical resistivity test was performed on 100 by 100 by 100 mm specimens according to ASSHTO T358 [48]. Figure 3 provides information on the effect of SRA on electrical resistivity. Here it can be seen that adding SRA to concrete, as well as decreasing the w/c ratio, caused an increment in electrical resistivity. However, the effect of changes to the w/c ratio was greater than the addition of SRA. The average increase in electrical resistivity from decreasing the w/c ratio was 14.26%, while this increment was 3.18% when adding SRA. Adding SRA to concrete reduces interlayer water (hydration-induced water) in the mixture, thereby reducing electrical resistivity. Figure 2. Tensile strength in specimens with three different w/c ratios with and without SRA after 7 and 28 days. Figure 3. Electrical resistivity of specimens for three different w/c ratios with and without SRA after 28 days. 3.2.4. Dynamic Elastic Modulus Young’s modulus testing was performed on specimens of 200 by 100 mm according to ASTM C469 at 28 days. Figure 4 illustrates the elastic modulus test instrument. Figure 5 shows that the w/c ratio had a greater effect on the modulus of elasticity compared to adding SRA. The highest modulus of elasticity observed in the specimens with lower w/c ratio. The specimens with SRA reduced the Young’s modulus compared to the similar specimens without SRA. These results are consistent with the results found by Haitao in 2013 [50]. ![Elastic modulus measuring device.](image) Figure 4. Elastic modulus measuring device. ![Modulus of elasticity in specimens with different w/c ratios in plain concrete and concrete containing SRA.](image) Figure 5. Modulus of elasticity in specimens with different w/c ratios in plain concrete and concrete containing SRA. 3.2.5. Free Drying Shrinkage A free-drying shrinkage test was performed in line with ASTM C157, according to which the specimens were stored in a chamber with a relative humidity of 50 ± 5 and 23 ± 2. Length of the specimens was also read at intervals of 1, 4, 7, 14, and 28 days, and of 8, 16, 32, and 64 weeks [51]. Figure 6 shows the specimen in the chamber with standard conditions. The drying-induced free shrinkage test was performed on all the specimens, as shown in Figure 7. This figure shows that the free shrinkage of the mixture had a 1.5% SRA weight in a w/c ratio of 0.4, which is approximately similar to the drying-induced free shrinkage of the mixture without the SRA material in a w/c ratio of 0.5. This was due to the effect of SRA on drying-induced free shrinkage. Generally, SRA at the age of 224 days compensated for drying shrinkage by about 27%, 30%, and 50%, in the w/c ratios of 0.6, 0.5, and 0.4, respectively. Shrinkage due to a loss of excess water caused by internal stresses results in cracking. SRA reduced shrinkage stresses. It should be noted that the higher the w/c ratio, the greater the effect of the SRA material and the greater the effect on compensating for the drying shrinkage. The results indicate that reducing drying-induced shrinkage does not necessarily require a reduction in the w/c ratio and can be achieved by using SRA. ![Figure 6. (a) Measurement of dry shrinkage and (b) specimens in the standard room.](image) ![Figure 7. Free drying shrinkage over time for three different w/c ratios with and without SRA.](image) 3.2.6. Water Absorption The water absorption test for concrete specimens was performed according to BS 188: Part 122 [52]. Figure 8 shows the results of the comparison of changes in the mixtures’ water absorption percentage over time. As the immersion time increased, the percentage of the concrete’s water absorption increased, where the 24-h water absorption was about 2.57 times that of the half-hour water absorption. The use of SRA reduced the water absorption of the concrete. However, it is worth noting that as the immersion time increases, the impact of SRA on reducing the concrete’s water absorption increases. This may be due to the higher volume of filled pores with increased immersion time. The use of SRA reduces the surface tension stress of water with the wall of capillary pores, thereby reducing capillary suction of water into cavities, and decreasing the water absorption of concrete [53]. As the immersion time increases, more concrete pores contribute to the water absorption process. Therefore, due to the effect of SRA, the difference in water absorption percentage increases with a longer immersion time. As the w/c ratio decreases, the water absorption rate of concrete decreases. The results indicate that the effect of a w/c ratio reduction on the decrease of water absorption rate in the mixture containing SRA was approximately similar to the control design, namely the design without SRA. Furthermore, by adding SRA and increasing the w/c ratio, water penetration depth (calculated according to BS EN 12390-8 [52]) in 28 days specimens decreased, see Figure 9. The decrease in the water penetration depth is due to the effect of the SRA on the pores system of concrete. Figure 8. Water absorption in different mix designs after 0.5, 1, and 24 h. Figure 9. Water penetration depth in different mix designs. 3.3. Artificial Neural Networks Many researchers have proposed models in various fields of study using soft computing methods [54–59], especially by employing artificial neural networks [28,60–63]. Artificial neural network is an artificial intelligence (AI) based method that simulates human brain to learn machines. ANN can solve new problems using past experiences like human brain. One of the most basic neural models available is multi-layer perceptron (MLP) model, which simulates the transfer function of the human brain. An artificial neural network consists of three layers: Input, output, and processing. Each layer contains a group of neurons that are generally associated with all the neurons in the other layers. After receiving the input, each neuron processes it and transmits the result to another cell. This behavior continues until a definite result is reached, which eventually leads to a decision, process, thought, or move. This is to compare the output of a network with the output that is desired and expected. The difference between the two outputs is used to change and modify the connection weights between the network units. Learning neural networks using a feedback process are called feedforward networks. Feedforward networks proceed by decreasing the difference between the actual output and the desired output until the two outputs become the same. In this study, ANN is performed to propose a model to predict the dry shrinkage of the tested specimens. To create a network, a total of eight parameters, including the w/c ratio, type of admixture, weight of sand, gravel, and superplasticizer, were considered as input. The dry shrinkage of concrete specimens was considered to be the output parameter. The network properties used in this model are described in Table 6 below. \| Network Type \| Feed-Forward Backprop \| \|------------------------------\|-----------------------\| \| Training function \| TRAINLM \| \| Adaption learning function \| LEARNGDM \| \| Performance function \| MSE \| \| Number of layers \| 2 \| \| Transfer function (layer 1) \| TANSIG \| \| Transfer function (layer 2) \| PURELIN \| Different hidden nodes were examined (1 to 10) and their mean square error (MSE) value and the regression value for training, testing, validation, and the whole dataset, were obtained. The criterion for choosing the best network was having at least MSE (in this study the minimum MSE was equal to 0.00047), with the regression values being as close as possible to one. According to this criterion, in this study, the two-layer network was selected as the optimal network. The validation performance and training state and the values of the regressions are presented in Figures 10 and 11, respectively. The values predicted by the optimal network and its prediction errors are given in Table 7 below. Figure 10. Value of mean square error (MSE) in the selected network. Figure 11. Values of regression for training, validation, testing, and the whole dataset for the selected network to predict shrinkage. The values predicted by the optimal network and its prediction errors are given in Table 7 below. Table 7. Predicted shrinkages by artificial neural network along with its error. \| Mix Design \| w/c \| SRA (%) \| Fine Aggregate (kg/m³) \| Coarse Aggregate (kg/m³) \| Superplasticizer % (Weight of Cement) \| Exp. Shrinkage \| Predicted Shrinkage \| Error (%) \| \|------------\|-----\|---------\|------------------------\|--------------------------\|-------------------------------------\|---------------\|---------------------\|-----------\| \| Plain-0.6 \| 0.6 \| 0 \| 1099 \| 593 \| 0 \| 0.63 \| 0.63 \| 0.88 \| \| SRA-0.6 \| 0.6 \| 1.5 \| 1099 \| 593 \| 0 \| 0.30 \| 0.3 \| 0.23 \| \| SCA-0.6 \| 0.6 \| 0 \| 1099 \| 593 \| 0 \| 0.27 \| 0.27 \| 0.31 \| \| PRA-0.6 \| 0.6 \| 0 \| 1099 \| 593 \| 0 \| 0.28 \| 0.28 \| 0.02 \| \| Plain-0.5 \| 0.5 \| 0 \| 1159 \| 610 \| 0.7 \| 0.43 \| 0.43 \| 0.37 \| \| SRA-0.5 \| 0.5 \| 1.5 \| 1159 \| 610 \| 0.7 \| 0.28 \| 0.28 \| 0.06 \| \| SCA-0.5 \| 0.5 \| 0 \| 1159 \| 610 \| 0.7 \| 0.22 \| 0.22 \| 0.74 \| \| PRA-0.5 \| 0.5 \| 0 \| 1159 \| 610 \| 0.7 \| 0.25 \| 0.25 \| 0.347 \| \| Plain-0.4 \| 0.4 \| 0 \| 1189 \| 639 \| 3.15 \| 0.38 \| 0.36 \| 4.62 \| \| SRA-0.4 \| 0.4 \| 1.5 \| 1189 \| 639 \| 3.15 \| 0.24 \| 0.29 \| 18.61 \| \| SCA-0.4 \| 0.4 \| 0 \| 1189 \| 639 \| 3.15 \| 0.18 \| 0.13 \| 29.77 \| \| PRA-0.4 \| 0.4 \| 0 \| 1189 \| 639 \| 3.15 \| 0.21 \| 0.21 \| 0.36 \| The network is selected in a way that the error values for training, validation, test, and all data are the minimum values. The other networks had shown a higher number of errors than this network. The purpose of using neural network in this study is to investigate the predicted results for shrinkage using limited available experimental data. As shown in Table 7, the maximum and minimum errors of the predicted values by artificial neural network are 0.02% and 29.77%, respectively, and the average error is 4.69%, which show the acceptable accuracy of ANN in predicting the dry shrinkage of specimens despite the low numbers of data. The highest errors have been observed in the specimen with w/c ratio of 0.4; it means that this network did not perform well in predicting the shrinkage of specimens with w/c ratio equal to 0.4. To improve the network in this case, more experimental data are required. 4. Conclusions The present study investigates the effect of liquid propylene glycol ether on mechanical properties and free shrinkage induced by drying at different water-cement ratios. Furthermore, the effect of shrinkage-reducing admixtures on the properties of hardened concrete such as compressive and tensile strength, electrical resistivity, modulus of elasticity, free drying shrinkage, water absorption, and depth of water penetration was investigated. Based on the experiments, the following conclusions regarding the effect of SRA on different properties of concrete in low, medium, and high w/c ratios are drawn. - The use of SRA reduced the slump compared to the control specimen, and the higher the w/c ratio, the greater the decrease of the slump. - The use of SRA reduced compressive strength and tensile strength as compared to the control specimen. The higher the ratio of water to cement is, the greater the reduction in compressive strength. Using SRA caused a decrease in the Young’s modulus of the concrete and had a greater effect in a w/c ratio of 0.4. - The use of SRA increased the electrical resistivity of the concrete, which has the same effect on the electrical resistivity of concrete in low, medium and high w/c ratios. - Using SRA caused a decrease in the depth of penetration of water under pressure. It decreased less in a low w/c ratio compared to other ratios. - Using SRA caused a decrease in the water absorption rate of concrete. It was observed that the effect of SRA on the reduction of water absorption of concrete is dependent on the immersion time of the concrete in water. - The use of SRA caused a 50% decrease in free shrinkage induced by drying. - Prediction of the dry shrinkage of specimens was performed using an artificial neural network, with low and acceptable mean error, indicating the high accuracy of ANN in predicting dry shrinkage based on experimental results. 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[CrossRef] Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3536, 1 ], [ 3536, 8259, 2 ], [ 8259, 11296, 3 ], [ 11296, 15990, 4 ], [ 15990, 18318, 5 ], [ 18318, 19262, 6 ], [ 19262, 20766, 7 ], [ 20766, 22566, 8 ], [ 22566, 23573, 9 ], [ 23573, 26445, 10 ], [ 26445, 26849, 11 ], [ 26849, 32161, 12 ], [ 32161, 36465, 13 ], [ 36465, 41411, 14 ], [ 41411, 45844, 15 ], [ 45844, 46082, 16 ] ] }
969cb9f762599a9398001c6e5592ec6352a48b09	{ "olmocr-version": "0.1.59", "pdf-total-pages": 14, "total-fallback-pages": 0, "total-input-tokens": 45049, "total-output-tokens": 12132, "fieldofstudy": [ "Physics" ] }	Invariant distributions and collisionless equilibria Henry E. Kandrup Department of Astronomy and Department of Physics and Institute for Fundamental Theory, University of Florida, Gainesville, FL 32611 USA and Observatoire de Marseille, 2 Place Le Verrier, F-13248 Marseille Cedex 4, France Abstract This paper discusses the possibility of constructing time-independent solutions to the collisionless Boltzmann equation which depend on quantities other than global isolating integrals such as energy and angular momentum. The key point is that, at least in principle, a self-consistent equilibrium can be constructed from any set of time-independent phase space building blocks which, when combined, generate the mass distribution associated with an assumed time-independent potential. This approach provides a way to justify Schwarzschild’s (1979) method for the numerical construction of self-consistent equilibria with arbitrary time-independent potentials, generalising thereby an approach developed by Vandervoort (1984) for integrable potentials. As a simple illustration, Schwarzschild’s method is reformulated to allow for a straightforward computation of equilibria which depend only on one or two global integrals and no other quantities, as is reasonable, e.g., for modeling axisymmetric configurations characterised by a nonintegrable potential. 1 MOTIVATION Conventional wisdom holds that galaxies in or near equilibrium can be modeled as time-independent solutions to the collisionless Boltzmann equation. In this context, the modeling of galaxies would seem to break logically into two reasonably distinct components, namely (i) constructing time-independent solutions to the collisionless Boltzmann equation and then (ii) determining whether said solutions are linearly stable and otherwise viable as reasonable models of what one actually sees. The principal focus of this paper is primarily on the former component, the construction of time-independent solutions, although the concluding section will comment on issues related to viability. Given an assumed equilibrium mass distribution $\rho_0$, and an associated potential $\Phi_0$ generated by the gravitational Poisson equation, $$\nabla^2 \Phi_0 = 4\pi G \rho_0, \quad (1)$$ there is a globally conserved quantity (isolating integral) $E$ reflecting time translational invariance. If the configuration is time-independent in an inertial frame, this quantity is the ordinary energy $E = \frac{1}{2}v^2 + \Phi_0$ (here, and henceforth, units have been chosen so that the stellar mass $m = 1$). If instead the configuration is time-independent in a suitably chosen rotating frame, $E$ is the Jacobi integral. If $\Phi_0$ manifests other continuous symmetries as \[\text{current address}\] well (e.g., spherical or axial symmetry), Noether’s Theorem (cf. Arnold 1989) implies that there will be one or more additional globally conserved quantities, say $ \{I_i\} $. If there exist three independent global integrals, motion in the potential $ \Phi_0 $ is integrable. If fewer than three independent global integrals exist, the motion is nonintegrable. Jeans’ Theorem implies that any function $ f_0(E, \{I_i\}) $ that reproduces the assumed $ \rho_0 $, i.e., for which \[ \rho_0 = \int d^3v f_0(E, \{I_i\}), \] yields a self-consistent equilibrium (cf. Binney and Tremaine 1987). Indeed, many workers have gone further and assumed that all time-independent equilibria must depend on such global isolating integrals. If, however, one demands that every $ f_0 $ be a function only of some set of global isolating integrals, there is an obvious critique which can be leveled towards numerical model-building based on Schwarzschild’s (1979) method. This method, which involves selecting ensembles of orbit segments that self-consistently reproduce the mass density associated with an imposed potential, says nothing \textit{a priori} about any global integrals; and, as such, for generic potentials nothing intrinsic to the method imposes explicitly the demand that the equilibrium $ f_0 $ be a function of one or more global isolating integrals. For the special case of integrable potentials, e.g., spherical configurations or triaxial equilibria characterised by Staeckel (1890) potentials, there \textit{is} a direct, albeit not completely trivial, connection between Schwarzschild’s method and global integrals. As discussed by Vandervoort (1984) in a slightly different language, if orbits are constrained by three independent global integrals, say $ I_1(r, v) $, $ I_2(r, v) $, and $ I_3(r, v) $, fixing the values of these integrals as $ I_{1,0}, I_{2,0}, $ and $ I_{3,0} $ determines completely a collection of one or more multiply periodic orbits in the three-dimensional configuration space, each of which must in principle be included in an equilibrium model with the proper relative weight.\footnote{Consider, for example, a spherical system with global integrals $ E, J^2, $ and $ J_z $, and focus on motion in the equatorial plane, i.e., $ J_x = J_y = 0 $. Here there are an infinite number of possible orbits, characterised by initial conditions corresponding to all possible points $(r, \varphi)$ located in an annulus with inner and outer radii fixed by $ E $ and $ J_z^2 $. The weighting implicit in eq. (3) means that all values of $ \varphi $ should be treated equally, but that the relative weighting of different $ r $’s must reflect the fact that, because of conservation of angular momentum, orbits spend different amounts of time at different radii. As a practical matter, however, this subtlety is arguably unimportant, and it may suffice computationally to consider a single orbit: If the radial and azimuthal periods are incommensurate, any $(x, y)$ yields an orbit that densely fills the annulus with the proper weight; and, even if the periods are not incommensurate, unless they are in a relatively low order resonance the orbit will generally fill a region which, to the level of accuracy associated with one’s configuration space discretisation, is essentially dense in the annulus.} More precisely, specifying a triplet $ \{I_{1,0}, I_{2,0}, I_{3,0}\} $ defines a phase space density \[ g_{I_{1,0},I_{2,0},I_{3,0}}(r, v) \propto \delta_D[I_1(r, v) - I_{1,0}] \delta_D[I_2(r, v) - I_{2,0}] \delta_D[I_3(r, v) - I_{3,0}] \] and a corresponding configuration space density \[ n_{I_{1,0},I_{2,0},I_{3,0}}(r) = \int d^3v g_{I_{1,0},I_{2,0},I_{3,0}}(r, v) \] \[ = \int \int \int dI_1 dI_2 dI_3 \frac{\partial(v_1, v_2, v_3)}{\partial(I_1, I_2, I_3)} g_{I_{1,0},I_{2,0},I_{3,0}}(r, v), \] which, when evolved into the future using the Hamilton equations associated with $ \Phi_0 $, remains unchanged. The assumption that the desired $ \rho_0 $ is generated from some $ f_0(I_1, I_2, I_3) $ depending only on global integrals means that the equilibrium distribution must be constructed as a superposition of solutions of the form given by eq. (3). In this context, the proper construction of an equilibrium model using Schwarzschild’s method thus entails three stages, namely (i) selecting all the orbits entering into each $ g_{I_1,0,I_2,0,I_3,0}(r,v) $ with the weights implicit in eq. (3), (ii) performing the integration of eq. (4) to extract $ n_{I_1,0,I_2,0,I_3,0}(r) $, which incorporates the fact that each point in configuration space is weighted in proportion to the amount of time orbits spend there, and then (iii) choosing a superposition of $ n_{I_1,0,I_2,0,I_3,0}(r) $’s which yields the imposed $ \rho_0 $. At least in the specific setting described by Vandervoort (1984), this interpretation breaks down for the case of nonintegrable potentials, where one cannot identify three global integrals, or, more generally, whenever one relaxes the demand that $ f_0 $ be realisable as a function of global isolating integrals. However, as described more carefully later on in this paper, one can still capture the essential aspect of Vanderv oort’s analysis, namely that appropriately identified orbit segments yield the natural time-independent building blocks in terms of which to construct a self-consistent model. Nonintegrable potentials generically admit two different classes of orbits, namely regular and chaotic. Regular orbits in a nonintegrable potential behave qualitatively like orbits in an integrable potential in that they are multiply periodic and, even more importantly, are restricted to a three- (or lower-)dimensional hypersurface in the six-dimensional phase space. It follows that, even though they do not admit three global integrals, they must be constrained (cf. Lichtenberg and Lieberman 1992) by what are sometimes termed “local integrals.” For this reason, regular orbits in nonintegrable potentials define time-independent building blocks in the same sense as do orbits in integrable potentials. Chaotic orbits are very different in that they are intrinsically aperiodic and densely fill phase space regions that are necessarily higher than three-dimensional. However, chaotic phase space regions can still be characterised by invariant distributions which, when evolved into the future, remain unchanged; and one can use these invariant distributions as an additional set of building blocks when constructing self-consistent equilibria. This alternative “orbital” interpretation of the building blocks for self-consistent equilibria is important for at least two reasons. (1) It is possible to generate analytically exact two-integral models for axisymmetric configurations which are characterised by nonintegrable potentials (cf. Hunter and Qian 1993), including potentials where motion in the meridional plane is chaotic. However, reproducing these models numerically using Schwarzschild’s method must entail sampling a collection of time-independent building blocks more complex than those associated with integrable potentials. (2) Because global integrals are associated with continuous symmetries, one might expect generically that, for genuinely three-dimensional potentials, there will not exist any global integral aside from the energy (or the Jacobi integral). If, however, one demands that the equilibrium distribution be a function only of the energy $ E $, so that $ f_0 = f_0(E) $, one concludes (cf. Binney and Tremaine 1987) that the mass distribution $ \rho_0 $ must be spherical. (This is the analogue of the well known theorem from stellar structure that all static perfect fluid stars are spherical.) --- $^3$ A good example of a local integral is the so-called third integral associated in some cases with a nonintegrable, time-independent, axisymmetric potential, where the only global integrals are energy $ E $ and rotational angular momentum $ J_z $. How regular orbits in a nonintegrable potential differ from orbits in an integrable potential is clearly stated on p. 49 of Lichtenberg and Lieberman (1992): “Since the regular trajectories depend discontinuously on initial conditions, their presence does not imply the existence of an isolating integral (global invariant) or symmetry of the system. However, regular trajectories, when they exist, represent exact invariants of the motion.” other words, every nonrotating triaxial equilibrium must depend on something other than the energy, either additional global integrals, as for Staeckel potentials, or “local” integrals, as is implicit in the construction of cuspy triaxial models by Merritt and Fridman (1996) or Siopis (1997). Section 2 discusses more carefully the basic building blocks of a self-consistent equilibrium, allowing explicitly for the possibility of nonintegrable potentials that admit chaotic orbits. Section 3 then illustrates how, for the simple case of nonintegrable equilibria depending only on one or two global isolating integrals (and nothing else), Schwarzschild’s method can be reformulated in terms of an appropriate set of time-independent building blocks. Section 4 concludes by describing straightforward generalisations to construct equilibria that do not depend simply on global integrals and then discussing the issue of whether such “more complex” equilibria are physically viable. 2 INVARIANT DISTRIBUTIONS AND SELF-CONSISTENT EQUILIBRIA It is often asserted glibly that “any equilibrium solution $f_0$ to the collisionless Boltzmann equation must be given as a function of the time-independent integrals of the motion associated with the potential $\Phi_0$ generated self-consistently from $f_0$.” In point of fact, however, this statement is an oversimplification and requires some careful thought. Should one demand, as is often assumed, at least tacitly, that $f_0$ depends only on the global isolating integrals, such as energy $E$ (or the Jacobi integral for a rotating configuration) and angular momentum $J_z$, or can one instead allow for equilibria $f_0$ that depend on the “local” isolating integrals which, in a generic nonintegrable potential, make regular orbits regular, i.e., restrict them to a lower-dimensional phase space hypersurface (cf. Lichtenberg and Lieberman 1992)? Could one, for example, try to construct models which assign regular and chaotic orbits on the same $E$-$J_z$ hypersurface different weights, or must one sample each constant $E$-$J_z$ hypersurface uniformly? Arguably, the only crucial point is that a time-independent solution to the collisionless Boltzmann equation must be constructed from time-independent building blocks, so as to ensure that, if initial data be evolved into the future along the characteristics associated with the self-consistent potential, the form of $f_0$ will remain unchanged. The easiest way to do this, both conceptually and practically, is to demand that $f_0$ be given as a function of one or more global isolating integrals, say $E$ and $I$. The obvious point is that any $f_0(E, I)$ which implies the proper mass density $\rho_0$, and hence the proper potential $\Phi_0$, will yield a time-independent solution since, by assumption, both $E$ and $I$ are time-independent constants of the motion. In other words, $dE/dt = dI/dt = 0$ implies $\partial f_0/\partial t = 0$. This is of course the standard way of showing that time-independent conserved quantities can be used to construct a self-consistent equilibrium. However, there is another, more “microscopic,” viewpoint. Specifically, viewed in terms of the orbits associated with the equilibrium (i.e., characteristics associated with the Boltzmann equation), this construction works because such an $f_0$ implies that the phase space number density is constant on hypersurfaces of constant $E$ and $I$. This constancy means that the orbit ensemble that generates $f_0$ must involve a uniform, i.e., microcanonical, sampling of each constant $E-I$ phase space hypersurface, but Hamilton’s equations for motion in a fixed $\Phi_0$ imply that such a population is invariant under time translation. It would seem clear from this latter viewpoint that choosing $f_0$ to be a function only of global isolating integrals is not necessary, at least in principle. A priori, a self-consistent equilibrium $f_0$ can be constructed from any collection of time-independent building blocks. which successfully reproduces the assumed potential $\Phi_0$. The key point, then, as stressed, e.g., by Ott (1993), is that, assuming the validity of the Ergodic Theorem, for flows in a fixed time-independent potential any orbit is ergodic in an appropriately interpreted subspace, so that a microcanonical population of the appropriate subspace yields a time-independent building block. Regular orbits are multiply periodic and, as such, are characterised (in an orbit-averaged sense) by a density that is time-independent, so that they can be treated individually as time-independent building blocks, with a density $\rho$ proportional to the time that the orbit spends in the neighborhood of each point. In this sense, regular orbits in a nonintegrable potential can be exploited in the same way as the orbits in an integrable potential, even though it is seemingly impossible to identify explicitly the forms of the “local integrals,” and even though regularity is not attributable directly to a continuous symmetry. Chaotic orbits are not periodic, so that this naive argument does not hold. However, it would still seem possible to identify an appropriate set of time-independent chaotic building blocks. For a fixed value of $E$ (and any other global integral), the constant $E$ (or $E-I$) phase space hypersurface divides naturally into regular and chaotic regions. The chaotic region divides in turn into one or more subregions which are connected in the sense that an orbit starting in any part of a subregion will eventually pass arbitrarily close to every other part of that subregion. The important point then is that a uniform, i.e., microcanonical, population of any connected chaotic domain defines a time-independent building block. Why this should be so is easy to understand: Time translation using Hamilton’s equations moves each phase space point in the chaotic domain to another point in the same domain, but the only initial distribution invariant under time translation using Hamilton’s equations is a constant density distribution. Integrating this phase space building block over the allowed range of velocities yields a configuration space density which, as for the regular orbits, is proportional to the amount of time that a representative chaotic orbit in the domain spends in the neighborhood of each point $r$. Assuming the validity of the Ergodic Theorem for individual connected chaotic domains, it is relatively simple to generate such invariant distributions numerically. Specifically, one knows that, when evolved into the future, a generic ensemble of initial conditions located anywhere in the domain will evidence a coarse-grained approach towards the invariant microcanonical distribution. In fact, this has been confirmed by numerical experiments (cf. Kandrup and Mahon 1994, Mahon, Abernathy, Bradley, and Kandrup 1995, Merritt and Valluri 1996) which have shown that, for chaotic flows in a variety of different potentials, reduced distribution functions (like $f(r)$ or $f(v)$) exhibit an apparent exponential in time approach towards an invariant reduced distribution on a time scale $\tau$ that correlates with the value of the largest Lyapunov exponent. Viewed in this fashion, regular and chaotic orbits can be used to define time-independent building blocks in exactly the same way, the only difference being that chaotic building blocks are intrinsically higher-dimensional. When evolved into the future, initial conditions corresponding to regular and chaotic orbits both yield trajectories which, in an asymptotic, late time limit, converge towards time-independent invariant distributions. The crucial point in all of this is that, in principle, a library comprised of all possible invariant distributions, both those corresponding to individual regular orbits and those corresponding to individual connected chaotic phase space regions, should constitute a complete set of building blocks in terms of which to construct self-consistent models of a galaxy with the specified potential $\Phi_0$. In the real world, one cannot construct such a library, which would contain an infinite number of building blocks. However, one can construct a large, but finite, library and then sample that library in an attempt to select appropriate combinations that reproduce a suitably discretised version of the assumed $\Phi_0$. This is the essence of what Schwarzschild’s (1979) method can, and should, do when applied to a generic nonintegrable potential that admits both regular and chaotic orbits. It is also evident that, in principle, nothing stops one from trying to construct equilibria that contain only regular (or perhaps only chaotic) orbits, although one might imagine that it would be very hard to reproduce a smooth potential $\Phi_0$ with a collection of orbits that systematically avoids significant phase space regions or, especially, probes the phase space in an exceedingly irregular fashion. For the case of a generic rotating, axisymmetric equilibrium, there are two global isolating integrals, namely $E$ and $J_z$, associated respectively via Noether’s Theorem with symmetries with respect to time translations and rotations about the $z$-axis. The potential may in fact be integrable, so that there are three global isolating integrals, but this is not necessarily the case. In general, a rotating, axisymmetric, time-independent potential will be nonintegrable and admit both chaotic and regular orbits, each of which defines time-independent building blocks. It follows that, if one allows for local integrals, one can, at least in principle, try to construct equilibria that do not sample constant $E$-$J_z$ surfaces uniformly. One could, e.g., try to construct models which exclude all chaotic orbits. Analytic approaches to constructing self-consistent axisymmetric equilibria, as developed, e.g., by Hunter and Qian (1994), neglect this possibility altogether and focus exclusively on solutions for which $f_0 = f_0(E, J_z)$, so that the phase space density is constant on hypersurfaces of constant $E$ and $J_z$. Whether this is well motivated physically, or whether this is only a useful analytic simplification, is not completely clear at the present time. It should be stressed that great care must be taken in identifying the invariant distributions associated with (ensembles of) chaotic orbits. As has long been known from numerical investigations of simple maps (cf. Lieberman and Lichtenberg 1972), the presence of cantori (cf. Aubry and Andre 1978, Mather 1982) or an Arnold (1964) web allows for the possibility of chaotic near-invariant distributions which, albeit not strictly time-independent, can, at least in the absence of any perturbations, behave for very long times as if they were essentially time-independent distributions. As discussed, e.g., in Mahon, Abernathy, Bradley, and Kandrup (1995), the crucial point here that cantori and Arnold webs serve as partial obstructions which, although they cannot completely block motion between different phase space regions, can significantly impede phase space transport. It follows that, even if a single chaotic region is connected, it may appear partitioned into disjoint regions even over relatively long time scales. This phenomenon is problematic. A putative self-consistent equilibrium generated with a near-, rather than true, invariant distribution cannot be a true self-consistent equilibrium. On sufficiently long time scales, the orbital population associated with the distribution will change, occasioning changes in the mass distribution, the potential, and so forth. One might nevertheless want to argue that, if the time scale associated with this phenomenon is sufficiently long, this very slow effect will be irrelevant astronomically, so that one can speak of nearly self-consistent equilibria that can exist for times much longer than the age of the Universe, $t_H$. However, this argument is probably wrong. Real astronomical systems involve $N$-body realisations of self-consistent equilibria which, heuristically, are presumed to behave like smooth three-dimensional Hamiltonian systems perturbed by friction and noise. However, numerical experiments involving perturbations of motion in a fixed poten- tial indicate (Habib, Kandrup, and Mahon 1996, 1997) that even very weak friction and noise can dramatically accelerate phase space transport through cantori or along an Arnold web, occasioning significant changes in an initial near-invariant distribution on comparatively short time scales. Trying to estimate the longevity of a near-invariant distribution without allowing for the effects of perturbations is unquestionably a very bad idea. 3 A VARIANT OF SCHWARZSCHILD’S METHOD FOR ONE- AND TWO-INTEGRAL DISTRIBUTIONS The objective of this Section is to reformulate Schwarzschild’s method in terms of the natural set of building blocks so as to permit the construction of equilibrium models $f_0$ which are assumed to depend on one or two global integrals and to exhibit no additional dependence on any nonclassical local integrals. This is a straightforward generalisation of an approach proposed by Vandervoort (1984) for the construction of three-integral equilibria. Start by specifying a time-independent potential $\Phi_0(r)$, and hence a configuration space density $\rho_0(r)$ which admits (say) two constants of the motion, $E$ and $I$, where $E$ is the particle energy (or, perhaps, the Jacobi integral) and $I$ is some other isolating integral, the form of which is assumed to be known explicitly. By assumption, the desired equilibrium (or equilibria) $f_0$ must be given exactly as a function $f_0 = f_0(E, I)$. The object, therefore, is to construct a discretised approximation to a smooth $f_0$ of this form which reproduces the assumed $\rho(r)$ self-consistently. This can be done in two stages, viz: 1. First grid $E$-$I$ space into a collection of cells and, for each pair $\{E_i, I_j\}$, write down the invariant distribution $g_{ij}(r, v)$ on the constant $E_i$-$I_j$ hypersurface. Use these $g_{ij}$’s to derive reduced configuration space densities $n_{ij}(r)$. 2. Then construct the desired numerical approximation to $f_0$ as a sum of contributions from the different invariant distributions $g_{ij}$, with the relative weights of the different $g_{ij}$’s fixed by the requirement of self-consistency for the configuration space density. This construction proceeds without explicit reference to individual orbits and, as such, provides no insight into the orbital building blocks entering into the equilibrium. If this be perceived as a serious lacuna, the natural tack numerically is to consider separately the different constant $E$-$I$ hypersurfaces and, on each hypersurface, to construct ensembles of orbit segments that reproduce self-consistently the invariant $g_{ij}$’s. 3.1 Construction of the invariant distribution for fixed $E$ and $I$ A uniform population of the phase space hypersurface of fixed $E_i$ and $I_j$ corresponds to an invariant distribution of the form $$g(E_i, I_j) \equiv g_{ij}(r, v) = K \delta_D[E_i - E(r, v)] \delta_D[I_j - I(r, v)],$$ where $\delta_D$ denotes a Dirac delta, and the quantities $E$ and $I$ are viewed explicitly as functions of the phase space coordinates. The quantity $K$ is a constant, whose value is fixed by the --- 4 Although it is the density, rather than the potential, that astronomers are wont to specify, it is more natural conceptually to view $\Phi_0$ as the fundamental object, since it is the Hamiltonian associated with $\Phi_0$ that defines the time-invariant building blocks. 5 Reformulating the following for equilibria admitting only one isolating integral is completely straightforward. If the equilibrium admits three independent integrals, it is integrable and can be addressed using the approach described by Vandervoort (1984). normalisation \[ \int d^3x \int d^3v \, g_{ij}(\mathbf{r}, \mathbf{v}) = 1, \] where the integral extends over the allowed phase space regions. In other words, the invariant distribution corresponds to a normalised microcanonical population of the constant $E_i-I_j$ hypersurface. Given such a $g_{ij}(\mathbf{r}, \mathbf{v})$, it is straightforward to integrate over the velocity dependence to extract a reduced configuration space density $n_{ij}(x, y, z)$. Because $E_i$ and $I_j$ are known functions of $r$ and $v$, one can choose to view any two of the phase space coordinates, say $v_y$ and $v_z$, as functions of $E$, $I$, and the remaining four phase space coordinates. However, the Dirac deltas in eq. (5) make $dv_y$ and $dv_z$ integrations trivial, so that one can immediately write down analytically a reduced $\tilde{g}_{ij}(x, y, z, v_x)$ \[ \tilde{g}_{ij}(x, y, z, v_x) \equiv K \int dv_y dv_z \delta_D[E_i - E(\mathbf{r}, \mathbf{v})] \delta_D[I_j - I(\mathbf{r}, \mathbf{v})]. \] It follows that the configuration space density, \[ n_{ij}(x, y, z) = \int dv_x \, \tilde{g}_{ij}(x, y, z, v_x), \] associated with each constant $\{E_i, I_j\}$ pair is given as a simple quadrature. In general, it may be impossible to perform the integral in eq. (8) analytically. This, however, is not a serious difficulty. Even if known analytically, the $n_{ij}$'s must eventually be approximated by a set of values on a configuration space grid so as to facilitate a comparison between the imposed density $\rho_0(\mathbf{r})$ and the inferred density $n(\mathbf{r})$ constructed from the invariant $n_{ij}$'s. ### 3.2 Construction of $f_0(E, I)$ from the invariant distributions In the continuum limit, one knows that the true equilibrium distribution \[ f_0(\mathbf{r}, \mathbf{v}) = \int \int dE dI \, A(E, I) \, g_{E,I}(\mathbf{r}, \mathbf{v}), \] where $g_{E,I}$ is the invariant distribution for fixed $E$ and $I$, viewed as a function of $\mathbf{r}$ and $\mathbf{v}$, and $A(E, I)$ is an expansion coefficient, which gives the relative weights of the different values of $E$ and $I$ entering into $f_0$. The discretised construction thus involves \[ f_0(\mathbf{r}, \mathbf{v}) = \sum_i \sum_j A_{ij} g_{ij}(\mathbf{r}, \mathbf{v}). \] The proper choice of weights $A_{ij}$ derives from the demand of self-consistency: Given $f_0$, one can define a density \[ n(\mathbf{r}) = \int \, d^3v \, f_0(\mathbf{r}, \mathbf{v}) \] which, when discretised, becomes \[ n(x, y, z) = \sum_i \sum_j A_{ij} n_{ij}(x, y, z) \] $^6$ The choice of Cartesian coordinates, implicit in the following, is only for specificity: as far as this algorithm is concerned, the coordinate system is completely irrelevant. in terms of the unknown expansion coefficients $A_{ij}$. However, demanding that this $n(x, y, z)$ correspond as closely as possible to the density $$\rho_0(x, y, z) = \frac{1}{4\pi G} \nabla^2 \Phi_0$$ (13) associated with the assumed potential $\Phi_0$ then enables one to determine the “best” values for the $A_{ij}$’s. This construction is very much analogous to the ordinary Schwarzschild method, save only that the basic building blocks are now the reduced invariant distributions $n_{ij}$, rather than individual orbits. ### 3.3 Orbital building blocks for the invariant distributions One way in which to obtain insights into the orbital building blocks of a self-consistent model constructed using this algorithm is by proceeding numerically to construct ensem- bles of orbit segments which reproduce self-consistently the invariant distributions $g_{ij}$. In general, $g_{ij}$ will contain contributions from both regular and chaotic orbits, each of which is characterised separately by its own invariant distribution. The easiest way to construct $g_{ij}$ is probably to (1) obtain an invariant distribution for the chaotic orbits and then (2) augment this by another (sub)distribution comprised of segments of regular orbits, the latter so chosen that the combination of regular and chaotic orbits yields a satisfactory approximation to the true invariant distribution. The invariant distribution is approximated numerically by binning the six-dimen-sional phase space into a collection of six-dimensional hypercubes, and then assigning occupation numbers to the different hypercubes which are proportional to the time that orbits sampling the true invariant distribution reside in each cell. (This is justified by the Ergodic Theorem [cf. Lichtenberg and Lieberman 1992].) In the continuum limit, the invariant distribution corresponds to a uniform population on a four-dimensional phase space hypersurface. Given a discretisation of the phase space coordinates, the invariant distribution corresponds instead to a four-dimensional shell in the six-dimensional phase space. The invariant (sub-)distribution of chaotic orbits is especially easy to compute if, as is often the case, for fixed $E_i$ and $I_j$ the entire chaotic region is connected in the sense that, eventually, every chaotic orbit will pass arbitrarily close to every point in the chaotic region. (For simplicity, ignore the tiny measure of chaotic orbits trapped permanently inside invariant KAM tori.) All that one need do is specify a (more or less arbitrary) ensemble of initial conditions, each corresponding to a chaotic orbit, evolve each initial condition into the future, and wait until the evolved ensemble approaches an invariant distribution, i.e., a uniform sampling of the chaotic portions of the $E_i$-$I_j$ hypersurface (cf. Kandrup and Mahon 1994, Mahon, Abernathy, Bradley, and Kandrup 1995). To expedite the calculation, it is useful to evolve the initial conditions in the presence of very weak amplitude friction and noise, sufficiently weak that the values of $E$ and $I$ are almost constant (cf. Habib, Kandrup, and Mahon 1996, 1997). The advantage of intro- ducing weak friction and noise is that such small perturbations can dramatically accelerate the overall approach towards a true invariant distribution by facilitating extrinsic diffusion through cantori and/or along an Arnold web (cf. Lichtenberg and Lieberman 1992). If one does not either (a) integrate for a very long time and/or (b) allow for such perturbing influ- ences, one faces the problem that the initial ensemble may evolve towards a near-invariant distribution which, albeit not strictly time-independent, only changes significantly on a very long time scale. The contribution of different regular orbits to the invariant distribution can be generated using an analogue of the original Schwarzschild method. Specify a large number of regular initial conditions and integrate each into the future to generate a library of regular orbits. Then use a linear programming algorithm, or some variant thereof, to select a weighted ensemble of regular orbits which, when combined with the chaotic (sub)distribution, yields a satisfactory approximation to the true invariant distribution on the constant $E_i - I_j$ hypersurface. This construction of invariant distributions $g_{ij}$, and the corresponding densities $n_{ij}$, is admittedly tedious numerically (albeit presumably straightforward), since it involves repeating Schwarzschild's method for each pair $\{E_i, I_j\}$. However, it is arguably a crucial step in obtaining a proper understanding of the orbital structure associated with the self-consistent model since, as discussed already, one knows that the $g_{ij}$'s are the proper building blocks in terms of which to construct an equilibrium $f_0(E, I)$. ### 3.4 A simple two-dimensional example Consider as a pedagogical example the case of two-dimensional gravity, this corresponding physically to a collection of infinite rods aligned along the $z$-axis, and suppose that the configuration is rotating uniformly about the $z$-axis with angular velocity $\Omega$. It then follows that, in the rotating frame, the configuration is characterised by a potential $\Psi(x, y)$ and a surface density $\sigma(x, y)$ related by $$\nabla^2 \Psi(x, y) = 4\pi G \sigma(x, y).$$ (15) Suppose then that there is only one global isolating integral, namely the Jacobi integral $E$, which, in terms of phase space coordinates defined in the rotating frame, takes the form $$E = \frac{1}{2} v_x^2 + \frac{1}{2} v_y^2 + \Psi(x, y) - \frac{1}{2} \Omega^2 (x^2 + y^2) = \frac{1}{2} v_x^2 + \frac{1}{2} v_y^2 + \Psi_{eff}(x, y).$$ (16) To the extent that one demands that any equilibrium $f_0$ associated with this mass distribution be a function only of the isolating integral $E$, the fundamental building block is the microcanonical phase space density on a constant Jacobi integral hypersurface, which, for any $E_i$, takes the form $$g(E_i) = g_i(r, v) = K \delta_D[E_i - E(r, v)].$$ (17) As will be evident from below, the normalisation constant $K$ can be written as $$K = \frac{1}{2\pi V(E_i)}$$ (18) in terms of $V(E_i)$, the area of the configuration space region with $\Psi_{eff} \leq E_i$. The reduced configuration space density $n_i$ associated with this $g_i$ satisfies $$n_i(x, y) = K \int \int dv_x dv_y \delta_D[E_i - E(r, v)],$$ (19) where the integrals extend over the values of $v_x$ and $v_y$ that are allowed energetically, i.e., for which $E_i \geq \Psi_{eff}$. The $dv_y$ integration can be performed trivially by implementing the Dirac delta, allowing for nonzero contributions at two values, namely $v_y = \pm \sqrt{2(E_i - \Psi_{eff}) - v_x^2} \equiv \alpha$. It follows that, for those regions in configuration space for which $\Psi_{eff}(x, y) \leq E_i$, $$n(x, y) = 2K \int_{-\alpha}^{\alpha} \frac{dv_x}{\sqrt{\alpha^2 - v_x^2}}.$$ (20) The remaining integral can then be performed trivially, leading to a reduced configuration space density on the constant $E_i$ hypersurface of the form $$n_i(x, y) = 2\pi K \Theta[E_i - \Psi_{\text{eff}}(x, y)] = \frac{1}{V(E_i)} \Theta[E_i - \Psi_{\text{eff}}(x, y)],$$ (21) where $\Theta(z) = 1$ for $z \geq 0$ and $\Theta = 0$ otherwise. It follows from eq. (21) that, independent of the specific form of the potential $\Psi(x, y)$, the total configuration space surface density, given as a sum of contributions on different constant Jacobi integral hypersurfaces, must be of the form $$n(x, y) = \sum_i A_i \frac{1}{V(E_i)} \Theta[E_i - \Psi_{\text{eff}}(x, y)].$$ (22) where the $A_i$'s give the relative weights of the different $E_i$ hypersurfaces. The demand that the $n(x, y)$ of eq. (22) agree as closely as possible with the $\sigma(x, y)$ associated with $\Psi$ may then be used to identify the “best” values of the $A_i$’s. 4 DISCUSSION There are a number of different ways in which the algorithm described in the preceding Section can be generalised to permit the construction of more complex equilibria, which do not depend simply on the global integrals $E$ and $I$. For fixed values of $E$ and $I$, it is straightforward to locate the general locations of (at least the large) chaotic regions and, by evolving arbitrary ensembles of initial conditions located in these regions into the future, it is easy to derive a numerical approximation to the invariant distribution associated with each of these chaotic regions. Given these invariant distributions, one can then integrate over velocities to extract the chaotic contribution $n_{ij}^c(x, y, z)$ to total density $n_{ij}(x, y, z)$ associated with any pair $E_i$ and $I_j$. Subtracting $n_{ij}^c$ from the full $n_{ij}$ then yields the regular contribution $n_{ij}^r(x, y, z)$ to the density. However, given a knowledge of $n_{ij}^c$ and $n_{ij}^r$ separately, one can then attempt to construct models which assign different relative weights to the regular and chaotic portions of the $E_i-I_j$ hypersurface, thus allowing one to test the prejudice of some workers that self-consistent models should contain few, if any, chaotic orbits. Similarly, one can identify those portions of the $E_i-I_j$ hypersurface that correspond to different types of regular orbits, e.g., boxes and tubes, and compute their relative densities, say $n_{ij}^b$ and $n_{ij}^t$, which can in turn be used as separate building blocks. In particular, given such a collection one can try to construct models which associate different relative weights to boxy and/or tuby and/or chaotic orbits, and, to the extent that such models can be constructed, one can investigate whether the different phase space densities $f_0$ have obvious observational signatures which could be compared with real astronomical data. Is there, e.g., some natural signature which, when observed in real galaxies, can be interpreted as evidence that $f_0$ contains a significant measure of chaotic orbits? In principle, one can continue this process of refinement more or less ad infinitum, identifying increasing numbers of time-independent building blocks associated with different regular orbits, although one’s freedom to deal with chaotic orbits is limited by the fact that there is only one natural notion of a time-independent invariant distribution. However, it is not clear that such a procedure is well motivated physically. At least heuristically, it would seem that building an equilibrium by “picking and choosing” amongst individual orbits in a strongly nonintegrable potential with different values of local isolating integrals is akin to selecting orbits in an integrable potential which yield a distribution function that is a highly irregular function of the $ I_i $'s. This latter procedure might strike one as contrived and, in any event, one knows that, in many cases, such irregular $ f_0 $'s are linearly unstable. Thus, e.g., it is well known that, for a spherical equilibrium with $ f_0 = f_0(E, J^2) $, stability or lack thereof often correlates with the sign of the partial derivatives $ \partial f_0 / \partial E $ and/or $ \partial f_0 / \partial J^2 $. In particular, population inversions can trigger instabilities. If any discrete construction based on Schwarzschild's method is to be reasonable, there must be a sense in which, as the discretisation of the density becomes more refined and as the number of building blocks becomes larger, the solution constructed numerically converges towards a continuous self-consistent equilibrium. However, identifying the precise sense in which this is so would most likely be very difficult. Mathematically, establishing such a convergence would probably involve a study of sequences of discrete Banach spaces, along the lines that have been used to study the convergence of finite difference schemes for solving partial differential equations. In that setting, a good deal is known about linear differential equations but, if one incorporates nonlinearities and/or allows for an integro-differential equation – recall that the collisionless Boltzmann is a quadratically nonlinear integro-differential equation – things become much harder! It is evident, both intuitively and from painful experience (cf. Siopis, Athanassoula, and Kandrup 1997), that it is easier to approximate comparatively smooth quantities on a finite lattice than quantities that manifest intricate structures on a variety of different scales. For this reason, one might expect that it is much easier to construct a satisfactory numerical representation of an $ f_0 $ that is a function only of smoothly varying global isolating integrals than an $ f_0 $ that depends sensitively on “local” integrals that manifest the details of the complex phase space structure associated with a generic nonintegrable potential. Moreover, even if one allows for local integrals, the numerical construction should be more straightforward if, for example, on a constant energy hypersurface, the phase space population is reasonably smooth, e.g., perhaps avoiding chaotic regions but weighting different regular regions in a fashion that varies smoothly with their phase space location. Suppose that there is in fact a “true” $ f_0 $ involving local integrals, generated (in principle) as an exact time-independent solution to the collisionless Boltzmann equation, to which one has constructed a latticized $ f_0 $ via some analogue of Schwarzschild’s method, and that this latticized $ f_0 $ has been used to generate an ensemble of initial conditions to populate an $ N $-body realisation of the model. There are then two potentially serious sources of error: (1) The latticized approximation to $ f_0 $ could miss important microscopic structures associated with local integrals. If the “true” $ f_0 $ is a function only of smoothly varying integrals like the energy $ E $, allowing for as few as 20 different energies, as did Schwarzschild (1979), Merritt and Fridman (1996), and Siopis (1997), may be adequate to capture the essence of the analytic model. If, however, $ f_0 $ involves a complex combination of local integrals as well as the energy, allowing for 20 values may not be enough. (2) Even if most/all the important microscopic structures are adequately represented in the discretised model, the $ N $-body realisation could fail to sample them adequately. Even for very large particle number, $ N \sim 10^6 $ or more, there is no guarantee that a complex phase space will be adequately sampled. If, however, it is difficult for galactic astronomers to construct $ N $-body realisations of “complex” equilibria $ f_0 $ that involve local integrals in a highly irregular way, nature too may find it hard. If $ N \sim 10^6 $ is not enough to generate a “fair” sampling, $ N \sim 10^{11} $ may also be inadequate to probe the complex phase space associated with a smooth potential. generated as a Boltzmann equilibrium. Both statistical fluctuations, which will obviously be present, and small non-Hamiltonian irregularities, which can be important in complex Hamiltonian systems (cf. Lichtenberg and Lieberman 1992) may tend to “smooth out” a complex would-be equilibrium into something substantially simpler. ACKNOWLEDGMENTS Work on this paper began while I was a visitor at the Observatoire de Marseille, where I was supported by the C.N.R.S. Additional support was provided by the National Science Foundation through PHY92-03333. Portions of this paper were written while I was a visitor at the Aspen Center for Physics. I am grateful to Evangelia Athanassoula, Chris Hunter, Christos Siopis, and Haywood Smith for useful comments and interactions. Arnold, V. I. 1964, Russ. Math. Surveys 18, 85. 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Schwarzschild, M. 1979, ApJ 232, 236. Siopis, C. 1997, University of Florida Ph. D. dissertation. Siopis, C., Athanassoula, E., and Kandrup, H. E. 1997, A&A, in preparation. Staeckel, P. 1890, Math. Ann 35, 91. Vandervoort, P. O. 1984, ApJ 287, 475.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2772, 1 ], [ 2772, 6853, 2 ], [ 6853, 11249, 3 ], [ 11249, 15265, 4 ], [ 15265, 19365, 5 ], [ 19365, 23536, 6 ], [ 23536, 27180, 7 ], [ 27180, 29953, 8 ], [ 29953, 33787, 9 ], [ 33787, 36905, 10 ], [ 36905, 40589, 11 ], [ 40589, 44904, 12 ], [ 44904, 45677, 13 ], [ 45677, 46970, 14 ] ] }
a9c6894e13d1ae8c314ff40938c689017d2b1200	{ "olmocr-version": "0.1.59", "pdf-total-pages": 12, "total-fallback-pages": 0, "total-input-tokens": 48155, "total-output-tokens": 11881, "fieldofstudy": [ "Chemistry", "Biology" ] }	Discovery and Optimization of Small-Molecule Ligands for the CBP/p300 Bromodomains Duncan A. Hay,‡‡ Oleg Fedorov,‡§ Sarah Martin,‡§ Dean C. Singleton,‡§ Cynthia Tallant,‡§ Christopher Wells,‡§ Sarah Picaud,‡ Martin Philpott,‡§ Octovia P. Monteiro,‡§ Catherine M. Rogers,‡§ Stuart J. Conway,‡ Timothy P. C. Rooney,‡ Anthony Tumber,‡§ Clarence Yapp,‡§ Panagis Filippakopoulos,‡ Mark E. Bunnage,⊥ Susanne Müller,‡§ Stefan Knapp,‡ Christopher J. Schofield,‡ and Paul E. Brennan‡‡⊥§ ‡Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3TA, U.K. ‡Structural Genomics Consortium, University of Oxford, Old Road Campus Research Building, Roosevelt Drive, Oxford, OX3 7DQ, U.K. §Target Discovery Institute, University of Oxford, NDM Research Building, Roosevelt Drive, Oxford, OX3 7LD, U.K. ⊥Worldwide Medicinal Chemistry, Pfizer, Cambridge, Massachusetts 02139, United States ABSTRACT: Small-molecule inhibitors that target bromodomains outside of the bromodomain and extra-terminal (BET) sub-family are lacking. Here, we describe highly potent and selective ligands for the bromodomain module of the human lysine acetyl transferase CBP/p300, developed from a series of 5-isoxazolyl-benzimidazoles. Our starting point was a fragment hit, which was optimized into a more potent and selective lead using parallel synthesis employing Suzuki couplings, benzimidazole-forming reactions, and reductive aminations. The selectivity of the lead compound against other bromodomain family members was investigated using a thermal stability assay, which revealed some inhibition of the structurally related BET family members. To address the BET selectivity issue, X-ray crystal structures of the lead compound bound to the CREB binding protein (CBP) and the first bromodomain of BRD4 (BRD4(1)) were used to guide the design of more selective compounds. The crystal structures obtained revealed two distinct binding modes. By varying the aryl substitution pattern and developing conformationally constrained analogues, selectivity for CBP over BRD4(1) was increased. The optimized compound is highly potent (K\text{d} = 21 nM) and selective, displaying 40-fold selectivity over BRD4(1). Cellular activity was demonstrated using fluorescence recovery after photo-bleaching (FRAP) and a p53 reporter assay. The optimized compounds are cell-active and have nanomolar affinity for CBP/p300; therefore, they should be useful in studies investigating the biological roles of CBP and p300 and to validate the CBP and p300 bromodomains as therapeutic targets. INTRODUCTION CBP and p300. The CREB (cyclic-AMP response element binding protein) binding protein (CBP) and E1A binding protein (p300) are ubiquitously expressed pleiotropic lysine acetyl transferases that play a key role as transcriptional co-activators in human cells.1--5 CBP and p300 possess nine conserved functional domains which bind to general and genespecific transcription factors such as the hypoxia-inducible transcription factor (HIF) and the human tumor suppressor protein p53 (Figure 1A).6--15 Both CBP and p300 possess a single bromodomain (BRD) and a lysine acetyltransferase (KAT) domain, which are involved in the post-translational modification (PTM) and recruitment of histones and non-histone proteins.16--20 The BRD is an acetyl-lysine (Kac)-selective recognition module, whereas the KAT domain transfers an acetyl group from acetyl coenzyme A to unmodified lysine side chains. These processes enable CBP/p300 to exert context-dependent regulation of transcriptional control. The sequence similarity between CBP and p300 is high in the conserved functional domains, with the BRD having 96% similarity (Figure 1A). CBP and p53. Mutations of the p53 gene are common, with around 50% of human cancers encoding such mutations.21--23 In response to cellular stress, p53 undergoes PTMs of the C- and N-terminal regions, including acetylation at the C-terminal region, which results in changes in the p53-dependent activation of target genes leading to cell cycle arrest, senescence, or apoptosis.23--25 Lysine acetylation at lysine 382 (K382) of p53 is responsible for recruitment of CBP via its... BRD, as shown by NMR titration of the CBP BRD with acetylated p53 peptides, and transfection of p53−/− cells with mutated p53.12 Additionally, in a p21 luciferase assay, the CBP-Kac interaction was shown to be crucial for p53-induced p21-mediated G1 cell cycle arrest. Additionally, chemo- and radio-therapy can cause p53-mediated tissue damage of non-cancerous tissue, implying that p53 inhibition could be used to protect healthy tissue during these therapies.26 Thus, inhibition of the CBP BRD, and therefore p53-mediated p21 activation, has potential clinical applications. In addition to its important tumor suppressor role, hyperactive p53 is implicated in Alzheimer’s disease, Parkinson’s disease, spinal cord diseases, multiple sclerosis, ischemic brain injury, infectious and auto-immune diseases, and myocardial ischemia.32–37 Thus, inhibitors of p53 activity represent potential points of intervention in multiple diseases. The CBP/p300 Bromodomain. Bromodomains are made up of ~110 residues arranged in a characteristic structure made up of four α-helices (αZ, αA, αB, αC) and the ZA and BC loops that form the Kac binding pocket (derived from PDB 3P1C).27 (C) Structure of an acetyl lysine (yellow, only partial structure shown) and CBP BRD complex. Key interactions are shown, including the hydrogen bond (dotted lines) from the Kac carbonyl to N1168 and a water-mediated hydrogen bond from the Kac carbonyl to Y1125 (PDB 3P1C).27 (D) CBP BRD ligands with reported affinities.28–31 Figure 1. (A) Percent conservation and domain organization of human CBP (accession no. Q92793) and p300 (accession no. Q09472). Abbreviations: ZF TAZ 1 and 2, zinc finger transcription adaptor putative zinc finger-type; KIX, kinase-inducible domain interacting domain; BRD, bromodomain; RING, really interesting new gene; PHD, plant homeodomain; KAT, lysine acetyltransferase domain; ZF ZZ, zinc finger, ZZ-type; NRC, nuclear receptor co-activator interlocking domain; CH1−3, cysteine–histidine-rich regions 1−3. (B) CBP BRD-fold depicting the four α-helices (αZ, αA, αB, αC) and the ZA and BC loops that form the Kac binding pocket (derived from PDB 3P1C).27 could serve as tools to elucidate the function of these proteins, and these have started to emerge in recent years. In particular, potent and selective inhibitors of the BRD and extra-terminal (BET) sub-family are now available from several different structural classes.43–49 Pioneering work on the inhibition of the CBP BRD emerged from the Zhou group, which reported several compounds with micromolar affinities (Figure 1D).28–30 The N-acetylindole MS7972 (compound 1, $K_d = 19.6 \mu M$) was shown to block the p53–CBP interaction at 50 $\mu M$ in a competition assay.28 Ischemin (compound 2, $K_d = 19 \mu M$) inhibited p53-induced p21 activation in a luciferase reporter-gene assay ($IC_{50} = 5 \mu M$) and down-regulated p53 target gene expression under oxidative stress conditions.29 The cyclic peptide 3 has also been shown to bind the CBP BRD ($K_d = 8 \mu M$) and to inhibit p53 in the reporter assay.50 These compounds demonstrated the potential of CBP BRD inhibitors to modulate p53-mediated expression; however, they are not very potent or well characterized in terms of selectivity against other BRD-containing proteins. Recent reports also describe potent but non-selective or moderately selective CBP BRD inhibitors, including the sub-micromolar dihydroquinazolinone inhibitor 4.43,51,50 We now report on the discovery of a series of potent and selective CBP/p300 BRD inhibitors, and we demonstrate their inhibition of the CBP–p53 interaction in cells. In addition, we demonstrate how compounds from the series bind in the Kac binding pocket using X-ray crystallography. Our starting point for developing selective CBP/p300 inhibitors was the reported non-selective 3,5-dimethylisoxazole BRD inhibitor, 5 (Figure 2).43 Compound 5 was considered to be an attractive fragment to develop CBP BRD-selective inhibitors because it has a low molecular weight (213 Da) and reasonable LipE51 (3.5) and ligand efficiency (0.45)52,53 for CBP, and because it has various points useful for the introduction of diversity to the core scaffold. Our aim was to develop the scaffold of compound 5 with the goal of achieving potent compounds ($K_d \leq 0.1 \mu M$) with selectivity over other BRD sub-families (≥30-fold) in vitro and displaying target-based cellular activity ($IC_{50} \leq 1 \mu M$) to enable functional studies in cellular systems. Several reports describe 1,3-dimethylisoxazoles as potent inhibitors of the BET BRDs, including the benzimidazole compound 6.43,45,46,55 Therefore, it was recognized that obtaining selectivity for CBP/p300 over the BET BRDs could represent a substantial challenge. Compounds would therefore initially be screened against both CBP and BRD4(1) BRDs as representative examples of their respective sub-families. All in vitro screening and X-ray crystallography was carried out using recombinant BRDs as surrogates of full-length protein. RESULTS AND DISCUSSION An X-ray crystal structure of the reported dimethylisoxazole compound 7 in complex with the CBP BRD illustrated two potential regions which substituted analogues of 5 could interact with, potentially leading to improvements in potency and selectivity (Figure 3).43 Figure 3B shows how the dimethylisoxazole of compound 7 mimics the key Kac binding interactions of the CBP BRD with an H-bond to N1168 and a water-mediated H-bond to Y1125. Figure 3C highlights the two regions targeted for analogues of 5. Region 1 is comprised of part of the “ZA-channel” and is largely hydrophobic, except for ![Image](https://example.com/image.png) backbone carbonyls and the carboxamide of Q1113. Region 2 is analogous to the WPF shelf of BRD4(1).58 The surface is mostly hydrophobic but also has the side-chain of R1173 as a potential site for ligand interactions that could give selectivity for CBP over BRD4(1). On the basis of this analysis, it was anticipated that analogues of compound 5 which possessed substitution on the N-1 and C-2 may be able to interact with regions 1 and 2, with the aim of improving potency and selectivity. However, in initially library chemistry, other substitution patterns were also included in anticipation that unexpected interactions may occur. Library Chemistry. In order to identify more potent and selective leads for the CBP/p300 BRD, a set of Suzuki couplings was carried out in parallel with a commercially acquired 3,5-dimethylisoxazole-4-boronic acid pinacol ester and a set of heteroaryl bromides (Scheme 1). The heteroaryl bromides were chosen from the Pfizer compound collection and were selected so that products obtained would have Lipinski rule of 5 compliant properties (e.g., clogP < 5 and MW < 500), with the majority of the compounds targeted at around clogP = 2–4 and MW = 300–400.57 The set chosen consisted of 101 heteroaryl bromides, which had a variety of substituents on the heterocyclic core in order to maximize diversity. Reactions and workups were carried out in parallel, and products were purified by automated preparative HPLC. Product purity was assessed by UV, evaporative light scattering, and MS. The 101 reactions delivered 83 target compounds in sufficient yield and purity for biochemical testing using differential scanning fluorimetry (DSF, DTm), a high-throughput assay used as a surrogate for displacement assays.47 From this initial library, compound 8 emerged as a promising hit, with ΔTm = 4.5 °C against CBP and 3.2 °C against BRD4(1) at a compound concentration of 10 μM (Figure 4). To improve potency and selectivity for CBP, analogues of compound 8 varied in the C-2 position were then prepared using parallel synthesis for the coupled reduction/cyclization step (Scheme 2). Dithionite-mediated reduction of the aryl nitro group of compound 11 in the presence of R-aldehydes efficiently afforded the desired benzimidazole targets which were purified by automated HPLC. The most promising compound from this set was compound 12, with an increased ΔTm = 6.3 °C (4.5 °C for compound 8) against CBP while maintaining BRD4(1) potency at ΔTm = 2.9 °C (3.2 °C for compound 8) (Figure 4). A pIC50 = 6.3 was measured for compounds 8 and 12, using a peptide displacement AlphaScreen (amplified luminescent proximity homogeneous assay screen).58 The CBP potency represents a significant improvement on compound 5 (pIC50 = 5.4). These results implied that differential 1,2-disubstitution of benzimidazoles could lead to compounds with improved potency and selectivity. It was therefore decided to optimize the substituents on this template via focused synthesis to further improve potency and selectivity. N-1 Amine Optimization. Late-stage variation of the amino moiety was achieved by reductive amination of an aldehyde, obtained from the dimethyl acetal 13 (Scheme 2). The compounds obtained were screened by DSF and AlphaScreen (Table 1). Comparison of the screening --- Scheme 1. Parallel Suzuki Couplings ![Scheme 1](image) Scheme 2. Synthesis of Trisubstituted Benzimidazoles ![Scheme 2](image) --- Figure 4. CBP-selective hits from initial parallel chemistry. Mean values ± SEM (number of measurements). ![Figure 4](image) techniques confirmed that DSF was an effective tool for ranking the potency of compounds. The correlation was high enough that the general and operationally simple DSF assay was felt to be a useful surrogate for the more complex AlphaScreen in further efforts to increase the potency of the compounds. The results suggest that simple cyclic amino analogues 14–16 (CBP $ \Delta T_m = 0.27 \pm 5.4 ^\circ C $, pIC50 = 3.3–6.2) are not as potent as the dimethyamino variant 12 (CBP $ \Delta T_m = 6.3 ^\circ C $, pIC50 = 6.3). However, the morpholine-containing analogue 17 gave a slight improvement with $ \Delta T_m $ values of 6.5 and 2.7 $^\circ C$ for CBP and BRD4(1) respectively and was potent in CBP AlphaScreen (Table 2). The $ K_d $ determined by ITC for this set of compounds. The results are given as mean \pm SEM (number of measurements). ### Table 2. ITC Results for Compound 17 \| Cmpd \| R \| DSF $ \Delta T_m (^\circ C) $ \| CBP pIC50 \| BRD4(1) pIC50 \| \|------\|---\|-------------------------------\|-----------\|--------------\| \| 14 \| -N \| 0.27 \pm 0.13 $ (3) $ \| 0.60 \pm 0.076 $ (3) $ \| 3.3 \pm 1.1 $ (2) $ \| \| 15 \| -N \| 4.4 \pm 0.15 $ (3) $ \| 2.6 \pm 0.35 $ (3) $ \| 6.2 \pm 0.21 $ (2) $ \| \| 16 \| -N \| 5.4 \pm 0.45 $ (3) $ \| 2.7 \pm 0.22 $ (3) $ \| 6.2 \pm 0.20 $ (4) $ \| \| 17 \| -N \| 6.5 \pm 0.18 $ (2) $ \| 2.7 \pm 0.64 $ (3) $ \| 6.8 \pm 0.074 $ (12) $ \| \| 18 \| -N Me \| 3.9 \pm 0.17 $ (3) $ \| 2.1 \pm 0.14 $ (3) $ \| 5.7 \pm 0.048 $ (2) $ \| \| 19 \| -N NH \| 2.0 \pm 0.24 $ (3) $ \| 1.2 \pm 0.23 $ (3) $ \| 5.4 \pm 0.076 $ (2) $ \| \| 20 \| -N S \| 6.5 \pm 0.12 $ (3) $ \| 4.0 \pm 0.23 $ (3) $ \| 6.1 \pm 0.083 $ (2) $ \| \| 21 \| -N O \| 6.5 \pm 0.20 $ (3) $ \| 3.9 \pm 0.31 $ (3) $ \| 6.3 \pm 0.10 $ (2) $ \| Selectivity Optimization. In order to identify potential avenues for improving the selectivity of the series, high-resolution crystal structures were determined for compound 17 in complex with CBP and BRD4(1) (Figure 5). The results suggested that differences in the observed binding modes could be exploited to improve selectivity. In the CBP complex, the morpholine moiety of compound 17 occupies an area in the ZA channel, between the targeted regions 1 and 2. The phenethyl group of compound 17 appears to be in a hydrophobic region on the edge of the pocket. In BRD4(1), compound 17 adopts a flipped binding mode with respect to side-chain orientation; notably, a water-mediated hydrogen bond from the NH of the Q85 carbamidomethyl N-3 nitrogen is apparent. The morpholine moiety points out toward solvent, whereas the phenethyl group fits into a hydrophobic region comprising the WPF shelf and ZA channel of BRD4(1). ### C-2 Aryl Optimization. As the phenethyl moiety of compound 17 was observed to occupy different regions in the CBP and BRD4(1) structures, it was decided to explore the synthesis of a diverse set of compounds with substituted aryl rings to test effects on selectivity. Additionally, it was considered that the C-2 linked aryl group would be amenable to late-stage variation, allowing for an efficient synthesis of analogues. The targeted compounds were synthesized according to Scheme 2. Thus, the phenylenediamine compound 22 was formed by an S$_\text{N}$Ar reaction of compound 10 followed by dithionite-mediated nitro reduction. Precursor 22 was then reacted with substituted carboxylic acids under dehydrating conditions (propylphosphonic anhydride (T3P) or 6 M aqueous HCl) to yield the target compounds 23–36 (Table 3) and s101–s116 (see SI). The DSF results for compounds 23–25 (Table 3) suggest that an electron-donating methyl group on the aryl ring is tolerated, with the para-methyl analogue 25 showing an increased $ \Delta T_m $ for CBP of 7.4 $^\circ C$. The more strongly electron-donating para-methoxy group in compound 26 gave a further increase with $ \Delta T_m = 8.1 ^\circ C$, and showed a larger window over BRD4(1). Conversely, the strongly electron-withdrawing nitro groups in compounds 27 and 28 were detrimental to CBP binding. The results for compounds 29–31 indicated that halogens are tolerated on the phenyl ring, with the meta-substituted fluorine analogue 30 appearing optimal, with $ \Delta T_m = 7.1 ^\circ C$ against CBP. Compounds 32 and 33 combined the para-methoxy and meta-halogen moieties, resulting in a further increase in CBP $ \Delta T_m $ to 9.0 and 9.6 $^\circ C$, respectively. Analogues 34–36 demonstrated that the phenyl group can be substituted for a heteroaryl group, with the electron-rich indole-containing compound 36 representing the optimal compound from this set with $ \Delta T_m = 8.9 ^\circ C$ against CBP. It was encouraging that increases in CBP potency for the best compounds in Table 3 were not accompanied by increases in BRD4(1) potency. Since the four aryl analogues 26, 32, 33, and 36 all indicated improved potency in the $ \Delta T_m $ assay, the pIC50 against CBP was determined using AlphaScreen (Table 4). The results were in the range of 7.0–7.3, indicating that these were all promising analogues warranting more detailed biophysical investigations on their selectivity for CBP over BRD4(1). Thermodynamic parameters for binding to CBP and BRD4(1) were therefore determined by ITC for this set of compounds. The results are summarized in Table 4. Gratifyingly, the substituted aryl analogues are more potent against CBP than compound 17, with $ K_d $ in the range of 0.022−0.050 $ \mu $M. Additionally, the selectivity for CBP over BRD4(1), as determined by ITC $ K_d $ values, had improved to 11−22-fold for these analogues, with the best results being those of compound 36, which had a CBP $ K_d $ = 30 nM and was 22-fold selective over BRD4(1). Although the selectivity had improved, efforts continued in order to achieve a greater window over BRD4(1). To achieve this objective, the obtained crystal ![Figure 5](image) Figure 5. Views from X-ray crystal structures of compound 17 complexed to CBP (PDB 4NR5) and BRD4(1) (PDB 4NR8) BRDs. For CBP: (A) view showing the H-bond interactions between the oxygen of the isoxazole of 17 and N1168 (3.02 Å), and between the nitrogen of the isoxazole and a water (2.75 Å) (water = red spheres), and (B) surface view with shaded regions indicating regions targeted by N-1 and C-2 benzimidazole substitution according to Figure 3. For BRD4(1): (C) view showing the H-bond interactions between the oxygen of the isoxazole of 17 and N140 (3.08 Å), and between the nitrogen of the isoxazole and a water (2.91 Å); the H-bond between the benzimidazole N-3 of 17 and a water molecule is also shown (2.71 Å), and W81 from other ligand-bound structures (carbon = magenta) is overlaid to illustrate the shift in W81 side-chain position (PDB 3MXF, 4E96, 4C67),47,49,60 and (D) surface view. Table 3. Structure—Activity Relationships for CBP and BRD4(1) Binding As Determined by DSF Assay for a Selection of the C-2 Analogues \| Cmpd \| R \| DSF $ \Delta T_m $ (°C) \| \|------\|-----------\|---------------------------\| \| \| \| CBP \| BRD4(1) \| \| 23 \| H$ _2 $C \| 6.4 ± 0.30 (3) 3.8 ± 0.45 (3) \| \| 24 \| CH$ _3 $ \| 6.3 ± 0.23 (3) 2.7 ± 0.085 (2) \| \| 25 \| CH$ _3 $ \| 7.4 ± 0.21 (3) 3.8 ± 0.24 (3) \| \| 26 \| OMe \| 8.1 ± 0.27 (4) 2.4 ± 0.57 (4) \| \| 27 \| NO$ _2 $ \| 5.2 ± 0.15 (3) 1.9 ± 0.58 (3) \| \| 28 \| NO$ _2 $ \| 5.2 ± 0.60 (3) 2.0 ± 0.55 (3) \| \| 29 \| F \| 6.2 ± 0.31 (4) 2.6 ± 0.069 (3) \| \| 30 \| F \| 7.1 ± 0.39 (4) 2.8 ± 0.27 (3) \| \| 31 \| F \| 6.4 ± 0.092 (4) 3.1 ± 0.27 (3) \| \| 32 \| Cl \| 9.0 ± 0.27 (4) 1.9 ± 0.10 (3) \| \| 33 \| F \| 9.6 ± 0.17 (3) 3.2 ± 0.10 (2) \| \| 34 \| OMe \| 6.0 ± 0.47 (2) 3.4 ± 0.30 (2) \| \| 35 \| S \| 6.2 ± 0.52 (2) 3.1 ± 0.80 (2) \| \| 36 \| N \| 8.9 ± 0.17 (3) 2.8 ± 0.10 (2) \| Values are given as mean $ \Delta T_m $ ± SEM (number of measurements). structures (Figure 5) were employed in order to further guide design. Indole Analogue. The structure of compound 17 complexed to BRD4(1) reveals a water-mediated hydrogen bond from the benzimidazole N-3 to the protein backbone (P82) and to the carboxamide side chain of Q85; analogous interactions are absent in the equivalent CBP structure (Figure 5A,C). These observations imply that, in the absence of other effects, replacing the benzimidazole ring with an indole that does not contain the nitrogen in compound 17 should negatively impact BRD4(1) binding, but not CBP. The synthesis of the targeted indole analogue 40 is shown in Scheme 3. Aminophosphonium salt 38 was synthesized according to known procedures and then acylated. Base-promoted cyclization yielded the indole intermediate 39, which was alkylated and cross-coupled to give the target molecule 40. As hoped, indole 40 was completely inactive against BRD4(1) with a $\Delta T_m < 1$ °C (Table 5). Disappointingly, it also gave a significantly lower $\Delta T_m$ for CBP (2.0 °C) than the equivalent benzimidazole analogue 32. This implies that although the crystal structure of compound 17 bound to CBP shows no H-bond to the protein backbone, interaction of the electron-poor benzimidazole with the CBP protein is favored over that of the electron-rich indole. Conformationally Constrained Analogues. The ethylene moiety of compound 17, which links the benzimidazole C-2 and phenyl groups, sits in a hydrophobic region in BRD4(1) and partly occupies the space termed the WPF shelf, which contains a tryptophan residue protruding out of the pocket (Figure 5C,D). The orientation of W81 in BRD4(1) in the complex with compound 17 is unusual when compared to other BRD4(1) ligand-bound structures (Figure 5C) and shows how BRD4(1) can accommodate hydrophobic groups in orientations other than those that occupy the typical WPF shelf. \| Cmpd \| CBP AlphaScreen pIC50 \| ITC Kd (μM) \| BRD4(1) \| Selectivity \| \|------\|------------------------\|-------------\|---------\|-------------\| \| 26 \| 7.0 ± 0.17 (4) \| 0.050 ± 0.0039 \| 0.55 ± 0.0033 \| 11-fold \| \| 32 \| 7.2 ± 0.0080 (2) \| 0.028 ± 0.0024 \| 0.48 ± 0.038 \| 17-fold \| \| 33 \| 7.0 ± 0.069 (2) \| 0.022 ± 0.0017 \| 0.44 ± 0.025 \| 20-fold \| \| 36 \| 7.3 ± 0.18 (2) \| 0.030 ± 0.0021 \| 0.66 ± 0.055 \| 22-fold \| Values are given as mean pIC50 ± SEM (number of measurements). tionally constrained linkers with reduced degrees of freedom, as they would be less able to avoid a steric clash with the WPF shelf by bond rotation. Synthesis of the oxygen-linked targets is shown in Scheme 4. 1,1'-Carbonyldiimidazole (CDI)-mediated cyclization of phenyleneamine 22 gave a 2-oxo precursor. Alkylation tended to favor N-substitution, but use of Ag₂CO₃ as base gave a mixture of N- and O-alkylated isomers, which could be separated to yield the desired target 41. Compound 22 was also used to prepare a hydroxymethyl precursor, which was reacted with a phenol using Tsunodou’s Mitsunobu conditions to yield target compound 42. Analogues 43–51, which possess additional substitution or conformational constraints on the ethylene moiety linking the benzimidazole and aryl groups, were synthesized by methodology analogous to that described in Scheme 2. Disappointingly, screening using DSF showed no improvement in potency and selectivity for the O-linked analogues (41, 42) or conformational constrained compounds (43–51) over the analogous ethylene linked compounds (Table 5). Without indication of an improvement in selectivity, attention shifted to modification of the N-1 ethylene linker between the morpholine moiety and the N-1 position of the benzimidazole ring. It was again proposed that by constraining the conformation of the linker it would force unfavorable interactions in BRD4(1) due to steric interactions with the WPF shelf or by changing the orientation of the phenethyl group (Figure 5). Racemic analogues containing methyl groups on the N-1 ethylene linker (compounds 52–55) were prepared according to the methodology in Scheme 2. Screening results for these compounds are shown in Table 6. While methyl groups were not well tolerated next to the benzimidazole ring (compounds 52 and 54), they were tolerated next to the morpholine ring (compounds 53 and 55). The ΔTᵢₗ and AlphaScreen values for the racemic compounds were encouraging enough to prompt synthesis of the single enantiomers, according to the route shown in Scheme 5. Commercially acquired chiral (R)- and (S)-1,2-diaminopropane reacted via SnAr with 10, predominantly at the less sterically hindered 1-amino group. This reaction gave an inseparable 4:1 mixture of isomers in favor of the desired compound. The morpholine ring was formed by Scheme 4. Synthesis of O-Linked Targets* ``` 41 42 ``` “Reagents and conditions: (a) CDI, THF, reflux, 78%; (b) BnBr, Ag₂CO₃, toluene, 80 °C (18%); (c) 2-hydroxyacetic acid, 6 M aq. HCl, microwave 180 °C, 62%; (d) 3-fluoro-4-methoxyphenol, 1,1'-(azodicarbonyl)dipiperidine, P(n-Bu)₃, CH₂Cl₂, 67%. Table 6. Structure–Activity Relationships for CBP and BRD4(1) Binding As Determined by DSF and AlphaScreen for Conformationally Constrained N-1 Linkers \| Cmpd \| 1 \| 2 \| 3 \| ΔTᵢₗ (°C) \| CBP \| BRD4(1) \| CBP AlphaScreen pIC₅₀* \| \|------\|-----\|-----\|-----\|-----------\|--------------\|--------------\|-------------------------\| \| 52 \| A \| CH₃ \| H \| 5.8 ± 0.02 (3) \| 1.9 ± 0.27 (2) \| ND \| \| \| 53 \| A \| H \| CH₃ \| 9.4 ± 0.58 (5) \| 2.0 ± 0.33 (3) \| 7.6 ± 0.046 (2) \| \| \| 54 \| B \| CH₃ \| H \| 5.6 ± 0.29 (3) \| 1.2 ± 0.070 (2) \| ND \| \| \| 55 \| B \| H \| CH₃ \| 9.1 ± 0.44 (5) \| 2.4 ± 0.25 (3) \| 7.0 ± 0.15 (2) \| \| \| 58 \| A \| H \| (R)-CH₃ \| 7.5 ± 0.10 (3) \| 2.0 ± 0.040 (2) \| 6.3 ± 0.10 (2) \| \| \| 59 \| A \| H \| (S)-CH₃ \| 9.7 ± 0.31 (4) \| 1.8 ± 0.71 (4) \| 7.1 ± 0.049 (2) \| \| \| 60 \| B \| H \| (R)-CH₃ \| 7.2 ± 0.21 (3) \| 2.3 ± 0.25 (2) \| 6.3 ± 0.054 (2) \| \| \| 61 \| B \| H \| (S)-CH₃ \| 11 ± 0.17 (3) \| 3.3 ± 0.57 (2) \| 7.3 ± 0.050 (2) \| \| \| 62 \| C \| H \| (R)-CH₃ \| 7.3 ± 0.058 (3) \| 3.4 ± 0.54 (2) \| 6.7 ± 0.065 (2) \| \| \| 63 \| C \| H \| (S)-CH₃ \| 10 ± 0.11 (3) \| 2.3 ± 0.25 (2) \| 7.2 ± 0.033 (2) \| \| “Compounds are racemic except where indicated. Values are given as mean ± SEM (number of measurements). alkylation with 2-bromoethyl ether. At this stage, the isomeric compounds could be separated by chromatography. Nitro-reduction and benzimidazole formation yielded the target compounds 58–63 in >99% ee, as determined by chiral HPLC. Gratifyingly, the (R)- and (S)-enantiomers displayed clearly different affinities for CBP, with the (S)-form giving a large ΔT_m of around 10 °C and high potency (pIC_{50} > 7.0) in AlphaScreen for the three aryl variants tested (compounds 59, 61, and 63). The (S)-enantiomers were therefore analyzed by ITC, and the results are shown in Table 7. The K_d for these compounds indicated high potency (0.021–0.039 μM). The most selective compound, 59, was shown to be 40-fold selective for CBP over BRD4(1) and 250-fold over BRD4(2). Compound 59 was also potent against p300, with K_d = 0.032 μM (see SI for details). Introducing a chiral methyl onto the morpholino-ethylene moiety had the desired effect of improving selectivity over BRD4(1) while maintaining CBP/p300 potency, and validated the design strategy of introducing conformational restraints into the ethylene linker of the target compounds. Compound 59 was crystallized with CBP (Figures 6). Although the binding mode is similar to that observed for compound 17 (Figure 5A,B), the orientation of the ethylene-linked aryl group is different. In the complex with CBP and 59, there is an apparent cation–π interaction between the guanidino group of R1173 and the aryl ring. This is made possible because the R1173 side chain moves with respect to the guanidino group of R1173 and the aryl ring, possibly helping to lock the ring in position. The induced pocket has been reported for another series of CBP inhibitors which also form cation–π interactions between the inhibitors and the R1173 side chain. The combined findings perhaps suggest that the interaction of aromatic groups with R1173 represents an important feature of potent CBP inhibitors. In order to investigate the wider selectivity of inhibitors in the series, compounds 17 and 59, were screened against representative members of the other BRD sub-families using DSF (Figure 7). The values obtained correlated well with available AlphaScreen IC_{50} values (Spearman rank correlation, ρ 0.94, see SI). In the DSF panel, both compounds were selective for CBP/p300 BRDs. Compound 59 was particularly selective, with no significant ΔT_m (≥ 2 °C) against any other BRDs apart from the BETs: BRD2(1), BRD3(1), and BRD4(1) with ΔT_m between 1 and 2 °C. Table 7. ITC Determination of K_d for the Binding of (S)-Methyl Analogues to CBP and BRD4(1) \| Cmpd \| CBP K_d (μM) \| BRD4 K_d (μM) \| CBP selectivity \| \|------\|--------------\|---------------\|-----------------\| \| 59 \| 0.021 ± 0.0022 \| 0.85 ± 0.096^a \| 40-fold \| \| \| 5.2 ± 0.14^b \| 250-fold \| \| \| 61 \| 0.026 ± 0.0026 \| 0.53 ± 0.074^a \| 20-fold \| \| 63 \| 0.039 ± 0.0029 \| 0.61 ± 0.054^a \| 16-fold \| ^BRD4(1). BRD4(2). Cellular Assays. On-target cellular efficacy for the CBP BRD was investigated using a fluorescence recovery after photo-bleaching (FRAP) assay (Figure 8A). HeLa cells transfected with a construct encoding a green fluorescent protein (GFP)-tagged multimerized (3×) CBP BRD showed a rapid recovery time (t_{1/2} = 0.59 s) upon photobleaching of a small area of the nucleus. The broad-spectrum histone deacetylase inhibitor, SAHA, was used to increase the extent of global lysine acetylation, so increasing recovery time (t_{1/2} = 0.79 s) and expanding the assay window. An equivalent increase in the recovery time was not observed in cells transfected with a CBP BRD construct carrying the N1168F mutation, (see SI, Figure S1), consistent with the critical role of N1168 in Kac binding, and supporting the proposal that the increase in assay window due to SAHA addition is due to BRD binding. Treatment of SAHA-treated cells with compound 59 at 0.1 μM was sufficient to reduce FRAP recovery times back to unstimulated levels (t_{1/2} = 0.60 s), equivalent to the N1168F mutant. The effect is indicative of displacement of the CBP BRD from acetylated chromatin. The weaker and less selective CBP inhibitor, compound 17 and the BRD4(1)-selective inhibitor 6 were unable to significantly alter the FRAP at this concentration (t_{1/2} = 0.66 and 0.74 s, respectively). Conversely, in an equivalent assay using GFP-tagged BRD4, only the BRD4-selective inhibitor 6 significantly affected FRAP recovery times, with CBP inhibitors 17 and 59 showing no significant effect at 0.1 μM (Figure 8B) demonstrating the specificity of the compounds on their respective targets. To investigate the effect of compound 59 on the CBP–p53 association in a cellular context, a luciferase reporter assay for p53 induction was used. Doxorubicin induced p53 activity was effectively inhibited by compound 59 in a dose-dependent manner (IC50 = 1.5 μM) (Figure 8C). These results suggest that the CBP BRD inhibitor 59 inhibits the CBP co-activation of p53 target genes in cells and demonstrate the utility of 59 in a cellular context. The effect on p53 regulation by compound 59 is most likely due to its CBP inhibition, not its weaker BRD4 inhibition, as the much more potent BRD4 inhibitor, JQ1, shows p53-mediated effects at similar concentrations.64,65 However, it was not possible to analyze the effects of less selective CBP inhibitors in the p53 reporter gene assay due to the confounding effects of BRD4 inhibition on p53.64,66 To test if CBP BRD inhibition was cytotoxic at the concentrations where on-target efficacy was observed, U2OS osteosarcoma cells were treated with compound 59 for 24 h, and cell viability was determined using a standard 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) turnover assay (see SI, Figure S2). This showed that compound 59 had modest cytotoxicity (CC50 = 80 μM), well above the levels where on-target efficacy was observed in the FRAP and p53 reporter gene assays. After 72 h of treatment with compound 59, cytotoxicity in U2OS cells increased (CC50 = 8.1 μM). µM), consistent with the effect of BRD4 inhibition at higher concentration as previously reported.$^6$ In order to investigate if compound $S9$ could also serve as a probe in animals, it was tested in \textit{in vitro} ADME (absorption, distribution, metabolism, and excretion) assays (see SI, Table S6). In a human liver microsome (HLM) stability assay, no compound was detected after 60 min, implying that the metabolism of compound $S9$ may be too rapid for it to be useful as an oral \textit{in vivo} probe. The selectivity of compound $S9$ against other target classes was assessed using wide ligand profiling (see SI, Table S7).$^6$ When tested against 136 GPCR, ion channel, enzyme, and kinase targets, compound $S9$ showed IC$_{50}$ < 1 µM only for the adrenergic receptors $α2C$ (0.11 µM) and $α2A$ (0.57 µM), phosphodiesterase-5 (PDE5) (0.15 µM), and platelet-activating factor (PAF) (0.54 µM). CONCLUSIONS* In summary, potent, selective, and cell-active inhibitors of the CBP/p300 BRD have been described. There is a lack of potent and selective inhibitors that target bromodomains outside the BET sub-family. The optimal compound, $S9$, is a highly potent inhibitor of the CBP and p300 BRDs ($K_i = 0.021$ and 0.032 µM, respectively) and is 40-fold selective for CBP over BRD4(1), and highly selective over the other BRD sub-family members screened. In cells, $S9$ inhibits CBP-mediated p53 activity in a luciferase-based reporter assay and has low cytotoxicity. Compound $S9$ is expected to be useful in furthering the understanding of the role of the CBP/p300 BRD in transcriptional regulation. In the context of p53, compound $S9$ could serve to validate the potential of CBP BRD inhibitors as a clinical approach in the treatment of disorders related to hyperactive p53 transcription and could serve as a starting point for developing bioavailable \textit{in vivo} probes and clinical candidates. ASSOCIATED CONTENT Supporting Information Experimental procedures and characterization data. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The SGC is a registered charity (number 1097737) that receives funds from AbbVie, Bayer, Boehringer Ingelheim, the Canada Foundation for Innovation, the Canadian Institutes for Health Research, Genome Canada, GlaxoSmithKline, Janssen, Lilly Canada, the Novartis Research Foundation, the Ontario Ministry of Economic Development and Innovation, Pfizer, Takeda, and the Wellcome Trust [092809/Z/10/Z]. P.F. and S.P. are supported by a Wellcome Trust Career-Development Fellowship (095751/Z/11/Z). The authors thank the European Union, the Biotechnology and Biological Sciences Research Council (BBSRC), and the British Heart Foundation for funding. We also thank Diamond Light Source for beamtime (proposals mx8421 and mx6391), and the staff of beamlines I02 and 124 for assistance with crystal testing and data collection; Cerep for ligand profiling and ADME assays; Prof. Darren Dixon and Peter Clark for help with ee determinations; and Yue Zhu at Changchun Discovery Sciences Ltd for synthesis of selected monomers.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4179, 1 ], [ 4179, 6339, 2 ], [ 6339, 9884, 3 ], [ 9884, 13473, 4 ], [ 13473, 18871, 5 ], [ 18871, 21484, 6 ], [ 21484, 23927, 7 ], [ 23927, 28088, 8 ], [ 28088, 32727, 9 ], [ 32727, 34165, 10 ], [ 34165, 37470, 11 ], [ 37470, 37470, 12 ] ] }
aa6ffe65362ea2ded90e4b88af9e68d8dfe4a1b2	{ "olmocr-version": "0.1.59", "pdf-total-pages": 8, "total-fallback-pages": 0, "total-input-tokens": 28865, "total-output-tokens": 11613, "fieldofstudy": [ "Business" ] }	Model Selection of the Effect of Binary Exposures over the Life Course Andrew D. A. C. Smith, Jon Heron, Gita Mishra, Mark S. Gilthorpe, Yoav Ben-Shlomo, and Kate Tilling Abstract: Epidemiologists are often interested in examining the effect on a later-life outcome of an exposure measured repeatedly over the life course. When different hypotheses for this effect are proposed by competing theories, it is important to identify those most supported by observed data as a first step toward estimating causal associations. One method is to compare goodness-of-fit of hypothesized models with a saturated model, but it is unclear how to judge the “best” out of two hypothesized models that both pass criteria for a good fit. We developed a new method using the least absolute shrinkage and selection operator to identify which of a small set of hypothesized models explains most of the observed outcome variation. We analyzed a cohort study with repeated measures of socioeconomic position (exposure) through childhood, early- and mid-adulthood, and body mass index (outcome) measured in mid-adulthood. We confirmed previous findings regarding support or lack of support for the following hypotheses: accumulation (number of times exposed), three critical periods (only exposure in childhood, early- or mid-adulthood), and social mobility (transition from low to high socioeconomic position). Simulations showed that our least absolute shrinkage and selection operator approach identified the most suitable hypothesized model with high probability in moderately sized samples, but with lower probability for hypotheses involving change in exposure or highly correlated exposures. Identifying a single, simple hypothesis that represents the specified knowledge of the life course association allows more precise definition of the causal effect of interest. (Epidemiology 2015;26: 719–726) Medical research over the past two decades has examined fetal and early life antecedents of disease, and their interaction with other exposures throughout the life course to influence later-life conditions. Several hypothetical relations between repeated covariate measures (e.g., repeated measures of socioeconomic position in childhood) and a subsequent outcome (e.g., adult blood pressure) can be proposed, based on theoretical models or mechanisms of action. For example, a hypothesized “critical period” in early childhood specifies that socioeconomic position during this period has lasting effects on blood pressure. An alternative hypothesis is of an “accumulation” of risk across the life course (i.e., that adverse social circumstances at any time increases subsequent risk of high blood pressure). The hypotheses examined should inform the analytic methods used. The first step in estimating a causal association is to specify knowledge about the system—in this case the life course being studied. This knowledge will be incomplete unless the hypothesized relation between exposures and outcome has been investigated. The initial investigation may be thought of as exploratory: determining the most likely relation, while later analyses may be thought of as confirmatory: verifying the hypothesized relation and checking that no other relations are present. There has been growing interest in a structured approach to life course hypotheses, in which a closed set of hypotheses is proposed and tests conducted to identify best-fitting hypotheses. One such approach uses an F test to compare a saturated model with hypothesized models concerning the association between binary exposure variables, measured over the life course, and an outcome. This method has been used in several studies with continuous outcomes and adapted for binary outcomes. A hypothesis may be thought of as supported by observed data if the F test yields a P value above a certain threshold, although a large P value cannot be considered to “prove” the hypothesis. If more than one hypothesis passes the threshold, the hypothesis that renders the largest P value, or smallest Akaike information criterion, may be selected. The performance of these methods in the life course setting has not been formally assessed. We describe an alternative model selection strategy that identifies which hypothesis, selected from an a priori-compiled set of hypotheses, explains the most variation in... the outcome. We illustrate how the proposed method can be used in both exploratory and confirmatory studies. The performance is contrasted with the structured F test approach in data from a previously published example,9 and also through simulation. METHODS The proposed strategy involves selecting from an a priori-compiled set of potential hypotheses describing the association between exposure over the life course and outcome. Each hypothesis is encoded into one or more variables, which are then all included in a regression model, and the subset of variables that explains the greatest proportion of the outcome variation is selected. The number of hypotheses is not limited; any hypothesis may be examined provided there are enough exposure measurements to identify it. Several variations of similar hypothesis may be considered (e.g., a set of critical period hypotheses covering a range of possibly overlapping periods). The choice of hypotheses to examine may be informed by knowledge of causal mechanisms, perhaps using a directed acyclic graph. Examples of typical hypotheses for binary exposures are described below. An accumulation hypothesis states that there is a linear association between the outcome and the cumulative sum of the exposure over the life course. A critical period hypothesis states that only exposure during one period is associated with the outcome. Under a sensitive period hypothesis, the outcome is associated with the amount of exposure, as in the accumulation hypothesis, but the association is stronger in a particular period.21 A mobility hypothesis states that the outcome is associated with changes in the exposure over time. The simplest mobility hypotheses relate the outcome only to unidirectional changes. A more complex mobility hypothesis may relate the outcome to bidirectional changes (e.g., a positive association with increased exposure and a negative association with decreased exposure). This would in general enhance the plausibility of a causal association. The related interaction hypothesis states that the outcome is associated with the exposure in a particular period, but that this association is altered by the exposure in a different period. Encoding of Variables Each hypothesis is encoded as a variable that is proportional to the hypothesized outcome as the exposure varies. Simpler hypotheses may be encoded by a single variable; more complex hypotheses need multiple variables. Below, we give details of the single variables that encode the simple hypotheses discussed above. We assume a set of $m$ repeated binary measures of exposure $X_1,\ldots,X_m$. The accumulation hypothesis is encoded by the variable $A = X_1 + \cdots + X_m$. If there is only one measurement occasion during a hypothesized critical period then only that measurement will be associated with the outcome. A hypothesis of a critical period at the $j$th measurement occasion is encoded by the variable $C_j = X_j$. If there are several measurement occasions during the critical period (e.g., $X_j,\ldots,X_k$), then the critical period hypothesis may be encoded by $C_{jk} = X_j + \cdots + X_k$, i.e., as accumulation within the critical period. Under the simplest mobility hypothesis, the outcome varies with a unidirectional change in the exposure. A mobility hypothesis between the $j$th and $k$th measurement occasions may be encoded by $M_{jk} = (1 - X_j)X_k$ if it is hypothesized that a positive change from $j$ to $k$ is associated with the outcome, or by $\bar{M}_{jk} = X_j(1 - X_k)$ if it is hypothesized that a negative change from $j$ to $k$ is associated with the outcome. Some hypotheses require more than one variable to encode, and can therefore be thought of as compound hypotheses. All of these can be encoded by combinations of variables encoding simple hypotheses; some quite complex hypotheses can be encoded with two variables. The combinations of variables that encode compound hypotheses are described below, with further details provided in eAppendix A (http://links.lww.com/EDE/A940). A sensitive period hypothesis can be encoded by the combination of the accumulation variable and the relevant critical period variable. Two simple mobility variables can, together, encode a more complex mobility hypothesis. For instance, mobility hypotheses may combine a variable encoding positive change with a variable encoding negative change, or variables encoding change at different pairs of measurement occasions over the life course.9 An interaction hypothesis can be encoded by combining critical period and mobility variables. For example, combining the critical period variable $C_j$ with mobility variable $M_{jk}$ encodes a hypothesis that the outcome is associated with the exposure measurement at occasion $j$, but this association is modified by the exposure measurement at occasion $k$. Choosing Hypotheses Most Strongly Supported by Observed Data After encoding potential hypotheses, our approach is to examine the association between all encoded variables and the outcome, and select only those encoded variable combinations that have the strongest association with the outcome. Since there are potentially more variables than available degrees of freedom it is inappropriate to put all encoded hypotheses into a linear model and choose the variable(s) with the largest parameter estimates. Instead, we propose placing an absolute value penalty on parameter estimates, whereby unimportant variables have their estimated association shrunk to zero. Hence, the resulting fit will provide the fullest explanation of the observed data from the fewest parameters. The Least Absolute Shrinkage and Selection Operator (lasso)23 which minimizes the residual sum of squares plus an absolute value penalty, provides a suitable method, but requires selection of a smoothing parameter. This can be simplified by implementing the Least Angle Regression (LARS) approach to the lasso,24 which provides lasso estimates for all smoothing parameter values and indicates the best lasso fit for each number of selected variables, reducing the problem to that of choosing the number of variables. The lasso is a constrained version of linear regression and may be used whenever the assumptions of linear regression are satisfied. The LARS algorithm first selects the variable with the strongest association with the outcome,25 hence this approach will always select first the hypothesis, or component of a compound hypothesis, that offers the strongest explanation for the observed data. Using an absolute value penalty causes subsequent variables to be added in order of strength of association with outcome variation.26 The overall hypothesized view of the data is thus built from the most relevant simple hypotheses or components of compound hypotheses. When little is known regarding the association between the exposures and outcome over the life course, the structured approach can be used to suggest the most likely of an a priori-defined set of hypothesized associations. This set may extend to several hypotheses if we have little a priori information about which are likely. In this exploratory setting, the choice of hypothesis is somewhat subjective and we require a method for choosing how many variables to include in our selected hypothesis. We use an elbow plot—a plot of the proportion of outcome variation explained by the lasso fit (the $ R^2 $ value) against number of variables selected at each stage in the LARS procedure. The “elbow”—a sharp concave bend at which adding more variables does not substantially increase the $ R^2 $ value—is used to choose the number of variables. Provided enough variables are included in the procedure, the elbow plot will show how the lasso selections approach a saturated model. It is useful to see the $ R^2 $ value for a saturated model to check whether there is any association between the outcome and all exposure measurements over the life course. An alternative method for selecting the number of variables is provided by the lasso covariance hypothesis test.27 At each stage of the LARS procedure, this test checks the null hypothesis that adding the next variable does not improve the $ R^2 $ value. The covariance hypothesis test accounts for the fact that the next variable will have the greatest association out of the variables not already selected. An alternative option, a nested $ F $ test to discriminate between simple and complex hypotheses,22 may be biased by the selection of the simpler model due to its greater association. In the exploratory setting, it may be necessary to reject more compound hypotheses in favor of simpler ones to maintain plausibility. We may have a firmer idea of the nature of the life course association between exposures and outcome, and perhaps some causal information. In this setting, we might specify quite a small number of possible hypotheses a priori, and rather than choose the number of variables in our selected hypothesis we might simply choose the first variable or hypothesis selected by the LARS algorithm, to confirm our causal assumptions. EXAMPLE The proposed approach, in the exploratory setting, is illustrated using data on socioeconomic position and body mass index (BMI) from a cohort of 2,192 men and women, with binary measurements of the exposure, socioeconomic position, at ages 4, 26, and 43 years, and a continuous measurement of the outcome, BMI, at age 53 years. These data were previously used to illustrate the structured approach, and full details are given in the original study.9 Issues such as confounding and measurement error were not the focus of the original study and are therefore ignored here for sake of simplicity and comparison with the alternative structured method. Figure 1 shows a possible directed acyclic graph for this example. While there are many potential confounders of the life course association between exposure and outcome, which in this example are unmeasured (as they were in the original study), the focus in this exploratory setting is to identify likely life course associations between exposure and outcome, whether or not they are confounded. We considered the set of six hypotheses that have been previously proposed for this data: three critical period hypotheses corresponding to the three exposure measurement occasions, two mobility hypotheses concerning change between adjacent measurement occasions, and an accumulation hypothesis.9 Encoding of Variables Each hypothesis was encoded based on the binary exposure measurements $ X_1, X_2, $ and $ X_3 $ at the three time points, where zero represents a manual socioeconomic position and one a nonmanual socioeconomic position. The simple hypotheses, requiring one variable each, were the three critical period hypotheses, encoded by $ C_1, C_2, $ and $ C_3, $ and the accumulation hypothesis, encoded by $ A = X_1 + X_2 + X_3. $ The two mobility hypotheses required two variables each, with $ M_{12} $ and $ M_{12} $ encoding mobility between ages 4 and 26 years, and $ M_{23} $ and $ M_{23} $ encoding mobility between ages 26 and 43 years. Use of Elbow Plot Figure 2 shows the elbow plot for men. The variance explained by the model with the greatest number of variables was 1.7%, which approached the 2% explained by the saturated model; hence the maximum $ R^2 $ value on the plot is close to the maximum $ R^2 $ value achievable. There is a clear elbow where one variable is selected; adding additional variables did not considerably improve the $ R^2 $ value. In addition, the $ P $ value for adding a second variable was 0.90, indicating no evidence that one variable was insufficient. The first variable selected encoded the hypothesis of an age 4 critical period; choosing this elbow point identified this hypothesis as offering the best explanation for the observed data in men. Figure 3 shows the elbow plot for women. The maximum $ R^2 $ value on the plot is 3.8%; that of the saturated model was 3.9%. Therefore, socioeconomic position explained a greater proportion of the BMI variation in women than men. The position of an elbow point was less clear for women. The first variable selected encoded the accumulation hypothesis; the $ P $ value for adding a second variable was 0.52. It could thus be concluded that the accumulation hypothesis is the primary explanation for the observed data in women. The plot might also be considered to have an elbow at three variables, selecting variables that encoded the accumulation, childhood critical period, and adult nonmanual to manual mobility variables. Our interpretation of this is a hypothesis of two sensitive periods: sensitivity (to manual socioeconomic position) in childhood and sensitivity to change (from nonmanual to manual socioeconomic position) in adulthood. In the exploratory setting, further study would be required to clarify these hypotheses and examine causal mechanisms. SIMULATION STUDY To investigate how frequently the LARS algorithm selects the correct hypothesis in a confirmatory setting, we simulated data with two and three repeated binary exposures. The performance indicator is the selection probability: the proportion of simulations where the correct hypothesis is identified. Two Exposure Measurements Two exposure measurements were simulated as binary random variables, being zero or one with equal probability (see eAppendix B for details; http://links.lww.com/EDE/A940). We considered the situation in which the outcome is known to be associated with change in the exposure, but it is yet to be confirmed whether a mobility or interaction hypothesis defines the true association. We simulated mobility and interaction models, varying the correlation, $ \rho $, between exposure variables, and the residual variance, $ \sigma^2 $. In each simulation, we selected from six proposed compound hypotheses (four interaction hypotheses, full mobility, and an additive model). We compared three approaches for identifying the hypotheses offering the best explanation for the simulated data. The first was the LARS algorithm for the lasso, which was considered to have identified the correct hypothesis if the first two selected variables encoded that hypothesis. The second approach chose the hypothesized model with the largest $ F $ test $ P $ value when compared with the saturated model, and the third approach selected the hypothesized model yielding the smallest Akaike information criterion of those models with an $ F $ test $ P $ value not less than 0.05. We varied the sample size from 400, which might represent a subset of a study, to 2,500, which might represent a moderate-sized study. We ran 500 simulations for each combination of residual variance, correlation, model, and sample size. With 500 simulations, the 95% confidence interval for the selection probability will have a radius of less than 2% for a selection probability of 95%, and less than 5% for a selection probability of 50%. Table 1 shows the selection probabilities, in simulation, of the three methods. The selection probability of the LARS algorithm is very good in situations with low residual variance or large sample size: it was at least 83.6% when the $ R^2 $ value was at least 100/$ n $. This approach always outperformed the alternative methods, except for a difference of 0.4% in one situation with the largest residual variance and smallest sample size. Three Exposure Measurements This hypothetical example considered that prior knowledge provided evidence for either a critical or a sensitive period; the aim being to confirm the correct association using new data. Three measurements were simulated as binary variables as before, with adjacent measurements having correlations of $ \rho $, and the first and last measurements having correlation $ \rho^2 $. The models used to generate the outcome were: an early critical period, an accumulation model, and an early sensitive period model. The simple hypotheses that the LARS algorithm was allowed to choose from were three critical period hypotheses and an accumulation hypothesis. The LARS algorithm was considered to have chosen a simple hypothesis if it first selected the variable encoding that hypothesis, and the covariance test $ P $ value for including another variable was not less than 0.05. The LARS algorithm was considered to have identified a compound hypothesis if the first two selected variables encoded that hypothesis and the $ P $ value for including the second variable was less than 0.05. While we do not necessarily advocate using $ P $ value thresholds to select hypotheses, this allowed comparisons with other approaches. The other two approaches used the $ F $ test and Akaike information criterion as before, choosing between an accumulation model, three critical period models and three sensitive period models. There was some evidence that selection probabilities decreased as the exposure correlation increased (Table 2). The selection probability of the LARS algorithm was very good with low residual variance or large sample size: it was at least 90.2%, and higher than that of other methods, when the $ R^2 $ value was at least 100/$ n $. The only exception to this was in sensitive period simulations with strong exposure correlation, where there was less distinction between accumulation and critical period hypotheses. The alternative methods had better selection probabilities in compound models than simple models; it appears that Akaike information criterion or $ F $ test selection is more likely to select compound hypotheses over simple ones, regardless of the true underlying model. Confidence Intervals We repeated the simulation experiment with three exposure measurements, testing a null model in place of a sensitive period model. In each simulation, we calculated the usual 95% confidence interval for the regression parameter in the hypothesized model with the largest $ F $ test $ P $ value (coincidentally the model with smallest Akaike information criterion) when compared with the saturated model. We also calculated an adjusted confidence interval based on the covariance test (see eAppendix B for details; http://links.lww.com/EDE/A940). Table 3 shows the coverage of these confidence intervals. In the null model, the coverage of the usual confidence intervals was always less than 95%, showing that the $ F $ test or Akaike information criterion approach generates bias due to the fact that they consider the largest observed association to be selected at random. However, the adjusted confidence intervals have coverage between 92.2% and 96.2% in the null model, confirming that the covariance test corrects for selection of the variable with greatest association. ### DISCUSSION A causal life course association between exposure and outcome cannot be estimated without identifying knowledge of the system being studied. This can be achieved by assessing prespecified competing hypotheses regarding that system and the life course association. We have described a strategy for this, which involves encoding a set of hypotheses as covariates, and then using the LARS procedure for the lasso to identify the most appropriate covariate subset that accounts for the outcome variation. Variable selection is aided visually with an elbow plot, or guided by a hypothesis test. We showed that, for one example dataset, the LARS procedure identified the same hypotheses as earlier research using a structured approach. Furthermore, simulation showed, for reasonably large sample sizes, the LARS algorithm, even when combined with a naive $ P $ value threshold, effectively identified the correct hypotheses. Alternative methods, based on $ F $ tests and Akaike information criterion, did not identify the correct hypotheses as often and were more likely to favor compound hypotheses over simple ones. Our proposed approach is part of the process toward estimation of causal effects. The set of hypotheses proposed a priori can be chosen using previous knowledge and theory regarding the plausibility of various hypotheses. We have demonstrated techniques for choosing the best-fitting of those hypotheses, which can then be further investigated both for ### Table 1. Percentage of 500 Simulations in Which the Correct Model Was Identified, in Simulations with Two Binary Exposure Measurements, by Three Different Structured Approaches \| $ \sigma^2 = 1 (R^2 = 0.50) $ \| Mobility \| Interaction \| Mobility \| Interaction \| \| --- \| --- \| --- \| --- \| --- \| \| $ \rho $ \| LARS \| $ F $ test \| LARS \| $ F $ test \| \| 0 \| 99.4 \| 51.6 \| 100 \| 100 \| \| 0.4 \| 100 \| 50.8 \| 100 \| 100 \| \| 0.8 \| 99.8 \| 50.8 \| 100 \| 100 \| \| $ \sigma^2 = 9 (R^2 = 0.10) $ \| Mobility \| Interaction \| Mobility \| Interaction \| \| --- \| --- \| --- \| --- \| --- \| \| $ \rho $ \| LARS \| $ F $ test \| LARS \| $ F $ test \| \| 0 \| 62.8 \| 49.4 \| 97.2 \| 80.6 \| \| 0.4 \| 70.8 \| 48.8 \| 97.2 \| 75.0 \| \| 0.8 \| 61.0 \| 39.8 \| 84.2 \| 50.0 \| \| $ \sigma^2 = 24 (R^2 = 0.04) $ \| Mobility \| Interaction \| Mobility \| Interaction \| \| --- \| --- \| --- \| --- \| --- \| \| $ \rho $ \| LARS \| $ F $ test \| LARS \| $ F $ test \| \| 0 \| 38.4 \| 38.8 \| 82.2 \| 49.8 \| \| 0.4 \| 46.2 \| 37.6 \| 80.0 \| 45.6 \| \| 0.8 \| 39.2 \| 27.4 \| 62.4 \| 31.4 \| AIC indicates Akaike information criterion; LARS, least angle regression. replication and to estimate causal effects. Advantages of the structured approach are that it requires the hypotheses to be carefully specified a priori, and can accommodate complex compound hypotheses that involve interactions. For example, Forsdahl\textsuperscript{28} argued that a poor standard of living in early years followed by later life prosperity would increase the risk of arteriosclerotic disease. In this example, the highest risk would be seen in those who change exposure between earlier and later time periods. Other hypotheses, such as nonlinear accumulation, can also be investigated. The flexibility of our approach allows many hypotheses even if they are epidemiologically implausible: it is important to triangulate the statistical findings with knowledge about biological and social plausibility. If suggested hypotheses are thought to be “too complex,” our procedure allows for retreat to simpler, more interpretable, hypotheses if necessary. In further investigation, only the identified hypothesis need be considered, allowing precise definition of the causal effect(s) of interest and reducing their number, leading to improved estimation by marginal structural or structural nested models.\textsuperscript{7,29} Our approach has the advantage that the selected hypothesis will always be easy to interpret, provided that interpretable hypotheses are proposed a priori. This is in contrast to methods that provide a plot and invite interpretation based on \| TABLE 2. Percentage of 500 Simulations in Which the Correct Model Was Identified, in Simulations with Three Binary Exposure Measurements, by Three Different Structured Approaches \| \| --- \| \| $ \sigma^2 = 1 (R^2 = 0.50) $ \| $ \rho $ \| $ n = 400 $ \| $ n = 1,000 $ \| $ n = 2,500 $ \| \| Critical period \| LARS \| 97.2 \| 97.0 \| 97.2 \| 98.2 \| 97.4 \| 97.2 \| 96.6 \| 96.8 \| 97.8 \| \| \| $ F $ test \| 67.2 \| 66.2 \| 67.8 \| 68.4 \| 66.4 \| 68.2 \| 66.4 \| 66.4 \| 64.0 \| \| \| AIC and $ F $ test \| 83.6 \| 82.2 \| 79.6 \| 81.4 \| 81.8 \| 83.2 \| 83.6 \| 81.4 \| 79.0 \| \| Accumulation \| LARS \| 93.6 \| 92.8 \| 92.4 \| 94.4 \| 92.4 \| 90.2 \| 91.6 \| 93.0 \| 91.2 \| \| \| $ F $ test \| 40.8 \| 37.4 \| 38.4 \| 40.0 \| 38.4 \| 33.8 \| 38.4 \| 35.6 \| 35.6 \| \| \| AIC and $ F $ test \| 66.0 \| 65.4 \| 65.4 \| 66.0 \| 67.2 \| 64.2 \| 66.8 \| 66.6 \| 65.2 \| \| Sensitive period \| LARS \| 100 \| 100 \| 99.6 \| 100 \| 100 \| 99.6 \| 100 \| 100 \| 100 \| \| \| $ F $ test \| 100 \| 99.8 \| 96.8 \| 100 \| 100 \| 99.6 \| 100 \| 100 \| 100 \| \| \| AIC and $ F $ test \| 96.8 \| 95.2 \| 93.0 \| 94.4 \| 95.4 \| 95.0 \| 96.4 \| 95.0 \| 94.2 \| \| $ \sigma^2 = 9 (R^2 = 0.10) $ \| $ \rho $ \| $ n = 400 $ \| $ n = 1,000 $ \| $ n = 2,500 $ \| \| Critical period \| LARS \| 97.2 \| 97.0 \| 92.2 \| 98.2 \| 97.4 \| 97.2 \| 96.6 \| 96.8 \| 97.8 \| \| \| $ F $ test \| 67.0 \| 64.6 \| 58.4 \| 68.4 \| 66.4 \| 64.8 \| 66.4 \| 66.4 \| 64.0 \| \| \| AIC and $ F $ test \| 83.2 \| 81.0 \| 72.8 \| 81.4 \| 81.8 \| 80.8 \| 83.6 \| 81.4 \| 79.0 \| \| Accumulation \| LARS \| 93.6 \| 92.8 \| 90.2 \| 94.4 \| 92.4 \| 90.2 \| 91.6 \| 93.0 \| 91.2 \| \| \| $ F $ test \| 40.8 \| 38.4 \| 33.8 \| 40.0 \| 38.4 \| 33.8 \| 38.4 \| 35.6 \| 35.6 \| \| \| AIC and $ F $ test \| 66.0 \| 65.4 \| 65.4 \| 66.0 \| 67.2 \| 64.2 \| 66.8 \| 66.6 \| 65.2 \| \| Sensitive period \| LARS \| 71.8 \| 62.8 \| 17.6 \| 99.4 \| 98.0 \| 69.2 \| 100 \| 100 \| 98.4 \| \| \| $ F $ test \| 84.6 \| 77.4 \| 48.6 \| 98.8 \| 94.2 \| 71.8 \| 100 \| 100 \| 91.8 \| \| \| AIC and $ F $ test \| 78.4 \| 70.8 \| 34.6 \| 93.8 \| 90.2 \| 66.8 \| 96.4 \| 95.0 \| 87.2 \| \| $ \sigma^2 = 24 (R^2 = 0.04) $ \| $ \rho $ \| $ n = 400 $ \| $ n = 1,000 $ \| $ n = 2,500 $ \| \| Critical period \| LARS \| 95.2 \| 93.0 \| 79.8 \| 98.2 \| 97.2 \| 92.8 \| 96.6 \| 96.8 \| 97.8 \| \| \| $ F $ test \| 62.0 \| 59.4 \| 48.4 \| 68.0 \| 65.4 \| 56.6 \| 66.4 \| 66.4 \| 61.2 \| \| \| AIC and $ F $ test \| 79.4 \| 76.0 \| 62.6 \| 81.4 \| 81.6 \| 74.4 \| 83.6 \| 81.4 \| 77.2 \| \| Accumulation \| LARS \| 88.8 \| 90.2 \| 71.8 \| 94.4 \| 92.4 \| 88.0 \| 91.6 \| 93.0 \| 91.2 \| \| \| $ F $ test \| 40.8 \| 37.4 \| 37.8 \| 40.0 \| 38.4 \| 33.8 \| 38.4 \| 35.6 \| 35.6 \| \| \| AIC and $ F $ test \| 65.2 \| 65.2 \| 58.6 \| 66.0 \| 67.2 \| 64.0 \| 66.8 \| 66.6 \| 65.2 \| \| Sensitive period \| LARS \| 11.4 \| 9.8 \| 0.0 \| 66.8 \| 63.6 \| 13.8 \| 98.8 \| 97.8 \| 66.8 \| \| \| $ F $ test \| 47.2 \| 38.8 \| 17.6 \| 83.4 \| 75.6 \| 44.2 \| 98.0 \| 94.2 \| 76.0 \| \| \| AIC and $ F $ test \| 30.2 \| 24.6 \| 2.8 \| 74.6 \| 67.2 \| 30.8 \| 95.0 \| 90.2 \| 68.6 \| AIC indicates Akaike information criterion; LARS, least angle regression. curves on the graph. The LARS algorithm has the advantage of choosing the most important hypothesis first: that corresponding to the greatest proportion of the variability in the outcome, while unimportant effects are deselected. Unlike the structured F test approach, our approach can be employed without using P values. Using the covariance test for the lasso, we calculated confidence intervals with coverage unaffected by the fact that the selected hypothesis offers the best fit to the observed data. The covariance test for the lasso should be used in preference to an F test between simple and compound hypothesized models. If the association between exposure and outcome is weak, with little variation in the outcome explained by the exposure, then the reliability of structured approaches in identifying the true model is diminished. It is therefore important to extend this approach to continuous exposures and categorical outcomes, consider measurement error in the exposure, and accommodate possible confounding. Within the same overall structure, other variable selection methods might be used instead of the lasso. One possibility is the elastic net, although this could select more variables than parameters in the saturated model, which would not be an advantage in understanding the hypothesized life course association, as less parsimonious models are less interpretable. The grouped lasso would allow all variables encoding a compound hypothesis to be selected at the same time, and prevent only one component variable of a compound hypothesis being identified on its own. However, if compound hypotheses are misspecified, for example not all of their components are associated with the outcome, then not grouping variables still allows the important components to be extracted and the hypothesis to be identified. Our conclusion is that the LARS procedure, implementing the lasso, can select hypotheses from a prespecified set, identifying the optimal hypothesis that offers the greatest consistency with the data. Compound hypotheses can be built from simpler hypotheses in a straightforward way, using \| TABLE 3. Percentage of 500 Simulations in Which a 95% Confidence Interval Contained the True Parameter Value, in Simulations with Three Binary Exposure Measurements, Calculated by Two Different Structured Approaches \| \|-----------------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\|-------\| \| \| n = 400 \| \| n = 1,000 \| \| n = 2,500 \| \| \| \| 0 \| 0.4 \| 0.8 \| 0 \| 0.4 \| 0.8 \| 0 \| 0.4 \| 0.8 \| \| σ² = 1 \| \| \| \| \| \| \| \| Null \| LARS \| 95.0 \| 94.2 \| 95.2 \| 93.8 \| 95.0 \| 96.2 \| 92.2 \| 94.6 \| 94.4 \| \| \| AIC and/or F test \| 86.2 \| 87.8 \| 92.4 \| 86.8 \| 89.0 \| 92.2 \| 84.2 \| 84.2 \| 87.2 \| \| Critical period \| LARS \| 95.6 \| 96.2 \| 96.2 \| 96.0 \| 96.2 \| 95.6 \| 94.8 \| 94.4 \| 94.0 \| \| \| AIC and/or F test \| 95.6 \| 96.2 \| 96.2 \| 96.0 \| 96.2 \| 95.6 \| 94.8 \| 94.4 \| 94.0 \| \| Accumulation \| LARS \| 95.2 \| 96.0 \| 97.0 \| 97.4 \| 97.6 \| 97.0 \| 94.4 \| 93.8 \| 94.0 \| \| \| AIC and/or F test \| 95.2 \| 96.0 \| 97.0 \| 97.4 \| 97.6 \| 97.0 \| 94.4 \| 93.8 \| 94.0 \| \| σ² = 9 \| \| \| \| \| \| \| \| Null \| LARS \| 95.0 \| 94.2 \| 95.2 \| 93.8 \| 95.0 \| 96.2 \| 92.2 \| 94.6 \| 94.4 \| \| \| AIC and/or F test \| 86.2 \| 87.8 \| 92.4 \| 86.8 \| 89.0 \| 92.2 \| 84.2 \| 84.2 \| 87.2 \| \| Critical period \| LARS \| 95.6 \| 95.6 \| 89.2 \| 96.0 \| 96.2 \| 94.4 \| 94.8 \| 94.4 \| 94.0 \| \| \| AIC and/or F test \| 95.6 \| 95.8 \| 89.2 \| 96.0 \| 96.2 \| 94.4 \| 94.8 \| 94.4 \| 94.0 \| \| Accumulation \| LARS \| 95.4 \| 95.8 \| 92.2 \| 97.4 \| 97.6 \| 96.0 \| 94.4 \| 93.8 \| 94.0 \| \| \| AIC and/or F test \| 95.0 \| 95.8 \| 92.2 \| 97.4 \| 97.6 \| 96.0 \| 94.4 \| 93.8 \| 94.0 \| \| σ² = 24 \| \| \| \| \| \| \| \| Null \| LARS \| 95.0 \| 94.2 \| 95.2 \| 93.8 \| 95.0 \| 96.2 \| 92.2 \| 94.6 \| 94.4 \| \| \| AIC and/or F test \| 86.2 \| 87.8 \| 92.4 \| 86.8 \| 89.0 \| 92.2 \| 84.2 \| 84.2 \| 87.2 \| \| Critical period \| LARS \| 93.2 \| 90.2 \| 83.5 \| 96.0 \| 95.2 \| 90.0 \| 94.8 \| 94.4 \| 93.0 \| \| \| AIC and/or F test \| 93.2 \| 90.8 \| 83.8 \| 96.0 \| 95.2 \| 90.0 \| 94.8 \| 94.4 \| 93.0 \| \| Accumulation \| LARS \| 94.8 \| 90.2 \| 70.4 \| 97.4 \| 97.4 \| 89.2 \| 94.4 \| 93.8 \| 93.6 \| \| \| AIC and/or F test \| 94.8 \| 89.2 \| 70.4 \| 97.4 \| 97.4 \| 89.0 \| 94.4 \| 93.8 \| 93.6 \| AIC indicates Akaike information criterion; LARS, least angle regression. a small number of variables. 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b7e1bf6dbc56f55ea948c3666fbcfb56f0e5cff6	{ "olmocr-version": "0.1.59", "pdf-total-pages": 17, "total-fallback-pages": 0, "total-input-tokens": 40668, "total-output-tokens": 12731, "fieldofstudy": [ "Computer Science" ] }	Probing Limits of Information Spread with Sequential Seeding Jarosław Jankowski¹, Boleslaw K. Szymanski²-⁴, Przemysław Kazienko³, Radosław Michalski³, Piotr Bródka³ Abstract We consider here information spread which propagates with certain probability from nodes just activated to their not yet activated neighbors. Diffusion cascades can be triggered by activation of even a small set of nodes. Such activation is commonly performed in a single stage. A novel approach based on sequential seeding is analyzed here resulting in three fundamental contributions. First, we propose a coordinated execution of randomized choices to enable precise comparison of different algorithms in general. We apply it here when the newly activated nodes at each stage of spreading attempt to activate their neighbors. Then, we present a formal proof that sequential seeding delivers at least as large coverage as the single stage seeding does. Moreover, we also show that, under modest assumptions, sequential seeding achieves coverage provably better than the single stage based approach using the same number of seeds and node ranking. Finally, we present experimental results showing how single stage and sequential approaches on directed and undirected graphs compare to the well-known greedy approach to provide the objective measure of the sequential seeding benefits. Surprisingly, applying sequential seeding to a simple degree-based selection leads to higher coverage than achieved by the computationally expensive greedy approach currently considered to be the best heuristic. Keywords: diffusion, social network, seed selection, influence maximization, sequential seeding Introduction Making decisions is often difficult; this is why it is often worth to split it into consecutive stages to reduce potential risk. Such approach gives the decision maker an opportunity to learn the outcomes of the previous stages and adjust accordingly the current stage. This approach applies also to influence maximization and information spread in complex networks. One of the main challenges there is the selection for initial and activation network nodes referred to as seeds, to maximize the spread of information within the network [1]. E-mail: [email protected] Various factors affecting the diffusion and social influence in complex networks were analyzed including the role of different centrality measures in selection of initial influencers [2], impact of homophily for successful seeding [3] and others [4]. While most of the relevant research is related to marketing, the problem is more generally defined as a target set selection in combinatorial optimization in theoretical computer science [5–7]. The influence maximization problem is also explored in physics from the perspective of network structures [8]. Some other studies discuss the role of communities [9] or propose to use optimal percolation [10]. Initial research has been carried out to identify seeds for temporal [11,12] and multi-layered social networks [13]. Several comparative studies on seeding strategies were presented in [14,15]. Since the seed selection process is NP-hard [1], several heuristics have been proposed. Most of them use network structural properties like degree or eigenvector measure to rank seed candidates [14]. Seeding strategies have been applied to word-of-mouth marketing, social and political campaigns and diffusion of information in social media. Vast majority of them are based on the assumption that all seeds are activated at the beginning of the process or campaign and then diffusion starts and continues naturally without any additional support [14]. Some recent research proposes to apply adaptive approaches with two-stage stochastic model exploring the potential of neighboring nodes [16], further extended towards more scalable approach [17]. Using some seeds after the first stage was preliminary proposed in [18,19] and potential of multi-period spraying for routing in delay-tolerant networks was discussed as an effective solution for propagation in computer networks in [20]. On top of that, the concept of sequential seeding was introduced [21]. It takes the advantage of delayed seeding by interweaving activating seeds with diffusion. Here we firm the foundations of sequential seeding and address a number of research questions that have not been studied before [21–23]. First, we prove formally and confirm experimentally on real networks that the sequential seeding is at least as good as the single stage method and under modest conditions, it is provably better. Then, we evaluate the realistic benefits of this method by comparing its capabilities to both greedy and optimal (maximal) solutions to obtain some measure of improvements provided by this approach. Finding optimal seed sets and computing the maximal coverage for various scenarios allow us to represent gains from sequential seeding as a fraction of the space between coverage of other algorithms and the maximal coverage. This has been investigated empirically for directed and undirected networks using independent cascades model [1]. \| Strategy \| Description \| No. of seeding stages \| \|----------\|-------------\|-----------------------\| \| SN \| Single Stage Seeding – all seeds are activated in one stage at the beginning \| 1 \| \| SQ \| Sequential Seeding – one seed activation starts the stage and revives the previously stopped diffusion; each stage ends when diffusion stops \| n \| Table 1: Seeding strategies with n number of seeds In the first phase, we ran simulations on six real complex networks with sizes in the range of 1.5k-17k nodes. The visualization of the networks and their basic properties are provided in the Supplementary Material. The independent cascades model (IC) [1] was used with a given propagation probability $PP(a, b)$ that node $a$ activates (influences or infects) node $b$ in step $t + 1$ under the condition that node $a$ was activated at time $t$ [24]. The results for undirected networks assume that $PP(a, b) = PP(b, a)$ for all edges. This simplification allowed us to obtain the optimal seed set through the complete search even for largest networks among those used for experimentation. To explore the directed networks without this assumption, another large set of extensive experiments were performed on the smaller network, for which it was also possible to compute optimal solutions, see the next section. Figure 1: Undirected networks: (A) The averaged performance of sequential SQ and single stage seeding SN with greedy based nodes selection as a fraction of the maximum coverage $C_{Max}$ and as a function of the network size $N$, probability of propagation PP across each edge, and the fraction of nodes selected as seeds (seed selection percentage) SP; see (A1) Performance of sequential SQ and single stage seeding SN with degree-based ranking in comparison with maximum coverage and the upper bound as a function of the individual configurations, each defined by $N$, PP, SP, and the random binary choice made at simulation initialization for each edge to propagate or not information across this edge; (B) Coverage of sequential method SQ as percentage of $C_{Max}$ placed between single stage seeding SN and Max for greedy nodes selection; (B1), (B2) Sequential seeding performance SQ between single stage seeding SN and Max for random and degree-based node selection, respectively; (B3) Performance of sequential SQ and single stage seeding SN represented by percentage of activated nodes within network (coverage) for random seed selection, degree-based ranking and greedy seed selection in comparison with maximum coverage as a function of the individual configurations; (C) Gain for different propagation probabilities PP averaged over all cases; (D) Gain for different seeding percentages SP; (E) Gain for node ranking strategies based on random, greedy and degree selection; (F) Gain for networks N1 - N6. With the independent cascades model (IC) even a single seed can induce diffusion (which is crucial for sequential approaches), while in the linear threshold model [1] (LT), a small seed set could have no effect. For that reason, experiments were carried out on the IC model. Results achieved by sequential seeding (SQ) were compared with the single stage approach (SN) and the maximum coverage (Max) for the same setup: network and parameters: the propagation probability, the seeding percentage, and the seed ranking strategies: degree, greedy and random. The sequential coverage $C_{SQ}$ was on average 7.1% better than the single stage coverage $C_{SN}$. The positive gain of SQ over SN was also confirmed by statistical tests, see Section Material and Methods. Results for greedy based ranking for 50,000 simulations represented as percentage of maximum coverage $C_{Max}$ averaged over individual configurations and ordered by the ratio $C_{SN} / C_{Max}$ are presented in Fig. [A]. Additionally, the upper bound $C_{Greedy SN} * e/(e - 1)$ [1] is for many configurations up to 50% greater than real maximum value observed, see Fig. [A1] (A). These results demonstrate that upper limit derived from greedy approach is not tight. Sequential methods always outperform single stage ones, if we consider averaged coverage, for any strategy as well as for every configuration. Moreover, degree SQ is able to cover more nodes than greedy SN, especially for configurations with coverage significantly lower than $C_{Max}$, as shown in Fig. [A] (A1). There were 8,100,000 individual simulation cases defined during simulation initialization, each case by its $N$, PP, SP, and binary random choice selected for each edge to propagate information or not across this edge. These cases are ordered by coverage obtained in the single stage method. The resulting plots demonstrate that $C_{SQ}$ performs better than $C_{SN}$ in almost every case. The greatest increase is observed for $C_{SN} \in [30\%, 85\%]$; simply the space for improvement is larger in such cases. The global results for all networks, strategies, parameters and random binary choices for each edge to propagate information or not across this edge made at the simulation initialization yield better values of $C_{SQ}$ than of $C_{SN}$ in 96.7% of cases. The increase over 5% was achieved in 20.2% of cases. The results were dependent on node ranking strategy with 96.0% better results for random rankings, 100% for degree based rankings and 93.9% for greedy approach based ranking. The improvement over 5% was observed for 11.2% cases for random strategy and as much as 38.7% cases for degree-based selection and 10.9% for greedy method. It should be also noted that, surprisingly, the random selection performs slightly better than the expensive greedy selection. Results for individual cases with respect to maximum coverage are presented in Fig. 1(B). The sequential results are localized above the single stage border, filling the space towards maximum (100%). The dispersion is the highest for degree based rankings Fig. 1(B1). The lowest dispersion of results is observed for random based node selection, see Fig. 1(B2). Moreover, if the single stage coverage is at least at the level of 90%, all strategies are able to provide sequential cases very close to maximum. For lower coverage, only degree-based rankings can improve results so much. The results revealed an important phenomenon: sequential seeding based on degree selection in 92.2% of cases outperforms single stage greedy approach. A similar improvement is also observed for the averaged values. It means that sequential approach almost always is able to boost performance of the simple degree-based ranking over computationally expensive greedy heuristic. Moreover, $C_{degreeSQ}$ is greater than $C_{greedySQ}$ in 62.6% of cases but for single stage methods such superiority can be observed in only 0.01% of cases. Hence, the main finding is that the computationally ineffective greedy strategy is suitable for single stage approach, while degree based selection for sequential seeding is significantly better than other selection methods. In general, the obtained results were dependent on the network profile and parameters of the diffusion. Space between the maximum coverage $C_{Max}$ and the single stage seeding $C_{SN}$ is an area in which sequential approaches deliver improvement. This area on average is $(C_{Max} - C_{SN})/C_{SN}$ so only 25%, of the all simulation cases. To evaluate the improvement, a gain measure $G$ was defined; it is based on average coverage values: $$G = ((C_{SQ} - C_{SN})/(C_{Max} - C_{SN})) \times 100\%.$$ It shows what part of the improvement area is reachable by sequential approach. Depending on process parameters and network, the gain varies from 30% to 83%. In general, the greater propagation probability value, the greater coverage and gain, see Fig. 1(C). The same phenomenon arises for seeding percentages, as seen in Fig. 1(D). Regarding node selection strategies, the highest average gain 74% was observed for degree based selection, while for greedy and random strategies it is much lower: 27% and 33% respectively, as shown in Fig. 1(E). The gain strongly depends on network structure, see Fig. 1(F). The highest gain (83%) was achieved for network N6, whereas the least gain (30%) was achieved for network N3. Results Experimental results for directed networks As in case of undirected networks, coordinated execution experiments for a real directed network were run to analyze gain from sequential seeding compared to greedy approach and maximal possible coverage. Since they requires computationally expensive search for the optimal seed sets, only a small network with 16 nodes and 58 edges was used [25]. Following the coordinated execution principles, 10k instances of the network were randomly generated to assign binary choices of propagation or not for each directed edge, i.e., independently for $a \rightarrow b$ and $b \rightarrow a$ activation. One of these instances is presented in Fig 2. For each instance and propagation probability PP, an optimal 4-node seed set was computed to estimate the maximum coverage for this instance and PP. Results for all probabilities and ranking strategies (degree, greedy, random) show that the highest increase of coverage was observed for the sequential degree based selection, see Fig. 3 (B), (D). Moreover, the sequential approach with the degree rankings delivered better results than greedy-based selection regardless if used in single stage or sequential mode, as shown in Fig. 3 (A), (D). It means that the degree approach should be among the first choices considered when selecting the node ranking method. The average performance (gain in coverage) is strongly dependent on propagation probabilities (PP) and it increases with PP values, see Fig. 3 (C), even though higher probabilities leave less space for improvements, since they also raise the single stage coverage. This effect is present for all selection strategies. The reason is that although the processes with high PP reaches more than 80% of nodes for all strategies and the area for gain is much smaller, the savings from the sequential approaches are even greater than for smaller PP’s, as shown in Fig. 3 (E), benefiting the final results. In general, the sequential approach enables us to save seeds and allocate them to other network regions. This gain varies for different propagation probabilities and ranking strategies, as shown in Fig. 3 (E), and it comes from activation of seed candidates by inter-stage diffusion. The degree ranking reveals its superiority over other ranking methods also in seed saving, which may, in fact, be the reason why the sequential degree method outperforms the single stage greedy, as seen in Fig. 3 (A). More than 25% of seeds can be saved even for smallest propagation probabilities and up to 48% for PP=0.25 and degree-based selection. These results may guide future research on methods to find the minimal number of seeds used sequentially to achieve the same coverage as in the single stage seeding. Overall, the main findings for directed networks are similar to the ones for undirected graphs: (1) sequential approach almost always significantly increases coverage of spreading and reaches beyond the current limits (never makes it worse), (2) sequential degree-based selection is commonly better than the greedy selection and (3) it is often close to the maximum, (4) usually, the greater propagation probability, the greater gain, and (5) sequential approach enables us to replace some of the initial seeds with the additional ones thereby increasing coverage, especially for greater PP and degree selection. Discussion The presented results lay firm foundation for the earlier studies related to sequential seeding and address currently unanswered research questions [21–23]. Averaging the coverage obtained by the typical agent based simulations delivers improvement in about 90% of the cases [21], the formal proof relying on the coordinated execution and corroborated by the new empirical studies shows that sequential seeding delivers at least as large coverage as the widely used single stage seeding; under modest assumption this coverage is provably larger. The performance of sequential seeding is compared with both greedy seed selection (which may be treated as the current limit) and the optimal seed set providing maximal possible coverage for a given number of seeds and the given network configuration. Experiments were performed for directed and undirected networks by means of independent cascades model [1]. Sequential usage of seeds selected by the simplest degree-based heuristics delivers better coverage than the greedy algorithm used in the single stage mode. However, coverage achieved by the greedy selection can also be further improved, if seeds are used sequentially instead of being all activated at the beginning of execution, even though the resulting coverage still remains worse than the one that the sequential degree selection delivers. Overall, the results confirm that sequential allocation of seeds improves the coverage of information diffusion in both directed and undirected complex networks. The measure of improvements provided by this approach is showed. It helps to substitute seeding nodes activated by diffusion by selecting new seeds based Figure 2: One of the experimental cases for the directed network (run 4336) with the number of seeds $n = 4$ and the propagation probability $PP = 0.05$. For clarity and high network density only edges assigned the random choice of propagating information for them by coordinated execution are shown. Degree- and greedy-based rankings are computed for the full initial network with all edges. (A) Single stage seeding (SN) with degree-based ranking, the coverage $C_{SN} = 6$, a diffusion cascade is visible when node 11 activates nodes 9 and 10. (B) Diffusion with sequential seeding and degree-based selection; the ranking is the same as in (A); one seed is activated in each of four stages; in the first stage node 6 is activated according to its highest degree. It activates node 11 which in turn activates nodes 15 and 9; finally, node 9 activates node 10 and diffusion stops. The two seeds used in (A) are already activated by diffusion in this case. In the second stage node 16 is selected since it has the highest degree among not activated yet nodes. Its only neighbor, node 11, is already active so the process stops. In the next stage node 1 is selected as a seed but it lacks active edges so diffusion cannot progress. Fourth seed is node 12 and it activates node 14. Sequential seeding avoids using nodes 11 and 15 seeds which are activated as seeds in single stage seeding. This allow sequential seeding to activate two more seeds and three more nodes in total compared to single stage seeding. (C) Single stage seeding with greedy-based ranking and coverage $C_{SN} = 7$. (D) Single stage seeding based on the seed set optimal for this individual case, including knowledge of which edges are active for propagation, with the resulting coverage $C_{SN} = 11$. on node’s ranking which may activate new regions, see Fig. 2 (B). As a result, sequential seeding commonly provides better coverage than the single stage approach, no matter which initial node selection strategy is used. In the worst case, the results remain the same but the experimental studies show that it happens in fewer than 10% of all cases. For single stage mode the greedy approach is commonly better than typical ranking selections based on structural measures, e.g. degree and it can be treated as the method defining the current limit. However, it requires extensive prior simulations, which in practice are hardly possible due to (1) high computational complexity, and (2) feasibility of simulations for real data – very rarely we can run thousands of diffusion processes when the results need to be delivered in the real-time of the campaign. Sequential seeding outperforms the greedy search method. Moreover, sequential seeding using structural network measures like degree, for seed selection yields coverage greater than obtained by greedy, without necessity of any prior simulations. In our experiments, it happened in over 92% of cases. It appears that using degree-based rankings with sequential strategy is better than using the computationally expensive greedy approach. We observed that the main factor that defines performance of sequential seeding versus single stage seeding is to what extent seed selection method avoids selecting nodes that will be activated through diffusion. The gain of sequential seeding arises when the selected seed to be activated in the current stage is already active. In such a case, this seed is removed from the seed list and replaced by a highest ranking node which is not yet activated. It should be noted that we compare the resulting coverage with the real maximum coverage, which very often is much lower than the theoretical upper bound for the average maximum coverage suggested in [1,26], see red line in Fig. 1(A1) and 3(A). Presented study has several implications for practice. Instead of introducing the product to large number of customers at the outset of commercial campaign, better strategy is seeding a small fraction of nodes and giving the chance to natural diffusion driven by social influence mechanisms to spread the content. Marketing budgets can be optimized if additional seeds are utilized only if campaign fails and revival is needed. Moreover, the knowledge gain from the initial spreading may improve seed selection for revival. Increased coverage of spreading might be crucial for campaigns with limited budgets, such as spreading security information, or disease warnings and awareness. During massive campaigns habituation phenomenon can arise among customers resistant to marketing messages. It can be avoided by limiting the intensity of marketing activity. While campaigns with higher intensity can be perceived negatively as unsolicited massive communication, sequential strategies may avoid making such negative impact on customers. Sequential seeding is also a low risk strategy with possible high gains because, as we proved, results will never be worse when compared to single stage seeding. Figure 3: The directed network: (A) Performance of sequential SQ and single stage seeding SN with degree-based ranking in comparison with maximum coverage; (B) The coverage achieved by sequential strategies in comparison to coverage obtained by a single stage approach; (C) Averaged gain for all used propagation probabilities; (D) Averaged gain for node ranking strategies based on random, greedy and degree selections; (E) Percentage of saved seeds for degree, random and greedy based selections. Figure 4: Diffusion processes for the number of seeds $n = 3$; the classical single stage method (SN) compared with sequential seeding strategy (SQ). Methods Independent cascade model We consider an independent cascade that is a stochastic diffusion model of information spread in the network initiated by seeds [1]. A basic, commonly used, single stage seeding (SN) consists of only one activation stage in which the fixed number of $n$ seeds are activated, see Table 1. They initiate diffusion which runs until no more nodes can be activated. In the independent cascade model each diffusion step consists of a single attempt by all nodes activated in the previous step, to activate their direct not yet active neighbors with a given propagation probability (PP). We measure diffusion time in the number of such steps, assuming that each lasts a unit of execution time. Sequential seeding Let $T_{SN}$ denote the time the whole process of the single stage seeding lasts, see Fig. 4. Often, some seeds activated at the beginning could have been naturally activated later on. The sequential seeding strategy (SQ) uses the same number of seeds $n$ as SN [21]. Its idea is to take the same initial ranking of nodes as in case of single stage seeding, but activate them sequentially in $n$ consecutive stages each with one seed activated. After each activation, the diffusion proceeds. The next activation is suspended until the current diffusion process stops, i.e., when the last diffusion step does not increase the coverage. In the independent cascade model, each recently activated node has only one chance to infect its neighbors. Hence, if the diffusion stops, the only way to continue activation is activating a seed. In the sequential method, it is the highest ranking node not yet activated. It means that nodes already activated by diffusion are omitted. The gain of sequential approach comes from the new areas activated by additional seeds substituting the already activated ones. Hence, the set of seeds activated in sequential seeding often differs from the one activated in the single stage approach. Sequential approach may be applied to any initial node ranking computed once at the beginning of the process. Such ranking may utilize random choice, any structural measures like commonly used degree or any other heuristic, e.g., greedy [1][26]. Some questions arise here: what is the increased coverage $C_{SQ}$; is $C_{SQ}$ always greater than $C_{SN}$ and what is the gain achieved comparing with the estimate of the maximum coverage $C_{Max}$ for a given configuration. Coordinated execution and maximal coverage The need often arises to compare algorithms which during execution make random choices, e.g., to break ties, simulate random outcomes according to the given distribution, or are randomized in nature. In such cases often average values of performance are measured over many runs of each algorithm and used for comparison between them. Here, we propose coordinated execution as the more direct alternative, in which we compare performance of runs with the same choices made during executions with different algorithms, providing run by run comparison of the results. This requires that all random choices are made and recorded before each run for all compared algorithms. The subsequent runs for comparison of algorithms simply execute preprocessing of choices with unique seeds for random number generator. When applied to comparing various seeding methods uses, the coordinated execution requires that each node activated in any execution makes the same edge diffusion transmission decision. To ensure that all edges randomly select their activity status before the coordinated executions are run for all variants of single stage and sequential strategies. It enables us to make fair comparisons between different seeding strategies. Coordinated execution in the undirected network uses only one edge between two nodes. A propagation probability between two nodes $a \rightarrow b$ is the same as for $b \rightarrow a$ transmission. Coordinated execution in directed network replaces each edge with two directed edges, and then decides which directed edges will be activated in diffusion. The edge states are sampled from the binary set $\{0, 1\}$ with state 1 being chosen with uniform probability PP. Edges assigned value of 0 are removed, while edges with value 1 stay, creating an instance of an active edge graph. Two instances of execution of sequential and single stage methods are coordinated if all edges originating from node activated in both instances have the same states. Such coordinated instances are used to compute the maximum coverage $C_{Max}$ for a given network and active edge choices. Such computation requires identification of all connected components in the active edge graph, which can be done in $O(e)$ steps, where $e$ is the number of active edges. Then, the maximum coverage $C_{Max}$ for a given seed size $n$ is equal to the total number of nodes within $n$ largest components. Many instances of active edge graph are then created by simply using a different random number generator seed for each instance. The number of instances needed to collect the reliable estimate of the average coverage of the tested seeding methods is provided in [26]. Computing the average of the maximum coverage over these instances provides a reliable estimate of an upper bound for the maximum average coverage of any seeding method. As shown in Fig. 1 (A1) and 3 (A), this upper bound is in most cases tighter than the one derived from the greedy seed selection. Formal proof of non-decreasing coverage In a formal proof, we show that the sequential seeding always provides at least as large coverage as the classical single stage approach does. Using coordinated execution, we also demonstrate that under modest assumptions the former approach is provably better than the latter when both use the same number of seeds and node ranking method. To do that, we demonstrate that there exist network configurations for which sequential seeding coverage is larger than the coverage yielded by the single stage seeding. Configurations are defined at simulation initialization by choosing randomly the diffusion transmission status for each edge. Theorem: For arbitrary node ranking and number of seeds, a sequential seeding execution has at least the same coverage $C_{SQ}$ as the corresponding single stage execution $C_{SN}$ coordinated with it. Moreover, if there is an initial seed $u$ which is reachable in the original graph from a seed $s$ with rank lower than rank of $u$, then there exists a configuration of the original graph for which the coverage for sequential seeding is larger than it is for single stage seeding. Proof: For clarity, we assume that seeds are activated in the increasing order of their ranks. We start by observing that in sequential seeding, the seed ranked $r$ is activated no later than in stage $r$. It can be activated in the earlier stage either by diffusion or by having a seed with rank lower than $ r $ activated by diffusion, thereby decreasing the ranks of all seeds ranked higher than the activated seed. If neither of these two cases happens before stage $ r $ starts, in this stage, the seed ranked $ r $ will be the highest ranking not yet activated seed and therefore it will be chosen for activation. We observe also that not yet activated node will be activated by diffusion in a single stage execution of a given configuration if and only if this node is reachable from a seed by the edges active in this configuration. Indeed, if a node $ m $ is reachable from a seed, this seed will be activated in the first and only stage of activation. Then, by the rules of diffusion, this seed’s activation cascade will reach node $ m $ and activate it, if it is still non-active. Conversely, the seed activated in step $ t $ of diffusion in sequential seeding activates only not yet activated nodes that are distance $ t $ from it. The upper bound for the number of diffusion steps before the diffusion stops is the diameter of the configuration. Hence, no node that is not reachable from any seed in the given configuration will be activated by diffusion. Since in sequential seeding all original seeds will be activated no later than by stage $ n $, all nodes reachable from these seeds will also be activated by this stage, proving the first part of the Theorem. Regarding the second part of the Theorem, let $ H $ be a configuration in which all the edges on the reachability path from seed $ s $ to node $ u $ defined in the Theorem are active. At the end of stage $ n - 1 $ of sequential execution of configuration $ H $, all seeds activated in the single stage seeding are activated. Indeed by definition, all seeds ranked $ n - 1 $ has to be activated by then, and the seed of rank $ n $ has to be activated either by diffusion from seed $ s $ when rank of $ u $ is $ n $ or by lowering of its rank by activation of seed $ u $ from seed $ s $ when rank of $ u $ is less than $ n $. Consequently, diffusion at stage $ n - 1 $ comes from all seeds, and therefore all nodes activated in single stage seeding will be activated in sequential seeding by then. In the next stage $ n $, not yet activated node will be activated as a seed, making the overall coverage of the sequential seeding larger for this configuration than the coverage of the single stage seeding; QED. Greedy seed set search Greedy method requires many simulations to estimate the potential of a single node, i.e., its ability to activate other nodes via diffusion [1,26]. Here, the greedy method is based on approach presented in [26]. Averaged results of the greedy algorithm (coverage $ C_{\text{greedy}} $ - the average total number of nodes activated by the process) are no worse than $ C_{\text{Max}} \ast (1 - 1/e) $, where $ C_{\text{Max}} $ is the expected maximum coverage [26]. It means that the greedy approach also defines the theoretical upper bound for maximum coverage: $ C_{\text{greedy}} \ast e / (e - 1) $. Due to its great coverage, the greedy algorithm is currently treated as the benchmark to beat and reference to. Since it requires prior simulations to compute the node potential, it is also very inefficient thus hardly applicable in practice, especially for large networks. Experimental setup: undirected networks The experiments were carried out on six real complex networks: N1 - Condensed Matter collaboration [27], N2 - Communication network at University of California [28], N3 - High-Energy Theory collaboration network [29], N4 - Political blogs [30], N5 - ego-Facebook [31] and N6 - wiki-Vote [32]. The parameters used in experimental configurations define diffusion, networks and seed selection strategy as shown in Table 2. Three commonly used strategies were exploited: the highest degree, greedy [26] and random selection. Simulation parameters create configuration space $ N \times PP \times SP \times R $ with 162 configurations, each were independently applied to both single stage (SN) and sequential seeding strategies (SQ) using coordinated execution repeated 50,000 times, resulting in 16250,0002=16,200,000 simulation cases; 8,100,000 cases for each single stage and sequential strategies. For the greedy approach, finding the seed sets required another 10,000 simulations computed independently for each configuration, as defined in [1,26]. The nodes were ranked according to their average coverage \| Parameter \| Values \| Variants \| \|---------------------------------\|--------\|--------------\| \| Network - N \| 6 \| N1-N6 real networks \| \| Propagation probability - PP \| 3 \| 0.05, 0.1, 0.20 \| \| Seeds percentage - SP \| 3 \| 1%, 3%, 5% \| \| Seed ranking strategy - R \| 3 \| random, degree, greedy \| Table 2: Configuration space of the simulated diffusion processes over all 10,000 simulations; a separate greedy ranking was computed for each of the 162 parameter combinations. Statistical tests The positive gain of sequential approach (SQ) over single stage (SN) for experiments on undirected networks was also confirmed by the Wilcoxon signed rank test, with $ p<2.2e-16 $ and $ \Delta = 1.9 $, with the Hodges-Lehmann estimator used as a difference measure. Values $ \Delta > 0 $ demonstrate significantly larger coverage for $ C_{SQ} $ than $ C_{SN} $. Regarding seeding strategies based on node ranking methods, sequential approach increases coverage for random ranking on average by 3.2\%, with $ p<2.2e-16 $ and $ \Delta = 1.6 $. Sequential seeding based on degree delivered coverage results 15.5\% better than single stage seeding, with $ p$-value<2.2e-16 and $ \Delta = 4.2 $. For sequential seeding and greedy based ranking 2.5\% average coverage improvement was achieved with $ p$-value<2.2e-16 and $ \Delta = 0.7 $. Experimental setup: a directed network As much as 10,000 instances of coordinated execution for the small real network of 16 nodes were randomly selected, to ensure stability of the solutions; further instances would not affect results [1]. Due to a small number of network nodes, only four seeds were used arbitrarily. Five propagation probabilities (PP) with values 0.05, 0.1, 0.15, 0.2 and 0.25 were applied. Similarly to the undirected version, three ranking strategies were analyzed: degree, greedy and random. 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Acknowledgment This work was partially supported by the National Science Centre, Poland, grant no. 2017/27/B/HS4/01216 (JJ), 2016/21/B/ST6/01463 (PK), 2015/17/D/ST6/04046 (RM), and 2016/21/D/ST6/02408 (PB), the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 691152 (RENOIR); the Polish Ministry of Science and Higher Education fund for supporting internationally co-financed projects in 2016–2019 (agreement no. 3628/H2020/2016/2); the Army Research Laboratory under Cooperative Agreement Number W911NF-09-2-0053 (the ARL Network Science CTA); and the Office of Naval Research Grant No. N00014-15-1-2640. Author contributions Author contributions: All authors contributed to the study design and manuscript preparation, BKS contributed proof of sequential seeding properties and the concept of coordinated execution, both JJ and RM conducted simulations and analyzed the data, PB prepared illustrative simulation cases. Competing interests Authors declare no conflict of interest. Supplementary Information Experimental results for undirected networks Each from 162 combinations from configuration space $N \times PP \times SP \times R$ was applied as a simulation configuration to single stage SN and sequential seeding SQ with the use of coordinated execution. Repeated simulations resulted in 16,200,000 simulation cases. Results from individual simulation cases are presented in Fig. 5 (A). They show that $C_{SQ}$ performs better than $C_{SN}$ for most cases with coverage $C_{SQ} \in [30\%, 85\%]$. Fig. 5 (B) shows coverage for sequential approaches $C_{SQ}$ compared to single stage methods $C_{SN}$. The maximum coverage $C_{Max}$ for optimal seed set is presented as well as the upper bound $C_{GreedySN} \ast e/(e-1)$ for all cases. The results show that sequential seeding based on simple degree-based ranking in 92.2% of cases outperforms single stage computationally expensive greedy heuristic, see Fig. 5 (B1). Moreover, sequential seeding based on degree $C_{degreeSQ}$ is greater than sequential greedy approach $C_{greedySQ}$ in 62.6% of cases. For all simulation cases $C_{SQ}$ shows better results than $C_{SN}$ in 96.7% of cases what as presented in Fig. 5 (C). Increase above 5% was achieved in 20.2% of simulation cases. The obtained coverage was dependent on seed selection strategy with 96.0% better results for random selection, 100% for degree based selection and 93.9% for greedy based selection, see Fig. 5 (C1). Fig. 5 (D) shows one of real diffusion cases with visible differences between sequential (SQ) and single stage seeding (SN). As a result of better usage of natural diffusion processes sequential approach outperforms the single stage approach. Apart from user rankings the results were dependent on the network characteristics with visible differences seen in Fig. 5 (E). Network N6 delivered the highest gain (83%) while the least gain (30%) was achieved for network N3. Figure 5: (A) Coverage for sequential approach $C_{SQ}$ compared with single stage $C_{SN}$ and maximum coverage $C_{Max}$ for all configurations and all simulation cases; ordered by $C_{SN}$; (B) Coverage as percentage of all activated network nodes for greedy and degree-based single stage and sequential strategies and their relation to $C_{Max}$ and the upper bound; ordered by $C_{SN}$; (B1) Performance of sequential and single stage approaches with degree-based selection in relation to single stage greedy ranking; (C) Performance of sequential seeding $SQ$ in the relation to single stage seeding $SN$, a vertical tick denotes percentage of cases with no gain: $C_{SQ} = C_{SN}$; (C1) Performance of random, degree and greedy based sequential seeding compared with single stage seeding $SN$; (D) Steps of one sequential and one single stage diffusion process in the coordinated execution for one configuration; (E) Coverage values for sequential $C_{SQ}$ and single stage seeding $C_{SN}$ as well as maximum coverage $C_{Max}$ for networks N1-N6 and all simulation cases. Experimental results for directed network Performance of sequential seeding within directed network was analyzed for random node selection, degree based selection and greedy approach. Detailed results for all used probabilities and strategies for single stage and sequential seeding are presented in Table 3. The highest increase of coverage was observed for sequential degree based selection with results better than greedy selection for both single and sequential seeding. The highest gain for degree based selection was observed for low propagation probabilities 0.05, 0.01, 0.15. For higher probabilities differences between strategies are smaller. ### Coverage for random seed selection \| PP \| Single stage \| % of Max \| Sequential \| Increase \| Gain \| \|-----\|--------------\|----------\|------------\|----------\|-------\| \| 0.05\| 5.43 \| 62.2% \| 5.67 \| 1.04 \| 7.4% \| \| 0.1 \| 7.43 \| 61.5% \| 8.17 \| 1.09 \| 16.0% \| \| 0.15\| 9.65 \| 67.4% \| 11.03 \| 1.14 \| 29.5% \| \| 0.2 \| 11.76 \| 75.9% \| 13.56 \| 1.15 \| 48.3% \| \| 0.25\| 13.34 \| 83.9% \| 15.07 \| 1.13 \| 68.0% \| ### Coverage for degree based seed selection \| PP \| Single stage \| % of Max \| Sequential \| Increase \| Gain \| \|-----\|--------------\|----------\|------------\|----------\|-------\| \| 0.05\| 5.59 \| 64.0% \| 5.99 \| 1.07 \| 12.5% \| \| 0.1 \| 7.54 \| 62.4% \| 8.60 \| 1.15 \| 23.4% \| \| 0.15\| 9.56 \| 66.7% \| 11.39 \| 1.21 \| 38.5% \| \| 0.2 \| 11.45 \| 73.9% \| 13.75 \| 1.22 \| 57.0% \| \| 0.25\| 12.96 \| 81.5% \| 15.14 \| 1.19 \| 74.5% \| ### Coverage for greedy seed selection \| PP \| Single stage \| % of Max \| Sequential \| Increase \| Gain \| \|-----\|--------------\|----------\|------------\|----------\|-------\| \| 0.05\| 5.73 \| 65.6% \| 5.88 \| 1.02 \| 5.0% \| \| 0.1 \| 7.88 \| 65.2% \| 8.47 \| 1.08 \| 14.2% \| \| 0.15\| 10.14 \| 70.8% \| 11.08 \| 1.09 \| 22.4% \| \| 0.2 \| 12.22 \| 78.9% \| 13.59 \| 1.12 \| 42.0% \| \| 0.25\| 13.72 \| 86.3% \| 15.09 \| 1.11 \| 62.9% \| Table 3: Coverage for single stage and sequential seeding for used seed selection methods and propagation probabilities \| No. \| Network name \| Ref \| Nodes \| Edges \| Edge type \| Components \| CC \| Diameter \| \|-----\|----------------------------------------------\|-----\|--------\|---------\|-----------\|------------\|---------\|----------\| \| 1 \| N1 - Condensed Matter collaboration \| [27] \| 16,264 \| 47,594 \| Undirected\| 726 \| 0.638 \| 18 \| \| 2 \| N2 - Communication network at University of California \| [28] \| 1,899 \| 20,296 \| Undirected\| 4 \| 0.109 \| 8 \| \| 3 \| N3 - High-Energy Theory collaboration network \| [29] \| 7,610 \| 15,751 \| Undirected\| 581 \| 0.486 \| 19 \| \| 4 \| N4 - Political blogs \| [30] \| 1,224 \| 19,090 \| Undirected\| 2 \| 0.320 \| 8 \| \| 5 \| N5 - ego-Facebook \| [31] \| 4,039 \| 88,234 \| Undirected\| 1 \| 0.606 \| 8 \| \| 6 \| N6 - wiki-Vote \| [32] \| 7,115 \| 103,689 \| Undirected\| 24 \| 0.141 \| 7 \| \| 7 \| N7 - Social network of tribes \| [25] \| 16 \| 114 \| Directed \| 1 \| 0.519 \| 3 \| Table 4: Description of networks used in the experiments Figure 6: Degree distribution for networks N1-N6	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2264, 1 ], [ 2264, 6460, 2 ], [ 6460, 9737, 3 ], [ 9737, 13873, 4 ], [ 13873, 18449, 5 ], [ 18449, 20784, 6 ], [ 20784, 23919, 7 ], [ 23919, 26511, 8 ], [ 26511, 30960, 9 ], [ 30960, 35543, 10 ], [ 35543, 38408, 11 ], [ 38408, 41426, 12 ], [ 41426, 42978, 13 ], [ 42978, 45973, 14 ], [ 45973, 47709, 15 ], [ 47709, 49344, 16 ], [ 49344, 50610, 17 ] ] }
277ae019cd94f8e8a3d3dfb616d45c9959902609	{ "olmocr-version": "0.1.59", "pdf-total-pages": 6, "total-fallback-pages": 0, "total-input-tokens": 31120, "total-output-tokens": 11867, "fieldofstudy": [ "Computer Science" ] }	Abstract—Tensors are a fundamental operation in distributed computing, e.g., machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall completion time. Recent works in coded computing provide a novel strategy to mitigate stragglers with coded tasks, with an objective of minimizing the number of tasks needed to recover the overall result, known as the recovery threshold. However, we demonstrate that this strict combinatorial definition does not directly optimize the probability of failure. In this paper, we focus on the most likely event and measure the optimality of a coding scheme more directly by its probability of decoding. Our probabilistic approach leads us to a practical construction of random codes for matrix multiplication, i.e., locally random alloy codes, which are optimal with respect to the measures. Furthermore, the probabilistic approach allows us to discover a surprising impossibility theorem about both random and deterministic coded distributed tensors. I. INTRODUCTION Machine learning has become a dominant tool in the broader computing community. Its success has been due to the availability of large datasets and more recently the use of hardware optimized to perform multi-linear functions such as GPU’s and TPU’s, which are a fundamental building block for a large number of deep neural network architectures. If the dataset has many data points then the overall computation, or job, is distributed as tasks amongst workers, which model a distributed network of computing devices. This solution creates a new problem; stragglers and other faults can severely impact the performance and overall training time. The model we consider is the master-worker model of distributed computing where there is a centralized node, i.e., the master, which sends out the computational tasks to the workers and then receives their results. This paper offers a novel information-theoretic approach for analyzing the communication complexity of distributed fault-tolerant tensors computation and matrix multiplication in this model. Our scheme leads us to construct two families of practical code constructions which we call the globally random alloy codes and the locally random alloy codes; furthermore, we prove that our constructions give better performance than many benchmarks, e.g., the state-of-the-art algorithms in coded distributed computing. Our algorithm gives an explicit construction that archives the theoretical bound in [1] with (arbitrarily) high probability. We give an implementation that achieves a (probabilistic) bound of $ O(x^{1-\alpha}) $ for matrix multiplication of two $ x \times x $ block matrices, where $ \alpha = 0.321334... $ is the current bound for the dual exponent given in [2]. We consider schemes that satisfy the weaker but more general condition “with probability close to 1, results from the first $ k $ out of $ n $ workers allow the algorithm to terminate correctly”; i.e., this paper considers the typical fault pattern. Our main contributions are: 1) constructing random codes that work for arbitrary fields (cf. [3] which only works for characteristic 0 fields), 2) constructing codes that allow for more than $ q $ evaluation points over a finite field, 3) proving that a very large class of outer product codes do not exist over finite fields, and 4) constructing codes that can use less than a factor of 2 many machines in comparison with their un-coded algorithm (cf. [1] which needs at least 2 times as many machines in comparison to their uncoded counterpart). A. Motivating examples: initial demonstration of alloy codes Suppose that we wish to multiply matrices $ A = \begin{pmatrix} A_1 & A_2 \end{pmatrix}^T, B = \begin{pmatrix} B_1 & B_2 \end{pmatrix} $. If we have 5 or more workers (i.e., $ n \geq 5 $), then we can give worker $ k $ the coded task \[ \left( (gA_1)^k_1 A_1 + (gA_1)^k_2 A_2 \right) \left( (gB_1)^k_1 B_1 + (gB_2)^k_2 B_2 \right) \] where the $ g^k $ are i.i.d. according to the distribution in Eq. 5. Then the workers will return the values \[ (gC)^k_{i,j} A_i B_j := (gA_1)^k_i (gB_1)^k_j A_i B_j. \] We will see in Thm. 2 that: the probability of the $(gC)^k_{i,j}$ being an invertible matrix, where $ k $ indexes the rows and the $(i,j)$ indexes the columns, gets arbitrarily close to 1 for a large enough field size $ q $; and that this coding scheme works for all fields, e.g., in the case of bytes (i.e., $ 2^8 $) the probability for this example is 0.99 (i.e., it gets close to 1 fast). In particular, any 4 workers allow us to solve the linear system given by $ gC $. We will see that the coefficients $(gA)^k_i, (gB)^k_j, (gC)^k_{i,j}$ form what we term a globally random alloy code and satisfy the relationship: \[ gC = \begin{pmatrix} (gA)^1_1 (gB)^1_1 & (gA)^1_1 (gB)^1_2 & (gA)^1_2 (gB)^1_1 & (gA)^1_2 (gB)^1_2 \\ (gA)^1_1 (gB)^2_1 & (gA)^1_1 (gB)^2_2 & (gA)^1_2 (gB)^2_1 & (gA)^1_2 (gB)^2_2 \\ ... & ... & ... & ... \end{pmatrix}. \] To illustrate the simplest form of locally random alloy code, suppose that instead want to multiply the following: \[ A = \begin{pmatrix} A_{1,1} & A_{1,2} & A_{1,3} & A_{1,4} \\ A_{2,1} & A_{2,2} & A_{2,3} & A_{2,4} \end{pmatrix}, \quad B = \begin{pmatrix} B_{1,1} & B_{1,2} & B_{1,3} & B_{1,4} \\ B_{2,1} & B_{2,2} & B_{2,3} & B_{2,4} \end{pmatrix}. \] If we let \[ A^1 = \begin{pmatrix} A_{1,1} & A_{2,1} \end{pmatrix}, \quad A^2 = \begin{pmatrix} A_{1,2} & A_{2,2} \end{pmatrix}, \quad A^3 = \begin{pmatrix} A_{1,3} & A_{2,3} \end{pmatrix}, \quad A^4 = \begin{pmatrix} A_{1,4} & A_{2,4} \end{pmatrix}, \] \[ B^1 = \begin{pmatrix} B_{1,1} & B_{1,2} \end{pmatrix}, \quad B^2 = \begin{pmatrix} B_{1,3} & B_{1,4} \end{pmatrix}, \quad B^3 = \begin{pmatrix} B_{2,1} & B_{2,2} \end{pmatrix}, \quad B^4 = \begin{pmatrix} B_{2,3} & B_{2,4} \end{pmatrix}, \] then Strassen’s algorithm gives $ AB = T_1 + \cdots + T_7 $, where \[ T_1 = (A^1 + A^4)(B^1 + B^4), \quad T_2 = (A^1 + A^4)B^1, \quad T_3 = A^1(B^2 - B^4), \quad T_4 = A^4(B^3 - B^5), \] \[ T_5 = (A^1 + A^4)B^2, \quad T_6 = (A^3 - A^4)(B^1 + B^2), \quad T_7 = (A^2 - A^4)(B^3 + B^4). \] Conversely, there are fault patterns where the recovery threshold for the locally random alloy code is less than $ \text{Entangled Polynomial} (EP) $. Furthermore, the master can drop communication with workers returning useless data so that the master always can receive a maximum of 28 results from the workers. In fact, suppose that the total number of workers is 35. We will see that the recovery threshold for the locally random alloy code is 34, since there exists a fault pattern that returns 5 workers from groups $ T_1 $ through $ T_6 $ and only 3 from the last group $ T_7 $; however, fault patterns of this type are highly improbable. Conversely, there are fault patterns where 28, 29, 30, 31, 32, 34 and 35 workers can compute the product; however, for the EP codes [1], only the patterns with 33, 34, 35 workers returning will work. In this paper, we describe codes inspired by these examples. Before doing so, we set the notation to be used throughout. ### B. Background If $ A $ is a $ x \times z $ matrix with entries in $ F^{P \times R} $ (equivalently, $ A $ is a $ P \times zR $ matrix that has been partitioned into $ x \times z $ parts) and $ B $ is a $ z \times y $ matrix with entries in $ F^{R \times Q} $, then, if $ T $ is the matrix multiplication operator takes the form $ T : (F^{P \times R})^{x \times z} \times (F^{R \times Q})^{x \times y} \rightarrow (F^{P \times Q})^{x \times y} $, then we define the tensor rank as the smallest number $ r $ of $ x \times z $-dimensional linear functionals $ E_0^i : (F^{P \times R})^{x \times z} \rightarrow F^{P \times R} $, $ z \times y $-dimensional linear functionals $ E_1^i : (F^{R \times Q})^{x \times y} \rightarrow F^{R \times Q} $, and coefficients $ D_i \in F $ such that $ T(A, B) = \sum_{i \in [r]} D_i E_0^i(A) E_1^i(B) $. This modification is a straightforward modification of the usual definition and is implicitly used for recursive fast matrix multiplication algorithms. In practice, the parameters $ P, Q, R $ are determined by the amount of memory/computing power available at the worker nodes. Suppose we are given some family of subsets, $ R \subset [n] $, where $ n $ is the number of workers, which we take to be the recoverable subsets. Then we have a family of coefficients $ D_i^R $ so that the coded matrix multiplication tensor is given by \[ T_R(A, B) = \sum_{i \in R} D_i^R E_0^i(A) E_1^i(B). \] In particular, the master first encodes (and sends out) $ E_0^i(A), E_1^i(B) $ for all $ i $, then worker $ i $ computes $ E_0^i(A) E_1^i(B) $, and finally when some recoverable subset $ R $ of workers return, the master decodes by Eq. 1. This easily generalizes to higher order products \[ T_R(A_1, \ldots, A_t) = \sum_{i \in R} D_i^R \prod_{j \in [t]} E_j^i(A_j). \] The works [4]–[6] established the use of coding theory for distributed coded matrix-vector and vector-vector multiplication; shortly after and concurrently, the works [1], [7] further improved on these techniques by using alignment to come up with efficient constructions for general matrix-matrix multiplication. In particular, the authors of [1] established the equivalence of the recovery threshold for general partitions to the tensor rank of matrix multiplication (which they call the bilinear complexity). The most similar approaches to our work are the codes presented in [3] and the codes in [1] as well as the impossibility results in [8]. The works [6], [7], [9]–[15] also worked on improving coded distributed matrix multiplication. Further work has been extended to include batch matrix multiplication as well [16]–[19]. The work [20] considered the extra constraint of private/secure multiplication and the work [21] considered a trade-off between the size of the entries of the matrix and the recovery threshold, and parallel integer multiplication [22]. The works [23], [24] considered coding for distributed gradient descent in machine learning applications. The channel model used for the matrix multiplication problem is defined as a probability distribution $ p(Y = c \| X = a) $ where the random variables $ X $ and $ Y $ take values in the sets \[ X = \{ (a_1, a_2) : a_1 \in F_{PS}^x, a_2 \in F_{SQ}^y \} \subset F_{PS + SQ}^{x \times y}, \] \[ Y = \{ c = a_1 a_2 : a_1 \in F_{PS}^x, a_2 \in F_{SQ}^y \} \subset F_{PS}^x \cup \{ E \} \subset F_{PS}^{x \times y}. \] $ E $ is a placeholder symbol for an erasure (i.e., when a node in the network has a fault), $ a_1, a_2 $ are all matrices, and $ c $ is matrix multiplication. We call $ M = \{ (M_1, M_2) : M_1 \in F_{SQ}^P(zS), M_2 \in F_{PS}^y \} $ a set of message pairs, and $ M' = \{ M_1, M_2 : M_1 \in F_{SQ}^P(zS), M_2 \in F_{PS}^y \} $ the input message set and output message set respectively. $ A $ is a code of pairs of functions $ (E, D) $ where $ E : M \rightarrow X^n $ is the --- 1 The set of matrices that we wish to multiply and $ M' $ is their product; $ i.e., $ the values of $ M $ are $ (A, B) $ where $ A $ is an $ x \times z $ block matrix with blocks of size $ P \times R $ and $ B $ is an $ z \times y $ block matrix with blocks of size $ R \times Q $. The product has dimensions $ x \times y $ with blocks of size $ P \times Q $. encoder and $ D : Y^m \rightarrow M' $ is the decoder. The meaning of $ n $ is that we break down a large task $ M_1M_2 $ into a sequence of $ n $ multiplications $ a_1^1a_2^1, a_1^2a_2^2, \ldots, a_1^n a_2^n $ which corresponds to using the channel $ n $ times. We assume that each worker’s failure probability, $ p_f $, is i.i.d.; which is a weak assumption in a distributed environment with simple 1-round master-to-worker communication. For simplicity, we define Random codes as probability distributions over all possible codes $ C = (E, D) $. The deterministic case is a special case of the non-deterministic case. Tensor codes for matrix multiplication are codes of the form $ E = gA_1gB $ and $ D $ which solves the equation $ gC(A \cdot B)^{\text{flat}} = M $ where $ gA \ast gB = gC $. $ A, B $ are block matrices, and $ \text{flat} $ converts a matrix to a vector; i.e., \[ (gC)_{i,j} = (gA)_{i}^{k} (gB)_{j}^{k}, \] where $ k $ corresponds to the $ k^{th} $ worker. For higher order tensors the code is defined as \[ (gC)_{i_1, \ldots, i_k} = (gA_{i_1})_{i_1}^{k_1} \cdots (gA_{i_k})_{i_k}^{k_k}. \] It is important to note that the operation $ \ast $ is not matrix multiplication but instead defined by Eq. 2. Given $ C = (E,D) $ and the channel above, we define our probability of error as $ p^C_n(M_1M_2) := p(D(Y^n) \neq M_1M_2 \mid X^n = E(M_1, M_2)) $. A code $ C $ with $ M = \|M\| $ input messages, codewords of length $ n $, and probability of error $ \epsilon $ is said to be a $(M,n,\epsilon)$-code or $(M,n,\epsilon)$-code for short. We give the definition of the (computational) rate of a $(M,n)$-code as $ R = \frac{\log(\|M\|)}{\log(\|E\|)} = \frac{\log(\|M\|)}{\log(\|E\|)} $ where $ E $ is the set of output sequences with an erasure. The typical recovery threshold, $ R(x, y, z, p_f, \epsilon, C) $, is the number of workers needed for the code $ C $ to have less than $ \epsilon $ probability of error for a partition of type $ (x, y, z) $ if each worker has a probability of fault equal to $ p_f $. The typical recovery threshold and the rate satisfy the following relationship \[ R = \frac{\log(\|M\|)}{\log(\|E\|)} = \log(\|Y\| - 1) \frac{1}{R}. \] II. CODE CONSTRUCTIONS AND ANALYSIS Before giving the main construction we give the key lemma of this paper which computes the rank of a matrix whose rows are given by the flattening of rank 1 tensors. Theorem 1. Suppose that $(g^1, \ldots, g^d)$ are i.i.d. uniformly random rank 1 tensors where $ d = d_1 \cdot \cdots \cdot d_{\ell} $, and $(g)^k \in \mathbb{F}^{d_1} \otimes \cdots \otimes \mathbb{F}^{d_\ell} $. Let $ G $ be the matrix formed by flattening the $(g)^i $ and so that the $ i^{th} $ row of $ G $ is $ \text{flat}((g)^k) $. In particular, in the case where $ \ell = 2 $, we have that \[ (G)_{k, i d_2 + j} = (g)^k_{i,j} \] if we use standard matrix notation. If $ d_1 + \ldots + d_\ell \geq d_1 \cdot \cdots \cdot d_\ell $, then we have that the probability that $ G $ is full rank is greater than or equal to \[ \prod_{i \in [d]} \left( \prod_{j \in [\ell]} 1 - q^{-d_j} \right) - q^{-d_1 - \cdots - d_\ell}. \] Proof. For simplicity let us abuse notation and identify the tensor $ g $ with its flattening $ G $. Let $ N(k, d) $ be the number of $ k \times d $ full rank matrices whose rows are (a flattening of) rank 1 tensors (where $ k \leq d $). We proceed to prove that \[ N(k, d) \geq \prod_{i \in [k]} \left( \prod_{j \in [\ell]} q^{-d_j} - 1 \right) - q^k - 1 \] by induction. For the base case, a $ 1 \times d $ matrix $ g $ is full rank iff its first and only row $(g)^1$ is a non zero vector. There are a total of $ \prod_{i \in [\ell]} q^{-d_i} $ non-zero rank 1 vectors since $(g)^{1_i} = (g_1)^{1_i}, \ldots, (g_{\ell})^{1_i} $ for some $ g_i \in \mathbb{F}^{d_i} $ by definition and there are $ q^{d_1} - 1 $ choices for $(g)^1$, $ q^{d_2} - 1 $ choices for $(g)^2$ and so on we subtract out the 0 vector $(0, \ldots, 0) $ times. Now assume that \[ N(k + 1, d) \geq \prod_{i \in [k+1]} \left( \prod_{j \in [\ell]} q^{-d_j} - 1 \right) - q^{k+1} \] To make a full rank $ k + 1 $ row matrix we must first choose $ k $ many linearly independent rows of flattened rank 1 matrices and then for the choice of the $(k + 1)^{th} $ row we must subtract out all possible linear combinations of the previous $ k $ rows; this is bounded by $ q^{k+1} $. There are $ \prod_{i \in [\ell]} q^{-d_i} - 1 $ many such linear combinations and thus an induction gives us that \[ N(k + 1, d) \geq N(k, d) \left( \prod_{j \in [\ell]} q^{-d_j} - 1 \right) - q^{k+1} \] Finally the proof is completed by dividing the number of full rank matrices by the number of total matrices whose rows are flattened rank 1 tensors. Indeed, we have that the total number is equal to \[ T(k, d) = (q^{d_1 + \cdots + d_\ell})^k = \prod_{i \in [k]} q^{d_i + \cdots + d_{\ell}} \] since there are $ q^{d_i + \cdots + d_{\ell}} $ many choices for a row and each of the rows can be chosen independently and we have $ k $ many rows where we repeat the same sequences of choices and thus taking the ratio of the two we get the probability is equal to \[ \frac{N(k, d)}{T(k, d)} = \prod_{i \in [k]} \left( \prod_{j \in [\ell]} q^{-d_j} - 1 \right) - q^{k+1} \] \[ = \prod_{i \in [k]} \left( \prod_{j \in [\ell]} 1 - q^{-d_j} \right) - q^{-d_1 - \cdots - d_{\ell}} \] as was needed to be shown. A. Globally Random Alloy Codes for Order 2 Outer Products Consider the uniformly random 2-product distribution \[ p^(g_{j}^1, z) = \begin{cases} 1 - \sqrt{\frac{q-1}{q}} & \text{for } z = 0 \\ \frac{\sqrt{q(q-1)}}{q} & \text{for } z \neq 0. \end{cases} \] Then we can define our random codes as \[ \tilde{A}_k = \sum_{i \in [x]} (g_A)_i^k A_i, \quad \tilde{B}_k = \sum_{i \in [u]} (g_B)_i^k B_i, \] for matrix multiplication. The intuition behind the code construction is that we wish to define probability distributions for the coefficients of $ g_A $ and $ g_B $ in such a fashion that the resulting product code $ g_C $ is i.i.d. uniformly randomly distributed. If one were to naively encode the coefficients of $ g_A $ and $ g_B $ using the uniformly random distribution, then the resulting code $ g_C $ would be skewed towards 0. This is because 0 is not invertible and thus multiplication by zero does on form a permutation on $ \mathbb{F}_q $. By slightly skewing $ g_A $ and $ g_B $ towards non-zero coefficients, we get that the resulting coefficients of the code $ g_C $ is i.i.d. by the uniform random distribution. Since the decodability of the code only depends on the invertibility of $ g_C $, the only important distribution is the resulting product distribution; Thm. 2 gives us that this is exactly the case. Theorem 2 (Existence of Random Tensor Codes for Outer Products of Order 2).* There exists a probability distribution on $ g_A, g_B $ such that $ g_C = g_A \circ g_B $ has its coefficients uniformly i.i.d.; in particular, the probability of success for scheme over a finite field with $ q = p^k $ many elements is $ \prod_{i \in [d]} (1 - q^{1-i-d_i}) $, where $ d_1 $ is the maximum possible rank of $ g_C $. Proof. Taking the distribution $ p^* $ from Eq. 5 on $ g_A, g_B $ gives \[ p((g_C)_{ij}^k = z) = \sum_{g_A = x} p((g_A)_i^k = x) p((g_B)_j^k = y), \] so $ (g_C)_{ij}^k = (g_A)_i^k (g_B)_j^k $ and the $ p^_A, p^_B $ are independent. Since $ p^_A, p^_B $ are identically distributed, we can set \[ u = p^(g_j^k = 0) = 1 - \frac{q^{-1}}{q}, \] \[ (\forall z \neq 0) \quad v = p^(g_j^k = z) = \frac{1}{q(q-1)}, \] where we replace $ g_A, g_B $ with $ g $ above for simplicity (since they are identically distributed). A simple combinatorial argument gives us that \[ p^((g_C)_{ij}^k = z) = \begin{cases} u^2 + 2(q-1)uv & \text{for } z = 0 \\ (q-1)v^2 & \text{for } z \neq 0 \end{cases} \] Therefore, the probability of a 0 is equal to \[ p^((g_C)_{ij}^k = 0) = u^2 + 2(q-1)uv = \left(1 - \frac{q^{-1}}{q}\right)^2 + 2(q-1) \left(1 - \frac{q^{-1}}{q}\right) \left(\frac{1}{q(q-1)}\right) = \frac{1}{q}. \] Similarly, we have that \[ p^((g_C)_{ij}^k = z) = (q-1)v^2 = (q-1) \left(\frac{1}{q(q-1)}\right)^2 = \frac{1}{q}, \] for a non-zero $ z $. Because $ p^((g_C)_{ij}^k = z) $ is a function of the values $ p^((g_A)_i^k = 0), \ldots, p^((g_A)_i^k = q-1) $ and $ p^((g_B)_j^k = 0), \ldots, p^((g_B)_j^k = q-1) $ we have that $ k \neq k' $ implies that $ p^((g_C)_{ij}^k = z) $ and $ p^((g_C)_{ij}^{k'} = z) $ are independent. Thus, any two rows of $ g_C $ are independent. The proof is completed by applying Theorem 1, but in order to apply this theorem we must first show that our code does indeed generate random rank 1 tensors uniformly. If either $ i \neq i' $ or $ j \neq j' $, then $ p^((g_C)_{ij}^k = z) $ and $ p^((g_C)_{ij'}^{k'} = z) $ are independent. Thus if we fix an $ i $ (or respectively fix a $ j $) we have that $ p^((g_C)_{ij}^k = z) $ is a uniformly randomly generated over $ \mathbb{F}^{d_i} $, respectively $ \mathbb{F}^{d_j} $. Since this is true as we fix any $ i $ or $ j $ we have that for a fixed $ k $ every possible rank 1 tensor is generated with equal probability and Theorem 1 completes the proof. B. General Globally Random Alloy Codes of Order $ \ell $* If we let the uniformly random l-product tensor distribution, be defined as \[ p^(g_j^k = z) = \begin{cases} 1 - \sqrt[1]{q-1} & \text{for } z = 0 \\ \sqrt[1]{q(q-1)^\ell-1} & \text{for } z \neq 0 \end{cases} \] then we can define our random codes as \[ (\tilde{A}_1, \ldots, \tilde{A}_k) = \left( \sum_{i \in [x]} (g_A)_i^k A_{1,i}, \ldots, \sum_{i \in [x]} (g_A)_i^k A_{k,i} \right). \] Theorem 3 (Existence of Random Tensor Codes for Outer Products of Order $ \ell $).* There exists a probability distribution on $ g_A, \ldots, g_A $ such that $ g_C = g_A \circ \cdots \circ g_A $ has its coefficients uniformly i.i.d.; in particular, the probability of success for scheme over a finite field with $ q = p^k $ many elements is $ \prod_{i \in [d]} (1 - q^{1-i-d_i}) $, where $ d_1 $ is the maximum possible rank of $ g_C $. Proof. Taking the distribution $ p^* $ from Eq. 7 on $ g_A, g_B $ gives \[ p((g_C)_{ij}^k = z) = \sum_{x_1, \ldots, x_\ell = z} \prod_{i \in [\ell]} p((g_A)_i^k = x_i), \] so $ (g_C)_{ij}^k = (g_A)_i^k (g_C)_j^k $ and the $ p^_A, p^_B $ are independent. Since $ p^_A, p^_B $ are identically distributed, we can set \[ u = p^(g_j^k = 0) = 1 - \sqrt[1]{q-1} \] \[ (\forall z \neq 0) \quad v = p^(g_j^k = z) = \sqrt[1]{q(q-1)^\ell-1}, \] where we replace the $ g_A, g_B $ with $ g $ above for simplicity (since they are identically distributed). A simple combinatorial argument gives us that \[ p^((g_C)_{ij}^k = z) = \begin{cases} u^\ell + (q-1)uv & \text{for } z = 0 \\ (q-1)v^\ell & \text{for } z \neq 0 \end{cases} \] Therefore, the probability of a 0 is equal to \[ p^((g_C)_{ij}^k = 0) = (u + (q-1)v)^\ell - ((q-1)v)^\ell = 1 - \frac{q-1}{q} = \frac{1}{q} \] Similarly, we have that \[ p^(gc)^k_{i_1, \ldots, i_t} = z = (q - 1)^{-1} q^\ell \] \[ = (q - 1)^{-1} \left( \frac{1}{\sqrt{q(q - 1)^{t-1}}} \right)^\ell = \frac{1}{q} \] (10) for a non-zero $ z $. Because $ p^(gc)^k_{i_1, \ldots, i_t} = z $ is a function of the values $ p^(gc)^k_{i_1, \ldots, i_t} = 0 $, $ \ldots $, $ p^(gc)^k_{i_1, \ldots, i_t} = q - 1 $, \ldots \), $ p^(gc)^k_{i_1, \ldots, i_t} = q - 1 $ we have that $ k \neq k' $ implies that $ p^(gc)^k_{i_1, \ldots, i_t} = z $ and $ p^(gc)^k'_{i_1, \ldots, i_t} = z $ are independent. Thus, any two rows of $ gc $ are independent. The proof is completed identically to the proof of Theorem 2. Lemma 1. The codes given by Thm. 2 exist for all fields. Proof. Suppose $ \text{char}(F) = p $ for some prime $ p $ and $ \|F\| > p^k $. Then $ F $ contains a subfield isomorphic to $ F_p $, for all $ q = p^k $, and $ k' \| k $, which is the setting described in Theorem 2. Thus, it remains to prove the result for $ \text{char}(F) = 0 $. In this case, $ F $ contains a copy of $ \mathbb{Z} $. Because the determinant function and the function $ \text{mod}_p : \mathbb{Z} \rightarrow \mathbb{F}_p $ defined by $ n \rightarrow (n \mod p) $ are homomorphisms, a full rank matrix $ G $ over $ \mathbb{F}_p $ may be considered as a full rank matrix $ g_\mathbb{Z} $ with entries in $ \mathbb{Z} $, reducing to the previous case. C. An Impossibility Theorem Theorem 4. There do not exist linear outer product codes (of neither the deterministic nor random type) if $ \left( \prod_{j \in [t]} 1 - q^{-d_j} \right) \leq q^{1-d_1 - \ldots - d_t} \cdot d_1 \cdot \ldots \cdot d_t $. Proof. A modification of the proof of Theorem 1 gives us that the total number of full rank $ (k + 1) \times d $ matrices that can be created by flattening outer products satisfies the recursion \[ \mathcal{N}(k + 1, d) \leq \mathcal{N}(k, d) \left( \prod_{j \in [t]} q^{d_j} - 1 \right) - q(k + 1) \], which counts the number of $ k + 1 $ linearly independent sets of flattened rank 1 matrices by taking a set of $ k $ many such matrices and subtracting out all the possibly linearly dependent choices. However, plugging in $ d $ gives us $ \mathcal{N}(d, d) / T(d, d) \leq 0 $, and thus there cannot exist any matrix rank 1 tensors if $ \left( \prod_{j \in [t]} 1 - q^{-d_j} \right) < q^{1-d_1 - \ldots - d_t} \cdot d_1 \cdot \ldots \cdot d_t $. D. Locally Random Alloy Codes Given a tensor $ T $ with a tensor decomposition $ T_1, \ldots, T_r $, and general block matrices $ A_0, A_1 $, where $ T = T_1 + \ldots + T_r $, $ T_i(A) = D_i(T_i(E_0^i(A_0), E_1^i(A_1))) $, and the workers perform outer products $ T_i $ for a non-coded algorithm, we show how to convert it into a coded algorithm. The master node generates $ r $ many codes $ q^t := (g_A^t)^k $ for $ t \in [r] $ according to Eq. 5. The workers are indexed by $ (t, k) $ where $ t \in [r] $, $ k \in [n/r] $. The master and sends worker $(t, k)$ the data $ \tilde{A}_{k,0}, \tilde{A}_{k,1} $, where $ \tilde{A}_{k,t} = \sum_{i \in \text{dim}(A_j)} (g^t_A)^k_i E_j(A_j) $. Each worker $(t, k)$ computes $ T_i(\tilde{A}_{k,0}, \tilde{A}_{k,1}) $. The master then solves for $ T_i(E_0^i(A_0), E_1^i(A_1)) $ for each $ t \in [r] $ by inverting $ g_e^t $ (if possible) and returns $ (D_1 T_1 + \ldots + D_r T_r)(A_0, A_1) $. Theorem 5 (Theorem for General 3-D Distributed Matrix Multiplication). If $ R = \frac{p_1}{p_2} \cdot 2^{-\beta} \cdot \alpha < c $, then by standard arguments by the method of strong types, i.e., Hoeffding’s inequality, as found in [25]. To simplify the proof we prove it for a probability of failure $ p = p_f \geq 1 $. If we give each worker group a factor of $ \lambda $ extra workers and we want to know what is that probability that a percentage of $ (p + \Delta)\% $ of them will fail, then we have that \[ P((p + \Delta)\% \text{ of workers will fail}) \leq \exp \left( -\frac{\Delta^2 \chi}{2p(1 - p)} \right) \] by the Chernoff-Hoeffding inequality. We need $ p + \Delta = \frac{\lambda^{1+m}}{1 + \lambda^{1+m}} = \frac{\lambda}{1 + \lambda} $ so that $ \Delta = \frac{\lambda}{1 + \lambda} - p $. Therefore if we want the probability of the $ z^2 $ large tasks $ T_1, \ldots, T_z $ tasks (see [26] for a proof that $ z^2 $ rank-one tensors are needed for $ \frac{z^2}{p^2}, z, z $ size rectangular multiplication) to fail with less than $ 1 - \epsilon $ probability the following bound \[ 1 - \exp \left( -\frac{\lambda}{1 + \lambda} - p \right)^2 \chi \leq z^2 \] is sufficient. Algebraic manipulation and the facts that \[ 1 - \exp \left( -\frac{\lambda}{1 + \lambda} - p \right)^2 \chi < 1 \] and $ c < 1 \implies 1 - c \geq \log(1 - c) $ together imply that \[ -\exp \left( -\frac{\lambda}{1 + \lambda} - p \right)^2 \chi \geq \frac{\ln(1 - \epsilon)}{z^2} - 1 \] which in turn gives \[ \frac{1}{1 + \lambda} \geq p + \sqrt{-\chi - 12p(1 - p) \ln \left( 1 - \frac{\ln(1 - \epsilon)}{z^2} \right)} \] Fixing $ p, \epsilon $ and letting $ x, y, z, \chi \rightarrow \infty $ gives us that for any $ c' \rightarrow 0 $, the inequality $ \frac{1}{1 + \lambda} \geq p + c' $ is satisfied. Thus we have that asymptotically we only need that $ \frac{1}{1 + \lambda} \geq p $ which is equivalent to the desired inequality $ \lambda \geq \frac{p}{1 - p} $. $ \square $ REFERENCES [1] Q. Yu, M. A. Maddah-Ali, and A. S. Avestimehr, “Straggler mitigation in distributed matrix multiplication: Fundamental limits and optimal coding,” ISIT, pp. 2022–2026, 2018. [2] V. V. Williams, Y. Xu, Z. Xu, and R. Zhou, New Bounds for Matrix Multiplication: from Alpha to Omega, pp. 3792–3835. [Online]. Available: https://epubs.siam.org/doi/abs/10.1137/1.9781611977912.134 [3] A. M. Subramaniam, A. Heidarzadeh, and K. R. Narayanan, “Random khatri-rao-product codes for numerically-stable distributed matrix multiplication,” Allerton, pp. 253–259, 2019. [4] K. Lee, M. Lam, R. Pedarsani, D. Papailiopoulos, and K. Ramchandran, “Speeding Up Distributed Machine Learning Using Codes,” IEEE Trans. Inf. Theory, pp. 1514–1529, 2018. [5] Q. Yu, M. A. Maddah-Ali, and A. S. 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Shroff, “Coded sparse matrix multiplication,” in ICML, 2018, pp. 5152–5160. [12] P. Soto, J. Li, and X. Fan, “Dual entangled polynomial code: Three-dimensional coding for distributed matrix multiplication,” in ICML, 2019. [13] S. Dutta, V. Cadambe, and P. Grover, “‘short-dot’: Computing large linear transforms distributedly using coded short dot products,” IEEE Trans. Inf. Theory, pp. 6171–6193, 2019. [14] A. B. Das and A. Ramamoorthy, “Distributed matrix-vector multiplication: A convolutional coding approach,” in ISIT, 2019, pp. 3022–3026. [15] S. Hong, H. Yang, Y. Yoon, T. Cho, and J. Lee, “Chebyshev polynomial codes: Task entanglement-based coding for distributed matrix multiplication,” in ICML, 2021, pp. 4319–4327. [16] Q. Yu, S. Li, N. Raviv, S. M. M. Kalan, M. Soltanolkotabi, and S. A. Avestimehr, “Lagrange coded computing: Optimal design for resiliency, security, and privacy,” in AISTATS, 2019, pp. 1215–1225. [17] Z. Jia and S. A. Jafar, “Generalized cross subspace alignment codes for coded distributed batch matrix multiplication,” in ICC, 2020, pp. 1–6. [18] P. Soto and J. Li, “Straggler-free coding for concurrent matrix multiplications,” in ISIT, 2020, pp. 233–238. [19] P. Soto, X. Fan, A. Saldívia, and J. Li, “Rook coding for batch matrix multiplication,” IEEE Trans. Commun., pp. 1–1, 2022. [20] R. G. L. D’Oliveira, S. E. Rouayheb, and D. A. Karpuk, “Gasp codes for secure distributed matrix multiplication,” ISIT, pp. 1107–1111, 2019. [21] L. Tang, K. Konstantinidis, and A. Ramamoorthy, “Erasure coding for distributed matrix multiplication for matrices with bounded entries,” IEEE Commun. Lett., vol. 23, pp. 8–11, 2019. [22] R. Nissim, O. Schwartz, and Y. Spitzer, “Fault-tolerant parallel integer multiplication,” in Proceedings of the 36th ACM Symposium on Parallelism in Algorithms and Architectures, ser. SPAA ’24. New York, NY, USA: Association for Computing Machinery, 2024, p. 207–218. [Online]. Available: https://doi.org/10.1145/3626183.3659961 [23] R. Tandon, Q. Lei, A. G. Dimakis, and N. Karampatziakis, “Gradient coding: Avoiding stragglers in distributed learning,” in ICML, 2017, pp. 3368–3377. [24] P. J. Soto, I. Imer, H. Guan, and J. Li, “Lightweight projective derivative codes for compressed asynchronous gradient descent,” in ICML, 2022, pp. 20444–20458. [25] I. Csiszár and J. Körner, “Information theory - coding theorems for discrete memoryless systems, second edition,” 1997. [26] P. L. Gall and F. Urrutia, Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor*, pp. 1029–1046.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5156, 1 ], [ 5156, 11559, 2 ], [ 11559, 17337, 3 ], [ 17337, 22756, 4 ], [ 22756, 28203, 5 ], [ 28203, 32613, 6 ] ] }
d0a54c09611e67dc4eaa5abc9844c765ea7dd4da	{ "olmocr-version": "0.1.59", "pdf-total-pages": 13, "total-fallback-pages": 0, "total-input-tokens": 56158, "total-output-tokens": 14320, "fieldofstudy": [ "Physics" ] }	This is the accepted manuscript made available via CHORUS. The article has been published as: Phase transitions and ordering structures of a model of a chiral helimagnet in three dimensions Yoshihiko Nishikawa and Koji Hukushima Phys. Rev. B 94, 064428 — Published 25 August 2016 DOI: 10.1103/PhysRevB.94.064428 Phase transitions and ordering structures of a model of chiral helimagnet in three dimensions Yoshihiko Nishikawa$^{1,}$ and Koji Hukushima$^{1,2,†}$ $^1$Department of Basic Science, University of Tokyo 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan $^2$Center for Materials Research by Information Integration, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan (Dated: July 5, 2016) Phase transitions in a classical Heisenberg spin model of a chiral helimagnet with the Dzyaloshinskii–Moriya (DM) interaction in three dimensions are numerically studied. By using the event-chain Monte Carlo algorithm recently developed for particle and continuous spin systems, we perform equilibrium Monte Carlo simulations for large systems up to about $10^6$ spins. Without magnetic fields, the system undergoes a continuous phase transition with critical exponents of the three-dimensional XY model, and a uniaxial periodic helical structure emerges in the low temperature region. In the presence of a magnetic field perpendicular to the axis of the helical structure, it is found that there exists a critical point on the temperature and magnetic-field phase diagram and that above the critical point the system exhibits a phase transition with strong divergence of the specific heat and the uniform magnetic susceptibility. I. INTRODUCTION Frustration and competition between interactions and/or fields often induce complicated spin structures into magnetic materials such as spin ice, magnetic skyrmion, and spin liquid. Phase transitions and phase diagrams in magnetic materials driven by various interactions and fields have been extensively studied in condensed matter physics and also statistical physics. Among them, chiral magnets such as MnSi and Cr$_{1/3}$NbS$_2$ have recently attracted great interests to experimental and theoretical studies not only for its fundamental properties but also for applications [1–9]. Chiral helimagnet is a magnetic system in which a uniaxial helical structure emerges in the low temperature region. The helical structure is induced by the Dzyaloshinskii–Moriya (DM) interaction [10, 11] which is an antisymmetric interaction breaking a chiral symmetry, and thus, the two same helical structures with different winding directions do not degenerate. By a variational analysis of a one-dimensional continuum model [6–9], it is revealed theoretically that a chiral magnetic soliton lattice (CSL) is formed with a finite magnetic field perpendicular to the axis of the helical structure (see Fig. 1), and a continuous phase transition to forced ferromagnetic phase occurs with increasing the magnetic field. A mean-field analysis shows that a phase transition into the CSL phase occurs at a finite temperature under the magnetic field even in a three-dimensional system[12]. While recent experiments [2, 3] have reported the existence of the CSL state at finite temperatures in three dimensions, finite-dimensional effects beyond the mean-field theory on the nature of the finite-temperature phase transitions of the system are still less clear. In the absence of magnetic fields, renormalization-group approaches [13, 14] predict that the system undergoes a continuous phase transition with critical exponents of the ferromagnetic XY model. Other theoretical studies [15, 16] also indicate that the system belongs to the same universality class of the ferromagnetic XY model. On the other hand, with the magnetic field perpendicular to the axis of the helical structure, the system no longer has any continuous symmetry in the spin space. Therefore, the nature of a possible phase transition in three dimensions is nontrivial and possibly different from the three-dimensional XY model. In this paper, we study a three-dimensional classical Heisenberg spin model of a chiral helimagnet by equilibrium Monte Carlo simulations. We especially focus on its phase transitions and ordering structures in the low temperature region with and without the magnetic field. Because of the competition among the DM interaction, the symmetric exchange interaction, and the magnetic field, complicated ordering structures emerge in the low temperature region. In particular, there are many CSL states with different numbers of chiral solitons which are separated with each other by large energy barrier. Hence, a FIG. 1. A schematic picture of the chiral-soliton-lattice structure. Each arrow represents a spin. The magnetic field is in the upward direction of the figure. $^$ [email protected] $^†$ [email protected] transition between the different CSL states hardly occurs by means of conventional Monte Carlo algorithms such as the Metropolis and the heat-bath algorithm. In order to reduce the difficulty of the slow relaxation, we use the event-chain Monte Carlo algorithm [17–21] which is a recently proposed rejection-free and efficient algorithm for equilibrium simulations. This algorithm enables us to equilibrate quite large systems with more than $10^6$ spins so as to avoid suffering from its strong finite-size effects particularly in the presence of the magnetic field. This paper is organized as follows. In Section II we define a classical Heisenberg spin model of a chiral helimagnet and various physical quantities. The details of the event-chain Monte Carlo algorithm are presented in Section III. In Section IV, results of our Monte Carlo simulations are shown, and properties of phase transitions and ordering structures of the system with and without a magnetic field are discussed. In Section V we discuss a possible phase diagram and summarize our results. II. MODEL AND PHYSICAL QUANTITIES In this paper, we study a classical Heisenberg model of a chiral helimagnet in a three-dimensional simple cuboidal lattice. The system is defined by the Hamiltonian $$H \{ \{ S_i \} \} = -J \sum_{\langle i,j \rangle} S_i \cdot S_j - D \sum_i (S_i \times S_{i+\hat{y}}) - h \cdot \sum_i S_i; \quad (1)$$ where $S_i$ is a unit vector with three components, $J$ is a positive coupling constant, $D = D\hat{y}$ is the DM vector, and $h = h\hat{z}$ is a magnetic field perpendicular to the DM vector $D$. The summation in the first term runs over all the neighboring pairs of sites, and the other summations run over all the sites. The lattice on which the system is defined is a cuboid where the linear size of $y$ direction is $\alpha$ times as long as $x$ and $z$ directions. The linear size of $x$ and $z$ directions of the lattice is denoted by $L$ and the total number of sites is $N = \alpha L^3$. We set $\alpha = 8$ in the following of this paper. Periodic boundary conditions are imposed on $x$ and $z$ directions and a free boundary condition on $y$ direction. The second term in the Hamiltonian (1) represents the Dzyaloshinskii–Moriya interaction [10, 11] which induces a helical spin structure. In the ground state of the system without magnetic fields, all spins in each $x$-$z$ plane align ferromagnetically and the spins in each plane make a canted angle $\theta = \arctan(D/J)$ with respect to its nearest neighbor plane along the DM vector. The wave vector $q_{\text{chiral}}$ corresponding to the helical structure in the ground state is determined by $D/J$ via $$q_{\text{chiral}} = \arctan \left( \frac{D}{J} \right) \hat{y}. \quad (2)$$ At a finite temperature, the system undergoes a phase transition from a paramagnetic phase to a chiral helimagnetic phase as temperature decreases. Following the previous works [15, 16], the system without magnetic fields can be exactly mapped onto another system defined by the Hamiltonian $$H' \{ \{ S_i \} \} = -J \sum_{\langle i,j \rangle} S_i \cdot S_j - \sum_i S_i \cdot CS_{i+\hat{y}}, \quad (3)$$ where $$C = \left( \frac{\sqrt{J^2 + D^2}}{J} \frac{J}{\sqrt{J^2 + D^2}} \right), \quad (4)$$ and the summation in the first term runs over all the neighboring pairs of two sites which are in the same $x$-$z$ plane. This Hamiltonian (3) for a finite value of $D$ has the same symmetry with the XY model, and therefore, the original system is expected to belong to the same universality class of the three-dimensional ferromagnetic XY model [16]. In the presence of the magnetic field $h$ perpendicular to the DM vector, the structure of the ground state is modulated depending on $h = \|h\|$. For $0 < h < h_c$, the CSL is formed, and all spins are parallel to the magnetic field for $h > h_c$. The precise value of $h_c$ is unclear for arbitrary value of $D/J$ while that for $D/J \ll 1$ is calculated by a continuum approximation [1, 6–9]. In the CSL state at zero temperature, there are more than one local length scales such as the distance between two chiral solitons and the length of one chiral soliton, and hence, multiple wave vectors are expected to be required to characterize the CSL structure. For the chiral helimagnetic system, we define the wave-vector-dependent magnetization which captures the helical structure of the system as $$m(q) = \frac{1}{N} \sum_i S_i \exp(i q \cdot r_i), \quad (5)$$ where $q$ is a three-component wave vector. The wave-vector-dependent susceptibility associated with $m(q)$ is defined as $$\chi(q) = \beta N \left( \langle \|m(q)\|^2 \rangle - \langle m(q) \rangle^2 \right), \quad (6)$$ where $\beta$ is an inverse temperature and the bracket $\langle \cdots \rangle$ denotes the thermal average. Note that $\chi(q)$ is proportional to a Fourier component of the spin correlation function $$C(r) = \frac{1}{N} \sum_i \langle S_i \cdot S_{i+r} \rangle - \langle S_i \rangle \cdot \langle S_{i+r} \rangle. \quad (7)$$ In particular, the susceptibility with a wave vector $q$ parallel to the DM vector $D$ is denoted as $\chi^D(q)$, where $q = \|q\|$. Although the ground state of the system with no magnetic fields is obviously characterized by $ \mathbf{m}(q = \mathbf{q}_{\text{chiral}}) $, it is unclear that which $ q $'s characterize the structure at finite temperature with/without a magnetic field $ \mathbf{h} \neq 0 $. We thus calculate the wave-vector dependence of $ \chi^\parallel(q) $, which yields the wave vectors $ q_0 $ at which $ \chi^\parallel(q_0) $ gives a maximum value. By using $ \chi(q) $, the wave-vector-dependent finite-size correlation length is defined as \[ \xi_L(q) = \frac{1}{2 \sin(\frac{\|q_{\text{min}}\|}{2})} \left( \frac{\chi(q)}{\chi(q + q_{\text{min}})} - 1 \right), \] (8) where $ q_{\text{min}} $ is the minimum wave vector parallel to $ q $. Similarly to the susceptibility, the finite-size correlation length depending on a wave vector $ q $ parallel to $ \mathbf{D} $ is defined as $ \xi_L^D(q) $, where $ q_{\text{min}} $ in Eq. (8) is set to $ q_{\text{min}} = (0, 2\pi/\alpha L, 0) $. We also define a distribution function of the energy density $ e $ as \[ P(e) = \left\langle \delta \left( e - \frac{1}{N} H(\{S_i\}) \right) \right\rangle, \] (9) which is evaluated by Monte Carlo simulations. From the distribution, the specific heat $ c $ is calculated. When the system exhibits a first-order phase transition, the distribution has a double-peak structure at the transition temperature. We study the phase transitions of the system with $ D/J = 1 $ by equilibrium Monte Carlo (MC) simulations using the event-chain Monte Carlo (ECMC) algorithm [17–21] combined with the heat-bath algorithm, the over-relaxation updates [22, 23] and the exchange Monte Carlo method (or parallel tempering) [24]. The details of the ECMC algorithm in our simulations are presented in the next section. III. EVENT-CHAIN MONTE CARLO ALGORITHM The ECMC algorithm was originally developed for particle systems [17–19], and recently applied to continuous spin systems [20, 21]. In every step of the algorithm, only one particle (or spin) is moved, and another interacting particle (or spin) starts to move instead of rejecting a proposal. Thus, a series of local updates called “event chain” is formed, in which many particles (or spins) are updated in a cooperative manner. This dynamics breaks the detailed balance condition, but still satisfies the global balance condition. For various systems, the ECMC algorithm outperforms conventional algorithms such as the Metropolis algorithm [25] and the heat-bath algorithm [26, 27]. In particular, it is revealed that the algorithm reduces the value of the dynamical critical exponent $ z $ of the three-dimensional ferromagnetic Heisenberg model to $ z \approx 1 $ from the conventional value $ z \approx 2 $ [21]. This reduction enables us to simulate systems with much larger degrees of freedom in equilibrium than those attained with the conventional algorithms previously. In this algorithm, the state of the system is represented by $ \{\{S_i\}, U\} $, where $ \{S_i\} $ is the spin configuration and $ U $ is a “lifting parameter.” The lifting parameter $ U $ specifies the current rotation site and the direction vector of the rotation axis. Explicitly, the lifting parameter is given as an $ N \times 3 $ matrix of the form $ U = e_j v^T $, where $ e_j $ is an $ N $-dimensional unit vector with components $ (e_j)_k = \delta_{j,k} $ and $ v $ is a three-component unit vector. For concreteness, we assume that the Hamiltonian can be written as a summation of interactions \[ H(\{S_i\}) = \frac{1}{2} \sum_{i,j} E_{ij}^{(a)}(S_i, S_j) + \sum_{i,a} E_{i}^{(a)}(S_i), \] (10) where the suffix “$ a $” is the type of interaction. Note that any decompositions of the Hamiltonian in the form of Eq. (10) are allowed in the following argument. An elementary step of this algorithm is to propose an infinitesimal rotation $ d\phi $ of the moving spin $ S_j $ around the axis $ v $, and to accept the proposal with probability of the factorized Metropolis filter [19] \[ W_U(d\phi) = \prod_{k \in \partial j} \exp \left( -\beta \max_a \left[ \frac{d}{d\varphi} \left( \Delta E_{jk}^{(a)}(\varphi = 0; v) \right), 0 \right] d\phi \right) \times \prod_{a} \exp \left( -\beta \max_a \left[ \frac{d}{d\varphi} \left( \Delta E_{i}^{(a)}(\varphi = 0; v) \right), 0 \right] d\phi \right), \] where $ \partial j $ means the set of sites interacting with $ j $-th spin, $ \Delta E_{jk}^{(a)}(\varphi; v) = E_{jk}^{(a)}(R_{\varphi}(v) S_j, S_k) - E_{jk}^{(a)}(S_j, S_k) $, $ \Delta E_{i}^{(a)}(\varphi; v) = E_{i}^{(a)}(R_{\varphi}(v) S_j) - E_{i}^{(a)}(S_j) $, and $ R_{\varphi}(v) $ is a rotation matrix around $ v $ with an angle $ \varphi $. Thanks to the factorization, whether the proposal is accepted can be determined by each factor independently, i.e., the proposal is accepted only if all the factorized potentials avoid the rejection. When the proposal is rejected by a factor with the potential $ E_{jk}^{(a)}(R_{\varphi}(v) S_j, S_k) $, then a lifting event occurs and the lifting parameter is updated as $ U \rightarrow L_j^{(a)} U (U \rightarrow L_j^{(a)} U) $, where $ L_j^{(a)} $ (or $ L_j^{(a)} $) is a lifting matrix. The balance condition requires that $ L_j^{(a)} $ and $ L_j^{(a)} $ satisfy [18] \[ L_j^{(a)} g_j^{(a)} = -g_j^{(a)}, \] (11) \[ L_j^{(a)} g_j^{(a)} = -g_j^{(a)}, \] (12) where \[ g_j^{(a)} = \frac{d}{d\varphi} \left( \Delta E_{jk}^{(a)}(\varphi; v) e_j + \Delta E_{jk}^{(a)}(\varphi; v) e_k \right) \big\|_{\varphi = 0}, \] \[ g_j^{(a)} = \frac{d}{d\varphi} \left( \Delta E_{j}^{(a)}(\varphi; v) e_j \right) \big\|_{\varphi = 0}. \] respectively. In general, $L_{jk}^{(a)}$ and $L_j^{(a)}$ which satisfy Eq. (11) and Eq. (12) are rewritten by using an $N \times N$ regular matrix $A$ and the identity matrix $I$ as $$L_{jk}^{(a)} = I - 2A^{(a)}g_{jk}^{(a)} \left( g_{jk}^{(a)} \right)^T, \quad (13)$$ $$L_j^{(a)} = I - 2A^{(a)}g_j \left( g_j \right)^T. \quad (14)$$ In principle, any matrix $A$ is available but a class of $A$ leading to a simple lifting event is desired in practice. To make the algorithm into practice, an event-driven approach [28] is adopted, which allows to move the spins with a finite displacement. In the conventional ECMC algorithm for continuous spin systems only with isotropic interactions [20, 21] and a magnetic field, the Hamiltonian is decomposed as $$H_{iso} (\{S_i\}) = \frac{1}{2} \sum_{i,j,a} E_{ij}^{(a)} (S_i, S_j) + \sum_{i} E_i^{(a)} (S_i), \quad (15)$$ where $$E_{ij}^{(a)} (S_i, S_j) = -J_{ij}^{(a)} S_i \cdot S_j, \quad (16)$$ $$E_i^{(a)} (S_i) = -h_i^{(a)} S_i. \quad (17)$$ The isotropic interactions have a simple relation as $$\left. \frac{d}{d\varphi} \Delta E_{jk}^{(a)} (\varphi; \nu) \right\|_{\varphi=0} = -\left. \frac{d}{d\varphi} \Delta E_{kj}^{(a)} (\varphi; \nu) \right\|_{\varphi=0} \quad (18)$$ for all $j$, $k$ and $\nu$. This relation yields that by choosing the matrix $A$ in Eq. (13) and Eq. (14) as the identity $I$, the lifting matrices are determined as $$\left( L_{jk}^{(a)} \right)_{p,q} = \delta_{p,q} - \delta_{j,p} \delta_{k,q} + \delta_{j,q} \delta_{k,p}, \quad (19)$$ $$\left( L_j^{(a)} \right)_{p,q} = \delta_{p,q} (1 - 2\delta_{j,p}). \quad (20)$$ respectively. These lifting matrices make the lifting parameter $U$ have one non-zero row, and thus, only a single spin moves at any time. The master equation in this case is explicitly written down in Appendix A. For anisotropic interactions including the DM interaction, however, Eq. (18) does not hold in general. In these cases, $L_{jk}^{(a)}$ depends on the spin configuration, and the updated lifting parameter $L_{jk}^{(a)} U$ has more than one non-zero rows, meaning that multiple spins start to move after a lifting event. Although we could implement another Monte Carlo algorithm in which multiple spins move simultaneously [18, 29], we apply the ECMC algorithm only with the rotation axis $\nu = \hat{y}$, where Eq. (18) holds for the DM interaction and thus the single spin update is still kept. Instead, the ergodicity condition is not satisfied by the ECMC algorithm only with a single rotation axis. In order to recover the ergodicity condition in the Markov chain, the over-relaxation and the heat-bath algorithms are combined with this ECMC algorithm. The ECMC algorithm enables us to sample different structures of the system efficiently by inducing cooperative spin updates of the same $x$-$z$ plane in each event chain. We demonstrate that the ECMC algorithm works efficiently in the chiral helimagnetic model defined by the Hamiltonian (1) with $D/J = 1$ and $h/J = 0$. We measure the autocorrelation function $C_O (t)$ of a physical quantity $O$ at Monte Carlo time $t$ defined by $$C_O (t) = \frac{\langle O(t) O(0) \rangle - \langle O(t) \rangle \langle O(0) \rangle}{\langle O^2 (0) \rangle - \langle O(0) \rangle^2}. \quad (21)$$ Monte Carlo simulations for the measurements are performed with and without the ECMC algorithm. One Monte Carlo step (MCS) is defined as exactly one update per spin while the number of updated spins in each event chain of the ECMC algorithm is determined in a probabilistic way. Because the wave vector $\mathbf{q}_{chiral}$ characterizes the order parameter of the finite-temperature phase transition of the model without magnetic fields as shown in the next section, we adopt the square of the wave-vector-dependent magnetization $\|\mathbf{m} (\mathbf{q}_{chiral})\|^2$ as a physical quantity in Eq. (21). Fig. 2 shows MCS dependence of the autocorrelation function $C_{\|\mathbf{m} (\mathbf{q}_{chiral})\|^2} (t)$ for $L = 4, 8$ and $16$ at the critical temperature $T_c$ which is estimated in the next section. In the combined method for the calculation of the autocorrelation function, we use the heat-bath algorithm once in approximately 10 MCS by the ECMC algorithm. One can see in the figure that $C_{\|\mathbf{m} (\mathbf{q}_{chiral})\|^2} (t)$ decays much faster by combining the ECMC algorithm with the conventional heat-bath algorithm and the acceleration by the ECMC algorithm is more significant with increasing $L$. IV. RESULT In this section, we present results of our Monte Carlo simulations of the system with and without the magnetic field. The linear size of the system in the simulations ranges from $L = 2$ (the total number of spins $N = 2 \times 16 \times 2$) to $L = 64$ ($N = 64 \times 512 \times 64$). The total number of MCS in our simulations is about $5 \times 10^4 - 5 \times 10^5$ depending on the system size, where one MCS is defined as 1 update by ECMC with 5 over-relaxation sweeps per spin. One heat-bath update per spin is performed for every 10 MCS. We checked the equilibration by confirming that the average values of physical quantities measured during an interval coincide with those measured during another interval twice longer within statistical uncertainty. Error bars are evaluated by results of multiple independent simulations. A. Universality class of the system without magnetic fields First, we present the specific heat $c$ of the system for various system sizes in Fig. 3. One can see in the figure that the specific heat shows a sharp peak at about $T/J \simeq 1.68$, and thus, a phase transition is expected to occur at around this temperature. Around and below this temperature, the wave-vector-dependent susceptibility $\chi(\mathbf{q})$ has two peaks at $q = \pm q_{\text{chiral}}$, see Fig. 4. This fact is insensitive to the system size in our simulations. Therefore, the wave vector $\mathbf{q}_{\text{chiral}}$ also characterizes the ordering structure of the system at finite temperature and $m(\mathbf{q}_{\text{chiral}})$ can be considered as an order parameter of the system. ![Figure 3](image3.png) FIG. 3. (Color online) Temperature dependence of the specific heat $c$ of the chiral helimagnetic model in three dimensions without magnetic fields. ![Figure 4](image4.png) FIG. 4. (Color online) Wave-number dependence of $\chi(\mathbf{q})$ of the three-dimensional chiral helimagnetic model without magnetic fields (a) for various system sizes at $T/J = 1.680645$, which is close to the critical temperature, and (b) with $L = 32$ at various temperatures above and below the critical temperature. We show the wave-vector-dependent finite-size correlation length $\xi_L(q_{\text{chiral}})$ divided by $\alpha L$ in Fig. 5. One can see in the figure that each pair of curves for $\xi_L(q_{\text{chiral}})/\alpha L$ and $\xi_{2L}(q_{\text{chiral}})/2\alpha L$ intersects at a temperature and that the intersection converges to a certain temperature point for larger sizes while it slightly shifts for smaller sizes. This implies that the correlation length with the wave vector $\mathbf{q}_{\text{chiral}}$ diverges at a finite temperature in the thermodynamic limit. Here, we assume that $\xi_L(q_{\text{chiral}})/\alpha L$ follows a finite-size scaling (FSS) form $$\frac{\xi_L(q_{\text{chiral}})}{\alpha L} = F \left[ (T - T_c)(\alpha L)^{1/\nu} \right],$$ where $F$ is a scaling function and $\nu$ is the critical exponent of the correlation length. By using a recently proposed method based on Bayesian inference [30, 31], FSS analyses are performed for four sets of the data con- FIG. 5. (Color online) Temperature dependence of the finite-size correlation length $\xi_L(q_{\text{chiral}})$ divided by $\alpha L$ of the three-dimensional chiral helimagnetic model without magnetic fields. The inset presents an enlarged view around the critical temperature. FIG. 6. (Color online) A finite-size scaling plot of the finite-size correlation length $\xi_{\parallel}^L(q_{\text{chiral}})$ divided by $\alpha L$ of the three-dimensional chiral helimagnetic model without magnetic fields. The smallest system size of this FSS plot is $L_{\text{min}} = 16$. The critical temperature $T_c$ and the critical exponent $\nu$ are estimated as $T_c/J = 1.68672(4)$ and $\nu = 0.676(3)$, respectively. FIG. 7. (Color online) (a): Temperature dependence of the wave-vector-dependent susceptibility $\chi_{\parallel}^L(q_{\text{chiral}})$ for the same data sets. The susceptibility is assumed to follow a scaling form $$\chi_{\parallel}^L(q_{\text{chiral}}) = (\alpha L)^{(\gamma/\nu)} G \left[ (T - T_c)(\alpha L)^{1/\nu} \right],$$ where $G$ is a scaling function and $\gamma$ is the critical exponent of the susceptibility. One can see in Fig. 7 temperature dependence of the susceptibility $\chi_{\parallel}^L(q_{\text{chiral}})$ and the resultant FSS plot. The exponents are estimated as $\nu = 0.670(2)$ and $\gamma = 1.320(4)$, respectively. The estimated values of the critical temperature and exponents are shown in Table I. As seen in the table, the values of the critical exponents approach those of the three-dimensional ferromagnetic $XY$ model $\nu = 0.67155(27)$ and $\gamma = 1.3177(5)$ [32] as $L_{\text{min}}$ increases. We conclude that the system without magnetic fields undergoes a phase transition from a paramagnetic phase to a chiral helimagnetic phase as temperature decreases with critical exponents of the three-dimensional $XY$ model, as predicted in Ref. 13–16. B. Phase transition under a magnetic field perpendicular to the DM vector In this subsection, we focus on the effect of a magnetic field perpendicular to the DM vector. The wave-number dependence of the susceptibility $\chi_{\parallel}(q)$ at $h/J = 0.1, 0.2, \text{and} 0.3$ for various temperatures and various sizes is shown in Fig. 8 and Fig. 9, respectively. In contrast to the case without the magnetic field shown in Fig. 4, $\chi_{\parallel}(q)$ has several peaks at $\pm q_0$ and integral multiples of $q_0$ in the presence of the magnetic field in the low tem- FIG. 8. (Color online) Wave-number dependence of $\chi^\parallel(q)$ of the chiral helimagnetic model in three dimensions for various temperatures with $L = 32$. The values of the magnetic fields perpendicular to the DM vector are (a) $h/J = 0.1$, (b) $h/J = 0.2$, and (c) $h/J = 0.3$. The vertical line represents $q_{\text{chiral}}/2\pi$. FIG. 9. (Color online) Wave-number dependence of $\chi^\parallel(q)$ of the chiral helimagnetic model in three dimensions for various system sizes near the estimated transition temperature depending on the magnetic field. The values of the magnetic fields perpendicular to the DM vector are (a) $h/J = 0.1$, (b) $h/J = 0.2$, and (c) $h/J = 0.3$. \| $L_{\text{min}}$ \| $T_c/J$ \| $\nu_\parallel$ \| $\nu_\perp$ \| $\gamma$ \| \|------------------\|----------\|------------------\|-------------\|---------\| \| 2 \| 1.688(1) \| 0.72(2) \| 0.711(5) \| 1.45(1) \| \| 4 \| 1.6871(2)\| 0.696(5) \| 0.682(2) \| 1.314(4)\| \| 8 \| 1.68683(5)\| 0.681(4) \| 0.671(1) \| 1.303(3)\| \| 16 \| 1.68672(4)\| 0.6763(3) \| 0.670(2) \| 1.320(4)\| TABLE I. The estimated values of the critical temperature and the critical exponents of the correlation length and the susceptibility by finite-size scaling analyses. The values of the critical temperature $T_c$, and the exponent of the correlation length denoted as $\nu_\parallel$ are estimated using the data of the finite-size correlation length $\xi_L(q_{\text{chiral}})/\alpha L$. Using the estimated value of $T_c$, the value of critical exponents of the susceptibility $\gamma$ and that of the correlation length denoted as $\nu_\perp$ are estimated by FSS analyses of the susceptibility $\chi^\parallel(q_{\text{chiral}})$. temperature region with $q_0$ being the positive wave number which gives the largest value of the susceptibility. The value of $q_0$ for finite magnetic fields is significantly smaller than that of $q_{\text{chiral}}$, although the difference is tiny for small fields as shown in Fig. 8 and Fig. 9. Furthermore, not only the largest peaks but also other small peaks are enhanced with increasing the system size, as seen in Fig. 9. These indicate that a periodic order, e.g., chiral soliton lattice (CSL) which cannot be characterized by a single wave vector emerges at low temperatures in the thermodynamic limit. The distance between two chiral solitons in the low temperature region is characterized by the value of the wave number $q_0$ as $q_0 = 2\pi/\|q_0\|$. In Fig. 8(c), for instance, one can see that $\|q_0\|/2\pi \sim 0.1$ at a sufficiently low temperature for $h/J = 0.3$, and hence, the distance between two chiral solitons along the DM vector is about 10 lattice spacings. Other wave numbers of the peak in $\chi^\parallel(q)$ in the low temperature region are considered to characterize shorter length scales within one chiral soliton. One may consider naively the order parameter of the CSL order to be $m(q_0)$. The value of $q_0$ weakly depends on temperature and also the values of the wave numbers of the peaks in finite systems with the magnetic field slightly deviate from those in the thermodynamic limit. The latter is due to the fact that the wave number in finite-size lattices can take only discrete values. As discussed above, the existence of the CSL phase characterized by the multiple wave vectors is strongly suggested at low temperatures. It is, however, difficult to identify the precise value of $q_0$ in numerical simulations and the order parameter in the CSL phase. While the CSL emerges in the presence of the magnetic field, qualitatively different behavior is observed in thermodynamic quantities at a relatively large magnetic field, particularly at $h/J = 0.3$ in our study. One of the striking features is the existence of the sharp peak of $\chi^\parallel(0)$ at a certain temperature which is not the intrinsic suscepti- FIG. 10. (Color online) System-size dependence of the peak value of the susceptibility $\chi_{\parallel}^\star(0)$ (a) and the specific heat $c_\star$ (b) of the chiral helimagnetic model in three dimensions with a magnetic field perpendicular to the DM vector $h/J = 0$, 0.1, 0.2, and 0.3. The black dotted lines are proportional to $L^3$. The insets show enlarged views. bility conjugated with the CSL order and also the chiral helimagnetic order parameter. Temperature dependence of the specific heat has a diverging peak at that temperature simultaneously. We denote the peak values of the uniform susceptibility and the specific heat in the temperature dependence as $\chi_{\parallel}^\star(0)$ and $c_\star^\star$, respectively. We show in Fig. 10 the system-size dependence of $\chi_{\parallel}^\star(0)$ and $c_\star^\star$. For $h/J = 0.1$ and 0.2, the peak values of $\chi_{\parallel}^\star(0)$ and $c_\star$ do not seem to diverge even in the thermodynamic limit. This is compatible with the result of $h/J = 0$, where the system belongs to the universality class of the three-dimensional $XY$ model and hence the critical exponent $\alpha$ is negative. Without the magnetic field, the specific heat $c$ does not diverge, but shows a cusp singularity at the critical temperature in the thermodynamic limit as the three-dimensional $XY$ model. When a cusp singularity exists in the specific heat, its peak value $c_\star^\star$ scales as $c_\star^\star \sim c_\star^\infty - sL^{\alpha/\nu}$, where $c_\star^\infty$ is the peak value of the specific heat in the thermodynamic limit and $s$ is a constant. We can see in the inset of Fig. 10(b) that the peak values $c_\star$ of the system with $h/J = 0$, 0.1 and 0.2 have very similar system size dependence. This fact suggests that the system under the magnetic fields also belongs to the universality class of the three-dimensional ferromagnetic $XY$ model. On the other hand, for $h/J = 0.3$, the peak values $\chi_{\parallel}^\star(0)$ and $c_\star$ show very strong tendencies to diverge in the thermodynamic limit. In particular, $\chi_{\parallel}^\star(0)$ and $c_\star$ at $h/J = 0.3$ seem to diverge as a power law with $L^3$ or FIG. 11. (Color online) Temperature dependence of specific heat $c$ of the chiral helimagnetic model in three dimensions with a magnetic field perpendicular to the DM vector $h/J = 0.3$. The system size $L = 64$ is the largest size in our simulations and the temperatures are close to the transition temperature. FIG. 12. (Color online) The energy-density distribution function $P(e)$ of the chiral helimagnetic model in three dimensions with a magnetic field perpendicular to the DM vector $h/J = 0.3$. The system size $L = 64$ is the largest size in our simulations and the temperatures are close to the transition temperature. even faster than a power low in larger system sizes. These indicate the existence of a critical point $(T_d, h_d)$ where $0.2 < h_d/J < 0.3$ on the phase boundary between the paramagnetic phase and the CSL phase in the magnetic phase diagram of the system. In other words, the system is expected to have finite values of the specific heat $c$ and the susceptibility $\chi^\parallel (0)$ at the transition temperature for $h < h_d$, and presumably belongs to the same universality class of the system without the magnetic field, while the system undergoes a phase transition at a finite temperature with the diverging specific heat $c$ and diverging magnetic susceptibility $\chi^\parallel (0)$ for $h > h_d$. A possible explanation of the strong divergence of the specific heat found at $h/J = 0.3$ might be an occurrence of the first-order phase transition. Then, the specific heat has a delta-function type divergence at the transition temperature and the peak value of the specific heat is expected to diverge as $L^d$ where $d = 3$ is the spatial dimension [35]. Also the energy-density distribution has two peaks at the transition temperature. In Fig. 11, we present temperature dependence of the specific heat $c$ of the system with $h/J = 0.3$. One can see in the figure that the specific heat $c$ shows a very sharp peak at about $T/J \approx 1.445$, and the width of the peak becomes narrower as the system size increases. This is consistent with the occurrence of the first-order transition and the size dependence of $c_s$ shown in Fig. 10(b) is marginally compatible with $L^3$. However, as seen in Fig. 12, the energy-density distribution function $P(e)$ does not have a double-peak structure near the transition temperature. No clear evidence of the first-order transition is found in our numerical results. We could not completely rule out the possibility of a weak first-order transition with a finite correlation length at the transition temperature larger than the largest system size in our simulations. Therefore, we tentatively conclude that this phase transition found at $h/J = 0.3$ is a continuous one. Our results suggest that the expected universality class has a ratio of the critical exponents of the specific heat and the correlation length $\alpha/\nu > 3$, assuming that $c_s$ of the system diverges faster than $L^3$ also in larger systems. Unfortunately, we could not determine the critical exponents of the transition and the precise location of the critical point $(T_d, h_d)$, which requires larger scale simulations of the system. V. DISCUSSION AND SUMMARY A possible phase diagram of the system is presented in Fig. 13, where we denote the paramagnetic phase and the CSL phase as “P” and “CSL”, respectively. The filled square at $h/J = 0$ is estimated by the FSS analysis in Sec. IV A, and other squares are estimated by the peak temperature of $\chi^\parallel (0)$ at $h/J = 0.1, 0.2$ and $0.3$ for $L = 64$ and at $h/J = 0.35$ for $L = 16$. The circle represents an expected location of the critical point $(T_d/J, h_d/J)$. One can see in the phase diagram that the phase boundary $h_{\text{CSL}}(T)$ between the paramagnetic phase and the CSL phase has a finite slope, which is compatible with the experimental phase diagram of a chiral helimagnet [3]. Imposing differentiability on the free-energy density of the infinite system at a point $(T_0, h_{\text{CSL}}(T_0))$ where a second-order phase transition occurs, the finite tangent of the phase boundary yields the relation \[ \Delta\chi \Delta c - T (\Delta \omega)^2 = 0, \tag{25} \] where $\omega$ and $\chi$ are the temperature derivative and the magnetic-field derivative of the magnetization parallel to the field, and $\Delta X = X_{\text{CSL}} - X_P$ for any $X \in \{c, \chi, \omega\}$ at $(T_0, h_{\text{CSL}}(T_0))$, respectively. If the system under the magnetic field with $0 < h < h_d$ belongs to the universality class of the three-dimensional ferromagnetic $XY$ model as discussed above, the specific heat is continuous on the phase boundary. In this system for a fixed $h < h_d$, the uniform susceptibility has a finite value. Therefore, Eq. (25) requires $\Delta \omega = 0$, meaning that the magnetization parallel to the magnetic field is smooth at the transition temperature. For $h > h_d$, however, the strong divergence is found in the specific heat. The difference $\Delta c$ is infinitely large unless the critical amplitude ratio is accidentally 1 with the same critical exponent above and below the critical temperature which may unlikely occur in finite dimensions. Then, the relation of Eq. (25) allows typically two cases: (i) $\Delta \chi = 0$ and $\Delta \omega$ is finite and (ii) \[ \Delta \chi = \infty \text{ and } \Delta \omega = \infty. \] Our result of the divergence of $ \chi_{\parallel} (0) $ indicates the latter case. Precisely speaking, $ \chi $ is not identical with $ \chi_{\parallel} (0) $ but $ \Delta \chi $ likely diverges when $ \chi_{\parallel} (0) = \infty $. This implies that the exponent of the divergence of $ \chi_{\parallel} (0) $ coincides with that of the specific heat. Furthermore, the temperature dependence of the magnetization is also described by the same singularity at least either above or below the critical temperature. Thus, the critical singularity of the specific heat appears in other observables unrelated to the critical nature through the relation of Eq. (25), while in a conventional system where $ \chi $ is an order-parameter susceptibility, the relation yields the scaling relation $ \alpha + 2 \beta + \gamma = 2 $ among the critical indices. We should note here that Dzyaloshinskii predicts by analyzing the one-dimensional continuum model of the chiral helimagnet in the presence of the magnetic field that a continuous phase transition occurs at a finite temperature $[8]$. It is also shown that the specific heat diverges from below the transition temperature with a logarithmic correction as \[ c \propto \frac{1}{(T_s - T) \log^2 (T_s - T)}, \tag{26} \] where $ T_s $ is the transition temperature, while no divergence of $ c $ displays from above $ T_s $. In this case, $ \Delta c $ is infinity at $ T_s $ and the critical exponent of the specific heat $ \alpha' = 1 $ below $ T_s $ and $ \alpha = 0 $ above $ T_s $. Although no definite conclusion can be drawn on the validity of this peculiar prediction, our numerical data of the specific heat is not inconsistent with the asymmetric behavior between above and below the critical temperature. One of the main difficulties in determining the critical indices is due to the logarithmic-correction term, which makes the critical region narrow. Assuming the hyperscaling relation $ d \nu = 2 - \alpha $ and $ \alpha = 1 $, the critical exponent of the correlation length is $ \nu = 1/3 $, and hence, the peak value of the specific heat is expected to diverge as $ \sim L^{\alpha'/\nu} = L^3 $. It also coincides with that in the system with the first-order transition. As discussed in IV B, the power-law divergence of $ c_* $ with $ L^3 $ is marginally consistent with our numerical result. Further investigations are required to clarify the nature of the phase transition of the system with $ h > h_d $ and examine the validity of Dzyaloshinskii’s theory $[8]$. In summary, we have numerically studied the classical Heisenberg spin model of a chiral helimagnet in three dimensions by equilibrium Monte Carlo simulations using the event-chain algorithm. We have particularly focused on its finite-temperature phase transitions with and without a magnetic field perpendicular to the axis of the helical structure. Without the magnetic field, it is shown by the FSS analysis that the system undergoes a continuous phase transition with critical exponents of the three-dimensional ferromagnetic $ XY $ model as predicted by some theoretical studies. It is found that the nature of phase transitions changes in the presence of the magnetic field, although we speculate that the phase transition is continuous irrespectively with the value of the magnetic field $ h $. While the specific heat $ c $ and the magnetic susceptibility $ \chi_{\parallel} (0) $ have finite values at the transition temperature for $ h/J = 0.1 $ and 0.2, they diverge at the transition temperature for $ h/J = 0.3 $. Consequently, it is suggested that the critical point $(T_d, h_d)$ exists in the region where $ 0.2 < h_d/J < 0.3 $ in the phase diagram of the system. The critical exponents of the phase transitions at and above $ h_d $ remain unclear, and thus it would be interesting to reveal the universality class of the phase transition in high fields by determining the critical exponents. A promising way for studying the phase structure might be the method of renormalization group. Our results suggest that the phase transition, distinct from the transition at the low fields, can be detected as a strong singularity in the specific heat, uniform susceptibility and also magnetization curve, which are measurable in experiments. However, the amplitude of the DM interaction studied in this paper is rather large from viewpoint of experiments. Thus, the dependence of the critical point is to be clarified in comparison with the experiments. ACKNOWLEDGMENTS The authors thank S. Hoshino and Y. Kato for very useful discussions and S. Takabe and J. Takahashi for carefully reading the manuscript. Numerical simulation in this work has mainly been performed by using the facility of the Supercomputer Center, Institute for Solid State Physics, the University of Tokyo. This research was supported by the Grants-in-Aid for Scientific Research from the JSPS, Japan (No. 25120010 and 25610102), and JSPS Core-to-Core program “Nonequilibrium dynamics of soft matter and information.” This work was also supported by “Materials research by Information Integration” Initiative (MPI) project of the Support Program for Starting Up Innovation Hub from Japan Science and Technology Agency (JST). Appendix A: Master equation of the ECMC algorithm The dynamics of the ECMC algorithm for continuous spin systems including the lifting parameter $ U $ is explained in this appendix. As used in this work, only one spin specified by the lifting parameter $ U $ is allowed to rotate at any time in our simulations. We denote the probability density of a state $ \langle \{S_i\}, U \rangle $ at time $ s $ as $ \rho (\{S_i\}, U, s) $. 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B 26, 2507 (1982).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 313, 1 ], [ 313, 4918, 2 ], [ 4918, 10127, 3 ], [ 10127, 15786, 4 ], [ 15786, 20236, 5 ], [ 20236, 23406, 6 ], [ 23406, 25878, 7 ], [ 25878, 29813, 8 ], [ 29813, 32644, 9 ], [ 32644, 37452, 10 ], [ 37452, 43353, 11 ], [ 43353, 46021, 12 ], [ 46021, 46972, 13 ] ] }
cdadbca72b38682b09c7f4594604a31c71c8f306	{ "olmocr-version": "0.1.59", "pdf-total-pages": 8, "total-fallback-pages": 0, "total-input-tokens": 27575, "total-output-tokens": 5050, "fieldofstudy": [ "Engineering" ] }	On the oscillations of spatial vibration-isolating system of mining machines under the action of impact loads Mykola Lysytsia 1 Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine, 49005, Dnipro, Simferopolska Str., 2a, Ukraine Abstract. Theoretical and experimental results concerning interaction between lumpy loads and loading sections of a belt conveyer have been represented. The rational parameters of the loading section of the conveyer belt are determined from the point of view of reducing the amplitude of oscillations after the interaction. The regularities of oscillation amplitude of a loading section after interaction with a single lump have been identified. 1 Introduction Since conveyer transport is high-productive, it is the integral part of schemes of cyclic and continuous flow process technology as well as continuous flow process technology in mining. Loading of lumpy product and its conveyance is the restricting factor to apply belt conveyers efficiently. Currently, loading sections of belt conveyers with the use of steel ropes to support rollers and carrying rollers are very popular. Effect of lumpy product on carrying rollers of loading section of a conveyer is characterized by pressure of dice load as well as impact of lumps with certain time interval. After the lump impact, carrying rollers of the section oscillate relative to balance position. When following lump is falling, relative velocity of interaction of the bodies (i.e. load-carrying roller) may either increase or decrease to compare with the initial impact due to carrying roller oscillations. The fact results in the increased dynamic loads both on the belt and the carrying rollers. To decrease the loads, it is necessary for time of suspension system of carrying rollers balancing to be less than a period during which lumps pass. In this context, it is necessary to know displacement mode of carrying rollers, and determine effect of structure of the section and its parameters on its displacement mode in time. Consideration of the problem is of prime importance while designing supporting loading elements taking into consideration a flow of the material being loaded. The paper analyzed oscillations of the two basic types of loading sections – with conveying ropes, and nonrigid carrying rollers designed by Institute of Geotechnical Mechanics named by N. Poljakov of National Academy of Sciences of Ukraine (Fig. 1). Corresponding author: [email protected] © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). 2 Theoretical study While forming oscillation equation of nonrigid carrying roller section, the following has been hypothesized: movement value of central roller cannot depend upon load point along the section length, and longitudinal movements of the rollers are more than by an order of magnitude lesser than vertical ones; and when nonrigid carrying rollers interact with a lump, rope tension varies if only suspension achieves its maximum displacement. Further oscillations of the section take place in terms of practically constant rope tension. That makes it possible to consider a section of nonrigid carrying rollers as a constant density string on an elastic foundation; in this context, at a first approximation, damping of the system is not considered. Figure 2,a demonstrates analytical model where $ U $ is string deviation from its balance; $ L $ is string length; $ T $ and $ \rho $ are string tension and linear density respectively; and $ C_0 $ is rigidity coefficient of the elastic foundation. Figure 2,b shows original form of the string bend where $ b $ is distance between central rollers and $ h $ is the string bend. Original form of the string bend depends upon design features of the section of nonrigid carrying rollers; moreover, experimental data confirm the fact. Using the principles of d’Alembert [1] for the string section we obtain the equations of oscillations: \[ \frac{\partial^2 U}{\partial x^2} = \beta^2 \frac{\partial^2 U}{\partial t^2} + k^2 U, \] where $ \beta^2 = \frac{\rho}{T}; \ k^2 = \frac{C_0}{T}, $ in terms of following initial conditions: \[ U(x,0) = \begin{cases} 0, & 0 < x < \frac{L}{2} - b; \\ -\frac{h}{b}x + h\left(\frac{L}{2} - b\right), & \frac{L}{2} - b < x < \frac{L}{2}; \\ \frac{h}{b}x - \frac{h}{b}\left(\frac{L}{2} + b\right), & \frac{L}{2} < x < \frac{L}{2} + b; \\ 0, & \frac{L}{2} + b < x < L; \end{cases} \] and boundary conditions: \[ U(0,t) = 0; \quad U(L,t) = 0. \tag{3} \] The solution of equation (1) by the Fourier method is presented in general form: \[ U(x,t) = X(x)T(t), \tag{4} \] where \[ X(x) = A \cos(\sqrt{\lambda} x) + B \sin(\sqrt{\lambda} x), \] \[ T(t) = C_n \cos \left( \sqrt{\frac{k^2}{\beta^2} + \frac{\lambda}{\beta^2}} \cdot t \right) + D_n \sin \left( \sqrt{\frac{k^2}{\beta^2} + \frac{\lambda}{\beta^2}} \cdot t \right); \tag{5} \] \[ \lambda = \left( \frac{\pi n}{L} \right)^2, \quad (n = 1, 2, 3\ldots), \] $ A, B, C_n, D_n $ – arbitrary constants. Insert expression (5) into equation (4). While using conditions (2), and (3) we obtain: \[ U(x,t) = \sin \left( \frac{n\pi}{L} x \right) \left[ C_n \cos \left( \sqrt{\frac{k^2}{\beta^2} + \frac{(n\pi)^2}{(L\beta)^2}} \cdot t \right) + D_n \sin \left( \sqrt{\frac{k^2}{\beta^2} + \frac{(n\pi)^2}{(L\beta)^2}} \cdot t \right) \right]. \] Relying upon $ \frac{\partial U(x,0)}{\partial t} = 0 $ condition, we identify that $ D_n = 0. $ Then, \[ U(x,t) = \sum_{n=1}^{\infty} C_n \cos \left( \sqrt{\frac{k^2}{\beta^2} + \frac{(n\pi)^2}{(L\beta)^2}} \cdot t \right) \sin \left( \frac{n\pi}{L} x \right). \tag{6} \] In terms of equation (9), constant $C_n$ is determined using the expression: $$C_n = 2 \frac{L}{L_0} \int f(x) \sin \left( \frac{n\pi}{L} x \right) dx,$$ where $f(x)$ is a function corresponding to initial conditions (2). It follows from initial conditions (2) that: $$f(x) = \begin{cases} 0, & 0 \leq x < \frac{L}{2} - b; \\ - \frac{h}{b} x + \frac{h}{b} \left( \frac{L}{2} - b \right), & \frac{L}{2} - b \leq x < \frac{L}{2}; \\ \frac{h}{b} x - \frac{h}{b} \left( \frac{L}{2} + b \right), & \frac{L}{2} \leq x < \frac{L}{2} + b; \\ 0, & \frac{L}{2} + b \leq x < L. \end{cases}$$ Inserting expressions (8) into (7), we obtain $$C_n = \frac{8hL}{b^2 \pi^2 n^2} \sin \left( \frac{n\pi}{2} \right) \sin^2 \left( \frac{n\pi b}{2L} \right).$$ Taking into consideration that $\beta^2 = \rho / T$, and inserting (9) into (6), we obtain definitely: $$U(x,t) = - \frac{8hL}{b \pi^2} \sum_{n=1}^{\infty} \sin \left( \frac{n\pi}{2} \right) \sin \left( \frac{n\pi b}{2L} \right) \cos \left( \frac{C_0}{\rho} + \frac{T}{\rho L^2} (n\pi)^2 \right) \sin \left( \frac{n\pi}{L} x \right).$$ According to [2], rigidity coefficient of elastic foundation is determined using the expression $$C_0 = \frac{p}{f b^2},$$ where $p$ is a load acting on the roller; and $f$ is displacement of the roller under the load action. Consider oscillations of loading section with conveying ropes. In this context, boundary conditions remain previous ones, and initial conditions are: $$U(x,t) = \begin{cases} - \frac{2h}{L} x, & 0 < x < \frac{L}{2}; \\ \frac{2h}{L} (x - L), & \frac{L}{2} < x < L; \end{cases}$$ $$\frac{\partial U(x,0)}{\partial t} = 0.$$ If initial boundaries (11), and boundary ones (3) are taken into consideration, then solution of equation (1) is Hence, expressions have been developed to determine displacements of loading section points for nonrigid carrying rollers (10), and sections with conveying ropes (12). We will analyze the solutions obtained. Study the effect of loading section length, and initial deviation nature on its oscillation mode within a point of maximum bend, i.e. if $ x = L/2 $, and $ U(x,0) = -h $. 1. Suppose that $ L = 2b $, i.e. initial deviation corresponds to (11) conditions. Then, expression (10) is \[ U\left(\frac{L}{2}, t\right) = -\frac{16h}{\pi^2} \sum_{n=1}^{\infty} \frac{1}{n^2} \sin^2\left(n\pi\right) \cos\left[\frac{C_0}{\rho} + \frac{T}{\rho L^2} (n\pi)^2 \cdot t\right] \sin^2\left(\frac{n\pi}{2}\right). \] If $ n $ values are even ones, then expression (13) is equal to 0. If $ n $ values are odd ones, then $ \sin^2 \frac{n\pi}{4} = \frac{1}{2} $. Hence, expression (13) is as follows \[ U\left(\frac{L}{2}, t\right) = -\frac{8h}{\pi^2} \sum_{n=1}^{\infty} \frac{1}{n^2} \sin^2\left(n\pi\right) \cos\left[\frac{C_0}{\rho} + \frac{T}{\rho L^2} (n\pi)^2 \cdot t\right]. \] The generated dependence coincides completely with expression (12) for section with conveying ropes. In accordance with (12), string points with coordinate $ x = L/2 $ oscillate harmonically with following frequency \[ \omega = \sqrt{\frac{C_0}{\rho} + \frac{T}{\rho L^2} (n\pi)^2} \] and amplitude being equal to $ \pm \frac{8h}{\pi^2} $. While setting $ C_0 = 0 $ in (12), we arrive at the known expression of oscillations of finite-length string with fixed ends [1]. 2. Determine displacement if $ L \to \infty $. While applying L’Hospital rule, we identify that \[ U\left(\frac{L}{2}, t\right) = \lim_{L \to \infty} \left[ \sum_{n=1}^{\infty} \frac{1}{n^2} \sin^2\left(\frac{n\pi b}{2L}\right) \right]^{11} = 0, \] i.e. in terms of considerable $ L $, oscillations of sections decay within a point of maximum bend. Calculations on formula (10) have been performed to determine effect of the section parameters on its oscillations. The section parameters varied as follows: distance between rollers $ b $ was 0.8 and 1.0 m; rope tension $ T $ was 6.0; 8.0 and 10.0 kN; section length $ L $ was 5; 10; 15 and 20 m; linear density $ \rho $ – 50; 80; 110 kg/m; rigidness of nonrigid carrying rollers $ C $ was 60.0; 90; 120 and 150 kN/m² and initial deviation was $ h = 0.09 $ m. The number of series terms was determined with 10% calculation accuracy and amounted 11; 21; 31 and 43 respectively for such section lengths as 5; 10; 15 and 20 m. For 1% calculation accuracy, 129, 257 and 385 series terms $ L = 5; 10; 15 $ m required respectively. However, comparison of the obtained results has shown that the number of series terms effects calculation accuracy of initial ratio $ h_{ at \ t = 0} $ time moment. If $ t > 0 $, then displacement calculation divergence is up to 1.5%. The calculations results helped construct graphs of vertical displacements of the section in time if its parameters vary. Figure 3, a, demonstrates graphs of lateral oscillations of the sections in terms of its varied length as well as rigidness (Fig. 3, b) of elastic foundation. The graphs explain that in the course of time, the section oscillates with constant amplitude decreasing along with the increase in the section length. To compare with the initial disturbance, the amplitude decrease of subsequent oscillations is connected with the fact that at $ t = 0 $ time moment, deviation from the balance concerns limited section area only. Then, the whole its length is involved in the oscillations. Analysis of curves in Figure 3,b shows that the increased rigidness of elastic foundation results in the increase of subsequent oscillations (curve 2). The increased amplitude can be explained by the increased potential energy of the section area with the initial deviation. Analysis of the calculation results has shown: - changes in line load has minor effect on the amplitude of subsequent oscillations; - increase in rope tension decreases amplitude of subsequent oscillations; and - 1.0 m down to 0.8 m decrease in distance between rollers results in 25-30% decrease of subsequent section oscillations. The research has made it possible to determine the effect of the loading section design and parameters on the mechanism of roller displacement reduction in the context of vertical oscillations of the loading section after its interaction with falling material. To compare with initial displacement, the mechanism intended to decrease amplitude of roller oscillation is as follows: during the first time moment, falling load localized bend within a small distance of the section length; subsequently, the energy, accumulated by the area, is consumed by longitudinal oscillations along the section length. Further, point along the section length oscillate. Amplitude of their oscillations is 8-10 times less to compare with the initial deviation amplitude resulted from the load impact. Consideration of frictional losses within the system will result in the damped oscillations while complicating the solution significantly. However, neither qualitative nor quantitative analysis may involve consideration of the losses. It has been determined that 6-8 times decrease in amplitude of vertical oscillations of rollers during 0.4-0.5 s is provided owing to following section parameters: length should not be less than 10 m; rope tension should be 8-10 kN, rigidness should be 100-120 kN, and distance between rollers should be 0.7-0.8 m. 3 Experiments The experiments were carried out by means of a belt conveyor set-up with 80 m length, 0° inclination angle, and 800 mm belt width. Granite was loaded. Its maximum lump size was 400-800 mm; drop height was 0.5 m and 1.0 m; nonrigid carrying rollers were used within loading area. Objective of the experiments is to substantiate analytical model, and to make qualitative evaluation of the results of theoretical studies as for interaction between load and nonrigid carrying rollers. Figure 4 demonstrates a scheme of arrangement of sensors within a section of nonrigid carrying rollers. Hereinafter, following symbols are applied: - $D_1$, $D_3$, and $D_4$ are sensors of vertical displacements of central rollers; - $D_2$ is a sensor of vertical displacements of central roller interacting with the falling load; - $P_1$, and $P_2$, $C_1$, and $C_2$ are sensors of angular displacements of side rollers; - $K_1$, and $K_2$ rope tension sensors. Fig. 4. Scheme of arrangement of sensors. Values of displacement of rollers as well as their oscillation mode after impact with a lump load were determined if variations concerned: loading height (0.5 m; 0.6 m; 0.8 m and 1.0 m); falling lump weight (16 kg and 29 kg); preliminary rope tension (2.0 kN; 3.0 kN; and 4.0 kN and distance between rollers (1 m). Figure 5 explains interaction of 16 kg lump when rope tension is 4.0 kN. Analysis of the obtained data shows that after impact, a roller performs rapidly damping oscillations during 0.4-0.5 s. Amplitude value of oscillations, following the interaction, are 6-10 times less to compare with maximum displacement during impact. Movement of other central rollers (sensors $D_1$, and $D_4$) starts when a roller, experiencing the impact (sensor $D_2$), achieves maximum displacement. Hence, weight of one roller takes place in the impact; loading section bends in terms of length being equal to a twofold pitch of arrangement of rollers. After the interaction, roller oscillations take place in the context of almost constant rope tension. Preliminary rope tension increase results in oscillation amplitude of the roller after interaction. Availability of a belts is not very important for maximum roller displacements (difference is up to 10 %) having minor effect on the section oscillation mode. Fig. 5. Oscillorgams of interaction between a lump and nonrigid carrying rollers. Conclusions* 1. The experiments have confirmed adequacy of the assumptions originated during the analytical model substantation. 2. The results of theoretical studies, concerning the effect of loading section parameters on the mode of vertical oscillations, and on their amplitude after interaction with a single lump, have been supported. 3. The regularities of oscillation amplitude of a loading section after interaction with a single lump have been identified. References 1. Aramanovich, I.G., Levin, V.I. (1969). Uravneniya matematicheskoy fiziki. Moskva: Nauka 2. Timoshenko, S.P. (1946). Soprotivleniye materialov. Moskva: Gostekhizdat	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2724, 1 ], [ 2724, 4232, 2 ], [ 4232, 5822, 3 ], [ 5822, 7575, 4 ], [ 7575, 9978, 5 ], [ 9978, 12704, 6 ], [ 12704, 15245, 7 ], [ 15245, 16199, 8 ] ] }
57c737969c7f78eff471f5a87e232dd4d1639179	{ "olmocr-version": "0.1.59", "pdf-total-pages": 11, "total-fallback-pages": 0, "total-input-tokens": 40839, "total-output-tokens": 16093, "fieldofstudy": [ "Medicine", "Biology" ] }	Current progress in the prevention of mother-to-child transmission of hepatitis B and resulting clinical and programmatic implications Abstract: There is currently no cure for hepatitis B chronic infections. Because new hepatitis B infections result mainly from perinatal transmission, preventing mother-to-child transmission is essential to reach by 2030 the goal of hepatitis B elimination set by the World Health Organization. The universal administration of hepatitis B vaccine to all infants, regardless of maternal status, starting with the birth dose, is the cornerstone of the strategy for elimination. Additional interventions, such as hepatitis B immune globulin administered to newborns and antiviral prophylaxis administered to hepatitis B infected pregnant women, may contribute to reaching the goal earlier. Hepatitis B immune globulin may remain out of reach of many pregnant women in low- and middle-income countries due to cost and logistic issues, but antivirals are cheap and do not require a cold chain for distribution. However, it has been observed that some viruses harbor mutations associated with escape from vaccine-elicited antibodies following immunization or administration of hepatitis B immune globulin. Also, resistance associated mutations have been described for several drugs used for treatment of hepatitis B infected patients as well as for the prevention of mother-to-child transmission. Whether these mutations have the potential to compromise the prevention of mother-to-child transmission or future treatment of the mother is a question of importance. We propose a review of important recent studies assessing tenofovir disoproxil fumarate for the prevention of mother-to-child transmission, and provides detailed information on the mutations possibly relevant in this setting. Keywords: hepatitis B, mother-to-child transmission, prevention, antiviral, resistance Introduction The World Health Organization (WHO) estimated that, in 2015, 257 million individuals, ie, more than 3% of the global population, were affected by chronic hepatitis B virus (HBV) infection, resulting in almost 900,000 deaths. Typically, HBV is acquired early in infancy after exposure to an infected individual, and the infection remains asymptomatic for decades before the apparition of life threatening complications: liver cirrhosis (about 20–30%) and hepatocellular carcinoma (HCC) (about 1%). In 2010, the World Health Assembly adopted the WHA63.18 resolution recognizing the burden of viral hepatitis and expressing the need for more prevention and control of viral hepatitis, and WHO released its first ever guidelines for the prevention, care, and treatment of persons with chronic hepatitis B infection in 2015. Risk of mother-to-child transmission In the absence of any prophylactic measure, mother-to-child transmission (MTCT) of HBV is frequent. Without immunization, about 20%-40% of infants born to HB surface antigen (HBsAg) carrier mothers are found to be infected by 1 year of age, with large variations, depending on maternal risk factors; in particular, infants born to HBe antigen (HBeAg) positive mothers have a 70–90% risk of being infected. While 90% of infants infected during delivery or in infancy become HBsAg chronic carriers, 25–30% of children infected later, between 1 and 5 years of age, develop chronic infection. Route and timing of transmission HBV may be transmitted from an infected mother to her infant in utero, during delivery, or thereafter through close contact. It remains unclear what specific close contacts are most involved in HBV transmissions. HBV is highly contagious. For example, it can be transmitted to humanized mice using tears from HBV infected children. In contrast, it seems unlikely that breast feeding is associated with MTCT of HBV. The World Health Organization (WHO) recommends that HBsAg positive mothers breastfeed their infants, based on studies finding similar rates of HBV infection in breastfed compared to bottle fed children. Most often, the exact timing and route of transmission – vertical versus horizontal – cannot be determined. First, the time needed to establish HBV infection in the liver after virus entry into the fetus or infant body is unknown, and may be variable. While, in adults, symptoms appear on average 90 days after exposure with large variations (8 weeks to 5 months), infant HBV infection is usually asymptomatic. Second, unless a phylogenetic analysis is performed, it remains impossible to know whether the virus originates from the mother or someone else. HB vaccine for the prevention of perinatal infection Most new cases of chronic infections are acquired early in life, and the infant’s mother is the most frequent source of infection. An efficient vaccine has been available since the early 1980s, and is now produced with recombinant DNA techniques. It contains the highly immunogenic HBsAg “a” determinant, which elicits neutralizing anti-HBsAg antibodies and long-term cellular immunity with cross genotype protection in healthy individuals. Produced in high quantities, the cost of the vaccine is low, less than USD 0.5 a dose. Children who have not been immunized are susceptible to HBV infection through contacts with infected individuals (parents, siblings, other family members, etc.). Worldwide, about half of the infants are born in countries where chronic HBV infection is highly endemic, therefore they are at high risk of early infection. In 1992, the incorporation of hepatitis B vaccine in the Expanded Programs for Immunization (EPI) was recommended by the World Health Assembly (WHA 45.17). Hepatitis B vaccine is often administered as one of five or six individual vaccines conjugated into one vial (pentavalent or hexavalent vaccine) to immunize infants against life-threatening infections, ie, diphtheria, tetanus, poliomyelitis, pertussis, Haemophilus influenzae type B, and hepatitis B, with the first administration of the multivalent vaccine scheduled at 6 weeks or 2 months of age. Less developed member states receive support from the Global Alliance for Vaccines and Immunizations (GAVI). This resulted in a dramatic increase in vaccine coverage in infants from 1% in 1990 to 84% in 2015. All countries where hepatitis B vaccine has been integrated in the EPI have seen dramatic decreases in HBV prevalence in children. However, globally, the prevalence of chronic hepatitis B infection in children under 5 years remains relatively high, 1.3% in 2015, with large variations between WHO regions and up to 3.0% in the African Region. Indeed, newborns are susceptible to infection before the first administration of the multivalent vaccine at 2 months of age and those born to HBV infected mothers are the most at risk. As the determination of whether an infant may be exposed to persons with HBV infection is practically impossible, the need for immunization of all infants regardless of HBV maternal status starting at birth (birth dose, using a monovalent vaccine) has been recognized since the 1980s. WHO recommendations have been more and more insistent on the need for a timely birth dose, ie, administered within 24 hours of birth. A timely birth dose seems more effective in preventing perinatal infection than if administered in the following days, though a late birth dose may still prevent infection before the administration of the first pentavalent vaccine at 2 months of age, as long as the infant has not already been infected. In addition, studies in the USA and in China have shown that the administration of the birth dose was associated with an increased likelihood of completing the HB vaccine series. Pregnancy tracking, coordination with traditional birth attendants to ensure timely administration of the vaccine by village-based healthcare workers, and the use of compact, prefilled autodisable devices are among innovative approaches to ensure the timely administration of the HBV birth-dose vaccine that have been evaluated in rural settings in countries such as Vietnam, Indonesia, and China. These strategies have enabled districts to achieve between 84% and 97% vaccination coverage in home-based birth settings.20–22 HBlg in association to HB vaccine to prevent perinatal HBV infection Immunization using the vaccine starting at birth has been shown to decrease the risk of perinatal transmission, but the addition of immune globulin administration after birth is more efficacious to prevent transmission, though this strategy cannot prevent all transmissions.14,23 However, the administration of HBlg to infants born to HBV chronically infected mothers is more challenging than the administration of HB vaccine at birth, a basic preventive measure that has still not been implemented in many health facilities in the world.24 As noted in the 2015 WHO Guidelines,25 HBlg “may not be feasible in most settings.” This is related to multiple factors, including the need for maintenance of refrigerated HBlg stocks, short shelf life, cost considerations, and access to a reliable source of HBlg production from immunized donors. Although the situation has improved for infants born in health facilities, the implementation of the vaccine+HBlg strategy is challenging in settings where pregnant women deliver at home, usually at significant distance from health facilities. The concomitant administration of HBlg and vaccine will remain probably out of reach for a large proportion of infants born to HBV infected women for a long time. Antivirals Therefore, several studies have been conducted to clarify whether alternative or additional approaches could help reduce mother-to-child transmission, in particular using antenatal maternal administration of HBlg or antivirals. Several studies that have investigated the effect of immune globulin administered to the mother during pregnancy on HBV transmission to the fetus/newborn have not demonstrated the efficacy of this approach.26 In contrast, maternal antiviral agents administered during the end of pregnancy may decrease the risk of transmission of HBV from a mother to her infant. An extensive review and meta-analysis of the efficacy and safety of the approach by Brown et al27 was published in 2016. Three oral antiviral drugs, lamivudine (Pregnancy Category C), telbivudine (Category B), and tenofovir disoproxil fumarate (TDF) (Category B) were found to reduce the rates of MTCT in HBeAg-positive women with high viral loads (>10^6 copies IU/mL). However, this conclusion was considered of “moderate to low quality of evidence, rated down due to risk of bias”. As for the safety for the mothers, there were no significant differences in occurrence of severe adverse events, but the quality of the evidence was “very low due to the observational nature of the studies, imprecision, and indirectness”. In infants, there were no differences in congenital malformation rate, prematurity rate, and Apgar scores, with the quality of the evidence considered as “moderate to low, down-rated due to risk of bias and imprecision”. The authors concluded that the results of larger-scale randomized clinical trials were eagerly awaited. Later in 2016, the results of a randomized, open label, clinical trial conducted in academic tertiary care centers in east, south, west, north, and southwest China from March 2012 to June 2013 were reported by Pan et al.28 All infants received vaccine and immune globulin starting at birth, then following national recommendations. None of the 92 infants born to mothers who received TDF from 30–32 weeks of gestation until week 4 postpartum were infected, compared to six of 88 infants (7%) born to mothers who received usual care without antiviral therapy. In 2018, Jourdain et al29 reported the results of a larger, randomized, double blind, placebo-controlled, clinical trial (iTAP-1) conducted in 17 provincial and community hospitals in Thailand from January 2013 to August 2015. The trial was designed both to assess the efficacy of maternal course of TDF from 28 weeks gestational age to 2 months postpartum for the prevention of MTCT and its safety for the mothers and infants with a 1-year mothers’ and infants’ follow-up after delivery/birth. In this trial also, there were no infections among 147 infants born to mothers in the TDF arm, and only three infections (2%) among those 147 infants born to mothers in the placebo arm. The reasons for the differences in rates of infection between the two studies remain unclear (see Table 1 for a comparison of selected characteristics of the two trials). Infants in China received immune globulin twice compared to the once in Thailand. In Thailand, HB vaccine was administered very early after birth (a median 1.2 hours), with four boosters after the birth dose (at 1, 2, 4, and 6 months of age), compared to two in China (2 and 6 months). In both studies, there were no safety concerns. In the Thai study, postpartum ALT elevations above 300 IU/L were observed in both placebo and TDF groups at a similar frequency, and none was associated with clinical symptoms. Altogether, these data suggest that maternal TDF is effective in preventing perinatal transmission of HBV and that the use of TDF is not associated with safety issues. This approach is recommended by the major associations for the study of liver diseases.30–32 However, this recommendation was not included in the WHO Hepatitis B Guidelines in 2015,5 and the use of antivirals for the prevention of PMTCT remains “off-label” in the US due to a lack of data demonstrating the superiority of this approach compared to active-passive immunization. Of note, two studies have suggested that infant development delays may be related to telbivudine in utero exposure.33,34 Effects of pregnancy on viral replication HBV seems to have little effect on pregnancy, but HBV replication tends to increase during pregnancy, probably in relation to immune-suppression and increased production of adrenal corticosteroids, estrogen, and progesterone.35,36 Clinical studies have shown that, within the first months after delivery, some women experience hepatitis flares, with or without HBeAg seroconversion,37 presumably in relation with the rapid decrease in immunosuppression post-partum.38 Comparative clinical studies have confirmed that ALT elevations do occur during the postpartum period in the absence of any antiviral treatment, and that the discontinuation of antiviral treatment in the postpartum period does trigger ALT elevations, but no clinical consequences have been reported.28,29,39 Table 1 Comparison of selected characteristics of two recent clinical trials to assess the efficacy and safety of tenofovir disoproxil fumarate (TDF) for the prevention of mother-to-child transmission of hepatitis B virus \| Studies \| Pan et al24 \| Jourdain et al (iTAP-I)25 \| \|---------\|-------------\|---------------------------\| \| ClinicalTrials.gov registration \| NCT01488526 \| NCT01745822 \| \| Intervention studied \| Maternal TDF 300 mg once a day versus usual care From 30–32 weeks gestational age until week 4 postpartum \| Maternal TDF 300 mg once a day versus placebo From 28 weeks gestational age until 2 months postpartum \| \| Concealment of intervention \| Allocation concealment and open label after randomization and enrollment \| Double blind of the randomized treatment throughout the study \| \| Planned sample size \| 100 pregnant women in each group (total: 200) for ≥85% power to detect a difference of at least 18 percentage points in the transmission rate (expected rate: 20% in the control group (2-sided alpha 0.05) \| 164 pregnant women in each arm (total: 328) for 90% power to detect a difference of at least 9 percentage points in the transmission rate (expected rate: 12% in the placebo group) (1-sided alpha 0.049) \| \| Main inclusion criteria \| HBeAg-positive HBV DNA level >200,000 IU/mL History of abortion, pregnancy loss, or congenital malformation Chronic HBV infection in the biologic father \| HBeAg-positive ALT <60 IU/L \| \| Main exclusion criteria \| Not allowed \| Encouraged \| \| Breastfeeding \| At birth and 1 month of age \| At birth \| \| Planned HBV administration to infants \| At birth, 1, and 6 months of age \| At birth, 1, 2, 4, 6 months of age \| \| Planned HBV vaccine administration to infants \| Multicenter: 4 academic tertiary care centers in China \| Multicenter: 17 provincial and community hospitals in Thailand \| \| Implementation sites \| Period of enrollment \| Month 2012–June 2013 \| January 2013–August 2015 \| \| Number of pregnant women enrolled \| 100 in the TDF group; 100 in the “usual Care” group \| 168 in the TDF arm; 163 in the placebo arm \| \| Amniocentesis performed \| Not specified \| None \| \| Cesarean sections \| 50% \| 26% \| \| Number of infants evaluated \| 92 in the TDF group; 88 in the “usual Care” group 0/92 (0%) in the TDF arm; 6/88 (7%) in the “Usual Care” group \| 147 in the TDF arm; 147 in the placebo arm 0/147 (0%) in the TDF arm; 3/147 (2%) in the placebo arm \| \| Frequency and percentage of infants found HBV infected at 6 months of age \| 0/92 (0%) in the TDF arm; 6/88 (7%) in the “Usual Care” group \| HBV mutations HBV is a partially double-stranded DNA virus which replicates via a reverse transcription step using its polymerase enzyme, which lacks proofreading ability. Errors occur throughout the whole HBV DNA genome at a rate of approximately $2 \times 10^4$ base substitutions/site/year, at least 100-fold higher than for other DNA viruses, but about 1,000-times lower than for RNA viruses. As a result of a high replication rate, 10$^{11}$ virions per day, genetically distinct but closely related variants called quasi species are produced at each replication cycle in the host. Because of specific selection pressure, HBV mutants with a survival advantage over wild type viruses are selected. While some mutant viruses harbor a modified S gene associated with HBV vaccine or HBIg escape, others present polymerase gene mutations conferring resistance to specific antiviral drugs. HBV mutations possibly associated with immunoprophylaxis failure The small HBsAg (S-HBsAg), composed of 226 amino acids (aa), is the major envelope lipoprotein. Its central core (aa 99–169), the major hydrophilic region (MHR), is exposed at the virus surface and involved in binding to anti-HBs antibodies. The immunodominant and immunoprotective determinant is called “a” determinant. It spans the sequence from aa 124 to 147, which includes five cysteine residues crucial for its conformation. The “a” determinant is the main target of neutralizing antibodies either vaccine-induced or passively acquired (HBIg) from HB vaccinated subjects. It is also the target of antibodies used in diagnostic assays. Any change in the “a” determinant modifying the conformation of the HBsAg is critical for antigenicity. Such changes may allow the virus to escape neutralizing antibodies or cause HBV infection misdiagnosis. Failures of hepatitis B vaccine and/or immunoglobulin prophylaxis have been associated with the emergence of mutations in infants. The most common escape mutation is a glycine to arginine substitution at amino acid 145 (sG145R), originally identified in vaccinees and patients receiving active-passive prophylaxis for liver transplantation. Studies have also reported a glycine to alanine substitution at this position (sG145A). Several other mutations (sT116N, sP120E/S, sT125M/A, sT126A/S/N/T/M, sQ129H/R, sT/N131I, sM133L, sK141E, sP142S, sT/S143W, and sD144A/E), occurring either alone or in combination, have also been associated with vaccine failure. From a public health perspective, these mutations are concerning because the efficacy of HB vaccine may be compromised if vaccine escape mutants were to spread out. An evaluation of large scale HB vaccination programs in eastern China during 2005–2013 showed a 9% prevalence of vaccine escape mutants, particularly the s126S/N, sT126A, and sG145R/A, with a significantly upward trend of the sG145R/A mutant from 9% in 2005 to 44% in 2013. The long-term consequences of this increase are still unclear. HBsAg diagnostic tests may turn negative in patients infected with a virus harboring HBsAg mutations in the “a” determinant region. New generations of HBsAg diagnostic kits have been developed to overcome this problem; however, there is still a concern from a public health perspective, in particular regarding MTCT, that infection in these patients may not be diagnosed although they are potentially contagious. In that case, the infection remains detectable by HBV-DNA PCR or HBeAg testing, as these tests are not affected by these mutations. This suggests that the performance over time of the diagnostics kits to detect HBsAg should be monitored. In conclusion, HBsAg mutations in the “a” determinant region remain of concern for the prevention of HBV infection. Impact of immune escape mutants on HBV replication Due to the overlap of the envelope and polymerase genes regions, mutations in the S gene may result in mutations in the polymerase gene. The s145R and the corresponding rTR153Q may affect polymerase activity and HBV replication. In vitro analysis showed that immune escape mutations in the “a” determinant region, sS117T, sK122R, sI126N/S/T, and sG145R, were associated with lower levels of HBsAg as compared to wild-type virus. Practically, it is unclear whether this could increase or decrease the risk of transmission: lower HBV load levels would decrease the risk, but escaping antibodies and HBIg would have the opposite effect, even at lower levels of viral load. Mutations associated with resistance to antivirals Current anti-HBV drugs mostly target the polymerase and include oral nucleos(t)ide analogs with various levels of genetic barrier to resistance. Drugs that have been used for the prevention of MTCT of HBV include lamivudine, $^68–70$ telbivudine, $^71–74$ and TDF.$^27–29,75$ These three drugs have different genetic barriers to resistance, the lowest for lamivudine and the highest for tenofovir, as established in patients treated for HBV infection (Figure 1: Rates of HBV resistance among HBeAg positive patients on HBV monotherapy). The use of lamivudine selects HBV resistance mutations in up to 46% of patients treated for 2 years.$^76–78$ Resistance has been reported in up to 22% in patients on telbivudine for 2 years,$^79$ but less than 1% in patients on entecavir for 2 years.$^80$ No clinical resistance has been reported in HBV-antiviral treatment naïve patients after 8 years on TDF.$^81$ In the context of HIV-HBV co-infection, the use of TDF has been associated with high rates of virological suppression.$^82,83$ However, a small percentage of co-infected patients on TDF-containing antiretroviral treatment have experienced suboptimal responses after long-term therapy and, in rare cases, possible resistance to tenofovir has been suspected.$^82,84$ The emergence of such viral mutations, or genotypic resistance, may trigger an increase in HBV replication that can be evidenced by an increase in HBV DNA levels, ie, a virological breakthrough. In some cases, a severe exacerbation of the underlying liver disease may occur and, in rare cases, lead to acute liver failure. However, pregnant women with indications for antiviral treatment for the prevention of MTCT of HBV usually have high viral loads and are in the immune tolerance phase of the infection. Therefore, it is unclear whether the selection of such mutation during the short course of antiviral prophylaxis can trigger clinically significant exacerbations. Mutations on the polymerase gene conferring resistance to nucleoside analogs The HBV polymerase is composed of four domains. The reverse transcriptase (rt) domain is responsible for the polymerase activity and is the target of nucleoside analogs. Specific mutations associated with resistance to lamivudine include the mutations at position 204 of the reverse transcriptase domain where the wild-type position is a methionine (rtM204) in the YMDD locus of the catalytic C box of the polymerase.$^76,78,85,86$ Other mutations can occur in the A and B boxes (rtL80V/I, rtV173L, and rtL180M) and are often found along with the rtM204V/I mutations. Some ![Figure 1 Risk of HBV resistance in HBeAg positive patients on lamivudine, telbivudine, entecavir or tenofovir disoproxil fumarate (TDF) monotherapy according to duration on treatment.](image-url) of these mutations reduce susceptibility to other NAs: rtM204I/V mutations confer virus cross-resistance to telbivudine, and the rtA181T/V mutations confer cross-resistance to telbivudine and adefovir. The rtN236T mutation selected for by adefovir may confer resistance to tenofovir when present with the rtA181T/V mutations.87 (see Table 2). Due to potential cross-resistance to lamivudine and entecavir, it is not recommended to use lamivudine for treatment and prophylaxis as entecavir is currently the only option for patients who cannot tolerate TDF. As noted above, tenofovir resistance in HBV mono-infected patients has not been identified in patients on treatment and, to our knowledge, there has been no report of such resistance in women receiving TDF to prevent MTCT. However, several mutations associated with resistance to tenofovir have been described in HIV-HBV co-infected patients, though the clinical relevance of these mutations remains unclear. The rare cases described were co-infected patients previously exposed to lamivudine who achieved incomplete HBV suppression on TDF.84,88 The rtA194T mutation was detected in co-infected TDF treated patients also exhibiting lamivudine-resistance mutations. In vitro phenotypic analysis showed that viruses with the rtA194T along with the lamivudine resistance rtL180M and rtM204V mutations had a 10-fold increase in the IC50 for TDF as compared with wild type viruses.89 However, it has been reported that a patient with the rtA194T achieved HBV replication suppression on TDF.90 In another study of 111 HIV-HBV co-infected patients on long-term TDF-containing antiretroviral therapy, some polymerase resistance mutations selected during antiviral therapy can concomitantly alter the antigenicity of HBsAg. The rtM204V mutation, selected by lamivudine treatment, is associated with an amino acid residue change at position 195 of the HBsAg (sI195M), while the rtM204I mutation can result in three possible changes; sW196S, sW196L, or a stop codon.93 The triple lamivudine resistance mutations (rtV173L +rtL180M+rtM204V) are linked with the changes of two amino acids in the surface gene (sE164D +sI195M).94,95 As a consequence of the conformation change of the surface antigen, mutant HBsAg binding to anti-HBs is greatly reduced to levels similar to that observed with the vaccine escape mutant sG145R.96 These mutations were found in up to 25% of HIV-HBV co-infected individuals and 10% of HBV mono-infected patients with HBV replication on lamivudine treatment.97 The polymerase mutations, rtA181T and rtA181V, induced by adefovir, result in envelope mutations: top codon (sW172stop) and sL173F, respectively. Mutations conferring resistance to entecavir (ie, rtI169T, rtS184G, and rtS202I) also result in amino acid changes of HBsAg (sF161L, sL/V176G, and sV194F). However, their effect on the envelope structure, particularly in the “a” determinant region, and their significance for diagnostics and vaccine escape need further investigation. ### Impact of resistance mutations selected by antiviral therapy on surface antigen Due to the overlap of the envelope and polymerase genes reading frames, some polymerase resistance mutations selected during antiviral therapy can concomitantly alter the antigenicity of HBsAg. The rtM204V mutation, selected by lamivudine treatment, is associated with an amino acid residue change at position 195 of the HBsAg (sI195M), while the rtM204I mutation can result in three possible changes; sW196S, sW196L, or a stop codon.93 The triple lamivudine resistance mutations (rtV173L +rtL180M+rtM204V) are linked with the changes of two amino acids in the surface gene (sE164D +sI195M).94,95 As a consequence of the conformation change of the surface antigen, mutant HBsAg binding to anti-HBs is greatly reduced to levels similar to that observed with the vaccine escape mutant sG145R.96 These mutations were found in up to 25% of HIV-HBV co-infected individuals and 10% of HBV mono-infected patients with HBV replication on lamivudine treatment.97 The polymerase mutations, rtA181T and rtA181V, induced by adefovir, result in envelope mutations: top codon (sW172stop) and sL173F, respectively. Mutations conferring resistance to entecavir (ie, rtI169T, rtS184G, and rtS202I) also result in amino acid changes of HBsAg (sF161L, sL/V176G, and sV194F). However, their effect on the envelope structure, particularly in the “a” determinant region, and their significance for diagnostics and vaccine escape need further investigation. ### Table 2 Polymerase gene mutations associated with resistance to one or several nucleos(t)ide analogs \| Polymerase boxes \| A \| B \| C \| D \| E \| \|------------------\|---\|---\|---\|---\|---\| \| Lamivudine \| rtL80I \| rtV173L, rtL180M, rtA181T/V \| rtM204V/I \| rtN236T, rtI233T \| rt250I/V \| \| Telbivudine \| rtL217R \| rtL180M, rtA181T/V \| \| \| \| \| Adefovir \| rtI169T, rtL180M, rtA181T/V \| rtM204V/I \| \| \| \| \| Entecavir \| rtI169T, rtL180M, rtT184G, rtA194T \| \| \| \| \| \| TDF \| \| rtL180M, rtA181T/V \| rtS202G \| \| \| Of concern for the prevention of MTCT, it has been suggested that these mutants selected by lamivudine treatment could escape recognition by anti-HBs antibodies elicited by HB vaccine and, also, cause false negative HBsAg test results despite active HBV replication. However, since 2017, TDF is no longer protected, and the price of generics has dramatically decreased, which makes the use of lamivudine less attractive. Therefore, the incidence of HBsAg mutants selected by lamivudine should decrease over time. HBV resistance to nucleos(t)ide analogs and prevention of MTCT Information about the percentage of pregnant women with nucleos(t)ide analog-resistant viruses at the initiation of antiviral prophylaxis or later is scarce, and this may vary across settings depending on the extent of the use of these drugs. Transmission despite antiviral prophylaxis and associated with antiviral resistance have not been reported to our knowledge. As for emergence of resistance during a short prophylactic course of antiviral, the issue has not been fully investigated in older MTCT clinical trials but, in 2014, Ayres et al reported the emergence of low frequency rtM204I/V and rtA181T resistant viruses to lamivudine or minor variants using ultra-deep pyrosequencing in seven of 21 pregnant women who received lamivudine during the third trimester of pregnancy. Conclusion Maternal antiviral prophylaxis during pregnancy, in addition to active-passive immunization, has been proposed to further prevent MTCT of HBV. Recent clinical trials assessing TDF in this setting have suggested the efficacy and safety of the approach. Major associations for the study of liver diseases have included this approach in their guidelines for PMTCT of HBV but, to date, not WHO, and the use of TDF for the prevention of MTCT of HBV remains “off-label” in the US. Immune escape mutants and nucleos(t)ide analog resistant viruses do not seem to represent a major threat to this approach, but need to be monitored. The question of whether the administration of HB Ig is needed when a mother receives antiviral prophylaxis remains unanswered. As new infections are essentially the results of perinatal transmission, reaching by 2030 the goal of hepatitis B elimination set by WHO, ie, 90% reduction in new chronic infections, relies first on the accurate administration of HB vaccine to all infants starting with the birth dose, which has the potential of lifelong protection. Additional interventions, such as antiviral prophylaxis in pregnant women or HB Ig to infants, may help but not replace the vaccine. Disclosure The authors declare that they have no conflicts of interest in this work. References 1. World Health Organization. Global Hepatitis Report 2017. Geneva: World Health Organization & Global Hepatitis Programme; 2017. 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J Med Virol. 2005;78(Suppl 1):S76–81. doi:10.1002/jmv.20608	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2743, 1 ], [ 2743, 7831, 2 ], [ 7831, 12903, 3 ], [ 12903, 17147, 4 ], [ 17147, 21773, 5 ], [ 21773, 24476, 6 ], [ 24476, 29553, 7 ], [ 29553, 35037, 8 ], [ 35037, 41745, 9 ], [ 41745, 49136, 10 ], [ 49136, 52476, 11 ] ] }
7f9508df6d7db8033dfb3713eb3b5def943b085a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 13, "total-fallback-pages": 0, "total-input-tokens": 45989, "total-output-tokens": 14616, "fieldofstudy": [ "Engineering", "Materials Science" ] }	Electromechanical impedance instrumented circular piezoelectric-metal transducer for corrosion monitoring: modeling and validation Weijie Li1, Jianjun Wang2, Tiejun Liu1 and Mingzhang Luo3 1 School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, People’s Republic of China 2 Department of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, People’s Republic of China 3 Electronics and Information School, Yangtze University, Jingzhou 434023, People’s Republic of China E-mail: [email protected] Received 3 August 2019, revised 13 November 2019 Accepted for publication 3 January 2020 Published 27 January 2020 Abstract Corrosion induced thickness loss of metallic structures is one of the most common issues across multiple industries. In our previous work, a new type of corrosion sensor based on lead zirconate titanate (PZT) using electromechanical impedance (EMI) technique was proposed. The sensor is fabricated by bonding a PZT patch onto a metal plate. The previous work has demonstrated that the peak frequencies in the conductance signatures decrease linearly with the increase of the corrosion induced thickness loss. However, a theoretical model that fully describe the coupled vibration between piezoelectric element and the metal plate, and the EMI characteristics has not been established. This paper presents the theoretical modeling of the EMI instrumented circular piezoelectric-metal transducer for corrosion monitoring purpose. Based on electro-elastic and Kirchhoff plate theory, the EMI responses of the transducer operated in transverse bending modes with free boundary conditions were modeled. Finite element modeling calculations and experimental measurement were conducted to validate the theoretical results with good agreement. Keywords: piezoelectric-metal transducer, electromechanical impedance (EMI), corrosion monitoring, electro-elastic modeling, finite element modeling (Some figures may appear in colour only in the online journal) 1. Introduction Corrosion is the deterioration of metallic materials as a result of chemical or electrochemical reaction between them and their environment. Corrosion is one of the most common issues in multiple industries, including oil and gas, civil, mechanical, aerospace, mining, and processing. Generally, corrosion can be classified into two types, the uniform corrosion and localized corrosion. The uniform corrosion leads to the thinning of metallic materials, which is the most common form of corrosion and represents the greatest destruction on metals. The corrosion induced thickness loss on the metallic structures poses great threat to the safety and serviceability of the structures, and in severe situations, it is responsible for the huge amount of economic loss and even the loss of human life. It is reported that the global cost of corrosion is about 2.5 trillion US dollars each year (Koch et al... Various methods are under development for corrosion monitoring. For example, the development of guided wave tomography (Huthwaite and Simonetti 2013, Rao et al 2016a, 2016b, Brath et al 2017, Rao et al 2017a) has enabled the quantification of corrosion in plates and pipes (Nagy et al 2014, Rao et al 2017b, 2017c). On the other hand, the piezoelectric based structural health monitoring (SHM) has received increasing research attention over the past decades. A piezoelectric transducer acts as both sensor and actuator due to the direct and inverse piezoelectric effects. Piezoelectric material, the lead zirconate titanate (PZT) in particular, offers many advantages such as noninvasive, low cost, high sensitivity, wide bandwidth, quick response, and online monitoring capability. The piezoelectric based SHM methods have been adopted in the monitoring of damages in various engineering structures. For example, the rock bolt health monitoring (Song et al 2017, Wang et al 2017b), interlayer slide detection (Wu et al 2017), water seepage monitoring in concrete structures (Liu et al 2013, Zou et al 2014), concrete crack monitoring (Dumoulin et al 2014, Tsangouris et al 2015), debonding detection (Xu et al 2013, Li et al 2016a, Luo et al 2016, Xu et al 2018, Chen et al 2019), crack detection in aluminum plate (Kudela et al 2018), concrete hydration and strength gain monitoring (Dumoulin et al 2012, Kong et al 2013, Lu et al 2018b, Lu et al 2019), novel smart aggregate based health monitoring methods for concrete structures (Li et al 2016b, Zou et al 2017, Du et al 2018), and novel signal processing approaches were also proposed for extracting useful damage related information (Fan et al 2016, 2018b). The electromechanical impedance (EMI) technique has been extensively recognized as a promising and powerful tool for damage detection and evaluation of a variety of engineering structures, such as pre-stressed structures (Wang et al 2017a, Fan et al 2018a, Huyhn et al 2018, Ryu et al 2019), concrete structures (Liang et al 2016, Li et al 2018, Lu et al 2018a, Shi et al 2018, Talakokula et al 2018), metal plates (Giurgiutiu and Zagari 2005, Vieira Filho et al 2011, Fan et al 2018c), and interlayer slide (Wu et al 2018). In this technique, the PZT patch is either surface-bonded on or embedded into the structure to be examined. The vibration of the PZT patch and the host structure are thus coupled. The PZT patch is collocated as sensor and actuator and the EMI signals are measured by an impedance analyzer. If variations presented in the EMI signals of current condition as compared to those of pristine condition, structural damages are detected. The EMI method is fast, accurate, and has the potential to provide real-time, remote and autonomous monitoring at low cost with large scale application capability. Up to now, literature survey showed that limited studies have been carried out on corrosion monitoring using the EMI technique. Talakokula et al evaluated the corrosion process of rebars of reinforced concrete using the surface-bonded PZT patches and the EMI technique (Talakokula et al 2013). It was shown that the equivalent parameters derived from the admittance signatures were correlated to the corrosion amount of the reinforced concrete. Zhu et al introduced the concept of structural mechanical impedance for corrosion detection of steel structures using the EMI method (Zhu et al 2016). The experimental results showed that the structural mechanical impedance is sensitive to corrosion damage despite the limited sensing range. Na investigated the possibility of detecting wall thickness loss of metal based pipeline facilities using the EMI technique (Na 2017). It was found that the resonance peaks in the impedance signatures is shifted due to the reduction in wall thickness. However, the common issue with these studies is that the PZT patch is usually attached to the host structures which have complex geometry, loading conditions, and boundary conditions. Thus, it is difficult to build up the physical relation between the resonant peaks in the EMI signatures and the structural parameters. Also, it is difficult to isolate the other influencing factors, such as variations in loading and boundary conditions, from the corrosion induced damages. Since the resonant frequency range are deeply affected by the geometry shape, loading conditions, and boundary conditions of the host structure, choosing the appropriate frequency range for the EMI signatures would be a challenging task. Furthermore, the damage induced variations in the EMI signatures are quantified by the statistical metrics, such as root-mean-square deviation and correlation coefficient, which may not work well if the selected frequency range is inadequate. In our previous studies, a new type of EMI based corrosion sensor was proposed to overcome the shortcomings of the abovementioned EMI corrosion monitoring methods (Li et al 2019a, 2019b). The proposed corrosion sensor is essentially a piezoelectric-metal transducer, which consists of a metal plate with a PZT patch attached onto it. Previous studies demonstrated that the peak frequencies decrease linearly with the increase of the corrosion induced thickness loss. And the finite element modeling (FEM) based modal analysis showed that the vibration modes of the piezoelectric-metal transducer corresponding to the shifted peak frequencies are the bending modes. However, a theoretical model that fully describe the coupling vibration between piezoelectric element and the metal plate and the EMI characteristics has not been established. In the present study, the theoretical model accounts for the transverse bending vibration of the piezoelectric-metal transducer was established. The EMI characteristics of the transducer was investigated and the validity of using the proposed transducer as corrosion sensor was verified theoretically. The theoretical calculations were compared with FEM and experimental results. The results showed that theoretical predictions, FEM calculations and experimental measurements agree well with each other. 2. Theoretical modeling The EMI based corrosion sensor to be modeled is considered as a circular piezoelectric-metal transducer fabricated by bonding a piezoelectric disk to a metal plate, as shown in figure 1. The piezoelectric disk is polarized in the thickness direction, and its major surfaces are completely covered with electrodes with negligible thickness. When the electrodes are connected to an sinusoidal actuating voltage of magnitude $V_0$ and circular frequency $\omega$, the in-plane extension of the piezoelectric disk excites the bending vibration of the transducer. The thickness reduction of the metal plate will reduce the bending resonant frequencies of the transducer, and thus the transducer can be used for corrosion monitoring. In the following analysis, the piezoelectric-metal transducer is treated as a single electromechanical body operated in transverse bending modes. 2.1. Basic equations The thicknesses of the piezoelectric disk and the metal plate are $h_p$ and $h_m$, respectively, and their radii are both $a$. The total thickness is then expressed as $h_{total} = h_p + h_m$. Subscripts $p$ and $m$ indicate the piezoelectric disk and the metal plate, respectively. The neutral surface of the whole sensor is chosen as the coordinate $z = 0$. Thus, the distance from the top surface to the neutral surface is $h_0$ and the distance from the bottom surface to the neutral surface is $h_1$. The total thickness is also expressed as $h_{total} = h_0 + h_1$. Based on Kirchhoff’s hypotheses, the strain-displacement relationships can be expressed as (Mo et al 2006, Deshpande and Sagare 2007, Li et al 2009) $$\varepsilon_r = -z \frac{dw}{dr}, \quad \varepsilon_\theta = -z \frac{dv}{dr},$$ where $\varepsilon_r$ and $\varepsilon_\theta$ are the radial and circumferential strains, respectively; $w$ is the transverse displacement. For the piezoelectric disk polarized along its thickness direction, its constitutive equations can be expressed as (Mo et al 2006, Dong et al 2007, Wang and Shi 2013, Wang et al 2018) $$\sigma_p = \frac{E_p}{1 - \nu_p^2} (\varepsilon_r + \nu_p \varepsilon_\theta) - \varepsilon_{31} E_z, \quad \sigma_m = \frac{E_m}{1 - \nu_m^2} (\varepsilon_r + \nu_m \varepsilon_\theta) - \varepsilon_{31} E_z,$$ where $\sigma_p$ and $\sigma_m$ are the radial and circumferential stresses, respectively; $D_z$ and $E_z$ are the electric displacement and electric field, respectively; $E_p = 1/s_{11}^p$ is Young’s modulus of the piezoelectric disk; $\nu_p = -s_{12}^p/s_{11}^p$ is Poisson’s ratio; $e_{31} = d_{31}/(s_{11}^p + s_{12}^p)$ is the effective piezoelectric stress constant; $\varepsilon_{33} = \varepsilon_{33}^s - 2d_{31}^s/(s_{11}^p + s_{12}^p)$ is the effective dielectric permittivity at constant strain; $s_{11}^p, s_{12}^p, d_{31}^p$ and $\varepsilon_{33}^s$ are the elastic compliances at constant electric field, the piezoelectric strain constant, the dielectric permittivity at constant stress, respectively. For the metal plate, its constitutive equations can be expressed as (Mo et al 2006, Dong et al 2007) $$\sigma_m = \frac{E_m}{1 - \nu_m^2} (\varepsilon_r + \nu_m \varepsilon_\theta), \quad \sigma_m = \frac{E_m}{1 - \nu_m^2} (\varepsilon_r + \nu_m \varepsilon_\theta),$$ where $E_m$ and $\nu_m$ are Young’s modulus and Poisson’s ratio of the metal plate, respectively. The resultant radial and circumferential bending moments $M_r$ and $M_\theta$ are $$M_r = \int_{-h_1}^{h_0} \sigma_m dz + \int_{h_0}^{h_1} \sigma_m dz, \quad M_\theta = \int_{-h_1}^{h_0} \sigma_m dz + \int_{h_0}^{h_1} \sigma_m dz.$$ The equilibrium equations for the axisymmetric bending problem are $$Q_r = \frac{dM_r}{dr} + \frac{M_r - M_\theta}{r}, \quad \frac{dQ_\theta}{dr} + \frac{Q_\theta}{r} = m \frac{d^2w}{dt^2},$$ where $Q_r$ is the resultant shear force; $\rho_p$ and $\rho_m$ are the densities of the piezoelectric disk and the metal plate, respectively; $m = \rho_p h_p + \rho_m h_m$ is the mass per unit area; $t$ is the time. 2.2. Solution In order to solve the equilibrium equations together with constitutive equations in view of strain-displacement relationships, the location of the neutral surface needs to be determined based on the force equilibrium of the resultant radial force $N_r$, that is $$N_r = \int_{-h_1}^{h_0} \sigma_m dz + \int_{h_0}^{h_1} \sigma_m dz = 0. \quad (12)$$ To simply the problem, the electrical effect is usually assumed to be negligible when determining the neutral surface. Under this condition, the second term in equation (3) is neglected for the piezoelectric disk. Upon solving equation (12), the distances $h_0$ and $h_1$ can be derived as (Dong et al 2007, Li et al 2009) $$h_0 = \frac{Y_m h_m^2 + Y_p h_p^2 + 2Y_m h_m h_p}{2(Y_m h_m + Y_p h_p)},$$ $$h_1 = \frac{Y_m h_m^2 + Y_p h_p^2 + 2Y_m h_m h_p}{2(Y_m h_m + Y_p h_p)},$$ where $Y_m = E_m/(1 - \nu_m^2), Y_p = E_p/(1 - \nu_p^2).$ Substituting equations (1)–(4), (6), (7), (13) and (14) into equations (8) and (9), the resultant radial and circumferential bending moments $M_r$ and $M_ heta$ can be expressed in terms of the transverse displacement $w$ as follows: $$M_r = \bar{D} \left[ - \frac{d^2 w}{dr^2} \right] + \bar{D}_r \left( \frac{1}{r} \frac{dw}{dr} \right) - e_{31} E_z h_{pr},$$ (15) $$M_{\theta} = \bar{D} \left[ - \frac{d^2 w}{dr^2} \right] + \bar{D}_\theta \left( \frac{1}{r} \frac{dw}{dr} \right) - e_{31} E_z h_{pr},$$ (16) where $$\bar{Y}_n = \frac{1}{3} Y_m [ (h_m - h_i)^3 + h_i^3 ],$$ $$\bar{Y}_p = \frac{1}{3} Y_p [ h_0^3 - (h_m - h_i)^3 ];$$ $\bar{D} = \bar{Y}_m + \bar{Y}_p$ is the flexural rigidity of the whole structure; $\bar{D}_r = \bar{Y}_m v_m + \bar{Y}_p v_{pr}$ Substituting equations (15) and (16) into (10), the resultant shear force $Q_r$ can also be expressed in terms of the transverse displacement $w$ as follows: $$Q_r = \bar{D} \left[ - \frac{d^3 w}{dr^3} \right] + \left( \frac{1}{r^2} \frac{d^2 w}{dr^2} \right) + \left( \frac{1}{r} \frac{dw}{dr} \right).$$ (17) Substituting equation (17) into (11) yields $$-\bar{D} \left[ \frac{d^2 w}{dr^3} + 2 \frac{d^2 w}{r \, dr^2} - \left( \frac{1}{r} \frac{d^2 w}{dr^2} + \frac{1}{r} \frac{dw}{dr} \right) \right] = m \frac{d^2 w}{dr^2}.$$ (18) Considering a harmonic actuating voltage $V(t) = V_0 e^{j \omega t}$ ($E = -(V_0 / h_p) e^{j \omega t}$) applied to the piezoelectric disk, the transverse displacement $w$ can be written as $$w = w(r) e^{j \omega t},$$ (19) where $V_0$ is the actuating voltage amplitude, $j = \sqrt{-1}$ is the imaginary unit, $f$ is the excitation frequency, and $\omega = 2 \pi f$ is the circular frequency. Substituting equation (19) into (18), results in the following governing equation $$\frac{d^3 w(r)}{dr^3} + 2 \frac{d^2 w(r)}{r \, dr^2} - \left( \frac{1}{r^2} \frac{d^2 w(r)}{dr^2} \right) + \frac{1}{r} \frac{dw(r)}{dr} - k^4 w(r) = 0,$$ (20) where $k^4 = \omega^2 m / \bar{D}$. Solving equation (20), yields $$w(r) = A_1 J_0 (kr) + B_1 Y_0 (kr) + C_1 I_0 (kr) + D_1 K_0 (kr),$$ (21) where $A_1$, $B_1$, $C_1$ and $D_1$ are the undetermined coefficients; $J_0 (kr)$ and $Y_0 (kr)$ are Bessel functions of the first and second kinds, respectively; $I_0 (kr)$ and $K_0 (kr)$ are Modified Bessel functions of the first and second kinds, respectively. When $r \to 0$, $Y_0 (0)$, $K_0 (0) \to \infty$. Thus, $B_1 = 0$, $D_1 = 0$. Then equation (21) becomes $$w(r) = A_1 J_0 (kr) + C_1 I_0 (kr).$$ (22) At $r = a$, the free boundary conditions must be satisfied, which are expressed as $$M_r \|_{r=a} = 0,$$ (23) $$Q_r \|_{r=a} = 0.$$ (24) Combining equations (23) and (24), yields $$A_1 \delta_1 - C_1 \delta_2 = -e_{31} V_0,$$ (25) $$A_1 \delta_3 - C_1 \delta_4 = 0,$$ (26) where $$\delta_1 = (\bar{D} + \bar{D}_r) (1 / a) k J_1 (ka) - \bar{D} k^2 J_2 (ka),$$ (27) $$\delta_2 = (\bar{D} + \bar{D}_r) (1 / a) k I_1 (ka) + \bar{D} k^2 I_2 (ka),$$ (28) $$\delta_3 = \bar{D} k^2 [ - (4 / a) J_2 (ka) + k J_3 (ka) ],$$ (29) $$\delta_4 = \bar{D} k^2 [ (4 / a) I_2 (ka) + k I_3 (ka) ].$$ (30) Solving equations (25) and (26), the undetermined coefficients $A_1$ and $C_1$ are $$A_1 = \delta_5 V_0,$$ (31) $$C_1 = \delta_6 V_0,$$ (32) where $$\delta_5 = -e_{31} \delta_3 / (\delta_1 \delta_4 - \delta_2 \delta_3),$$ (33) $$\delta_6 = -e_{31} \delta_4 / (\delta_1 \delta_3 - \delta_2 \delta_4).$$ (34) Further, combining equations (1), (2), (5), (22), (31), (32), and performing the integration over the upper electrode area of the piezoelectric disk gives the electrical charge $$Q(t) = \int_0^{2 \pi} \int_0^a D_2 \left[ -h_0 r dr d\theta \right] = \tilde{C}_0 V_0 e^{j \omega t},$$ (35) where $\tilde{C}_0$ is the effective electric capacitance, and is defined as $$\tilde{C}_0 = 2 \pi \varepsilon_3 \varepsilon_0 k a [ \delta_5 J_1 (ka) - \delta_6 \delta_2 (ka) ] - C_0.$$ (36) In equation (36), $C_0 = \pi a^2 \varepsilon_{33} / h_p$ is the clamped electric capacitance of the piezoelectric disk. Thus, the currents $I(t)$ can be solved as $$I(t) = - \frac{dQ(t)}{dt} = -j \omega \tilde{C}_0 V_0 e^{j \omega t}. $$ (37) Then, the electrical admittance $Y$, which is the inverse of impedance $Z$, can be expressed as $$Y = \frac{1}{Z} = G + jB = \frac{I(t)}{V(t)} = -j \omega \tilde{C}_0,$$ (38) where $G$ and $B$ are the conductance (real part of admittance) and susceptance (imaginary part of admittance), respectively. The local maxima appearing in the admittance curve or conductance curve corresponds to resonance. 3. Numerical results 3.1. Theoretical calculations Using the theoretical analysis described in the previous section, the EMI responses of the piezoelectric-metal transducer with different metal thicknesses can be calculated numerically. The piezoelectric-metal transducers considered in this study are listed in table 1. Transducers with two different diameters are considered, that is, 30 and 40 mm. The thickness of the piezoelectric disk is 0.5 mm. The thickness of the metal plate is reduced from 3.0 to 1.0 mm with an interval... Table 1. Sizes of piezoelectric-metal transducer. \| Specimen \| Metal plate (mm) \| PZT thickness (mm) \| Diameter (mm) \| \|----------\|-----------------\|-------------------\|---------------\| \| D30T30 \| 3.0 \| 0.5 \| 30 \| \| D30T25 \| 2.5 \| \| \| \| D30T20 \| 2.0 \| \| \| \| D30T15 \| 1.5 \| \| \| \| D30T10 \| 1.0 \| \| \| \| D40T30 \| 3.0 \| 0.5 \| 40 \| \| D40T25 \| 2.5 \| \| \| \| D40T20 \| 2.0 \| \| \| \| D40T15 \| 1.5 \| \| \| \| D40T10 \| 1.0 \| \| \| Table 2. Material properties of the piezoelectric disk and the metal plate. \| Material \| Properties \| Symbols \| Values \| \|----------\|---------------------\|---------\|---------\| \| PZT \| Density (kg m$^{-3}$) \| $\rho$ \| 7450 \| \| \| Dielectric loss factor \| $\tan \delta$ \| 0.023 \| \| \| Compliance (10$^{-12}$ m$^2$ N$^{-1}$) \| $s_{ii}$ \| 13 \| \| \| Relative permittivity \| $\varepsilon_{ii}/\varepsilon_0$ \| 5800 \| \| \| Piezoelectric strain coefficients (10$^{-12}$ C/N) \| $d_{31}$, $d_{32}$ \| -186 \| \| \| Damping ratio \| $\zeta$ \| 0.014 \| \| Metal plate \| Density (kg m$^{-3}$) \| $\rho$ \| 7800 \| \| \| Poisson’s Ratio \| $\nu$ \| 0.26 \| \| \| Young’s modulus (GPa) \| $E$ \| 200 \| of 0.5 mm, so as to simulate thickness loss and observe the corresponding EMI responses. The diameter-to-thickness ratio is larger than 10 except for specimen D30T30. The material for the piezoelectric disk is PZT-5H and those for metal plate is mild steel. The material properties are listed in table 2. The conductance signatures of transducers with different metal plate thickness in the frequency range 1–200 kHz are shown in figure 2. Since some of the peaks for different metal thickness are overlapped, the conductance signatures for different metal plate thickness are plotted in separate subplots. The first peak corresponds to the resonant frequency of first bending mode and the same goes for the second and the third. In this study, only the first and the second bending modes were investigated since these modes are within 200 kHz frequency range that can be easily measured using a common impedance analyzer. It can be observed that the peak frequency shows leftward movement due to the reduction in metal plate thickness. That is to say, the resonant frequency reduced with the decrease in metal thickness, or the increase in thickness loss of the metal plate. Such property in the EMI response can be utilized for corrosion monitoring. Such phenomenon were also observed in our previous studies (Li et al 2019a, 2019b). The peak frequencies calculated from the theory are listed in table 3 for comparison. The peak frequencies of the first two bending modes as a function of thickness loss of the metal plate, together with the linear fitted curves, are shown in figure 3. The expressions and the coefficients of determination ($R^2$) of the fitted curves are also presented. The linearity between the peak frequency and the thickness loss is very good as evidenced by the fact that all the coefficients of determination of the fitted curves are very close to one. The linear relationship between the peak frequency of bending modes and the thickness loss of the metal plate is an advantageous feature of the proposed transducer. The slope of the fitted curve is the sensitivity of the transducer. For the 30 mm diameter transducer, the sensitivity for the first and the second bending modes are 9.12 kHz mm$^{-1}$ and 39.30 kHz mm$^{-1}$, respectively. And for the 40 mm diameter transducer, the sensitivity for the first peak and the second peak are 5.10 kHz mm$^{-1}$ and 22.12 kHz mm$^{-1}$, respectively. As can be seen, the second mode is much more sensitive than the first mode. In addition, when comparing the same mode, that of the 30 mm diameter transducer is more sensitive than that of the 40 mm diameter transducer. Consequently, higher order modes and transducer with smaller diameter, are more sensitive to the thickness loss of the metal plate. Thus, it is possible to adjust the sensitivity of the transducer by selecting the proper mode as well as the size of the transducer. Given that the sampling resolution of the impedance analyzer can be as high as 1 Hz/sample, the proposed transducer is able to achieve sub-micrometer accuracy technically. The results demonstrate that the EMI instrumented piezoelectric-metal transducer can be utilized as corrosion sensor for quantitative determination of corrosion induced thickness loss. 3.2. Finite element modeling The theoretical analysis described in the above section has advantages in terms of using expressions to calculate the EMI signatures. However, such analysis has drawbacks because some assumptions were adopted to simplify the real physical phenomenon. Therefore, the theoretical analysis was validated by FEM and impedance measurement results. The FEM of the EMI responses of the piezoelectric-metal transducer were performed using ANSYS software. Modal analysis was also carried out to identify the vibration modes corresponding to the peaks in the EMI signatures. The sizes and material properties of the transducers are in accordance with theoretical analysis. The coupled field element SOLID5 was used to model the piezoelectric disk and the structural element SOLID45 was used to model the metal plate. The finite element model of the transducer is shown in figure 4. The model was meshed with a size of 1 mm. The adjacent nodes between the PZT disk and the metal plate were glued so that their displacement degrees of freedom were coupled. Only one quarter of the transducer was modeled due to symmetry. Harmonic analysis was carried out to obtain the EMI signatures of the transducer under different thicknesses of the metal plate. The voltage degrees of freedom of the nodes at both the top and bottom surfaces of the PZT were coupled to one master node to simulate the electrodes. A harmonic excitation $V(t) = V_0 e^{j\omega t}$ with $V_0 = 1$ V was applied to the The conductance signatures of transducers with different metal plate thickness are shown in figure 5. The first peak is not noticeable in the graph, so a refined frequency range was scanned for EMI signatures and the results are shown in figure 6. The refined frequency interval is 25 Hz. The peak frequencies of the first two bending modes as a function of thickness loss of the metal plate obtained by FEM, together with the linear fitted curves, are shown in figure 7. It should be noted that the first two peaks correspond to the first two bending modes of the transducer, while the third peak corresponds to the in-plane extension mode which is confirmed in the following modal analysis. The in-plane extension mode was not presented in the theoretical results since only bending modes were considered in the theoretical modeling. For the 30 mm diameter transducer, the sensitivity for the first and the second bending modes are 8.32 kHz mm$^{-1}$ and 27.32 kHz mm$^{-1}$, respectively. And for the 40 mm diameter transducer, the sensitivity for the first and the second bending modes are 4.86 kHz mm$^{-1}$ and 17.72 kHz mm$^{-1}$, respectively. The characteristics of the first two peaks is the same as those obtained by theory. The peak frequencies calculated using FEM are listed in table 3 for comparison. In the modal analysis, the top and bottom electrodes of the PZT were short-circuited by setting voltage to 0 V so as to obtain the resonant frequencies and the corresponding modes. The first two bending mode shapes of the transducer (Mode 1 and Mode 2), along with the in-plane extension mode (Mode 3), are shown in figure 8. The modal frequencies of these three modes versus the thickness loss are shown in figure 9. The modal frequencies match well with the peak frequencies in the conductance signatures. It can also be observed that Mode 1 and Mode 2 are sensitive to thickness loss while Mode 3 is not sensitive to the thickness loss. The physical explanation for such phenomenon is that the thickness loss reduces the plate rigidity of the piezoelectric-metal transducer and therefore the resonant frequencies associate with bending modes. 4. Experimental study 4.1. Impedance measurement The piezoelectric-metal transducers were fabricated by bonding the PZT disk onto the circular metal plate using epoxy, as shown in figure 10. The size configurations of the transducers were in accordance with the theoretical analysis and FEM. The transducer was placed on a soft foam so that the free boundary conditions were satisfied. The transducer was then connected to an impedance analyzer (PV520A, Beijing Band Era Co., Beijing) to acquire the EMI signatures which were stored in a personal computer for further processing. The frequency range is from 10 to 200 kHz with an interval of 200 Hz. The conductance signatures obtained by the impedance measurement are shown in figure 11. The first peak of specimens D40T15 and D40T10 is below 10 kHz, which is outside the measurement range of impedance analyzer PV520A. The first peak of 40 mm diameter transducer was scanned from 1 to 20 kHz with an interval of 25 Hz using another impedance analyzer (Agilent 4291A, Hewlett Packard, USA). The conductance signatures are shown in figure 12. The peak frequencies of the first two bending modes versus thickness loss of the metal plate obtained by measurement, together with the linear fitted curves, are shown in figure 13. For the 30 mm diameter transducer, the sensitivity for the first and the second bending modes are 8.20 kHz mm$^{-1}$ and 27.48 kHz mm$^{-1}$, respectively. And for the 40 mm diameter transducer, the sensitivity for the first and the second bending modes are 4.90 kHz mm$^{-1}$ and 17.88 kHz mm$^{-1}$, respectively. The characteristics of the first two peaks is the same as those obtained by theory and FEM. The peak frequencies obtained by measurement are listed in table 3 for comparison. 5. Comparisons and discussion The peak frequencies for the first two bending modes obtained by theory, FEM and impedance measurement are plotted in figure 14 and summarized in table 3. The comparison of these peak frequencies are listed in table 4. The FEM calculations agree well with the measurement results, with the discrepancies within 4.29%. The difference between FEM results and impedance measurements may be attributed to the accuracy of the materials constants and defects of the piezoelectric-metal transducer that generated during the fabrication or adhesion process. The theoretical calculations of Mode 1 are in good agreement with the FEM and the measurement results, with the discrepancies within 6.03%. However, those of Mode 2 present large difference with the FEM and the measurement results, with the largest difference of 26.48%. It is worthy to note that for the theoretical calculations, the higher the mode, and/or the smaller the diameter, and/or the thicker the thickness, the larger the difference with the FEM and measurement results. The reason for such differences is that the Kirchhoff plate hypotheses may not be well satisfied for transducers with small diameter-to-thickness ratio. Such differences can be minimized by using transducers with larger diameter-to-thickness ratio. Another factor that could also contribute to the differences is that the electrical effect is neglected when determining the neutral surface in order to simplify the calculation. These consequences imply that the thickness and diameter of the piezoelectric-metal transducer are important factors for the theoretical investigation. As can be concluded from the results obtained by theoretical analysis, FFM, and impedance measurement, the EMI instrumented piezoelectric-metal transducer can be utilized as corrosion sensor for quantitative determination of corrosion induced thickness loss. The theoretical analysis was validated by FEM and experimental measurement. Good agreements among them were achieved. The principle of the transducer for corrosion monitoring is that the thickness loss of the metal plate reduces the bending resonant frequencies of the transducer, and it is measured by the EMI technique. The relationship between the thickness loss and the peak frequency shift is linear, which is an advantageous feature of the proposed transducer. The sensitivity of the transducer is at several kHz mm$^{-1}$, which can be tuned by adjusting the thickness and diameter of the transducer. The transducer is very sensitive and accurate to thickness loss. Considering that the resolution of the most commonly used impedance analyzer can be as high as 1 Hz/sample, the transducer is able to achieve sub-micrometer accuracy technically. In the theoretical analysis, only the bending vibration of the transducer was considered. The in-plane extension vibration, which was presented in the FEM and impedance measurement analysis, was not modeled. It is showed from the FEM and impedance measurement results that the in-plane extension mode is not sensitive to the thickness loss of the transducer. Such insensitivity of the in-plane extension mode can also be utilized in the design of the transducer. The rule-of-thumb is that the resonant frequency of the selected bending mode should not exceed the resonant frequency of the in-plane extension mode. Otherwise, the resonant frequency of in-plane extension mode may complicate the process of peak frequency identification. One may notice that the amplitude of conductance signatures from theoretical calculations are in several tens of siemens (s), while those for FEM and experimental measurement are in several hundreds of millisiemens (ms). The difference in amplitude can be attributed to the different calculation interval or sampling interval used. Smaller interval usually results in higher frequency accuracy and higher amplitude. Since the resonant frequency was used to indicate the thickness loss, the variation in the amplitude has negligible effect on the performance of the transducer. It should be pointed out that the proposed corrosion sensor is composed of a PZT disk and a metal plate of same diameter attached to it. The PZT disk is not meant to be separated from the metal plate and attached onto the structure directly for corrosion monitoring. Instead, the corrosion sensor is installed in distributed and critical locations on the structure. The corrosion sensor measures the corrosion amount on the structure at that specific location. Commonly used EMI corrosion monitoring techniques are the direct bonding of PZT on the metallic structures, which suffer from several issues. Firstly, the metallic structures usually have complex geometry shape, loading conditions, boundary conditions, and the influences of other environmental factors, and it is very difficult to establish the accurate theoretical model of the electromechanical system. Instead, the over simplified one degree-of-freedom model for electromechanical interaction between a PZT and a host structure by Liang et al. (1994) is adopted. This model states that the variation in the EMI signatures are related to the variation of the mechanical properties of the host structure, such as stiffness, mass, and damping. However, there are many factors can contribute to the variation in the stiffness, mass, and damping of the metallic structure, and therefore the physical meaning between the variation in the EMI signatures and the change in structural properties is not clear. Secondly, since the physical meaning of the peaks in the EMI signatures is not clear, selecting the suitable scanning frequency range is usually done by trial and error. Thirdly, damage assessment is made by quantifying the variations in the EMI signature via statistical metrics, such as root-mean-square deviation and correlation coefficient. The assessment results are qualitative by nature. In a word, there is no direct meaning between the variations in the EMI signatures and the damage of the metallic structure. In our proposed piezoelectric-metal transducer as corrosion sensor, the direct physical meaning between the peaks in the EMI signature and the thickness of the metal was established. The peak frequencies of bending modes are directly related to the thickness of metal disk. And therefore, for the first time, the theoretical model for the electromechanical coupling of the piezoelectric-metal transducer derived, and the results were validated by FEM calculations and experimental measurement. In this way, the corrosion induced thickness loss of the metal disk is measured by the peak frequency. And more importantly, the relationship between them is linear and the assessment results are quantitative, without needing to find a suitable scanning frequency range and relying on statistical metrics for damage assessment. The main scope of the current study is the modeling and validation of the EMI instrumented circular piezoelectric-metal transducer as a kind of corrosion sensor. The influence of environmental factors, such as the temperature, humidity, and loading and boundary conditions are not investigated in the current study. It is certain that the temperature will induce small amount frequency shift. If precise determination of corrosion amount is required, the temperature effect needs to be compensated. Further studies will conduct experiments on the practical issues related to the application of the corrosion sensor, such as waterproofing materials, influences of temperature and humidity, encapsulation and isolation schemes for the sensors to satisfy free boundary, and strategies for uneven thickness loss. 6. Conclusions In this study, theoretical analysis of the EMI responses of the EMI instrumented circular piezoelectric-metal transducer as a new type of corrosion sensor was carried out, and was validated by FEM and impedance measurement. The piezo-electric-metal transducer was fabricated by bonding a piezo-electric disk to a metal plate. According to the electro-elastic and Kirchhoff plate theory, the EMI responses of the transducer operated in transverse bending modes with free boundary conditions were demonstrated. The results showed that the peak frequency in the conductance signatures is linearly reduced with increase of thickness loss. Transducers using higher order modes or with smaller diameter-to-thickness ratio are generally more sensitive to thickness loss. Therefore, it is possible to adjust the sensitivity of the transducer by selecting proper mode and tuning the size of the transducer. The theoretical calculations were validated by harmonic analysis and modal analysis using FEM, as well as impedance measurement. Comparisons among them were made. The FEM calculations show good agreement with the measurement results, with the discrepancies within 4.29%. The theoretical calculations of the first bending mode are in \| Diameter (mm) \| Thickness (mm) \| Theory/FEM \| Theory/measurement \| FEM/measurement \| \|---------------\|----------------\|------------\|--------------------\|-----------------\| \| \| \| Mode 1 \| Mode 2 \| Mode 1 \| Mode 2 \| \| 30 \| 3.0 \| 6.03 \| 24.52 \| 0.00 \| 1.57 \| \| \| 2.5 \| 4.55 \| 18.08 \| 20.71 \| 0.00 \| 2.23 \| \| \| 2.0 \| 3.00 \| 12.03 \| 1.98 \| 15.23 \| −0.99 \| 2.86 \| \| \| 1.5 \| 1.90 \| 6.99 \| 0.63 \| 10.42 \| −1.25 \| 3.21 \| \| \| 1.0 \| 0.86 \| 2.88 \| −0.85 \| 7.30 \| −1.69 \| 4.29 \| \| 40 \| 3.0 \| 3.07 \| 14.40 \| 3.70 \| 15.87 \| 0.62 \| 1.28 \| \| \| 2.5 \| 2.16 \| 10.51 \| 2.90 \| 12.13 \| 0.72 \| 1.47 \| \| \| 2.0 \| 0.87 \| 6.41 \| 1.75 \| 9.21 \| 0.88 \| 2.63 \| \| \| 1.5 \| 1.11 \| 3.74 \| 2.25 \| 7.18 \| 1.12 \| 3.31 \| \| \| 1.0 \| 0.00 \| 1.08 \| 3.12 \| 4.85 \| 3.12 \| 3.73 \| Note. Difference of $(a / b) = 100 \times (a - b) / b$ (%). good agreement with the FEM and the measurement results, with the discrepancies within 6.03%. Those of the second bending mode show larger discrepancies, which are mainly due to the limitations of Kirchhoff plate hypotheses. The findings of the present study are encouraging. The proposed corrosion sensor has the advantages of low cost, linear, quantitative corrosion assessment, and on-line and remote monitoring. Future works will concentrate on the encapsulation, optimization, and performance under practical conditions. Acknowledgments The research reported in this paper was partially supported by the National Natural Science Foundation of China (No. 51808170, No. 51678200), China Postdoctoral Science Foundation (No. 2018M630362). 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c6e77765cf69ba818de50187296357288aaa6eb6	{ "olmocr-version": "0.1.59", "pdf-total-pages": 11, "total-fallback-pages": 0, "total-input-tokens": 31349, "total-output-tokens": 6637, "fieldofstudy": [ "Physics" ] }	Abstract We show that a simple gravitational theory can provide a holographically dual description of a superconductor. There is a critical temperature, below which a charged condensate forms via a second order phase transition and the (DC) conductivity becomes infinite. The frequency dependent conductivity develops a gap determined by the condensate. We find evidence that the condensate consists of pairs of quasiparticles. 1 Introduction A most remarkable result to emerge from string theory is the AdS/CFT correspondence [1], which relates string theory on asymptotically anti de Sitter spacetimes to a conformal field theory on the boundary. In recent years, it has become clear that this holographic correspondence between a gravitational theory and a quantum field theory can be extended to describe aspects of nuclear physics such as the results of heavy ion collisions at RHIC [2] and to certain condensed matter systems. Phenomena such as the Hall effect [3] and Nernst effect [4, 5, 6] have dual gravitational descriptions. One can ask if there is a dual gravitational description of superconductivity. Conventional superconductors, including many metallic elements (Al, Nb, Pb, ...), are well described by BCS theory [7]. However, basic aspects of unconventional superconductors, including the pairing mechanism, remain incompletely understood. There are many indications that the normal state in these materials is not described by the standard Fermi liquid theory [8]. We therefore hope that a tractable theoretical model of a strongly coupled system which develops superconductivity will be of interest. Several important unconventional superconductors, such as the cuprates and organics, are layered and much of the physics is 2+1 dimensional. Our model will also be 2+1 dimensional. To map a superconductor to a gravity dual, we introduce temperature by adding a black hole [9] and a condensate through a charged scalar field. To reproduce the superconductor phase diagram, we require a system that admits black holes with scalar hair at low temperature, but no hair at high temperature. While Hertog has shown that neutral AdS black holes can have neutral scalar hair only if the theory is unstable [10], Gubser has recently suggested that a charged black hole will support charged scalar hair if the charges are large enough [11]. We consider a simpler version of Gubser’s bulk theory (in which the black hole can remain neutral) and show that it indeed provides a dual description of a superconductor. 2 The model: condensing charged operators We start with the planar Schwarzschild anti-de Sitter black hole \[ ds^2 = -f(r)dt^2 + \frac{dr^2}{f(r)} + r^2(dx^2 + dy^2), \] where \[ f = \frac{r^2}{L^2} - \frac{M}{r}. \] $L$ is the AdS radius and $M$ determines the Hawking temperature of the black hole: $$T = \frac{3M^{1/3}}{4\pi L^{1/3}}. \quad (3)$$ This black hole is 3+1 dimensional, and so will be dual to a 2+1 dimensional theory. In this background, we now consider a Maxwell field and a charged complex scalar field, with Lagrangian density $$\mathcal{L} = -\frac{1}{4} F^{ab} F_{ab} - V(\|\Psi\|) - \|\psi - iA\psi\|^2. \quad (4)$$ For simplicity and concreteness, we will focus on the case $$V(\|\Psi\|) = -\frac{2\|\Psi\|^2}{L^2}. \quad (5)$$ Although the mass squared is negative, it is above the Breitenlohner-Freedman bound [12] and hence does not induce an instability. It corresponds to a conformally coupled scalar in our background (1) and arises in several contexts in which the $AdS_4/CFT_3$ correspondence is embedded into string theory. For instance, the truncation of M theory on $AdS_4 \times S^7$ to $\mathcal{N} = 8$ gauged supergravity has scalars and pseudoscalars with this mass, dual to the bilinear operators tr$\Phi (I\Phi)$ and tr$\Psi (I\Psi)$ in the dual $\mathcal{N} = 8$ Super Yang-Mills theory, respectively. However, we should note that our Lagrangian (4) has not been obtained from M theory. We expect that our choice of mass is not crucial, and qualitatively similar results will hold, e.g., for massless fields. We will work in a limit in which the Maxwell field and scalar field do not backreact on the metric. This limit is consistent as long as the fields are small in Planck units. (Recall that in the analogous case one dimension higher, only Yang-Mills states with energy of order $N^2$ have finite backreaction in the bulk.) Alternatively, this decoupled Abelian-Higgs sector can be obtained from the full Einstein-Maxwell-scalar theory considered in [11] through a scaling limit in which the product of the charge of the black hole and the charge of the scalar field is held fixed while the latter is taken to infinity. Thus we will obtain solutions of non-backreacting scalar hair on the black hole. As we shall see, our simple model captures the physics of interest. Taking a plane symmetric ansatz, $\Psi = \Psi(r)$, the scalar field equation of motion is $$\Psi'' + \left(\frac{f'}{f} + \frac{2}{r}\right) \Psi' + \frac{2}{f^2} \Phi^2 + \frac{2}{f^2 L^2} \Psi = 0, \quad (6)$$ 1Introducing a gauge coupling $1/e^2$ in front of the $\|F\|^2$ term in the action is equivalent to rescaling the fields $\Psi \to e\Psi$ and $A_\mu \to eA_\mu$. Setting $e = 1$ is a choice of units of charge in the dual 2+1 theory. where the scalar potential $A_t = \Phi$. With $A_r = A_x = A_y = 0$, the Maxwell equations imply that the phase of $\Psi$ must be constant. Without loss of generality we therefore take $\Psi$ to be real. The equation for the scalar potential $\Phi$ is the time component of the equation of motion for a massive vector field $$\Phi'' + \frac{2}{r} \Phi' - \frac{2\Psi^2}{f} \Phi = 0,$$ (7) where $2\Psi^2$ is the, in our case, $r$ dependent mass. The charged condensate has triggered a Higgs mechanism in the bulk theory. At the horizon, $r = r_0$, for $\Phi dt$ to have finite norm, $\Phi = 0$, and (6) then implies $\Psi = -3r_0 \Psi'/2$. Thus, there is a two parameter family of solutions which are regular at the horizon. Integrating out to infinity, these solutions behave as $$\Psi = \frac{\Psi^{(1)}}{r} + \frac{\Psi^{(2)}}{r^2} + \cdots.$$ (8) and $$\Phi = \mu - \rho \frac{1}{r} + \cdots.$$ (9) For $\Psi$, both of these falloffs are normalizable [13], so one can impose the boundary condition that either one vanishes. After imposing the condition that either $\Psi^{(1)}$ or $\Psi^{(2)}$ vanish we have a one parameter family of solutions. It follows from (7) that the solution for $\Phi$ is always monotonic: It starts at zero and cannot have a positive maximum or a negative minimum. Note that even though the field equations are nonlinear, the overall signs of $\Phi$ and $\Psi$ are not fixed. We will take $\Phi$ to be positive and hence have a system with positive charge density. The sign of $\Psi$ is part of the freedom to choose the overall phase of $\Psi$. Properties of the dual field theory can be read off from the asymptotic behavior of the solution. For example, the asymptotic behavior (9) of $\Phi$ yields the chemical potential $\mu$ and charge density $\rho$ of the field theory. The condensate of the scalar operator $\mathcal{O}$ in the field theory dual to the field $\Psi$ is given by $$\langle \mathcal{O}_i \rangle = \sqrt{2} \Psi^{(i)}, \quad i = 1, 2$$ (10) with the boundary condition $\epsilon_{ij} \Psi^{(j)} = 0$. The $\sqrt{2}$ normalization simplifies subsequent formulae, and corresponds to taking the bulk-boundary coupling $\frac{1}{2} \int d^3 x \left( \bar{\mathcal{O}} \Psi + \mathcal{O} \bar{\Psi} \right)$. Note that $\mathcal{O}_i$ is an operator with dimension $i$. From this point on we will work in units in which --- 2One might also imagine imposing boundary conditions in which both $\Psi^{(1)}$ and $\Psi^{(2)}$ are nonzero. However, if these boundary conditions respect the AdS symmetries, then the result is a theory in which the asymptotic AdS region is unstable [14]. the AdS radius is $ L = 1 $. Recall that $ T $ has mass dimension one, and $ \rho $ has mass dimension two so $ \langle O_i \rangle / T^i $ and $ \rho / T^2 $ are dimensionless quantities. An exact solution to eqs (6,7) is clearly $ \Psi = 0 $ and $ \Phi = \mu - \rho / r $. It appears difficult to find other analytic solutions to these nonlinear equations. However, it is straightforward to solve them numerically. We find that solutions exist with all values of the condensate $ \langle O \rangle $. However, as shown in figure 1, in order for the operator to condense, a minimal ratio of charge density over temperature squared is required. ![Figure 1: The condensate as a function of temperature for the two operators $ O_1 $ and $ O_2 $. The condensate goes to zero at $ T = T_c \propto \rho^{1/2} $.](image) The right hand curve in figure 1 is qualitatively similar to that obtained in BCS theory, and observed in many materials, where the condensate goes to a constant at zero temperature. The left hand curve starts similarly, but at low temperature the condensate appears to diverge as $ T^{-1/6} $. However, when the condensate becomes very large, the backreaction on the bulk metric can no longer be neglected. At extremely low temperatures, we will eventually be outside the region of validity of our approximation. By fitting these curves, we see that for small condensate there is a square root behaviour that is typical of second order phase transitions. Specifically, for one boundary condition we find \[ \langle O_1 \rangle \approx 9.3 T_c (1 - T/T_c)^{1/2}, \quad \text{as} \quad T \to T_c, \tag{11} \] where the critical temperature is $ T_c \approx 0.226 \rho^{1/2} $. For the other boundary condition \[ \langle O_2 \rangle \approx 144 T_c^2 (1 - T/T_c)^{1/2}, \quad \text{as} \quad T \to T_c, \tag{12} \] where now $ T_c \approx 0.118 \rho^{1/2} $. The continuity of the transition can be checked by computing the free energy. Finite temperature continuous symmetry breaking phase transitions are only possible in 2+1 dimensions in the large $N$ limit (i.e. the classical gravity limit of our model), where fluctuations are suppressed. These transitions will become crossovers at finite $N$. Thus for $T < T_c$ a charged scalar operator, $\langle \mathcal{O}_1 \rangle$ or $\langle \mathcal{O}_2 \rangle$, has condensed. It is natural to expect that this condensate will lead to superconductivity of the current associated with this charge. ### 3 Maxwell perturbations and the conductivity We now compute the conductivity in the dual CFT as a function of frequency. As a first step, we need to solve for fluctuations of the vector potential $A_x$ in the bulk. The Maxwell equation at zero spatial momentum and with a time dependence of the form $e^{-i\omega t}$ gives $$A''_x + \frac{f'}{f}A'_x + \left(\frac{\omega^2}{f^2} - \frac{2\Psi^2}{f}\right)A_x = 0.$$ (13) To compute causal behavior, we solve this equation with ingoing wave boundary conditions at the horizon \[16]: $A_x \propto f^{-i\omega/3r_0}$. The asymptotic behaviour of the Maxwell field at large radius is seen to be $$A_x = A_x^{(0)} + \frac{A_x^{(1)}}{r} + \cdots$$ (14) The AdS/CFT dictionary tells us that the dual source and expectation value for the current are given by $$A_x = A_x^{(0)}, \quad \langle J_x \rangle = A_x^{(1)}.$$ (15) Now from Ohm’s law we can obtain the conductivity $$\sigma(\omega) = \frac{\langle J_x \rangle}{E_x} = -\frac{\langle J_x \rangle}{A_x} = -\frac{i\langle J_x \rangle}{\omega A_x} = -\frac{iA_x^{(1)}}{\omega A_x^{(0)}}.$$ (16) In figure 2 we plot the frequency dependent conductivity obtained by solving (13) numerically. The horizontal line corresponds to temperatures at or above the critical value, where there is no condensate. The fact that the conductivity in the normal phase is frequency independent is a characteristic of theories with $AdS_4$ duals \[15\]. The subsequent curves describe successively lower values of the temperature (for fixed charge density). We see that as the temperature is lowered, a gap opens. The gap becomes increasingly deep until the (real part of the) conductivity is exponentially small. There is also a delta function at $\omega = 0$ which appears as soon as $T < T_c$. This can be seen by looking at the imaginary part of the conductivity. The Kramers-Kronig relations Figure 2: The formation of a gap in the real, dissipative, part of the conductivity as the temperature is lowered below the critical temperature. Results shown for both the $\mathcal{O}_1$ operator (left) and the $\mathcal{O}_2$ operator (right). There is also a delta function at $\omega = 0$. The rightmost curve in each plot corresponds to $T/T_c = 0.0066$ (left) and $T/T_c = 0.0026$ (right). 3 The superfluid density is usually defined as the coefficient of $\delta(\omega)$ multiplied by the mass of the electron. In simple two fluid models, this density is related to the London magnetic penetration depth, $n_s = 1/4\pi\lambda_L^2$. Our scaling (19) thus implies $\lambda_L \sim (T_c - T)^{-1/2}$, consistent with Landau-Ginzburg theory. In figure 3 we rescaled the small $T/T_c$ plots of figure 2 by plotting the frequency in units of the condensate rather than the temperature. The curves tend to a limit in which the width of the gap is proportional to the size of the condensate. The differing shapes of the plots in figure 3 are precisely what is expected from type II and type I coherence factors, respectively [7]. Type II coherence suppresses absorption near the edge of the gap, explaining the slower rise of $\text{Re}[\sigma]$ in the left hand plot. It is possible that this difference is due to the operator $O_1$ being a pair of bosons and $O_2$ a pair of fermions, as in the case of $AdS_4 \times S^7$. ![Figure 3](image-url) Figure 3: The gap at small $T/T_c$, with the frequency normalised in terms of the condensate. On the right the gap is finite, but since $\langle O_1 \rangle$ becomes large at small $T$, the gap on the left is also becoming large. The dashed curve on the left plot is (22). The Ferrell-Glover sum rule states that $\int \text{Re}[\sigma]d\omega$ is a constant independent of temperature. Thus the area missing under the curve $\text{Re}[\sigma]$ due to the gap must be made up by the delta function at $\omega = 0$. That $\text{Re}[\sigma]$ exceeds the value one in figure 3 (right) implies then that the superfluid density $n_s$ must be correspondingly reduced for the $O_2$ system compared with the $O_1$ system for $T \ll T_c$. We can also compute the contribution of the normal, non-superconducting, component to the DC conductivity. Let us define $$n_n = \lim_{\omega \to 0} \text{Re}[\sigma(\omega)].$$ \hspace{1cm} (20) From our numerics we obtain $$n_n \sim e^{-\Delta/T}, \quad \text{for} \quad \frac{\Delta}{T} \gg 1,$$ where we have $\Delta = \langle O_1 \rangle/2$ and $\Delta = \sqrt{\langle O_2 \rangle}/2$. Numerically this factor of $1/2$ is accurate to at least 4%. From (21), $\Delta$ is immediately interpreted as the energy gap for charged... excitations. The gap we found previously in the frequency dependent conductivity was $2\Delta$. The extra factor of two is expected if the gapped charged quasiparticles are produced in pairs, suggesting that there is a ‘pairing mechanism’ at work in our model. Our results for $\Delta$ are suggestive of strong pairing interactions. Note that for figure 1 (right) at $T = 0$ we find $2\Delta \approx 8.4T_c$, which might be compared with the BCS prediction $2\Delta \approx 3.54T_c$. The larger value is what one expects for deeply bound Cooper pairs. Indeed, in our other model, figure 1 (left), we see that $\Delta$ actually diverges at low $T$. Finally in figure 4 we plot the imaginary part of the conductivity in this limiting, low temperature, regime. Again we see that the curves rapidly approach a limiting curve. We also see the advertised pole at $\omega = 0$. \begin{figure}[h] \centering \includegraphics[width=\textwidth]{fig4.png} \caption{The imaginary part of the conductivity at small $T/T_c$, with the frequency normalised in terms of the condensate. The analytic expression (22) is also shown on the left, but is indistinguishable from the numerics.} \end{figure} It is natural to ask if one can reproduce this limiting low temperature behavior by just taking $M = 0$ in our background metric, and considering our matter fields in anti de Sitter space. One problem is that there are no solutions to the field equations (6,7) which are smooth on the horizon of the Poincare patch. Nevertheless, for the $O_1$ case, we have observed numerically that at low temperatures, $\Psi \approx \langle O_1 \rangle / \sqrt{2r}$. Taking $M \to 0$ where $f \approx r^2$, (13) can be solved exactly to yield $A_x = A_x^{(0)} \exp(\pm \sqrt{\langle O_1 \rangle^2 - \omega^2 / r})$. This exact result then produces the nonzero conductivities $$\text{Re}[\sigma] = \frac{\sqrt{\omega^2 - \langle O_1 \rangle^2}}{\omega} \quad \text{for} \quad \omega > \langle O_1 \rangle , \quad \text{Im}[\sigma] = \frac{\sqrt{\langle O_1 \rangle^2 - \omega^2}}{\omega} \quad \text{for} \quad \omega < \langle O_1 \rangle , \quad (22)$$ via (16). The curves on the left hand sides of figures 3 and 4 are well approximated by the conductivity (22). We have included (22) as a dashed curve in these plots. 4 Discussion We have shown that a simple 3+1 dimensional bulk theory can reproduce several properties of a 2+1 dimensional superconductor. Below a second order superconducting phase transition the DC superconductivity becomes infinite and an energy gap for charged excitations is formed. There are many extensions of this model that we hope to consider elsewhere: 1) By probing the system with spatially varying fields and an external magnetic field, one can compute the superconducting coherence length and penetration depth, respectively. 2) One would like to consider a wider class of models by allowing for more general masses for the charged scalar field. 3) One should study the effects of backreaction on the bulk spacetime metric. 4) Perhaps the most interesting question is to understand the ‘pairing mechanism’ in field theory that leads to a condensate in these systems. Acknowledgements We would like to thank A. Bernevig, S. Gubser, D. Huse, P. Kovtun and D. Mateos for discussion. This work was supported in part by NSF grants PHY-0243680, PHY-0555669 and PHY05-51164. References [1] J. M. Maldacena, “The large N limit of superconformal field theories and supergravity,” Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [arXiv:hep-th/9711200]. [2] D. Mateos, “String Theory and Quantum Chromodynamics,” Class. Quant. Grav. 24, S713 (2007) [arXiv:0709.1523 [hep-th]]. [3] S. A. Hartnoll and P. Kovtun, “Hall conductivity from dyonic black holes,” Phys. Rev. D 76, 066001 (2007) [arXiv:0704.1160 [hep-th]]. [4] S. A. Hartnoll, P. K. Kovtun, M. Muller and S. Sachdev, “Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes,” Phys. Rev. B 76, 144502 (2007) [arXiv:0706.3215 [cond-mat.str-el]]. [5] S. A. Hartnoll and C. P. Herzog, “Ohm’s Law at strong coupling: S duality and the cyclotron resonance,” Phys. Rev. D 76, 106012 (2007) [arXiv:0706.3228 [hep-th]]. [6] S. A. Hartnoll and C. P. Herzog, “Impure AdS/CFT,” arXiv:0801.1693 [hep-th]. [7] R. D. Parks, Superconductivity, Marcel Dekker Inc. (1969). [8] E. W. Carlson, V. J. Emery, S. A. Kivelson and D. Orgad, “Concepts in high temperature superconductivity,” arXiv:cond-mat/0206217. [9] E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:hep-th/9802150]. [10] T. Hertog, “Towards a novel no-hair theorem for black holes,” Phys. Rev. D 74, 084008 (2006) [arXiv:gr-qc/0608075]. [11] S. S. Gubser, “Breaking an Abelian gauge symmetry near a black hole horizon,” arXiv:0801.2977 [hep-th]. [12] P. Breitenlohner and D. Z. Freedman, “Stability In Gauged Extended Supergravity,” Annals Phys. 144, 249 (1982). [13] I. R. Klebanov and E. Witten, “AdS/CFT correspondence and symmetry breaking,” Nucl. Phys. B 556, 89 (1999) [arXiv:hep-th/9905104]. [14] T. Hertog and G. T. Horowitz, “Towards a big crunch dual,” JHEP 0407, 073 (2004) [arXiv:hep-th/0406134]; T. Hertog and G. T. Horowitz, “Holographic description of AdS cosmologies,” JHEP 0504, 005 (2005) [arXiv:hep-th/0503071]. [15] C. P. Herzog, P. Kovtun, S. Sachdev and D. T. Son, “Quantum critical transport, duality, and M-theory,” Phys. Rev. D 75, 085020 (2007) [arXiv:hep-th/0701036]. [16] D. T. Son and A. O. Starinets, “Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications,” JHEP 0209, 042 (2002) [arXiv:hep-th/0205051].	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 429, 1 ], [ 429, 2750, 2 ], [ 2750, 5295, 3 ], [ 5295, 7941, 4 ], [ 7941, 9998, 5 ], [ 9998, 12345, 6 ], [ 12345, 13092, 7 ], [ 13092, 15065, 8 ], [ 15065, 17360, 9 ], [ 17360, 19320, 10 ], [ 19320, 20769, 11 ] ] }
1366209765c57a7362a929f744825bef5f312b0f	{ "olmocr-version": "0.1.59", "pdf-total-pages": 14, "total-fallback-pages": 0, "total-input-tokens": 36403, "total-output-tokens": 10987, "fieldofstudy": [ "Biology", "Medicine" ] }	Identification of potential agents for thymoma by integrated analyses of differentially expressed tumour-associated genes and molecular docking experiments XIAO-DONG WANG¹, PENG LIN², YU-XIN LI¹, GANG CHEN², HONG YANG¹, YUN HE¹, QING LI¹ and RUO-CHUAN LIU¹ Departments of ¹Medical Ultrasonics and ²Pathology, The First Affiliated Hospital of Guangxi Medical University, Nanning, Guangxi Zhuang Autonomous Region 530021, P.R. China Received February 8, 2019; Accepted June 20, 2019 DOI: 10.3892/etm.2019.7817 Abstract. Thymoma, derived from the epithelial cells of the thymus, is a rare malignant tumour type. Following diagnosis with thymoma, patients generally undergo surgical treatment. However, patients with advanced-stage disease are only candidates for chemotherapy and have poor survival. Therefore, it is urgently required to explore effective chemotherapeutic agents for the treatment of thymoma. In the present study, a Bioinformatics analysis was performed to identify novel drugs for thymoma. Differentially expressed genes (DEGs) in thymoma were obtained by Gene Expression Profiling Interactive Analysis. Subsequently, these genes were processed by Connectivity Map analysis to identify suitable compounds. In addition, Metascape software was used to verify drug and target binding. Molecular docking technology was used to verify drug and target binding. Finally, absorption, distribution, metabolism and excretion parameters in the Traditional Chinese Medicine Systems Pharmacology Database and Analysis Platform database were used for drug screening and for evaluation of the potential clinical value. In total, 2,447 DEGs, including 2,204 upregulated and 243 downregulated genes, were identified from 118 thymoma patients and 339 normal samples. The top 10 drugs displaying the most significant negative correlations were fulvestrant, hesperetin, zidovudine, hydrocortisone, rolitetracycline, ellipticine, sirolimus, quinisocaine, oestradiol (estradiol) and harmine. The predicted targets of these drugs were then confirmed. The score for the association between estrogen receptor 1 (ESR1) and fulvestrant was 0.99. According to the molecular docking analysis, the total scores for the interaction between ESR1 were 10.26, and those for the interaction between tamoxifen and ESR1 were 6.60. The oral bioavailability (%), drug-likeness and drug half-life for hesperetin were 70.31, 0.27 and 15.78, respectively; those for oestradiol were 53.56, 0.32 and 3.50, respectively; and those for harmine were 56.80, 0.13 and 5.04, respectively. In conclusion, several potential therapeutic drugs for thymoma were identified in the present study. The results suggested that the compounds, including fulvestrant, estradiol, hesperetin and ellipticine, represent the most likely drugs for the treatment of thymoma. Future studies should focus on testing these novel compounds in vitro and in vivo. Introduction Thymoma, which is derived from the epithelial cells of the thymus, is a rare malignant tumour type. At the time of diagnosis, patients are usually between 40 and 60 years of age (1); certain patients present with myasthenia gravis or other symptoms, including superior vena cava syndrome, dysphagia, cough or chest pain (2). In general, upon diagnosis with thymoma, patients undergo surgical treatment. However, for patients with stage III and IV disease, the 5-year overall survival rates are 74% and <25%, respectively (3), indicating that those patients require further treatment. Furthermore, even after post-operative radiotherapy, the overall survival rates of patients were not significantly improved (4). Therefore, patients with advanced disease are candidates for chemotherapy. According to certain international guidelines, the first-line combination chemotherapy regimens for thymoma include the following: i) Cisplatin, doxorubicin and cyclophosphamide (CAP), ii) CAP with prednisone, iii) cisplatin, doxorubincin, cyclophosphamide and vincristine, iv) cisplatin and etoposide, v) etoposide, ifosfamide and cisplatin and vi) carboplatin/paclitaxel, while the second-line chemotherapy regimens include etoposide, ifosfamide, pemetrexed, 5-fluorouracil or its analogues, gemcitabine and paclitaxel, separately (5). However, even after chemotherapy, the 10-year disease-free survival rate is only 56% for patients with stage III thymoma and 33% for patients with stage IV disease (6). Therefore, exploration of effective chemotherapeutic agents to treat thymoma is required. However, most drug development strategies primarily involve determining a novel therapeutic target and then searching for compounds that fit the target. Therefore, agent discovery is an expensive endeavor that frequently involves issues with bioavailability first and toxicity later (7). However, drug repositioning, with the aim of identifying novel applications for existing drugs, has been established as a cost-effective strategy. Over the last decade, burgeoning computer technologies have made structure-based compound screening a prevalent tool in early drug identification (8). Among them, Connectivity Map (CMap), which is based on RNA chip technology, is a useful data resource for studying drug mechanisms and drug reallocation (9). Furthermore, all drugs in the database are ranked according to a score, which is derived from conventional measures, including the Pearson correlation coefficient. For instance, those with a score of 1 are the most strongly positively correlated with the query signature, and those with a score of -1 are most strongly negatively correlated. Consequently, by using the differentially expressed genes (DEGs) between thymoma and normal tissues, CMap is able to identify the affected pathways and small-molecule drugs that may be considered potential therapeutic agents for treating thymoma. Accordingly, the use of RNA chip technology may provide novel ideas for the treatment of thymoma. In the present study, connectivity mapping was performed based on DEGs identified in a large population of patients with thymoma in The Cancer Genome Atlas (TCGA) and GTEx databases, accompanied by the procurement of prospective candidate drugs for the future treatment of thymoma. Materials and methods Screening of DEGs in thymoma. Gene expression profiling interactive analysis (access: August 9, 2018; GEPIA; http://geopia.cancer-pku.cn/) was used to identify the DEGs in thymoma. GEPIA uses data from TCGA and GTEx projects and is a freely available tool to consign customizable functionalities (10). Four-way analysis of variance (ANOVA) was used to calculate differential expression based on variables, including sex, age, ethnicity and disease stage. First, on the website, all the expression profiles were transformed to the log2 (transcripts per million (TPM)+1) scale for further calculations. Simultaneously, the median (tumour-normal) was defined by the log2 [fold change (FC)]. The adjusted q-value was then obtained after multiple adjustments using the Benjamini and Hochberg false discovery rate method for each variable. The cut-off values for overexpressed genes were a log2FC of >4.0 and a q-value of <0.05 were selected as cut-off values for overexpressed genes. Cutoff values for the downregulated expression of mRNAs were a log2FC of >3.0 and a q-value of <0.05. After the data were inputted into CMap (access time: April 6, 2018, https://portals.broadinstitute.org/cmap/), the corresponding compounds with scores of <0.75 were considered potential drugs for the treatment of thymoma. Finally, the top 10 compounds were subjected to further analysis, and their molecular structures were obtained from PubChem (access time: April 6, 2019, https://pubchem.ncbi.nlm.nih.gov/compound) (19). Construction of the drug-target network. A drug-target network was constructed to further examine the potential mechanisms of action of the compounds. The freely available STITCH software (access time: April 11, 2019, http://prion.bchs.uh.edu/stitch/) was used to construct the drug-target \| Clinicopathological feature \| Number \| \|----------------------------\|--------\| \| Age (years) \| \| \| <40 \| 10 \| \| 40-60 \| 51 \| \| >60 \| 57 \| \| Sex \| \| \| Male \| 62 \| \| Female \| 56 \| \| Ethnicity \| \| \| White \| 98 \| \| Black \| 6 \| \| Asian \| 12 \| \| Not specified \| 2 \| \| Stage \| \| \| I \| 35 \| \| II \| 60 \| \| III \| 15 \| \| IV \| 6 \| \| Not available \| 2 \| Table I. Clinicopathological features of the thymoma patients (n=118). network and to provide genetic identification (20). A higher score indicated a greater likelihood that the drug targeted the tested gene product (21). Molecular docking analysis of the interactions between proteins and compounds. The Surflex-Dock program in Sybyl version X-2.0 was used to verify the interactions between drugs and targets. The program obtained particular information on how these novel drugs exert their anti-tumour activity. Simultaneously, the docking scores and crash were calculated to represent binding affinities and the degree of inappropriate penetration into the protein by the ligand (22-24). Functional annotation of the targets. To further explore the functions of the compounds in combination with the target, KEGG pathway and GO term analyses of the targets were performed using the tools mentioned above. Screening compounds based on absorption, distribution, metabolism and excretion (ADME) parameters in the Traditional Chinese Medicine Systems Pharmacology Database and Analysis Platform (TCMSP) database. The ADME parameters were used for drug screening and evaluation to further determine the potential clinical value of the compounds. The TCMSP database (access time: April 6, 2018, http://sm.nwsuaf.edu.cn/lsp/tcmsp.php) was used to query the ADME parameters of the top 10 drugs identified above (25). The compounds were then screened with the following criteria: Oral bioavailability (OB) ≥30%, drug-likeness (DL) ≥0.18 and drug half-life (HL) ≥4 h. --- Figure 1. DEGs between thymoma and normal tissues. (A) Locations of the DEGs based on GRCh38.p2 (NCBI). (B) Volcano plot displaying the DEGs. DEG, differentially expressed gene; NCBI, National Center for Biotechnology Information. Figure 2. GO terms and KEGG pathway analysis for the differentially expressed genes. (A-C) GO terms in the categories (A) biological process, (B) molecular function and (C) cellular component; (D) KEGG pathway analysis. GO, Gene Ontology; KEGG, Kyoto Encyclopedia of Genes and Genomes; hsa, Homo sapiens. Results GO and pathway analyses of the DEGs associated with thymoma. In total, 2,447 DEGs, including 2,204 upregulated and 243 downregulated genes, were identified in 118 thymoma patients and 339 normal samples (2 normal tissues and 337 normal blood samples) (Fig. 1; Table I). A GO analysis was further employed to determine the possible molecular mechanisms of the DEGs. In the category biological process (BP), these genes were most enriched in 'translation', 'SRP-dependent co-translational protein targeting to membrane', 'viral transcription', 'nuclear-transcribed mRNA catabolic process, nonsense-mediated decay' and 'rRNA processing' (Fig. 2A). In the category cellular component (CC), 'ribosome', 'extracellular exosome', 'mitochondrial inner membrane', 'mitochondrion' and 'cytosolic large ribosomal subunit' were the most prominent terms (Fig. 2B). In the category molecular function (MF), these genes were significantly involved in 'poly(A) RNA binding', 'structural constituent of ribosome', 'protein binding', 'RNA binding' and 'NADH dehydrogenase (ubiquinone) activity' (Fig. 2C). In the KEGG pathway analysis, 'ribosome', 'oxidative phosphorylation', 'Huntington's disease', 'Parkinson's disease' and 'Alzheimer's disease' were the most prominent pathways (Fig. 2D). Among these pathways, 'ribosome', with 93 genes included, was the most significant pathway. The PPI networks comprising the DEGs revealed that certain genes, including complement C3 (C3), Serum amyloid A1 (SAA1), C-X-C motif chemokine receptor 1 (CXCR1), C-X-C motif chemokine receptor 2 (CXCR2), C-X-C motif chemokine... ligand 12 (CXCL12), C-C motif chemokine ligand 19 (CCL19), C-C motif chemokine ligand 25 (CCL25) and Formyl peptide receptor were closely linked with a high degree (Fig. 3). Potential therapeutic drugs identified from the CMap database. CMap analysis identified 5,000 compounds correlated with the DEGs. According to the score rankings, 769 drugs scored < -0.75 and were considered potential thymoma therapeutics. The top 10 compounds displaying the strongest negative correlation were fulvestrant, hesperetin, zidovudine, hydrocortisone, rolitetracycline, ellipticine, sirolimus, quinisocaine, oestradiol and harmine (Fig. 4; Table II). \| Drug name \| Dose \| Connectivity score \| Up score \| Down score \| \|---------------\|-------\|--------------------\|----------\|------------\| \| Fulvestrant \| 1 µM \| -1.00 \| -0.25 \| 0.38 \| \| Hesperetin \| 13 µM \| -0.99 \| -0.25 \| 0.37 \| \| Zidovudine \| 15 µM \| -0.99 \| -0.25 \| 0.37 \| \| Hydrocortisone\| 11 µM \| -0.99 \| -0.24 \| 0.38 \| \| Rolitetracycline\| 8 µM \| -0.98 \| -0.23 \| 0.38 \| \| Ellipticine \| 16 µM \| -0.98 \| -0.22 \| 0.40 \| \| Sirolimus \| 100 nM\| -0.98 \| -0.23 \| 0.39 \| \| Quinisocaine \| 13 µM \| -0.98 \| -0.23 \| 0.38 \| \| Estradiol \| 100 nM\| -0.97 \| -0.24 \| 0.37 \| \| Harmine \| 16 µM \| -0.97 \| -0.21 \| 0.40 \| Table II. Connectivity map results for the 10 strongest negative correlation compounds according to CMap. All data are for the MCF7 cell line. Up score and down score represent induced and repressed of the expression in the list respectively. The connectivity score combines the up score and the down score. Figure 5. Drug-target networks of five compounds curated from the STITCH database. Pill-shaped and spheres nodes represent the compounds and proteins respectively. Construction of the drug-target network. The targets of the test drugs were identified from the STITCH database (20) (Fig. 5). The predicted targets of the top 10 drugs predicted for thymoma were confirmed, and the predicted scores for the interactions of DNA topoisomerase IIα (TOP2A), TOP2B and tumour protein 53 with ellipticine were 0.93, 0.86 and 0.84, respectively. Similarly, the scores for the interactions of estrogen receptor 1 (ESR1), ESR2 and cytochrome P450 family 19 subfamily A member 1 (CYP19A1) with fulvestrant were 0.99, 0.99 and 0.99, respectively. The score for the interaction of CYP11B1 and s-cortisol (hydrocortisone) was 0.90. Furthermore, the scores for the interactions between C-C motif chemokine ligand 18 and regulatory factor X-associated ankyrin-containing protein with azidothymidine (zidovudine) were 0.44 and 0.40, respectively. The score for the interaction of monoamine oxidase A with CHEMBL14355 (harmine) was 0.52 (Table III). Molecular docking analysis of the interactions between proteins and compounds. Molecular docking analysis was performed to confirm the interactions between drugs and protein targets. The total scores, crash and polar for the fulvestrant and ESR1 interaction were 10.26, -3.72 and 2.08 respectively (Fig. 6A). The total scores, crash and polar for the tamoxifen and ESR1 interaction were 6.60, -4.02 and 0, respectively (Fig. 6B). Functional annotation of the drug targets. To further explore the functions of the compounds in combination with the target, functional annotation, including GO and KEGG pathway analyses, were performed. The results revealed that the targets for fulvestrant in the category BP were significantly involved in ‘mammary gland alveolus development’, ‘transcription initiation from RNA polymerase II promoter’, ‘transcription, DNA-templated’, ‘positive regulation of transcription, DNA-templated’ and ‘signal transduction’ (Fig. 7A). However, in the CC category, the targets were only significantly involved in ‘nucleoplasm’ (Fig. 7B). In the category MF, the targets were mainly enriched in ‘steroid binding’, ‘steroid hormone receptor activity’, ‘enzyme binding’, ‘RNA polymerase II transcription factor activity, ligand’ and ‘transcription factor binding’ (Fig. 7C). Finally, in the KEGG pathway analysis of fulvestrant, ‘prolactin signaling pathway’, ‘prostate cancer’, ‘glioma’, ‘melanoma’ and ‘oocyte meiosis’ were the most prominent pathways (Fig. 7D; Table IV). Target genes of ellipticine in the category BP were mainly enriched in ‘omega-hydroxylase P450 pathway’, ‘epoxygenase P450 pathway’, ‘drug metabolic process’, ‘steroid metabolic process’ and ‘monoterpenoid metabolic process’ (Fig. 8A). In the CC category, the targets were mainly enriched in ‘organelle membrane’, ‘intracellular membrane-bound organelle’, ‘endoplasmic reticulum membrane’, ‘nucleoid’ and ‘DNA topoisomerase complex (ATP-hydrolyzing)’ (Fig. 8B). Regarding the enrichment of targets of ellipticine in the category MF, they were mainly enriched in ‘mitochondrion’, ‘membrane’, ‘endoplasmic reticulum membrane’, ‘nucleoid’ and ‘DNA topoisomerase complex (ATP-hydrolyzing)’ (Fig. 8C). In the KEGG pathway analysis ### Table III. Predicted targets of the drugs identified from the STITCH database. \| Drug/targets \| Combined score \| \|-------------------------\|----------------\| \| Ellipticine \| \| \| TOP2A \| 0.93 \| \| TOP2B \| 0.86 \| \| TP53 \| 0.84 \| \| CYP1A1 \| 0.78 \| \| MDM2 \| 0.75 \| \| CYP1B1 \| 0.74 \| \| CYP3A4 \| 0.73 \| \| CYP1A2 \| 0.73 \| \| CASP7 \| 0.70 \| \| CYP2C19 \| 0.70 \| \| Fulvestrant \| \| \| ESR1 \| 1.00 \| \| ESR2 \| 0.99 \| \| CYP19A1 \| 0.99 \| \| AR \| 0.97 \| \| PGR \| 0.97 \| \| TFF1 \| 0.95 \| \| PRL \| 0.94 \| \| CCND1 \| 0.92 \| \| IGF1R \| 0.92 \| \| RB1 \| 0.91 \| \| S-cortisol \| \| \| CYP11B1 \| 0.90 \| \| Azidothymidine (zidovudine) \| \| \| CCL18 \| 0.44 \| \| RFXANK \| 0.40 \| \| CHEMBL14355 \| 0.52 \| \| MAOA \| \| TOP2A, DNA topoisomerase II alpha; TP53, Tumor protein P53; CYP1A1, Cytochrome P450 family 1 subfamily a member 1; MDM2, MDM2 proto-oncogene; CASP7, Caspase 7; ESR1, Estrogen receptor 1; AR, Androgen receptor; PGR, Progesterone receptor; TFF1, Trefoil factor 1; PRL, Prolactin; CCND1, Cyclin D1; IGF1R, Insulin like growth factor 1 receptor; RB1, RB transcriptional corepressor 1; CCL18, C-C motif chemokine ligand 18; RFXANK, Regulatory factor X associated ankyrin containing protein; MAOA, Monoamine oxidase A. of ellipticine, 'chemical carcinogenesis', 'steroid hormone biosynthesis', 'metabolism of xenobiotics by cytochrome P450', 'linoleic acid metabolism' and 'tryptophan metabolism' were the most prominent pathways (Fig. 8D; Table V). Screening of compounds based on ADME parameters in the TCMSP database. Hesperetin, oestradiol and harmine were searched in the TCMSP database. The OB (%), DL and HL for hesperetin were 70.31, 0.27 and 15.78, respectively; those for oestradiol were 53.56, 0.32 and 3.50, respectively; and those for harmine were 56.80, 0.13 and 5.04, respectively (Table VI). Discussion In the present study, it was speculated that the potential therapeutic drugs for thymoma are compounds that are matched with DEGs known to be associated with the occurrence and development of tumours. First, by using the DEG data from the GEPIA database, correlations between the genes and previously known pharmaceutical compounds were revealed in CMap. Subsequently, the top 10 molecules with the lowest negative correlations were obtained and they were considered as potential therapeutic drugs for further analysis. In addition, a drug-target network was constructed to examine the potential mechanisms of action of the compounds. Molecular docking analysis was then performed to confirm the interactions between the drugs and protein targets. Furthermore, the ADME parameters were inquired to determine the potential clinical value of the compounds. According to the GEPIA tool, 2,447 DEGs were identified in 118 thymoma patients and 339 normal samples. After functional annotation analysis, it was determined that the DEGs were enriched in ‘ribosome’, ‘oxidative phosphorylation’, ‘spliceosome’, ‘DNA replication’ and ‘cell cycle’, which indicated that the DEGs may affect cell growth and have an important role in the occurrence and development of thymoma. Then, based on the DEGs, potential therapeutic drugs were identified using the CMap database, including fulvestrant, hesperetin, zidovudine, hydrocortisone, rolitetracycline, Then, to examine the effect of the potential drugs, a drug-target network was constructed and a molecular docking analysis was performed. Compared with the docking score of tamoxifen and ESR1, the score of fulvestrant and ESR1 was high, which indicates a high interaction between fulvestrant and ESR1. Among these compounds, tamoxifen, as an ESR1 inhibitor, remains the first-line of medication for the treatment of ESR1+ breast cancer (26). In addition, the ESR1 protein localizes to the nucleus and has been proven important in the pathological processes of several cancer types, including breast and endometrial cancers (27,28). Furthermore, functional enrichment analysis indicated that the targets of fulvestrant significantly accumulated in ‘prolactin signaling pathway’, ‘prostate cancer’, ‘glioma’ and ‘melanoma’. The results indicated that fulvestrant may combine with ESR1 to affect the treatment of thymoma. Finally, using the TCMSP database, it was determined that the compounds oestrogen, oestradiol and harmine may potentially be of high clinical value. In summary, the compounds may have an important role in the treatment of thymoma. Among these compounds, fulvestrant has been used to treat breast and prostate cancers. Regardless of endocrine tolerance or the levels of hormone receptor expression, fulvestrant significantly improves the survival of patients with non-progressive breast cancer (29-31). In addition, fulvestrant also represents a treatment option for patients with recurrent hormone receptor-positive or HER2-negative metastatic breast cancer (32). Hesperetin is a bioflavonoid from citrus fruit. Based on experimental evidence, hesperetin possesses anti-oxidant and free radical-quenching activities. This compound also induces apoptotic cell death. In addition, hesperetin reportedly exerts an anti-cancer effect on various cancer cell lines, including breast cancer, prostate cancer, human colon adenocarcinoma and hepatocellular carcinoma cells (33-37). Based on ADME values of the compound molecules from the TCMSP database, it was revealed that hesperetin, estradiol and harmine may have good prospects. Among them, hesperetin caught our attention. The consequence of it for oral bioavailability was 70.31. A high OB (%) is frequently considered a key factor to judge the drug-like properties of compounds as therapeutic agents. Furthermore, as hesperetin is derived from citrus fruit, it may be easy to produce on a large scale. However, due to its poor water solubility, its clinical use is restricted. Numerous studies have been undertaken to improve the bioavailability of flavonoids (33). In summary, hesperetin may not only be used as a promising compound to treat thymoma in the future, but may also be commonly used in the treatment of other tumour types. Zidovudine is an inhibitor of HIV replication that may reverse neurological dysfunction induced by HIV and ameliorate certain clinical abnormalities (38,39). Hydrocortisone is the major glucocorticoid and its synthetic counterpart is used to treat inflammation, allergy, shock and certain neoplasms (40). Rolitetracycline is a broad-spectrum antibiotic (41). Sirolimus is a potent immunosuppressant (42). Quinisocaine blocks nerve conduction when applied to nervous tissues at appropriate concentrations. Estrogen has been consistently reported to affect the advancement of thymoma (43-45). However, the therapeutic value of fulvestrant and hesperetin for thymoma has not been previously reported. Simultaneously, the other compounds among the top 10 have also not been reported to be suitable for the treatment of cancer. The limitations to the present study include the following: First, the DEGs should be further validated in vitro to determine their specific expression in thymoma. In addition, the exact DEGs between the different groups of patients and at different stages of the disease should be determined in vitro to further identify potential compounds, particularly in patients aged 40-60 years and in stage III/IV. Finally, further research should focus on in vitro and in vivo tests prior to the clinical application of these compounds. In summary, the development of compounds or combinations of drugs remains a requirement in order to improve chemotherapy. The present study identified compounds that may represent novel treatments for thymoma and may reduce the range of potential drugs for treating thymoma. Acknowledgements Not applicable. Funding No funding was received. Availability of data and materials The datasets used and/or analysed during this study are available from the corresponding author on reasonable request. Authors' contributions The study was designed by GC, HY, QL and RL. XW, PL, YL, GC, HY, YH and QL were involved in the statistical analysis. HY, YH, QL and RL were involved in drafting the manuscript and critically revising it for important intellectual content. YH, QL and RL gave final approval for the version of the manuscript to be published. Table VI. Absorption, distribution, metabolism and excretion parameters for three drugs from the Traditional Chinese Medicine Systems Pharmacology Database and Analysis Platform database. \| Drug name \| Oral bioavailability (%) \| Drug-likeness (0-1) \| Drug half-life (h) \| \|-----------\|--------------------------\|---------------------\|--------------------\| \| Hesperetin \| 70.31 \| 0.27 \| 15.78 \| \| Estradiol \| 53.56 \| 0.32 \| 3.5 \| \| Harmine \| 56.8 \| 0.13 \| 5.04 \| Each author sufficiently participated in the work to take public responsibility for appropriate portions of the content and agreed to be accountable for all aspects of the work to ensure that questions regarding the accuracy or integrity of any part of the work are appropriately investigated and resolved. Ethics approval and consent to participate Not applicable. Patient consent for publication Not applicable. Competing interests The authors declare that they have no competing interests. References 1. 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65912cd42dc527d3c542d4b535140e33c2069074	{ "olmocr-version": "0.1.59", "pdf-total-pages": 22, "total-fallback-pages": 0, "total-input-tokens": 25900, "total-output-tokens": 13464, "fieldofstudy": [] }	The History and values of tolerance in Tabot traditional ceremonies in Bengkulu society by Buyung Surahman The Strategy of farming religious charakters on the children; Study at special schools in Rejang Lebong by Buyung Surahman The Strategy of Forming Religious Characters on the Deaf Children: Study at Special Schools in Rejang Lebong Ahmad Suradi ) Institut Agama Islam Negeri Bengkulu, Indonesia. Email: [email protected] Buyung Surahman Institut Agama Islam Negeri Bengkulu, Indonesia. Email: [email protected] Mawardi Universitas Syah Kuala Banda Aceh, Indonesia. Email: [email protected] Abstract: The study aims to determine the strategy used in forming religious characters on the deaf children in Elementary Special School. A qualitative method was used where the data taken from observation, interview and document analysis. The result showed that the learning strategy of Islamic religious education in the development of morals for children with special needs in special schools is by implementing expository strategy, adding hours of study using the habituation method. The finding also showed that the supporting factors in the learning process to form moral guidance are the involvement of school’s principal who is very concern on the development of students’ morals; the teachers who have great patience in dealing with children with special needs. Then, it was also found that there were some inhibiting factors that faced by the school. They were on the absence of a special curriculum for children with special needs, Islamic education teachers who are not teachers who are graduates of special service schools, as well as the lack of supporting facilities as learning media, doing the learning process run monotonously. Keywords: Strategy; religious characters; deaf children INTRODUCTION Education is an important factor for the creation of a harmonious life and based on clear values (Galindo et al., 2007; Lipman, 2003). Without education, human life patterns cannot run properly, follow the passions and are far from the ideal values that must be fought for and accounted for. Therefore, teaching knowledge about Islam is very important for all Muslims. This is in line with the concept of the Qur'an in surah Hajj: 3. All humans are in equality to have the right on education and require religious education and science (Harahap, 2019; Mumtahanah, 2011). Basically every human being has the right to have education in order to develop the potential capability. Thus, he or she needs assistance from others who are able to guide him or her. This is no exception for children who have physical deficiencies in the form of partially or partially deformed (abnormal) limbs such as hearing impaired. Children who have physical or psychological disabilities or differences are often referred to as people with disabilities (Buhler, 2013; Farokhi & Hashemi, 2011; Hager & Runtz, 2012). This is usually caused by lack of oxygen at birth which causes brain damage or neurological disorders, which can make a child suffer from brain paralysis (cerebral palsy) (Rafferty, 2008). Todays, education for the deaf children should be given more attention so that they are not further away from the community, because as citizens they have equal right to have education and teaching in accordance with their respective conditions and abilities (Morton, 2000; Powers, 2002; Winkens & Hehir, 2008). As for obtaining education for children who have juridical disorders mentioned in Article 5 paragraph 2 of the Law on the National Education System, it states that citizens who have physical, emotional, mental, intellectual and/or social disabilities are entitled to special education (Syahrizal & Sugianto, 2013). Provisions in Republic of Indonesia Law Number 20 of 2003 is a foundation for Children with Special Needs because the law explains that children who have special needs need to get the same opportunities as those given to other normal children in terms of education and teaching. Nugroho & Mareza (2016) mentioned that every citizen has the same right to obtain quality education. Citizens who have physical, emotional, mental, intellectual or social disabilities are entitled to special education. For those who have disabilities or include the deaf children, the government has provided special schools which is well-known as Sekolah Luar Biasa so that children who have special needs can get education and skills that can be used as provisions for their lives so as not to become a burden for others, especially parents and families, especially to reach their goals (Rahardja, 2016). As the word of God in Q.S. At-Tin: 4. In the book of commentary Ibn Kathir this verse is interpreted that, this is the object of oath, namely that Allah has created man in the best form and form with perfect stature and normal body members (Katsir, 2004). The Word of God above, God does not discriminate between His creatures (humans), humans are created as well as possible so that before God all humans are equally dependent on their deeds. Therefore, it is true that children with special needs or their physical or mental disabilities need to get the same treatment especially in the field of education. Education plays a very important position to form characters (Avramidis et al., 2000; Cook et al., 2015; Guha et al., 2008; Hastings & Oakford, 2003). It is specifically for them to get religious education because this education is a necessity for them to perform their worship that are applied in everyday life. Religious education is a fundamental one that must be given to all students as a provision of life in the world and the hereafter (Afdal, 2008; Holley, 2016; Vermeer, 2010). In the schools, it is given in Islamic religious education that is subjects that are compulsory curriculum to be studied by all Muslim students. Islamic religious education is an effort in the form of guidance and care for students so that after completion of education they can understand and practice the teachings of Islam and make it a way of life (Aat Syafaat, 2008; Nesbitt, 2004). The importance of studying religion has broad meaning, regardless of one’s condition whether he is normal or has physical, mental or behavioral limitations. The deaf children are also entitled to education. Basically, the deaf children face great obstacles in the field of personal, social, and academic formation. Seen from the general character, they tend to have unstable personalities, temperament, moody and others, especially in terms of their understanding of the lessons they receive at school. It must be realized that a teacher should know the characteristics of each student. Educating children with physical, mental or physical characteristics is not the same as educating normal children, because in addition to requiring a specific approach also requires a specific strategy (Aron & Lopresti, 2012; Carta et al., 1991; DeVore & Russell, 2007; Pivik et al., 2002). This is solely because it relies on the conditions experienced by these children with disabilities. Therefore, a teacher must try to create a pleasant learning atmosphere for all students, because a learning atmosphere that is not exciting and enjoyable for students will usually bring teaching and learning activities that are less harmonious, especially for deaf children (Swanwick & Marschark, 2010; Wauters & Knoors, 2008). A teacher must really have a specific strategy so that students who need guidance and special treatment can understand the lesson well. Good classroom management will influence good teaching and learning interactions, such as learning goals can be achieved without finding significant obstacles. In addition, the success of learning must be supported by the selection of the right strategy with the lessons to be delivered, also supported by adequate learning resource media so that the lessons delivered are achieved according to the intended educational goals. There are different things the writer witnessed during the initial survey, children with special needs in special school in Rejang Lebong, especially those with hearing impairment, they display something that attracts attention, where they have good character towards God with the habit of praying before and after learning, having good morals to teachers and older people by always shaking hands and kissing the hands of older people, they are also very concerned about others as evidenced by the quick response when seeing teachers who need help without being asked, they also care about the environment. Dispose of trash in its place, school infrastructure is well maintained. While the writer who is actually a lecturer and a teacher of Islamic Education in public schools with the majority of their students under normal conditions, but still always finds obstacles in providing moral guidance. For that reason, the writer is interested in wanting to know how the strategy is implemented in instilling morals for children with special needs in Special Schools. METHOD* A qualitative approach was used. This research approach is a research method that is based on the philosophy of postpositivism, used to examine natural conditions of objects where the researcher is a key instrument. The study was conducted at Elementary Special School for 3 months, starting on February 11 until April 11, 2019. While the type of research used is case study research. Case study research is research that seeks to describe a phenomenon, event, event that is happening right now. Case study research focuses on the actual problem as it was when the research took place. Through descriptive research, researchers try to describe the events and events that are the center of attention without giving special treatment to those events. The respondents of this study were the principal, teachers and deaf students at Special Schools in Rejang Lebong, by means of observation, interviews and documents. RESULTS AND DISCUSSION Learning Strategies for the Deaf Children There are actually so many learning strategies. The following are among the strategies that can be used by teachers to enable students in the learning process for children with hearing impairment according to Generals, Strategies commonly used for children with disabilities include; heuristic, expository, classical, group, individual, cooperative, and behavior modification strategies (Derawan, 2013). 1) The Heuristic Learning Strategies. Heuristic strategies are teaching and learning strategies that work around so that aspects of the components forming instructional systems lead to activating students can also be interpreted as reason in the work or practical instructions that can help shorten the path of problem solving (Seriti et al., 2013). 2) The Expository Learning Strategies. According to Jaya (2012) revealed that expository learning strategy is a form of teacher-oriented learning approach. It is said so because in this strategy the teacher plays a very important or dominant role. Almost in line with Safriadi’s statement that in expository learning the teacher presents the material in a form that has been prepared neatly, systematically and completely so that students stay listening and digesting it in an orderly and orderly manner (Safriadi, 2017). 3) The Cooperative Learning Strategies. Cooperative learning strategy is a series of learning activities carried out by students in certain groups to achieve the learning objectives that have been formulated. There are four important elements in cooperative learning strategies, namely the presence of participants in the group, the existence of group rules, the learning effort of each group member, and the existence of objectives that must be achieved (Johnson & Johnson, 2011; Slavin, 1987). So, the interesting thing from cooperative learning strategies is that there is hope that in addition to having a learning impact, that is in the form of an increase in student achievement (Student achievement) also has an accompanying impact such as social relations, acceptance of students considered weak, self-esteem, academic norms, respect for time, and like to give help to others. 4) The Collaborative Learning Strategies. The collaborative learning is a learning strategy where students with multilevel variations work together in small groups towards one goal. In this group the students help one another. So the collaborative learning situation there is an element of positive dependence to achieve success. 5) The Behavior Modification Learning Strategies. Behavior modification is the application of operant conditioning learning theory to change behavior. Operant conditioning discovered by B.F Skinner refers to the relationship between the environments that result in specific behavioral changes. Assumptions relating to behavior modification include the following. (1) Behavior is something that is learned. (2) Behavior is not permanent but can be trained, taught and changed or modified. (3) Most of the behavior is the result of certain stimuli, for example when a mosquito bites, people will be moved to hit it. Behavior does not occur randomly, but because of a stimulus. (4) Behavioral management programs should be specific, for each behavior to be modified. (5) Behavioral management programs must be focused on the child’s environment (Safriadi, 2017). Mahabbati (2014); Rahayu (2013) stated some special principles that must be considered in learning for children who have deficiencies in this case deaf, these principles are: 1) Position in conveying and explaining learning to students should deal with students (face to face) and do not turn their backs on students because deaf students will try to understand what the teacher explained through reading utterances. 2) In an inclusive or regular class, the deaf students should be placed in a sitting position in front so that they can understand the teacher’s words when explaining and should be placed with students who have good hearing so that they can help smooth learning. 3) The deaf students have obstacles in capturing teacher explanations due to lack of hearing, therefore teachers should provide an explanation slowly, clearly, loud voice, simple sentences or language used and record important things on the board. The teacher should also pay attention to the direction of the ray of light, so that the deaf student is not dazzled by the teacher's lip movements and expression. 4) The use of visual aids should be sought by the teacher in learning to facilitate students’ understanding of the deaf to the material presented because deaf students are known as visual children. 5) Avoid using the lecture method often because deaf students experience hearing impairments that make it difficult to understand the teacher's words. Teachers should use more visual methods such as demonstrations, role playing and so on. 6) The teacher needs to modify or simplify the use of language in verbal material so that deaf students can understand the material presented. 7) Provide additional vocabulary and ensure that deaf students understand correctly the terms that the teacher uses because deaf students are poor in vocabulary or less understanding in vocabulary compared to other regular students. Based on the explanation above, it is clear that deaf children are very complex in terms of learning, in addition to problems with their sense of hearing, they are also poor in vocabulary, difficult to understand material in the form of verbal and can not learn with the conditions of the room that dazzle their eyes. So for teachers who teach inclusion classes that are deaf children or indeed deaf classes, must really pay attention to the special principles of learning for deaf children as described above. The Forming the Religious Character of the Deaf Children in Special Schools Islamic Education is a subject that is in public schools including the Special Schools in Rejang Lebong, Bengkulu. Based on documentation and interview data, the curriculum implemented at this school uses the 2013 curriculum, where Islamic religious education gets a three-hour portion every week for all classes. The teacher who teaches Islamic Education at Special School in Rejang Lebong is not a teacher who is based on Special School Education, but the teacher is a teacher based on Islamic Education who comes from State Islamic Institute of Curup graduates, and as a support for teachers who will teach in Special School then the school provides special training for teachers who will teach. The purpose of Islamic education at the Special School in Rejang Lebong refers to the realization of the vision and mission of the school, namely Excellence in the field of skills to equip students for independence based on cultural and religious values. This is the uniqueness of the implementation of the curriculum in schools in learning as an effort to develop morals, so to achieve this vision Special Schools in Rejang Lebong has the following mission: 1) Improve the quality that is relevant in special education and special services; 2) Instilling belief/Aqeedah through the practice of religious teachings (EES of Rejang Lebong Document, 2019). The implementation of Islamic education learning carried out at special Schools in Rejang Lebong based on the 2013 curriculum with a total of three hours of learning in each class, while teachers who teach Islamic education subjects are teachers of State Islamic Institute of Curup graduates who are then equipped with special knowledge to communicate with students with special needs, this aims to realize the vision and mission of the school in which there is moral guidance, and Islamic education teachers are the teachers who are most in touch with it, so the role of Islamic religious teachers is very dominant, both in terms of providing material in class and the implementation of religious activities carried out. Expository Learning Strategies Using Modeling Methods and Exercises The deaf Children have limitations in terms of hearing, some are low, moderate, and some are totally unable to hear at all so special strategies are needed to deliver learning material; especially there are students who have doubts that are deaf and dumb. Delivering subject matter to deaf children requires a special way that is better known as commutal or total communication, besides that a teacher must really prepare adequate media to convey the material, such as pictures and videos related to the material even to teach about daily activities days like eating and eating should use pictures and at the time of evaluation or examination it is suggested that the questions given use more images. Based on the explanation from the teachers above, it seems that the expository strategy is indeed very suitable for use in the learning process for students with special needs, especially for people with hearing impairment, because the principle in this learning strategy a teacher really prepares everything related to the material to be taught, as expressed by Spiriadi (2017) that, in expository learning, the teacher presents the material in a form that has been prepared neatly, systematically and completely so that students stay listening and digesting it in an orderly and orderly manner. Almost the same as the expression of Ariani (2017) that expository learning strategy as a direct learning strategy (Direct Instruction), because learning is delivered directly by the teacher, students are not required to find the material because the subject matter seems to be ready and prepared by the teacher. The learning method used to carry out the expository learning strategy is very appropriate when the modeling and training methods are used where the teacher does not explain much verbally but the teacher shows more pictures, then students take turns. implementing the tasks given by the teacher such as showing the exact picture they have to select, this can be seen when the teacher provides learning about morals. The results of the study, that the modeling and assigning methods or exercises are very appropriate for students with hearing impairment because they are more interested in paying attention to the pictures that are displayed, and when they are instructed to choose the most appropriate picture, they look very enthusiastic, besides that there is a habit interesting thing that was done by Islamic Education teachers at Special Schools in Rejang Lebong, that students were assigned to paste the pictures given by the teacher to their notebooks that had previously been representative of students photocopied the pictures in the administration room, and that they could do well. The presentation from the teacher council regarding the use of modeling methods for deaf students is very effective, because this method provides more concrete learning and is easily understood by students, they can use the senses that they are the mainstay of vision besides teachers who provide explanations using total communication and voice hard, their interest in the image makes them very enthusiastic to follow the learning and carry out the tasks given by the teacher to them, so it is appropriate if we refer to the old adage, if students have enjoyed the lesson, then they will automatically love the teacher who teaches it, outside Usually it can be felt by the teacher is when his students are very obedient, and shows good morals to the teacher both in class and outside the classroom, from the results of interviews and observations conducted answered that there are advantages that are felt when the teacher provides learning with and using modeling methods and exercises. So, the modeling method basically expresses the ideas thought by the teacher and then can later be imitated or demonstrated by students through examples in the form of pictures or actions of a show. This method is very effective for students with special needs, especially those with hearing impairment, to create conducive learning situations and produce maximum learning outcomes. Adding Class Hours with the Habitation Method The method of habituation if done early on, according to Ihsani et al. (2018), will bring hobby and the habit will become a kind of custom so that it becomes an inseparable part of his personality, in developing the attitude the habituation method is quite effective. Moral development for children with special needs at Special Schools in Rejang Lebong. In addition to being done in the classroom at a predetermined hour, Islamic education teachers also do it outside of class hours by using the habituation method. Moral development with the habituation method consists of fostering morals to God, fostering morals to beings and fostering morals to the environment. Moral Guidance to Allah The Elementary Special School of Rejang Lebong carries out the moral character of students to Allah with the habituation method including: The habit of memorizing short letters The Koran is the greatest miracle revealed to the Prophet Muhammed, as a complete book from the previous book which has virtues for anyone who reads, learn let alone able to memorize it. One of the miracles that we feel from the Koran is that, although speaking Arabic, but whoever the person is, whatever the nation and language will be given convenience for those who want to learn it, even Allah gives convenience for those who are serious about memorizing it, as proven today few people are able to memorize the whole contents of the Koran, even children who are 5 years old Allah gives ease to memorize the Koran. This is proof that Allah sent him down and Allah also guarded him. Currently there are many attempts made by state and private educational institutions that encourage students to memorize the Koran, as well as those done by Special Schools in Rejang Lebong, although the desired target is not the same as public schools especially those based on Islam, but this school tries to targeting students to memorize short letters in the Koran, this is related to the limitations of students whose backgrounds have physical or even mental deficiencies. The method of teaching memorizing short letters that is appropriate for children with special needs is the classical method, as revealed by Maskur (2019). That teaching in a classical way will encourage students to be more enthusiastic. There is a nuance of learning that is fresher than the individual model. The classical way is also effective and efficient for teachers to convey theories, both about makhraj, the nature of letters, reading laws, and other aspects of recitation. Other positive effects, students will gain additional experience from the teacher, how the teacher reacts with students, train sensitivity to reading errors made by students and how the teacher straightens them and so on, during the learning process runs, each teacher should try to make students use the time learn. Aim to continue to use free time by repeating readings on lessons that are not yet mastered. Familiarize children to memorize the Koran, especially in short letters the right method is done classically, where the teacher as a mentor reads slowly then followed by children and it is done repeatedly, especially for children who have special needs. The habit of participating in Islamic holidays In addition to learning that is carried out formally with a predetermined schedule, it turns out that getting children used to participating in Islamic holidays has a positive impact on their moral development, as is done by Special Schools in Rejang Lebong, always holding religious activities in accordance with certain moments such as commemoration activities of the Prophet Muhammad’s Birthday, commemoration of Isra Mi’raj in which there is moral guidance especially in the example of the Prophet. According to Rahmi (2019), instilling morality with a story says that, example is important in moral education and example will be a powerful method in fostering children’s morals. Regarding the great example, God sent the Apostle to be the best example (Chaeruddin, 2016; Fitroh & Suri, 2015). Muhammad is the highest example as a role model in the context of moral development. Moral Guidance to Teachers At least there are four indicators of students said to have good character towards the teacher, that is, they are always polite in speaking and behaving, do not argue with the teacher and always carry out the tasks given by the teacher, always help teachers in need without being asked and feel happy when following the learning process. Good practice in speaking and acting There is a classic suggestion expressed by Rifan (2012) that, a very noble person is a person who pioneered a moral movement that is beneficial to one generation and the next generation. The advice indicates that humans have the same opportunity to do good, especially humans who work as teachers, because the teacher is big in the eyes of his students, what is seen from his teacher will be imitated, because the child will emulate what is seen from his teacher. Exemplary has an important meaning in educating children's morals and being a central point in educating and fostering morals. If the teacher has good character, there is a possibility that the students have good character. Conversely, if the teacher has a bad character there is a possibility that the student has a bad character too. The habit used by the teacher to educate children in the Elementary Special School of Rejang Lebong, seems to use the exemplary method especially in fostering politeness in speaking and behaving. As the results of research data that, fostering student morals is not only when giving lesson material in class but we also do it outside of class hours, by giving examples to them like to get used to good things in speaking gently, even though sometimes there are annoying student attitudes, we must show a high level of patience, giving direct advice we do as an example when meeting with an older person we instruct that the child shake hands and kiss his hand. Based on the results of the research, she revealed that, the role of parents and teachers is very dominant in fostering student morals; the simplest and most effective way is for the teacher to set a good example to student. When students commit violations then that's when students get lessons and reprimands, for example when they call parents and teachers using the word "hi hi" then given an example by calling the father or mother with polite words. Every time there is a case of moral violation, then it should be reprimanded and given a lesson at that time so as not to pile up the problem, because if there are too many problems done by a student, it will be difficult to provide coaching. The habit of carrying out the tasks given by the teacher One of the activities in the learning process is the teacher gives assignments to students who function as exercises or evaluation materials for the level of achievement of the learning process. For children with special needs, of course there is a separate way for them to want to carry out every task given to them. Based on the results of research data in the field, found some tricks from Islamic education teachers, among them, the teacher gave assignments in a fun way such as students directed to photocopy copies of the material taught, then paste it in the exercise book they have, besides that the teacher also gave task with a very gentle way of persuading them to do their work with words that educate. The method of persuading or seducing children in educating children is apparently very effective for children with special needs, because mentally they are eager to get praise when they do well, and do not threaten them when they make mistakes. The habit of paying attention to the teacher when talking in and out the classroom Reciprocal communication must occur when the learning process takes place between the teacher and students, so for children with special needs total communication is needed in conveying educational messages especially for children who have a hearing deficiency, special ways are needed to provide information to the deaf, in this spelling of the finger is very functioning to support the development of the ability to read and write. So by using the finger alphabet and supported by total communication by amplifying the sound volume can convey messages to students so that they continue to be interested to pay attention to the explanation delivered by the teacher both in and out the classroom. Likewise what is done by teachers in Elementary Special School? According to experts that if a deaf child has mastered the spelling of the fingers, then this ability will also support the ability to read and write (Somat & Herawati, 2004) The Habit of helping teachers who need help without being asked Behavior of helping others who need help in Islam is called good character, as Mucharomah (2017); Rasyid (2016) revealed, that when character is connected with Allah, then character is carrying out all the commands of Allah and away from His prohibitions with full sincerity. Allah's command that is carried out is not a burden and Allah's prohibition is shunned not because of compulsion, but all of it is lived with full awareness and sincerity. Helping is one of the items of character recommended in Islam, so as a formal educational institution for foreign Special schools in Curup Mejang Lebong also implements this habit in the learning process, as revealed on the results of research data, that the majority of children in this school have physical and mental limitations, but that does not mean moral guidance in terms of being accustomed to helping other people in need we don't teach, but we as teachers here provide direction so that children are sensitive and quick to help if there are teachers or other people who need help. The same with the results of observations, it is clearly seen that the children in this school have tremendous sensitivity in terms of helping people who need help, at that time the researcher witnessed a teacher who had just come down from the car carrying goods, and one of the children with hearing impairment rushed to help the teacher without any instructions or requests for help from his teacher, this indicates one of the habits that teachers have successfully done towards their students. The habit of creating a sense of joy when attending Islamic religious lessons The joy of the child while attending the lesson is happiness for a teacher, because in reality a teacher has managed to create a pleasant mood for their students. Excitement according to Ahmadi (2009) is an expression of relief that is feeling free from tension. Usually the excitement is caused by things that are suddenly (Surprise) and the excitement is usually social in nature, which involves other people around the person being excited. Creating an atmosphere of joy, it is not possible not to use a method or the method that makes a condition that can be happy, meaning there are certain factors that can make a condition that is a happy atmosphere, so it happens in class. Based on the results of research data at Special Schools in Rejang Lebong, it was clearly seen that the children in this school condition the classroom into a class that is not saturated for children by using fun learning strategies, starting from preparing everything related to learning media such as pictures, props and so on, to how the teachers delivered the material with great patience, and occasionally interspersed with light humor that tickled students so that they seemed enthusiastic about learning and excited when studying Islamic education. Fostering Student Morals on the Environment Giving students an understanding of how to care for the environment is an obligation for a teacher, because according to Rasyid (2016), Allah has created nature in a balanced and harmonious manner. Therefore humans are obliged to maintain the harmony of Nature. There are at least two things coaching conducted by the teacher to students in order to foster a sense of concern and maintain environmental harmony, namely: Habitation of students to throw trash in its place Based on the results of research data at Special Schools in Rejang Lebong, it appears that students in this school already have good habits in terms of caring for the environment as evidenced by their habit of throwing trash in the space provided, and if a violation occurs the teacher immediately makes repairs by reprimanding the student is directly at the scene, so students immediately realize that what they did was wrong. So, clean will also have a good psychological impact on activities, as revealed by Setyaka in his book the secret habits of successful people from waking up to before breakfast say, that successful people also have clean habits-clean in the morning before starting work. In other words, successful people always do it, because with cleanliness, comfort and safety in work can be enjoyed. Feeling comfortable will give a psychological feel of calm. This calmness gives a positive effect in doing work (Setyaka, 2014) The habit of students taking care of school facilities and infrastructures Giving an understanding to students to feel they have school facilities and infrastructures such as their own is one of the ways done by the teacher, so that students want to maintain the existing facilities and infrastructure, this is evidenced by the results of research data, it appears that facilities and infrastructure at Special Schools in Rejang Lebong is neatly maintained, there are no visible classroom doors, broken school glass, scratches on the walls of the school were not found, this is usually found in public schools, especially at the elementary school level. This shows that, there is seriousness on the part of the school, and the awareness of the students to maintain the facilities and infrastructure available at school. The results of the study above, seen their seriousness to provide moral guidance to their students, meaning that learning is not only focused on the cognitive realm, where children are expected to memorize or explain the theories provided, but more than that good personality or character is emphasized to be applied by children wherever they are, and the process of coaching is done every day at school using the habituation method. In addition, the role of parents is also expected to support this habituation movement, especially parents are directly involved and witnessing how teachers provide learning to their children, because the majority of parents wait for their children until the end of class. So when there are violations committed by their children, the teacher asks parents to participate in providing guidance to their children. The implementation of Islamic education at the Special Schools in Rejang Lebong Regency refers to the 2013 curriculum with the vision, mission and objectives of the school being designed. One of them is to make this school superior in skills and independence through inculcation of cultural and religious values, and supported by adequate learning methods and media, because educating children with special needs is very different from normal children, the teacher must be really mature in preparing teaching material, so that later students will easily understand the material delivered by the teacher in class. Especially for children with hearing impaired special needs, teachers at the Elementary Special School of Rejang Lebong, using learning strategies in moral development is using expository strategies. Safridi (2017) named this expository strategy with the term direct learning strategies (Direct Instruction), in this system the teacher presents material in a form that is prepared neatly, systematically and completely so that students pay listening and digesting it in an orderly and orderly manner. Students are also required to master the material that has been prepared. Based on the results of research data, it can be explained the steps prepared by the teacher in implementing expository learning strategies as follows: 1) The teacher prepares a lesson plan; 2) The teacher prepares learning materials as complete as possible; 3) The teacher carries out learning by using total communication; 4) The teacher displays pictures relating to the material; 5) Students are instructed to choose the right picture for a statement; 6) Students are instructed to stick pictures into a notebook; 7) Teachers and students draw conclusions from the learning process. While a very supportive method for implementing this strategy in the classroom used by Islamic education teachers is to use modeling and training methods, bearing in mind the children who are given lessons are children with special hearing impairments, the teacher prepares materials suitable for deaf students, namely using visual media such as pictures related to the subject matter, besides that the teacher must also really understand the material being taught extensively especially the material relating to moral development, based on the results of observations made very clear that Islamic religious education teachers are able to modify the material by displaying examples that occur in real life. So in the learning process students seem enthusiastic to follow the ongoing subject matter, this is shown when in turn students are asked to choose a picture that matches the good character and they are able to show the right choice, they do it with a happy mental condition especially when they are instructed to photograph the copy of the picture and paste it in their respective notebooks, but in the process of course the teacher who teaches must have a high level of patience, because students with conditions have limitations, especially hearing impaired sometimes they have when they like the process learning and sometimes boredom appears. Moral development carried out at Special Schools in Rejang Lebong Regency, is not only done formally in the classroom, but as long as students are in the school environment, using the strategy of adding hours of study with the habituation method, the teacher and parents of students who every day waiting for their children to be involved in the process of moral formation, from the results of interviews with both the teacher and the students' parents, it appears that when outside the classroom students make mistakes that violate the moral provisions, directly the teacher and student parents give a reprimand, which according to them this warning is more effective and impressing the child that this is wrong and should not be done. To increase the student's knowledge about religion, the school adopted a special policy to carry out religious activities in the school by presenting outside da'i who delivered a sermon, this is usually done at moments of Islamic holidays, such as the Birthday of the Prophet, Isra’Mi‘raj and the Islamic new year, in the process of its implementation students were enthusiastic about participating in the activity. Each learning process certainly has things that support and hinder its journey, then in Special Schools, based on interviews, documentation and observations found at least four things that support the learning process in moral development for deaf students, namely: 1) Headmaster who are in fact graduates of special service schools, are very concerned about the creation of human beings who have noble character so he fully supports any activities oriented to the formation of morals, this can be seen from the vision and mission of the school, as well as the policies taken to hold religious activities as supporting activities to realize it. 2) Teachers who teach at the Special Schools in Rejang Lebong Regency especially Islamic education teachers have the seriousness to foster student morals, even though they do not have the basic knowledge of teaching children with special needs, but through activities carried out by the school by providing guidance specifically how to teach at Special Schools, the teachers follow it well, so that when teaching they are accustomed to dealing with students with various limitations in a tenacious and patient manner. 3) Concern of students' parents towards the progress of their children is also felt to be very supportive of the learning process especially in terms of moral development, this is in accordance with the results of an interview with one of the students' parents, that they are very supportive of the activities carried out at school, they never protest when their children reprimanded when they make mistakes and they even support their teacher by directly reprimanding when their children make mistakes. 4) Students show high enthusiasm when the learning process takes place, they learn calmly and are happy this is certainly supported by the strategies and methods of teachers who teach in their class, so that they respond positively to the teacher and the material being taught. Then there are five components that are felt as obstacles, in the implementation of learning in the Elementary School of Rejang Lebong Regency, namely: 1) The absence of a special curriculum for students with special needs so that this school uses the 2013 curriculum, the Graduation Standards, Core Competencies and Competencies are essentially equated with public schools, with this condition the teaching teacher finds it difficult to pursue it all, which ultimately teachers take the initiative to transfer knowledge adapted to the child's condition; 2) Especially for Islamic education teachers, the dominant ones who provide moral guidance to children should be religious teachers graduated from Special Service Schools, but this is not the case in this school, Islamic religious education teachers at this school who are graduates of State Islamic Institute of Cunup, Rejang Lebong; 3) The learning process does not go according to a predetermined schedule, which should enter at 08.00 PM and they go home at 12.00 PM, but at 10:00 PM on average students have asked to go home, this happens because of the limitations they have, and based on observations students do it seems that they are already getting nervous around 09.30 PM, this is due to the limitations they have, and it turns out that people with special needs, get tired more quickly and feel bored when compared to those who are normal; 4) Supporting facilities in learning are still lacking, this is based on observations and interviews that education in special schools will be easier if supported by means as a learning medium for example for deaf children, they are very easy to catch the message conveyed if the material is conveyed through audio, visual, or both, this is evident when getting learning with teachers who use drawing media students are very enthusiastic, it would be better if the teacher uses electronic media such as infocus, but the availability is very limited, for six classes there are only two infocus so that the teacher the teacher must take turns using it; 5) The distance between the domicile of students and the majority of schools is far, this results in frequent students not attending school, especially on rainy days and schools do not have a car as a means of transportation for students. CONCLUSIONS AND RECOMMENDATION The teaching strategy of Islam education teachers in moral guidance for children with special needs at Special Schools is expository strategy. In addition the strategy used is to increase the hours of study by using the habituation method. Supporting factors in the learning process are mainly moral development in Elementary Special Schools, namely principals who are very concerned about the development of student morals, teachers who are enthusiastic in providing learning and moral guidance, and have great patience in dealing with children with special needs. Besides that, parents who play an active role in helping with moral development activities, students seem calm and happy to take lessons in class, especially when the teacher who teaches them uses media that attracts their attention so that the material delivered is easy to understand, as well as moral messages that are delivered they can receive well. 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N., & Knoors, H. (2008). Social integration of deaf children in inclusive settings. Journal of Deaf Studies and Deaf Education, 13(1), 21-36. Wilkens, C. P., & Hehir, T. P. (2008). Deaf education and bridging social capital: A theoretical approach. American Annals of the Deaf, 153(3), 275-284. The Strategy of farming religious charakters on the children; Study at special schools in Rejang Lebong \| PRIMARY SOURCES \| SIMILARITY INDEX \| INTERNET SOURCES \| PUBLICATIONS \| STUDENT PAPERS \| \|-----------------\|------------------\|------------------\|--------------\|----------------\| \| 1 \| Submitted to Academic Library Consortium \| 2% \| \| \| \| 2 \| N A Hidayati, S Fahmi, K Farida. "The comparative of mathematics learning using guided discovery method and expository method to mathematics learning outcomes", Journal of Physics: Conference Series, 2019 \| 1% \| \| \| \| 3 \| repository.uhamka.ac.id \| 1% \| \| \| \| 4 \| Rizza Megasari, Rizky Dwi Putri, Dian Rachmawati. "Improvement of Subjects Understanding Development of Teaching Materials Through Project Based Learning", KnE Social Sciences, 2020 \| 1% \| \| \| \| 5 \| theses.uin-malang.ac.id \| <1% \| \| \| Submitted to Universitas Muria Kudus M. Arif Rahman Hakim, Mohamad Jafre Zainol Abidin, Nur Ilianas Adnan. "Chapter 32 Using the ASSURE Model in Developing an English Instructional Module for Indonesian Migrant Workers in Penang, Malaysia", Springer Science and Business Media LLC, 2020 \| \| Title \| Publication \| \|---\|-----------------------------------------------------------------------\|--------------------------------------------\| \| 15\| System for Object Vocabulary Mastery for Students with Hearing Impairment Based on Augmented Reality \| Journal of Physics: Conference Series, 2019\| \| 16\| Zulvia Misykah, M.Syarif Sumantri, Deasyanti. "The Effect of PQ4R Strategy and Intellectual Intelligence on Higher Thinking Ability in Mathematics in Elementary Schools" \| International Journal of Advances in Scientific Research and Engineering, 2018 \| \| 17\| Encyclopedia of Cross-Cultural School Psychology, 2010. \| \| \| 18\| en.wikipedia.org \| \| \| 19\| jurnal.uinsu.ac.id \| \| \| 20\| Submitted to UIN Raden Intan Lampung \| \| \| 21\| www.inderscienceonline.com \| \| \| 22\| garuda.ristekbrin.go.id \| \| 24 J Maknun, M S Barliana, D Cahyani. "How to Improve Engineering Competencies for Students with Special Needs?", IOP Conference Series: Materials Science and Engineering, 2018 25 e-journal.unipma.ac.id 26 Nur Hidayanti. "Analysis of Student Mistakes in Completing Matrix Problems in The Linear Algebra Course", Journal of Physics: Conference Series, 2020 27 pdfs.semanticscholar.org 28 core.ac.uk 29 Teguh Prasandy, Ika Nurlaila, Titan Titan, Lena Lena. "Implementation of "ADAB" to Hearing Impaired Student as Learning Innovation in the Data and Text Mining Course, Information System Distance Learning, Binus Online Learning", International Journal of Emerging Technologies in Learning (iJET), 2020 Oussama Metatla, Clare Cullen. ""Bursting the Assistance Bubble"", Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems - CHI '18, 2018 Richard P. Hastings, Suzanna Oakford. "Student Teachers' Attitudes Towards the Inclusion of Children with Special Needs", Educational Psychology, 2003 # The History and values of tolerance in Tabot traditional ceremonies in Bengkulu society ## Originality Report \| Similarity Index \| Internet Sources \| Publications \| Student Papers \| \|------------------\|------------------\|--------------\|----------------\| \| 16% \| 16% \| 0% \| 0% \| ## Primary Sources \| Rank \| Source \| Percentage \| \|------\|------------------------------------------------\|-------------\| \| 1 \| repository.radenintan.ac.id \| 7% \| \| 2 \| repository.unair.ac.id \| 4% \| \| 3 \| repository.usu.ac.id \| 3% \| \| 4 \| repositori.uin-alauddin.ac.id \| 2% \| Exclude quotes: Off Exclude bibliography: Off Exclude matches: Off	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 108, 1 ], [ 108, 232, 2 ], [ 232, 3261, 3 ], [ 3261, 7578, 4 ], [ 7578, 11733, 5 ], [ 11733, 15843, 6 ], [ 15843, 19931, 7 ], [ 19931, 23960, 8 ], [ 23960, 28036, 9 ], [ 28036, 32007, 10 ], [ 32007, 36017, 11 ], [ 36017, 40110, 12 ], [ 40110, 44549, 13 ], [ 44549, 48100, 14 ], [ 48100, 51021, 15 ], [ 51021, 53785, 16 ], [ 53785, 54949, 17 ], [ 54949, 55199, 18 ], [ 55199, 56595, 19 ], [ 56595, 57308, 20 ], [ 57308, 57620, 21 ], [ 57620, 58466, 22 ] ] }
0c6decc40ed6b3b0b76b92a0f2616e35b016ba5a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 10, "total-fallback-pages": 0, "total-input-tokens": 29199, "total-output-tokens": 10681, "fieldofstudy": [ "Biology" ] }	SirT3 is a nuclear NAD$^+$-dependent histone deacetylase that translocates to the mitochondria upon cellular stress Michael B. Scher$^1,2,3$ Alejandro Vaquero$^1,3,4$ and Danny Reinberg$^1,2,3,5$ $^1$Howard Hughes Medical Institute, New York University Medical School, New York, New York 10016, USA; $^2$Department of Biochemistry, New York University Medical School, New York, New York 10016, USA; $^3$Department of Biochemistry, Division of Nucleic Acids Enzymology, Robert Wood Johnson Medical School, University of Medicine and Dentistry of New Jersey, Piscataway, New Jersey 08854, USA In humans, there are at least seven Sir2-like proteins (SirT1–7) with diverse functions, including the regulation of chromatin structure, and metabolism. SirT3 levels have been shown to correlate with extended life span, to localize to the mitochondria, and to be highly expressed in brown adipose tissue. In humans, SirT3 exists in two forms, a full-length protein of $\sim 44$ kDa and a processed polypeptide lacking 142 amino acids at its N terminus. We found that SirT3 not only localizes to the mitochondria, but also to the nucleus under normal cell growth conditions. Both the full-length and processed forms of SirT3 target H4-K16 for deacetylation in vitro and can deacetylate H4-K16 in vivo when recruited to a gene. Using a highly specific antibody against the N terminus of SirT3, we found that SirT3 is transported from the nucleus to the mitochondria upon cellular stress. This includes DNA damage induced by Etoposide and UV-irradiation, as well as overexpression of SirT3 itself. Keywords: Histone deacetylation; chromatin; mitochondria; SirT3 Received December 31, 2006; revised version accepted February 21, 2007. SirT3 is a member of the Sir2 family of NAD$^+$-dependent protein deacetylases (Frye 1999). This family of proteins is implicated in chromatin structure, transcriptional silencing, and aging in organisms ranging from yeast to humans. It has been proposed that human sirtuins generally have nonhistone substrates. Yet the SirT proteins (especially SirT1, SirT2, and SirT3) are highly related to the yeast Sir2 protein, a dedicated histone deacetylase with specificity for Lys 16 of histone H4 (H4-K16), a residue important in attaining a repressed chromatin state in yeast upon its deacetylation (Suka et al. 2002; Shogren-Knaak et al. 2006). Recent speculations suggest a function for SirT1 (and other SirTs) in caloric restriction and life span [Haigis and Guarente 2006]. SirT1 initially was found to deacetylate the tumor suppressor p53 [Luo et al. 2001; Vaziri et al. 2001; Langley et al. 2002], as well as other transcription factors [Brunet et al. 2004; Giannakou and Partridge 2004; Haigis and Guarente 2006]. However, SirT1 was later found to function in the formation of facultative heterochromatin through its deacetylation of core histones, specifically acetyl-Lys 16 of histone H4 [H4-K16ac] [Vaquero et al. 2004]. SirT1 also interacts with histone H1 and deacetylates acetyl-Lys 26 [Vaquero et al. 2004]. The ability of sirtuins to deacetylate H4-K16ac is not restricted to SirT1, as SirT2 has been shown to deacetylate H4-K16ac during mitosis (Vaquero et al. 2006). SirT3 is the only Sirtuin with an apparent direct link to extended life span in humans. Mutations in an enhancer region of the $\text{SirT3}$ gene that potentially up-regulate its expression were found at a high frequency in long-lived individuals, suggesting that high expression of SirT3 can be an important marker in life extension [Bellizzi et al. 2005]. Overexpression of murine SirT3 also has been shown to increase the expression of genes involved in mitochondrial biogenesis and metabolism in brown fat cells, linking SirT3 concentration to the regulation of nuclear gene expression [Shi et al. 2005]. However, SirT3 has been reported to localize exclusively to the mitochondria, and it has been speculated that this localization may have important implications in SirT3 function in life span [Onyango et al. 2002; Schwer et al. 2002]. It has also been reported that once SirT3 enters the mitochondria the protein becomes processed at the N terminus, resulting in the activation of its enzymatic activity (Schwer et al. 2002). Finally, studies demonstrated that SirT3 is able to deacetylate and activate the enzyme acetyl-CoA synthetase 2 within the mitochondria, showing an important role of SirT3 at this organelle (Hallows et al. 2006; Schwer et al. 2006). The previous studies used overexpressed SirT3 and did not address whether or not the endogenous SirT3 also resides exclusively in the mitochondria. Using highly specific antibodies against the N terminus of SirT3 and hence specific to the full-length human protein, we show that under normal cellular conditions, full-length SirT3 resides in the nucleus. Full-length SirT3 does, indeed, localize to the mitochondria; however, we show that such translocation occurs upon stress caused by either environmental conditions or by the massive overexpression of SirT3 itself. We further observe that SirT3 completely exits the nucleus upon these conditions in a manner sensitive to Leptomycin B (LMB). In characterizing the biochemical activity of SirT3, we show that both the full-length and processed forms of SirT3 have a strong NAD⁺-dependent histone deacetylation activity in vitro with specificity for acetyl-Lys 16 of histone H4 and to a lesser extent acetyl-Lys 9 of histone H3. We further show that SirT3 is an in vivo histone deacetylase (HDAC), which can repress transcription of a gene when recruited to its promoter. Our work complements studies that revealed a mitochondrial function for SirT3 by showing that SirT3 also localizes to the nucleus and deacetylates acetyl-Lys 9 and acetyl-Lys 16 of histones H3 and H4, respectively. Results Full-length SirT3 is a nuclear protein In order to study SirT3 function in vivo, we initially sought to generate a highly specific antibody. We used the N terminus of human SirT3 (hSirT3) as it does not share homology with other Sirtuins and it is specific to the human protein, as the mouse protein lacks this domain (Fig. 1A). After affinity purification of the antibodies, we examined SirT3 localization in several cell lines (Fig. 1A). Using immunofluorescence studies, we observed that the SirT3 antibodies recognize a protein that resides exclusively in the nucleus and is excluded from the dark DAPI regions (Fig. 1B). Since the murine SirT3 is devoid of the N-terminal region, no immunofluorescence signal was observed in the mouse cell line NIH3T3, demonstrating specificity of the antibodies. Moreover, in competition experiments only recombinant SirT3 competed away the signal, further verifying the specificity of the antibody (Fig. 1C). Since the antibody is generated against the N terminus, it is not possible to probe for the localization of endogenous SirT3 that has been processed. Using a highly specific antibody generated against the C terminus of SirT3 (Schwer et al. 2002), we demonstrated using Western blot analysis the presence of full-length and processed forms of SirT3 in the nucleus (Fig. 6B [below], lane 1). However, and in agreement with previous studies, we also observed that a large population of the N-terminal-processed SirT3 is lo- Figure 1. Full-length SirT3 is nuclear. (A) Schematic representation of full-length human and mouse SirT3. (B) Immunofluorescence analyses of the cell lines indicated using antibody specific to the N terminus of human SirT3. DAPI was used to visualize the nuclei. (C) HeLa cells analyzed as in B but in the presence of the competitors indicated. localized to the mitochondria (Fig. 6B, below). Therefore, from these observations, we conclude that SirT3 is localized in the nucleus and mitochondrion. SirT3 has NAD$^+$-dependent histone deacetylase activity In order to understand the nuclear function of SirT3, we examined its enzymatic activity and substrate specificity. Only the processed SirT3 is considered biochemically active (Schwer et al. 2002). Yet given our findings that full-length SirT3 exists in the nucleus, we re-examined whether both forms of SirT3 have detectable NAD$^+$-dependent activity. Recombinant SirT3 expressed in Escherichia coli generated exclusively full-length protein, but it was highly aggregated and exhibited very weak enzymatic activity; therefore, we generated a baculovirus SirT3 (bSirT3), which contained both a histidine and a Flag tag at the N terminus. After double affinity purification, only full-length bSirT3 was observed (Fig. 2A). We compared the bSirT3 to SirT3 purified from human cells (hSirT3) after transfection of a SirT3 expression plasmid containing an HA-tag at the C terminus. After HA affinity purification, $>90\%$ of the hSirT3 was in the processed form (Fig. 2A). Both SirT3 preparations displayed strong NAD$^+$ -exchange activity (Vaquero et al. 2004) to either acetylated BSA or hyperacetylated core histones (Fig. 2B, top panel). As expected, unacetylated BSA as a substrate was inactive. Most importantly, SirT5, which localizes exclusively to the mitochondria (Haigis and Guarente 2006), displayed NAD$^+$-exchange activity with specificity for acetylated BSA but not to hyperacetylated core histones. These observations collectively demonstrate that the histone-dependent exchange activity observed with SirT3 is specific. We next compared the SirT3 preparations in a histone deacetylation assay using hyperacetylated core histones purified from TSA and sodium butyrate-treated HeLa cells as substrate, coupled with Western blot analyses using antibodies against specific histone acetylated residues. In the absence of SirT3, deacetylation of histones was not observed (Fig. 2C, top panel). However, the addition of equivalent amounts of nicotinamide exchange units of both forms of SirT3 (full-length and processed forms shown in Fig. 2B, bottom panel) revealed a strong specificity for deacetylation of H3-K9ac and H4-K16ac in each case (Fig. 2C, top panel). We further analyzed the specificity and NAD$^+$ dependence of baculovirus-derived, full-length SirT3 and human-derived, processed SirT3 by titrating down the enzymes, in the presence and absence of NAD$^+$ (Fig. 2C, bottom panel). In each case, SirT3 exhibits apparently a higher specificity for H4-K16ac, and this HDAC activity is NAD$^+$-dependent. As well, full-length SirT3 containing a Flag tag at the N terminus and isolated from human cells using anti-Flag affinity purification exhibited equivalent HDAC activity and specificity (data not shown), demonstrating that its expression in mammalian cells has no effect on its activity. SirT3 deacetylates histones in vivo The results described above indicate that SirT3 is localized to the nucleus and that it deacetylates histone H4-K16ac and H3-K9ac in vitro. To analyze whether the above observations are biologically relevant, we analyzed whether SirT3 can deacetylate histones in vivo. We first tested if RNA interference (RNAi)-mediated reduction of cellular SirT3 would affect the overall levels of acetylated H3-K9 and H4-K16; these results were negative (data not shown). We then speculated that SirT3-mediated deacetylation of histone residues may be gene-specific. To test whether SirT3 can repress transcription in a gene-specific manner and in a deacetylation-dependent manner, we transfected a luciferase reporter directed by the TK promoter with Gal4 DNA-binding sites and Gal4-SirT3 expression plasmids into 293F cells. Recruitment of wild-type full-length Gal4-SirT3 to the luciferase reporter led to its repression (Fig. 3A). Transfection of a SirT3 mutant protein with a single substitution in the catalytic domain was ineffectual, demonstrating that the repression is dependent on SirT3 enzymatic activity. Since the N terminus of SirT3 may have an important role in the nucleus, we tested whether a truncated Gal4-SirT3 could repress transcription. Surprisingly, the N terminus was required for repression (Fig. 3A). Gal4-SirT3 fusion proteins were expressed and remained almost exclusively nuclear as shown by fractionation of cells transfected with full-length and processed forms of SirT3 (Fig. 3B). We next tested a cell line in which the full-length Gal4-SirT3 is stably integrated and its expression is regulated by tetracycline. Recruitment of Gal4-SirT3 to an integrated luciferase reporter was analyzed by chromatin immunoprecipitation (ChIP) experiments (Fig. 3C). After tetracycline induction, Gal4-SirT3 was present at the luciferase reporter gene as expected. Importantly, the levels of acetylated H4-K16 and H3-K9 were clearly reduced, relative to the uninduced case. Of note, tetracycline treatment was without effect at the actin promoter with respect to the levels of acetylated H4-K16 (Fig. 3C). Figure 3. SirT3 directed to a promoter mediates gene repression and HDAC activity toward H4-K16ac. (A) Results of luciferase assays performed using a stable cell line containing an integrated luciferase reporter under the TK promoter with GAL4 DNA-binding sites. Transient expression of the GAL4 fusion proteins indicated was performed. (B) Western blots of extracts fractionated into nuclear and mitochondrial fractions after transfection with expression vectors for the indicated protein. (C) ChIP experiments performed with a stable cell line containing both an integrated luciferase reporter and an integrated tetracycline-inducible GAL4-SirT3 fusion protein. The experiment was performed in the presence or absence of tetracycline as indicated and with the specific antibodies shown at the top. Primers targeted to the luciferase reporter as well as the actin promoter were used to assay the immunoprecipitations. Overexpression of SirT3 leads to its relocalization to the mitochondria We next sought to rationalize previous results showing the exclusive localization of SirT3 to the mitochondria. These previous studies used conditions under which SirT3 was overexpressed. Toward this end, we generated a stable cell line that constitutively expresses SirT3 containing an HA tag at its C terminus. Consistent with the current literature, when SirT3 was overexpressed, the protein localized to the mitochondria as evident with anti-HA antibodies (Fig. 4A). Interestingly, when SirT3 antibodies that recognize the N terminus of either endogenous or overexpressed protein were used for immunofluorescence, we no longer observed any signal in the nucleus and found SirT3 only in the mitochondria. This result led us to postulate that prolonged overexpression of SirT3 created an environment that provoked nuclear SirT3 to vacate the nucleus. It also is evidence of a mechanism whereby SirT3 function in the nucleus can be rapidly and negatively controlled through its potential physical exclusion from this site. Hst2, the closest homolog of SirT2, has recently been shown to contain an NES and its cytoplasmic localization to be sensitive to LMB [Wilson et al. 2006]. LMB inhibits CRM1 (chromosomal region maintenance 1), a protein required for nuclear export of proteins containing a nuclear export signal (NES). Examination of the primary sequence of SirT3 did not reveal an NES; however, it is possible that SirT3 export is mediated through an interaction with a protein containing an NES. We tested the possibility that LMB would inhibit SirT3 export from the nucleus upon its overexpression. After transfection of SirT3-HA, cells were treated with LMB followed by immunofluorescence. Since transfection of SirT3 leads to constitutive expression of SirT3, we reasoned that treatment with LMB would inhibit newly expressed protein from leaving the nucleus. Following transfection of SirT3 under normal conditions, we did not observe any cells containing nuclear SirT3; however, upon treatment with LMB, we observed many cells that contained a nuclear SirT3 signal (Fig. 4B). This result suggests that SirT3 is actively transported from the nucleus to the mitochondria by a pathway dependent on CRM1. Full-length SirT3 resides in the nucleus and translocates to the mitochondria upon cellular stress In light of the results presented above as well as the proposal that the main function of sirtuins might be to promote survival and stress resistance in times of adversity (Guarente and Picard 2005), we hypothesized that SirT3 localization to the mitochondria may be biologically relevant during cellular stress—a condition attained by its overexpression. Toward this end, we analyzed SirT3 localization under other conditions that lead to cellular stress: UV-irradiation or treatment with Etoposide, an inhibitor of topoisomerase II that causes DNA damage. In agreement with the results presented above, untreated cells displayed most of the endogenous full-length SirT3 in the nucleus (Fig. 5). However, upon UV or Etoposide treatment, a large population of the endogenous SirT3 was now localized to the mitochondria, as detected using the antibodies directed against its N terminus recognizing full-length human protein (Fig. 5). Since the SirT3 antibodies used in the last two experiments (Figs. 4, 5) are directed toward the N terminus of SirT3 and give rise to a strong mitochondrial signal under the conditions used (cellular stress induced by SirT3 overexpression, UV irradiation, or Etoposide treatment), we surmised that the full-length SirT3 protein is transported into the mitochondria after stress (see below). Newly synthesized SirT3 is processed in the nucleus To analyze the fate of SirT3 upon its overexpression, we used a stable cell line encoding a tetracycline-inducible SirT3 harboring an HA-tag at its C terminus. We examined SirT3 localization as a function of time after tetracycline induction using anti-HA antibodies in immunofluorescence experiments (Fig. 6). Early after induction (10 min), SirT3 localized primarily to the nucleus, and at subsequent time points, SirT3 starts to accumulate in the mitochondria (Fig. 6A). After 1 h of induction, a large fraction of SirT3 localized to the mitochondria, but de- detectable amounts in the nucleus were also observed. At 2 h of SirT3 induction, most of the protein was localized to the mitochondria (Fig. 6A). This result is consistent with the observation shown above demonstrating that prolonged overexpression of SirT3 results in its complete translocation to the mitochondria. Similar results were observed when cells were fractionated into nuclear and mitochondrial fractions and SirT3’s localization analyzed by Western blots (Fig. 6B). Normal uninduced 293 cells displayed endogenous SirT3 in the nucleus and mitochondria as detected using an antibody against the C terminus of the SirT3 protein. The presence of SirT3 in the nucleus was not due to mitochondrial contamination in the nuclear fraction, as Western blots using antibodies against the mitochondria-specific protein Cox IV demonstrate its absence in the nuclear fraction (Fig. 6B, lanes 1,2). Consistent with the immunofluorescence studies presented above, after induction of SirT3-HA, most of the nontagged, endogenous SirT3 quickly localized to the mitochondria (Fig. 6B, lane 4). The C-terminal HA-tagged SirT3 protein can still be detected in the nuclear fraction as this represents the newly synthesized protein before it translocates to the mitochondria. That SirT3 is still detected in the nucleus by Western analysis and not by immunofluorescence may be due to the differences in the two methods. The normalization of the protein loaded for Western blot may not accurately represent the physiological ratio that is present in the fixed cells used for immunofluorescence. These observations further stress the presence of full-length SirT3 in the nucleus. Moreover, they suggest a path by which newly synthesized SirT3 translocates to the nucleus and then to the mitochondria. Interestingly, both the truncated and full-length forms of SirT3 were present in the nuclear fraction, while only the truncated form was detected in the mitochondria (Fig. 6B, lanes 1,2). The most likely explanation for the presence of truncated SirT3 in the nucleus is that SirT3 becomes cleaved at this site. Overexpression causes the cell to become stressed (and oversaturated with SirT3), and this signals the full-length SirT3 to translocate to the mitochondria. Discussion In this study, we analyzed SirT3, a protein related to the yeast Sir2 (Frye 1999), which is involved in the formation of repressive chromatin structures through its ability to deacetylate histone H4-K16ac (Imai et al. 2000; Landry et al. 2000). In agreement with previous results (Onyango et al. 2002; Schwer et al. 2002), we found that SirT3 exists in two different forms, a full-length protein and a protein in which the N-terminal 142 amino acids are removed. However, in contrast to previous studies demonstrating that SirT3 localizes exclusively to the mitochondria, we found that the full-length SirT3 actually resides completely in the nucleus. It is intriguing that conditions that foster cellular stress such as those that induce apoptosis and even those caused by overloading the cell with ectopic expression of SirT3 result in the expulsion of full-length SirT3 from the nucleus. This suggests that the nuclear function of SirT3 can be completely and quickly halted and, in keeping with this, that the enzyme has an extremely important and time-sensitive role in the nucleus. Since a large amount of processed SirT3 is localized to the mitochondria, it certainly performs important roles there. However, we posit that this role is not as sensitive as the nuclear one in that most of the cellular processed SirT3 resides in the mitochondria already. Thus the small increase of SirT3 in the mitochondria from the pool of nuclear SirT3 would not be expected to lead to a strong effect on its concentration there. On the other hand, the exclusion of 100% of the full-length SirT3 from the nucleus would create a dramatic change in concentration at this site. The nuclear full-length SirT3 protein is enzymatically active and deacetylates histones H3-K9ac and H4-K16ac both in vivo and in vitro. Previous reports indicated that only the processed SirT3 is enzymatically active (Schwer et al. 2002). In this case, SirT3 was generated by in vitro translation using rabbit reticulocyte extract and was tested for activity by using a histone H4 peptide that was chemically labeled in vitro. Our results were obtained using endogenous core histones that were acetylated in vivo. That the previous studies used a chemically labeled H4 peptide as opposed to using core histones isolated from cells may have in part led to the results obtained. Another possible explanation of the difference observed could be due to expression of SirT3 in reticulocyte extracts. We found that the bacterially expressed SirT3 protein tends to aggregate, prompting us to generate a baculovirus vector for SirT3 expression. The possibility exists that the SirT3 protein used in previous studies was misfolded, thereby inhibiting its enzymatic activity, and that treatment with peptidase removes the N terminus and this putative block. Our studies also indicate that SirT3 is processed in the nucleus. This finding is consistent with studies of the mouse SirT3 (Shi et al. 2005), which lacks the N terminus and localizes to the mitochondria. This is in contrast to previous studies of the human SirT3 that reported a requirement for the N terminus in its localization to the mitochondria based on immunofluorescence studies and using a SirT3-GFP fusion protein (Schwer et al. 2002). Rather than the suggested possibility that mouse and human SirT3 proteins use two different pathways to localize to the mitochondria (Shi et al. 2005), it is more likely that both proteins are transported to the mitochondria by the same process. Should this be the case, the mouse protein would initially go to the nucleus and then travel to the mitochondria, while the human protein goes to the nucleus, where it is cleaved, and then the Figure 6. Full-length endogenous SirT3 is expelled from the nucleus upon SirT3 overexpression. (A) Immunofluorescence experiment showing the localization of HA-tagged SirT3 as a function of induction time with tetracycline in a stable cell line, using antibody specific to the HA tag. (B) Western blot using antibody specific to the SirT3 C terminus and nuclear or mitochondrial fractions derived from either 293F cells or from a 293F stable cell line expressing tetracycline-inducible HA-tagged SirT3 after treatment with tetracycline overnight. Arrows on the right indicate both tagged and endogenous SirT3. Large arrows on the left indicate the sizes of endogenous SirT3. The antibodies used for Western analysis are indicated on the left. processed protein travels to the mitochondria via the same pathway. Furthermore, a possible explanation as to why truncated SirT3-GFP lost its localization to the mitochondria (Schwer et al. 2002) is that the N terminus is required for the human SirT3 to correctly localize to the nucleus before it can be transported to the mitochondria. Our results also show that the N terminus of human SirT3 is required for transcription repression, further suggesting a regulatory role in the nucleus for this domain. It is possible that in mice, a murine adapter protein performs a similar function as the human SirT3 N terminus. The N terminus of human SirT3 might mediate protein recruitment and substrate specificity in the nucleus as compared with the mitochondria. For example, the N terminus might facilitate SirT3 activity in histone deacetylation in vivo through the recruitment of chromatin remodeling factors or an intrinsic chromatin-related activity. It is also possible that other HDACs are recruited to the gene and that the SirT3 activity is required for deacetylation of another transcription factor required for full repression. Since Sirtuins, like Sir2, are dependent on NAD+ for enzymatic activity (Imai et al. 2000; Landry et al. 2000), SirT3-mediated gene repression is probably regulated by changes in metabolism and NAD+/NADH levels during normal cell conditions, and, as such, SirT3 functions in the mitochondria to deacetylate acetyl-CoA synthetase 2, leading to metabolic changes. Furthermore, given that upon cellular stress SirT3 completely leaves the nucleus, this might cause the rapid activation of nuclear genes involved in mitochondrial function. Hence, SirT3 may autoregulate itself between the nucleus and the mitochondria. From diverse studies (Vaqüero et al. 2004, 2006; Haigis and Guarente 2006), it is clear that the sirtuin family of proteins uses NAD+ for at least two functions, histone/protein deacetylation and protein ADP-ribosylation (Haigis and Guarente 2006). Three members, SirT3, SirT4, and SirT5, have been directly implicated in mitochondrial activity through their localization to the mitochondria and in the case of SirT1 through its ability to deacetylase and thereby enhance the activity of the nuclear coactivator PGC-1α, which regulates the expression of proteins involved in oxidative phosphorylation and mitochondrial biogenesis in skeletal muscle and brown adipose tissue (Koo and Montminy 2006; Lagouge et al. 2006). That sirtuins use NAD+ as a cofactor for enzymatic activity prompted speculations that these proteins, including SIR2, may be involved in the response to caloric restriction and in prolonging life span (Haigis and Guarente 2006). This speculation gained credibility when resveratrol, a naturally existing compound enriched in red grapes and thus in red wine, was found to specifically stimulate SirT1 activity. Further precise biochemical studies uncovered that the resveratrol effect was actually specific for one among several types of assays that measure SirT1-mediated protein deacetylation, and thus disputed the resveratrol effects both in mammals [Borra et al. 2005] and in yeast [Kaeberlein et al. 2005]. However, recent studies performed in mice suggest that resveratrol does function in regulating caloric restriction by stimulating the activity of SirT1, which, in turn, deacetylates PGC-1α and stimulates the expression of nuclear genes involved in mitochondrial function and biogenesis (Lagouge et al. 2006). Certainly, the possible role of resveratrol in caloric restriction and in prolonging life span requires further studies. However, despite the existence of contradictory data, it is surprising and certainly encouraging that independent studies uncovered that increasing SirT1 activity through resveratrol or SirT3 expression through enhancer mutations is associated with prolonged life span. Our results predict that increased SirT3 expression would result in its expulsion from the nucleus and translocation to the mitochondria. Perhaps future experiments should concentrate on understanding how the SirT3 nuclear function together with its mitochondrial function participate in the processes of aging, metabolism, mitochondrial biogenesis, and thermogenesis (Bellizzi et al. 2005, Shi et al. 2005). Based on the studies described herein, it appears that drugs targeted toward the regulation of SirT3 activity and/or its expression as well as to the protease responsible for its cleavage may have important consequences in a cell’s response to stress and its life span. Materials and methods Plasmids and antibodies All constructs were generated using standard PCR-based cloning strategy, and the identities of individual clones were verified through DNA sequencing using an ABI prism DNA sequencer. SirT5 was cloned into pET30α [Novagen], SirT3-HA was cloned into pcDNA4/TO, and baculovirus SirT3 was cloned into pAcHHT-B. Site-directed mutagenesis was performed to change histidine 247 of SirT3 to tyrosine to generate SirT3 HY. N-terminal SirT3 antibodies were generated in rabbits using the N-terminal peptide sequence [H2-N-VFPQCAGCRCLVLGGRDDVYSAGLRSHGARGEPDLPARQPRPEFVR-1COOH]. SirT3 C-terminal antibodies were a gift from Eric Verdin and are described in Schwer et al. [2002]. The antibodies used in HDAC assays and CHIP were previously described [Vaqüero et al. 2004]. Anti-HA antibodies and HA peptide were purchased from Sigma. Anti-H3 acK9 antibodies were purchased from Abcam. Mitotracker was purchased from Molecular Probes. Preparation of nuclear- and mitochondrial-enriched extracts To generate fractions enriched in nuclear and mitochondrial proteins, 5.0 × 10⁶ cells were harvested and washed in PBS. Cells were resuspended in 0.2 mL of buffer MgRSB [10 mM NaCl, 1.5 mM MgCl₂, 10 mM Tris-HCl at pH 7.5, 0.1 mM PMSF, 1 mM DTT] and incubated on ice for 10 min. Cells were dounced to yield free nuclei, and 0.034 mL of sucrose buffer (2 M sucrose, 35 mM EDTA, 50 mM Tris-HCl at pH 7.5) was immediately added. Free nuclei were collected by centrifugation at 800 rcf for 10 min. Mitochondria were collected by centrifugation at 10,000 rcf for 10 min. Nuclei were resuspended in buffer C (20 mM Tris-HCl at pH 7.9, 25% glycerol, 0.42 M NaCl, 1.5 mM MgCl₂, 0.2 mM EDTA, 0.1 mM PMSF, 0.5 mM DTT) and incubated on ice for 20 min. To generate nuclear extract, nuclei were spun down at 20,000 rcf, and the supernatant was collected. Mitochondria were resuspended in buffer C to be used in Western blots. Immunofluorescence Mitotracker Red and Green were incubated with cells at a concentration of 0.1 nM and 0.4 nM, and the cells were allowed to grow for 45 min prior to fixation. For Etoposide treatment, cells were incubated in medium containing 50 μM Etoposide for 4 h. For UV treatment, media was removed from the cells that were then irradiated with 40,000 μJ/cm² UV followed by the addition of fresh media. The cells were allowed to grow for 4 h after UV treatment. Immunofluorescence was performed as described [Vaquero et al. 2006]. For LMB experiments, 293F cells were transfected on coverslips with a vector expressing SirT3-HA overnight. The following day, cells were treated with 5 ng/mL LMB for 120 min, and immunofluorescence was performed as described. In vitro enzymatic assays and cell-based assays All assays were as previously described [Vaquero et al. 2004, 2006]. Stable cell lines Cells harboring a Gal4-inducible luciferase reporter were generated by transfecting 293F TREX cells [Invitrogen] with a plasmid containing the luciferase gene downstream from Gal4-binding sites described previously [Vaquero et al. 2004] and selected for G418 resistance. After selection for luciferase expression, cells were transfected with pcDNA4/TO Gal4-SirT3 and were selected for G418 and Zeocin resistance. Inducible SirT3 stable cells were generated by transfection of pcDNA4/TO SirT3-HA into 293F TREX cells and selected for resistance. Acknowledgments We thank Dr. Eric Verdin and Dr. Bjorn Schwer for α-SirT3 C-terminal antibodies. We also thank Dr. Lynne Vales for comments on the manuscript and members of the Reinberg laboratory for helpful discussions. This work was supported by grants from NIH GM64844 (to D.R.) and the HHMI (to D.R.). References Bellizzi, D., Rose, G., Cavalcante, P., Covello, G., Dato, S., De Rango, F., Greco, V., Maggiolini, M., Feraco, E., Mari, V., et al. 2005. A novel VNTR enhancer within the SIRT3 gene, a human homologue of SIR2, is associated with survival at old ages. Genomics 85: 258–263. Borra, M.T., Smith, B.C., and Denu, J.M. 2005. Mechanism of human SIRT1 activation by resveratrol. J. Biol. Chem. 280: 17187–17195. 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Scher, Alejandro Vaquero and Danny Reinberg Genes Dev. 2007, 21: Access the most recent version at doi:10.1101/gad.1527307 References This article cites 25 articles, 13 of which can be accessed free at: http://genesdev.cshlp.org/content/21/8/920.full.html#ref-list-1 License Email Alerting Service Receive free email alerts when new articles cite this article - sign up in the box at the top right corner of the article or click here.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4304, 1 ], [ 4304, 7670, 2 ], [ 7670, 11292, 3 ], [ 11292, 15272, 4 ], [ 15272, 18126, 5 ], [ 18126, 21358, 6 ], [ 21358, 24842, 7 ], [ 24842, 31352, 8 ], [ 31352, 38048, 9 ], [ 38048, 38620, 10 ] ] }
f22fdc3909619a13c0dd4019a6504e72550f3132	{ "olmocr-version": "0.1.59", "pdf-total-pages": 5, "total-fallback-pages": 0, "total-input-tokens": 15819, "total-output-tokens": 3303, "fieldofstudy": [ "Education" ] }	Challenges and opportunities for a CAMPEP-accredited Medical Physics Graduate Program in Galway, Ireland C Kleefeld\textsuperscript{1,2}, M Alaswad\textsuperscript{1,3} and M Foley\textsuperscript{1} \textsuperscript{1}School of Physics, National University of Ireland Galway, Galway, Ireland \textsuperscript{2}Department of Medical Physics and Clinical Engineering, University Hospital Galway, Saolta University Healthcare Group, Galway, Ireland \textsuperscript{3}Comprehensive Cancer Centre, Radiation Oncology, King Fahad Medical City, Riyadh, 11525, Kingdom of Saudi Arabia E-mail: [email protected] Abstract. Established in 2002, this long running MSc in Medical Physics program was awarded CAMPEP accreditation in 2015, thus being one out of only two CAMPEP approved graduate programs outside North America. The program is a full-time, one-year taught master course delivered by a close university–hospital collaboration. This paper will give an outline of the current program structure and will identify challenges likely affecting the areas of teaching, research and course administration. Strategies to address these challenges will be discussed. Since the accreditation, the number of students enrolled in the program increased from 8 in 2015/16 and 16 in 2016/17 to 21 in 2017/18 and 25 in 2018/19. The number of non-EU students in these cohorts was 2, 5, 4, and 9 respectively. Non-EU students predominantly originate from North America and Saudi-Arabia. The total number of applicants averages at approximately 55 per year. A further increase in student intake has been advocated but might impact negatively on the quality of the clinical training which forms a vital part of the program. Students are given access to clinical systems for laboratory exercises as well as for pursuing research projects, thus gaining some clinical experience which will increase their employability. However, local clinical access has to be limited. In order to mitigate the situation, the program cooperates with medical physics departments nationwide and internationally. Curricular challenges arising from clinical implementations of ever-evolving technologies and from a rapidly changing medical physics landscape in general will be expanded on. 1. Introduction In the early 2000s the rapid expansion in radiotherapy services and the introduction of significant quantities of high end medical technology into many hospitals throughout the Republic of Ireland created the need for further development and expansion of existing medical physics and clinical engineering services. These developments also required increased efforts in the education and training of the next generation of medical physics and clinical engineering professionals. This was recognized by the late Professor Wil van der Putten in 2002 and to address these requirements he established a Master of Science (MSc) in Medical Physics program based at the National University of Ireland, Galway (NUIG), located at the West coast of the Republic of Ireland (Figure 1). The MSc program is a full-time one-year taught master course (90 credits) delivered in close collaboration between the School of Physics, NUIG, and the Department of Medical Physics and Clinical Engineering (MPCE) of University Hospital Galway (UHG), with hospital-based medical physics staff playing an active role in teaching individual modules. Initially accredited by the Institute of Physics and Engineering in Medicine (IPEM), UK, from 2002 to 2014, in 2015 the program received accreditation by the North American Commission on Accreditation of Medical Physics Education Programs (CAMPEP). This article will give an outline of the current program structure and governance, will identify challenges to the program, and will discuss strategies to address these challenges. ![Figure 1. Location of Galway, Republic of Ireland [1].](image) 2. Course Syllabus and Delivery The training of medical physicists requires the acquisition of a body of knowledge and the skills and competencies to apply this knowledge in the clinical practice. In compliance with the CAMPEP curriculum [2], the program introduces students to traditional medical physics topics, including Human Body Structure (Anatomy), Human Body Function (Physiology), Radiation Fundamentals and Dosimetry, Fundamentals of Medical Imaging, Physics of Radiation Therapy and Concepts of Radiobiology, as well as Radiation Protection and Safety. Students are also exposed to other areas that are crucial in a clinical setting, including Clinical Instrumentation, Risk and Safety Management with human factors engineering, Monitoring for Health Hazards at Work, Introduction to Biostatistics as well as Professionalism and Ethics. The latter is a valuable addition to the course, instilling in the student the patient-focused approach of the profession at an early stage in their careers. The course content is delivered through a mixture of traditional lectures, online lectures, tutorials and self-directed learning. The Medical Imaging module is taught through the concept of self-directed learning, that is, each sub-module (e.g., Theory of Image Formation, X-Ray Imaging) is introduced by a lecture. Subsequently, the students are asked to complete topic-related assignments and are be examined on these through short viva exams. The viva interviews are perceived by the students as a helpful preparation for job interviews after graduation [3], thus contributing to the employability of the MSc graduates. In order to give students the skills to be able to apply their theoretical knowledge in the clinical practice the program offers a series of demonstrations and practical exercises, both university-based and hospital-based. Physics laboratory exercises (e.g. γ-ray spectroscopy, α and β radiation attenuation measurements and Monte Carlo simulation of radiation interactions) complement the lectures on radiation and dosimetry fundamentals. Moreover, to take just two examples, dose output measurements at a linear accelerator and brachytherapy source calibrations conducted in a hospital setting deliver some – albeit limited – practical clinical training. The practical component of the program is further strengthened by the curricular requirement that students have to complete a research project, further discussed below. Demonstrations of quality assurance procedures in diagnostic radiology and radiotherapy as well as a computer workshop on practical radiotherapy treatment planning complete the clinical training component of the program. All elements of the program are delivered in close collaboration between university-based and hospital-based medical physics staff. Hospital-based staff will share their clinical experience with students but also have the opportunity to further develop their own professional skill set through lecturing as well as lab and project supervision thereby engaging in continuing professional development. 3. Program Governance The management, further development and quality assurance of the MSc in Medical Physics program is conducted and overseen by two Program Directors and a Program Board. The appointment of two program directors reflects the close collaboration between university and hospital. The Academic Director is responsible for liaising with the College of Science and the wider university in matters of course administration while the Clinical Director will develop the clinical aspects of the program and will interact with the accrediting body. The program board is composed of the program directors, the respective heads of the School of Physics, NUIG and the Medical Physics and Clinical Engineering department, UHG, hospital-based and university-based teaching staff, and an external academic clinician. There will also be a student representative, providing feedback from the current class. The board meets three times per year to discuss student admission and progression throughout the course, to deal with past courses, and to review upcoming courses and future course developments. In order to identify deficiencies and areas for improvement within the program and thereby enabling evidence-based course developments, different feedback procedures have been put into place, complementing the tasks of the program board. In compliance with university policy students are asked to fill out an anonymous online feedback form after completion of each program module. However, on average, only about 25% of the students avail of this feedback mechanism. On an annual basis, the program is assessed by an external examiner. The role of the external examiner is not only to certify that academic standards, student performance and the quality of the program are appropriate to meet national and international expectations, the examiner will also meet the class without the presence of faculty. The students’ responses are anonymized and relayed to the program board and the university. Informal feedback will be obtained through direct staff-student engagements but also through the wider medical physics community which is involved in the supervision of student research projects and also in the recruitment of program graduates. A scientific study on the effectiveness of the MSc, based on a survey among graduates from the first 10 years of the program was conducted and published by van der Putten [3]. In response to the study and feedback received, improvements to the program have been implemented. These include the addition of a comprehensive practical laboratory practice, the expansion of the statistics module and the revision of the medical imaging curriculum. 4. Research Project Although designed as a taught master course, the curriculum requires the completion of a research project. Students are encouraged to pursue their research projects on clinically relevant subjects. The choice of clinical projects is hospital service driven and generally relates to the implementation and performance evaluation of new technologies and treatment techniques or the evaluation of therapeutic or diagnostic outcomes. Recently, a project establishing guidelines for patient precaution times after brachytherapy prostate cancer treatments with radioactive sources received the local Health Care Group award for outstanding research [4]. During their clinical project work most students are based full-time in the Medical Physics and Clinical Engineering Department, UHG. Pursuing their research projects in a clinical environment provides students with additional first-hand experiences of the routine work of a medical physicist. It also provides them with an understanding of the clinical workflow in a busy university affiliated teaching hospital. Experiences such as these add to the student’s future employment prospects. MSc projects are not only conducted in the local public and private hospitals but are also performed in cooperation with Medical Physics departments outside of Galway, thereby contributing to an active Irish research landscape. In addition, it is important to note that in compliance with the internationalization strategy of the university, individual projects have been conducted in collaboration with Canadian and German medical centres as well as with student’s respective home institutions. Several of the past MSc graduates have been awarded PhD scholarships to further their research careers. In preparation of the research component students will give a short oral presentation about their projects to faculty for early feedback. Typically, the presentation will include the motivation, a literature review, the student’s scientific method for approaching the research question, and a project timeline. The project will be examined through another oral presentation towards the end of the practical work as well as a research thesis. 5. Challenges The expansion in terms of student numbers enrolled on the MSc program since its commencement in 2002 is presented in Figure 2. ![Figure 2. Development of student numbers 2002 – 2018.](image) The time series shows a variation in student numbers with an absolute minimum of 3 students in the class of 2011/2012, coinciding with a general economic downturn in the Republic of Ireland. Since receiving CAMPEP accreditation in 2015, the student intake has continuously increased from 9 in 2015/16 to 25 in 2018/19. The CAMPEP accreditation allows recruitment of applicants from North America who after graduating from the MSc program are eligible to continue their clinical careers in the US or Canada. However, the prestigious CAMPEP accreditation also attracts international students from other world regions. Thus, on average, about one third of the students enrolled are international, non-EU students, predominately from Saudi Arabia and North America. Generally, the accreditation creates opportunities for all MSc graduates to pursue their clinical careers not only in Ireland or their respective home countries but also in the US and Canada. Challenges to the program are arising from several factors. The accessibility of practical clinical training constitutes a vital part of the program however the availability of clinical placement opportunities at a local level has to be limited and will be even further compromised by the high student numbers observed. Additionally, on a local level, access to the latest technologies for teaching purposes might be inadequate given a rapidly evolving clinical landscape. Therefore the MSc program intensified collaborations with clinical medical physics departments in Ireland and internationally, providing further placements for student research projects and access to technologies that might not be available locally. A lack of dissemination of results from research projects has been identified as a development opportunity. Although the students have the opportunity to present results at the annual scientific meeting of the national medical physics society, the Irish Association of Physicists in Medicine (IAPM), the number of scientific journal publications is scarce. Therefore, in 2017 the program established three-month write-up stipends, which are available after course completion. Two stipends were awarded to outstanding student projects with a presumed high publication probability [5, 6]. With a multi-national student cohort the program has to embrace diverse educational backgrounds. Noticeably, students have different levels of experience with practical laboratory exercises. Consequently, the already comprehensive practical laboratory practice has been further advanced and project supervision in terms of contact hours has been increased. 6. Conclusions This highly successful CAMPEP accredited medical physics graduate program has a strong practical clinical component with about 75% of its graduates pursuing a medical physics-based career [3], including PhD studentships and radiotherapy residencies. With its dynamic structure the MSc program is well placed to respond to the challenges of an ever changing medical physics landscape. References [1] Google Map 2018 Location of Galway, Republic of Ireland (accessed 05.11.2018). [2] AAPM 2018 Standards for Accreditation of Graduate Educational Programs in Medical Physics http://campep.org/GraduateStandards.pdf (accessed 05.11.2018). [3] van der Putten W J 2014 Fit for purpose? Evaluation of an MSc. in Medical Physics. Phys. Med. 30 358-364. [4] O’Neill M 2016 Patient Isotope Measurements. Evaluating the need for patient specific radiation protection guidelines following Iodine-125 seed implantation MSc Thesis National University of Ireland Galway. [5] Davey K, Moore M, Cleary S, Kleefeld C, Foley M Off-axis dose distribution with stand-in and stand-off configurations for superficial radiotherapy treatments (under peer review). [6] Flynn R, Moore M, Alaswad M, Golden A, Kleefeld C, Foley M A pilot clinical study for an in-house solution for non-standard fractionation re-treatment (under peer review).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3239, 1 ], [ 3239, 5531, 2 ], [ 5531, 9675, 3 ], [ 9675, 12286, 4 ], [ 12286, 16044, 5 ] ] }
310a174089d6394c848a6be79f459f15679c01bc	{ "olmocr-version": "0.1.59", "pdf-total-pages": 15, "total-fallback-pages": 0, "total-input-tokens": 46472, "total-output-tokens": 14304, "fieldofstudy": [ "Medicine" ] }	REVIEW ARTICLE HIV Prevention in Adolescents and Young People in the Eastern and Southern African Region: A Review of Key Challenges Impeding Actions for an Effective Response Kaymarlin Govender1, Wilfred G.B. Masebo1, Patrick Nyamaruze2, Richard G. Cowden3, Bettina T. Schunter4 and Anurita Bains4 1Health Economics and HIV and AIDS Research Division, University of KwaZulu-Natal, Durban, South Africa 2School of Applied Human Sciences, University of KwaZulu-Natal, Durban, South Africa 3Department of Psychology, Middle Tennessee State University, Murfreesboro, United States of America 4UNICEF, Eastern and Southern Africa Regional Office, Nairobi, Kenya Received: February 26, 2018 Revised: April 27, 2018 Accepted: May 7, 2018 Abstract: The global commitment to ending the AIDS epidemic by 2030 places HIV prevention at the centre of the response. With the disease continuing to disproportionately affect young populations in the Eastern and Southern African Region (ESAR), particularly adolescent girls and young women, reducing HIV infections in this group is integral to achieving this ambitious target. This paper examines epidemiological patterns of the HIV epidemic among adolescents and young people, indicating where HIV prevention efforts need to be focused (i.e., adolescent girls and young women, adolescent boys and young men and young key populations). Key innovations in the science of HIV prevention and strategies for dealing with programme implementation are reviewed. The paper also discusses the value of processes to mitigate HIV vulnerability and recommends actions needed to sustain the HIV prevention response. Stemming the tide of new HIV infections among young people in the ESAR requires an amplification of efforts across all sectors, which will safeguard past achievements and advance actions towards eliminating AIDS as a public health threat. Keywords: HIV, Prevention, Adolescents, Young people, Africa, SRH services. 1. INTRODUCTION Substantial progress has been made in the AIDS response under the Millennium Development Goals framework. Yet, adolescents and young people1 are still heavily affected by the disease, accounting for 37% of all new HIV infections in 2017 and 15% of all people living with HIV [1, 2]. While the overall number of AIDS-related deaths declined by 48% between 2005 and 2017, AIDS-related deaths among all adolescents and young people increased by 50% to approximately 55,000 deaths [2]. The greatest number of new infections in the Eastern and Southern African Region (ESAR) (Fig. 1) occur among adolescents and young people [3]. In this region, access to HIV and sexual and reproductive health (SRH) services is limited and social stigma and human rights violations are widespread [4, 5]. If the target of reducing the number of new HIV infections by 75% by 2030 is to be achieved [6], amplified HIV prevention efforts are necessary. Accordingly, this paper outlines some of the key challenges impeding efforts to reduce the number of new HIV infections among adolescents and young people in the ESAR. The paper begins by describing epidemiological patterns in the HIV epidemic among adolescents and young people, populations where HIV prevention efforts are necessary, current approaches to HIV prevention programming and their limitations. Further, consideration is Address correspondence to this author at the Health Economics and HIV and AIDS Research Division, University of KwaZulu, Natal, Durban, South Africa; Tel: 031-2602468; E-mail: [email protected] given on the broader developmental priorities for sustaining the HIV prevention response, including social protection programming to mitigate HIV vulnerability, innovative ways in which to finance HIV prevention activities, and areas where civil society involvement can be strengthened. ![Map showing countries in Eastern and Southern Africa Region](image1) Fig. (1). Map showing countries in Eastern and Southern Africa Region [1]. 2. EPIDEMIOLOGICAL PATTERNS OF HIV IN THE ESAR Recent evidence suggests that the global burden of HIV in young populations is predominant in the ESAR. In 2017, the estimated number of new infections among young people in the ESAR aged between 15 and 24 years was 300,000, with the number of AIDS-related deaths in this age group approximately 36,000. [2]. Examining the HIV infection rates among children and young people in the ESAR over a period of 16 years (Fig. 2), sub-epidemic age-related patterns indicate that while there are declines in new infections in both cohorts, new infections among young people are comparatively higher. Almost two in five (300,000 out of 790,000) new infections in the ESAR in 2015 were among young people between 15 and 24 years old, and one in five (130,000 out of 790,000) among adolescents between 15 and 19 years of age [2]. ![Estimated number of new HIV infections among children and young people in the ESAR, 2000-2016](image2) Fig. (2). Estimated number of new HIV infections among children and young people in the ESAR, 2000-2016 [2]. 1 WHO defines people between 10 and 19 years of age as adolescents, and those between 10 and 24 years of age as young people. Although AIDS-related deaths in the ESAR among adolescents and young people have generally been decreasing, the mortality rate remains high among adolescent girls and young women and is increasing among adolescent boys and young men (Fig. 3). A closer look at the data on AIDS-related deaths points to age and gender patterns. The 2017 data indicated that mortality levels were higher among young women 20 to 24 years old (21,000) as compared to their male counterparts (7,300), yet were lower for adolescent girls (7,900) than for adolescent boys (9,000) [2]. Higher mortality rates for adolescent boys (as compared to adolescent girls) may be due to undiagnosed cases of HIV in this vertically infected population. This means that although more women acquire HIV, more men die of AIDS. Part of the explanation could be that women have more interactions with health facilities (pregnancy, taking children for immunisation) so have opportunities to be tested and treated. Also, it could be that older adolescent boys and young men are just not being captured in the HIV response. For example, adolescent boys and adolescent girls differ in their HIV status knowledge. Demographic Health Surveys (DHS) data suggest that more adolescent girls have had an HIV test and are aware of their HIV status as compared to adolescent boys (Fig. 4). ![Fig. (3). HIV-related deaths among young women and young men in the ESAR, 2000-2016 [2].](image) ![Fig. (4). Percentage of adolescent girls and adolescent boys (15 to 19) tested for HIV and received results in the last 12 months, in the ESAR, 2010-2015 [2, 7].](image) Given the complex factors that drive HIV risk among young people in the ESAR, current epidemiological evidence is limited in several ways. First, there are a number of methods to measuring HIV incidence (e.g., cohort estimation, mathematical modelling, inference incidence from antenatal clinic data, laboratory tests, a combination of HIV testing algorithms), each with benefits and limitations [8]. More recently, these methods have been complemented by phylogenetic and geospatial epidemiology [8, 9]. Given that some of these methods employ newer technologies, more expertise and resources are required for implementation especially in low resourced settings. In addition, most national surveillance systems are not fully equipped to implement location-based approaches at sub-national or at health facility levels [8], which results in a lack of context-specific data (by age and gender) to inform locally-based programming. The challenges in tracking the epidemic at local levels is further compounded by low rates of HIV testing [5]. Second, there is a lack of data on younger adolescents (those below 15 years) because of challenges in getting valid (and ethically sanctioned) information. Understanding issues of sexuality and sexual risk in young children is important for informing HIV and sexual and reproductive health (SRH) risk mitigation strategies (e.g., delaying sex, using condoms, regular health screening) before they get older and more exposed to the risk of HIV infection. In addition, when one takes into consideration adolescent key populations (e.g., adolescent girls engaged in sex work, men who have sex with men, people who inject drugs and the lesbian, gay, bisexual, transgender and intersex [LGBTI] community), there is much debate on accuracy of population size estimates at country level, which ultimately has a bearing on resource allocations for HIV programming [5]. Third, self-reported behavioural data (when it is available) is plagued by measurement issues. Coupled with small sample sizes, especially among younger cohorts, the generalisability of such findings is questionable. Scant data also exists on the broader health and social issues of young populations (e.g., mental health, developmental adjustments to social environments and decision-making skills). Fourth, there are few efforts devoted to interrogating conflicting data reported on adolescents and young people. For example, in Botswana, condom use is reportedly high and exceeds national targets for both sexes, yet adolescent HIV incidence rates and early pregnancy rates are increasing [10]. There is a clear need for triangulation of different data sources to obtain a well-defined picture of the epidemic and trends over time at country and regional levels. HIV data that is collected should be integrated with data on the prevalence of pregnancies and access (SRH) facilities. Data shows that antenatal attendance rates in the ESAR are relatively high at 77% [11 - 14], with some clients being older adolescent girls and young women. This finding is not surprising given that adolescent pregnancy rates in the ESAR are among the highest in the world, ranging from 19% to 29% in Lesotho, Kenya, Malawi, Mozambique, South Africa and Zambia [11 - 14]. Finally, data gathered in different settings need to be extended to planning interventions, including target setting, monitoring and advocacy. 3. YOUNG POPULATIONS THAT REQUIRE TARGETED HIV PREVENTION INTERVENTIONS 3.1. Adolescent Girls and Young Women In 2017, HIV prevalence among young women (15 to 24 years) was double that of young men in the ESAR (3.4% compared to 1.6%), although in some countries the disparity between women and men was even greater [2]. In the ESAR, the gender differentiation of the HIV epidemic appears to start at an early age. For example, in Swaziland, among 15- to 19-year old adolescent girls and adolescent boys, 6,900 and 2,500 were infected, respectively [2]. This discrepancy was higher in Lesotho, with 8,400 adolescent girls between 15 and 19 years of age infected compared to boys of the same age cohort (3,700) [2]. The 2017 data for the ESAR indicates that 98,000 of new HIV infections occurred among adolescent girls aged 15 to 19 years, and 110,000 new HIV infections occurred among young women aged 20 to 24 years [2]. The number of 15- to 19-year-olds living with HIV in the ESAR was as high as 490,000 among adolescent girls and 270,000 among adolescent boys [2]. Despite comprising 10% of the population, young women aged 15 to 24 years accounted for 26% of new HIV infections in the ESAR in 2017 [2]. These data point to the high-level vulnerability of adolescent girls and young women. The inability to negotiate for condom use and vulnerability to multiple and concurrent sexual partnerships, age disparity in sexual relationships, transactional sex, as well as gender-based violence (GBV) are some of the drivers of these trends in the region [15]. Country-level data reveals that age-disparate sexual relationships are common, with many adolescent girls being infected by young men who are at least five years older than they are. Data from Swaziland, Lesotho and Zambia point to a significant association between a young woman’s HIV status and the number and age of her partners [11, 13, 16]. In Swaziland, for instance, a young woman with more than one older partner is three times more likely to be HIV positive than those not having older partner then those not having older partner [16]. Adolescent girls who often engage in such a relationship for economic and other material reasons usually have very limited possibilities to negotiate for safe sex [17]. A recent phylogenetic analysis of the HIV virus in KwaZulu-Natal, South Africa [18] found evidence of the high-risk nature of age-disparate sexual relationships, while another study in the same region did not support the relationship between age-disparate sex and HIV acquisition in adolescent girls and young women [19]. Clearly, more research is needed to understand contextual factors that influence the choice of sexual partners and how these choices are associated with HIV risk. 3.2. Young Key Populations Young Key Populations (YKP) in the ESAR face significant barriers to accessing HIV and SRH services. Key populations, which refer to sex-workers, people who inject drugs, the imprisoned population, and the LGBTI community, are extremely diverse groups. Young people, who are also members of key populations, are a frequently neglected subset of this group. YKP, which often include adolescents, face additional legal, policy and social barriers to accessing HIV and SRH services [5]. While regional and international treaties guarantee a number of rights to SRH services for young people, including those who identify as members of key populations, there are weaknesses in the legal environments of many countries in the ESAR. For young people who belong to one or more YKP, age-related barriers to accessing HIV and SRH services are further compounded by in-country laws and policies that criminalise their sexual activities, identities and behaviours [20, 21]. Designation of sexual activities and identities as illegal impacts access to healthcare, which can increase vulnerability to HIV. YKP are especially vulnerable to risks associated with limited access to quality SRH services through widespread discrimination, stigma and violence, which are often compounded by vulnerabilities (e.g., youth-power imbalances in relationships), and, sometimes, alienation from family and friends [22]. Young female sex workers, for example, are at risk of unwanted teenage pregnancies and sexually transmitted infections [23], while young transgender and lesbian women are sometimes the targets of so-called ‘corrective’ rape [24]. Young prisoners are often exposed to enduring sexual abuse, which goes largely unrecognised and unpunished [25]. Despite exposure and vulnerability to these circumstances, YKP tend to be reluctant to seek support from healthcare providers [20, 26, 27]. YKP are rarely involved in policy development or consulted during law reforms. As a result, inadequate government funding is directed towards research, prevention, treatment and care programmes that are responsive to their needs. Given the punitive legal and socio-cultural contexts in the region, which are intolerant to the diversity of identities and sexual practices [20, 26, 27], more work needs to be done to document experiences of such populations. This would strengthen legal and policy environments that help accelerate access to HIV and SRH services, as well as reduce human rights violations and health risks within these groups. Progressive steps have been made towards achieving this, with the Global Fund now requiring grant applicants consult KP when developing their applications for funding [24]. 3.3. Boys and Young Men HIV prevalence rates remain much lower among adolescent boys and young men compared to their female counterparts, particularly before the age of 20 years [2]. Owing to these low prevalence rates, inadequate attention has been directed towards HIV prevention and treatment programmes for this population [28, 29]. While adolescent boys might not be drivers of HIV infections among girls and young women, data shows that HIV incidence rates among young men steadily increase between 20 and 30 years of age [2, 3, 5]. This is attributed to the internalisation of traditional masculine values and misogynistic gender attitudes espoused in the region, which are closely linked to sexual practices that predisposes young men to the risk of HIV infection (e.g., unprotected sex, multiple and concurrent sexual partnerships, sex while under the influence of alcohol, and gender-power relations linked to sexual violence) [30 - 33]. Previous research indicates that these normative behaviours are developed during identity formation stages in early adolescence [31, 34 - 37]. Therefore, understanding masculine identities associated with transitioning to adulthood that influence sexual risk behaviours need to be a central part of HIV prevention intervention. In most African countries, SRH services are essentially considered women’s domain, thereby, neglecting men. Adolescent boys and young men are less likely to know their HIV status and utilise HIV services [2, 7, 29]. Therefore, engaging in approaches to promote the health of adolescent girls and young women requires efforts that cultivate a sense of gender equality among men at a young age [32, 33]. Engaging boys and young men in HIV prevention interventions requires a generalised understanding of the health-seeking behaviours of young men. Evidence suggests that well-implemented and developmentally appropriate behaviour change communication programmes, which promote gender equality, can potentially influence attitudes and behaviours of young men [34]. However, programming of this nature needs to consider age and cultural differences and similarities across sub-populations of young African men. Accordingly, prevention programming should factor in processes to understand masculinities and HIV risk in different contexts to more clearly inform the development of locally-based gender-sensitive interventions [35]. Gender-sensitive interventions (e.g., Stepping-Stones, livelihood strengthening, peer networks) [36, 37] require intensive and prolonged engagement with men. While there are no swift solutions to changing men’s behaviours, encouraging adolescent boys and young men to participate in HIV prevention activities at an early age is essential for not only promoting healthy masculinities, but also the health of adolescent girls and young women [28]. In addition, there is a need to increase the participation of young men and their uptake of HIV services, including Prevention of Mother to Child Transmission (PMTCT), family index testing, and pre-exposure prophylaxis (PrEP) for discordant couples [38]. Voluntary Medical Male Circumcision (VMMC) is seen as one key entry point for HIV prevention among adolescent boys and young men [39]. Although the number of circumcised males has tripled in the last two years, seven out of ten males have not yet had the chance to be circumcised in the 14 priority countries in the ESAR [33]. The demand for VMMC services is greater among adolescent boys under the age of 19 years in the ESAR [33, 40, 41]. VMMC performed before the age of sexual debut has maximum long-term impact on reducing individual HIV risk, and, consequently (if scaled up), reduces the risk of transmission in the population [42]. Offered as a comprehensive package, adolescent VMMC can potentially increase public health benefits and offers opportunities for addressing gender norms. However, additional research is needed to assess whether current VMMC services address the specific needs of adolescent clients, to test adapted tools, and to assess linkages between VMMC and other adolescent-focused HIV, health and social services. 4. CHALLENGES ASSOCIATED WITH HIV PREVENTION PROGRAMMING AND RESEARCH 4.1. Multifaceted and Cascaded HIV Programming The science of combination approaches to HIV prevention, including VMMC, comprehensive sexuality education and access to SRH services, is considered as an optimal response and is meant to reflect a coordinated implementation of behavioural, structural and biomedical strategies targeting a particular population [43]. While this approach is conceptually sound, success of such strategies are limited by underlying gender-power dynamics, insufficient sexuality education and the absence of quality health services [44]. Even when interventions are introduced, they are often applied asynchronously or combined without synergy [27, 45]. The importance of recognising the heterogeneity of a single population and the need for differentiated HIV prevention approaches [46] has prompted some researchers to consider interventions from an HIV prevention cascade perspective. The prevention cascade guides the design and monitoring of HIV prevention programmes through a multi-pronged approach that includes demand-side interventions, supply-side interventions and adherence interventions [47, 48]. Demand-side interventions are aimed at improving risk perception and awareness and acceptability of prevention approaches [48]. Supply-side interventions are aimed at making prevention products and procedures more accessible and available [48]. Adherence interventions support ongoing adoption of prevention behaviours [48]. The advantage of the cascade approach is that it identifies population-level constraints to adopting proven biomedical, behavioural, and structural strategies for HIV prevention [49], while also serving as a useful tool for planning interventions and monitoring gaps in HIV prevention. So far, the cascade approach has been successfully used in PMTCT and in monitoring HIV treatment for viral load suppression [49]. The challenge for HIV prevention programming is addressing the behavioural and structural factors that influence the uptake of and adherence to biomedical regimens [49]. These include issues such as acceptability, demand, perceived efficacy for self-care, stigma and discrimination, and life challenges (e.g., poverty, violence) that may impede an individual’s ability to adopt and adhere to prevention regimens [48,] (Table 1). Table 1. Categorization of HIV prevention activities according to the HIV prevention cascade [46]. \| Table 1: Categorization of HIV prevention activities according to the HIV prevention cascade [46]. \| \|---------------------------------------------------------------\| \| Demand side interventions \| \| Type of Intervention \| \| • Psycho-social and behavioural \| \| Subcategory (if applicable) \| \| • Young men and women, males who have sex with males, female sex workers, people who use drugs including alcohol \| \| Supply side interventions \| \| Type of Intervention \| \| • Integration of HIV services \| \| • Condom distribution \| \| • Community level STI (sexually transmitted infections) interventional \| \| Subcategory (if applicable) \| \| • Young people, males who have sex with males, female sex workers, people who use drugs including alcohol \| \| Adherence interventions \| \| Type of Intervention \| \| • Counselling \| \| • Socio-economic \| \| • HIV testing and counselling, HIV positive prevention \| \| • Cash transfer interventions \| \| Subcategory (if applicable) \| \| • Males to females transmission, females to males transmission, males who have sex with males \| \| Direct mechanisms of HIV prevention \| \| Type of Intervention \| \| • Voluntary medical male circumcision \| \| • Condom \| \| • PrEP (pre-exposure prophylaxis) \| \| • STI treatment \| \| • HIV treatment \| \| Subcategory (if applicable) \| An illustration of these challenges has been aptly demonstrated with the introduction of antiretroviral medicines (ARVs), both to prevent HIV acquisition (PrEP) and to minimise onward transmission. This new biomedical prevention modality has introduced renewed hope for eradicating HIV [50], with studies showing that daily oral PrEP is safe and efficacious among populations at substantial risk of becoming infected with HIV, including young men and women [51]. However, low adherence levels to PrEP among adolescents in pilot and experimental interventions raise concerns about its feasibility as a public health strategy [50, 51]. Issues associated with medication adherence include inadequate use, lack of instruction comprehension, influence of partner beliefs, unfavourable side-effects, low HIV risk perceptions and living in poor socioeconomic conditions [3, 52]. In addition, issues related to the need for criteria on who should be eligible, length of eligibility or treatment, and the cost effectiveness of scaling-up treatment are important considerations. As indicated, biomedical HIV prevention offers much promise as a component of comprehensive prevention strategy packages. However, this method poses a number of challenges for programme implementers. How can combination prevention programmes be tailored for specific contexts? Young people have very different HIV risk profiles, HIV service access needs, and socio-developmental challenges relative to sexual decision-making compared to adults older than 24 years. Further, these factors vary widely among young people, especially based on age and gender. Therefore, there is no universal, ‘one-size-fits-all’ approach to delivering HIV services for young people. Ongoing complex, multi-component intervention trials and programmes that are being implemented in different settings can provide the necessary guidance on the type and degree of combinations appropriate for different populations in their specific context [53]. An example is the Determined, Resilient, Empowered, AIDS-free, Mentored, and Safe women (DREAMS) programme, which aims to reduce HIV infections among adolescent girls and young women (aged 15 to 24 years) by 40% in ten ESAR countries [54]. Although this modality of prevention programming is promising, implementation often varies conditionally based on location (e.g., high HIV prevalent zones) and strength of community systems. Therefore, interventions need to be coupled with ongoing situational analyses to improve HIV delivery platforms that ensure these interventions reach the intended populations. Evidence from both scientific and operational research needs to be collated in order to shape the policy environment, which will facilitate large-scale implementation with high quality and intensity [48]. 4.2. Issues of Consent Related to Research and Access to HIV and SRH Services Research on HIV prevention among adolescents and young populations is needed to understand the determinants of specific patterns of sexual behaviour, predictors of sexual activity debut, and the health and psychosocial needs that result from these issues [55]. Undertaking such research, however, requires appropriate ethical guidelines to ensure these vulnerable groups are adequately protected while undertaking research that is relevant and appropriate to their needs [27]. Current ethical and legal standards in most countries in the ESAR make it difficult to conduct health research with people under the age of 18 years [56]. People younger than 18 years of age are often legally designated as incapable of consenting to research participation [55], with consent only possible through parents or legal guardians [57]. The current approach results in a lack of adequate data, and, when data becomes available, the indicators of HIV risk and sexual behaviours are likely biased. Recently, some progress on biomedical HIV research with children and adolescents has been made, but there still exists a reluctance to involve adolescent participants in clinical research in many countries because of the complex legal and ethical requirements [57, 58]. These complexities include researchers studying illegal behaviours (e.g., underage or other forms of criminalised sex, intravenous drug use, or sex work), researchers needing to provide access to HIV and SRH health services, which may be illegal in some countries, and minors having privacy expectations regarding their health status as part of ongoing studies. Researchers also need to ensure field staff are adequately trained to conduct research with minors and have the necessary medical and psycho-social mechanisms in place to manage adverse events that may be encountered during research [58]. Given these complexities, there is a need to simultaneously ensure protection of minors from any form of harm when undertaking research that is highly beneficial to them. A related concern is the obstacles faced by adolescents in accessing HIV and SRH services and information [59]. In many ESAR countries, the legislation is often contradictory. Usually, there are minimum ages of consent for sex (typically 15 or 16 years of age), but also minimum age restrictions for accessing SRH services independent of parents (usually above 18 years when a potential client is recognised legally as an adult). In some countries, the minimum age for sex (in teens) is contradicted by statutory definitions of a ‘child’ and associated laws for child protection [60]. Although parents have the legal right to make health decisions on behalf of their children, this can hinder their child’s access to and threatens their confidentiality when seeking SRH services [3]. In Fig. (4), there are low rates of HIV testing among adolescents in some countries, with less than 5% reported in Madagascar and Comoros. One explanation for this is that the legal age of consenting to SRH services in some countries (e.g., HIV testing and counselling and contraceptive access) is unclear or unspecified. Consequently, service providers may apply “age-appropriateness” of consent to HIV testing at their discretion, and there is likely to be confusion about the situations and treatment types for which minors do and do not require parental consent [60]. Therefore, it is imperative that countries clearly set out the minimum age of consent to sexual activity and ensure that this aligns to the age of consent to SRH services, including contraceptives. The criminalisation of consensual sexual activity among minors in some countries in the ESAR also hinders access to SRH services, such as preventative measures (e.g., contraception) [60]. The low rates of HIV testing are also attributed to social stigma, concern over being HIV positive, risk-naïvety and a lack of awareness about testing facilities [61]. Those who are unaware of their HIV positive status are unlikely to seek antiretroviral treatment, and, are predisposed to transmit HIV unintentionally [62]. In addition, inadequate management of learner pregnancies often restricts access to education and health [63]. Only half of the countries in the ESAR have legislation and policies on the management of learner pregnancy and re-entry to school [63]. Excluding learners because of their pregnancy limits their access to education and health, and perpetuates gender inequality [63]. While HIV and SRH information and services need to target those with the highest risk of infection, such interventions should be designed on the premises that young people are capable of understanding information, appreciating risks and making informed decisions about their SRH [59]. Further, age-based criteria for independent access to health services needs to be standardised across settings, with consent also taking into account developmental and contextual factors that relate to the vulnerability of young people, which are not necessarily chronological. Consequently, it is important to accommodate the evolving capacities of young people, especially minors, with procedures in place that allow service providers to assess consent capabilities of minors. This needs to be accompanied by supportive social change mechanisms and engagement of service providers who can offer friendly services. 5. MITIGATING VULNERABILITY AND SUSTAINING THE HIV PREVENTION RESPONSE 5.1. Keeping Social Protection on the Agenda Social protection is a mechanism for addressing the structural barriers experienced by the poor and vulnerable. More specifically, HIV-sensitive social protection addresses the socio-economic determinants of vulnerability, where financial protection programmes support access to affordable quality services, and country policies and legislation to uphold the rights of the most vulnerable people in high HIV prevalence contexts [64]. Many countries in the ESAR provide financial protection (e.g., cash transfers), which has been influential in reducing poverty [65, 66]. Cash transfers can increase household income and the affordability of healthcare and nutrition, which ultimately improve health outcomes [67]. Several studies have shown the benefits of cash transfers and other economic incentives for preventing HIV among adolescent girls and young women [68, 69], which have also been used successfully to encourage safer sexual practices in the ESAR [65, 67]. Cash transfers are more likely to have an effect on reducing HIV if they can increase school attendance or meet survival needs, thereby deterring adolescent girls from engaging in transactional and age-disparate relationships [66]. While cash transfers are proving to be a key component of interventions aimed at HIV prevention, available evidence supports augmenting financial support with social support from parents and teachers, free education and support services rather than cash alone [70]. In a South African-based study from 2009-2012, past-year incidence of sexually risky behaviour was higher among both adolescent girls and adolescent boys who received cash transfers alone, as compared to those that received a combination of cash, free education, and parental monitoring. The likelihood of engaging in unprotected sex was reduced by approximately 40% when adolescents between 12 and 18 years of age were provided a combination of social protection factors, including access to education, parental monitoring and sensitive clinical care. When cash, free education and parental monitoring were combined, condom use at last sex increased from 47.1% to 60.8% among young men, and from 50% to 64.3% among young women. Testing for HIV also increased from 46% to 56% among young males and from 63% to 73% among young females [70]. Although evidence points to the need for a combination approach to providing social protection [71], these approaches require more well-developed evidence that focuses on outcomes from diverse contexts. Social protection systems need to appreciate the unique and nationally specific needs of adolescents and young people in the ESAR [72]. However, funding for social protection remains a significant challenge for many countries in the ESAR, as resources for investing in social protection programmes are scant and depend on donor projects [73]. The challenge of ensuring adequate and sustainable financing for social protection is compounded by economic uncertainties and competing agendas in these countries, resulting in reluctance among donors to enter into long-term funding commitments [73]. Despite these issues, there is a need to move away from short-term project funding towards providing longer-term domestic resources for combined social protection programmes. Such programmes should move beyond cash alone to in-kind components combined with care and building individual capabilities in young people. Social protection programmes for the poor should also do away with categorically targeting the most vulnerable groups and rather focus on the entire community [70, 74, 75]. Simply, social protection programmes have to be linked to basic social services of cash, care, health, nutrition, education and protection. Locally-based implementers should lean on the current evidence to design and implement intervention in their communities. These programmes also require coherence and integration into stronger social welfare policy that extend beyond safety nets [69] by drawing on the technical and financial capacities of governments. The Government of Zambia, which uses its national budget for its social protection programme, is one example of country-level ownership [75, 76]. Further considerations for financing social welfare systems include raising domestic tax revenues and reallocation of public funds for social protection programming. 5.2. Funding HIV Prevention Programmes Despite the Global Fund’s calls for investments towards HIV prevention, funding for the HIV response in the ESAR has been on the decline and driven primarily by donor agendas. The ESAR, which is home to 50% of people living with HIV worldwide, obtains 55% of its HIV-related funding from international donors [54]. The region accounts for 82% of funding received directly from the United States of America under PEPFAR [54]. Other donor-supported HIV programmes for youth in the region include the DFID-Youth Agenda and SIDA-Investing in Future Generations [77]. To maximise impact, HIV treatment and combination prevention efforts must be complementary. With the increasing demand for HIV treatment, funding for HIV prevention is falling behind. Currently, only 20% of global resources for HIV programming are being spent on HIV prevention [77, 78]. Political leaders in the 2016 United Nations Political Declaration on Ending AIDS agreed that member states should be spending at least 25% of their total HIV budget on HIV prevention [79]. Investing more in HIV prevention is critical. UNAIDS modelling has revealed that investing around a quarter of all the resources required for the AIDS response in HIV prevention services would be sufficient to provide a range of HIV prevention programmes, including condom programmes, PrEP, VMMC, programmes to empower adolescent girls and young women, and mobilising key populations and providing them with essential service packages [80]. Data shows that donor contributions declined from US$8.62 billion in 2014 to US$7.53 billion in 2015, a 13% decline [81]. The US, which contributes the majority of funding towards combatting HIV (66%), decreased its financing from $5.6 billion in 2014 to $5 billion in 2015 [54, 82]. Notwithstanding the lack of precise data on funding directed towards HIV prevention among young people, the general reduction in HIV funding is likely to have a negative impact on access to HIV prevention services for young populations. The current decline in funding has occurred when there is still a wide gap in ensuring universal access to key HIV prevention services for young people in the ESAR, including the provision of age-appropriate education and essential sexual and reproductive health and treatment services [34]. This further contributes to the challenge of lowering HIV incidence and mortality rates [34, 82]. Efforts to meet the objective of ending the global HIV epidemic by 2030 requires sustained fiscal commitment. HIV funding needs to be addressed by framing a vision that focuses on mobilising local resources for evidence-based prevention interventions among young people. For HIV prevention interventions to be sustainable in the long-term (e.g. DREAMS), donor commitments need to be paralleled by country-level investments with local ownership. Some countries (e.g., South Africa and Namibia) significantly fund their HIV treatment programmes, [77, 83]. Other countries could also implement domestic financing initiatives, with one option being to institute an HIV tax/levy, similar to the one used in Zimbabwe [83]. Other innovative financing instruments that could be utilised include remittances and diaspora bonds, social and development impact bonds, sovereign wealth funds, and risk and credit guarantees [84]. Additionally, innovations could include public-private sector partnerships, surcharges on international calls and international flights [82]. In this environment, improving the targeting, efficiency, effectiveness and financial sustainability of HIV programmes is essential. Governments should ensure that each dollar invested achieves the highest return on investment and improved health outcomes. This can be done through optimised allocation of resources, public accountability of funds, and the implementation of cascades to monitor HIV programming. 5.3. Civil Society: Service Providers or Advocates for Legal Reform? The single most effective way to reduce the financial burden of AIDS is to revitalise and scale-up HIV prevention initiatives [85]. The history of AIDS has shown the central importance of civil society organisations (CSOs) in shaping global, regional and national HIV responses, enabling accessible and cost-effective provision of services including treatment and PMTCT, as well as education in areas that are largely inaccessible to government. CSOs have also been instrumental in advocating for the rights of young people and LGBTI, and lobbying donors to fund the AIDS response [86]. CSOs are various associations, both formal and non-formal that represent the broad voluntary interests, purposes and ties that characterise a society [87]. Previous research has documented the influence of CSOs advocacy in developing health policies particularly in areas of influencing leadership, networking, credibility and resources [88]. Given the central importance of civil action in the HIV prevention response, the actions of CSOs are challenged on many fronts. In most cases, their work is considered apolitical, thereby, minimising chances of addressing from a policy change perspective [88 - 90]. Although governments tolerate advocacy, the participation of CSOs in policy and decision-making is mostly tokenistic and largely driven by libertarian service provision agendas, which makes long-term advocacy challenging [90]. Effective CSO policy engagement is also limited by government corruption, lack of openness to CSO engagement [89], and under-resourced CSOs with limited advocacy capacity. Further, a sense of fear and mistrust between CSOs and respective governments stifles the establishment of ‘state-society synergy’ [88, 89]. Consequently, a shift from advocacy towards service delivery is seen as a more comfortable option for some CSOs. Given their history in promoting perspectives of vulnerable groups in national HIV and AIDS policies and programmes [90], an important role for CSOs is advocacy for legal reform. However, prohibitive laws (e.g., age of consent for sexual activity, age of consent to medical treatment, criminalisation of consensual sexual activity between adolescents, criminalisation of HIV transmission) make advocacy for legal reform a complex and hostile space to work in. Advancing the rights of marginalised and vulnerable populations in contexts where legislative and normative conditions prevent access to HIV and SRH services, care and support modalities is seen as a necessary component of an evolved HIV prevention response. An example of a regional NGO initiative is the Southern African Litigation Centre [91], which uses public interest litigation, training and advocacy to advance human rights in 11 southern African countries. Good practices of like-minded organisations include creating progressive jurisprudence, which advances human rights, instigates reform of national laws that do not comply with international human rights law, documenting human rights violations by the judiciary and enabling individuals to seek remedies for human rights violations. Clearly, there is a need for resources (fiscal and technical) to support communities to strengthen their engagement in policymaking and reform on removing legal barriers to accessing HIV and SRH services [92, 93]. CONCLUSION The global commitment to ending the AIDS epidemic by 2030 invariably places HIV prevention at the heart of the response. Reducing the new tide of infections in young populations in the ESAR is integral to the prevention response if this ambitious target is to be achieved. However, a number of challenges lie ahead. These challenges include gaps in epidemiological and behavioural profiles of young populations, complexities in HIV research with adolescents and young people, discriminatory (and contradictory) age-related legislature and policies on consent to sex, access to HIV testing and counselling and SRH services. Availability and sharing of information (e.g., epidemic dynamics, programming successes and lessons learned) across sectors, countries and stakeholders, in an effective and timely manner, is a continuous challenge for effective programming. Furthermore, the rigid legislative and normative environments in the countries in the ESAR are major obstacles to accessing services for marginalised populations. While the science of HIV combination prevention offers hope, implementation and scale-up of HIV programmes remain challenges. The resources that are required to drive and sustain the HIV prevention response require effective cross-sector partnerships with a regional vision and country-led processes enabled through strong participation and accountability from all stakeholders. CONSENT FOR PUBLICATION Not applicable. CONFLICT OF INTEREST The authors declare no conflict of interest, financial or otherwise. ACKNOWLEDGEMENTS The study team acknowledges the Swedish International Development Agency (SIDA) for supporting this work. We also thank the team at The Eastern and Southern Africa Regional Inter-Agency Task Team on Children Affected by AIDS (RIATT-ESA) and Renato Pinto (UNICEF, ESARO) and Michael Strauss (HEARD) for their insightful comments on draft versions of the manuscript. REFERENCES [1] UNICEF. Children and AIDS: Statistical update. UNICEF 2017; [cited 2018 May 23]. Available from: https://www.unicef.org/esaro/theregion.html [2] UNICEF. Children and AIDS: statistical update. UNICEF 2017; [cited 2018 May 23]. Available from: https://data.unicef.org/wp-content/uploads/2017/11/HIVAIDS-Statistical-Update-2017.pdf [3] Bekker LG, Johnson L, Wallace M, Hosek S. Building our youth for the future. J Int AIDS Soc 2015; 18(2): 20027. [PMID: 25724512] [4] Centre for Reproductive Rights. Adolescents’ access to reproductive health services and information. 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[http://dx.doi.org/10.1186/s12913-016-1598-9] [PMID: 27484178]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3546, 1 ], [ 3546, 5196, 2 ], [ 5196, 6806, 3 ], [ 6806, 12433, 4 ], [ 12433, 17651, 5 ], [ 17651, 22233, 6 ], [ 22233, 28473, 7 ], [ 28473, 34003, 8 ], [ 34003, 39343, 9 ], [ 39343, 44543, 10 ], [ 44543, 48756, 11 ], [ 48756, 54105, 12 ], [ 54105, 54105, 13 ], [ 54105, 54105, 14 ], [ 54105, 58335, 15 ] ] }
c2dbe90f3668ed85143f803bfd13190cf63d419a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 10, "total-fallback-pages": 0, "total-input-tokens": 31447, "total-output-tokens": 11601, "fieldofstudy": [ "Medicine" ] }	Original Research Paper Productivity loss among people with early multiple sclerosis: A Canadian study Elisabet Rodriguez Llorian, Wei Zhang, Amir Khakban, Scott Patten, Anthony Traboulsee, Jiwon Oh, Shannon Kolind, Alexandre Prat, Roger Tam and Larry D Lynd Abstract Objectives: To analyze work productivity loss and costs, including absenteeism (time missed from work), presenteeism (reduced productivity while working), and unpaid work loss, among a sample of employed people with multiple sclerosis (pwMS) in Canada, as well as its association with clinical, sociodemographic, and work-related factors. Methods: We used cross-sectional data collected as part of the Canadian Prospective Cohort Study to Understand Progression in MS (CanProCo) and information from the Valuation of Lost Productivity questionnaire. Results: Among 512 pwMS who were employed, 97% showed no or mild disability and 55% experienced productivity loss due to MS in the prior 3 months. Total productivity time loss over a 3-month period averaged 60 hours (SD = 107; 23 from presenteeism, 19 from absenteeism, and 18 from unpaid work), leading to a mean cost of lost productivity of CAD$2480 (SD = 4282) per patient, with an hourly paid productivity loss greater than the wage loss. Fatigue retained significant associations with all productivity loss outcomes. Conclusion: Unpaid work loss and productivity losses exceeding those of the employee alone (due to teamwork and associated factors) are key additional contributors of the high economic burden of MS. Workplace accommodations and treatments targeted at fatigue could lessen the economic impact of MS. Keywords: Multiple sclerosis, work productivity loss, unpaid productivity loss, fatigue Date received: 26 October 2021; revised: 18 November 2021; accepted: 2 December 2021 Introduction Multiple sclerosis (MS), a chronic disease of the central nervous system with variable severity and disability duration,1 not only impacts health and well-being but also represents a major economic burden.2,3 Since MS affects people in their most productive years of life (typically, diagnosis occurs between 20 and 40 years of age),4 productivity loss has been found to be the main cost driver for most severe cases of the disease.2,5 Typically, productivity loss due to illness comprises absenteeism (time missed from work) and presenteeism (reduced productivity while working) for people who are employed, as well as unpaid work productivity loss (from activities such as housework, shopping, or childcare) for all people.6 However, previous studies have applied a wide variety of definitions and instruments.7 Notably, common practice is to use respondents’ income to quantify costs of lost time attributable to presenteeism and absenteeism,8–12 and unpaid work losses have been ignored from existing MS productivity loss monetary valuations. While the use of income fails to account for additional costs resulting from team productivity loss and other job and workplace features,13 failing to account for unpaid work loss can further underestimate the burden of MS. In Canada, even though indirect costs have been identified as a major component of MS costs,14–16 last available estimates are based on data that are almost a decade old16 and only considered productivity loss associated with absenteeism by accounting for sick leave and retirement due to MS. The objective of this study was to characterize work productivity loss and costs in a sample of employed Canadians with MS, as... well as its association with a set of clinical, sociodemographic, and work-related factors. Methods Data and design We used baseline, cross-sectional data collected between January 2019 and April 2021 as part of the Canadian Prospective Cohort Study to Understand Progression in MS (CanProCo). CanProCo is a 5-year prospective cohort study conducted in five sites across four Canadian provinces (Alberta, British Columbia, Quebec, and Ontario) with the primary aim to better understand MS disease progression. CanProCo obtained local research ethics board approval before study initiation, and all participants provided written informed consent. Details on CanProCo inclusion criteria, ethics, and informed consent are provided as supporting information (S1). Productivity loss Productivity loss components were measured using the Valuation of Lost Productivity questionnaire (VOLP), previously validated and applied in other diseases.\textsuperscript{13,17} The key outcomes of interest for this study, all measured for the last 3 months, were (1) paid work productivity loss (hours) due to absenteeism; (2) paid work productivity loss (hours) due to presenteeism; (3) unpaid work productivity loss (hours); and (4) total cost of lost productivity (the sum of the cost of paid and unpaid work productivity losses). To calculate the total cost of lost productivity (i.e. attaching a monetary value to time loss), different aspects of each individual’s work environment including team size, contribution to team productivity, and availability of perfect substitutes were used to obtain wage multipliers. Costs of paid work lost productivity were calculated as “time lost × hourly wage × multiplier.” As for costs of unpaid work loss, we used hourly earnings of CAD$15.60 reported by Statistics Canada for home childcare and home support workers.\textsuperscript{18} Additional details on measuring productivity loss and costs are provided in S1. Variables associated with productivity loss We evaluated the association between productivity loss and costs with sociodemographic, clinical, quality of life, and work-related characteristics based on previous research.\textsuperscript{19–21} Sociodemographic variables included sex and age. In terms of clinical predictors, the severity of disease was measured using the Expanded Disability Status Scale (EDSS) which ranges from 0 to 10 in 0.5 increments, which indicate a higher level of disability. The Modified Fatigue Impact Scale (MFIS)\textsuperscript{22} that contains physical, cognitive, and psychosocial items was used to measure fatigue; the Patient Health Questionnaire (PHQ)-9\textsuperscript{23,24} was used for depression and the seven-item Generalized Anxiety Disorder (GAD-7) questionnaire\textsuperscript{25} for anxiety, with higher scores signaling greater levels of distress. Other clinical variables included in the analysis were time since diagnosis in years; whether the patient was using a disease-modifying therapy (DMT); number of comorbidities; whether the patient had a relapse in the past 3 months; and MS phenotype. We also included health-related quality of life utility using health states from the EQ-5D-5L instrument\textsuperscript{26} and associated value set for Canada,\textsuperscript{27} as well as work habits (usually sitting, standing, or walking during the day; lifting either light or heavy loads) and type of employment (full-time, part-time, and self-employed). Statistical analysis The analysis centered on those participants who were employed at the time information was collected. Given the zero-inflated and skewed nature of the data, we evaluated the association of all productivity loss outcomes with the selected group of variables using two-part models. The model was first composed of a logistic regression for the probability of observing a positive-versus-zero productivity loss outcome, followed by a generalized linear model (GLM) with log link and gamma distribution, fitted for those participants showing non-zero (i.e. some) productivity loss. To improve the interpretation of the coefficients from the two-part models, we generated a marginal (or incremental) effect of each factor on productivity loss.\textsuperscript{28} To determine which factors to include in the multivariate analysis, univariate two-step models were first created. Only those variables with a $p$ value $\leq 0.1$ in the resulting univariate analysis joint test of significance\textsuperscript{28} were included in the final multivariate two-part model. Furthermore, given the high statistical correlation (see S2) and conceptual overlap between considered distress variables (fatigue, depression, and anxiety),\textsuperscript{29} the multivariate model only included the MFIS indicator of physical, cognitive, and psychosocial fatigue. Results Study cohort and patient characteristics Figure 1 presents the study sample selection process. From a total of 693 pwMS enrolled in the CanProCo study who had completed the required questionnaires... by April 2021, 512 (74%) were working for pay, 148 (21%) were not doing any paid work, and 33 (5%) did not specify their employment status. Of those employed, 72% were working full-time, 16% part-time, and 12% were self-employed. As shown in Table 1, the sample of 512 employed pwMS was mostly female (71%) with RRMS (83%) and mild disability (EDSS 1–3.5: 72%). The mean age of participants was 39 (SD = 9.5) years, and the mean duration of MS was 3.4 (SD = 2.7) years. In addition, 56% of participants were receiving a DMT, 7% had a recent relapse, and 37% declared having no comorbidities, while 20% had more than three comorbidities. Most jobs required participants to be mostly sitting (53%), while 31% had jobs that required them to stand and/or walk, and 16% had occupations that required some type of lifting. Among the 512 eligible employed pwMS, 392 had no missing information for all three productivity loss components. A comparison between employed pwMS depending on whether they had at least one missing productivity loss component shows no substantial differences (see S3). Figure 1. Study cohort. Productivity loss Table 2 shows a characterization of productivity loss and work-related variables. The average working time among participants was 5 days, 37 hours/week. Wage multipliers for absenteeism and presenteeism were 1.43 and 1.38, respectively, indicating an hourly work productivity loss greater than the wage loss. Fifty-five percent of participants experienced at least some productivity loss in the past 3 months. In addition, 44% of participants missed work for health reasons (absenteeism) and 24% reported being able to complete the same work in less time had they not had any health problems (presenteeism). Overall, absenteeism and presenteeism accounted for 7% and 5% of participants’ regular work time, respectively. Average total productivity lost over a 3-month period was 60 hours (SD = 107; 23 from presenteeism, 19 from absenteeism, and 18 from unpaid work) among the 392 pwMS with non-missing values for all three productivity loss components, leading to a mean value of lost productivity of CAD$2480 (SD = 4282) per patient. By only using wages, the mean monetary cost was lower by CAD$632. Table 1. Characteristics of employed pwMS. \| Variable \| No \| Statistic \| \|-----------------------------------------------\|------\|--------------\| \| Sociodemographic \| \| \| \| Sex, % female \| 512 \| 364 (71%) \| \| Age (years), Mean (SD) \| 512 \| 38.74 (9.51) \| \| Clinical \| \| \| \| No disability EDSS 0 \| 510 \| 128 (25%) \| \| Mild disability EDSS 1–3.5 \| 510 \| 367 (72%) \| \| Moderate disability EDSS 4–6 \| 510 \| 15 (3%) \| \| Time since diagnosis (years), mean (SD) \| 511 \| 3.35 (2.72) \| \| MS type, % by phenotype \| \| \| \| RRMS \| 512 \| 426 (83%) \| \| PPMS \| 512 \| 27 (5%) \| \| RIS \| 512 \| 29 (6%) \| \| CIS \| 512 \| 30 (6%) \| \| Current DMT users, % \| 512 \| 284 (56%) \| \| Relapsed in the past 3 months, % \| 475 \| 35 (7%) \| \| Comorbidities, % \| \| \| \| 0 \| 512 \| 191 (37%) \| \| 1 \| 512 \| 139 (27%) \| \| 2 \| 512 \| 84 (16%) \| \| +3 \| 512 \| 98 (20%) \| \| Fatigue, median (max–min)$^b$ \| 492 \| 24 (0–81) \| \| Depression, median (max–min)$^c$ \| 503 \| 5 (0–26) \| \| Anxiety, median (max–min)$^d$ \| 500 \| 4 (0–21) \| \| Quality of life \| \| \| \| EQ-5D utility score, mean (SD) \| 508 \| 0.86 (0.10) \| \| Work-related characteristics \| \| \| \| Usually sits \| 497 \| 262 (53%) \| \| Stand/walk \| 497 \| 152 (31%) \| \| Light/heavy lifting \| 497 \| 83 (16%) \| \| Full-time \| 512 \| 366 (72%) \| \| Part-time \| 512 \| 84 (16%) \| \| Self-employed \| 512 \| 62 (12%) \| CIS: clinically isolated syndrome; DMT: disease-modifying therapy; EDSS: Expanded Disability Status Scale; EQ-5D: EuroQol-5D; MS: multiple sclerosis; RRMS: relapsing-remitting MS; PPMS: primary-progressive MS; RIS: radiologically isolated syndrome; SD: standard deviation. $^{b}$Respondents with non-missing information included in the analysis of each variable (out of a total of 512 employed pwMS). $^{c}$Measured using Modified Fatigue Impact Scale, score ranging from 0 to 84. $^{d}$Measured using Patient Health Questionnaire-9, index ranging from 0 to 27. $^{e}$Measured using seven-item Generalized Anxiety Disorder questionnaire with a possible maximum score of 21 points, cut points of 5, 10, and 15 might be interpreted as representing mild, moderate, and severe levels of anxiety, respectively. Differences in productivity time lost across key variables (namely, disease type, severity, and sex) are shown in S4. There are sharp differences between severity levels; pwMS with an EDSS > 0 showed higher productivity loss for all components, on average. Interestingly, while those with no disability (EDSS = 0) showed higher hours lost attributable to absenteeism than to presenteeism, the opposite happened for those with some level of disability. Among all MS phenotypes, PPMS showed the highest total productivity loss. As for sex, females showed higher losses across all three categories. Factors associated with productivity loss Table 3 shows which variables were found to be associated with each productivity loss outcome and thus were incorporated into the multivariate two-part Neither sex nor work characteristics were found to be associated with any productivity loss outcome in univariate analysis. After multivariate adjustment, each additional point in the EDSS scale (signaling higher severity) averaged an additional 5 hours (95% confidence interval (CI): 0.21, 9.23) of presenteeism and 6 hours (95% CI: 0.88, 10.93) of unpaid work. Absenteeism, on the other hand, was found not to be associated with severity. Notably, fatigue was consistently significantly associated with all productivity loss outcomes. Specifically, each one unit increase in the MFIS index (i.e. increasing fatigue) resulted in an average increase in lost productivity of 0.62 (95% CI: 0.18, 1.05), 0.96 (95% CI: 0.64, 1.29), and 0.64 (95% CI: 0.27, 1.01) hours lost due to absenteeism, presenteeism, and unpaid work, respectively. Likewise, one additional point in the MFIS index represented a cost of CAD$95 (95% CI: 61, 128). Those patients who had a relapse within the past 3 months lost 39 (95% CI: −0.07, 78.74) more hours due to absenteeism, 17 (95% CI: −24.47, −9.26) less hours due to presenteeism and showed costs of CAD$2851 (95% CI: −701, 6402) higher. Comorbidities, on the other hand, were not significantly associated with work productivity loss hours, but those pwMS having over three comorbidities showed a cost of lost productivity CAD$176 (95% CI: −849, 1201) higher than those with no comorbidities. Similarly, use of DMTs and quality of life utility, after adjusting for other variables, was not found to have a significant association with productivity loss. Finally, employment status was associated with absenteeism and presenteeism, but not with unpaid work. Participants with a full-time job lost 36 (95% CI: 18.82, 52.79) and 18 (95% CI: 8.37, 27.89) more hours due to absenteeism and presenteeism, respectively, relative to those that were self-employed. Similarly, full-time job holders showed a cost of lost productivity CAD$2190 (95% CI: 1333, 3048) higher than self-employed workers. Table 3. Factors associated with productivity loss—unadjusted association (marginal effect). \| Variable \| Absenteeism \| Presenteeism \| Unpaid work productivity loss \| Total costs of lost productivity \| \|---------------------------------\|-------------\|--------------\|--------------------------------\|----------------------------------\| \| Sociodemographic \| \| \| \| \| \| Female \| -4.37 (-19.76, 11.03) \| 3.71 (-7.14, 14.57) \| 7.40 (-4.87, 19.66) \| 557.59 (-313.13, 1428.30) \| \| Age \| -0.16 (-0.85, 0.54) \| 0.54 (-0.02, 1.11) \| 0.43 (-0.22, 1.08) \| 18.88 (-27.93, 65.68) \| \| Clinical \| \| \| \| \| \| Severity \| 4.09 (-2.21, 10.38) \| 9.79 (5.16, 14.43) \| 11.51 (5.31, 17.70) \| 721.88 (337.69, 1106.06) \| \| Time since diagnosis \| -5.37 (-8.00, -2.75) \| 0.42 (-1.39, 2.23) \| 2.44 (-0.13, 5.01) \| -102.79 (-253.53, 47.94) \| \| MS phenotype \| \| \| \| \| \| RRMS \| 11.35 (-5.33, 28.02) \| -10.21 (-29.89, 9.47) \| 1.01 (-21.50, 23.51) \| 159.57 (-1259.71, 1578.85) \| \| PPMS \| 5.85 (-37.51, 49.21) \| 14.11 (-25.55, 53.77) \| 18.91 (-29.34, 67.15) \| 1518.73 (-1556.24, 4593.70) \| \| RIS \| -17.14 (-28.82, -5.46) \| -14.52 (-29.14, 0.10) \| -16.36 (-27.56, -5.15) \| -1412.44 (-2984.14, 159.27) \| \| CIS \| Ref. \| Ref. \| Ref. \| Ref. \| \| Current DMT use \| 4.04 (-8.80, 16.89) \| 6.99 (-2.81, 16.80) \| 12.36 (0.07, 24.66) \| 580.03 (-251.35, 1411.40) \| \| Relapse \| 49.64 (-1.38, 100.66) \| -18.18 (-25.73, -10.62) \| 7.82 (-13.98, 29.62) \| 2467.81 (-1190.31, 6125.93) \| \| Number of comorbidities \| \| \| \| \| \| 0 \| Ref. \| Ref. \| Ref. \| Ref. \| \| 1 \| -5.99 (-21.90, 9.92) \| -0.02 (-13.21, 13.16) \| 0.81 (-21.15, 22.77) \| -204.10 (-1386.95, 978.75) \| \| 2 \| -11.36 (-23.78, 1.05) \| 5.04 (-10.95, 21.03) \| 5.94 (-14.30, 26.18) \| -26.24 (-1150.82, 1098.34) \| \| 3+ \| 12.65 (-7.98, 33.29) \| 15.24 (-1.52, 32.01) \| 20.77 (-0.66, 42.19) \| 1645.69 (334.20, 2957.18) \| \| Quality of life \| \| \| \| \| \| EQ-5D utility score \| -3.20 (-8.49, 2.09) \| -11.64 (-16.99, -6.29) \| -11.52 (-18.56, -4.48) \| -1040.78 (-1457.77, -623.79) \| \| Work characteristics \| \| \| \| \| \| Work habits \| \| \| \| \| \| Usually sits \| 6.18 (-10.60, 22.97) \| 2.07 (-10.57, 14.70) \| 15.73 (-4.90, 36.36) \| 311.06 (-803.88, 1425.99) \| \| Stand/walk \| 5.66 (-14.33, 25.64) \| -3.75 (-17.75, 10.24) \| 10.50 (-15.67, 36.66) \| -417.54 (-1555.99, 720.91) \| \| Light/heavy loads \| Ref. \| Ref. \| Ref. \| Ref. \| \| Employment status \| \| \| \| \| \| Full-time \| 35.70 (20.76, 50.64) \| 21.63 (9.83, 33.43) \| 5.62 (-13.02, 24.26) \| 2301.83 (1454.32, 3149.34) \| \| Part-time \| 59.45 (0.91, 117.99) \| 13.03 (-26.59, 52.66) \| 18.96 (-14.30, 52.22) \| 1888.27 (-622.48, 4399.01) \| \| Self-employed \| Ref. \| Ref. \| Ref. \| Ref. \| Bold values indicate a joint $p$ value $\leq 0.1$. CIS: clinically isolated syndrome; DMT: disease-modifying therapy; EDSS: Expanded Disability Status Scale; EQ-5D: EuroQol-5D; GAD-7: seven-item Generalized Anxiety Disorder; MFIS: Modified Fatigue Impact Scale; MS: multiple sclerosis; PHQ: Patient Health Questionnaire; PPMS: primary-progressive MS; RIS: radiologically isolated syndrome; RRMS: relapsing-remitting MS. Table 4. Factors associated with productivity loss—adjusted association (marginal effect). \| Variable \| Absenteeism \| Presenteeism \| Unpaid work productivity loss \| Total costs of lost productivity \| \|---------------------------------\|-----------------\|---------------\|-------------------------------\|----------------------------------\| \| Age \| 0.21 (-0.53, 0.94) \| — \| 0.20 (-0.32, 0.72) \| 1.08 (-46.43, 48.59) \| \| Severity \| — \| 4.72 (0.21, 9.23) \| — \| 185.12 (-201.54, 571.78) \| \| Time since diagnosis \| -5.32 (-7.93, -2.72) \| — \| 1.55 (-0.80, 3.90) \| — \| \| MS phenotype \| \| \| \| \| \| RRMS \| 18.00 (2.02, 33.97) \| — \| — \| — \| \| PPMS \| 2.68 (-38.87, 44.23) \| — \| — \| — \| \| RIS \| -14.75 (-28.09, -1.42) \| — \| — \| — \| \| CIS \| Ref. \| \| \| \| \| Current DMT use \| — \| — \| 6.37 (-4.56, 17.31) \| — \| \| Relapse \| 39.33 (-0.07, 78.74) \| -16.87 (-24.47, -9.26) \| — \| 2850.56 (-701.05, 6402.18) \| \| Number of comorbidities \| \| \| \| \| \| 0 \| Ref. \| Ref. \| Ref. \| Ref. \| \| 1 \| -12.70 (-25.31, -0.09) \| -5.14 (-15.43, 5.14) \| -3.69 (-16.94, 9.56) \| -670.18 (-1616.95, 276.59) \| \| 2 \| -12.45 (-25.23, 0.33) \| 3.94 (-9.59, 17.47) \| 3.78 (-14.11, 21.68) \| -285.43 (-1330.38, 759.53) \| \| 3+ \| 2.42 (-17.56, 22.41) \| 0.29 (-12.21, 12.79) \| 7.07 (-10.18, 24.32) \| 175.65 (-849.40, 1200.71) \| \| Fatigue index MFIS \| 0.62 (0.18, 1.05) \| 0.96 (0.64, 1.29) \| 0.64 (0.27, 1.01) \| 94.59 (61.32, 127.87) \| \| EQ-5D utility score \| 1.86 (-4.67, 8.38) \| 3.39 (-3.33, 10.12) \| -2.11 (-8.17, 3.95) \| 285.52 (-297.00, 868.03) \| \| Employment status \| \| \| \| \| \| Full-time \| 35.80 (18.82, 52.79) \| 18.13 (8.37, 27.89) \| — \| 2190.24 (1332.93, 3047.54) \| \| Part-time \| 60.94 (-14.60, 136.49) \| 1.95 (-23.75, 27.64) \| — \| 1895.71 (-1485.38, 5276.80) \| \| Self-employed \| Ref. \| Ref. \| Ref. \| Ref. \| Bold values indicate a joint p value <=0.1. CIS: clinically isolated syndrome; DMT: disease-modifying therapy; EDSS: Expanded Disability Status Scale; EQ-5D: EuroQol-5D; MFIS: Modified Impact Scale; MS: multiple sclerosis; PPMS: primary-progressive MS; RIS: radiologically isolated syndrome; RRMS: relapsing-remitting MS. Discussion This study characterizes productivity loss in a Canadian sample of employed pwMS including paid work productivity loss attributable to absenteeism and presenteeism and unpaid work productivity loss, and conducts a comprehensive monetary valuation of lost time. Overall, among a total work productivity loss of 60 hours in a 3-month period, presenteeism accounted for most (38%), followed by absenteeism (32%) and unpaid work loss (30%), of total loss. Assuming an 8-hour workday, our findings translate to approximately 2.5 days lost in a month. PwMS in our cohort lost approximately 7% of work time due to absenteeism and 5% due to presenteeism. Finally, lost hours represented an average total monetary cost of CAD$2480 over 3 months per MS patient when incorporating wage multipliers accounting for frequency of working with a team, team size, and influence on team function; and CAD$1848 when only using wages. Two prior non-Canadian studies have measured productivity time loss using the work productivity and activity impairment questionnaire (WPAI). In the US study by Glanz et al.30 and the Australian study by Chen et al.10 the authors found that approximately 3.6% and 3.4% of productivity time loss was due to absenteeism and 11.9% and 10.8% due to presenteeism, respectively. Discrepancies with our findings are most likely explained by differences in the instrument used and variations in study subjects. A previous study found that WPAI provided the highest estimate of presenteeism (14.2 hours per 2 weeks) among four different instruments; while the health and labor questionnaire, using a similar direct hour estimation method to VOLP, provided the lowest presenteeism estimate (1.6 hours per 2 weeks).31 In addition, while our cohort is relatively young and at a very early stage of disease progression, those of Glanz et al.30 and Chen et al.10 included older patients who were approximately 12 years postdiagnosis. There are no available comparisons for unpaid work productivity loss, which was not included by Chen et al.10 and only provided as a mean percent activity impairment by Glanz et al.30 As for monetary valuations of lost time, existing costs attributable to absenteeism and presenteeism vary greatly across regions and MS severity levels as shown in a past systematic review and meta-analysis.7 Overall, current estimates of the value of lost productivity face two crucial gaps. First, they failed to account for unpaid work productivity loss, which based on our results is not a negligible component of productivity time loss. Other study findings that MS is more prevalent among women combined with greater unpaid work productivity losses for females11 could further affect total productivity loss estimations. Second, existing research in MS assigns a monetary value to time loss using reported personal income, which severely underestimates productivity loss as shown by our wage multipliers. The difference between the two cost approaches as shown for this study’s cohort at an early stage of disease progression is approximately CAD$632 per patient in a 3-month period, or an annual mean cost of CAD$2528. This illustrates how underestimated the overall burden of MS is when not accounting comprehensively for productivity losses beyond those of the MS employee alone. We also explored statistically significant associations between productivity loss and a group of sociodemographic, clinical, and work-related factors. Contrary to previous findings in Germany,11 we found no association between gender and productivity loss, although females showed higher losses in each component, on average. Interestingly, work habits were also found not to be significantly associated with productivity loss outcomes. It could be that pwMS self-select into jobs that match their disability level, hence not significantly affecting their paid work productivity. The use of DMTs was also not significant, which is probably a reflection that DMTs tend to be more often used in people with more disease activity. As for relapses, consistent with published research,12 we found costs and absenteeism hours to be higher for those participants who experienced at least one relapse within the last 3 months. However, an opposite effect was found on presenteeism. That those with relapses showed lower productivity losses while working is likely driven by the fact that participants exhibiting relapses in our cohort are also younger and with a shorter disease duration. The severity of MS as measured using EDSS was found to be associated with presenteeism, and unpaid work productivity loss, but not absenteeism. Several publications have studied the effect of EDSS on employment status, but evidence on its relationship with specific productivity loss outcomes is limited.20 Given the overall low severity of our cohort, participants might not need to take additional days from work, only experiencing reduced productivity while working. The one factor consistently associated with all productivity loss outcomes was fatigue which is highly prevalent among pwMS,32 and has been consistently observed to be strongly associated with both leaving employment and hours lost.20 Notably, we also found that associations of productivity loss with fatigue were greater for presenteeism and unpaid work, confirming previous findings in the United States\textsuperscript{30} that fatigue could have a greater impact on regular daily activities than on paid work. There are several limitations of this study. First, our productivity loss estimations and associations with key factors were developed using participants exclusively from the CanProCo study, with overrepresentation of patients at an early stage of MS (and even those who are asymptomatic), resulting in a cohort with low disease severity. Additional validation in other healthcare settings is therefore warranted to ensure generalizability. It is important to note that, given the low severity observed in our cohort, productivity losses in the general MS population are likely higher than our conservative estimates. Second, since we only used cross-sectional information, we were not able to examine changes in clinical factors and productivity loss over time. It is expected that, as the MS progresses, participants reduce their routine hours, and/or change jobs, further underestimating productivity loss estimates. Third, productivity loss is sensitive to the instrument used.\textsuperscript{31,33} Most previous studies in MS used the WPAI, which provides a higher presenteeism estimate as mentioned above and makes a comparison of our results with prior studies difficult. Future research on a standardized instrument for productivity loss will be informative. Future studies could also use a longitudinal design to explore patterns of employment and productivity changes and to identify differences across MS phenotypes and a wider range of severity levels. Likewise, extending the study beyond employed individuals, the focus of this paper, will allow for the incorporation of costs of early retirement, work disability, and unemployment due to MS. Overall, this study shows the importance of a comprehensive measure of productivity loss in determining the societal economic impact of MS, and the need to account for additional losses surpassing the wage loss of the person with MS. Effective interventions including workplace accommodations, psychosocial and pharmacological treatments, aimed at addressing the factors found to be associated with productivity loss, could enhance patient-oriented care, and potentially reduce the economic burden of MS. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The Canadian Prospective Cohort Study to Understand Progression in MS (CanProCo) is funded by the MS Society of Canada, Brain Canada, Roche, Biogen-Idec, and the Government of Alberta. Funders do not have any role in the design of the study and collection, analysis, and interpretation of data and in writing this manuscript. ORCID iD Elisabet Rodriguez Llorian https://orcid.org/0000-0002-3207-8916 Supplemental material Supplemental material for this article is available online. References 1. MS Society of Canada. About MS, https://mssociety.ca/about-ms/what-is-ms 2. Paz-Zulueta M, Parás-Bravo P, Cantarero-Prieto D, et al. 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3017bea34a2b53f0b17b42313ebe461a2620d628	{ "olmocr-version": "0.1.59", "pdf-total-pages": 17, "total-fallback-pages": 0, "total-input-tokens": 78493, "total-output-tokens": 23817, "fieldofstudy": [ "Computer Science", "Mathematics" ] }	Weak Concurrent Kleene Algebra with Application to Algebraic Verification Annabelle McIver1 Tahiry Rabeaja1 Georg Struth3 1 Department of Computing Macquarie University, Sydney, Australia Email: \{annabelle.mciver, tahiry.rabeaja\}@mq.edu.au 2 Department of Computer Science University of Sheffield, United Kingdom, Email: [email protected] Abstract We propose a generalisation of concurrent Kleene algebra [2] that can take account of probabilistic effects in the presence of concurrency. The algebra is proved sound with respect to a model of automata modulo a variant of rooted $\eta$-simulation equivalence. Applicability is demonstrated by algebraic treatments of two examples: algebraic may testing and Rabin’s solution to the choice coordination problem. 1 Introduction Kleene algebra generalises the language of regular expressions and, as a basis for reasoning about programs and computing systems, it has been used in applications ranging from compiler optimisation, program refinement, combinatorial optimisation and algorithm design [2, 6, 7, 8, 10]. A number of variants of the original axiom system and language of Kleene algebra have extended its range of applicability to include probability [12] with the most recent being the introduction of a concurrency operator [2]. Main benefits of the algebraic approach are that it captures some essential aspects of computing systems in a simple and concise way and that the calculational style of reasoning it supports is very suitable for automated theorem proving. In this paper we continue this line of work and propose weak concurrent Kleene algebra, which extends the abstract probabilistic Kleene algebra [12] with the concurrency operator of concurrent Kleene algebra [5] and thus supports reasoning about concurrency in a context of probabilistic effects. This extension calls for a careful evaluation of the axiom system so that it accurately accounts for the interactions of probabilistic choice, nondeterministic choice and the treatment of concurrency. For example probabilistic Kleene algebra accounts for the presence of probability in the failure of the original distributive law $x(y + z) = xy + xz$ which is also absent in most process algebras. That is because when the terms $x, y, z$ are interpreted as probabilistic programs, with $xy$ meaning “first execute $x$ and then $y$” and + interpreted as a nondeterministic choice, the expression on the left hand side exhibits a greater range of nondeterminism than the right in the case that $x$ includes probabilistic behaviours. For example if $x$ is interpreted as a program which flips a bit with probability 1/2 then the following nondeterministic choice in $y + z$ can always be resolved so that $y$ is executed if and only if the bit was indeed flipped. This is not a behaviour amongst those described by $xy + xz$, where the nondeterminism is resolved before the bit is flipped and therefore its resolution is unavoidably independent of the flipping. Instead, in contexts such as these, distributivity be replaced by a weaker law: Sub-distributivity: $xy + xz \leq x(y + z)$. (1) Elsewhere [9] we show that this weakening of the original axioms of Kleene algebra results in a complete system relative to a model of nondeterministic automata modulo simulation equivalence. The behaviour of the concurrency operator of concurrent Kleene algebra [5] is captured in particular by the Interchange law: \[ (x\\|y)(u\\|v) \leq (xu)\|(yv) \] which expresses that there is a lesser range of nondeterministic executions on the left where, for example, the execution of $u$ is constrained to follow a complete execution of $x$ run concurrently with $y$ but on the right it is not. Our first contribution is the construction of a concrete model of abstract probabilistic automata (where the probability is at the action level) over which to interpret terms composed of traditional Kleene algebra together with concurrent composition. In this interpretation, each term represents an automaton. For example in Equation (1), $x, y$ and $z$ are automata and so is $xy + xz$. We show that the axiom system of concurrent Kleene algebra weakened to allow for the presence of probability is sound with respect to those probabilistic automata. Our use of probabilistic automata is similar to models where the resolution of probability and nondeterminism can be interleaved; concurrent composition of automata models CSP synchronisation [4] in that context. Finally we use a notion of rooted $\eta$-simulation to interpret the inequality $\leq$ used in algebraic inequations. Our second contribution is to explore some applications of our axiomatisation of weak concurrent Kleene algebra, to explain our definition of rooted $\eta$-simulation in terms of may testing [14], and to demonstrate the proof system on Rabin’s distributed consensus protocol [15]. One of the outcomes of this study is to expose the tensions between the various aspects of system execution. Some of the original concurrent Kleene algebra axioms required for the concurrency operator now fail to be in place in the presence of probabilistic effects and synchronisation supported by the interchange law. For example, the term 1 from Kleene algebra (interpreted as "do nothing") can no longer be a neutral element for the concurrency operator \|\| — we only have the specific equality 1\|\|1 = 1 and not the more general 1\|\|x = x. In fact we chose to preserve the full interchange law in our choice of axioms because it captures so many notions of concurrency already including exact parallel and synchronisation, suggesting that it is a property about general concurrent interactions. A feature of our approach is to concentrate on broad algebraic structures in order to understand how various behaviours interact rather than to study precise quantitative behaviours. Thus we do not include an explicit probabilistic choice operator in the signature of the algebra — probability occurs explicitly only in the concrete model as a special kind of asynchronous probabilistic action combined with internal events (events that the environment cannot access). This allows the specification of complex concurrent behaviour to be simplified using applications of weak distributivity embodied by Equation (1) and/or the interchange law as illustrated by our case study. Finally we note that the axiomatisation we give is entirely in terms of first-order expressions and therefore is supported by first-order reasoning. Thus all of our algebraic proofs has been implemented within the Isabelle/HOL theorem proving environment. These proofs can be found in a repository of formalised algebraic theorems. In Section 2 we explore the axiomatisation of the new algebra. It is essentially a mixture of probabilistic and concurrent Kleene algebras. Sections 3 and 4 are devoted to showing the consistency of our approach. A concrete model based on automata and q-simulation is constructed. In Section 5 we compare our approach with probabilistic automata (automata that exhibit explicit probability) and probabilistic simulation. We conclude that, up to some constraint, the concrete model is a very special case of that more general model. In sections 6 and 7, we present some applications, in particular an algebraic version of may testing is studied and variations of the specification of Rabin's protocol are explored. In this paper x, y, etc represent algebraic expressions or variables. Terms are denoted s, t, etc. Letters a, b, etc stand for actions and τ represents an internal action. An automaton associated with a term or an expression is usually denoted by the same letter. Other notation is introduced as we need it. In this extended abstract we can only explain the main properties of weak concurrent Kleene algebra and sketch the construction of the automaton model. Detailed constructions and proofs of all statements in this paper can be found in an appendix. 2 Axiomatisation A Kleene algebra is a structure that encodes algebraically the sequential behaviour of a system. It is generally presented in the form of an idempotent semiring structure (K, +, , 0, 1) where x · y (sequential composition) is sometimes written using juxtaposition xy in expressions. The term 0 is the neutral element of + and 1 is the neutral element of ·. The semiring is then endowed with a unary Kleene star * representing finite iteration to form a Kleene algebra. This operator is restricted by the following axioms: Left unfold: \[ 1 + xx^* = x^* \] (2) Left induction: \[ xy \leq y \Rightarrow x^y \leq y \] (3) where $ x \leq y $ if and only if $ x + y = y $. In the sequel our interpretations will be over a version of probabilistic automata. In particular we will interpret ≤ as q-simulations. Often, the dual of (2-3) i.e. $ 1 + x^x = x^* $ and $ xy \leq y \Rightarrow yx^* \leq y $ are also required. However, (2) and (3) are sufficient here and the dual laws follow from continuity of sequential composition for finite automata. In a Kleene algebra, the semiring structure supports two distributivity laws: Left distributivity: \[ xy + xz = x(y+z) \] (4) Right distributivity: \[ (x+y)z = xz + yz \] (5) Equation (4) however is not valid in the presence of probability. For example, compare the behaviour of probabilistic choice in the diagrams below. Here, $ \text{flip}_p $ denotes the process that flips a $ p $-biased coin, which we can represent by a probabilistic automaton (details are given in Section 5). In the right diagram, the choice between $ a $ and $ b $ can be based on the outcome of the coin flip but such resolution is not possible in the left-hand diagram. We express the greater range of possible outcomes by the general inequation (1), specifically here it becomes \[ (\text{flip}_p)y + (\text{flip}_p)z \leq (\text{flip}_p)(y + z) \] (6) As mentioned above, the zero of a Kleene algebra satisfies: Left annihilation: \[ 0x = 0 \] (7) Right annihilation: \[ x0 = 0 \] (8) In our interpretation that includes concurrency, we assume that $ 0 $ captures deadlock. However, axiom (8) is no longer appropriate because we should be able to differentiate between the process doing an action and deadlocking from a process that is just deadlocked. Definition 1. A weak probabilistic Kleene algebra is a structure $ (K, +, \cdot, 0, 1) $ that satisfies the axioms of Kleene algebra except there is no left distributivity (it is replaced by (1)) and Equation (3) does not hold generally. A concurrency operator was added to Kleene algebra by Hoare et al [5]. Our concurrency operator \|\| satisfies the following standard axioms: \[ \begin{align} \text{Associativity:} & & x \|\| (y \|\| z) &= (x \|\| y) \|\| z, \\ \text{Commutativity:} & & x \|\| y &= y \|\| x, \\ \text{One-idenpotence:} & & 1 \|\| 1 &= 1. \end{align} \] In CSP, $ \|\| $ satisfies the identity $ 1 \|\| x = x $ which we do not have here because in the concrete model, we will interpret $ \\| $ as the synchronisation operator found in CSP. However, we still maintain the instance of that law in the special case $ x = 1 $ (see axiom (11)) where $ 1 $ is interpreted as “do nothing”. Next we have the axioms dealing the interaction of $ \\|, + $ and $ . $: \[ \begin{align} \text{Monotonicity} : & & x \|\| y + x \|\| z &\leq x \|\| (y + z), \\ \text{Interchange-law:} & & (x \|\| y)(u \|\| v) &\leq (xu)(yv). \end{align} \] The interchange law is the most interesting axiom of concurrent Kleene algebra. That is the vending machine performs a coin flip where $ \text{coin} $ and $ \text{tea} $, $ \text{coffee} $, $ \tau_h $ and $ \text{flip}_p $ are all represented by automata. That is the vending machine accepts a coin and then decides internally whether it will enable the button coffee or tea. The decision is determined by the action $ \text{flip}_p $ which (as explained later) enables either $ \tau_h $ or $ \tau_t $. The actions $ \tau_t $ and $ \tau_h $ are internal and the user cannot access them. Now, a user who wants to drink tea is specified as \[ U = \text{coin}(\cdot)(\text{tea} + 1). \] The system becomes $ U \|\| VM $ where the concurrent operation is CSP like and synchronises on $ \text{coin} $, $ \text{tea} $ and $ \text{coffee} $. The interchange law together with the other axioms and some system assumptions imply the following inequation: \[ U \|\| VM \geq \text{coin} \cdot \text{flip}_p \cdot (\tau_h \cdot (\text{tea} + 1) + \tau_t \cdot (\text{coffee} + 1)) \] which is proved automatically in our repository. In other words, the user will only be satisfied with probability at least $ p $ since the right-hand side equation says that the tea action can only be enabled provided that $ \tau_h $ is enabled, and in turn that is determined by the result of the $ \text{flip}_p $ action. Now we are ready to define our algebra. Definition 2. A weak concurrent Kleene algebra is a weak probabilistic Kleene algebra $(K, +, \cdot, , 0, 1)$ with a concurrency operator $ \|\| $ satisfying $ \Box \Box $. We assume the operators precedence $ < \cdot < \|\| < + $. Proposition 3. Let $ s, t $ be terms, the following equations holds in weak concurrent Kleene algebra. 1. All the operators are monotonic. 2. $ (s^* \|\| t^)^ = s^* \|\| t^* $. 3. $ s\|\|t\|^* \leq s^* \|\| t^* $. 4. $ (s + t)^* = (s^* t^)^ $. \[\Box\Box\] i.e. the automaton that performs a \text{flip}_p action. ### 3 Concrete Model #### 3.1 Semantic Space We use nondeterministic automata to construct a concrete model. An automaton is denoted by a tuple $(P, \rightarrow, i, F)$ \[ (P, \rightarrow, i, F) \] where $ P $ is a set of states. The set $ \rightarrow \subseteq P \times \Sigma \times P $ is a transition relation and we write $ x \rightarrow a y $ when there is a transition, labelled by $ a $, from state $ x $ to state $ y $. The alphabet $ \Sigma $ is left implicit and considered to be fixed for every automaton. The state $ i \in P $ is the initial state and $ F \subseteq P $ is the set of final states of the automaton. In the sequel, we will denote an automaton $(P, \rightarrow, i, F)$ by its set of states $ P $ when no confusion is possible. The actions in the alphabet $ \Sigma $ are categorised into three kinds: - internal: actions that will be “ignored” by the simulation relation (as in $ \tau_h $ and $ \tau_t $). Internal actions are never synchronised by $ \|\| $. - external: actions that can be synchronised. Probabilistic actions are external (as in $ \text{flip}_p $) but they are never synchronised. - synchronised: external actions that will be synchronised when applying $ \|\| $ (as in $ \text{coin}, \text{tea} $ and $ \text{coffee} $). These actions are determined by a set of external actions $ A $. More specifically, $ \|\| $ refers to $ x\|y $ which we assume is fixed and given beforehand. The special case of probabilistic choice is modelled by combining probabilistic and internal actions. That is a process that does $ a $ with probability $ p $ and does $ b $ with probability $ 1 - p $ is interpreted as the following automaton where $ \text{flip}_p \in \Sigma $ represents the action of flipping a $ p $-biased coin which produces head with probability $ p $ and tail with probability $ 1 - p $. The internal actions $ \tau_t $ and $ \tau_h $ are enabled according to the result of $ \text{flip}_p $. Hence only one of $ \tau_h $ and $ \tau_t $ will be enabled just after the coin flip. Since $ \tau_t $ and $ \tau_h $ are internal actions, the choice is internal and based upon the outcome of $ \text{flip}_p $. The important facts here are that the choice after $ \text{flip}_p $ is internal so could be based on the probabilistic outcome of $ \text{flip}_p $ and that the environment cannot interfere with that choice. These two behavioural characteristics are what we consider to be the most general features of probability in a concurrent setting and they are those which we axiomatise and record in our concrete model. Next, we impose some conditions on the automata to ensure soundness. - reachability: every state of the automaton is reachable by following a finite path from the initial state. - initiality: there is no transition that leads to the initial state. This means that $a^$ corresponds to the automaton associated to $1 + aa^$ rather than a self loop labeled by $a \in \Sigma$. We denote by $\text{Aut}$ the set of automata satisfying these two conditions. The next step is to define the operators that act on $\text{Aut}$. We use the standard inductive construction found in [1, 17, 9] and the diagrams illustrating the constructions are given in the appendix. Deadlock: 0 This is the automaton that has only one state, namely the initial state, and no transition at all. It is the tuple $((i),\emptyset,\emptyset,\emptyset)$. Skip: 1 This is the automaton that has only one state $i$ which is both initial and final. This automaton has no transition i.e. is denoted by $((i),\emptyset,\emptyset,\emptyset)$. Single action: The automata associated with $a$ is $i \xrightarrow{a} \circ$ where $i$ is the initial state and $\circ$ is a final state. It is the tuple $((i,\circ),(i\xrightarrow{a}\circ),i,\emptyset)$. Addition: $P + Q$ This automaton is obtained using the standard construction of identifying the initial states of $P$ and $Q$. (This is possible due to the initiality property.) Multiplication: $PQ$ (or $P \cdot Q$) This automaton is constructed in the standard way of identifying copies of the initial state of $Q$ with final states of $P$. Concurrency: $P \|\| Q$ This automaton is constructed as in CSP [9]. It is a sub-automaton of the Cartesian product of $P$ and $Q$. The initial state is $(i_P, i_Q)$ and final states are reachable elements of $F_P \times F_Q$. Notice that the set $A$ never contains probabilistic actions. Further explanation about $\\| \\|$ is given below. Kleene star: $P^$ This automaton is the result of repeating $P$ allowing a successful termination after each (possibly empty) full execution of $P$. The initial state of $P^$ is final and copies of the initial state of $P$ are identified with the final states of $P$. All automata begin with an initial state and end in some final or deadlock state. Our main use of final states is in the construction of sequential composition and Kleene star. The concurrency operator $\\| \\|$ synchronises transitions labeled by an action in $A$ and interleaves the others (including internal transitions). As in CSP, a synchronised transition waits for a corresponding synchronisation action from the other argument of $\\| \\|$. This is another reason we do not have $1 \\| P = P$ because if $P = i_P \xrightarrow{a} \circ$ and $i_P$ is not a final state, then $$1 \\| P = ((i, i_P),\emptyset, (i, i_P),\emptyset) = 0.$$ Proposition 4. These operations of weak concurrent Kleene algebra are well defined on $\text{Aut}$ that is if $P, Q \in \text{Aut}$ then $P + Q, PQ, P \|\| Q$ and $P^$ are elements of $\text{Aut}$. The proof consists of checking that $P + Q, PQ, P \|\| Q$ and $P^$ satisfy the reachability and initiality conditions whenever $P$ and $Q$ satisfy the same conditions. (See Proposition 20 in the appendix.) In the sequel, whenever we use an unframed concurrency operator $\\|$, we mean that the frame $A$ has been given and remains fixed. ### 3.2 Equivalence The previous subsection has given us the objects and operators needed to construct our concrete model. Next we turn to the interpretation of equality for our concrete interpretation. Following the works found in [1, 4, 13], we again use a simulation-like relation to define valid equations in the concrete model. More precisely, due to the presence of internal actions, we will use an $\eta$-simulation as the basis for our equivalence. Before we give the definition of simulation, we need the following notation. Given the state $x$ and $y$, we write $x \Rightarrow y$ if there exists a path, possibly empty, from $x$ to $y$ such that it is labelled by internal actions only. This notation is also used in [14] with the same meaning. Definition 5. Let $P, Q$ be automata, a relation $S \subseteq P \times Q$ (or $S : P \rightarrow Q$) is called $\eta$-simulation if - if $(i_P, i_Q) \in S$, - if $(x, y) \in S$ and $x \xrightarrow{a} x'$ then a) if $a$ is internal then there exists $y'$ such that $y \Rightarrow y'$ and $(x', y') \in S$, b) if $a$ is external then there exists $y_1$ and $y'$ in $Q$ such that $y \Rightarrow y_1 \xrightarrow{a} y'$ and $(x, y_1) \in S$ and $(x', y') \in S$. - if $(x, y) \in S$ and $x \in F_P$ then $y \in F_Q$. A simulation $S$ is rooted if $(i_P, y) \in S$ implies $y = i_Q$. If there is a rooted simulation from $P$ to $Q$ then we say that $P$ is simulated by $Q$ and we write $P \leq Q$. Two processes $P$ and $Q$ are simulation equivalent if $P \leq Q$ and $Q \leq P$, and we write $P \equiv Q$. In the sequel, rooted any $\eta$-simulation will be referred simply as a simulation. Relations satisfying Definition 5 are also $\eta$-simulation in the sense of [17] where property (a) is replaced by: $$\text{if } a \text{ is internal then } (x', y) \in S.$$ (15) The identity relation (drawn as dotted arrow) in the following diagram is a simulation relation satisfying Definition 5 but it is not a simulation in the sense of [14]. We need the identity relation to be a simulation here because in our proof of soundness, more complex simulations are constructed from identity relations. Proposition 6. The following statements hold. 1. The relational composition of two rooted $\eta$-simulations is again a rooted $\eta$-simulation. That is, if $S, T$ are rooted $\eta$-simulations then $S \circ T$ is also a rooted $\eta$-simulation, where $\circ$ denotes relational composition. 2. The simulation relation $\leq$ is a preorder on $\text{Aut}$. Proposition 6 is proven in Proposition 21 of the appendix. Therefore, $\equiv$ as determined by Definition 5 is an equivalence. In fact, we prove in the following proposition that it is a congruence with respect to $\tau$. Proposition 7. The equivalence relation $\equiv$ is a congruence with respect to $+$ and $P \leq Q$ iff $P + Q \equiv Q$. The proof adapts and extends the one found in [17] and the specialised version for our case is Proposition 22 in the appendix. It is well documented that $\eta$-simulation is not a congruence without the rootedness condition [17]. A typical example is given by the expressions $\tau a + \tau b$ and $\tau(a + b)$. The automata associated to these expressions are equivalent under non-rooted $\eta$-simulation. The manipulation of probabilistic actions is also an important facet of our model. We assume that probabilistic actions are not synchronised and in that respect they are similar to internal actions. However probabilistic actions cannot be treated as internal as the following examples illustrates. Consider the action $\text{flip}_{1/2}$ which flips a fair coin. If $\text{flip}$ is an internal action then the inequality $$(\text{flip}_{1/2})(\tau a + \tau b) \leq (\text{flip}_{1/2})\tau a + (\text{flip}_{1/2})\tau b$$ would be valid when interpreted in the concrete model. In other words, we would have the following simulation: But this relationship (which implies distributivity of $\text{flip}_p$ through $+$) does not respect the desired behaviour of probability which, as we explained earlier, satisfies only a weaker form of distributivity. Whence, we assume that probabilistic actions such as $\text{flip}_{1/2}$ are among the external actions which will never be synchronised. 4 Soundness In this section, we prove that the set $\text{Aut}$ endowed with the operators defined in Subsection 3.3 modulo rooted $\eta$-simulation equivalence (Subsection 3.3) forms a weak concurrent Kleene algebra. The first part is to prove that $\text{Aut}$ is a weak probabilistic Kleene algebra. Proposition 8. $(\text{Aut}, +, \cdot, , 0, 1)$ is a weak probabilistic Kleene algebra. The proof consists of detailed verifications of the axioms for weak probabilistic Kleene algebra (see Proposition 23 in the appendix). The second part consists of proving that $\parallel$ satisfies the equations (19). Associativity depends heavily on the fact that both concurrent compositions involved in $x[y]z$ have the same frame set. For instance, let $\Sigma = \{a, b, c\}$. $$a(a \|\| b)(c) \|\| a = ab0 + ba0$$ and $$a(a \|\| b)(c) \|\| a = ab + ba$$ are valid in the concrete model. Hence, the first process will always go into a deadlock state though the second one will always terminate successfully. Therefore, to have associativity, the concurrency operator must have a fixed frame. Proposition 9. $(\text{Aut}, +, \cdot, , \\|, 1)$ satisfies equations (19) modulo rooted $\eta$-simulation equivalence for any set of synchronisable actions $A \subseteq \Sigma$ (i.e. no probabilistic actions). Associativity is mainly a consequence of the fact that there is only one frame for $\parallel$. The other axioms need to be checked thoroughly (see Proposition 24). Our soundness result directly follows from these two propositions. Theorem 10. $(\text{Aut}, +, \cdot, , \\|, 0, 1)$ is a weak concurrent Kleene algebra for any set of synchronisable actions $A \subseteq \Sigma$. In this theorem, the frame $A$ is fixed beforehand. In other words, a model of weak concurrent Kleene algebra is constructed for each possible choice of $A$. In particular, if $A$ is empty then the concurrency operator is interleaving all actions i.e. no actions are synchronised. This particular model satisfies the identity $1_A[x = x]$ of the original concurrent Kleene algebra found in [8]. The sequential and concurrent composition actually have stronger properties in the concrete model. If we consider finite automata only — automata with finitely many states and transitions — then we show that these two operators are conditionally Scott continuous in the sense of [1] (see Proposition 25 and 27 in the appendix). 5 Relationship to Probabilistic Processes Firstly, it is shown in [11] that a probabilistic choice $\text{flip}_p \triangleright \parallel b$ simulates the nondeterministic choice $a + b$. A similar result also holds in our setting. In the absence of internal transitions, simulation has been also defined elsewhere [1, 17] which we will refer to as strong simulation. Recall that $(\text{flip}_p)(a + (\text{flip}_p)b \leq (\text{flip}_p)(a + b)$ is a general property of probabilistic Kleene algebra [12] so it is valid under strong simulation equivalence [18]. Due to the absence of internal actions, the middle part of the diagram of Figure 4 does not exist with respect to strong simulation equivalence. In the context of Definition 5 the right-hand simulation of Figure 1 is the refinement of probabilistic choice by nondeterminism. This example gives an explicit distinction between $(\text{flip}_p)(a + b)$ and $(\text{flip}_p)a + (\text{flip}_p)b$ by considering the fact that the choice in $(\text{flip}_p)(a + b)$ can depend on the probabilistic outcome of $(\text{flip}_p)b$, but this is not the case for $(\text{flip}_p)a + (\text{flip}_p)b$. Secondly, we discuss about the relationship between our concrete model and probabilistic automata. Remind that our interpretation of probability lies in the use of actions that implicitly contain probabilistic information. In its most general form, a probabilistic choice between $n$ possibilities can be written as $$\text{flip}_{p_1, \ldots, p_n} \cdot (\tau_1 \cdot a_1 + \ldots + \tau_n \cdot a_n)$$ where $\sum_i p_i = 1$. In this algebraic expression, we implicitly ensure that each guard $\tau_i$ is enabled with a corresponding probability $p_i$. Therefore, if these $\tau_i$’s are not found directly after the execution of the probabilistic action then matching them with the corresponding $p_i$ becomes a difficult task. We call $p$-automaton a transition system as per the definition of Subsection 3.1 such that if a probabilistic action has associated $\tau$ transitions then all of them follow that action directly. Another complication also arises from the use of these $\tau_i$’s. Consider the following two processes $$\text{flip}_{p_1, p_2} \cdot (\tau_1 \cdot a + \tau_2 \cdot b)$$ and $$\text{flip}_{p_1, p_2} \cdot (\tau_1 \cdot b + \tau_2 \cdot a)$$ where $p_1 + p_2 = 1$. We can construct a (bi)simulation relation between the corresponding automata though the probabilities of doing an $a$ are different. Hence we need to modify the definition of $\eta$-simulation (Definition 5) to account for these particular structure. Definition 11.* A $p$-simulation $S$ between two $p$-automata $P, Q$ is a $\eta$-simulation such that if - $x \xrightarrow{\text{flip}_{p_1, \ldots, p_n}} x'$ is a transition in $P$, - $y \xrightarrow{\text{flip}_{p_1, \ldots, p_n}} y'$ is a transition in $Q$, - and $(x, y) \in S$ then $(x_i', y_i') \in S$, for each $i = 1, \ldots, n$. This definition ensures that the probability of doing a certain action from $y$ is greater than doing that action from $x$. With similar proofs as in the previous Sections, we can show that the set of $p$-automata modulo $p$-simulation forms again a weak concurrent Kleene algebra. We denote $p$-$\text{Aut}$ the set of $p$-automata modulo $p$-simulation. We will now show that this definition is a very special case of probabilistic simulation on probabilistic automata. To simplify the comparison, we assume that $\tau$ transitions occur only as part of these probabilistic choices in $p$-automata. Definition 12. A probabilistic automaton is defined as a tuple $(P, \rightarrow, \Delta, F)$ where $P$ is a set of states, $\rightarrow$ is a set of labelled transitions from state to distributions of states i.e. $\rightarrow \subseteq P \times \Sigma \times DP$, $\Delta$ is the initial distribution and $F \subseteq P$ is a set of final states. The notion of simulation also exists for probabilistic automata and, in particular, simulation and failure simulation is discussed in $\mathbb{k}$ where they are proven to be equivalent to may and must testing respectively. To give a proper definition of probabilistic simulation, we need the following notations which are borrowed from $\mathbb{k}$ and $\mathbb{17}$. Given a relation $R \subseteq P \times DQ$, the lifting of $R$ is a relation $\hat{R} \subseteq DP \times DQ$ such that $\phi \hat{R} \psi$ if: - $\phi = \sum_x p_x \delta_x$, - for each $x \in \text{supp}(\phi)$ (the support of $\phi$) there exists $\psi_x \in DQ$ such that $x \hat{R} \psi_x$, - $\psi = \sum_x p_x \psi_x$. Similarly, the lifting of a transition relation $\rightarrow$ is denote $\rightarrow$ whose reflexive transitive closure is denote $\rightarrow$. For each external action $a$, we write $\rightarrow a$ for the sequence $\rightarrow \rightarrow \rightarrow \rightarrow \rightarrow \rightarrow a$. Definition 13. A probabilistic simulation $S$ between two probabilistic automata $P$ and $Q$ is a relation $S \subseteq R \times DQ$ such that: - $(\Delta_P, \Delta_Q) \in S$, - if $(x, \phi) \in S$ and $x \xrightarrow{\phi} \psi$ then there exists $\psi' \in DQ$ such that $\psi \xrightarrow{\phi} \psi'$ and $(\phi, \psi') \in S$ (for every $a \in \Sigma \cup \{\tau\}$). - if $x \in F_P$ and $(x, \psi) \in S$ then $\text{supp}(\psi) \subseteq F_Q$. We denote by $\text{ProbAut}$ the set of probabilistic automata modulo simulation equivalence. We can now construct a mapping $\epsilon : p$-$\text{Aut} \rightarrow \text{ProbAut}$ such that each instance of structure similar to $\text{flip}_{p_1, \ldots, p_n} \cdot (\tau_1 \cdot a_1 + \ldots + \tau_n \cdot a_n)$ is collapsed into probabilistic transitions. More precisely, let $P \in p$-$\text{Aut}$ and $\rightarrow$ be its transition relation. The automaton $\epsilon(P)$ has the same state space as $P$ (up to accessibility with respect to the transitions of $\epsilon(P)$). The initial distribution of $\epsilon(P)$ is $\delta_I$, and the set of final states of $\epsilon(P)$ is $F_P$ again $\mathbb{k}$. \footnote{We assume that all distributions are finitely supported.} \footnote{We denote by $\delta_x$ the point distribution concentrated on $x$.} \footnote{Notice that by assuming the structure $\text{flip}_{p_1, \ldots, p_n} \cdot (\tau_1 \cdot a_1 + \ldots + \tau_n \cdot a_n)$ the state between the flip action the corresponding $\tau$ transitions is never a final state. Hence we are safe to use $F_P$ as the final state of $\epsilon(P)$} The set of transitions $ \rightarrow_{c(P)} $ is constructed as follow. Let $ x \xrightarrow{a} x' $ be a transition of $ P $, there are two possible cases: a) if $ a $ is probabilistic i.e. of the form $ \text{flip}_{p_1, \ldots, p_n} $ and is followed by the $ \tau $'s, then the transition \[ x \xrightarrow{\tau} p_1 \delta_{x'_1} + \ldots + p_n \delta_{x'_n} \] is in $ \rightarrow_{c(P)} $ where $ x' \xrightarrow{\tau} x'_i $ is a transition in $ P $. b) else the transition $ x \xrightarrow{a} x' $ is in $ \rightarrow_{c(P)} $. We now prove that $ c $ is a monotonic function from $ P\text{-Aut} $ to $ \text{ProbAut} $. Proposition 14. If $ P \leq Q $ then $ c(P) \leq c(Q) $. Proof. Assume that $ S $ is a $ P $-simulation from $ P $ to $ Q $. Consider the exact same relation but restricted to the state space of $ c(P) $ and $ c(Q) $. We show that this restriction holds. - Obviously, $ (\delta_{x'_1}, \delta_{y'_1}) \in \hat{S} $. - Let $ x \xrightarrow{\phi} (x, \psi) \in \hat{S} $. Since $ \tau $ transitions only occur as part of probabilistic choices, we have two possibilities: \[ x \xrightarrow{\tau} p_1 \delta_{x'_1} + \ldots + p_n \delta_{x'_n} \] is a transition in $ c(P) $ and $ (x, \psi) \in S $ where $ \psi = \delta_{y} $. Since $ (x, y) $ belongs to the original $ S $. In this case, $ y \xrightarrow{\tau} p_1 \delta_{y'_1} + \ldots + p_n \delta_{y'_n} $ is a transition in $ c(Q) $ and each $ (x'_i, y'_i) $ belongs to the original $ S $ (Definition of $ \text{p-simulation} $). - Conservation of final states follows easily from the $ S $ is a $ P $-simulation. Since our Definition \[13\] implies the definition of probabilistic simulation in \[3\], we conclude that maximal probability of doing a particular action in $ P $-automata is increased by $ \text{p-simulation} $. This remark provides a formal justification of our earlier example. That is, Equation \[13\] ensures that the maximal probability that a buyer will be satisfied when using the probabilistic vending machine is at least 1/2 because the maximal probability of a trace containing \text{tea} in the automata described by \[ \text{coin} \cdot \text{flip} \cdot (\tau_1 \cdot (\text{tea} + 1) + \tau_1) \] is 1/2. In the proof of proposition \[14\] the simulation constructed is a very particular case of probabilistic simulation so it is too weak to establish certain relationships between $ p $-automata. For instance, the automaton represented by $ a_1 \mathbb{P} (a_2 \mathbb{P} b) $ should be equivalent to $ a_1 a_2 + a_2 b $ but Definition \[11\] will not provide such equality. This line of research is part of our future work where we will study proper probabilistic automata and simulations against weak concurrent Kleene algebra. ## 6 Algebraic Testing In this section, we describe an algebraic treatment of testing. Testing is a natural ordering for processes that was studied first in \[11\]. The idea is to “measure” the behaviour of the process with respect to the environment. In other words, given two processes $ x $ and $ y $ and a set of test processes $ T $, the goal is to compare the processes $ x\|_T $ and $ y\|_T $ for every $ t \in T $. In our case, the set $ T $ will contain all processes. We consider a function $ o $ from the set of terms to the set of internal expressions $ I = \{x \mid x \leq 1\} $. The function $ o : T \Sigma \xrightarrow{\text{c}} I $ is defined by \[ o(x) = x \quad \text{if} \quad x \in I \] \[ o(s) = o(s) o(t) \quad \text{if} \quad a \in \Sigma - I \] \[ o(s + t) = o(s) + o(t) \quad \text{if} \quad s + t \leq \Sigma \] \[ o(s t) = o(s) o(t) \quad \text{if} \quad s t \leq \Sigma \] In the model, the function $ o $ is interpreted by substituting each external action with the internal action $ \tau (o(a) = \tau $ for any $ a \in \Sigma - I $). Then any final state is labelled by 1 and deadlock states are labelled by 0. Inductively, we label a state that leads to some final state by 1, else it is labelled by 0. This is motivated by the fact that $ x \phi = 0 $ for any $ x \in I $ so each transition leading to \text{deadlock states} only will be removed. Therefore, only states labelled by 1 will remain and the transitions between them. Hence, $ o(s) \neq 0 $ iff the resulting automaton contains at least one state labelled by 1. In other words, $ o(s) = 0 $ iff $ x $ must not terminate successfully. Without loss of generality (by considering automata modulo simulation), we assume that $ \tau $ is the only internal action in $ \Sigma $ and it satisfies $ \tau \tau = \tau $. This equation is valid in the concrete model. The existence of a well-defined function $ o $ satisfying these conditions depends on our definition of simulation. That is, we can show that if $ P \leq Q $ then $ o(P) \leq o(Q) $ where we have abused notation by writing $ o(P) $ as the application of $ o $ on the term associated to $ P $. A detailed discussion about this can be found in the appendix under Remark \[25\]. Definition 15. The may testing order is given by \[ x \leq_{\text{may}} y \iff \forall t \in T \Sigma. \{ o(y) \| t = 0 \Rightarrow o(x) \| t = 0 \} \] We now provide some results about algebraic may testing. It follows from monotonicity of $ \mid $ with respect to $ \leq $ (Proposition \[3\]) that may ordering $ \leq_{\text{may}} $ is weaker than the rooted $ \eta $-simulation order. Proposition 16. $ x \leq y $ implies $ x \leq_{\text{may}} y $. In fact, $ \leq_{\text{may}} $ is too weak compared to $ \leq $ : may testing is equivalent to language equivalence. Given a term $ s $, the language $ T \tau(s) $ of $ s $ is the set of finite words formed by external actions and are accepted by the automata represented by $ s $. In other word, it is the set of finite traces in the sense of CSP which lead to final states. The precise definition of this language equivalence can be found in the appendix and so is the proof of the following proposition (Proposition \[20\] of the appendix). Proposition 17. In $ \text{Aut} $, $ \leq_{\text{may}} $ reduces to language equivalence. \[\text{Notice} \|\| \text{ should be framed because some external actions are not synchronised. But in the setting of testing, we can also assume that all external actions are synchronised which permits to follow up all external actions present in the process.}\] We have shown that $\sqsubseteq_{eq}$ is equivalent to language equivalence and hence it is weaker than our simulation order. This is also a consequence of the fact that our study of may testing is done in a qualitative way because the probabilities are found implicitly within actions. A quantitative study of probabilistic testing orders can be found in [8]. 7 Case Study: Rabin’s Choice Coordination The problem of choice coordination is well known in the area of distributed systems. It usually appears in the form of processes voting for a common goal among some possibilities. Rabin has proposed a probabilistic protocol which solves the problem [14] and a sequent. Some possibilities. Rabin has proposed a probabilistic protocol which solves the problem [15] and a sequent. The whole specification of the protocol executed by each tourist is described by the automata of Figure 2. We are ready to specify the whole system. Assume we have two tourists $P$ and $Q$ (our result generalises easily to $n$ tourists). The tourists’ joint action is specified as $(P + Q)\ast$. This ensures that when a tourist has started his turn by reading the board, he will not be interrupted by any other tourist until he is done and goes inside the current place or to the other place. This condition is crucial for the protocol to work properly. The actions of the locations process are specified by $(M + C)\ast$ which ensures that each tourist can be at one place at a time only — this is a physical constraint. Now, the whole system is specified by \[ \text{init} \cdot \left( (P(\alpha, u) + Q(\beta, v))\ast[c,m] \right)[(M + C)\ast] (16) \] where init is the initialisation of the values on the boards, notepads and initial locations. Specification [10] describes the most arbitrary behaviour of the tourists compatible with visiting and interacting with the locations in the manner described above. Rabin’s design of the protocol means that this behaviour is equivalent to a serialised execution where first one location is visited, followed by the other. We can write that behaviour behaviour as $\left( (P + Q)(M)\ast (P + Q)(C)\ast \right)$, where the concurrent and sequential compositions are continuous in the the concrete model. The composition only we denote the concurrency operator by $\parallel$ instead of $[c,m]\|\|$ to make the notation lighter. The next theorem says that this more uniform execution is included in $S = [P(\alpha, u) + Q(\beta, v)\ast][(M + C)\ast]$, described by Specification [10]. Theorem 18. We have \[ S \geq \left( (P + Q)(M)\ast (P + Q)(C)\ast \right)\ast \] The proof is a simple application of Proposition [3]. Theorem [18] means $S$ could execute all possible actions related to door $M$, and then those at door $C$, and then back to door $M$ and so one. In fact, we can also prove the converse i.e. Proposition [18] could be strengthened to equality. But for that, we need the continuity of the operators $\cdot$ and $\parallel$. Theorem 19. In the concrete model, the specification of Rabin’s protocol satisfies \[ S = \left( (P + Q)(M)\ast (P + Q)(C)\ast \right)\ast \] The proof of this theorem depends heavily on the fact that the concurrent and sequential compositions are continuous in the the concrete model. The complete proof can be found in the appendix. In the proof, if we stopped at the distribution over $\parallel$, we obtain the equivalent specification \[ S = [(P + Q)\parallel M + (P + Q)\parallel C]\ast \] which describes a simpler situation where $P$ or $Q$ interacts at the Museum or at the Church. This is similar to the sequential version found in [11], which can be treated by standard probabilistic invariants to complete a full probabilistic analysis of the protocol. 8 Conclusion An algebraic account of probabilistic and concurrent system has been presented in this paper. The idea was to combine probabilistic and concurrent Kleene algebra. A soundness result with respect to automata and rooted $\eta$-simulation has been provided. The concrete model ensures not only the consistency of the axioms but provides also a semantic space for systems exhibiting probabilistic, nondeterministic and concurrent behaviour. We also showed that the model has stronger properties than just the algebraic axiomatisation. For instance, sequential and concurrent compositions are both continuous in the case of finite automata. We provided some applications of the framework. An algebraic account of may testing has been discussed in Section 6. It was shown that may ordering reduces to language equivalence. We also provided a case study of Rabin’s solution to the choice coordination problem. A concurrent specification was provided and it was shown to be structurally equivalent to the sequential one given in [13]. Though the algebra was proven to be powerful enough to derive non-trivial properties for concrete protocols, the concrete model still needs to be refined. For instance, the inclusion of tests is important especially for the construction of probabilistic choices. Tests need to be introduced carefully because their algebraic characterisation are subtle due to presence of probability. We also need to improve and refine the manipulation of quantitative properties in the model as part of our future work. Finally, it is customary to motivate automated support for algebraic approaches. The axioms system for weak concurrent Kleene algebra is entirely first-order, therefore proof automation is supported and automated version of our algebraic proofs can be found in our repository. References [1] E. Cohen. Weak Kleene algebra is sound and (possibly) complete for simulation. CoRR, abs/0910.1028, 2009. [2] J. H. Conway. Regular Algebra and Finite Machines. Chapman and Hall, Mathematics series, 1971. [3] Y. Deng and R. Van Glabbeek. Characterising testing preorders for finite probabilistic processes. In In LICS'07: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, CA, pages 313–325, 2007. [4] C. A. R. Hoare. Communicating sequential processes. Commun. ACM, 21:666–677, August 1978. [5] C. A. R. Hoare, B. Möller, and I. Struth, G.and Wehrman. Concurrent Kleene algebra. In Proceedings of the 29th International Conference on Concurrency Theory, CONCUR 2009, pages 399–414, Berlin, Heidelberg, 2009. Springer-Verlag. [6] D. Kozen. A completeness theorem for Kleene algebras and the algebra of regular events. Infor. and Comput., 110(2):366–390, May 1994. [7] D. Kozen. On Hoare logic and Kleene algebra with tests. Trans. Computational Logic, 1(1):60–76, July 2000. [8] D. Kozen and M. C. Patron. Certification of compiler optimizations using Kleene algebra with tests. In John Lloyd, Veronica Dahl, Ulrich Furbach, Manfred Kerber, Kung-Kiu Lau, Catuscia Palamidessi, Luis Moniz Pereira, Yehoshua Sagiv, and Peter J. Stuckey, editors, Proc. 1st Int. Conf. Computational Logic (CL2000), volume 1861 of LNAI, pages 568–582, London, July 2000. Springer-Verlag. [9] A. McIver, T. M. Rabehaja, and G. Struth. On probabilistic Kleene algebras, automata and simulations. In Proceedings of the 12th international conference on Relational and algebraic methods in computer science, RAMICS'11, pages 264–279, Berlin, Heidelberg, 2011. Springer-Verlag. [10] A. K. McIver, E. Cohen, and C. C. Morgan. Using probabilistic Kleene algebra for protocol ver- ification. In Relmics/AKA 2006, volume 4136 of LNCS. Springer Verlag. [11] A. K. McIver and C. C. Morgan. Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science). Springer Verlag, 2004. [12] A. K. McIver and T. Weber. Towards automated proof support for probabilistic distributed systems. In Proceedings of Logic for Programming and Automated Reasoning, volume 3835 of LNBI, pages 534–548. Springer, 2005. [13] R. Milner. An algebraic definition of simulation between programs. Technical report, Stanford, CA, USA, 1971. [14] R. De Nicola and M. Hennessy. Testing equivalence for processes. In Proceedings of the 10th Colloquium on Automata, Languages and Programming, pages 548–560, London, UK, 1983. Springer-Verlag. [15] M. O. Rabin. The choice coordination problem. Acta Inf., 17:121–134, 1982. [16] R. Segala and N. Lynch. Probabilistic simulations for probabilistic processes. In Nordic Journal of Computing, pages 481–496. Springer, 1994. [17] R. G. van Glabbeek. The linear time-branching time spectrum (extended abstract). In J. C. M. Baeten and J. W. Klop, editors, CONCUR 1990, volume 458 of LNCS, pages 278–297. Springer, 1990. Appendix The following proofs, diagrams, remarks and other results are only included to add further clarification of the contents of the present paper. It is left to the discretion of the reviewers to choose whether they will read these proofs or not. A Diagrams, Theorems and Proofs Diagram of the Operators: The construction are done inductively from 0, 1 and elements of the alphabet $\Sigma$. - Deadlock: 0. This is the automaton that has only one state, no transition and no final state. - Skip: 1 This is the automaton $\circ$ which has only one state which is both initial and final and has no transition. - Single action: The automaton associated to $a \in \Sigma$ is $i \xrightarrow{a} \circ$ where $i$ is the initial state and $\circ$ is a final state. - Addition: $P + Q$. This is constructed by identifying the initial states of $P$ and $Q$. This construction is allowed because of the initiality condition (Figure 3). - Multiplication: $PQ$. This is constructed by identifying each final state of $P$ with the initial state of $Q$ (Figure 4). - Concurrency: $P\|Q$. This is constructed as a sub-automaton of the Cartesian product of $P$ and $Q$ following CSP [3]. Assuming $a \in A$ and $b, d \notin A$, the concurrent composition $P_A\|Q$ is inductively constructed as in Figure 5. Notice that $A \subseteq \Sigma$ is a set of synchronised action and does not contain any (strictly) probabilistic actions such as $\text{flip}(p)$, for $p \in [0, 1]$. - Kleene star: $P^$ This is the result of repeating $P$ allowing a successful termination after each (possibly empty) full execution of $P$. In the diagram of Figure 6 we just picture one transition from the initial state and one final state. The construction needs to be performed for each initial transition and final state. Notice the initial state of $P^$ is a final state too. Proposition 20. These operations are well defined on $\text{Aut}$ that is if $P, Q \in \text{Aut}$ then $P + Q, PQ, P\parallel Q$ and $P^$ are elements of $\text{Aut}$. Proof.* The proof is by induction on the structure of the automata $P$ and $Q$. For the base case, it is obvious that 0, 1 and $i \xrightarrow{a} \circ$ satisfy the reachability and initiality conditions. Let $P, Q \in \text{Aut}$. It is easy to see from the diagrams that $P + Q, P\parallel Q$ and $P^$ belongs to $\text{Aut}$ too. $PQ$ satisfies the initiality condition because the initial state is $i_P$. For reachability, let $x \in Q$. Then $x$ is reachable from $i_Q$ which in turn is reachable from $i_P$ by the definition of sequential composition. Proposition 21.* The following statements hold: 1. The relational composition of two rooted $\eta$-simulations is again a rooted $\eta$-simulation. That is, if $S, T$ are rooted $\eta$-simulations then $S \circ T$ is also a rooted $\eta$-simulation, where $\circ$ denotes relational composition. 2. The simulation relation $\leq$ is a preorder on $\text{Aut}$. Proof. Let $S : P \rightarrow Q$ and $T : Q \rightarrow R$ be simulations and let us show that $ST : P \rightarrow R$ is a simulation. - Evidently, $(i, i) \in ST$. - Let $(x, z) \in ST$ and $x \xrightarrow{a} x'$. By definition of the relational composition there exists $y \in Q$ such that $(x, y) \in S$ and $(y, z) \in T$. a) if $a$ is internal, there exists $y' \in Q$ such that $y \Rightarrow y'$ and $(x', y') \in S$. Since $y \Rightarrow y'$ consists of a sequence of finite internal transition, there exists $z' \in T$ such that $(y', z') \in T$ and $z \Rightarrow z'$. Hence $(x', z') \in ST$ and $z \Rightarrow z'$. b) If $a$ is external, there exists $y_1, y' \in Q$ such that $y \Rightarrow y_1 \xrightarrow{a} y'$ and $(x, y_1) \in S$ and $(x', y') \in S$. Since $(y, z) \in T$ and $y \Rightarrow y_1$, there exists $z_1 \in R$ such that $(y_1, z_1) \in T$ and $z \Rightarrow z_1$. Again, since $T$ is a simulation and $y_1 \xrightarrow{a} y'$, there exists $z, z' \in R$ such that $z_1 \Rightarrow z_2 \xrightarrow{a} y'$ and $(y_1, z_2) \in T$ and $(y', z') \in T$. Hence, by transitivity of $\Rightarrow$, we have $z_2 \xrightarrow{a} z'$ and $(x, z_2) \in ST$ and $(x', z') \in ST$. - Let $(x, z) \in ST$ and $x \in F_P$, there exists $y \in Q$ such that $(x, y) \in S$ and $(y, z) \in T$. a) If $y \in F_Q$ and hence $z \in F_R$. b) If $y \in S$ and $(y, z) \in T$. So $y = i$ and hence $z = i$. 2. For reflexivity, the identity relation is a rooted $\eta$-simulation and transitivity follows from 1. Proposition 22. The equivalence relation $\equiv$ is a congruence with respect to + and $P \leq Q \iff P + Q \equiv Q$. Proof. Let $S : P \rightarrow Q$ and $S' : P' \rightarrow Q'$ be rooted $\eta$-simulations. We show that $S \cup S' : P + P' \rightarrow Q + Q'$ is again a rooted $\eta$-simulation. - Since initial states are identified in the construction of $+$, we have $(i_P + i_{P'} , i_Q + i_{Q'}) = (i_P, i_Q) \in S \cup S'$. - Let $(x, y) \in S \cup S'$ and $x \xrightarrow{a} x'$ be a transition of $P$ (the case where this transition belongs to $P'$ is dealt with the exact same way). We have two cases: 1. if $(x, y) \in S$, then either $a$ is internal and hence $(x', y') \in S$ (so in $S \cup S'$ too) or there exists $y_1, y' \in Q$ such that $y \Rightarrow y_1 \xrightarrow{a} y'$ is a path in $Q$ and $(x, y_1) \in S$ and $(x', y') \in S$. By definition of $+$, $y \Rightarrow y_1 \xrightarrow{a} y'$ is again a path in $Q + Q'$ such that $(x, y_1) \in S \cup S'$ and $(x', y') \in S \cup S'$. Proposition 22. The equivalence relation $\equiv$ is a congruence with respect to + and $P \leq Q \iff P + Q \equiv Q$. Figure 3: Automaton for $P + Q$. Figure 4: Automaton for $PQ$. The symbol $\circ$ denotes a final state and the symbol $\bullet$ is final if and only if $i_Q$ is final in $Q$. Notice that this construction is done for each final state of $P$. Figure 5: Automaton for $P\\|Q$. The action $a$ has been synchronised and $b,d$ were interleaved. Notice that $b$ or $d$ could be internal. The initial state of the automata is the pair $(i_P,i_Q)$ and the final states are the elements of $F_P \times F_Q$. Figure 6: Automaton for $P^$. 2. if $(x, y) \in S'$, then $x = i_P$ because $x \xrightarrow{a} x'$ is assumed to be a transition in $P$. Since the initial states are merged, $i_{P'}, y \in S'$ and therefore $y = i_{Q'} = i_{Q+Q'} = i_Q$. Therefore $(x, y) \in S$ and we are back to Case 1. - Let $(x, y) \in S \cup S'$ and $x \in F_P$ (the case $x \in F_{P'}$ is similar). We have two cases again, $(x, y) \in S$ and $y \in F_{P'}$. Or $(x, y) \in S'$ and then $x \in P \cap P'$. Hence $x = i$ and we are back to the first case again. - $S \cup S'$ is rooted because $S$ and $S'$ are both rooted. Now assume $P \subseteq Q$. Then $P + Q \subseteq Q + Q \equiv Q$ follows from the fact that $\leq$ is a congruence and the idempotence of $+$ in Proposition 8. Moreover, since $id_Q : Q \rightarrow Q$ is a simulation, we have $P + Q \equiv Q$. Conversely, assume $P + Q \equiv Q$, since $id_P : P \rightarrow P + Q$ is a simulation we have $P \leq Q$ by transitivity of $\leq$. Proposition 23.* $(+, \cdot, \cdot, , 0, 1)$ is a weak probabilistic Kleene algebra. Proof.* Associativity and commutativity of $+$ and $0 + x = x$ follows easily from the fact that $+$ is base on $\cup$. - Idempotence of $+$: since the union is made disjoint, we assume $P$ is a copy of $P$ where every states is indexed by $c$. Then $id_P : P \rightarrow P + P$ is a simulation and $\{\{y, x\} \mid y = x = x\} = x$ is a simulation from $P + P$ to $P$. - Associativity of $:$; associativity follows from the same proof found in 8 because identity relations are simulation and our multiplication here is exactly the $\varepsilon$-free version of the multiplication there. - 1 is neutral for $:$; it follows easily from the construction that $1P = P$ and $P1 = P$. - Subdistributivity $[\ref{subdistributivity}]$ to show that $PQ + PR \leq P(Q + R)$, it suffices to show that $PR \leq P(Q + R)$ and derive the result from idempotence of $+$. Remind that $id_P$ and $id_Q$ are simulation so it suffices to show that $id_P \cup id_Q : PQ \rightarrow P + Q$ is again a simulation. Obviously, $(i, i) \in S$ and it is rooted and conserves final states. Moreover $\rightarrow P_{(Q + R)} \supseteq \rightarrow P_{Q}$. Hence $id_P \cup id_Q$ is a simulation. - Right distributivity $[\ref{right_distributivity}]$ let $P_{c}$ be a disjoint copy of $P$, then the relation \[ S = \{(x, y) \mid y = x \text{ or } y = x\} \] from $(Q + R)P$ to $Q_{P_{c}} + RP$ is rooted and preserves final states. Let $(x, y) \in S$ and $x \xrightarrow{a} x'$ then $\rightarrow_{(Q + R)P}$. Remind that \[ \rightarrow_{(Q + R)P} = \rightarrow_{Q} \cup \rightarrow_{R} \cup \rightarrow_{P} - \{i \xrightarrow{a} z \in \rightarrow_{P}\} \cup \{z \xrightarrow{a} z' \mid z \in F_{Q} \cup F_{R} \text{ and } i \xrightarrow{a} z' \in \rightarrow_{P}\}\] If the transition belongs to the first three sets then we are done, else we can assume $x \in F_{Q}$ and $i \xrightarrow{a} x' \in \rightarrow_{P}$ i.e. $y = x$ and $x' \in P$. We have $\rightarrow_{Q_{P_{c}} + RP} \supseteq \{z \xrightarrow{a} z' \mid z \in F_{Q} \text{ and } i \xrightarrow{a} z' \in \rightarrow_{P}\}$ so $x \xrightarrow{a} x' \in \rightarrow_{Q_{P_{c}} + RP}$ and $(x', x') \in S$. Similarly, we can prove that if $(x, y) \in S$ and $y \xrightarrow{a} y'$ then there exists $x'$ such that $(x', y') \in S$ and $x \xrightarrow{a} x'$. Hence $S$ is a bisimulation. - Left unfold $[\ref{left_unfold}]$ Let $x$ be a state in $P^$ and $x$ the corresponding state in the unfolded version $(1 + PP^)$ i.e. $x$ is considered as a state of $P$. The rooted version of relation $S = id_P \cup \{(x, x)\}$ is a rooted $\eta$-bisimulation from $P^$ to $1 + PP^$. - Left induction $[\ref{left_induction}]$ as in (10), the proof is again similar to $[\ref{left_unfold}]$ because rooted $\eta$-simulation are stable by union. Proposition 24. $(+, \cdot, \cdot, , 0, 1)$ satisfies equations $[\ref{prop_24}]$ modulo rooted $\eta$-simulation equivalence for any set of synchronisable actions $A \subseteq \Sigma$ (i.e. no probabilistic actions). Proof.* 1$(\\\| 1 = 1$ follows directly from the definition of $\\|$ and the simulation used for the commutativity is $\{(x, y, (y, x)) \mid x \in P \text{ and } y \in Q\}$. For associativity, we show that if $(x, (y, z)) \xrightarrow{a} (x', (y', z'))$ then $(x, y) \xrightarrow{a} (x', y')$ $\in \rightarrow_{(P_{(Q_{A}\|\|Q)})}$. \[ - \text{ if } a \notin A, \text{ then } x \xrightarrow{a} x' \text{ and } y = y', z = z'. \] \[ \text{So } ((x, y), z) \xrightarrow{a} ((x', y'), z) \in \rightarrow_{(P_{(Q_{A}\|\|Q)})}\text{ and hence } ((x, y), z) = ((x', y'), z) \in \rightarrow_{(P_{(Q_{A}\|\|Q)})}\text{ because } a \notin A. \] \[ \text{or } x = x' \text{ and } (y, z) \xrightarrow{a} (y', z'). \] \[ \text{So } x \xrightarrow{a} x' \text{ and } (y, z) \xrightarrow{a} (y', z'). \text{ Since } a \notin A \text{ we have } \] \[ (x, y) \rightarrow_{(P_{(Q_{A}\|\|Q)})}\text{ and hence } ((x, y), z) \rightarrow_{(P_{(Q_{A}\|\|Q)})}\text{ and hence } ((x, y), z) = (y', z') \in \rightarrow_{(P_{(Q_{A}\|\|Q)})}. \] \[ \text{If } a \in A, \text{ then } x \xrightarrow{a} x' \text{ and } (y, z) \xrightarrow{a} (y', z'). \text{ Since } a \text{ is again synchronised in } Q_{A\|\|Q}\text{ and } z \rightarrow_{(P_{(Q_{A}\|\|Q)})}\text{ and hence } ((x, y), z) \rightarrow_{(P_{(Q_{A}\|\|Q)})}\text{ and hence } ((x, y), z) = (y', z') \in \rightarrow_{(P_{(Q_{A}\|\|Q)})}. \] Since $\\|$ is commutative, we deduce that $\rightarrow_{(P_{(Q_{A}\|\|Q)})}\rightarrow_{(P_{(Q_{A}\|\|Q)})}$ so the identity relations could again be used for the simulation. To prove monotonicity, we consider the relation $S : P_{Q_{A}} + P_{Q_{A}}(R) \rightarrow P_{Q_{A}}(Q + R)$ as in the case of multiplication i.e. $S = \{(x, y, (x, y)) \mid x \in P \text{ and } y \in Q \} \in P_{(Q_{A}\|\|Q)}$ and $x_{c}$ is the copy of the state $x \in P$ in $P_{c}$. Let $(x_{c}, y) \in S$ (the case $(x, y) \in S$ is easier and can be handled in the same way) and $(x_{c}, y) \rightarrow_{(x_{c}, y', z')} \rightarrow_{P_{(Q_{A}\|\|Q)}}\text{ By definition of } +\text{, that transition belongs to } \rightarrow_{P_{(Q_{A})}}\text{ or } \rightarrow_{P_{(Q_{A})}}\text{. Since the first component is a copy of } x, \text{ we have } (x_{c}, y) \rightarrow_{(x_{c}, y', z')} \rightarrow_{P_{(Q_{A})}}\text{ that is } y, y' \in R.$ Firstly notice that the set of states of $(P\parallel Q)(P'\parallel Q')$ (where the frame $A$ of the concurrency operator is left implicit) is a subset of $(P \times Q) \cup (P' \times Q')$ which is in turn a subset of $(P \cup P') \times (Q \cup Q')$. Hence we consider the injection id of the former set to the latter one and the relation defined in Figure A. We show that $S$ is a simulation in our sense. - Since $(i, i) = i$ is related to itself. In particular, $S$ is rooted because $x \neq i$ in the second set in the definition of $S$ (resp. for the third set) and HCI. - Let $(x, y) \in (P \parallel Q)(P' \parallel Q')$ such that $(x, y) \xrightarrow{a} (x', y')$. We have the following cases. * The transition is in $\rightarrow_{P \parallel Q}$, in which case $(x, y), (x', y') \in P \times Q$. - if $a \notin A$, then $x \xrightarrow{a} x' \in \rightarrow_P$ and $y = y'$, so $x \xrightarrow{a} y \in \rightarrow_{P \parallel Q}$ and $(x', y) \in S$ by definition of $S$. - or $x_c = x_c'$ and $y \xrightarrow{a} y'$, so $(x, y) \xrightarrow{a} (x', y') \in \rightarrow_{P \parallel (Q + R)}$ and $(x', y') \in S$. - if $a \in A$, then $x_c = x_c'$ and $y \xrightarrow{a} y$ $\in \rightarrow_R$. So $x \xrightarrow{a} x' \in \rightarrow_P$ and $y \xrightarrow{a} y' \in \rightarrow_{Q}$. Hence $(x', y') \in S$ by definition of $S$. * The case $(i, y'), (x, y')$ is similar. - Let $(x, y, (u, v)) \in S$ such that $(x, y) \in F_{(P \parallel Q)(P' \parallel Q')\}$. That is, \[ x \in (F_{P - \{i\}} \cup Q \parallel Q') (i, i) F_P \subseteq (F_{P - \{i\}} \cup Q \parallel Q') F_P \] and similarly for $y$. Hence, if tuple belongs to $id$ then we are done. Assume $i \xrightarrow{a} x \in \rightarrow_P$ and $y = i$ (the other case is proved in exactly the same way), then $u = x$ and $v \in F_Q$. Since $(x, i)$ is a final state, we have $F_{Q \parallel Q'} = (F_{Q' - \{i\}}) F_Q$ and $x' \in F_{P - \{i\}}$. Hence $(u, v) \in F_{P \parallel Q} \times F_{Q' \parallel Q'}$. Finally, since simulation preserves reachability, the reachable part of $(P \parallel Q)(P' \parallel Q')$ is simulated by the reachable part of $PP' \parallel QQ'$. Proposition 25. The sequential composition is (conditionally) continuous from the left and the right in $\text{Aut}$. That is, if $(\bar{P})_i$ is a $\leq$-directed set of finite automata with limit $P$ then sup, $P_i K = PK$ and sup, $K P_i = KP$. We denote $\text{Aut}_f$ the set of finite automata satisfying the reachability and initiality conditions. $\text{Aut}_f$ is a subalgebra of $\text{Aut}$. The proof is similar to our proof in [9]. The only difference is from the manipulation of 0 (because we do not have $x0 = 0$ in this setting) and hence Proposition 25 is a generalised version of the continuity in [9]. Proof. We first define a notion of residuation on $\text{Aut}_f$. For automata $P$ and $Q$ we define the automaton $P \parallel Q$ with initial state $iP/\parallel Q = iP$, final states $F_{P \parallel Q} = \{x \in P \mid Q \leq P_{x}\}$, where $P_x$ is constructed from $P$ by making its initial state into $x$. We make the resulting automaton reachable by discarding all states not reachable from $x$. Notice that $P_x$ does not necessarily satisfy HCl. In this case, we unfold each transition from $x$ once and isolate $x$ but keeping a disjoint copy of it to make sure that the resulting automaton is bisimulation equivalent to the non-rooted version. We now show that $RQ \leq P$ iff $R \leq P/\parallel Q$. Assume $S$ is a simulation from $R$ to $P$. That means $S$ generates a simulation from $Q$ to $P_x$ for some $x$. It follows from the definition of $P/\parallel Q$ that $S$ generates a simulation from $R$ to $P/\parallel Q$, since the state $x$ become yielding indeed a simulation of precisely all $Q_i$ for some is simulated. Obviously, that is, the set of all those states in hence there is a set of states $X$ for all final states $x \in F_{P/Q}$. Moreover, there is a relation $T : P/Q \to P$ satisfying all properties of simulation except the final state property, namely a restriction of the identity relation $id_P$. We can show that $T' = (\cup_i S_x) \cup T$ is indeed a simulation from $(P/Q)Q$ to $P$ and $S' \circ T'$ is a simulation from $Q$ to $P$. It then follows from general properties of Galois connections that $(H)$ is (conditionally) additive, hence right continuous. It remains to show left continuity. Let $(Q_i)_i$ be a directed set of automata such that $sup_i Q_i = Q$ and let $P$ be any automaton. Then $sup_i (PQ_i) \leq PQ$ because multiplication is monotone and it remains to show $PQ \leq sup_i (PQ_i)$. Let us assume that $sup_i (PQ_i) \leq R$. We will show that $PQ \leq R$. By definition of supremum, $PQ_i \leq R$ for all $i$, hence there is a set of states $X_i = \{x \in R \mid Q_i \leq R_x\}$, that is, the set of all those states in $R$ from which $Q_i$ is simulated. Obviously, $X_i \subseteq X_j$ if $Q_j \leq Q_i$ in the directed collection. But since $R \in \text{Aut}_f$, it has only finitely many states, there must be a minimal set $X$ in that directed set such that all $Q_i$ are simulated by $R_x$ for some $x \in X$. Therefore $Q = sup_i Q_i \leq R_x$ for all $x \in X$. There exists a simulation $S_X : PQ_i \to R$ for some $i$ such that the residual automaton $R/Q_i$ has precisely $X$ as its set of final states. We can thus take the union of $S_X$ restricted to $P$ with all simulations yielding $Q \leq R_x$ for all $x \in X$ and verify that this is indeed a simulation of $PQ$ to $R$. We denote $L(P) = \{t \mid t$ is a tree and $t \leq P\}$ the tree language associated to $P$. We have Lemma 26. $P \leq Q$ iff $L(P) \subseteq L(Q)$. A specialized version of this theorem could be found in [3]. In this paper, we prove it for our rooted $\eta$-simulation. Proof. By transitivity of simulation, we have $P \leq Q$ implies $L(P) \subseteq L(Q)$ so it suffices to show the converse. Let $L(P) \subseteq L(Q)$ and consider the relation $S : P \to Q$ such that $(x, y) \in S$ if $L(P_x) \subseteq L(Q_y)$, where $P_x$ is the automata constructed from $P$ with initial state $x$ as in the previous proof. We now show that the rooted version of $S$ is a simulation. - Since $L(P) \subseteq L(Q)$, we have $(ip, iq) \in S$. - Let $(x, y) \in S$ and $x \in F_P$, then $1 \in L(P_x) \subseteq L(Q_y)$. Hence $y \in F Q_i$. - Let $(x, y) \in S$, $L(P_x) \subseteq L(Q_y)$ and $x \overset{x}{\to} x'$ be a transition of $P$. There are two cases: a) $a$ is internal: for any tree $t$, $at \leq t$. Hence $L(P_{x'}) \subseteq L(Q_y)$ i.e. $(x', y) \in S$. b) $a$ is external: assume for a contradiction that for each $y' \in Q$ such that $y \overset{a}{\to} y'$, there exists $t_i \in L(P_{x'})$ such that $t_i \notin L(Q_{y'})$. Since $Q \in \text{Aut}_f$, there are only finitely many such $y'$. It then follows from general properties of Galois connections that $P$ is indeed a simulation from $R$ to $P/Q$. By construction of $P/Q$, we know that there exists a simulation $S_f$ from $Q$ to $P$ for all final states $x \in F_{P/Q}$. Hence $R = R \leq P/Q \leq P$. - Making the relation $S$ rooted does not affect the well-definedness of $S$ as a simulation because the automata $P, Q$ are rooted. Proposition 27. The concurrency operator $\parallel$ is (conditionally) continuous in $\text{Aut}_f$. Proof. We need to show that for any $\leq$-directed sequence $(Q_i)_i \subseteq \text{Aut}_f$ such that $sup_i Q_i = Q$, we have $sup_i (P\parallel Q_i) = P\parallel Q$, where the frame is left implicit. Firstly, we show that $L(P \parallel Q) = \downarrow (L(P) \parallel L(Q)) = \downarrow \{t \parallel t' \mid t \in L(P) \land t' \in L(Q)\}$. where $\downarrow X$ is the down closure of $X$. Since $\parallel$ is monotone, $t \parallel t' \in L(P \parallel Q)$. Conversely, let $t \in L(P \parallel Q)$. By unfolding $P$ and $Q$ up to the depth of $t$, we can find two tree $t_P, t_Q$ such that $t \leq t_P \parallel t_Q$ and hence $t \in \downarrow (L(P) \parallel L(Q))$. Secondly, we have $$L(P \parallel Q) = \downarrow \{t \parallel t' \mid t \in P \land t' \in L(Q)\} = \downarrow \cup_i \{t \parallel t' \mid t \in P \land t' \in L(Q_i)\} = \cup_i L(P \parallel Q_i)$$ and directedness ensures that $L(Q) = \cup_i L(Q_i)$. Therefore, Lemma 26 ensures that $P \parallel Q = sup_i (P \parallel Q_i)$. Remark 28. The following remarks ensures the existence of an $\omega$ function satisfying the properties listed in Section 6. 1. The axiom $\pi \tau = \tau$ ensures that $o(x) \in \{0, \tau, 1\}$ for any $x \in T \Sigma$. If $o(x) = 0$ then $x$ will never terminate successfully. If $o(x) = 1$, then $x$ may terminate successfully without the execution of any 2. The interpretation of $o$ in the concrete model respects simulation. In fact, let $P, Q$ be the automata representing some terms in $T_{\Sigma}$ and $S : P \rightarrow Q$ a simulation. After replacing each action in $P, Q$ by $\tau$, $S$ remains a simulation by Property (a) of Definition\[12\] Therefore - if $o(P) = 1$ then the initial state of $P$ is final and so is the initial state of $Q$, - if $o(P) = \tau$ then the initial state of $P$ leads to some final state and so is the initial state of $Q$ i.e. $1 \leq o(Q)$, - if $o(P) = 0$ then we are done, and in all three cases $o(P) \leq o(Q)$. Hence, it is safe to assume that $o$ is well defined on $T_{\Sigma}$ modulo the axioms of weak concurrent Kleene algebra. In particular, $o$ is monotonous with respect to the restriction of the natural order of the algebra on $I$. 3. The last property $o(x\|\|y) \leq o(x)o(y)$ is in general a strict inequality. For instance, if $a, b$ are synchronised actions then $o(a\|\|b) = o(0) = 0$ but $o(a)b(0) = \tau\tau = \tau$. Proposition 29. In $\text{Aut}$, $\sqsubseteq_{\text{sy}}$ reduces to language equivalence. Remind that we assume there is only one non-trivial internal action, namely $\tau$, and it satisfies $\tau\tau = \tau$. Proof. Firstly, the language of the automata associated to $x$ is given by $$Tr(x) = \{t \mid t \text{ is linear, loop-free, has only } \tau \text{ as non-synchronised action and } t \leq x\}$$ where $x \leq y$ if there is a simulation between the automata represented by $x$ and $y$ such that all non-synchronised actions are replaced by $\tau$. This ensures for instance that $Tr(\tau) = \tau$. Remind that $Tr(x\|\|y) = Tr(x) \cap Tr(y)$ because elements of $Tr(x)$ are of the form $w\tau$ or $w$ (modulo the equivalence from $\leq_{\tau}$) where $w$ is a word formed of synchronised actions only. For the direct implication, assume $x \sqsubseteq_{\text{sy}} y$ and let $t \in Tr(x)$. Then $o(x)[t] \neq 0$ and since $x\|\|t \leq y\|\|t$, we have $o(y)[t] \neq 0$. Since $t$ has synchronised actions only (or possibly ends with $\tau$) and $o(y)[t] \neq 0$, then $t \in Tr(y)$ that is $Tr(x) \subseteq Tr(y)$. Conversely, let $Tr(x) \subseteq Tr(y)$ and $z \in T_{\Sigma}$. $$Tr(x\|\|z) = Tr(x) \cap Tr(z) \subseteq Tr(y) \cap Tr(z) = Tr(y\|\|z).$$ So if $o(y)[z] = 0$ then $y\|\|z$ has no final state and hence $Tr(y\|\|z) = \emptyset$. Hence $Tr(x\|\|z) = \emptyset$ i.e. $x\sqsubseteq_{\text{sy}} y$ has no final state that is $o(x\|\|z) = 0$. B Specification of Rabin’s Protocol. Remind that $P(\alpha, k)$ is the specification of a tourist in from of the door $\alpha \in \{m, c\}$ and has $k$ written on his notepad (Figure 8). ![Diagram](image-url) Figure 8: Interpretation of $P(\alpha, k)$ in term of automata with implicit probability. Any action of the form $[a]$ are considered internal. The symbol $o$ denotes final states and $\bullet$ is a deadlock state. In this protocol, deadlock state is used to specify that the tourist has come to a decision and the common place would be the value of $a$ when the deadlock state is reached. Theorem 30. In the concrete model, the specification of Rabin’s protocol satisfies $$S = [[[P + Q]M]^n(P + Q)[C]^]$$ Firstly, notice that if $\cdot$ is (conditionally) continuous then $x^ = \sup_{\alpha \in \gamma}(1 + x)^n$. The proof relies on the fact that $f^n_{\tau}(0) = (1 + x)^n$ where $f_{\tau}(y) = 1 + x \cdot y$ and the result follows by taking the limit. Proof. The above property allows us to express $x^*$ as the limit of finite iterations of $x$ interleaved with successful termination. We have $$(P + Q)^n \|\| (M + C)^n = \sup_{m \leq n} (1 + P + Q)^m \|\| (1 + M + C)^n$$ The processes $P$ and $Q$ are essentially delimited by $\alpha?K$ and $\alpha!K$ which ensures the following properties of the system $$X \cdot A \|\| Y \cdot B = [X][Y] \cdot [A][B] \quad (17)$$ $$X \cdot A \|\| 1 = 0 \quad (18)$$ $$Y \cdot B \|\| 1 = 0 \quad (19)$$ for every processes $A, B$ and where $X = P + Q$ is the collection of tourists and $Y = M + C$ is the collection of places. In particular, $$1 \|\| (1 + X)^n = 1 \|\| (1 + X)^n - 1 + 1 \|\| X \cdot (1 + X)^n = 1 \|\| (1 + X)^{n-1}$$ and by induction, since $1\\|1 = 1$, \[ 1\\|(1+X)^n = 1 \quad (20) \] for every $n \in \mathbb{N}$. Similarly, $1\\|(1+Y)^n = 1$. On the other hand, let us denote $T_{m,n} = (1+X)^m\\|(1+Y)^n$, then \[ T_{m,n} = \left[ (1+X)^{m-1} + X \cdot (1+X)^{m-1} \right] \left( [1+Y]^{n-1} + Y \cdot (1+Y)^{n-1} \right) \] \[ = T_{m-1,n-1} + X \cdot (1+X)^{m-1} \\|[1+Y]^{n-1} + (1+X)^{m-1}Y \cdot (1+Y)^{m-1} + [X\\|Y] : T_{m-1,n-1} \] \[ = (1+X\\|Y) \cdot T_{m-1,n-1} + U_{m-1,n-1} + V_{m-1,n-1} \] where \[ U_{m-1,n-1} = X \cdot (1+X)^{m-1} \\|[1+Y]^{n-1} \] \[ = U_{m-1,n-2} + [X\\|Y] \cdot T_{m-1,n-2} \] \[ = U_{m-1,n-3} + [X\\|Y] \cdot T_{m-1,n-3} + [X\\|Y] : T_{m-1,n-3} \] Since the sequence $(1+Y)^n$ is monotone, $T_{m,n} \leq T_{m,n'}$ for every $n \leq n'$ and therefore $U_{m-1,n-1} \leq U_{m-1,0} + [X\\|Y] \cdot T_{m-1,n-1}$. But Property 18 implies that $U_{m-1,0} = 0$. Similarly, $V_{m-1,n-1} \leq [X\\|Y] \cdot T_{m-1,n-1}$. Hence \[ T_{m,n} = (1 + [X\\|Y]) \cdot T_{m-1,n-1}. \] By induction, we show that \[ T_{m,n} = (1 + [X\\|Y])^{\inf(m,n)} \] because $T_{0,n} = T_{m,0} = 1$ by Equation 20. Finally, we have \[ X^\ast\\|Y^\ast = \sup_m \sup_n (1+X)^m\\|(1+Y)^n \] \[ = \sup_n (1 + [X\\|Y])^n \] \[ = (X\\|Y)^\ast \]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4931, 1 ], [ 4931, 10676, 2 ], [ 10676, 16356, 3 ], [ 16356, 21782, 4 ], [ 21782, 27416, 5 ], [ 27416, 32782, 6 ], [ 32782, 39320, 7 ], [ 39320, 43556, 8 ], [ 43556, 46743, 9 ], [ 46743, 47941, 10 ], [ 47941, 53637, 11 ], [ 53637, 54170, 12 ], [ 54170, 60731, 13 ], [ 60731, 64663, 14 ], [ 64663, 69676, 15 ], [ 69676, 73870, 16 ], [ 73870, 75090, 17 ] ] }
3d5f4a6565ff99f8962bbf1c76e803d2d68456e0	{ "olmocr-version": "0.1.59", "pdf-total-pages": 11, "total-fallback-pages": 0, "total-input-tokens": 58735, "total-output-tokens": 10112, "fieldofstudy": [ "Medicine", "Education" ] }	Randomized Controlled Trial Targeting Obesity-Related Behaviors: Better Together Healthy Caswell County Jamie Zoellner, PhD, RD; Jennie L. Hill, PhD; Karissa Grier; Clarice Chau, MS; Donna Kopec; Bryan Price; Carolyn Dunn, PhD Suggested citation for this article: Zoellner J, Hill JL, Grier K, Chau C, Kopec D, Price B, et al. Randomized Controlled Trial Targeting Obesity-Related Behaviors: Better Together Healthy Caswell County. Prev Chronic Dis 2013;10:120296. DOI: http://dx.doi.org/10.5888/pcd10.120296. Abstract Introduction Collaborative and multilevel interventions to effectively address obesity-related behaviors among rural communities with health disparities can be challenging, and traditional research approaches may be unsuitable. The primary objective of our 15-week randomized controlled pilot study, which was guided by community-based participatory research (CBPR) principles, was to determine the effectiveness of providing twice-weekly access to group fitness classes, with and without weekly nutrition and physical activity education sessions, in Caswell County, North Carolina, a rural region devoid of medical and physical activity resources. Methods Participants were randomly divided into 2 groups: group 1 was offered fitness sessions and education in healthful eating and physical activity; group 2 was offered fitness sessions only. Outcome measures were assessed at baseline and immediately after the intervention. Standardized assessment procedures, validated measures, and tests for analysis of variance were used. Results Of 91 enrolled participants, most were African American (62%) or female (91%). Groups were not significantly different at baseline. Group 1 experienced significantly greater improvements in body mass index ($F = 15.0, P < .001$) and waist circumference ($F = 7.0, P = .01$), compared with group 2. Both groups significantly increased weekly minutes of moderate physical activity ($F = 9.4, P < .003$). Participants in group 1 also had significantly greater weight loss with higher attendance at the education ($F = 14.7, P < .001$) and fitness sessions ($F = 18.5, P < .001$). Conclusion This study offers effective programmatic strategies that can reduce weight and increase physical activity and demonstrates feasibility for a larger scale CBPR obesity trial targeting underserved residents affected by health disparities. This study also signifies successful collaboration among community and academic partners engaged in a CBPR coalition. Introduction Obesity is a widely recognized public health concern in the United States (1). Various individual, social, community, and environmental factors contribute to obesity-related behaviors (2). For rural areas with few resources, such as the Dan River Region in south-central Virginia and north-central North Carolina, providing collaborative and multilevel interventions to effectively address obesity-related behaviors is challenging. The Dan River Region includes Pittsylvania and Henry counties in Virginia and Caswell County in North Carolina. A rural area with health disparities, the Dan River Region is classified as a medically underserved area (3–7). Despite the need for health evaluation data in vulnerable regions, using traditional research approaches can be difficult because of geographic location and lack of 1) community trust, 2) local health professionals and services, and 3) local qualified researchers to oversee research activities. However, the community-based participatory research (CBPR) approach can be used to overcome these obstacles. The CBPR approach is designed to build equitable community-academic partnerships, encourage community participation in all aspects of the research process, and promote program sustainability (8–10). The intervention reported here was planned and implemented in the context of a CBPR coalition, the Dan River Partnership for a Healthy Community (DRPHC). The DRPHC’s mission is to foster community partnerships to combat obesity in the Dan River Region through healthy lifestyle initiatives. As described elsewhere, community stakeholders developed 6 obesity causal models (11). This 15-week randomized controlled study is the first pilot intervention from the physical activity priority area. The primary aim is to determine the effectiveness of providing twice-weekly access to group fitness classes, with and without weekly nutrition and physical activity education sessions. Weight and physical activity are the primary outcomes of interest; secondary outcomes are waist circumference, blood pressure, dietary behaviors, and psychosocial variables. A secondary aim is to explore relationships among attendance levels at fitness and education sessions and the anthropometric and biologic outcomes. Methods The study was conducted in Caswell County, North Carolina, which is classified as an 8 on the 9-point Rural-Urban Continuum Codes (1 = urban, 9 = completely rural) (12). The median household income of $34,747 is below average for the state ($39,061) and the nation ($41,994) (13). The county is approximately 34% African American and 63% white. Caswell County has fewer than 2 recreation and fitness facilities and high rates of obesity and diabetes compared with the rest of North Carolina (14). After a physical activity program was selected as the intervention (11), a DRPHC physical activity subgroup was formed. Through regular committee meetings, community partners provided feedback on the design of the study, the selection of the education curriculum, logistics of providing group fitness and education classes, processes for randomization, and data assessment procedures including the selection and review of psychosocial measuring instruments. The committee held a 90-minute listening session with a convenience sample of 12 Caswell County residents (11 female, 1 male; 8 African American, 4 white). Semistructured questions were used to ask residents about their preferences for session days and times, topics of interest, types of fitness offerings, recruitment methods, barriers to program participation, participant accountability, and data collection procedures. Recruitment procedures and eligibility Participants were recruited through an advertisement in the local paper, flyers posted around town, and word of mouth. Interested community members called the local health department and were screened. Eligibility criteria were being aged 18 or older, speaking English, and having no self-reported exercise contraindications. Study design and intervention Participants in this 15-week randomized controlled pilot study were randomly assigned to 1 of 2 groups. All participants received access to 2 weekly group fitness classes, offered free of charge at the Caswell County Parks and Recreation Building. Zumba classes were offered 1 night a week, and the other evening was a “potluck” night designed to increase participants’ exposure to other classes (eg, aerobics, kickboxing, line dancing). Participants in the intervention group (group 1) were enrolled in Eat Smart, Move More, Weigh Less (ESMMWL) and received weekly 1-hour classes on healthy eating and physical activity (15,16). The ESMMWL curriculum was established on evidence-based weight loss principles and strategies. The curriculum is guided by the theory of planned behavior, which empowers and motivates participants to live mindfully as they make choices about eating and physical activity (17). Each lesson includes discussion related to 1) a behavior (eg, controlling or decreasing portion sizes; eating more meals at home; increasing physical activity) and its importance to the participant’s weight goal; 2) how family and friends can support the behavior change; and 3) strategies for adopting the behavior (eg, interpreting food labels, keeping a food and physical activity record). The program has been field tested and disseminated through the North Carolina extension system; however, this study is the first known to document effects in a randomized controlled study (15,16). All phases of this research were approved by Virginia Tech’s institutional review board, and participants provided written informed consent forms. Attendance was tracked at all sessions. Among the 50% of participants who provided e-mail addresses, 10 reminder e-mails were sent via a listserv. Participants who were absent for 2 or more consecutive weeks received approximately 1 weekly reminder or encouragement telephone call or a personalized e-mail. Raffle prizes (eg, measuring utensils, exercise DVDs) to reward attendance were provided at regular intervals in both the group fitness and education session. Education sessions were led by 1 Caswell County Health Department employee who had completed certification for the ESMMWL curriculum. The fitness sessions were delivered by local experienced instructors, including 1 who taught Zumba and 3 others who led the potluck night. Outcome measures and randomization All outcome measures were assessed at baseline and immediately after the intervention. A data collection manual of procedures was developed to standardize all assessments. Data were collected in person, in a private setting, and questionnaires were read aloud by trained and certified research staff who were blinded to the participants’ group assignment. To promote transparency in the randomization procedures, an equal number of cards marked “group 1” or “group 2” were concealed in an envelope, and participants drew their own random assignment at the end of baseline enrollment. Participants were provided a $10 gift card for completing each assessment time point. Anthropometric variables and blood pressure Height, weight, waist circumference, and blood pressure were measured, respectively, with a portable stadiometer, Tanita body fat analyzer model TBF-310GS (Tanita, Arlington Heights, Illinois), nonstretchable flexible measuring tape, and an OMRON HEM-907XL (OMRON Group, Lake Forest, Illinois) automatic inflation sphygmomanometer. Participants received a personal assessment that compared their values with healthy ranges. Self-reported variables The valid and reliable Godin measure and the National Cancer Institute’s Five-Factor Screener were used to assess self-reported physical activity and nutrition behaviors (18–20). Health-related quality of life was assessed with the Centers for Disease Control and Prevention’s (CDC’s) Healthy Days core module (http://www.cdc.gov/hrqol/hrqol14_measure.htm). The validated Newest Vital Sign was used to assess health literacy (21). Validated psychosocial measuring instruments (22,23) were used, including instruments to measure self-efficacy and social support for both physical activity and nutrition. Cronbach’s alphas calculated on the baseline data indicated strong internal consistency for each psychosocial scale (α ≥ .90). The follow-up data collection concluded with 7 open-ended questions to explore participants’ opinions of the project and to inform future programming. Data analyses Descriptive statistics were used to summarize variables. Tests for analysis of variance (ANOVA) and generalized linear models were used to examine effects. Two analytical approaches were used: an intent-to-treat analysis that uses the last observation carried forward method (eg, for noncompleters, baseline value is substituted for postintervention value [assumes a zero change]), and complete cases-only analysis (24). Findings did not vary by approach; therefore, intent-to-treat results are presented. Analyses were performed using SPSS 20.0 software (IBM, Chicago, Illinois). A critical value of α = .05 was adopted for significance testing. For the open-ended questions, comments were first coded as specific to group fitness, to education, or nonspecific. Comments were then further coded as positive or negative and subsequently examined for emerging themes. Results Of the 102 people who called to inquire about the study, all were screened, met the screening inclusion criteria, and were scheduled for an enrollment appointment (Figure 1). At enrollment, 2 participants with blood pressure higher than 180/110 mm Hg were referred for immediate medical attention; both received medical release and were enrolled. In total, 91 participants completed enrollment and were randomly assigned to a group in the trial (44 in group 1 and 47 in group 2). Attendance at group fitness sessions averaged 10.3 of 28 sessions (standard deviation [SD], 9.6) for group 1 and 7.6 of 28 (SD, 8.7) for group 2 (F = 1.85; P = 0.18) (Figure 1). Attendance at education sessions for group 1 averaged 6.6 (SD, 5.4) of 14 sessions. Postintervention data was available on 58 participants (64%). Figure 1. Recruitment, screening, and participation in Better Together Healthy Caswell County, North Carolina, 2011. [A text description of this figure is also available.] Most participants were women (91%) and African American (62%) (Table 1). Education and income levels indicate a broad representation of socioeconomic status. Most participants were obese (31%) or morbidly obese (49%). Approximately 40% of the participants had a high likelihood of limited health literacy. No significant group differences were noted at baseline. Furthermore, demographics were not significantly different among postintervention completers and noncompleters. Body mass index and waist circumference improved significantly between baseline and follow-up (Table 2). Group 1 participants achieved significantly greater improvements in BMI and waist circumference than did those in group 2. We found no significant effects on blood pressure. For self-reported physical activity, moderate activity increased from baseline to follow-up, yet we found no significant differences between groups on the physical activity measures. For self-reported dietary intake, with the exception of a decrease in amount of sugar used, we noted no changes in dietary variables. Significant time effects were seen for self-efficacy for physical activity (decrease) and friend support for healthy eating (increase); however, there were no significant effects for other psychosocial variables. Group 1 had significant weight loss effects by level of attendance at sessions (<50% or ≥50%): education attendance ($F = 14.7, P < .001$) and fitness attendance ($F = 18.5, P < .001$) (Figure 2). Significant effects for waist circumference were found by education attendance ($F = 11.6, P < .001$) and fitness attendance ($F = 5.8, P = .02$) (Figure 3). For group 2, effects were not significant by group fitness attendance (Figure 3). ![Figure 2](image2.png) Figure 2. Weight change by attendance at group education sessions and group fitness sessions (N = 91), Better Together Healthy Caswell County, North Carolina, 2011. [A text description of this figure is also available.] ![Figure 3](image3.png) Figure 3. Change in waist circumference by attendance at group education sessions and group fitness sessions (N = 91), Better Together Healthy Caswell County, North Carolina, 2011. [A text description of this figure is also available.] Waist circumference differed significantly by percentage of education and fitness sessions attended. Group 1 members who attended 50% or more of the education sessions decreased waist circumference more than did those who attended less than 50% of the sessions, $P < .001$. Group 1 members who attended 50% or more of the fitness sessions also had greater changes in waist circumference than did those who attended less than 50% of the sessions, $P = .02$. Fifty-eight participants completed the qualitative exit questionnaire. Responses indicated that group fitness was well received and Zumba was the favored activity. The nutrition classes were also well received, although many participants requested a personalized planning component. Group cohesion and accountability also contributed to an enjoyable experience. Participants recommended that future programs have more sessions and serve more people. Discussion Our findings are congruent with those of systematic reviews that found that exercise plus diet programs tend to be superior at producing and maintaining weight loss compared with programs that promote weight loss through diet alone or physical activity alone (25,26). Although both groups reported increases in moderate physical activity and experienced significant changes in weight, participants in the intervention group (group 1), who could attend weekly classes on healthy eating and physical activity in conjunction with twice-weekly group fitness classes, had significantly greater weight loss than did participants who had access only to fitness classes (group 2). On average, participants in group 1 lost about 3% of their baseline weight, whereas those in group 2 lost <0.5%. Clinically meaningful weight loss is typically defined as a 5% to 10% reduction in baseline weight, an amount that improves numerous risk factors associated with obesity (26,27). Although our study did not reach this threshold of clinical significance, our 15-week pilot trial was shorter than most weight loss programs (eg, 6–18 months); longer programs generally result in more weight loss (26,27). Likewise, although on average participants did not achieve CDC’s recommendation of 150 min/wk of moderate-to-vigorous physical activity, participants’ combined amount of moderate and vigorous physical activity nearly doubled. These improvements resulted in a naturally occurring community setting, where conditions were much less controlled than in clinical trials. Although our primary outcomes improved as hypothesized, several secondary outcomes did not change. For example, we hypothesized a greater improvement in dietary variables among the participants randomized to receive the ESMMWL curriculum (group 1). Null findings may be due, in part, to limitations of the screener used to assess dietary changes (19). The screening instrument was selected because of its low respondent burden and ease of use and scoring; however, the instrument was developed for use at the population level and was not validated for use at the individual level. Future studies should include dietary methods sensitive enough to detect changes at the individual level. Similarly, we hypothesized that participants receiving the ESMMWL curriculum would achieve greater improvements in the psychosocial variables related to healthy eating. Although this curriculum was grounded in the theory of planned behavior, related measures to evaluate changes in theoretical constructs associated with the curriculum have not been developed (15–17). The chosen instruments and underlying constructs (self-efficacy and family and friend support) were determined to be the most culturally relevant for the participants and consistent with the efforts of the DRPHC physical activity subcommittee. Future research is needed to develop and evaluate culturally appropriate psychosocial instruments that are matched to the goals and underlying theoretical constructs of the ESMMWL curriculum. In addition, self-efficacy for physical activity significantly decreased from baseline to follow-up among both groups. This phenomenon has been observed in other behavioral trials, as participants engage in physical activity and realize the difficulty in maintaining such efforts (28). The relationship among levels of participation and outcomes also help inform future sustainable programs. The attendance expectations for the 15-week program were high. Although arguably necessary to help meet physical activity recommendations and provide adequate education time, engaging participants in structured activities 3 nights a week may be unrealistic. Nonetheless, group 1 participants who attended more than 50% of the sessions achieved clinically significant weight reductions (5.5%–6.3%) compared with those who attended less than 50% of the sessions. This positive relationship between high attendance and the desired outcome is consistent with findings of other studies (29). Future study is needed to develop scalable approaches that can provide educational content and motivational support yet adequately reach geographically dispersed residents with hectic lifestyles. In the qualitative exit questionnaire, several participants spoke of the need for personal customization of both the fitness and eating regimens. Many participants who were motivated to be physically active but could not attend the fitness sessions regularly because of scheduling conflicts expressed frustration over not receiving recognition for physical activity performed outside of the group fitness sessions. To address these concerns, regular collection and review of the participants’ records and diaries of all food and physical activity behaviors, along with a feedback loop and reward system, should be considered for future programs. Furthermore, many members of group 1 commented on the relationships they built with their peers. Incorporating evidence-based principles on group dynamics (30) may strengthen the delivery process, enhance the participants’ experiences and retention rates, and improve future intervention effects. In the context of guiding CBPR principles, the less tangible outcomes are perhaps the most important (8,9). For most DRPHC stakeholders and participants involved in this study, this was their first exposure to any aspect of research. The collaborative process involved in this study helped create an atmosphere of shared ownership in the research process and in the evaluation components. Study procedures, enrollment and participation rates, and outcome data were disseminated at the monthly DRPHC coalition meetings. This procedure allowed the researchers to understand the unique needs and dynamics of the community and make protocol adjustments accordingly, and it helped community stakeholders gain an appreciation for the research process. Collaborating with and gaining trust of vulnerable communities are essential elements of CBPR and are necessary to promote program sustainability. Obesity prevalence among the enrolled community sample and the lack of regional physical activity resources (14) signify the need for evidence-based weight-management programs in this region. The relationships forged through this pilot study created a critical alliance that was used as leverage when proposals were submitted for other obesity-related intervention grants. This study has limitations. These findings may be generalizable only to women and individuals who are motivated to change behavior and lose weight. Our attrition rates also have the potential to bias our results. We explored this concern by using both intent-to-treat and present-at-follow-up analyses, and findings did not vary by analytical approach. Nevertheless, we purposefully chose to present data from the intent-to-treat analysis and to account for all enrolled participants because this method is the more conservative and produces the more generalizable estimate of effects. Furthermore, although the study was adequately powered to determine primary outcome effects, it may be underpowered to determine secondary outcome effects. Likewise, although we used validated instruments, they may not have been the best fit for the curriculum. Despite these limitations, this pilot study sufficiently achieved the desired outcomes of informing the feasibility of implementing larger scale community-based experimental interventions in the region and promoting collaboration and resource-sharing among members of the CBPR coalition. Future programs of similar design should attempt to account for potential contamination across groups (e.g., group randomization, postassessments to determine information sharing with acquaintances in different groups). Our pilot findings suggest that giving people access to 15 weeks of free group fitness can increase minutes of moderate physical activity in a region that has health disparities and lacks physical activity resources, but such access alone is insufficient to improve weight outcomes. To effectively improve weight outcomes, access to both physical activity and educational programs is needed. This study also signifies a successful collaboration among several community–academic partners engaged in a CBPR coalition. Future studies are needed to determine the long-term clinical effectiveness and cost-effectiveness of similar efforts and the ability of the DRPHC coalition and local organizations to sustain programs that provide access to free physical activity and weight management. Acknowledgments The authors declare that they have no competing interests. We thank the members of the DRPHC physical activity subcommittee and larger DRPHC coalition for their time, effort, and enthusiasm in the development and execution of this project. We thank Ashley Williams from Caswell County Parks and Recreation Department and the staff with Get Fit (Stephanie Ferrugia and Ciji Moore) for their contributions in executing the group fitness sessions. We thank Frederick Moore, MD, for his collaboration and for allowing events to take place at the Caswell County Health Department. We thank Terri Corsi for her project management contributions and review of the manuscript. Finally, we thank all the Virginia Tech graduate and undergraduate students who assisted with data collection and data management, including Ashley Zanko, Monica Motley, Lauren Noel, Emily Cook, Kacie Allen, Jess Floro, Maggie Reinhold, and Kathleen Collins. Author Information Corresponding Author: Jamie Zoellner, PhD, RD, Associate Professor, Virginia Tech, Human Nutrition, Foods, and Exercise, Integrated Life Sciences Bldg 23, Room 1034 (0913), 1981 Kraft Dr, Blacksburg, VA 24061. Telephone: 540-231-3670. E-mail: [email protected]. Author Affiliations: Jennie L. Hill, Karissa Grier, Clarice Chau, Virginia Tech, Blacksburg, Virginia; Donna Kopec, Caswell County Senior Center, Yanceyville, North Carolina; Bryan Price, Danville City Parks and Recreation, Danville, Virginia; Carolyn Dunn, 4H Youth Development and Family and Consumer Science, North Carolina State University, Raleigh, North Carolina. References 1. Flegal KM, Carroll M, Ogden C, Curtin L. Prevalence and trends in obesity among US adults, 1999–2008. JAMA 2010;303(3):235–41. CrossRef PubMed 2. Sallis JF, Owen N, Fisher EB. Ecological models of health behavior. In: Glanz K, Rimer BK, Viswanath K, editors. Health behavior and health education: theory, research and practice. 4th edition. San Francisco (CA): Jossey-Bass; 2008. p. 465–86. 3. Virginia Department of Health. Unequal health across the commonwealth: a snapshot. 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Demographic Characteristics of Participants at Baseline (N = 91), Better Together Healthy Caswell County (North Carolina), 2011 \| Characteristic \| Group 1a (n = 44) \| Group 2b (n = 47) \| P Valuec \| \|--------------------------------\|-------------------\|-------------------\|----------\| \| Sex \| \| \| \| \| Female \| 38 \| 45 \| .11 \| \| Male \| 6 \| 2 \| \| \| Race \| \| \| \| \| African American \| 25 \| 31 \| .37 \| \| White \| 19 \| 16 \| \| \| Education level \| \| \| \| \| High school graduate or less \| 16 \| 18 \| .98 \| \| Some college \| 15 \| 16 \| \| \| College degree \| 13 \| 13 \| \| \| Annual income, $ \| \| \| .90 \| \| <19,999 \| 10 \| 14 \| \| \| 20,000–49,999 \| 22 \| 21 \| \| \| ≥50,000 \| 11 \| 11 \| \| \| Did not answer \| 1 \| 1 \| \| \| Body mass index group \| \| \| .65 \| \| Normal (18.5–24.9 kg/m²) \| 1 \| 0 \| \| \| Overweight (25–29.9 kg/m²) \| 8 \| 9 \| \| \| Obese (30–34.9 kg/m²) \| 15 \| 13 \| \| \| Morbidly obese (≥35 kg/m²) \| 20 \| 25 \| \| \| Health literacyd \| \| \| .22 \| \| High likelihood of limited health literacy \| 5 \| 11 \| \| \| Possibility of limited health literacy \| 11 \| 7 \| \| \| Adequate health literacy \| 28 \| 29 \| \| a Twice-weekly access to group fitness classes plus weekly nutrition and physical activity education sessions. b Twice-weekly access to group fitness classes. c χ² tests. d Assessed using the Newest Vital Sign (21): 0–1 correct answer, high likelihood of limited literacy; 2–3 correct answers, possibility of limited literacy; and 4–6 correct answers, adequate literacy skills. Table 2. Overall and Between Group Effects for Anthropometrics, Blood Pressure, Physical Activity, Dietary Intake, and Psychosocial Constructs (N = 91), Better Together Healthy Caswell County (North Carolina), 2011 \| Variable \| Group 1<sup>a</sup> (n = 44) \| Group 2<sup>b</sup> (n = 47) \| Time Effects<sup>c</sup> \| Group by Time Effects<sup>c</sup> \| \|---------------------------------------\|------------------------------\|------------------------------\|--------------------------\|-----------------------------------\| \| Anthropometrics and blood pressure\| \| \| \| \| \| Body mass index, kg/m<sup>2</sup> \| 35.9 (7.2) \| 34.7 (7.2) \| 36.6 (8.1) \| 36.4 (8.0) \| <.001 \| <.001 \| \| Weight, kg \| 99.6 (24.1) \| 96.5 (23.9) \| 98.0 (20.4) \| 97.6 (20.5) \| <.001 \| <.001 \| \| Waist circumference, cm \| 109.1 (15.7) \| 106.2 (15.9) \| 110.7 (16.5) \| 110.0 (17.1) \| <.001 \| .01 \| \| Systolic blood pressure, mm Hg \| 132.6 (20.6) \| 131.2 (21.0) \| 128.2 (14.7) \| 126.4 (16.0) \| .15 \| .84 \| \| Diastolic blood pressure, mm Hg \| 80.2 (12.1) \| 80.4 (12.7) \| 78.1 (8.0) \| 77.1 (8.0) \| .55 \| .40 \| \| Leisure-time physical activity (min/wk) \| \| \| \| \| \| Moderate activity \| 37.3 (67.6) \| 74.1 (114.6) \| 21.8 (57.9) \| 49.7 (80.5) \| .003 \| .67 \| \| Vigorous activity \| 36.5 (89.1) \| 49.2 (96.6) \| 9.7 (29.7) \| 25.8 (52.3) \| .06 \| .82 \| \| Strength activity \| 8.9 (25.9) \| 14.6 (29.7) \| 11.5 (38.6) \| 7.6 (19.5) \| .79 \| .17 \| \| Dietary intake \| \| \| \| \| \| Sugar, teaspoon \| 17.3 (8.9) \| 13.5 (7.5) \| 17.9 (10.2) \| 15.6 (9.6) \| <.001 \| .24 \| \| Calcium, mg \| 671.7 (111.2) \| 670.0 (110.2) \| 675.9 (86.8) \| 671.4 (91.2) \| .70 \| .87 \| \| Fiber, g \| 20.8 (5.7) \| 20.7 (5.4) \| 21.6 (4.9) \| 21.3 (5.1) \| .75 \| .80 \| \| Fruits and vegetables, servings \| 4.5 (2.3) \| 4.6 (1.8) \| 4.5 (2.2) \| 4.8 (2.2) \| .35 \| .53 \| \| Fruits and vegetables, cup \| 5.4 (8.2) \| 5.0 (4.1) \| 6.0 (9.5) \| 6.8 (9.0) \| .75 \| .46 \| \| Dairy, servings \| 1.0 (0.5) \| 1.1 (0.9) \| 1.1 (0.7) \| 1.1 (0.7) \| .28 \| .31 \| \| Psychosocial measures for physical activity \| \| \| \| \| \| Self-efficacy<sup>e</sup> \| 75.07 (13.88) \| 71.23 (15.24) \| 73.51 (17.43) \| 70.01 (19.46) \| .003 \| .89 \| \| Family support<sup>f</sup> \| 2.96 (1.22) \| 2.98 (1.26) \| 2.81 (0.99) \| 2.86 (1.00) \| .57 \| .83 \| \| Friend support<sup>r</sup> \| 3.42 (0.85) \| 3.48 (0.90) \| 3.11 (1.09) \| 3.14 (1.01) \| .46 \| .76 \| \| Psychosocial measures for nutrition \| \| \| \| \| \| Self-efficacy<sup>e</sup> \| 81.95 (12.53) \| 80.70 (15.26) \| 81.78 (14.07) \| 80.21 (16.00) \| .19 \| .88 \| \| Family support<sup>f</sup> \| 2.61 (0.85) \| 2.61 (0.85) \| 2.53 (0.74) \| 2.69 (0.84) \| .15 \| .15 \| \| Friend support<sup>r</sup> \| 2.96 (0.89) \| 3.08 (0.99) \| 2.77 (0.82) \| 2.89 (0.89) \| .05 \| >.99 \| <sup>a</sup> Twice-weekly access to group fitness classes plus weekly nutrition and physical activity education sessions. <sup>b</sup> Twice-weekly access to group fitness classes. <sup>c</sup> Calculated by F-test for analysis of variance. <sup>d</sup> Groups 1 and 2 were not significantly different (P < .05) at baseline. <sup>e</sup> 100-point continuum scale (0 = certain I cannot, 100 = certain that I can). Defined as confidence in being physical active and eating healthfully under different conditions. <sup>f</sup> Five-point Likert scale (1 = strongly disagree, 5 = strongly agree). Defined as the social influence of people on physical activity and eating behaviors. The opinions expressed by authors contributing to this journal do not necessarily reflect the opinions of the U.S. Department of Health and Human Services, the Public Health Service, the Centers for Disease Control and Prevention, or the authors' affiliated institutions. The RIS file format is a text file containing bibliographic citations. These files are best suited for import into bibliographic management applications such as EndNote, Reference Manager, and ProCite. A free trial download is available at each application's web site.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3419, 1 ], [ 3419, 8954, 2 ], [ 8954, 12729, 3 ], [ 12729, 14187, 4 ], [ 14187, 16058, 5 ], [ 16058, 22491, 6 ], [ 22491, 27482, 7 ], [ 27482, 31762, 8 ], [ 31762, 35134, 9 ], [ 35134, 40862, 10 ], [ 40862, 41403, 11 ] ] }
b1d03aa201ad80fd0d81e6366816b7a7fa381f9a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 8, "total-fallback-pages": 0, "total-input-tokens": 21624, "total-output-tokens": 7577, "fieldofstudy": [ "Medicine" ] }	Treatment-Related Death in Patients with Small-Cell Lung Cancer in Phase III Trials over the Last Two Decades Nobuaki Ochi, Katsuyuki Hotta, Nagio Takigawa, Isao Oze, Yoshiro Fujiwara, Eiki Ichihara, Akiko Hisamoto, Masahiro Tabata, Mitsune Tanimoto, Katsuyuki Kiura 1 Department of Respiratory Medicine, Okayama University Hospital, Okayama, Japan, 2 Department of General Internal Medicine 4, Kawasaki Hospital, Kawasaki Medical School, Okayama, Japan Abstract Introduction: Treatment-related death (TRD) remains a serious problem in small-cell lung cancer (SCLC), despite recent improvements in supportive care. However, few studies have formally assessed time trends in the proportion of TRD over the past two decades. The aim of this study was to determine the frequency and pattern of TRD over time. Methods: We examined phase 3 trials conducted between 1990 and 2010 to address the role of systemic treatment for SCLC. The time trend was assessed using linear regression analysis. Results: In total, 97 trials including nearly 25,000 enrolled patients were analyzed. The overall TRD proportion was 2.95%. Regarding the time trend, while it was not statistically significant, it tended to decrease, with a 0.138% decrease per year and 2.76% decrease per two decades. The most common cause of death was febrile neutropenia without any significant time trend in its incidence over the years examined (p = 0.139). However, deaths due to febrile neutropenia as well as all causes in patients treated with non-platinum chemotherapy increased significantly (p = 0.033). Conclusions: The overall TRD rate has been low, but not negligible, in phase III trials for SCLC over the past two decades. Introduction Chemotherapy is the mainstay of treatment for small-cell lung cancer (SCLC); it is widely accepted that patients with limited-stage SCLC (LD-SCLC) have prolonged survival with systemic chemotherapy when combined with thoracic irradiation [1,2]. Even in patients with extended-stage SCLC (ED-SCLC), chemotherapy has yielded a survival advantage, with a median survival time of over 1 year [3–5]. However, chemotherapy-related toxicity sometimes leads to treatment-related death (TRD) and often to deterioration in the patient’s quality-of-life. Thus, toxicity profile information as well as data on efficacy from phase III trials are essential for a full discussion by physicians and patients in clinical practice. Although there have been many phase III trials involving SCLC patients investigating the efficacy of chemotherapy, few studies have focused specifically on the frequency or pattern of chemotherapy-related fatal toxicity. The aim of this study was to clarify this issue and its time trends over the last two decades, using data from phase III systemic treatment trials that included about 25,000 patients. Materials and Methods Trials We conducted a search for trials reported from January 1990 to March 2010. To avoid publication bias, we identified both published and unpublished trials through a computer-based search of the PubMed database and abstracts from ten past conferences of the American Society of Clinical Oncology, European Society for Medical Oncology, and the International Association for the Study of Lung Cancer. We used the following search terms: lung cancer, chemotherapy, and randomized controlled study. The search was extended by a thorough examination of reference lists from original articles, review articles, relevant books, and the Physician Data Query registry of clinical trials. Trial Selection Phase III trials that investigated the systemic treatment of previously untreated LD- and ED-SCLC patients with cytotoxic agents were eligible. Trials designed with concurrent thoracic radiotherapy (TRT) or prophylactic cranial irradiation sequentially after the induction of chemotherapy were included. Some phase III trials incorporated patients with both LD- and ED-SCLC. Trials that provided data for TRD in each report were included. Clinical trials of salvage chemotherapy (second-line or later-setting) were ineligible. Data collection and data items To avoid bias in the data abstraction process, four medical oncologists (NO, IO, YF, and KH), three of whom (NO, IO, and KH) hold board certificates in medical oncology, abstracted data independently from the trials and subsequently compared the results, as described previously [5–13]. The following information was obtained from each report: year of trial initiation, year of publication, number of patients enrolled and randomized, proportion of patients with a good performance status, proportion of male patients, type of disease stage included (LD only/others), number of treatment arms, published year, and trials designed to assign TRT (yes/no). Table 1. Characteristics of the 97 trials. \| Variables \| Values \| \|------------------------------------------------\|-----------------\| \| Proportion of randomized patients with a good performance status (%) \| \| \| <80 \| 43.3 \| \| 80–90 \| 27.8 \| \| >90 \| 19.6 \| \| Median proportion (range) \| 80.0 (23.0–100) \| \| Proportion of male patients (%) \| \| \| <80 \| 63.0 \| \| 80–90 \| 19.0 \| \| >90 \| 12.0 \| \| Median proportion (range) \| 71.0 (41.0–99.0) \| \| Type of disease stage included (LD only/others)\| 19/78 \| \| No. of treatment arms \| \| \| 2 \| 84 \| \| 3 \| 10 \| \| 4 \| 3 \| \| Published year (median; range) \| 1997 (1990–2009) \| \| Trials designed to assign TRT (yes/no) \| 53/44 \| A good performance status (PS) was defined as an Eastern Cooperative Oncology Group (ECOG) PS of 0 or 1. LD, limited disease; TRT, thoracic radiotherapy. doi:10.1371/journal.pone.0042798.t001 status (PS), proportion of male patients, median age of patients, number of chemotherapeutic regimens, description of the administration of concurrent or sequential thoracic irradiation, treatment regimens in each treatment arm, total number of patients with TRD, cause of TRD in each treatment arm, and the definition of LD or ED (the definitions of LD- and ED-SCLC varied somewhat from trial to trial, but we did not reallocate each patient strictly in this study because we were unable to access individual patient data). All data were checked for internal consistency, and disagreements were resolved by discussion among the investigators. Definition of TRD We defined TRD should satisfy all the followings: 1) death occurring within 4 weeks of the completion of treatment, 2) death ‘possibly,’ ‘probably,’ or ‘definitely’ related to treatment reported by investigators, as defined previously [6,7]. 3) death without clear evidence of any other cause of death (i.e., disease progression). We also defined febrile neutropenia (FN)-associated death, the most common cause of fatal toxicity during chemotherapy [7], as death related to fever of unknown origin without clinically or microbiologically documented infection with absolute neutrophil count <1.0×10⁹/L and fever >38.3°C. In general, more recent trials included in this study defined TRD and/or FN-related death clearly in their reports. However, previous studies tended to be left their definitions vague and not to state them specifically. In response to that situation, we tried best to contact the principal authors of the reports for each trial to clarify this and to get precise number of TRD and FN-related death. In case we could not obtain any additional information despite these intensive efforts, we accepted the number of TRDs and FN-related deaths as was described in those reports. The data we collected from each trial also included the number stratified by representative cause of toxic death other than FN-related one. On the basis of our previous study, the causes of TRD were collected as follows [7]: FN, hemorrhage, renal failure, central nervous system (CNS) disorder, cardiovascular disorder and pulmonary disorder. Hemoptysis, upper and lower gastrointestinal hemorrhages, and disseminated intravascular coagulation- Figure 3. Time trends in chemotherapeutic regimen.* All analyses were weighted by sample size. A. Cisplatin-containing regimen. B. Carboplatin-containing regimen. C. Non-platinum regimen. D. CAV (cyclophosphamide, doxorubicin and vincristine)-based regimen. doi:10.1371/journal.pone.0042798.g003 Figure 4. Time trend in the incidence of TRDs (treatment-related deaths). The analysis was weighted by sample size. A. Overall incidence of TRDs. B. Incidence of FN (febrile neutropenia)-related TRDs. doi:10.1371/journal.pone.0042798.g004 related hemorrhage were all categorized as “hemorrhage”, while both CNS ischemia and hemorrhage were classified as “CNS disorder”. “Cardiovascular disease” included ischemia, infarction, or embolism in any organ other than the CNS (i.e., myocardial infarction and pulmonary embolism). “Pulmonary disorders” included all pulmonary diseases other than pulmonary embolisms, including infection without neutropenia (i.e., pneumonia) [7]. Quantitative Data Synthesis The incidence of TRD was defined as the number of TRDs divided by the number of randomized patients. To derive the annual change in TRD incidence during the observation period, we calculated this number for each year of publication. The association between the year of publication and incidence of TRD was analyzed using linear regression analysis, weighted by sample size. All p-values corresponded to two-sided tests, and significance was set at p<0.05. Statistical analyses were conducted using STATA software (ver. 10; StataCorp, College Station, TX, USA). Results Trial flow and characteristics of the eligible trials Figure 1 shows a flow chart for this study. In total, we identified 97 trials as a result of computer-based and manual searches (File S1). In total, 24,152 patients were randomized and allocated to 208 treatment arms. Table 1 shows the characteristics of all eligible trials. The median proportion of randomized patients with a good PS (0 or 1) and that of male patients in all trials was 80.0 and 71.0%, respectively. Most trials had two chemotherapy arms (86.6%). The number of trials designed to assign TRT in addition to chemotherapy was 53 (54.6%). The median number of randomized patients and proportion of patients with a good PS in each trial increased significantly, with 8.489 patients and 1.075% per year, respectively (regression coefficients = 8.489 and 1.075, corresponding to an 8.489 and 1.075% increase per year; p = 0.003 and 0.009, respectively; Fig. 2A and B). The proportion of male patients, however, showed no particular change over time (Fig. 2C). Time trends in treatment regimens Figure 3 shows the changes in treatment regimens over the past two decades. Regarding platinum-based regimens, the proportion of cisplatin use was largely constant during the period (regression coefficient = 0.599, corresponding to a 0.599% increase per year; p = 0.549; Fig. 3A), while carboplatin (CBDCA)-containing regimens increased yearly (regression coefficient = 2.527 [2.527% increase per year]; p = 0.004; Fig. 3B). In contrast, the use of non-platinum combination regimens and that of cyclophosphamide, doxorubicin, and vincristine (CAV)-based regimens decreased significantly during the two decades, at 3.438% (p = 0.001) and 3.300% (p = 0.001) per year, respectively (Fig. 3C and D). Time trends in overall TRD incidence Data for the calculation of the overall incidence of TRD were available for all 97 trials with their 208 chemotherapy arms (24,152 patients), whereas information about the causes of death were provided for 154 arms (74.0%; 17,570 patients). The crude TRD proportion in the overall cohort was 2.95%. Of these, the most common cause of death was febrile neutropenia (FN) (1.25%), followed by pulmonary disorder (0.45%). The crude TRD proportions of other causes collected in this study were very low compared with FN and pulmonary disorder (hemorrhage 0.03%, renal failure 0.05%, CNS disorder 0.02%, cardiovascular disorder 0.12%, and others 0.18%). Next, we assessed the time trends in TRD incidence. It was stable over the last two decades, with no statistically significant difference (regression coefficient = −0.138; p = 0.15). This corresponds to a 0.138% decrease per year; however, it does mean that, theoretically, the TRD incidence decreased by 2.76% per two decades (Fig. 4A). Further, we assessed which clinical factor affected this time trend (Table 2). In most clinical settings, there was no particular difference in the time trend, whereas, interestingly, when limited to patient cohorts treated with a non-platinum regimen, there was a significant increase in TRD incidence (0.146% increase per year; p = 0.033). We observed no significant increase or decrease in TRD incidence with other treatment regimens, including cisplatin-, carboplatin-, and CAV-based regimens (p = 0.270, 0.390, and 0.570, respectively). Because FN was the most common cause of fatal toxicity during chemotherapy, we focused specifically on the incidence and pattern of FN-related deaths. Overall, there was no significant time trend in TRD, with a regression coefficient of 0.035 and p-value of 0.259 (Fig. 4B). Through the entire period, the proportion of FN-related deaths was similar across the four regimens (cisplatin-based 0.649%, carboplatin-based 0.652%, non-platinum 0.645%, and CAV-based regimens 0.704%). However, the pattern of the time trend was different among the regimens (Fig. 5A-D). Non-platinum regimens were associated with a significant increase in death over the years, with a 0.155% increase per year (regression coefficient = 0.155; p = 0.037; Fig. 5C), while no yearly change in the proportion was observed for the other treatment regimens (cisplatin-, carboplatin- and CAV-based regimens; p = 0.337 [Fig. 5A], 0.857 [Fig. 5B], and 0.123 [Fig. 5D], respectively). Discussion We found that the incidence of overall TRDs tended to decrease over the past two decades, although it was not statistically significant (p = 0.15; Fig. 4A). In contrast, the incidence of FN-related death was fairly stable (Fig. 4B). Additionally, stratified by treatment regimen, non-platinum chemotherapy produced an increased incidence of both TRD (Table 2) and FN-related deaths (Fig. 5C) year by year. In this study, the overall TRD incidence seems to have decreased over the last two decades, with a regression coefficient of −0.138, meaning a decrease of 0.138% per year and 2.76% per two decades (Fig. 4A). This phenomenon might be partly correlated with the observation that the number of trials designed to assess TRT, which included potentially induced fatal pulmonary fibrosis, decreased over the years, with a regression coefficient of −0.162 (0.162% decrease per year; p = 0.042). Another hypothesis is the improvement in supportive care. In NSCLC, even in patients allocated to the best supportive care alone arm, the median survival time was prolonged [14]. Similarly, in SCLC, supportive care improved over time, resulting in a decrease in the incidence of overall TRD. Further exploration is warranted to clarify the essential factors that contributed to this trend. On the other hand, FN-related death was similar over the study period (Fig. 4B). One possible reason for this is that chemotherapeutic agents with relatively high myelotoxicity, such as etoposide or anthracyclines, have been repeatedly studied in clinical trials over the past two decades in SCLC [3,15,16]. Second, one would wonder consider the potential impact of the use of granulocyte colony stimulating factor (G-CSF) on reduction in the risk of FN-related death [17], but G-CSF has been used in phase III trials since the early 1990s, corresponding approximately to the beginning of the target period investigated here [18–20]. Thus, G-CSF usage would likely have equally influenced the incidence of FN-related deaths throughout the study period. Further, controversy persists as to the impact of the prophylactic or routine use of G-CSF on clinical outcome, including treatment-related and overall mortality [21,22]; there is as yet no definitive evidence regarding the impact of its use on outcome. Finally, we have no definitive data to validate the above hypotheses. Novel agents that possess less myelotoxic profiles should be developed to decrease FN-related deaths. Meanwhile, both the overall incidence of TRD and incidence of FN-related death have increased in non-platinum regimens over the years (Table 2 and Fig. 5C). Most of the non-platinum regimens investigated here consisted of multiple agents (i.e., alternating regimens, switching regimens, and combination regimens with three or more drugs) [23–28], which seemed to be more toxic [7]. Assuming that the proportion of FN-related deaths accounted for a large fraction of overall TRDs, the overall TRD incidence in non-platinum regimens may have simply increased in accordance with the increase in FN-related deaths. The absolute number of trials investigating non-platinum regimens has decreased; thus, these findings seem to have less importance for clinical practice. Our study has several limitations. First, this analysis tried to cast a wide net to capture several heterogeneous studies for the database, and the results of this study have several potential confounders and a degree of uncertainty. Second, our analyses were not based on individual patient data. Differences in patient clinical characteristics, unlike differences in the characteristics of the trial arms (chemotherapy regimen), would directly have affected the toxicity profiles. Third, a publication bias may exist. Severely toxic agents or regimens may not have been reported, resulting in an underestimation of the TRD incidence. To reduce this bias, we included both published and unpublished (abstract only) trials. Fourth, actual TRD numbers in this study seemed to be low compared with that was seen in clinical practice [29]. One explanation for this discrepancy may be that the patients eligible in such clinical studies generally tend to have better general conditions than those patients treated in clinical practice. Another explanation is that, in clinical trials, investigators might tend to produce “positive” results; that is, they would deal with true treatment-related deaths as treatment-unrelated deaths unconsciously. Thus, observed TRD numbers in the clinical trials might be smaller than the true value. Finally, the definition of TRD and/or FN-related death might have been somewhat vague. We initially defined both TRD and FN-related death in this study as described in Methods section. However, all the trials we included here did not have identical TRD and FN definitions, which was the major limitation in our abstracted data-based analysis. Given that mentioned above, all our results should be interpreted cautiously. In conclusion, the overall TRD proportion was low and has decreased quite gradually, but is still not negligible in phase III trials for SCLC. Physicians should be aware of these trends and do their best to reduce the risk of fatal toxicity. Supporting Information File S1 The list of 97 trials included in this study and its characteristics. (DOCX) Acknowledgments We thank Drs. Rodrigo Arriagada, Angel Artal-Cortes, Linda Aucroft, Jeffrey Crawford, Allan K. Hackshaw, Nasser Hanna, David F. Heigener, Andreas Hermes, Peter W.M. Johnson, Risako Komaki, Primo N. Lara, Jr., Nathalie Leclercq, Serge Levyraz, Heliee Lichitopoulou, Paul Lorigan, Kell Osterlind, Jean-Louis Pujol, Jean-Paul Sculier, Richard J. Stephens, Nicholas Thatcher, Johanna N. Timmer-Bonte, Thierry Urban and Konstantinos Zarogoulidis for providing valuable information on overall TRD numbers and the causes of TRD in their trials. Author Contributions Conceived and designed the experiments: NO KH YF. Performed the experiments: NO KH YF IO. Analyzed the data: NO KH. Contributed reagents/materials/analysis tools: NO KH YF IO YF EI AH M. Tabata M. Tanimoto KK. References 1. Pigoun JP, Arriagada R, Bide DC, Johnson DH, Perry MC, et al. (1992) A meta-analysis of thoracic radiotherapy for small-cell lung cancer. N Engl J Med 327: 1618–1624. 2. Aupérin A, Arriagada R, Pigoun JP, Le Péhoux C, Gregor A, et al. (1999) Prophylactic cranial irradiation for patients with small-cell lung cancer in complete remission. Prophylactic Cranial Irradiation Overview Collaborative Group. N Engl J Med 341: 476–481. 3. Noda K, Nishiwaki Y, Kawahara M, Negoro S, Sugirua T, et al. 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(1999) The addition of cisplatin to cyclophosphamide-doxorubicin-etoposide combination chemotherapy in the treatment of patients with small cell lung carcinoma: A randomized study of 457 patients. “Petites Cellules” Group. Cancer 86: 2238–2245. 29. Ohe Y, Yamamoto S, Suzuki K, Hojo F, Kakimura R, et al. (2003) Risk factors of treatment-related death in chemotherapy and thoracic radiotherapy for lung cancer. Eur J Cancer 37:54–63.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3994, 1 ], [ 3994, 6354, 2 ], [ 6354, 8661, 3 ], [ 8661, 9204, 4 ], [ 9204, 12814, 5 ], [ 12814, 15062, 6 ], [ 15062, 22626, 7 ], [ 22626, 28032, 8 ] ] }
036f4aa904ff5bf0e87333d585da5f94b2dd581b	{ "olmocr-version": "0.1.59", "pdf-total-pages": 8, "total-fallback-pages": 0, "total-input-tokens": 28761, "total-output-tokens": 8894, "fieldofstudy": [ "Environmental Science", "Agricultural And Food Sciences" ] }	Thermogenesis, Flowering and the Association with Variation in Floral Odour Attractants in Magnolia sprengeri (Magnoliaceae) Ruohan Wang¹, Sai Xu¹,², Xiangyu Liu², Yiyuan Zhang¹, Jianzhong Wang¹, Zhixiang Zhang⁵ ¹ National Engineering Laboratory for Tree Breeding, Key Laboratory for Genetics and Breeding of Forest Trees and Ornamental Plants, Ministry of Education, College of Biological Sciences and Biotechnology, Beijing Forestry University, Beijing, China, ² Lab of Systematic Evolution and Biogeography of Woody Plants, College of Nature Conservation, Beijing Forestry University, Beijing, China, ³ School of Environment, Tsinghua University, Beijing, China Abstract Magnolia sprengeri Pamp. is an ornamental and ecologically important tree that blooms at cold temperatures in early spring. In this study, thermogenesis and variation in the chemical compounds of floral odours and insect visitation in relation to flowering cycles were studied to increase our understanding of the role of floral thermogenesis in the pollination biology of M. sprengeri. There were five distinct floral stages across the floral cycle of this species: pre-pistillate, pistillate, pre-staminate, staminate and post-staminate. Floral thermogenesis during anthesis and consisted of two distinct peaks: one at the pistillate stage and the other at the staminate stage. Insects of five families visited M. sprengeri during the floral cycle, and sap beetles (Epuraea sp., Nitidulidae) were determined to be the most effective pollinators, whereas bees (Apis cerana, Apidae) were considered to be occasional pollinators. A strong fragrance was released during thermogenesis, consisting of 18 chemical compounds. Although the relative proportions of these compounds varied at different floral stages across anthesis, linalool, 1-iodo-2-methylundecane and 2,2,6-trimethyl-6-vinyltetrahydropyran-3-ol were important. Importantly, we found that the floral blends released during the pistillate and staminate stages were very similar, and coincided with flower visitation by sap beetles and the two thermogenic episodes. Based on these results, we propose that odour acts as a signal for a reward (pollen) and that an odour mimicry of staminode-stage flowers occurs during the pistillate stage. Introduction Recent studies have confirmed that thermogenic activity occurs in the reproductive organs of some flowering plants and is crucial for various phases of sexual reproduction, insect–plant interactions and the adaptation of plants to environmental conditions [1]. Thermogenesis is not a by-product of floral development but has been suspected to serve specific functions such as the volatilisation of floral fragrances [2],[3], enhanced blooming in cool weather [4], inflorescence unfolding, pollen maturation or release [5], provision of a warm environment for pollinating insects that temporarily reside in the flower [6],[7] and facilitation of fertilisation and seed set [8]. Thermogenic activity occurs in various structures of many plant families, including the cones of gymnosperms (Cycadaceae and Zamiaaceae) and flowers or inflorescences of some angiosperms (Annonaceae, Araceae, Arecaceae, Aristolochiaceae, Cyclanthaceae, Hydroraceae, Illiciaceae, Magnoliaceae, Nelumbonaceae, Nymphaeaceae, Rafflesiaaceae, and Schisandraceae) [9–14]. Previous studies on the families Araceae and Nelumbonaceae have focused on patterns of thermogenesis in terms of pollination biology, fertilisation and the biochemical regulation of heat production [15],[16], while only a few reports have linked thermogenic activity with the release of odours [2],[7],[17]. Magnolia species are early diverging angiosperms having thermogenic flowers with floral cycles of 2–4 days [18–20]. In these species, thermogenesis during anthesis commonly consists of two episodes, which are related to the male and female phases, respectively, in Magnolia species [3],[17],[21]. Floral fragrances are emitted during the anthesis of Magnolia [22],[23], and the scents are generally dominated by one chemical class of compounds, e.g. monoterpenes, benzenoids or hydrocarbons [23],[24]. In addition, pollination biology has been extensively studied, with beetles regarded as major pollinators [17],[22],[25]. Thermogenesis, floral scent emission and insect visitation occur simultaneously during anthesis, but our current knowledge of these phenomena in Magnolia is primarily derived from independent studies of thermogenesis patterns, floral scent and the species of visiting insects [22],[23],[26]. Very few combined studies have been performed to explore the relationship of thermogenesis with insect–plant interactions in Magnoliaceae or how thermogenesis is related to floral odour [3],[10],[17]. In our study, we focused on the association between thermogenesis and floral odour attractants in Magnolia sprengeri. Based on a description of the floral cycle, temperature measurements of floral thermogenicity and analyses of floral odour compounds, we investigated the visiting insects during different flowering stages. and the relationships among floral thermogenesis, floral scent and pollinator visitation. The mutual relationships among thermogenic activity, variation in floral odour compounds and visiting frequency of pollinators during flowering uncovered in this study will increase our understanding of how Magnoliaceae ensures reproductive success at low temperatures in early spring. Materials and Methods Ethics statement We obtained permission to perform this investigation from the Dalaoling National Nature Reserve Bureau, Hubei Province, China. No specific permission was required for this study since it did not involve any endangered or protected species in the sampled area. Study site and plant material Magnolia sprengeri (Magnoliaceae) is an indigenous species distributed mainly in Shaanxi Province, west Hubei Province and the north-east part of Guizhou Province in China [27–29]. This study was conducted at Dalaoling Natural Reserve (30°50′–30°92′N, 110°52′–110°83′E) in Hubei Province, China. There are four distinct seasons in the study area, though spring and autumn are comparatively longer. The climate is moderate and humid, with 900–1500 mm of annual precipitation. In this population, M. sprengeri trees grow to 20–30 m in height and 20–30 cm in diameter at breast height. The trees typically flower from mid-March to the end of April, with peak blooming in mid-April. Determination of the floral cycle This study was conducted from March 18 to April 26 of 2012. Movements of the petals, stigmas and anthers of individual flowers were recorded every day at anthesis for 30 flowers. The floral cycle was determined according to these floral characteristics. Insect visitation to flowers Visiting insects were recorded during anthesis for 46 flowers on two trees (23 flowers per tree). This experiment was initiated on April 10, 2012. During the daytime, insects were collected in polyethylene bags (Reynolds, Lake Forest, IL, USA) from 10:00 to 18:30 at intervals of 1.5–2.0 h. At night, before the flowers closed to form a temporary chamber, we smeared Vaseline (Fuda Company, China), which is colourless, odourless and viscous, evenly to the basement of the inner petals to trap visiting insects. The trapped insects were recorded the following morning. The insects collected were totalled by floral stages. As individual flowers had very small variation (<1.5 h) in the duration of anthesis and floral stages (Table 1), we divided the floral stages of the 46 flowers as follows: pre-pistillate stage, 10:00 day 1 (April 10) to 10:00 day 2; pistillate stage, 10:00 day 2 to 18:30 day 2; pre-staminate stage, 18:30 day 2 to 10:00 day 3; staminate stage, 10:00 day 3 to 18:00 day 3; and post-staminate stage, 18:30 day 3 to 10:00 day 4. All collected insects were sent for identification to the Beijing Natural History Museum or the Institute of Zoology of the Chinese Academy of Sciences. As sap beetles and bees visited the flowers at both the pistillate and staminate stages (see results), suggesting that they were potential pollinators, we made additional observations of the visiting frequencies of sap beetles and bees to flowers at the pistillate and staminate stages. On April 15, 2012, 3 flowers at the pistillate stage and 3 flowers at the staminate stage were arbitrarily chosen in an individual tree. During the experiment, we made 0.5-h-long observations every 1.5 h. We recorded the number of sap beetles and bees landing on the chosen flowers. \| Table 1. Description of the flowering stages of individual flowers of Magnolia sprengeri. \| \|-----------------------------------------------\|-----------------------------------------------\|-----------------------------------------------\|-----------------------------------------------\|-----------------------------------------------\| \| Petals \| Pre-pistillate stage \| Pistillate stage \| Pre-staminate stage \| Staminate stage \| Post-staminate stage \| \|--------\|----------------------\|------------------\|---------------------\|------------------\|----------------------\| \| Folded tightly \| Loose to open \| Closed at night \| Re-opened in the morning \| Became brown \| \| Pistil \| Appressed tightly \| Immature with anthers non-dehiscent \| Loosened, but anthers do not dehisce \| Radiated, all anthers dehisced \| Became brown and abscising \| \| Starting time \| day 1 \| 10:00–11:00 on day 2 \| 18:30–20:00 on day 2 \| 10:00–11:00 on day 3 \| 21:30–22:00 on day 3 \| \| Ending time \| 10:00–11:00 on day 2 \| 18:30–20:00 on day 2 \| 10:00–11:00 on day 3 \| 21:00–21:30 on day 3 \| 7:00–9:00 on day 4 \| \| Duration \| 22.5±1.2 h \| 8.5±0.9 h \| 15.2±1.2 h \| 11.2±0.8 h \| 10.2±1.0 h \| Figure 1. Morphology of an individual flower of Magnolia sprengeri at the pre-pistillate (A), pistillate (B), pre-staminate (C, D), staminate (E) and post-staminate (F) stages. (A) Pre-pistillate stage: petals folded tightly with pistils opened. (B) Pistillate stage: functionally female flowers with receptive stigmas and immature stamens with no dehiscent anthers. (C) and (D) Pre-staminate stage: a floral chamber with appressed and unreceptive stigmas and non-dehiscent anthers. (E) Staminate stage: functionally male flowers with gynoecium starting to fade; stamens detached from the axis and the anthers dehisced. (F) Post-staminate stage: withered flowers with the petals and stamens becoming brown and abscised; the stigma withered. Abbreviations: An, androecium; Gy, gynoecium; Ip, inner petals; Op, outer petals; Tw, twig. doi:10.1371/journal.pone.0099356.g001 Floral thermogenesis The floral temperature of 20 individual anthetic flowers on one tree was measured at 0.5-h intervals. A portable infrared thermal imaging radiometer [Ti55FT and FlexCam (±0.5°C under 30°C); Fluke, Everett, WA, USA] was used to record the locations of flowers with the highest temperatures upon opening. Then, floral and ambient temperatures were recorded using thermocouples (0.3 mm in diameter) connected to a portable, battery-powered, digital thermometer (OS 685 L; Omega, Stamford, CT, USA) accurate to ±0.5°C. The thermocouples were inserted into the tissue at the basal part of the inner petals and gynoecium, which showed the highest temperature according to infrared thermal imaging radiometry (see the result). Each measurement was repeated three times, and the mean value was recorded. The air-temperature probe was hung freely at the same height. The flowers were shaded to avoid any influence from sunflecks and wind. Floral scents Odour production was studied during the flowering period under natural conditions. Seven flowers were arbitrarily selected in the middle canopy of one tree, and floral scents were collected and analysed for each of the seven flowers during the five floral stages (10:00 for the pre-pistillate stage, 15:00 and 18:00 for the pistillate stage, 10:00 for the pre-staminate stage, 15:00 and 18:00 for the staminate stage and 08:00 for the post-staminate stage). Floral odours were collected using the dynamic headspace technique [2]. Each flower was enclosed in a polyethylene bag (Reynolds), and the open end of the bag was bound around the stalk. The scent was collected in a glass tube containing 60 mg of Tenax-GR (mesh 80/100; CAMSCO, Houston, TX, USA) connected to the bag with an odourless silicone tube. Air was pumped at 200 ml/min. Circumambient air without flowers was collected as a control in the same manner. The trapped floral scents were stored in a freezer at −20°C before analysis. Gas chromatography–mass spectrometry (GC-MS) was performed using a TurboMatrix 650 ATD thermal desorber, and a Clarus 600 gas chromatograph (Perkin-Elmer, Waltham, MA, USA) coupled to a Clarus 600 mass spectrometer (Perkin-Elmer). The gas chromatographic column used was the DB-5MS (30 m × 0.25 mm × 0.25 µm; Clarus 600, Perkin-Elmer). The temperature was kept at 50°C for 8 min, programmed to 5°C/min to 150°C, and finally raised to 250°C at 1°C/min where it was kept for 8 min. The split value was 20:1. Data analysis was performed using NIST 08 with TurboMass ver. 5.4.2. Results Determination of the floral cycle Flowers of M. sprengeri appeared before the leaves, and were erect, cup-shaped and 15 cm wide with 12–14 petals that were white to rosy red in colour. The flowers were protogynous and the anthesis of an individual flower lasted for almost 4 days. According to the movements of the petals, stigmas and anthers of the flowers, the floral cycle could be divided into five distinct stages: pre-pistillate, pistillate, pre-staminate, staminate and post-staminate. (Table 1). The pre-pistillate stage commenced 1 day before flower opening and ended in the following morning at 10:00–11:00. During this stage, the outer petals opened first, followed by the internal petals (Fig. 1A). Upon opening, the outer petals were initially held erect along with the inner petals, and then opened fully at 11:00 when the pistillate stage commenced. At the pistillate stage, the flowers were functionally female: the pistil was open and the receptive stigmas produced nectar-like exudates (Fig. 1B). The pistillate stage lasted until 18:30 in the afternoon. The flowers then closed to form a floral chamber (Fig. 1D), entering the pre-staminate stage. This stage was characterised by open stamens with non-dehisced anthers and a closed stigma (Fig. 1C) and lasted until 10:00–11:00 of the following morning. Then, the flower reopened, the surfaces of the stigmas shrank and the anthers began to dehisce, which indicated the start of the staminate stage (Fig. 1E). After about 11.5 h of pollen shedding, the stigmas began to turn brown and wither (Fig. 1F), which was indicative of the onset of the post-staminate stage. Floral pollinators The floral visitors to M. sprengeri included bibionid flies (Bibio sp., Bibionidae, Diptera), sap beetles (Epuraea sp., Nitidulidae, Coleoptera), bees (Apis cerana, Apidae, Hymenoptera), paper wasps (Polistes chinensis, Vespidae, Hymenoptera) and brown lacewings (Hemerobiidae, Neuroptera) (Table 2 and Fig. 2). Different insects visited the flowers at different floral stages (Table 2). The visiting frequencies of some insects varied during the anthesis. At the pre-pistillate stage, many bibionid flies (Bibio sp.) landed on the bud surfaces (Fig. 2A), particularly on partly exposed petals. However, they were absent during the pistillate stage; 187 sap beetles (Epuraea sp.) were observed both in the pistillate and staminate stages (Fig. 2B) and 89 of them landed on the pistillate-stage flowers and crawled on the stamens and gynoecia without foraging pollen (no pollen was produced during the pistillate stage). During the staminate stage, we recorded 72 sap beetles; some of them stayed inside the flowers for longer than 30 min and then flew into the loose stamens. We observed pollen on their bodies in both the pistillate and staminate stage flowers (Fig. 2B). Therefore, they were considered to be the most effective pollinators of M. sprengeri. In addition, bees (A. cerana) also visited flowers at both the pistillate and staminate stages; however, when compared with sap beetles, far fewer bees were observed at the pistillate stage (Fig. 3). Thus, they were considered to be occasional pollinators. The majority of flies (Bibio sp.) were observed on the surface of swollen buds during the pre-pistillate stage; a small number of paper wasps (P. chinensis) and brown lacewings (Hemerobiidae) also foraged at the staminate and post-staminate stages (Fig. 2C and D), but none of them visited pistillate-stage flowers. Thus, these insects were not considered effective pollinators. Floral thermogenesis Thermogenesis in M. sprengeri consisted of two distinct peaks (Fig. 4). The first peak occurred between 12:00 and 18:30 on the second day of anthesis, corresponding with the pistillate stage when stigmas were receptive (Fig. 4). During this peak, the floral temperature was 1.0–5.5°C above the ambient air temperature (Fig. 4). The second peak occurred between 14:00 and 18:30 in the third day of anthesis. This peak was lower (0.9–4.1°C) and synchronised with pollen liberation and dispersion during the staminate stage. Floral scent variation during different stages of flowering Magnolia sprengeri flowers produced a strong fragrance. Floral scent analyses were conducted during the four developmental stages (Table 3). In total, 18 compounds were identified in the floral scents. Three compounds, linalool, 1-iodo-2-methylundecane and 2,2,6-trimethyl-6-vinyltetrahydro-2H-pyran-3-ol (epoxy-linalool), accounted for more than 5% of the total scent of each As expected, floral stage was an important factor influencing the relative amount of compounds in floral scents (p = 0.001; Table 4). Table 4 clearly shows that no significant difference in the odour compounds was detected among the seven flowers sampled (p = 0.558). In addition, the interaction between “floral stage” and “flower” showed no significant cross effect on the compounds within floral scents (p = 0.922; Table 4), meaning that the variation in odour between the stages was the same for each flower. According to the post hoc tests, the scent composition of different floral stages was significantly different (Fig. 4C). With regard to the dominant compounds, the scents sampled at 15:00 during the pistillate stage were not significantly different to those sampled at 15:00 during the staminate stage. Such similarity was also found in floral scents sampled at 18:00 during the pistillate and staminate stages (Fig. 4C). Discussion Similar to other early diverging angiosperms [12],[19],[32], the flowers of M. sprengeri are bisexual, protogynous, fragrant and pollinated by insects (especially beetles). When the flowers opened for the first time during the daytime, they were functionally female with a receptive stigma and non-dehiscent stamen. The flowers then closed overnight, forming floral chambers, until their reopening the following morning. In some thermogenic plants, e.g. Philodendron solimoesense and Symplocarpus foetidus, heated floral chambers provide shelter for beetle pollinators where they can mate, feed and pollinate the flowers at night during cold periods, and benefit from the energy provided by the flower’s heat in the cool mornings [6],[33],[34]. In our study, some sap beetles remained inside the floral chambers at night during the prestamine stage. We thus suggest that M. sprengeri flowers may act as shelter for sap beetles during the cold night. Heat production in gynoecia of M. sprengeri flowers occurred during anthesis and consisted of two distinct peaks. Distinct Table 3. Retention time and relative proportions (%) of chemical compounds identified in scents collected on M. sprengeri flowers at different flowering stages (values in this table are means ± s.e.). \| Retention time (min) \| Pre-pistillate stage \| Pistillate stage \| Pre-staminate stage \| Staminate stage \| Post-staminate stage \| \|----------------------\|----------------------\|------------------\|---------------------\|-----------------\|----------------------\| \| \| A \| B \| A \| B \| A \| B \| \| Heptanal \| 5.67 \| 0.22±0.08\| - \| - \| 0.53±0.02\| - \| \| Acetophenone \| 7.05 \| 0.11±0.05\| 0.18±0.07\| 0.22±0.01\| - \| - \| \| Methyl heptenone \| 7.66 \| - \| 0.74±0.03\| 0.18±0.01\| 0.31±0.02\| 0.27±0.06\| \| Myrcene \| 7.74 \| 0.12±0.03\| 0.47±0.01\| 0.74±0.01\| - \| 0.57±0.02\| \| Caprylic aldehyde \| 8.09 \| - \| 0.22±0.09\| 0.47±0.01\| 0.22±0.01\| 0.92±0.19\| \| Cyclohexene \| 8.67 \| 0.33±0.08\| 0.32±0.03\| 0.74±0.01\| - \| 0.57±0.02\| \| Pelargonic aldehyde \| 10.62 \| 1.25±0.15\| 0.64±0.02\| 0.95±0.02\| 0.22±0.01\| 0.92±0.19\| \| Linalool \| 10.64 \| 2.37±1.28\| 3.82±1.87\| 2.68±1.60\| 3.62±1.60\| 3.71±1.57\| \| Phenylethanol \| 10.95 \| 1.15±0.25\| 1.72±0.19\| 1.40±0.02\| 0.76±0.02\| 1.06±0.01\| 0.48±0.12\| \| Tridecyl aldehyde \| 12.19 \| - \| - \| - \| - \| 0.21±0.06\| - \| \| epoxylinalool \| 12.29 \| 8.25±0.60\| 6.22±0.39\| 7.91±0.49\| 13.57±0.53\| 7.67±0.31\| 10.51±0.42\| 18.67±0.28\| \| (L)-Alpha-terpineol \| 12.80 \| 1.97±0.18\| 1.21±0.15\| 1.30±0.01\| 1.12±0.02\| 0.27±0.01\| 1.01±0.17\| 1.15±0.08\| \| Decyl aldehyde \| 13.04 \| - \| - \| - \| - \| 0.41±0.08\| - \| \| Indole \| 14.98 \| 1.07±0.21\| 0.71±0.15\| 2.24±0.02\| 1.87±0.03\| 1.21±0.02\| 1.84±0.18\| 5.18±0.09\| \| Undecyl aldehyde \| 15.35 \| - \| - \| - \| - \| 0.21±0.06\| - \| \| 2-Phenylethyl 2-methylbutyrate \| 19.10 \| 1.93±0.25\| 1.83±0.25\| 3.25±0.02\| 2.35±0.03\| 2.05±0.02\| 3.29±0.19\| 3.59±0.18\| \| Alpha-farnesene \| 19.23 \| 2.11±0.19\| 3.1±0.21 \| 2.86±0.20\| 3.35±0.21\| 1.29±0.12\| 12.95±0.35\| \| 1-Iodo-2-methylundecane \| 19.55 \| 57.77±0.72\| 46.27±1.75\| 52.48±0.87\| 39.05±0.81\| 43.79±0.83\| 53.13±0.97\| 35.56±2.10\| Note: The floral odours were sampled at 10:00 for the pre-pistillate stage, 15:00 (A) and 18:00 (B) for the pistillate stage, 10:00 for pre-staminate stage, 15:00 (A) and 18:00 (B) for the staminate stage, and 8:00 for the post-staminate stage. doi:10.1371/journal.pone.0099356.t003 heating patterns have been reported in different thermogenic species [35],[36]. In some thermogenic plants, floral temperature is maintained at a constant range, independent of ambient temperature, for a long period throughout anthesis [8],[35],[36]. Floral temperature stability of these plants is achieved by means of physiological thermoregulation [35],[36]. In this study, floral temperature of \textit{M. sprengeri} changed constantly throughout anthesis and major thermogenic episodes were short, which indicated that \textit{M. sprengeri} was not thermoregulated. Our result is in agreement with a previous study on floral thermogenesis of \textit{M. ovata} in Brazil [3]. Thermogenesis is generally linked to volatilisation of floral scent [37]. Like many other \textit{Magnolia} species [23], floral scent was emitted during the thermogenesis of \textit{M. sprengeri}. Floral scents have been well documented to play an important role in plant-pollinator interactions through various effects on visiting insects, e.g. as a feeding cue and nectar guide [38]. Beetles are important pollinators of many early diverging angiosperms, including \textit{Magnolia} [32]. In this study, we found that many sap beetles (\textit{Epuraea} sp.) visited \textit{M. sprengeri} flowers at both the pistillate and staminate stages and were identified as effective pollinators. When the sap beetles were in the flowers, they were frequently observed foraging pollen grains during the staminate stages. We thus concluded that the floral odours of \textit{M. sprengeri} may act as a signal of food resources for sap beetles. Floral scents are complexes of chemical compounds [39], and different odours are selected by different insects [2],[40]. Intriguingly, we found a similarity in dominant compounds of different odours are selected by different insects [2],[40]. ### References 1. Seymour RS, Ito Y, Onda Y, Ito K (2009) Effects of floral thermogenesis on pollen function in Asian skunk cabbage \textit{Symplocarpus renifolius}. Biology Letters 5: 560–570. 2. 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Plant Species Biology 18: 123–127.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5120, 1 ], [ 5120, 10644, 2 ], [ 10644, 13690, 3 ], [ 13690, 17733, 4 ], [ 17733, 19770, 5 ], [ 19770, 22431, 6 ], [ 22431, 25196, 7 ], [ 25196, 28415, 8 ] ] }
f0c4595798a546cc65b3e83f098eccdf409c466e	{ "olmocr-version": "0.1.59", "pdf-total-pages": 5, "total-fallback-pages": 0, "total-input-tokens": 21374, "total-output-tokens": 4756, "fieldofstudy": [ "Psychology" ] }	ATTESTATION OF A TEST SAMPLE OF PIRACETAM TO DETERMINE THE ACCOMPANYING IMPURITIES WITHIN THE PROFESSIONAL TESTING PROGRAM Abstract: The attestation of the test sample to determine the accompanying impurities in testing a professional testing program. The attribute value has obtained the content of the accompanying impurities in the test sample of piracetam. Confirmed the homogeneity and stability of the piracetam content test sample accompanying impurities. Criteria for evaluating participants' results were developed, testing a professional testing program to determine the content of the accompanying impurities. Forms of tables have been developed to populate the test results participants. Key words: professional testing program, test sample, certification, high-performance liquid chromatography, suitability testing chromatographic system, evaluation criteria. Language: English Citation: Yurchenko, O. I., Chernozhuk, T. V., & Kravchenko, O. A. (2020). Attestation of a test sample of piracetam to determine the accompanying impurities within the professional testing program. ISJ Theoretical & Applied Science, 03 (83), 257-261. Soi: http://s-o-i.org/1.1/TAS-03-83-49 Doi: https://dx.doi.org/10.15863/TAS.2020.03.83.49 Scopus ASCC: 1600. Introduction Medicines Quality Control Laboratories have a great responsibility for authorized government agencies and customers to provide right and accurate analytical research findings that base their conclusions on the quality of medicines. Therefore, such laboratories must continuously confirm their competence and the reliability of the data they receive following the officially recognized mechanisms and demonstrate it to both the state accredited accrediting bodies and directly to the customers. One of the standards and accepted ways of doing this is the participation of the laboratory in inter-laboratory comparative tests [1, p.9]. There are many programs in the world between comparative laboratory tests for control laboratories in various fields - medical, food, environmental, and others. In the pharmaceutical area, popular overseas relative research programs are being developed and implemented by such well-known international organizations as the European Directorate for Quality of Medicinal Products (EDQM), the World Health Organization (WHO), and others. However, for most Ukrainian laboratories, participation in these programs involves some difficulties - material (cost of the involvement in the program), logistics (time and cost of delivery of test samples from abroad), and language (understanding and providing information in English only). Therefore, in Ukraine since 2001, a national program for laboratory comparisons, called the Professional Testing Program of Laboratories for Quality Assurance in Medicinal Products (PTP), has been developed and successfully implemented in 2001 and has 13 annual rounds of testing. This program has some peculiarities in comparison with its foreign counterparts, in particular, regarding approaches to the choice of testing method, attestation of test samples provided to test participants, and criteria for evaluating the results of participants. Unlike most similar programs that evaluate the effects of testing the participants on the statistical 3s-criterion, the PTP proceed from the specific pharmacopoeial requirements to the actual drugs described in the pharmacopoeia in formulating their evaluation criteria. Controlling laboratories of pharmaceutical enterprises, state and independent laboratories for quality control of drugs, both domestic and from abroad, take part in the PTP. According to the concept of PTP, when the attestation of the testing sample (TS) is taken, it is necessary not only to determine the attributable value of a specific quality characteristic and the level of uncertainty with which this value is obtained but also to make sure that the attested TS provides an opportunity to trace the compliance of participants with pharmacopoeial requirements. Thus, with a sufficient degree of reliability to obtain the test results are in line with the test results. Besides, according to the methodology with which the certification is conducted and following the results of the accreditation, form a protocol for filling in the test participants to monitor the quality of the test participants test and identify violations and non-compliance with pharmacopoeial requirements [1, p.15, 2, p.33, 3, p.876, 4, p.1085, 5, p.29, 6, p.10, 7, p.5, 8, 9, 2, p.41, 10, p.13, 11, p.436, 12, p.85, 13, p.3, 14, p.13, 15, p.112, 16, p.23, 17, p.532]. The purpose of this work is to certify the test sample of piracetam. Accompanying impurities in the test sample of piracetam should be determined. Also, there is a strong need for the study of the homogeneity and stability of the test sample of piracetam. The reproducibility of the test of the suitability of the chromatographic system is important to be determined. The experimental part. Piracetam. Pharmacopoeial quality indicators. Piracetam substance was selected as a candidate for PTP certification. Piracetam is a nootropic drug, historically the first and foremost representative of this group of drugs. Chemically, it is a derivative of pyrrolidone and is the ancestor of the group of "racetam", a class of psychoactive nootropic substances which have the pyrrolidone core. The pharmacopoeial quality requirements of this substance are represented in the Piracetam monograph included in Ph.Eur. and SPU (National Pharmacopoeia of Ukraine). Properties: Powder is white or almost white. Easily soluble in water P, soluble in ethanol (96%) P. Quality/purity indicators are transparency of solution; the color of the solution; accompanying impurities; heavy metals; weight loss on drying; ash sulfates. Quantitative determination. Famous impurities Specified impurities: A, B, C, D. • D. $ R=\text{CH}_2 - \text{CO}_2\text{H} $: (2-Oxypropylidin-1-yl) acetic acid. Equipment: - Scales analytical MC 210 S, firms Sartorius, Germany. - Scales analytical AUW220D, from Shimadzu, Japan. - 713 pH Meter, Metrohm, Switzerland. - Chromatograph with diode-matrix detector Waters Alliance. - Measuring dishes of accuracy of class A for solution preparation. Chromatographic columns: - Column 1: Waters X TerraRP 18,4,6 * 250 mm, 5 μm with pre-column; - Column 2: Agilent Zorbax Eclipse XDB-C18, 4.6 * 250 mm, 5 μm with pre-column; - Column 3: Supelco Discovery C18, 4.6 * 250 mm, 5 μm with front column (1); Standard sample: - Pharmacopoeial standard samples of SPU of piracetam with a content of the basic substance 99.8% (uncertainty of attestation does not exceed 0.5%). Reagents: - Water P; - Acetonitrile P; - Dicalium Hydrophosphate P; - Phosphoric acid diluted R. Test sample: - The substance used was Piracetam, a product of the People's Republic of China, provided by the Health Pharmaceutical Company LLC, Ukraine, 20110520, as a test sample. Methods The determination of the accompanying impurities was carried out according to the method of the indicator "Compound impurities" of the monograph of SPU "Piracetam", in accordance with the requirements of the general article of the SPU "2.2.29. Liquid chromatography" [16, p.21], SPU “2.2.46.Chromatographic separation methods”. Accompanying impurities. Liquid chromatography (2.2.29). Verification of the suitability of the chromatographic system According to the SPU, the Chromatographic System Verification Test (CSVT) is an integral part of the procedure and is used to ensure the required quality of the chromatographic system. The method of the indicator "Compound impurities" of the monograph of SPU "Piracetam" regulates only two parameters of CSVT, which is determined from the chromatogram of the comparison solution (a): - a degree of separation of at least 3.0 between the peaks of piracetam and impurity A; - symmetry coefficient: no more than 2.0 for the piracetam peak. However, under the requirements of the general article Ph.Eur./SPU “2.2.29. Liquid chromatography" typically uses parameters such as nominal efficiency, retention factor (mass partition coefficient), degree of separation, relative retention, and symmetry coefficient to evaluate the functioning of the column, as well as, in tests for the content of accompanying impurities, except should be controlled by such an important parameter as the limit of quantification (LQ). It should be observed that the pharmacopoeial requirements [15, p. 111], LQ should be no more than the boundaries that are not taken into account. According to the method of the Piracetam monograph [17,p.532], the unaccounted limit is 0.05%, that is, the LQ should be no more than 0.05%, from which it follows that the calculated S / N ratio should be not less than 20. The calculation of these parameters for various analytical columns is given in table 1. For the reliable certification of the substance piracetam as a TS for testing on the indicator "Compound impurities", it is necessary to analyze the sample, which is certified on as many chromatographic columns as possible. Also, the method of indicator should be checked. Therefore, the suitability of the chromatographic system, which is an integral part of the technique, was tested for six chromatographic columns. The results of the definition, as well as the regulation (if any), are given in Table 1, where bold indicates the parameters of the CSVT that do not meet the requirements. It turned out that not all columns with the sorbent type, particle size, and geometric parameters that meet the requirements of the method meet the needs of the suitability of the chromatographic system. The following studies were performed on columns 2 and 6, which do not meet the requirements. According to the information above, when testing in PTP, it was necessary to monitor how test participants understand the requirements for CSVT and comply with them. Thus, on the basis of the CSVT data obtained from the TS certification of piracetam, tables on the performance of CSVT for the chromatograph of the comparison solution (a) (Table 2) and the comparison solution (b) (Table 3) were developed and were included in the testing protocol. ### Determination of the content of the accompanying impurities in TS of piracetam The presence of impurities in the substance of piracetam was determined by the method of the indicator "Compound impurities" monograph SPU "Piracetam" on columns 2 and 6. Initially, two parallel determinations of three samples of the sample, selected from different packing cities, thereby determining the homogeneity of the sample. Also, the stability of the substance piracetam over time was monitored at intervals of about one month and three months, respectively. The results of determining the content of impurities are shown in table 4. As can be seen from the table, no accompanying impurities in the TS of piracetam were found. The same conclusion was reproduced by the results of all definitions, thus confirming that the piracetam was homogeneous and stable over the testing. ### Conclusion According to the results of the certification, it can be concluded that the TS of piracetam complies with the requirements of SPU of "Piracetam" monograph due to the content of the accompanying impurities. There are no accompanying impurities. It means that their content does not exceed the unaccounted for limit (0.05%). Test participants should draw the same conclusion to obtain satisfactory test results in PTP. --- Table 1. Parameters of the suitability of the chromatographic system \| Reglamentation \| Time of staying \| Number of theoretical plates \| Staying factor (k) \| Symmetry coefficient (As) \| Measure of separation (Rs) \| Signal \| MKV, % \| \|---------------\|-----------------\|------------------------------\|-------------------\|--------------------------\|---------------------------\|--------\|-------\| \| Column 1 \| 3,248 \| 6278 \| 0,624 \| 0,98 \| 1,40 \| 22 \| 0,045 \| \| Column 2 \| 3,177 \| 8638 \| 0,59 \| 1,84 \| 3,03 \| 27 \| 0,037 \| \| Column 3 \| 3,641 \| 5812 \| 0,82 \| 1,23 \| 1,63 \| 16 \| 0,063 \| \| Column 4 \| 3,978 \| 7297 \| 1,00 \| 1,31 \| 2,21 \| 30 \| 0,033 \| \| Column 5 \| 2,96 \| 5356 \| 0,48 \| 1,48 \| 2,12 \| 15 \| 0,067 \| \| Column 6 \| 3,245 \| 7563 \| 0,622 \| 1,16 \| 3,16 \| 25 \| 0,04 \| Table 2. CSVT from chromatograms of comparison solution (a) to be filled by participants \| Sample, mg \| Volume of pirolidone, ml \| Number of theoretical plates \| Staying factor (k) \| Symmetry coefficient (As) \| Measure of separation (Rs) \| \|------------\|--------------------------\|-------------------------------\|-------------------\|--------------------------\|---------------------------\| Table 3. CSVT from chromatograms of comparison solution (b) to be filled by participants \| Dilution \| Peaks square \| An average value of peak square \| Relation S/N \| Limit of quantitative determination \| \|----------\|--------------\|---------------------------------\|--------------\|-------------------------------------\| ### Impact Factor: \| \| ISRA (India) \| SIS (USA) \| ICV (Poland) \| PIF (India) \| IBI (India) \| ESJI (KZ) \| SJIF (Morocco) \| OAJI (USA) \| \|----------------\|--------------\|-----------\|--------------\|-------------\|-------------\|-----------\|----------------\|-----------\| \| JIF \| 1.500 \| \| \| \| \| \| 5.667 \| 0.350 \| Table 4. The results of the determination of the accompanying impurities in TS of piracetam \| The date of the experiment \| Availability of chromatographic system \| Content of individual impurities \| Sum of impurities \| Result \| \|----------------------------\|----------------------------------------\|---------------------------------\|--------------------\|--------\| \| 11.08.2019 \| Fit for \| An additional peaks are absent on chromatograms \| Absent \| No impurities \| \| 17.08.2019 \| Fit for \| An additional peaks are absent on chromatograms \| Absent \| No impurities \| \| 06.09.2019 \| Fit for \| An additional peaks are absent on chromatograms \| Absent \| No impurities \| \| 18.01.2020 \| Fit for \| An additional peaks are absent on chromatograms \| Absent \| No impurities \| References: 1. Leontev, D. A. (2007), Farmakom. V.2, pp 16 – 25. 2. Dmitrieva, M. V. (2012). Farmakom. V. ½, pp. 33 – 38. 3. Sur, S. V. (2011). Programi profesijnogo testuvannja jak zasib standartizacii roboti laboratorii z kontrolju jakosti likars'kih zasobiv U kn. [Harkiv: vidavnictvo «NTMT»], pp. 3 – 1064. 4. Leontev, D. A. (2011). Farmacevtichni standartni zraki. (pp.1085-1104). Harkiv: vidavnictvo «NTMT». 5. (2010). ST – N MOZU 42-4.0:2011. – Likarski zasobi. Naležhna virobnichna praktika. (p.281). Kiyv, MOZ Ukraini. 6. (n.d.). ICH Topic Q10. - Pharmaceutical Quality System. 7. (n.d.). The Rules Governing Medicinal Products in the Europian Union, Volume 3A: Quality Guidelines. – Guideline 3AQ11a: Specifications and Control Tests on the Finished Products. 8. (2008). Validacija analytichnih metodik i viprobuvani': Derzhavnaya Farmakopeja Ukraini, (pp. 85 – 100). 9. Grizodub, A. I. (2006). Farmakom. V.2, pp. 35 – 44. 10. Orlov, V. I., & Aratskov, A. A. (1997). Ridinna hromatografija. Teoretichni osnovi. (p.14). Dzerzhins'k, Naukovoy – tehnologichna kompanija «Sinetko». 11. Bekker, Ju. (2009). Hromatografiya. Instrumental'na analitika: metodi hromatografiy ta kapiljarnogo elektroforezu. (p.473). Moscow, Tehnosfera. 12. Sichov, K. S. (2010). Praktichne kerivnictvo z ridinnoi hromatografii. (p.272). Moscow, Tehnosfera. 13. Sadek, P. S. (1999). Jak uniknuti pomilok u visokoeffektivnij ridinij hromatografii. (p.335). Kiyv: Alsi. 14. Shatc, V. D., & Sahartova, O. V. (1988). Visokoeffektivna ridinna hromatografija: Osnovi teorii. Metodologija. Zastosuvannja u likars'kij himii. (pp.11-21). Riga: Zinatne. 15. (2015). Metodi hromatografichnogo rozdiлення : Derzhavna Farmakopeja Ukraini «Naukovoy – ekspertnyj farmakopejnij centru», p.126. 16. Henke, H. (2010). Ridinna hromatografija. (pp.20-22). Moscow: Tehnosfera. 17. (2015). "Piracetam" Derzhavna Farmakopeja Ukraini «Naukovoy – ekspertnyj farmakopejnij centru», p.532."	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2212, 1 ], [ 2212, 5906, 2 ], [ 5906, 9820, 3 ], [ 9820, 13652, 4 ], [ 13652, 17036, 5 ] ] }
929cb0ee862d5f272bddeab85f9bd281494a5af7	{ "olmocr-version": "0.1.59", "pdf-total-pages": 9, "total-fallback-pages": 0, "total-input-tokens": 14564, "total-output-tokens": 2772, "fieldofstudy": [ "Physics", "Chemistry" ] }	Abstract A structural phase transition has been found using electron diffraction technique in PrRu$_4$P$_{12}$ accompanied by a metal - insulator (M - I) transition ($T_{MI} = 60$K). Weak superlattice spots appeared at $(H, K, L)$ $(H + K + L = 2n + 1; n$ is an integer) position at a temperature of $T = 12$ K and 40 K. Above $T = 70$ K, the spots completely vanished. The space group of the low temperature phase is probably $Pm\overline{3}$. This is the first observation of a symmetry other than $Im\overline{3}$ in skutterudite compounds. 1. Introduction Filled skutterudite compounds RM$_4$X$_{12}$ (R = rare - earth; M = Fe, Ru and Os; X = P, As and Sb) show various physical properties, such as magnetic ordering, semiconducting transport property, superconductivity and metal - insulator (M - I) transition. For several years, a great effort has been taken to clarify the origin of the various properties of the skutterudites particularly from the viewpoint of 4f instability. It is expected that further knowledge of the 4f instability can be obtained by studying the physics of the skutterudites. In this paper, we particularly focus our attention on the M - I transition in PrRu$_4$P$_{12}$. PrRu$_4$P$_{12}$ shows a M - I transition at $T_{MI} = 60$ K [1]. Although several studies have been carried out, the origin of the M - I transition is still a controversial issue. The temperature dependence of the magnetic susceptibility shows no anomaly at $T_{MI}$, suggesting that the M - I transition is not caused by magnetic ordering [1]. Pr L$_2$ - edge XANES measurements indicate that the Pr atoms are almost trivalent independent of temperature [2]. According to powder X - ray diffraction measurements using synchrotron radiation, PrRu$_4$P$_{12}$ shows no structural phase transition down to $T = 25$ K [3]. To date, no cause for the M - I transition has been found. To clarify the mechanism of the M - I transition, determination of the precise crystal structure in the low temperature insulator phase is very important. We expect that there is still a possibility of a small lattice distortion which has been undetected by the powder X - ray diffraction. Thus, we have performed electron diffraction measurements which are very sensitive to lattice distortion, in order to find a structural phase transition at $T_{MI}$. 2. Experimental Details Single crystals of PrRu$_4$P$_{12}$ were grown by the Sn flux method. High quality Pr (99.9%), Ru (99.9%), P (99.999%) and Sn (99.999%) powders were mixed with the atomic ratio Pr : Ru : P : Sn = 1 : 4 : 20 : 50 and sealed in quartz tubes under a pressure of 150 mm Hg of argon gas. The mixtures were calcined at 1000 °C for one week and then cooled down slowly to 600 °C at 2 °C / h. As - grown samples were treated with aqua regia to dissolve the Sn matrix. The dimensions of the obtained single crystals were typically 0.3 × 0.3 × 0.3 mm³. The samples were characterized by powder X - ray diffraction at room temperature using Cu Kα1 radiation. The crystal structure of PrRu₄P₁₂ was cubic with a lattice parameter of a = 8.0424 Å, which is consistent with the reported value [4]. For the electron diffraction measurements, the single crystals were mechanically polished and ion etched. Electron diffraction measurements were carried out by using a transmission electron microscope (JEOL 4000FX) operated at 200 kV. A double tilt liquid He holder was equipped for cooling samples down to around 10 K. Specimens could be tilted up to ± 15° along two axes in the microscope. 3. Results Figure 1 shows [0, 0, 1] zone - axis electron diffraction patterns at T = 70 K, 40 K and 12 K. For T = 70 K (Figure 1 (a)), the diffraction pattern is consistent with the Im3 structure. No spot that was inconsistent with the Im3 structure was observed at T = 70 K, suggesting that the single crystal was of high quality. At T = 12 K well below T_{MI} (Figure 1 (c)), weak superlattice spots appeared, for example at the (1, 0, 0) position as indicated by the arrow. This type of superlattice spots was also observed in higher order Laue zones. The positions of the superlattice spots were (H, K, L) (H + K + L = 2n + 1; n is an integer). The clear observation of superlattice spots over a wide Q range suggests that this phase transition is accompanied by a lattice distortion. At T = 40 K (Figure 1 (b)), the superlattice spots can still be seen but the intensity becomes very weak, suggesting that a structural phase transition occurs between T = 40 K and 70 K. The precise transition temperature is hard to determine owing to difficulty of quantitative analysis of weak reflections. 4. Discussion Since the intensity of the observed superlattice spots was very weak, the structural distortions in the low temperature phase must be relatively small. Thus, we have assumed that the low temperature phase retains the same point group as the high temperature phase (m$\overline{3}$). Under this assumption, we can show that the crystal structure of the low temperature phase is Pm$\overline{3}$. A minor change in the crystal structure is consistent with the lack of observation of a structural phase transition in the powder X-ray diffraction data. In Figure 2, the crystal structure of PrRu$_4$P$_{12}$ with the space group Pm$\overline{3}$ is shown. As can be seen in the figure, two sites exist for the Pr and P atoms in the Pm$\overline{3}$ structure, while the Im$\overline{3}$ structure has only one site for each Pr and P atom. In the Pm$\overline{3}$ structure, one possible distortion is the displacement of P (1 or 2) atoms toward or away from the Pr (1 or 2) atoms. An increase or decrease in the bond length of P (1) - P (1) or P (2) - P (2) atoms is also possible. As shown above, the M - I transition and the structural phase transition occur almost at the same temperature. At present, several models are consistent with the mechanism of the M - I transition taking the structural phase transition into account. Among them, charge ordering with an energy gap is a candidate to explain the M - I transition. According to the XANES measurements, the valence of the Pr atoms remains constant from 300 K down to 20 K [2]. Thus, charge ordering on the Pr sites can be excluded. On the other hand, since two sites also exist for the P atoms in the Pm$\overline{3}$ structure, charge ordering on P sites seems to be more plausible. In this case, the electron rich P site can be expected to shift towards either a Pr or Ru cation. Another possibility is the opening of a band gap owing to the P displacement. The P displacement makes the volume of Brillouin zone decrease by half and may change the band structure. According to band calculations for LaFe$_4$P$_{12}$ [5, 6], hole carriers exist mainly on a single Fermi surface. Thus, using the analogy of LaFe$_4$P$_{12}$, carriers in PrRu$_4$P$_{12}$ in the Im$\overline{3}$ phase are also expected to be on a single Fermi surface, which suggests that a band gap can easily open by a P displacement. Precise site information is required for further discrimination between possible mechanism. 5. Conclusion We have performed electron diffraction measurements on PrRu$_4$P$_{12}$ and found weak superlattice spots at (H, K, L) (H + K + L = 2n + 1) below $T_{MI}$. The crystal structure of the low temperature phase is probably Pm$\overline{3}$. The M - I transition appears to be induced by a structural phase transition. Acknowledgements The authors thank I. Hase, T. Yanagisawa and H. Harima for delightful discussions. This work was supported by the NEDO project with contact number of #98E-a-05-003-2 and funds from the Ministry of International Trade and Industry, Japan. Figure Captions Figure 1 Electron diffraction patterns of PrRu$_4$P$_{12}$ along the [0, 0, 1] zone-axis at (a) $T = 70$ K, (b) $T = 40$ K and (c) $T = 12$ K. Weak superlattice spots are observed at $T = 40$ K and 12 K. An arrow depicts one of the superlattice spots. Figure 2 The crystal structure of PrRu$_4$P$_{12}$ with the space group Pm$\bar{3}$. References [1] C. Sekine, T. Uchiumi, I. Shirotani and T. Yagi, Phys. Rev. Lett. 79, 3218 (1997). [2] C. H. Lee, H. Oyanagi, C. Sekine, I. Shirotani and M. Ishii, Phys. Rev. B 60, 13253 (1999). [3] C. Sekine et al. (unpublished). [4] W. Jeitschko and D. Braun, Acta Cryst. B33, 3401 (1977). [5] H. Harima, J. Magn. Magn. Mater. 177-181 (1998) 321 [6] H. Sugawara, Y. Abe, Y. Aoki, H. Sato, M. Hedo, R. Settai, Y. Onuki and H. Harima J. Phys. Soc. Jpn. 69 (2000) 2938 $T=70\text{K}$ $T=40\text{K}$ $T=12\text{K}$	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 545, 1 ], [ 545, 2739, 2 ], [ 2739, 4662, 3 ], [ 4662, 7162, 4 ], [ 7162, 7737, 5 ], [ 7737, 8094, 6 ], [ 8094, 8562, 7 ], [ 8562, 8609, 8 ], [ 8609, 8609, 9 ] ] }
a627b2dafec2c4ff3744ffc054c23a17735a6331	{ "olmocr-version": "0.1.59", "pdf-total-pages": 23, "total-fallback-pages": 0, "total-input-tokens": 116086, "total-output-tokens": 26564, "fieldofstudy": [ "Mathematics" ] }	LOCAL WELL-POSEDNESS OF ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH VACUUM HUAJUN GONG, JINKAI LI, XIAN-GAO LIU, AND XIAOTAO ZHANG Abstract. In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is that the well-posedness is established without assuming any compatibility condition on the initial data, which was widely used before in many literatures concerning the well-posedness of compressible Navier-Stokes equations in the presence of vacuum. 1. Introduction The isentropic compressible Navier-Stokes equations read as \[ \rho (u_t + (u \cdot \nabla) u) - \mu \Delta u - (\lambda + \mu) \nabla \text{div} u + \nabla P = 0, \] \[ \rho_t + \text{div} (\rho u) = 0, \] in $ \mathbb{R}^3 \times (0, T) $, where the density $ \rho \geq 0 $ and the velocity field $ u \in \mathbb{R}^3 $ are the unknowns. Here $ P $ is the scalar pressure given as $ P = a \rho^\gamma $, for two constants $ a > 0 $ and $ \gamma > 1 $. The viscosity constants $ \lambda, \mu $ satisfy the physical requirements: \[ \mu > 0, \quad 2\mu + 3\lambda \geq 0. \] System (1.1)–(1.2) is complemented with the following initial-boundary conditions \[ (\rho, \rho u)\|_{t=0} = (\rho_0, \rho_0 u_0), \] \[ u(x, t) \to 0, \quad \text{as} \quad \|x\| \to \infty. \] There are extensive literatures on the studies of the compressible Navier-Stokes equations. In the absence of vacuum, that is the density has positive lower bound, the system is locally well-posed for large initial data, see, e.g., [23, 41, 48, 43, 51]; however, the global well-posedness is still unknown. It has been known that system in one dimension is globally well-posed for large initial data, see, e.g., [2, 26, 22, 57, 58] and the references therein, see [35] for the large time behavior of the solutions, and also [34, 37, 38] for the global well-posedness for the case that with nonnegative density. For the multi-dimensional case, the global well-posedness holds for small initial data, see, e.g., [6, 10, 13, 19, 30, 42, 45, 47, 50]. In the presence of vacuum, that is the density may vanish on some set, global existence (but without uniqueness) of weak solutions has been known, see [1, 14, 16, 25, 39, 40]. Local well-posedness of strong solutions was proved for suitably regular initial data under some extra compatibility conditions (being mentioned in some details below) in [7–9]. In general, when the vacuum is involved, one can only expect solutions in the homogeneous Sobolev spaces, that is, the $L^2$ integrability of $u$ is not expectable, see [31]. Global well-posedness holds if the initial basic energy is sufficiently small, see [20, 21, 36, 54]; however, due to the blow-up results in [55, 56], the corresponding entropy of the global solutions in [20, 54] must be infinite somewhere in the vacuum region, if the initial density is compactly supported. In this paper, we focus on the well-posedness of the Cauchy problem to system (1.1)–(1.2) in the presence of vacuum. As mentioned in the previous paragraph, local well-posedness of strong solutions to the compressible Navier-Stokes in the presence of vacuum has already been studied in [7–9], where, among some other conditions, the regularity assumption $$\rho_0 - \rho_\infty \in H^1 \cap W^{1,q}, \quad u_0 \in D^1 \cap D^2,$$ for some constant $\rho_\infty \in [0, \infty)$, and the compatibility condition $$-\mu \Delta u_0 - (\mu + \lambda) \nabla \text{div} u_0 + \nabla P(\rho_0) = \sqrt{\rho_0} g,$$ for some $g \in L^2$, were used. Similar assumptions as (1.4) and (1.5) were also widely used in studying many other fluid dynamical systems when the vacuum is involved, see, e.g., [3–5, 17, 18, 20–22, 32, 36, 52–54]. Assumptions (1.4) and (1.5) are so widely used when the initial vacuum is taken into consideration, one may ask if the regularities on the initial data stated in (1.4) can be relaxed and if the compatibility condition (1.5) is necessary for the local well-posedness of strong solutions to the corresponding system. In a previous work [33], the second author of this paper considered these questions for the inhomogeneous incompressible Navier-Stokes equations, and found that the compatibility condition is not necessary for the local well-posedness. The aim of the current paper is to give the same answer for the isentropic compressible Navier-Stokes equations. As will be shown in this paper that we can indeed reduce the regularities of the initial velocity in (1.4) and remove the compatibility condition (1.5), without loosing the existence and uniqueness, but the prices that we need to pay are the following: (i) the corresponding strong solutions do not have as high regularities as those in [7–9] where both (1.4) and (1.5) were assumed; (ii) one can only ask for the continuity, at the initial time, of the momentum $\rho u$, instead of the velocity $u$ itself. Before stating our main results, let us introduce some notations. Throughout this paper, we use $L^r = L^r(\mathbb{R}^3)$ and $W^{k,r} = W^{k,r}(\mathbb{R}^3)$ to denote, respectively, the standard Lebesgue and Sobolev spaces in $\mathbb{R}^3$, where $k$ is a positive integer and $r \in [1, \infty]$. When $r = 2$, we use $H^k$ instead of $W^{k,2}$. For simplicity, we use $\\| \cdot \\|_r = \\| \cdot \\|_{L^r}$. We denote $$D^{k,r} = \left\{ u \in L^1_{loc}(\mathbb{R}^3) \mid \\| \nabla^k u \\|_r < \infty \right\}, \quad D^k = D^{k,2},$$ \[ D_0^1 = \{ u \in L^6 \big\| \\| \nabla u \\|_2 < \infty \}. \] For simplicity of notations, we adopt the notation \[ \int f dx = \int_{\mathbb{R}^3} f dx. \] Our main result is the following: Theorem 1.1. Suppose that the initial data $(\rho_0, u_0)$ satisfies \[ \rho_0 \geq 0, \quad \rho - \rho_\infty \in H^1 \cap W^{1,q}, \quad u_0 \in D_0^1, \quad \rho_0 u_0 \in L^2, \] for some $\rho_\infty \in [0, \infty)$ and some $q \in (3, 6)$. Then, there exists a positive time $T$, depending only on $\mu, \lambda, a, \gamma, q$, and the upper bound of $\psi_0 := \\| \rho_0 \\|_{\infty} + \\| \rho_0 - \rho_\infty \\|_2 + \\| \nabla \rho_0 \\|_{L^2 \cap L^q} + \\| \nabla u_0 \\|_2$, such that system (1.1)–(1.2), subject to (1.3), admits a unique solution $(\rho, u)$ on $\mathbb{R}^3 \times (0, T)$, satisfying \[ \rho - \rho_\infty \in C([0, T]; L^2) \cap L^\infty(0, T; H^1 \cap W^{1,q}), \quad \rho_t \in L^\infty(0, T; L^2), \quad \rho u \in C([0, T]; L^2), \quad u \in L^\infty(0, T; D_0^1) \cap L^2(0, T; D^2), \quad \sqrt{\rho} u_t \in L^2(0, T; L^2), \quad \sqrt{\rho} u_t \in L^2(0, T; D_0^1). \] Remark 1.1. (i) Compared with the local well-posedness results established in [7, 8], in Theorem 1.1, $u_0$ is not required to be in $D^2$ and we do not need any compatibility conditions on the initial data. (ii) The same result as in 1.1 also holds for the initial boundary value problem if imposing suitable boundary conditions on the velocity. ### 2. Lifespan Estimate and Some a Priori Estimates As preparations of proving the main result being carried out in the next section, the aim of this section is to give the lifespan estimate and some a priori estimates, under the condition that the initial velocity $u_0 \in D_0^1 \cap D^2$ and some compatibility condition; however, it should be emphasized that all these estimates depend neither on $\\| \nabla^2 u_0 \\|_2$ nor on the compatibility condition. We start with the following local existence and uniqueness result, which has been essentially proved in [7, 8]. Proposition 2.1. Let $\rho_\infty \in [0, \infty)$ and $q \in (3, 6)$ be fixed constants. Assume that the data $\rho_0$ and $u_0$ satisfy the regularity condition \[ \rho_0 \geq 0, \quad \rho_0 - \rho_\infty \in H^1 \cap W^{1,q}, \quad u_0 \in D_0^1 \cap D^2, \] and the compatibility condition \[ -\mu \Delta u_0 - (\mu + \lambda) \nabla \text{div} u + \nabla P_0 = \sqrt{\rho_0} g, \] for some $g \in L^2$, where $P_0 = a \rho_0^{\gamma/2}$. Proposition 2.2. The following estimates hold generic constant depending only on (1.1)–(1.2), subject to (1.3), such that \[ \rho - \rho_\infty \in C([0, T_]; H^1 \cap W^{1,q}), \quad u \in C([0, T_]; D_0^1 \cap D^2) \cap L^2(0, T_; D^2), \] \[ \rho_t \in C([0, T_]; L^2 \cap L^q), \quad u_t \in L^2(0, T_; D_0^1), \quad \sqrt{\rho u_t} \in L^\infty(0, T_; L^2). \] As will be shown in this section, the existence time $ T_* $ in the above proposition can be chosen depending only on $ \mu, \lambda, a, \gamma, q $, and the upper bound of \[ \Psi_0 := \|\|\rho_0\|\|_\infty + \|\|P_0 - P_\infty\|\|_2 + \|\|P_0\|\|_\infty + \|\|\nabla P_0\|\|_2 + \|\|\nabla P_0\|\|_q + \|\|\nabla u_0\|\|_2, \] with $ P_\infty = a \rho_\infty^2 $, and, in particular, independent of $ \|\|\nabla^2 u_0\|\|_2 $ and $ \|\|g\|\|_2 $. The following quantity plays the key role in this section \[ \Psi(t) := (\|\|\rho\|\|_\infty + \|\|P - P_\infty\|\|_2 + \|\|P\|\|_\infty + \|\|\nabla P\|\|_2 + \|\|\nabla P\|\|_q + \|\|\nabla u\|\|_2 + \|\|\sqrt{t} \sqrt{\rho u_t}\|\|_2) \cdot (t + 1). \] In the rest of this section, until the last proposition, we always assume $(\rho, u)$ is a solution to system (1.1)–(1.2), subject to (1.3), on $ \mathbb{R}^3 \times (0, T) $, satisfying the regularities stated in Proposition 2.1 with $ T_* $ there replaced with $ T $. Throughout this section, except otherwise explicitly mentioned, we denote by $ C $ a generic constant depending only on $ \mu, \lambda, a, \gamma, q $, and the upper bound of $ \Psi_0 $. Proposition 2.2. The following estimates hold \[ \|\|\nabla^2 u\|\|_2^2 \leq C(\Psi^{10} + \Psi \|\|\sqrt{\rho} u_t\|\|_2^2), \] \[ \|\|\sqrt{\rho} (u \cdot \nabla) u\|\|_2 \leq C(\Psi^9 + \Psi^5 \|\|\sqrt{\rho} u_t\|\|_2), \] \[ \|\|\nabla^2 u\|\|_q \leq C(\sqrt{t} \|\|\nabla u_t\|\|_2^2 + \|\|\sqrt{\rho} u_t\|\|_2^2 + t^{-\frac{5q-6}{4q}} + \Psi^{a_1}), \quad q \in (3, 6), \] with $ a_1 := \max \left\{ 12, \frac{(5q-6)^2}{2q(6-q)} \right\} $. Proof. Applying the elliptic estimates to (1.1) yields \[ \|\|\nabla^2 u\|\|_2^2 \leq C \|\|\rho\|\|_\infty (\|\|\sqrt{\rho} u_t\|\|_2^2 + \|\|\sqrt{\rho} (u \cdot \nabla) u\|\|_2^2) + C \|\|\nabla P\|\|_2^2. \] By the Hölder and Sobolev inequality, one has \[ \|\|\sqrt{\rho} (u \cdot \nabla) u\|\|_2 \leq \|\|\rho\|\|_\infty \|\|u\|\|_6^2 \|\|\nabla u\|\|_2 \|\|\nabla u\|\|_6 \leq C \Psi^4 \|\|\nabla^2 u\|\|_2. \] Substituting the above inequality into the previous one and using the Cauchy inequality, one gets \[ \|\|\nabla^2 u\|\|_2^2 \leq C (\Psi \|\|\sqrt{\rho} u_t\|\|_2^2 + \Psi^5 \|\|\nabla^2 u\|\|_2 + \Psi^2) \] \[ \leq \frac{1}{2} \|\|\nabla^2 u\|\|_2^2 + C (\Psi \|\|\sqrt{\rho} u_t\|\|_2^2 + \Psi^{10}), \] that is \[ \|\|\nabla^2 u\|\|_2^2 \leq C (\Psi^{10} + \Psi \|\|\sqrt{\rho} u_t\|\|_2^2), \quad (2.1) \] and, consequently, \[ \\| \sqrt{\rho} (u \cdot \nabla) u \\|_2^2 \leq C (\Psi^5 + \Psi^6 \\| \sqrt{\rho} u_t \\|_2), \] proving the first two conclusions. It follows from the Hölder and Gagliardo-Nirenberg inequalities that \[ \\| \rho (u \cdot \nabla) u \\|_q \leq \\| \rho \\|_\infty \\| u \\|_{\frac{6q}{6q-9}} \\| \nabla u \\|_6 \] \[ \leq C \\| \rho \\|_\infty \\| u \\|_6^\frac{3}{q} \\| \nabla u \\|_6^\frac{3}{q} \leq C \\| \rho \\|_\infty \\| \nabla u \\|_2^\frac{3}{q} \\| \nabla^2 u \\|_2^\frac{2q-3}{q}, \tag{2.2} \] from which, by the Young inequality and using (2.1), one has \[ \\| \rho (u \cdot \nabla) u \\|_q \leq C \Psi^{\frac{q+3}{q}} (\Psi^{10} + \Psi \\| \sqrt{\rho} u_t \\|_2^2)^{\frac{2q-3}{2q}} \] \[ \leq C \Psi^{3} (\Psi^{9} + \\| \sqrt{\rho} u_t \\|_2^2)^{\frac{2q-3}{q}} \] \[ \leq C (\Psi^{3q} + \Psi^9 + \\| \sqrt{\rho} u_t \\|_2^2) \leq C (\Psi^{12} + \\| \sqrt{\rho} u_t \\|_2^2). \] It follows from the Hölder and Sobolev inequalities that \[ \\| \rho u_t \\|_q \leq \\| \rho \\|_\infty \\| \sqrt{\rho} u_t \\|_2^\frac{q-6}{q} \\| u_t \\|_6^\frac{6q-6}{2q} \leq C \\| \rho \\|_\infty \\| \sqrt{\rho} u_t \\|_2^\frac{q-6}{q} \\| u_t \\|_2^\frac{6q-6}{2q}, \tag{2.3} \] and further by the Young inequality that \[ \\| \rho u_t \\|_q \leq C \Psi^{\frac{q-6}{q} - \frac{3q-6}{2q}} \\| \sqrt{\nabla u_t} \\|_2^{\frac{3q-6}{2q}} \\| \sqrt{\rho u_t} \\|_2^{\frac{6q-6}{q}} \] \[ \leq C (\\| \sqrt{\nabla u_t} \\|_2^2 + \\| \sqrt{\rho u_t} \\|_2^2 + \Psi^{\frac{q-6}{2q}} + \Psi^{\frac{q-6}{2q}}). \] Thanks to the above two, and applying the elliptic estimates to (1.1), one obtains \[ \\| \nabla^2 u \\|_q \leq C (\\| \rho u_t \\|_q + \\| \rho (u \cdot \nabla) u \\|_q + \\| \nabla P \\|_q) \] \[ \leq C (\\| \sqrt{\nabla u_t} \\|_2^2 + \\| \sqrt{\rho u_t} \\|_2^2 + \Psi^{\frac{q-6}{2q}} + \Psi^{\alpha_1}), \] proving the conclusion. $ \square $ Proposition 2.3. The following estimate holds \[ \sup_{0 \leq t \leq T} \left( \\| \nabla u \\|_2^4 + \\| P - P_{\infty} \\|_2^2 \right) + \int_0^T \\| \sqrt{\rho} u_t \\|_2^2 dt \leq C + C \int_0^T \Psi^{10} dt. \] Proof. Multiplying (1.1) with $ u_t $, it follows from integration by parts that \[ \frac{1}{2} \frac{d}{dt} (\mu \\| \nabla u \\|_2^2 + (\mu + \lambda) \\| \nabla u \\|_2^2) + \\| \sqrt{\rho} u_t \\|_2^2 = - \int (\rho (u \cdot \nabla) u + \nabla P) \cdot u_t dx. \] Integration by parts and noticing that \[ P_t + u \cdot \nabla P + \gamma \text{div} u P = 0, \tag{2.4} \] on one deduces \[ - \int \nabla P \cdot u_t dx = \int (P - P_{\infty}) \text{div} u_t dx \] \[ \begin{align} &= \frac{d}{dt} \int (P - P_\infty) \text{div } u \, dx - \int P_t \text{div } u \, dx \\ &= \frac{d}{dt} \int (P - P_\infty) \text{div } u \, dx + \int (u \cdot \nabla P + \gamma \text{div } uP) \text{div } u \, dx. \end{align} \] Therefore \[ \frac{d}{dt} \left( \mu \\|\nabla u\\|_2^2 + (\mu + \lambda) \\|\text{div } u\\|_3^2 - 2 \int (P - P_\infty) \text{div } u \, dx \right) + \\|\sqrt{\rho} u_t\\|_2^2 \\ = \int (u \cdot \nabla P + \gamma \text{div } uP) \text{div } u \, dx - \int \rho (u \cdot \nabla) u_t \, dx =: I_1 + I_2. \] By the Hölder, Sobolev, and Young inequalities, and applying Proposition 2.2, one has \[ I_1 \leq \\|u\\|_6 \\|\nabla P\\|_2 \\|\text{div } u\\|_3 + \gamma \\|\text{div } u\\|_3 \\|P\\|_\infty \\ \leq C \\|\nabla u\\|_2 \\|\nabla P\\|_2 \\|\nabla u\\|_2^\frac{1}{2} \\|\nabla^2 u\\|_2^\frac{1}{2} + C \Psi^3 \\ \leq C \Psi^\frac{3}{2} (\Psi^\frac{5}{2} + \Psi^\frac{7}{2} \\|\sqrt{\rho} u_t\\|_2^\frac{3}{2}) + C \Psi^3 \\ \leq \frac{1}{4} \\|\sqrt{\rho} u_t\\|_2^2 + C \Psi^5, \] and \[ I_2 \leq \\|\sqrt{\rho} u_t\\|_2 \\|\sqrt{\rho} (u \cdot \nabla) u\\|_2 \\ \leq C (\Psi^\frac{9}{2} + \Psi^\frac{1}{2} \\|\sqrt{\rho} u_t\\|_2^\frac{5}{2}) \\|\sqrt{\rho} u_t\\|_2 \\ \leq \frac{1}{4} \\|\sqrt{\rho} u_t\\|_2^2 + C \Psi^{10}. \] Therefore \[ \frac{1}{2} \frac{d}{dt} \left( \mu \\|\nabla u\\|_2^2 + (\mu + \lambda) \\|\text{div } u\\|_2^2 - 2 \int (P - P_\infty) \text{div } u \, dx \right) + \\|\sqrt{\rho} u_t\\|_2^2 \leq C \Psi^{10}, \] from which, one obtains by the Cauchy inequality that \[ \sup_{0 \leq t \leq T} \\|\nabla u\\|_2^2 + \int_0^T \\|\sqrt{\rho} u_t\\|_2^2 \, dt \leq C \left( 1 + \sup_{0 \leq t \leq T} \\|P - P_\infty\\|_2^2 + \int_0^T \Psi^{10} \, dt \right). \tag{2.5} \] Multiplying (2.3) with $P - P_\infty$, it follows from integration by parts and the Sobolev inequality that \[ \frac{d}{dt} \\|P - P_\infty\\|_2^2 = -(\gamma - \frac{1}{2}) \int \text{div } u(P - P_\infty)^2 \, dx - \gamma P_\infty \int \text{div } u(P - P_\infty) \, dx \\ \leq C \\|\nabla u\\|_2 \\|P - P_\infty\\|_2 \\|\nabla P\\|_2^\frac{1}{2} + C \\|\nabla u\\|_2 \\|P - P_\infty\\|_2 \leq C \Psi^3, \] which gives \[ \sup_{0 \leq t \leq T} \\|P - P_\infty\\|_2^2 \leq C + C \int_0^T \Psi^3 \, dt. \] This, combined with (2.5), leads to the conclusion. The $ t $-weighted estimate in the next proposition is the key to remove the compatibility condition on the initial data. Proposition 2.4. The following estimate holds \[ \sup_{0 \leq t \leq T} \\| \sqrt{t} \rho u_t \\|_2^2 + \int_0^T \\| \sqrt{t} \nabla u_t \\|_2^2 dt \leq C + C \int_0^T \psi^{16} dt. \] Proof. Differentiating (1.1) in $ t $ and using (1.2) yield \[ \rho_t + (u \cdot \nabla) u - \mu \Delta u - (\lambda + \mu) \nabla \text{div} u = -\nabla P + \text{div} (\rho u)(u_t + (u \cdot \nabla) u) - \rho (u_t \cdot \nabla) u. \] Multiplying it by $ u $, integrating by parts over $ \mathbb{R}^3 $ and then using the continuity equation (1.2), one has \[ \frac{1}{2} \frac{d}{dt} \\| \sqrt{\rho} u_t \\|_2^2 + \mu \\| \nabla u_t \\|_2^2 + (\lambda + \mu) \\| \text{div} u_t \\|_2^2 \] \[ = \int P_t \text{div} u_t dx + \int (\rho u_t \cdot \nabla) \|u_t\|^2 dx + \int (\rho u_t \cdot \nabla) u \cdot u_t dx \] \[ - \int \rho (u_t \cdot \nabla) u \cdot u_t dx =: II_1 + II_2 + II_3 + II_4. \] Recalling (2.4) and using the Sobolev and Young inequalities, one deduces \[ II_1 = -\int (\gamma \text{div} u P + u \cdot \nabla P) \text{div} u_t dx \] \[ \leq C (\\| P \\|_\infty \\| \nabla u \\|_2 \\| \nabla u_t \\|_2 + \\| u \\|_6 \\| \nabla P \\|_3 \\| \nabla u_t \\|_2) \] \[ \leq C (\psi^4 + \\| \nabla u \\|_2^2 \\| \nabla P \\|_{L^2(\mathbb{R}^3)}^2) + \frac{\mu}{8} \\| \nabla u_t \\|_2^2 \] \[ \leq C \psi^4 + \frac{\mu}{8} \\| \nabla u_t \\|_2^2. \] Integrating by parts, using the Hölder, Sobolev and Young inequalities, and applying Proposition 2.2, we have \[ II_2 = -\int_{\mathbb{R}^3} \rho u \cdot \nabla \|u_t\|^2 dx \] \[ \leq C \\| \rho \\|_{\frac{3}{2}} \\| u \\|_6 \\| \sqrt{\rho} u_t \\|_2 \\| \nabla u_t \\|_2 \] \[ \leq C \\| \rho \\|_{\frac{3}{2}} \\| \nabla u \\|_2 \\| \sqrt{\rho} u_t \\|_2 \\| \nabla u_t \\|_2 \] \[ \leq C \psi^7 \\| \sqrt{\rho} u_t \\|_2^2 + \frac{\mu}{8} \\| \nabla u_t \\|_2^2. \] \[ II_3 \leq \int_{\mathbb{R}^3} \rho \|u\| (\|\nabla u\|^2 + \|u\| \|\nabla^2 u\| + \|u\|\| \nabla u\| \|\nabla u\|) dx \] \[ \leq C\\|\rho\\|_\infty (\\|u\\|_6 \\|\nabla u\\|_3^2 \\|u_t\\|_6 + \\|u\\|_2^2 \\|\nabla^2 u\\|_2 \\|u_t\\|_6 \\ + \\|u\\|_6^2 \\|\nabla u\\|_6 \\|\nabla u_t\\|_2) \leq C\\|\rho\\|_\infty \\|\nabla u\\|_2^2 \\|\nabla^2 u\\|_2 \\|\nabla u_t\\|_2 \leq C \Psi^6 \\|\nabla^2 u\\|_2^2 + \frac{\mu}{8} \\|\nabla u_t\\|_2^2 \leq C(\Psi^{16} + \Psi^7 \\|\sqrt{\rho} u_t\\|_2^2) + \frac{\mu}{8} \\|\nabla u_t\\|_2^2 \] and \[ II_4 \leq \int_{\mathbb{R}^3} \rho \|u_t\|^2 \|\nabla u\| \, dx \leq C\\|\rho\\|_\infty^{\frac{1}{3}} \\|\nabla u\\|_2 \\|\sqrt{\rho} u_t\\|_2^{\frac{1}{3}} \\|\sqrt{\rho} u_t\\|_6^{\frac{1}{3}} \\|u_t\\|_6 \leq C\\|\rho\\|_\infty^{\frac{3}{4}} \\|\nabla u\\|_2 \\|\sqrt{\rho} u_t\\|_2^{\frac{3}{2}} \\|\nabla u_t\\|_2^{\frac{3}{2}} \leq C \Psi^7 \\|\sqrt{\rho} u_t\\|_2^2 + \frac{\mu}{8} \\|\nabla u_t\\|_2^2. \] Therefore, we have \[ \frac{d}{dt} \\|\sqrt{\rho} u_t\\|_2^2 + \mu \\|\nabla u_t\\|_2^2 \leq C(\Psi^{16} + \Psi^7 \\|\sqrt{\rho} u_t\\|_2^2), \] which, multiplied by $ t $, gives \[ \frac{d}{dt} \\|\sqrt{t} \sqrt{\rho} u_t\\|_2^2 + \mu \\|\sqrt{t} \nabla u_t\\|_2^2 \leq C(\Psi^{16} + \Psi^7 \\|\sqrt{t} \sqrt{\rho} u_t\\|_2^2 + \\|\sqrt{\rho} u_t\\|_2^2) \leq C(\Psi^{16} + \\|\sqrt{\rho} u_t\\|_2^2). \] Integrating this in $ t $ and applying Proposition 2.3, the conclusion follows. Proposition 2.5. The following estimate holds \[ \int_0^T (\\|\nabla u\\|_\infty + \\|\nabla^2 u\\|_q) \, dt \leq C + C \int_0^T \Psi^\alpha_2 \, dt, \] with $ \alpha_2 := \max \{16, \alpha_1\} = \max \left\{16, \frac{(5q-6)^2}{2q(6-q)}\right\} $. Proof. Noticing that $ t^{-\frac{5q-6}{4q}} \in (0, 1) $, for $ q \in (3, 6) $, and recalling the following estimate by Proposition 2.2 \[ \\|\nabla^2 u\\|_q \leq C(\\|\sqrt{t} \nabla u_t\\|_2^2 + \\|\sqrt{\rho} u_t\\|_2^2 + t^{-\frac{5q-6}{4q}} \\|\nabla u\\|_2^2 + \Psi^{\alpha_1}), \] it follows from the Gagliardo-Nirenberg and Young inequalities and Propositions 2.3 and 2.4 that \[ \int_0^T \\|\nabla u\\|_\infty \, dt \leq C \int_0^T \\|\nabla u\\|_2^{1-\theta} \\|\nabla^2 u\\|_q^\theta \, dt \] $$\leq C \int_0^T (\\|\nabla u\\|_2 + \\|\nabla^2 u\\|_q) dt$$ $$\leq C \int_0^T (\\|\sqrt{t} \nabla u_t\\|_2^2 + \\|\sqrt{\rho} u_t\\|_2^2 + t^{-\frac{5q-6}{4q}} + \Psi^{\alpha_1}) dt$$ $$\leq C + C \int_0^T \Psi^{\alpha_2} dt,$$ where $ \theta = \frac{3q}{5q-6} \in (0,1) $, proving the conclusion. \[\Box\] Proposition 2.6. The following estimate holds $$\sup_{0 \leq t \leq T} (\\|\rho\\|_\infty + \\|P\\|_\infty) \leq C \exp \left( C \int_0^T \Psi^{\alpha_2} dt \right),$$ where $ \alpha_2 $ is the number in Proposition 2.5. Proof. Define $ X(t; x) $ as $$\begin{cases} \frac{d}{dt}X(t; x) = u(X(t; x), t), \\ X(0; x) = x. \end{cases}$$ One can show that for any $ t \in (0, T) $, and for any $ y \in \mathbb{R}^3 $, there is a unique $ x \in \mathbb{R}^3 $, such that $ X(t; x) = y $, and, in particular, $ X(t; \mathbb{R}^3) = \mathbb{R}^3 $; in fact, to show this, it suffices to consider the backward problem $ \frac{d}{dt}Z(t) = u(Z(t), t), X(T; x) = y $. Then, by (1.2), it has $$\frac{d}{dt} \rho(X(t; x), t) = \partial_t \rho(X(t; x), t) + u(X(t; x), t) \cdot \nabla \rho(X(t; x), t)$$ $$= -\text{div} u(X(t; x), t) \rho(X(t; x), t),$$ and, thus, $$\rho(X(t; x), t) = \rho_0(x) \exp \left(- \int_0^t \text{div} u(X(\tau; x), \tau) d\tau \right). \quad (2.6)$$ Therefore, $$\\|\rho\\|_\infty(t) = \\|\rho(X(t; x), t)\\|_\infty(t)$$ $$\leq \\|\rho_0\\|_\infty \exp \left( \int_0^T \\|\nabla u\\|_\infty dt \right),$$ and the conclusion follows by applying Proposition 2.4. \[\Box\] Proposition 2.7. The following estimate holds $$\sup_{0 \leq t \leq T} (\\|\nabla P\\|_2 + \\|\nabla P\\|_q) \leq C \exp \left( C \int_0^T \Psi^{\alpha_2} dt \right), \quad q \in (3, 6),$$ where $ \alpha_2 $ is the number in Proposition 2.5. Proof. From (2.4), one has \[ \partial_t \nabla P + \gamma \text{div} u \nabla P + \gamma P \nabla \text{div} u + (u \cdot \nabla) \nabla P + \nabla P \nabla u = 0. \] Multiplying the above by $\|\nabla P\|^{p-2} \nabla P\|$, integrating over $\mathbb{R}^3$, one has \[ \frac{d}{dt} \\| \nabla P \\|_p \leq C (\\| \nabla u \\|_{\infty} \\| \nabla P \\|_p + \\| P \\|_{\infty}^p \\| \nabla^2 u \\|_p \\| \nabla P \\|_p^{p-1}), \] which gives \[ \frac{d}{dt} \\| \nabla P \\|_p \leq C (\\| \nabla u \\|_{\infty} \\| \nabla P \\|_p + \\| P \\|_{\infty} \\| \nabla^2 u \\|_p). \] By the Gronwall inequality, one has \[ \sup_{0 \leq t \leq T} \\| \nabla P \\|_p \leq C \left( \\| \nabla P_0 \\|_p + \int_0^T \\| \nabla \\|_p \\| \nabla^2 u \\|_p dt \right) \exp \left( C \int_0^T \\| \nabla u \\|_{\infty} dt \right) \] \tag{2.7} Thanks to the above, it follows from Proposition 2.5 and Proposition 2.6 that \[ \sup_{0 \leq t \leq T} \\| \nabla P \\|_q \leq C \left( 1 + \int_0^T \\| \nabla^2 u \\|_p dt \right) \exp \left( C \int_0^T \Psi^{\alpha_2} dt \right) \] where we have used the fact that $ e^z \geq 1 + z $ for $ z \geq 0 $. By Proposition 2.2 and Proposition 2.3, it follows from (2.7) and the Cauchy inequality that \[ \sup_{0 \leq t \leq T} \\| \nabla P \\|_2 \leq C \left[ 1 + \int_0^T (\Psi^5 + \Psi^{\frac{5}{2}} \\| \sqrt{\rho u_t} \\|_2) dt \right] \exp \left( C \int_0^T \Psi^{\alpha_2} dt \right) \] This proves the conclusion. $ \square $ Proposition 2.8. The following estimates hold \[ \sup_{0 \leq t \leq T} (\\| \rho - \rho_\infty \\|_2 + \\| \nabla \rho \\|_2 + \\| \nabla \rho \\|_q) \leq C \exp \left( C \int_0^T \Psi^{\alpha_2} dt \right), \quad q \in (3, 6), \] with constant $C$ depending also on $\\|\rho_0 - \rho_\infty\\|_2 + \\|\nabla \rho_0\\|_2 + \\|\nabla \rho_0\\|_q$, and \[ \sup_{0 \leq t \leq T} \\|\sqrt{t} \nabla^2 u\\|_2^2 \leq C \sup_{0 \leq t \leq T} (\Psi^{10} + \Psi \\|\sqrt{t} \rho u_t\\|_2^2), \] where $\alpha_2$ is the number in Proposition 2.7. Proof. The estimate of $\\|\rho - \rho_\infty\\|_2$ follows in the same way as that for $\\|P - P_\infty\\|_2$ in Proposition 2.3, while those for $\\|\nabla \rho\\|_2$ and $\\|\nabla \rho\\|_q$ can be proved similarly as in Proposition 2.7. The conclusion for $\\|\sqrt{t} \nabla^2 u\\|_2^2$ follows from combining Propositions 2.2 and 2.4. $\square$ We end up this section with the following proposition on the lifespan estimate and a priori estimates. Proposition 2.9. Assume in addition to the conditions in Proposition 2.1 that $\rho \geq \rho$ for some positive constant $\rho$. Then, there are two positive constants $T$ and $C$ depending only on $\mu$, $\lambda$, $a$, $\gamma$, $q$, and the upper bound of $\psi_0 := \\|\rho_0\\|_\infty + \\|\rho_0 - \rho_\infty\\|_2 + \\|\nabla \rho_0\\|_{L^2 \cap L^q} + \\|\nabla u_0\\|_2$, and, in particular, independent of $\rho$ and $\\|\nabla u_0\\|_2$, such that system (1.1)–(1.2), subject to (1.3), has a unique solution $(\rho, u)$ on $\mathbb{R}^3 \times (0, T)$, enjoying the regularities stated in Proposition 2.4, with $T_$ there replaced by $T$, and the following a priori estimates \[ \sup_{0 \leq t \leq T} (\\|\rho\\|_\infty + \\|\rho_0 - \rho_\infty\\|_2 + \\|\nabla \rho\\|_2 + \\|\nabla \rho\\|_q + \\|\rho\\|_2) \leq C, \] \[ \sup_{0 \leq t \leq T} \\|\nabla u\\|_2^2 + \int_0^T (\\|\nabla^2 u\\|_2^2 + \\|\sqrt{t} \rho u_t\\|_2^2) dt \leq C, \] \[ \sup_{0 \leq t \leq T} (\\|\sqrt{t} \rho u_t\\|_2^2 + \\|\sqrt{t} \nabla^2 u\\|_2^2) + \int_0^T (\\|\sqrt{t} \nabla u_t\\|_2^2 + \\|\sqrt{t} \nabla^2 u\\|_q^2) dt \leq C. \] Proof. Define the maximal time $T_{\text{max}}$ as \[ T_{\text{max}} := \max \{ T \in \mathcal{T} \}, \] where \[ \mathcal{T} := \{ T \in [T_, \infty) \mid \text{There is a solution } (\rho, u) \text{ in the class } \mathcal{D}_T \text{ to system (1.1)–(1.2), subject to (1.3), on } \mathbb{R}^3 \times (0, T) \}, \] where $\mathcal{D}_T$ is the class of $(\rho, u)$ enjoying the regularities as stated in Proposition 2.1 with $T_$ there replaced with $T$. By Proposition 2.1, it is clear that $T_{\text{max}}$ is well defined and $T_{\text{max}} \geq T_$. Moreover, by the uniqueness result, see the proof of the uniqueness part of Theorem 1.1 in the next section, one can easily show that any two solutions $(\bar{\rho}, \bar{u})$ and $(\tilde{\rho}, \tilde{u})$ to system (1.1)–(1.2), subject to (1.3), on $\mathbb{R}^3 \times (0, \bar{T})$ and on $\mathbb{R}^3 \times (0, \tilde{T})$, respectively, coincide on $\mathbb{R}^3 \times (0, \min\{\bar{T}, \tilde{T}\})$. Choose $T_k \in \mathcal{T}$ with $T_k \uparrow T_{\max}$ as $k \uparrow \infty$. By definition of $\mathcal{T}$, there is a solution $(\rho_k, u_k)$ to system (1.1)–(1.2), subject to (1.3), on $\mathbb{R}^3 \times (0, T_k)$. Define $(\rho, u)$ on $\mathbb{R}^3 \times (0, T_{\max})$ as $$(\rho, u)(x, t) = (\rho_k, u_k)(x, t), \quad x \in \mathbb{R}^3, t \in (0, T_k), k = 1, 2, \cdots.$$ Applying the uniqueness result again, the definition of $(\rho, u)$ is independent of the choice of the sequence $\{T_k\}_{k=1}^{\infty}$. By the construction of $(\rho, u)$, one can verify that $(\rho, u)$ is a solution to (1.1)–(1.2), subject to (1.3), on $\mathbb{R}^3 \times (0, T_{\max})$, and $(\rho, u) \in \mathcal{X}_T$, for any $T \in (0, T_{\max})$. By Propositions 2.3, 2.4, 2.6, and 2.7, it is clear that $$(\rho, u)(x, t) \in \mathbb{R}^3 \times (0, T_{\max}),$$ where $C_m$ is a positive constant depending only on $\mu, \lambda, a, \gamma, q,$ and the upper bound of $\psi_0$. Here we have used the fact that $\Psi_0$ can be controlled by $\psi_0$. One can easily derive from the above inequality that $$(\rho, u)(x, t) \leq 2^{\frac{1}{\alpha^2}} C_m, \quad \forall t \in (0, \min \{T_{\max}, (2^{\alpha^2} C_m^{\alpha+1})^{-1}\}).$$ (2.8) Thanks to the above estimate, one can get by applying Propositions 2.5 and 2.8 that $$\left(\\|\rho - \rho_\infty\\|_2 + \\|\nabla \rho\\|_2 + \\|\nabla u\\|_q + \\|\sqrt{\nabla^2 u}\\|_{\alpha}\right) (t) + \int_0^t \\|\nabla u\\|_{\infty} d\tau \leq C.$$ (2.9) for any $t \in (0, \min \{T_{\max}, (2^{\alpha^2} C_m^{\alpha+1})^{-1}\})$, and for a positive constant $C$ depending only on $\mu, \lambda, a, \gamma, q,$ and the upper bound of $\psi_0$. Thanks to (2.8)–(2.9) and using (1.2) one can further obtain $$\\|\nabla u\\|_2 \leq C(1 + \\|\nabla \rho\\|_3 + \\|\nabla u\\|_2) \leq C_1,$$ (2.10) for any $0 < t < \min \{T_{\max}, (2^{\alpha^2} C_m^{\alpha+1})^{-1}\}$. Using the estimate $\int_0^t \\|\nabla u\\|_{\infty} d\tau \leq C$ in (2.9) and recalling (2.6), it is clear that $$(\rho, u)(x, t) \geq C \rho_0, \quad x \in \mathbb{R}^3, \quad 0 < t < \min \{T_{\max}, (2^{\alpha^2} C_m^{\alpha+1})^{-1}\}.$$ (2.11) We claim that $T_{\max} > (2^{\alpha^2} C_m^{\alpha+1})^{-1}$. Assume in contradiction that this does not hold. Then, all the estimates in (2.8)–(2.11) hold for any $t \in (0, T_{\max})$. Estimates (2.8)–(2.11), holding on time interval $(0, T_{\max})$, guarantee that $(\rho, u)(\cdot, t)$ can be uniquely extended to time $T_{\max}$, with $(\rho, u)(\cdot, T_{\max})$ defined as the limit of $(\rho, u)(\cdot, t)$ as $t \uparrow T_{\max}$, and that $$(\rho - \rho_\infty)(\cdot, T_{\max}) \in H^1 \cap W^{1,q}, \quad u(\cdot, T_{\max}) \in D^{1} \cap D^2.$$ Thanks to this and recalling (2.11), it is clear that the compatibility condition holds at time $T_{\max}$. Therefore, by the local well-posedness result, i.e., Proposition 2.1, one can further extend solution $(\rho, u)$ beyond the time $T_{\max}$, which contradicts to the definition of $T_{\max}$. This contradiction proves the claim that $T_{\max} > (2^{\alpha^2} C_m^{\alpha+1})^{-1}$. As a result, one obtains a solution $(\rho, u)$ on time interval $(0, (2^{\alpha_2}C^{\alpha_2+1})^{-1})$ satisfying all the a priori estimates in (2.8)-(2.10), except $\int_0^T \\|\sqrt{t}\nabla^2 u\\|^2_q dt \leq C$, on the same time interval. It remains to verify $\int_0^T \\|\sqrt{t}\nabla^2 u\\|^2_q dt \leq C$. To this end, recalling (2.2) and (2.3), it follows from the elliptic estimate, the estimates just obtained, and the Young inequality that \[ \\|\nabla^2 u\\|_q \leq C(\\|\rho u_t\\|_q + \\|\rho(\nabla)u\\|_q + \\|\nabla P\\|_q) \] \[ \leq C(1 + \\|\nabla^2 u\\|^2_2 + \\|\sqrt{\rho}u_t\\|_2 + \\|\nabla u_t\\|_2), \] and further that \[ \int_0^T \\|\sqrt{t}\nabla^2 u\\|^2_q dt \leq C \int_0^T (1 + \\|\nabla^2 u\\|^2_2 + \\|\sqrt{\rho}u_t\\|^2_2 + \\|\sqrt{\nabla}u_t\\|^2_2) dt \leq C, \] proving the conclusion. $\square$ ### 3. Proof of Theorem 1.1 This section is devoted to proving Theorem 1.1. The following lemma, proved in [33], will be used in proving the uniqueness. Lemma 3.1. Given a positive time $T$ and nonnegative functions $f, g, G$ on $[0, T]$, with $f$ and $g$ being absolutely continuous on $[0, T]$. Suppose that \[ \begin{cases} \frac{d}{dt} f(t) \leq \delta(t) f(t) + A \sqrt{G(t)}, \\ \frac{d}{dt} g(t) + G(t) \leq \alpha(t) g(t) + \beta(t) f^2(t), \\ f(0) = 0, \end{cases} \] where $\alpha, \beta$ and $\delta$ are three nonnegative functions, with $\alpha, \delta, t, \beta \in L^1((0, T))$. Then, then following estimates hold \[ f(t) \leq AB \sqrt{tg(0)} \exp \left(\frac{1}{2} \int_0^t (\alpha(s) + A^2 B^2 s \beta(s)) ds\right), \] \[ g(t) + \int_0^t G(s) ds \leq g(0) \exp \left(\int_0^t (\alpha(s) + A^2 B^2 s \beta(s)) ds\right), \] where $B = 1 + e^{\int_0^T \delta(r) dr}$. In particular, if $g(0) = 0$, then $f \equiv g \equiv 0$ on $(0, T)$. We are now ready to prove Theorem 1.1. Proof of Theorem 1.1. We first prove the uniqueness and then the existence. Uniqueness: Let $(\hat{\rho}, \hat{u}), (\tilde{\rho}, \tilde{u})$ be two solutions of system (1.1)-(1.2), subject to (1.3), on $\mathbb{R}^3 \times (0, T)$, satisfying the regularities stated in the theorem. For $u \in \{\hat{u}, \tilde{u}\}$, by the Gagliardo-Nirenberg and Hölder inequalities, one has \[ \int_0^T \\| \nabla u \\|_\infty \, dt \leq C \int_0^T \\| \nabla u \\|_2^{1-\theta} \\| \nabla^2 u \\|_q^\theta \, dt \leq C \left( \int_0^T \\| \sqrt{t} \nabla^2 u \\|_q^{\theta} \, dt \right)^{\frac{1-\theta}{2}} \left( \int_0^T \sqrt{t} \, dt \right)^{\frac{\theta}{2}} < \infty, \] where $ \theta = \frac{3q}{2q-6} \in (0, 1) $. Therefore, $ \nabla \hat{u}, \nabla \check{u} \in L^1(0, T; L^\infty) $. Denote $ \sigma = \hat{\rho} - \check{\rho} $, $ W = \hat{P} - \check{P} $, $ v = \check{u} - \hat{u} $. Then, straightforward calculations show \[ \begin{align} \sigma_t + v \cdot \nabla \hat{\rho} + \check{u} \cdot \nabla \sigma + \text{div } \hat{u} \sigma + \text{div } v \check{\rho} &= 0, \quad (3.1) \\ \hat{\rho}(v_t + \hat{u} \cdot \nabla v) - \mu \Delta v - (\lambda + \mu) \nabla \text{div } v + \nabla W &= -\sigma \check{u}_t - \sigma \check{u} \cdot \nabla \check{u} - \check{\rho} v \cdot \nabla \check{u}, \quad (3.2) \\ W_t + v \cdot \nabla \hat{P} + \check{u} \cdot \nabla W + \gamma \text{div } \check{u} W + \gamma \text{div } v \check{P} &= 0. \quad (3.3) \end{align} \] Testing (3.1) with $ \sigma $ and using the Hölder inequality, we have \[ \frac{d}{dt} \int \|\sigma\|^2 \, dx \leq C \int (\|v \cdot \nabla \hat{\rho}\| \|\sigma\| + \|\text{div } \hat{u}\| \|\sigma\|^2 + \|\text{div } v \check{\rho}\| \|\sigma\|) \leq C(\|\nabla \hat{\rho}\|_3 \|\|\sigma\|\|_2 \|v\|_6 + \|\|\nabla \hat{u}\|_\infty \|\|\sigma\|\|_2^2) + C\|\|\hat{\rho}\|_\infty \|\|\nabla v\|\|_2 \|\|\sigma\|\|_2 \leq C\|\|\nabla \hat{u}\|_\infty \|\|\sigma\|\|_2^2 + C(\|\|\hat{\rho}\|_\infty + \|\|\nabla \hat{\rho}\|_3\|\|) \|\|\nabla v\|\|_2 \|\|\sigma\|\|_2, \] and, thus, \[ \frac{d}{dt} \|\|\sigma\|\|_2 \leq C\|\|\nabla \hat{u}\|_\infty \|\|\sigma\|\|_2 + C(\|\|\hat{\rho}\|_\infty + \|\|\nabla \hat{\rho}\|_3\|\|) \|\|\nabla v\|\|_2. \quad (3.4) \] Similarly, by testing (3.3) with $ W $ yields \[ \frac{d}{dt} \|\|W\|\|_2 \leq C\|\|\nabla \hat{u}\|_\infty \|\|W\|\|_2 + C(\|\|\nabla \hat{P}\|_3 + \|\|\check{P}\|_\infty\|\|) \|\|\nabla v\|\|_2. \quad (3.5) \] Testing (3.2) with $ v $ and using the Hölder and Young inequalities, we have \[ \frac{1}{2} \frac{d}{dt} \int \|\hat{\rho}\|\|v\|^2 \, dx + \int [\mu\|\nabla v\|^2 + (\lambda + \mu)(\text{div } v)^2] \, dx \leq \int (\|\|W\|\| \|\|\nabla v\|\| + \|\|\|\sigma\|\| \check{u}_t \|\|v\|\| + \|\|\|\sigma\|\| \hat{u} \|\|\nabla \hat{u}\|\| \|\|v\|\| + \|\hat{\rho}(v \cdot \nabla \hat{u}) \cdot v\|) \, dx =: \text{RHS.} \quad (3.6) \] We proceed the proof separately for the cases $ \rho_\infty = 0 $ and $ \rho_\infty > 0 $. Case I: $ \rho_\infty = 0 $. By the Hölder, Sobolev, and Young inequalities, we can control $ \text{RHS} $ as \[ \text{RHS} \leq \|\|W\|\|_2 \|\|\nabla v\|\|_2 + \|\|\|\sigma\|\|_2 \hat{u}_t \|\|v\|\|_6 + \|\|\|\sigma\|\|_2 \check{u}_t \|\|\nabla \hat{u}\|\|_6 + \|\|\nabla \hat{u}\|\|_\infty \sqrt{\check{\rho} v} \|\|v\|\|_2^2 \leq C(\|\|W\|\|_2 \|\|\nabla v\|\|_2 + \|\|\|\sigma\|\|_2 \|\|\nabla \hat{u}\|\|_2 \|\|\nabla v\|\|_2 \] which plugged into (3.6) leads to \[ \frac{d}{dt} \\| \sqrt{\rho v} \\|_2^2 + \mu \\| \nabla v \\|_2^2 \leq C \\| \nabla \tilde{u} \\|_\infty \\| \sqrt{\rho v} \\|_2^2 + C (1 + \\| \nabla \tilde{u} \\|_2^2 + \\| \nabla \tilde{u} \\|_2 \\| \nabla \tilde{u} \\|_2^2) \] \[\times (\\|W \\|_2^2 + \\| \sigma \\|_2^2 + \\| \sigma \\|_2^3).\] (3.7) The appearance of $ \\| \sigma \\|_\frac{3}{2} $ in the above inequality requires the energy estimate for $ \\| \sigma \\|_\frac{3}{2} $ given in the below. Testing (3.1) with $ \text{sign}(\sigma) \|\sigma\|^{\frac{3}{2}} $ and using the H"older and Sobolev inequalities that \[ \frac{d}{dt} \int \|\sigma\|^{\frac{3}{2}} \, dx \leq C \int (\|v \cdot \nabla \rho\| \|\sigma\|^{\frac{3}{2}} + \|\text{div} \tilde{u}\| \|\sigma\|^{\frac{3}{2}} + \|\text{div} \tilde{\rho}\| \|\sigma\|^{\frac{3}{2}}) \] \[\leq C (\\| \|\nabla \tilde{\rho}\|\|_2 \|\sigma\|^{\frac{3}{2}} \|v\|\|_6 + \\| \nabla \tilde{u} \\|_\infty \|\sigma\|^{\frac{3}{2}} + C \\| \|\tilde{\rho}\|\|_6 \|\nabla v\|\|_2 \|\sigma\|^{\frac{3}{2}}) \] \[\leq C \\| \nabla \tilde{u} \\|_\infty \|\sigma\|^{\frac{3}{2}} + C \\| \|\nabla \tilde{\rho}\|\|_2 \|\nabla v\|\|_2 \|\sigma\|^{\frac{3}{2}},\] which gives \[ \frac{d}{dt} \int \|\sigma\|^{\frac{3}{2}} \, dx \leq C \\| \nabla \tilde{u} \\|_\infty \|\sigma\|^{\frac{3}{2}} + C \\| \|\nabla \tilde{\rho}\|\|_2 \|\nabla v\|\|_2.\] (3.8) Denote \[ f_1(t) = (\\| \|\sigma\|^{\frac{3}{2}} + \\| \|\sigma\|\|_2 + \\| \|W\|\|_2 \|\|(t), \quad g_1(t) = \\| \|\sqrt{\rho v}\|\|_2^2 \|\|(t), \quad G_1(t) = \mu \\| \|\nabla v\|\|_2^2 \|\|(t), \] \[ \delta_1(t) = C \\| \nabla \tilde{u} \\|_\infty \|\|(t), \quad A_1 = C \sup_{0 \leq t \leq T} (\\| \|\tilde{\rho}\|\|_\infty + \\| \|\tilde{\rho}\|\|_\infty + \\| \|\nabla \tilde{\rho}\|\|_{L^2 \cap L^1} + \\| \|\nabla \tilde{\rho}\|\|_3 \|\|(t), \] \[ \alpha_1(t) = C \\| \nabla \tilde{u} \\|_\infty \|\|(t), \quad \beta_1(t) = C (1 + \\| \|\nabla \tilde{u}\|\|_2^2 + \\| \|\nabla \tilde{u}\|\|_2 \\| \nabla \tilde{u} \|\|_2^2 \|\|(t), \] then, it follows from (3.1), (3.5), (3.7), and (3.8) that \[ \left\{ \begin{array}{l} \frac{d}{dt} f_1(t) \leq \delta_1(t) f_1(t) + A_1 \sqrt{G_1(t)}, \frac{d}{dt} g_1(t) + G_1(t) \leq \alpha_1(t) g_1(t) + \beta_1(t) f_1^2(t), \end{array} \right. \] \[ f_1(0) = 0. \] By the regularities of $ (\tilde{\rho}, \tilde{u}) $ and $ (\tilde{\rho}, \tilde{u}) $, and recalling $ \nabla \tilde{u} \in L^1(0, T; L^\infty) $, one can easily verify that $ \alpha_1, \delta_1, t \beta_1 \in L^1((0, T)) $. Therefore, one can apply Lemma 3.1 to get $ f_1(t) = g_1(t) = G_1(t) = 0 $, on $ (0, T) $, which implies the uniqueness for Case I. Case II: $ \rho_\infty > 0 $. By the H"older and Sobolev inequalities, it follows for $ (\rho, u) \in \{(\tilde{\rho}, \tilde{u}), (\tilde{\rho}, \tilde{u})\} $ that \[ \rho_\infty^4 \int \|u_t\|^2 \, dx = \int \|\rho_\infty - \rho + \rho\|^4 \|u_t\|^2 \, dx \] implies the uniqueness for Case II. By the Hölder, Sobolev, and Cauchy inequalities, we deduce $$ \int_0^T t\\|u_t\\|^2 dt \leq C \sup_{0 \leq t \leq T} (\\|\nabla \rho\\|^2 + \\|\rho\\|^3) \int_0^T (\\|\sqrt{T} u_t\\|^2 + \\|\sqrt{T} u_t\\|^2) dt < \infty, $$ that is, $\sqrt{T} u_t \in L^2(0, T; L^2)$, for $u \in \{\hat{u}, \check{u}\}$. By the Hölder, Sobolev, and Cauchy inequalities, we deduce $$ RHS \leq \\|W\\|_2 \\|\nabla v\\|_2 + \\|\sigma\\|_2 \\|\bar{u}_t\\|_3 \\|v\\|_6 \\ + \\|\sigma\\|_2 \\|\bar{u}_0\\| \nabla \bar{u}_0 \\|v\\|_6 + \\|\nabla \bar{u}\\|_\infty \\|\sqrt{T} v\\|_2^2 \\ \leq \\|W\\|_2 \\|\nabla v\\|_2 + \\|\nabla \bar{u}\\|_\infty \\|\sqrt{T} v\\|_2^2 \\ + (\\|\bar{u}_t\\|^2 + \\|\nabla \bar{u}_t\\|_2^{3/2}) \\|\nabla \bar{u}\\|_2 \\|\nabla \bar{u}_t\\|_2 \\ \leq \frac{\mu}{2} \\|\nabla v\\|_2^2 + C \\|\nabla \bar{u}\\|_\infty \\|\sqrt{T} v\\|_2^2 + C(1 + \\|\bar{u}_t\\|_2 \\|\nabla \bar{u}_t\\|_2 \\ + \\|\nabla \bar{u}\\|_2 \\|\nabla \bar{u}_t\\|_2^2)(\\|\sigma\\|^2 + \\|W\\|_2^2). $$ Plugging this into (3.6) leads to $$ \frac{d}{dt} \\|\sqrt{T} v\\|_2 + \mu \\|\nabla v\\|_2^2 \leq C \\|\nabla \bar{u}\\|_\infty \\|\sqrt{T} v\\|_2^2 + C(1 + \\|\bar{u}_t\\|_2 \\|\nabla \bar{u}_t\\|_2 \\ + \\|\nabla \bar{u}\\|_2 \\|\nabla \bar{u}_t\\|_2^2)(\\|\sigma\\|^2 + \\|W\\|_2^2). \tag{3.9} $$ Denote $$ f_2(t) = (\\|\sigma\\|_2 + \\|W\\|_2)(t), \quad g_2(t) = \\|\sqrt{T} v\\|_2^2(t), \quad G_2(t) = \mu \\|\nabla v\\|_2^2(t), $$ $$ \delta_2(t) = C \\|\nabla \bar{u}\\|_\infty(t), \quad \alpha_2(t) = C(1 + \\|\bar{u}_t\\|_2 \\|\nabla \bar{u}_t\\|_2 + \\|\nabla \bar{u}\\|_2^2 \\|\nabla \bar{u}_t\\|_2^2)(t), $$ then, it follows from (3.4), (3.5), and (3.9) that $$ \begin{cases} \frac{d}{dt} f_2(t) \leq \delta_2(t) f_2(t) + A_2 \sqrt{G_2(t)}, \\ \frac{d}{dt} g_2(t) + G_2(t) \leq \alpha_2(t) g_2(t) + \beta_2(t) f_2^2(t), \\ f_2(0) = 0. \end{cases} $$ By the regularities of ($\hat{\rho}, \hat{u}$) and ($\check{\rho}, \check{u}$), and recalling $\nabla u \in L^1(0, T; L^\infty)$ and $\sqrt{T} u_t \in L^2(0, T; L^2)$, for $u \in \{\hat{u}, \check{u}\}$, one can easily verify that $\alpha_2, \delta_2, \beta_2 \in L^1((0, T))$. Therefore, one can apply Lemma 3.1 to get $f_2(t) = g_2(t) = G_2(t) = 0$, on $(0, T)$, which implies the uniqueness for Case II. Existence: Set $\rho_{0n} = \rho_0 + \frac{1}{n^2}, \rho_{n\infty} = \rho_\infty + \frac{1}{n}$, and choose $u_{0n} \in D_0^1 \cap D^2$, such that $u_{0n} \to u_0$ in $D_0^1$, as $n \to \infty$. Denote $$ \psi_0 = \\|\rho_0\\|_\infty + \\|\rho_0 - \rho_\infty\\|_2 + \\|\nabla \rho_0\\|_{L^2 \cap L^q} + \\|\nabla u_0\\|_2, $$ $$ \psi_{0n} = \\|\rho_{0n}\\|_\infty + \\|\rho_{0n} - \rho_{n\infty}\\|_2 + \\|\nabla \rho_{0n}\\|_{L^2 \cap L^q} + \\|\nabla u_{0n}\\|_2. $$ Then, one can easily check that $\psi_{0n} \leq \psi_0 + 1$, for sufficiently large $n$. By Proposition 2.9 there are two positive constants $T$ and $C$ depending only on $\mu$, $\lambda$, $\alpha$, $\gamma$, $q$, and $\psi_0$, such that system (1.1)–(1.2), subject to (1.3), has a unique solution $(\rho_n, u_n)$, on $\mathbb{R}^3 \times (0, T)$, satisfying $$ \sup_{0 \leq t \leq T} \left( \\|\rho_n\\|_\infty + \\|\rho_n - \rho_{n\infty}\\|_2 + \\|\nabla \rho_n\\|_2 + \\|\nabla \rho_n\\|_q + \\|\partial_t \rho_n\\|_2 \right) \leq C, \quad (3.10) $$ $$ \sup_{0 \leq t \leq T} \left( \\|\nabla u_n\\|_2^2 + \int_0^T \left( \\|\nabla^2 u_n\\|_2^2 + \\|\sqrt{\rho_n} \partial_t u_n\\|_2^2 \right) dt \right) \leq C, \quad (3.11) $$ $$ \sup_{0 \leq t \leq T} \left( \\|\nabla \sqrt{t} \nabla^2 u_n\\|_2^2 + \int_0^T \left( \\|\nabla \sqrt{t} \partial_t \nabla u_n\\|_2^2 + \\|\nabla \sqrt{t} \nabla^2 u_n\\|_q^2 \right) dt \right) \leq C. \quad (3.12) $$ Thanks to (3.10)–(3.12), there is a subsequence, still denoted by $(\rho_n, u_n)$, and a pair $(\rho, u)$, satisfying $$ \rho - \rho_\infty \in L^\infty(0, T; H^1 \cap W^{1,q}), \quad \rho_t \in L^\infty(0, T; L^2), \quad (3.13) $$ $$ u \in L^\infty(0, T; D_0^1) \cap L^2(0, T; D^2), \quad (3.14) $$ $$ \sqrt{t} \nabla^2 u \in L^\infty(0, T; L^2), \quad \nabla u_t \in L^2(0, T; L^2), \quad \sqrt{t} \nabla^2 u \in L^2(0, T; L^q), \quad (3.15) $$ such that $$ \rho_n - \rho_{n\infty} \overset{}{\rightharpoonup} \rho - \rho_\infty, \quad \text{in } L^\infty(0, T; H^1 \cap W^{1,q}), \quad (3.16) $$ $$ \partial_t \rho_n \overset{}{\rightharpoonup} \rho_t, \quad \text{in } L^\infty(0, T; L^2), \quad (3.17) $$ $$ u_n \overset{}{\rightharpoonup} \nu, \quad \text{in } L^\infty(0, T; D_0^1), \quad (3.18) $$ $$ u_n \rightharpoonup \nu, \quad \text{in } L^2(0, T; D^2), \quad (3.19) $$ $$ \partial_t u_n \rightharpoonup \nu_t, \quad \text{in } L^2(\delta, T; D_0^1), \quad (3.20) $$ for any $\delta \in (0, T)$. Note that $W^{1,q} \hookrightarrow C(\overline{B_k})$, for any positive integer $k$. With the aid of (3.16)–(3.20), by the Aubin-Lions lemma, and using the Cantor’s diagonal argument, there is a sequence, still denoted by $(\rho_n, u_n)$, such that $$ \rho_n \to \rho, \quad \text{in } C([0, T]; C(\overline{B_k})), \quad (3.21) $$ $$ u_n \to \nu, \quad \text{in } L^2(\delta, T; H^1(\overline{B_k})) \cap C([\delta, T]; L^2(B_k)), \quad (3.22) $$ for any positive integer $k$, and for any $\delta \in (0, T)$, where $B_k$ is the ball in $\mathbb{R}^3$ centered at the origin of radius $k$. By the aid of (3.20), (3.21) and (3.22), one has $$ \rho_n u_n \rightharpoonup \rho u, \quad \text{in } L^2(B_k \times (0, T)), \quad (3.23) $$ $$ \rho_n \partial_t u_n \rightharpoonup \rho \nu_t, \quad \text{in } L^2(B_k \times (\delta, T)) \quad (3.24) $$ \[ \rho_n(u_n \cdot \nabla)u_n \to \rho(u \cdot \nabla)u, \quad \text{in } L^1(B_k \times (\delta, T)), \] (3.25) \[ \alpha \rho_n^\gamma \to \alpha \rho^\gamma, \quad \text{in } C(\bar{B}_k \times [0, T]), \] (3.26) for any $\delta \in (0, \mathcal{T})$, and for any positive integer $k$. Due to (3.17), (3.19), and (3.23)–(3.26), one can take the limit to the system of $(\rho_n, u_n)$ to show that $(\rho, u)$ is a strong solution to system (1.1)–(1.2), on $\mathbb{R}^3 \times (0, \mathcal{T})$, satisfying the regularities (3.13)–(3.15). The convergence (3.21) implies that the initial value of $\rho = \rho_0$. The regularity of $\rho - \rho_\infty \in C([0, \mathcal{T}]; L^2)$ follows from (3.13). The regularity $\sqrt{\rho}u \in L^2(0, \mathcal{T}; L^2)$ is verified as follows. It follows from (3.20) and (3.21) that $\sqrt{\rho_n}\partial_t u_n \to \sqrt{\rho}u_t$ in $L^2(0, \mathcal{T}; L^2(B_k))$, for any positive integer $k$. Then, the weakly lower semi-continuity of the norms implies \[ \int_0^\mathcal{T} \\|\sqrt{\rho}u_t\\|_{L^2(B_k)}^2 dt \leq \liminf_{n \to \infty} \int_0^\mathcal{T} \\|\sqrt{\rho_n}\partial_t u_n\\|_{L^2(B_k)}^2 dt \leq C, \] for a positive constant $C$ independent of $k$. Taking $k \to \infty$ in the above inequality yields $\sqrt{\rho}u \in L^2(0, \mathcal{T}; L^2)$. Finally, we show that $\rho u \in C([0, \mathcal{T}]; L^2)$ and $\rho u\|_{t=0} = \rho_0 u_0$. By (1.2) and (3.13)–(3.14), and noticing that $\\|u\\|_\infty \leq C\\|\nabla u\\|_2^\frac{1}{2}\\|\nabla^2 u\\|_2^\frac{3}{2}$, guaranteed by the Gagliardo-Nirenberg and Sobolev embedding inequalities, it follows \[ \int_0^\mathcal{T} \\|\partial_t (\rho u)\\|_2^2 dt \\ = \int_0^\mathcal{T} \\|-(u \cdot \nabla \rho + \text{div } \rho u)u + \rho u_t\\|_2^2 dt \\ \leq \int_0^\mathcal{T} \left(\\|u\\|_\infty^2 \\|\nabla \rho\\|_2 + \\|u\\|_\infty \\|\nabla u\\|_2 \\|\rho\\|_\infty + \\|\rho\\|_\frac{3}{2} \\|\sqrt{\rho}u_t\\|_2 \right)^2 dt \\ \leq C \int_0^T \left(\\|\nabla u\\|_2^2 \\|\nabla^2 u\\|_2^\frac{1}{2} + \\|\nabla u\\|_2^3 \\|\nabla^2 u\\|_2 + \\|\sqrt{\rho}u_t\\|_2^2 \right) dt \\ \leq C \int_0^T \left(1 + \\|\nabla^2 u\\|_2^2 + \\|\sqrt{\rho}u_t\\|_2^2 \right) dt \leq C. \] (3.27) Similarly, it follows from (3.10)–(3.11) that $\int_0^T \\|\partial_t (\rho_n u_n)\\|_2^2 dt \leq C$, for a positive constant $C$ independent of $n$. Thanks to these, we deduce by the Hölder inequality that \[ \\|(\rho u)(\cdot, t) - \rho_0 u_0\\|_{L^2(B_R)} \\ \leq \\|\rho u - \rho_n u_n\\|_{L^2(B_R)} + \\|\rho_n u_n - \rho_0 u_0\\|_{L^2(B_R)} + \\|\rho_0 u_0 - \rho_0 u_0\\|_{L^2(B_R)} \\ \leq \\|\rho u - \rho_n u_n\\|_{L^2(B_R)} + \int_0^t \\|\partial_t (\rho_n u_n)\\|_{L^2(B_R)} d\tau + \frac{C}{n} \\|u_0\\|_{L^2(B_R)} \\ \leq \\|\rho u - \rho_n u_n\\|_{L^2(B_R)} + C\sqrt{t} + \frac{C}{n} \\|u_0\\|_{L^2(B_R)}, \] for a positive constant $C$ independent of $n$ and $R$. Noticing that $\rho_n u_n \to \rho u$ in $C([\delta, \mathcal{T}]; L^2(B_R))$, for any $\delta \in (0, \mathcal{T})$, guaranteed by (3.21)–(3.22), one can pass the limits $n \to \infty$ first and then $R \to \infty$ to the above inequality, and end up with $\\| (\rho u)(\cdot, t) - \rho_0 u_0 \\|_2 \leq C\sqrt{t}$. This implies $\rho u \in L^\infty(0, \mathcal{T}; L^2)$ and $\rho u\|_{t=0} = \rho_0 u_0$. 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COLLEGE OF MATHEMATICS AND STATISTICS, SHENZHEN UNIVERSITY, SHENZHEN, CHINA E-mail address: [email protected] SOUTH CHINA RESEARCH CENTER FOR APPLIED MATHEMATICS AND INTERDISCIPLINARY STUDIES, SOUTH CHINA NORMAL UNIVERSITY, ZHONG SHAN AVENUE WEST 55, GUANGZHOU 510631, CHINA E-mail address: [email protected] SCHOOL OF MATHEMATIC SCIENCES, FUDAN UNIVERSITY, SHANGHAI, 200433, CHINA E-mail address: [email protected] SOUTH CHINA RESEARCH CENTER FOR APPLIED MATHEMATICS AND INTERDISCIPLINARY STUDIES, SOUTH CHINA NORMAL UNIVERSITY, ZHONG SHAN AVENUE WEST 55, GUANGZHOU 510631, CHINA E-mail address: [email protected]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2393, 1 ], [ 2393, 5578, 2 ], [ 5578, 8099, 3 ], [ 8099, 10782, 4 ], [ 10782, 13276, 5 ], [ 13276, 15480, 6 ], [ 15480, 17562, 7 ], [ 17562, 19560, 8 ], [ 19560, 21317, 9 ], [ 21317, 22966, 10 ], [ 22966, 25822, 11 ], [ 25822, 28936, 12 ], [ 28936, 31140, 13 ], [ 31140, 34063, 14 ], [ 34063, 36863, 15 ], [ 36863, 39068, 16 ], [ 39068, 42342, 17 ], [ 42342, 45163, 18 ], [ 45163, 47879, 19 ], [ 47879, 50643, 20 ], [ 50643, 53537, 21 ], [ 53537, 56401, 22 ], [ 56401, 57026, 23 ] ] }
a3f70527e930f145081b17010e22d6f6a1bb930e	{ "olmocr-version": "0.1.59", "pdf-total-pages": 3, "total-fallback-pages": 0, "total-input-tokens": 9960, "total-output-tokens": 3511, "fieldofstudy": [ "Medicine", "Biology" ] }	Anaesthetic management of infants posted for repair of anomalous origin of left coronary artery from pulmonary artery Chitralekha Patra, Naveen G Singh, N Manjunatha, Anand Bhatt Department of Cardiac Anaesthesiology, Sri Jayadeva Institute of Cardiovascular Sciences and Research, Bengaluru, Karnataka, India ABSTRACT First described in 1908, anomalous origin of left coronary artery from pulmonary artery is a very rare congenital anomaly. Here, the right coronary artery is usually enlarged and has a normal origin from aorta. Numerous collaterals connect the two coronary arteries over right ventricular outflow tract or interventricular septum. It is one of the most common causes of myocardial ischaemia and infarction in children. Key words: Anomalous origin of left coronary artery from pulmonary artery, coronary steal, left ventricular assist device, myocardial ischemia INTRODUCTION Anomalous origin of left coronary artery from pulmonary artery (ALCAPA) is a rare entity occurring 1 in 3,00,000. It is characterised by anomalous origin of the left main coronary artery (LMCA) from pulmonary artery (PA).$^1$$^2$ Blood supply to the myocardium is derived through collaterals arising from the right coronary artery (RCA) and exiting into the PA which is liable for coronary steal. Endocardial fibrosis and scarring may involve the papillary muscle of the mitral valve resulting in valvular insufficiency.$^2$$^3$ Anaesthetic management poses a unique challenge as ALCAPA patients have increased chances of perioperative myocardial ischaemia, cardiac arrest and sudden death. Here, we discuss the anaesthetic management and post-operative outcome of a series of three cases over 1 year in our institution. CASE REPORTS Case 1 A 6-month-old, 3 kg boy presented with resting tachypnoea and diaphoresis while feeding and failure to thrive. The heart rate (HR) was 160/min and blood pressure (BP) was 90/60 mmHg. No murmur was present. Electrocardiogram (ECG) showed T-wave inversion in lead II, III and AVF and chest radiograph showed significant cardiomegaly. Transthoracic echocardiography revealed retrograde flow in LMCA draining into the PA. There was dilatation of left atrium and ventricle with Grade II mitral regurgitation (MR). There was severe left ventricular (LV) dysfunction with ejection fraction (EF) of 20%. Since the diagnosis was clear, cardiac catheterisation and angiography were not done. His medications included digoxin, spironolactone and ramipril. This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License, which allows others to remix, tweak, and build upon the work non-commercially, as long as the author is credited and the new creations are licensed under the identical terms. For reprints contact: [email protected] How to cite this article: Patra C, Singh NG, Manjunatha N, Bhatt A. Anaesthetic management of infants posted for repair of anomalous origin of left coronary artery from pulmonary artery. Indian J Anaesth 2017;61:676-8. The child was taken to operating room, where non-invasive monitors such as 5 lead ECG, Pulse oximetry and non-invasive BP (NIBP) were attached. BP was 90/50 mmHg, HR was 135/min and SpO₂ was 100%. There was no evidence of ischaemia on ECG. General anaesthesia was induced with intravenous (iv) injection ketamine (2 mg/kg), followed by iv injection fentanyl (2 μg/kg) and iv injection atracurium (0.5 mg/kg) and the trachea was intubated with 4.0 mm cuffed endotracheal tube (CETT). The femoral artery was cannulated for invasive arterial BP monitoring, and the right internal jugular vein was cannulated for central venous pressure monitoring. Anaesthesia was maintained with isoflurane and intermittent fentanyl. The ventilatory settings were aimed to prevent hypocarbia, hyperoxia and alkalosis. An FiO₂ of 0.5 was targeted to maintain normoxia, with a PaO₂ of 80-100 mmHg which was used to maintain pulmonary vascular resistance (PVR). End-tidal carbon dioxide was maintained between 40 and 45 mmHg. Re-implantation of the LMCA was performed under cardiopulmonary bypass (CPB). During weaning from CPB, dopamine (5 μg/kg/min) and milrinone (0.33 μg/kg/min) were started. Patient remained haemodynamically stable throughout the perioperative period. The child was ventilated for 24 h and discharged to ward on 5th post-operative day. Case 2 An 8-month-old, 5.5 kg baby girl presented with a history of excessive crying and difficulty in breathing since 3 months. HR was 106/min, regular and BP was 80/46 mmHg. Transthoracic echocardiography revealed ALCAPA, reduced LV global function and EF 20%. She was on ramipril (5 mg/day) and furosemide (10 mg/day). The child was taken to OT, where non-invasive monitors such as ECG, NIBP and SpO₂ were attached. Anaesthesia was induced with iv injection etomidate (0.3 mg/kg), iv injection fentanyl (2 μg/kg) and iv injection atracurium (0.5 mg/kg) and intubated with CETT (3.5 mm). Femoral artery and vein were cannulated for invasive monitoring. Anaesthetic goals of maintaining a slightly higher PVR and higher EtCO₂ of 40–45 mmHg was done by preventing hypocarbia, hyperoxia and alkalosis. Relocation of LMCA was performed under CPB where bypass time was 106 min and cross-clamp time was 73 min. After rewarming was complete, inotropes such as dopamine 5 μg/kg/min and dobutamine 5 μg/kg/min were started. Sinus rhythm returned, and patient was haemodynamically stable throughout post-operative period. The patient was ventilated for 36 h and shifted to ward on 8th post-operative day. Transeosophageal echocardiogram (TOE) after 1 week revealed LMCA arising from aorta and slightly improved EF of 30%. Case 3 A 1-month-old, 3.5 kg baby girl presented with breathlessness. Her HR was 150/min and BP was 64/35 mmHg. Auscultation revealed S1, S2 and pansystolic murmur. ECG revealed ST depression and T-wave inversion in leads aVL, I and II. TTE showed ALCAPA, severe LV dysfunction, severe MR and EF of 20%. In the OT, HR was 145/min, BP was 60/38 mmHg and ECG revealed T-wave inversion. Anaesthesia was induced with iv injection ketamine (2 mg/kg), injection fentanyl (2 μg/kg) and injection atracurium (0.5 mg/kg) and intubated with CETT (3.0 mm). Femoral artery and vein were cannulated. The anaesthetic goals of preventing hypocarbia, hyperoxia and alkalosis and maintaining the PVR were achieved by keeping FiO₂ of 0.5 to maintain PaO₂ between 80-100 mmHg, and EtCO₂ of 40–45 mmHg. Re-implantation of LMCA was performed under CPB. After the patient was rewarmed completely, the heart did not beat for a long time, and pacing of the ventricle was commenced. Inotropic supports i.e. dopamine (5 μg/kg/min) and adrenaline (0.1 μg/kg/min) were started. The heart started to beat in sinus rhythm, however, with very poor contractility. An attempt was made to wean off CPB, but there was severe distension of the ventricles with low systemic pressures of around 45/30 mmHg. CPB was recommenced and later three more attempts were made to wean off CPB again but was unsuccessful due to severe myocardial dysfunction. The total CPB time was 300 min and cross-clamp time was 126 min. Finally, the patient was weaned off CPB with very high inotropic support of Dopamine 10 μg/kg/min, Noradrenaline 0.1 μg/kg/min and Milrinone 0.99 μg/kg/min. Patient was shifted to paediatric intensive care unit (PICU) with a BP of 50/34 mmHg and poor contractility of heart. Patient had unstable haemodynamics, severe metabolic acidosis with low cardiac output inspite of high inotropic support resulting in cardiac arrest after one hour of shifting to PICU. DISCUSSION There are unique anaesthetic considerations for patients presenting with ALCAPA repair. Of utmost importance is maintaining adequate coronary perfusion pressure through the single coronary artery and minimising myocardial oxygen consumption. Hence, laryngoscopy... and intubation should be smooth and rapid, and swings in BP and HR should be avoided as tachycardia can alter myocardial oxygen supply and demand and predispose to myocardial infarction (MI).\textsuperscript{[2,3]} Coronary blood flow in ALCAPA is dependent on pressure gradient between RCA and PA, and low PA pressures can worsen the steal phenomenon. Hence, factors decreasing PVR such as hyperventilation, hypocarbia or hyperoxia must be avoided. Patients are ventilated using oxygen and air mixture, with an aim to maintain normoxia targeting a $ \text{PaO}_2 $ of 80-100 mmHg. An $ \text{etCO}_2 $ of 40-45 mmHg is achieved to maintain PVR. An increase in afterload is prevented, to optimize the stroke volume.\textsuperscript{[3]} However, aggressive reduction in afterload may be deleterious as it attenuates perfusion of the RCA, thus decreasing blood flow to LMCA. Inotropes such as dopamine, dobutamine and milrinone should be used cautiously as they increase myocardial oxygen consumption and increase the risk of MI.\textsuperscript{[3,4]} Isoflurane is the inhalation agent of choice as it causes less myocardial depression. In our case series, case 1 and 2 showed remarkable recovery post-bypass. A possible mechanism for the recovery of cardiac function after repair is myocyte hyperplasia in young infants. In addition, there may be compensatory hypertrophy of remaining viable myocytes if muscle necrosis occurs. Alternatively, phenomenon of hibernation may explain the complete myocardial recovery after revascularisation.\textsuperscript{[5]} Hibernating myocardium specifically refers to the occurrence of persistent contractile dysfunction associated with chronic ischaemia but preserved myocardial viability. It has been suggested that the chronic myocardial hypoperfusion of ALCAPA leads to myocyte adaptation rather than diffuse infarction.\textsuperscript{[5,6]} The finding of complete recovery of LV function in these patients without evidence of infarction supports this hypothesis. However, at times, the recovery may be prolonged or may not occur at all as in case 3 which represents a reversal of these adaptive cellular changes. Cardiac dysfunction may be acutely compounded by prolonged CPB time and post-operative myocardial stunning, the transient mechanical dysfunction that persists after reperfusion and restoration of normal coronary blood flow. Myocardial stunning may contribute to some patient dependence on left ventricular assist device (LVAD) in the immediate post-operative period. ALCAPA patients with severe LV dysfunction exacerbated with prolonged CPB time are ideal candidates for successful use of a LVAD when separation from bypass cannot be achieved.\textsuperscript{[5,6]} The advantages of LVAD are its simplicity, better ventricular decompression, absence of oxygenator and low anticoagulation requirements. Alternatively, extracorporeal membrane oxygenator (ECMO) can be considered as a strategy for recovery of poor LV function in ALCAPA patients. Survival has been found to be 33% when ECMO was initiated.\textsuperscript{[7]} However, it is associated with complications such as bleeding and intracerebral haemorrhage. Mild and moderate MR usually improves with post-operative recovery of LV function. However, it remains possible that patients with severe pre-operative MR, as in case 3 would have a better outcome if MV was repaired at the time of coronary revascularisation. Furthermore, better results could be expected with minimal bypass and cross-clamp time. Moreover, mechanical support of LV with a LVAD or ECMO could have helped for better management in the above case. CONCLUSION Survivors of perioperative period in ALCAPA repair have excellent prognosis for functional recovery of LV regardless of pre-operative state. Normalisation of LV function occurs once dual coronary circulation is restored, which may take as long as 2 years. Financial support and sponsorship Nil. Conflicts of interest There are no conflicts of interest. REFERENCES 1. Gupta K, Gupta M, Mehrotra M, Prasad J. Anaesthesia for repair of anomalous origin of left coronary artery from pulmonary artery. Indian J Anaesth 2015;59:136-7. 2. Cormac J, Richard J, Frank H, O’Hara B. Anaesthetic management and physiologic implications in infants with anomalous origin of left coronary artery from pulmonary artery. J Clin Virol 2011;26:286-90. 3. Bland EF, White PD, Garland J. Congenital anomalies of the coronary arteries. Am Heart J 1933;8:787-801. 4. Cherian KM, Bharati S, Rao SG. Surgical correction of anomalous origin of the left coronary artery from the pulmonary artery. J Card Surg 1994;9:386-91. 5. Schwartz ML, Jonas RA, Colan SD. Anomalous origin of left coronary artery from pulmonary artery: Recovery of left ventricular function after dual coronary repair. J Am Coll Cardiol 1997;30:547-53. 6. Wesselhoeft H, Fawcett JS, Johnson AL. Anomalous origin of the left coronary artery from the pulmonary trunk. Its clinical spectrum, pathology, and pathophysiology, based on a review of 140 cases with seven further cases. Circulation 1968;38:403-25. 7. Singh P, Kapoor PM, Devagourou V, Bhuvana V, Kiran U. Use of integrated extracorporeal membrane oxygenator in anomalous left coronary artery to pulmonary artery: Better survival benefit. Ann Card Anaesth 2011;14:240-2.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3070, 1 ], [ 3070, 7949, 2 ], [ 7949, 13302, 3 ] ] }
b90486459aafef52eb6b1903a8d598da10ccfaf6	{ "olmocr-version": "0.1.59", "pdf-total-pages": 12, "total-fallback-pages": 0, "total-input-tokens": 44813, "total-output-tokens": 12562, "fieldofstudy": [ "Computer Science", "Business" ] }	Reducing Complexity in Next-Generation Multi-User MIMO Systems KONSTANTINOS NTOUGIAS DIMITRIOS NTAIKOS CONSTANTINOS B. PAPADIAS Athens Information Technology (AIT), 44 Kifissias Avenue, 15125 Maroussi, Greece. kontou \| dint \| cpap @ait.gr Abstract Recently, several advanced multi-antenna radio communications technologies have emerged to meet the increased capacity demands in wireless multiuser networks. Despite their great potential, the extent of these techniques’ practical applicability still remains questionable, since they have to face either backhaul limitations or cost and hardware constraints. In this paper, we propose a new system solution which includes network architecture, antenna technology and radio transmission protocol to reduce drastically the hardware complexity and cost as well as the channel state information / user data feedback requirements of multi-user multi-antenna wireless networks. We focus on the forward link of an interference channel in a cloud radio access network setup wherein an arbitrary number of remote radio heads are each equipped with a single radio frequency module parasitic antenna array and wish to send data to their respective single-antenna user terminals, while co-existing in time and frequency. Base stations select cooperatively the optimal combination of pre-determined beams prior transmission. Our proposed approach is able to achieve the aforementioned goals, while offering significant downlink sum-rate gains due to the available spatial degrees of freedom. Index terms— Remote Radio Head (RRH), Electronically Steerable Parasitic Array Radiator (ESPAR) Antenna, Channel State Information (CSI), Zero-Forcing (ZF) Precoding, Interference Channel (IFC). 1 Introduction Over the last decade, an enormous growth of mobile data traffic has been witnessed. As several studies indicate [1][2], this trend is likely to continue in the years to come in an even more abrupt pace. In view of the well-known scarcity and high cost of the radio spectrum, current cellular mobile broadband networks incorporate multiple-input multiple-output (MIMO) technology as a response to the increased capacity demands. Traditional single-user MIMO (SU-MIMO) focuses on the physical layer performance of the communication between a base station (BS) and a mobile terminal (MT) over a point-to-point link. It exploits the additional degrees of freedom (DoFs) provided by the use of multiple antennas to enhance spectral efficiency through spatial multiplexing of individual data streams or to reduce co-channel interference by spatially focusing transmissions and separating co-channel signals. Multi-user MIMO (MU-MIMO) is an evolution of SU-MIMO that enhances link-level performance by exploiting DoFs to spatially separate users, thus enabling a BS to communicate simultaneously with multiple mobile users (MUs) over a multipoint-to-point (uplink) or a point-to-multipoint (downlink) channel. Recently, new MIMO paradigms, which aim at improving system-level performance, have been introduced. Their common characteristic is that they increase significantly the available DoFs to boost the performance of the system. More specifically, cooperative MIMO [3][4] enables the cooperation between different BSs to mitigate inter-cell interference and increase area spectral efficiency and system capacity, while massive MIMO [5][6] makes use of an excessive number of antennas at the cell site to orthogonalize MUs in the spatial domain. It is expected that both these technologies will be an integral part of future fifth generation (5G) systems. However, their transition from theory into implementation requires the addressing of some important practical issues. Cooperative MIMO refers to a collection of techniques with varying level of cooperation, from network MIMO which requires the sharing of user data and global channel state information (CSI) between the individual BSs to cooperative beamforming which requires only the exchange of precoding matrices between the cooperating nodes. In practice, backhaul latency limits the effectiveness of these techniques, while backhaul capacity constraints reduce the achievable level of cooperation. and the corresponding performance gains. Massive MIMO, on the other hand, places a heavy burden, in terms of cost, to the mobile network operators due to the large number of radio-frequency (RF) chains (one per active antenna element) that is required for its implementation. Moreover, the tight spacing of antenna elements may lead to reduced efficiency due to spatial correlations. In addition, as the number of BSs or/and antennas increases, channel estimation becomes a challenging task. In this paper, we describe a system setup that is promising in its ability to address these challenges. We focus on the study of a radio transmission protocol that takes advantage of the attributes of the employed technologies to achieve substantial performance gains, while reducing significantly system complexity. The structure of the remainder of the paper is as follows: In Section 2, the considered system architecture and antenna technology is presented. Next, the system and channel model is described in Section 3. We continue in Section 4 with a presentation of the proposed radio protocol. In Section 5 we present numerical performance results for different flavors of the proposed transmission scheme and compare them against performance bounds. We then discuss in Section 6 about the complexity reduction that is achieved with the considered radio protocol as well as about the relevant complexity-feedback overhead and complexity-performance tradeoffs. In Section 7 we study the performance of the transmission scheme when CSI is imperfect. Finally, in Section 8 we present our conclusions and discuss about future extensions of our work. 2 System Architecture and Technologies According to the discussion in Section 1, we define three main criteria that are important to be met in order to enable the use of Cooperative / Massive MIMO in practice: 1. Low-cost implementation of systems with many antennas. 2. Low-delay communication between cooperating nodes. 3. Minimization of the information that has to be exchanged between the cooperating base stations. In order to fulfill these requirements, all aspects of system design have to be taken into account, that is, network architecture, antenna technologies, and radio transmission protocols. In this Section, we describe two proposed components that can meet the first two of these objectives. Next, we will focus on a proposed radio scheme that can be employed by this system to reduce feedback complexity. 2.1 ESPAR Antennas Advanced parasitic antenna arrays, often called electronically steerable parasitic array radiators (ESPARs), provide multi-antenna functionality using fewer active elements (and, as a consequence, fewer RF units) than conventional antenna arrays. They accomplish this by adjusting the loads of parasitic elements that are placed in the vicinity of the active element(s), thus controlling the corresponding induced currents caused by mutual coupling to form and steer beams [7]. This concept is illustrated in Fig. 1. ESPAR technology can be viewed as an attractive enabler of massive MIMO, since it allows the implementation of large antenna systems with much reduced complexity, size and cost. 2.2 Cloud-RAN/RRH Cloud Radio Access Network (Cloud-RAN or C-RAN) [8][9] is a split base station architecture which separates the baseband unit (BBU) from the radio unit. More specifically, in C-RAN, remote radio units (RRUs), also called remote radio heads (RRHs), remain at the cell site, while BBUs are centralized and virtualized using cloud technology. Baseband and radio resources are allocated to “virtual base stations” in real time according to processing and radio coverage needs. Remote radio heads are connected with the centralized BBU pool through optical fibers. Protocols such as Common Public Radio Interface (CPRI) [10] are used to enable the communication between the virtualized baseband pool and the RRHs over this new network segment, which is often referred to as the mobile fronthaul. C-RAN is hence considered to be a compelling candidate technology for bringing cooperative MIMO communication into reality, due to the centralization and virtualization of the baseband and the use of optical transmission technologies at the fronthaul which have the potential to meet the stringent delay and bandwidth requirements of these advanced techniques [11]. 3 System and Channel Model In this Section, we introduce the system and channel model of our setup. Before getting in the details, let us present the notation that we follow throughout the paper. Notation: With a, a, and A we denote a (in general, complex-valued) scalar, vector, and matrix, respectively. A<sub>i,j</sub> denotes the (i, j) (row, column) element of A. The Hermitian (transpose conjugate), determinant, and rank of A are denoted by A<sup>†</sup>, det(A) and rank(A), respectively, while the inverse and the Moore-Penrose pseudoinverse of A are denoted by A<sup>−1</sup> and A<sup>+</sup>, respectively. Tr(A) represents the trace of A and ∥A∥<sub>F</sub> denotes its Frobenius norm, whereas diag(a) represents a diagonal matrix with the elements of vector a at its main diagonal. \|a\| stands for the Euclidean norm of vector a. E<sub>·</sub> denotes the set of complex numbers, E{·} represents the expectation operator, X ∼ CN(0, σ<sub>a</sub>2) refers to a complex-valued random variable (RV) X following the Gaussian distribution with zero mean (i.e., E{X} = 0) and variance σ<sub>a</sub>2, and a ∼ CN(0, σ<sub>a</sub>2I) represents a complex-valued Gaussian vector with mean vector E{a} = 0 and covariance matrix R<sub>aa</sub> = E{aa<sup>†</sup>} = σ<sub>a</sub>2I, i.e., the elements of a are complex-valued RVs with zero mean and variance σ<sub>a</sub>2. 3.1 System Model We consider the downlink of a C-RAN system with K RRHs, each representing an individual BS and being equipped with a single-RF ESPAR antenna, where each one of them wishes to communicate with a user equipment (UE) having a single antenna. All transmissions take place simultaneously and over the same frequency band. Note that due to the C-RAN architecture, the BSs can efficiently share information. The MUs, on the other hand, do not cooperate. Each ESPAR antenna is able to generate L distinct predetermined beams. According to some criterion, the best K-tuple of beams is selected for transmission from the L<sup>K</sup> different beam combinations in total, with each one of these beams being generated at a different RRH, as seen in Fig. 2. (The beam selection criteria are presented in Section 4.) The corresponding “beam-domain transformed” channel between these K transmitter-receiver (TX-RX) pairs is equivalent to a single-input single-output (SISO) K-user interference channel (IFC), since each TX has a single active antenna. However, we should not ignore the fact that the TXs are equipped with parasitic antenna arrays and make use of beamforming, in contrast to conventional SISO TXs which utilize omni-directional antennas. Mathematically, this SISO IFC with K TXs and K RXs having $ \{N_{T,k}\}_{k=1}^K = 1 $ and $ \{N_{R,k}\}_{k=1}^K = 1 $ active antennas each, respectively, can be viewed as a multi-user multiple-input single-output (MU-MISO) K-user IFC formed by a composite TX with $ N_T = \sum_{k=1}^K N_{T,k} = K $ antennas and K RXs, each with $ \{N_{R,k}\}_{k=1}^K = 1 $ antenna. We assume narrowband transmission (i.e., flat-fading channel), such that no inter-symbol interference is caused by multipath. This is the case, for example, in indoor environments with relatively small delay spread as well as when orthogonal frequency division multiplexing (OFDM) transmission is employed to convert a frequency-selective channel into parallel frequency-flat sub-channels. We also assume block-fading, such that the channel remains fixed during the transmission of each symbol. Therefore, we can omit time dependence in the system model. Under these assumptions, the baseband received signal at user k, where $ k = 1, \ldots, K $, for a selected beam combination, can be expressed as \[ y_k = \sum_{m=1}^K h_{k,m} s_m + n_k, \quad k = 1, \ldots, K \tag{1} \] where $ s_m \in \mathbb{C} $ is the complex symbol transmitted by TX<sub>m</sub>, $ y_k \in \mathbb{C} $ is the complex received symbol at RX<sub>k</sub>, $ n_k \sim \mathcal{CN}(0, \sigma_n^2) $ is complex additive Gaussian noise with zero mean and variance $ \sigma_n^2 $, and $ h_{k,m} $ is the complex channel coefficient from $Tx_m$ to $Rx_k$. Equivalently, we can write $$y_k = h_k^\dagger s + n_k, \quad k = 1, \ldots, K$$ \hspace{1cm} (2) where $h_k \in \mathbb{C}^{K \times 1}$ is the vector of the channel coefficients between $Rx_k$ and $\{Tx_m\}_{m=1}^K$ and $s \in \mathbb{C}^{K \times 1}$ is the vector of transmitted symbols. The input-output model of the overall channel is $$y = Hs + n,$$ \hspace{1cm} (3) where $y \in \mathbb{C}^{K \times 1}$ is the vector of received symbols; $n \in \mathbb{C}^{K \times 1}$ is a complex-valued Gaussian noise vector with $n \sim \mathcal{CN}(0, \sigma^2_n I_K)$, i.e., with mean matrix $E\{n\} = 0_K$ and covariance matrix $R_{nn} = E\{nn^\dagger\} = \sigma^2_n I_K$; and $H \in \mathbb{C}^{K \times K}$ is the channel matrix expressed as $$H = [h_1, \ldots, h_K]^\dagger.$$ \hspace{1cm} (4) The total transmitted power is constrained to $P$, i.e., $$\text{Tr}(R_{ss}) = \text{Tr}(E\{ss^\dagger\}) \leq P,$$ \hspace{1cm} (5) where $R_{ss} = E\{ss^\dagger\}$ is the covariance matrix of the transmitted signal vector $s$. For convenience, and without loss of generality, we assume that all transmitted symbols $\{s_k\}_{k=1}^K$ have equal variance $\sigma^2_s = P/K = 1$ such that $R_{ss} = \sigma^2_s I_K = I_K$ and $P = \text{Tr}(R_{ss}) = K$. ### 3.2 Channel Model In order to capture the effect of the beam radiation patterns, we consider, without loss of generality, a geometry-based single-bounce scattering statistical model \[12\],[13]. In the single-bounce approach, each transmit/receive path is broken into two sub-paths: transmitter-to-scatterer and scatterer-to-receiver (described by their direction of departure, direction of arrival, and path distance). The scatterer itself is modeled typically via the introduction of a random attenuation and phase shift. In this paper, we assume that the scatterers are randomly distributed on the surface of a sphere that is placed in the middle of the distance between the TXs and the RXs, as seen in Fig. 3. This model has been selected because, while it is relatively simple in comparison with other models, it captures small-scale fading and shadowing effects sufficiently well. In order to facilitate performance analysis, we normalize the channel matrix. More specifically, for fixed $H$ (e.g., when a given channel realization over the coherence time of the channel is considered), the normalized channel matrix $\tilde{H}$ is given by \[14\]: $$\tilde{H} = aH,$$ \hspace{1cm} (6) where, in the approach that we followed, the normalization constant is expressed as $$\|a\|^2 = N_T N_R \\|H\\|_F^2 = K^2 \\|H\\|_F^2,$$ \hspace{1cm} (7) such that the power gain of the channel is $$\text{Tr}(\tilde{H}\tilde{H}^\dagger) = \\|H\\|_F^2 = N_T N_R = K^2.$$ \hspace{1cm} (8) Of course, when the channel coefficients are RVs (e.g., longer time intervals are of interest), the expectation over $H$ should be taken in the appropriate expressions. Note that in Eqs. (1)–(5), as well as throughout the paper, we denote the normalized channel matrix simply as $H$, for convenience. ### 4 Radio Transmission Protocol System operation is divided into three phases, namely, the learning phase, the selection phase, and the transmission phase. In the learning phase, each UE acquires information about the quality or the coefficients of each channel formed by the $L^K$ different beam combinations at the TXs. In the selection phase, the BSs select jointly the best $K$-tuple of beams, according to the information that has been fed back to them by the UEs. Finally, in the transmission phase, communication takes place. The transmission strategy depends on the channel information available at the TXs. 4.1 Learning Phase There exist two different types of channel information that a UE may send back to the corresponding BS: 1. Its signal to interference plus noise ratio (SINR) for each beam combination at the TXs. 2. The CSI for the resulting “beam-domain transformed channel”, i.e., the complex-valued coefficients for the self- and cross-channels of the total $K \times K$ channel. 4.2 Beam Selection Phase According to the type of channel information that the BSs acquired through feedback, the following beam selection criteria apply: Beam Selection Rule #1: Select the $K$-tuple of beams that results in the largest sum of SINRs, i.e., the beam combination that maximizes $\sum_{k=1}^{K} \gamma_k$. Beam Selection Rule #2: Select the $K$-tuple of beams that results in the equivalent channel matrix with the largest product $\mathbf{H}^\dagger \mathbf{H}$. We should note that, even though our goal in this work is to generate beams using parasitic antenna arrays, since ESPAR technology reduces the cost, size, and complexity of the system, the general principle holds also for beams generated by conventional antenna arrays. 4.3 Transmission Phase In this phase, the transmission strategy that will be followed to send information symbols over the selected beams is determined. The performance metric that we wish to increase as much as possible while maintaining complexity and CSI feedback overhead low is the sum-rate throughput. If beam selection is based on the measured SINRs at the RXs (i.e., the beams that maximize the sum of the received SINRs have been selected), then there is no additional processing taking place at the TXs. The sum-rate in this non-precoded transmission case is given by: $$R_{NP} = \sum_{k=1}^{K} R_k^{(NP)} = \sum_{k=1}^{K} \log_2 \left(1 + \gamma_k^{(NP)}\right),$$ where $$R_k^{(NP)} = \log_2 \left(1 + \gamma_k^{(NP)}\right)$$ is the rate achieved by user $k$ and $\gamma_k$ is the SINR of user $k$ which is expressed as $$\gamma_k^{(NP)} = \frac{\|h_{k,k}\|^2 \sigma^2_k}{\sum_{m \neq k} \|h_{k,m}\|^2 \sigma^2_m + \sigma^2_n}$$ $$= \frac{\|h_{k,k}\|^2}{\sum_{m \neq k} \|h_{k,m}\|^2 + \sigma^2_n}.$$ since $\{\sigma^2_k\}_{k=1}^K = \sigma^2_n = 1$. If, on the other hand, the channel matrices have been fed back to the TXs (i.e., the beams that result... in an equivalent channel with the largest product $\mathbf{HH}^\dagger$ have been selected), then the TXs jointly precode the transmit vector $\mathbf{s}$, thus transforming the MU-MISO IFC into a MU-MISO broadcast channel (BC). We assume that linear precoding is employed by the system, in order to avoid the high RX complexity required by more advanced transmission techniques \cite{13}. Linear precoding includes a family of simple but sub-optimal pre-processing techniques that exploit CSI at the transmitter (CSIT) to improve MU-MIMO performance--e.g., to increase the sum-rate throughput or to minimize the aggregated bit error rate. (Unless stated otherwise, perfect CSIT is assumed.) A linear precoder generates a precoded signal vector as a linear transformation of the original symbol vector: $$\mathbf{s}' = \mathbf{Ws}. \quad (12)$$ Hence, the received signal vector is expressed as $$\mathbf{y} = \mathbf{Hs}' + \mathbf{n}. \quad (13)$$ That is, $$\mathbf{y} = \mathbf{H} \left[ \begin{array}{c} \mathbf{W} \\ \vdots \\ \mathbf{W} \end{array} \right] \left[ \begin{array}{c} \mathbf{s} \\ \vdots \\ \mathbf{s} \end{array} \right] + \mathbf{n} \quad (14)$$ Equivalently, we can write $$y_k = \mathbf{h}_k^\dagger \mathbf{w}_k s_k + \sum_{m \neq k} \mathbf{h}_k^\dagger \mathbf{w}_m s_m + n_k. \quad (15)$$ where $\mathbf{h}_k \in \mathbb{C}^{K \times 1}$, $\mathbf{w}_k \in \mathbb{C}^{K \times 1}$ and $s_k$ are the channel vector, precoding vector, and data stream of user $k$, respectively; $\mathbf{H}$ is the channel matrix; and $\mathbf{W}$ is the precoding matrix expressed as $$\mathbf{W} = \left[ \mathbf{w}_1 \ \cdots \ \mathbf{w}_K \right]. \quad (16)$$ Note that the second term at the right-hand side of Eq. \ref{eq:15} represents the multi-user interference (MUI). The SINR of user $k$ for this linear precoding scheme is given by $$\gamma^{(LP)}_k = \frac{\left\| \mathbf{h}_k^\dagger \mathbf{w}_k \right\|^2}{\sum_{m \neq k} \left\| \mathbf{h}_k^\dagger \mathbf{w}_m \right\|^2 + \sigma_n^2}. \quad (17)$$ The expressions of the $k$th user’s rate $R^{(LP)}_k$ and the sum-rate of the system $R^{(LP)}$ are similar with the ones given in Eq. \ref{eq:10} and \ref{eq:9}, respectively, for the non-precoded system. The Tx power constraint is $$\text{Tr} \left( \mathbb{E} \left\{ \mathbf{s}' (\mathbf{s}')^\dagger \right\} \right) = \text{Tr} \left( \mathbb{E} \left\{ (\mathbf{W}s) (\mathbf{Ws})^\dagger \right\} \right) = \text{Tr} \left( \mathbb{E} \left\{ \mathbf{Wss}^\dagger \mathbf{W}^\dagger \right\} \right) = \text{Tr} \left( \mathbf{WRss}^\dagger \mathbf{W}^\dagger \right) \leq P. \quad (18)$$ We propose the use of zero-forcing (ZF) precoding, which provides a promising compromise between complexity and performance \cite{15}, especially at the high signal to noise ratio (SNR) regime \cite{16}. The reasoning behind ZF precoding is to employ a linear transformation to the transmit signal vector, according to Eq. \ref{eq:12}, such that MUI becomes null, i.e., so that each user $k = 1, \ldots, K$ receives no interference from the signals intended for the other users \cite{13}: $$\left\\| \mathbf{h}_k^\dagger \mathbf{w}_m^{(ZF)} \right\\| = 0, \quad m \neq k \quad (19)$$ Interference suppression at the TX is important in this setup, since single-antenna, non-cooperating RXs are unable to eliminate interference--the best they can do is to treat it as noise. A common approach to accomplish this goal involves the inversion of the channel matrix at the TX in order to create orthogonal channels between the TX and the RXs (i.e., to diagonalize the effective channel). Channel inversion implies, under the flat-fading assumption, the multiplication of the original transmit vector signal with the right Moore-Penrose pseudo-inverse of the channel matrix $\mathbf{H}$, such that the matrix of the composite channel is the identity matrix. That is, $$\mathbf{W}_{ZF} = \mathbf{H}^+ \Rightarrow \mathbf{s}' = \mathbf{W}_{ZF}s = \mathbf{H}^+ \mathbf{s} \quad (20)$$ where $$\mathbf{H}^+ = \mathbf{H}^\dagger (\mathbf{HH}^\dagger)^{-1}. \quad (21)$$ In practice, though, we typically normalize the precoding matrix $\mathbf{W}_{ZF}$ in order to set the transmit power (after precoding) to a fixed value, independent of the channel $\mathbf{H}$, according to the given power constraint. An often used normalization, which is referred to as equal receive power (ERP) normalization, takes the following form \cite{17}: $$\mathbf{W}_{ERP} = \sqrt{\beta} \mathbf{H}^+ = \sqrt{\beta} \mathbf{H}^\dagger (\mathbf{HH}^\dagger)^{-1}. \quad (22)$$ Under our assumption $\sigma_n^2 = 1 \Rightarrow \mathbb{E} \left\{ \mathbf{s}s^\dagger \right\} = \mathbf{R}_{ss} = \mathbf{I}_K \Rightarrow \text{Tr} (\mathbf{R}_{ss}) = K$ and by forcing the total transmit power after precoding to remain equal to $P = K$, that is, $$\text{Tr} \left( \mathbf{W}_{ERP} \mathbf{R}_{ss} \mathbf{W}_{ERP}^\dagger \right) = K, \quad (23)$$ the power normalization factor $\beta$ is given by \cite{18}: $$\beta = \frac{1}{\text{Tr} \left( (\mathbf{HH}^\dagger)^{-1} \right)} \quad (24a)$$ $$= \frac{1}{\left\\| (\mathbf{HH}^\dagger)^{-1} \right\\|_F} \quad (24b)$$ $$= \frac{1}{\sum_{k=1}^K 1/ (\lambda_k^2)} \quad (24c)$$ where $ \lambda_k $ is the $ k $th singular value of $ \mathbf{H} $. When the channel matrix is square, as it is in our case where $ N_T = K $, then the precoding matrix is simply given by \cite{19}: \[ \mathbf{W}_{\text{ERP}} = \sqrt{\beta} \mathbf{H}^{-1}. \] (25) In any case, the corresponding received signal vector is given by: \[ \mathbf{y} = \mathbf{Hs}^t + \mathbf{n} = \mathbf{H} (\mathbf{W}_{\text{ERP}} \mathbf{s}) + \mathbf{n} = (\mathbf{HW}_{\text{ERP}}) \mathbf{s} + \mathbf{n} = \sqrt{\beta} \mathbf{s} + \mathbf{n}. \] (26) Note that the scaling factor in Eq. (26) may lead to reduced SNR at the receiver if the channel matrix is ill-conditioned, i.e., if one of its singular values is very large. The SINR at user $ k $ is given by Eq. (17) by setting the MUI at the denominator equal to zero and noting that $ \mathbf{HW}_{\text{ERP}} = \sqrt{\beta} \mathbf{I} $: \[ \gamma_k^{(\text{ERP})} = \frac{\beta}{\sigma_k^2}. \] (27) Therefore, all MUs experience the same SNR as expected, since the scaling factor is the same for all transmitted signals, and achieve the same rate \[ R_k^{(\text{ERP})} = \log_2 \left( 1 + \gamma_k^{(\text{ERP})} \right). \] (28) Hence, the sum-rate of this ZF precoding scheme is given by: \[ R_{\text{ERP}} = \sum_{k=1}^{K} R_k^{(\text{ERP})} = \sum_{k=1}^{K} \log_2 \left( 1 + \gamma_k^{(\text{ERP})} \right) = \sum_{k=1}^{K} \log_2 \left( 1 + \frac{\beta}{\sigma_k^2} \right) = K \log_2 \left( 1 + \frac{\beta}{\sigma_k^2} \sum_{k=1}^{K} \frac{1}{(\lambda_k^2)} \right). \tag{29a} \] Another commonly used normalization, which results in higher sum-rate than ERP normalization, is the so-called equal transmit power (ETP) normalization which is obtained by setting \[ \mathbf{F} = \mathbf{H}^+ = \mathbf{H}^\dagger (\mathbf{HH}^\dagger)^{-1} \] (30) (or $ \mathbf{F} = \mathbf{H}^{-1} $ in case of a square channel matrix) and then dividing the elements of column $ k $ of $ \mathbf{F} $ with the norm of the corresponding column vector \cite{20}: \[ \mathbf{W}_{\text{ETP}} = \mathbf{F}(; k) / \\| \mathbf{F}(; k) \\|, \quad k = 1, \ldots, K. \] (31) The SINR in this case is \[ \gamma_k^{(\text{ETP})} = \frac{1}{\sigma_k^2 \\| \mathbf{F}(; k) \\|^2} \] (32) and the sum-rate is given as \[ R_{\text{ETP}} = \sum_{k=1}^{K} \log_2 \left( 1 + \gamma_k^{(\text{ETP})} \right) = \sum_{k=1}^{K} \log_2 \left( 1 + \frac{1}{\sigma_k^2 \\| \mathbf{F}(; k) \\|^2} \right). \tag{33} \] Both these normalization methods set MUI to zero and have the same total transmit power. These ZF precoding design schemes aim at minimizing transmit power. Another design approach is to set \[ \mathbf{W}_{\text{WF}} = \mathbf{H}^\dagger (\mathbf{HH}^\dagger)^{-1} \text{diag} \left( \sqrt{P_1}, \ldots, \sqrt{P_K} \right) \] (34) and perform water-filling (WF) to optimally allocate transmit power per antenna $ \{P_k\}_{k=1}^{K} $ such that the sum-rate is maximized, under the total power constraint \[ \sum_{k=1}^{K} \\| \mathbf{w}_k \\| P_k = P. \tag{35} \] However, this optimal ZF method is not applicable in the considered system setup due to the fact that it does not only increase the complexity of the cooperation between the BSs, but it requires also cooperation between the UEs (i.e., joint decoding). 5 Performance Results In this section we evaluate the sum-rate performance of the proposed radio protocol via numerical simulations for the system setup described in Section 3 with $ K = 2 $ and $ L = 4 $. The performance results in Fig. 4 represent ergodic sum-rates achieved over a range of target SNR values at the receiver, from 0dB up to 30dB. These results have been obtained after 1,000 simulation runs by taking the expectation of the corresponding sum-rate equations. Also, in each simulation run, 100 sub-runs are used for the normalization of the channel matrices, as described in Section 3.2. We consider transmission over the “beam-domain” channel with and without ZF precoding. That is, we study non-precoded transmission over the beams (which have been selected according to the SINRs that the MTs have fed back to the BSs) as well as the case where the MTs feed back the complex coefficients of the equivalent 2 × 2 “beam-domain” channel and ZF precoding is incorporated in the transmission process. For comparison purposes, we illustrate also the performance of the system when communication does not take place over a selected pair of beams, but we have instead conventional (non-precoded or precoded) “omni-channel” transmission. Of course, this type of non-precoded transmission would not take place in practice, since it is not a multi-user communication scheme, i.e., it does not take into account MUI; it is just included in the simulation as a lower performance bound. In our simulations we have set, for mathematical tractability and without loss of generality, $ P = K $. We note that non-precoded transmission over the “beam-channels” outperforms significantly “omni-channel” transmission methods, even when the latter employ ZF precoding, especially at high SNR values. This is due to: (a) The gain that is introduced to the system as a result of the use of beams. (b) The fact that the TXs are informed about the SINR at the RXs and select the best beam combination each time. We also note that the knowledge of the CSI at the transmitter for the equivalent “beam-domain transformed” channel and the joint precoding of the transmit vector that is performed based on that CSIT further improves the performance of the system at the high SNR regime. Finally, it is worth noting that the sum-rate of the transmission schemes that incorporate ZF precoding keeps increasing linearly within the considered SNR range, whereas the non-precoded techniques experience an expected flooring of their performance due to the residual interference that they incur, which is not accounted for. 6 Complexity-Overhead and Complexity-Performance Tradeoffs In Section 2, a brief overview of ESPAR and C-RAN technologies was given. In this Section, we present the complexity reduction accomplished by the use of the proposed radio transmission scheme described in Section 4, mainly in terms of channel estimation / channel information feedback, and the relevant complexity-overhead as well as complexity-performance tradeoffs. But first, let us summarize the main points of Section 2: - ESPAR antennas reduce the size, complexity and cost of antenna arrays due to the fact that they use fewer active antenna elements and RF units than conventional antenna solutions and thus can be viewed as an enabler of massive MIMO. - C-RAN facilitates the efficient cooperation between individual BSs in Coordinated Multi-Point (CoMP) setups since the centralization and virtualization of the BBUs as well as the use of optical fibers at the fronthaul for the connection of the BBUs with the RRHs is capable of meeting the stringent delay and bandwidth requirements that are imposed by this family of cooperative MIMO communication techniques. The interested reader is encouraged to refer to the corresponding references cited in Section 2 for a more detailed presentation of the benefits and drawbacks / challenges of these technologies. As we mentioned in Section 3, our focus is on the downlink transmission in a system setup with $ K $ cloud-based RRHs/BSs, each equipped with a single-RF ESPAR, and $K$ single-antenna UEs. Since the $K$ RRHs can be viewed as a composite BS with $K$ antennas due to the C-RAN architecture, MU-MISO communication techniques over a BC are applicable. The use of ESPARs instead of conventional antenna arrays reduces significantly channel estimation complexity due to the decreased number of active antenna elements which is translated into a correspondingly decreased number of direct- and cross-channels. In the remaining Section, we will compare “omni-channel” and “beam-channel” transmission methods in terms of complexity assuming in both cases the use of ESPARs at the BSs, but we should keep in mind this important note, that is, that the replacement of antenna arrays by ESPARs already provides complexity reduction regarding channel estimation. Initially, let us assume conventional transmission over “omni-channels”. The optimum precoding technique in terms of sum-rate is dirty paper coding (DPC) [13]. However, the computational complexity of this non-linear precoding scheme makes it impractical. ZF precoding, on the other hand, is a low-overhead scheme that completely eliminates MUI, but it amplifies noise power. Minimum mean square error (MMSE) considers noise in the precoding process, leading to better performance than ZF in low SNR conditions, at the cost of increased complexity [9]. Hence, ZF precoding is the MU-MISO transmission method with the smaller overhead. ZF precoding requires full CSIT. Since we have $K$ active antennas at the composite TX (and recalling that we are considering narrowband channels), the equivalent channel is described by a $K \times K$ matrix. In other words, each one of the $K$ UEs should feed back to its corresponding BS a vector of size $K$ containing the coefficient of the direct channel with that BS and the $K - 1$ coefficients of the cross-channels with the other $K - 1$ BSs. If we assume non-precoded transmission, as a low complexity bound, then each UE should feed back to its BS only its SINR. Thus, the composite BS would have to collect $K$ SINR values (real numbers), as opposed to the $K^2$ channel coefficients (complex numbers) required in the ZF precoding scenario. Of course, as we mentioned in the previous Section, such a transmission scheme would not be used in practice due to its poor performance. Now, let us consider the proposed radio protocol. Each one of the $K$ RRHs is able to generate $L$ distinct beams. Thus, there exist $L^K$ possible beam combinations. Assuming non-precoded transmission (i.e., the beams to be used during transmission are selected according to criterion #1 described in Section 4), each UE should feed back to its BS its SINR for each one of the beam combinations. That is, each one of the $K$ UEs should send to its corresponding BS $L^K$ SINR values. Therefore, $K$ ($L^K$) real values will be sent back to the composite BS in total. In contrast, when ZF precoding is used over “omni-channels”, $K^2$ complex values have to be send back to the composite BS. However, in the latter case, accurate channel estimation is challenging when the number of BSs (and active TX antenna elements) is high, while the measurement of the received SINR value at each UE is a rather trivial task. Also, while non-precoded, SINR-based transmission over “omni-channels” presents the lowest overhead (the feedback of only $K$ real values is required), it is not suitable for multi-user communication as we have already mentioned. Let us turn our attention into ZF precoding-based transmission over the “beam-channels” (i.e., beam selection criterion #2 is applied). For each beam-combination, the required CSIT is represented by a $K \times K$ complex-valued matrix. Thus, in total $K^2$ ($L^K$) complex values have to be fed back to the composite BS instead of only $K^2$ complex values that are required in the corresponding “omni-channels” case. However, a performance-complexity tradeoff is expected due to the “beam-gains” and the selection of the optimal “composite beam-domain channel”, as we have seen in Section 5. Let us summarize: Non-precoded and precoded transmission over “beam-channels” results in an increase of the feedback overhead by $L^K$ in comparison with the corresponding “omni-channel” schemes due to the fact that each UE should send back to its BS its SINR or channel matrix for each beam combination. However, it outperforms transmission over “omni-channels” and it simplifies (or even eliminates the need for) channel estimation. More specifically: - “Beam-channel” communication techniques present a significant performance gain against their “omni-channel” counterparts. - Even non-precoded “beam-channel” transmission outperforms ZF “omni-channel” transmission. Thus, by using predetermined beams, we could simply collect SINR values instead of estimating channel matrices, which is a much simpler procedure - and therefore, it is easier to be used in practice, even in large setups. - The increase in the channel information overhead caused by the use of beams can be partly compensated by the use of ESPARs instead of conventional antenna arrays, depending on \[1\] In high mobility environments, it is possible to update the SINR value corresponding to each beam combination every time it is used to serve a user. Then, a record of time-windowed SINR values can be kept, thus further reducing the feedback requirements. the ratio “reduction in the number of active antenna elements / increase in the number of beams”. 7 ZF Precoding-based Transmission over “Beam-Channels” with Imperfect CSIT So far, we have assumed perfect CSIT. In practice, though, various sources of error (e.g., channel estimation errors, channel quantization errors, feedback errors etc.) may result in imperfect CSIT. In this case, the imperfect channel matrix that is fed back to the TX is expressed as \[ H_e = H + E, \] where $ H $ is the actual channel matrix and $ E $ is an additive error matrix whose entries are independent and identically distributed (i.i.d.) RVs that are independent of $ H $ and follow a $ \mathcal{CN}(0, \sigma_e^2) $ distribution. Then, the precoded signal vector is expressed as \[ s' = \sqrt{\beta} W_{ZF} H_e^, \] where the power normalization factor $ \beta $ is given by \[ \beta = \frac{1}{\text{Tr}\left((H_e H_e^)^{-1}\right)} \] \[ = \frac{1}{\left\\| (H_e H_e^)^{-1} \right\\|_F} \] \[ = \frac{1}{\sum_{k=1}^K 1 / \lambda_k^2}, \] and $ \lambda_k $ is the $ k $th singular value of $ H_e $. The received signal vector is expressed as \[ y = H s' + n \] \[ = \sqrt{\beta} H H_e^ s + n \] \[ = \sqrt{\beta} (H_e - E) H_e^* s + n \] \[ = \sqrt{\beta} s - \sqrt{\beta} E H_e^* s + n. \] The SINR of each user, given that $ \sigma_s^2 = 1 $, is \[ \gamma_k^{(ZF)} = \frac{\beta}{P \sigma_s^2 + \sigma_n^2} = \frac{1}{(\sigma_s^2 + 1/P) \sum_{k=1}^K 1 / \lambda_k^2}, \] while the sum-rate is expressed as \[ R_{ZF} = K \log_2 \left( 1 + \frac{1}{(\sigma_s^2 + 1/P) \sum_{k=1}^K 1 / \lambda_k^2} \right). \] Note that the variance of the error, $ \sigma_e^2 $, limits the sum-rate, i.e., as $ P \to \infty $, \[ R_{ZF} = K \log_2 \left( 1 + \frac{1}{\sigma_s^2 + 1/P} \sum_{k=1}^K 1 / \lambda_k^2 \right). \] We conclude this Section by evaluating the sum-rate performance of ZF precoding transmission over pre-determined beams for the considered setup in the case where CSIT is imperfect and for a range of error variance values $ P_e $ from $ 10^{-3} $ up to $ 10^{-1} $ via simulations and we compare these results with the performance obtained when CSIT was assumed to be perfect. As we see in Fig. 5, when the error variance is small, the degradation in the sum-rate throughput is negligible and only noticeable at the high SNR regime. However, as the error variance increases, the sum-rate is decreased and at some point floors (the higher the error variance, the sooner this flooring takes place). 8 Conclusions In this paper, we proposed a new radio transmission protocol for a system setup that could be an enabler of next-generation MU-MIMO systems. The proposed scheme performs extremely well in terms of the achieved sum-rate while it reduces significantly the complexity of the system. In the future, we plan to extend this work by studying larger setups and cases with imperfect CSI feedback. Acknowledgments This work has been supported by the EC FP7 project HARP (http://www.fp7-harp.eu/) under grant number 318489. References [1] ITU-R, “Assessment of the global mobile deployments and forecasts for international mobile telecommunications,” Report M.2243, November 2011. [2] “Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update 2014-2019,” Cisco, White Paper, February 2015. [3] M. Sawahashi et al., “Coordinated Multi-point Transmission/reception Techniques for LTE-Advanced [Coordinated and Distributed MIMO],” IEEE Wireless Communications Magazine, vol. 17, no. 3, pp. 26–34, 2010. Figure 5: Sum-rate of ZF precoding-based transmission over “beam-channels” for the case of imperfect CSIT and for various values of error variance. [4] D. Lee et al., “Coordinated Multipoint Transmission and Reception in LTE-Advanced: Deployment Scenarios and Operational Challenges,” IEEE Communications Magazine, vol. 50, no. 2, pp. 148–155, 2012. [5] Massive MIMO Project. [Online]. Available: www.massivemimo.eu [6] T. L. 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Papadias, “Low-feedback Cooperative Opportunistic Transmission for Dynamic Licensed Shared Access,” in EUSIPCO, 2015, to appear.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4208, 1 ], [ 4208, 8778, 2 ], [ 8778, 12682, 3 ], [ 12682, 15978, 4 ], [ 15978, 18732, 5 ], [ 18732, 23987, 6 ], [ 23987, 28114, 7 ], [ 28114, 31366, 8 ], [ 31366, 36782, 9 ], [ 36782, 40359, 10 ], [ 40359, 43143, 11 ], [ 43143, 43551, 12 ] ] }
d2d12cdeb6311968880dbd4bddbf7c11c0cf0898	{ "olmocr-version": "0.1.59", "pdf-total-pages": 15, "total-fallback-pages": 0, "total-input-tokens": 50639, "total-output-tokens": 9598, "fieldofstudy": [ "Physics" ] }	Charge Carriers Relaxation Behavior of Cellulose Polymer Insulation Used in Oil Immersed Bushing Yu Shang 1, Qiang Liu 1, Chen Mao 1, Sen Wang 1, Fan Wang 1, Zheng Jian 2, Shilin Shi 2 and Jian Hao 2 1 Shaanxi Electric Power Research Institute, State Grid Shaanxi Electric Power Co., Xi’an 710100, China; [email protected] (Y.S.); [email protected] (Q.L.); [email protected] (C.M.); [email protected] (S.W.); [email protected] (F.W.) 2 State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400044, China; [email protected] (S.S.); [email protected] (J.H.) * Correspondence: [email protected] Abstract: Cellulose polymer insulation material is widely used in oil immersed bushing. Moisture is one of the important reasons for the deterioration of cellulose polymer insulation, which seriously threatens the safe and stable operation of bushing. It is significant to study the polarization and depolarization behavior of oil-immersed cellulose polymer insulation with different moisture condition under higher voltage. Based on polarization/depolarization current method and charge difference method, the polarization/depolarization current, interfacial polarization current and electrical conductivity of cellulose polymer under different DC voltages and humidity were obtained. Based on molecular-dynamics simulation, the effect of moisture on cellulose polymer insulation was analyzed. The results show that the polarization and depolarization currents become larger with the increase in DC voltage and moisture. The higher applied voltage will accelerate the charge carrier motion. The ionization of water molecules will produce more charge carriers. Thus, high DC voltage and moisture content will increase the interface polarization current. Increased moisture content results in more charge carriers ionized by water molecules. In addition, the invasion of moisture will reduce the band width of cellulose polymer and enhance its electrostatic potential, so as to improve its overall electrical conductivity. This paper provides a reference for analyzing the polarization characteristics of charge carriers in cellulose polymer insulation. Keywords: cellulose polymer insulation; polarization/depolarization current; charge carrier; moisture; molecular dynamics simulation 1. Introduction The oil-immersed transformer is the core equipment of power transmission in the power grid, wherein safety and stability are significantly important to energy security and social stability. According to statistics, fault of bushing is one of the main causes for transformer faults, and the cellulose polymer paper, as the main insulation material of bushing, is the main factor contributing to the fault of bushing after moisture invaded [1–3]. To ensure the safe operation and stability of the transformer, it is necessary to analyze the time-domain relaxation behavior of carriers at high applied voltage with various moisture contents. To date, some scholars have studied the effect of moisture on cellulose polymer paper. Wenyu Ye, et al. found that the structure of liquid-solid interface is determined by the interaction between insulating oil and cellulose polymer paper, which is based on the Van der Waals effect, and water molecules will gather at the interface because of the interaction of the liquid-solid interface at certain electric field value [4]. Guanwei Long, et al. have simulated the distribution of H+ and OH− for oil and cellulose polymer paper insulation when moisture invaded, explaining the effect of moisture on the cellulose polymer paper... and oil insulation from a microscopic point of view [5]. Haoxiang Zhao et al. found that when charge carriers pass through the interface between cellulose polymer paper and oil, the insulating paper has an obstruction effect, while the existence of water molecules would produce more charge carriers and reduce the obstruction effect, resulting in lower conductivity of cellulose polymer paper and different dielectric response characteristics [6]. The above research shows that moisture will have a great influence on the dielectric properties of cellulose polymer paper. In order not to damage the sealing performance of bushing, nondestructive testing methods based on dielectric relaxation theory have been widely used by scholars, among which polarization and depolarization current (PDC) method and frequency domain spectroscopy (FDS) method are the most popularly used [7–9]. Both methods have the advantages of simple operation and rich insulation information. However, FDS is usually used to study the dielectric response characteristics at different frequencies, focusing on the analysis of dielectric constant and dielectric loss factor. While PDC is used to analyze the charge accumulation and charge carrier relaxation behavior of cellulose polymer paper because it can measure the time domain dielectric response characteristics of insulating oil and cellulose polymer paper. Quanmin Dai et al. found that the dielectric response of bushing changes when moisture invaded, which provided a basis for judging the moisture content of cellulose polymer paper by PDC [10]. Feng Yang tested the cellulose polymer paper by PDC and found that the polarization and depolarization current increases with higher moisture content; they established a relationship between the moisture content of bushing and the PDC results [11]. T. K. Saha et al. proposed a method to calculate the conductivity of cellulose polymer paper by the polarization and depolarization current, providing a method to analyze charge accumulation by conductivity [12]. Although some scholars have studied the correlation between the dielectric characteristic parameters of bushing insulating paper in time domain and moisture, most of the research is based on low excitation voltage, resulting in low signal-to-noise ratio, which is easy to be interfered by environmental noise. Additionally, and yet worse, the cellulose paper in the bushing works at a higher voltage, which means the traditional low-voltage measurement results and rules are not applicable to a higher excitation voltage. In addition, there is little research on analyzing the charge accumulation at the interface of oil-paper insulation in bushing based on PDC measurement results. Therefore, it is necessary to analyze the time-domain relaxation behavior of the bushing insulating paper with various moisture contents at high voltage. This paper studies the time domain relaxation behavior of charge carriers for cellulose polymer insulation used in oil immersed bushing under higher voltage. Firstly, the polarization and depolarization currents of cellulose polymer insulation with different moisture conditions are obtained. Then, the influence of moisture and applied voltage on the characteristics of interface polarization behavior is studied; the motion of the interface charge carriers during the process of polarization and depolarization and the relationship between the steady state time of electrical conductivity are analyzed. Finally, based on molecular dynamics simulation, the effect of moisture on the insulation properties of cellulose polymers is analyzed. 2. Experiment and Theoretical Analysis 2.1. Experiment Cellulose is a natural polymer compound, its chemical structure is a linear polymer composed of many β-D-glucopyranosyl groups connected to each other by 1, 4-β glycoside bonds. Cellulose polymer insulation is mainly composed of cellulose macromolecular chains composed of cellulose monomers, as shown in Figure 1. Because cellulose polymer insulation has excellent insulation performance, it is widely used in the field of high voltage insulation. The chemical structure of cellulose macromolecular chain is shown as Figure 1 [13,14]. In this paper, an oil immersed bushing with cellulose polymer insulation, where the maximum voltage is 40.5 kV, is tested. The structure diagram of the bushing is shown in Figure 2. The insulation performance of this bushing may be reduced due to moisture in the oil and cellulose polymer insulation. In order to study the influence of moisture on the time domain relaxation behavior, the cellulose polymer insulation and insulation oil are treated with moisture absorption before the bushing is manufactured and packaged. PDC tests in different DC voltages are carried out; the schematic diagram and physical diagram of PDC test is shown in Figure 3. In this paper, the DC high voltage power supply (AU-2060, Matsusada, Osaka, Japan) is used to excite the bushing, and the high-precision electrometer (6517 B, Keithley, OH, USA) is used to collect the current signal at the end screen of the bushing. The polarization/depolarization process of the bushing cellulose polymer can be further explained by analyzing the changes in the excitation voltage and response current. The charge and discharge process for bushing lasts for 3000 s, and the applied voltages are 200 V, 500 V, 1000 V, 2000 V and 4000 V, respectively, and the environmental temperature and relative humidity are 20 °C and 62%, respectively. ![Chemical structure of cellulose macromolecular chain.](image1) Figure 1.* Chemical structure of cellulose macromolecular chain. ![Structure diagram of oil immersed bushing.](image2) Figure 2. Structure diagram of oil immersed bushing. ![PDC test.](image3) Figure 3. PDC test: (a) Schematic diagram; (b) Physical diagram. ### 2.2. Polarization/Depolarization Principle and Charge Analysis for Composite Polymer Medium By applying and removing DC voltages to the insulating medium, the dielectric response characteristics in time domain from the polarization and depolarization current... can be extracted based on a PDC test. The schematic diagram is shown as Figure 4. By connecting the switch to point a and then point b, the insulating medium is charged and then discharged, these two processes are polarization and depolarization processes of the insulating medium, respectively, and the current generated in these two processes are called polarization current $i_{\text{pol}}$ and depolarization current $i_{\text{depol}}$, correspondingly. Figure 4. Schematic diagram. For the insulating medium, the polarization process mainly includes dipole polarization and interface polarization. Due to the difference of dielectric constant and electrical conductivity of composite insulating mediums, the free charge will accumulate at the interface and will not dissipate easily, resulting in the asymmetry of polarization process and depolarization process. Polarization current consists of dipole relaxation current $i_{\text{pol}}$ and interface polarization current $i_{\text{interface-pol}}$. The depolarization current mainly consists of dipole relaxation current $i_{\text{dipole-depol}}$. In general, the dipole polarization current is equal to dipole relaxation current. The polarization current and depolarization current are shown in Equations (1) and (2). \[ \begin{align} i_{\text{pol}} &= i_{\text{dipole-pol}} + i_{\text{conductance}} + i_{\text{interface-pol}} \quad (1) \\ i_{\text{depol}} &= i_{\text{dipole-depol}} \quad (2) \end{align} \] Electrical conductivity can reflect the degree of moisture content of insulating materials. Charge difference analysis method (CDA) can effectively calculate the electrical conductivity of insulating materials by analyzing the change characteristics of the charge amount difference in charge and discharged process [15–18]. By integrating the difference of polarization and depolarization current curve over time, charge amount difference can be obtained, as shown in Equations (3) and (4) [19,20]. \[ \begin{align} q_{\text{pol}}(t_i) &= \sum [i_{\text{pol}}(t_i) \times t_i] \quad (3) \\ q_{\text{depol}}(t_i) &= \sum [i_{\text{depol}}(t_i) \times t_i] \quad (4) \end{align} \] Thus the charge amount difference at any time is as Equation (5), and the difference between polarization current and depolarization current at any time is as Equation (6): \[ \begin{align} \Delta Q(t_i) &= \sum i_{\text{dc}}(t_i) \times t_i \quad (5) \\ i_{\text{dc}}(t_i) &= i_{\text{pol}}(t_i) - i_{\text{depol}}(t_i) \quad (6) \end{align} \] The charge amount difference is numerically the integral of the conductance current over time. As the conductance current changes little with time, the slope $k$ of charge amount difference function with time is approximately constant, as shown in Equation (7). \[ k = \frac{[q_{\text{pol}}(t_2) - q_{\text{depol}}(t_2)] - [q_{\text{pol}}(t_1) - q_{\text{depol}}(t_1)]}{t_2 - t_1} \quad (7) \] From Equations (6) and (7), $ i_{dc}(t_f) $ can be expressed as Equation (8): \[ i_{dc}(t_f) = \frac{q(t_f)}{t_f} = k \] (8) When the time of polarization and depolarization process is equal and long enough, the current difference at the final moment is equal to the conductance current, as shown in Equation (9). The electrical conductivity $ \sigma_r $ of the composite insulating medium can be obtained from the conductance current, as shown in Equation (10). \[ i_{dc}(t_{final}) = i_{pol}(t_{final}) - i_{depol}(t_{final}) = i_{\text{conductance}} \] (9) \[ \sigma_r \approx \frac{\varepsilon_0}{C_0U_0} [i_{pol}(t_{final}) - i_{depol}(t_{final})] = \frac{\varepsilon_0i_{\text{conductance}}}{C_0U_0} \] (10) 2.3. Electrical Conductivity Calculation for Cellulose Polymer Insulation The composite insulation structure in the bushing is composed of aluminum foil and oil immersed cellulose polymer wrapped closely, as shown in Figure 5. The electrical conductivity of the cellulose polymer insulation can be obtained by using simplified X-Y model when the electrical conductivity of the whole insulating material is known [20]. As for simplified X model, the electrical conductivity of the composite insulating structure is shown as Equation (11), where X is the thickness ratio. \[ \sigma_r = \frac{\sigma_{cellulose}C_{Al}}{\sigma_{cellulose}(1 - X) + \sigma_{Al}X} \] (11) Since the electrical conductivity of aluminum foil is much greater than that of cellulose polymer and the thickness of aluminum foil is negligible compared with that of cellulose polymer insulation, which means $ X $ equals to 1, the electrical conductivity of cellulose polymer insulation can be simplified, and the electrical conductivity of the cellulose polymer is as shown in Equation (12). \[ \sigma_{cellulose} = \frac{\varepsilon_0k}{C_0U_0} \] (12) 2.4. Modeling of Molecular Dynamics Simulation In order to study the effect of moisture on the insulation properties of cellulose polymer, the models of cellulose without moisture and after moisture were constructed by using Materials Studio software [21]. Three cellulose chains with a degree of polymerization of 10 were used as the cellulose polymer insulation model without moisture, while 3.5% water molecules were added. into three cellulose chains with a degree of polymerization of 10 as the cellulose polymer insulation model with moisture. The two cellulose polymer insulation models are shown in Figure 6. ![Cellulose chains](image1) ![Water molecules](image2) Figure 6. The two cellulose polymer insulation models: (a) Cellulose model; (b) Cellulose model with 3.5% water. First, 10,000 steps of geometric optimization were carried out for the two models by using the Steepest descent method. Then, the two models were annealed to make the model reach the most realistic condition; the annealing temperature was 300–500 K. Under Compass force field, constant-pressure and constant-temperature ensemble (NPT ensemble), with a constant number of molecules, pressure, and temperature, was used to balance each model and to make the model more reasonable with 500 ps. Based on the density functional theory (DFT), the calculations for two cellulose models were analyzed by DMol3 Tool in Materials Studio. The geometry optimization, molecule orbitals and electrostatic potential were calculated by employing the PBE function under the generalized gradient approximation (GGA) exchange-correlation term. The double numerical plus polarization (DNP) basis set was applied for setting the parameters of C, H, O atoms in this computational work. The all-electron method was adopted for core electron calculation. 3. Results 3.1. Polarization and Depolarization Current Characteristics for Cellulose Polymer Insulation The polarization and depolarization current of bushings with different moisture conditions and applied voltages are shown in Figures 7–9. For normal bushing, the polarization current will hardly change significantly with time under any polarization voltage. The depolarization current decreases rapidly to a stable value in the first 10 s. For dampened oil bushing, under any polarization voltage, the polarization current decreases slowly in the first 10 s, and then tends to be almost stable. The depolarization current decreases rapidly in the first 50 s, and with the passage of time, the decreasing trend gradually slows down and finally tends to be stable. For dampened cellulose polymer bushing, under any polarization voltage, the polarization current will gradually decrease with time in a short time, and then gradually tend to be stable. The depolarization current decreases rapidly in the first 100 s, and with the passage of time, the decreasing trend gradually slows down and finally tends to be stable. This phenomenon can be explained by the differing hydrophilic qualities of oil and cellulose polymer. Since the hydrophilic quality of cellulose polymer is much higher than that of insulation oil, when water is present, most water molecules in the insulation oil will migrate to the cellulose polymer with the invasion of moisture. As polar molecules, the more moisture infiltrates into the cellulose polymer insulation, the more polar molecules are involved in the polarization reaction, leading to a larger polarization intensity difference. The moisture content, on one hand, can increase the electrical conductivity of the insulation system, whereas, on the other hand, it can enhance the response speed of the interface This phenomenon can be explained by the differing hydrophilic qualities of oil and cellulose polymer. When the applied voltage is lower than 1000 V, the current fluctuates significantly with time. This is because the polarization process of oil-immersed cellulose polymer insulation system inside the bushing cannot be fully stimulated by low DC voltage in such a large size. Therefore, the polarization and depolarization currents of the insulation are small and susceptible to the interference of environmental noise, which has an obvious influence on the accuracy of the test results. When the applied DC voltage increases, the corresponding current becomes larger and the fluctuation of that decreases. The development trend of polarization and depolarization current is not affected by applied DC voltage, which means the applied DC voltage has little influence on the general trend of the dielectric polarization process. Thus, a high applied DC voltage test can not only improve the signal-to-noise ratio, but also reflect the polarization process of bushing more clearly, resulting in a more accurate and effective test result. ![Figure 7](image1.png) Figure 7. Polarization/depolarization current of normal bushing: (a) Polarization current; (b) Depolarization current. ![Figure 8](image2.png) Figure 8. Polarization/depolarization current of bushing with damped oil: (a) Polarization current; (b) Depolarization current. Figure 8. Polarization/depolarization current of bushing with damped cellulose polymer insulation: (a) Polarization current; (b) Depolarization current. 3.2. Interface Polarization Characteristics of Cellulose Polymer Insulation The interface polarization current of the three bushings can be calculated by Equations (1)–(3), as shown in Figures 10 and 11. Figure 10 shows that the interface polarization current of the bushing with different moisture condition decreases to zero with time. While for normal bushing, the interface polarization current does not change significantly and always tends to be zero. Compared with dampened oil bushing, the initial interface polarization current of the bushing with dampened cellulose polymer insulation is larger and takes longer time to decay to zero. Figure 11 reflects that with the increase in applied DC voltage, the interface polarization current increases, and the current decreases slowly with the time. The insulation system of the bushing is composed of aluminum foil and cellulose polymer, and the dielectric constants of both are different. When applying DC voltage in the insulation system, the interface polarization process occurs, and an interface polarization current is generated. When the voltage increases, the electric field becomes larger, accelerating the motion of the charge carriers. When the moisture infiltrates into the insulation medium, the water molecules are ionized to produce more charge carriers under the effect of electric field. This explains the characteristic of interface polarization current under the influence of moisture content and applied DC voltage. The migration process of charge carriers at the cellulose polymer interface is shown in in Figure 12. Figure 9. Polarization/depolarization current of bushing with damped cellulose polymer insulation: (a) Polarization current; (b) Depolarization current. Figure 10. Interface polarization current of bushings with different moisture conditions. Figure 10. Interface polarization current of bushings with different moisture conditions. The slopes of the polarization/depolarization charge amount difference at 200 V, 500 V, 1000 V, 2000 V and 4000 V are shown in Figures 13–15, respectively. The results show that the charge difference curves of the three bushings have similar characteristics. According to Equation (8), the slope of the charge difference curve is approximately equal to the conductance current, indicating that the accumulation rate of the charge difference tends to be constant. With the increase in the excitation voltage, the faster is the accumulation rate of the charge difference. However, under the same excitation voltage, the slope of the charge difference curve is less than that of the moistened bushing, indicating that water will also affect the accumulation rate of the charge difference. The charge difference spectrum of normal bushing, dampened oil bushing and dampened cellulose polymer paper bushing under different voltages are shown in Figures 13–15, respectively. The results show that the charge difference curves of the three bushings have similar characteristics. According to Equation (8), the slope of the charge difference curve is approximately equal to the conductance current, indicating that the accumulation rate of the charge difference tends to be constant. With the increase in the excitation voltage, the faster is the accumulation rate of the charge difference. However, under the same excitation voltage, the slope of the charge difference curve of the normal bushing is always less than that of the moistened bushing, indicating that water will also affect the accumulation rate of the charge difference. The slopes of the polarization/depolarization charge amount difference at 200 V, 1000 V and 4000 V are shown in Figure 16. It is indicated that the slopes at larger applied DC voltage are much higher and more distinguished than those at lower applied DC voltages, which indicates that the moisture condition can be confirmed by the slope of charge amount difference curve at high applied DC voltage in PDC test. Figure 13. Polarization/depolarization charge amount difference curve of normal bushing. Figure 14. Polarization/depolarization charge amount difference curve of dampened oil bushing. Figure 15. Polarization/depolarization charge amount difference curve of damped cellulose polymer paper bushing. The electrical conductivity change behavior of cellulose polymer insulation with different moisture conditions is shown in Figure 17. It is shown that the electrical conductivity increases with time and tends to be stable after 1000 s. The stable value of electrical conductivity is the real electrical conductivity $ \sigma $. The geometric capacitance of the insulation in the bushing is 228 pF, thus the real electrical conductivity of normal, bushings with dampened oil and dampened cellulose polymer insulation are $ 7.9748 \times 10^{-13} $ S/m, $ 9.7884 \times 10^{-13} $ S/m and $ 1.1672 \times 10^{-12} $ S/m, respectively. The results indicate that electrical conductivity increases when the moisture content in the insulation material is higher, leading to the deterioration of the insulation performance. ![Figure 16. Slopes of charge amount difference curve at different applied DC voltages.](image) For normal bushing, electrical conductivity is stabilized the fastest because the interface polarization current dissipates faster with time, resulting in the electrical conductivity current taking less time to stabilize. However, the polarization process can be influenced by the invasion of moisture when the insulation material is dampened, resulting in a longer time that the interface polarization current dissipates and the higher value of the interface polarization current. Additionally, moisture content can also lead to a longer time that the conductance current takes to be stable and can decrease the initial value of polarization and depolarization charge amount difference. The polarization current increases significantly while the depolarization current is less affected under the influence of moisture content, leading to the increase in slope of polarization/depolarization charge amount difference. Because the electrical conductivity is linear with the slope of the polarization/depolarization charge amount difference curve, the electrical conductivity of the bushing with dampened oil and dampened cellulose polymer in the stable state is larger than that of normal bushing. These reasons explain that normal bushing has a larger electrical conductivity than that of bushing with dampened oil and cellulose polymer insulation, and that the electrical conductivity of normal bushing takes less time to stabilize. 3.4. Molecular Dynamics Analysis Based on Band Structure and Electrostatic Potential The band structure of unmoistened cellulose and moistened cellulose is shown in Figure 18. It can be seen that the band width ($\Delta E$) of unmoistened cellulose is 5.657 eV, while the band gap width of moistened cellulose is 5.546 eV. The wider the band width, the weaker the electrical conductivity. The energy band width of cellulose is narrowed after the water content of cellulose is increased, so the moistened cellulose polymer insulation electrical conductivity is stronger. ![Figure 18: The band structure of two cellulose polymer insulation models](image) The electrostatic potential of unmoistened cellulose and moistened cellulose is shown in Figure 19. The red is the positive electrostatic potential, and the blue is the negative electrostatic potential. It can be seen that with the increase of water content in cellulose, water molecules would increase the positive electrostatic potential in the model, so the polarity of the model increases. Due to the existence of a large number of hydroxyl groups in cellulose, these hydroxyl groups can easily form hydrogen bonds with each other. It is precisely because of the existence of hydrogen bonds that cellulose has strong intermolecular and intramolecular interaction forces, and the ability of cellulose to resist external damage is also closely related to the concentration of hydrogen bonds. The molecular simulation results show that the presence of water destroys the intramolecular and intermolecular hydrogen bonds in the cellulose chain, and forms a new hydrogen bond interaction with the oxygen atom on the cellulose hydroxyl group. Water mainly acts on the hydroxyl and glycoside bonds of cellulose and destroys their stability. Therefore, the motion of charge carriers in the insulating paper cellulose is more intense under the action of the electric field. This is consistent with the conclusion in [25] that charge carriers have a significant accelerating effect on the hydrolysis of cellulose. The polarization/depolarization current of bushings increases when the applied voltage becomes higher. High applied voltage can decrease the influence of noise. Moisture can aggravate the polarization/depolarization process, leading to higher polarization/depolarization current. 2. When applied voltage is higher, the speed of charge carriers increases, leading to the increase of interface polarization current. Water molecules are ionized under the effect of electric field, producing more charge carriers, thus increasing the interface polarization current as well. With the increase of interface current, the relaxation behavior will be further intensified. 3. The charge amount difference of polarization and depolarization current is linearly aligned with the time, and the slope becomes larger with the increase in moisture, which is more obvious under high applied voltage. Water molecules produce more charge carriers after being ionized and provide more paths for charge movement. 4. With the invasion of moisture, the band width of cellulose polymer insulation becomes narrower, and its electrostatic potential increases, which improves the electrical conductivity of cellulose polymer insulation, and the polarization characteristics under DC electric field are more significant. In conclusion, with the invasion of moisture, the electrical conductivity and polarity of cellulose polymer insulation will increase. Under the excitation of DC electric field, the polarization/depolarization process is more intense, which is specifically reflected in the experiment by the polarization/depolarization current being greater. In addition, the electrostatic potential of cellulose polymer is stronger after moisture invasion, indicating that its electrical conductivity characteristics are better under the action of electric field, that is, the electrical conductivity is greater, which verifies the calculated electrical conductivity of cellulose polymer insulation in different oil-immersed bushings above. 4. Conclusions This paper studies the time domain relaxation behavior of charge carriers for cellulose polymer insulation used in oil-immersed bushing, and the characteristics of dielectric response and motion of charge carriers have been analyzed. The conclusions drawn are as follows: 1. The polarization/depolarization current of bushings increases when the applied voltage becomes higher. High applied voltage can decrease the influence of noise. Moisture can aggravate the polarization/depolarization process, leading to higher polarization/depolarization current. Figure 19. Electrostatic potential of two cellulose models: (a) Cellulose model; (b) Cellulose model with 3.5% water. Author Contributions: Formal analysis, Y.S. and Z.J.; Investigation, Q.L. and S.S.; Methodology, C.M. and J.H.; Software, S.W. and F.W.; Writing—original draft, all authors; Writing—review and editing, all authors. All authors have read and agreed to the published version of the manuscript. Funding: This work is supported by State Grid Shaanxi Electric Power Co., Shaanxi Electric Power Research Institute (SGSNKYOOSP)S2000308, Time/Frequency Domain Dielectric Response Combined Diagnosis and Analysis Technology and Application Research on High Voltage Bushing Defects and Health Margin—Research on Combined Diagnosis Method of Dielectric Response of Bushing). Conflicts of Interest: All the authors declare no conflict of interest. References 1. Mikulecky, A.; Stih, Z. Influence of Temperature, Moisture Content and Ageing on Oil Impregnated Paper Bushings Insulation. IEEE Trans. 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5aa7dedcf7c5e3cfb5cb8fae65bcfac4414bf2e2	{ "olmocr-version": "0.1.59", "pdf-total-pages": 9, "total-fallback-pages": 0, "total-input-tokens": 30167, "total-output-tokens": 11272, "fieldofstudy": [ "Biology" ] }	Specific expression of proton-coupled oligopeptide transporter 1 in primary hepatocarcinoma-a novel strategy for tumor-targeted therapy YANXIA GONG1,2, JIE ZHANG1, XIANG WU3, TAO WANG1, JIA ZHAO4, ZHI YAO5, QINGYU ZHANG1, XI LIU1 and XU JIAN3 1Department of Gastroenterology, Tianjin Medical University General Hospital, Tianjin 300052; 2Department of Gastroenterology, Tianjin Nankai Hospital, Tianjin 300100; 3Central Laboratory and 4Clinical Laboratory, Tianjin Medical University General Hospital, Tianjin 300052; 5Department of Immunology, School of Basic Medical Science, Tianjin Medical University, Tianjin 300070, P.R. China Received December 11, 2015; Accepted May 16, 2017 DOI: 10.3892/ol.2017.6724 Abstract. Proton-coupled oligopeptide transporter 1 (PEPT1) is a membrane protein which expressed predominantly in intestine and recognized as the target of dietary nutrients (di/tripeptide) or peptidomimetic drug for delivery. The information on the existence of PEPT1 in carcinomas were limited. Our study aimed to investigate the expression profile and transport activity of PEPT1 both in human hepatocarcinoma tissues and cell lines. Western blotting and an immunofluorescence assay revealed the high level of PEPT1 protein expression in hepatocarcinoma Bel-7402, SMMC-7721, HepG2, HEP3B, SK-HEP-1 cell lines. Quantitative real time PCR showed the mRNA expression of PEPT1 in Bel-7402, SMMC-7721, HepG2, HEP3B, SK-HEP-1 cells. High level PEPT1 expression in hepatocarcinoma patient samples were observed by Immunohistology and showed a significant correlation between protein level and pathological grade. Functional activities were also studied using D-Ala-Lys-AMCA (a substrate of peptide transporter) in above five hepatocarcinoma cell lines. The uptake tests performed by fluorescent microscopy suggested that PEPT1 can transport both D-Ala-Lys-AMCA into the hepatocarcinoma cells and the uptake can be competitively inhibited by three PEPT1 substrates (Gly-sar, Gly-gln and Glyglygly). In conclusion, our findings provided the novel information on the expression and function of PEPT1 in human hepatocarcinoma and expanded the potential values for tumor specific drug delivery. Introduction Primary hepatocarcinoma, which arises from liver cells or intrahepatic bile duct epithelial cells, is one of the most fatal types of malignant tumors worldwide (1), causing 250,000 to 1,000,000 mortalities per year, and has become the fifth and seventh most common malignant tumor in males and females, respectively (2). The majority of hepatocarcinoma cases occur in a number of developing countries (3). China has the highest morbidity and mortality associated with hepatocarcinoma; the number of patients with hepatocarcinoma in China accounts for 54% of the cases worldwide (4). The preferred treatment for hepatocarcinoma is liver resection, but this is restricted to early stages of hepatocarcinoma (5). Due to the difficulty of early detection, the rapid progression of the disease and the fact that the majority of patients exhibit liver cirrhosis, only a limited number of patients are able to undergo surgery, resulting in the majority of patients exhibiting a poor prognosis (6). Therefore, the identification of a specific tumor marker, for early diagnosis and targeted therapy, is required. Proton-coupled oligopeptide transporter 1 (PEPT1) is one of the four members of the peptide transporter superfamily in mammalian cells (7). PEPT1 is expressed predominantly in the intestine and mediates the absorption of dietary nutrients (di/tripeptide) or peptidomimetic drugs (8). As PEPT1 is able to transport a broad spectrum of substrates, it is an attractive target for drug delivery (9). Previous studies on the presence and function of PEPT1 in carcinomas was limited in a number of carcinoma cell lines, including colon carcinoma Caco-2 cells (10), pancreatic carcinoma cell lines AsPC-1 and Capan-29 (11), gastric cancer (12), prostate cancer (13,14) and fibroblast-derived tumor cells (15), which indicates that PEPT1 may be expressed in other types of cancer cells. The overexpression of PEPT1 in cancer cells may enable the identification of a specific pathway for therapeutic agents to exploit. Therefore, clarifying the expression patterns of PEPT1 in other types of cancer cell may expand the value of peptide transporters in cancer therapy. Correspondence to: Dr Xu Jian, Central Laboratory, Tianjin Medical University General Hospital, 154 Anshan Road, Heping, Tianjin 300052, P.R. China E-mail: [email protected] Key words: proton-coupled oligopeptide transporter 1, primary hepatocarcinoma, expression, tumor-targeted therapy In the present study, the expression profile and function of PEPT1 in hepatocarcinoma were investigated in hepatocarcinoma cells and tissues. The results of the present study may provide novel information on the expression and function of PEPT1 in human hepatocarcinoma, and expand the values for hepatocarcinoma early diagnosis and tumor specific drug delivery. Materials and methods Materials. D-Ala-Lys-AMCA (2.5 mg/ml) was purchased from BIOTREND Chemikalien GmbH (Köln, Germany), and glycine (Gly)-sarcosine (Sar), Gly-glutamine (Gln) and Gly-Gly-Gly were obtained from Sigma-Aldrich (Merck KGaA, Darmstadt, Germany). The PCR primers used in the present study were synthesized by Integrated DNA Technologies, Inc. (Coralville, IA, USA). A rabbit polyclonal antibody against PEPT1 (anti-PEPT1 antibody; catalog no. 78020; dilution, 1:50) was provided by Abcam (Cambridge, UK). Additionally, the human liver cancer Bel-7402, SMMC7721, Hep3B, HepG2, and SK-HEP-1 cell lines, the human gastric cancer BGC-823 cell line and the human colon cancer Caco-2 cell line were obtained from the Academia Sinica Cell Repository (Shanghai, China). Cell culture. Bel-7402 cells were grown in RPMI-1640 medium (Gibco; Thermo Fisher Scientific, Inc., Waltham, MA, USA) containing 10% fetal bovine serum (FBS; Gibco; Thermo Fisher Scientific, Inc.), whereas SK-HEP-1 cells were cultured in Dulbecco's modified Eagle medium (DMEM; Gibco; Thermo Fisher Scientific, Inc.) supplemented with 10% FBS (Gibco; Thermo Fisher Scientific, Inc.), 1% 100 µg/ml penicillin and 100 µg/l streptomycin. Concurrently, SMMC7721, Hep3B, HepG2 and Caco-2 cell lines were maintained in DMEM (Gibco; Thermo Fisher Scientific, Inc.) supplemented with 10% FBS (Gibco; Thermo Fisher Scientific, Inc.), 1% 100 µg/ml penicillin (Sigma-Aldrich; Merck KGaA) and 100 µg/ml streptomycin (Sigma-Aldrich; Merck KGaA). All of the cells were maintained at 37˚C in 5% CO2. The culture media were changed every other day, and cells were passaged once they reached 80-90% confluence, at which point the cells were collected for protein or RNA extraction. Immunofluorescence of cell lines. Subsequent to attachment onto a plate, 1x10^5 cells/ml (Bel-7402, SK-HEP-1, SMMC7721, Hep3B, HepG2 and Caco-2) were washed with medium, fixed with 4% paraformaldehyde for 5 min at room temperature, washed three times with PBS, treated with bovine serum albumin, (Wuhan Boster Biological Technology, Ltd., Wuhan, China) for 1 h, and subsequently incubated with the rabbit anti-humananti-PEPT1 primary antibody (1:50 dilution) overnight at 4˚C. Following three washes with PBS, the cells were incubated with a fluorescent goat anti-rabbit IgG secondary antibody (dilution, 1:100; catalog no. ZF036; Beijing ZSGB-BIO Co. Ltd., China) for 1 h at 37°C, washed with PBS, stained with DAPI (5 µg/ml) for 5 min at room temperature, fixed, mounted, and observed using a fluorescent microscope (magnification, x20) to determine blue (nucleus) and red (PEPT1) fluorescence. Each experiment was repeated three times and Caco-2 cell lines was used as the positive control. Western blotting. All the cell types (Bel-7402, SK-HEP-1, SMMC7721, BGC-823, Hep3B, HepG2 and Caco-2) were seeded (1x10^7 cells/ml) in 100-mm cell culture dishes. Total protein was then extracted from the cells using 1% Nonidet P-40 lysis buffer (Sigma-Aldrich; Merck KGaA). The protein concentration was measured using the Lowry method. The protein lysates (30 µg protein/lane) were subsequently separated using 10% SDS-PAGE and transferred to polyvinylidene fluoride membranes (PVDF; EMD Millipore, Billerica, MA, USA). The blocking reagent used was 5% bichinonic acid, and the PVDF membranes were blocked at 37°C for 1 h. These membranes were incubated with the primary antibody, as aforementioned (dilution, 1:100), followed by incubation with a horseradish peroxidase-conjugated secondary antibody (dilution, 1:100; catalog no. ZB-2301; Beijing ZSGB-BIO Co. Ltd) at room temperature. Protein expression was visualized using a Super Signal Protein Detection kit (Pierce; Thermo Fisher Scientific, Inc.). The membranes were then stripped and re-probed with anti-PEPT1 (dilution, 1:1,000), and an anti-β-actin primary antibody (dilution, 1:1,000; catalog no. sc-47778; Santa Cruz Biotechnology, Inc.) served as a loading control. Each experiment was repeated three times. Reverse transcription-quantitative-polymerase chain reaction (RT-qPCR) analysis. Total RNA was extracted from all of the cell types (Bel-7402, SK-HEP-1, SMMC7721, BGC-823, Hep3B, HepG2 and Caco-2) using the TRIzol reagent (Invitrogen; Thermo Fisher Scientific, Inc.) and then used for cDNA synthesis by RT with M-MLV Reverse Transcriptase (Promega Corporation, Madison, WI, USA) in a total volume of 10 µl according to the manufacturer's protocol. The reverse transcription-PCR products were separated by electrophoresis on a 2% agarose gel. The gel was then stained with ethidium bromide, digitally photographed, and scanned with a UV 1 gel analysis system (UVItec, Cambridge, UK). Using a 7500 ABI RT-PCR machine (Applied Biosystems; Thermo Fisher Scientific, Inc.), expression levels were quantitatively analyzed. The TaqMan assay kit (Applied Biosystems; Thermo Fisher Scientific, Inc.) was used to detect gene expression. Quantification was also performed using amplification efficiencies derived from cDNA standard curves to obtain the relative gene expression. The data are presented as fold changes (2^(-ΔΔCq)) (16) and were initially analyzed using the Opticon Monitor V2.02 analysis software (MJ Research; Bio-Rad Laboratories, Inc., Hercules, CA, USA). Specific RT-qPCR primers were obtained from Fulen Gene BioEngineering Inc. (Guangdong, China). The primers for PEPT1 were 5'-GCTCGGTCTTATACATCTC-3' (forward) and 5'-TCTCCATCTCCTAGTGGCT-3' (reverse) (10). The primers for GAPDH as the reference gene were: 5'-AGGTCC GTGTCAGTCTTCCG-3' (forward) and 5'-GGGGTGTCT GTGGCAACAA-3' (reverse). Each was performed in triplicate. The thermocycling conditions were as follows: 95°C for 3 min; 45 cycles of 95°C for 15 sec, 58°C for 30 sec and 72°C for 30 sec; and 72°C for 2 min. Verification of D-Ala-Lys-AMCA. D-Ala-Lys-AMCA is a known PEPT1 substrate that emits blue fluorescence. All cell types were cultured in 24-well plates for 1 day, and the culture medium was then aspirated. Following one wash with PBS, D-Ala-Lys-AMCA (1 mM in PBS) was added for 2 h at 37°C. D-Ala-Lys-AMCA fluorescence was then observed through a fluorescence microscope (magnification, x20). The uptake of D-Ala-Lys-AMCA was detected under different conditions. First, the uptake of D-Ala-Lys-AMCA at different times (0, 15, 30, 60, 120 and 180 min) but at the same pH value (6.0) and concentration (25 µmol/l) was detected. Second, D-Ala-Lys-AMCA uptake at different pH levels (5.4, 6, 7.4 and 8.4) but at the same time (2 h) and concentrations (25 µmol/l) was detected. Third, the effects of different initial concentrations of D-Ala-Lys-AMCA (25, 50 and 150 µmol/l) were analyzed, and these tests were performed at a pH of 6.0 for 2 h. Inhibition tests were conducted by pre-incubating the cells with competitive compounds (Gly-Sar, Gly-Gln, Gly-Gly-Gly) for 30 min and then with D-Ala-Lys-AMCA (25 µmol/l) for 1 h at 37°C prior to the detection of fluorescence. Subsequent to removing the buffer and rapidly washing 3 times with ice-cold PBS, the cellular uptake of D-Ala-Lys-AMCA was examined with a BioTek Synergy 2 Multi-Mode reader (BioTek Instruments, Inc., Winooski, VT, USA) with excitation at 350 nm, and emission at 460 nm. All analyses were performed in triplicate. Immunohistochemistry and immunofluorescence staining. A total of 82 human hepatocarcinoma tissue chips were purchased from Xi'an Alenabio Technology Co., Ltd. (Xi'an, China), which included 50 cases of hepatocarcinoma tissues (pathological grade 1, 4 cases; grade 2, 20 cases; and grade 3, 26 cases), 13 cases of adjacent cancer tissues and 19 cases of normal liver tissues. Pathological grades 1, 2 and 3 were equivalent to well-, moderately- and poorly-differentiated, respectively (17). The expression of PEPT1 in these tissues was detected by immunohistochemistry. For immunohistochemical staining, formalin-fixed tissue samples were prepared as paraffin-embedded sections (thickness, 3 µm), and immunostaining of the sections was performed using the avidin-biotin-complex method: Primary antibody directed against PEPT1 (1:100 dilution) was diluted in PBS with 0.1% Tween and incubated with the sections overnight at 4°C. The sections were then incubated with biotinylated secondary antibodies (dilution, 1:100; catalog no. ZB-2010; Beijing ZSGB-BIO Co. Ltd.) for 1 h at 37°C, followed by the avidin-biotin complex for an additional 1 h at 37°C. Protein expression was detected via coloration with 3,3'-diaminobenzidine in buffer, and the sections were counterstained with hematoxylin (2 mg/ml) at room temperature for 5 min. Using a microcamera computational image analysis system (CellSens standard; version 1.6; Olympus Corporation, Tokyo, Japan), a nucleus or cytoplasm containing brown-colored particles was considered positive. A total of five high-power fields were randomly selected for each group, and a total of 250 cells were counted. Sections with no labeling, or with <5% labeled cells, were scored as 0. Sections with 5-30% positive cells were scored as 1, 31-70% positive cells as 2, and ≥71% positive cells as 3. Staining intensity was scored similarly, with 0 for negative staining, 1 for weakly positive, 2 for moderately positive, and 3 for strongly positive. Scores for the percentage of positive tumor cells and staining intensity were used to generate an immunoreactive score for each specimen. The quantity and intensity scores were calculated such that a final score of 0-1 indicated negative expression (-), 2-3 indicated weak expression (+), 4-5 indicated moderate expression (++), and 6 indicated strong expression (+++) (11). Statistical analysis. Significance of Kaplan-Meier statistics was tested by calculating the log-rank. Data are expressed as the mean ± standard deviation. SPSS software (version 16.0; SPSS, Inc., Chicago, IL, USA) was used for all calculations. P<0.05 was considered to indicate a statistically significant difference. Results Immunofluorescence. Cell nuclei were labeled with blue fluorescence and red fluorescence indicated the presence of PEPT1 using the image system CellSens standard (version 1.6; Olympus Corporation). All types of liver cancer cells emitted red fluorescence, as determined using microscopy (Fig. 1). Western blotting. The results demonstrated that PEPT1 was expressed in the five liver cancer cell types studied (Bel-7402, SMMC7721, Hep3B, HepG2 and SK-HEP-1) to different degrees with SK-HEP-1 cells expressing the highest levels of PEPT1 (Fig. 1). RT-qPCR. The results revealed that increased PEPT1 mRNA expression was present in the majority of liver cancer cells compared with Caco2 cell lines. Furthermore, a markedly increased expression of the PEPT1 protein was observed in HepG2 cells compared with the other cell types, as determined by RT-qPCR (Fig. 1). Verification of D-Ala-Lys-AMCA Fluorescence of D-Ala-Lys-AMCA. D-Ala-Lys-AMCA is a well-known PEPT1 substrate that emits blue fluorescence. The results of the present study validated that D-Ala-Lys-AMCA may be transported into liver cancer and Caco-2 cells, on the basis of the emission of blue fluorescence (Fig. 2). Uptake of D-Ala-Lys-AMCA. The uptake of Ala-Lys-AMCA was time-dependent and also concentration-dependent, but not pH-dependent. The maximum uptake occurred at a pH value of 7.4. Additionally, uptake was significantly decreased by the presence of Gly-Sar, Gly-Gln or Gly-Gly-Gly inhibitors (Fig. 3). Immunohistochemistry. The results suggested that each group exhibited PEPT1 expression to different degrees (Fig. 4). Specifically, the expression of PEPT1 in hepatocarcinoma tissue was significantly higher compared with the expression observed in adjacent and normal liver tissue samples (P=0.0193 and P=0.0057, respectively, Table I). Significant differences in the expression of PEPT1 between three different pathological grades of liver cancer were observed, with tissues with a higher pathological grade demonstrating greater expression of PEPT1 (P=0.0093; Table II). Discussion Hepatocarcinoma is one of the most common malignant tumors worldwide (17). Each year, >700,000 incident patients are diagnosed, and ~250,000 people succumb to liver cancer (18). In China, the hepatocarcinoma incidence is expected to markedly increase over the prospective decades, due to the increasing incidence of viral hepatitis infection, which is one of the most important pathogenic factors for the development of hepatocarcinoma (19). The preferred treatment for hepatocarcinoma is liver resection, but this treatment is restricted to patients with the very early stages of hepatocarcinoma (5). Due to the difficulty associated with achieving early diagnosis, the rapid progression of the disease and the fact that the majority of patients exhibit liver cirrhosis, few patients are able to undergo the operation, resulting in the majority of patients having a poor prognosis. Thus, non-operative therapy is an important treatment strategy for advanced hepatocarcinoma (19). At present, chemotherapy drugs commonly used in the clinical treatment of primary hepatocarcinoma include 5-fluorouracil, mitomycin, doxorubicin and epirubicin, among others (20). However, as chemotherapy is not specific to tumor cells, it may also affect normal cells and result in serious adverse effects. Transcatheter arterial chemoembolization and other local treatments may transport drugs directly to lesions, but the effects of the dissemination of satellite foci and portal vein tumor thrombi are limited, and these therapies rarely control metastases that are distant from the lesions (21). Sorafenib is one targeted agent that serves an essential role in the treatment of advanced hepatocarcinoma, but high concentrations are required (22). Other novel targeted agents remain in the trial stage and require additional investigation (23). Therefore, the currently available therapies offer limited benefits to patients. As a result, there is a need for the development of novel and improved therapeutic strategies. A targeted drug delivery system that may be used as an effective specific treatment may have good application prospects. In particular, targeted drug delivery is a system that uses a drug carrier that transports chemotherapy drugs to the specific location of a tumor, and may achieve directional and focal inhibition of the tumor cells, thus causing less injury to normal cells. This system has numerous advantages. For example, the drug may be specifically transported to the target area, reach the maximum drug concentration in the target area, and react directly at the lesion site. Thus, this may promote the highest treatment effects with minimal toxic effects on normal cells, resulting in increased overall efficacy, safety and patient compliance with chemotherapy (24). The identification of a safe and effective targeted drug carrier is a focus of ongoing study. Previous studies have suggested that peptide-targeted gold nanoparticles may serve as drug carriers for the treatment of brain cancer (25) and that biodegradable nanoparticles may deliver docetaxel to airway cancer cells in a targeted manner (26). In addition, a study of drug carriers for prostate cancer revealed that a peptide-drug conjugate exhibited markedly higher uptake by prostate cancer cells in comparison with the parent drug (27). Thus, the selection of an effective targeted carrier based on its specific oligopeptide transport activity is essential (28). If PEPT1 is specifically expressed in liver cancer cells and tissues, it may be a promising carrier for the delivery of chemotherapy drugs to a targeted region, with increased efficacy and decreased adverse effects on healthy tissues. Peptides and peptide analogs may enter the cells of the body via peptide transporters in the membrane. The most widely studied peptide transporters are PEPT1 and PEPT2, which are members of the POT family (29). In mammals, the POT family comprises the following 4 members, which are encoded by Solute carrier family 15 (SLC15) genes: PEPT1 (SLC15A1), PEPT2 (SLC15A2), peptide/histidine transporter 1 (PHT1; SLC15A4), and PHT2 (SLC15A3) (30). The functional expression of PEPT1 and PEPT2 has been identified. These peptide transporters are primarily expressed in the digestive tract and kidney, respectively (31,32). The former demonstrates low affinity and high capacity, such that it may absorb a wide range of di/tripeptides (33,34). PEPT1, which is phylogenetically conserved, serves as an integral membrane protein in the cellular uptake of di/tripeptides and certain pharmacologically active drugs (35), and mediates the uptake of peptides and peptide-like molecules using the inwardly directed H⁺ gradient across the membrane (36). PEPT1 is specifically a type of active transport protein with low affinity and high transport capacity that is almost exclusively expressed in humans, and several other mammalian species, including rats and mice (37,38). This protein was first identified in the small intestine of a rabbit during cloning (39,40). The PEPT1 molecule recognizes a wide range of oligopeptides and other compounds with similar structures, and its range of drug substrates is extensive, including β-lactam antibiotic drugs, angiotensin-converting enzyme inhibitors, antitumor and antiviral agents, thrombin inhibitors, dopamine receptor antagonists, and renin inhibitors (41,42). The cellular uptake of these types of small peptides is an important physiological process mediated by proton-coupled peptide transporters (43). PEPT1 in particular may be involved in the transport of endogenous molecules and affects drug absorption, distribution, metabolism, and excretion, ultimately affecting the efficacy and toxicity of drugs. A loss of PEPT1 activity may therefore lead to a decrease in the intestinal absorption of di/tripeptides, peptidomimetics and peptide-like drugs (44). As PEPT1 is a proton-coupled carrier, it has a close association with the proton concentration. To summarize, oligopeptide transporters maybe regarded as putative therapeutic targets in cancer cells (45). \| Tissue type \| PEPT1 expression \| Positive rate, % \| \|----------------------\|------------------\|-----------------\| \| Hepatocarcinoma \| 50 - 7 6 12 25 \| 86.00 \| \| Adjacent cancer \| 13 6 4 2 1 \| 53.85* \| \| Normal liver \| 19 9 5 4 1 \| 52.63* \| SPSS version 16.0 was used for all calculations. P=0.0193 hepatocarcinoma vs. adjacent cancer tissue; *P=0.0057 hepatocarcinoma vs. normal liver tissue; -, negative expression; +, weak expression; ++, moderate expression; ++++, strong expression; PEPT1, proton-coupled oligopeptide transporter 1. The results of the present study demonstrated that PEPT1 has relatively limited expression in normal tissues, but is highly expressed in various types of tumor cells (46,47). PEPT1 was already known to exhibit high expression in the pancreatic cancer cell lines AsPC-1 and Capan-2, and low expression in adjacent tissues (47,48). Nakashishi et al (15) first revealed the expression of PEPT1 in the human fibro sarcoma HT1080 cell line. In addition, the expression of PEPT1 in the gastric cancer MKN45 cell line was previously suggested (49), and an additional study identified high expression of PEPT1 in prostate cancer cells (13). However, at present, little is known about the expression of PEPT1 in primary hepatocarcinoma or its significance for targeted drug delivery. Caco-2 is a human colon cancer cell line that was used as a positive control in the present study as it is generally considered to exhibit high expression of PEPT1 (50,51). In the immunofluorescence analysis, it was observed that the PEPT1 protein (red fluorescence) was localized to the plasma membrane of the liver cancer cells Bel-7402, SMMC7721, Hep3B, HepG2 and SK-HEP-1, similar to what was observed for Caco-2 cells. These results directly demonstrated the expression of PEPT1 in liver cancer. A previous study identified the expression of PEPT1 in gastric cancer cells (12). In the present study, the expression of PEPT1 in the gastric cancer cell line BGC-823 was examined, and the results were consistent with a previous study (12). In the case of BGC-823 and Caco-2 cells, which were used as a positive control, universal expression of PEPT1 was observed, similar to data previously demonstrated for PEPT1 in other cancer cells (11-15). Although PEPT1 demonstrated different functional activities in the liver cell lines, the expression of PEPT1 in SK-HEP-1 cells was highest, as determined by western blotting. In contrast, the highest expression detected by RT-qPCR was observed in HepG2 cells. The potential for experimental error was eliminated by repeating experiments three times. The reasons underlying this discrepancy may be associated with differences in cellular status, the presence of protein isoforms and the regulation of protein transcription or translation. To study the functional activity of PEPT1 in liver cancer cells and to determine the role of PEPT1 in the uptake of PEPT1 substrates, the specific fluorescence substrate Ala-Lys-AMCA, a well-known PEPT1 substrate, was studied in the absence and presence of PEPT1 (30). The fluorescence analysis of D-Ala-Lys-AMCA confirmed that D-Ala-Lys-AMCA may be transported into liver cancer cells and Caco-2 cells, which indirectly demonstrated the expression of PEPT1 in hepatocarcinoma cells. A previous study investigated the function of PEPT1 in the mouse intestine through electrophysiological methods (52). In the present study, the absorption of substrates at different times, pH values and concentrations were determined. It was also identified that the uptake of Ala-Lys-AMCA was time- and concentration-dependent. All of these data confirm that the transport of PEPT1 may be affected by time, pH and substrate inhibitors, as observed in previous studies (53,54). Gly-Sar is a small peptide that also serves as a substrate for PEPT1, which specifically recognizes and transports it (47). A study conducted by Berthelsen et al (55) demonstrated that basolateral Gly-Sar transport in the intestinal cell line Caco-2 is specifically proton-coupled via PEPT1. The dipeptide Gly-Gln is also known as a high-affinity substrate for PEPT1, which transports it into the cell in an inward direction (13). In the present study, Gly-Sar, Gly-Gln and Gly-Gly-Gly were all used as competitive substrates in a competition inhibition test (56,57), which demonstrated that the uptake of D-Ala-Lys-AMCA was significantly decreased by all three inhibitors. Thus, this suggests that the liver cancer cells examined expressed functionally active PEPT1 in the plasma membrane, and that PEPT1 serves an important role in the transport of the substrate Ala-Lys-AMCA. A tissue microarray analysis was performed in the present study to provide a preliminary investigation of the expression of PEPT1 in normal liver tissues, liver cancer tissues with different pathological grades and tissues adjacent to liver cancer. The analysis demonstrated that the expression of PEPT1 in cancer tissues was higher compared with that in normal tissues (P<0.05), whereas a low expression of PEPT1 was observed in adjacent tissues. In addition, the expression levels were associated with the pathological grade of the liver cancer tissues. In summary, it was demonstrated that PEPT1 is expressed in liver cancer tissues, and that PEPT1 overexpression is associated with more aggressive tumor malignancy and a poor prognosis. Therefore, PEPT1 may serve as an indicator of the nature of liver cancer (benign or malignant) and the differentiation degree of liver cancer cells, making it an attractive target for cancer therapy. In the present study, initial exploration of the specific overexpression of PEPT1 in primary hepatocarcinoma cells and liver cancer tissues was performed using various approaches, and different conditions. The correlation between tumor tissues and PEPT1 indicates that PEPT1 represents a promising molecular target for targeted drug delivery. The selection of a drug carrier must meet the following criteria: First, the carrier should be able to transport the drug into the body and to avoid attack by the immune systems of the body. Secondly, the carrier should deliver the drug specifically to a particular location and cell type, and should guarantee drug release (58). Furthermore, the targeted drug should exhibit the highest bioavailability possible, and reach its appropriate site of action through efficient transport by drug carriers (59). Current tumor therapy primarily relies on highly toxic chemical drugs, which lead to numerous serious side effects. For example, paclitaxel and doxorubicin may induce neurotoxicity, cardiac toxicity and bone marrow suppression during treatment of a tumor. An effective approach to reduce the side effects of chemotherapy would be the selective delivery of antitumor drugs to tumor tissues (60). As its substrate-binding site may accommodate a wide range of molecules of different sizes, hydrophobicities and charges, PEPT1 is regarded as an excellent target for the delivery of pharmacologically-active compounds (61). Due to its high expression in hepatocarcinoma, PEPT1 may serve as a good transporter-mediated drug delivery target, to improve the treatment of primary hepatocarcinoma. Generally, the design of a drug carrier that may specifically deliver drugs to a tumor site is of importance. 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04bb042e46449605a3ad025d2644a362e825c6ed	{ "olmocr-version": "0.1.59", "pdf-total-pages": 4, "total-fallback-pages": 0, "total-input-tokens": 10572, "total-output-tokens": 3155, "fieldofstudy": [ "Business", "Computer Science" ] }	Welcome to this special issue of the EURASIP Journal on Wireless Communications and Networking (JWCN). This special issue is devoted to the topic of the latest research and development on Orthogonal Frequency-Division Multiple Access (OFDMA) from physical and network layers to practical applications. OFDMA technologies are currently attracting intensive attention in wireless communications to meet the ever-increasing demands arising from the explosive growth of Internet, multimedia, and broadband services. OFDMA-based systems are able to deliver high data rate, operate in the hostile multipath radio environment, and allow efficient sharing of limited resources such as spectrum and transmit power between multiple users. OFDMA has been used in the mobility mode of IEEE 802.16 WiMAX, is currently a working specification in 3GPP Long Term Evolution downlink, and is the candidate access method for the IEEE 802.22 “Wireless Regional Area Networks.” Clearly recent advances in wireless communication technology have led to significant innovations that enable OFDMA-based wireless access networks to provide better Quality-of-Service (QoS) than ever with convenient and inexpensive deployment and mobility. However, regardless of the technology used, OFDMA networks must not only be able to provide reliable and high-quality broadband services but also be implemented cost-effectively and be operated efficiently. OFDMA presents many of the advantages and challenges of OFDM systems for single users, and the extension to multiple users introduces many further challenges and opportunities, both on the physical layer and at higher layers. These requirements present many challenges in the design of network architectures and protocols, which have motivated a significant amount of research in the area. Also, many critical problems associated with the applications of OFDMA technologies in future wireless systems are still looking for efficient solutions. The aim of this special issue is to present a collection of high-quality research papers that report the latest research advances in OFDMA communications, networks, systems, and its application in future wireless systems. In this special issue, we selected 17 papers from 36 submissions. The selected papers may be classified into four categories: Channel Estimation, Coding and Modulation, QoS and resource allocation, and Systems and Implementation. In the first part, 4 papers were included. In the second part, there are 3 papers on the coding and modulation. There are 7 papers about QoS and resource allocation management, and 3 papers were selected for systems and implementation issues. A detailed overview of the selected works is given below. Channel Estimation. This part describes the recent advances on channel estimation in OFDMA systems. The first paper, “A fast LMMSE channel estimation method for OFDM systems,” reports a fast linear minimum mean square error (LMMSE) channel estimation method for OFDM systems. In comparison with conventional LMMSE channel estimation, the proposed channel estimation method does not require statistical knowledge of the channel in advance and avoids the inverse operation of a large dimension matrix by using the FFT operation. Therefore, the computational complexity can be reduced significantly. Numerical results show that the NMSE of the proposed method is very close to that of the conventional LMMSE method. In addition, computer simulation shows that the performance of the proposed method is almost the same as that of the conventional LMMSE method in terms of bit error rate. The second paper, “Linearly time-varying channel estimation and symbol detection for OFDMA uplink using superimposed training,” addresses superimposed training-based linearly time-varying (LTV) channel estimation and symbol detection for OFDMA systems. The study estimates the LTV channel transfer functions over the whole frequency band by using a weighted average procedure, thereby providing validity for adaptive resource allocation. In addition, an iterative symbol detector is presented to mitigate the superimposed training effects on information sequence recovery. The third paper, “DFT-based channel estimation with symmetric extension for OFDMA systems,” presents a partial frequency response channel estimator for OFDMA systems. The partial frequency response is obtained by using the least square (LS) method. A symmetric extension method is proposed to reduce the leakage power. After IDFT of the symmetric extended signal, the leakage power of channel impulse response is self-cancelled. Simulation results show that the accuracy of the estimator has increased significantly compared with the conventional DFT-based channel estimator. The fourth paper, “Near optimum detection with low complexity for uplink virtual MIMO systems,” proposes two efficient MIMO decoding schemes that achieve near-optimum performance with low complexity for uplink virtual MIMO systems. The system has an iterative channel decoder using bit log-likelihood ratio information. The simulation results show that the proposed schemes achieve almost the same block error rate performance as that of the optimal MLD with only minor increased computational complexity. Coding and Modulation. The first paper, “Separate turbo code and single turbo code adaptive OFDM transmissions,” studies adaptive modulation and adaptive rate turbo-coding in OFDM to increase throughput on the time and frequency selective channel. The adaptive turbo-code scheme is based on a subband adaptive method and compares two adaptive systems: a conventional approach where a separate turbo code is used for each subband and a single turbo code adaptive system which uses a single turbo code over all subbands. Simulation results show that the single turbo code adaptive system provides a significant performance improvement. The second paper, “Multiresolution with hierarchical modulations for long term evolution of UMTS,” investigates mobile TV services over UMTS Long Term Evolution (LTE). By using multiresolution with hierarchical modulations, this service is expected to be broadcasted to larger groups achieving significant reduction in power transmission or increasing the average throughput. The presence of interactivity will allow for a certain amount of link quality feedback for groups or individuals. This study performs a system level simulation of multicellular networks considering broadcast/multicast transmissions using the OFDM/OFDMA-based LTE technology with respect to the number of TV channels with given bit rate and total spectral efficiency and coverage. Multiresolution with hierarchical modulations is able to achieve much higher throughput gain compared to single resolution systems of Multimedia Broadcast/Multicast Service (MBMS) standardized in Release 6. The third paper, “An opportunistic error correction layer for OFDM systems,” proposes a cross-layer approach to reduce the power consumption of ADCs in OFDM systems. The scheme is based on resolution-adaptive ADCs and Fountain codes. The key part of the proposed system is that the dynamic range of ADCs can be reduced by discarding subcarriers that are attenuated by the channel. Correspondingly, the power consumption in ADCs can be decreased. The receiver only decodes subcarriers (i.e., Fountain encoded packets) with the highest SNR. Others are discarded. With the approach, more than 70% of the energy consumption in the ADCs can be saved compared with the conventional IEEE 802.11a WLAN system under the same channel conditions. QoS and Resource Allocation. The third part focuses on resource allocation and QoS issues. The issues cover medium access control, cross-layer design, service differentiation, and admission control in IEEE 802.11 WirelessLAN and IEEE 802.16 WirelessMAN (or WiMAX). The first paper, “Service differentiation in OFDM-based IEEE 802.16 networks,” proposes several service differentiation approaches, which are based on the contention-based bandwidth request scheme and achieved by means of assigning different channel access parameters and/or bandwidth allocation priorities to different services. Additionally, the study proposes an effective analytical model to study the impacts of the service differentiation approaches, which can be used for the configuration and optimization of the service differentiation services. The service differentiation approaches and the analytical model are evaluated by simulation. It is observed that the analytical model has high accuracy. Service can be efficiently differentiated by initial backoff window in terms of throughput and channel access delay. And the service differentiation can be improved if combined with the bandwidth allocation priority approach without adverse impact on the overall system throughput. The second paper, “Multiuser radio resource allocation for multiservice in OFDMA-based cooperative relay networks,” studies multiservice transmission over OFDMA-based cooperative relay networks. The work proposes a framework to adaptively allocate power, subcarriers, and data rate to maximize system spectral efficiency under QoS constraints. The single user scenario is first investigated in a point-to-point cooperative relay network. Then multiservice transmission is investigated in a multiuser point-to-multipoint scenario. Several suboptimal resource allocation algorithms are proposed to reduce the computational complexity. Simulation results show that the proposed algorithms yield both high spectral efficiency and low outage probability. The third paper, “Throughput analysis of band AMC scheme in broadband wireless OFDMA system,” performs an analysis of the maximum system throughput for a band-AMC under various system parameters. In particular, the practical features of resource management for OFDMA system are modeled and evaluated within the current analytical framework. The results demonstrate that the band-AMC mode outperforms the diversity mode only by providing the channel qualities for a subset of good subbands, confirming the multiuser and multiband diversity gain that can be achieved by the band-AMC mode. The fourth paper, “Continuous frequency-time resource allocation and scheduling for wireless OFDMA systems with QoS support,” presents a joint scheduling and resource allocation scheme for the OFDMA system with continuous subcarrier permutation. The proposed algorithm provides continuous sets of frequency-time resource units following a rectangular shape, yielding a reduction of the required burst signalling. The joint scheme has two phases: the QoS requirements and the input buffers emptying status. For each phase, a specific prioritization function is defined in order to obtain a trade-off between the fairness and the spectral efficiency maximization. The fifth paper, “OFDMA-based medium access control for next-generation WLANs,” studies a new adaptive MAC design based on OFDMA technology. The design uses OFDMA to reduce collision during transmission request phases and makes channel access more predictable. To improve throughput, the study combines the OFDMA access with a Carrier Sense Multiple Access (CSMA) scheme. Data transmission opportunities are assigned through an access point that can schedule traffic streams in both time and frequency (subchannels) domains. The results demonstrate the effectiveness of the proposed MAC and compare it to existing mechanisms through simulation experiments and by deriving an analytical model for the operation of the MAC in saturation mode. The sixth paper, “Multiuser resource allocation maximizing the user perceived quality,” addresses multiuser resource allocation for time/frequency-slotted wireless communication systems. A framework for application driven cross-layer optimization (CLO) between the application (APP) layer and medium access control (MAC) layer is developed. The objective is to maximize the user perceived quality by joint optimization of the rate of the information bit-stream provided by the APP layer and the adaptive resource assignment on the MAC layer. Assuming adaptive transmission with long-term channel state information at the transmitter (CSIT), the optimization problem is analyzed mathematically, which is then used as the basis for a CLO algorithm. The proposed CLO framework supports user priorities such that premium users perceive a better service quality than ordinary users and have a higher chance to be served. The seventh paper, “Admission control threshold in cellular relay networks with power adjustment,” designs admission capacity planning in a cellular network using a cooperative relaying mechanism called decode-and-forward. The work mathematically formulates the dropping ratio using the randomness of “channel gain.” With this, the admission threshold planning problem is formulated as a simple optimization problem. The simplicity of the problem formulation facilitates its solution in real-time. The proposed planning method can provide an attractive guideline for dimensioning a cellular relay network with cooperative relays. Systems and Implementation. The first paper, “Advanced receiver design for quadrature OFDMA systems,” investigates various detection techniques such as linear zero forcing (ZF) equalization, minimum mean square error (MMSE) equalization, decision feedback equalization (DFE), and turbo joint channel estimation and detection, for Q-OFDMA systems to mitigate the noise enhancement effect and improve the bit error ratio (BER) performance. It is shown that advanced detection, for example, DFE and turbo receiver, can significantly improve the performance of QOFDMA. The second paper, “Residue number system arithmetic assisted coded frequency-hopped OFDMA,” presents a residue number system arithmetic-based frequency-hopped (FH) pattern design. The proposed FH scheme guarantees orthogonality among intracell users while randomizing the intercell interferences and providing frequency diversity gains. Simulation results demonstrate the gains due to frequency diversity and intercell interference diversity on the system bit error rate (BER) performance. Furthermore, the BER performance gain is consistent across all cells, which is superior to other FH pattern design schemes since they have larger performance variations across cells. The third paper, “Implementation of a smart antenna base station for mobile-WiMAX based on OFDMA,” presents the implementation of a smart antenna base station for OFDMA-based WiMAX. To implement the Base Station, the paper addresses a number of key issues in baseband signal processing related to symbol-timing acquisition, the beamforming scheme, and calibration. Experimental tests were performed to verify the validity of the solutions. Results showed a 3.5-time (5.5 dB) link-budget enhancement on the uplink compared to a single antenna system. In conclusion, this issue of EURASIP JWCN offers a ground-breaking view into the recent advances in OFDMA communications and networks. The popularity of submissions indicates that OFDMA is a worldwide focus that has universal appeal in terms of research, industry, and standardization. This issue offers both academic and industry appeal—the former as a basis toward future research directions and the latter toward viable commercial applications. OFDMA communications and networks in the longer-term will be characterized by their criticalness in consumer, business, and government applications in the areas of radio communications, LTE, LTE Advanced, WiMAX, and cognitive radio applications. Finally, we would like to express our gratitude to the Editor-in-Chief of EURASIP JWCN, Dr. Luc Vandendorpe for his advice, patience, and encouragement from the beginning until the final stage. We thank all anonymous reviewers who spent much of their precious time reviewing all the papers. Their timely reviews and comments greatly helped us select the best papers in this special issue. We also thank all authors who have submitted their papers for consideration for this issue. We hope you will enjoy reading the great selection of papers in this issue. Victor C. M. Leung Alister G. Burr Lingyang Song Yan Zhang Thomas Michael Bohnert	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3131, 1 ], [ 3131, 9421, 2 ], [ 9421, 15640, 3 ], [ 15640, 16280, 4 ] ] }
de0376a00d51af5cd8ca59d640e073e53db97f5b	{ "olmocr-version": "0.1.59", "pdf-total-pages": 9, "total-fallback-pages": 0, "total-input-tokens": 25098, "total-output-tokens": 7076, "fieldofstudy": [ "Agricultural And Food Sciences" ] }	Original Research Article Allelopathic potential of Lantana camara for weed control in cowpea (Vigna unguiculata L. Walp) Linda Chikeyi Muchimba a,, Tamara Tonga Kambikambi a,b, Kalaluka Munyinda c, Paul W. Kachapulula a a Department of Plant Science, School of Agricultural Sciences, University of Zambia, P.O Box 32379, Lusaka Zambia. b Cavendish University, P.O Box 34625, Lusaka, Zambia. ARTICLE INFORMATION Received: 4 September 2019 Revised: 10 November 2019 Accepted: 7 December 2019 Available online: 9 December 2019 DOI: [10.26655/JRWEEDSCI.2020.3.1](https://doi.org/10.26655/JRWEEDSCI.2020.3.1) KEYWORDS Allelopathy Genotypes Lantana camara Weed control Weed population density ABSTRACT Smallholder farmers have challenges of weed control and mostly they use cultural control methods because chemical control with herbicides is usually costly. However, Lantana camara L. is known to be allelopathic to other plants hence a worthy candidate for biological control of weeds under cowpea production. A field study was conducted to determine the potential for L. camara to control weeds in cowpea at the University of Zambia Agricultural Experimentation Station. Leaves were harvested from two genotypes of L. camara (G1: Pink-flowered and G2: Orange-flowered genotypes) dried and pulverized to form a powder and applied at different rates (R0C: 0 kg ha⁻¹, R1: 100 kg ha⁻¹, R2: 200 kg ha⁻¹, R3: 400 kg ha⁻¹) using the following types of application: T0C: No application, T1: broadcasting, T2: incorporation in the soil and T3: spraying of soaked ground L. camara. The research was conducted at the University Of Zambia School Of Agricultural Sciences Field Station. The experiment was arranged in a split split-plot design with three replications. Weed population density and weed weight were reduced the most (38% and 12.5%, respectively) at the highest rate (R3: 400 kg ha⁻¹) of L. camara application. The cowpea grain yield was higher (P < 0.05) in fields treated with G1 (mean = 876.90 kg ha⁻¹) than for G2 (mean = 672.10 kg ha⁻¹). G1 increased cowpea grain yield by 36.04%. Lantana camara holds great potential to increase food security by reducing losses associated with weeds in cowpea. Introduction In many agricultural systems around the world, competition between crops and weeds is one of the major factors reducing crop yield and farmers’ income (Ward et al. 2008). In cowpea production, weeds are a serious problem. When cowpea is left un-weeded, it can be completely smothered by weeds resulting in total yield loss. Weeds can cause greater yield reduction than all... the other pests and may lower quality of crop production (Ngalamu et al. 2014). Many strategies have been developed in order to control weeds including cultural, chemical, biological, mechanical and integrated weed control (Ngalamu et al. 2014). Although many smallholder farmers mostly use cultural control methods, such approaches are tedious and re-infestation of weeds is very rapid especially during the peak growing period. Chemical control with herbicides, though effective, is usually costly and sometimes unsafe to both human health and the environment (Mehdizadeh et al. 2019). Biological control of weeds has been achieved through the use of parasites, predators, or pathogens to maintain weed populations at a density lower than would occur without these natural enemies (Huffaker and Messenger, 2012; Van Driesche et al. 2008). Allelopathy has also been used to control weeds (Jabran et al. 2015). Many plants are known to have allelopathic effects, and some of these include Asters, Sorghum bicolor, Triticum aestivum and L. camara (Jabran, 2017). Despite being regarded as both a notorious weed and a popular ornamental garden plant, L. camara also has allelopathic properties that have been studied and exploited in weed management (Mishra, 2015). Lantana was found to inhibit the metabolism, germination and growth of susceptible plants (Mishra, 2015). Lantana camara therefore has potential for the control of weeds in a sustainable and environmentally friendly manner. The objective of the study was to determine the effect of L. camara on weed control in cowpea production. More specifically, the study sought to compare effect of genotype of L. camara on weed control in cowpea, to identify the rate of application of L. camara on weed control in cowpea and to identify the effective rate and type of application for the control of weeds in cowpea. Materials and Methods Study Site The research was conducted at the University of Zambia, School of Agricultural Sciences experimental station, falling between latitude 15°23’ 24” S and longitude 28° 19’ 48” E, with an elevation of 1,260 m above the sea level. The station experiences tropical weather and falls under agro-ecological region IIa of Zambia, characterized by total annual rainfall between 800–1000 mm and annual temperature between 16°C-26°C. Soil texture grades from sandy loam in the top soil to clay loam in the subsoil. Experimental Design and Treatments The leaves of genotypes of L. camara L. were room dried under ambient temperatures, milled using a mortar and pestle, sieved through a 0.1 mm sieve and the powder was weighed according to rates: Rate zero with cowpea (R0C): 0 kg ha⁻¹, Rate one (R1):100 kg ha⁻¹, Rate two (R2): 200 kg ha⁻¹ and Rate three (R3): 400 kg ha$^{-1}$, equivalent, respectively. The experiment was conducted in three replicates in a split-split plot design with two genotypes (G1 and G2), four rates of application (R0C, R1, R2 and R3) and four types of application (Type zero with cowpea (T0C), Type one (T1): broadcasting, Type two (T2) incorporation in the soil and, Type three (T3): spraying of soaked ground $L.\ camara$ powder) as main plot, sub plot and sub-sub plot factors respectively. The control was rate zero (R0C) with cowpea while the treatments (rate of application of $L.\ camara$) were applied in subplots as follows: i) 400 kg ha$^{-1}$ equivalent of dry powdered leaves of $L.\ camara$, ii) 200 kg ha$^{-1}$ equivalent of dry powdered leaves of $L.\ camara$, and iii) 100 kg ha$^{-1}$ equivalent of dry powdered leaves of $L.\ camara$. Land preparation comprised of hand hoeing, after which raking was done to smoothen the tilth and flatten the land in readiness for planting. Cowpea ($Vigna\ unguiculata$ L.) variety, Bubebe was planted on 26$^{th}$ February, 2018 at the rate of 25 kg ha$^{-1}$. Spacing was 60 cm inter-row (with 30 cm on each side) with 15 cm and 2 cm intra row and depth, respectively. One seed was planted on each station. 300 kg ha$^{-1}$ of basal dressing fertilizer (Compound – D with a percentage of Nitrogen (N) 10: Phosphorus (P) 20: and Potassium (K) 10) was applied at planting on the 26$^{th}$ February, 2018 as recommended. Supplementary irrigation was given when there was no rainfall in week five and week six after planting using overhead irrigation. Plant protection was done using insecticides which included: i) Phorate with active ingredient phorate applied at 2 g per plant. Phorate was broadcasted in the second week after planting (7$^{th}$ of March, 2018) at recommended rate to protect the plants against insect pests and birds after germination. It controls insects as well as birds that feed on cowpea seedlings, ii) Thunder with imidacloprid and beta-cyfluthrin as active ingredients applied at 400 ml ha$^{-1}$ and iii) Ninja plus 5EC an emulsifiable concentrate containing five percent of Lambda-cyhalothrin applied at 400 ml ha$^{-1}$. Cowpea pods where harvested at physiological maturity, signified by pods turning yellow during the final stage of growth, and becoming brown and brittle when they reached maturity at a moisture content of 12%. Cowpea yield was done by removing mature pods by hand and they were packed in harvesting bags from the field to the Botany laboratory where they were allowed to dry completely. Cowpea was then threshed and the cowpea grain yield was weighed in plastic papers per plot to determine the effect of $L.\ camara$ on weed control in cowpea. Data Collection and analysis Parameters measured were weed population density (WPD), weed weight (WW), crop stand (CS) and crop yield (CY). A 1 m$^{2}$ quadrant was used for sampling weeds around the research area as a baseline. A quadrant was thrown randomly in 15 different areas, three days before planting. The collected weeds per 1 m$^{2}$ quadrant were counted physically to obtain the weed population density and weighed using an electronic balance to determine weed weight. Identification of weeds was done in order to determine the types of weeds present per quadrant around the research area. Emergence count was done by counting the number of cowpea seedlings in each row per plot in the second week after planting. All the cowpea seeds which were planted germinated. Crop stand was also done in the second week after planting. Cowpea pods where harvested at physiological maturity, signified by pods turning yellow during the final stage of growth, and becoming brown and brittle when they reached maturity at a moisture content of 12%. Cowpea yield was done by removing mature pods by hand and they were packed in harvesting bags from the field to the Botany laboratory where they were allowed to dry completely. Cowpea was then threshed and the cowpea grain yield was weighed in plastic papers per plot to determine the effect of L. camara on weed control in cowpea. Data analysis was conducted with ANOVA and treatment means were separated using LSD calculated at P ≤ 0.05 using GenStat 14th Edition. Results and Discussion *Effect of genotype of L. camara* L. on cowpea grain yield** There were significant differences (P < 0.05) in cowpea grain yield between fields treated with the different genotypes of Lantana, rates of application and types of application (Table 1). All the interactions were also significant (Table 1). Table 1. Analysis of Variance (ANOVA) for cowpea grain yield. \| Source of variation \| df \| MS \| \|---------------------\|----\|-------------\| \| Replication \| 2 \| 539 \| \| Genotype (G) \| 1 \| 1007334.00\| \| Error \| 2 \| 1583.00 \| \| Rate (R) \| 3 \| 946548.00\| \| G x R \| 3 \| 151852.00\| \| Error \| 12 \| 802.00 \| \| Type (T) \| 3 \| 619394.00\| \| G x T \| 3 \| 107095.00\| \| Rate x Type \| 9 \| 41383.00* \| \| G x R x T \| 9 \| 25715.00* \| \| Error \| 48 \| 1282.00 \| \| Total** \| 95 \| \| P was calculated at P ≤ 0.05. G: Genotype, R: Rate of application, T: Type of application, ** means significant at P = 0.01, while *** means highly significant at P < 0.001. The cowpea grain yield was higher in plot treated with G1 (876.90 kg ha⁻¹) than in those treated with G2 (672.10 kg ha⁻¹). The difference in cowpea grain yield of genotype 1 over genotype 2 was 30.47% (Table 2). allelopathic potential of Lantana camara for weed control... 258 Table 2. Means of cowpea grain yield (kg ha$^{-1}$) responses on different genotypes, rates of application and types of application of Lantana camara L. \| Genotype \| Means (Kg ha$^{-1}$) \| Rate \| Means (Kg ha$^{-1}$) \| Type \| Means (Kg ha$^{-1}$) \| \|----------\|-------------------------\|------\|-------------------------\|------\|-------------------------\| \| G1 \| 876.90 \| R0C \| 533.90$^d$ \| T0C \| 579.60$^d$ \| \| G2 \| 672.10 \| R1 \| 724.30$^c$ \| T1 \| 823.70$^b$ \| \| \| \| R2 \| 831.60$^b$ \| T2 \| 732.40$^c$ \| \| \| \| R3 \| 1008.30$^a$ \| T3 \| 962.30$^a$ \| \| LSD \| 34.940 \| LSD \| 17.810 \| LSD \| 20.780 \| Means within the same column followed by the same letter are not significantly different from each other at Ps ≤ 0.05. Both genotypes of L. camara were associated with higher cowpea grain yield as compared to control plots. This effect on cowpea yield could be attributed to the allelopathic effect of L. camara on weeds in treated fields, consistent with trends observed by Qasem (2006) who found that allelopathic plants release chemicals into the surrounding soil which prevent germination and competition from other plant species (Ambika et al. 2003). Competition from weeds is one of the major factors reducing crop yield and farmers’ income (Ward et al. 2008) and as such, reducing this competition is expected to result in increased yields. The genotype of L. camara with pink flowers (G1) decreased (by 64%) weed population density more than G2 and was associated with higher cowpea grain yield than the latter. This superiority of G1 over G2 in weed control could be that G1 produced more of the allelopathic chemicals than G2. Future studies should seek to verify the concentrations of allelopathic chemicals produced by the two genotypes of L. camara. Effect of rate of application of L. camara on cowpea grain yield Rate of application of L. camara had a significant impact on cowpea grain yield (P < 0.05, Table 2). Grain yield increased with increase in quantity of Lantana applied with R3 (400 kg ha$^{-1}$ rate) having the highest cowpea grain yield (1008.30 kg ha$^{-1}$) and R0C having the least (533.90 kg ha$^{-1}$, Table 2). These findings were in agreement with those by Mishra, (2015), who reported that, the high concentration of L. camara caused marked inhibition of germination and growth of weeds and eventually led to increase in yield as compared to the lower rates. The current study shows that smallholder farmers would get the most weed reduction and thus cowpea yields by using L. camara with pink flowers (G1), at the highest rate (R3: 400 kg ha$^{-1}$), by spraying socked ground L. camara (T3) to control weeds in cowpea. Type of application is discussed in the section below. Effect of type of application of L. camara on cowpea grain yield The type of application had an effect on cowpea grain yield. The findings of the study showed variation in plots treated with type of application on cowpea grain yield ($P < 0.05$) (Table 2). Cowpea grain yield increased by 66\% at T3 (962.30 kg ha$^{-1}$) as it was compared to the control (579.60 kg ha$^{-1}$) and it was also significant from T1 (823.70 kg ha$^{-1}$). T3 was the most effective and it showed variation with T1. Soaked ground $L$. camara (T3) was more effective in that, it controlled more WPD which resulted to high yield. Similarly, other authors ascribed that yield losses caused by weeds alone in cowpea production can range from 25\% to 76\% (Adigun et al. 2014; Gupta et al. 2016; Osipitan et al. 2016; Ugbe et al. 2016). Contrary to the findings Marinov-Serafimov (2015), who suggested that weeds such as $L$. camara may also reduce crop yield by releasing allelopathic compounds into the environment. Soaked ground $L$. camara appeared to control more weeds maybe because grinding and soaking it made the allelopathic compound more readily available and diffusible to weeds than direct application. Variation of genotype, rate and type of application of $L$. camara on cowpea grain yield The highest cowpea grain yield was obtained from interaction of G1 at its highest rate (R3: 400 kg ha$^{-1}$) with socked ground $L$. camara (T3). In addition, the cowpea grain yield was significant different when G1, R3 and T1 was applied. In the case of G2, the highest yield was obtained from a combination of R3 and T1. Although it was higher, but it was still lower than what was obtained in G1 by 48.12\% (Table 3). Table 3. Effect of genotype, rate and type of application of $L$. camara on cowpea grain yield. \| Genotype \| Rate \| Type of application \| Cowpea grain yield (kg ha$^{-1}$) \| \|----------\|------\|---------------------\|----------------------------------\| \| \| \| TOC \| T1 \| T2 \| T3 \| \| G1 \| R0C \| 440.40$^{p}$ \| 583.60$^{lm}$ \| 550.30$^{mn}$ \| 668.80$^{ij}$ \| \| \| R1 \| 657.10$^{jk}$ \| 858.60$^{g}$ \| 760.10$^{h}$ \| 980.70$^{ef}$ \| \| \| R2 \| 496.40$^{nop}$ \| 1026.10$^{e}$ \| 952.30$^{f}$ \| 1165.90$^{d}$ \| \| \| R3 \| 735.80$^{h}$ \| 1350.08$^{b}$ \| 1249.60$^{c}$ \| 1554.70$^{a}$ \| \| G2 \| R0C \| 506.70$^{no}$ \| 483.10$^{nop}$ \| 454.10$^{op}$ \| 584.20$^{lm}$ \| \| \| R1 \| 467.10$^{op}$ \| 643.00$^{jk}$ \| 602.70$^{k}$ \| 824.90$^{s}$ \| \| \| R2 \| 616.00$^{jk}$ \| 871.30$^{g}$ \| 655.50$^{jk}$ \| 869.50$^{s}$ \| \| \| R3 \| 717.70$^{hi}$ \| 772.80$^{h}$ \| 635.00$^{jd}$ \| 1049.70$^{e}$ \| LSD = 56.910 $P$ was calculated at $P \leq 0.05$. The findings of the current study differ from what was noticed by Gantayet et al. (2014), where all the concentrations of leaf-litter dust of $L$. camara considerably reduced the yield efficiency of the test crops compared with their respective control plants. It could be that allelopathic chemicals released by L. camara in the study targeted the weeds and not the crop as it was similar with observations by Wafaa et al. (2016). Weeds were mostly controlled where L. camara was applied as compared to where it was not applied (control) which eventually increased cowpea yield. Conclusion The findings indicate that cowpea emergence and crop stand were not affected by L. camara and that L. camara reduced weeds in cowpea. G1 was more effective in that it increased cowpea grain yield by 36.04% than the G2 and the control (35.59%). However, different genotypes exhibited different effects in that G1 had better control resulting in significantly higher yield (876.90 kg ha$^{-1}$) than both the control (533.90 kg ha$^{-1}$) and G2 (672.10 kg ha$^{-1}$) which were in turn significantly different from each other. WPD and WW were reduced the most at the highest rate of application (400 kg ha$^{-1}$) or 14% aqueous extract of ground L. camara was found to be most effective. L. camara holds great potential to increase food security by reducing losses associated with weeds in cowpea. Acknowledgement Authors wish to thank the staff from the Departments of Plant and Soil Sciences, under the School of Agricultural Sciences, University of Zambia, for the provision of necessary facilities and the Ministry of General Education for the study leave given to the first author. This study was financed by a grant from under the Agricultural Productivity Program for Southern Africa (APPSA). The authors did not have conflict of interest. Conflicts of Interest No conflicts of interest have been declared. References Adigun J, Osipitan A.O, Lagoke S.T, Adeyemi R.O, Afolami S.O. 2014. Growth and yield performance of cowpea (Vigna unguiculata L. Walp) as influenced by row-spacing and period of weed interference. J Agric Sci. 6(4):188-198. Ambika S.R, Poornima S, Palaniraj R, Sati S.C, Narwal S.S. 2003. Allelopathic plants. Jnana Bharathi Campus, Bangalore University, India. Jabran, K. 2017. Manipulation of Allelopathic Crops for Weed Control. Springer Briefs in Plant Science, Springer International Publishing AG, Switzerland. Muchimba et al. 2015. Allelopathy for weed control in agricultural systems. J Crop Prot. 72: 57-65. Gantayet P.K, Adhikary S.P, Lenka K.C, Padhy B. 2014. Allelopathic Impact of Lantana Camara on Vegetative Growth and Yield Components of Green Gram (Phaseolus radiatus). Int J current microbiolappl Sci. 3(7): 327-335. Gupta K.C, Gupta A.K, Rani S. 2016. Weed management in cowpea [Vigna unguiculata L. Wasp] under rainfed conditions. Int J Agri Sci. 12(2): 238-240. Huffaker C.B, Messenger P.S. 2012. Theory and practice of biological control. Academic Press. Marinov-Serafimov P. 2015. Determination of allelopathic effect of some invasive weed species on germination and initial development of grain legume crops. Pesticidi I Fitomedicina. 25(3): 251-259. Mehdizadeh M, Izadi-Darbandi E, Naseri Pour Yazdi M.T, Rastgoo M, Malaekheh-Nikouei B, Nassirli H. 2019. Impacts of different organic amendments on soil degradation and phytotoxicity of metribuzin. International Journal of Recycling of Organic Waste in Agriculture. https://doi.org/10.1007/s40093-019-0280-8 Mishra A. 2015. Allelopathic properties of Lantana camara. Int Res J Basic Clinical Stud. 3(1): 13-28. Ngalamu T, Odra J, Tongun N. 2014. Cowpea production handbook. College of Natural Resources and Environmental Studies, University of Juba, Southern Sudan. Osipitan O.A, Adigun J.A, Kolawole R.O. 2016. Row spacing determines critical period of weed control in crop: Cowpea (Vigna unguiculata L. Walp) as a case study. Azarian J Agri. 3(5): 90-96. Qasem J.R. 2006. Response of onion (Allium cepa L.) plants to fertilizers, weed competition duration and planting times in the central Jordan Valley. Weed Biol Manag. 6: 212-220. Ugbe L.A, Ndaeyo N.U, Enyong J.F. 2016. Efficacy of Selected Herbicides on Weed Control, Cowpea (Vigna unguiculata L. Walp) Performance and Economic Returns in Akamkpa, South-eastern Nigeria. Int J. 19: 19-27. Van Driesche R.L, Hoodle M, Centre T. 2008. Control of pests and weeds by natural enemies; an introduction to biological control. Blackwell Publishing. Wafaa M.A.E, Youssef M.M.A, Kowthar G.E. 2016. Department of Plant Pathology, Nematology Labolatory. Int J Chem Tech Res. 9(6): 55-62. Ward S.M, Gaskin J.F, Wilson L.M. 2008. Ecological Genetics of Plant Invasion: What do We Know? Invasive Plant Sci and Manag. 1: 98-109. Cite this article as: Linda Chikeyi Muchimba, Tamara Tonga Kambikambi, Kalaluka Munyinda, Paul W. Kachapulula. 2020. Allelopathic potential of Lantana camara for weed control in cowpea (Vigna unguiculata L. Walp). Journal of Research in Weed Science, 3(3), 254-262. DOI: 10.26655/JRWEEDSC12020.3.1	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2640, 1 ], [ 2640, 5420, 2 ], [ 5420, 8805, 3 ], [ 8805, 11110, 4 ], [ 11110, 14247, 5 ], [ 14247, 17314, 6 ], [ 17314, 19592, 7 ], [ 19592, 21795, 8 ], [ 21795, 22230, 9 ] ] }
c3dbfba8e6ad8de005365d88e1057e7770d3821a	{ "olmocr-version": "0.1.59", "pdf-total-pages": 6, "total-fallback-pages": 0, "total-input-tokens": 21287, "total-output-tokens": 4447, "fieldofstudy": [ "Engineering" ] }	Flame-Oxidized Stainless-Steel Anode as a Probe in Bioelectrochemical System-Based Biosensors to Monitor the Biochemical Oxygen Demand of Wastewater Qiaochu Liang 1, Takahiro Yamashita 2, Ryoko Yamamoto-Ikemoto 1 and Hiroshi Yokoyama 2,* 1 Graduate School of Nature Science & Technology, Kanazawa University, Kakumamachi Kanazawa, Ishikawa 920-1192, Japan; [email protected] (Q.L.); [email protected] (R.Y.-I.) 2 Division of Animal Environment and Waste Management Research, Institute of Livestock and Grassland Science, National Agriculture and Food Research Organization (NARO), 2 Ikenodai, Tsukuba 305-0901, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-(0)29-838-8679; Fax: +81-(0)29-838-860 Received: 16 January 2018; Accepted: 14 February 2018; Published: 16 February 2018 Abstract: Biochemical oxygen demand (BOD) is a widely used index of water quality in wastewater treatment; however, conventional measurement methods are time-consuming. In this study, we analyzed a novel flame-oxidized stainless steel anode (FO-SSA) for use as the probe of bioelectrochemical system (BES)-based biosensors to monitor the BOD of treated swine wastewater. A thinner biofilm formed on the FO-SSA compared with that on a common carbon-cloth anode (CCA). The FO-SSA was superior to the CCA in terms of rapid sensing; the response time of the FO-SSA to obtain the value of $R^2 > 0.8$ was 1 h, whereas the CCA required 4 h. These results indicate that the FO-SSA offers better performance than traditional CCAs in BES biosensors and can be used to improve biomonitoring of wastewater. Keywords: biochemical oxygen demand; bioelectrochemical system; biosensor; flame oxidation; livestock wastewater; metal anode; stainless steel 1. Introduction Biochemical oxygen demand (BOD) is a widely used index for measuring the amount of biodegradable organic matter in wastewater. Since the conventional BOD measurement method is time-consuming (5 days), more rapid techniques are required to support advances in wastewater-treatment processes. BOD biosensors based on microbial fuel cells (MFCs) have emerged as an alternative to the conventional method [1]. In MFCs, exoelectrogenic bacteria adhere to the anode surface and transfer electrons from organic matter to the anode under anaerobic conditions. Kim et al. [2] reported on a mediator-free MFC-based BOD biosensor for the first time. Di Lorenzo et al. [3] reported on a single-chamber MFC-based biosensor that measured chemical oxygen demand values up to 350 ppm with a coefficient of determination ($R^2 > 0.96$) using artificial wastewater. Recently, a self-powered MFC-based biosensor was developed for online BOD monitoring [4]. At present, there is only one MFC-based biosensor available for sale by a Korean company (KORBI, Seoul, Korea). Current generation in MFC-based biosensors depends not only on the anode reaction, but also on the cathode reaction, and changes in cathode conditions can potentially affect current generation in a BOD-independent manner. To circumvent the cathode dependency, we recently developed a novel bioelectrochemical system (BES)-based BOD biosensor equipped with a potentiostat [5]. The anodic potential of the biosensor is kept constant by the potentiostat; therefore, the current generation is expected to depend on only the anode reaction based on the potential control. Usually, carbonaceous electrodes, such as carbon cloth, carbon felt, and carbon fiber, are used as the anodes in MFCs, since they have large effective surface areas and high biocompatibility with microbes. A new method that oxidizes the surface of a stainless steel anode (SSA) using fire reportedly improves the current output in BESs [6] and power production in MFCs [7]. The maximum power density using a flame-oxidized (FO)-SSA in MFCs was 24% higher than that using a carbon-cloth anode (CCA) [7]. Flame oxidation of stainless steel leads to the formation of Fe oxide nanoparticles on the surface, which have been suggested to attract exoelectrogenic bacteria that prefer Fe oxides, such as Geobacter spp., onto the surface in MFCs [7]. Geobacter spp. are representative exoelectrogenic bacteria with Fe oxide-reducing activity [8]. The performance of FO-SSAs has been characterized in MFCs, but not in BOD biosensors. Therefore, in the present study, we analyzed the utility of an FO-SSA as the probe of a BES-based biosensor for BOD measurements. Most studies on BOD biosensors have used artificial wastewater. However, evaluations using real wastewater are ultimately necessary for the practical application of biosensors, since the structure of the anode biofilm is dependent on the medium supplied. Therefore, we fed real treated swine wastewater into the BES-biosensor, and the performance of the FO-SSA was compared with that of a typical CCA. 2. Materials and Methods 2.1. Biosensor Construction The biosensor was rectangular (dimensions: 80 mm length $\times$ 50 mm width $\times$ 70 mm height; Figure 1). A mesh-shaped FO-SSA (70 mm $\times$ 80 mm $\times$ 0.2 mm) or CCA (70 mm $\times$ 80 mm $\times$ 0.2 mm) was placed inside the reactor. The FO-SSA was prepared by flame-oxidizing stainless-steel mesh (#60 mesh, SUS304) for 10 min, as described previously [7]. A plate-shaped stainless-steel cathode (SUS304, 50 mm $\times$ 80 mm $\times$ 0.2 mm) was placed opposite the anode in the reactor. An Ag/AgCl double-junction type reference electrode was inserted into the reactor, and the three electrodes were connected to a potentiostat (HA-151B; Hokuto Denko, Tokyo, Japan). A syringe was inserted in the top of the reactor to prevent increases in the inner pressure due to CO$_2$ production. ![Figure 1](image_url) Figure 1. (a) Schematic representation and (b) photograph of the BES-based BOD biosensor used in this study. 2.2. Biosensor Operation and Analysis The anode potential was set to $-0.2$ V (vs. Ag/AgCl). The reactor was inoculated with active sludge collected from an animal wastewater treatment plant at the Institute of Livestock and Grassland... Science (Tsukuba, Japan) as seed sludge. During an acclimation period of 3 weeks, raw swine wastewater (>500 mg BOD/L) was fed into the reactors, and medium exchange was conducted three times per week. Treated swine wastewater, purified using a conventional activated sludge process, was settled for 1 h, and the supernatant (8–90 mg BOD/L) was subsequently supplied to the biosensors. The biosensors were operated at 30 °C under repeated-batch culture mode. The whole volume of the reactor content was manually replaced with fresh medium using a syringe for each batch culture. Current generation was recorded every 15 min with a data logger. BOD was measured using a conventional respirometric method (BOD5) at 20 °C using an apparatus equipped with a pressure sensor. To quantify the biofilm amount, the anodes after culture were dried at 110 °C for 24 h and then cooled in a desiccator for 24 h. The mass of the attached biofilm was estimated by subtracting the weight of the anodes before use from the weight after use. 3. Results and Discussion 3.1. BOD Monitoring Figure 1 shows the configuration of the BES-based BOD biosensor. To analyze current response, various BOD5 concentrations were supplied to biosensors equipped with an FO-SSA or a CCA. The current intensity of both biosensors increased as the concentration of BOD5 increased (Figure 2). The time course of current generation was similar between the biosensors; in both, the current increased linearly and did not reach a plateau within 20 h. The $R^2$ values of the correlation between coulombs (current $\times$ time) with BOD5 in both biosensors ($n = 14$) increased with increasing response time and reached $> 0.9$ (Table 1). The FO-SSA showed higher $R^2$ values than CCA at all response times. The response time to obtain $R^2 > 0.8$ was 1 h for the FO-SSA, whereas the CCA required 4 h to reach $R^2 > 0.8$. In addition, $R^2 > 0.9$ was achieved within a shorter time (8 h) with the FO-SSA than the CCA (12 h). Figure 3 presents the correlation between BOD5 and coulombs at a response time of 8 h using the FO-SSA. The FO-SSA showed a linear correlation within the tested range of 8–90 mg BOD5/L ($R^2 > 0.9$). These results clearly show that FO-SSA offers superior performance to the CCA in terms of the rapid detection of BOD in wastewater. Table 1. $R^2$ values of the correlation between coulomb and BOD$_5$ at the indicated response times for biosensors equipped with an FO-SSA or a CCA ($n = 14$). \| Response Time (h) \| FO-SSA \| CCA \| \|------------------\|---------\|--------\| \| 1 \| 0.805 \| 0.696 \| \| 2 \| 0.823 \| 0.752 \| \| 3 \| 0.845 \| 0.789 \| \| 4 \| 0.860 \| 0.803 \| \| 5 \| 0.874 \| 0.820 \| \| 6 \| 0.884 \| 0.836 \| \| 7 \| 0.894 \| 0.851 \| \| 8 \| 0.902 \| 0.867 \| \| 10 \| 0.918 \| 0.895 \| \| 12 \| 0.924 \| 0.912 \| \| 16 \| 0.937 \| 0.930 \| \| 20 \| 0.941 \| 0.939 \| Figure 3. Correlation between coulomb and BOD$_5$ at a response time of 8 h in the FO-SSA-equipped biosensor. 3.2. Efficacy of the FO-SSA as a BES-Based BOD Biosensor Probe Metal-based anodes are rarely used in BESs, since bacteria adhere poorly to metal electrodes compared with carbon electrodes, and some metals are toxic to microbes. Nevertheless, we found that the FO-SSA enabled rapid BOD sensing. The biofilm on the FO-SSA appeared to be thinner than that on the CCA (Figure 4). To confirm this observation, the dry weight of the biofilms on the FO-SSA and CCA were determined. The biofilm on the FO-SSA (0.5 mg/cm$^2$ projected surface area) was less than one-third of that on the CCA (1.8 mg/cm$^2$ projected surface area). Owing to the thinness of the biofilm, substrates for current production in the wastewater might penetrate the biofilm on the FO-SSA more quickly than the CCA, resulting in a faster response of the FO-SSA-equipped biosensor to changes in BOD concentration. The structure of biofilms on BES anodes is dependent on the medium used. For example, when minimal medium with acetate for exoelectrogenic bacteria was supplied to BESs, a thin biofilm dominated by Geobacter spp. frequently formed on the anode [9]. In another case using real wastewater, a thick biofilm with a two-layer structure formed on the anode of BESs [5]. Exoelectrogenic bacteria are present inside the biofilm, and non-exoelectrogenic bacteria decomposing organic matter into smaller molecules are present outside the biofilm. Generally, the high biocompatibility of carbon electrodes, which leads to the abundant and rapid attachment of bacteria, is an advantageous feature in BESs. However, in the case of BOD biosensors for real wastewater, carbon electrodes might result in an overly thick biofilm layer, resulting in inaccurate and delayed sensing. We speculate that the anode biofilm thickness might be a critical parameter for the rapid sensing of BOD in real wastewater. Further studies are required to verify this hypothesis. ![Image of FO-SSA and CCA before and after culturing](image) Figure 4. Images of the FO-SSA and CCA before and after culturing, showing biofilm attachment. 3.3. Potential Applications of FO-SSA-Equipped BOD Biosensors Stainless steel is highly conductive compared with standard carbonaceous electrodes and is a low-cost material with good chemical and mechanical strength. FO-SSA preparation is a relatively simple process, which requires the short application of flame to stainless steel mesh. In this study, a BES-based biosensor was equipped with an FO-SSA in a manner that enabled the anode potential to be kept constant for accurate sensing. Water pollution is a major problem that damages water resources, such as rivers, ponds, and ground water, and various practical applications of the biosensor presented herein are expected. For example, the biosensor could be placed in the final sedimentation tank of wastewater treatment plants to prevent discharge of inadequately treated wastewater with high BOD concentrations into the surrounding aquatic environment linking an alarm to the biosensor. Acknowledgments: This research was supported by a grant from the Project of the NARO Bio-oriented Technology Research Advancement Institution for the special scheme project on vitalizing management entities of agriculture, forestry and fisheries (k037). Author Contributions: Q.L., T.Y., performed the experiments and analyzed the data. R.Y.-I. and H.Y. designed the research. Q.L. and H.Y. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest. References 1. Sun, J.Z.; Kingori, G.P.; Si, R.W.; Zhai, D.D.; Liao, Z.H.; Sun, D.Z.; Zheng, T.; Yong, Y.C. Microbial fuel cell-based biosensors for environmental monitoring: A review. Water Sci. Technol. 2015, 71, 801–809. [CrossRef] [PubMed] 2. Kim, B.H.; Chang, I.S.; Gil, G.C.; Park, H.S.; Kim, H.J. Novel BOD (biological oxygen demand) sensor using mediator-less microbial fuel cell. Biotechnol. Lett. 2003, 25, 541–545. [CrossRef] [PubMed] 3. Di Lorenzo, M.; Curtis, T.P.; Head, I.M.; Scott, K. A single-chamber microbial fuel cell as a biosensor for wastewaters. Water Res. 2009, 43, 3145–3154. [CrossRef] [PubMed] 4. Pasternak, G.; Greenman, J.; Ieropoulos, I. Self-powered, autonomous Biological Oxygen Demand biosensor for online water quality monitoring. Sens. Actuator B-Chem. 2017, 244, 815–822. [CrossRef] [PubMed] 5. Yamashita, T.; Ookawa, N.; Ishida, M.; Kanamori, H.; Sasaki, H.; Katayose, Y.; Yokoyama, H. A novel open-type biosensor for the in-situ monitoring of biochemical oxygen demand in an aerobic environment. Sci. Rep. 2016, 6, 38552. [CrossRef] [PubMed] 6. Guo, K.; Donose, B.C.; Soeriyadi, A.H.; Prevoteau, A.; Patil, S.A.; Freguia, S.; Gooding, J.J.; Rabaey, K. Flame oxidation of stainless steel felt enhances anodic biofilm formation and current output in bioelectrochemical systems. Environ. Sci. Technol. 2014, 48, 7151–7156. [CrossRef] [PubMed] 7. Yamashita, T.; Ishida, M.; Asakawa, S.; Kanamori, H.; Sasaki, H.; Ogino, A.; Katayose, Y.; Hatta, T.; Yokoyama, H. Enhanced electrical power generation using flame-oxidized stainless steel anode in microbial fuel cells and the anodic community structure. Biotechnol. Biofuels 2016, 9, 62. [CrossRef] [PubMed] 8. Bond, D.R.; Lovley, D.R. Electricity production by Geobacter sulfurreducens attached to electrodes. Appl. Environ. Microbiol. 2003, 69, 1548–1555. [CrossRef] [PubMed] 9. Yokoyama, H.; Ishida, M.; Yamashita, T. Comparison of Anodic Community in Microbial Fuel Cells with Iron Oxide-Reducing Community. J. Microbiol. Biotechnol. 2016, 26, 757–762. [CrossRef] [PubMed] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3412, 1 ], [ 3412, 6121, 2 ], [ 6121, 8444, 3 ], [ 8444, 11014, 4 ], [ 11014, 13648, 5 ], [ 13648, 15122, 6 ] ] }
dadd309199855b14d887bfaee46340e03a11578c	{ "olmocr-version": "0.1.59", "pdf-total-pages": 5, "total-fallback-pages": 0, "total-input-tokens": 17184, "total-output-tokens": 4379, "fieldofstudy": [ "Medicine" ] }	Short Term Outcomes of Early Term Neonates in a Tertiary Care Centre: A Descriptive Study P. Ragasudhin¹, Harish Sudarsanan¹* and J. Kumutha² ¹Saveetha Medical, College and Hospital, India. ²Department of Neonatology, Saveetha Medical, College and Hospital, India. Authors’ contributions This work was carried out in collaboration among all authors. All authors read and approved the final manuscript. Article Information DOI: 10.9734/JPRI/2021/v33i47B33207 Editor(s): (1) Ana Cláudia Coelho, University of Trás-os-Montes and Alto Douro, Portugal. Reviewers: (1) Uchenna Ekwochi, Enugu State University of Science & Technology, Nigeria. (2) Anil Kumar Tiwari, Aryabhatt Knowledge University, India. Complete Peer review History: https://www.sdiarticle4.com/review-history/75491 Original Research Article ABSTRACT Introduction: The number of babies delivered between 37 weeks to 38 weeks and 6 days has been on the rise with increase in lower segment caesarian section (LSCS). These early term neonates have increased risk of developing respiratory distress syndrome, neonatal hyperbilirubinemia, transient tachypnoea, prolonged hospital stays, hypothermia, and feeding difficulty, when compared to a term neonate. An audit of early term neonatal short-term outcomes was undertaken at our institute. Methodology: A retrospective descriptive cross-sectional study was carried out between July 2020 and December 2020 at a private medical college Neonatal Intensive Care Unit. Neonates with a gestation age of 37 weeks and 0 days to 38 weeks and 6 days born were included. Results: A total of 137 early term delivery data were obtained. Hypothyroidism (23%) and gestational diabetes (23%) were found to be the most common associated antenatal problems. The most common morbidity out of 137 early term neonates was neonatal jaundice 91 (66.4%) followed by respiratory distress which affected 38 (28%) neonates. Conclusion: This study establishes the high incidence of neonatal jaundice and respiratory morbidities in early term neonates. Hence it is better to avoid elective LSCS before 39 weeks of gestation provided there are no medical indications for the same. Keywords: Early term neonate; neonatal jaundice; respiratory morbidity. 1. INTRODUCTION A child’s risk of death is 15 times greater in the first 4 weeks of life [1], which may be due to various causes. It is important to know the various preventable causes of neonatal mortality for timely intervention and reduction of perinatal morbidity. Although prematurity has been the most common cause of perinatal morbidity [2], more recent evidences suggest that early term deliveries contribute to an extent to neonatal morbidity [3,4,5]. American College of Obstetricians and Gynecologist defines early term delivery as delivery of baby between the gestational periods from 37 weeks to 38 weeks and 6 days [6]. Incidence of Respiratory Distress syndrome, Neonatal hyperbilirubinemia, Transient Tachypnoea, prolonged hospital stays, hypothermia, feeding difficulty has been increased [7], when compared to a term neonate. The reason behind these is physiological immaturity of the baby. The indications of elective Lower Segment Caesarian Section (LSCS) in early term pregnancy can range from unavoidable circumstances such as, previous LSCS in labor, breech in labour, cephalopelvic disproportion to avoidable scenarios such as maternal request of LSCS in view of anxiety or wishing to have their child on an auspicious day. According to a study done by Pirjani, R et al, 28% of women requested for LSCS [8]. A study was undertaken at our institute to audit the early term neonatal short-term outcomes. Though it is impossible to drastically decrease the incidence of early term deliveries as there will be absolute indications making an early term delivery inevitable, we can still try and avoid early term deliveries that are done for maternal request or non-medical and non-emergent indications provided if we establish a relationship between bad outcomes and early term neonates. 2. METHODOLOGY A retrospective descriptive cross-sectional study was carried out between July 2020 and December 2020 at a private medical college neonatal intensive care unit. Neonates with a gestation age of 37 weeks and 0 days to 38 weeks and 6 days born during the above period of 6 months were included. The identity details of the babies were obtained from department database. Information on maternal age, parity, antenatal risk factors, mode of delivery, resuscitation was obtained from case records. The early neonatal outcomes that were studied included incidence of respiratory distress, hypoglycemia, feeding problems including restricted breastfeeding and tub feeding, neonatal jaundice and duration of hospital stay. The data was compiled using Microsoft Office 365 Excel and analyzed with Microsoft Excel data analysis tool kit. Qualitative data was presented as frequencies and percentages. Mean, standard deviation, median an interquartile range were used to represent quantitative data. 3. RESULTS A total of 137 early term babies were delivered between July 2020 and December 2020. Table 1 shows maternal characteristics. The mean age of the mother who gave birth to early term neonates was 26.8 years [SD ±4.2]. Hypothyroidism (23%) and gestational diabetes (23%) were found to be the most common antenatal problem. 73% of the deliveries were through LSCS. Neonatal characteristics are given in Table 2. The mean gestational age of the neonates was 37.4 [SD ±0.5] and mean weight of the neonates was 2822g [SD±471]. Out of 137 neonates 80 [58%] of them were male babies and 57 [42%] of them were female babies. The median value for the time taken for giving the first feed was around 30 minutes with interquartile range of 18-36. Table 3 shows early neonatal outcomes of the study population. The most common morbidity in early term neonates was neonatal jaundice which affected 91 [66.4%] of the neonates, with mean peak bilirubin value of 14.1mg/dl, followed by respiratory morbidity which affected 38 [28%] of the neonates. None of the babies had feeding problem. 4. DISCUSSION In our study we aimed to highlight the short term outcomes with early term deliveries and associated risk factors. In our study the mean age of the mothers is 26.8, which is comparatively lower than the study done by Tita ATN et al [9] in which the median age was 30 and is similar to study done by Dilek Ulubaş-Işık et al in which the mean age was 28.2 [10]. According to a study done by Palanivel et al. [11], 73% of the mothers were between the age of 21-30 years. Maternal hypothyroidism (23%), gestational diabetes (GDM) (23%) followed by pregnancy induced hypertension (PIH) (15%) were the antenatal risk factors associated with early term deliveries in our study. These findings are in contrast to the study done by Dilek Ulubaş-Işık et al in which 22% of PIH and 35% of GDM accounted for early term deliveries [10]. The mode of delivery in our study is 73% via LSCS and 27% by NVD, which implies that early term deliveries are associated with LSCS. Our incidence of LSCS is more than three fourths of total delivery when compared to study done by Sengupta S et al where the frequency of LSCS for early term gestation was 38.4% [12]. According to our study the mean gestational age of the babies is 37.4 weeks and the mean birth weight is 2822 grams which is almost similar to study done by Bulut et al [13] where the mean weight is 3124 grams. This implies that incidence of low birth weight is not that significant in early term according to our study. The frequency of male baby in this study is 58% which is similar to the study done by Dilek Ulubaş-Işık et al [10] in which there was 61% of male babies. The mean 1-minute APGAR score is 7.5 and 5-minute APGAR score is 8.6 which is lesser when compared to study done by Ozgul Bulut et al where the 1 minute APGAR was 7.9 and 5 minute APGAR was 9.1[13]. Our study results showed high incidence of respiratory morbidity and neonatal jaundice. The most common adverse outcome was neonatal jaundice which accounted for 66.4% with mean peak bilirubin value of 14.1 mg/dl followed by respiratory morbidity which accounted for 28%. A study done by Gharkey K et al showed that there is 2 fold increase in incidence of respiratory morbidity in early term neonates when compared to term neonates [14] and this fact is also supported by the study done by Thomas J et al[15]. The increase in respiratory morbidity is probably due to decreased clearance of lung fluid which is secondary to delayed pulmonary fluid absorption due to decreased maturity and increased rate of LSCS. The incidence of neonatal hypoglycemia is 5% which is similar to the study done by Sengupta S et al in which the incidence was 4.9% [12]. In our study population, the low incidence could be due to the practice of first hour feeding. None of the neonates needed intravenous fluids for hypoglycemia correction and correction of feeds along with prescription of pasteurized donor human milk from our human milk bank was sufficient for hypoglycemia correction. Jaundice is the most common condition requiring medical attention in the neonates. According to a study done by Woodgate P, about 50% of term babies and 80% of preterm babies develop neonatal jaundice. This shows that as the gestational age decreases the incidence of jaundice increases. The incidence of neonatal jaundice in our study is 66.4% which is comparatively higher than the study done by Dilek Ulubaş-Işık et al [10] in which the incidence was 45% which might be due to higher study population. The higher incidence was probably due to decreased feeding ability of early term neonates that is compounded by hepatic immaturity. The mean duration of hospital stay in our study is 7 which is higher when compared to study done by Ozgul Bulut et al [13], where the mean duration was 4.4. the higher incidence of neonatal jaundice needing phototherapy and respiratory morbidity probably lead on to increase in duration of stay. 5. CONCLUSION Our study is limited by the sample size used and long-term data, which is being done as a follow up project in our unit. This study establishes the high incidence of neonatal jaundice and respiratory morbidities in this population. This will in turn cause maternal anxiety, mother child separation and increased hospital stay. Hence it is better to avoid elective LSCS before 39 weeks of gestation provided there are no medical indications for the same. CONSENT It is not applicable. ETHICAL APPROVAL Institutional Ethical Committee approval was obtained prior to retrieving case records from Hospital Medical Records Department. COMPETING INTERESTS Authors have declared that no competing interests exist. REFERENCES 1. Sources: World Health Report: Make Every Mother and Child Count (WHO) and The Lancet’s Newborn Survival Series (2005) and UNICEF (2008); 2005. 2. Beck S, Wojdyla D, Say L, Bertran AP, Merialdi M, Requejo JH, et al. The worldwide incidence of preterm birth: a systematic review of maternal morbidity and mortality. Bull World Health Organ. 2010;88(1):31–8. DOI:10.2471/BLT.08.062554. Epub 2009 Sep 25. 3. Engle WA. Morbidity and mortality in late preterm and early term newborns: a continuum. Clin perinatol 2011;38:493-516. 4. Seikku L, Gissler M, Andersson S, Rahkonen P, Stefanovic V, Tikkanen M, Paavonen J, Rahkonen L. Asphyxia, neurologic morbidity, and perinatal mortality in early-term and postterm birth. Pediatrics. 2016;137(6). 5. Sengupta S, Carrion V, Shelton J, Wynn RJ, Ryan RM, Singhal K, Lakshminrusimha S. Adverse neonatal outcomes associated with early-term birth. JAMA pediatrics. 2013;167(11):1053-9. 6. Spong CY. Defining "term" pregnancy: recommendations from the Defining "Term" Pregnancy Workgroup. JAMA. 2013;309(23):2445-6. DOI: 10.1001/jama.2013.6235. PMID: 23645117 7. Murray SR, Shenkin SD, McIntosh K, Lim J, Grove B, Pell JP, Norman JE, Stock SJ. Long term cognitive outcomes of early term (37-38 weeks) and late preterm (34-36 weeks) births: A systematic review. Wellcome Open Res. 2017;2:101. DOI: 10.12688/wellcomeopenres.12783.1. PMID: 29387801; PMCID: PMC5721566. 8. Pirjani R, Afrahydro M, Sepidarkhish M, et al. Elective caesarean section at 38–39 weeks gestation compared to > 39 weeks on neonatal outcomes: a prospective cohort study. BMC Pregnancy Childbirth 2018;18:140. Available:https://doi.org/10.1186/s12884-018-1785-2 9. Tita ATN, Jablonski KA, Bailit JL, Grobman WA, Wapner RJ, Reddy UM, Varner MW, Thorp JM Jr, Leveno KJ, Caritis SN, Iams JD, Saade G, Sorokin Y, Rouse DJ, Blackwell SC, Tolosa JE; Eunice Kennedy Shriver National Institute of Child Health and Human Development Maternal-Fetal Medicine Units Network. Neonatal outcomes of elective early-term births after demonstrated fetal lung maturity. Am J Obstet Gynecol. 2018 Sep;219(3):296.e1-296.e8. DOI: 10.1016/j.ajog.2018.05.011. Epub 2018 May 22. PMID: 29800541; PMCID: PMC6143365. 10. Ulubaş-Işık D, Erol S, Demirel N, Kale Y, Çelik İH, Tapisiz ÖL, Yırıcı B, Baş AY. Early-term delivery and adverse neonatal outcomes at a tertiary center in Turkey. Turkish Journal of Pediatrics. 2015;57(6). 11. Palanivelraja T. Immediate Neonatal Outcomes in Early Term Birth in Tertiary Care Hospital, Tirunelveli Medical College and Hospital (Doctoral dissertation, Tirunelveli Medical College, Tirunelveli). 12. Sengupta S, Carion V, Shelton J, et al. Adverse Neonatal Outcomes Associated With Early-Term Birth. JAMA Pediatr. 2013;167(11):1053–1059. DOI:10.1001/jamapediatrics.2013.2581 13. Bulot O, Buyukkayhan D. Early term delivery is associated with increased neonatal respiratory morbidity. Pediatrics International. 2021;63:60-64. Available:https://doi.org/10.1111/ped.14437 14. Gharkey K, Coletta J, Lizaraga L, Murphy E, Ananth CV, G Yam-F-Bannerman C. Neonatal respiratory morbidity in the early term delivery. Am J Obstet Gynecol. 2012;207(4):292.e1-4. DOI: 10.1016/j.ajog.2012.07.022. Epub 2012 Jul 20. PMID: 22902075. 15. Thomas J, Olukade TO, Naz A, Salama H, Al-Qubaisi M, Al Rifai H, Al-Obaidly S. The neonatal respiratory morbidity associated with early term caesarean section - an emerging pandemic. J Perinat Med. 2021;49(7):767-772. DOI: 10.1515/jpm-2020-0402 PMID: 33962503. © 2021 Ragasudhin et al.; This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Peer-review history: The peer review history for this paper can be accessed here: https://www.sdiarticle4.com/review-history/75491	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2173, 1 ], [ 2173, 6150, 2 ], [ 6150, 7791, 3 ], [ 7791, 11754, 4 ], [ 11754, 14767, 5 ] ] }
e79de5ff356a000e6c0fef6785db419a6886bebc	{ "olmocr-version": "0.1.59", "pdf-total-pages": 10, "total-fallback-pages": 0, "total-input-tokens": 31913, "total-output-tokens": 11178, "fieldofstudy": [ "Biology", "Engineering", "Materials Science" ] }	Effect of Strain Magnitude on the Tissue Properties of Engineered Cardiovascular Constructs RALF A. BOERBOOM, MIRJAM P. RUBBENS, NIELS J. B. DRIESSEN, CARLJN V. C. BOUTEN, and FRANK P. T. BAAIJENS Department of Biomedical Engineering, Soft Tissue Biomechanics and Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands (Received 24 April 2007; accepted 26 November 2007; published online 8 December 2007) Abstract—Mechanical loading is a powerful regulator of tissue properties in engineered cardiovascular tissues. To ultimately regulate the biochemical processes, it is essential to quantify the effect of mechanical loading on the properties of engineered cardiovascular constructs. In this study the Flexercell FX-4000T (Flexcell Int. Corp., USA) straining system was modified to simultaneously apply various strain magnitudes to individual samples during one experiment. In addition, porous polyglycolic acid (PGA) scaffolds, coated with poly-4-hydroxybutyrate (P4HB), were partially embedded in a silicone layer to allow long-term uniaxial cyclic mechanical straining of cardiovascular engineered constructs. The constructs were subjected to two different strain magnitudes and showed differences in biochemical properties, mechanical properties and organization of the microstructure compared to the unstrained constructs. The results suggest that when the tissues are exposed to prolonged mechanical stimulation, the production of collagen with a higher fraction of crosslinks is induced. However, straining with a large strain magnitude resulted in a negative effect on the mechanical properties of the tissue. In addition, dynamic straining induced a different alignment of cells and collagen in the superficial layers compared to the deeper layers of the construct. The presented model system can be used to systematically optimize culture protocols for engineered cardiovascular tissues. Keywords—Tissue engineering, Collagen organization, Cell orientation, Biochemical properties, Mechanical properties. INTRODUCTION Load bearing (soft) tissues are composed of a highly organized extracellular matrix (ECM), which primarily consists of collagen, elastin and proteoglycans. Predominantly, the collagen architecture (i.e., content, crosslinks, and orientation) determines the mechanical behavior of these tissues.3,8 In addition, model studies show that the collagen organization is strongly coupled to the mechanical loading condition of these tissues.9,16 Several load bearing tissues become dysfunctional and need replacement. Frequently replaced load bearing cardiovascular soft tissues include coronary arteries and heart valves.40 The currently used replacement strategies all have several shortcomings35,45 and the most important drawback of the replacement tissue is the inability to remodel in response to the dynamic biological environment. Tissue engineering (TE) is a promising technique that has the potential to overcome these shortcomings. However, engineered tissues often lack sufficient amounts of properly organized ECM and consequently do not meet mechanical demands. An often applied technique in TE comprises the use of autologous cell sources and biodegradable carrier materials (synthetic or biological). These tissue engineered constructs are most often mechanically conditioned and are ultimately placed in the human body. Successful attempts have been performed to create strong vessels by engineering vessels using the self assembled vascular graft approach,34 growing vessels in the recipients peritoneal cavity12 and using a porous biodegradable scaffold seeded with cells.26,41 Tissue engineered heart valves have been cultured using either a biological scaffold that will attract endogenous cells1,43 or using a biodegradable synthetic scaffold on which cells are seeded.19,25 Recently, Mol et al.38 have cultured tissue engineered heart valves that demonstrated sufficient mechanical strength for placement at the aortic position. The valves were cultured using mechanical stimulation of cell seeded scaffolds in a bioreactor by mimicking the diastolic phase of the heart cycle. However, the mechanical stimulation... CARDIOVASCULAR TISSUES, in which mechanical loading on the properties of engineered studies have focused on the effect of well defined controlled deformation. Only a limited amount of tubular constructs in the presence of accurately ECM. Cells have been stimulated by using a variety of culture systems such as longitudinal stretching devices and vacuum driven devices. Several studies have been performed looking at the effect of mechanical stimulation on tissue remodeling in complex geometries. Similar experiments in well defined simple geometries were performed. Seliktar et al. cultured fibroblast populated collagen gels (tubular constructs) in the presence of accurately controlled deformation. Only a limited amount of studies have focused on the effect of well defined mechanical loading on the properties of engineered cardiovascular tissues, in which de novo formation of ECM is studied (e.g., polyglycolic acid (PGA) scaffolds seeded with cells). Mechanical control of tissue properties in engineered constructs is desired. This requires a detailed study on the effects of well defined loading conditions on ECM synthesis and ECM organization in order to optimize the loading regimen. The first aim of this paper was to develop a model system, which allowed long term dynamic loading of cardiovascular engineered constructs. Previously, PGA in combination with cells deformed plastically and straining of the constructs required continuous adjustment of the applied strain. By supporting the scaffolds with a silicone layer, a technique was developed that enabled continuous straining of engineered cardiovascular constructs. Local tissue strains were measured during culture using digital image correlation (DIC). These constructs, consisting of PGA coated with poly-4-hydroxybutyrate (P4HB) and seeded with human saphenous vein cells (HSVC), were attached to flexible membranes, which were strained using a Flexercell FX-4000T (Flexcell International, USA) straining system. The scaffold consisted of non-woven PGA scaffold (density 72.76 mg/cm³; Cellon, Luxemburg), which was coated with 1% (w/v) poly-4-hydroxybutyrate (P4HB; Symetis Inc., Switzerland) dissolved in tetrahydrofuran (THF; Merck, Germany). The scaffold consisted of non-woven PGA scaffold (density 72.76 mg/cm³; Cellon, Luxemburg), which was coated with 1% (w/v) poly-4-hydroxybutyrate (P4HB; Symetis Inc., Switzerland) dissolved in tetrahydrofuran (THF; Merck, Germany). The scaffold was supported by a 0.5 mm thick layer of elastic silicone (Silastic MDX4-4210, Dow Corning, USA). After curing, rectangular scaffolds were cut (34 × 5 × 1 mm³) and the constructs were attached at the outer 5 mm to the flexible membrane by using Silastic MDX4-4210 (Fig. 1b). The strain applied to the constructs was de novo formation. quantified $(n = 6)$ after 2 weeks of dynamic culture using a similar protocol as was used for the membrane strains in the section “Straining System”. Cell and Tissue Culture Human saphenous vein cells (HSVC, myofibroblasts) were acquired from a 44-year-old woman and were grown using regular cell culture methods.$^4$ The cells were expanded in medium consisting of advanced Dulbecco’s Modified Eagle Medium (DMEM; Gibco, USA) supplemented with 10% fetal bovine serum (FBS; Greiner Bio one, The Netherlands), 1% l-glutamax (Gibco, USA) and 0.1% gentamycin (Biochrom, Germany). The scaffolds were vacuum dried for 48 h, followed by exposure to ultra violet light for 1 h and were subsequently placed in 70% ethanol for 4–5 h to obtain sterility. The scaffolds were allowed to dry overnight, followed by washing three times with phosphate buffered saline (PBS; Sigma, USA). Prior to cell seeding, tissue culture medium was added to the scaffolds for 16 h to facilitate cell attachment. HSVC cells at passage 7 were seeded on these scaffolds using fibrin gel (Sigma, Germany) as a cell carrier.$^3$ The cells were seeded at a concentration of approximately 20 million cells per cm$^2$ and the tissue constructs were subsequently cultured in tissue culture medium (at 37 °C and 5% CO$_2$). The tissue culture medium was changed every 3–4 days and consisted of advanced DMEM (Gibco, USA) supplemented with 10% FBS, 1% l-glutamax, 0.3% gentamycin and L-ascorbic acid 2-phosphate (0.25 mg/L; Sigma, USA). Straining Protocol The engineered cardiovascular constructs were cultured for 3 weeks, comprising 6 days of no applied loading to allow the cells to adapt after seeding, followed by 2 weeks of dynamic straining at a frequency of 1 Hz. Three different strain conditions were applied: 0% strain, 4% dynamic strain and 8% dynamic strain $(n = 8)$. The measurements of the applied strain were performed on separate samples strained at 4 and 8% strain for 2 and 3 weeks $(n = 6)$. Mechanical Testing The constructs were sacrificed after 3 weeks of culture and were tested for their mechanical properties within 1 h $(n = 6)$. The silicone layer was removed from the samples and the remaining tissues were placed in tissue culture medium to moisturize the samples. Thickness and width of the samples were determined using a Plu 2300 non contact optical image profiler (Sensofar Tech S.L., Spain). A representative area measuring 8.35 $\times$ 7.85 mm$^2$ was scanned using a 5x objective (Nikon, Japan) at a scanspeed of 1x. Thickness and width were obtained by averaging over the representative area. Uniaxial tensile tests in the longitudinal direction were performed on the engineered tissues using a tensile stage (Kammrath & Weiss Gmbh, Germany) equipped with a 20 N loadcell. The tissues were tested at a constant strainrate of 1/60 s$^{-1}$ and were tested until break. Simultaneously, the force and elongation were measured, which were converted to Cauchy stress and strain, respectively. The linear slope of the resulting curve was defined as the tangent stiffness of the sample. Biochemical Assays on Tissue Formation The tissues that were used for mechanical testing $(n = 6)$ were subsequently analyzed with biochemical assays for the amount of DNA, glycosaminoglycan (GAG), collagen and hydroxylysyl pyridinoline (HP) cross-links. The amount GAG and hydroxyproline (Hyp) were expressed per µg DNA and the amount of DNA was expressed per mg dryweight. Furthermore, the amount of collagen cross-links was normalized per collagen triple helix. The lyophilized samples were digested in papain solution (100 mM phosphate buffer, 5 mM L-cystein, 5 mM ethylenediaminetetraacetic acid (EDTA) and 125–140 µg papain per mL) at 60 °C for 16 h. The samples were then centrifuged and subsequently analysed. A portion of the supernatant was used for the DNA assay, a portion was used for the GAG assay and another portion was used for Hyp and cross-link analysis. The amount of DNA was determined using the Hoechst dye method. In short, TE cross-link analysis. The amount of DNA was determined using the Hoechst dye method. In short, TE buffer (10 mM Tris, 1 mM EDTA, pH 7.4) was used to dilute the samples and 100 µL was pipetted into a black 96 wells plate (Corning, USA). An equal amount of working solution containing the Hoechst dye (10 mM Tris, 1 mM EDTA, 2 M NaCl and 2.5 µg Hoechst dye per mL) was added to each well. To allow binding of the Hoechst dye to the DNA, the plate was incubated at room temperature for 10 min and was protected from light. Subsequently, the fluorescence was measured (excitation wavelength 355 nm, emission wavelength 460 nm). The amount of DNA in the samples was determined from a standard curve prepared from calf thymus DNA (Sigma, USA). The GAG content was determined using a modification of the assay described by Farndale et al. Briefly, 40 µL of each sample was pipetted into a flat bottom 96 well plate. 150 µL of DMMB color reagent (46 µM dimethylmethylene blue, 40.5 mM glycine, 40.5 mM NaCl, pH 3.0) was added to each well and the plate was gently shaken. The absorbencies at 540 and 595 nm were read within 5–10 min and extracted from one another. The amount of GAG in the samples was determined from a standard curve prepared from chondroitin sulfate of shark cartilage (Sigma, USA). Digested tissue samples were hydrolyzed by adding 25% HCl (Merck, Germany) to 200 µL of sample volume to obtain a final concentration of 6 M HCl. These samples were hydrolysed at 110 °C for 22 h and were subsequently used for amino acid and cross-link analyses. Hyp residues were measured on the acid hydrolysates by reverse-phase high-performance liquid chromatography (HPLC) after derivatization with 9-fluorenylmethyl chloroformate (FMOC, Fluka, Switzerland) as previously described by Bank et al. Residues of the same samples were used to measure the number of HP cross-links using HPLC as described by Bank et al. The amount of Hyp was converted to the amount of collagen using a conversion factor of 7.26. Histology and Multiphoton Microscopy One sample per group was used for histology. Tissues were fixed in phosphate-buffered formalin (Fluka, USA) and embedded in paraffin. 10 µm transverse sections were cut and these sections were stained with Haematoxylin and Eosin (H&E) to study general tissue formation. In addition, one living sample per group was stained for multiphoton microscopy. Cell Tracker Blue CMAC (CTB; Invitrogen, the Netherlands) and CNA35-OG488 were used as specific fluorescent markers for cell cytoplasm and collagen, respectively. CTB and CNA35-OG488 were excitable with two-photon microscopy and exhibited broad emission spectra at 466 and 520 nm. Labeling of the tissue was performed with tissue culture medium, which was supplemented with CTB (15.0 µM) and CNA35-OG488 (2.0 µM). The CTB solution was applied for 5 h, followed by CNA35-OG488 (3.0 µM) for 16 h. The samples were then placed in tissue culture medium. An inverted Zeiss Axiovert 200 microscope (Carl Zeiss, Germany) coupled to an LSM 510 Meta (Carl Zeiss, Germany) laser scanning microscope was used to image the tissue engineered construct. A chameleon ultra 140 fs pulsed Ti:Sapphire laser (Coherent, USA), was tuned to 760 nm to image the applied fluorescent probes. A 63× water-immersion objective (1.2 N.A.; Carl Zeiss, Germany) was used and the channels for the two photo multiplier tubes (PMT) were defined as follows: 435–485 nm, CTB (PMT1) and 500–530 nm, CNA35-OG488 (PMT2). Separate images were obtained from each PMT (coded blue and green, respectively) and combined into a single image. Statistics Quantitative data are represented as mean ± standard deviation (Table 1), except for graphical representations, where data are depicted as mean ± standard error of the mean (SEM, n = 6). The data were analysed with an analysis of variance (ANOVA), followed by a Bonferroni post-hoc test to indicate significant differences between experimental groups (SPSS 12.01, SPSS Inc., USA). RESULTS Strain Field Characterization By placing polycarbonate rings around the Flexcell loading posts, the straining system was modified to simultaneously apply various strain magnitudes to individual samples during one experiment. The strain profile, applied to the membranes, was calibrated for three different ring heights (8.16, 7.47, and 7.05 mm) using round loading post geometries and showed reproducible homogeneous strain fields (Fig. 2). The average strains (%) and standard deviation were 3.84 ± 0.61, 8.08 ± 0.72 and 12.48 ± 0.45, respectively. The strain fields at the surface of the strained engineered cardiovascular constructs (n = 6) were validated for two different strain rings (8.16 and 7.47 mm) after 2 weeks of dynamic culture. After 2 weeks of culture the average strain (%) measured 4.57 ± 1.34 and 8.04 ± 2.81, respectively. Typical strain fields after 2 weeks of culture for both ring heights (Figs. 3a and 3b, respectively) showed a more inhomogeneous distribution than the strain applied to the membrane without the tissue construct. The measured average applied strain in the tissue constructs is nearly equal to the membrane only situation (two dimensional), but the standard deviations are larger, reflecting the more inhomogeneous nature of the strain field. Furthermore, the major strain direction for both straining conditions (Fig. 3) is uniaxial. Effect of Cyclic Strain on Tissue Properties To characterize the effect of different strain magnitudes on engineered cardiovascular tissue properties, the tangent stiffness of the constructs and the amount of DNA, GAG, collagen, and HP crosslinks (Table 1) were quantified. Cyclic strain did not increase the amount of DNA per dryweight within the engineered tissue constructs relative to unstrained engineered tissue constructs. However, collagen per DNA and GAG per DNA in mechanically strained constructs, were significantly reduced compared to unstrained tissue constructs. The number of HP crosslinks per triple helix on the other hand were significantly increased for both strain conditions. The tangent stiffness of the 4% strained constructs was equal to the stiffness of the unstrained tissue constructs, whereas the 8% strained constructs showed a significant reduction in stiffness relative to both the unstrained and the 4% strained constructs (Fig. 4). Histology and Multiphoton Microscopy The H&E stain was performed to obtain a general overview of matrix formation within the engineered cardiovascular constructs after 3 weeks of culture (Figs. 5a–c). In general the constructs showed a dense layer of cells and ECM at the surface of the construct. Deeper into the tissues less cells and a faint staining of the ECM was seen, which illustrates a reduced production of ECM per cell. The bottom of the engineered tissue, which was attached to the silicone support layer, did not show much production of matrix due to an insufficient supply of nutrients. Comparing the different straining conditions showed that the superficial layer appeared thinner in unstrained tissues relative to the strained tissues. In addition, the superficial layer of the 4% strained construct appeared more dense. compared to the superficial layer of the 8% strained construct. Multiphoton microscopy was performed to visualize the organization of cells and collagen within the engineered cardiovascular tissues. The surface of the construct was covered with a layer of cells with a small amount of collagen in between the cells (Figs. 5d–f). The cells and collagen at the surface of the strained tissues were aligned oblique or perpendicular with respect to the strain direction. However, the cells and the collagen at the surface of the unstrained construct were oriented more parallel to the longitudinal axis of the construct compared to the cells in the strained construct. Slightly deeper into the tissue more collagen and less cells (Figs. 5g–i) were present, which were both aligned almost parallel to the straining direction. DISCUSSION Mechanical loading is an important regulator of biochemical processes within living tissues. In order to regulate these biochemical processes, it is essential to quantify the effect of mechanical loading on the properties of engineered cardiovascular constructs. In this study an experimental framework was presented in which an adapted version of the Flexercell FX-4000T (Flexcell Int. Corp., USA) straining system was used to simultaneously apply various strain magnitudes to individual samples during one experiment. The flexercell system allows a high throughput of samples and is easily kept sterile for prolonged periods of time. Porous PGA/P4HB scaffolds were partially embedded in a silicone layer, which allowed repeated and uniaxial long term mechanical straining of these constructs. The constructs were attached to Bioflex wells (Flexcell Int. Corp., USA), subjected to two different strain magnitudes for several weeks and showed differences in biochemical properties, mechanical properties and organization of the microstructure compared to the unstrained constructs. The results suggest that prolonged mechanical stimulation induces the production of collagen with a higher fraction of crosslinks, which improves the intrinsic mechanical properties of the collagen. However, too large straining resulted in detrimental effects of straining on the mechanical properties of the tissue. In addition, straining induced a different alignment of cells and collagen in the superficial layers compared to the deeper layers of the construct. By using polycarbonate rings of different height placed around the Flexercell loading posts, various strain magnitudes could be applied to individual samples while only one vacuum pressure was applied. This eliminates the risk of inter-experimental differences, as the number of experiments to culture cells at different strain magnitudes can be reduced. However, using these rings imposes limitations to the applied waveform, as with vacuum controlled devices the shape of the vacuum waveform can be controlled. When rings are used to limit deformation this type of waveform control is pointless. Therefore, an input signal of a square waveform with an amplitude of maximum vacuum pressure was chosen. In order to allow stretching of three dimensional engineered cardiovascular constructs the model system was further developed. One of the components of the tissue construct was PGA coated with P4HB, which previously did not show elastic material behavior. Therefore, part of the porous PGA scaffold was embedded in a thin layer of liquid silicone. This allowed dynamic stretching of these engineered tissues. The strain fields were validated after 2 weeks of culture (1 week strain) and the presence of the supporting silicone layer resulted in an elastic response of the engineered constructs, which is illustrated by the fact that after 2 weeks of culture the initially applied strain was preserved. However, the strain distribution after 3 weeks could not be ascertained as constructs partially detached from the supporting silicone layer, which approximately corresponds to the loss of mechanical integrity of PGA. Although the strain was not entirely defined, a dynamic component was still present. This means that controlled strain can ultimately be applied over a period of 2.5–3 weeks. Analyzing the different strain fields showed that the average strain constitutes the applied strain, which was validated for the membrane without tissue construct. However, the strain distribution was much more inhomogeneous for the tissue constructs. Possibly, the inhomogeneous deformation can be attributed to inhomogeneous tissue properties resulting from non-uniform tissue formation. A limitation to the setup is that the tissue formation (Figs. 5a–c) is constricted to FIGURE 5. Histology and microstructure of 3-weeks-old engineered cardiovascular constructs. The straining direction is from left to right. (a–c) H&E staining of engineered cardiovascular constructs cultured at 0, 4, and 8% strain, respectively. (d–f) Multiphoton images of cells (blue) and collagen (green) visualized at the surface of the engineered constructs, approximately 3 μm into the tissue. (g–i) Multiphoton images of cells and collagen visualized approximately 25 μm into the engineered tissue constructs. the surface of the construct due to the reduced supply of nutrients in the presence of the silicone layer. In the present study dynamic straining did not have an effect on proliferation. The amount of DNA per dryweight did not differ between the dynamically strained constructs and the unstrained constructs. Previously, cell proliferation was not influenced by mechanical loading in relatively long term studies. However, Mol et al. did show an elevated level of proliferation in free floating engineered cardiovascular constructs, which were not constrained mechanically. It is essential to realize that in this study the unstrained constructs were not entirely stress free. The HSVC belong to the myofibroblast phenotype and these myofibroblasts produce a continuous isometric tension. An internal tension is generated in the construct due to the fact that the engineered construct is restricted to contract by the supporting silicone layer. The internal stress generated by (myo)fibroblast contraction is sufficient to limit cell proliferation. In general, studies on biosynthesis of collagen and GAG most often show upregulation in response to mechanical straining. However, these results are often observed in short term studies, whereas for prolonged straining of engineered tissue constructs an increase in collagen production is not always observed. Our results show that the production of both GAGs and collagen per cell was even reduced in response to strain. This reduced collagen production per DNA was similar to Mol et al., who also observed a decrease in collagen production per DNA. In contrast, the fraction of HP crosslinks per collagen triple helix were increased compared to the unstrained culture condition. Crosslinks are often related to the mechanical properties of tissues. The mechanical properties of the 4% strained constructs were equal to the unstrained constructs, whereas the tangent stiffness of the 8% strained constructs was significantly reduced. Equal mechanical properties combined with an increased fraction of crosslinks and a decreased production of collagen indicates that the cells produced collagen with different intrinsic mechanical properties in order to resist the effect of mechanical straining more effectively. Increasing the strain even further resulted in equal collagen production and collagen fraction compared to the 4% strained sample. However, a decrease in mechanical properties was observed, which possibly indicates that damage was introduced to the immature collagen fibers within the engineered construct. The upregulation of crosslink formation by mechanical loading is potentially explained by an increased TGF-β secretion due to mechanical loading. TGF-β upregulates lysyl hydroxylase 2 (LH2) expression, which in its turn facilitates HP crosslink formation. In contrast to previous studies, dynamic mechanical loading did not result in an increase of the mechanical properties. Similar to Mol et al. the tangent stiffness of the constructs, created using fibrin as a cell carrier, became high in a relatively short period of time. Mol et al. showed that the effect of mechanical loading only came to expression after 4 weeks of culture. The microstructure of the strained engineered cardiovascular constructs showed a striking difference in cell and collagen orientation between the superficial layers and the deeper layers, whereas in the unstrained constructs this typical orientation was almost absent (Fig. 5). An oblique and perpendicular cell orientation has also been observed in studies where two dimensional substrates seeded with cells were subjected to strain. Similar to the superficial layers of the engineered construct, a relatively low amount of ECM was present in the 2D cultures. However, cells embedded in a 3D environment subjected to strain aligned parallel to the direction of strain. This corresponds to the alignment of cells deeper into the engineered constructs (Fig. 5). The orientation response of cells has been attributed to a strain avoidance mechanism (present in superficial layer of the construct) and cell contact guidance (present in deeper layers of the construct). Potentially the orientation response is determined by the amount of collagen surrounding the cells. In addition, in the strained samples the characteristic waviness of collagen seemed to be more present. The waviness might be related to the appearance of the non-linear behavior in engineered cardiovascular tissues (i.e., uncrimping of collagen fibers). As can be observed from the histology, the amount of collagen and cells in the layer of the construct close to the silicone is much lower. When the layer is observed with two photon microscopy (data not shown), much more scaffold compared to the superficial layer is observed. In addition, the limited amount of collagen is both randomly oriented and oriented in the direction of the scaffold fibers (contact guidance). Furthermore, only a very limited amount of cells could be detected, most likely due to the limited supply of nutrients. In this study an adapted form of the Flexercell straining system was developed, which allows simultaneous straining of individual engineered cardiovascular constructs at various strain magnitudes during one experiment. The used system and the used analyses techniques are valuable tools to obtain an improved understanding of the effects of mechanical loading on tissue formation. This will help us to elucidate the effect of mechanical strain on tissue remodeling and ultimately optimize loading protocols for TE. ACKNOWLEDGMENT The authors wish to thank Jessica Snabel and Ruud Bank of TNO Leiden for analyzing our samples for collagen content and crosslink fraction. 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Ther. 4(6):801–812, 2004.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4212, 1 ], [ 4212, 7015, 2 ], [ 7015, 10436, 3 ], [ 10436, 15405, 4 ], [ 15405, 18300, 5 ], [ 18300, 21100, 6 ], [ 21100, 23475, 7 ], [ 23475, 29059, 8 ], [ 29059, 35122, 9 ], [ 35122, 40895, 10 ] ] }
d60944292ec2e2edc20fc35da4b457bb65c2b416	{ "olmocr-version": "0.1.59", "pdf-total-pages": 15, "total-fallback-pages": 0, "total-input-tokens": 31991, "total-output-tokens": 11281, "fieldofstudy": [ "Economics" ] }	Premature Deindustrialization Risk in Thailand Ni Lar, Saitama University, Japan Hiroyuki Taguchi, Saitama University, Japan* ABSTRACT This study investigates the possibility of premature deindustrialization risk in Thailand, where the pressure of globalization and uneven industrial policies remain. This study adopts the latecomer index to materialize premature deindustrialization risk, which is expressed as the downward shift of the manufacturing-income relationship at the earlier level of income. The results of the empirical analysis confirm the presence of premature deindustrialization risk in Thailand’s regions as a result of globalization pressure (represented by China’s entry into the World Trade Organization) and uneven industrial policies conducted by the Thai government. Thus, the current industrial policies of the Thai government should be reconsidered to overcome premature deindustrialization risk in remote regions. KEYWORDS Globalization, Import Deindustrialization, Inclusive Growth, Industrial Policies, Latecomer Index, Manufacturing-Income Relationship, Premature Deindustrialization Risk, Thailand INTRODUCTION Conventionally, scholars attempt to outline economic developments by referring to the system of improving the economic and social well-being of people. Lewis (1955) presented the two-sector growth model of structural changes with an unlimited supply of labor, and Petty-Clark’s law (Clark, 1940) presented the three-sector hypothesis for the developed and developing world. Developing countries, such as those classified as low and middle incomers, however, still experience from poverty traps and income inequalities among their provinces, regions, or districts within territories, and search for ways to mitigate them. In the literature, the flying geese model by Akamatsu (1962) is renowned for charting Asian countries’ growth paths after its success in Japan, while the balanced growth (Nurkse, 1953) and the imbalanced growth (Hirschman, 1958) are also practical theories for regional development of a country. From the industrial perspective, the manufacturing sector is considered the engine of growth for a country. Kaldor (1966, 1967) found a positive relationship between the growth of manufacturing output and growth of GDP, now called Kaldor’s law. Manufacturing sector expansion improves the primary sector’s labor productivity by shifting oversupplied labor from the primary to the manufacturing sector. Therefore, the manufacturing output expands quickly, and the productivity growth, employment creation, and income growth persist. Thus, various forms of industrialization strategies and growth models have been adopted for regional development. The premature deindustrialization issue among regions/provinces, however, has not yet been fully discussed. Recently, the concept of “Premature Deindustrialization” has gained attention among scholars, economists, and policy-makers. Specifically, Dasgupta and Singh (2007) and Rodrik (2016) have stressed developing countries’ quick transition into the services sector with the reduction or destruction of the manufacturing sector. Advanced countries have already been experiencing this line of deindustrialization. However, labor productivity achievement rather than not prematurity has led to the structural changes from the secondary sector to the tertiary sector. This has resulted in employment loss but not output loss. It has, however, not been the case for developing countries since the 1980s. Developing countries have experienced a reduction in their manufacturing share of output with a reduction in their income levels. The theoretical framework of Rodrik (2016) considered developing countries as the price taker with a lack of comparative and competitive advantages; thus, they are compelled to import considerable amounts of manufacturing products from developed countries, which is called “import deindustrialization.” This premature deindustrialization should be examined since the interruption in manufacturing output would lessen the catching-up effect for developing countries. This paper examines the premature deindustrialization risk with a focus on Thailand’s regions for 1995-2019. Specifically, this study concerns manufacturing output and the latecomer index represented by the ratio of a region’s per capita gross regional product (GRP) relative to that of a benchmark region. Bangkok is selected as the benchmark region because it records the highest per capita GRP at the 2002 constant prices. The latecomer index makes it possible to identify the downward shift of the manufacturing-income relationship, thereby suggesting the existence of premature deindustrialization risk. The estimation methodology in this study follows Rodrick (2016), and Taguchi and Tsukada (2021). The ultimate objective of this study is to evaluate the industrial policies’ performance and the degree of its inclusive growth in Thailand by examining whether premature deindustrialization risk has been emerging in its local regions. The research area and scope in this study are crucial in business and academic circles and policy makers in that alleviating premature deindustrialization risk in the latecomer’s regions would lead to attaining “inclusive growth,” one of the Sustainable Development Goals established by the United Nations. The remainder of this paper is organized as follows. Section 2 briefly describes the manufacturing trends in Thailand’s economy. Section 3 reviews the literature related to premature deindustrialization and clarifies this study’s contributions. Section 4 presents the framework of econometric analysis with the methodology and data. Section 5 discusses the empirical results on the premature deindustrialization risk in Thailand. Section 6 concludes and summarizes this study. THAILAND’S ECONOMY AND ITS MANUFACTURING TRENDS Thailand is a developing country and is attempting to overcome its middle-income trap. Its per capita GDP has been higher than the East Asia and Pacific average (excluding high-income countries), with a substantial rise during the 1960s and 1980s. Its economic structure has changed from agriculture to manufacturing. The share of manufacturing export out of total exports rose from 1.2% in 1960 to 77.8% in 1992 (Falkus, 1995). Thailand’s economic growth rate had been on a rise until the late 1990s. Its growth rate was one of the highest, at more than 7% during the boom, and an average of 5% even in the severe recession period of 1999–2005 (Glassman, 2007; World Bank, 2021). However, it started facing growth slow-down in 2013, and the growth rate fell to lower than the East Asia and Pacific country average (excluding high-income countries) until 2020. Thailand’s economy has been severely impacted by COVID-19. Since the early 1960s, industrialization and urbanization have been the driving forces toward Thailand’s modernization (Biggs et al., 1990; Cuyvers et al., 1997; Panpiemras, 1988; World Bank, 1993). In particular, Thailand’s industrialization has been impressive since it has been accompanied by job creation in the millions, welfare improvement, longer years of education and enrolment, and improvements in health security status (World Bank, 2021). This sector’s contributions to GDP surpassed that of the agriculture sector during 1986. Thailand’s growth path became export-led industrialization in 1975-78, although it had been practicing import-substitution strategy during 1966-1972 (Falkus, 1995). However, the focus of Thailand’s industrialization policies and strategies has been inadequate with regard to rural areas, sectoral linkage, and economic distribution, despite its import-substitution industrialization strategy propelling the rapid industrialization (Panpiemras, 1988; Poapongsakorn, 1995; and Pansuwan, 2010). Consequently, income inequality increased due to massive domestic migration from rural regions to industrial areas, since the industrialization strategies were primarily concentrated in the Bangkok Metropolis Region (Hussey, 1993). The shift in the industrial policy from centralization to decentralization began in 1987 to encourage private investors to invest in remote areas. The policy effects had, however, been confined to the Central and Northeast regions in the early 1990s (Poapongsakorn, 1995). The regions that the Thai government did not focus on for industrialization faced slow growth, income disparity, and a dominance of the agriculture sector, even though Thailand’s Ministry of Industry intended to promote provincial and rural industry development1 by supporting infrastructure and other related facilities (Pansuwan, 2010). ADB (2015) also warned against unbalanced growth among various regions: the North, Northeast, and Southern regions lag behind Bangkok and the Central region. The structural transformation of Thailand’s economy depicted in Figure 1-a reveals that the agricultural share of value-added reduces between 1995-2019, while the share of services continues to be the highest contributor among the four sectors. Figure 1-b illustrates the relationship between the manufacturing share in GDP and GDP per capita (2002 constant prices). GDP per capita grows from 85,900 Baht in 1995 to 157,700 Baht in 2019. Manufacturing share in GDP forms an inverted-U shape with the turning point being 31% and 113,000 Baht in GDP per capita in 2006-2007. From this nationwide relationship, Thailand appears to have experienced technological-driven deindustrialization, and ordinary transformation from agriculture to services through manufacturing along with income growth, just like that in advanced economies. The regional manufacturing-income relationship, however, has not necessarily followed the nationwide relationship because some regions lag in development due to the insufficient effects of Thailand’s industrial policies. Thus, the regional manufacturing-income relationship is worth investigating. Figure 2 presents the industrial transformation in Thailand by region. There is a clear contrast between the two groups (Eastern and Central regions and the other regions): the Eastern and Central regions concentrate on the manufacturing sector, whereas in the others, the service sector has a dominant share. Bangkok and its vicinities appear to have entered a mature stage with an increase in the service sector’s share, as their GRP per capita (2002 constant prices) is the highest among the regions. The Eastern and Central regions appear to follow the robust industrialization process as their manufacturing shares reach a high level, namely, above 50%. In the other regions, the manufacturing shares stay at lower levels, implying the existence of premature deindustrialization risk. The additional observation is the degree of convergence in GRP per capita among regions in Thailand’s regions. The Organisation for Economic Co-operation and Development (OECD; 2016) argued that convergence depends on labor productivity and industrial policies. Figure 3 illustrates the gap in GRP per capita between Bangkok and other regions. It shows that the convergence is realized slowly, but its pattern has stopped (the gap levels off or even widens slightly in the Northeastern and Northern regions) since 2011. From these observations on industrial transformation and income gap among Thailand’s regions, the question that arises is whether there has been premature deindustrialization risk in underdeveloped regions, and if this related to the uneven industrial policies in Thailand. This section reviews the literature related to the issue on premature deindustrialization and clarifies this study’s contributions. The reviewed literature is organized in Table 1. The seminal works as the origin of the study of premature deindustrialization are Dasgupta and Singh (2007) and Rodrik (2016). Dasgupta and Singh (2007) initially proposed the concept of premature deindustrialization. They examined the role of manufacturing and services sectors in developing countries and argued that manufacturing is still a core contributor of growth in developing countries, as in Kaldor’s law. They used the term “premature deindustrialization” in the sense of a fall in the share of manufacturing output and employment, with an increase in service share taking place at the lower income levels in developing countries. However, they argued that deindustrialization Figure 2. Structural Transformation Trends in Thailand's regions (Sources: NESDC stat (https://www.nesdc.go.th/nesdb_en/main.php?filename=index)) in developing countries could be classified into two types: technological-driven and pathological. India, for instance, belongs to the former type, and several Latin American and African countries fall into the latter type, where their economies have faced balance-of-payment problems under import substitution industrialization strategies. Rodrik (2016) polished the concept and implication of premature deindustrialization. He constructed a simple two-sector theoretical model with manufacturing and non-manufacturing sectors, and demonstrated that the developing countries opening up to trade tend to be price-takers in global markets for manufacturing, and those who lack a strong comparative advantage in manufacturing must become net importers of manufacturing under a decline in the relative price of manufacturing and the rise of China, thereby leading to deindustrialization in both employment and output. He also conducted empirical estimations for cross countries and different country groups during the late 1940s to post 2010. The empirical results showed that Latin American and African countries suffered from both employment- and output-deindustrialization as these countries discovered their resources and experienced a rise in commodity prices. However, Asian countries that maintained a comparatively stronger advantage in manufacturing avoided premature deindustrialization. The results of the pre- pre-and post-1990 estimations also indicated that late industrializers reach their peak levels of industrialization, as measured by manufacturing employment and output shares at lower income level, which is around 40% of the level gained by early industrializers. Fujiwara and Matsuyama (2020), extending the theoretical model of Rodrik (2016), constructed the model of “technology gaps” representing the heterogenous capacity to adopt the frontier technology to describe premature deindustrialization. Based on the theoretical model of Rodrih (2016), a lot of empirical studies have been conducted for identifying the existence of premature deindustrialization in the levels of multi and specific countries. Regarding multi-country analyses, Sato and Kuwamori (2019), targeting non-OECD and OECD countries as samples, confirmed the existence of premature deindustrialization in non-OECD countries in that their share of manufacturing employment and output hit a peak at their lower income levels than those of OECD countries. Daymard (2020) suggested the occurrence of premature Table 1. Literature Review \| Sample \| Methodology \| Message \| \|--------\|-------------\|---------\| \| [Origins of PD studies] \| \| \| \| Dasgupta & Singh 2006 \| Panel with 14 countries for 1986-2000 \| Inverse U-shape for manufacturing-income nexus \| - Pathological PD in Latin America & Africa<br>- Technology-driven PD in Latin America<br>- PD in Latin America & Africa<br>- No PD in Asia with comparative advantage in manufacturing \| \| Rodrik 2016 \| Panel with 42 countries for 1960s-2010s \| Inverse U-shape for manufacturing-income nexus \| - PD in Latin America & Africa<br>- No PD in Asia with comparative advantage in manufacturing \| \| [Theoretical study] \| \| \| \| Fujisaki & Matsumoto 2020 \| Theoretical Model: A Technology-Gap Model \| \| - PD is driven by a technology gap: the frontier technology whose productivity growth rate differs across the sectors. \| \| [Empirical studies: multi-country analyses] \| \| \| \| Sato & Kramm 2019 \| Panel with 42 countries for 1950-2014 \| Inverse U-shape for manufacturing-income nexus \| - PD in non-OECD<br>- No PD in OECD \| \| Dayand 2020 \| Panel with 41 countries for 1950-2013 \| Panel fixed-effect model with two-stage least square estimation \| - The difficult creation of manufacturing jobs in Latin America and Africa—a trait commonly referred to as PD \| \| Nayyar et al. 2021 \| 43 countries for 2000-2014 \| Growth Decomposition Exercise \| - The rising share of services is largely not driven by a statistical artifact. The prospect of service-led development in lower-income countries is limited. \| \| Ravidran & Babu 2021 \| Panel with 54 middle-income countries for 1992-2017 \| Panel fixed-effects and bootstrap-corrected dynamic fixed-effect models \| - The rise of income inequality with PD if the displaced workers are absorbed into less productive and informal market services \| \| Botts et al. 2022 \| Panel with 36 countries for 1980-2017 \| Inverse U-shape for manufacturing-income nexus \| - Net capital inflows as a potential source of PD \| \| [Empirical studies: regional multi-country analyses] \| \| \| \| Caldentey & Vasquez 2020 \| 8 Latin American countries \| Descriptive analysis \| - Premature fiscalization connected with the process of PD in Latin America \| \| Iseri & Howard 2018 \| Panel with Sub-Saharan Africa 35 countries for 1993-2016 \| Panel fixed-effect model with General Method of Moments estimation \| - The transition into an industrial economy is constrained not only international competition and the poor business climate, but also the low participation in the global value chains. \| \| Taguchi & Tsukada 2021 \| Panel with 14 Asian countries for 1970-2018 \| Inverse U-shape for manufacturing-income nexus and intra-sectoral index \| - PD risk in Asia \| \| [Empirical studies: specific-country analyses] \| \| \| \| Lee 2020 \| Malaysia \| GVC analysis for 2006-2015 & micro analysis of 581 firms in 2015 \| - PD in Malaysia has been accompanied by a decline in the country's participation in GVCs \| \| Hameed & Khan 2015 \| Pakistan \| Descriptive sectional analysis for 1959-2014 \| - Pakistan is on the brink – if not already in the process – of PD, as a result of stagnation in manufacturing since 2007 \| \| Andriansyah & Irawati 2018 \| Indonesia panel with 4 islands for 1986-2015 \| Regional panel analysis \| - The speed of deindustrialization varies between islands and PD is identified in Indonesia \| \| Ismail & Hadiadi 2020 \| Indonesia panel with 26 provinces for 1987-2018 \| Inverse U-shape for manufacturing-income nexus \| - PD in Indonesia (the peak is lower than the threshold value of Rodrik 2016) \| Note: PD means premature deindustrialization. <br>Source: Author's description. deindustrialization in Latin America and Africa from the viewpoint of manufacturing jobs. Nayyar et al. (2021) argued that premature deindustrialization matters in lower-income countries because the prospect of their service-led development is limited. Ravindran and Babu (2021) identified the rise of income inequality with premature deindustrialization in case that workers are absorbed into low-productive and informal market services. Botta et al. (2022) found that net capital inflows are as a potential source of premature deindustrialization. As for regional multi-country analyses, Caldentey and Vemengo (2021) analyzed premature financialization in connection with the process of premature deindustrialization in Latin America. Ssozi and Howard (2018) discussed the premature deindustrialization in Sub-Saharan Africa in relation to the low participation in global value chains. Taguchi and Tsukada (2021) presented the risk of premature deindustrialization with a focus on Asian developing economies by applying the latecomer index to demonstrate downward shifts in the latecomers’ manufacturing-income relationship. They showed that the risk is higher for manufacturing trade-deficit countries and South Asian countries, and also suggested the need for greater participation in global value chains to avoid premature deindustrialization. There have been also specific-country studies that also verified the existence of premature deindustrialization: in Malaysia (Lee, 2020), Pakistan (Hamid and Khan, 2015), and Indonesia (Andriyani and Irawan, 2018; Islami and Hastiadi, 2020). The two studies in Indonesia conducted a regional panel analysis to verify the existence of premature deindustrialization. In sum, there are a limited number of specific-country empirical studies of premature deindustrialization, particularly, with regional panel analyses (only Andriyani and Irawan, 2018; Islami and Hastiadi, 2020), whereas a large number of multi-country studies exist. In addition, it is only Taguchi and Tsukada (2021) that applied the latecomer index to explicitly identify the risk of premature deindustrialization. This study’s contributions to fill the literature gap could be highlighted as follows. First, this study targets Thailand with a regional panel analysis as in the two studies in Indonesia, thereby contributing to enriching empirical evidence in specific-country studies. Second, this study applies the latecomer index to verify the risk of premature deindustrialization as in Taguchi and Tsukada (2021). The majority of previous empirical studies have concentrated on the comparison in industrialization peaks between developed and developing economies and have proved its lower peak with a lower income stage in developing economies to show premature deindustrialization. However, all developing economies and regionally local economies do not necessarily reach the industrialization peak. The latecomer index makes it possible to identify downward shifts in latecomers’ manufacturing–income relationship regardless of the existence of the peak in manufacturing ratio. For the economies that have not reached the peak yet, its downward shift suggests the upcoming peak-out at a lower manufacturing ratio in a lower income stage, namely, the symptom and risk of premature deindustrialization. This study applies the latecomer index to the regional manufacturing–income analysis for the first time. The application of the index in regional analysis also contributes to evaluating a country’s industrial policies’ performance and the degree of its inclusive growth. METHODOLOGY This study follows the theoretical framework and the empirical specification presented by Rodrik (2016). He constructed a simple two-sector theoretical model with manufacturing and non-manufacturing sectors, and derived the different outcomes for a closed economy in advanced countries (exogenous in net manufacturing exports $x$ and endogenous in manufacturing price $P_m$) and a small open economy for developing countries (exogenous in $P_m$ and endogenous in $x$; namely, price takers in global manufacturing markets), as Table 2 shows. This model could explain premature deindustrialization in the case of a developing country as a small open economy that liberalizes trade. Suppose that the global supply of manufacturing exceeds that of non-manufacturing with technological progress in manufacturing, and the relative price of manufactured goods $(P_m < 0)$ declines for all countries under globalization. In this case, developing countries with less technological progress in manufacturing (the increase in $\theta_m - \theta_n$ is less than the decline in $P_m$) witness a decline in the output and employment share of manufacturing. Then, only countries with a manufacturing productivity growth sufficient to offset the relative-price decline (having a comparative advantage in manufacturing) can avoid premature deindustrialization. Regarding the empirical specification, this study applies the equation with the inverted U-shaped manufacturing-income nexus proposed by Rodrik (2016), which controls for the effect of demographic and income trend with their quadratic terms. However, this study modifies the Rodrik specification by adopting the latecomer index as in Taguchi and Tsukada (2021) to demonstrate downward shifts in the regional latecomers’ manufacturing-income relationship to verify the risk of premature deindustrialization: \[ \ln \text{ manrit} = q_0 + q_1 \ln \text{ popit} + q_2 (\ln \text{ popit})^2 + q_3 \ln \text{ grppit} + q_4 (\ln \text{ grppit})^2 + d_1 \text{ lacit} + d_2 \text{ lacit} d_99 + d_3 \text{ lacit} d_{02} + d_4 \text{ lacit} d_{06} + d_5 \text{ lacit} d_{12} + f_i + \varepsilon_{i,t} \] (1) where the subscripts i and t denote the regions (the seven regions in Thailand) and years (1995–2019), respectively; $\text{manr}$ represents the output ratios of manufacturing in GRP in 2002 constant prices; $\text{pop}$ and $\text{grpp}$ indicate the region’s population size and GRP per capita in 2002 constant prices; $\text{lac}$ denotes the latecomer index; $d_{99}, d_{02}, d_{06}, d_{12}$ represent time dummies for 1999–2019, 2002–2019, 2006–2019, and 2012–2019, respectively; $f_i$ shows a time-invariant regional-specific fixed effect; $\varepsilon$ denotes a residual error term; $\theta_{0…4}$ and $\delta_{1…5}$ stand for estimated coefficients, respectively; and $\ln$ shows a logarithm form. The key variable in Equation (1) is the latecomer index $(\text{lac})$ proposed by Taguchi and Tsukada (2021) for examining premature deindustrialization risk in their cross-country panel analysis. In this study, the index is expressed as the ratio of GRP per capita of a region relative to that of a benchmark region in each year. Bangkok is selected as the benchmark region because it records the highest per capita GRP at the 2002 constant prices. Thus, the index shows the degree of delayed development of a region relative to Bangkok. The significance and sign of the latecomer index’s coefficient ($\delta$) are critical for identifying the premature deindustrialization risk. The regions are considered to be at premature deindustrialization risk if the coefficient ($\delta$) is significantly positive, since it reveals... the linkage between a region’s delayed development and its lower manufacturing output ratio. This relationship is called the risk of premature deindustrialization because it implies that the regions would reach their peak in manufacturing output ratio at a lower-income level than Bangkok. Equation (1) also equips the cross-terms of the latecomer index $ \text{lac} $ with the time dummies for 1999–2019 ($ d_{99} $), 2002–2019 ($ d_{02} $), 2006–2019 ($ d_{06} $), and 2012–2019 ($ d_{12} $). This is because the regional manufacturing activities related to premature deindustrialization also appears to have been affected by the following events. First, Thailand suffered from the 1997-98 financial crisis, and continuous capital flights depressed the manufacturing activities at the regional level as well. Second, China’s entry into the World Trade Organization (WTO) in 2001 affected manufacturing in Thailand because it led to massive inflows of lower priced manufactured products from China. Third, the political crisis during 2005–06, and the flood in 2011 also dampened the Thai manufacturing sector. Regarding the variable of GRP per capita, if the coefficients hold $ \theta_3 > 0 $ and $ \theta_4 < 0 $ at the conventionally significant level, the relationship between the regions’ manufacturing output share and GRP per capita would form an inverted U-shaped curve. Equation (1) contains the region-specific fixed effect, $ f_i $, as a control variable for the panel estimation. Each region is embedded with time-invariant factors such as geography and resource endowments (not distributed randomly among the regions), affecting manufacturing activities. The fixed effect absorbs all these factors, including unobservable ones, and contributes to avoiding biased estimation. The estimation does not include the time-specific dummy because the sample period is limited, and the aforementioned time dummies cover most economic fluctuations. A panel dataset is then constructed for the seven Thailand regions for 1995–2019. All the data for the estimation of Equation (1) are retrieved from the Office of the National Economic and Social Development Council (NESDC) Stat, which is the most reliable authority of statistics in Thailand. The descriptive statistics for the data are presented in Table 3. RESULTS AND DISCUSSION Table 4 reports the estimation result with estimation (a) being without any time dummies as the cross-terms, and estimations (b), (c), (d), and (e) being those with the time dummies adding $ d_{99} $, $ d_{02} $, $ d_{06} $, and $ d_{12} $ as the cross-terms, respectively. In all the results, the coefficients of GRP per capita satisfy $ \theta_3 > 0 $ and $ \theta_4 < 0 $ at the conventionally significant level, thereby showing the inverted U-shaped relationship between the regions’ manufacturing output share and GRP per capita. The turning point can be computed by the simplified equation: \[ \ln \text{manr}_{it} = \varphi_0 + \varphi_1 \ln \text{grpp}_{it} + \varphi_2 \left( \ln \text{grpp}_{it} \right)^2 \] (2) Table 3. Descriptive Statistics \| Variables \| Observations \| Mean \| Median \| Standard Deviation \| Minimum \| Maximum \| \|-----------\|--------------\|-------\|--------\|--------------------\|---------\|---------\| \| Dependent Var \| \| \| \| \| \| \| \| $ \ln \text{manr} $ \| 175 \| 3.203 \| 3.221 \| 0.557 \| 2.214 \| 4.127 \| \| Explanatory Var \| \| \| \| \| \| \| \| $ \ln \text{pop} $ \| 175 \| 8.924 \| 9.070 \| 0.663 \| 7.966 \| 9.966 \| \| $ \ln \text{grpp} $ \| 175 \| 11.468 \| 11.340 \| 0.778 \| 9.991 \| 12.726 \| \| $ \text{lac} $ \| 175 \| 0.453 \| 0.286 \| 0.327 \| 0.078 \| 1.003 \| Sources: NESDC stat at https://www.nesdc.go.th where the GRP per capita at the turning point is $ \exp \left( \varphi_1 / 2 \varphi_2 \right) $. It is calculated as 221,562 Bath in 2002 constant prices per capita, which is a reasonable level among the regions. This income level at the peak of industrialization can be converted into around 5,000 US dollars using exchange rate in 2002. Islami and Hastiadi (2020) also estimated the level of GDP per capita at the maximum industrialization as 6,285 US dollars in Indonesia. Thus, the peak-incomes in Thailand and Indonesia are similar, and both are far below 47,099 US dollars in the pre-1990 and 20,537 US dollars in the post-1990, estimated as the maximum industrialization income level by Rodrik (2016). This implies the existence of premature deindustrialization as a nation-wide level in both countries. Figure 4 displays the relationship between manufacturing output share and GRP per capita in each of the seven regions in Thailand. Bangkok and the Eastern region already surpass the turning point, and the Central region is approaching it. The rest of the regions are far behind the turning point with their lower share of manufacturing output. All the estimation results from (a) to (e) contain significant coefficients with positive signs on the latecomer index and its cross-terms with the time dummies. This indicates the downward shift of Table 4. Estimation Results \| Estimation \| a \| b \| c \| d \| e \| \|------------\|---\|---\|---\|---\|---\| \| Const. \| 27.202* \| 21.143 \| 22.919 \| 24.304* \| 24.242* \| \| ln pop \| 2.647 \| 2.341 \| 2.951 \| 3.709 \| 3.428 \| \| (ln pop)^2 \| -0.160* \| -0.152 \| -0.192 \| -0.242** \| -0.233 \| \| ln grpp \| 3.406* \| 2.678* \| 2.609* \| 2.403* \| 2.768* \| \| (ln grpp)^2\| -0.150* \| 0.116* \| 0.114* \| -0.106* \| -0.125* \| \| lac \| 0.911* \| 0.643* \| 0.497** \| 0.276 \| 0.386 \| \| lacd99 \| 4.469 \| (2.894) \| (2.192) \| (1.108) \| (1.485) \| \| lacd02 \| 0.108*** \| 0.068 \| 0.083* \| 0.086** \| \| lacd06 \| (2.758) \| (1.615) \| (1.970) \| (2.047) \| \| lacd12 \| 0.103* \| 0.105 \| 0.128*** \| \| Regional fixed effect \| Yes \| Yes \| Yes \| Yes \| Yes \| \| Period fixed effect \| - \| - \| - \| - \| - \| \| Number of regions \| 7 \| 7 \| 7 \| 7 \| 7 \| \| Number of observations \| 175 \| 175 \| 175 \| 175 \| 175 \| Note. , , and ** denote the rejection of null hypothesis at 90%, 95%, and 99% levels of significance respectively. t-statistics are in parentheses. Sources: Author’s estimation the manufacturing-income relationship for the latecomer regions, thereby suggesting the existence of premature deindustrialization risk in the latecomer regions. The subsequent description focuses only on the estimation result (e) because it contains all the variables on the latecomer index. In this result, the coefficients are significantly positive in the cross-terms of $ lac_{it} d99 $, $ lac_{it} d02 $, and $ lac_{it} d06 $. Thus, it implies that the 1997-98 financial crisis, China’s entry into the WTO in 2001, and the political crisis during 2005-06 depressed manufacturing activities in the latecomer regions, thereby contributing to the rise of premature deindustrialization risk. Among the coefficient sizes, $ lac_{it} d02 $ is the largest, suggesting that the globalization effect caused by China’s entry into the WTO in 2001 is the major factor that contributed to the premature deindustrialization risk in the latecomer regions’ economies. This result has a similarity to the outcomes of Taguchi and Tsukada (2021) that could showcase downward shifts of the latecomers’ manufacturing-income relationship with the progress in globalization (the rise of premature deindustrialization risk) in the Asian country panel analysis. Both results are in line with theoretical framework of “import deindustrialization” proposed by Rodrick (2016). Then, the largest contribution of this study is that it could verify the existence of premature deindustrialization risk in regional level in a specific country, thereby being able to bring this result to industrial-policy discussion and evaluation. Once premature deindustrialization risk is identified in the latecomer regions in Thailand, the question of how to avoid it comes up. As discussed in Section 2, the current industrial policies by the Thai government have not necessarily focused on the industrial development of the latecomer regions. In fact, the Northern and Northeastern regions are still far behind others in manufacturing development, as shown in Figures 2 and 4. The suggestion provided by Rodrick (2016) for avoiding premature deindustrialization even under “import deindustrialization” is to create comparative and competitive advantages in manufacturing sectors in a country’s economy. In the context of regional development within a country, overcoming the premature deindustrialization in latecomer regions appears to lead to attaining “inclusive growth” in an economy. Inclusive growth is defined by the OECD as the economic growth that is distributed fairly across society and creates opportunities for all². Ianchovichina and Lundstrom (2009) also argued that the focus of inclusive growth is on ![Figure 4. Turning Point in Thailand’s regions (Sources: Author’s estimation based on NESDC stat)](image-url) productive employment rather than on direct income distribution as a means of increasing income for excluded groups. Thus, the fundamental role of government policies for avoiding premature deindustrialization is to prioritize the regional development of infrastructure and human resources. It will enable the latecomer regions to materialize their comparative and competitive advantages in the manufacturing sector. CONCLUSION This study confirms the presence of premature deindustrialization risk in Thailand’s regions as a result of the pressure of globalization (represented by China’s entry into the WTO) and uneven industrial policies conducted by the Thai government. From a regional perspective, the Northeastern and Northern regions are still far behind other regions in manufacturing development, which suggests that latecomer regions are under premature deindustrialization risk. Thus, the current industrial policies of the Thai government should be reconsidered to overcome this risk in the latecomer regions. Specifically, the government should prioritize regional development of infrastructure and human resources so that the latecomer regions can realize their comparative and competitive advantages in the manufacturing sector. A limitation of this study is the lack of detailed analyses in individual provinces and manufacturing sectors, including the impact of globalization and strategic policy analysis to overcome premature deindustrialization in the latecomer regions. Thus, further research should be conducted by collecting more detailed data and factual evidence. FUNDING AGENCY This research received a research support allowance from the Japan Society for the Promotion of Science. The authors have covered the Open Access Processing fee for this article in full. REFERENCES Akamatsu, K. (1962). A historical pattern of economic growth in developing countries. 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A World Bank Policy Research Report. Oxford University Press. World Bank. (2021). World Development Report 2021: Data for Better Lives. World Bank. ENDNOTES 1 Nine provinces were chosen for development target according to Pansuwan 2010: Nakhon Ratchasima, Khon Kaen, Nakhon Sawan, Phitsanulok, Chiang Mai, Saraburi, Ratchaburi, Surat Thani, and Songkhla. 2 See the website: https://www.oecd.org/inclusive-growth/.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2589, 1 ], [ 2589, 6972, 2 ], [ 6972, 11559, 3 ], [ 11559, 12429, 4 ], [ 12429, 12575, 5 ], [ 12575, 15076, 6 ], [ 15076, 18712, 7 ], [ 18712, 23110, 8 ], [ 23110, 26048, 9 ], [ 26048, 29979, 10 ], [ 29979, 32447, 11 ], [ 32447, 35249, 12 ], [ 35249, 37046, 13 ], [ 37046, 40530, 14 ], [ 40530, 42461, 15 ] ] }
f78189245d7a021c509358193697f0e83cc646bc	{ "olmocr-version": "0.1.59", "pdf-total-pages": 15, "total-fallback-pages": 0, "total-input-tokens": 35359, "total-output-tokens": 9904, "fieldofstudy": [ "Biology", "Medicine" ] }	HMMR potential as a diagnostic and prognostic biomarker of cancer—speculation based on a pan-cancer analysis Junyi Shang1†, Xiaoju Zhang1†, Guangjie Hou2 and Yong Qi1† 1Department of Respiratory and Critical Care Medicine; Henan Provincial People’s Hospital; People’s Hospital of Zhengzhou University, Zhengzhou, China, 2Department of Thoracic Surgery; Henan Provincial People’s Hospital; People’s Hospital of Zhengzhou University, Zhengzhou, China Background: Although the status of universal upregulation for the Hyaluronan-Mediated Motility Receptor (HMMR) in pan-cancer is still unknown, HMMR is upregulated and associated with poor prognosis for some tumors. Methods: Exploring HMMR expression in different tumor types using The Cancer Genome Atlas (TCGA) or other public databases for a pan-cancer analysis, exploring the relationship between HMMR and tumor prognosis, and exploring the role of HMMR in tumor immunity. Results: No matter the pairing or unpairing of data, HMMR expression generally increased compared to corresponding normal tissue. Based on a CCLE study, our results indicated that HMMR is widely expressed in various tumor cells. For most tumor types, high HMMR expression was associated with reduced Overall Survival (OS), Return to Functional Status (RFS), and Platinum Free Interval (PFI). ROC curves indicated that HMMR displays high prediction potential for most tumor types. In pan-cancer, HMMR is correlated with some clinical staging, immune cells, and immune checkpoints for some tumors. The GO/KEGG enrichment analysis results for proteins most closely related to HMMR indicate that the most highly enriched pathways are all related to tumor development. Conclusions: Our pan-cancer analysis of HMMR suggests that HMMR can be used as a potential diagnostic and prognostic indicator of pan-cancer and that HMMR may be involved in tumor development. KEYWORDS HMMR, pan-cancer, prognosis, immune infiltration, TCGA Introduction Cancer occurrence caused by multiple biologic processes is a life-threatening disease and, worldwide, imposes a substantial economic burden (1–3). Each year, tens of thousands of people die of cancer. Due to the lack of adequate diagnosis and therapy, cancer causes a higher mortality rate in less developed countries. Early diagnosis and treatment can significantly reduce cancer morbidity, and effective treatments can increase patient survival rates. Cancer treatments include surgery, chemotherapy, radiation, targeted therapy, immunotherapy, and so forth. Accurate cancer diagnosis requires useful predictive markers. Implementing immune therapy from immune- suppressor checkpoints, such as Programmed Cell Death Protein 1/Programmed Death-Ligand 1 (PD1/PDL1) expression, is often beneficial. Although radical surgery is the most effective treatment, many cancer patients do not benefit from surgery (4). Chemotherapy, radiotherapy, targeted therapies, and immunotherapies do not apply to all patients (5). As such, the discovery and application of new diagnostic markers and therapeutic targets are never out-of-date. Exposing general phenomena related to cancer has become one of the major hotspots in cancer research. Bioinformatics has made it easier to conduct commonality research related to tumors. One such commonality is the role of the Hyaluronan-Mediated Motility Receptor (HMMR) in breast cancer (6, 7), pancreatic cancer (8), and lung adenocarcinomas (9). HMMR, also called cluster of differentiation 168 (CD168), to date, the role of HMMR in pan-cancer has not yet been explored. The purpose of this study was to analyze the expression of HMMR in pan-cancer and its potential value for diagnostic and prognostic use. Materials and methods The expression of HMMR in pan-cancer The GTEx dataset was obtained from TCGA (https://portal.gdc.cancer.gov/) and processed through Toil. RNAseq data were downloaded from the HTSeq-FPKM data of TCGA Pan-Cancer. The abbreviations for cancer types are shown in Supplementary Table S1. The RNAseq data of tumors and paracancerous tissues in different cancers also came from the HTSeq-FPKM data of TCGA Pan-Cancer for retention paired samples. The differential expressions of HMMR in GTEx, in paired or unpaired samples from TCGA, were all statistically processed using R (Version 3.6.3) and ggplot2 [Version 3.3.3] for visualization. For analyzing differential HMMR expression between the tumor and adjacent normal tissue, we also used TIMER (https://cistrome.shinyapps.io/timer/) (10). To validate the reliability of TCGA, we used ONCOMINE (https://www.oncomine.org), a public database for retrieving HMMR expression in different cancers. Finally, the HMMR expression matrix for 946 cell lines from 22 types of cancers was obtained from the CCLE (https://portals.broadinstitute.org/ccle/about). To construct HMMR distributions in different tumoral tissues, we used R (v4.0.3) and ggplot2 (v3.3.3). The relationship between HMMR and overall survival (OS) We used the Kaplan-Meier Plotter (https://www.kmplot.com) to analyze the association between HMMR and OS in pan-cancer. Next, prognostic data for 33 types of cancer were downloaded from TCGA. Samples were then distributed into low and high groups based on HMMR expression. The R survminer package (Version 0.4.9) was used for visualization, and the survival package (Version 3.2–10) was used for statistical analyses of the survival data. The HR and p values for each tumor prognosis-based HMMR expression were determined using the Cox regression model, then constructed the forest plots. The relationship between HMMR and recurrence free survival (RFS), constructed the forest plot for progress free interval (PFI) The Kaplan Meier plotter was also used for analyzing the relationship between HMMR and RFS in pan-cancer. We downloaded pan-cancer clinical data from TCGA, divided the data into a high HMMR expression group and a low HMMR expression group, and then obtained the HR and P for each type of cancer-based on HMMR expression using a Cox regression model. Statistical analyses and visualization were determined using the R survminer package (Version 0.4.9) and the survival package (Version 3.2–10). We employed forest plots to display the PFI for each tumor type. ROC curves based on HMMR expression RNAseq data were obtained from the TCGA dataset. ROC curves were constructed to predict normal cells or cancer. We used R (Version 3.6.3) for statistical analyses and visualization. The pROC package (Version 1.17.0.1) and the ggplot2 package (Version 3.3.3) were also simultaneously used for analyses, visualization, and for the calculation of the confidence intervals and curve areas. The correlation between HMMR and clinical stage RNAseq and clinical information were obtained from TCGA. Normal and control samples were removed. We retained samples using clinical information. An analysis was implemented for HMMR and the T-stage, with a Kruskal-Wallis test employed for statistical analyses. For statistical analyses and visualization, we utilized R (Version 3.6.3). The program ggplot2 (Version 3.3.3) was also used for visualization. The relationship between HMMR and immune infiltration The RNA-seq data of 33 tumor types were downloaded from the TCGA database. mRNA expression data was also downloaded from 33 tumors with paired normal tissue samples. The immune-related assessment was performed using the immuneDEconv package. The package consists of six integrated algorithms, including TIMER, xCell (11), MCP-counter (12), CIBERSORT (13), EPIC (14), and quanTseq (15). R (v4.0.3) was used for statistical analyses. The significance of the two groups was performed using a Wilcoxon rank sum test. The correlation between HMMR and immune checkpoints SIGLEC15, IDO1, CD274, HAVCR2, PDCD1, CTLA4, LAG3, and PDCD1LG2 are immune checkpoint-related transcripts. We extracted these eight gene expressions of 33 tumor types from TCGA and calculated correlations between HMMR and checkpoint-related transcripts. We used R (Version 4.0.3) for statistical analyses. A rank sum test was used to detect two sets of data. p-values ≤ 0.05 were considered statistically significant. The correlation between HMMR and tumor mutation burden (TMB) and microsatellite instability (MSI) Downloaded The RNA-seq database of 33 tumor patients from TCGA, and each tumor matched mRNA expression data Derived TMB from the article by Thorsson et al. (16). and derived MSI from the article by Bonneville et al. (17). Then performed statistical analyses by using R software (Version 4.0.3). A rank sum test was employed on two sets of data. p value < 0.05 was considered statistically significant. Analysis of molecular correlates The STRING Database (https://string-db.org/) is a Protein-Protein Interaction (PPI) analysis database that can predict protein-protein interactions of known proteins. Entered HMMR into the STRING website by selecting Homo sapiens. Then obtained the top ten HMMR-related proteins and downloaded the results. For constructing the PPI network, we employed R (Version 3.6.3) and the igraph package (Version 1.2.6) for statistical analyses and visualization. Similarly, we obtained the top 50 proteins most tightly associated with HMMR. Then performed enrichment analysis for GO and KEGG terms. The ggplot2 package (Version 3.3.3) and the clusterProfile package (Version 3.14.3) were used for statistical analysis and visualization. The protein expression of HMMR in pan-cancer The Human Protein Atlas (https://www.proteinatlas.org/) is the most extensive collection of immunohistochemistry (IHC) data mapping all human proteins. First, we collected the protein expressions of HMMR in different cancer types and the corresponding normal organs from this website. Selected samples of 5 tumor types to represent the antibody stains in 20 different cancers. HMMR expression is low or not detected in these five cancer types’ corresponding normal organs but was the medium or high expression in tumor tissues. The stack bar plot shows the proportion of moderate or increased expression of HMMR in these five tumors; the stack bar plot was plotted by http://www.bioinformatics.com.cn, which is a free online platform for data analysis and visualization. Meanwhile, We collected cancer tissues and paired adjacent normal tissues from eight lung adenocarcinoma patients with pathologic stage I or II. Western blotting detected the HMMR expression, and paired t-test was used to analyze the difference between cancer and paired adjacent normal tissues. This study was approved by Henan Provincial People’s Hospital ethics committees. Results Differential HMMR expression in various cancers HMMR mRNA expression levels in ACC, BLCA, BRCA, CESC, CHOL, COAD, DLBC, ESCA, GBM, HNSC, KICH, KIRC, KIRP, LGG, LIHC, LUAD, LUSC, OV, PAAD, PCPG, PRAD, READ, SKCM, STAD, THCA, THYM, UCEC, and UCS were determined to be higher than in normal tissues, except for LAML and TGCT (Figure 1A). A Wilcoxon rank sum unpaired test for TCGA data indicated that the expression of HMMR mRNA in BLCA, BRCA, CESC, CHOL, COAD, ESCA, GBM, HNSC, KIRC, KIRP, LIHC, LUAD, LUSC, PAAD, PCPG, PRAD, READ, SKCM, STAD, THCA, THYM, UCEC, and UCS were determined to be higher than in normal tissues, except for LAML and TGCT (Figure 1B). For TCGA paired samples, HMMR mRNA expression in BLCA, BRCA, CHOL, ESCA, HNSC, KICH, KIRC, KIRP, LIHC, LUAD, LUSC, PRAD, READ, STAD, THCA, and UCEC was higher than in normal tissue (Figure 1B). For TCGA paired samples, HMMR mRNA expression in BLCA, BRCA, CHOL, ESCA, HNSC, KICH, KIRC, KIRP, LIHC, LUAD, LUSC, PRAD, READ, STAD, and UCEC were all at higher levels in tumor tissues than in matched normal adjacent tissues (Figure 1C). The expression of HMMR in pan-cancer was also analyzed using the TIMER database. HMMR expression was at a higher FIGURE 1 HMMR expression in different types of tumors. The abscissa represents samples in different groups, and the ordinate shows the distribution of HMMR expression. ns, $p \geq 0.05$; , $p < 0.05$; , $p < 0.01$; , $p < 0.001$. (A) HMMR expression analysis in pan-cancer for GTEx datasets. (B) Differential HMMR expression in tumor tissues as compared to normal tissues. (C) Different HMMR expressions between the tumor and paired adjacent normal tissues were utilized from the TCGA dataset. (D) HMMR expression for the TIMER dataset. (E) HMMR expression in different tissues for the ONCOMINE dataset, blue represents low expression, and red represents high expression. (F) HMMR expression in different tumor types using the CCLE database. FIGURE 2 The relationship between HMMR gene expression and OS (A–M). (N) is the forest plot of HRs for OSs in different tumor types. FIGURE 3 An RFS survival analysis of HMMR expression in pan-cancer (A–K). (L) is PFI forest plot for HMMR expression in pan-cancer. FIGURE 4 The ROC curve of HMMR predicting tumor and normal outcomes. For Areas Under the ROC Curve (AUC) which are between 0.5 and 1, the closer the value is to 1, the better the diagnostic value. HMMR displays poor accuracy for AUCs between 0.5 and 0.7. HMMR displays certain accuracy when AUC is between 0.7 and 0.9, and good accuracy when AUC is above 0.9. level in BLCA, BRCA, CESC, CHOL, COAD, ESCA, GBM, HNSC, KIRC, KIRP, LIHC, LUAD, LUSC, PRAD, READ, SKCM, STAD, THCA, and UCEC as compared to normal tissue (Figure 1D). We also verified differential HMMR expression between tumor and normal tissue using the ONCOMINE software. Except for leukemia and some other cancers, HMMR expression in tumor tissues was significantly higher than in normal tissues (Figure 1E). Finally, we used the Cancer Cell Line Encyclopedia (CCLE) to profile HMMR expression across various types of cancer (Figure 1F). The relationship between HMMR expression and overall survival (Os)* Figures 2A–N represents the relationship between HMMR expression and OS across different tumor types. High HMMR expression indicated a reduced OS for bladder carcinoma, breast cancer, esophageal adenocarcinoma, head-neck squamous cell carcinoma, kidney renal clear cell carcinoma, kidney renal papillary cell carcinoma, liver hepatocellular carcinoma, lung adenocarcinoma, pancreatic ductal adenocarcinoma, sarcoma, and stomach adenocarcinoma. For thymoma and uterine corpus endometrial carcinoma, high HMMR expression predicted better OS. The relationship of HMMR to RFS and PFI For bladder carcinoma, breast cancer, esophageal adenocarcinoma, kidney renal clear cell carcinoma, kidney renal papillary cell carcinoma, liver hepatocellular carcinoma, lung adenocarcinoma, pancreatic ductal adenocarcinoma, sarcoma, thyroid carcinoma and uterine corpus endometrial carcinoma, patients with higher HMMR expression were predicted to have a reduced RFS (Figures 3A–K). Figure 3L shows the correlation between HMMR and PFI for the various tumor types using forest plots. ROC curves constructed by HMMR expression For LAML, BRCA, CESC, CHOL, ESCA, GBM, GBMLGG, HNSC, LGG, LIHC, LUAD, LUSC, OV, PAAD, STAD, UCEC, and UCS, HMMR has high accuracy in predicting tumor and normal outcomes. For BLCA, COAD, COADREAD, KIRC, PRAD, READ, and TGCT, HMMR also has a certain accuracy in predicting tumor and normal outcomes (Figure 4). The correlation between HMMR expression and tumor stage Based on a correlation analysis between HMMR and different tumor stages, ACC, BRCA, KIRC, KIRP, LUAD, LIHC, LUADLUSC, LUSC, TGCT, and HMMR had certain predictive accuracy for the T stage (Figures 5A–I). The correlation analysis between HMMR and immune cells Our research separately used CIBERSORT (Figure 6A), xCell (Figure 6B), EPIC (Figure 6C), TIMER (Figure 6D), quanTIseq (Figure 6E), and MCP-counter (Figure 6F) to calculate the correlation between HMMR and immune cells in various tumor types. Figure 6 indicates that HMMR has correlations with multiple different types of immune cells for 33 tumor types (p < 0.05). Heat maps for the relationship between HMMR expression and immune checkpoint-related genes for various tumor types SIGLEC15, IDO1, CD274, HAVCR2, PDCD1, CTLA4, LAG3, and PDCD1LG2 are immune checkpoint-related genes. Figure 7 provides a heatmap of the correlation between immune checkpoints and HMMR in 33 tumor types from TCGA. In addition to PCPG, MESO, ESCA, and CHOL, HMMR was associated with multiple immune checkpoint-related genes ($p < 0.05$) (Figure 7). The correlation of HMMR with TMB and MSI Figure 8 provides a Pearson correlation analysis for HMMR expression correlated with TMB (Figure 8A) and MSI (Figure 8B). The abscissa provides the correlation coefficient between the gene and TMB or MSI. The ordinate provides various tumors. Colors represent various $p$-values. The darker the blue color, the smaller the $p$-value. Molecular correlation analyses We performed a STRING database pathway analysis. The strongest associated proteins to HMMR were LYVE1, TPX2, STAB2, ASPM, AURKA, BRCA1, BUB1, CD44, CDK1, and DLGAP5. The results are provided as a Protein-Protein Interaction (PPI) network (Figure 9A). We then performed a gene GO/KEGG analysis for the top 50 protein associations to HMMR (Figure 9B). Nuclear division and regulation of the cell cycle phase transition were the most enriched GO molecular function term. The most enriched KEGG pathway was the Cell cycle. The protein expression of HMMR in pan-cancer IHC detected the expression of HMMR in different organs in The Human Protein Atlas. Except for the medium expressed in the placenta and highly expressed in the testis, HMMR is not detected or has low expression in other organs (Figure 10A). In Figure 10B, we showed the proportion of high or medium expression of HMMR in 20 cancer types. We selected colorectal cancer, breast cancer, prostate cancer, lung cancer, and liver cancer to represent the antibody stains in 20 different cancers; HMMR expression can be detected in these five cancer types while not being detected in their corresponding normal organs (Figures 1C,D). Finally, we validated the results in eight patients with lung adenocarcinoma. HMMR expression was higher in cancer tissues compared with the cancer-adjacent tissues for eight patients with lung adenocarcinoma (Figure 1E). Discussion HMMR is a type of hyaluronic acid receptor associated with cell movement (18). HMMR influences brain development by regulating the spindle (19). Elevated HMMR expression is always associated with poor prognosis in breast cancer (20, 21). Some bioinformatics analysis findings have indicated that HMMR is the hub gene for some tumors (22, 23). However, the role of HMMR in all cancer types is largely unknown. The purpose of our study was to explore HMMR in pan-cancer. HMMR is expressed at low levels in most healthy tissues. Our study of HMMR expression in pan-cancer found that HMMR was upregulated in most tumor types compared to normal tissues. normal tissues. Therefore, HMMR has the potential to be a tumor marker. In order to verify this hypothesis, we separately repeated the analysis using TCGA, TIMER, and ONCOMINE and found the outcomes to be similar. Tumor heterogeneity includes intratumoral and intertumoral heterogeneity. Tumor tissues are composed of multiple and complex cell types. Currently, the Cancer Cell Line Encyclopedia (CCLE) is the largest tumor cell database (24). As such, a thorough analysis of various tumor cells using the database can reflect the heterogeneity of tumor cells. HMMR was found to be an independent prognostic indicator for prostate cancer (25). However, the prognostic significance of HMMR in pan-cancer is not entirely clear. Based on our prognosis analysis, high HMMR expression predicts inferior survival for bladder carcinoma, breast cancer, esophageal adenocarcinoma, head-neck squamous cell carcinoma, kidney renal clear cell carcinoma, kidney renal papillary cell carcinoma, liver hepatocellular carcinoma, lung adenocarcinoma, pancreatic ductal adenocarcinoma, sarcoma, and stomach adenocarcinoma. Likewise, based on our pan-cancer analysis, a high level of HMMR is associated with inferior RFS and PFI for various tumor types. ROC curves revealed the predictive power of HMMR regarding tumors. When the area under the ROC curve is close to 1, the predictive power of HMMR is more substantial. With the TCGA database analysis, we found that the area under ROC curves was all above 0.9 for most tumor types, indicating that HMMR could be a potential diagnostic marker for these tumors. Although HMMR is predictive in most tumor types, it did not display the exact potential prediction in some tumor types; this illustrates tumor is a heterogeneous disease. Past researchers have outlined HMMR levels that are upregulated in breast cancer and are accompanied by poor pathologic stages and tumor size (26). In our pan-cancer analysis of the tumor stage, we determined associations of HMMR with some tumor stages. Immunotherapy is an essential hot treatment for cancer therapy and has become the first-line therapy for cancer patients. The essence of immunotherapy is the mobilization of immune cells to kill tumor cells. Changes within the tumor microenvironment inhibit immune cell function and stop immune cells from engulfing tumor cells, thereby, promoting tumor progression and migration. The immune escape of tumors can also suppress or block the immune response. Immunotherapy began in 1983 (27). Targeting immune checkpoint inhibitors is the most common type of immunotherapy, and PD1 and PDL1 are the most commonly used immune checkpoints (28). In recent years, additional potential immune checkpoints have also been determined (29, 30). The immune checkpoints expressed on immune cells belong to a class of immunosuppressive molecules that can regulate the activation of immunity. Immune checkpoint molecules cause the immune system to remain within a normal range; thus, the immune system does not become over-activated. Our research analyses included the correlation between HMMR expression and different types of immune cells. Our results indicate that HMMR could become a new therapeutic target for tumors. With the exception of PD1 and PDL1, Tumor Mutational Burden (TMB) (31) and Microsatellite Instability (MSI) (32) are also commonly used as predictive markers for immunotherapy. We also performed a correlation analysis between HMMR and MSI/MSI. Studies of molecular interaction are favorable for analyzing molecular mechanisms. The purpose of the PPI network analysis was to explore protein-protein interactions. The STRING database provides a tool for analyzing the interaction between known and predicted proteins. Using a PPI analysis, we obtained the top 10 and top 50 proteins most closely related to HMMR. The imbalance of the cell cycle may cause persistent excessive cell division, resulting in tumorigenesis. GO and KEGG analyses were performed for functional analysis, the largest cluster pathways display the regulation of cell cycle phase transitions, nuclear division, cell cycle checkpoints, cell cycle, spindle, condensed chromosomes, and spindle poles. All of these pathways are closely related to the occurrence and development of cancer (33–35). Different tumor types share some similar pathophysiology, including gene mutations, immune infiltration, and other aspects. It is now identified tumors with different subtypes or organs have similarities. For example, TP53 mutations can drive multiple tumor types, such as endometrial cancer. But there are also differences manifest in some genetic changes, which shows tumor heterogeneity. Our results showed that HMMR represents different performances among different tumors, prompting us to think that these differ must be viewed separately. The limitations of our study is that restricted by the professionals we engaged, pan-cancer analyses are difficult to obtain simultaneously for many types of tumor specimens. As such, Some of the results could not be verified with our own clinical samples. Altogether, we performed bioinformatics analysis and came to the conclusion that HMMR is an oncogene for most cancer types. Data availability statement The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author/s. Ethics statement The studies involving human participants were reviewed and approved by Henan Provincial People’s Hospital ethics committees. The patients/participants provided their written informed consent to participate in this study. Author contributions (I) Conception and design: YQ, JS, XZ; (II) Administrative support: YQ; (III) Provision of study materials or patients: JS, XZ, GH; (IV) Collection and assembly of data: YQ, JS, XZ, (V) Data analysis and interpretation: JS, XZ; (VI) Manuscript writing: All authors; (VII) Final approval of manuscript: All authors. All authors contributed to the article and approved the submitted version. Acknowledgments This title has been posted as a preprint on Research Square, the DOI is 10.21203/rs.3.rs-1091833/v2 (36). The preprint in the reference section of the manuscript with the intext citation to that reference. 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PREPRINT (Version 2) available at Research Square. doi: 10.21203/rs.3.rs-1091833/v2	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2632, 1 ], [ 2632, 7141, 2 ], [ 7141, 11857, 3 ], [ 11857, 12605, 4 ], [ 12605, 12738, 5 ], [ 12738, 12870, 6 ], [ 12870, 13230, 7 ], [ 13230, 14292, 8 ], [ 14292, 15949, 9 ], [ 15949, 17894, 10 ], [ 17894, 18272, 11 ], [ 18272, 18938, 12 ], [ 18938, 22410, 13 ], [ 22410, 26748, 14 ], [ 26748, 33729, 15 ] ] }
af0dbed60d88f008771678b5ba9cf889f6dc7a67	{ "olmocr-version": "0.1.59", "pdf-total-pages": 13, "total-fallback-pages": 0, "total-input-tokens": 38949, "total-output-tokens": 14727, "fieldofstudy": [ "Medicine", "Biology" ] }	Clinical and prognostic value of tumor volumetric parameters in melanoma patients undergoing $^{18}$F-FDG-PET/CT: a comparison with serologic markers of tumor burden and inflammation Christian Philipp Reinert 1, Sergios Gatidis 1, Julia Sekler 1, Helmut Dittmann 2, Christina Pfannenberg 1, Christian la Fougère 2,3,4, Konstantin Nikolaou 1,3,4 and Andrea Forschner 5 Abstract Background: To investigate the association of tumor volumetric parameters in melanoma patients undergoing $^{18}$F-FDG-PET/CT with serologic tumor markers and inflammatory markers and the role as imaging predictors for overall survival. Methods: A patient cohort with advanced melanoma undergoing $^{18}$F-FDG-PET/CT for planning metastasectomy between 04/2013 and 01/2015 was retrospectively included. The volumetric PET parameters whole-body MTV and whole-body TLG as well as the standard uptake value (SUV) peak were quantified using 50%-isocontour volumes of interests (VOIs) and then correlated with the serologic parameters lactate dehydrogenase (LDH), S-100 protein, c-reactive protein (CRP) and alkaline phosphatase (AP). PET parameters were dichotomized by their respective medians and correlated with overall survival (OS) after PET/CT. OS was compared between patients with or without metastases and increased or not-increased serologic parameters. Results: One hundred seven patients (52 female; 65 ± 13.1yr.) were included. LDH was strongly associated with MTV ($r_P = 0.73$, $p < 0.001$) and TLG ($r_P = 0.62$, $p < 0.001$), and moderately associated with SUV peak ($r_P = 0.55$, $p < 0.001$). S-100 protein showed a moderate association with MTV ($r_P = 0.54$, $p < 0.001$) and TLG ($r_P = 0.48$, $p < 0.001$) and a weak association with SUV peak ($r_P = 0.42$, $p < 0.001$). A strong association was observed between CRP and MTV ($r_P = 0.66$, $p < 0.001$) and a moderate to weak association between CRP and TLG ($r_P = 0.53$, $p < 0.001$) and CRP and SUV peak ($r_P = 0.45$, $p < 0.001$). For differentiation between patients with or without metastases, receiver operating characteristic (ROC) analysis revealed a cut-off value of 198 U/l for serum LDH (AUC 0.81, sensitivity 0.80, specificity 0.72). Multivariate analysis for OS revealed that both MTV and TLG were strong independent prognostic factors. TLG, MTV and SUV peak above patient median were accompanied with significantly reduced estimated OS compared (Continued on next page) to the PET parameters below patient median (e.g. TLG: 37.1 ± 3.2 months vs. 55.9 ± 2.5 months, p < 0.001). Correspondingly, both elevated serum LDH and S-100 protein were accompanied with significantly reduced OS (36.5 ± 4.9 months and 37.9 ± 4.4 months) compared to normal serum LDH (49.2 ± 2.4 months, p = 0.01) and normal S-100 protein (49.0 ± 2.5 months, p = 0.01). Conclusions: Tumor volumetric parameters in 18F-FDG-PET/CT serve as prognostic imaging biomarkers in patients with advanced melanoma which are associated with established serologic tumor markers and inflammatory markers. Keywords: Malignant melanoma, 18F-FDG-PET/CT, Tumor volumetric parameter, Overall survival, Biomarker Background Malignant melanoma incidence is increasing worldwide. At time of diagnosis, most patients have localized disease that can be successfully treated by complete surgical resection, however, 28% of stage IV melanoma patients develop visceral metastases [1]. Recently, new treatment approaches such as antibodies targeting the immune checkpoints T-lymphocyte-associated protein 4 (CTLA-4) or the programmed cell death protein 1 (PD-1) either used alone or as combined immunotherapy remarkably improved prognosis of advanced melanoma. However, about 40–50% of patients fail to respond to therapy [2–5]. Serum lactate dehydrogenase (LDH) is released through cell damage and has been established as a biochemical marker of tumor load in various tumor entities including malignant melanoma [6]. Serum LDH is part of the AJCC melanoma staging guideline for metastatic melanoma patients [6]. Elevated serum LDH level is associated with poor survival and poor therapy response rates [5, 7, 8]. The calcium-binding, acidic cytoplasmic S-100 protein has been shown to be a specific and reliable immunohistochemical marker in malignant melanoma which correlates with clinical melanoma stage and poor survival [9–13]. Besides, several studies have found that the inflammatory markers c-reactive protein (CRP) and alkaline phosphatase (AP) are independent prognostic biomarkers in patients with both early-stage and advanced-stage melanoma [14–16]. Whole-body 18F-FDG-PET/CT is the imaging modality of choice for staging of advanced (stage III and IV) melanoma to provide information on the presence and location of metastases [17]. For assessing the degree of 18F-FDG accumulation in diverse cancer types, the volumetric parameters MTV and TLG have been proposed, as they reflect the whole volume of the tumor rather than the maximum standardized uptake value (SUVmax) which represents only the most active part of the tumor [18–20]. The point spread function (PSF) reconstruction as used in modern PET scanners not only improves sensitivity but it overestimates SUVmax [21]. The SUVpeak has been shown to provide a slightly more robust alternative for assessing the most metabolically active region of a tumor [22–25]. In a recent study of Ito et al., whole-body MTV obtained from baseline PET/CT scans has been shown to be a strong independent prognostic factor among other clinical prognostic factors in melanoma patients treated with ipilimumab [26]. Son et al. observed that among patients with primary cutaneous melanoma, both MTV and TLG are strong prognosticators of survival [27]. Melanoma patients with an elevated serum LDH level have a higher tumor 18F-FDG uptake, however, without full coincidence [8]. The prediction of patient prognosis and the assessment of early response to immunotherapy have become areas of intensive investigation, because unnecessary toxicities or aggressive treatments should be avoided [28]. In this study we investigated the association of tumor volumetric parameters in melanoma patients undergoing 18F-FDG-PET/CT with serologic tumor markers and inflammatory markers and the role as independent imaging predictors for overall survival. Methods Ethics approval was obtained from the local ethics committee (Project number: 064/2013B01). Informed consent was obtained from all patients included in the study. Patient cohort The underlying study population consisted of patients with advanced melanoma, who were enrolled in a local PET/CT registry between April 2013 and January 2015 [29, 30]. All patients were initially intended for radical metastasectomy based on conventional imaging prior to the PET/CT examination. According to the melanoma guideline, PET/CT imaging is routinely recommended for patients with stage III and IV melanoma and in case of high risk melanoma (ulceration or tumor thickness above 4 mm) or suspect findings in the follow-up (i.e. US or serologic tumor markers) in patients with stage I and II [31]. After having performed the PET/CT scan, patients were re-evaluated regarding the intended management plan (surgery, systemic therapy, watchful watching). The final treatment was a consensus decision of a tumor-board on the basis of the PET/CT result in agreement with the patients. In case of 18F-FDG avid metastases, a corresponding surgical or systemic therapy was initiated. If no vital metastases were confirmed, patients underwent watchful waiting. 18F-FDG-PET/CT imaging All PET/CT examinations were performed on a state-of-the-art clinical scanner (Biograph mCT®, Siemens Healthineers). All patients fasted overnight before examination. Approximately 300 MBq 18F-FDG were injected intravenously 60 min prior to image acquisition. Standardized CT examination protocols included weight-adapted 90–120 ml intravenous CT contrast agent (Ultravist 370®, Schering AG). Portal-venous phase acquisitions were obtained with 70s delay time using a tube voltage of 120 kV and a reference dose of 200 mAs. Image reconstruction was performed using iterative CT reconstruction (Siemens SAFIRE®, Forchheim). PET was acquired from the skull to the mid thigh level over six to eight bed positions and reconstructed using a 3D ordered subset expectation maximization algorithm (two iterations, 21 subsets, Gaussian filter 2.0 mm, matrix size 400 × 400, and slice thickness 2.0 mm). In case of known metastases at the extremities, PET acquisition was expanded accordingly. PET acquisition time was 2–3 min per bed position. Quantification of tumor lesion 18F-FDG uptake and serologic markers Segmentation of metastatic tumor lesions was performed by two readers in consensus using approved software for quantification of PET parameters on Syngo.via VB 30A (Siemens Healthineers). Metastatic lesions included all lesions which were characterized by substantially increased 18F-FDG uptake. Segmentation of each lesion was manually performed using 50%-isocontour VOIs for quantification. Whole-body MTV and whole-body TLG were calculated as the sum of all quantified metastatic lesions per patient. The SUVpeak of the metastatic lesion with the highest 18F-FDG uptake in a patient was calculated using an automated computed maximal mean SUV in a 1.0-cm³ spherical volume within the tumor [24]. The documented patient’s SUVpeak is defined as the highest value derived from all lesions within a patient. As part of the staging procedures in melanoma patients, serum LDH, serum S-100 protein and the acute-phase proteins CRP and AP were routinely determined by the in-house laboratory. Serologic tumor markers were extracted from the clinical data base within 45 days before up to 7 days after PET/CT and acute-phase-proteins 20 days before up to 7 days after PET/CT. The upper limits of the reference ranges were: 250 U/l for serum LDH, 0.1 µg/l for serum S-100 protein, 0.5 µg/dl for CRP and 130 U/l for AP. Data analysis Statistical analyses and graphical illustrations were performed using SPSS Version 22 (IBM Corporation). Association of PET parameters and serologic markers First, we checked for potential associations between the serum parameters and the whole-body MTV, whole-body TLG and SUVpeak by direct correlation of the absolute values. Second, we analyzed these associations separately in patients undergoing surgical or systemic treatment after PET/CT. Interactions between PET parameters and serologic markers were analyzed by bivariate correlation. Further, a multiple linear regression was calculated to predict the whole-body MTV, whole-body TLG and SUVpeak based on serologic markers. The strength of the linear relationships between the variables was measured by calculating the Pearson correlation coefficient which was denoted by rP. The predictive value of serum LDH for differentiation between patients with and without metastases and between patients with whole-body MTV, whole-body TLG and SUVpeak above or below the cohort’s median was assessed by computing a receiver operating characteristic (ROC) curve and by calculation of the area under the curve (AUC). Survival analysis Overall patient survival recorded between date of PET/CT and death was assessed for all patients based on patient records. In a first step, we performed an univariate analysis to identify PET markers including whole-body MTV, whole-body TLG and SUVpeak as well as serologic parameters including LDH, serum-100, AP and CRP associated with OS. In a second step, the factors that were identified as being significant by univariate analysis (p < 0.05) were entered into a Cox multivariate regression analysis model. A forward stepwise multivariate regression analysis was carried out to identify the factors that remained significant after multivariate analysis. The variables with p < 0.05 were entered and those with p > 0.10 were removed. Third, we compared the OS between patients with and without metastases on PET/CT, between patients with whole-body MTV, whole-body TLG and SUVpeak above or below the cohort’s median and between patients with normal or elevated serologic parameters (serum LDH, serum S-100 protein, CRP, AP). Fourth, OS was analyzed in the patient subgroups undergoing surgical or systemic treatment after PET/CT for normal and elevated PET parameters and serologic markers. To analyze differences of overall survival between the groups, we performed Kaplan-Meier analyses. The differences between the Kaplan Meier survival curves were evaluated by non-parametric log-rank tests. Optimal thresholds were identified for each marker, which best separated the subgroups (lowest p-value from log-rank test). The significance level was set at a p-value of < 0.05. Estimated mean survival times were derived from Kaplan-Meier analyses. Results Study population 107 consecutive patients (52 female; mean age 65 ± 13.1 years) with malignant melanoma who were selected for potential surgical metastasectomy prior PET/CT were evaluated. Tumors were staged according to the eighth edition AJCC Cancer Staging Manual [32]. Five patients had stage I, three patients stage II, 42 patients stage III and 57 patients stage IV melanoma according to PET/CT. The eight early stage (I and II) patients had been scheduled for surgery for suspicious findings in CT or US. On the basis of clinical findings and PET/CT results, 52 patients (48.6%) were selected for surgical treatment whereas 32 patients (29.9%) were selected for systemic therapy. Two patients (1.9%) underwent palliative radiotherapy and one patient (0.9%) underwent isolated extremity perfusion. 20 patients (18.7%) underwent watchful waiting. Detailed patient characteristics are listed in Table 1. Association of PET parameters and serologic markers PET/CT findings and results of the laboratory are shown in Table 2. A total of 87/107 patients (81.3%) had histologically confirmed metastases. 18F-FDG avid lesions have been identified in 76/107 patients (71.0%) by PET/CT allowing for manual segmentation. 11/107 patients (10.3%) had small cutaneous in-transit metastases which were either not completely recorded by PET/CT scan or not clearly quantifiable (Fig. 1). Current serologic parameters were available as follows: - Serum LDH was available in 84/107 patients (78.5%), which could be correlated with PET parameters in 67 patients. - Serum S-100 protein was available in 82/107 patients (76.6%), which could be correlated with PET parameters in 68 patients. - CRP was available in 72/107 patients (67.3%), which could be correlated with PET parameters in 59 patients. - AP was available in 68/107 patients (63.6%), which could be correlated with PET parameters in 60 patients. Serum LDH and serum S-100 protein showed a significantly positive correlation (r_p = 0.82, p < 0.001). In the whole patient cohort, serum LDH was strongly associated with whole-body MTV (r_p = 0.73, p < 0.001) and moderately associated with whole-body TLG (r_p = 0.62, p < 0.001) and SUV_{peak} (r_p = 0.55, p < 0.001) (Fig. 2). S-100 protein showed a moderate association with MTV (r_p = 0.54, p < 0.001) and TLG (r_p = 0.48, p < 0.001) and a weak association with SUV_{peak} (r_p = 0.42, p < 0.001). A strong association was observed between CRP and MTV (r_p = 0.66, p < 0.001) and a moderate to weak association between CRP and TLG (r_p = 0.53, p < 0.001) and CRP and SUV_{peak} (r_p = 0.45, p < 0.001). A weak association was also observed between AP and MTV (r_p = 0.39, p < 0.001) and AP and TLG (r_p = 0.29, p < 0.01). AP and SUV_{peak} were not associated (r_p = 0.16, p = 0.2). The separate analysis for patients receiving surgical treatment after PET/CT revealed strong associations between serum LDH and MTV (r_p = 0.82, p < 0.001) and serum LDH and TLG (r_p = 0.74, p < 0.001) and between serum S-100 protein and MTV (r_p = 0.66, p < 0.001). Moderate associations were observed between S-100 protein and TLG (r_p = 0.60, p < 0.001), SUV_{peak} and serum LDH (r_p = 0.60, p < 0.001) and SUV_{peak} and S-100 protein (r_p = 0.48, p < 0.001). ### Table 1 Patient characteristics \| Characteristic \| No. of patients \| % \| \|--------------------------------\|-----------------\|-----\| \| Sex \| \| \| \| Male \| 52 \| 48.6\| \| Female \| 55 \| 51.4\| \| Age, years \| \| \| \| Mean \| 65 \| \| \| Interquartile range (25–75) \| 55–74 \| \| \| Stage (AJCC 2009) \| \| \| \| Stage I \| 5 \| 4.7 \| \| Stage II \| 3 \| 2.8 \| \| Stage III \| 42 \| 39.3\| \| Stage IV \| 57 \| 53.3\| \| Histological melanoma type \| \| \| \| Superficial \| 35 \| 32.7\| \| Nodular \| 21 \| 19.6\| \| Lentigo maligna \| 7 \| 6.5 \| \| Acral lentiginous \| 15 \| 14.0\| \| Mucosal \| 6 \| 5.6 \| \| Other \| 23 \| 21.4\| \| Treatment after PET/CT \| \| \| \| Surgical \| 52 \| 48.6\| \| Systemic \| 32 \| 29.9\| \| Other \| 3 \| 2.8 \| \| None \| 20 \| 18.7\| Reinert et al. Cancer Imaging (2020) 20:44 Page 4 of 13 In the subgroup of patients undergoing systemic treatment after PET/CT, MTV and serum LDH (r_P = 0.61, p < 0.001) and MTV and S-100 protein were moderately associated (r_P = 0.56, p < 0.001). Moderate associations were also observed between TLG and serum LDH (r_P = 0.47, p < 0.001), TLG and S-100 protein (r_P = 0.42, p < 0.001), SUV_peak and serum LDH (r_P = 0.51, p < 0.001) and SUV_peak and S-100 protein (r_P = 0.43, p < 0.001). The results of the bivariate correlation analyses are listed in Table 3. The ROC analysis for differentiation between patients with and without metastases revealed a cut-off value of 198 U/l for serum LDH with an AUC of 0.81 (sensitivity 0.80; specificity 0.72). A significant regression equation was found: F (4,52) = 26.9, p < 0.0001, with R^2 of 0.67. Both serum LDH and CRP were significant predictors of whole-body MTV. Whole-body MTV increased 0.84 cm^3 for each U/l serum LDH and 1.83 cm^3 for each mg/dl CRP. Overall survival* At the time of analysis in February 2020, 55/107 patients (51.4%) had died, whereas 47/107 patients (43.9%) were still alive. In 5/107 patients (4.7%) survival data were not available. Univariate analysis revealed that whole-body MTV (< 2.74 cm^3 vs. > 2.74 cm^3), whole-body TLG (< 13.0 vs. > 13.0), SUV_peak (< 6.7 vs. > 6.7), as well as the serologic parameters LDH (normal vs. increased), and S-100 protein (normal vs. increased) were significant predictors of overall survival. Multivariate analysis for overall survival --- Table 2 PET/CT and laboratory findings \| PET/CT and laboratory findings \| No. of patients \| % \| \|-------------------------------\|----------------\|---\| \| Metastases \| 87 \| 81.3 \| \| 18F-FDG avid metastases quantifiable by PET/CT \| 76 \| 71.0 \| \| Whole body metabolic tumor volume (MTV, cm^3) \| \| 48.6 \| \| Median \| 2.74 \| \| Interquartile range (25–75) \| 0.30–9.22 \| \| Whole-body total lesion glycolysis (TLG) \| \| \| \| Median \| 13.0 \| \| Interquartile range (25–75) \| 1.17–64.30 \| \| SUV_peak \| \| \| Median \| 6.7 \| \| Interquartile range (25–75) \| 2.53–12.60 \| \| Serum lactate dehydrogenase (mean: 241 [130–960] U/l) \| 84 \| 78.5 \| \| Normal \| 64 \| 76.2 \| \| Increased \| 18 \| 21.4 \| \| Serum S-100 protein (mean: 0.14 [0.02–3.0] μg/l) \| 82 \| 76.6 \| \| Normal \| 64 \| 76.2 \| \| Increased \| 18 \| 21.4 \| \| C-reactive protein (mean: 3.0 [0.01–16.7] mg/dl) \| 72 \| 67.3 \| \| Normal \| 59 \| 72.0 \| \| Increased \| 23 \| 28.0 \| \| Alkaline phosphatase (mean: 91 [36–175] μg/l) \| 68 \| 63.6 \| \| Normal \| 56 \| 82.4 \| \| Increased \| 12 \| 17.6 \| --- Fig. 1 Patient flowchart Fig. 2 a Bivariate correlation curves between serum LDH and whole-body TLG ($r_P = 0.62, p < 0.001$), between serum LDH and whole-body MTV ($r_P = 0.73, p < 0.001$) b and between serum LDH and $SUV_{peak}$ ($r_P = 0.55, p < 0.001$) c. including the significant parameters revealed that whole-body TLG greater than 13 (hazard ratio [HR], 3.30; 95% CI, 1.6–6.80; p = 0.001), and whole-body MTV greater than 2.74 cm³ (HR, 2.29; 95% CI, 1.12–4.70; p = 0.02) remained independent prognostic factors (Table 4). Patients with ¹⁸F-FDG avid metastases had a significantly reduced estimated OS (43.1 ± 2.7 months) compared to patients without ¹⁸F-FDG avid metastases (55.7 ± 2.8 months, p < 0.01) (Fig. 3a). Patients with whole-body MTV, whole-body TLG or SUV peak above the cohort’s median had a significantly (p < 0.001) reduced estimated OS compared to patients with corresponding PET parameters below cohort’s median (MTV: 42.8 ± 3.3 months vs. 51.2 ± 2.7 months; TLG: 37.1 ± 3.2 months vs. 55.9 ± 2.5 months; SUVpeak: 39.9 ± 3.2 months vs. 54.1 ± 2.7 months) (Fig. 3). Correspondingly, an elevated serum LDH was accompanied with a significantly lower OS (36.5 ± 4.9 months) compared to patients with normal serum LDH (49.2 ± 2.4 months, p = 0.01), which was also observed in Table 3 ### Table 3 Bivariate correlation analysis between PET and serologic parameters \| All patients (n = 107) \| MTV (cm³) \| p-value \| TLG \| p-value \| SUVpeak \| p-value \| \|------------------------\|-----------\|---------\|-----\|---------\|---------\|---------\| \| Serum LDH (U/l) \| 0.73 \| < 0.001 \| 0.62 \| < 0.001 \| 0.55 \| < 0.001 \| \| Serum S-100 protein (μg/l) \| 0.54 \| < 0.001 \| 0.48 \| < 0.001 \| 0.42 \| < 0.001 \| \| C-reactive protein (mg/dl) \| 0.66 \| < 0.001 \| 0.53 \| < 0.001 \| 0.45 \| < 0.001 \| \| Alkaline phosphatase (μg/l) \| 0.39 \| < 0.001 \| 0.29 \| < 0.001 \| 0.16 \| 0.2 \| ### Surgical treatment (n = 52) \| Serum LDH (U/l) \| 0.82 \| < 0.001 \| 0.74 \| < 0.001 \| 0.60 \| < 0.001 \| \| Serum S-100 protein (μg/l) \| 0.66 \| < 0.001 \| 0.60 \| < 0.001 \| 0.48 \| < 0.001 \| \| C-reactive protein (mg/dl) \| 0.62 \| < 0.001 \| 0.50 \| < 0.001 \| 0.13 \| 0.4 \| \| Alkaline phosphatase (μg/l) \| 0.44 \| 0.007 \| 0.21 \| 0.2 \| 0.12 \| 0.1 \| ### Systemic treatment (n = 32) \| Serum LDH (U/l) \| 0.61 \| < 0.001 \| 0.47 \| < 0.001 \| 0.51 \| < 0.001 \| \| Serum S-100 protein (μg/l) \| 0.56 \| < 0.001 \| 0.42 \| < 0.001 \| 0.43 \| < 0.001 \| \| C-reactive protein (mg/dl) \| 0.41 \| 0.06 \| 0.31 \| 0.2 \| 0.48 \| 0.02 \| \| Alkaline phosphatase (μg/l) \| 0.34 \| 0.06 \| 0.37 \| 0.04 \| 0.21 \| 0.3 \| Table 4 Univariate and multivariate survival analyses of PET and serologic parameters \| PET parameters \| Hazard ratio \| 95% CI \| p-value \| Hazard ratio \| 95% CI \| p-value \| \|----------------\|--------------\|--------\|---------\|--------------\|--------\|---------\| \| Whole-body MTV \| < 2.74 cm³ \| 1.00 \| – \| – \| – \| – \| \| \| > 2.74 cm³ \| 4.90 \| 1.93–12.46 \| 0.001 \| 2.29 \| 1.12–4.70 \| 0.02 \| \| Whole-body TLG \| < 13.0 \| 1.00 \| – \| – \| – \| – \| \| \| > 13.0 \| 3.86 \| 1.98–7.55 \| < 0.0001 \| 3.30 \| 1.60–6.80 \| 0.001 \| \| SUVpeak \| < 6.7 \| 1.00 \| – \| – \| – \| – \| \| \| > 6.7 \| 2.81 \| 1.48–5.33 \| 0.002 \| 2.29 \| 1.16–4.52 \| 0.02 \| \| Serologic parameters \| Hazard ratio \| 95% CI \| p-value \| Hazard ratio \| 95% CI \| p-value \| \|----------------------\|--------------\|--------\|---------\|--------------\|--------\|---------\| \| LDH \| normal \| 1.00 \| – \| – \| – \| – \| \| \| increased \| 2.18 \| 1.17–4.05 \| 0.01 \| 1.18 \| – \| – \| \| S-100 protein \| normal \| 1.00 \| – \| – \| – \| – \| \| \| increased \| 2.09 \| 1.14–3.82 \| 0.02 \| 1.33 \| 0.63–2.81 \| 0.46 \| \| Alkaline phosphatase \| normal \| 1.00 \| – \| – \| – \| – \| \| \| increased \| 1.32 \| 0.69–2.52 \| 0.40 \| – \| – \| \| C-reactive protein \| normal \| 1.00 \| – \| – \| – \| – \| \| \| increased \| 0.89 \| 0.44–1.81 \| 0.74 \| – \| – \| patients with an elevated serum S-100 protein (37.9 ± 4.4 months) compared to patients with a normal serum S-100 protein (49.0 ± 2.5 months, p = 0.01) (Fig. 4). No differences in OS could be observed between patients with an elevated (43.3 ± 4.4 months) or normal AP (45.3 ± 3.2 months, p = 0.48) and an elevated (47.8 ± 3.5 months) or normal CRP (41.9 ± 4.4 months, p = 0.41). In the subgroup of patients undergoing surgical treatment after PET/CT, OS was significantly reduced in case of $^{18}$F-FDG avid metastases ($n = 41$, $51.7 \pm 4.0$ months) compared to patients without $^{18}$F-FDG avid metastases ($n = 11$, $60.9 \pm 7.2$ months, $p < 0.05$). This observation was similar to patients with elevated serum S-100 protein ($41.8 \pm 5.9$ months) compared to patients with normal serum S-100 protein ($50.2 \pm 3.4$ months), however, without statistical significance ($p = 0.07$). Discussion In this study, we investigated the clinical and prognostic value of volumetric PET parameters in a patient cohort with advanced melanoma undergoing $^{18}$F-FDG-PET/CT by direct correlation with the established serologic tumor markers LDH and S-100 protein and the inflammatory markers AP and CRP. A strong association was observed between the whole-body MTV and LDH, whereas whole-body TLG was moderately associated with LDH. Moderate associations were also detected between LDH and SUV peak and between S-100 protein and both MTV and TLG. Similar associations were observed in the patient subgroups who underwent surgical or systemic treatment after PET/CT. To the best of our knowledge, there are no reports so far reporting on direct correlations of volumetric imaging markers and the established serologic tumor markers LDH and S-100 protein in melanoma. A possible explanation for the strong association between MTV, TLG and LDH is that the conversion of pyruvate... to lactate by LDH produces NAD$^+$, and the NADH/NAD$^+$ ratio is thought to be important in various oxidoreductase-based metabolic reactions which are up-regulated in melanoma cells [33]. Increasing serum values of LDH are correlated with tumor progression and are therefore found in higher tumor stages [13]. However, it has been shown that LDH is less sensitive in early disease stages and as a predictor of metastatic relapse [34, 35]. The volumetric parameters MTV/TLG and the SUV$_{\text{peak}}$ showed a stronger association with serum LDH as with CRP. This is in concordance with the study results of de Heer et al. showing significantly higher MTV, TLG and SUV$_{\text{peak}}$ in melanoma patients with elevated LDH [8]. CRP is synthetized in response to cytokines such as interleukin-6 (IL-6), which is produced by melanoma cells [36]. However, CRP might also be synthetized by activated T cells, macrophages or monocytes which are also responsible for elevated IL-6 levels in response to inflammation [37]. Therefore, CRP is not a marker which is exclusively increased in melanoma. We observed a strong association between the serum markers LDH and S-100 protein. Therefore, it is not surprising, that S-100 protein was also associated with MTV, TLG and SUV$_{\text{peak}}$. It has been observed that S-100 protein has a prometastatic attribute in melanoma by influencing cell growth and differentiation and interaction with coexpressed receptor for advanced glycation endproducts (RAGE) [38, 39]. It has been shown that serum concentrations of S-100 correlate with clinical melanoma stage [13]. In asymptomatic melanoma patients, S-100 protein has been proven to be a useful tool for discovering tumor progression which could be confirmed by PET/CT [40]. However, abnormal elevated S-100 levels may attributed to other causes such as inflammatory and infectious diseases [41–43]. Our survival analysis revealed that both whole-body MTV and whole-body TLG are independent prognostic factors. Patients with $^{18}$F-FDG avid metastases or MTV/TLG and SUV$_{\text{peak}}$ above the cohort’s median had a significantly reduced survival, which was similarly observed in patients with an elevated serum LDH or elevated serum S-100 protein. Patients undergoing surgical treatment after PET/CT had a reduced OS in case of $^{18}$F-FDG avid metastases, which was similarly observed in patients with elevated serum S-100 protein above the cohort’s median. This is in concordance with other studies demonstrating that both whole-body MTV, whole-body TLG, SUV$_{\text{peak}}$ and serum LDH are independent prognostic factors in patients with malignant melanoma [8, 26, 27]. Ito et al. combined information about PET parameters and clinical factors showing that melanoma patients with high serum LDH in combination with elevated whole-body MTV had a worse prognosis than patients with a high serum LDH or an elevated MTV alone [25]. Differences in survival between patients with a sum of SUV$_{\text{peak}}$ above and below the cohort’s median were not significant, however, a trend was noted. In their study, patients were divided into subgroups with increased or not increased LDH referring to the upper limit of the normal range. We could additionally show that serum LDH and PET parameters are directly associated which may help clinicians to early identify melanoma patients who would particularly benefit from PET/CT imaging for staging. Further, Ito et al. included only patients with unresectable melanoma who were planned for ipilimumab immunotherapy and a part of their patient cohort had already undergone previous systemic therapy [44]. Son et al. evaluated the prognostic relevance of MTV, TLG and SUV$_{\text{max}}$ in patients with primary cutaneous malignant melanoma [27]. The volumetric parameters MTV and TLG were significant prognostic factors for melanoma-specific survival, whereas SUV$_{\text{max}}$ was not a significant factor [27]. Tumor volumetric parameters assessed on baseline PET/CT have been proven to be of prognostic value in various malignancies, including non-small cell lung cancer [45], lymphoma [46], breast cancer [47], head and neck cancer [48], and pancreatic cancer [20]. The clinical applicability of standard uptake value (SUV) for prognostic purposes in melanoma patients is still under discussion [49, 50]. The intra- and inter-patient heterogeneity in tumor lesion $^{18}$F-FDG uptake (SUV) among metastatic melanoma patients are major limitations [8]. S-100 protein and LDH have been reported as early prognostic markers for response and overall survival in melanoma patients treated with anti-PD-1 or combined anti-PD-1 plus anti-CTLA-4 antibodies [51]. Our observation that increased MTV is directly associated with serum LDH and S-100 in patients being accompanied with worse prognosis might therefore be a help for clinicians to early identify patients with an increased risk of relapse and which deserve particularly close monitoring. Perhaps, these would also be the patients who particularly benefited from a neoadjuvant therapy approach. No differences in OS could be observed between patients with elevated or normal acute-phase proteins (AP and CRP). An explanation is the low specificity of CRP and AP which may be elevated due to other reasons, for instance, inflammatory disorders [52, 53]. In our study, a cut-off value of 198 U/l for serum LDH could be defined which best differentiates between patients with or without $^{18}$F-FDG avid metastases (sensitivity 0.80; specificity 0.72). If the serum LDH rises above this cut-off value, vital tumor burden can be reasonably assumed. This finding is of great diagnostic relevance as an increasing serum LDH above this cut-off value may influence patient prognosis and it is below the generally accepted cut-off of 250 U/l. The early decision to perform a PET/CT in a clinical diagnostic setting should be considered. Our study has limitations. Due to the retrospective design, a selection bias cannot be excluded. In addition, serologic parameters and survival data were not available for all patients. Volumetric parameters such as the MTV require an accurate lesion segmentation using a standardized segmentation method which has still not been established across clinical institutions. As all patients of our study cohort were examined at our institution, MTV was measured using the same segmentation method which includes a fixed relative threshold for all lesions. Further, we used a 50% threshold for the isocontour VOIs instead of the EANM recommended 41% threshold, which may underestimate volumetric PET parameters [54]. The rationale for this choice was that our mCT system uses PSF modeling, producing higher values of SUV compared to standard OSEM. Our data are the first to demonstrate that there is an association between the absolute values of PET parameters and established serologic tumor markers in melanoma patients. Further prospective studies with more patients and consideration of neoadjuvant therapy approaches should be conducted. Conclusions Tumor volumetric parameters in 18F-FDG-PET/CT serve as prognostic imaging biomarkers in patients with advanced melanoma which are associated with established serologic tumor markers and inflammatory markers. Abbreviations AP: Alkaline phosphatase; AUC: Area under the curve; AJCC: American Joint Committee on Cancer; CTLA-4: T-lymphocyte-associated protein 4; CRP: C-reactive protein; EANM: European Association of Nuclear Medicine; 18F-FDG: (18)F-fluoro-2-deoxy-D-glucose; LDH: Serum lactate dehydrogenase; MBq: Megabecquerel; MTV: Metabolic tumor volume; OS: Overall survival; PET/CT: Positron emission tomography/computed tomography; PD-1: Programmed cell death protein 1; PSF: Point spread function; RAGE: Receptor for advanced glycation endproducts; ROC: Receiver operating characteristic; SUV: Standardized uptake value; VOI: Volume of Interest Acknowledgements Not applicable. Authors’ contributions CR and AF conceived of the presented idea. CR and JS performed the patient data research. CR performed the segmentations and measurements. SG, HD, CP and AF verified the analytical methods. CR performed the analysis, drafted the manuscript and designed the figures. AF, SG and CP supervised the findings of this work. Both KN and CF contributed to the conceptual idea and final version of the manuscript. All authors provided critical feedback and helped shape the research, analysis and manuscript. The authors read and approved the final manuscript. Funding This study was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2180 - 39090677. The study was supported by the Junior Clinician Scientist Program of the Medical Faculty, University of Tübingen. Availability of data and materials The datasets generated and analyzed during the current study are not publicly available due to sensitive information but are available in anonymous form from the corresponding author on reasonable request. Ethics approval All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. For this type of study formal consent is not required. Consent for publication Not applicable. Competing interests Konstantin Nikolaiou received institutional research funds and speaker’s honorarium from Siemens Healthineers and is a scientific advisor of Siemens Healthcare Germany. The other authors have declared that no competing interests exist. Author details 1Department of Radiology, Diagnostic and Interventional Radiology, University Hospital Tübingen, Hoppe-Seyler-Str.3, 72076 Tübingen, Germany. 2Department of Radiology, Nuclear Medicine and Clinical Molecular Imaging, University Hospital, Tübingen, Hoppe-Seyler-Str.3, 72076 Tübingen, Germany. 3Cluster of Excellence IIT (EXC 2180) “Image Guided and Functionally Instructed Tumor Therapies”, University of Tübingen, Tübingen, Germany. 4German Cancer Consortium (DKTK). Partner Site Tübingen, Tübingen, Germany. 5Department of Dermatology, University Hospital Tübingen, Liebermeisterstrasse 25, 72076 Tübingen, Germany. Received: 16 April 2020 Accepted: 29 June 2020 Published online: 06 July 2020 References 1. Duncan LM. The classification of cutaneous melanoma. Hematol Oncol Clin North Am. 2009;23:501–13. https://doi.org/10.1016/j.hoc.2009.03.013. 2. Ribas A, Hamid O, Daud A, Hodi FS, Wolchok JD, Kefford R, et al. 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Boellaard R, Delgado-Bolton R, Oyen WJG, Giammarie F, Tatsch K, Eschner W, et al. FDG PET/CT: EANM procedure guidelines for tumour imaging: version 2.0. Eur J Nucl Med Mol Imaging. 2015;42:528–54. https://doi.org/10.1007/s00259-014-2961-x. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2439, 1 ], [ 2439, 7267, 2 ], [ 7267, 12506, 3 ], [ 12506, 17690, 4 ], [ 17690, 20687, 5 ], [ 20687, 20922, 6 ], [ 20922, 24460, 7 ], [ 24460, 24838, 8 ], [ 24838, 26343, 9 ], [ 26343, 32125, 10 ], [ 32125, 38917, 11 ], [ 38917, 43812, 12 ], [ 43812, 45862, 13 ] ] }
21e9a8ba524d463f1b90e76c9d7e8b2118e07784	{ "olmocr-version": "0.1.59", "pdf-total-pages": 4, "total-fallback-pages": 0, "total-input-tokens": 9623, "total-output-tokens": 2153, "fieldofstudy": [ "Physics" ] }	e-ASTROGAM: a space mission for MeV-GeV gamma-ray astrophysics R Rando\textsuperscript{1,2}, A De Angelis \textsuperscript{2,3,4,5}, M Mallamaci\textsuperscript{2}, on behalf of the e-ASTROGAM collaboration\textsuperscript{‡} \textsuperscript{1} Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, I-35131 Padova, Italy E-mail: [email protected] \textsuperscript{2} INFN, Sezione di Padova, I-35131 Padova, Italy \textsuperscript{3} INAF - Osservatorio Astronomico di Padova, I-35122, Padova, Italy \textsuperscript{4} Dipartimento di Matematica, Informatica e Fisica, Università di Udine, I-33100 Udine, Italy \textsuperscript{5} Laboratorio de Instrumentacao e Particulas and Instituto Superior Tecnico, Lisboa, Portugal Abstract. e-ASTROGAM is an observatory space mission dedicated to the study of the gamma radiation in the range from 0.3 MeV to 3 GeV. The detector is composed by a Silicon tracker, a calorimeter, and an anticoincidence system. The mission is based on an advanced space-proven detector technology, with unprecedented sensitivity, angular and energy resolution, combined with polarimetric capability. Thanks to its performance in the MeV-GeV domain, substantially improving its predecessors, e-ASTROGAM will open a new window on the non-thermal Universe. In particular it will determine the origin of key isotopes fundamental for the understanding of supernova explosions and the chemical evolution of our Galaxy. It will also shed light on the processes behind the acceleration of cosmic rays in our Galaxy. 1. The scientific objectives e-ASTROGAM [1] is a concept for a gamma-ray space observatory operating in the energy range from 0.3 MeV to 3 GeV, aiming to provide gamma-ray data to a broad astronomical community in a decade of powerful observatories for multiwavelength astronomy and for the detection of gravitational waves, neutrinos and ultra-high-energy cosmic rays (UHECRs). The expected scientific return for such an observatory is substantial [2]. In particular, e-ASTROGAM will address the outstanding issue of the origin and propagation of cosmic rays. It will measure cosmic-ray diffusion in interstellar clouds and their impact on gas dynamics and state, thus providing crucial diagnostics about the impact of cosmic rays on star formation, structures of the interstellar medium, galactic winds and outflows. The improved sensitivity and angular resolution will be \textsuperscript{‡} See http://eastrogam.iaps.inaf.it e-ASTROGAM ![Graph showing sensitivity of different instruments](image) Figure 1. Point source continuum differential sensitivity of different X- and γ-ray instruments, from [2] It is crucial to probe the interplay between cosmic rays and the turbulent medium of star forming regions (e.g. the Cygnus Cocoon) during the early steps of their Galactic voyage. Sensitive e-ASTROGAM observations of a set of cosmic-ray sources, such as young supernova remnants, will allow for the first time to distinguish the emission produced by the interactions of cosmic-ray nuclei with the ambient gas and the non-thermal emission from cosmic-ray electrons, helping in the discrimination among models of hadronic and leptonic production. 2. The instrument The e-ASTROGAM instrument operates over more than four orders of magnitude in energy (from about 150 keV to 3 GeV) by detecting photons in both the Compton (0.15 – 30 MeV) and pair-production (> 10 MeV) regimes. The telescope is made up of three detection systems: a silicon tracker, a scintillator calorimeter and an anti-coincidence system, for a mass of 1.2 tons. The Si tracker comprises 5600 double-sided strip detectors (DSSDs) arranged in 56 layers, divided in four units of 5×5 DSSDs. Each DSSD has a geometric area of 9.5×9.5 cm², a thickness of 500 μm, and a strip pitch of 240 μm. Stacking relatively thin detectors enables efficient tracking of the electrons and positrons produced by pair conversion, and of the recoil electrons produced by Compton scattering. The DSSD signals are read out by 860,160 independent, ultra low-noise and low-power electronics channels with self-triggering capability. The calorimeter is a pixelated detector made of 33,856 Thallium-activated Cesium Iodide bars of 8 cm length and 5×5 mm² cross section. Each element is read out by silicon drift detectors (SDDs) at both ends, the depth of interaction along each e-ASTROGAM ![Diagram](image) Figure 2. Left panel – overview of the scientific instrument. Right panel – the scientific instrument on top of the platform. From [1]. ...crystal is measured from the different light amount collected at both ends. The accurate measurement of the 3D position and deposited energy of each interaction is essential for a proper reconstruction of the Compton events. The total thickness – 4.3 radiation lengths – guarantees an 88% absorption probability for a 1-MeV photon on-axis. The anti-coincidence system is composed of two parts: a standard anti-coincidence detector (Upper-AC), made of segmented panels of plastic scintillators covering the top and four lateral sides of the instrument, and a time-of-flight system (ToF) placed on the bottom of the instrument, to reject the particle background produced by the mass in the platform. The Upper-AC detector is segmented in 33 plastic tiles (6 tiles per lateral side and 9 tiles for the top) coupled to silicon photomultipliers (SiPM) by optical fibers, the ToF unit is composed of two plastic scintillator layers separated by 50 cm, read out by SiPMs with a timing resolution of 300 ps. ### 3. Performance e-ASTROGAM is to be launched into a quasi-equatorial (inclination $i < 2.5^\circ$) low Earth orbit at a typical altitude of 550 – 600 km. Extensive simulations based on the mass model of the satellite and on the model of the background environment [3, 4] have demonstrated the performance of the instrument [1]: - broad energy coverage ($\sim$0.15 MeV to 3 GeV), with nearly two orders of magnitude improvement of the continuum sensitivity in the range 0.15 – 100 MeV compared to previous missions (Figure 1); - excellent sensitivity for the detection of key gamma-ray lines e.g. sensitivity for the 847 keV line from thermonuclear supernovae 70 times better than that of the INTEGRAL spectrometer (SPI); - unprecedented angular resolution, improving not only on the angular resolution of CGRO-COMPTEL in the MeV regime, but also on that of Fermi-LAT in the GeV regime (68% containment radius at 1 GeV is 9'). e-ASTROGAM ![Diagram showing angular resolution and energy resolution comparison between COMPTEL, Fermi/LAT, and e-ASTROGAM.] Figure 3. Left panel – e-ASTROGAM on-axis angular resolution compared to that of COMPTEL and Fermi/LAT. Right panel – 1σ energy resolution of COMPTEL and e-ASTROGAM in the Compton domain. From [1]. - large field of view (> 2.5 sr), ideal to detect transient Galactic and extragalactic sources, such as X-ray binaries and GRBs; - timing accuracy of 1 μs (at 3σ), ideal to study the physics of magnetars and rotation-powered pulsars, as well as the properties of terrestrial gamma-ray flashes; - pioneering polarimetric capability for both steady and transient sources. References [1] De Angelis A, Tatischeff V, Tavani M et al. 2017 Exp. Astr. 44 25–82 [2] De Angelis A, Tatischeff V, Grenier I A et al. submitted to J. High Energy Phys. arXiv:1711.01265 [3] Zoglauer A, Andritschke R and Schopper F 2006 New Astr. Rev. 50, 629–632 [4] Bulgarelli A, Fioretti V, Malaguti P, Trifoglio M and Gianotti F 2012 Proc. SPIE 8453 845335	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2492, 1 ], [ 2492, 4400, 2 ], [ 4400, 6508, 3 ], [ 6508, 7566, 4 ] ] }
1ecf89314b65d99a98037f11ca758992ea108a84	{ "olmocr-version": "0.1.59", "pdf-total-pages": 11, "total-fallback-pages": 0, "total-input-tokens": 33076, "total-output-tokens": 13608, "fieldofstudy": [ "Psychology" ] }	Factors Associated with Happiness among Malaysian Elderly Shamsul Azhar Shah 1,, Nazarudin Safian 1, Saharuddin Ahmad 2, Wan Abdul Hannan Wan Ibadullah 3, Zulkefley bin Mohammad 1, Siti Rohani Nurumal 1, Juliana Mansor 1, Mohd Fairuz Addnan 1 and Yugo Shobugawa 3,4 1 Department of Community Health, Faculty of Medicine, Universiti Kebangsaan Malaysia, Cheras, Kuala Lumpur 56000, Malaysia; [email protected] (N.S.); [email protected] (W.A.H.W.I.); [email protected] (S.R.N.); [email protected] (J.M.); [email protected] (M.F.A.) 2 Department of Family Medicine, Faculty of Medicine, Universiti Kebangsaan Malaysia, Cheras, Kuala Lumpur 56000, Malaysia; [email protected] 3 Division of International Health (Public Health), Niigata University Graduate School of Medical and Dental Sciences, Niigata 950-2181, Japan; [email protected] 4 Department of Active Ageing, Niigata University Graduate School of Medical and Dental Sciences, Niigata 951-8510, Japan Correspondence: [email protected] Abstract: Happiness is an essential component to experience healthy ageing. Hence, understanding the factors that contribute to happiness is important. This study aimed to determine the factors associated with happiness among the elderly population in Malaysia. In this study, 1204 respondents were recruited from urban and rural areas in Selangor. A face-to-face interview was conducted using the Bahasa Malaysia version of the Japan Gerontological Evaluation Study questionnaire. The inclusion criteria include Malaysians who are 60-years old and above and can converse in the Malaysian language. Those who encounter less than seven scores for the Abbreviated Mental Test were excluded from the study. Among the 1204 respondents, 953 (79.2%) were happy. Sociodemographic characteristics showed that being a men, age of 60 to 74 years, and living in urban areas were significantly associated with happiness. A logistic regression model showed that locality (aOR 1.61), income category (Bottom 40% aOR 0.49; Middle-class group 40% aOR 1.40), social engagement (active aOR 1.77; less active aOR 1.25), receiving emotional support (aOR 2.11) and handgrip strength (aOR 1.02) were significantly associated with happiness. Thus, ensuring the elderly population in receiving emotional support and active social engagement among them can enhance their happiness level. Keywords: happiness; factor; elderly; Japan gerontological evaluation study 1. Introduction As the population of the world is turning into an aged population, elderly health has become one of the priority aspects [1]. This demographic transition will have an impact on all aspects of society. By 2050, it is estimated that 20% of the world population will be 60-years or older, amounting to two billion people. The 2030 Agenda for Sustainable Development targeted healthy life for all; thus, everyone has the right to health regardless of their age [2]. Healthy life involves not only the physical health but also the mental and social well-being of the person, and is not only restricted to the presence of disease or infirmity [3] but includes also happiness. Happiness is an essential factor for healthy ageing [4]. It is defined as a positive inner experience that results from an emotional interpretation of one’s lives and also the individuals’ cognitive function [5], or in short how a person likes the life he or she has [6]. The emotional component refers to pleasure (balance between comfort and pain... or unpleasant effect), whereas the cognitive component is attributed to mental health [6]. The term happiness sometimes is interchangeable with life satisfaction. However, life satisfaction is mostly used for overall happiness. Life satisfaction related to happiness does not mean quality of life (QOL). The satisfaction in quality-of-life concept denotes life results’ inner qualities, which is the subjective QOL; yet, it does not represent life satisfaction. The concept of life satisfaction comprises the components of enduring and life-as-a-whole [6]. The term happiness is typically used for the affective appraisal of life, and it is synonymous with the hedonic level of effect [7]. Steptoe et al. divided subjective well-being into three components, namely “affective well-being”, “eudaimonic well-being” and “evaluative well-being”. Within this taxonomy, the positive feelings experienced by a person, such as happiness and joy, were classified as affective well-being. The eudaimonic well-being focuses on evaluations of meaning and purpose in life, including personal growth, positive relations with others and self-acceptance. Meanwhile, the evaluative well-being concept is related to the appraisals of how satisfied people are with their QOL [8]. Steptoe et al. have summarized eight factors that contribute to happiness, namely education, socioeconomic status, social network, time use and activities, stress exposure, marital status and family, personality and genetics [9]. There are many ways to assess happiness that depend on the type of subjective well-being components that they intend to measure and the time period considered. The responses can be either in verbal scales, numerical scales or graphical scales [6]. In Malaysia, study of happiness among the elderly population has not been well investigated. A study done in the year 2016 of the Malaysian adult population with an average age of 40 years noted that most of the respondents (96%) were happy [10]. Happiness was significantly associated with high household income, employment, high education level and being female. However, it was not significantly associated with age. Meanwhile, a study by Park et al. [11] showed that happiness declined with age in Malaysia and was especially low for those who were 50 years and older. Previous studies on life satisfaction have been performed; however, in view of the period of the study, the fast-growing numbers of elderly people in Malaysia and current changes in the socioeconomic surrounding, we believe it is necessary for us to have a more updated study in order to plan for proper elderly policy to be implemented. Hence, this study aimed to determine the overall happiness and its associated factors among the elderly population in Malaysia, focusing on social engagement and support, education, socioeconomic status, time use and activities, depression status, marital status and family. 2. Materials and Methods 2.1. Design and Population of the Study A cross-sectional study was conducted among older adults aged 60-years and above in four areas in Selangor, Malaysia from 1 December 2018 to 30 April 2020. Selangor is a state that surrounds the capital city of Kuala Lumpur on the west coast of Peninsular Malaysia. Selangor is the most populous state in the country with 6.53 million inhabitants in 2020 [12]. It reflects the nation’s diversity of people and living conditions and includes all major ethnic groups, such as Malays, Chinese people and Indians. The method used in this study was similar to that of Safian et al. [13], whereby the official public data on district administrative units and their population were used as sampling frame. There are nine districts and 177 sub-districts in Selangor. Hulu Langat district, with more than one million inhabitants, was picked as a representative of urban regions. Meanwhile, Kuala Selangor, with 0.2 million inhabitants, was chosen as a representative of rural regions. Multi-stage cluster sampling was performed, with a probability proportionate to the size of the elderly population. Districts, specifically Hulu Langat and Kuala Selangor, are the primary sampling units, whereas sub-districts are the secondary sampling units. Six sub-districts were chosen, respectively, from Hulu Langat (seven sub-districts) and Kuala Selangor (nine sub-districts). Ten towns/villages were randomly chosen from each sub-district at the third sampling point. There are around 30–50 towns/villages in a typical sub-district. With permission from the appropriate village head, the household ledgers for the selected areas were obtained and used as the sampling system for households and individuals. A random sampling of households with an older individual from the areas selected was carried out. The Kish grid table was used to pick the sample when more than one older adult in a chosen household was eligible for the analysis. The sample size was determined using the equation $ n = \frac{Z^2[(P(1-P))/e^2]}{1} $ [14], where $ Z $ is the confidence level, $ P $ is the prevalence of ‘good health’ among older people, and $ e $ is the error margin. Using $ Z = 1.96 $, $ P = 0.3 $ (estimate from a previous analysis of older individuals in Japan) [15] and $ e = 0.05 $, the initial sample size measurement was 322. The design effect of 1.5 and the two groups of estimates (urban and rural) needed for the survey results = 966 were then multiplied by this initial sample size. Finally, 966 was divided by 0.80 to account for an estimated 20% non-response rate, resulting in a total sample size of 1207. Finally, with a response rate of 99.8%, we successfully recruited 1204 respondents. Before the interview, respondents were given a detailed description of the study, including information sheets and consent forms. The interviews were conducted in a private environment, face-to-face, by professional research assistants immediately after the respondents signed the consent document and lasted 40–50 min. The study used the Bahasa Malaysia variant of the questionnaire for the Japan Gerontological Assessment Study (BM-Japan Gerontological Evaluation Study (JAGES)) [16], which incorporates multidimensional variables for healthy ageing. The inclusion criteria for respondents were (1) being at least 60-years of age and able to speak the Malaysian language; (2) being registered residents of Malaysia (as the sampling frame was used for household ledgers); (3) living at home and (4) being able to understand and consent to comply with the study. However, if the respondent was unable to cooperate and had an Abbreviated Mental Test score of less than seven in the screening questions, the individual was excluded. Those who were institutionalized in nursing or old folks’ homes were also excluded. The study has been approved by the Research Ethics Committee of the National University of Malaysia (FF-2018-532). 2.2. Variables The self-perceived happiness was subjectively determined by the respondents using a single question with a scale from 0 to 10 points. In this study, happiness refers to the overall happiness in life. The question was as follows: To what degree do you feel you are currently happy? (Score “0” for “Very unhappy” and “10” for “Very happy”). Based on this scale, happiness was defined as a self-rated score of 7–10 points, whereas unhappiness 0–6 points. This level of the cut points was finalized using a previous survey among the elderly in Japan on their average happiness score, which was six points [11]. This single question was used to measure happiness in a previous article in Japan using the JAGES questionnaire [17]. Sociodemographic variables included age, sex, marital status and locality. Age was categorized into the following three levels: 60–74, 75–84 and ≥85 years. On the basis of the article by Steptoe et al., we were able to include five components, namely marital status, socioeconomic status, education, social network and physical activities. Marital status was categorized into married living together, married living separately, widowed and divorced and never married. Locality was divided into rural and urban. Socioeconomic status includes household income, education level and current employment status. For household income classification, we used the Income Structure 2019 by the Department of Statistics Malaysia [18]. B40 refers to the base group or bottom 40%, with a monthly household income of less than RM4850, whereas M40 refers to the middle-class group or middle 40%, with earnings between RM4851 and RM10,959 per month. Conversely, T20 is the upper-class group or top 20%, with monthly earnings of more than RM10959 [12]. In the study, we used social engagement and social support in measuring social network. Social network was measured with the frequency of engagement in group activities. The activities that were measured were religious, volunteering, sports or clubs, hobbies, community meetings and political meetings or events. Participation at least once a week in any one of these activities was considered active engagement. Meanwhile, social support was measured by asking respondents if they have someone to talk to regarding concerns or complaints (emotional support) and who looked after them when they felt sick and were confined for a few days (instrumental support). These variables were also used by Park et al. in defining social support [10]. We also asked if they listen to someone’s concerns or complaints and whether they look after someone when he/she is sick and confined for a few days. Physical measurements comprised the body mass index (BMI) and handgrip strength (HGS). Weight and height were measured twice to calculate the BMI. The Malaysian BMI classification was used as a reference [13], in which underweight is defined as BMI < 18.5 kg/m$^2$, normal weight as BMI = 18.5–22.9 kg/m$^2$, overweight as BMI ≥ 23 kg/m$^2$, pre-obese as BMI = 23.0–27.4 kg/m$^2$, obese I as BMI = 27.5–34.9 kg/m$^2$, obese II as BMI = 35.0–39.9 kg/m$^2$ and obese III as BMI ≥ 40 kg/m$^2$ [19]. HGS was measured using a handgrip dynamometer with the dominant hand (T.K.K. 5001 GRIP-A; Takei Scientific Instrument Co. Ltd., Japan). The HGS of each of the respondents was measured twice, and the mean was taken as reading. Physical activities for older adults were evaluated through questions regarding the frequency of moderate exertion activities such as brisk walking, golf, dancing, farming, gardening or car washing. This later was translated to an average of 150 min of moderate-intensity aerobic physical activity throughout the week based on the WHO recommendation [20]. Respondents were asked about their diseases or comorbidities. These include stroke, heart disease, diabetes, hyperlipidaemia, respiratory disease, gastrointestinal, liver or gallbladder disease, kidney or prostate gland disease, musculoskeletal disease, including osteoporosis and arthritis, traumatic injury, cancer, blood or immune disease, depression, dementia, Parkinson’s disease, eye and ear disease, malaria and HIV infection and gynecological problem. 2.3. Data Analyses To determine the associations among the study variables, chi-squared and independent t-tests were conducted. Simple logistic and multiple logistic regressions were used to calculate the crude and adjusted odds ratios, respectively. A p-value of <0.003 (Bonferroni correction) was considered significant. Any variables from the simple logistic regression with a p-value of <0.25 were candidates for the multivariable model [21]. Once the multivariable analysis was completed, the preliminary model was checked for multicollinearity and interactions. Analyses were conducted using IBM SPSS version 21.0 (IBM Corp., Armonk, NY, USA). 3. Results Among 1204 respondents, 953 (79.2%) reported to be happy. Of these, 57.4% were male, the majority (82.7%) was 60 to 74 years old, 65.6% was married and 94.2% stayed with blood-related family members (Table 1). Table 1. Descriptive and bivariate analysis of factors associated with happiness. \| Variables \| N (%) \| Happiness, N (%) \| $ p $-Value \| \|----------------------------\|--------\|------------------\|----------------\| \| Age group \| \| Happy \| Unhappy \| \| \| Young old (60–74 years) \| 996 \| 82.7 \| 801 (80.4) \| 195 (19.6) \| 0.031 \| \| Middle old (75–84 years) \| 186 \| 15.4 \| 138 (74.2) \| 48 (25.8) \| \| \| Old old (≥85 years) \| 22 \| 1.8 \| 14 (63.6) \| 8 (36.4) \| \| \| Sex \| \| \| \| \| \| \| Male \| 691 \| 57.4 \| 562 (81.3) \| 129 (18.7) \| 0.031 \| \| Female \| 513 \| 42.6 \| 391 (76.2) \| 122 (23.8) \| \| \| Marital status \| \| \| \| \| \| \| Married \| 790 \| 65.6 \| 653 (81.4) \| 1469 (18.6) \| 0.023 \| \| Widowed or divorced \| 384 \| 1.8 \| 287 (74.7) \| 97 (25.3) \| \| \| Never married \| 18 \| 1.5 \| 13 (72.2) \| 5 (27.8) \| \| \| Household composition \| \| \| \| \| \| \| Stay alone \| 64 \| 5.3 \| 54 (84.4) \| 10 (15.6) \| 0.253 \| \| Stay with blood-related family \| 1134 \| 94.2 \| 893 (78.7) \| 241 (21.3) \| \| \| Stay with other family (non-blood-related) \| 6 \| 0.5 \| 6 (100.0) \| 0 (0) \| \| \| Locality \| \| \| \| \| \| \| Rural \| 602 \| 50.0 \| 450 (74.8) \| 152 (25.2) \| <0.001 \| \| Urban \| 602 \| 50.0 \| 503 (83.6) \| 99 (16.4) \| \| \| Education level \| \| \| \| \| \| \| Primary or less \| 665 \| 55.2 \| 513 (77.1) \| 152 (22.9) \| 0.035 \| \| Secondary \| 426 \| 35.4 \| 341 (80.0) \| 85 (20.0) \| \| \| Tertiary \| 113 \| 9.4 \| 99 (87.6) \| 14 (12.4) \| \| \| Current employment status \| \| \| \| \| \| \| Employed \| 169 \| 14.0 \| 139 (82.2) \| 30 (17.8) \| 0.560 \| \| Retired from job \| 868 \| 72.1 \| 682 (78.6) \| 186 (21.4) \| \| \| Never had a job \| 167 \| 13.9 \| 132 (79.0) \| 35 (21.0) \| \| \| Household income \| \| \| \| \| \| \| B40 \| 1094 \| 90.9 \| 851 (77.8) \| 243 (22.2) \| 0.001 \| \| M40 \| 98 \| 8.1 \| 91 (92.9) \| 7 (7.1) \| \| \| T20 \| 12 \| 1.0 \| 11 (91.7) \| 1 (8.3) \| \| $ a $ Chi-squared test, $ p $-value < 0.003 considered significant. 3.1. Association of Happiness with Sociodemographic Factors Happiness was significantly associated with sociodemographic factors such as age, sex and locality, as shown in Table 1. Individuals of the younger age group (60–74 years) were happier than those in the other two groups ($ p = 0.031 $). In terms of sex, being male was significantly associated with happiness compared with being female ($ p = 0.031 $). In terms of the location of residence, the elderly who lived in urban places were happier in their daily life ($ p < 0.001 $). 3.2. Association of Happiness with Socioeconomic Status The household income was categorized into three main groups in this study; the respondents in the M40 group showed to be significantly happier than those in the other two groups. In the same group, those who were employed considered themselves happier than those in the other two groups, although the difference was not statistically significant. 3.3. Association of Happiness with Health Parameters Happiness was significantly associated with health parameters such as moderate physical activity, comorbidities and HGS as shown in Table 2. BMI was not significantly associated with happiness. In terms of presence of chronic diseases or comorbidities, those who did not have comorbidities were significantly happier ($ p = 0.042 $). Meanwhile, for HGS measurement, those who were happy demonstrated higher HGS (mean = 26.0 kg, $ SD = 8.61 $) than those who were unhappy. Table 2. Descriptive and bivariate analysis of health parameters associated with happiness. \| Variables \| N \| (%) \| Happiness, N (%) \| p-Value \| \|----------------------\|----\|-----\|------------------\|---------\| \| \| \| \| Happy \| Unhappy \| \| Physical activity \| \| \| \| \| \| Yes \| 632\| 52.5\| 516(81.6)\| 116(18.4)\| 0.025 \| \| No \| 572\| 47.5\| 437(76.4)\| 135(23.6)\| \| \| BMI class \| \| \| \| \| \| Normal \| 223\| 18.5\| 167(74.9)\| 56(25.1)\| 0.145 \| \| Obese I \| 410\| 34.1\| 329(80.2)\| 81(19.8)\| \| \| Obese II \| 61 \| 5.1 \| 44(71.2)\| 17(27.9)\| \| \| Obese III \| 17 \| 1.4 \| 15(88.2)\| 2(11.8)\| \| \| Pre-obese \| 454\| 37.7\| 370(81.5)\| 84(18.5)\| \| \| Underweight \| 39 \| 3.2 \| 28(71.8)\| 11(28.2)\| \| \| Comorbidity \| \| \| \| \| \| Yes \| 941\| 78.2\| 733(77.9)\| 208(22.1)\| 0.042 \| \| No \| 263\| 21.8\| 220(83.7)\| 45(16.3)\| \| \| Handgrip strength \| \| \| \| \| \| Mean (SD) in kilograms\| \| \| 26.0(8.61)\| 23.5(7.89)\| <0.001 \| $a$ Chi-squared test, $b$ Student t-test. 3.4. Association of Happiness with Social Network Most of the respondents had engaged in social group activities as shown in Table 3. Only 17.9% of them were not involved in any kind of group activity. Frequent engagement in social activity was significantly associated with happiness $(p \leq 0.001)$. The majority of the participants (60.6%) engaged in religious group activities, followed by community meetings (9.6%), hobbies (5.8%), political meetings or events (2.6%), sports or clubs (2.0%) and volunteer group activities (1.6%). Table 3. Descriptive and bivariate analysis of social network associated with happiness. \| Variables \| N \| (%) \| Happiness, N (%) \| p-Value \| \|--------------------------------\|----\|-----\|------------------\|---------\| \| \| \| \| Happy \| Unhappy \| \| Social engagement \| \| \| \| \| \| Active \| 687\| 57.1\| 574(83.6)\| 113(16.4)\| <0.001 \| \| Less active \| 301\| 25.0\| 230(76.4)\| 71(23.6)\| \| \| Never \| 216\| 17.9\| 149(69.0)\| 67(31.0)\| \| \| Receiving social support \| \| \| \| \| \| Emotional \| \| \| \| \| \| Yes \| 1126\| 93.5\| 902(80.1)\| 224(19.9)\| 0.002 \| \| No \| 78 \| 6.5 \| 51(65.4)\| 27(34.6)\| \| \| Instrumental \| \| \| \| \| \| Yes \| 1117\| 92.8\| 892(79.9)\| 225(20.1)\| 0.031 \| \| No \| 87 \| 7.2 \| 61(70.1)\| 26(26.9)\| \| \| Providing social support \| \| \| \| \| \| Emotional \| \| \| \| \| \| Yes \| 1080\| 89.7\| 860(79.6)\| 220(20.4)\| 0.229 \| \| No \| 124 \| 10.3\| 93(75.0)\| 31(25.0)\| \| \| Instrumental \| \| \| \| \| \| Yes \| 982 \| 81.6\| 783(79.7)\| 199(20.3)\| 0.295 \| \| No \| 222 \| 18.4\| 170(76.6)\| 52(23.4)\| \| $a$ Chi-squared test. Most of the respondents received and acted as providers of social support. However, having someone to talk to regarding their concerns and problems $(p = 0.002)$ and someone to look after them when sick $(p = 0.031)$ were significantly associated with happiness. The main person who was accountable for providing emotional support to the respondents was their spouse (50.2%). Conversely, the main persons that provide instrumental support to the respondents were their children who are living with them (56.5%). In the multivariable analysis, there were five factors associated with happiness as follows: location, comorbidities, social engagement, receiving emotional support and HGS (Table 4). The model correctly classified 79.1% of the respondents. Neither interaction nor collinearity was present. Table 4. Factors associated with happiness. \| Variables \| Crude OR (95% CI) \| d p-Value \| Adj OR (95% CI) \| d p-Value \| \|----------------------------\|-------------------\|-----------\|-----------------\|-----------\| \| Locality \| \| \| \| \| \| Urban \| 1.72 (1.29, 2.28) \| <0.001 \| 1.61 (1.21, 2.16)\| 0.001 \| \| Rural \| 1.00 \| \| 1.00 \| \| \| Income category \| \| \| \| \| \| B40 \| 0.32 (0.04, 2.48) \| <0.274 \| 0.49 (0.62, 3.95)\| <0.506 \| \| M40 \| 1.18 (0.13, 10.52)\| <0.881 \| 1.40 (0.15, 12.72)\| <0.767 \| \| T20 \| 1.00 \| \| 1.00 \| \| \| Comorbidities \| \| \| \| \| \| No \| 1.45 (1.01, 2.08) \| 0.043 \| 1.46 (1.01, 2.11)\| 0.047 \| \| Yes \| 1.00 \| \| 1.00 \| \| \| Social engagement \| \| \| \| \| \| Active \| 2.28 (1.61, 3.25) \| <0.001 \| 1.77 (1.21, 2.59)\| <0.003 \| \| Less Active \| 1.46 (0.98, 2.16) \| <0.060 \| 1.25 (0.83, 1.87)\| <0.283 \| \| Never \| 1.00 \| \| 1.00 \| \| \| Receiving emotional support\| \| \| \| \| \| Yes \| 2.13 (1.31, 3.48) \| 0.002 \| 2.11 (1.28, 3.50)\| 0.004 \| \| No \| 1.00 \| \| 1.00 \| \| \| Handgrip Strength \| 1.04 (1.02, 1.05) \| <0.001 \| 1.02 (1.00, 1.04)\| 0.017 \| * Wald test; d likelihood ratio test. Model adjusted for age group, sex, marital status, household composition, education level, current employment status, physical activity, BMI, receiving instrumental social support and providing emotional and instrumental social support. In terms of locality, those living in urban areas had 61% higher odds of being happy compared with those in rural areas. Those reported to have no comorbidities had 46% higher odds of being happy compared with those suffering from comorbidities. Those receiving emotional support were twice more likely to be happy compared with those not receiving any emotional support. 4. Discussion The findings of this study showed that 79.2% of the elderly who participated in the study were happy and the factors that contributed to their happiness were significantly associated with their locality, comorbidities, social engagement with the community, HGS and receiving any emotional support. Comparatively, the BM-JAGES conducted in Japan involving Japanese older adults aged 65 years and above showed that 68% of the participants self-rated themselves to have overall happiness. [17]. The percentage of overall happiness in Japan is slightly lower than that in Malaysian elderly based on our study. With greater life expectancy in both men and women in Japan, the elderly are prone to loneliness and social isolation. The famous Japanese word “kodokushi”, which refers to dying alone with the corpse that remained undiscovered for a long period of time, commonly makes Japanese elderly anxious as they age [22]. This might contribute to the lower percentage of overall happiness among Japanese elderly compared with the Malaysian elderly. Peer-based intervention as one of the methods to overcome loneliness and social isolation among the elderly has been shown to enhance happiness among them [23]. In terms of locality, the elderly living in urban areas are happier. This is similar to the finding in a previous study conducted among elderly of age 60-years old and above at Chon- buri Province, Thailand, as they can have access to some hobbies or activities. The elderly living in urban areas receive regular monthly retirement pension, whereas those in rural areas still have to work at an advanced age as they only have subsistence allowance [24]. Multivariable analysis showed that there is no significant association between household income and happiness. A similar finding was found in a study done in Brazil involving 236 people [25]. In general, a person with a higher income is happier than one with a lower income. Having enough money will allow one to fulfill his/her material needs, thus affecting his/her happiness. A study done among Turkish elderly showed that low-income levels increased the odds of being unhappy by four times [26]. By contrast, having an income beyond one’s needs does not affect happiness [27]. The low socioeconomic status among older people is detrimental and directly affects their mental health and subsequently increase the risk for suicidal ideation [28]. A Korean national-level study noted that household income is associated with interpersonal trust and depressive symptoms [29,30]. In this study, the less depressive a person is the happier he/she is. A study noted that adjusting for depression and pension types has an effect on the happiness status [17]. Considering receiving support, older people receiving emotional support showed a more positive view of happiness, and this was similar to that shown in studies in Iran and Japan [31,32]. In 2018, a study was conducted in Thailand to determine the factors that affect the QOL among the elderly population; it showed that emotional support did contribute significantly to improving the QOL of elderly people [33]. Emotional loneliness among the elderly has been shown to be associated with increased risk of all-cause mortality. Emotional loneliness or not receiving any emotional support happens due to loss or absence of a close emotional attachment figure that can provide a sense of belonging, of companionship, and of being a member of the community [34]. A study done in the United States showed that a community-based intervention for elderly individuals consisting of 90-min group sessions involving elderly receiving emotional support in terms of having positive relationships among others led to a significant increase in life satisfaction and happiness and lowered the levels of depression among the participants [35]. This showed that emotional support among the elderly is crucial to achieve higher levels of happiness leading to healthy ageing. Having family and friends as support has been shown to lead to a better level of overall happiness over a stable period during the ageing process [36]. This study also found that not having any comorbidities significantly contributed to happiness among the elderly. A cross-sectional study conducted among elderly Nepalese showed a similar result, i.e., that elderly individuals without depression based on a geriatric depression scale were happier [37]. A similar finding in Iran showed elderly individuals diagnosed with hypertension had lower happiness levels compared with those without hypertension [38]. A similar result was obtained in one of the studies conducted among older Korean women living alone to determine the predictors of their happiness. The study found that happiness was negatively correlated with the number of comorbidities and having depressive symptoms [39]. Interestingly, a study in Brazil among people with end-stage renal failure undergoing hemodialysis showed that even though they suffered from chronic kidney diseases, a high level of religiosity led to higher happiness [40]. Based on the result, having active social engagement is significantly associated with happiness among the elderly. Social engagement or participation among elderly individuals refers to community-based activities and interpersonal interactions, revolving around resource sharing, active participation and individual satisfaction. It has the elements of individual, environmental and social background, as well as implications on the individual and environment [41]. Individuals with low social participation were found to have a steep decline in psychological well-being, which was not buffered by social support [42]. A similar finding was noted among Chinese elderly whereby social participation had a profound effect on life satisfaction and depression compared with social support [43]. Moreover, individuals with high social participation tend to have more social support than those with low participation [43] since they actively interact and mingle around. Hence, having active social participation was more crucial than having social support [42,43] in determining happiness status among the elderly. In term of HGS, the higher the mean score associated with happiness among the elderly. This is an anthropometric measurement that is also known as arm strength that specify the health of the arm muscle. The HGS also as the indicators of the elderly well-being [44]. Thus, it includes the fundamental of their QOL as well the happiness in daily living [45]. In consequence the HGS, can establish happiness among the elderly population following healthy life style such as being physically active [46]. This was also shown in a study conducted in the younger generation of 145 University students in British, which showed that HGS correlated significantly (r = 0.43) with happiness as the participants perceived themselves on the emotion [47]. Hence, HGS can either directly or indirectly determine the happiness among the population, the young as well the elderly. This study has its own limitations. The older people are not a homogeneous group of frail individuals who progress rapidly towards disease and need of care. Successful and healthy ageing can also be determined by their personality traits, which were not explored in this study. According to Kahlbaugh et al., to have a successful ageing, being open and teachable and having low neuroticism are important factors [48]. Therefore, the personality traits of each elderly individual are additional factors that might contribute to their happiness level. Second, the overall happiness level measure among the respondents was based on a single-item questionnaire and it is a self-rated questionnaire. No confirmatory questions followed. Nonetheless, this method of assessing overall happiness has been commonly used in previous published studies and it is moderately reliable [49–51]. This is the limitation in the JAGES questionnaire. Thus, in the future, we plan to conduct more studies on the life style/well-being and QOL domains among the elderly population in Malaysia. When considering who shall provide emotional support for the elderly, family members are the first to be thought of. Hence, more awareness programs must be initiated among family members regarding emotional support for their elderly. However, there are several circumstances in which family members cannot provide support; hence, having various sources of support is essential. Community-based services are useful for the elderly especially for those who are living alone. Support for the elderly can be found in several places including assisted living facilities, homes or care centers for the elderly, meal delivery or even religious affiliations. These services can provide positive support, either emotional or instrumental, which can help the elderly defeat loneliness and isolation. 5. Conclusions To conclude, for the benefit of the next generation of older people, emotional support and active social engagement among them should be assured to promote lifelong happiness. This study has shown some determinants that we need to look at and explore further to achieve happiness among the Malaysian elderly. Therefore, programs or activities should be structured and established with the aim of strengthening the emotional support and active social engagement in the elderly population. Author Contributions: S.A.S. conceptualized the study and supervised all aspects of its implementation. W.A.H.W.I. and S.R.N. completed the statistical analyses and led the writing of the manuscript. N.S., S.A., Z.b.M. and J.M. assisted in conducting the study and in analyzing the data. Y.S. and M.F.A. assisted in critical revision. All authors contributed to conceptualizing ideas, interpreting findings and reviewing the drafts of the manuscript, and they approved the final version of the manuscript. Funding: This research was funded by the World Health Organization Centre for Health Development (WHO Kobe Centre—WKC), grant number 2018/863819-1. Institutional Review Board Statement: The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Research Ethics Committee of the National University of Malaysia (FF-2018-532; 14 September 2018). Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Data Availability Statement: The research datasets analysed during the current study are available in the Mendeley dataset repository. [https://data.mendeley.com/datasets/5nb6g859m/1] (accessed on 9 February 2021). 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[CrossRef]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3530, 1 ], [ 3530, 7850, 2 ], [ 7850, 12231, 3 ], [ 12231, 15538, 4 ], [ 15538, 20599, 5 ], [ 20599, 24390, 6 ], [ 24390, 28815, 7 ], [ 28815, 33483, 8 ], [ 33483, 37851, 9 ], [ 37851, 43614, 10 ], [ 43614, 48509, 11 ] ] }
2c0d8fa18ce7b3b31603602238c0c5dc3165d0f6	{ "olmocr-version": "0.1.59", "pdf-total-pages": 4, "total-fallback-pages": 0, "total-input-tokens": 13061, "total-output-tokens": 4256, "fieldofstudy": [ "Medicine" ] }	Public Health and Epidemiology Informatics: Recent Research Trends Moving toward Public Health Data Science Sébastien Cossin1,2, Rodolphe Thiébaut1,2,3, Section Editors for the IMIA Yearbook Section on Public Health and Epidemiology Informatics 1 Univ. Bordeaux, Inserm, Bordeaux Population Health Research Center, UMR 1219, Bordeaux, France 2 Centre Hospitalier Universitaire de Bordeaux, Service d’Information Médicale, Bordeaux, France 3 Inria, SISTM, Talence, France Summary Objectives: To introduce and summarize current research in the field of Public Health and Epidemiology Informatics. Methods: PubMed searches of 2019 literature concerning public health and epidemiology informatics were conducted and the returned references were reviewed by the two section editors to select 14 candidate best papers. These papers were then peer-reviewed by external reviewers to allow the Editorial Committee a curated selection of the best papers. Results: Among the 835 references retrieved from PubMed, two were finally selected as best papers. The first best paper leverages satellite images and deep learning to identify remote rural communities in low-income countries; the second paper describes the development of a worldwide human disease surveillance system based on near real-time news data from the GDELT project. Internet data and electronic health records are still widely used to detect and monitor disease activity. Identifying and targeting specific audiences for public health interventions is a growing subject of interest. Conclusions: The ever-increasing amount of data available offers endless opportunities to develop methods and tools that could assist public health surveillance and intervention belonging to the growing field of public health Data Science. The transition from proofs of concept to real world applications and adoption by health authorities remains a difficult leap to make. Keywords Public health, epidemiology, surveillance, medical informatics, International Medical Informatics Association, data science, ethics Introduction The increasing digitization of health data and the recent advances in several fields of computer science such as natural language processing and deep learning offer more opportunities for applications in the domain of public health and epidemiology. Data generated on the Internet can be used to measure the prevalence and incidence of diseases and allows the development of real-time applications to serve the early detection of epidemics [1]. Although easy and cheap to access, Internet data is often noisy and extracting good quality data for decision makers is often very challenging and requires strong and multidisciplinary expertise. Harder to access, electronic health records (EHRs) and clinical data registries contain very high quality data generated by health professionals. Several international initiatives like the Observational Health Data Sciences and Informatics (OHDSI, https://ohdsi.org) aim at facilitating the interoperability and the exploitation of clinical data while guaranteeing data protection and ownership. Recently, the feasibility of building a cohort of hundreds of millions patients across the globe has been demonstrated [2] and the activity opens up new research perspectives at the global scale. A promising technology for public health is the increasing use of mobile phones. The surge of computing power and the ubiquity of mobile phones around the globe make it possible for large populations to participate in public health surveillance and prevention campaigns [3]. Further research is expected to fully leverage this technology for the benefit of public health. This synopsis looks at the literature published in 2019 in the domain of medical informatics applied to public health and epidemiology. The aim is to identify new topics and trends as compared to previous years and describe the selection process of the best papers published in 2019 based on quality and originality of articles. Methods A comprehensive literature search was performed using PubMed/Medline database from NCBI, National Center for Biotechnology Information. Using a large set of MeSH descriptors, the queries targeted public health or epidemiological journal articles over the year 2019 that included medical informatics topics. Returned references addressing topics of the other sections of the Yearbook, e.g., those related to sensors, were excluded from our search. The study was performed at the beginning of January 2020, and the search returned a total of 835 references. Articles were separately reviewed by the two section editors and were first classified into three categories: keep, discard, or leave pending with the BibReview tool [4]. Then, the two lists of references were merged yielding 90 references that were retained by at least one reviewer or classified as “pending” by both of them. The Results The trend towards the increase in the number of publications in infodemiology noticed in 2018 [5] continued in 2019 with new emerging use cases like the monitoring of physical activity using Twitter Data [6], the surveillance of plague outbreak with Google Trends [7], the identification of patients with diabetes or the detection of conjunctivitis epidemics worldwide based on search engine queries [8,9]. One selected best paper describes the development of a global infectious disease database using natural language processing, machine learning, and human expertise [10]. The original idea of this paper was to exploit the publicly available data of the GDELT project that monitors in near real time the world’s broadcast, print, and web news. The system developed was capable of analyzing news in 65 languages to early detect onset of epidemics worldwide. Disease surveillance systems based on social media and search queries aim to measure current disease activity, aka nowcasting, but are still prone to errors due to the imperfect features of the models they rely upon. Priedhorsky et al. [11] proposed the metric of deceptiveness which quantifies the noise in the features of a model. This metric could improve in the future the measurement of disease prevalence and incidence. In order to be adopted by health authorities, there is much room for further research to improve the performance of these statistical models as accurate and reliable estimations of disease activity based on Internet data. EHRs are still a source of high quality information for public health researchers. Post marketing drug surveillance [12, 13] and healthcare-associated outbreaks detection [14, 15] continue to be hot topics of research. Also, as quoted by the survey paper of the Public Health and Epidemiology Informatics section of the 2020 International Medical Informatics Association (IMIA) Yearbook [16], the targeting of sub-populations for dedicated public health interventions is a growing subject of interest. Digital segmentation aims to reach audiences using digital technologies offering new opportunities to deliver appropriate prevention messages. Several studies have already shown the interest of social media for public health campaigns such as smoking cessation [18]. A way to maximize their impact and efficiency could be to identify and target specific audiences. To do so, natural language processing, data mining, and machine learning have been used to classify user traits [19]. The strategy is similar to that of online targeted advertising except that the goal is to deliver dedicated public health, rather than advertising, messages. The second selected best paper applied deep learning on satellite images to identify rural and hard-to-reach remote communities in low-income countries and help community health workers deliver health services [20]. The geographical segmentation of population based on their access to healthcare is needed to organize specific healthcare delivery and to reduce inequalities. Despite the obvious need of these new approaches, the use of phenotyping algorithms to classify individuals raises ethical issues about data privacy, confidentiality, and informed consent. Interestingly, these issues are rarely discussed when information is retrieved from social media, unlike from EHRs where an institutional review board authorization is often mandatory to carry out such analyses. A consensus has yet to emerge to handle Internet data [21]. In the meantime, public health researchers must do their utmost to protect user data and to keep confidential the models of individual prediction. Conclusion The huge amount of data available from Internet, from EHRs, and upcoming from mobile phones, is the fuel for a lot of research on different topics covering statistics, informatics, and epidemiology defining public health Data Science. Acknowledgements We would like to thank the reviewers for their participation in the selection process of the Public Health and Epidemiology Informatics section of the IMIA Yearbook. References 1. Eysenbach G. Infodemiology and infoveillance tracking online health information and cyberbehavior for public health. Am J Prev Med 2011 May;40(5 Suppl 2):S154-8. 2. Hripcsak G, Duke JD, Shah NH, Reich CG, Huser V, Schuemie MJ, et al. Observational Health Data Sciences and Informatics (OHDSI): Opportunities for Observational Researchers. Stud Health Technol Inform 2015;216:574-8. 3. Steinhubl SR, Muse ED, Topol EJ. The emerging field of mobile health. Sci Transl Med 2015 Apr Public Health and Epidemiology Informatics: Recent Research Trends. Moving toward Public Health Data Science 4. Lamy JB, Séroussi B, Griffon N, Kerdelhué G, Jaulet MC, Bouaud J. Toward a Formalization of the Process to Select IMIA Yearbook Best Papers. Methods Inf Med 2015;54:135–44. 5. Thiebaut R, Cossin S. Section Editors for the IMIA Yearbook Section on Public Health and Epidemiology Informatics. Artificial Intelligence for Surveillance in Public Health. Yearb Med Inform 2019 Aug;28(1):232-4. 6. Liu S, Chen B, Kao A. Monitoring Physical Activity Levels Using Twitter Data: Infodemiology Study. J Med Internet Res 2019 Jun 3;21(6):e12394. 7. Bragazzi NL, Mahroum N. Google Trends Predicts Present and Future Plague Cases During the Plague Outbreak in Madagascar: Infodemiological Study. JMIR Public Health Surveill 2019 Mar 8;5(1):e13142. 8. Hochberg I, Daoud D, Shehadeh N, Yom-Tov E. Can internet search engine queries be used to diagnose diabetes? Analysis of archival search data. Acta Diabetol 2019;56(10):1149-54. 9. Deiner MS, McLeod SD, Wong J, Chodosh J, Lietman TM, Porco TC. Google Searches and Detection of Conjunctivitis Epidemics Worldwide. Ophthalmology 2019 Sep;126(9):1219-29. 10. Feldman J, Thomas-Bachli A, Forsyth J, Patel ZH, Khan K. Development of a global infectious disease activity database using natural language processing, machine learning, and human expertise. J Am Med Inform Assoc 2019 Nov;26(11):1355-9. 11. Priedhorsky R, Daughton AR, Barnard M, O’Connell F, O’Sheus D. Estimating influenza incidence using search query deceptiveness and generalized ridge regression. PLoS Comput Biol 2019 Oct 1;15(10):e1007165. 12. Banerji A, Lai KH, Li Y, Saff RR, Camargo CA, Blumenthal KG, et al. Natural Language Processing Combined with ICD-9-CM Codes as a Novel Method to Study the Epidemiology of Allergic Drug Reactions. J Allergy Clin Immunol Pract 2020 Mar;8(3):1032-1038.e1. 13. Lin F-C, Huang S-T, Shang RJ, Wang C-C, Hsiao F-Y, Lin F-J, et al. A Web-Based Clinical System for Cohort Surveillance of Specific Clinical Effectiveness and Safety Outcomes: A Cohort Study of Non-Vitamin K Antagonist Oral Anticoagulants and Warfarin. JMRI Med Inform 2019 Jul 3;7(3):e13329. 14. Bush K, Barbosa H, Faroq S, Weisenthal SJ, Trayhan M, White RJ, et al. Predicting hospital-onset Clostridium difficile using patient mobility data: A network approach. Infect Control Hosp Epidemiol 2019;40(12):1380-6. 15. Sundermann AJ, Miller JK, Marsh JW, Saul MI, Shutt KA, Pacey M, et al. Automated data mining of the electronic health record for investigation of healthcare-associated outbreaks. Infect Control Hosp Epidemiol 2019;40(3):314-9. 16. Bucheridge DL. Precision, Equity, and Public Health and Epidemiology Informatics – A Scoping Review. Yearb Med Inform 2020:226-30. 17. Evans WD, Thomas CN, Favatas D, Snyser J, Briggs J. Digital Segmentation of Priority Populations in Public Health. Health Educ Behav 2019;46(2_suppl):81-9. 18. Naslund JA, Kim SJ, Aschbrenner KA, McCulloch LJ, Brunette MF, Dallery J, et al. Systematic review of social media interventions for smoking cessation. Addict Behav 2017;73:81-93. 19. Chu K-H, Colditz J, Malik M, Yates T, Primack B. Identifying Key Target Audiences for Public Health Campaigns: Leveraging Machine Learning in the Case of Hookah Tobacco Smoking. J Med Internet Res 2019 Jul 21(7):e12443. 20. Bruzelius E, Le M, Kenny A, Downey J, Danilett M, Baum A, et al. Satellite images and machine learning can identify remote communities to facilitate access to health services. J Am Med Inform Assoc 2019 Aug 1;26(8-9):806-12. 21. Hunter RF, Gough A, O’Kane N, McKeeown G, Fitzpatrick A, Walker T, et al. Ethical Issues in Social Media Research for Public Health. Am J Public Health 2018;108(3):343-8. Correspondence to: Sébastien Cossin Univ. Bordeaux, Inserm Bordeaux Population Health Research Center UMR 1219 F-33000 Bordeaux, France E-mail: [email protected] Appendix: Content Summaries of Selected Best Papers for the 2020 IMIA Yearbook, Section ‘Public Health and Epidemiology Informatics’ Brzelius E, Le M, Kenny A, Downey J, Danieleto M, Baum A, Doupe P, Silva B, Landrigan PJ, Singh P Satellite images and machine learning can identify remote communities to facilitate access to health services J Am Med Inform Assoc 2019;26(8-9):806-12 In low-income countries, a promising strategy for improving care access among remote rural population is via the expansion of community health worker (CHW) programs. In settings where census data is missing and vital registration systems are weak, a persistent barrier of the expansion of CHW programs has been the difficulty to accurately enumerate population catchment areas. The authors used satellite-based neural network methods to automate the identification of communities in very rural areas. Training data came from the publicly available SpaceNet corpus and a rural satellite image dataset specifically built for this project. External validation data was provided by a geographic information system dataset identifying all known Liberian communities within the health service catchment area of Last Mile Health, a non-profit organization. Community geolocation data was obtained by sending a team into the field with handheld GPS devices to collect community locations. Then 26,180 candidate rural images were labeled for this project and split into training and testing sets using an 80:20 ratio. The community prediction approach involved recognition of individual buildings from satellite imagery with TensorFlow that output a set of coordinates describing the bounding box of each building. In a second phase, a clustering method was used to identify groups of densely connected buildings indicative of a community. The source code of their program is published. Compared with existing health system community census data, the study method detected 75% of registered communities and identified an additional 167 building groupings that had not previously been identified. This new method for identifying communities in rural and remote settings using satellite imagery and deep learning has the potential to facilitate greater targeting of health services in low-income countries. Feldman J, Thomas-Bachli A, Forsyth J, Patel ZH, Khan K Development of a global infectious disease activity database using natural language processing, machine learning, and human expertise J Am Med Inform Assoc 2019;26(11):1355-9 Rapid onset of infectious disease epidemics can significantly reduce cases and deaths. Online media reports can facilitate timelier identification. The huge volume of media reports and the different languages make the identification of disease activity very challenging. The authors collected media records from the Global Database of Events Language and Tone (GDELT), that monitors the world’s broadcast, print, and web news from nearly every country. Its global coverage and its updates every 15 minutes make it an invaluable source. The authors used Google Translate to translate every media report they found into English. A dictionary containing a curated list of disease names was created. If an article didn’t contain a disease name in its title, the article was deemed irrelevant. To distinguish articles talking about general infectious disease information and about disease activity, a supervised classification model was trained on 8,322 manually labeled articles. Finally, a user interface was built to allow clinical experts to verify articles clustered by disease, location, and time. The authors compared their GDELT-derived feed to the WHO disease Outbreak News reports from July 2017 to June 2018. Their classification model achieved a F1 score of 0.87. On the study period, 37 outbreaks were reported by the WHO. Out of the 37 outbreaks, 89% were covered by online news outlets before the WHO reported the outbreak and the system correctly detected 94% of these events before reported by the WHO with a mean of 43.4 days earlier. Since it takes time for health authorities to investigate and confirm a disease, outbreak media reports can provide timelier information, but news reports fail often to distinguish between suspected and confirmed cases and are prone to false positive errors. Combining natural language processing, machine learning, and human expertise, the authors created an international and near real-time event-based infectious disease activity database.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 4907, 1 ], [ 4907, 9483, 2 ], [ 9483, 13445, 3 ], [ 13445, 17974, 4 ] ] }
2d83b8e412504a56efb0b1e1c3a0bc68520a2f3f	{ "olmocr-version": "0.1.59", "pdf-total-pages": 34, "total-fallback-pages": 0, "total-input-tokens": 150951, "total-output-tokens": 44742, "fieldofstudy": [ "Mathematics", "Physics" ] }	Finite Conformal Quantum Gravity and Nonsingular Spacetimes Leonardo Modesto and Leslaw Rachwał Center for Field Theory and Particle Physics and Department of Physics, Fudan University, 200433 Shanghai, China We explicitly prove that a class of finite quantum gravitational theories (in odd as well as in even dimension) is actually a range of anomaly-free conformally invariant theories in the spontaneously broken phase of the conformal Weyl symmetry. At classical level we show how the Weyl conformal invariance is likely able to tame the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. This latter statement is rigorously proved by a singularity theorem that applies to a large class of weakly non-local theories. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions conformally equivalent to the Schwarzschild metric. Furthermore, we show that the FRW cosmological solutions and the Belinski, Khalatnikov, Lifshitz (BKL) spacetimes, which exactly solve the classical equations of motion, are conformally equivalent to regular spacetimes. Finally, we prove that the Oppenheimer-Volkov gravitational collapse is an exact (singularity-free) solution of the non-local conformally invariant theory compatible with the bounce paradigm. Contents I. Introduction II. The theory A. Propagator and Unitarity B. Super-renormalizability and Finiteness III. Theories in different bases A. The theory in Weyl basis B. The four dimensional theory in Bach basis C. The theory in Einstein basis IV. Singularity Theorem in non-local gravity V. Local higher derivative quantum gravity VI. Non-local conformal gravity VII. Conformal quantum gravity A. Power-counting renormalizability of $[51]$ B. Conformal quantum gravity in odd dimension C. Conformal quantum gravity in $D = 4$ D. Evaluating Feynman diagrams E. Perturbative unitarity F. Unitarity bound and Causality VIII. Spacetime singularities IX. Geodesic completion A: non-conformally coupled point particle probe X. Geodesic completion B: conformally coupled point particle probe Electronic address: [email protected]; Electronic address: [email protected] †Electronic address: [email protected] The problems of quantum gravity are long-standing and probably the most difficult problems of theoretical physics. Many ingenious ideas were proposed in order to find a fully consistent framework for it. One direction of these developments amounted to enlarging the symmetry group governing the gravitational dynamics. Obviously, this group should be fully gauged, so the new gauge symmetry should be realized in a local manner. The original hope was that the Ward identities of this new symmetry could constrain the quantum dynamics and hopefully provide more control over quantum divergences, which typically beset the quantum field theory of gravity. This was only partially successful with the inclusion of supersymmetry and the realization of supergravity models. However, there is still one symmetry, which was often neglected as not pertaining to our world. This is the conformal symmetry relating things at small and large scales. In the most naive version this symmetry was realized as invariance with respect to global transformations of the scale, according to the formula $$x^\mu \rightarrow \Omega x^\mu,$$ (here applied to controvariant dimensionful coordinates on flat Minkowski spacetime.) Later in a fully diffeomorphism (Diff.) covariant framework of general relativity (GR) this was promoted to a local transformation on the metric tensor according to the law $$g_{\mu\nu}(x) \rightarrow \Omega^2(x)g_{\mu\nu}(x).$$ This transformation bears the name of Weyl rescaling and as it is clear it preserves only the angles (normalized scalar products of vectors), but not the spacetime distances (magnitudes of vectors), hence the other name of the symmetry is conformal. Since the scales are not absolute notions in conformally invariant theories, then it is possible to think that this symmetry may be instrumental in solving problems of quantum divergences and classical singularities in gravitational theories. Actually for the first part of the problem the conformal symmetry realized on the quantum level is the solution, because its presence (in both unbroken or spontaneously broken phase) is equivalent to the absence of all divergences. In this paper we make this argument precise and relate it on the other hand to the absence of conformal anomaly. One of the problem with conformal quantum gravity was that it was very difficult to keep conformal invariance on all loop quantum levels, when it was secured on the classical level or to some lower loop levels. In other words this was seen as the problem with returning loop divergences appearing at every level due to non-renormalizability of quantum Einstein-Hilbert (E-H) gravity. Some control over divergences was gained in renormalizable gravitational theories with higher derivatives, however, the problem with unitarity spoiled the physical interpretation of them and rendered them inconsistent. The rescue to this situation came after the invention of weakly non-local gravitational theories \[1–6\]. In this paper we briefly review them and expand about a range of them, in which they are unitary (ghost-free) and perturbatively super-renormalizable in the quantum field theory framework \[1–13\]. Moreover, a recent mild extension of these theories has been proved to be completely finite at any order in the loop expansion \[6\]. In this way for the first time a class of quantum gravity theories was found completely free of any divergences. Therefore, they are candidates to be conformally invariant quantum gravity theories. Originally, they were not written in a form showing explicitly the conformal invariance and this is why later in the article, we propose a conformally invariant reinterpretation of these theories based on the following requirements: (i) general covariance; (ii) explicit conformal invariance (in broken or unbroken phase); (iii) weak non-locality (or quasi-polynomiality); (iv) unitarity (freedom from ghosts) and (v) finiteness at quantum level. In comparison with Einstein gravity we enlarge the symmetry group of gravitational dynamics by the inclusion of conformal invariance, which we believe to be crucial also in removing all kind of spacetime singularities in the classical physical solutions. At classical level in the wake of numerous approximate and exact “singularity-free” solutions [16–20] we were led to believe that the non-locality in the kinetic terms for the fluctuations in the gravitational action was enough to solve the issue of spacetime singularities. However, in [21] we showed that all Einstein spaces, including the singular Schwarzschild and Kerr spacetimes [21], are exact solutions of the non-local theory. Therefore, non-locality is not sufficient to remove the singularities and we need a new (actually old) symmetry principle to get rid out of them. Let us here bring up an analogy between conformal invariance and the role played by Diff. invariance in general relativity. It is well known that the Schwarzschild metric in Schwarzschild coordinates is singular at the event horizon. However, after years of fighting experts of general relativity figured out that such singularity was not physical, but was just an artefact of an unlucky choice of coordinate system. Indeed, by changing coordinates to the Kruskal-Szekeres ones the singularity disappears and the spacetime can be easily extended beyond the event horizon. In this case singularity was of the coordinate type and was removed thanks to the invariance with respect to coordinate transformations. We believe that in the same way, conformal invariance should remove all the spacetime essential singularities. We may consider here a first simple example of spacetime singularities: the initial Big Bang singularity in FRW models. The Weyl tensor for any FRW spacetime is exactly zero, which means that in a conformally invariant theory the flat spacetime and any FRW spacetime are actually the same indistinguishable objects, because they are in the same equivalence class of conformally related metrics. This is in the same way like different coordinate systems describe the same differential manifold, if they are related by a differentiable map in differential geometry. Phrasing differently FRW spacetime is conformally flat, because the tensor of the conformal curvature (Weyl tensor) vanishes there identically. The FRW metrics are to the Weyl tensor like the Minkowski spacetime is to the Riemann tensor. Therefore, there is no invariant physical content in the initial Big Bang singularity in these models in the same way as there is no physical content in the coordinate singularity at the event horizon of a Schwarzschild or Kerr back hole. These arguments are not very new, but actually there is an old [30] and also new very inspiring literature about conformal gravity and its role in removing spacetime singularities [32, 34, 39]. However, our main contribution in this paper lies in proposing a conformally invariant theory that is finite at quantum level, and therefore, a theory that is devoid of any conformal anomaly. Moreover at classical level we have discovered a new class of exact singularity-free black hole solutions in a wide range of conformally invariant theories. These configurations are related by conformal transformations to the original singular Schwarzschild metric and constitute a core of the proposal for a conformal resolution of the black hole singularity. Coming back to the hypotheses listed at the beginning of this section, the other difference with Einstein gravity lies in the third requirement from the above list, namely in the weak non-locality. It makes possible to achieve unitarity and finiteness at the same time of the full quantum theory. This is a solid statement confirmed by numerous studies [1, 2, 4, 5]. The paper is organized as follows. In the second section we remind and expand about a class of ghost-free weakly non-local gravitational theories. We explicitly compute the propagator for wide class of theories that mainly vary for the appearance or not of the Weyl tensor in the action. Power-counting super-renormalizability is in short proved. In the third section we present three range of weakly non-local theories in different basis: Weyl, Bach, and Einstein. In section four we prove a simple but rigorous singularity theorem to be valid for a large class of weakly non-local theories ultraviolet complete. In section five we show the structure of the second variation of the action with respect to the graviton fluctuations in any dimension and we schematically display the one-loop counterterms. In the sixth section a range of classical conformally invariant actions is proposed, while in section seven such theories are studied at quantum level in odd dimension and for the particular case of four spacetime dimensions. It is shown, how the recently proposed finite quantum gravity can take the explicit form of a conformally invariant theory being, moreover, in its spontaneously broken phase. Finally, in sections eight, nine, and ten the spacetime singularities are taken by the horns and we get rid out of them with the help of the conformal symmetry on the footprint of the Narlikar and Kembhavi paper [30]. As an example of singularity resolution we expressly construct a class of singularity-free spherically symmetric black hole solutions and BKL spacetimes. Finally, we study the gravitational collapse for dust matter. In particular in the sections nine and ten we explicitly show the geodesic completion of the above spacetimes making use of two different kind of probes: a massive particle and a conformally coupled particle. The FRW spacetime turns out to be automatically singularity-free in a conformally invariant theory because Weyl flat. At the end we write conclusions and speculate about possible applications of our finite conformal quantum gravity. We wish to emphasize once again that all the results about the resolution of a wide class of spacetime singularities are general features of any conformally invariant theory. However, the quasi-polynomial theories are, at the moment, the only ones compatible with quantum finiteness [6], freedom from conformal anomaly, and perturbative unitarity [8]. For their application to cosmology of early universe we refer the reader to the recent paper [23]. II. THE THEORY The Lagrangian density of the most general $D$-dimensional theory weakly non-local (or quasi-local) and quadratic in the Riemann curvatures reads \[ \mathcal{L}_\gamma = -2\kappa_D^{-2} \sqrt{g} \left( R + \text{Riem} \, \gamma(\Box) \text{Riem} + V \right) = \sqrt{g} \left( R + R_{\mu\nu\rho\sigma} \gamma(\Box)^{\mu\nu\rho\sigma}_{\alpha\beta\gamma\delta} R^{\alpha\beta\gamma\delta} + V \right), \] (3) where the weakly non-local function of the d’Alembertian operator $\gamma(\Box)$ is defined by \[ \gamma(\Box)^{\mu\nu\rho\sigma}_{\alpha\beta\gamma\delta} = g^{\mu\rho} g^{\nu\sigma} g_{\alpha\gamma} g_{\beta\delta} \gamma(\Box) + g^{\mu\rho} g_{\nu\sigma} g_{\alpha\gamma} g^{\beta\delta} \gamma(\Box) + \delta^{\mu\nu} \delta^{\rho\sigma} \delta^{\alpha\gamma} \delta^{\beta\delta} \gamma_4(\Box). \] (4) The theory consists of a kinetic weakly non-local operator quadratic in the curvature, three entire functions $\gamma_0(\Box)$, $\gamma_2(\Box)$, and a potential $V$, which we choose hereby to be local and at least cubic in the curvature. In general dimension $D$ it is made up of the following three sets of operators, \[ V = \sum_{j=3}^{N+2} \sum_{k=3}^{j} c_{k,i} \left( \nabla^2(j-k) R^k \right)_i + \sum_{j=N+3}^{j} \sum_{k=3}^{j} d_{k,i} \left( \nabla^2(j-k) R^k \right)_i + \sum_{k=3}^{j} s_{k,i} \left( \nabla^2(j+N+2-k) R^k \right)_i, \] (5) where operators in the third set are called killers, because they are crucial in making the theory finite in any dimension. The coefficients, $c_{k,i}$, $d_{k,i}$, $s_{k,i}$ are coupling constants (only $c_{k,i}$ are undergoing RG running), while the tensorial structure of operators present in $V$ have been neglected.\footnote{Definitions \textendash\ The metric tensor $g_{\mu\nu}$ has signature $(-\cdots)$ and the curvature tensors are defined as follows: $R_{\mu\nu\rho\sigma} = -\partial_\nu \Gamma_{\rho\sigma}^\mu + \cdots$, $R_{\mu\nu} = R_{\rho\mu\rho\nu}$, $R = g^{\rho\sigma} R_{\rho\mu\nu}$. With symbol $R$ we generally denote one of the above curvature tensors.} The minimal choice compatible with unitarity and super-renormalizability corresponds to the form factor $\gamma_0(\Box)$. As a matter of fact we can also add other operators quadratic in the curvature and equivalent to the above operators up to interaction vertices. These operators correspond to a different ordering of derivatives in the form factors in-between the Riemann, Ricci, and scalar curvatures. We name these operators “terminators”. However, such non-local operators can be crucial in making the theory finite.\footnote{Definitions \textendash\ The metric tensor $g_{\mu\nu}$ has signature $(-\cdots)$ and the curvature tensors are defined as follows: $R_{\mu\nu\rho\sigma} = -\partial_\nu \Gamma_{\rho\sigma}^\mu + \cdots$, $R_{\mu\nu} = R_{\rho\mu\rho\nu}$, $R = g^{\rho\sigma} R_{\rho\mu\nu}$. With symbol $R$ we generally denote one of the above curvature tensors.} The form factor $\gamma_0(\Box)$ must take the following particular forms, if we require the same spectrum as in the quantum Einstein-Hilbert gravity around Minkowski spacetime. We write them in terms of exponentials of entire functions $H_\ell(z)$ ($\ell = 0, 2$), namely \[ \gamma_0(\Box) = \frac{-(D-2)(e^{H_0} - 1) + D(e^{H_2} - 1)}{4(D-1)\Box} + \gamma_4(\Box), \quad \gamma_2(\Box) = \frac{e^{H_2} - 1}{\Box} - 4\gamma_4(\Box). \] (6) The form factor $\gamma_4(\Box)$ stays arbitrary, but is only constrained by renormalizability to have the same (or lower in number of derivatives) asymptotic UV behaviour as the other two form factors $\gamma_0(\Box)$ ($\ell = 0, 2$). Due to dimensional reasons the form factor $\gamma_4(\Box)$ can be written as $\gamma_4(\Box)/D$, where now $\gamma_4(\Box)$ as well as $e^{H_0}$ and $e^{H_2}$ are dimensionless functions. The minimal choice compatible with unitarity and super-renormalizability corresponds to $\gamma_0(\Box) = 0$. As a matter of fact we can also add other operators quadratic in the curvature and equivalent to the above operators up to interaction vertices. These operators correspond to a different ordering of derivatives in the form factors in-between the Riemann, Ricci, and scalar curvatures. We name these operators “terminators”. However, such non-local operators can be crucial in making the theory finite.\footnote{Definitions \textendash\ The metric tensor $g_{\mu\nu}$ has signature $(-\cdots)$ and the curvature tensors are defined as follows: $R_{\mu\nu\rho\sigma} = -\partial_\nu \Gamma_{\rho\sigma}^\mu + \cdots$, $R_{\mu\nu} = R_{\rho\mu\rho\nu}$, $R = g^{\rho\sigma} R_{\rho\mu\nu}$. With symbol $R$ we generally denote one of the above curvature tensors.} Finally, the entire functions $V_\ell^{-1}(z) \equiv \exp H_\ell(z)$ ($z \equiv -\Box / \Lambda^2$) ($\ell = 0, 2$) introduced in $\Box$ are required to be real and positive on the real axis and without zeros on the whole complex plane $\|z\| < +\infty$. This requirement implies that there are no other gauge-invariant poles than the transverse massless pole of the physical graviton (the same like in E-H theory). We note that $\Lambda$ is an invariant mass scale in our fundamental theory, which later will be called the scale of non-locality. Moreover, there exists an angle $\Theta$ ($0 < \Theta < \pi/2$ ), such that asymptotically \[ \|V^{-1}(z)\| \to \|z\|^{\gamma + N + 1}, \text{ when } \|z\| \to +\infty \text{ with } \gamma > \frac{D_{\text{even}}}{2} \text{ or } \gamma > \frac{D_{\text{odd}} - 1}{2}, \] (8) for the complex values of $z$ in the conical regions $C$ defined by: $C = \{ z \| -\Theta < \arg z < +\Theta, \pi - \Theta < \arg z < +\pi + \Theta \}$. The last condition is necessary to achieve the maximum convergence of the theory in the UV regime and at the same time to avoid non-local counterterms. One example of such function is: \[ V^{-1}(z) = e^{\frac{1}{2} \left[ 1 + \log((p(z)^2) + \gamma e^{1+\log(p(z)^2}) \right]}, \] (9) where $p(z)$ is a polynomial of degree $\gamma + N + 1$. To achieve (super-)renormalizability the degrees of the polynomials appearing in the definitions of $V_0^{-1}(z)$ and $V_2^{-1}(z)$ must be equal. In the rest of the paper we will denote the common degree by $\gamma + N + 1$. ### A. Propagator and Unitarity Now we want to obtain the propagator of the gravitational fluctuations around flat Minkowski background and discuss the issue of unitarity of the theory. Splitting the spacetime metric into the background and the fluctuation $h_{\mu\nu}$ defined by $g_{\mu\nu} = \eta_{\mu\nu} + \kappa_D h_{\mu\nu}$, we can expand the action $^{(3)}$ to the second order in $h_{\mu\nu}$. The result of this expansion together with the usual harmonic gauge fixing term reads $^{(40)}$ $$\mathcal{L}_{\text{quad}} + \mathcal{L}_{\text{GF}} = h^{\mu\nu} \mathcal{O}_{\mu\nu,\rho\sigma} h_{\rho\sigma}/2,$$ where the operator $\mathcal{O}$ is made up of two terms, one coming from the quadratization of $^{(3)}$ and the other one from the following gauge-fixing term, $\mathcal{L}_{\text{GF}} = \xi^{-1} \partial^\rho h_{\mu\nu} \omega(-\Box) \partial^\sigma h_{\rho\sigma}$, where $\omega(-\Box)$ is a weight functional $^{(41–43)}$ and $\xi$ a gauge parameter. The d’Alembertian operator in $\mathcal{L}_{\text{quad}}$ and the gauge fixing term are written in terms of flat spacetime metric and partial derivatives. Inverting the operator $\mathcal{O}$ $^{(40)}$ and making use of the form factors defined in $^{(6)}$, we find the two-point function in the harmonic gauge ($\partial^\rho h_{\mu\nu} = 0$), $$O^{-1} = \frac{\xi(2P^{(1)} + \tilde{P}^{(0)})}{2k^2 \omega(k^2/\Lambda^2)} + \frac{P^{(2)}}{k^2 e^{2H_2(k^2/\Lambda^2)}} - \frac{P^{(0)}}{(D - 2) k^2 e^{2H_0(k^2/\Lambda^2)}}.$$ Above we omitted the tensorial indices for the propagator $O^{-1}$ and the usual projectors $\{P^{(2)}, P^{(1)}, P^{(0)}, \tilde{P}^{(0)}\}$ are defined in $^{(40–44)}$. We have also replaced $-\Box \rightarrow k^2$ in the quadratized action, thus writing it in momentum space. The propagator $^{(11)}$ describes the most general p-spectrum compatible with unitarity without any other degree of freedom besides the massless spin 2 graviton field. We see that gauge-invariant are only terms proportional to $P^{(2)}$ and $P^{(0)}$. Unitarity is satisfied, because the propagator is given by multiplication of these two projectors by entire functions, respectively $e^{H_2}$ and $e^{H_0}$, which do not give rise to any additional pole. Moreover, the optical theorem for the interaction between two gravitational sources $T_{1,2}(k)$ is trivially satisfied, namely $$2 \text{Im} \{T_1(k)^{\mu\nu} O_{\mu\nu,\rho\sigma}^{-1} T_2(k)^{\rho\sigma}\} = 2\pi \text{Res} \{T_1(k)^{\mu\nu} O_{\mu\nu,\rho\sigma}^{-1} T_2(k)^{\rho\sigma}\} \big\|_{k^2 = 0} > 0,$$ where $T^{\mu\nu}(k)$ is the most general conserved energy-momentum tensor written in momentum space. In the appendix B we give two more examples of theories written in different bases, which nonetheless give rise to the same propagator as computed in this section. Unitarity is proved by perturbing the Minkowski spacetime and the absence of ghosts and tachyons tells us about the stability of the flat spacetime. We can not exclude at the moment the presence of ghosts around other exact backgrounds. However, the theory is weakly non-local and the analysis developed in $^{(46, 47)}$ can be applied to the stability of the flat spacetime. We can not exclude at the moment the presence of ghosts around other exact backgrounds, because non-locality avoids the “ghost catastrophe”. This observation is quite remarkable, because it clarifies once and for all about the perturbative stability of gravitational fluctuations around any background. Indeed, the non-locality scale $\Lambda$ regularizes in a Lorentz-invariant way the decay probability $^{(46, 48)}$ and the eventual presence of a real ghost tells about the lifetime of such spacetime, which can be very short or very long, but not identically zero, depending on the mass of the ghost developing around the peculiar background (the value of the mass can be read from the quadratic action and could be related to the mass scale $\Lambda$ and/or the form factor.) If there is such occurrence, unitarity is safe because the optical theorem can be satisfied whether it is taken the opposite prescription respect to normal particles to move out the real axis the pole, i.e \| physical particle \| ghost (negative norm state) \| ghost (positive norm state) \| \|-------------------\|-----------------------------\|-----------------------------\| \| $\frac{-1}{k^2 + i\epsilon}$ \| $\frac{-1}{k^2 + i\epsilon}$ \| $\frac{-1}{k^2 + i\epsilon}$ \| Indeed, we can calculate the scattering amplitude $T$, which is defined in terms of the $S$–matrix through the definition $S = 1 + iT$, to show that the optical theorem is satisfied, namely $$\frac{-1}{k^2 + i\epsilon} = P \left(\frac{-1}{k^2}\right) + i\pi\delta(k^2) \quad \Rightarrow \quad 2\text{Im} T_{if} = 2\text{Im} \left[(-i)(-i)^2 \frac{1}{i k^2 + m^2 + i\epsilon}\right] \rightarrow 2\pi\delta(k^2 + m^2).$$ where the first factor $(-i)$ in the second equivalence above comes from the definition of $T$ and the second $(-i)^2$ keeps track of the second order expansion of the $S$-matrix. The tensorial structure and the contraction of the propagator $[12]$ with the energy-momentum tensor are the same of $[11, 40]$. The price to be paid is that the particles with negative energy are the ones that propagate forward in time, therefore the ghosts possess negative energy. This implies that in a scattering process involving normal particles and ghosts the energies of the normal particles can increase leading to a catastrophic instability of the vacuum (background) $[51]$. However, in a non-local theory the catastrophe is avoided as explained above and in $[46, 47]$. Let us consider a local theory consisting of a massless normal particle and a ghost-like particle with mass $m$. The propagator reads, \[ \frac{1}{k^2 - i\epsilon} = \frac{1}{k^2} - \frac{1}{k^2 + m^2}. \] (13) When we adopt the unitary prescription to avoid the pole in $k^2 = -m^2$ the high energy convergence of the theory due to the propagator scaling $\sim 1/k^4$ is spoiled. This is due to the difference between the convergent propagator and the unitary one $[41]$, namely \[ \frac{1}{k^2} - \frac{1}{k^2 + m^2} = -2\pi \delta(k^2 + m^2). \] (14) When the extra $\delta(k^2 + m^2)$ is integrated inside loop diagrams new non-renormalizable divergences are generated $[41]$. The same argument applies to a weakly non-local theory where likely the distribution $e^{-H(k^2)}\delta(k^2 + m^2)$ is actually equivalent to the distribution $e^{-H(m^2)}\delta(k^2 + m^2)$. We end up with a non-renormalizable theory when we quantize the action around an unstable shortly- or longly-lived vacuum. The lifetime of the vacuum sets the shorter distance that can be measured and the effective action keeps track of the second order expansion of the $\mathcal{L}$ in momentum space scales schematically as: \[ g \propto \frac{1}{k^2} \quad \text{at leading order in } \frac{1}{k^2}. \] B. Super-renormalizability and Finiteness We now review the power-counting analysis of quantum divergences. In the high energy regime, the above propagator $[10]$ in momentum space scales schematically as: $O^{-1}(k) \sim k^{-(2\gamma + D)}$. The vertices can be collected in different sets that may or may not involve the entire functions $e^{\int \mathcal{L}(z)}$. However, to find a bound on the quantum divergences it is sufficient to concentrate on the leading operators in the UV regime. These operators scale as the propagator giving the following upper bounds on the superficial degree of divergence of any graph $\omega(G)$ in even dimension $[4, 44]$, \[ \delta^D(K) \Lambda^{2\gamma(L-1)} \int (d^D p)^L \left( \frac{1}{p^{2\gamma+D}} \right)^I (p^{2\gamma+D})^V = \delta^D(K) \Lambda^{2\gamma(L-1)} \int (d^D p)^L \left( \frac{1}{p^{2\gamma+D}} \right)^L - \omega(G) \equiv D - 2\gamma(L - 1), \] (15) where we have introduced the following notation: $V$ for the numbers of vertices, $I$ for the number of internal lines, $L$ for the number of loops, $K$ for the sum of external momenta, $\Lambda_{\text{cut-off}}$ for the cut-off scale. We also used the topological relation valid for any graph: $I = V + L - 1$. Thus, if $\gamma > D/2$, only 1-loop divergences survive. Therefore, in even dimension the theory is super-renormalizable $[1, 2, 3, 42]$ and only a finite number of operators of mass dimension up to $D$ has to be included in the action in the renormalization procedure. In spacetimes of odd dimension we have defined $D_{\text{odd}} + 1 = 2N + 4$ and therefore \[ \omega(G)_{\text{odd}} = D_{\text{odd}} - (2\gamma + 1)(L - 1), \] (16) and for $\gamma > (D_{\text{odd}} - 1)/2$ there are at most one loop divergences. However, in odd dimension we can not construct any curvature invariant with an odd number of derivatives and the theory is completely finite (see also $[43]$. For the sake of simplicity we can assume that at the end of section in section (II) (see formulas (18)) with form factors defined by a curvature potential. Further specifications of this theory are possible in order to achieve finiteness at quantum level. It is enough to include D even dimension. In Riemann or Weyl tensors are sufficient to end up with all beta functions identically zero, namely \[ V(R) = s^{(1)}_R R_{\mu\nu} R^{\mu\nu} \Box^{-2} R_{\alpha\beta} R^{\alpha\beta} + s^{(2)}_R R^2 \Box^{-2} R^2, \] or in terms of Weyl tensor solely. \[ V(C) = s^{(1)}_C C_{\mu\nu\rho\sigma} C^{\mu\nu\rho\sigma} \Box^{-2} C_{\alpha\beta\gamma\delta} C^{\alpha\beta\gamma\delta} + s^{(2)}_C C_{\mu\nu\rho\sigma} C^{\alpha\beta\gamma\delta} \Box^{-2} C_{\alpha\beta\gamma\delta} C^{\mu\nu\rho\sigma}. \] These operators give contributions to the beta functions for $ R^2 $ and $ \text{Ric}^2 $ linear in the front coefficients $ s^{(1)}_R, s^{(2)}_R $ or $ s^{(1)}_C, s^{(2)}_C $. Therefore, we can always make zero the beta function with a suitable choice of the non-running coefficients. This is evident in the background field method because at one loop we need the second order variation of the action respect to $ h_{\mu\nu} $, and such variation can be at least quadratic in the curvature for the operators (17) and (18) because they are quartic in the Riemann tensor. Contributions to the second order variation higher in curvature do not affect the beta functions $ \beta_{R^2} $ and $ \beta_{\text{Ric}^2} $. See the references [5–7] for more details about super-renormalizability, finiteness, and killer operators. ### III. THEORIES IN DIFFERENT BASES In this section we consider three weakly non-local gravitational actions out of the general ones introduced in section [III]. All these theories will contain three operators: the Einstein-Hilbert local operator and two non-local operators quadratic in the curvature. The first theory is quadratic in the Ricci tensor and the Weyl tensor, the second one is quadratic in the Ricci scalar and the Bach tensor, the third one is quadratic in the Ricci tensor and Ricci scalar. All these theories are ghost free, perturbative unitary, and super-renormalizable or finite at quantum level. #### A. The theory in Weyl basis We hereby define a class of theories in the Weyl basis. These theories are equivalent to the previous ones [3] for everything about unitarity (the propagator is given again by (10)) and super-renormalizability. Also finiteness can be easily gotten, if we slightly modify the killer operator terms. The general Lagrangian density reads, \[ L_C = -2 \kappa^{-2}_D \sqrt{\|g\|} \left[ R + C \gamma_C(\Box) C + R \gamma_S (\Box) R + \text{Riem} \gamma_R (\Box) \text{Riem} + V(C) \right], \] with form factors defined by \[ \gamma_C = \frac{D - 2}{4} \gamma_2, \quad \gamma_S = \gamma_0 + \frac{1}{2(D - 1)} \gamma_2 \quad \text{and} \quad \gamma_R = \gamma_4 + \frac{D - 2}{4} \gamma_2, \] where all the form factors $ \gamma_\ell (\ell = 0, 2) $ are defined in [3]. Solving for $ \gamma_C, \gamma_S $ and $ \gamma_R $ we find \[ \gamma_C = \frac{(2 - D) \left( e^{H_2} - 1 - 4 \gamma_4 \Box \right)}{4 \Box}, \] \[ \gamma_S = \frac{(2 - D) \left( e^{H_0} + e^{H_2} - 2 \right) + 4 \gamma_4 (D - 3) \Box}{4(D - 1) \Box}, \] \[ \gamma_R = \frac{(D - 2) \left( e^{H_2} - 1 \right) - 4 \gamma_4 (D - 3) \Box}{4 \Box}. \] For the sake of simplicity we can assume $ \gamma_R = 0 $, and the theory (19) reduces to \[ L_C = -2 \kappa^{-2}_D \sqrt{\|g\|} \left[ R + C \gamma_C(\Box) C + R \gamma_S (\Box) R + V(C) \right], \quad \gamma_C = \frac{D - 2}{4(D - 3)} \frac{e^{H_2} - 1}{\Box}, \quad \gamma_S = -\frac{D - 2}{4(D - 1)} \frac{e^{H_0} - 1}{\Box}. \] Further specifications of this theory are possible in order to achieve finiteness at quantum level. It is enough to include a curvature potential $ V $ that is built up with only Weyl tensors, namely $ V(C) $. This can always be done as explained at the end of section in section [III] (see formulas [18].) ingularity, has no general validity, and only a new symmetry can definitely remove the spacetime singularities. Therefore, the non-local smearing of the source, so successful in removing the Newtonian singularity, are exact solutions in extra dimension too. Notice that all the Ricci flat and the FRW spacetimes for the case of traceless matter are exact solutions in extra dimension. The above claim will be rigorously proved later in this paper making use of a simple theorem. It is straightforward to see from the first variation of the action that all Ricci flat spacetimes and the FRW spacetimes, whether they are sourced by a traceless energy tensor, are exact solutions of the classical equations of motion. This completes and makes even stronger the claim in the paper [21], namely we have here an example of finite spacetimes, whether they are sourced by a traceless energy tensor, are exact solutions of the classical equations of motion. In this section we publish for the first time a super-renormalizable or finite theory of gravity in $D = 4$ making use of the Ricci scalar and the Bach tensor that is defined by $$B_{ac} = \nabla^b \nabla^d C_{abcd} - R^{bd} C_{abcd}$$ $$\equiv \frac{1}{2} R_{ac} - \frac{1}{12} g_{ac} \Box R - \frac{1}{6} \nabla^c \nabla_a R - R^{bd} C_{abcd} - \frac{1}{3} R R_{ac} - \frac{1}{4} g_{ac} R_{bd} R^{bd} + \frac{1}{12} g_{ac} R^2.$$ \hspace{1cm} (25) The Bach tensor has zero divergence and conformal weight $-2$, i.e. $$\nabla^c B_{ac} = 0 , \quad B^{\Omega}_{ab} = \Omega^{-2} B_{ab}.$$ \hspace{1cm} (26) Notice that $B_{ab}$ is identically zero for Ricci flat and FRW metrics. The four dimensional Lagrangian reads $$\mathcal{L}_B = -2 \kappa_4^{-2} \sqrt{\|g\|} \left[ R + B \gamma_B(\Box)B + R \gamma_S(\Box)R + V(B) \right], \quad \gamma_B = \frac{4}{\Box^3} \frac{e^{H_2} - 1}{\Box^3} , \quad \gamma_S = - \frac{1}{6} \frac{e^{H_0} - 1}{\Box}.$$ \hspace{1cm} (27) It is straightforward to see from the first variation of the action that all Ricci flat spacetimes and the FRW spacetimes, whether they are sourced by a traceless energy tensor, are exact solutions of the classical equations of motion. This completes and makes even stronger the claim in the paper [21], namely we have here an example of finite quantum gravity with the same black hole and cosmological Big Bang singularities of Einstein gravity present in exact solutions on classical level. Therefore, the non-local smearing of the source, so successful in removing the Newtonian singularity, has no general validity, and only a new symmetry can definitely remove the spacetime singularities. The above claim will be rigorously proved later in this paper making use of a simple theorem. We can use the tensor defined in (24) also in any dimension, but the conformal properties of $B_{ab}$ are not preserved in extra dimension. The multidimensional theory reads$^2$, $$\mathcal{L}_B = -2 \kappa_D^{-2} \sqrt{\|g\|} \left[ R + B \gamma_B(\Box)B + R \gamma_S(\Box)R + V(B) \right], \quad \gamma_B = \frac{(D - 2)}{(D - 3)} \left( \frac{e^{H_2} - 1}{\Box^3} \right), \quad \gamma_S = - \frac{(D - 2)(D - 3) (e^{H_0} - 1) + D(D - 4) (e^{H_2} - 1)}{4(D - 1)(D - 3)\Box}.$$ \hspace{1cm} (29) Notice that all the Ricci flat and the FRW spacetimes for the case of traceless matter are exact solutions in extra dimension too. C. The theory in Einstein basis Last but not least, we express the theory in the original basis introduced in [3, 4]. For the sake of simplicity we assume $\gamma_4 = 0$ in (24), $$\mathcal{L}_E = -\frac{2}{\kappa_D^2} \sqrt{\|g\|} \left[ R + G \gamma_G(\Box)\text{Ric} + R \gamma_{S'}(\Box)R + V \right].$$ \hspace{1cm} (31) $^2$ A useful formula we made use to compute the propagator is: $$B_{ac} = \nabla^b \nabla^d C_{abcd} - R^{bd} C_{abcd} = \frac{D - 3}{D - 2} R_{ac} - \frac{D - 3}{2(D - 1)} R_{ac} + \frac{D(D - 3)}{(D - 2)^2} R_{ab} R_{cd} - \frac{D - 3}{D - 2} R^{bd} C_{abcd} - \frac{D - 3}{(D - 2)^2} g_{ac} R_{bd} R^{bd}$$ $$- \frac{D(D - 3)}{(D - 1)(D - 2)^2} R R_{ac} - \frac{D - 3}{2(D - 1)(D - 2)} g_{ac} \Box R + \frac{D - 3}{(D - 1)(D - 2)^2} g_{ac} R^2 - R^{bd} C_{abcd}.$$ \hspace{1cm} (28) with form factors given by \[ \gamma_G = \gamma_2 = \frac{e^{H_2} - 1}{\Box}, \quad \gamma_{S'} = \frac{1}{2} \gamma_2 + \gamma_0 = \frac{D - 2}{4(D - 1)} \frac{e^{H_2} - e^{H_0}}{\Box}. \] (32) We can make the further minimal choice $ H_0 = H_2 $ and the theory reduces to \[ \mathcal{L}_E = -2\kappa_D^{-2} \sqrt{\|g\|} \left[ R + G \gamma_G(\Box)\text{Ric} + V \right], \] (33) where $ \gamma_G $ is given in (32). Notice that for $ H_0 = H_2 $ the spacetime dimension $ D $ disappears from the action. IV. SINGULARITY THEOREM IN NON-LOCAL GRAVITY Throughout all the paper we pointed out more times that almost on all spacetime singularity of Einstein gravity remain in non-local theories. In this section we explicitly prove a simple singularity theorem based on the very general theory (29). Theorem.* Given the EOM $ E_{\mu\nu} = 8\pi G_N T_{\mu\nu} $ for the theory (29), which we derive below in a very compact form, the following implication turns out to be true, - $ R_{\mu\nu} = 0 $ \& $ T_{\mu\nu} = 0 $ $ \implies $ $ E_{\mu\nu} = 0 $; - $ R_{\mu\nu} = 8\pi G_N T_{\mu\nu} $ \& $ T_{\mu}^{\mu} = 0 $ $ \implies $ $ E_{\mu\nu} = 8\pi G_N T_{\mu\nu} $. Therefore, - all Ricci flat spacetimes are exact solutions of the theory (29); - all the FRW spacetime sourced by conformally coupled matter are exact solutions of the theory (29). The theorem works for any potential at least quadratic in the Bach tensor. Proof. Let us start writing the exact EOM in a short and very compact notation, namely \[ E_{\mu\nu} = \frac{\delta}{\delta g^{\mu\nu}} \left[ \sqrt{\|g\|} \left( R + R\gamma_S(\Box)R + B_{\alpha\beta} B^{\alpha\beta} + V(B) \right) \right] \] \[ = G_{\mu\nu} - \frac{1}{2} g_{\mu\nu} (R\gamma_S(\Box)R) - \frac{1}{2} g_{\mu\nu} (B_{\alpha\beta} B^{\alpha\beta}) + 2 \frac{\delta R}{\delta g^{\mu\nu}} (\gamma_S(\Box)R) + \frac{\delta B_{\alpha\beta}}{\delta g^{\mu\nu}} (\gamma_B(\Box) B^{\alpha\beta}) + \frac{\delta B^{\alpha\beta}}{\delta g^{\mu\nu}} (\gamma_B(\Box) B_{\alpha\beta}) \] \[ + \frac{\delta \Box^r}{\delta g^{\mu\nu}} \left( \frac{\gamma_S(\Box^l)}{\Box^l} - \frac{\gamma_S(\Box^r)}{\Box^r} \right) R + \frac{\delta \Box^r}{\delta g^{\mu\nu}} \left( \frac{\gamma_B(\Box^l)}{\Box^l} - \frac{\gamma_B(\Box^r)}{\Box^r} \right) B_{\alpha\beta} B^{\alpha\beta}, \] \[ \frac{1}{\sqrt{\|g\|}} \delta V = 8\pi G_N T_{\mu\nu}, \] (34) where $ \Box^l, r $ act on the left and right arguments (on the right of the incremental ratio) as indicated inside the brackets. We observe that when we replace $ R_{\mu\nu} = 0 $ and $ T_{\mu\nu} = 0 $ in the above EOM (34) the tensor $ E_{\mu\nu} $ is identically zero. Indeed, the EOM contain operators linear and quadratic respectively in the Ricci or the Bach tensor and the Bach tensor vanishes when $ \text{Ric} = 0 $. Therefore, the first item of the theorem is proved. We now proceed with the second item. For the FRW spacetimes the Bach tensor is identically zero (see the definitions (24) and (28) and when radiation (or general conformal matter) is coupled to the gravitational theory (29) only the term quadratic in the Ricci scalar and the Einstein-Hilbert term in the action (29) give contribution to the EOM. This is clear looking at the EOM (34). Indeed, all the terms containing the Bach tensor (without variation respect to the metric) are identically zero for any FRW spacetime. Therefore, the EOM simplify to \[ G_{\mu\nu} - \frac{1}{2} g_{\mu\nu} (R\gamma_S(\Box)R) + 2 \frac{\delta R}{\delta g^{\mu\nu}} (\gamma_S(\Box)R) + \frac{\delta \Box^r}{\delta g^{\mu\nu}} \left( \frac{\gamma_S(\Box^l)}{\Box^l} - \frac{\gamma_S(\Box^r)}{\Box^r} \right) R = T_{\mu\nu}. \] (35) We now evaluate the trace of the above EOM (35), \[ R + \frac{D}{2} R\gamma_S(\Box)R - 2 g^{\mu\nu} \frac{\delta R}{\delta g^{\mu\nu}} (\gamma_S(\Box)R) - g^{\mu\nu} \frac{\delta \Box^r}{\delta g^{\mu\nu}} \left( \frac{\gamma_S(\Box^l)}{\Box^l} - \frac{\gamma_S(\Box^r)}{\Box^r} \right) R = 0. \] (36) Notice that the right hand side is identically zero because for radiation (and any other conformal matter coupled to gravity) the trace of the energy tensor vanishes. The trace of the EOM is solved by $ R = 0 $ that we can replace in (35) and we finally end up with the Einstein equations. Therefore, we end up with exactly the same reduced EOM as for Einstein gravity and the usual Big Bang singular solution for a radiation dominated universe is unavoidable. In short we can summarize the proof of the second item with the following chain of implications, \[ \text{tr} \, \mathbf{T} = 0 \implies R = 0 \implies G = 8\pi G_N \, \mathbf{T} \implies \text{Big Bang Singularity}. \] (37) At this level we have proved that the spacetime singularities show up also in a finite theory of quantum gravity. We believe that only a fundamental symmetry principle may sweep away the spacetime singularities. V. LOCAL HIGHER DERIVATIVE QUANTUM GRAVITY In this technical section we study a quite general local super-renormalizable quantum gravity. The results will be exported later to our unitary weakly non-local super-renormalizable gravitational theory. For our goals the theory in this section can be consider as a kind of prototype. This is possible, because the local and weakly non-local theories under investigation have the same divergences and therefore the same beta functions. Let us start with the following general prototype for a local super-renormalizable action, \[ S_{\text{HD}} = \int d^D x \sqrt{\|g\|} \left[ \lambda - 2\kappa^2 R + 2\kappa^2 \sum_{n=0}^{\gamma+N} \omega R_{\text{Ric},n} R_{\mu\nu} \Box_n R_{\mu\nu} + 2\kappa^2 \sum_{n=0}^{\gamma+N} \omega R_{\nu} R \Box_n^\nu R \right]. \] (38) In background field method the metric $ g_{\mu\nu} $ is split into a background metric $ \bar{g}_{\mu\nu} $ and a quantum fluctuation $ h_{\mu\nu} $, \[ g_{\mu\nu} = \bar{g}_{\mu\nu} + h_{\mu\nu}. \] (39) Sometimes below we will denote these metrics by $ g, \bar{g} $ and $ h $ without writing covariant indices explicitly. Additionally from now on we will not speak, in this section, about the full metric $ g $ and for simplicity of notation the background metric will be denoted again by $ g $. Since the theory is diff. invariant we have to fix the gauge and in the quantization procedure we must introduce Faddeev-Popov (FP) ghosts. The gauge-fixing and FP-ghost actions read as follows, \[ S_{\text{gf}} = \int d^D x \sqrt{\|g\|} \frac{1}{2} \chi_\mu C^{\mu\nu} \chi_\nu, \quad \chi_\mu = \nabla_\sigma h^\sigma_{\mu} - \beta_\mu \nabla_\mu h, \quad C^{\mu\nu} = -\frac{1}{\alpha_\beta} (g^{\mu\nu} \Box + \gamma_\mu \nabla^\mu \nabla^\nu - \nabla^\nu \nabla_\mu) \Box^{N+\gamma}_\Lambda, \] (40) \[ S_{\text{gh}} = \int d^D x \sqrt{\|g\|} \left[ \bar{C}_\alpha M^\alpha_{\beta} C^\beta + \frac{1}{2} b_\alpha C^{\alpha\beta} b_\beta \right], \quad M^\alpha_{\beta} = \Box \delta^\alpha_\beta + \nabla^\alpha \nabla^\beta - 2\beta_\gamma \nabla^\alpha \nabla^\beta. \] (41) In (40) and (41) we used covariant gauge-fixing condition $ \chi_\mu $ with weight function $ C^{\mu\nu} $ (the special case of it is an $ \omega(\Box) $ appearing in the harmonic gauge fixing as introduced in section (11A)). The standard (complex) FP-ghost and anti-ghost fields we denote by $ C^{\beta} $ and $ \bar{C}_\alpha $, respectively. Due to the higher derivative character of our theory we are forced to introduce also a third (real-)ghost field $ b_\alpha $, which we appoint $ b_\alpha $. The gauge-fixing parameters $ \beta_\mu $ and $ \gamma_\mu $ are dimensionless, while $ \alpha_\beta = M^{4-D} $. We notice right here that in our theory the beta functions are independent of these gauge parameters (see [42] for a rigorous proof). The partition function of the full quantum theory with the right functional measure compatible with BRST invariance [54, 50] reads \[ Z[g] = \mu(g, h) \prod_{\mu \leq \nu} \mathcal{D} h_{\mu\nu} \prod_\alpha \mathcal{D} \bar{C}_\alpha \prod_\beta \mathcal{D} C^\beta \prod_\gamma \mathcal{D} b_\gamma e^{[S_{\text{HD}} + S_{\text{gf}} + S_{\text{gh}}]}. \] (42) At one loop we can evaluate the functional integral explicitly and express the partition function as a product of functional determinants, namely \[ Z[g] = e^{iS_{\text{g}[g]}} \left\{ \frac{\text{Det} \left[ \frac{\delta^2 (S_{\text{HD}}[g+h] + S_{\text{gf}}[g+h])}{\delta h_{\mu\nu} \delta h_{\sigma\rho}} \right]_{h=0} }{\text{Det} \left[ \delta^2 (S_{\text{HD}}[g+h] + S_{\text{gf}}[g+h]) \right]_{h=0} } \right\}^{\frac{1}{2}} \left( \text{Det} \left[ M^\alpha_{\beta} \right] \left( \text{Det} \left[ C^{\mu\nu} \right] \right) \right)^{-\frac{1}{2}}. \] By symbol $ S_{\text{g}[g]} $ we understand classical functional of the gravitational action of the theory for the background metric $ g $. To calculate the one-loop effective action we need first to expand the action plus the gauge-fixing term to the second order in the quantum fluctuation $ h_{\mu\nu} $ \[ \hat{H}^{\mu\nu,\sigma\tau} = \left. \frac{\delta^2 S_{\text{HD}}}{\delta h_{\mu\nu} \delta h_{\rho\sigma}} \right\|_{h=0} + \left. \frac{\delta \chi_\delta}{\delta h_{\mu\nu}} \right\|_{h=0} C^{\delta\nu}_{\beta} \left. \frac{\delta \chi_\sigma}{\delta h_{\rho\sigma}} \right\|_{h=0}. \] (43) Following [42] we can recast [43] for the simpler four-dimensional case in the following compact form \[ \hat{H}^{\mu\nu,\alpha\beta} = \left( \frac{\omega_{\text{Ric}}}{4} g^{\mu\nu} \rho^\rho\sigma - \omega_{\text{Ric}} \left( \omega_{\text{Ric}} + 4 \omega_R \right) g^{\mu\nu} \rho^\rho\sigma \right) \times \left\{ \delta^\alpha_\rho \delta^\beta_\sigma \square^2 + V_{\rho\sigma} \alpha,\beta \lambda_1 \ldots \lambda_{2+2} \nabla_{\lambda_1} \cdots \nabla_{\lambda_{2+2}} + W_{\rho\sigma} \alpha,\beta \lambda_1 \ldots \lambda_{2+1} \nabla_{\lambda_1} \cdots \nabla_{\lambda_{2+1}} + U_{\rho\sigma} \alpha,\beta \lambda_1 \ldots \lambda_2 \nabla_{\lambda_1} \cdots \nabla_{\lambda_2} + O(\nabla^2 \gamma^{-1}) \right\}, \] (44) where $ \delta^\alpha_\rho \delta^\beta_\sigma \equiv \frac{1}{2} \left( \delta^\alpha_\rho \delta^\beta_\sigma + \delta^\alpha_\sigma \delta^\beta_\rho \right) $, and the tensors $ V, W $ and $ U $ depend on curvature tensors of the background metric and its covariant derivatives. In [44] the pre-factor in round brackets (called de Witt metric $ G^{\mu\nu,\rho\sigma} $) does not give any contribution to the divergences and, therefore, it can be omitted. The coefficients $ \omega_{\text{Ric}} $ and $ \omega_R $ stay for $ \omega_{\text{Ric},\gamma+N} $ and $ \omega_{\text{Ric},\gamma+N} $ respectively. The tensor $ V $ is linear in a curvature tensor $ (R) $, while the tensor $ U $ contains contributions quadratic in curvature $ (R^2) $ and also terms with two covariant derivatives on one curvature $ (\nabla^2 R) $. We obtain expressions for $ U, V $ and $ W $ tensors by contracting the operator $ \hat{H}^{\mu\nu,\alpha\beta} $ with the inverse de Witt metric and extracting at the end covariant derivatives. They have the canonical position of first matrix indices (two down followed by two up) thanks to the application of this metric in the field fluctuation space. The one-loop effective action is defined by [42] \[ \Gamma^{(1)}[g] = -i \ln Z[g] = S_{\text{HD}}[g] + \frac{i}{2} \ln \text{Det}(\hat{H}) - i \ln \text{Det}(\hat{M}) - \frac{i}{2} \ln \text{Det}(\hat{C}). \] (45) Once the relevant contributions to the operator $ \hat{H} $ are known we can apply the Barvinsky-Vilkovisky method [58] to extract any divergent part of $ \ln \text{Det}(\hat{H}^{\mu\nu,\alpha\beta}) $. The explicit calculation of $ \hat{H} $ in a $ D $-dimensional spacetime goes beyond the scope of this paper and here we only offer the schematic tensorial structure in terms of the curvature tensors of the background metric and its covariant derivatives. For the action [55], where we have only terms with a maximal number of $ 2\gamma + 2N + 4 $ derivatives on the metric tensor (case of a UV monomial theory), and with front coefficients of these terms given by $ \omega_{\text{Ric}} $ and $ \omega_R $, the matrix $ H^{\mu\nu,\rho\sigma} $ in fully covariant form consists solely of terms proportional to the non-running constants $ \omega_{\text{Ric}} $ and $ \omega_R $, \[ \hat{H}^{\mu\nu,\alpha\beta} = G^{-1}_{\mu\nu,\alpha\beta} \left( \square^\gamma + N + 2 \right) \left( \frac{\omega_{\text{Ric}}}{4} \gamma_{\mu\nu} \gamma^\rho \rho^\sigma - \omega_{\text{Ric}} \left( \omega_{\text{Ric}} + 4 \omega_R \right) \gamma_{\mu\nu} \gamma^\rho \rho^\sigma \right) \times \left\{ \delta^\alpha_\rho \delta^\beta_\sigma \square^2 + V_{\rho\sigma} \alpha,\beta \left( 4 \right) \lambda_1 \ldots \lambda_{2+2} \nabla_{\lambda_1} \cdots \nabla_{\lambda_{2+2}} + W_{\rho\sigma} \alpha,\beta \left( 3 \right) \lambda_1 \ldots \lambda_{2+1} \nabla_{\lambda_1} \cdots \nabla_{\lambda_{2+1}} + U_{\rho\sigma} \alpha,\beta \left( 2 \right) \lambda_1 \ldots \lambda_2 \nabla_{\lambda_1} \cdots \nabla_{\lambda_2} + O(\nabla^2 \gamma^{-1}) \right\}. \] (46) To avoid too much complicity we restricted ourselves above to the case of even dimensionality of spacetime. We wrote above only terms giving rise to quantum divergences. We explicitly showed the relationship of the tensors $ V^{(i)}, W^{(i)}, U_4^{(i)}, U_5^{(i)}, \ldots, U_D^{(i)} $ (for the case $ i = \gamma + N + 2 $) to the background curvature tensors and its covariant derivatives. Employing the universal trace formulae of Barvinsky and Vilkovisky [58] \[ \text{Tr} \ln \square \left\|_{\text{div}} \right\| \sim \frac{1}{\epsilon} \int d^Dx \sqrt{\|g\|} \left( R^{\rho\sigma} + \nabla^2 R^{\rho\sigma} - 1 + \ldots + \nabla^2 \square^2 \right), \] (47) \[ \nabla^p \frac{1}{\square^{N+\gamma+2}} \delta(x,y) \left\|_{\text{div}} \right\| \sim \frac{1}{\epsilon} \left( R^{p\sigma} - (\gamma+\nu+2) \delta^{\nu} + \ldots + \nabla^p - 2\gamma - 2N - 6 + D \right), \] (48) we can derive in a general case of UV-polynomial theory the following divergent contribution to the effective action, \[ \Gamma_{\text{div}}^{(1)} \sim \frac{-1}{\epsilon} \int d^Dx \sqrt{\|g\|} \left[ \beta - 2\beta^\gamma_{\kappa R^D} R + \sum_{n=0}^{N+2} \left( \beta_{\omega_{\text{Ric}},\nu} R^{p^\nu} R + \beta_{\omega_{\text{Ric}},\nu} R^\nu R^{\mu\nu} R^{\mu\nu} \right) + \sum_{j=3}^{i} \sum_{k=3}^{i} j c^{(j)}_{k,i} \left( \nabla^2 (j-k) R^{k} \right) \right], \] (49) where all the beta functions depend only on the “non-running” constants $ \omega_{\text{Ric},n} $ or $ \omega_{n} $ for $ n = N - \frac{d}{2}, \ldots, N $. VI. NON-LOCAL CONFORMAL GRAVITY We here use the compensating field method to make our finite or super-renormalizable gravitational theory “trivially” conformally invariant at classical level. Following the conventions in [31, 32], we replace the following definition, $$g^{\mu\nu} = \left(\phi^2 \kappa_D^2\right)^{\frac{2}{D-2}} \hat{g}^{\mu\nu},$$ (50) in the general action 3 and we end up with $$\mathcal{L}_g = -2\kappa_D^{-2} \sqrt{g} \left[ R(g) + \text{Riem}(g) \gamma(\Box) \text{Riem}(g) + V(g) \right] \bigg\|_{\phi \hat{g}} = -2 \sqrt{g} \left[ \phi^2 R(\hat{g}) + \frac{4(D-1)}{D-2} \hat{g}^{\mu\nu} \partial_\mu \phi \partial_\nu \phi \right]$$ $$-2\kappa_D^{-2} \sqrt{g} \left[ R(g) \gamma_0(\Box) R(g) + \text{Ric}(g) \gamma_2(\Box) \text{Ric}(g) + \text{Riem}(g) \gamma_4(\Box) \text{Riem}(g) + V(g) \right] \bigg\|_{\phi \hat{g}} .$$ (51) where by $ \|_{\phi \hat{g}} $ we mean that the metric $ \hat{g}^{\mu\nu} $ must be replaced with $ \left(\phi^2 \kappa_D^2\right)^{\frac{2}{D-2}} g^{\mu\nu} $. The requirement to have a theory completely independent on any scale forces us to identify $ \Lambda $ with the Planck mass, namely $ \Lambda^2 = \left(\kappa_D^2\right)^{\frac{2}{D-2}} $. The form factors $ \gamma_{0,2,4} $ are the same given in [30]. We now consider the case $ \gamma_4(\Box) = 0 $ in view of having the Schwarzschild spacetime as an exact solution of the theory. The theory simplify to $$\mathcal{L}_g = -2 \sqrt{\hat{g}} \left[ \phi^2 R(\hat{g}) + \frac{4(D-1)}{D-2} \hat{g}^{\mu\nu} \partial_\mu \phi \partial_\nu \phi \right] - \frac{2}{\kappa_D^2} \sqrt{\hat{g}} \left[ R(g) \gamma_0(\Box) R(g) + \text{Ric}(g) \gamma_2(\Box) \text{Ric}(g) + V(g) \right] \bigg\|_{\phi \hat{g}} .$$ (52) In the theory [52] we have an extra ghost-like degree of freedom. However, it can be eliminated using the extra symmetry of the theory, namely conformal invariance. When the unitary gauge $ \phi = \text{const.} $ is enplaned then we can come back to the super-renormalizable or finite quantum theory extensively studied in literatures. Moreover, the quantum properties of the theory can not change in different gauges, and the theory must be super-renormalizable or finite also when the scalar field is not completely gauged away, but another gauge is implemented. We remind that for the four dimensional local Weyl theory $ \sqrt{\|g\| C^2} $ [41] the conformal symmetry is usually gauge fixed imposing the graviton fluctuation to be traceless [24]. In this theory there are “9 + 1” degrees of freedom (d.o.f.) related respectively to the “9” metric components of $ \hat{g}_{\mu\nu} $ and “1” scalar field $ \phi $. However, the product [50] (and therefore the actions [51] or [52]) are invariant under 3 For the sake of simplicity we here assume $ \kappa_D = 1 $. There is another “equivalent” way to count the d.o.f. The metric $ \hat{g}_{\mu\nu} $ has 10 d.o.f given that it is the spacetime metric, while $ \phi $ counts for 1 d.o.f for a total of 11 d.o.f. On the other hand we have one more symmetry (Weyl conformal invariance) that can be used to fix $ \phi = 1 $. Therefore, we end up again with 10 d.o.f. This counting is perfectly consistent with the replacement [50] because we have the extra conformal symmetry that we can use to impose for example $ \sqrt{\|g\|} = 1 $ or $ \phi = 1 $ [25, 33]. Indeed, the number of d.o.f. on the left and right side of [50] do match when the gauge freedom is fixed. However, in this paper we would like to see [50] as a splitting of the metric tensor $ g_{\mu\nu} $, having 10 d.o.f., in 9 + 1 components (1 stays for the conformal overall factor, namely $ \gamma_0(\Box) = \phi^2 g_{\mu\nu} $) that, afterwards, shows up the new conformal invariance. Assuming this point of view, the conformal symmetry can only be spontaneously broken, when we want to avoid losing of one d.o.f. Let us compare the gravitational Higgs mechanism with an analog toy-model in gauge theory. We consider a Lagrangian invariant under local $ U(1) $ gauge transformations and based on a real scalar field $ \theta(x) $ plus an abelian gauge field $ A_\mu $ [29], $$\mathcal{L} = \frac{1}{4} F(A)^2 - \left\| D_\mu \phi \right\|^2,$$ (53) $$F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu ,$$ (54) $$D_\mu = \partial_\mu - ig A_\mu ,$$ (55) $$\phi(x) = \frac{1}{\sqrt{2}} v e^{i \phi(x)} \quad (v = \text{const.} \quad \text{and} \quad [v] = 1) ,$$ (56) where the fields $ A $ and $ \phi $ or $ \theta $ transform under $ U(1) $ as follows, $$\phi'(x) = e^{i \phi(x)} \phi(x) \quad \text{or} \quad \theta'(x) = \theta(x) + v g \phi(x) \quad \text{and} \quad A'_\mu = A_\mu + \partial_\mu \phi(x) ,$$ (57) $$D_\mu \phi = -\frac{1}{\sqrt{2}} g v e^{2i \phi(x)} \left( A_\mu - \frac{1}{v g} \partial_\mu \phi(x) \right).$$ (58) Introducing a new gauge-invariant field $$B_\mu = A_\mu - \frac{1}{v g} \partial_\mu \phi(x) ,$$ (59) the rescaling \[ \hat{g}_{\mu\nu} \to \Omega^2(x) \hat{g}_{\mu\nu}, \quad \phi \to \Omega^{-\frac{D}{2}}(x) \phi, \] meaning that $ \phi $ describes clocks are rulers while $ \hat{g}_{\mu\nu} $ contains information about the light cone causal structure of the spacetime. After the gauge fixing $ \phi $ is just a constant and the distances are now measured by the metric $ \hat{g}_{\mu\nu} $ or equivalently by the metric $ g_{\mu\nu} $. The two metrics are now identified and, therefore, they have the same number of d.o.f., namely 10. In other words the “effective number of d.o.f.” is actually 10 before and after spontaneous symmetry breaking of conformal invariance. The “Higgs” mechanism consist on moving the d.g.f., measuring time and space, from $ \phi $ to the metric $ \hat{g}_{\mu\nu} $. Such degree of freedom is the analog the the Higgs particle giving mass to the other fields in the standard model of particle physics (SM). We infer that the class of finite quantum gravitational theories (3) (in odd as well as in even dimension) is actually a range of anomaly-free conformally invariant theories in the spontaneously broken phase of the conformal Weyl symmetry. The conformally invariant theory is given in (51) or (52). In the next subsections we explicitly show that the weakly non-local theory is finite and then free of Weyl anomalies’ issue. However, at quantum level they are renormalizable, but not finite, implying that the Weyl symmetry is anomalous. In the next subsections we explicitly show that the weakly non-local theory is finite and then free of Weyl anomaly. Therefore, we have a good conformal quantum gravity candidate. \section{VII. CONFORMAL QUANTUM GRAVITY} Let us now explicitly prove that the theory is anomaly free, or, which is the same, that the theory is completely finite under quantization. There are two famous examples of conformally invariant gravitational theories in $ D = 4 $, namely \[ L_1 = aW + \alpha_v R^* R, \] \[ L_2 = -12\phi \left[-\square + \frac{1}{6} R \right] \phi + 2\lambda \phi^4 + aW + \alpha_v R^* R. \] These Lagrangians are useful tools for understanding the connection between conformal symmetry and the singularities’ issue. However, at quantum level they are renormalizable, but not finite, implying that the Weyl symmetry is anomalous. In the next subsections we explicitly show that the weakly non-local theory is finite and then free of Weyl anomaly. Therefore, we have a good conformal quantum gravity candidate. Besides weak non-locality, another attractive proposal to solve the unitarity problem that plagues the theory $64$ can be read in numerous papers by Mannheim \[49\]. A. Power-counting renormalizability of $51$ We hereby study the divergences of the theory $51$ when both the scalar and tensor perturbations propagate, without to take care, for the moment, of the gauge fixing we are going to implement later in the paper. To fix the notation, $h_{\mu\nu}$ is definite to be the fluctuation respect to $g_{\mu\nu}$, namely \[ \hat{g}_{\mu\nu} = \tilde{g}_{\mu\nu} + \hat{h}_{\mu\nu}. \tag{66} \] Let us first consider the case of the purely scalar interactions. We expand the action around a constant dimensionfull background, namely \[ \phi = \kappa^{-1}_D + \varphi, \quad \text{with} \quad \mid\varphi\mid = \frac{D}{2} - 1. \tag{67} \] In the subset of graphs involving only the scalar fluctuation $\varphi$, the kinetic operator and the $n$-scalars interactions respectively read \[ \mathcal{L}_{\text{Kin.}\varphi} \approx \frac{1}{\Lambda^{2\gamma+D-2}} \varphi \Box^{\gamma+\frac{D}{2}} \varphi, \quad \mathcal{L}_{\text{int.}\varphi} \approx \frac{1}{\Lambda^{2\gamma+D-2}} \frac{\varphi^{n-2}}{\Lambda^{(n-2)(\frac{D}{2}-1)}} \varphi \partial^2 \Box^{\gamma+\frac{D}{2}-1} \varphi, \tag{68} \] with $n \geq 3$ arbitrary large. The power-counting gives, \[ \delta^D(K) \Lambda^{(1-\frac{D}{2})E} \varphi^E \Lambda^{2\gamma(L-1)} \int (d^D p)^L \left(\frac{1}{p^{2\gamma+D}}\right)^{I} \left(p^{2\gamma+D}\right)^{1} = \delta^D(K) \Lambda^{(1-\frac{D}{2})E} \varphi^E \Lambda^{2\gamma(L-1)} \Lambda^{D-2\gamma(L-1)} \tag{69} \] where $E$ is the number of external scalar legs, and for the scalar sector the relation between $E, I, $ and $V$ is: $nV = 2I + E$. We end up the with the following superficial degree of divergence for an arbitrary Feynman diagram only involving the scalar field, \[ \omega_\varphi(G) = D - 2\gamma(L - 1). \tag{70} \] Notice that the number of external legs is arbitrary because the product $\Lambda^{(1-\frac{D}{2})E} \varphi^E$ is dimensionless. Although, there are only one loop divergences, it seems we have an infinite number of operators to renormalize, namely the counterterms read \[ \Lambda^{(1-\frac{D}{2})n} \int d^D x \varphi^{n-2} \varphi \Box^{\frac{D}{2}} \varphi, \tag{71} \] where we assumed the form factor to be asymptotically monomial. However, we expect these operators exactly to be generated expanding in the fluctuation $\varphi$ the curvatures $\mathcal{R}^{D/2}$, therefore, the operators we have to subtract are only a few when expressed in terms of $\phi$. Such operators can be obtained replacing the metric $\tilde{g}_{\mu\nu}$ in the Lagrangian operators with $D$ derivatives, namely $\mathcal{R}^{D/2}$. The operators at the orders 0, 1, and 2 in the curvature are given in $150$ we get the counterterms we advocated above on the base of the power-counting arguments and only involving the conformal factor. When all the interactions are taking into account the simpler way to carry out the power-counting is using the dimensionless fields $\hat{h}_{\mu\nu} = [\varphi] = 0$. In this case the power-counting is exactly the one given in $174$, we only have to rename the graviton fluctuation components \[ h_{\mu\nu} \rightarrow \{\hat{h}_{\mu\nu}, \varphi\}, \tag{72} \] and all the possible counterterms now include also the scalar field $\phi^4$. Therefore, in $D = 4$ and using DIMREG all \[\text{Footnote: Notice that expanding the action in } \varphi \text{ and } h_{\mu\nu}, \text{namely } \phi = \kappa^{-1}_D + \varphi \text{ and } \hat{g}_{\mu\nu} = \eta_{\mu\nu} + \hat{h}_{\mu\nu}, \text{we get quadratic mixing terms } (h_{\mu\nu} - \varphi). \] \[\text{Therefore, the quadratic part in } \hat{h}_{\mu\nu} \text{ and } \varphi \text{ has to be diagonalized by the transformation } 63: \] \[ \phi \rightarrow \phi + \hat{h}_{\mu\nu} \frac{\delta^2 \mathcal{L}_\phi}{\delta h_{\mu\nu} \delta \varphi} \left(\frac{\delta^2 \mathcal{L}_\phi}{\delta \varphi^2}\right)^{-1}. \tag{73} \] the possible counterterms of dimension four, up to total derivatives and topological terms, are: \[ \sqrt{\|g\|} R^2, \quad \sqrt{\|g\|} R^2_{\mu\nu}, \quad \sqrt{\|g\|} R, \quad \sqrt{\|g\|} = \sqrt{\|g\|} \phi^4, \quad (74) \] in which we have to replace again (50). Notice that the last operator gives rise to the cosmological constant through spontaneous symmetry breaking. However, if we choose a form factor asymptotically monomial only the first two operators are generated by a one-loop computation. At this level it is not obvious that the divergences collect all together with the right coefficients to reproduce exactly the curvature invariants (74). Indeed, we will proof that the combinatorics are the correct ones later in this section. For the case of even dimension, we will make this claim rigorous in the subsection (VII C) explicitly showing that the quantum dynamics of the fluctuation $ \varphi $ is actually trivial because of the conformal invariance. Finally, we want to point out that the main result of this section turns out to be the presence of only one loop divergences. Indeed, for the power-counting analysis, given the dimensionless fluctuations $ \hat{h}_{\mu\nu} $ and $ \varphi $, we basically need to look at the number of derivatives in the ultraviolet regime. B. Conformal quantum gravity in odd dimension In this section we show that we fairly easily achieve quantum finiteness in odd dimension and DIMREG. Indeed, in an odd dimensional spacetime there are no one-loop divergences made only of the Riemann tensor because we can not construct a curvature invariant out off an odd number of derivatives. Other operators involving also the scalar field (like the four operators in (74)) are not generated by the quantum corrections because the form factors are rational functions, namely all the one-loop integrals have the following structure, \[ I_{k,n} = \int d^D p \frac{(p^2)^k}{(p^2 + C)^n} = \frac{C^{D/2-(n-k)}}{(4\pi)^{D/2}} \frac{\Gamma(n-k-D/2)\Gamma(k+D/2)}{\Gamma(n)\Gamma(n-k-D/2)}. \quad (75) \] The above integrals (75) are convergent in odd dimension because the gamma function \[ \Gamma\left( n-k-D/2 \right) \] has no poles if $ n $ and $ k $ are both integer, but this is exactly the case of our theory, therefore, we do not have one-loop divergences. For $ L > 1 $ the gamma function in (76) is replaced by \[ \Gamma\left( n-k-LD/2 \right), \quad (77) \] which can be divergent, for example for $ L = 2 $, because the argument of the gamma function is now an integer number. We end up with a finite and anomaly free theory, which means that the quantum action is conformally invariant. In the next subsection we will show that the theory in even dimension and in particular in $ D = 4 $ is also quantum finite and anomaly free. C. Conformal quantum gravity in $ D = 4 $ In this section we quantize the theory in exactly the same way carried out by Fradkin and Tsytl in [24] (see also [25–27]) for the local theory $ (65) $.\footnote{In this subsection we define $ g_{\mu\nu} \equiv \phi^2 \hat{g}_{\mu\nu} $, which slightly differs from [20] because $ \|\phi\| = 0 $ and in particular its exponent is here independent on the spacetime dimension $ D $. This definition allows for less cumbersome formulas.} We first introduce the Faddeev-Popov determinant for the conformal symmetry. The scalar auxiliary field transforms as \[ \phi' = \Omega^{-1} \phi \equiv e^{-\sigma} \phi \approx (1-\sigma)\phi \quad \implies \quad \delta \phi = -\sigma \phi \equiv \xi R(\phi) \quad \implies \quad R(\phi) = \phi.\] We split the field in a background $\bar{\phi}$ plus fluctuation $\varphi$ and afterwards we impose the gauge condition, namely $$\varphi = \bar{\phi} + \varphi, \quad \chi(\varphi) = \varphi - \bar{\phi} = \varphi; \text{ gauge fixing: } \varphi = \ell = \text{const.}$$ Finally, the Fadeev-Popov determinant can be derived as follows, $$1 = \Delta_{\text{FP}}^\text{conf}(\bar{\phi}) \int D\xi \delta \left( \chi(\xi\bar{\phi} - \ell) \right) = \Delta_{\text{FP}}^\text{conf}(\bar{\phi}) \int D\xi \delta \left( \chi(\bar{\phi} + R\xi - \ell) \right) = \Delta_{\text{FP}}^\text{conf}(\bar{\phi}) \int D\xi \delta \left( \chi(\varphi - \ell) + \frac{\delta\chi}{\delta\varphi} R\xi \right)$$ $$= \Delta_{\text{FP}}^\text{conf}(\bar{\phi}) \det^{-1} \left( \frac{\delta\chi}{\delta\varphi} R(\bar{\phi}) \right) \bigg\|_{\varphi = \bar{\phi} + \ell} = \Delta_{\text{FP}}^\text{conf}(\bar{\phi}) \det^{-1} (\bar{\phi} + \ell) \implies \Delta_{\text{FP}}^\text{conf}(\bar{\phi}) = \int DcD\bar{c} e^\frac{i\delta\mathcal{F}(\bar{\phi})}{\delta\bar{\phi}} ,$$ where we used the gauge $\chi = \ell$ and the determinant is obtained integrating on the anticommuting fields $c, \bar{c}$. Since $\ell = \text{const.}$, the propagator is just a number and all the one loop diagrams are proportional to $\int d^4p = 0$ in dimensional regularization, then $\Delta_{\text{FP}}^\text{conf}(\bar{\phi}) = 1$. Since the scalar fluctuation is just a constant we can redefine the $\bar{\phi} + \ell = \bar{\phi}'$ and the quantum effective action will only be a function of $\varphi'$. $\Delta_{\text{FP}}^{\text{conf}}(\bar{\phi})$, the Fujikawa measure is recovered for $O = \bar{\phi}$. Where $$\chi = \bar{\phi} + \varphi$$ and $\varphi (\bar{\phi}) = \varphi - \bar{\phi}$ is a constant redefinitions of the background scalar field $\bar{\phi}$ plus quantum perturbations, namely $$\varphi = \bar{\phi} + \varphi = \bar{\phi} + \varphi$$ with $\varphi = \bar{\phi} + \varphi$. At quantum level we integrate in $\bar{\phi}$ and $\bar{\phi}$ with a proper conformally invariant measure $7$, $$Z(\bar{g}_{\mu\nu} = \bar{\varphi}^2 \bar{g}_{\mu\nu}) =$$ $$= \int D\left[ \left( \bar{\varphi} - \varphi \right)^{\frac{1}{2}} \right] \det(\varphi) \delta(\varphi) \Delta_{\text{FP}}^{\text{diff}}(\varphi) \Delta_{\text{FP}}^{\text{conf}}(\varphi)$$ $$\left\|_{\varphi = \varphi_0} \right\| \left\|_{\varphi = \varphi_1} \right\|$$ where $\Delta_{\text{FP}}^{\text{diff}}(\varphi)$ and $M_{\alpha\beta}^{\text{diff}}(\varphi)$ have been defined in section VII. In [83] the scalar field $\varphi$ and the metric $\bar{g}_{\mu\nu}$ are mean as the background fields $\varphi$ and $\bar{g}_{\mu\nu}$ plus quantum perturbations, namely $$\varphi = \bar{\varphi} + \varphi$$ In [83] we have multiplied by $$1 = \det(C_{\alpha\beta}(\bar{g}))^{1/2} \int D\ell \exp \frac{i}{2} \ell \Delta_{\text{FP}}^{\text{conf}}(\varphi)$$ and integrated in $\ell$. Now we replace in [83] the conf-determinant (79) and we integrate in $\varphi$. However, (79) is trivially constant in DIMREG, then we can just forget it and make the choice $\ell = 0$ [24] to avoid unnecessary constant redefinitions of the background scalar field $\varphi$. Moreover, $\delta^4(0) \equiv 0$ in DIMREG. The outcome reads $$Z(\bar{g}_{\mu\nu} = \varphi^2 \bar{g}_{\mu\nu}) = \int D\left[ \left( \bar{\varphi} - \varphi \right)^{\frac{1}{2}} \right] \det(\varphi) \delta(\varphi) \Delta_{\text{FP}}^{\text{diff}}(\varphi) \Delta_{\text{FP}}^{\text{conf}}(\varphi)$$ $$\left\|_{\varphi = \varphi_0} \right\| \left\|_{\varphi = \varphi_1} \right\|$$ 6 Given the following general operator, $$\mathcal{O} = \mathcal{O}_0 + \mathcal{O}_1$$ where $\mathcal{O}_0$ refers to the free part and $\mathcal{O}_1$ refers to the interaction part, $$\log \det \mathcal{O} = \text{Tr} \log \mathcal{O} = c + \text{Tr} \log(1 + \mathcal{O}^{-1}_0 \mathcal{O}_1)$$ $$= c + \sum_{n=1}^{+\infty} \left( \frac{-1}{n} \right)^{n+1} \int d^Dx_n \mathcal{O}_0^{-1}(x_1 - x_2) \mathcal{O}_1(x_2) \mathcal{O}_0^{-1}(x_2 - x_3) \mathcal{O}_1(x_3) \cdots \mathcal{O}_0^{-1}(x_n - x_1) \mathcal{O}_1(x_1),$$ where $c = \text{const.}$. If the propagator is just a constant and the interactions analytic functions, then every integral in the above sum is zero in DIMREG. 7 The most famous measures are ultralocals that do not depend on derivatives of the metric tensor $\varphi_{\mu\nu}$. Given two different ultralocal measures they are related by a Jacobian determinant that can be formally expressed as the exponential of a $\delta^D(0)$ divergence [50]. One possible measure reads $$\prod_{\mu<\nu} D[\varphi_{\mu\nu}(-g)]^{\frac{1}{2}} = \prod_{\mu<\nu} D[\varphi_{\mu\nu}] e^{\delta^D(0) \int d^Dx \log \varphi_{\mu\nu}}.$$ Since we completely integrated away the scalar fluctuation, we can now explicitly replace in (86) the following simplified splitting, \[ g_{\mu\nu} = \bar{g}_{\mu\nu} + h_{\mu\nu} = \delta^2(\bar{g}_{\mu\nu} + \bar{h}_{\mu\nu}) = \bar{\delta}^2 \bar{g}_{\mu\nu} + \bar{\delta}^2 \bar{h}_{\mu\nu} = \bar{\delta}^2 \bar{g}_{\mu\nu} + \bar{\delta}^2 \bar{h}_{\mu\nu}. \] However, since the measure is conformally invariant it is much simpler to replace the integration in $\bar{g}_{\mu\nu}$ with the one in $g_{\mu\nu}$ and only at the end to replace $\bar{g}_{\mu\nu}$ with $\bar{\delta}^2 \bar{g}_{\mu\nu}$. Here are the need steps, \[ Z(\bar{g}_{\mu\nu} = \bar{\delta}^2 \bar{g}_{\mu\nu}) = \\ = \text{det}(C_{\alpha\beta}(\bar{g}))^{\frac{1}{2}} \text{det}(M_{\alpha\beta}(\bar{g})) \int D\left[\bar{g}_{\mu\nu}(-\bar{g})^{-\frac{1}{2}}\right] e^{i[S(\bar{g}) + S_{\alpha\beta}(\bar{g})]} \|g_{\mu\nu} = \bar{\delta}^2 \bar{g}_{\mu\nu}\| \] \[ = \text{det}(C_{\alpha\beta}(\bar{g}))^{\frac{1}{2}} \text{det}(M_{\alpha\beta}(\bar{g})) \left\{ \int D\left[\bar{g}_{\mu\nu}(-g)^{-\frac{1}{2}}\right] e^{i[S(g) + S_{\alpha\beta}(\bar{g})]} \|g_{\mu\nu} = \bar{g}_{\mu\nu} + h_{\mu\nu}\| \right\} \|g_{\mu\nu} = \bar{\delta}^2 \bar{g}_{\mu\nu}\| \] \[ = \text{det}(C_{\alpha\beta}(\bar{g}))^{\frac{1}{2}} \text{det}(M_{\alpha\beta}(\bar{g})) \left\{ \int D\bar{h}_{\mu\nu} e^{i[S(\bar{g}) + S_{\alpha\beta}(\bar{g})]} \|g_{\mu\nu} = \bar{g}_{\mu\nu} + h_{\mu\nu}\| \right\} \|g_{\mu\nu} = \bar{\delta}^2 \bar{g}_{\mu\nu}. \] The divergent contributions to the above one-loop effective action are exactly the ones listed in (74) in agreement with [24]. The beta functions can be derived as explained in section [X] and read out of formula [19] specialized to the case $D = 4$. Therefore, we are quite close to achieve conformal invariance at quantum level because the quantum effective action, including all finite contributions, will be a function of $\bar{g}_{\mu\nu} = \bar{\delta}^2 \bar{g}_{\mu\nu}$ that keeps correctly hidden conformal invariance. However, we will shortly prove that in order to have conformal invariance at quantum level the path integral (89) must be free of any divergence in DIMREG.8 Now we are in the position to claim that the counterterms are the ones given in (74) and they are conformally invariant. However, since the presence of \[ \frac{1}{\epsilon} = \log \left( \frac{\Lambda_{\text{cut-off}}}{\mu} \right) \] (μ is the renormalization scale) in front of each operator in (74), conformal invariance is not preserved at quantum level. Indeed, it is obvious that an ultraviolet cut-off violates local conformal invariance. Equivalently, one may note that the operators (74) are conformally invariant in $D = 4$, but not in $4 - \epsilon$ because DIMREG does not preserve conformal invariance. Let us name the operators (74) by $O_i(\bar{g})$, then when the metric $g_{\mu\nu} = \phi^2 \bar{g}_{\mu\nu}$ is replaced in such operators we get the following anomalous contributions to the action, \[ \frac{1}{\epsilon} \phi^{-\epsilon} O_i(\phi^2 \bar{g}; \epsilon) \approx \frac{1}{\epsilon} (1 - \epsilon \log \phi) O_i(\phi^2 \bar{g}; \epsilon) = \frac{1}{\epsilon} O_i(\phi^2 \bar{g}) + \tilde{O}_i(\phi^2 \bar{g}) - \log(\phi) O_i(\phi^2 \bar{g}), \] where the $\epsilon$ among the slots of the operator $O_i(\phi^2 \bar{g}; \epsilon)$ comes from the replacement $D \rightarrow D - \epsilon$ in (150). Moreover, the contribution $\phi^{-\epsilon}$ comes from \[ \sqrt{\|g\|} = \phi^{D-\epsilon} \sqrt{\|\bar{g}\|} = \phi^{D} \sqrt{\|\bar{g}\|} \phi^{-\epsilon} = \sqrt{\|g\|} \phi^{-\epsilon}. \] The last two contributions in (74) are finite (independent on $\epsilon$) and explicitly violate conformal invariance. The operator $\tilde{O}_i(\phi^2 \bar{g})$ is the regular contribution to $O_i(\phi^2 \bar{g}; \epsilon)/\epsilon$, namely \[ \lim_{\epsilon \rightarrow 0} \frac{O_i(\phi^2 \bar{g}; \epsilon)}{\epsilon} = \tilde{O}_i(\phi^2 \bar{g}). \] 8 If we pretend to keep the Fujikawa measure in the path integral (80) the result does not change. In a $D$-dimensional spacetime the measure reads $D\left[\bar{g}_{\mu\nu}(-\bar{g})^{-\frac{D-4}{2}}\right]$, but in $D = 4$ it is just $D\left[\bar{g}_{\mu\nu}\right]$. Let us now change variable to $g_{\mu\nu} = \bar{\delta}^2 \bar{g}_{\mu\nu}$ or actually $g_{\mu\nu} = \bar{\delta}^{-2} \bar{g}_{\mu\nu}$, then the measure turns in $D\left[\bar{g}_{\mu\nu}\right] = D\left[g_{\mu\nu}\bar{\delta}^{-2}\right] = \exp \left\{ \delta^4(0) \int d^4x \log(\bar{\delta}^{-2}) \right\} D\left[\bar{g}_{\mu\nu}\right] \equiv D\left[\bar{g}_{\mu\nu}\right]$ in DIMREG. However, in our theory we have other contributions to the beta functions coming from the potential or killer operators. As explicitly shown in [6] and reminded in section II the killer operators contribute to the beta functions linearly in their front coefficients and it is always possible to make the beta functions to vanish. Therefore, there is no overall $1/\epsilon$ factor in (91) and we can take the limit $\epsilon \to 0$ consistently with conformal invariance (actually there are no counterterms because the theory is finite.) This result is not a fine tuning, but actually one loop exact because the theory is super-renormalizable with no divergences for $L > 1$. Generalization to any even dimension is straightforward once we proved the theory to be finite at quantum level. D. Evaluating Feynman diagrams The most general integral at the $L$-loops order has the following structure, $$ \int B(k_i, p_i) \prod_{i=1}^{L} d^Dk_i \prod_{j=1}^{I} \frac{i}{q_j - i\epsilon}, $$ (94) where $k_i$ are $L$ independent loop momenta, $q_j$ are linear combinations of the $k_i$ and external momenta $p_i$. $B(k_i, p_i)$ is an entire function without poles consisting of the product of exponential form factors $\exp -H(q_k)$ coming from the propagators times local and weakly non-local entire functions coming from the vertices, namely $$ B(k_i, p_i) = \prod_{i=1}^{I} e^{-H(q_k)} \mathcal{I}(k_i, p_i), $$ (95) where the entire function $\mathcal{I}(k_i, p_i)$ does not show any pole. The general integral (94) is convergent (up to sub-divergences) for $L > 1$ and can be calculated in Minkowski signature along the real axis because the contribution of the non-local functions to the integrand is even for $k_0 \to -k_0$ (this is not the case for $\exp \Box$, which is only convergent in Euclidean signature.) Moreover, the Feynman $i\epsilon$ prescription moves the poles outside the real axis. For $L = 1$ we can integrate in Minkowski signature, as just explained, whether the integral is convergent. On the other hand any divergent one-loop integral can always be written as the difference of a convergent integral and a divergent rational (by definition it is the ratio of polynomials) integral. The second one can be evaluated with any technique, with or without making use of the Wick rotation, because it is the usual divergence we meet in any local quantum field theory. E. Perturbative unitarity We can easily address the issue of perturbative unitarity following the original analysis by Cutkosky [33] and Tomboulis [3, 34]. We start by making a non singular field redefinition to bring the kinetic operator of the graviton field to be the same of the local Einstein-Hilbert theory, namely $$ h_{\mu\nu} \to \mathcal{F}(\Box)h_{\mu\nu} = e^{-H(\Box)}h_{\mu\nu} $$ (96) (the field redefinition is not essential whether we do not are interested in formulating the largest time equation.) Notice that the Jacobian of the transformation is trivially constant (see (81) in the footnote four) because the field redefinitions does not involve interactions) and all the scattering amplitudes are unchanged since the analytic form factors were all moved in the interaction vertexes [8]. Therefore, the Landau equations [35] for locating the singularities of any given amplitude are not changed by the presence of form factors in the integrand at any loop order. Their derivation in [32] is the same whether $\mathcal{F}(\Box)$ is a polynomial as in local theories, or a transcendental entire function as in our weakly non-local domain (see also formula (91) in the previous subsection.) Similarly, the derivation of the Cutkosky discontinuity cutting-rules [33] is unaffected because it only assumes the $\mathcal{F}(\Box)$-factor to be an entire function of its argument in any loop amplitude integrand. It follows that, at least order by order in the perturbative expansion, the theory is unitary. F. Unitarity bound and Causality In the unbroken phase it is very simple to infer about the unitarity bound and the Bogoliubov-Shirkov causality of the theory. Indeed, the scattering amplitudes $T_{if}$ (we remind the definition $S = 1 + iT$) are zero due to conformal invariance and in agreement with the Coleman-Mandula theorem, whose hypothesis are here satisfied. In particular it is not necessary that the $S$–matrix is governed by a local theory\textsuperscript{9}. Basically, in a conformally invariant theory the scale invariance is added to Poincaré invariance, hence physics at different scales is interconnected and the concept of asymptotic states does not make sense anymore and the $S$–matrix is trivially the identity. Therefore, we may conclude that conformal invariance is a kind of “strong” achievement of asymptotic freedom. Nevertheless, all the non-trivial dynamical nature of the theory is a consequence of the spontaneous symmetry breaking of the Weyl symmetry. It deserve to be noticed that an identically zero $T$–matrix in the unbroken phase makes intuitively clear why the theory should be free of classical and quantum spacetime singularities. Indeed, the gravitational collapse is just like a scattering process, but here the $S$–matrix is trivial and there is no interaction. Therefore, there is no way to produce a singularity in scattering processes, or, which is the same, from the gravitational collapse. We will expand on this point later from another prospective. VIII. SPACETIME SINGULARITIES As already pointed out in the abstract and in the introduction, conformal invariance seems to be the unique way to get rid out of the spacetime singularities in a gravitational theory. One can quite easily convince himself that in a conformally invariant theory there are no FRW singularities. Indeed, FRW spacetimes are equivalent, by a conformal transformation, to the Minkowski spacetime, which is of course regular everywhere. Less trivial is the case of the black hole singularities and numerous attempts have been done in this direction\textsuperscript{[37–39]}. As already pointed out in the abstract and in the introduction, conformal invariance seems to be the unique way to get rid out of the spacetime singularities in a gravitational theory. Indeed, FRW spacetimes are equivalent, by a conformal transformation, to the Minkowski spacetime, which is of course regular everywhere. Less trivial is the case of the black hole singularities and numerous attempts have been done in this direction\textsuperscript{[37–39]}. In this section we would complete the studies well displayed and developed by Narlikar and Kembhavi\textsuperscript{[30]} to include also the Schwarzschild metric in their list of singularity-free spacetimes. Let us first remind the logic introduced by the two authors. We start with a Riemannian spacetime manifold $\mathcal{M}$ with a metric tensor $\hat{g}_{\mu\nu}$ and a scalar field $\phi$ as discussed in the previous section. Then we derive the EOM for the theory\textsuperscript{[52]} that we give here only implicitly for the purpose of this section. Actually most of the results in this section is true for a general class of conformally invariant theories, including Einstein conformal gravity given by (65) with $\alpha_V = \alpha = 0$. The variation of the action with respect to $\hat{g}_{\mu\nu}$ is: $$\delta \left[ \sqrt{\|g\|} \left( R + R_{\gamma_0(\square)R} + R_{\alpha\beta\gamma_2(\square)R^{\alpha\beta} + V} \right) \right]_{\phi_0} = 0,$$ $$\phi^2 \hat{G}_{\mu\nu} = \nabla_\nu \partial_\mu \phi^2 - \hat{g}_{\mu\nu} \hat{\Box} \phi^2 - 4 \frac{D-1}{D-2} \left( \partial_\nu \phi \partial_\mu \phi - \frac{1}{2} \hat{g}_{\nu\mu} g^{\alpha\beta} \partial_\alpha \phi \partial_\beta \phi \right) - \delta \left[ \sqrt{\|g\|} \left( R_{\gamma_0(\square)R} + R_{\alpha\beta\gamma_2(\square)R^{\alpha\beta} + V} \right) \right]_{\phi_0}.$$ The variation with respect to $\phi$ is: $$\delta \left[ \sqrt{\|g\|} \left( R + R_{\gamma_0(\square)R} + R_{\alpha\beta\gamma_2(\square)R^{\alpha\beta} + V} \right) \right]_{\phi_0} = 0$$ $$\hat{\Box} \phi = \frac{D-2}{4(D-1)} \hat{R} \phi - \frac{1}{\sqrt{\|g_{\phi\phi}\|}} \frac{\delta \left( \sqrt{\|g\|} \left( R_{\gamma_0(\square)R} + R_{\alpha\beta\gamma_2(\square)R^{\alpha\beta} + V} \right) \right)}{\delta \phi}.$$ Since all the operators resulting from the variation are at least linear in the Ricci tensor $R_{\mu\nu}$ (notice that this is $\text{Ric}$ and not $\hat{\text{Ric}}$), then the Schwarzschild metric is an exact solution of the conformally invariant theory, namely $$g_{\mu\nu} = g_{\mu\nu}^{\text{Sch}} = \left( \phi \kappa_D \right)^{\frac{4}{D-2}} \hat{g}_{\mu\nu} \quad \text{and} \quad \phi = \kappa_D^{-1} \implies R_{\mu\nu} \left( \left( \phi \kappa_D \right)^{\frac{4}{D-2}} \hat{g}_{\mu\nu} \right) = 0 \implies E_{\mu\nu} \left( \left( \phi \kappa_D \right)^{\frac{4}{D-2}} \hat{g}_{\mu\nu} \right) = 0,$$ where by $E_{\mu\nu}$ we mean the set of equations (98) and (100). The EOM are conformally invariant, hence if we consider another manifold $\mathcal{M}'$ obtained from $\mathcal{M}$ by a conformal transformation $$\hat{g}_{\mu\nu}' = \Omega^2 \hat{g}_{\mu\nu}, \quad \phi' = \Omega^{\frac{2-D}{2}} \phi,$$ \textsuperscript{9} For a modern proof of the Coleman-Mandula theorem we refer the reader to: S. Weinberg, “The quantum theory of fields. Vol. 3: Supersymmetry”. then also $ \hat{g}^{\ast}_{\mu\nu} $ and $ \phi^\ast $ satisfy the EOM. The transformation $ \phi \rightarrow \phi^\ast $ is mathematically valid provided $ \Omega^{-1} $ does not vanish (or become infinite). It is assumed that $ \Omega = \Omega(x) $ is a twice differentiable function of the spacetime coordinates with the demand that always \[ 0 < \Omega < +\infty. \] (103) It is then shown for the Belinskii, Khalatnikov & Lifshitz (BKL) and for the Taub-Nut metrics that the manifold $ \mathcal{M}^* $ is geodesically complete while the original manifold $ \mathcal{M} $ is not. Notice that we here changed notation with respect to the original paper [30], namely for us the regular manifold is $ \mathcal{M}^* $. The Schwarzschild metric is an exact solution of the theory [52], and can be explicitly written in terms of $ \phi $ and $ \hat{g}_{\mu\nu} $, i.e. \[ \hat{g}^{\text{Sch}}_{\mu\nu} = (\phi \kappa_D)^{\frac{1}{D-2}} \hat{g}_{\mu\nu}. \] (104) However, as it is evident in the theory we can rescale both the scalar field $ \phi $ and the metric $ \hat{g}_{\mu\nu} $ to get an infinite class of solutions conformally equivalent to the Schwarzschild spacetime, i.e. \[ g^{\text{Sch}}_{\mu\nu} = (\phi \kappa_D)^{\frac{1}{D-2}} \hat{g}_{\mu\nu} \Leftrightarrow \hat{g}^_\mu\nu = \Omega^2 \hat{g}_{\mu\nu}, \quad \phi^ = \Omega^{\frac{2-D}{D}} \phi. \] (105) For $ \phi = \kappa_D^{-1} $ and $ \Omega = 1 $ we get the Schwarzschild spacetime $ \hat{g}^_\mu\nu = \hat{g}_{\mu\nu} = g^{\text{Sch}}_{\mu\nu} $. By making use of the conformal rescaling we can construct infinitely many other exact solutions conformally equivalent to the Schwarzschild metric. Moreover, \[ R_{\mu\nu}(g^{\text{Sch}}_{\mu\nu}) = 0 \Rightarrow \hat{R}_{\mu\nu}(\hat{g}^_\mu\nu) \neq 0. \] (106) We now explicitly provide an example of singularity-free exact black hole solution (in any conformally invariant gravity) obtained by rescaling the Schwarzschild metric by a suitable, singular warp factor $ \Omega $ (see also [53] for use of similar methods). For the sake of simplicity here we stay in $ D = 4 $. Indeed, we regard very educational to include here one regular black hole metric, namely one representative of the gauge conformal orbit, and to study its properties and the spacetime structure. The new singularity-free black hole metric looks like (later in this section we will prove the regularity of the spacetime) \[ ds^2 = \hat{g}^_\mu\nu dx^\mu dx^\nu = S(r)\hat{g}_{\mu\nu} dx^\mu dx^\nu = S(r) \left[ \left( 1 - \frac{2m}{r} \right) dt^2 + \frac{dr^2}{1 - \frac{2m}{r}} + r^2 d\Omega^2 \right], \] (107) \[ \phi^ = S(r)^{-1/2} \kappa_4^{-1}. \] (108) Let us consider the following scale factor $ \Omega $ depending only on the radial Schwarzschild coordinate, \[ \Omega^2(r) \equiv S(r) = \frac{L^4}{r^4} \left[ \frac{1}{2} \log (\frac{\hat{r}}{\hat{r}_0}) + \Gamma (0, (\frac{\hat{r}}{\hat{r}_0}) \right], \] (109) where $ L $ is a length scale introduced for dimensional reason, it could be $ L = L_P $ (Planck length) or $ L = 1/\Lambda $ or even $ L = 2m $. The first two are the scales already present in the theory, while the last one is the scale that breaks conformal symmetry on-shell. However, we believe that the spontaneous symmetry breaking of conformal symmetry should happen at the Planck mass scale, therefore, we are led to identify the scale $ L $ with $ L_P $. On the other hand, if we insist on obtaining exactly the Minkowski spacetime for $ m = 0 $, though we are not forced to do this identification in a conformally invariant theory, and then we can set $ L = 2m $. The scale factor $ S(r) $ given in [109] meets $ S^{-1}(0) = 0 $ while $ S^{-1}(\infty) = 1 $, and the Schwarzschild singularity appears exactly where the conformal transformation becomes singular, i.e. where $ S^{-1} = 0 $. However, the function $ S(r) $ is not a gauge-invariant observable in whatever conformally invariant gravitational theory, therefore, we should not be worried for the singularity present in the transformation law. This is just a gauge artefact and $ S(r) $ is not a physical quantity. We have to worry only about singularities appearing in physical observables. The situation is exactly the same like with the FRW spacetime, where the conformal factor is singular at the time of the Big Bang, but still the conformally equivalent metric is flat and regular everywhere and for any time. Notice that the metric $ \hat{g}_{\mu\nu} $ that we are tackling in this section has only few non-zero independent degrees of freedom. Indeed, for the Schwarzschild metric we have only four diagonal non-zero components, which are compatible with 9, the maximal number of components of $ \hat{g}_{\mu\nu} $. Of course there is an infinite class of such functions $S(r)$ that enables us to map the singular Schwarzschild spacetime in an everywhere regular one\textsuperscript{10}. However, as explained at the beginning of this section we must understand the singularity issue just like an artefact of the conformal gauge. Inter alia, there is a much simpler choice of $S(r)$ respect to \textbf{(109)} with exactly the same properties, $$S(r) = \frac{1}{r^2} \left( \frac{L^4}{r^2} + r^2 \right),$$ and the metric reads $$ds^2 = -\frac{1}{r^2} \left( \frac{L^4}{r^2} + r^2 \right) \left( 1 - \frac{2m}{r} \right) dt^2 + \frac{1}{r^2} \left( \frac{L^4}{r^2} + r^2 \right) \left( \frac{dr^2}{1 - \frac{2m}{r}} + \left( \frac{L^4}{r^2} + r^2 \right) d\Omega^2 \right).$$ The Kretschmann invariant $\hat{K} = \hat{Riem}^2$ is also simple and can be displayed here, $$\hat{K} = \frac{16r^2}{(L^4 + r^4)^3} \left[ L^{16} \left( 39m^2 - 20mr + 3r^2 \right) + 2L^{12}r^4 \left( 66m^2 - 32mr + 3r^2 \right) ight.$$ $$+ L^8r^8 \left( 342m^2 - 284mr + 63r^2 \right) + 12L^4m^2r^{12} + 3m^2r^{16} \big].$$ while the Ricci scalar reads $$\hat{R} = -\frac{12L^4r \left( L^4(r - 4m) + r^4(3r - 8m) \right)}{(L^4 + r^4)^3}.$$ (113) Therefore, $\hat{K}$ and $\hat{R}$ are regular for all $r$. Finally the Hawking temperature remains unchanged, namely $$T_H = \frac{1}{8\pi m}.$$ (114) We can even consider a more general range of spherically symmetric spacetimes by selecting out the following warp factor\textsuperscript{11}, $$S(r) = 1 + \left( \frac{L}{r} \right)^\alpha \quad \alpha \in \mathbb{N}, \quad \alpha > 2.$$ (117) For $\alpha = 4$ we get exactly \textbf{(110)}, but we explicitly check that the spacetime is singularity-free for any even value of the natural integer $\alpha$. For the sake of simplicity we did not consider the metric for general real values of $\alpha$. Notice that for the quite general scale factor \textbf{(117)} we get a minimum area of the spatial static sphere centred at the origin for $r = 2^{-1/\alpha} (\alpha - 2)^{1/\alpha} L$. The event horizon area and the minimum area are respectively, $$A_H = 4\pi(2m)^2 \left[ 1 + \left( \frac{L}{2m} \right)^\alpha \right], \quad A_{\text{min}} = \frac{4\pi}{\alpha^4} \left[ \left( 2^\frac{\alpha}{\alpha - 2} \right)^\frac{1}{\alpha - 2} \right]^\alpha + 1 \ (\alpha - 2)^\frac{\alpha}{\alpha - 2} \ L^{2}.$$ (118) If we wish to get back the flat spacetime for $m = 0$, the natural choice of the scale $L$ turns out to be $L = 2m$. Therefore in this case, the event horizon area is $A_H = 32\pi m^2$ for all $\alpha$, while minimal area $A_{\text{min}}$ simplifies to $$A_{\text{min}} = \pi \ 2^{4-\frac{\alpha}{\alpha - 2}} \left[ \left( 2^\frac{\alpha}{\alpha - 2} \right)^\frac{1}{\alpha - 2} \right]^\alpha + 1 \ (\alpha - 2)^\frac{\alpha}{\alpha - 2} \ m^2.$$ (119) \textsuperscript{10} It is worth to note here the crucial role played by the entire function $\hat{K}$ once again. \textsuperscript{11} Another scale factor that captures the same properties, but will simplify later the analysis of the spacetime geodesic completion, reads as follows, $$S(r) = \left( 1 + \frac{L^2}{r^2} \right)^2.$$ (115) Now, the Kretschmann invariant reads, $$\hat{K} = \frac{16r^2 \left[ L^8 \left( 39m^2 - 20mr + 3r^2 \right) + 2L^6r^2 \left( 42m^2 - 16mr + r^2 \right) + L^4r^4 \left( 150m^2 - 108mr + 23r^2 \right) + 12L^2m^2r^6 + 3m^2r^8 \right]}{(L^2 + r^2)^8},$$ (116) which is regular everywhere and zero in $r = 0$. It deserves to be noticed that $A_{\min} \leq A_H$ for all $\alpha$ and $A_{\min} = A_H$ only for $\alpha = 4$, which is the minimum value for the parameter $\alpha$ allowed for a singularity-free spacetime. Moreover, in this case a contracting two-dimensional sphere bounces back exactly at the position of the event horizon. Finally, for $L = 2m$ and $\alpha = 4$ the gravitational potential reads $$\Phi_{\text{gravity}}(r) = -\frac{1 + g_{00}}{2} = -\frac{m}{r} + \frac{8m^4}{r^4} - \frac{16m^5}{r^5}. \quad (120)$$ At a first sight the choice $L = 2m$ seems unacceptable. However, it is exactly the known black hole physics and in particular the trans-Planckian problem that support such identification. Indeed, the original derivation of the Hawking radiation involves field modes that, near the black hole horizon, have arbitrarily high frequencies. Therefore, it seems natural that the vacuum for the scalar field $\phi$ is significantly different from the Planck mass at such macroscopic quantum scale. If we take $L = \beta m$ with $\beta \in [0, +\infty)$, then the area of the event horizon $A_H$ is always bigger that the minimum area $A_{\min}$ and only for $\beta = 2$ they are equal. In general relativity we check the spacetimes’ regularity by looking at the singularities of Diff. invariant operators (the symmetry group is $GL(D)$) constructed out of the curvature and its covariant derivatives. In this way we assess the issue of the presence of curvature singularities only. About the relation of this kind of singularities to the geodesic singularities (which are the subject of powerful Hawking-Penrose theorems in GR) we comment elsewhere. When a spacetime is completely regular, then all invariants must be non-divergent. To prove that a spacetime singularity occurs, it is enough to find one divergent scalar operator. Conversely, in order to prove that no singularity occurs (in principle) all invariants should be examined and all should not exhibit curvature singularity in all spacetime points. Typically there are infinitely many diff-invariant scalar local operators, that can be constructed, hence the task of proving absence of singularities seems naively impossible. However, below we find a nice way out. In conformal gravity the symmetry group is enlarged to $GL(D) \times \text{Weyl}$, but still we only need to look for singularities in diff-invariant operators. Indeed, in $D = 4$ there is only one local conformal invariant scalar operator, namely $\sqrt{\|g\|}C^2$, but it is not diff-invariant. In higher dimensions all conformally invariant scalar invariants are already densitized, so they can not be invariant w.r.t. general coordinate transformation. We know that two metrics that differ by a conformal rescaling are located on the same conformal gauge orbit. Therefore, there is no physical difference between a singular metric and any regular one on the same orbit. We only have an operational issue because of the lack of scalar invariants under the full symmetry group $GL(D) \times \text{Weyl}$. Therefore, we do not know which invariants to examine, but we can still investigate some operators in a subgroup of the full symmetry group $GL(D) \times \text{Weyl}$. Nevertheless, we can easily overcome this problem every time we can explicitly construct the conformal map that turns a singular metric into a regular one. This is analogous to what was originally done at the event horizon by Kruskal and Szekeres for a Schwarzschild black hole in the Diff-invariant theory. Once more, the operator $\sqrt{\|g\|}C^2$ is not a good invariant because it changes under a general coordinate transformation (because $\sqrt{\|g\|}$ is a scalar density). If we insist on using such an operator to investigate the spacetime structure we are led to claim a persistence of singularity at $r = 0$. Indeed, the overall conformal factor resulting from the operator $C^2$ cancels out with exactly the same conformal factor coming from the square root of the determinant of the metric. For the metric (107) we get the following chain of identities, $$\sqrt{\|\hat{g}^\|} \hat{C}^2(\hat{g}_{\mu\nu}) = \sqrt{\|g\|}C^2(\hat{g}_{\mu\nu}) = \sqrt{\|g^{\text{Sch}}\|}C^2(g^\text{Sch}_{\mu\nu}) = \sqrt{\|g^{\text{Sch}}\|}\text{Riem}^2(g^\text{Sch}_{\mu\nu}). \quad (121)$$ However, we still have the freedom to make a coordinate transformation to rid of the singularity. Indeed, the Jacobian resulting from $\sqrt{\|\hat{g}^\|}$ plays a similar role to $S(r)$. Here we have considered curvature invariants made out of only the metric $\hat{g}_{\mu\nu}$. However, we can construct an infinite number of operators simultaneously invariant under coordinate and conformal transformations when they are built with the metric $\hat{g}_{\mu\nu}$ and the scalar field $\phi$. It is sufficient to take any diff-invariant operator of the metric $\hat{g}_{\mu\nu}$ and to replace in it $$g_{\mu\nu} \quad \text{by} \quad (\phi^2 \kappa_D^2)^{\frac{1}{2}} \hat{g}_{\mu\nu}. \quad (122)$$ Some examples are given in [150] of the Appendix A. Nevertheless, these operators do not help in understanding the singularities of the spacetime structure, exactly because of the presence of the scalar field $\phi$ that can be completely gauged away. In other words, in a conformally invariant theory the singularity is moved from the spacetime metric to the non-physical scalar field. Another proposal for an invariant quantity to consider in the case of Diff. and conformal invariant theories is given in the appendix. We conclude that to understand the spacetime singularities we need to explicitly construct a conformal map in such a way, if any, that all diff-invariant operators of $\hat{g}_{\mu\nu}$ are regular everywhere. Therefore, the singularity is non-physical. FIG. 1: The left panel shows the plot of the Kretschmann invariant for $m = 3$ and $L = 1$. The right panel shows the plot of the Ricci scalar invariant for $m = 3$ and $L = 1$. The dashed lines represent the Kretschmann invariant of the original Schwarzschild metric. FIG. 2: We have here depicted the components of the metric $g_{tt}$, $g_{rr}$, and $g_{\theta\theta}$. The dashed lines represent the components of the Schwarzschild metric. We assumed $m = 5$ and $L = 1$. We now apply this procedure to our new metric (107), namely we evaluate the Kretschmann scalar $\hat{R}_{\text{iem}}^2$ and the Ricci scalar for the metric (107). To avoid cumbersome formulas we only provide the limit of such curvature diff-invariant operators near $r = 0$, $$\hat{R} = \frac{48 m e^{\gamma E/2}}{L^4} r + O(r^2), \quad \hat{R}_{\text{iem}}^2 = \frac{624 e^{\gamma E} m^2}{L^8} r^2 + O(r^3).$$ Plots of the above operators for any value of the radial coordinate are given in Fig. 1. It deserves to be noticed that for the choice $L \propto m$ the curvature invariants and $T_H$ diverge at the last stage of the Hawking evaporation process when $m \to 0$. IX. GEODESIC COMPLETION A: NON-CONFORMALLY COUPLED POINT PARTICLE PROBE Having discussed in great extent the curvature singularities, the time has come to touch upon the issue of geodesic completeness of spacetime manifolds in conformal gravity. We will focus on the geodesic motion of some probe material point in the spacetime whose metric is given by (107). We now show that any probe massive particle can not fall in $r = 0$ in a finite proper time. We will later study the motion of a test point particle conformally coupled to conformal gravity, but the outcome will be essentially the same. We consider the radial geodesic equation for a massive point particle $$(-g_{tt} g_{rr}) \dot{r}^2 = E_n^2 + g_{tt},$$ (124) FIG. 3: Panel on the left. Spacetime structure of the Schwarzschild metric in conformal gravity. This diagram has been derived changing coordinates to Kruskal-Szekeres ones. The overall conformal factor $ S(r) $ does not change the diagram and all the curves $ r = \text{const.}, t = \text{const.} $, including $ r = 0 $, are located in exactly the same positions as in the well known Schwarzschild diagram. However, now the spacetime is regular in $ t = 0 $ and the horizontal line can never be reached in finite amount of proper time by any massive particle. If we identify the scale $ L $ present in the conformal factor $ S(r) $ with $ 2m $ the gauge orbit of the conformal transformations extends to the region $ 0 \leq r \leq 2m $. Panel on the right. Maximal extension of the singularity-free spacetime accessible only to massless particles. Indeed, the curvature invariants are regular for all $ r \leq r $ and we can extend the spacetime beyond $ r = 0 $. As a matter of comparison we consider the FRW spacetime in Einstein gravity. The photon does not see the conformal factor $ a(t) $, but we can not extend the light-like geodesics beyond the Big Bang moment $ t = 0 $, because $ a(0) = 0 $ and the metric is degenerate in $ t = 0 $. Generally, the points beyond which geodesics can not be extended occur as singularities of the curvature invariants. For the new rescaled Schwarzschild metric the curvature invariants constructed out of the $ \hat{g}_{\mu\nu} $ are regular and we are forced to extend the metric to all negative values of the radial coordinate. where the dot over quantity symbolizes the proper time derivative and $ E_n $ is the energy of the point particle. If the particle falls from infinity starting with zero initial radial velocity the energy is the rest energy of massive particle $ E_n = 1 $. We can write (124) in a more familiar form \[ \begin{align} E^2 & = \frac{E^2}{E} = S(r)^2 + S(r) \left( 1 - \frac{2m}{r} \right) = E, \quad r^2 + S(r)^{-1} \left( 1 - \frac{2m}{r} \right) = S(r)^{-2}E. \quad (125) \end{align} \] Very close to $ r = 0 $ the above equation simplifies to \[ \dot{r} \approx \frac{2mc}{L^4} r^3 \quad \Rightarrow \quad \dot{r} \approx -\frac{\sqrt{2mc}}{L} r^{3/2}, \] where the numerical constant is $ c = \exp(-\gamma E/2) $ for the the metric rescaled by a conformal factor $ S(r) $ given by (120) and $ c = 1 $ for the $ S(r) $ in (110). Above we assumed that the particle is falling on the black hole, hence the radial coordinate is decreasing with time $ \dot{r} \leq 0 $ and this is the reason why the minus sign was chosen. The plot of $ V_{\text{eff}} $ can be read out of the plot for $ g_{tt} $ in Fig. 2 From $ V_{\text{eff}} = -g_{tt} $ we infer that any massive particle can arrive in $ r = 0 $. However, integrating eq. (126) the proper time to reach the origin $ r \to 0^+ $ turns out to be infinite, \[ \Delta \tau \approx \frac{2L^2}{\sqrt{2mc}} \left( \frac{1}{\sqrt{r}} - \frac{1}{\sqrt{r_0}} \right) \quad \Rightarrow \quad \Delta \tau \equiv \tau (0^+) - \tau (r_0) \to +\infty. \] The maximal extension of the black hole spacetime is given in Fig. 3 In short, the Penrose diagram graphically shows that matter never (for none finite time) reaches the point $ r = 0 $. We remind that in the Schwarzschild background a point particle reaches the singularity in finite proper time (see also next section and Fig. 5). To derive the diagram we can write the metric in Kruskal-Szekeres coordinates, namely \[ ds^2 = S(r(X,T)) \left[ \frac{32m^3}{r(X,T)} e^{-\frac{r(X,T)}{2m}} (-dT^2 + dX^2) + r(X,T)^2d\Omega^2 \right]. \] where $r$ is implicitly defined in terms of $X$ and $T$ through the following equation, $T^2 - X^2 = (1 - r/2m) \exp(r/2m)$. The infinite amount of time needed to reach $r = 0$ is a universal property common to all regular spacetimes obtained by applying a conformal analytic transformation to the Schwarzschild metric. Let us now evaluate the volume of the black hole interior, namely the volume inside the event horizon. For $r < 2m$ the radial and time coordinates exchange their role, namely: $r = T$ and $t = R$. The metric belongs to the class of Kantowski-Sachs spacetimes, $$ds^2 = S(T) \left[ -\frac{dT^2}{2mT} - 1 + \left(\frac{2mT}{T} - 1\right) dR^2 + T^2 d\Omega^2 \right], \quad T < 2m,$$ and the interior spatial volume reads, $$V^{(3)} = 4\pi R_o S(T)^{3/2} T^2 \sqrt{\frac{2mT}{T} - 1}$$ that for the choice of the conformal factor $S(r)$ (110) turns in $$V^{(3)} = 4\pi R_o T^2 \sqrt{\frac{L^4}{T^4} + 1} \left(\frac{2mT}{T} - 1\right), \quad T < 2m,$$ where $R_o$ is an infrared cut-off due to the translational invariance in the radial variable $R$ of the metric inside the event horizon. The volume does not shrink to zero as in the Schwarzschild case, but reaches a minimum value and bounces back to infinity for $T \to 0$ (see Fig.4) X. GEODESIC COMPLETION B: CONFORMALLY COUPLED POINT PARTICLE PROBE In this section we study the geodesic completion probing the spacetime with a point particle conformally coupled to the Weyl invariant gravitational theory. The four dimensional action is obtained replacing again the metric $g_{\mu\nu}$ with $\phi^2 \kappa_4^2 \hat{g}_{\mu\nu}$ [60], $$S_{cp} = -\int \sqrt{-f^2 \phi^2 \hat{g}_{\mu\nu} dx^\mu dx^\nu} = -\int \sqrt{-f^2 \phi^2 \hat{g}_{\mu\nu}} \frac{dx^\mu}{d\lambda} \frac{dx^\nu}{d\lambda} d\lambda,$$ where $f$ is the constant coupling strength, $\lambda$ is a parameter, and $x^\mu(\lambda)$ is the trajectory of the particle. In the unitary gauge $\phi = \kappa_4^{-1}$ the action (132) turns in the usual one for a particle with mass $M = f\kappa_4^{-1}$. The Lagrangian reads $$L_{cp} = -\sqrt{-f^2 \phi^2 \hat{g}_{\mu\nu} \dot{x}^\mu \dot{x}^\nu},$$ and the translation invariance in the coordinate $t$ implies $$\frac{\partial L_{cp}}{\partial t} = \frac{f^4 \phi^2 g_{tt}}{L_{cp}} = \text{const.} = E \implies i = \frac{L_{cp} E}{f^2 \phi^2 g_{tt}}. \quad (134)$$ Since we are interested in evaluating the proper time the particle takes to reach the point $r = 0$, we must choose the proper time gauge, namely $$\frac{ds^2}{d\lambda^2} = -1 \implies \dot{x}^2 = -1. \quad (135)$$ Replacing (134) in (135) and using the solution of the EOM for $\phi$, namely $\phi = S^{-1/2} \kappa_4^{-1}$ we end up with $$S(r)^2 \dot{r}^2 + S(r) \left(1 - \frac{2m}{r}\right) - \frac{E^2 \kappa_4}{f^2} S(r) = 0. \quad (136)$$ For a particle at rest at infinity $E = f \kappa^{-1}$ and the above equation simplifies to $$S(r) \dot{r}^2 = \frac{2m}{r}. \quad (137)$$ For the scale factor (139) we can easily integrate (137) and the evaporation time to reach a general radial position $r$ starting from the event horizon in $r = 2m$ reads $$\tau = \frac{4m^2 - 3L^2}{3m} - \frac{(r^2 - 3L^2)}{3r} \sqrt{\frac{2m}{r}}. \quad (138)$$ Notice, that for any value of $L \neq 0$ the particle never reach the point $r = 0$, while for $L = 0$ we recover the finite amount of proper time need to reach the singularity in the Schwarzschild metric, namely $\tau_{Sch.} = 4m/3$ (see Fig.5) XI. BELINSKII, KHALATNIKOV, & LIFSHITZ SINGULARITY Another Ricci-flat spacetime is the generalized Kasner universe extensively studied by Belinskii, Khalatnikov & Lifshitz. It is commonly believed that such spacetime represents the most general way a spacetime cosmological singularity can be approached. The line element is $$ds^2 = g_{\mu\nu} dx^\mu dx^\nu = -dt^2 + a_1(t) dx_1^2 + a_2(t) dx_2^2 + a_3(t) dx_3^2,$$ $$a_i(t) = t^{2p_i} \quad (i = 1, 2, 3). \quad (139)$$ FIG. 5: Plot of the proper time as a function of the radial Schwarzschild coordinate for the regular spacetime and for the Schwarzschild spacetime. We here used $L = 2$, to amplify the difference between the two lines, and $m = 5.$ The condition to be Ricci-flat $ (R_{\mu\nu} = 0) $ implies that the metric must satisfy the condition \[ \sum_{i}^{3} p_{i} = \sum_{i}^{3} p_{i}^{2} = 1. \] (140) The metric $[139]$ is an exact solution of the theory $[52]$ as explained just after formula $[100]$. Indeed, all Ricci-flat spaces (again $ \text{Ric}(g) = 0 $, but $ \text{Ric}(g^{}) \neq 0 $) are exact solutions of the theory $[52]$. We now show that in conformal gravity the Kasner singularity is an artefact of the conformal gauge. Everything we have to do is to explicitly construct the proper conformal factor that rids of the spacetime singularity. The conformal factor we chose is: \[ S(t) = \frac{t^{2} + L^{2}}{t^{2}}, \] (141) and the metric reads \[ ds^{2} = \hat{g}_{\mu\nu}dx^{\mu}dx^{\nu} = \frac{t^{2} + L^{2}}{t^{2}}\left[-dt^{2} + a_{1}(t)dx_{1}^{2} + a_{2}(t)dx_{2}^{2} + a_{3}(t)dx_{3}^{2}\right], \] (142) where $ \hat{g}_{\mu\nu} $ is the BKL metric given in $[139]$. Notice that the metric $ S(t)\hat{g}_{\mu\nu} $ is not Ricci-flat, namely \[ \hat{\text{Ric}}(\hat{g}_{\mu\nu} = S(t)\hat{g}_{\mu\nu}) \neq 0, \] (143) but $ \text{Ric}(g_{\mu\nu}) = 0 $ by construction. For large $ t $ the metric $[142]$ approaches the metric $[139]$, but the Kretschmann invariant remains regular, \[ \hat{\text{Riem}}^{2}(\hat{g}_{\mu\nu}) = \frac{4\left(\frac{4(L^{2}+t^{2})^{2}}{u^{2}+u+1} - \frac{8(L^{2}+t^{2})}{u^{2}+u+1}\right)}{(L^{2}+t^{2})^{6}}, \] (144) where we introduced the usual BKL parametrization, namely \[ p_{1} = -\frac{u}{u^{2}+u+1}, \quad p_{2} = \frac{u+1}{u^{2}+u+1} \quad \text{and} \quad p_{3} = \frac{u(u+1)}{u^{2}+u+1}. \] (145) Therefore we proved that after the conformal transformation the BKL metric is without singularity. \[\text{XII. GRAVITATIONAL COLLAPSE AND COSMOLOGY}\] Concerning the black hole singularity problem at quantum level the outcome of Sec.VII F may be of some help. Indeed the gravitational collapse (and subsequent Hawking evaporation) is just like a scattering process, but the $ S $-matrix is trivial and there is no interaction in the conformal phase. Therefore, there is no way to produce a singularity. Let us expand on this point by explicitly constructing the spacetime metric for the gravitational collapse in a conformally invariant theory. Again, the theory manifests conformal invariance and any metric obtained from the Minkowski one up to a conformal rescaling is an exact vacuum solution. In particular, the metric \[ ds^{2} = \hat{g}_{\mu\nu}dx^{\mu}dx^{\nu} = -dt^{2} + 9t^{2}\hat{x}_{i}^{2}, \] (146) which represents a spacetime filled up with dust in Einstein gravity, is an exact solution of the weakly non-local theory. It is also a representative metric in the conformal gauge orbit of all conformally flat spacetimes. Indeed, we can first make the coordinate transformation $ t = \tau^{3} $ to get the metric \[ ds^{2} = -9\tau^{4}d\tau^{2} + 9\tau^{4}d\hat{x}_{i}^{2} \] (147) and second a conformal rescaling with the factor $ S(\tau) = 1/9\tau^{4} $ to finally end up with the Minkowski flat metric, namely \[ ds^{2} = \hat{g}_{\mu\nu}dx^{\mu}dx^{\nu} = S(\tau)ds^{2} = S(\tau)\hat{g}_{\mu\nu}dx^{\mu}dx^{\nu} \quad \Rightarrow \quad ds^{2} = \frac{1}{9\tau^{4}}\left(-9\tau^{4}d\tau^{2} + 9\tau^{4}d\hat{x}_{i}^{2}\right) = -d\tau^{2} + d\hat{x}_{i}^{2}, \] \[ \phi^{} = S(\tau)^{-1/2}\phi = 3\tau^{2}\phi. \] (148) Here $\phi^$ must be constant for consistency when the flat metric $\phi^{2}g_{\mu\nu} = g_{\mu\nu} = \eta_{\mu\nu}$ is an exact solution, then $\phi = 1/3r^2$. In other words we do not know what is the exact solution for $\phi$, but only the conformal relation between $\phi$ and $\phi^$ is known. Notice that the matter content must be coupled in a conformally invariant way directly in the EOM or in the action, but this is actually irrelevant for the aim of this section. However, only a physical source with traceless energy-momentum tensor can be consistently coupled in a conformally invariant theory as a consequence of the conformal invariance of the theory. Therefore, we can have a dust-like solution not for dust (pressureless) matter, but for collapsing massless radiation. We have shown that the Schwarzschild metric is an exact solution in vacuum, while the line element describes the spacetime inside the black hole filled with matter. We can impose the usual boundary conditions to make the metric and the extrinsic curvature continuous everywhere, and we finally end up with the simple Oppenheimer-Volkoff model for the gravitational collapse. Notice that the solution for $\phi$ is $1/3r^2$ in the matter region and is independent on time $\tau$ outside, but this shall not cause discomfort to the reader because $\phi$ is not a physical field. However, we advise the reader that we are here dealing with a non-local theory and a more strict study of the boundary conditions should be required or justified. This last issue is not present for the theories and . Nevertheless, there is no singularity in $t = 0$ because the spacetime is conformally equivalent to the flat one. In agreement with the previous section the radiation reaches the point $r = 0$ and goes beyond, while the regular black hole forms in a finite amount of time. The Hawking process allows radiation to evaporate out of the black hole after a finite amount of time, which is invariant independent on the conformal frame (because the surface gravity evaluated at the event horizon is invariant under a conformal rescaling of the metric.) All the radiation is bounces back in our universe in finite time throughout Hawking particles in a way that resembles what we would like to call “Planck Supernova”, on the footprint of the proposal in (see also and ). In a conformally invariant theory we can introduce a kind of dust matter in a conformally invariant way, whenever we have an action principle for dust . Indeed, we can make the same replacement also in the Lagrangian formulation of dust proposed in and we trivially achieve conformal invariance of the whole theory. If conformal invariance is spontaneously broken, namely $\phi = \kappa_D^{-1}$, then the Lagrangian for ordinary dust matter is recovered. Now we are ready to repeat for dust matter the analysis we have just provided for photons. The outcome of the previous section is that massive particles reach the point $r = 0$ in an infinite amount of time, but the regular black hole forms in finite time, just because matter crosses the event horizon in finite proper time. Through the Hawking mechanism, particles are emitted to finally make the black hole completely evaporate away. The dust matter never reaches the origin, but it bounces back in a finite amount of time throughout the process of emission of Hawking particles and they fill back the universe. We repeated several times that any FRW spacetime is an exact solution of the conformally invariant theory whatever is the scale factor $a(t)$. The quite involved EOM can be solved for the scalar field $\phi$, while the conformal invariance ensures that any solution is pure gauge and then non-physical. We extensively explained that the conformal invariance is spontaneously broken and the simpler constant solution for $\phi$ restores the Planck mass (or Newton constant) in the action without any change in the number of d.o.f. of the theory. This is actually a particular vacuum for the scalar field that, however, does not have any dynamics. In this paper we have found other less trivial vacua for the scalar field (see for example $S(r)$) in the black hole case) and in general we expect a general profile for the scalar field condensate instead of a constant one. In other words the EOM for $\phi$ can be read as equations for the vacuum of the theory. Since any FRW spacetime is an exact solution of the theory we can infer about the vacuum profile starting from the “observed” profile for the scale factor $a(t)$, namely $\phi^* = a(t)^{-1} \times \text{const}$. It turns out that the FRW background solutions of the theory are consistent with the whole spectrum of observations. However, here it is crucial a rigorous analysis of the linear perturbations to select out the physical vacuum. Moreover, the Penrose aeons’ theory is naturally embedded in any conformally invariant theory, but here we gain the conformal anomaly freedom. Finally, we point out again that the evolution of the universe in a conformally invariant theory is actually the spontaneous selection of a particular vacuum out of an infinite number of them. XIII. CONCLUSIONS AND REMARKS In this paper we have explicitly shown that a class of finite weakly non-local gravitational theories is the spontaneously symmetry broken phase of a range of conformally invariant gravities. The proof is straightforward in odd dimension, but it has been carried out also in $D = 4$ leaving for exercise the smooth generalization to any even dimension. Since theories are finite then conformal invariance is anomaly free or preserved at quantum level. Nevertheless, the conformal invariance is spontaneously broken in exactly the same way like the gauge symmetry is broken in the standard model of particle physics (SM). Our compensator scalar field $\phi$, need to implement conformal symmetry, plays exactly the same role of the Higgs field. After the symmetry breaking the $\phi$ degree of freedom is absorbed by the spacetime metric that increases its number of components from nine to ten. This is analog to the conservation of the degrees of freedom in the SM where three out of the four scalars move to the gauge boson sectors to generate their longitudinal modes. The only difference lies in the absence of any Higgs particle in gravity, as a mere consequence of the small number of gauge invariant degrees of freedom respect to the SM. In the last part of this paper we have explicitly shown how the conformal invariance tames the space time singularities. In particular all the FRW spacetimes, the BKL metric, and the Taub-Nut spacetime are singularity-free as shown by Narlikar and Kembhavi in [30]. On the footprint of such masterpiece we explicitly proved that the Schwarzschild metric is singularity free in a rather general class of conformally invariant gravitational theories. We explicitly construct a class of black hole metrics regular everywhere (including the point $r = 0$) that differ from the Schwarzschild metric only for an overall conformal rescaling, which approaches one for distances much bigger then the Planck length or any other scale the conformal factor depends on. The conformal map is well defined everywhere and singular in $r = 0$ as should be to cancel the singularity. The dust dominated universe is also an exact solution and, assuming such spacetime to be the interior of a collapsing star, the simple Oppenheimer-Volkoff model for the gravitation collapse turns out be compatible with the collapse with a subsequent bounce. Finally, we explicitly showed that the BKL spacetime is singularity-free in non-local conformal gravity as long as in Einstein conformal gravity. The main outcome of this paper is the compatibility of conformal invariance with quantum field theory. Indeed we explicitly constructed a class of conformally invariant gravitational theories free of conformal anomaly at quantum level. Therefore, we overcame the major impediment in believing to conformal invariance as a symmetry realized in nature, although such symmetry must be spontaneously broken. In other words the action is invariant under conformal invariance, but the vacuum is not. When we expand the action around the vacuum $\phi = \kappa_D^{-1}$ the action is no more manifestly conformally invariant. In analogy with the Higgs mechanism in the standard model, $\phi(x) = \kappa_D^{-1} + \varphi(x)$ plays the role of the forth component of the scalar field $\Phi_4(x) = v + H(x)$. However, here the symmetry is sufficient to completely remove the perturbation $\varphi(x)$ from the physical spectrum, while the spontaneous symmetry braking pattern in the standard model of particle physics, namely $SU(2) \times U(1)_Y$ broken to $U(1)_{\text{em}}$, fixes to zero three out of the four real scalars leaving one dynamical $H(x)$ degree of freedom. Notice that the three scalar degrees of freedom of the SM change into the longitudinal polarizations of the massive vectors $W^\pm$ and $Z^0$, while here the fluctuation $\varphi$ is absorbed in the metric $g_{\mu\nu}$ (namely $g_{\mu\nu} = \hat{g}_{\mu\nu}$) to make it sensitive to the distances and not only the causal structure of the spacetime. The last comments are about the quasi-polynomial non-local nature of the action. The reader could incorrectly objects about the ambiguous presence of form factors and therefore about the predictability of the theory. This objection has no physical foundation because in the majority of the experiments people are only able to observe form factors. If we have the same attitude in QED or QCD etc. then there is no way to prove or disprove such theories as long as we only make a finite number of measurements. Therefore, our non-local theory is testable on the same level of any other local theory. Nevertheless, one could assert that a non-local theory must be the effective theory of some, we would say, “mystic” extended underlying “fundamental object”. Whether we take seriously this point of view then we must find an underlying theory for any quantum effective action, which is severely non-local as repeatedly pointed out. However, we are quite happy with the standard model of particle physics (SM) and we are not forced to embed it in a more fundamental theory. However, let us assume for a moment that we do it, and we derive the standard model, for example, as a low energy limit sector of string theory. This is not enough to make the reductionist reader happy, because the quantum effective action of the string itself will be non-local, or actually double non-local, as evident in the string field theory framework when the quantum corrections are included. Indeed, the non locality is a feature of any field theory at quantum level and has nothing to do with the extended nature of the fundamental constituents. Whatever it is the extended object we base our theory, the quantization procedure will introduce extra non locality. Therefore, non locality is a feature of quantum field theory. The difference in our approach is that we start from a classical weakly non-local theory, while in the SM all the fundamental interactions are described by a local Lagrangian at classical level. However, the theory $\mathcal{S}_3$ presented in the first section for the minimal case $\gamma_4 = 0$ is astonishingly local at classical level. Indeed, it has been proved in [3] that with a field redefinition we can identically convert, at tree-level, such theory in the Einstein-Hilbert action. Notice that both the theories have the same perturbative spectrum.$^{13}$ It is only at one loop that the non $^{12}$ It is remarkable the similarity between the class of solution presented in this paper and the black hole spacetime structure derived in loop quantum gravity (LQG) in the minisuperspace approximation $^{14,15}$ (see also $^{16}$). Does LQG show a conformally invariant structure at the Planck scale? Preliminary results using weave states $^{14}$ and the ultra-locality of the Hamiltonian constraint are in favour of this interpretation. $^{13}$ Let us clarify the perturbative statement with one example. In Stelle’s quadratic gravity there are other perturbative degrees of freedom, namely one massive spin-2 ghost and one massive scalar, besides the graviton particle. Therefore, the field redefinition argument only locality becomes crucial in making the theory finite. However, it is not surprising that the quantum effective action is non-local. As matter of fact any quantum action is non-local whatever the classical action we start from is: local or non-local. In our case we have a kind of “hidden” non locality present in the classical action that shows up only at quantum level (one can track down the “hidden” non locality in the non ultra-local path integral measure resulting from the Jacobian of the field redefinition $ \hat{R} $). We infer that our theory is actually local at classical (perturbative) level and non-local at quantum level as well as any other theory. The only difference is in a kind of illusory non-locality at classical level, which only becomes real at quantum level when the path integral measure can not be left out. Again, at perturbative level we get the same tree-level scattering amplitudes if evaluated in the E-H theory or in the non-local one, which have also the same perturbative spectrum, therefore, the two theories are classically and perturbatively equivalent. At quantum level the form factors play a crucial role for the super-renormalizability or the finiteness and the effective action turns out to be non-local. However, this is not a novelty because every theory is non-local at quantum level. We can finally firmly assert that the non-local theory is “actually local” because of the reasons just explained. One more comment reads as follows. The following operators seem unavoidable at quantum level, \[ \text{Riem}^2 \text{Ric}, \quad \text{Ric} \mathcal{F}(\square) \text{Ric}, \quad \ldots \] \[\text{non analytic function}\] Indeed, they can not be removed by a field redefinition quadratic in the field EOM and/or perturbatively local. Moreover, we need the limit $ \Lambda \to \infty $ in (50) and in the full quantum action to be convergent. However, if one proves that the statements right above are incorrect then we can infer that Einstein gravity is finite at any perturbative order and the form factors just play the role of un-physical regulators. APPENDIX A: Curvature operators in conformal gravity In this section we remind the outcome of replacing the metric $ g_{\mu\nu} \equiv \phi^2 \hat{g}_{\mu\nu} $ in the operators linear and quadratic in the curvature. In a spacetime of general dimension $ D $ the the operators of order zero, one, and two in the curvature read [50] \[ \sqrt{\|g\|} = \phi^D \sqrt{\|\hat{g}\|}, \] \[ R = \phi^{-2} \left[ \hat{R} - 2(D - 1) \frac{\Box \phi}{\phi} - (D - 1)(D - 4) \hat{g}^{ab} \frac{\phi_{,a} \phi_{,b}}{\phi^2} \right], \] \[ R^2 = \phi^{-4} \left[ \hat{R}^2 + 4(D - 1)^2 \phi^{-2} (\Box \phi)^2 + (D - 1)^2 (D - 4)^2 \phi^{-4} \hat{g}^{ab} \phi_{,a} \phi_{,b} \hat{g}^{cd} \phi_{,c} \phi_{,d} \right. \] \[\left. - 4(D - 1) \hat{R} \phi^{-1} \Box \phi - 2 \hat{R} (D - 1) \phi^{-2} \hat{g}^{ab} \phi_{,a} \phi_{,b} + 4(D - 1)^2 (D - 4) \phi^{-3} \Box \phi \hat{g}^{ab} \phi_{,a} \phi_{,b} \right], \] \[ R_{ab} R^{ab} = \phi^{-4} \left\{ \hat{R}_{ab} \hat{R}^{ab} - 2 \phi^{-1} \left[ (D - 2) \hat{R}_{ab} \phi^{ab} + \hat{R} \Box \phi \right] \right. \] \[\left. + \phi^{-2} \left[ 4(D - 2) \hat{R}_{ab} \phi_{,a} \phi^{,b} - 2(D - 3) \hat{R} \phi_{,e} \phi^{,e} + (D - 2)^2 \phi_{,a} \phi_{,b} + (3D - 4) (\Box \phi)^2 \right] \right. \] \[\left. - \phi^{-3} \left[ (D - 2)^2 \phi_{,ab} \phi^{,a} \phi^{,b} - (D^2 - 5D + 5) \Box \phi \phi_{,e} \phi^{,e} \right] + \phi^{-4} (D - 1)(D^2 - 5D + 8) (\phi_{,a} \phi^{,a})^2 \right\}. \] (150) Notice that the definition $ g_{\mu\nu} \equiv \phi^2 \hat{g}_{\mu\nu} $ differs slightly from [50] because here $ [\phi] = 0 $ and its exponent is independent on the spacetime dimension $ D $. APPENDIX B: Local and non-local curvature invariants In this section we would like to expand on the inadequacy of using conformal invariant operators to verify the regularity of the spacetime. --- applying to the amplitudes with external graviton states. Indeed, these amplitudes coincide with the ones evaluated in Einstein gravity. In the case of the non-local theory the matching with Einstein gravity is one to one at perturbative level because the perturbative spectrum is the same. However, at the moment the non perturbative spectrum is unknown and the correspondence can not be pushed further. As already point out in the main text we can construct an infinite number of diffeomorphisms and at the same time conformal invariant operators, whether we make use of both the metric $\hat{g}_{\mu\nu}$ and the scalar field $\phi$. Indeed, it is sufficient to take any invariant built with the metric $g_{\mu\nu}$ and make the replacement $g_{\mu\nu} = \phi^2 \hat{g}_{\mu\nu}$ (for the sake of simplicity we here in deal with the $D = 4$ case.) All these operators are very ambiguous because involve the scalar field that can be gauged away exactly by a conformal rescaling. Moreover, these operator do not provide any information about the regularity of the physical metric $\hat{g}_{\mu\nu}$ because it is camouflaged with the scalar field. Making use of these operators you can only get information about $g_{\mu\nu}$, but not about $\hat{g}_{\mu\nu}$ solely. Indeed, all this operators diverge exactly as for the Schwarzschild metric. However, there is a subclass of conformal invariant operators involving the Bach tensor that has the special property to be “strongly” regular, namely they are identically zero. One example is: $$\phi^{-8} B_{ab} B^{ab}. \quad (151)$$ Moreover, $B_{ab} \equiv 0$ for any FRW and Ricci flat manifold. We could speculate that only vanishing invariants are good conformal invariant operators. Indeed, all the local Diff. invariant operators made of only the metric $\hat{g}_{\mu\nu}$ goes smoothly to zero near $r = 0$, while $d^{4}B_{ab}$ goes smoothly to zero near $r = 0$, while $d^{4}B_{ab}$ is zero everywhere. In other words these operators share the same behaviour near the classical singular point. Another more speculative idea to check the regularity of a spacetime is related to (strongly) non-local curvature invariants. They arise integrating some invariant densitized scalars over an region of the spacetime volume. We remark that they are not weakly non-local in the sense of containing infinitely many derivatives (such weakly non-local curvature invariants can be constructed as well.) They are integrals over a finite (or infinite) region, so they do not depend only on one point of the manifold. However, the advantage of using them to check the singularities is that they can be at the same time invariants with respect to the group of diffeomorphisms and the conformal transformations group. They are now full invariants, because the densities (coming always with local conformal invariants) are here integrated. One of the example of such non-local invariant in $D = 4$ is $$X = \int_{V_4} d^4x \sqrt{\|g\|} C^2. \quad (152)$$ Notice that the local operator $\sqrt{\|g\|} C^2$ is not invariant under diffeomorphisms as already pointed out in the main text. Namely, it is not a scalar unlike the Kretschmann invariant that we can also integrate on a spacetime region, but without to mix together the Diff. properties of the volume element and the curvature invariant. Thanks to the chain of equalities given in (121) the expression $X$ is a conformally invariant non-local scalar and the structural expression for it is the same for any metric $g_{\mu\nu}$, $\hat{g}_{\mu\nu}$ or $\hat{g}^{}_{\mu\nu}$. We need to discuss the issue about the domain of integration $V_4$ for such invariant. When a coordinate or conformal transformation is performed the domain of integration must be transformed accordingly. If we are interested in the problem of singularities, then we should choose a spacetime volume that includes the potential singular point. However, despite natural wishes to integrate over the whole manifold, this may be not a good strategy, because the integral may diverge because of the integration on an infinity region. Typically, it is better to restrict the domain to some finite manifold near the special point of the manifold where we expect the singularity. For the particular case of the Schwarzschild singularity, which is localized in the coordinate $r$, but not in coordinate $t$ (points $r = 0$ are singular for any time $t$) the convenient 4-volume $V_4$ to select is a cylinder. It may consist of a finite time interval of coordinate length $\Delta t$ and a 3-ball $B_3$ of finite radius centred at the origin of spatial reference system. We can choose the size of this ball uniformly along the whole cylinder in such a way that its boundary is at coordinate radius $r_1$. For such choice the manifold $V_4$ has the topology of $S_3 \times \mathbb{I}$, where $\mathbb{I}$ is the interval on the real axis. Since the potential dangerous point is at the origin, we have to cut out a little ball ending at the coordinate position $r_0$ and integrate over the remaining pipe-like shape bulk manifold $B_3 \times \mathbb{I}$. We will investigate the presence of singularities by analyzing the asymptotic behaviour of the invariant $X$, when $r_0 \rightarrow 0$ and keeping $\Delta t$ and $r_1$ fixed and non-zero. The explicit computation for the Schwarzschild metric shows that the densitized invariant $\sqrt{\|g\|} C^2$ does not depend on $t$, hence the invariant $X$ will be exactly proportional to the interval $\Delta t$. In what follows we can forget about this factor and study the more important $r_0$-dependence. This computation can be performed for any metric $g_{\mu\nu}$, $\hat{g}_{\mu\nu}$ or $\hat{g}^{}_{\mu\nu}$. For example in original $g_{\mu\nu}$ we find that near $r = 0$ the scaling is the following: $$C^2 = \frac{48 m^2}{r_6^2} \quad \text{and} \quad \sqrt{\|g\|} = r^2 \sin \theta. \quad (153)$$ Hence, the invariant $X$ reads $$X = \Delta t \int_{B_3} d^3x \sqrt{\|g\|} C^2 = 96\pi \Delta t m^2 \int_{r_0}^{r_1} \frac{dr}{r^2} \int_0^{\pi} \sin \theta d\theta = -64\pi \Delta t m^2 \left[ \frac{1}{r_0^3} \right]_{r_0}^{r_1} = 64\pi \Delta t m^2 \left( \frac{1}{r_1^3} - \frac{1}{r_0^3} \right). \quad (154)$$ One can see that $X$ is still divergent, when the internal coordinate radius $r_0$ of the modified ball $\tilde{B}_3$ is sent to zero. The invariant diverges like $64\pi \Delta t m^2 r_0^{-3}$. If we believe in the non-local invariant as a good one to identify the singularities, then the conclusion would be that Schwarzschild singularity is still there even in conformal gravity. However, we emphasize that the usage of strongly non-local invariants like $X$ is not so well motivated for the study of singularities. Moreover, we will show later with a counterexample that this invariant is in disagreement with the outcome of the explicit study of geodesic completion. However, if we take the principal value of $X$ the outcome of (154) is identically zero because the result of the indefinite integral is odd. This is actually in agreement with the value of (151), which is also zero. Moreover, it is not in disagreement with all the other Diff. curvature invariants. On the other hand the invariant $X$ has quite clear physical interpretation. It is a dimensionless quantity (because of scale-invariance) equal to the value of the conformal gravity action functional evaluated on the portion of the Schwarzschild solution that surrounds the singularity. In the result (154), we can easily send the external coordinate radius $r_1$ to infinity to end up with the value of the action for the whole Schwarzschild spacetime. In the case of an FRW spacetime the invariant $X$ is clearly zero for any 4-volume because the Weyl tensor in the integrand vanishes. It is not surprising that the action functional is a good invariant w.r.t. the Diff. and conformal group. The only problem is that it is non-local by construction. Requiring that it is well-defined and vanishes on the flat spacetime in $D = 4$ we have a unique choice for it, which is the familiar action of the 4-dimensional conformal gravity. In higher dimensions we can have more choices for conformally invariant actions satisfying the above condition, however, still finitely many. As it is known only non-local global invariants (like ADM mass for example) are true observables in pure classical GR. The invariant $X$ is one of such invariant for a 4-dimensional conformally invariant gravitational theory. A similar invariant can be constructed in conformally invariant 4-dimensional electrodynamics, namely $$X' = \int_{V_k} \sqrt{\|g\|} F^2,$$ where $F$ is the field strength of electromagnetism. We find that for the Coulomb potential $\Phi_{el} = Q/r$, the non-local invariant is also divergent $X' = 8\pi \Delta t Q^2 r^{-1}$ and it measures the energy stored in the field near the point-like charge multiplied by the time interval $\Delta t$. In this case, as for conformal gravity, the singularity is present because of the infinite energy stored in the gravitational field near the singularity. We notice that the non-local invariants are identically zero whether we shrink to zero the integration domain, namely $$\lim_{r_0 \to r_1} X = \lim_{t_0 \to t_1} X = 0.$$ A potential solution of this ambiguity is to define the invariant $X$ by taking the principle value of the integral, namely $$P(X) = P \left( \Delta t \int_{B_3} d^4x \sqrt{\|g\|} C^2 \right) = -64\pi \Delta t m^2 P \left( \frac{1}{r^3} \right) = 0.$$ Another drawback of using conformally invariant operators is related to the fact that conformal symmetry is in the broken phase for all the solutions analyzed here. The arguments presented in this section should persuade the reader that we can not infer about the regularity of the spacetime in a conformally invariant theory by the meaning of appropriate singularity-free curvature operators that are invariant under both conformal and general coordinate transformations. Only the Diff. invariant operators made of $\hat{g}_{\mu\nu}$ are appropriate to infer about the singularities of the spacetime, namely $$\hat{R}(g), \quad \hat{R}^2(g), \quad \hat{Ric}(g) \hat{Ric}(g), \quad \hat{Riem}(g) \hat{Riem}(g), \ldots.$$ Let us expand on this latter statement. In this section we presented two different kinds of operators. A first range of operators involve not only the metric, but also the scalar field. These operators are not able to single out the spacetime properties of the metric $\hat{g}_{\mu\nu}$. They are only sensitive to the metric $\hat{g}_{\mu\nu}$, but not to the sub-spacetime structure made of $\phi$ and $\hat{g}_{\mu\nu}$. A second range of operators involve only the metric $\hat{g}_{\mu\nu}$ (and not $\phi$), but are non-local and not suitable to infer about the regularity of the spacetime because the geodesic completion has to do with the local properties of the manifold. Finally, suppose that the regular metric $\hat{g}^_{\mu\nu}$ for a spherically symmetric body is not a solution of any conformally invariant theory. Therefore, nobody can object whether we use any local curvature invariants (158) to infer about the regularity of the spacetime. Indeed, it turns out that the metric $\hat{g}^_{\mu\nu}$ is singularity-free, because all the invariants (158) are regular everywhere. On the other side the spacetime is geodesically complete as explicitly shown in the text. Therefore, the outcomes of the Diff. invariant operators and of the geodesics completion perfectly agree. On the other hand if we use the non-local operator we find a singularity in the curvature invariant, while the geodesic motion is well defined. This argument is sufficient to rule out the non-local operator $\hat{g}_{\mu\nu}$ as a good tool to probe the spacetime singularity structure, because it is in disagreement with the geodesic completion. However, in this case the metric is not solution of any conformally invariant theory and in principle there is no reason to check the regularity of the spacetime by using general conformal invariant operators. Therefore, we could infer that only the local curvature invariants $\hat{g}_{\mu\nu}$ solely can eventually point out the presence of singularities in the spacetime.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2370, 1 ], [ 2370, 6571, 2 ], [ 6571, 12688, 3 ], [ 12688, 18635, 4 ], [ 18635, 23812, 5 ], [ 23812, 27835, 6 ], [ 27835, 31908, 7 ], [ 31908, 36076, 8 ], [ 36076, 40086, 9 ], [ 40086, 45404, 10 ], [ 45404, 50782, 11 ], [ 50782, 55741, 12 ], [ 55741, 58260, 13 ], [ 58260, 62393, 14 ], [ 62393, 65995, 15 ], [ 65995, 70757, 16 ], [ 70757, 75393, 17 ], [ 75393, 79584, 18 ], [ 79584, 84758, 19 ], [ 84758, 89571, 20 ], [ 89571, 93074, 21 ], [ 93074, 98851, 22 ], [ 98851, 100729, 23 ], [ 100729, 104402, 24 ], [ 104402, 106549, 25 ], [ 106549, 108586, 26 ], [ 108586, 112031, 27 ], [ 112031, 118042, 28 ], [ 118042, 124397, 29 ], [ 124397, 128773, 30 ], [ 128773, 134591, 31 ], [ 134591, 140030, 32 ], [ 140030, 140634, 33 ], [ 140634, 140634, 34 ] ] }
4eb66fde6d2295bfa689a2004e7f27dfe57361ef	{ "olmocr-version": "0.1.59", "pdf-total-pages": 25, "total-fallback-pages": 0, "total-input-tokens": 87214, "total-output-tokens": 21841, "fieldofstudy": [ "Engineering" ] }	Optimization of Operating Hydrogen Storage System for Coal–Wind–Solar Power Generation Rui Yan, Yuwen Chen and Xiaoning Zhu * School of Economics and Management, University of Science & Technology Beijing, Beijing 100089, China; [email protected] (R.Y.); [email protected] (Y.C.) * Correspondence: [email protected] Abstract: To address the severity of the wind and light abandonment problem and the economics of hydrogen energy production and operation, this paper explores the problem of multi-cycle resource allocation optimization of hydrogen storage systems for coal–wind–solar power generation. In view of the seriousness of the problem of abandoning wind and photovoltaic power and the economy of hydrogen production and operation, the node selection and scale setting issues for hydrogen production and storage, as well as decision-making problems such as the capacity of new transmission lines and new pipelines and route planning, are studied. This research takes the satisfaction of energy supply as the basic constraint and constructs a multi-cycle resource allocation optimization model for an integrated energy system, aiming to achieve the maximum benefit of the whole system. Using data from Inner Mongolia, where wind abandonment and power limitation are severe, and Beijing and Shanxi provinces, where hydrogen demand is high, this paper analyzes the benefits of the hydrogen storage system for coal–wind–solar power generation, and explores the impact of national subsidy policies and technological advances on system economics. Keywords: coal–wind–solar power; hydrogen storage; multi-cycle resource allocation; energy system optimization 1. Introduction In recent years, global climate change has caused a variety of environmental problems, which attracts the attention of various countries to develop clean energy to replace the fossil energy. Under the global energy transition and sustainable development, in September 2020, the Chinese government announced that China will strive to achieve peak carbon dioxide emissions by 2030 and carbon neutrality by 2060, demonstrating its great responsibility and commitment to building a community of shared future for mankind and its determination to address climate change [1]. Using clean energy to generate electricity, such as wind and solar power, is an important way to drive energy reformation in China. However, with the increase in fan installed capacity and photovoltaic installed capacity year by year, the phenomenon of abandoning wind and photovoltaic power has become an urgent problem to be solved, which directly affects the profits of wind and photovoltaic power plants, and wastes energy [2]. In 2015, China’s installed capacity for wind and photovoltaic power ranked first in the world. Meanwhile, the data on abandoning wind and photovoltaic power also hit a record high. Since 2015, the amount of abandoned wind and photovoltaic power in China has increased year by year. The situation did not ease until 2018, but the annual amount of abandoned wind and photovoltaic power was 27.7 billion kWh and 5.5 billion kWh, respectively. Hydrogen storage is the preferred solution to solve the problem of a large amount of centralized wind and solar combined with the grid [3,4]. Compared with hydraulic storage, compressed air storage, wind turbine storage, electrochemical storage, superconducting magnetic storage, etc., hydrogen storage has various advantages. The energy density of hydrogen is 140 MJ/kg, which is more than twice that of a typical solid fuel. Hydrogen is burned to produce water with no pollution gas produced during the production process. Furthermore, hydrogen has a large capacity and is easy to store for it can be stored as gas, liquid and solid [5]. The remaining hydrogen after combining with the grid can also be used as fuel for hydrogen vehicles without pollution. Therefore, the widespread use of hydrogen energy not only solves the problems of environmental pollution and abandoning wind and photovoltaic power, but also promotes the energy transition and mitigates climate change risks, creates work opportunities and enhances economic development, which in turn can contribute to the progress of the whole society [6]. The main obstacle to the large-scale application of hydrogen energy is the high cost of hydrogen production, storage and transport. The cost of hydrogen production accounts for about 70% of the total cost of hydrogen. A large number of domestic and foreign research institutions and related enterprises find that wind–hydrogen coupling and wind–solar–hydrogen coupling are two effective ways to reduce the cost of hydrogen [7]. Moreover, since coal provides a stable and continuous supply of electricity, wind–solar power, hydrogen storage and coal can complement each other and together improve the stability of the system. On this basis, in view of the seriousness of the problem of abandoning wind and photovoltaic power and the economy of hydrogen production and operation, this paper constructs a hydrogen storage system for wind–solar power generation, studies its economy and provides theoretical guidance for the large-scale adoption of hydrogen storage. The rest of this paper is organized as follows: the second part is a review of related literature; the third part is the construction of a multi-cycle resource allocation optimization model for the wind–solar–hydrogen integrated system; the fourth part is a case study on the construction of the hydrogen storage system for wind–solar power generation in Inner Mongolia, where the amount of abandoned wind and photovoltaic power is the largest in China, and in Beijing and Shanxi, where the demand for hydrogen is large; the last part is the conclusion of this paper and future research directions. 2. Literature Review The hydrogen storage system for wind–solar power generation uses wind and photovoltaic energy, instead of the fossil fuel, to generate power. To be specific, that system transmits the power that cannot be absorbed by the grid to the electrolyzer, and then generates hydrogen through the electrolysis of water, which transforms power into gas. When power is in short supply, the fuel cell can be used to convert it into power or export the hydrogen to the industrial or other consumer end. This paper explores the hydrogen storage of wind and photovoltaic power generation, the production, storage and transportation of hydrogen and the optimization of coal–wind–solar–hydrogen operation. 2.1. Research on Hydrogen Storage of Wind–Solar Power Generation Wind power generation is a commonly used method to generate power at present, but its instability affects the quality of wind power. Additionally, photovoltaic power generation was developed recently. However, it is more stable than wind power for it is affected by solar intensity. In 1981, Busch and Kallenbach proposed the concept of wind–solar power generation in view of the instability of wind and photovoltaic power supply, which is the first theoretical research on wind–solar coupled power generation. Subsequently, the system for wind–solar power generation was investigated by many scholars, such as Aspliden, Russell, Aksarni, Rajesh and Karki. The research on wind–solar coupled power generation in China began in 1982. Yu Huayang and others studied the energy conversion device of solar and wind power generators, which marked that the research on wind–solar power generation systems entered the stage of practical application. To solve the structural defects of the conventional wind–solar hybrid power generation system, Wei et al. [8] proposed a compact spherical wind–solar hybrid power generation system (CSWS-HPS) and achieved a considerable power generation efficiency. To improve the reliability and energy utilization of renewable energy generation systems, Liu et al. [9] investigated the optimal control method of wind–solar hybrid devices designed using the power prediction method and proposed an MPPT optimal control strategy. Wind and solar power generation has good temporal and spatial complementarity, which can ensure the stability and sustainability of electrical energy output, and thus achieve efficient utilization of resources and improve economic efficiency [10]. At present, many countries such as the United States, Germany and Spain have supported and planned to combine renewable energy with fuel cells to generate power in off-grid or grid systems. The U.S. Department of Energy NREL and Xcel Energy launched the Wind H2 plan, and the European Commission proposed the Fifth Framework Programme for Research, which aim to explore technologies which use renewable energy to produce and store hydrogen. As clean energy, hydrogen has high energy density, large capacity, long life and easy storage and transmission. In recent years, many scholars have verified the feasibility and necessity of hydrogen storage of wind–solar power generation through examples [11,12]. In addition, with the development of computer technology, more and more scholars have verified the effectiveness and reliability of hydrogen storage systems in wind–solar power generation through modeling and simulation [13–19]. Other scholars have designed the scheme on hydrogen storage of wind–solar power generation to optimize the system [20–24]. Hydrogen storage can provide frequency regulation and rotation reserve to effectively maintain the balance of grid generation and load [25]. 2.2. Production, Storage and Transportation of Hydrogen Energy At present, the main methods to produce hydrogen include thermochemical methods, natural gas reforming methods, coal gasification, steam methane reforming and water electrolysis [26], so there are more and more studies on hydrogen production systems [27–29]. In the Wind H2 plan which is proposed by the National Renewable Energy Laboratory (NREL) of the United States, the wind–hydrogen coupled system adopts electrolysis of water to produce hydrogen which is also adopted by other countries in hydrogen storage systems for the wind–solar power generation. That is because hydrogen production by water electrolysis has the advantages of simple operation, high hydrogen production efficiency and little environmental pollution. In recent years, it has been a useful way for hydrogen storage and hydrogen energy development to use hydrogen as secondary energy or fuel for industrial applications which is produced by abandoning water, wind and solar power. Hydrogen is extremely inconvenient to transport for it is gaseous at normal temperature and atmospheric pressure. Therefore, the hydrogen produced by electrolysis in the electrolyzer is generally stored in large storage tanks, compressed or cooled to liquefy and then transported to various hydrogen refueling stations by pipelines, trailers or tankers. Physical storage as compressed gas, physical storage as cryogenic liquid hydrogen and materials-based storage or solid-state storage are three typical methods of hydrogen storage, and the first two methods are the most mature and widely used methods. The main advantage of physical storage as compressed gas is the simplicity of the process and fast filling–releasing rate. Physical storage as cryogenic liquid hydrogen is expensive compared to compressed hydrogen storage, but provides a higher energy density. Materials-based storage or solid-state storage, on the other hand, can store a large amount of hydrogen in a relatively small volume [30]. In this process, how to minimize the cost of hydrogen storage has become a hot research topic [31]. According to the different states and storage methods of hydrogen, the transport methods of hydrogen can be divided into gas hydrogen transport, liquid hydrogen transport and metal hydride-form transport, of which the first two are the main methods. For transporting large quantities of hydrogen over long distances, using pipeline transport may be a preferable method. Liquid hydrogen is generally transported over long distances by road or sea, while low-pressure hydrogen stored in metal hydrides can only be transported in small quantities over short distances [32]. Transport by pipelines is divided into pipelines which have been built recently only for hydrogen and pipelines of natural gas which mix natural gas with hydrogen in order to transport. Sebastian and Timmerberg [33] demonstrated that the cost of using existing natural gas pipelines to transport hydrogen (10% mixing ratio) is lower than the cost of converting hydrogen into methane, diesel and gasoline. Deymi et al. [34] found that mixing hydrogen and natural gas increases the turbine compressor energy at the natural gas booster station, resulting in less fossil fuel consumption. However, the storage and transportation of hydrogen still present many technical challenges today. Even though the cost of transporting large quantities of gaseous hydrogen may be low, the construction of new pipelines incurs larger costs and there are associated safety issues, such as hydrogen embrittlement and leakage [35]. These technical challenges have been hindering the scaling up of the hydrogen supply chain, and optimizing operational strategies has become a key driver for it. 2.3. Optimization of Coal–Wind–Solar–Hydrogen Operation The optimization of a wind–solar–hydrogen operation mainly includes production, operation, evaluation and improvement of the system. Among them, the design and operation angle of the wind–solar–hydrogen system is reflected in the construction of the coupled system. It is an inevitable trend to design an operating model of the wind–solar–hydrogen system that maximizes profits [36]. Fan et al. [37] established a multi-energy hybrid coupled system including several systems such as a wind–energy hybrid system, power distribution system, hydrogen storage system and coal chemical system based on wind and solar resources in the Hami region, and studied the economic performance of the system. For the high volatility of wind power, Liang et al. [38] proposed a robust optimal dispatch model for integrated energy systems considering wind–hydrogen coupling and solved it by the column constraint generation method (C&CG). Zhao and Li [39] studied the influence of the capacity of wind turbines and photovoltaic arrays on the hydrogen production efficiency of the system under the analysis of the system dynamic model, conducted sensitivity and cost analysis to evaluate the cost of hydrogen production and found that wind turbines and photovoltaic arrays are the most important variable. The cost provides a reference for the capacity matching of various components of the hydrogen refueling station. Based on the model predictive control algorithm, Trifkovic et al. [40] realized the optimal operation of each sub-module of the hybrid system composed of fans, fuel cells, electrolyzers and hydrogen storage tanks under the condition of coordinating the balance of power generation. Yang et al. [41] proposed a generic optimal design method for planning and scheduling a multi-echelon HSCN based on an off-grid wind–hydrogen coupled system that accounts for uncertainty in wind and hydrogen demand, and the model involves both planning and operational issues. In the evaluation and improvement of the wind–solar–hydrogen system, the evaluation of the system cost has become a research hotspot [42,43]. When evaluating the dispatch of system energy, it is found that the model predictive control strategy is the most efficient [44]. In addition, Khalid et al. [45] proposed an integrated hydrogen storage system for wind and photovoltaic power which is applied in residence, in which wind and photovoltaic energy are used as power, and hydrogen is used as the stored energy, and evaluates the energy and exergy benefits of the system. In addition, based on the levelized cost and the net present value cost of power which have been determined, the integrated energy storage system of wind, solar and hydrogen is optimized. Won et al. [46] proposed the application of an integer linear programming model to optimize the capacity of wind power, photovoltaic and alkaline electrolyzers. At this stage, the research on the system of hydrogen production by wind and photovoltaic power mainly evaluates the reliability and economy of the hydrogen storage system for wind–solar power generation from the perspectives of model simulation, example verification and algorithm optimization. At present, there are few studies on the operation of the hydrogen storage system for wind–solar power generation and on the multi-cycle hydrogen storage system for wind–solar power generation. Therefore, based on previous research, this paper intends to introduce an optimization model of operating the multi-cycle hydrogen storage system for coal–wind–solar power generation, and then determines the optimal model of the hydrogen storage system for wind–solar power generation. Considering that coal generation is more stable and controllable, the electricity demand in this paper is the total social demand minus the coal generation. 3. Optimization of Operating the Hydrogen Storage System for Wind–Solar Power Generation and Construction of Dispatching Model As shown in Figure 1 below, the hydrogen storage system for wind power generation studied in this paper is a system for wind and photovoltaic power generation which combines with the grid, including a system for wind and photovoltaic power generation, a system for hydrogen production, a system for hydrogen storage, a system for hydrogen transport and a system for hydrogen operation (hydrogen refueling station). This paper mainly shows that the plant which generates power by wind and photovoltaic power is used to optimize the coupled system for power generation and the production, storage, transportation and operation of hydrogen. In the scenario where wind and photovoltaic power generation guarantees power demand and using abandoned wind and photovoltaic power to produce hydrogen and then transport it outside the system through trucks or pipelines, this paper explores the choice nodes of hydrogen production and storage, scale settings, the capacity of a new transmission line and new pipelines and their route planning so as to meet the energy supply and achieve the maximum profits of the whole system. ![Figure 1. Diagram of hydrogen storage of wind and photovoltaic power generation.](image) 3.1. Model Assumptions Considering the actual situation of production operation and the convenience of building the model, the assumptions of this model are given as follows: 1. When generating wind and photovoltaic power, wind power is mainly produced by wind turbines, while photovoltaic power is generated by solar panels, instead of solar thermal power generation. 2. The wind speed and solar radiation intensity in all decision-making cycles are known and remain unchanged in each decision-making cycle. 3. Within the sustainability of nature, all the equipment for wind and photovoltaic power generation is turned on, and all the remaining electricity is used for hydrogen production. (4) Without considering the power transport from the main transformer station to customers, the main transformer station is the end user of electricity; without considering the gas transport from the natural gas gate station to customers, the natural gas gate station is the end user of hydrogen energy. (5) The transmission lines between every two nodes have different degrees of loss which is only related to the transport amount of power. The gas pipeline between each two nodes has different degrees of loss which is only related to the amount of gas flow. (6) In each decision-making cycle, wind turbines, photovoltaic power generation equipment and hydrogen production electrolyzers only maintain the same state (start or stop), and all generators in the same station of wind power generation are synchronized. (7) The startup time of all devices is ignored. (8) Considering economy and convenience of operation, trucks only travel on fixed routes. (9) The maintenance cost per unit of the truck is unchanged which is only related to the distance. (10) The construction of new pipelines only depends on the construction of transformer stations and hydrogen demand stations. (11) The construction of new transmission lines only depends on stations of power generation, transformer stations and stations of hydrogen production. (12) The stations of hydrogen production and storage only depend on transformer stations, stations of hydrogen production, stations of hydrogen storage, natural gas stations and hydrogen demand stations. (13) During the period of electrolysis equipment, truck depreciation expenses are not considered. (14) Pipelines used in this system only transport hydrogen without storage. 3.2. Parameter Symbols and Their Descriptions In this section, this paper will present the parameter symbols and their descriptions in Tables 1–5. Table 1. Subscript parameter symbols and descriptions used in the model. \| Symbols \| Descriptions \| \|---------\|--------------\| \| m \| Symbols of transformer stations \| \| n \| Symbols of natural gas stations \| \| i \| Symbols of stations of wind power generation \| \| j \| Symbols of stations of photovoltaic power generation \| \| k \| Symbols of hydrogen demand stations \| \| l \| Symbols of all the nodes \| \| t \| Symbols of decision-making cycles \| Table 2. A collection of symbols and descriptions used in the model. \| Symbols \| Descriptions \| \|---------\|--------------\| \| $VI_m$ \| A collection of symbols which represents stations of wind power generation to transformer station $m$ \| \| $VJ_m$ \| A collection of symbols which represents stations of photovoltaic power generation to transformer station $m$ \| \| $VTS$ \| A collection of symbols which represents transformer stations \| \| $VNG$ \| A collection of symbols which represents natural gas stations \| \| $VPW$ \| A collection of symbols which represents stations of wind power generation \| \| $VPP$ \| A collection of symbols which represents stations of photovoltaic power generation \| \| $VHD$ \| A collection of symbols which represents hydrogen demand stations \| \| $V$ \| A collection of symbols which represents all the nodes, $V = VTS \cup VNG \cup VPW \cup VPP \cup VHD$ \| \| $T$ \| A collection of symbols which represents all the decision-making cycles \| Table 3. Symbols and descriptions of technical parameters used in the model. \| Symbols \| Descriptions \| \|---------\|-------------\| \| $ g_{wi} $ \| During the cycle $ t $, the amount of abandoned wind power in the station $ i $ of wind power generation, $ i \in VPW, t \in T $ \| \| $ g_{pj} $ \| During the cycle $ t $, the amount of abandoned solar power in the station $ j $ of photovoltaic power generation, $ j \in VPP, t \in T $ \| \| GEW $ i $ \| Power generating efficiency of the station $ i $ of wind power generation, $ i \in VPW $ \| \| GEP $ j $ \| Power generating efficiency of the station $ j $ of photovoltaic power generation, $ j \in VPP $ \| \| GHP $ t' $ \| During the cycle $ t $, the rated power amount of transmission lines from node $ l $ to node $ l', l, l' \in V, t \in T $ \| \| GTE $ t' $ \| During the cycle $ t $, the rated gas number of pipelines from node to node $ l', l, l' \in V, t \in T $ \| \| GTT \| The rated weight of trucks to transport gas \| \| $ d_{cil} $ \| The distance of transmission lines from node $ l $ to node $ l', l, l' \in V $ \| \| $ d_{sl} $ \| The original distance of pipelines from node $ l $ to node $ l', l, l' \in V, t \in T $ \| \| $ d_{rl} $ \| The original distance of pipelines from node $ l $ to node $ l', l, l' \in V, t \in T $ \| \| $ LE_{li} $ \| The loss rate per unit of transmission lines from node $ l $ to node $ l', l, l' \in V $ \| \| $ LG_{li} $ \| The loss rate per unit of pipelines from node $ l $ to node $ l', l, l' \in V $ \| \| $ LT_{li} $ \| The loss rate per unit of transmission lines from node $ l $ to node $ l', l, l' \in V $ \| \| GTEm $ t' $ \| The maximum amount of transmission lines from node $ l $ to node $ l', l, l' \in V $ \| \| GTGm $ t' $ \| The maximum number of pipelines from node $ l $ to node $ l', l, l' \in V $ \| \| RG $ t' $ \| The interval ratio of hydrogen to natural gas in the pipeline from node $ l $ to node $ l', l, l' \in V $ \| \| $ GGH_{li} $ \| During the cycle $ t $, the efficiency of hydrogen production at node $ l $ which is the hydrogen production station, $ l \in V, t \in T $ \| \| $ S_{min} $ \| During the cycle $ t $, the minimum demand amount of hydrogen demand station $ k, k \in VHD, t \in T $ \| \| $ S_{max} $ \| During the cycle $ t $, the maximum demand amount of hydrogen demand station $ k, k \in VHD, t \in T $ \| \| SL \| The mandatory scrap life of trucks \| \| TY \| The maximum working life of trucks \| Table 4. Symbols and descriptions of cost parameter used in the model. \| Symbols \| Descriptions \| \|---------\|-------------\| \| CPWi \| The cost per unit of power generation in the station $ i $ of wind power generation, $ i \in VPW $ \| \| CPPj \| The cost per unit of power generation in the station $ j $ of photovoltaic power generation, $ j \in VPP $ \| \| CPS $ t $ \| During the cycle $ t $, the startup cost of the node $ l $ which is the hydrogen production station, $ l \in V, t \in T $ \| \| CRS $ t $ \| During the cycle $ t $, the startup cost of the node which is the hydrogen storage station, $ l \in V, t \in T $ \| \| CPU $ t $ \| During the cycle $ t $, the construction cost of the unit output by the node $ l $ which is the hydrogen production station, $ l \in V, t \in T $ \| \| CRU $ t $ \| During the cycle $ t $, the construction cost of the unit output by the node $ l $ which is the hydrogen storage station, $ l \in V, t \in T $ \| \| CGU $ t $ \| During the cycle $ t $, the unit cost of hydrogen production by the node $ l $ which is the hydrogen production station, $ l \in V, t \in T $ \| \| CSU $ t $ \| During the cycle $ t $, the unit maintenance cost of the node $ l $ which is the hydrogen storage station, $ l \in V, t \in T $ \| \| CGMU $ t $ \| During the cycle $ t $, the unit maintenance cost of the node $ l $ as the hydrogen storage station, $ l \in V, t \in T $ \| Table 4. Cont. \| Symbols \| Descriptions \| \|---------\|--------------\| \| CCE\_t^l \| During the cycle $ t $, the construction cost per unit length of transmission lines from node $ l $ to node $ l', l', l' \in V, t \in T $ \| \| CCC\_t^l \| During the cycle $ t $, the construction cost per unit length of pipelines from node $ l $ to node $ l', l', l' \in V, t \in T $ \| \| CME\_t^l \| During the cycle $ t $, the maintenance cost per unit length of transmission lines from node $ l $ to node $ l', l', l' \in V, t \in T $ \| \| CMC\_t^l \| During the cycle $ t $, the maintenance cost per unit length of pipelines from node $ l $ to node $ l', l', l' \in V, t \in T $ \| \| CLU\_t^l \| During the cycle $ t $, the cost per unit length of upgrading pipelines from node $ l $ to node $ l', l', l' \in V, t \in T $ \| \| CSM\_n \| During the cycle $ t $, the unit cost of mixing hydrogen with natural gas at natural gas station $ n, n \in VNG, t \in T $ \| \| CSE\_n \| During the cycle $ t $, the unit cost of separating hydrogen from natural gas at natural gas station $ n, n \in VNG, t \in T $ \| \| CTC\_t^l \| During the cycle $ t $, the cost of compressing hydrogen at node $ l, l \in V, t \in T $ \| \| CTP\_t^l \| During the cycle $ t $, the unit cost of buying trucks, $ t \in T $ \| \| CTM\_t^l \| During the cycle $ t $, the maintenance cost per unit distance of trucks, $ t \in T $ \| \| CTD\_t^l \| During the cycle $ t $, the unit cost of transport by trucks, $ l, l' \in V, t \in T $ \| \| CUC\_t^l \| During the cycle $ t $, the unit cost of upgrading original pipelines from node $ l $ to node $ l', n, n' \in VNG, t \in T $ \| \| ps\_t^l \| During the cycle $ t $, the exit price of hydrogen, $ t \in T $ \| \| pb\_t^l \| During the cycle $ t $, the subsidized price of hydrogen, $ t \in T $ \| \| pp\_t^l \| During the cycle $ t $, the subsidized price of photovoltaic power generation, $ t \in T $ \| \| pp\_t^l \| During the cycle $ t $, the subsidized price of photovoltaic power generation, $ t \in T $ \| \| pn\_t^l \| During the cycle $ t $, the exit price of natural gas, $ t \in T $ \| \| r \| Discount rate \| \| $ \epsilon $ \| The power price \| Table 5. Symbols and descriptions of decision variables used in the model. \| Symbols \| Descriptions \| \|---------\|--------------\| \| BP\_t^l \| During the cycle $ t $, whether to select node $ l $ as the hydrogen production station, $ l \in V, t \in T $ \| \| BS\_t^l \| During the cycle $ t $, whether to select node $ l $ as the hydrogen storage station, $ l \in V, t \in T $ \| \| BE\_t^l \| During the cycle $ t $, constructing the transmission lines from node $ l $ to node $ l', l' \in V, t \in T $ \| \| BG\_t^l \| During the cycle $ t $, constructing the pipelines from node $ l $ to node $ l', l' \in V, t \in T $ \| \| BU\_t^l \| During the cycle $ t $, upgrading original pipelines from node $ l $ to node $ l', n, n' \in VNG, t \in T $ \| \| $ x_i^j $ \| During the cycle $ t $, the amount of power which is generated for hydrogen production in the station $ i $ of wind power generation, $ i \in VPW, t \in T $ \| \| $ y_j^t $ \| During the cycle $ t $, the amount of power which is generated for hydrogen production in the station $ j $ of photovoltaic power generation, $ j \in VPP, t \in T $ \| \| QPM\_t^l \| During the cycle $ t $, the effective capacity of hydrogen production equipment at node $ l, n \in VNG, t \in T $ \| \| QSM\_t^l \| During the cycle $ t $, the effective capacity of hydrogen storage equipment at node $ l, l \in V, t \in T $ \| \| $ u_l^t $ \| During the cycle $ t $, the amount of hydrogen production at node $ l, l \in V, t \in T $ \| \| $ v_l^t $ \| During the cycle $ t $, the amount of hydrogen storage at node $ l, l \in V, t \in T $ \| Table 5. Cont. \| Symbols \| Descriptions \| \|---------\|--------------\| \| $g_k^t$ \| During the cycle $t$, the amount of hydrogen consumption at node $k$, $k \in V_{HD}$, $t \in T$ \| \| $w_{l,l'}^t$ \| During the cycle $t$, the amount of power transport from node $l$ to node $l'$, $l,l' \in V$, $t \in T$ \| \| $zl_{l,l'}^t$ \| During the cycle $t$, the hydrogen amount transported by pipelines from node $l$ to node $l'$, $l,l' \in V$, $t \in T$ \| \| $zl_{n,n'}^t$ \| During the cycle $t$, the hydrogen amount transported by upgraded pipelines from node $l$ to node $l'$, $n,n' \in V_{NG}$, $t \in T$ \| \| $z_{lp}^t$ \| During the cycle $t$, the hydrogen amount transported by trucks from node $l$ to node $l'$, $l,l' \in V$, $t \in T$ \| \| $q^t$ \| During the cycle $t$, the amount of buying new trucks, $t \in T$ \| \| $f_{l,l'}^t$ \| During the cycle $t$, the frequency of operating trucks from node $l$ to node $l'$, $l,l' \in V$, $t \in T$ \| \| $h^t$ \| The number of scrapped trucks \| 3.3. Objective Function This paper establishes a linear programming equation with multi-decision variables during multiple periods based on the costs and proceeds during the full life cycle of hydrogen. Total profit = hydrogen sale proceeds + new energy subsidies − (cost of power generation + cost of hydrogen production + cost of hydrogen storage + cost of power transport + cost of hydrogen transport by pipelines + cost of hydrogen transport by trucks), $$\max GP = TIS + TIA - (TCG + TCH + TCS + TCE + TCLG + TCTG). \quad (1)$$ (1) Proceeds The total proceeds studied in this paper include hydrogen sale proceeds $TIS$ and new energy subsidies $TIA$. $$\text{Hydrogen sale proceeds } TIS = \sum_{t \in T} \left( \sum_{k \in V_{HD}} \frac{1}{(1 + r)^t} \cdot ps^t \cdot g_k^t \right) \quad (2)$$ $$\text{New energy subsidies } TIA = \sum_{t \in T} \left( \sum_{k \in V_{HD}} \frac{1}{(1 + r)^t} \cdot pb^t \cdot g_k^t \right) \quad (3)$$ (2) Costs of power generation and transport Since the wind and photovoltaic power plants are already in operation, there is no need to consider the costs of startup and construction of power plants. In addition, even if the hydrogen energy system is not introduced, the wind and photovoltaic power plants still need to complete the routine tasks of power generation which means it also needs to carry out routine maintenance. On this basis, there is no need to consider the maintenance cost of the wind and photovoltaic power generation equipment. Therefore, the cost of power generation in this model mainly refers to the cost per unit of power which is consumed by power generation equipment to produce hydrogen, including costs of wind power generation and photovoltaic power generation. $$\text{Cost of power generation } TCG = \sum_{i,t} \left( \frac{1}{(1 + r)^t} \cdot \left( \sum_{i \in V_{PW}} CPW_i \cdot x_i^t + \sum_{j \in V_{PP}} CPP_j \cdot y_j^t \right) \right) \quad (4)$$ where $ \sum_{i \in \mathcal{V}} CPW_i \cdot x_i^t $ represents the cost of power generation in the wind power plant in one year, and $ \sum_{j \in \mathcal{V}} CPP_j \cdot y_j^t $ the cost of power generation in the photovoltaic power plant in one year. The cost of power transport means all the costs involved in the power transport in this system, including costs of power transmission lines from power generation plants to transformer plants and from transformer plants to hydrogen production plants. Based on the cost analysis of power transport and the consideration for modeling, the cost of power transport in this model includes costs of constructing and maintaining power transmission lines and the cost of power transport loss. Costs of power transport: \[ TCE = \sum_{i \in \mathcal{I}} \sum_{l \in \mathcal{V}} \sum_{t \in \mathcal{T}} \frac{1}{(1 + r)^t} \cdot d_{el}^t \cdot \left( BE_{el}^t \cdot CCE_{el}^t + BE_{el}^t \cdot CME_{el}^t + LE_{el}^t \cdot w_{el}^t \cdot e^t \right) \] where $ BE_{el}^t \cdot CCE_{el}^t $ represents the cost of constructing power transmission lines per unit length in one year, and $ BE_{el}^t \cdot CME_{el}^t $ the loss cost of power transmission lines. (3) Costs of hydrogen production and storage The cost of hydrogen production in the model includes the cost of hydrogen production by electrolysis of water, the cost of starting the hydrogen production station in the early stage, the cost of constructing the hydrogen production station and the cost of maintaining the hydrogen production station during the period. Cost of hydrogen production: \[ TCH = \sum_{i \in \mathcal{I}} \sum_{l \in \mathcal{V}} \sum_{t \in \mathcal{T}} \frac{1}{(1 + r)^t} \cdot \left( CPS_i^t \cdot BP_i^t + CPU_i^t \cdot QPM_i^t + CGMU_i^t \cdot QPM_i^t + CGU_i^t \cdot u_i^t \right) \] where $ CPS_i^t \cdot BP_i^t $ represents the startup cost of the hydrogen production station, $ CPU_i^t \cdot QPM_i^t $ the construction cost of the hydrogen production station, $ CGMU_i^t \cdot QPM_i^t $ the maintenance cost of the hydrogen production station, and $ CGU_i^t \cdot u_i^t $ the cost of hydrogen production. The cost of hydrogen storage includes the cost of hydrogen storage, the startup cost of the hydrogen storage station, the construction cost of the hydrogen storage station and the maintenance cost of the hydrogen storage station during the period. Cost of hydrogen storage: \[ TCS = \sum_{i \in \mathcal{I}} \sum_{l \in \mathcal{V}} \sum_{t \in \mathcal{T}} \frac{1}{(1 + r)^t} \cdot \left( CRS_i^t \cdot BS_i^t + CRU_i^t \cdot QSM_i^t + CSMU_i^t \cdot QSM_i^t + CSU_i^t \cdot v_i^t \right) \] where $ CRS_i^t \cdot BS_i^t $ represents the startup cost of the hydrogen storage station, $ CRU_i^t \cdot QSM_i^t $ the construction cost of the hydrogen storage station, $ CSMU_i^t \cdot QSM_i^t $ the maintenance cost of the hydrogen storage station and $ CSU_i^t \cdot v_i^t $ the cost of hydrogen storage. (4) Cost of hydrogen transport The cost of hydrogen transport is the cost from the hydrogen production station to the hydrogen demand station, which can be transported by pipelines and trucks. The cost of hydrogen transport by pipelines includes the construction cost of new pipelines and the reconstruction cost of using existing natural gas pipelines. The cost of the new pipelines includes the construction and maintenance cost of the new pipelines and the cost of hydrogen loss when transporting by new pipelines. The reconstruction cost of using existing natural gas pipelines includes the cost of upgrading pipelines, the cost of hydrogen loss when transporting by existing pipelines, the cost of mixing gases and the cost of separating the gases. Cost of the new pipelines: $$\sum_{i \in T} \sum_{n \in VNG} \sum_{n' \in VNG} \frac{1}{(1 + r)^{l_{ij}}} \cdot d_{lnn'} \cdot \left( \frac{BG_{ij} \cdot CGG_{ij} + BG_{ij} \cdot CMG_{ij} + ps \cdot LGG_{ij} \cdot zl_{ij}}{} \right)$$ \hspace{1em} (8) where $BG_{ij} \cdot CGG_{ij}$ represents the construction cost per unit length of new pipelines, $BG_{ij} \cdot CMG_{ij}$ the maintenance cost per unit length of new pipelines, $ps \cdot LGG_{ij} \cdot zl_{ij}$ the cost per unit length of hydrogen loss when transporting by new pipelines. Cost of using existing natural gas pipelines: $$\sum_{i \in T} \sum_{n \in VNG} \sum_{n' \in VNG} \frac{1}{(1 + r)^{l_{ij}}} \cdot d_{lnn'} \cdot \left( \frac{BU_{ij} \cdot CUG_{ij} + (ps - pn) \cdot RG_{ij} \cdot LG_{ij} \cdot zl_{ij}}{} \right)$$ \hspace{1em} (9) where $BU_{ij} \cdot CUG_{ij}$ represents the cost of upgrading pipelines, $(ps - pn) \cdot RG_{ij} \cdot LG_{ij} \cdot zl_{ij}$ the cost of hydrogen loss when transporting by existing pipelines. Cost of mixing and separating the gases: $$\sum_{i \in T} \sum_{n \in VNG} \sum_{n' \in VNG} \frac{1}{(1 + r)^{l_{ij}}} \left( CSM_{n} \cdot zl_{ij} + CSE_{n} \cdot zl_{ij} \right)$$ \hspace{1em} (10) where $CSM_{n} \cdot zl_{ij}$ represents the cost of mixing hydrogen with natural gas, and $CSE_{n} \cdot zl_{ij}$ the cost of separating hydrogen from natural gas. The cost of transport by trucks includes the cost of buying trucks, the cost of repairing trucks, the cost of transport by trucks, the cost of hydrogen loss when transporting by trucks and the cost of compressing hydrogen. Cost of buying and repairing trucks: $$TCTG = \sum_{i \in T} \frac{1}{(1 + r)^{l_{ij}}} \cdot \left( CTP_{ij} \cdot q_{ij} + \sum_{i \in V} \sum_{l \in V} CTM_{ij} \cdot dt_{lj} \cdot f_{lj} \right).$$ \hspace{1em} (11) Cost of transport by trucks and hydrogen loss when transporting by trucks: $$TCTG = \sum_{i \in T} \frac{1}{(1 + r)^{l_{ij}}} \cdot \left( \sum_{i \in V} \sum_{l \in V} CTD_{ij} \cdot dt_{lj} \cdot zt_{lj} + \sum_{i \in V} \sum_{l \in V} LTr_{lj} \cdot ps \cdot dt_{lj} \cdot zt_{lj} \right).$$ \hspace{1em} (12) Cost of compressing hydrogen: $$\sum_{i \in V} \sum_{l \in V} CTC_{ij} \cdot zt_{ij}.$$ \hspace{1em} (13) 3.4. Constraint Conditions (1) Constraints on power generation and transport During the cycle $t$, the amount of power output from the station $i$ of wind power generation does not exceed that of abandoning wind power in that station: $$\sum_{i \in V} w_{ij} \leq GEW_{ij} \cdot g_{ij}, i \in VPW, t \in T.$$ \hspace{1em} (14) During the cycle $t$, the amount of power output from the station $j$ of photovoltaic power generation does not exceed that of abandoning photovoltaic power in that station: $$\sum_{i \in V} w_{ij} \leq GEP_{ij} \cdot gp_{ij}, j \in VPP, t \in T.$$ \hspace{1em} (15) During the cycle $ t $, the amount of power transport between node $ l $ and node $ l' $ does not exceed the maximum amount of power transport: \[ w_{ll'}^t \leq GTE_{ll',l,l'}^t, l, l' \in V, t \in T. \tag{16} \] If there are no transmission lines between two nodes, the amount of power transport between those two nodes is 0: \[ w_{ll'}^t \leq M \cdot BE_{ll',l}^t, l, l' \in V, t \in V. \tag{17} \] (2) Constraints on hydrogen production and storage During the cycle $ t $, the amount of hydrogen production at node $ l $ does not exceed the amount of hydrogen production of power which is transported: \[ u_l^t \leq GGH_{ll}^t \cdot w_{ll'}^t, l, l' \in V, t \in T. \tag{18} \] During the cycle $ t $, the amount of hydrogen production at node $ l $ does not exceed the maximum amount of hydrogen production: \[ u_l^t \leq QPM_{ll}^t, l \in V, t \in T. \tag{19} \] During the cycle $ t $, the amount of hydrogen storage at node $ l $ does not exceed the amount of hydrogen production at that node: \[ v_l^t \leq u_l^t, l \in V, t \in T. \tag{20} \] During the cycle $ t $, the amount of hydrogen storage at node $ l $ does not exceed the maximum amount of hydrogen storage: \[ v_l^t \leq QSM_{ll}^t, l \in V, t \in T. \tag{21} \] If a node is not selected as the station of hydrogen production, the amount of hydrogen production at that node is 0: \[ QPM_{ll}^t \leq M \cdot BP_{ll}^t, l \in V, t \in V. \tag{22} \] If a node is not selected as the station of hydrogen storage, the amount of hydrogen storage at that node is 0: \[ QSM_{ll}^t \leq M \cdot BS_{ll}^t, l \in V, t \in V. \tag{23} \] (3) Constraints on hydrogen transport The hydrogen constraints for balance at each node: \[ \sum_{l' \in V} (z_{ll'}^t + z_{l'l}^t) + u_l^t + v_l^t - 1 \geq \sum_{l' \in V} (z_{ll'}^t + z_{l'l}^t) + v_l^t, l \in V, t \in T, v_l^0 = 0. \tag{24} \] During the cycle $ t $, the amount of hydrogen for node $ k $ is not less than the minimum demand amount of hydrogen: \[ \sum_{l \in V} (z_{l'k}^t + z_{lk}^t) \geq S_{\text{min}}^t, k \in VHD, t \in T. \tag{25} \] During the cycle $ t $, the amount of hydrogen for node $ k $ does not exceed the maximum demand amount of hydrogen: \[ \sum_{l \in V} (z_{l'k}^t + z_{lk}^t) \leq S_{\text{max}}^t, k \in VHD, t \in T. \tag{26} \] During the cycle $t$, the amount of hydrogen transport by pipelines between node $l$ and node $l'$ does not exceed the maximum amount of hydrogen transport by pipelines between those two nodes: $$z_{rl}^t \leq G_{rl}^{ll'}, l, l' \in V, t \in T. \quad (27)$$ During the cycle $t$, the amount of hydrogen transport by trucks between node $l$ and node $l'$ does not exceed the maximum amount of hydrogen transport by trucks between those two nodes: $$z_{rl}^t \leq G_{lf} f_{lf}^t, l, l' \in V, t \in T. \quad (28)$$ During the cycle $t$, the total frequency of operating trucks among all the nodes does not exceed the maximum frequencies of operating trucks: $$\sum_{l \in V} \sum_{l' \in V} f_{lf}^t \leq O_{rl} g^t, t \in T. \quad (29)$$ If there is no new pipelines or ungraded pipelines between two nodes, the amount of the pipeline between two nodes is 0: $$z_{rl}^t \leq M \cdot (B_{rl} G_{rl}^{ll'} + B_{nn'} U_{nn'}), l, l' \in V, n, n' \in V, t \in V. \quad (30)$$ If there are no trucks between two nodes, the amount of hydrogen transport by trucks is 0: $$z_{rl}^t \leq M \cdot f_{lf}^t, l, l' \in V, t \in V. \quad (31)$$ During the cycle $t$, the number of available trucks is equal to the cumulative number of new purchased trucks minus the cumulative number of scrapped trucks: $$g^t = \sum_{\tau=0}^{t} (q^\tau - h^\tau), t \in T. \quad (32)$$ The maximum working life of trucks is $TY$, so: $$h^\tau = 0, 0 \leq \tau < TY, \tau \in T, \quad (33)$$ $$h^\tau = q^{\tau-TY}, \tau \geq TY, \tau \in T. \quad (34)$$ 4. Constraints on variables' range The constraints on the value range of binary variables, integer variables and continuous variables are as follows: $$BP_{rl}^t, BS_{rl}^t, BE_{rl}^t, BG_{rl}^t, BU_{nn'}^t \in \{0, 1\}, \quad (35)$$ $$q^l, g^l, f_{lf}^t \in \mathbb{N}, \quad (36)$$ $$QPM_{rl}, QSM_{ri}, u_i^l, v_i^l, w_i^l, z_i^t, zl_{rl}^t, zl_{ll'}^t \in \mathbb{R}^+. \quad (37)$$ 4. A Case Study on Optimization of Operating the Consumption of Abandoned Power in Inner Mongolia 4.1. Problem Description Inner Mongolia is rich in wind and photovoltaic energy, and the installed capacity of wind turbines and photovoltaics in Inner Mongolia ranks among the highest in China. However, there is an urgent phenomenon of abandoned wind and photovoltaic power in Inner Mongolia. To be specific, the abandoned wind power accounts for 10% of the total power generation. Figure 2 shows the amount of abandoned wind power in stations of wind and photovoltaic power generation in Inner Mongolia in 2017. In recent years, with the large-scale use of fuel cell vehicles, the demand for hydrogen energy has gradually increased. However, hydrogen at hydrogen refueling stations is expensive which is a key factor restricting the development of fuel cell vehicles. According to the previous research on hydrogen prices, it is concluded that costs of hydrogen production and transport account for 70% of the total cost and the power used to produce hydrogen costs the most. Therefore, it is necessary to optimize the operation of hydrogen production and transport so as to reduce the cost of hydrogen. Based on the previous analysis, this paper uses the abandoned wind and photovoltaic power in Bayan Nur, Baotou, and Ulanqab, Inner Mongolia autonomous region to produce hydrogen which will be transported to Beijing and Shanxi province with a large demand for hydrogen. This paper selects Beijing and Shanxi as hydrogen demand stations for Beijing has a large amount of hydrogen energy vehicles, but has insufficient hydrogen energy and Shanxi is adjacent to Inner Mongolia which is more practical to do this case study. Among many stations of wind power generation and photovoltaic power generation in Bayan Nur, Baotou, and Ulanqab, Inner Mongolia, this paper selects three wind power plants in Bayan Nur with a large amount of abandoned power, which are Huaneng Habutagai Wind Power Plant (the amount of abandoned wind power is 110.51 million kWh), CGN Hongyan Wind Power Plant (the amount of abandoned wind power is 108.43 million kWh), Guohua Chuanjing Wind Power Plant (the amount of abandoned wind power is 180.37 million kWh), and two photovoltaic power plants in Bayan Nur with a large amount of abandoned power, which are Guodian Hong Galu Photovoltaic Power Plant (the amount of abandoned photovoltaic power is 7.39 million kWh), Zhongli Taenghui Photovoltaic Power Plant (the amount of abandoned photovoltaic power is 8.13 million kWh); three wind power plants in Baotou with a large amount of abandoned power, which are Jinfeng Damao Wind Power Plant (the amount of abandoned wind power is 219.75 million kWh), Tianrunxing Shunxi Wind Power Plant (the amount of abandoned wind power is 122.49 million kWh), Zhongke Shiratu Wind Power Plant (the amount of abandoned power is 122.49 million kWh), and two photovoltaic power plants in Baotou with a large amount of abandoned power, which are Zhongke Shiratu Wind Power Plant (the amount of abandoned photovoltaic power is 122.49 million kWh), and Zhongke Shiratu Wind Power Plant (the amount of abandoned photovoltaic power is 122.49 million kWh). wind power is 118.04 million kWh), and two photovoltaic power plants in Baotou with a large amount of abandoned power, which are Mingao Huadu Photovoltaic Power Plant (the amount of abandoned photovoltaic power is 7.12 million kWh) and Chaer Lake Photovoltaic Power Plant (the amount of abandoned photovoltaic power is 7.39 million kWh); and three wind power plants in Ulanqab with a large amount of abandoned power, which are Sanxia Xingfu Wind Power Plant (the amount of abandoned wind power is 304.12 million kWh), Huarun Ruifeng Wind Power Plant (the amount of abandoned wind power is 106.64 million kWh) and Sanxia Changshun Wind Power Plant (the amount of abandoned wind power is 143.32 million kWh). It is assumed that those three cities each have a power plant and there is a natural gas pipeline from Baotou to Beijing that can be transformed into one mixing natural gas with hydrogen. The details are shown in Figure 3 below. Figure 3. The hydrogen storage system for wind–solar power generation in Inner Mongolia. The research objectives of this paper are to explore the optimal stations of hydrogen production and storage in Beijing and Shanxi when transporting the abandoned wind and photovoltaic power from Inner Mongolia corresponding to the different demands of hydrogen in Beijing and Shanxi and investigate the cost of transporting power. ### 4.2. Case Analysis Since the model involves 21 nodes of hydrogen production stations and hydrogen storage stations, the following assumptions are proposed on the basis of the existing assumptions in the model to prevent unrealistic situations: (1) The specific locations of hydrogen production stations and hydrogen storage stations are selected from transformer stations, natural gas stations and hydrogen demand stations. (2) The newly built pipelines generally transport directly to the hydrogen demand stations when the transformer station is the hydrogen production station. (3) Considering the economy of this model, if the existing natural gas pipelines are used for hydrogen transport, all existing natural gas pipelines will be upgraded to pipelines of mixing natural gas with hydrogen, and trucks will be used for transport from Beijing natural gas stations to Shanxi demand stations. (4) Coupling of hydrogen production stations and hydrogen storage stations. The values of the different variables are given in Table 6. \| Symbols \| Values \| Symbols \| Values \| \|---------\|----------------\|---------\|-----------------\| \| CCE_{il} \| 155 (yuan/km) \| GEP_{j} \| 0.6 \| \| CLU_{il} \| 5000 (yuan) \| LT_{il} \| 0.0015 \| \| CSE_{in} \| 0.3 (yuan) \| LG_{il} \| 0.05 \| \| CSM_{in} \| 0.2 (yuan) \| LE_{il} \| 0.025 \| \| CTC_{i} \| 0.65 (yuan/kg)\| r \| 0.1 \| \| CTD_{il} \| 3000 (yuan/km)\| pn_{i} \| 1.66 (yuan) \| \| GTE_{il} \| 400 (kg) \| RG_{il} \| 0.1 \| \| GTG_{il} \| 313,390,000 (kg)\| S_{min_{il}} \| 450 (kg) \| \| GGH_{i} \| 400 (kg) \| S_{max_{il}} \| 15,000 (kg) \| \| GEW_{i} \| 0.75 \| SL \| 10 (year) \| \| \| 0.75 \| TY \| 8 (year) \| 4.2.1. Results Analysis of This Model According to the above data, the optimal solution for the multi-cycle operation of hydrogen storage for wind–solar power generation is calculated by Lingo11 software (Lindo System Inc., Chicago, IL, USA), as shown in Table 7. \| Sale Proceeds \| Subsidizes \| Cost of Power Generation \| Cost of Power Transport \| \|---------------\|------------\|--------------------------\|------------------------\| \| 1,747,342 \| 18,811,940,000 \| 4,347,079,000 \| 11,455,000 \| \| Cost of Hydrogen Production \| Cost of Hydrogen Storage \| Cost of Transport by Pipelines \| Cost of Transport by Trucks \| \| 10,695,530 \| 32,307,130 \| 1,922,035 \| 35,353,970 \| In the system of transporting abandoned power from Inner Mongolia to Beijing and Shanxi within the consideration of labor cost changes in 30 years, hydrogen subsidies and technological progress, the total profit in the next 30 years will reach CNY $1.4 \times 10^{10}$. Compared with the new wind–solar–hydrogen coupling system, the profit has increased by about 20% [47]. The above data are calculated under the assumption that China will continue to increase hydrogen subsidies in the future, technological progress will make the rated amount of power transport continue to increase and the purchase cost of trucks will continue to decrease, which is more accurate and reliable when compared with only considering the operation results of one year. As new hydrogen pipelines are expensive, it is not economical to use existing natural gas pipelines to transform hydrogen for short- distance transport. Table 8 shows the changes in the location of hydrogen production stations, the fre- frequency of transport by trucks and the total cost which are all under different hydrogen demand stations. Table 8. Cost changes under different hydrogen demands. \| The Demand Amount of Hydrogen (m³/day) \| Demand Station \| The Location of the Hydrogen Production Station \| The Cost of Transport by Trucks (Million) \| The Cost of Hydrogen Transport (Million) \| The Total Cost (Million) \| \|--------------------------------------\|----------------\|-----------------------------------------------\|------------------------------------------\|-----------------------------------------\|--------------------------\| \| 500 \| K1, K2 \| M3, K2 \| 176.5 \| 0 \| 347 \| \| 1000 \| K1, K2 \| M3, K1 \| 346.8 \| 90.65 \| 589 \| \| 1500 \| K1, K2 \| M2, M3, K1 \| 478.6 \| 60.65 \| 641 \| As can be seen from Table 8, the locations of hydrogen production stations and hydrogen storage stations change corresponding to different amounts of hydrogen demand, and the position of hydrogen production stations will be closer to the hydrogen demand end. The results of the model are consistent with the conclusions of the existing literature on the hydrogen transport: the system of the direct power transport is superior to the system of transporting hydrogen produced by wind–solar power plants. The reasons are: 1. A hydrogen production station is established on the hydrogen demand end. If using the direct transport by wind and photovoltaic power, the cost of power transport is only taken into consideration. In this way, the cost of power transport is low. The loss of power transport is low when using a 500 kv ultra-high voltage circuit. Assuming power produced by wind and photovoltaic power plants is collected into the transformer stations, the power is more stable than that directly transported from the power field. 2. Stations of hydrogen production and hydrogen storage, modular structures, are more simple than normal structures. The startup cost of those stations is influenced by the environment, while the cost of construction, operation and maintenance is seldom influenced by location. Therefore, stations of hydrogen production and hydrogen storage located at the demand end better meet demand. Many of the existing hydrogen refueling stations produce hydrogen on-site, which reduces the cost of hydrogen storage and loss. Figure 4 is a combination diagram of stations of hydrogen production and storage and transmission lines in Beijing and Shanxi when the amount of hydrogen demand is 500 m³/day from 2020 to 2025. From 2020 to 2025, when the maximum demand amount of hydrogen in Beijing and Shanxi is 0.5 t/day, the hydrogen demand station in Beijing is located at the transformer stations in Ulanqab, which is relatively close to the hydrogen demand station, and the hydrogen production station in Shanxi is located at the hydrogen demand end. That result verifies the conclusion proposed by other scholars that the system of the direct power transport from the wind–hydrogen system is superior to the system that transports power from other places. However, in this paper, Beijing as a station of hydrogen demand does not build a hydrogen production station. That is because the startup cost of hydrogen production in Beijing is high because of its scarcity of land resources and high price level. However, when the demand amount of hydrogen in Beijing is 1 t/day, a station of hydrogen production will be built in Beijing. From 2020 to 2025, when the maximum demand amount of hydrogen in Beijing and Shanxi is 0.5 t/day, the hydrogen demand station in Beijing is located at the transformer stations in Ulanqab, which is relatively close to the hydrogen demand station, and the hydrogen production station in Shanxi is located at the hydrogen demand end. That result verifies the conclusion proposed by other scholars that the system of the direct power transport from the wind–hydrogen system is superior to the system that transports power from other places. However, in this paper, Beijing as a station of hydrogen demand does not build a hydrogen production station. That is because the startup cost of hydrogen production in Beijing is high because of its scarcity of land resources and high price level. However, when the demand amount of hydrogen in Beijing is 1 t/day, a station of hydrogen production will be built in Beijing. From 2025 to 2050, taking the increase in the amount of hydrogen demand and the limitation of the effective capacity to hydrogen production, two stations of hydrogen production (the transformer station and the station of hydrogen demand in Ulanqab) are selected to transport hydrogen to Beijing. With the increase in demand in Shanxi, hydrogen production and storage stations are established at the hydrogen demand station and the transformer station in Baotou. The details are shown in Figure 5. Based on the previous analysis, the hydrogen storage system for wind and photovoltaic power generation is useful and economical for places with a large amount of abandoned wind power and demand for hydrogen. In addition, the location of stations of hydrogen production and hydrogen storage will affect the cost of hydrogen. With the changes in hydrogen demand and the effective capacity of hydrogen production, priority will be given to the station of hydrogen production located at the transformer station which is close to the hydrogen demand station. When the amount of hydrogen demand is 1500 m³/day, Bayan Nur is not selected as a hydrogen production station for it is far away from other stations. Therefore, it only transmits power to transformer stations. Due to the high construction cost of new pipelines, there is little advantage to the hydrogen storage system for wind and photovoltaic power generation from Inner Mongolia to Beijing and Shanxi. This is a research topic for a future study on the economy of hydrogen transport by new pipelines in the hydrogen storage system for wind and photovoltaic power generation throughout the country. Based on the previous analysis, the hydrogen storage system for wind and photovoltaic power generation is useful and economical for places with a large amount of abandoned wind power and demand for hydrogen. In addition, the location of stations of hydrogen production and hydrogen storage will affect the cost of hydrogen. With the changes in hydrogen demand and the effective capacity of hydrogen production, priority will be given to the station of hydrogen production located at the transformer station which is close to the hydrogen demand station. When the amount of hydrogen demand is 1500 m$^3$/day, Bayan Nur is not selected as a hydrogen production station for it is far away from other stations. Therefore, it only transmits power to transformer stations. Due to the high construction cost of new pipelines, there is little advantage to the hydrogen storage system for wind and photovoltaic power generation from Inner Mongolia to Beijing and Shanxi. This is a research topic for a future study on the economy of hydrogen transport by new pipelines in the hydrogen storage system for wind and photovoltaic power generation throughout the country. 4.2.2. Analysis of Policy Influencing the Economy of the System The hydrogen storage system for wind and photovoltaic power is environmentally friendly, which realizes the efficient use of clean energy. According to the prospect of new energy in various countries, China will vigorously develop hydrogen production from clean energy such as wind power and photovoltaic power in the future. The cost of the system within 30 years is compared with consideration of policy changes and without consideration of policy changes, thereby providing support for the implementation of policies. In the cost of power generation, the unit cost of power generation and the amount of power generation (mainly affected by the amount of hydrogen demand) are greatly affected by the policy. The amount of demand is generally determined by market supply and demand, while the unit cost of power generation depends on the government’s subsidies. Figure 6 below shows the influence of policies on the unit cost of power generation by wind and photovoltaic power plants. Since 2019, China has decreased subsidies for wind and photovoltaic power plants. Due to the stability of power generation by photovoltaic power plants, places with rich wind and solar energy are encouraged to build photovoltaic power plants. Based on the previous analysis, the amount of photovoltaic power plants will increase from 2021 to 2030. Affected by the scale effect, the cost of power generation by wind and photovoltaic power plants will decrease and will stabilize after 2030. Figure 5. A combination diagram of stations of hydrogen production and storage when the amount of hydrogen demand is 1500 m$^3$/day. The cost of power transport is not significantly affected by the policy. The cost of power transport by transformer stations and hydrogen production stations is affected by the amount of hydrogen demand which is affected by market supply and demand. Based on the Figure 7, it can be seen that the changes of policies do not affect the cost of power transport directly. The cost of hydrogen production is greatly affected by national policies. In 2019, subsidies for hydrogen energy vehicles were canceled, while subsidies for hydrogen infrastructure were provided. Therefore, the hydrogen subsidies should be considered when setting the cost of hydrogen production. Figure 8 shows the little influence of the hydrogen production subsidy policy on the cost of hydrogen production in the early stage. However, the influence of subsidies on hydrogen production in the later period is prominent. It can be seen that the influence of subsidies on hydrogen energy infrastructure shows a certain lag. However, in the long run, the subsidies for hydrogen energy infrastructure will significantly reduce system costs. The cost of power storage ![Figure 8. Influence of policies on the cost of power production (CNY 10,000).](image) The cost of hydrogen storage is influenced by the policy as shown in Figure 9. Hydrogen is explosive so no subsidies are offered for hydrogen storage. On this basis, the cost of hydrogen storage is higher. The cost of hydrogen storage in 2030–2040 is high due to the large amount of hydrogen production. In order to effectively allocate hydrogen, the number of hydrogen storage stations increases, the amount of hydrogen storage increases and the cost of hydrogen storage is high in 2030–2040. ![Figure 9. Influence of policies on the cost of power storage (CNY 10,000).](image) Based on the above analysis, it can be concluded that costs of power generation and hydrogen production are mainly influenced by the degree of national support for hydrogen storage systems for wind and photovoltaic power generation. Therefore, for the cost of hydrogen production, the ratio of the abandoned power to hydrogen production should be increased, so as to reduce the cost of power generation. In addition, for hydrogen production, the degree of national support for hydrogen-related infrastructure should be increased, which is represented directly by the subsidies for hydrogen refueling stations. That is because the hydrogen subsidies for hydrogen influence the economy of the system. Figure 10 explores the changes in profits in the system corresponding to the degree of national support for hydrogen subsidies. This paper takes the influence of different hydrogen subsidies (0.1–1 yuan/m³) on the economy of hydrogen storage systems for wind and photovoltaic power generation into consideration. Figure 10 shows that the different hydrogen subsidies change profits in the system. Therefore, when applying the hydrogen storage system for wind and photovoltaic power generation throughout the world in the future, the hydrogen subsidies should be increased. Nowadays, hydrogen refueling stations at the hydrogen demand end are always subsidized by China. Therefore, in future, more hydrogen subsidies should be offered to stations of hydrogen production and storage, which will make the system more economical. ![Figure 10. Influence of hydrogen subsidies on profits.](image) 4.2.3. The Influence of Technological Progress on the Economy of the System The progress of system technology is represented by replacing old technology with advanced technology, and producing products with higher efficiency and better output. Technological progress mainly affects technical parameters in the model, including hydrogen production efficiency of hydrogen production equipment, rated gas weight of trucks, rated power amount of transmission lines and loss of power transport. Technological progress will improve the efficiency of hydrogen production by using hydrogen storage systems for wind and photovoltaic power generation. Figure 11 below shows the influence of different hydrogen production efficiencies on profits. ![Figure 11. Influence of electrolysis efficiency on system economy.](image) The objective function of this paper is to maximize the profit which means the sale proceeds will be more or the cost will be less. The sale proceeds are influenced by the amount of hydrogen sold, which is constrained by the hydrogen market and output, and the price of hydrogen. The research on the amount of hydrogen demand should connect... with the important nodes in the energy industry. In 2025, energy consumption in China will reach its peak; in 2030, carbon dioxide emissions in China will peak; and in 2050, the proportion of hydrogen production from renewable energy will account for 70%, which all show a vast market for hydrogen. Therefore, it is meaningful to study hydrogen. It can be seen from Figure 11 that electrolysis efficiency between 78% and 84% significantly improves the economy of the system. Therefore, increasing the research and development efforts on the efficiency of hydrogen production will make the system more economical. In this regard, factor analysis of hydrogen production by electrolyzers should be carried out by relevant institutions and colleges; electrolyzers should be innovated and upgraded by electrolyzer manufacturers; and electrolyzer manufacturers should be encouraged to cooperate with others and supported by the government so as to improve the hydrogen production efficiency and effective production capacity. 5. Conclusions In this paper, a multi-cycle model of optimizing the operation of hydrogen storage systems for wind and photovoltaic power generation is shown. Based on that model, a case study is given on Inner Mongolia with abandoned wind and photovoltaic power and Beijing and Shanxi province with high hydrogen demand to explore the influence of subsidy policy and technological progress on the economy of the system. Then, the following conclusions are drawn: (1) It is economical to build a hydrogen storage system for wind and photovoltaic power generation by using abandoned power, which not only solves the serious problem of power abandonment in wind and photovoltaic power plants, but also avoids the high cost of electrolysis of water. The profit by using a hydrogen storage system for wind and photovoltaic power generation is CNY $1.4 \times 10^{10}$ in the next 30 years. (2) The amount of hydrogen demand affects the location of hydrogen production stations. The most economical solution is to build stations of hydrogen production on the hydrogen demand end. Under the constraints of hydrogen production capacity, the stations of hydrogen production will be located close to the hydrogen demand stations. It can be seen that the system of direct power transport is prior to the system of hydrogen transport from the transformer stations where hydrogen is produced. (3) The results of optimizing the multi-cycle operation are more reliable than that of single-cycle operation. The influence of policy and technological progress on costs and proceeds is considered in a multiple-cycle system. To be specific, policy mainly affects the costs of power generation, hydrogen production and hydrogen subsidies. In addition, in terms of technological progress, the efficiency of electrolyzers has an impact on the economy of the system. Therefore, when the hydrogen storage system for wind and photovoltaic power generation is adopted commonly in the future, high-tech enterprises should update the electrolysis equipment and increase innovation subsidies. The government should also provide policy, and increase subsidies for the cost of power generation, hydrogen production and hydrogen sales. However, this paper still has shortcomings. First of all, this paper does not consider the instability of the abandoned power from wind and photovoltaic power plants. Second, in the case study, only the energy dispatched from Inner Mongolia to the surrounding cities is studied, without consideration of optimization of operating the hydrogen storage system for wind and photovoltaic power generation throughout the country. Third, only sale proceeds and subsidies are involved to calculate the profit in 30 years without consideration of the influence of inflation. In the long term, the proceeds of depreciation, carbon emission reduction and reducing the startup of wind turbines all have an important impact on the economy of the system which should be considered in follow-up studies. Author Contributions: Methodology, Supervision, Writing, Review and Editing, R.Y.; Investigation, Data Curation, Modeling and Experiment, Y.C.; Investigation and Supervision, X.Z. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant number 71802021. 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4334bb2263ce1006b92d5e5de61b8f16fbd2fa19	{ "olmocr-version": "0.1.59", "pdf-total-pages": 11, "total-fallback-pages": 0, "total-input-tokens": 33684, "total-output-tokens": 6867, "fieldofstudy": [ "Physics" ] }	Dual Ginzburg-Landau Theory for Quark Confinement and Dynamical Chiral-Symmetry Breaking* H. Toki\textsuperscript{a,b,c}, H. Suganuma\textsuperscript{a}, S. Sasaki\textsuperscript{b} and H. Ichie\textsuperscript{c} a) The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-01, Japan b) Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567, Japan c) Department of Physics, Tokyo Metropolitan University, Hachiohji, Tokyo 192, Japan ABSTRACT Nonperturbative features of QCD are studied using the dual Ginzburg-Landau (DGL) theory with QCD-monopoles. The linear quark potential appears in the QCD-monopole condensed vacuum. We find that QCD-monopole condensation plays an essential role to the dynamical chiral-symmetry breaking. We also investigate the QCD phase transition at finite temperature in the DGL theory. * To appear in Proc. of the International Symposium on “Intermediate Energy Nuclear Physics”, Beijing China, August 1994. 1. Introduction The asymptotic freedom of QCD enables us to use the perturbative QCD calculation in the ultraviolet region as the deep inelastic scattering, but it leads to a strong coupling system in the infrared region of the hadron physics. This strong interaction provides color confinement and also dynamical chiral-symmetry breaking ($D\chi_{SB}$) as the nonperturbative features of QCD. In particular, color confinement is one of the most unique features of the nonperturbative QCD, and therefore the understanding of the confinement mechanism is the central issue for the hadron physics. The $D\chi_{SB}$ is also an important feature in the nonperturbative QCD. Although recent lattice QCD studies support a close relation between color confinement and $D\chi_{SB}$, no clear physical interpretation has been presented yet. In this paper, we investigate these nonperturbative properties of QCD in terms of the dual Ginzburg-Landau theory [1,2], an infrared effective gauge theory of QCD based on the dual Higgs mechanism. 2. Dual Ginzburg-Landau Theory In 1981, ’t Hooft presented an interesting fact that a non-abelian gauge theory reduces to an abelian gauge theory with color-magnetic monopoles by the abelian gauge fixing [3]. The appearance of these color-magnetic monopoles in QCD, called as QCD-monopoles, would be important for the confinement mechanism, because the quark confinement can be interpreted by condensation of such monopoles as shown below. Since QCD-monopoles behave as singularities of vector potential $A_{\mu}$, we cannot introduce $A_{\mu}$ in the standard way. Instead, we can formulate the gauge theory without singularity following Zwanziger [4] by introducing the dual gauge field $B_{\mu}$, which satisfies $\partial_\mu B_\nu - \partial_\nu B_\mu = F_{\mu\nu}$. In this formalism, the duality of the gauge theory becomes manifest. The QCD-monopole current $k_{\mu}$ couples with the dual gauge field as $k_{\mu} B^\mu$ in the similar way as the ordinary color-electric current, $j_{\mu} A^\mu$. The self-interaction among QCD-monopoles is introduced to realize QCD-monopole condensation, which is strongly supported by the recent studies based on the lattice QCD [5]. The Lagrangian of the dual Ginzburg-Landau theory (DGL) is given as [1,2] \[ L_{DGL} = -\frac{1}{2n^2}[n \cdot (\partial \wedge A)]^\nu [n \cdot (\partial \wedge B)]^{ \nu} + \frac{1}{2n^2}[n \cdot (\partial \wedge B)]^\nu [n \cdot (\partial \wedge A)]^{* \nu} - \frac{1}{2n^2}[n \cdot (\partial \wedge A)]^2 - \frac{1}{2n^2}[n \cdot (\partial \wedge B)]^2 + \bar{q}(i\partial - e\vec{A} \cdot \vec{H} - m)q + \sum_{\alpha=1}^3 \left[ (i\partial_\mu - g\vec{\epsilon}_\alpha \cdot \vec{B}_\mu) \chi_\alpha \right]^2 - \lambda(\left\| \chi_\alpha \right\|^2 - v^2)^2 \] with $ \vec{A}_\mu = (A^3_\mu, A^8_\mu), \vec{B}_\mu = (B^3_\mu, B^8_\mu) $ and $ \vec{H} = (T_3, T_8) $. Here, $ g $ is the unit magnetic charge obeying the Dirac condition $ eg = 4\pi $, and $ \vec{\epsilon}_\alpha $ denotes the relative magnetic charge of the QCD-monopole field $ \chi_\alpha $ ($ \alpha = 1, 2, 3 $). The dual Meissner effect is caused by QCD-monopole condensation due to the self-interaction of $ \chi_\alpha $ in the case $ v^2 > 0 $. It provides the mass of the dual gauge field $ B_\mu $. In the QCD-monopole condensed vacuum, the DGL Lagrangian becomes \[ L_{MF} = -\frac{1}{2n^2}[n \cdot (\partial \wedge A)]^\nu [n \cdot (\partial \wedge B)]^{* \nu} + \frac{1}{2n^2}[n \cdot (\partial \wedge B)]^\nu [n \cdot (\partial \wedge A)]^{* \nu} - \frac{1}{2n^2}[n \cdot (\partial \wedge A)]^2 - \frac{1}{2n^2}[n \cdot (\partial \wedge B)]^2 + \bar{q}(i\partial - e\vec{A} \cdot \vec{H} - m)q + \frac{1}{2}m_B^2 B^2 \] with $ m_B = \sqrt{3}gv $. The QCD-monopole also becomes massive as $ m_\chi = 2\sqrt{\lambda}v $. Similar to the Higgs mechanism in the superconductivity, the color-electric field is then excluded in the QCD vacuum through the dual Meissner effect, and is squeezed between color sources to form the hadron flux tube. 3. Quark Confinement Potential We investigate the quark confinement in terms of the linear inter-quark potential, which is supported by the lattice QCD in the quenched approximation. By integrating over $ A_\mu $ and $ B_\mu $ in the partition functional of the DGL theory, the current-current correlation is obtained as $$\mathcal{L}_j = -\frac{1}{2} j_\mu D^{\mu\nu} j^\nu$$ \hspace{1cm} (3) with the nonperturbative gluon propagator, $$D_{\mu\nu} = \frac{1}{\partial^2} \left\{ g_{\mu\nu} + (\alpha_e - 1) \frac{\partial_\mu \partial_\nu}{\partial^2} - \frac{m_B^2}{\partial^2 + m_B^2 (n \cdot \partial)^2} \right\} \epsilon^\lambda_{\mu\alpha\beta} \epsilon_{\lambda\nu\gamma\delta} n^\alpha n^\gamma \partial^\beta \partial^\delta$$ \hspace{1cm} (4) in the Lorentz gauge. Putting a static quark with color charge $\vec{Q}$ at $x = a$ and a static antiquark with color charge $-\vec{Q}$ at $x = b$, the quark current is written as $j_\mu(x) = \vec{Q} g_{\mu0} \{ \delta^3(x - b) - \delta^3(x - a) \}$. We finally obtain the inter-quark potential including the Yukawa and linear terms, $$V(r) = -\frac{\vec{Q}^2}{4\pi} \frac{e^{-m_B r}}{r} + \frac{\vec{Q}^2 m_B^2}{8\pi} \ln\left(\frac{m_B^2 + m_B^2}{m_B^2}\right) \cdot r,$$ \hspace{1cm} (5) where $r = \|r\| = \|b - a\|$ is the relative distance. Here, we have identified $n//r$, which is also used in the similar context of the dual string theory [6], because of the axial symmetry of the system and the energy minimum condition. Otherwise, the energy of the system diverges. It should be noted that the expression for the string tension, the coefficient of the linear potential, agrees with the one for the energy per length of the vortex in the type-II superconductor. We compare the static potential with the phenomenological one, for example, the Cornell potential. We get a good agreement as shown in Fig.1 with the choice of $e = 5.5$, $m_B = 0.5\text{GeV}$ and $m_\chi = 1.26\text{GeV}$ corresponding to $\lambda = 25$ and $\nu = 126\text{MeV}$, which provide $k=1.0\text{GeV/fm}$ for the string tension and the radius of the hadron flux as $m_B^{-1} = 0.4\text{fm}$. 4. Dynamical Chiral-Symmetry Breaking The dynamical chiral-symmetry breaking (DχSB) is also important for the hadron properties as well as color confinement. We discuss here the DχSB in terms of the mass generation of light quarks in the QCD-monopole condensed vacuum [1,7]. We formulate the Schwinger-Dyson (SD) equation for massless quark as \[ S_q^{-1}(p) = \not{p} + \int \frac{d^4k}{i(2\pi)^4} \tilde{Q}^2\gamma^\mu S_q(k)\gamma^\nu D_{\mu\nu}^{sc}(k-p), \] where we assume the quark propagator $ S_q(p) $ as $ S_q(p) = \not{p} - M(-p^2) + i\eta $. In the presence of light quarks, there appears the screening effect in the long distance of the linear potential corresponding to the cut of the hadron flux tube by the light-quark pair creation. Hence, we introduce the corresponding infrared cutoff $ a $ in the gluon propagator $ D_{\mu\nu}^{sc} $ by the replacement, $ \frac{1}{(n\cdot k)^2} \rightarrow \frac{1}{(n\cdot k)^2 + a^2} $ [1]. Taking the trace and making the Wick rotation in the $ k_0 $-plane, we obtain the SD equation in the Euclidean metric, \[ M(p^2) = \int \frac{d^4k}{(2\pi)^4} \frac{M(k^2)}{k^2 + M^2(k^2)} D_{\mu\nu}^{sc}(k-p), \] where the gluon propagator including the screening effect is given as \[ D_{\mu\nu}^{sc}(k) = \frac{1}{(n\cdot k)^2 + a^2} \cdot \frac{1}{k^2} \cdot \frac{2m_B^2}{k^2 + m_B^2} \{ k^2 - (n\cdot k)^2 \} + \frac{3 + \alpha_e}{k^2} \] in the Lorentz gauge. After performing the angular integral, we obtain the final expression for the SD equation, \[ M(p^2) = \int_0^{\infty} \frac{dk^2}{16\pi^2 k^2 + M^2(k^2)} \frac{\tilde{Q}^2 M(k^2)}{k^2 + p^2 + m_B^2 + \sqrt{(k^2 + p^2 + m_B^2)^2 - 4k^2p^2}} \] \[ + \frac{(1 + \alpha_e)k^2}{\max(k^2, p^2)} + \frac{1}{\pi p_T} \int_{-k}^{k} dk_T \frac{1}{k_n^2 + a^2} \] \[ \times [(m_B^2 - a^2) \ln \left\{ \frac{k_T^2 + (k_T + p_T)^2 + m_B^2}{k_n^2 + (k_T - p_T)^2 + m_B^2} \right\} + a^2 \ln \left\{ \frac{k_T^2 + (k_T + p_T)^2}{k_n^2 + (k_T - p_T)^2} \right\}] \] with $ k_n \equiv k_n - p_n $ and $ k_T \equiv (k^2 - k_n^2)^{1/2} $. In solving the SD equation, we use the Higashijima-Miransky ansatz with a hybrid type of the running coupling constant, \[ \tilde{e} = e(\max\{p^2, k^2\}) \quad \tilde{e}^2(p^2) = \frac{48\pi^2(N_c + 1)}{(11N_c - 2N_f) \ln\left\{(p^2 + p^2_c)/\Lambda^2_{\text{QCD}} \right\}}. \] (10) Here, $ p_c $ is defined as $ p_c \equiv \Lambda_{\text{QCD}} \exp[\frac{24\pi^2}{e^2} \cdot \frac{N_c + 1}{11N_c - 2N_f}] $ with $ e = e(0) $. This ansatz naturally connects to the asymptotic freedom of the running coupling at large momentum. The coupling constant at low energy, $ e(p^2 \sim 0) \approx e $, controls the strength of the linear confinement potential. Fig. 2 shows the quark mass function $ M(p^2) $ with $ e=5.5 $ and $ a = 80\text{MeV} $. The QCD scale parameter is set to a realistic value $ \Lambda_{\text{QCD}} = 200\text{MeV} $. In order to see the effect of QCD-monopole condensation, we vary the mass of the dual gauge field, $ m_B $. There is no non-trivial solution for the case with small $ m_B < 300\text{MeV} $. A non-trivial solution is barely obtained at $ m_B = 300\text{MeV} $, and $ M(p^2) $ increases rapidly with $ m_B $ as shown in Fig. 2. Hence, QCD-monopole condensation provides a crucial contribution to $ D\chi_{\text{SB}} $. Taking the value for the mass of the dual gauge field as $ m_B = 0.5\text{GeV} $ extracted from the linear potential, we get the result for $ M(p^2) $ as shown in Fig. 3. The quark mass function $ M(p^2) $ in the space-like region is directly obtained from the SD equation. We extrapolate $ M(p^2) $ into the time-like region using a polynomial function as a simulation of the analytic continuation. This curve does not cross the on-shell condition $ M^2(p^2) + p^2 = 0 $ ($ p_\mu $: Euclidean momentum) and hence the quark propagator does not have a physical pole. This may indicate the light-quark confinement. We calculate the several quantities related to $ D\chi_{\text{SB}} $ from the solution of the SD equation. The constituent quark mass in the infrared region is found to be $ M(0)=348\text{MeV} $. The quark condensate is obtained as $ \langle \bar{q}q \rangle = -(229\text{MeV})^3 $. The pion decay constant is also calculated as $ f_\pi = 83.6\text{MeV} $ using the Pagels-Stoker formula [9]. These values are to be compared with the standard values; $ M(0)=350 \text{MeV}, \langle \bar{q}q \rangle = -(225 \pm 50\text{MeV})^3 $ and $ f_\pi = 93\text{MeV} $. 5. QCD Phase Transition at Finite Temperature The DGL theory is now able to describe many interesting quantities. Here, we study the change of the QCD vacuum at finite temperature [10] in terms of QCD-monopole condensation. To concentrate on the confinement properties, we consider the pure gauge case, where the quark degrees of freedom are frozen. In this case, we can drop the quark term in the DGL Lagrangian and perform integration over the gauge field $A_{\mu}$. Hence, we obtain the partition functional as $$Z[J] = \int \mathcal{D}\chi \mathcal{D}\vec{B}_{\mu} \exp \left( i \int d^4x \left\{ \mathcal{L}_{\text{DGL}} - J \sum_{\alpha=1}^{3} \|\chi_\alpha\|^2 \right\} \right). \quad (11)$$ where $\mathcal{L}_{\text{DGL}}$ has a simple form, $$\mathcal{L}_{\text{DGL}} = -\frac{1}{4} (\partial_\mu \vec{B}_\nu - \partial_\nu \vec{B}_\mu)^2 + \sum_{\alpha=1}^{3} \left[ (i\partial_\mu - g \vec{\epsilon}_\alpha \cdot \vec{B}_\mu) \chi_\alpha \right]^2 - \lambda (\|\chi_\alpha\|^2 - v^2)^2. \quad (12)$$ Here, we have introduced the quadratic source term instead of the linear source term, which is commonly used. Such an introduction of the quadratic source term is quite powerful for the formulation of the effective potential, especially in the negative-curvature region of the classical potential, where the use of the linear source term does not work well. The effective potential at finite temperature, which physically corresponds to the thermodynamical potential, is then obtained as $$V_{\text{eff}}(\bar{\chi}; T) = 3\lambda(\bar{\chi}^2 - v^2)^2 + \frac{3 T}{\pi^2} \int_0^\infty dk k^2 \ln \left( 1 - e^{-\sqrt{k^2 + m^2}/T} \right)$$ $$+ \frac{3 T}{2 \pi^2} \int_0^\infty dk k^2 \ln \left( 1 - e^{-\sqrt{k^2 + m^2}/T} \right). \quad (13)$$ Here, the masses of the QCD-monopole and the dual gauge field depend on the We provide the calculated results on the effective potential in Fig. 4. At $T = 0$, one minimum appears at a finite $\bar{\chi}$, which corresponds to the condensed phase of QCD-monopoles. As the temperature increases, the minimum moves toward a small $\bar{\chi}$ value, and the second minimum appears at $\bar{\chi} = 0$ above the lower critical temperature $T_{\text{low}} \simeq 0.39\text{GeV}$. The potential values at the two minima become equal at $T_c \simeq 0.49\text{GeV}$, which corresponds to the thermodynamical critical temperature for the QCD phase transition. In this case, it is of first order. Then the trivial vacuum stays as the absolute minimum above the critical temperature. When light dynamical quarks are included, we also expect the chiral-symmetry restoration as well as the deconfinement phase transition at this critical temperature, because QCD-monopole condensation is essential for $D\chi\text{SB}$ as demonstrated in the previous sections. Since the critical temperature seems too high in the above discussion, we consider the temperature dependence of the monopole coupling constant $\lambda$. This is very probable because the interaction among QCD-monopoles is weakened at finite temperature due to the asymptotic free behavior of QCD. Hence, we examine a simple case where $\lambda$ decreases linearly with $T$, $$\lambda(T) = \lambda \left( \frac{T_c - \alpha T}{T_c} \right),$$ where a constant $\alpha = 0.96$ is chosen so as to satisfy $T_c = 0.2\text{GeV}$. We find in this case also a weak first order phase transition. Here, we are able to compare with the numerical results with the pure-gauge lattice QCD on the string tension $k(T)$ [11]. The lattice QCD results are shown by black dots below the critical temperature in Fig. 5, while the results for the variable $\lambda(T)$ go through the dots. We also find that the masses of glueballs (QCD-monopoles, the dual gauge fields) drop largely toward $T_c$ with $T$ from those of order of 1 GeV at zero temperature. It would be very interesting to check this phenomena by the lattice QCD and also by experiment. 6. Summary We have studied the dual Ginzburg-Landau (DGL) theory as the effective theory of QCD. QCD is reduced to an abelian gauge theory with QCD-monopoles in 't Hooft’s abelian gauge. According to QCD-monopoles condensation, the dual Higgs mechanism works as the mass generation of the dual gauge field. We have derived the static inter-quark potential in the DGL theory. In the QCD-monopole condensed vacuum, there appears the linear potential responsible for the quark confinement. We have also studied the dynamical chiral-symmetry breaking (DχSB) in the DGL theory. We find an essential role of QCD-monopole condensation to DχSB. With the parameters extracted from the quark confining potential, we obtain reasonable values for the constituent quark mass $M(p = 0)=348\text{MeV}$, the quark condensate $\langle \bar{q}q \rangle = -(229\text{MeV})^3$ and the pion decay constant $f_\pi=83.6\text{MeV}$. The DGL theory predicts the existence of an axial-vector particle $B_\mu$ and the scalar QCD-monopole $\chi_\alpha$ with masses of $m_B \sim 0.5\text{GeV}$ and $m_\chi \sim 1.5\text{GeV}$ with admittedly a large error of about 1GeV. It would be important to look for these particles in the hadron spectra. Theoretically, we are investigating the decay properties of these particles. We have discussed also the properties of the QCD vacuum at finite temperature in terms of the DGL theory. We find a first order deconfinement phase transition in the pure gauge case. We are now making an effort to introduce dynamical quarks in the discussion of the QCD phase transition. REFERENCES 1. H. Suganuma, S. Sasaki and H. Toki, Nucl. Phys. B435 (1995) 207. H. Toki, H. Suganuma and S. Sasaki, Nucl. Phys. A577 (1994) 353c. 2. T. Suzuki, Prog. Theor. Phys. 80 (1988) 929 ; 81 (1989) 752. S. Maedan and T. Suzuki, Prog. Theor. Phys. 81 (1989) 229. 3. G. ’t Hooft, Nucl. Phys. B190 (1981) 455. 4. D. Zwanziger, Phys. Rev. D3 (1971) 880. 5. A. S. Kronfeld, G. Shierholz and U. -J. Wiese, Nucl. Phys.B293 (1987) 461. T. Suzuki and I. Yotsuyanagi, Phys. Rev.D42 (1990) 4257. 6. Y. Nambu, Phys. Rev. D10 (1974) 4262. 7. S. Sasaki, H. Suganuma and H. Toki, preprint, RIKEN-AF-NP-172 (1994). 8. K. Higashijima, Phys. Rev. D29 (1984) 1228; Prog. Theor. Phys. Suppl. 104 (1991) 1. V. A. Miransky, Sov. J. Nucl. Phys. 38(2) (1983) 280. 9. H. Pagels and S. Stoker, Phys. Rev. D20 (1979) 2947; D22 (1980) 2876. 10. H. Ichie, H. Suganuma and H. Toki, preprint, RIKEN-AF-NP-176 (1994). 11. M. Gao, Nucl. Phys. B9 (Proc. Suppl.) (1988) 368. Figure Captions Fig.1. The static quark potential $V(r)$ in the dual Ginzburg-Landau theory. The dashed curve denotes the Cornell potential. Fig.2. The dynamical quark mass $M(p^2)$ as a function of the Euclidean momentum squared $p^2$ for $m_B=300$, 400 and 500 MeV. Fig.3. The dynamical quark mass squared $M^2(p^2)$ as a function of $p^2$. The dotted straight line denotes the on-shell state. Fig.4. The effective potentials at various temperatures as functions of the QCD-monopole condensate $\bar{\chi}$. The crosses denote their minima. Fig.5. The string tensions $k(T)$ as functions of the temperature $T$ for a constant $\lambda$ and a variable $\lambda(T)$. The lattice QCD results in the pure gauge are shown by black dots.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 990, 1 ], [ 990, 3178, 2 ], [ 3178, 5348, 3 ], [ 5348, 7246, 4 ], [ 7246, 9275, 5 ], [ 9275, 11761, 6 ], [ 11761, 13603, 7 ], [ 13603, 15532, 8 ], [ 15532, 17298, 9 ], [ 17298, 18267, 10 ], [ 18267, 19005, 11 ] ] }
413d295f9c5657b83ddae4ee62e5390d0a0fe37b	{ "olmocr-version": "0.1.59", "pdf-total-pages": 6, "total-fallback-pages": 0, "total-input-tokens": 22413, "total-output-tokens": 7505, "fieldofstudy": [ "Physics" ] }	Actinide collisions for QED and superheavy elements with the time-dependent Hartree-Fock theory and the Balian-Vénéroni variational principle Cédric Simenel¹2, a, Cédric Golabek³, and David J. Kedziora² 1 CEA, Centre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette, France 2 Department of Nuclear Physics, Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 0200, Australia 3 GANIL (IN2P3/CNRS - DSM/CEA), BP 55027, F-14076 Caen Cedex 5, France. Abstract. Collisions of actinide nuclei form, during very short times of few zs (10⁻¹¹ s), the heaviest ensembles of interacting nucleons available on Earth. Such collisions are used to produce super-strong electric fields by the huge number of interacting protons to test spontaneous positron-electron pair emission (vacuum decay) predicted by the quantum electrodynamics (QED) theory. Multi-nucleon transfer in actinide collisions could also be used as an alternative way to fusion in order to produce neutron-rich heavy and superheavy elements thanks to inverse quasifission mechanisms. Actinide collisions are studied in a dynamical quantum microscopic approach. The three-dimensional time-dependent Hartree-Fock (TDHF) code of T3 is used with a full Skyrme energy density functional to investigate the time evolution of expectation values of one-body operators, such as fragment position and particle number. This code is also used to compute the dispersion of the particle numbers (e.g., widths of fragment mass and charge distributions) from TDHF transfer probabilities, on the one hand, and using the Balian-Veneroni variational principle, on the other hand. A first application to test QED is discussed. Collision times in ²³⁸U + ²⁵⁰Cf are computed to determine the optimum energy for the observation of the vacuum decay. It is shown that the initial orientation strongly affects the collision times and reaction mechanism. The highest collision times predicted by TDHF in this reaction are of the order of 4 zs at a center of mass energy of 1200 MeV. According to modern calculations based on the Dirac equation, the collision times at Ecm > 1 GeV are sufficient to allow spontaneous electron-positron pair emission from QED vacuum decay, in case of bare uranium ion collision. A second application of actinide collisions to produce neutron-rich transfermium is discussed. A new inverse quasifission mechanism associated to a specific orientation of the nuclei is proposed to produce transfermium. In a recent experiment, delay times in this reaction was searched analyzing kinetic energy loss and mass transfer [9]. Another application of actinide collisions is to form neutron-rich heavy and superheavy nuclei by multi-nucleon transfer [10][11][12]. Such reactions could be used to explore production. The life-time for such process is, however, longer than the collision-time between actinides. Then, the latter has to be optimized to allow for an experimental observation of vacuum decay. Recent calculations based on the time-dependent Dirac equation [3] show that two bare ²³⁸U need to stick together during at least 2 zs to allow for an observation of spontaneous positron emission. Although no pocket exists in the nucleus-nucleus potential of this system [4][6], nuclear attraction reduces Coulomb repulsion and dissipation mechanisms such as evolution of nuclear shapes may delay the separation of the system [3]. In a recent experiment, delay times in this reaction was searched analyzing kinetic energy loss and mass transfer [9]. 1 Introduction Actinide collisions are important tools to test our understanding of the nuclear many-body problem. They form nuclear systems in extreme conditions of mass and isospins. The prediction of the outcome of such collisions is a great challenge for nuclear theorists. In particular, the question of "How long can two actinides stick together" is of wide interests. The quantum-electrodynamic (QED) theory predicts that spontaneous pairs of e⁺ + e⁻ may be emitted due to the strong electric fields produced by the protons [12][13]. This process is also known as "QED vacuum decay". It occurs when an empty electron state dives into the Dirac sea. QED predicts that such a hole state is unstable and decays by e⁺ + e⁻ pair production. The life-time for such process is, however, longer than the collision-time between actinides. Then, the latter has to be optimized to allow for an experimental observation of vacuum decay. Recent calculations based on the time-dependent Dirac equation [3] show that two bare ²³⁸U need to stick together during at least 2 zs to allow for an observation of spontaneous positron emission. Although no pocket exists in the nucleus-nucleus potential of this system [4][6], nuclear attraction reduces Coulomb repulsion and dissipation mechanisms such as evolution of nuclear shapes may delay the separation of the system [3]. In a recent experiment, delay times in this reaction was searched analyzing kinetic energy loss and mass transfer [9]. Another application of actinide collisions is to form neutron-rich heavy and superheavy nuclei by multi-nucleon transfer [10][11][12]. Such reactions could be used to explore... the "blank spot" between decay chains of nuclei formed by "hot" and "cold fusion" around $Z = 105$ and $N = 160$. Theoretically, the complexity of reaction mechanisms and the high number of degrees of freedom to be included motivate the use of microscopic approaches. Early dynamical microscopical calculations of $^{238}\text{U}$ were performed with spatial symmetries and simplified effective interactions. Recently, this system has been studied within the Quantum Molecular Dynamics (QMD) model in which nucleon wave functions are constrained to be Gaussian wave packets and with the time-dependent Hartree-Fock approach which overcomes this limitation. 2 Formalism In general, the full quantum many-body problem cannot be solved exactly and, in most realistic cases, approximations have to be made. In general, variational principles are useful to build approximation schemes by reducing the variational space. 2.1 The Balian-Vénéroni variational principle The Balian and Vénéroni (BV) variational principle is based on the action $$ S_{BV} = \text{Tr} \left[ \hat{D}(t_1) \hat{B}(t_1) \right] - \int_{t_0}^{t_1} \text{Tr} \left[ \frac{\partial \hat{D}}{\partial t} - i \hat{D} [\hat{H}, \hat{B}] \right] dt, $$ where $\hat{B}$ and $\hat{D}$ are the time-dependent trial observable and density matrix of the trial state, respectively, and Tr denotes a trace in the Fock space. Both the state and the observable are allowed to vary between $t_0$ and $t_1$, corresponding to a mixture of the Schrödinger and Heisenberg pictures. They are constrained to obey the mixed boundary conditions $\hat{D}(t_0) = \hat{D}_0$ and $\hat{B}(t_1) = \hat{X}$, where $\hat{D}_0$ is the density matrix of the initial state of the system and $\hat{X}$ is the operator we want to evaluate at time $t_1$. Without restriction on the variational spaces, the variational principle $\delta S_{BV} = 0$, with the above conditions, is fully equivalent to the Schrödinger equation if the initial state is pure ($\hat{D}_0 = \|\Psi_0\rangle \langle \Psi_0\|$). 2.2 Mean-field approximation In most practical applications, mean-field models are considered in a first approximation. In mean-field theories, the interaction between the particles is replaced by a one-body mean-field potential generated by all the particles. It is then assumed that each particle evolves independently in this potential. For instance, $N$ independent fermions may be described by a Slater determinant $\|\psi\rangle = \prod_{i=1}^{N} \hat{a}_{\uparrow}^\dagger \|\rangle$, where $\hat{a}_{\uparrow}^\dagger$ creates a particle in the state $\|\varphi_i\rangle$ when it is applied to the particle vacuum $\|\rangle$. In such a Slater determinant, all the information is contained in the one-body density-matrix $\hat{\rho} = \sum_{i=1}^{N} \|\varphi_i\rangle \langle \varphi_i\|$. The BV variational principle is usually applied at the mean-field level where the variational space of $\hat{D}$ is restricted to independent particle states, i.e., with $\hat{D} = \|\varphi\rangle \langle \varphi\|$. 2.3 Expectation values of one-body operators In addition to the mean-field approximation, the variational space for $\hat{B}$ is usually constrained to belong to the same class of operators as the observable of interest. For instance, if one wants to predict expectation values of one-body observables $\hat{X} = \sum_{i=1}^{N} \hat{q}_X(i)$, then it is natural to restrict the variational space for $\hat{B}$ to one-body operators. In this case, one recovers the TDHF equation $$ \frac{i}{\hbar} \frac{\partial \rho}{\partial t} = \{ h[\rho], \rho \}, $$ where $h[\rho]$ is the Hartree-Fock (HF) single-particle Hamiltonian with matrix elements $h_{a\bar{a}} = \frac{\partial^2 E[\rho]}{\partial \rho_{a\bar{a}}}$. $\hat{H}$ is the full Hamiltonian, and $\rho_{a\bar{a}} = \langle \varphi_a \| \bar{\hat{\rho}} \| \varphi_{\bar{a}} \rangle = \langle \varphi_a \| \hat{a}_{\bar{a}}^\dagger \| \varphi_{\bar{a}} \rangle \| \varphi_{\bar{a}} \rangle \| \varphi_{\bar{a}} \rangle$. According to this variational approach, TDHF is an optimized mean-field theory to describe expectation values of one-body observables. However, TDHF may fail to reproduce their fluctuations $\sigma_{XX} = \sqrt{\langle \hat{X}^2 \rangle - \langle \hat{X} \rangle^2}$. 2.4 Fluctuations of one-body operators The BV variational principle can also be used with the variational space $\hat{B} \in \{ e^{i\alpha t}\hat{H} \}$ to determine an optimum mean-field prediction for correlations $\sigma_{XY}$ and fluctuations $\sigma'_{XX}$ of one-body operators, $$ \sigma'_{XX} = \sqrt{\langle \hat{X}^2 \rangle - \langle \hat{X} \rangle^2}, $$ In case of independent particle states, this leads to $$ \sigma'_{XY}(t_1) = \lim_{t_0 \to t_1} \frac{1}{2e^2} \text{tr} \left[ \left\{ \rho(t_0) - \rho_X(t_0, \epsilon) \right\} \left\{ \rho(t_0) - \rho_Y(t_0, \epsilon) \right\} \right], $$ where tr denotes a trace in the single-particle space. The one-body density matrices $\rho_X(t, \epsilon)$ obey the TDHF equation with the boundary condition $$ \rho_X(t_1, \epsilon) = e^{i\epsilon\hat{H}} \rho(t_1) e^{-i\epsilon\hat{H}}, $$ while $\rho(t)$ is the solution of Eq. (2) with the initial condition $\rho_{a\bar{a}}(t) = \text{Tr} a_{\bar{a}}^\dagger a_{\bar{a}} \hat{D}_0 = \langle \varphi_{\bar{a}} \| \hat{a}_{\bar{a}}^\dagger \| \varphi_{\bar{a}} \rangle \| \varphi_{\bar{a}} \rangle \| \varphi_{\bar{a}} \rangle$. The optimum mean-field prediction of $\sigma'_{XY}$ in Eq. (4) differs from the "standard" TDHF expression which is evaluated from Eq. (3) using $\rho(t_1)$. Eq. (4) has been solved numerically in the past with simple effective interactions and geometry restrictions. Modern three-dimensional TDHF codes with full Skyrme functionals can now be used for realistic applications of the BV variational principle. In this work, the fluctuations $\sigma_{NN}$, $\sigma_{ZZ}$, and $\sigma_{AA}$, are computed in fragments resulting from actinide collisions. The correlations $\sigma_{NZ}$, which are strictly zero in standard TDHF calculations, are also determined with this approach. Fig. 1. Isodensities at half the saturation density, i.e., $\rho_0/2 = 0.08$ fm$^{-3}$, in $^{238}$U+$^{238}$U central collisions at a center of mass energy $E_{c.m.} = 1200$ MeV. Evolutions associated to the four initial configurations $xx$, $yx$, $yy$, and $yz$ are plotted in columns (time runs from top to bottom). Consecutive snapshots are separated by 1.125 zs. 3 numerical details The use of a three-dimensional TDHF code with a full Skyrme energy-density-functional (EDF), modeling nuclear interactions between nucleons and including spin-orbit interaction [32,33], allows for a realistic prediction of these quantities. The TDHF equation (2) is solved iteratively in time, with a time step $\Delta t = 1.5 \times 10^{-24}$ s. The single-particle wave-functions are evolved on a Cartesian grid of $96 \times 32 \times 32/2$ points with a plane of symmetry (the collision plane) and a mesh-size $\Delta x = 0.8$ fm. The initial distance between collision partners is 22.4 fm. The $\tau$-nu$3d$ code is used with the SLy4d parameterization [26] of the Skyrme EDF, which is the only phenomenological ingredient, as it has been adjusted on nuclear structure properties [33]. Ref. [34] gives more details of the TDHF calculations. The numerical details for the evaluation of Eq. (4) can be found in [31]. 4 Collision time in $^{238}$U+$^{238}$U TDHF calculations have been performed to investigate the collision time in $^{238}$U+$^{238}$U [15]. The $^{238}$U nucleus exhibits a prolate deformation with a symmetry axis in its ground state. The effect of this deformation on collision is investigated in four configurations ($xx$, $yx$, $yy$ and $yz$) associated to different initial orientations. The letters $x$, $y$ and $z$ denote the orientation of the symmetry axis of the nuclei which collide along the $x$ axis [see Fig. 1]. We focus on central collisions as they lead to the most dissipative reactions with the longest collision times. Here, the collision time $T_{\text{coll}}$ is defined as the time during which the neck density exceeds $\rho_0/10$. It is shown in Figure 2 as function of the center of mass energy $E_{\text{cm}}$. At $E_{\text{cm}} \leq 900$ MeV, three distinct behaviors between the $xx$, $yx$ and $yy/yz$ configurations are seen. In particular, the last one needs more energy to get into contact as the energy threshold above which nuclear interaction plays a significant role is higher for such compact configurations. At all energies, the $yx$, $yy$ and $yz$ orientations exhibit roughly similar behaviors, i.e., a rise and fall of $T_{\text{coll}}$ with a maximum of $3 \times 10^{-21}$ s at $E_{\text{cm}} \sim 1200$ MeV. Dynamical evolution of nuclear shapes in these three configurations and a strong transfer in the $yx$ one (see next section) are responsible for these rather long collision times as compared to scattering with frozen shapes of the reactants [8]. The $xx$ configuration, however, behaves differently. For $700 < E_{\text{cm}} < 1300$ MeV, $T_{\text{coll}}$ exhibits a plateau which does not exceed $2 \times 10^{-21}$ s. This overall reduction of $T_{\text{coll}}$ in the $xx$ case is attributed to the strong overlap of the tips, producing a density in the neck higher than $\rho_0$ \cite{17}. The fact that nuclear matter is difficult to compress translates into a strong repulsive force between the fragments which decreases their contact time. This phenomenon is also responsible for the full of collision times in the other configurations, though higher energies are needed to strongly overlap. The calculations of Ref. \cite{3} show that the observation of spontaneous emission of $e^+ + e^-$ needs a contact time of at least 2 zs between the bare uranium nuclei. The TDHF calculations of Fig. \ref{fig:2} predict that such contact times are reached in central collisions for energies $E_{\text{cm}} > 1$ GeV. This lower energy limit should be taken into account in future experimental programs dedicated to the search of QED vacuum decay. Finally, it is worth mentioning that other approaches lead to comparable collision times in actinide collisions \cite{6,35}. 5 Formation of neutron-rich transfermium nuclei 5.1 $^{238}$U+$^{238}$U reaction We now analyze the proton and neutron numbers of the fragments produced in exit channels of actinide collisions. Strictly speaking, these fragments should be considered as primary fragments as they might decay by statistical fission. This decay is not studied here as it occurs on a much longer time scale than the collision itself. The importance of initial orientation on reaction mechanism is clearly seen in Fig. \ref{fig:1} for the $^{238}$U+$^{238}$U reaction. For symmetry reasons, the $xx$, $yy$, and $yz$ configurations give two symmetric distributions of fragments, although nucleon transfer is still possible thanks to particle number fluctuations. Nucleon transfer is expected to be stronger in the $yx$ configuration because, in addition to fluctuations, no spatial symmetry prevents from an average flux of nucleons. The $yx$ configuration is then expected to favor the formation of nuclei heavier than $^{258}$U. 5.2 $^{232}$Th+$^{250}$Cf reaction Similar calculations have been performed on the system $^{232}$Th+$^{250}$Cf \cite{35}. The same effect is observed, i.e., an important multi-nucleon transfer in the $xy$ and $yx$ configurations. The $xy$ configuration where the $^{250}$Cf nucleus receives nucleons (its deformation axis is perpendicular to the collision axis while the one of $^{232}$Th is parallel to the collision axis) corresponds to an "inverse quasifission" mechanism due to a specific orientation of the collision partners. Indeed, contrary to standard quasifission, the exit channel is more mass asymmetric than the entrance channel. Note that inverse quasifission may also occur due to shell effects in the exit channel \cite{8}. The effect is illustrated in Fig. \ref{fig:3} where the distribution of heavy fragments is shown at $E_{\text{cm}} = 916$ MeV. This distribution is computed after a TDHF calculation, using a particle number projection technique \cite{37}. The center of the distribution is located around $^{265}$Lr, i.e., in the neutron-rich side of the known Lawrencium isotopes. Note that, at the end of the TDHF calculation, the decay of the fragments by neutron emission is only partial \cite{36}. The width of such a distribution is known to be underestimated at the TDHF level \cite{19,20}. In addition, we see in Fig. \ref{fig:4} that the probability distributions for $N$ and $Z$ are uncorrelated at the TDHF level. This is not a feature of the TDHF formalism itself, but rather a limitation due to the fact that, for practical applications, one assumes $\phi = \|\phi_p\rangle \times \|\phi_n\rangle$, where $\|\phi_p\rangle$ and $\|\phi_n\rangle$ are Slater determinants of the proton and neutron single-particle wave-functions, respectively \cite{31}. If this constraint is released, as in \cite{38}, then non-zero correlations could be obtained at the TDHF level. The Balian-Vénéroni variational principle can be used, at the mean-field level, to optimize both widths of proton and neutron distributions as well as their correlations. Realistic calculations have been performed recently to study deep-inelastic collisions \cite{31}. Similar calculations have been done to investigate the inverse quasifission mechanism discussed above. Preliminary results are shown in Fig. \ref{fig:4} where the heavy-fragment distribution is shown for the same $xy$ orientation of $^{232}$Th+$^{250}$Cf as in Fig. \ref{fig:3}. As expected, much larger widths than in the TDHF case are observed in one hand, and, in the other hand, strong correlations between the proton and neutron number distributions are observed, which can be seen by the fact that the fragments are produced along the valley of stability. 6 Conclusions To conclude, this fully microscopic quantum investigation of actinide collisions exhibits a rich phenomenology strongly influenced by the shape of the nuclei. Two main conclusions can be drawn. (i) The giant system formed in bare uranium-uranium central collisions is expected to survive enough time with an energy $E_{\text{cm}} \geq 1000$ MeV, for the spontaneous positron emission to occur. (ii) The primary heavy-fragments produced by multinucleon transfer are more neutron-rich than in fusion-evaporation reactions. The width of these distributions, computed with the Balian-Vénéroni prescription, are much larger than with TDHF. Associated cross-sections need to be determined to estimate the experimental possibility of neutron-rich transfermium and SHE productions. Extension of the formalism need to be investigated. For instance, the role of pairing could be studied with Time-Dependent Hartree-Fock-Bogoliubov (or BCS) codes \cite{39,40,41}. Stochastic-mean-field methods might also be applied to investigate the role of initial beyond-mean-field correlations on fluctuations \cite{42}. 7 Acknowledgements We thank P. Bonche for providing his code. We are also grateful to M. 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Ayik, and D. Lacroix, Phys. Rev. C 80, 031602 (2009). 44. K. Washiyama et al., contribution to FUSION11.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5251, 1 ], [ 5251, 11375, 2 ], [ 11375, 14488, 3 ], [ 14488, 20505, 4 ], [ 20505, 20694, 5 ], [ 20694, 24543, 6 ] ] }
06408000a5383d52c56a3d14dd3524ed7e4218c2	{ "olmocr-version": "0.1.59", "pdf-total-pages": 4, "total-fallback-pages": 0, "total-input-tokens": 10230, "total-output-tokens": 2673, "fieldofstudy": [ "Materials Science" ] }	Fabrication of WO₃-based electrochromic displays using solid or gel-like organic electrolytes M Vasilopoulou¹, G Aspiotis², I Kostis², P Argitis¹ and D Davazoglou¹ ¹NCSR “Demokritos”, Institute of Microelectronics, POB 60228, 153 10 Agia Paraskevi, Attiki Greece ²Technological and Educational Institute (TEI) of Pereaus, Dpt. Of Electronics, Petrou Rali av., 12244 Aegaleo, Attiki Greece Abstract: New all solid-state electrochromic displays were fabricated by chemically vapor depositing and patterning a tungsten oxide film on SnO₂:F covered glass substrates. Aluminum sheets were used as counter electrodes to form electrochromic displays using solid or gel-like organic electrolytes. These ionically conductive and electronically insulating electrolytes were based on poly(methyl methacrylate) (PMMA) and poly(2-hydroxyethyl methacrylate) (PHEMA) into which phospho-tungstic acid was added at various concentrations. In some devices the electrolyte was formed by addition of photoacid generator into the polymeric matrix and exposure at deep UV light. It was found that displays exhibit an intense, reversible electrochromic effect with reflectivity varying by a factor of five between the uncolored to the colored state. The coloring voltage depends strongly on the polymeric matrix, the thickness of the electrolyte and post-apply baking conditions and is of the order of 6-9V. The response time was found to be of the order of 500 ms; coloration and bleaching times were comparable. 1. Introduction Electrochromism is defined as a reversible change in the transmittance and/or reflectance of a material caused by the application of an electrical current or potential. Its potential applications include smart windows [1] for the modulation of the incoming light and in large area displays [2]. Electrochromism is exhibited by a variety of organic [1, 3] and inorganic materials [1] in bulk and film form. Among the inorganic electrochromic films the most studied are those of WO₃ since they provide a memory effect, good contrast, high coloration efficiency and low switching voltage [4]. It has been suggested that electrochromism in WO₃ films is divided in two parts [5, 6]: a fast electronic one, during which the film is colored by electronic injection and a slower one associated with the insertion of ions in it. In this paper the fabrication of an electrochromic displays based on chemically vapor deposited (CVD) WO₃ films and novel solid or gel like electrolytes is described. Electrochromic performances are investigated and discussed when biased with DC voltages. 2. Experimental For the fabrication of electrochromic displays, W films were chemically vapor deposited on commercially available SnO₂:F covered glass substrates by decomposing W(CO)₆ vapors at a pressure of 0.1 Torr and a temperature of 400 °C [7]. After deposition the W films were patterned with AZ 5214™ photoresist, etched using aqueous solutions containing tetra-methyl ammonium hydroxide... (TMAH) [8] and oxidized to WO$_3$ in oxygen at 600 °C. Transparent electrochromic displays, like those shown in figure 1, were formed using another SnO$_2$:F covered glass substrate as counter electrode and solid or gel-like polymeric electrolytes formed as follows. In a polymeric solution composed either by poly-methyl methacrylate (PMMA) in methyl-iso-butyl ketone (MIBK) at concentrations of 2 or 4 % w/w or poly-hydroxy-ethyl methacrylate (PHEMA) in ethyl-lactate at a concentration of 2% w/w, phosphotungstic acid hydrate was added at concentrations varying between 1:1 to 1:8 of polymer mass. Displays using gel-like electrolytes were formed by dipping the electrochromic (EC) glass/SnO$_2$:F/WO$_3$ “sandwich” in the above solutions and then the counter electrode was pressed on the electrolyte. Solid electrolytes were applied by spinning electrolytes on the EC “sandwiches” at 2000 rpm followed by bake at 80 °C for min. A Perkin-Elmer Lamda 40 spectrophotometer running the WinLab software was used to record the optical transmission spectra of electrochromic devices within the range 300 to 1000 nm. 3. Results and Discussion In figure 2 typical reflection spectra are shown for WO$_3$-based EC displays using as electrolytes PMMA solutions 8% in MIBK containing acid at concentrations 1:1 (left) and 1:8 (right) of the polymer mass and Al sheets as counter electrodes. Spinning and curing as described before was used to deposit electrolytes. Displays were colored at various degrees with various voltages. For each measurement a DC voltage was applied on the display, which was remaining throughout the duration of the measurement (about 2 min). It can be observed that the reflection of the displays can be varied gradually and reversibly to the half of the initial value with a ![Figure 1. An electrochromic display in its uncolored (left), lightly (middle) and highly colored (right) state.](image1) ![Figure 2. Reflection spectra of electrochromic displays based on WO$_3$ films and using as electrolytes films applied by spinning from PMMA solutions 8% in MIBK containing acid at concentrations 1:1 (left) and 1:8 (right).](image2) voltage of 4 V. Moreover, it seems that the degree of coloration does not depend on the concentration of acid. It must be pointed out that for displays using such electrolytes coloration and bleaching times were comparable and equal to approximately 500 ms. This is contrary to what has been observed for EC displays using liquid electrolytes and may be explained assuming that after insertion of the protons generated from the acid decomposition in the electrolyte film into the WO₃, the last remains charged. This creates an internal electric field, which superimposes to the bleaching voltage facilitating this process. ![Figure 3](image-url) Reflectance spectra of electrochromic displays based on WO₃ films using as electrolytes films of PMMA solutions in MIBK 4 % (left) and 8 % (right). The acid concentration for both displays was the same and equal to 1:4. When the concentration of PMMA in the solution decreases the thickness of the electrolyte film also decreases. The EC displays using electrolytes containing PMMA at 4% need higher voltages to color at the same degree as displays using electrolytes containing PMMA at a concentration of 8% and similar acid concentrations as shown in figure 3. The thicknesses of the electrolyte films were 1 and 0.5 μm, respectively. Displays using electrolytes with low PMMA content are very hard to bleach. This result is somehow curious since thinner films means that higher voltages are applied on the mobile ions so the coloration and the bleaching, which are associated with the insertion and the extraction of these ions in and out of the WO₃ film respectively, should have to be facilitated. The phenomenon does not seem to be related to the lack of mobile ions in the thinner films since coloration occurs, hence it is rather related to the ionic mobility. Indeed, thinner PMMA films are easier to solidify at the curing temperature of 80 °C than thicker ones and this solidification implies a drop of mobility of ions. ![Figure 4](image-url) Reflectance spectra recorded on an EC display using gel-like electrolyte composed of PHEMA added phosphotungstic acid hydrate (1:2) 0.25 μm thick. In figure 4 reflectance spectra taken on an EC display using as electrolyte PHEMA 2\% in ethyl-lactate containing phosphotungstic acid at a concentration 1:2, colored and bleached with various voltages are shown. It can be seen that the voltages involved are higher than those used for PMMA-based displays. The thin electrolyte film was solidified and this is a possible explanation for the high voltages needed for the coloration of this display. Another possible explanation is that protons produced by the acid, the incorporation of which into the WO$_3$ causes the coloration, are now captured by the hydroxyl ions of the PHEMA. ![Figure 4](image1.jpg) Figure 5. Reflectance spectra recorded on an EC display using gel-like electrolyte composed PMMA 4\% added phosphotungstic acid hydrate at a concentration of 1:2. In figure 5 reflection spectra taken at the fully colored and bleached states on a display in the beginning of its operation and after 24 hours of operation are shown. It can be seen that the curves do not entirely coincide and this is probably due to protons that remain into the WO$_3$ film after every coloration cycle. However, in agreement with results made using liquid electrolytes the long-time use renders displays faster [9]. 4. Conclusions EC devices based on WO$_3$ LPCVD films have been fabricated using lithographic and etching techniques standard in Si technology and solid and gel-like electrolytes. A clear reproducible and stable electrochromic effect was observed on all devices. Devices using gel-like electrolytes exhibited a faster coloration and bleaching and at lower voltages than those using solid electrolytes. Coloration and bleaching times were comparable due to the creation of an internal field after insertion of protons in the WO$_3$ film, which superimposes on the bleaching voltage. 5. References [1] Lampert C 1984 Sol. Energy Mater. 11 828 [2] Dautremont-Smith W 1982 Displays 3 3 [3] See, for example, at http://dwww.epfl.ch/icp/ICP-2/elecr.html [4] Nagase K, Shimizu Y, Minya N and Yamazoe N 1994 Appl. Phys. Lett. 64 1059 [5] Donnadieu A, Davazoglou D and Abdellaoui A 1987 Th. Sol. Films 164 333-338 [6] Davazoglou D and Donnadieu A 1987 Th. Sol. Films 164 369-375 [7] Davazoglou D, Moutsakis A, Valamontes V, Psycharis V and Tsamakis D 1997 J. Electrochem. Soc., 144, 595 [8] Vassilopoulou M, Pappas D, Raptis I, Davazoglou D and Kostis I, Proc. Internat. Symp. Chem. Vapor Deposition CVD-XVI and EUROCVD 14 (Paris, 27 April - 2 May 2003) [9] Davazoglou D, Leveque G and Donnadieu A 1988 Sol. En. Mat. 17 379-390	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2986, 1 ], [ 2986, 5142, 2 ], [ 5142, 7293, 3 ], [ 7293, 9916, 4 ] ] }
4302db21447bc267eacdd15aba5fb2d5415332fe	{ "olmocr-version": "0.1.59", "pdf-total-pages": 19, "total-fallback-pages": 0, "total-input-tokens": 64084, "total-output-tokens": 18868, "fieldofstudy": [ "Medicine", "Biology" ] }	Ramulus Mori (Sangzhi) Alkaloids Alleviate High-Fat Diet-Induced Obesity and Nonalcoholic Fatty Liver Disease in Mice Yan-Min Chen, Chun-Fang Lian, Qian-Wen Sun, Ting-Ting Wang, Yuan-Yuan Liu, Jun Ye, Li-Li Gao, Yan-Fang Yang, Shuai-Nan Liu, Zhu-Fang Shen, and Yu-Ling Liu 1 Institute of Materia Medica, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100050, China; [email protected] (Y.-M.C.); [email protected] (C.-F.L.); [email protected] (Q.-W.S.); [email protected] (Y.Y.); [email protected] (L.-L.G.); [email protected] (Y.-F.Y.); [email protected] (S.-N.L.); [email protected] (Z.-F.S.) 2 State Key Laboratory of Bioactive Substance and Function of Natural Medicines, Institute of Materia Medica, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100050, China 3 Beijing Key Laboratory of Drug Delivery Technology and Novel Formulation, Institute of Materia Medica, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100050, China 4 School of Pharmaceutical Sciences, Tsinghua University, Beijing 100084, China; [email protected] (T.-T.W.); [email protected] (Y.-Y.L.) * Correspondence: [email protected] † These authors contributed equally to this work. Abstract: Nonalcoholic fatty liver disease (NAFLD), obesity, and type 2 diabetes mellitus (T2DM) have highly related mechanisms. Ramulus Mori (Sangzhi) alkaloids (SZ-A) from Morus alba L. were approved in 2020 for the treatment of T2DM. In this study, we examined the therapeutic effects and mechanism of SZ-A on obesity and NAFLD in mice. Mice (C57BL/6J) fed a high-fat diet (HFD) for 14 weeks were treated with SZ-A for another 6 weeks. HFD-induced weight gain was reduced by SZ-A in a dose-dependent manner. SZ-A treatment significantly stimulated adiponectin expression and secretion in adipose tissue and 3T3-L1 adipocytes. Additionally, SZ-A markedly reduced hepatic steatosis (triglyceride, total cholesterol) and expression of pro-inflammatory and pro-fibrotic genes. SZ-A regulated lipid metabolism and oxidative stress (malondialdehyde (MDA), superoxide dismutase (SOD), glutathione peroxidase (GPx), and glutathione (GSH)) in the liver. Palmitic acid-induced insulin resistance and lipid accumulation in HepG2 cells were also repressed by SZ-A. Collectively, SZ-A protected mice from HFD-induced NAFLD through an indirect effect of improved systemic metabolism reducing body weight, and a direct effect by enhancing the lipid metabolism of HepG2 cells. The weight-loss effect of SZ-A in mice was partly due to improved fatty oxidation instead of influencing food consumption. Keywords: NAFLD; obesity; Ramulus Mori (Sangzhi) alkaloids; steatosis; oxidative stress; adiponectin 1. Introduction Non-alcoholic fatty liver disease (NAFLD) has emerged as the most common cause of chronic liver disease worldwide, affecting approximately 25% of the population [1]. The prevalence of NAFLD has increased with the growing obesity epidemic. NAFLD is considered a hepatic manifestation of metabolic syndrome, ranging from steatosis and non-alcoholic steatohepatitis (NASH) to fibrosis and cirrhosis [2]. Obesity and obesity-related metabolic diseases such as NAFLD, type 2 diabetes mellitus (T2DM), and cardiometabolic diseases share common pathophysiological mechanisms, including a disturbed gut microbiome, insulin resistance, and chronic inflammation [3,4]. Obesity results when unbalanced energy intake and expenditure causes excessive energy to be stored in adipose tissue as triglycerides. When storage capacity is overwhelmed, lipotoxic metabolic stress promotes chronic inflammation and insulin resistance. Inappropriate ectopic lipid accumulation in the liver, caused by insulin resistance, induces metabolic stress, mitochondrial dysfunction, and endoplasmic reticulum (ER) stress, which leads to cell death and metabolic inflammation [5]. Hepatic fibrosis is thought to result from prolonged inflammation and hepatic stellate cell (HSC) activation [6,7]. Disturbed lipid homeostasis and metabolic stress-induced damage are the key pathogenic features of NAFLD [8,9]. AMP-activated protein kinase (AMPK), the guardian of metabolism, phosphorylates targets involved in lipid metabolism, protein metabolism, glucose metabolism, and mitochondrial homeostasis. Acetyl-CoA carboxylase (ACC) phosphorylation by activated AMPK regulates fatty acid synthesis and lipid β-oxidation. Peroxisome proliferator-activated receptor-γ co-activator 1α (PGC1α) is another downstream effector that regulates mitochondrial biogenesis [10]. When the balance between lipid production and breakdown is disturbed, free fatty acids (FFA) accumulated in the liver may be used as substrates for the production of lipotoxic species, which induce ER stress, mitochondrial dysfunction, oxidative stress, cell damage, and cytokine release. Mitochondria are a major cellular source of reactive oxygen species (ROS) [11]. Superoxide dismutase (SOD), glutathione peroxidase (GPx), and glutathione (GSH) are vital scavengers of ROS that relieve oxidative stress [12]. Excessive ROS induced by high fat diet (HFD) is harmful to hepatocytes, Kupffer cells, and hepatic stellate cells, which promotes the progression of NAFLD to NASH [13]. To date, no pharmacological therapies have been approved for NAFLD treatment. Given the complexity of NAFLD pathophysiology, agents targeting different molecular processes of hepatic metabolism, oxidative stress-induced cell death, inflammation, and fibrosis have been investigated in preclinical models and clinical trials [14]. These agents act through direct effect in the liver and indirect effect by improving systemic metabolic indexes. A number of anti-diabetic agents, such as thiazolidinedione insulin sensitizers, glucagon-like peptide 1 (GLP1) receptor agonists, and sodium-glucose cotransporter-2 (SGLT-2) inhibitors, are studied in NAFLD clinical trials by increasing insulin sensitivity, reducing bodyweight, and improving systemic metabolism [4,15,16]. In addition, combination therapies with different targets represent a new approach to treat NAFLD because the therapeutic effects of monotherapy drugs with a single target are limited [17]. Ramulus Mori (Sangzhi) alkaloid (SZ-A) tablets, extracted from Morus alba L. (mulberry twig), were approved by the China National Medical Products Administration in 2020 for T2DM treatment in China (approval number Z20200002). The main components of SZ-A powder (SZ-A tablet materials) are alkaloids (50% or more by weight), including 1-deoxynojirimycin (DNJ), 1,4-dideoxy-1,4-imino-D-arabinitol (DAB), and fagomine (FA). Though the prophylactic effects of DNJ have been reported to protect against high fat diet-induced liver steatosis through the regulation of the gut microbiota [18] and mitochondrial biogenesis [19], the application of DNJ is restricted, as industrial scale production of DNJ is difficult [20]. Enzymatic studies and molecular docking revealed that SZ-A inhibits α-glucosidases, especially disaccharidases [21]. Chronic treatment with SZ-A protects mice from HFD-induced insulin resistance and modulates gut microbiota and gut barrier integrity in type 2 diabetic KKAy mice [22]. In addition, the anti-inflammatory effects of SZ-A were also reported to result from blocking the activation of the p38 MAPK, ERK, and JNK signaling pathways in macrophages [23]. SZ-A exhibited hypoglycemic effects in the treatment of T2DM with fewer gastrointestinal side effects in a multicenter, randomized, double-blind clinical trial [24]. Tissue distribution analysis showed that the major alkaloids of SZ-A are well absorbed after oral administration and rapidly distributed to the liver and kidneys, in addition to the gastrointestinal tract [25], which revealed that SZ-A may have a direct effect on these tissues. In the present study, we investigated whether SZ-A mitigates obesity and NAFLD in HFD-fed mice by directly acting on the liver and adipose tissues. The direct effects and mechanisms of action of SZ-A and its major components on hepatocytes and adipocytes were studied in vitro. Our results demonstrate the potential of SZ-A as a natural anti-diabetic agent for the treatment of obesity and NAFLD in mice. 2. Materials and Methods 2.1. Chemical and Reagents Ramulus Mori (Sangzhi) alkaloids (SZ-A) powder (lot number: J202107010, the total polyhydroxy alkaloids content in SZ-A powder is 60.62%, which includes 40.75% DNJ, 8.99% FA, and 8.59% DAB, as shown in Supplementary Figure S1) was kindly provided by Beijing Wehand-Bio Pharmaceutical Co., Ltd. (Beijing, China). 1-Deoxynojirimycin (DNJ, purity > 98.5%) was kindly provided by Institute of Materia Medica, Chinese Academy of Medical Sciences and Peking Union Medical College. Fagomine (FA, purity > 98.0%) was obtained from MedChemExpress (Shanghai, China). 1,4-dideoxy-1,4-imino-D-arabinitol (DAB, purity > 98.0%), dexamethasone (DEX), 3-isobutyl-1-methylxanthine (IBMX) and insulin were purchased from Sigma-Aldrich (St Louis, MO, USA). Palmitic acid (PA) was purchased from Beijing Solarbio Science & Technology Co., Ltd. (Beijing, China). β-actin, AMPK, p-AMPK, ACC, p-ACC, peroxisome proliferator activated receptor γ (PPARγ), uncoupling protein 2 (UCP2), and adiponectin primary antibodies were purchased from Cell Signaling Technology (Danvers, MA, USA, cat nos.: 4970, 2532, 2535, 3676, 11818, 9475, 2435, 89326, and 2789, respectively). Peroxisome proliferator-activated receptor-α (PPARα) and peroxisome proliferator-activated receptor-γ co-activator 1α (PGC1α) primary antibodies were obtained from Abcam (Cambridge, MA, USA, cat nos.: ab126285 and ab54481, respectively). 2.2. Experimental Animals and Treatment All animal care and experimental procedures were approved by Beijing Laboratory Animal Research Center (ethical code: 2020001). Six-week-old male C57BL/6j mice were housed at 24 °C with a 12 h light/dark cycle. After 1 week of acclimatization to the environment, the mice were randomly divided into eight groups: a normal control group (NC; n = 10), an HFD control group by intragastrical administration of saline (HFD i.g.; n = 10), the SZ-A treatment groups by intragastrical administration (SZ-A 100; n = 10, SZ-A 200; n = 10, SZ-A 300; n = 10, SZ-A 400; n = 10), an HFD control group by peritoneal injection (HFD i.p. n = 10), and an SZ-A treatment group by peritoneal injection (SZ-A 200; n = 10). The mice in the NC group were given a standard diet, and the mice in other groups were fed with HFD (Research Diet, Cat No: D12492) for 14 weeks. Then the mice were given saline i.p., saline i.g., SZ-A 100 mg/kg/d i.g., SZ-A 300 mg/kg/d i.g., SZ-A 400 mg/kg/d i.g., and SZ-A 200 mg/kg/d i.p. for 6 weeks, respectively. Mice in the HFD and treatment groups were fed with HFD during the treatment. Bodyweights were measured weekly during the experimental period. Food intake was measured per cage. At the end of these experiments, mice were fasted overnight before being euthanized. Blood samples were collected and then kept at room temperature for half an hour before centrifugation at 3000 rpm for 15 min to obtain the serum samples. Tissues including liver, abdominal adipose tissue, perirenal fat, and subcutaneous fat were carefully collected, kept in liquid nitrogen, and then stored at −80 °C until analysis. Total body fat was measured using a Pharma Scan 70/16 US small animal MRI (Bruker, Ettlingen, Germany). 2.3. Serum Biochemical Parameters Serum total cholesterol (CHO), low-density lipoprotein cholesterol (LDL-C), C-reactive protein (CRP), high-density lipoprotein cholesterol (HDL-C), aspartate aminotransferase (AST), and alanine aminotransferase (ALT) levels were measured using automatic biochemistry analyzer (TOSHIBA TBA-40FR, Tokyo, Japan) with appropriate commercial assay kits from Biosino Biotechnology and Science Inc. (Beijing, China). Serum leptin level was determined using a mouse leptin ELISA kit (R&D Systems, Minneapolis, MN, USA) according to the manufacturer’s instruction. ### 2.4. Hepatic Lipid and Antioxidant Measurement The frozen liver tissues were homogenized in cold PBS (pH 7.4). The suspension was centrifuged at 3000 × g for 5 min at 4 °C, and the supernatant was collected for the assay. Hepatic total cholesterol (TC) and triglyceride (TG) were determined by COD-PAP and GPO-PAP with the commercial kits (Nanjing Jiancheng Bioengineering Institute, Nanjing, China). To measure the hepatic lipid peroxidation, the liver malondialdehyde (MDA) concentrations were monitored using a thiobarbituric acid reactive substances (TBARS) assay kit (Applygen Technologies Inc., Beijing, China), and calculated using a standard curve. The reduced glutathione (GSH) content was determined using a thiol-specific reagent, dithionitrobenzoic acid, according to the manufacturer’s protocol (Nanjing Jiancheng Bioengineering Institute, Nanjing, China), and the adduct was measured at 420 nm. Glutathione peroxidase (GPx) activity was determined using a glutathione peroxidase assay kit (Nanjing Jiancheng Bioengineering Institute, Nanjing, China). In brief, the activity of GPx was measured using the assay kit based on the principle that oxidation of glutathione and H₂O₂ could be catalyzed by GPx to produce oxidized glutathione (GSSG) and H₂O. According to the xanthine oxidase method, the activity of superoxide dismutase (SOD) was determined by superoxide dismutase activity colorimetric assay kit using water-soluble tetrazolium salt (Nanjing Jiancheng Bioengineering Institute, Nanjing, China). The concentration of proteins was estimated using a bicinchoninic acid (BCA) assay kit (Thermo Fisher Scientific, Waltham, MA, USA). ### 2.5. Histological Analysis Fresh liver tissue, inguinal adipose tissue (iWAT), epididymal adipose tissue (eWAT), and brown adipose tissue (BAT) were fixed in 10% paraformaldehyde solution, embedded in paraffin wax, and cut at 5 µm for hematoxylin–eosin (H&E) staining. Liver sections of each animal with volumes of approximately 1 cm³ were excised and placed in a tissue container, which was then filled with Tissue-Tek OCT compound gel (Sakura Finetek, CA, USA) and frozen in liquid nitrogen. The frozen samples were cut into 7 µm slices and stained with Oil Red O solution (Baso diagnostics Inc, Zhuhai, China) for evaluation of fat accumulation. After removing the staining solution with 70% ethanol and distilled water, the sections were counterstained by hematoxylin for 2 min, washed in tap water for another 5 min, and mounted with glycerin. Images of stained liver sections were obtained with an Olympus microscope–camera system. In order to observe the ultrastructure of liver, a small part of liver tissue was fixed in glutaraldehyde solution (2.5%) for 4 h at 4 °C and post-fixed in 1% osmic acid with 0.1 M phosphate buffer for 1 h at 4 °C. After dehydration, infiltration, and embedding, liver tissue samples were cut and stained with uranyl acetate. Images were taken under a transmission electron microscope (TEM; Hitachi H7650, Tokyo, Japan) at 80 kV. ### 2.6. Cell Culture and Differentiation Human hepatocellular carcinoma cell line (HepG2 cells) and 3T3-L1 cell line were obtained from the Cell Resource Center, Peking Union Medical College (which is the headquarter of National Infrastructure of Cell Line Resource, NSTI). The HepG2 cells were cultured in DMEM supplemented with 10% FBS and 1% penicillin/streptomycin, and maintained in 100 mm dishes in the presence of 5% CO₂ at 37 °C. The PA-induced medium was prepared with serum-free DMEM using the methods described by Arwa et al. [26]. A 100 mmol/L stock solution of PA was prepared in ethanol and then conjugated to 1% fatty acid free-bovine serum albumin (BSA). The cells were treated with different concentrations of SZ-A by adding appropriate amounts of the PA/BSA conjugate to the cultured cells in DMEM media. 3T3-L1 pre-adipocytes were grown to confluence in DMEM containing 10% calf serum and 1% penicillin–streptomycin for 4 days. Then the cells were induced to differentiate with DMEM containing 10% (v/v) fetal bovine serum, 1 µmol/L DEX, 10 µg/mL insulin, and 0.5 mmol/L IBMX every 2 days for an additional 4 days. Cells were incubated with fresh DMEM containing 10% fetal bovine serum and 10 mg/mL insulin for another 2 days. Finally, the media were replaced with DMEM containing only 10% FBS and 1% penicillin-streptomycin for 2 days, after which the cells were used. 2.7. Cellular Lipid Analysis HepG2 cells were plated in 6-well plates at $4 \times 10^5$ cells per well for 24 h. SZ-A (12.5, 25, and 50 µg/mL), DNJ (40 µg/mL), FA (10 µg/mL), DAB (10 µg/mL), and 0.125 mmol/L PA were added in the culture medium at the same time for 24 h. The cells were washed with PBS and lysed in lysis buffer (1% Triton X-100 and 1% PMSF in PBS) for 4 h at 4 °C. The TG level of the cells was measured by GPO-PAP (Nanjing Jiancheng Bioengineering Institute, Nanjing, China). The protein concentrations were measured using BCA, and results were expressed as a fold change of intracellular TG level compared to the non-treated control. 2.8. Glucose Consumption and Glycogen Concentration Measurement Glucose consumption and cellular glycogen concentration in HepG2 cells was assessed according to the previous report with a few modifications [27]. In short, cells cultured in six-well plates were treated with PA in the presence of SZ-A (12.5–50 µg/mL). After the treated HepG2 cells were incubated for 24 h, glucose content in the culture medium was measured by glucose oxidase using a glucose assay kit (Nanjing Jiancheng Bioengineering Institute, Nanjing, China). For the measurement of cellular glycogen, each group of cells was counted. The glycogen content of HepG2 cells was detected by anthrone–sulfuric acid using a glycogen assay kit (Nanjing Jiancheng Bioengineering Institute, Nanjing, China). Briefly, HepG2 cells were digested and centrifuged at 1000 rpm for 10 min, and the precipitates were transferred to glass tubes with 0.2 mL of alkaline liquor. Samples were incubated in boiling water for 10 min and diluted with distilled water. Thereafter, 1 mL of a colored-substrate solution and samples were incubated in boiling water for 5 min, according to the instructions. The absorbance values were measured at 620 nm by a microplate photometer (MultiSkan FC, Thermo Fisher Scientific, Rockville, MD, USA). 2.9. Supernent Adiponectin Measurement The 3T3-L1 cells were seeded into 6-well plates at $2 \times 10^4$ cells/mL and induced as described in cell culture and differentiation protocol. The differentiated 3T3-L1 preadipocytes were treated with different concentrations of SZ-A (100, 200 µg/mL), DNJ (40, 80 µg/mL), FA (10, 20 µg/mL), and DAB (10, 20 µg/mL) during differentiation. On the last day of the differentiation process, the media were collected, and concentrations of adiponectin were measured by ELISA (Elabscience, Wuhan, China). 2.10. Total RNA Preparation and Real-Time PCR Analysis Total RNA was isolated from liver tissues using TRIzol® (Invitrogen, Carlsbad, CA, USA). RNA was quantified by a Nano-300 Micro-Spectrophotometer (AllSheng, Hangzhou, China), and 1 µg RNA was reverse transcribed into cDNA using a reverse transcription system (Promega, Madison, WI, USA) according to the manufacturer’s protocol. The PCR amplification protocol consisted of 30 s at 95 °C, 10 s at 95 °C, and 30 s at 60 °C for 40 cycles. The purity of the PCR products was determined by melting curve analysis. The relative amount of each gene was calculated using $2^{-\Delta\Delta CT}$. The level of transcripts was normalized, using β-actin as an internal standard. The primers used are provided in Table S1. 2.11. Western Blot HepG2 cells, liver tissue, and iWAT were lysed in ice-cold lysis buffer containing protease inhibitor cocktail (Roche, Basel, Switzerland) and 1 mmol/L phenylmethanesulfonyl fluoride (PMSF) for 30 min, and were subjected to centrifugation at 10,000×g for 30 min at 4 °C. The protein concentration was detected by BCA assay. Equal amounts of protein samples were separated by 10% SDS-PAGE and transferred to polyvinylidene difluoride membranes. The membranes were blocked with blocking buffer (10% blocker... milk in PBS) for 1 h and incubated with first antibodies including β-actin (1:1000), p-AMPK (1:1000), AMPK (1:1000), PPARα (1:1000), PPARγ (1:1000), PGC1α (1:1000), adiponectin (1:1000), and UCP2 (1:1000) overnight at 4 °C, then washed three times with Tris-buffered saline with Tween 20 (TBST) and incubated with the secondary antibody conjugated to anti-mouse (1:5000) or anti-rabbit (1:5000) HRP-conjugated secondary antibodies for 1 h. Bands were detected using enhanced chemiluminescence (ECL) and visualized by Tanon-4600SF chemiluminescence imager (Tanon Science & Technology Co., Ltd., Shanghai, China). 2.12. RNA Sequencing and Data Analysis RNA extraction and RNA-seq analysis were carried out by Novogene (Beijing, China). Briefly, total RNA from liver tissues was isolated using TRIzol reagent according to the manufacturer’s instructions, and RNA integrity was assessed using the RNA Nano 6000 Assay Kit of the Bioanalyzer2100 system (Agilent Technologies, Santa Clara, CA, USA). The mRNA was purified using poly-T oligo-attached magnetic beads. After fragmentation, libraries were constructed using NEBNext® Ultra™ RNA Library Prep Kit for Illumina® according to the manufacturer’s instructions. Library quality was checked using the Agilent Bioanalyzer 2100 system. After cluster generation, the library was sequenced using an Illumina Novaseq platform, and 150 bp paired-end reads were generated. RNA sequencing data have been submitted to the Gene Expression Omnibus (GEO) under accession number (GSE199105). High quality reads were aligned to the Ensemble mouse (mm10/GRCm38) reference genomes with HISAT2 (version 2.0.5) software. Differential expression analysis was performed using the DESeq2 R package (1.20.0). The resulting p-values were adjusted using Benjamini and Hochberg’s approach for controlling the false discovery rate. Transcripts with a Padj <0.05 and a fold change >1.2 were assigned as differential expression genes (DEGs). Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analyses of DEGs were implemented by Novogene (Beijing, China). 2.13. Software and Statistical Analysis Image J software (NIH, Bethesda, MD, USA) was used to quantify the relative expression of proteins and adipocyte area. Graphs were produced using Prism 8 software (GraphPad Software Inc., San Diego, CA, USA). Numeric results are expressed as the mean ± SEM. Two experimental groups were analyzed using unpaired two-tailed Student’s t-test. Multiple groups were compared using one-way or two-way analysis of variance (ANOVA) followed by the Tukey’s test depending on the experiments. Differences where p < 0.05 were considered statistically significant. 3. Results 3.1. SZ-A Protects Mice from Hfd-Induced Obesity To examine the therapeutic effects of SZ-A on obesity and NAFLD, 6-week-old C57 mice were fed an HFD for 14 weeks and administered SZ-A (i.g.) for an additional 6 weeks with continuous HFD feeding (Figure 1A). After feeding the HFD, the bodyweight of the HFD group was significantly increased compared to that of the normal chow diet-fed control group. SZ-A protected the mice from HFD-induced obesity in a dose-dependent manner, with SZ-A (400 mg/kg) showing the most significant effect (Figure 1B). Next, we measured the total body fat mass using magnetic resonance imaging (MRI). Remarkably, administration of 400 mg/kg SZ-A reduced total fat mass (Figure 1C). However, food consumption was not altered by SZ-A treatment compared to the HFD control group (Figure 1D). The increased fasting blood glucose levels in the HFD-fed mice were significantly reduced by SZ-A (Figure 1E). In addition, treatment with SZ-A markedly reduced total cholesterol (CHO) and low-density lipoprotein cholesterol (LDL-C) levels in HFD-fed mice (Figure 1F,G). Compared with the NC group, HFD mice developed leptin resistance, which led to a compensatory increase in serum leptin levels. SZ-A-treated mice showed reduced serum leptin levels, which reflected increased leptin sensitivity (Figure 1H). These results show that SZ-A protects mice from obesity and hyperlipidemia. Figure 1. Effect of SZ-A on HFD-induced obesity. (A) Schematic diagram of the experimental procedure used to examine the protective effects of SZ-A on mice fed with HFD. HFD-fed mice were intragastrically administered (i.g.) saline or SZ-A (100, 300, and 400 mg/kg) once daily. (B) Bodyweight of mice treated with SZ-A (100, 300, and 400 mg/kg). (C) Total fat mass, (D) food consumption and (E) fasting blood glucose of mice. Effects of SZ-A (400 mg/kg) on serum levels of CHO (F), LDL-C (G), and leptin (H). Values are expressed as mean ± SEM (n = 10/group). ### p < 0.001 compared with the NC group (i.g.), and * p < 0.05, ** p < 0.01 compared with the HFD control group. NC, normal control; HFD; HFD, high-fat diet; SZ-A, Ramulus Mori (Sangzhi) alkaloids; TC, total cholesterol; LDL-C, low-density lipoprotein cholesterol. ### 3.2. SZ-A Stimulates Adiponectin Expression in Adipocytes Next, we examined the direct effect of SZ-A on adipose tissue and adipocytes. Fewer immune cells infiltrated the eWAT of the SZ-A-treated mice (Figure 2A). BAT from SZ-A-treated mice was redder in color and showed less lipid accumulation than BAT from HFD control mice (Figure 2A). Adipocyte size analysis in iWAT revealed that the area of the enlarged adipocytes in HFD-fed mice was considerably reduced in SZ-A-treated mice, while the adipocyte area in eWAT was not altered by SZ-A (Figure 2B). PPARα is a nuclear transcription factor regulating lipid metabolism. Western blot showed that PPARα expression in iWAT was increased by SZ-A treatment (Figure 2C). Adiponectin is an important adipokine, secreted mainly by adipocytes, that exerts anti-inflammatory and insulin-sensitizing effects by binding to its receptors. The expression of adiponectin in iWAT was increased by SZ-A treatment (Figure 2D). Treatment of differentiating 3T3-L1 cells with SZ-A, DNJ, or DAB resulted in increased secretion of adiponectin into the culture medium (Figure 2E). These results indicate that SZ-A might exert its protective effects on obesity in mice by enhancing fatty acid oxidation. The weight loss effect of SZ-A improves systemic metabolism in mice. were upregulated in the liver of the HFD group, and treatment with SZ-A significantly modulated the expression of these genes towards normal levels (Figure 3I). Markers of inflammation, and fibrosis. Liver weight and serum alanine aminotransferase (ALT), aspartate aminotransferase (AST), and C-reactive protein (CRP) levels were significantly elevated in mice administered an HFD diet. Here, we found that the serum levels of ALT, AST, and CRP were lower in SZ-A-treated mice than in control HFD mice (Figure 3A–C). Liver weight and hepatic triglyceride and total cholesterol levels were significantly reduced by SZ-A (Figure 3D–F). To determine the protective effects of SZ-A on fatty liver, liver sections were examined using hematoxylin and eosin (H&E) and Oil Red O staining. Histological results revealed that liver tissues were damaged by severe steatohepatitis, microvesicular fatty changes, and hypertrophy induced by HFD. SZ-A administration markedly blocked histopathological changes and reduced the number of hepatic lipid droplets (Figure 3G). 3.3. SZ-A Alleviates Hepatic Steatosis and Injury in Mice NAFLD is characterized by lipid overload, oxidative stress-induced cellular damage, inflammation, and fibrosis. Liver weight and serum alanine aminotransferase (ALT), aspartate aminotransferase (AST), and C-reactive protein (CRP) levels were significantly elevated in mice administered an HFD diet. Here, we found that the serum levels of ALT, AST, and CRP were lower in SZ-A-treated mice than in control HFD mice (Figure 3A–C). Liver weight and hepatic triglyceride and total cholesterol levels were significantly reduced by SZ-A (Figure 3D–F). To determine the protective effects of SZ-A on fatty liver, liver sections were examined using hematoxylin and eosin (H&E) and Oil Red O staining. Histological results revealed that liver tissues were damaged by severe steatohepatitis, microvesicular fatty changes, and hypertrophy induced by HFD. SZ-A administration markedly blocked histopathological changes and reduced the number of hepatic lipid droplets (Figure 3G). Next, we examined the effects of SZ-A on inflammation and fibrosis. Macrophage markers (F4/80 and CD68) and pro-inflammatory cytokines (tumor necrosis factor alpha (TNFα) and monocyte chemoattractant protein-1 (MCP1)) were significantly upregulated in the livers of HFD-fed mice. However, mRNA expression levels of macrophage markers and cytokines were attenuated in the SZ-A group (Figure 3H). Lectin, galactoside-binding, soluble 1 (Lgals1) and lectin, galactoside-binding, soluble, 3 (Lgals3), two members of the galectin family that reflect liver damage, were repressed by SZ-A (Figure 3I). Fibrosis-related genes collagen type I alpha 1 chain (Col1a1), collagen type I alpha 2 chain (Col1a2), collagen type III alpha 1 chain (Col3a1), and collagen type VI alpha 3 chain (Col6a3) were upregulated in the liver of the HFD group, and treatment with SZ-A significantly modulated the expression of these genes towards normal levels (Figure 3I). Markers of NASH-like tissue inhibitors of metalloproteinase-1 (Timp1), vimentin (Vim), matrix metallopeptidase 2 (Mmp2), and matrix metallopeptidase 9 (Mmp9) were significantly reduced by SZ-A (Figure 3I). These results suggest that supplementation with SZ-A at a dose of... 400 mg/kg/day restored impaired liver function and suppressed inflammation and fibrosis in mice suffering from HFD-induced oxidative toxicity. Figure 3. SZ-A alleviates hepatic steatosis and injury in mice fed with HFD. Effects of SZ-A on serum ALT (A), AST (B), and C-reactive protein (C) (n = 10/group). (D–F) Liver weight, hepatic triglyceride (TG), and total cholesterol (TC) in the three groups of mice (n = 10/group). (G) Histology of the livers stained with hematoxylin–eosin (H&E) and Oil Red O (scale bar, 200 μm). Relative mRNA expression levels of pro-inflammatory cytokines (H) and fibrosis (I) in livers (n = 6/group). Data are represented as mean ± SEM (n = 10/group). #p < 0.05, ##p < 0.01, ###p < 0.001 compared with the NC group (i.g.), and p < 0.05, p < 0.01, *p < 0.001 compared with the HFD group (i.g.). NC, normal control; HFD, high-fat diet; SZ-A, Ramulus Mori (Sangzhi) alkaloids; ALT, alanine aminotransferase; AST, aspartate aminotransferase; CRP, C-reactive protein; H&E, hematoxylin and eosin staining; TNFα, tumor necrosis factor alpha; MCP1, monocyte chemoattractant protein-1; Lgals1, lectin, galactoside-binding, soluble, 1; Lgals3, lectin, galactoside-binding, soluble, 3; Col1a1, collagen type I alpha 1 chain; Col1a2, collagen type I alpha 2 chain; Col3a1, collagen type III alpha 1 chain; Col6a3, collagen type VI alpha 3 chain; Timp1, tissue inhibitors of metalloproteinase-1; Vim, vimentin; Mmp2, matrix metalloproteinase 2; Mmp9, matrix metalloproteinase 9. 3.4. Intraperitoneal Administration of SZ-A Protects against Obesity and NAFLD To test whether SZ-A exhibited therapeutic effects outside the intestinal tract, HFD-fed mice were administered SZ-A (200 mg/kg) daily via intraperitoneal injection for 6 weeks. Bodyweight was significantly reduced by SZ-A at 200 mg/kg (Figure 4A), which was more effective in bodyweight control than intragastric administration. Serum ALT, AST, and TC levels were lower in SZ-A-treated mice than in HFD mice (Figure 4B–D). In addition, liver weight and hepatic TG levels were significantly decreased by intraperitoneal administration of SZ-A (Figure 4E,F). RT-PCR also showed that intraperitoneal administration of SZ-A decreased the mRNA levels of genes related to inflammation (MCP1 and TNFα) and fibrosis (Lgals1, Lgals3, Col1a1, Col3a1, and Timp1) (Figure 4G). These results show that the protective effects of SZ-A against HFD-induced obesity and NAFLD were independent of the inhibition of $\alpha$-glucosidase. Figure 4. Intraperitoneal administration of SZ-A exerts a protective effect. (A) Bodyweight of HFD mice with intraperitoneal administration (i.p.) of saline and SZ-A (200 mg/kg) $(n = 10\text{/group})$. Effects of SZ-A on serum levels of ALT (B), AST (C), and CHO (D) are shown. Liver weight (E) and hepatic triglyceride levels (F) of mice are shown. (G) Relative mRNA expression of genes involved in inflammation and fibrosis in livers. Data are represented as mean ± SEM. # $p<0.05$, ## $p<0.01$, ### $p<0.001$ compared with the NC group (i.p.), and $p<0.05$, $p<0.01$, * $p<0.001$ compared with the HFD group (i.p.). NC, normal control; HFD, high-fat diet; SZ-A, $Sangzhi$ alkaloids; ALT, alanine aminotransferase; AST, aspartate aminotransferase; TC, total cholesterol; TG, triglyceride; TNF$\alpha$, tumor necrosis factor alpha; MCP1, monocyte chemoattractant protein-1; Lgalsl1, lectin, galactoside-binding, soluble, 1; Lgalsl3, lectin, galactoside-binding, soluble, 3; Col1a1, collagen type I alpha 1 chain; Col1a2, collagen type I alpha 2 chain; Col3a1, collagen type III alpha 1 chain; Col6a3, collagen type VI alpha 3 chain; Timp1, tissue inhibitors of metalloproteinase-1. 3.5. Functional Analysis of Differentially Expressed Genes and Pathways in the Liver Tissues of NC, HFD Control, and SZ-A Groups To determine the transcriptional changes induced by SZ-A, we performed RNA-seq on the liver tissues of NC, HFD control, and SZ-A-treated HFD mice $(n = 6\text{ per group})$. A total of 436 genes were differentially expressed (FDR < 0.05, fold change > 1.2; Figure 5A) between the HFD control and SZ-A group, of which 174 genes were upregulated and 262 were downregulated. To identify the main biological pathways affected by SZ-A, we performed bioinformatic analysis. Gene ontology (GO) enrichment analysis showed that pathways involved in lipid transport and metabolism (cellular response to lipoprotein particle stimulus, lipid transport, lipid biosynthetic process, regulation of lipid localization), oxidative (superoxide metabolic process), inflammation (chemotaxis, cell activation involved in immune response, MyD88-dependent toll-like receptor signaling pathway), and fibrosis (extracellular structure organization, extracellular matrix organization) were significantly affected by SZ-A (Figure 5B). The top 20 pathways enriched from the DEGs in the livers from the HFD control and SZ-A group according to KEGG analysis are shown in Figure 5C. Lipid metabolism pathways including PPAR signaling pathway, cholesterol metabolism, and fatty acid metabolism were enriched. The top 20 upregulated and downregulated genes are shown in Figure 5D. SZ-A treatment significantly decreased mRNA levels of lipid uptake genes (CD36), proinflammatory genes (C-X-C motif chemokine ligand 9 (Cxcl9) and interferon alpha-inducible protein 27-like protein 2A (Ifi27l2a)), and fibrosis genes (Col1a1, Col3a1, and Col1a2) in the liver (Figure 5D). These results revealed that genes and pathways of lipid metabolism and metabolic stress-induced liver injury in mice were regulated by SZ-A. Figure 5. Gene expression signatures of SZ-A-treated mice. (A) Volcano plot of the differentially expressed genes (Padj < 0.05, fold change > 1.2) in livers of HFD control and SZ-A group (n = 6 per group). Red and blue represent high and low expression of genes in the SZ-A group, respectively. (B) GO analysis of biological processes related to NAFLD of differentially expressed genes. (C) The 20 highest-ranking terms from KEGG analysis of all differentially expressed genes (Padj < 0.05, fold change > 1.2) are shown. (D) Heatmap of the top 20 upregulated and downregulated genes is shown (Padj < 0.05). NC, normal control; HFD, high-fat diet; SZ-A, Ramulus Mori (Sangzhi) alkaloids. 3.6. SZ-A Protects Mice from Oxidative Stress Induced by HFD Oxidative stress stimulated by lipid overload is harmful to cells. MDA is a biomarker of lipid peroxidation. Cellular MDA levels reflect the degree of oxidative stress. We found that hepatic MDA in SZ-A-treated mice was lower than that of the HFD control group (Figure 6A). To evaluate the superoxide metabolic process, the functions of liver antioxidants in HFD-fed mice were measured. In the HFD group, the levels of SOD, GSH, and GPx were significantly downregulated compared with those in the control group (Figure 6B–D). SZ-A treatment restored the antioxidant capacity of the liver to normal levels. The homeostasis of energy metabolism is mainly regulated by mitochondria. Overload of free fatty acid into mitochondria leads to increased ROS production and alteration of mitochondrial functions. Transmission electron microscopy (TEM) analysis of liver sections showed that HFD induced a significant decrease in mitochondrial cristae density and mitochondria swelling. The mitochondrial double membrane structure and cristae damage induced by the HFD diet was ameliorated by SZ-A (Figure 6E). These results showed that SZ-A protected mice from oxidative damage induced by lipid overload. To further verify the mechanisms of action of SZ-A in hepatic steatosis, the expression of genes involved in lipid production and consumption was evaluated. Quantitative PCR assays showed that the hepatic mRNA levels of genes related to fatty acid uptake and synthesis (CD36 and peroxisome proliferator-activated receptor γ (PPARγ)) were significantly diminished after SZ-A treatment. Moreover, the mRNA levels of lipid β-oxidation genes (proliferator-activated receptor-α (PPARα) and PGC1α) were increased in SZ-A-treated mice (Figure 7A). SZ-A intervention also had a positive effect on liver adiponectin receptor expression. In particular, the mRNA levels of adiponectin receptor 1 (AdipoR1) and adiponectin receptor 2 (AdipoR2) were significantly higher in the SZ-A group than in the HFD group, which may mediate adiponectin/AMPK signaling (Figure 7B). Proteins involved in lipid metabolism were also evaluated (Figure 7C,D). The protein levels of the lipogenic gene PPARγ were highly upregulated by HFD, and SZ-A (400 mg/kg) significantly downregulated its expression. AMPK activation reduces NAFLD by regulating de novo lipogenesis, fatty acid oxidation, and promoting mitochondrial function. We found that SZ-A regulated lipid metabolism by increasing the protein levels of p-AMPK and p-ACC. Lipid β-oxidation proteins such as PGC1α and PPARα were markedly higher in the livers of the SZ-A group than those in the HFD group. Besides, SZ-A repressed uncoupling protein 2 (UCP2) expression in protein levels. Our results demonstrate that SZ-A treatment resulted in the activation of AMPK and upregulation of PPARα and PGC1α expression to improve β-oxidation of fatty acids. 3.8. SZ-A Regulates Lipid Accumulation and AMPK Signaling in HepG2 Cells Treated with Palmitic Acid To investigate the direct effects of SZ-A on hepatocytes, HepG2 cells stimulated with PA were used as models of insulin resistance and lipid accumulation. PA-stimulated HepG2 cells developed insulin resistance. Compared to the PA group, SZ-A significantly increased glycogen content and glucose consumption in HepG2 cells (Figure 8A,B). We also assessed the inhibitory effects of SZ-A on PA-induced intracellular lipid accumulation. in HepG2 cells. As shown in Figure 8C, SZ-A treatment resulted in a dose-dependent reduction in intracellular TG content. The main alkaloids in SZ-A are DNJ, FA, and DAB. The concentrations of the three ingredients were determined according to their proportions in SZ-A. In PA-stimulated HepG2 cells, both DNJ and DAB significantly decreased the intracellular lipid content, whereas the intracellular lipid content of the FA-treated group was inconspicuous (Figure 8D). SZ-A and DNJ markedly increased AMPK and ACC phosphorylation in PA-induced HepG2 cells. In addition, DAB markedly increased the phosphorylation of ACC, but FA had no obvious effect on the ratio of ACC phosphorylation (Figure 8E). These results indicate that SZ-A improved lipid metabolism by activating AMPK and inactivating ACC, which was mainly attributed to DNJ and DAB. Figure 7. SZ-A regulates lipid metabolism and oxidative stress. (A,B) Relative mRNA expression levels of genes, including CD36, PPARγ, PPARα, PGC1α, AdipoR1, and AdipoR2. (C,D) Hepatic PPARγ, p-AMPK, p-ACC, PGC1α, PPARα, and UCP2 protein expression were detected by Western blot with specific antibodies. Data are represented as mean ± SEM (n = 6/group). # p < 0.05, ## p < 0.01 compared with the NC mice (i.g.), and * p < 0.05, ** p < 0.01 compared with the HFD mice (i.g.). NC, normal control; HFD, high-fat diet; SZ-A, Ramulus Mori (Sangzhi) alkaloids; AMPK, AMP-activated protein kinase; ACC, acetyl-CoA carboxylase; p-AMPK, phospho-AMP-activated protein kinase; p-ACC, phospho-acetyl-CoA carboxylase; PPARγ, peroxisome proliferator-activated receptor γ; PPARα, proliferator-activated receptor-α; PGC1α, peroxisome proliferator-activated receptor-γ co-activator 1α; UCP2, uncoupling protein 2. reduction in intracellular TG content. The main alkaloids in SZ-A are DNJ, FA, and DAB. The concentrations of the three ingredients were determined according to their proportions in SZ-A. In PA-stimulated HepG2 cells, both DNJ and DAB significantly decreased the intracellular lipid content, whereas the intracellular lipid content of the FA-treated group was inconspicuous (Figure 8D). SZ-A and DNJ markedly increased AMPK and ACC phosphorylation in PA-induced HepG2 cells. In addition, DAB markedly increased the phosphorylation of ACC, but FA had no obvious effect on the ratio of ACC phosphorylation (Figure 8E). These results indicate that SZ-A improved lipid metabolism by activating AMPK and inactivating ACC, which was mainly attributed to DNJ and DAB. Figure 8. SZ-A regulates the AMPK signaling pathway in HepG2 cells. HepG2 cells were treated with PA (0.125 mmol/L) and/or SZ-A (12.5, 25, or 50 μg/mL), DNJ (40 μg/mL), FA (10 μg/mL), and DAB (10 μg/mL) for 24 h. Glucose consumption (A) and glycogen content (B) of each group was measured. (C, D) Levels of TGs in primary hepatocytes in the indicated groups. (E) Protein expression levels of p-AMPK, AMPK, p-ACC, ACC, and β-actin in HepG2 cells were analyzed by Western blot. β-Actin was used as an internal reference. Data are shown as the mean ± SEM (n = 4/group). # p < 0.05, ## p < 0.01 compared with cells treated with medium only, and * p < 0.05, p < 0.01 vs. cells treated with PA. TG, triglyceride; SZ-A, Ramulus Mori (Sangzhi) alkaloids; DNJ, 1-deoxynojirimycin; DAB, 1,4-dideoxy-1,4-imino-D-arabinitol; FA, fagomine; BSA, bovine serum albumin; PA, palmitic acid; AMPK, AMP-activated protein kinase; ACC, acetyl-CoA carboxylase; p-AMPK, phospho-AMP-activated protein kinase; p-ACC, phospho-acetyl-CoA carboxylase. 3.9. Graphic Illustration of the Mechanism Underlying SZ-A-Mediated Improvement of HFD-Induced Obesity and NAFLD Mice develop obesity and NAFLD when fed with HFD. Excessive lipids accumulate in the adipose tissue, which leads to obesity. Ectopic lipid accumulation in the liver induces oxidative stress and liver injury. Chronic inflammation and fibrosis occur because of metabolic stress. SZ-A is a group of alkaloids that undergo rapid distribution in liver and adipose tissues after administration. The weight-loss effect of SZ-A was partly mediated by activation of PPARα. Reduced fat mass is beneficial for systemic improvement of metabolism. SZ-A stimulates adiponectin expression and secretion, which mediates the crosstalk between liver and adipose tissue. AMPK is activated in the liver and HepG2 cells by direct and indirect effects of SZ-A. The phosphorylation of ACC by p-AMPK inhibits the function of ACC to inhibit lipogenesis and enhance lipid β-oxidation. PPARα and PGC1α are also increased in the liver. In conclusion, SZ-A protects mice from NAFLD through direct effect on hepatocytes and indirect effect mediated by weight loss. AMPK and PPAR signaling are involved in the protective effects of SZ-A (Figure 9). ![Figure 9. Graphic illustration of the mechanism underlying the SZ-A-mediated improvement of HFD-induced obesity and NAFLD. SZ-A is distributed in the liver and adipose tissue after intragastrical and intraperitoneal administration. SZ-A protects mice from HFD-induced obesity without affecting food consumption. The weight-loss effect contributes partly to the protective effect on NAFLD. Besides, SZ-A may also have direct effects on hepatocytes. AMPK and PPAR signaling pathways are involved in the protective effect. SZ-A, Ramulus Mori (Sangzhi) alkaloids; Ad, adiponectin; AMPK, AMP-activated protein kinase; ACC, acetyl-CoA carboxylase; PGC1α, peroxisome proliferator-activated receptor-γ co-activator 1α; PPARα, proliferator-activated receptor-α; FFA, free fatty acid. Dashed lines indicate indirect effect. Created in BioRender.com, accessed on 4 April 2022.] 4. Discussion NAFLD, obesity, and T2DM are common manifestations of metabolic syndrome that shares the same mechanisms, such as hyperlipidemia, insulin resistance, hyperglycemia, and inflammation. Increased hepatic gluconeogenesis promotes insulin resistance and T2DM, further aggravating NAFLD. Excessive fat leads to hypertrophy of adipocyte cells, necrosis, inflammation of adipose tissue, and increased FFA in the liver, which are risk factors for NAFLD [28]. SZ-A, the extract of Morus alba L., has been shown to reduce hyperglycemia in patients [24] and was approved for T2DM treatment in 2020, including the regulation of α-glucosidases, insulin sensitivity, microbiota, and inflammation. However, the therapeutic effects of SZ-A on HFD-induced liver injury have not yet been studied. In the present study, we used mice induced by HFD for 14 weeks as a model, followed by administration of SZ-A for another 6 weeks to study the therapeutic effect of SZ-A. We found that SZ-A ameliorated HFD-induced obesity and inhibited the increase in serum total cholesterol levels. Liver FFAs are derived from adipose tissue lipolysis, de novo lipogenesis, and diet. The fates of FFAs are β-oxidation and triglycerides formation. Excessive FFAs in the liver induce lipotoxicity when their supply and disposal are disturbed [14]. We found that SZ-A inhibited CD36 and PPARγ mRNA expression and promoted PPARα mRNA expression, suggesting that SZ-A may decrease hepatic lipid accumulation and steatosis by inhibiting de novo lipogenesis and fatty acid uptake, while promoting β-oxidation. Excessive fatty acids are toxic to hepatocytes by inducing inflammation and, ultimately, fibrosis. In our study, mRNA expression of inflammatory markers such as TNFα, MCP1, F4/80, and CD68 was restrained by SZ-A. Additionally, genes associated with collagen production, such as Col1a1, Col3a1, and Timp1, were downregulated by SZ-A. These results show that SZ-A has therapeutic effects on NAFLD in mice by inhibiting hepatic steatosis, inflammation, and fibrosis. To further investigate the target tissues that mediate the protective effect of SZ-A on obesity and NAFLD, SZ-A was intraperitoneally administered to HFD-induced mice for 6 weeks. We found that the bodyweight of mice treated with SZ-A was significantly lower than that of mice in the control group. Serum ALT and AST levels, hepatic steatosis, inflammation, and fibrosis were also reduced. These results imply that SZ-A may exert a protective effect on organs other than the intestinal tract. It has been reported that the major distribution tissues of DNJ, FA, and DAB are the gastrointestinal tract, liver, and kidney, which provide a rational basis for the direct effect in these tissues [25]. Here, we focused on the direct effects of SZ-A and its major constituents, DNJ, FA, and DAB, on hepatocytes and adipocytes. PA induces lipid accumulation and insulin resistance in hepatocytes. In vitro studies revealed that SZ-A alleviated PA-induced lipid accumulation in HepG2 cells, indicating a direct effect of SZ-A on hepatocytes. It is mainly DNJ and DAB that play a role in activating the p-AMPK/p-ACC pathway and lowering liver triglycerides and cholesterol. SZ-A and its different constituents were added during the differentiation of 3T3-L1 adipocytes. We found that SZ-A promoted adiponectin secretion in 3T3-L1 adipocytes. DNJ and DAB are major constituents that stimulate adiponectin secretion. In terms of its anti-inflammatory effects, it has been reported that DNJ and FA are effective in inhibiting supernatant IL-6, whereas DAB is more effective in suppressing TNFα [23]. These results suggest that the different components of SZ-A may exert different synergistic effects. Obesity is an important pathogenic factor for NAFLD and T2DM. Agents with mechanisms of insulin sensitization and bodyweight loss have been studied for NAFLD treatment. It is reported that treatment resulting in a 5% weight loss decreases hepatic fat content [29]. The effect of GLP1 receptor agonists on NASH endpoint are thought to be associated with weight loss and systemic improvements in metabolism [4]. In our study, the bodyweight of SZ-A-treated mice was significantly decreased compared with the HFD control group. The decreased bodyweight contributes partly to reduced fatty liver. However, food consumption was not affected. To elucidate the mechanism of reduced fat mass, we found that PPARα, a nuclear receptor important for lipid metabolism, is increased by SZ-A treatment. SZ-A promotes fatty acid oxidation in adipose tissue of mice. Adipose tissue plays an important role in systemic nutrient and energy homeostasis. Intercellular and interorgan communication is mediated by adipokines secreted by adipocytes. Adiponectin has been shown to inhibit inflammation, suppress oxidative stress, and accelerate fatty acid oxidation by binding to adiponectin receptors [30]. The synthesis of bioactive adiponectin is difficult, whereas agents that stimulate the secretion of adiponectin are promising [31]. In this study, we measured the effects of SZ-A and its major components on adiponectin expression both in vivo and in vitro. SZ-A promoted adiponectin secretion in 3T3-L1 adipocytes via its components DNJ and DAB. The protein levels of adiponectin also increased in the adipose tissue of SZ-A-treated mice. Increased adiponectin in circulation binds to adiponectin receptors on hepatocytes and exerts protective effects on lipid metabolism and inflammation. In the liver, adiponectin binds with AdipoR1 to activate AMPK pathways and AdipoR2 to activate PPARα pathways [32]. The anti-lipotoxic effects of adiponectin/AdipoR may also be mediated by enhanced activity of PPARα and PGC1α [33]. Lipid overload and oxidative stress-induced cellular damage are important factors in NAFLD pathogenesis. Hepatic lipid accumulation is the result of a disequilibrium between lipid production and consumption. AMPK is a master regulator of cellular energy homeostasis [34]. Phosphorylation of ACC by p-AMPK inhibits lipogenesis and enhances β-oxidation [35]. In this study, we found that SZ-A administration increased p-AMPK (Thr172) and p-ACC levels in SZ-A-treated HFD mice and HepG2 cells, which resulted in decreased lipogenesis and increased fatty acid oxidation. Activation of AMPK regulates PGC1α activation, and activation of Ca$^{2+}$/calmodulin-dependent protein kinase regulates PGC1α expression [36]. PGC1α is a coactivator of many transcription factors, including mitochondrial transcription factor A (TFAM) and nuclear respiratory factors (nuclear respiratory factor 1 (NRF1) and nuclear respiratory factor 2 (NRF2)) to regulate mitochondrial biogenesis, gluconeogenesis, and fatty acid $\beta$-oxidation [37]. We found that SZ-A upregulated the expression of PGC1α at mRNA and protein levels. UCP2 is a member of the anion carrier superfamily in the mitochondrial inner membrane. It has been reported that obesity-induced UCP2 expression in hepatocytes promotes hepatic ATP depletion and causes acute liver injury [38]. We found that SZ-A decreased liver UCP2 expression at the protein level to protect the mice from liver injury. These results are in accordance with the morphological changes of mitochondria. Oxidative stress reflects the imbalance between ROS production and scavenging [39]. ROS causes oxidative modifications to cellular macromolecules, leading to damage to macromolecules and liver injury. MDA is a lipid oxidation product of ROS. Hepatic lipid overload affects different ROS generators, including the mitochondria, endoplasmic reticulum, and NADPH oxidase. Enzymatic antioxidants such as SOD, glutathione peroxidase (GPx), catalase, and nonenzymatic antioxidants like glutathione (GSH) help to maintain a steady level of ROS [40]. The regulation of the antioxidant system has emerged as an interesting target for NAFLD treatment [41]. We found that HFD feeding led to reduced SOD, GPx, and GSH levels in the liver of NAFLD mice, which are major antioxidant biomarkers [42]. These effects were significantly restored by SZ-A treatment, suggesting that SZ-A may enhance ROS scavenging ability. These results demonstrate that SZ-A increased antioxidants to remove HFD-induced toxic oxidative stress in mice. Our study has some limitations. The protective effect of SZ-A on NAFLD cannot be separated from its weight-loss effect in this study. More studies are needed to compare the effect of SZ-A to food restriction resulting in the same weight loss on HFD-induced NAFLD. The mechanism of bodyweight loss is not clear, though we found that oxidation of fatty acid was influenced by SZ-A administration in mice. Mouse models such as methionine-choline deficient (MCD) diet-induced NASH should also be tested for effects of SZ-A in mice. We have tested the effect of SZ-A on HepG2 cells in vitro. However, the effect of SZ-A on hepatic stellate cells requires further investigation. Besides, the direct target and mechanism of individual components of SZ-A remains unknown, though the effects of SZ-A on adipocyte adiponectin expression and hepatocyte triglyceride metabolism were reported. 5. Conclusions In this study, HFD-induced obesity, hepatic steatosis, oxidative stress, inflammation, and fibrosis in mice were ameliorated by SZ-A administration. We speculate that SZ-A may act through multiple pathways. PPARα contributes partly to reduced bodyweight. SZ-A attenuates NAFLD by both weight loss and direct effects on HepG2 hepatocytes. AMPK and PPAR signaling pathways play important roles in the protective effects of SZ-A. In summary, the present study in mice revealed that SZ-A is a promising agent for the treatment of complex diseases, such as obesity and NAFLD. Supplementary Materials: The following supporting information can be downloaded at: [https://www.mdpi.com/article/10.3390/antiox11050905/s1](https://www.mdpi.com/article/10.3390/antiox11050905/s1), Table S1: Primers for RT-PCR. Figure S1: The major alkaloids in SZ-A determined using HPLC-MS. Miglitol is the internal standard. Author Contributions:** Conceptualization, Z.-F.S. and Y.-L.L.; Formal analysis, Y.-M.C. and C.-F.L.; Funding acquisition, Y.-M.C. and J.Y.; Investigation, Y.-M.C., C.-F.L. and Q.-W.S.; Methodology, Q.-W.S.; Project administration, L.-L.G.; Resources, Y.-Y.L.; Software, T.-T.W.; Supervision, Y.-F.Y. and S.-N.L.; Validation, T.-T.W. and J.Y.; Writing—original draft, Y.-M.C. and C.-F.L.; Writing—review and editing, Y.-L.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Beijing Postdoctoral Research Foundation (grant number 2021-ZZ-043) and CAMS Innovation Fund for Medical Sciences (grant number 2021-I2M-1-028). Institutional Review Board Statement: The animal study protocol was approved by the Ethics Committee of Beijing Laboratory Animal Research Center (ethical code: 2020001). Informed Consent Statement: Not applicable. Data Availability Statement: RNA sequencing data have been submitted to the Gene Expression Omnibus (GEO) under accession number (GSE199105). Acknowledgments: We are very thankful to the manufacturer (Guangxi Wehand-bio Pharmaceutical Co., Ltd., Yizhou, China) and the suppliers of SZ-A (Beijing Wehand-bio Pharmaceutical Co., Ltd.). We thank Editage (https://app.editage.cn, accessed on 10 March 2022) for its linguistic assistance during the preparation of this manuscript. Conflicts of Interest: The authors declare no conflict of interest. References 1. Gariani, K.; Jornayvaz, F.R. Pathophysiology of NASH in endocrine diseases. Endocr. Connect. 2021, 10, R52–R65. [CrossRef] [PubMed] 2. Chalasani, N.; Younossi, Z.; Lavine, J.E.; Charlton, M.; Cusi, K.; Rinella, M.; Harrison, S.A.; Brunt, E.M.; Sanyal, A.J. The diagnosis and management of nonalcoholic fatty liver disease: Practice guidance from the American Association for the Study of Liver Diseases. Hepatology 2018, 67, 328–357. 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[CrossRef] [PubMed]	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 3649, 1 ], [ 3649, 8134, 2 ], [ 8134, 12080, 3 ], [ 12080, 16276, 4 ], [ 16276, 20287, 5 ], [ 20287, 24248, 6 ], [ 24248, 26551, 7 ], [ 26551, 29858, 8 ], [ 29858, 32232, 9 ], [ 32232, 35187, 10 ], [ 35187, 37429, 11 ], [ 37429, 39643, 12 ], [ 39643, 41386, 13 ], [ 41386, 44078, 14 ], [ 44078, 46949, 15 ], [ 46949, 51440, 16 ], [ 51440, 55878, 17 ], [ 55878, 60852, 18 ], [ 60852, 65687, 19 ] ] }
6fa43e2862f3d1bd8e39da1a028687300a8dfb67	{ "olmocr-version": "0.1.59", "pdf-total-pages": 8, "total-fallback-pages": 0, "total-input-tokens": 30814, "total-output-tokens": 11196, "fieldofstudy": [ "Biology" ] }	The LIM-only Protein FHL2 Regulates Cyclin D1 Expression and Cell Proliferation* Charlotte Labalette‡§1, Yann Nouët‡§2, Joëlle Sobczak-Thepot, Carolina Armengol§, Florence Levillayer§, Marie-Claude Gendron∥, Claire-angélique Renard§, Béatrice Regnault, Ju Chen‡§, Marie-Annick Buendia§, and Yu Wei‡§4 From the ‡Unité d’Oncogenèse et Virologie Moléculaire and PT “Puce à ADN,” Institut Pasteur, 28 Rue du Dr. Roux, 75015 Paris, France, §Inserm U579, 28 Rue du Dr. Roux, 75015 Paris, France, ∥Université Paris VI, CNRS UMR7098, 7 Quai Saint-Bernard, 75005 Paris, France, ¶Institut Jacques Monod, 2 Place Jussieu, 75005 Paris, France, and the +†Department of Medicine, Institute of Molecular Medicine, University of California, San Diego, La Jolla, California 92093-0613 The LIM-only protein FHL2 acts as a transcriptional modulator that positively or negatively regulates multiple signaling pathways. We recently reported that FHL2 cooperates with CREB-binding protein/p300 in the activation of β-catenin/T cell factor target gene cyclin D1. In this paper, we demonstrate that FHL2 is associated with the cyclin D1 promoter at the T cell factor/CRE site, providing evidence that cyclin D1 is a direct target of FHL2. We show that deficiency of FHL2 greatly reduces the proliferative capacity of spontaneously immortalized mouse fibroblasts, which is associated with decreased expression of cyclin D1 and p16INK4a, and hypophosphorylation of Rb. Reexpression of FHL2 in FHL2-null fibroblasts efficiently restores cyclin D1 levels and cell proliferative capacity, indicating that FHL2 is critical for cyclin D1 activation and cell growth. Moreover, ectopic cyclin D1 expression is sufficient to override growth inhibition of immortalized FHL2-null fibroblasts. Gene expression profiling revealed that FHL2 deficiency triggers a broad change of the cell cycle program that is associated with down-regulation of several G1/S and G2/M cyclins, E2F transcription factors, and DNA replication machinery, thus correlating with reduced cell proliferation. This change also involves down-regulation of the negative cell cycle regulators, particularly INK4 inhibitors, which could counteract the decreased expression of cyclins, allowing cells to grow. Our study illustrates that FHL2 can act on different aspects of the cell cycle program to finely regulate cell proliferation. The LIM-only protein FHL2 is a member of the four-and-a-half LIM (FHL) family (1). Individual LIM domains consist of two zinc finger motifs rich in cysteine and histidine that serve as protein-binding interface for the assembly of multiprotein complexes. The zinc fingers of some transcriptional regulators can interact with DNA, but there is no evidence for DNA binding activity of a LIM domain. FHL2 interacts with multiple transcription factors, including the androgen receptor, AP1, CREB, PLZF, SKI, and β-catenin (2–8). It functions as either a coactivator or a corepressor, depending on cell type and promoter contexts (7, 9). Moreover, FHL2 can bind several transcription factors simultaneously and participates in the assembly of multiprotein complexes (10, 11). FHL2 is found in both the cytoplasm and the nucleus (8, 12). In the cytoplasm, FHL2 interacts with integrins and focal adhesion kinase at focal adhesions (13, 14). Integrins bind extracellular matrix proteins and certain cell surface receptors, serving as sensors for both chemical and mechanical cues (15). FHL2 shuttles between focal adhesions and nuclei to relay the flow of genetic information at different execution points. Serum response factor, which regulates the expression of immediate early genes, directly controls FHL2 expression in a RhoA-dependent manner (16), and the timing of FHL2 induction is coordinated with that of the early response proteins Fos and Jun (3). Following stimulation with RhoA or serum, FHL2 is induced and translocated to the nucleus, thereby linking extracellular signals to gene expression programs (3, 17). Studies in various biological systems have shown that FHL2 plays diverse roles in many aspects of cell life. Mouse deficient in FHL2 are viable (18) but display pathological phenotypes, including osteopenia, resulting from a decrease in the activity of osteoblasts (19), cardiac hypertrophy under β-adrenergic stimulation (20), and defects in skin wound healing (21). We have previously demonstrated that FHL2 is a coactivator of β-catenin and that it cooperates with CREB-binding protein/p300 to enhance transcription driven by the β-catenin-TCF complex β-catenin (8, 10, 22). We have shown that FHL2 and β-catenin synergistically increase the transcription of the β-catenin target gene cyclin D1. In addition, primary FHL2−/− mouse embryonic fibroblasts (MEFs) were found to express half the normal amount of cyclin D1 transcripts (10). Recent studies have shown that FHL2 antagonizes the p53-dependent antiproliferative effects of the transcription factor 5 The abbreviations used are: CREB, cAMP-response element-binding protein; CRE, cAMP-response element; MEF, mouse embryonic fibroblast; ChIP, chromatin immunoprecipitation; BrdUrd, bromodeoxyuridine; HA, hemagglutinin; RT, reverse transcription; WT, wild type; TCF, T cell factor. FHL2 Deficiency Impairs Cell Proliferation E4F1 (23) and regulates cell cycle-dependent p21 expression in breast cancer cells (24), thus linking FHL2 to cell cycle and proliferation. In this study, we used MEFs derived from FHL2-null embryos to investigate the role of FHL2 in the regulation of cyclin D1 and cell proliferation. By chromatin immunoprecipitation (ChIP), we show that FHL2 is associated with the cyclin D1 promoter. We found that disruption of FHL2 decreased the proliferative capacity of murine fibroblasts. Finally, we used microarray to analyze gene expression at the whole genome level and show down-regulation of both positive and negative regulators of the cell cycle in FHL2-null cells. Overall, our results provide evidence for the function of FHL2 as an important regulator of cell cycle and proliferation. EXPERIMENTAL PROCEDURES MEF Generation and Establishment of Immortalized Cell Lines—Primary MEFs from wild type (WT) or FHL2−/− mice (18) were derived from embryos on day 13.5 or 16.5. Spontaneously immortalized cell lines were generated from primary MEFs using a 3T3 protocol. The growth curves of immortalized clones were obtained by seeding 2.5 × 10⁶ cells into 12-well plates in triplicate. Cell numbers were determined every day for a total of 6 days. Flow Cytometry Analysis—Cells were pulsed for 30 min with 10 µM BrdUrd (Sigma). After fixation in 70% ethanol, cells were denatured in 2 M HCl, neutralized with 0.1 M sodium borate, and then incubated with fluorescein isothiocyanate-conjugated anti-BrdUrd monoclonal antibody (556028; BD Pharmingen). DNA was stained with 10 µg/ml propidium iodide (Sigma) and treated with DNase-free RNase (Roche Applied Science). Cells were analyzed by flow cytometry with excitation at 488 nm and monitored with BrdUrd-linked fluorescein isothiocyanate and propidium iodide at 514 and 575 nm, respectively, using appropriate filters. Serum Stimulation and Immunoblotting—1.5 × 10⁵ MEFs were seeded into 6-well plates and synchronized by incubation in 0.5% fetal bovine serum in Dulbecco’s modified Eagle’s medium for 96 h. Synchronized cells were stimulated by adding 10% fetal bovine serum in Dulbecco’s modified Eagle’s medium. Extracts were prepared at 0, 3, 9, 15, 18, 21, and 24 h post-stimulation and analyzed by immunoblotting as described previously (10). Antibodies against p16INK4a (sc-1207), p15INK4b (sc-613), p18INK4c (sc-1064), cyclin D1 (sc-450), cyclin D2 (sc-181), cyclin D3 (sc-182), cyclin A (sc-751), and cyclin E (sc-481) were purchased from Santa Cruz Biotechnology, Inc. (Santa Cruz, CA); FHL2 (ab123277), p27Kip1 (ab6547), and phospho-Rb (Thr1728) (ab4787) from Abcam; Rb (554136) from BD Pharmingen; Phospho-Rb (Ser780) (9307) and (Ser795) (9301) from Cell Signaling; and actin (A5441) from Sigma. Retroviral Vectors and Gene Transfer—pBabe-FHL2 was constructed by inserting full-length FHL2 cDNA in the pBabe-puro vector. pBabe puro cyclin D1 HA constructed by Dr. William Hahn was obtained from Addgene (Addgene plasmid 9050). Phoenix ecotropic virus packaging cells in 10-mm dishes were transfected by phosphate calcium precipitation with 10 µg of a retroviral plasmid. 24 h later, exponentially growing MEFs were infected with 5 ml of virus-containing supernatant supplemented with 8 µg/ml Polybrene/dish. This procedure was repeated three times every 3 h. Cells were selected in medium containing 4 µg/ml puromycin. ChIP Assay—Synchronized MEFs were starved in Dulbecco’s modified Eagle’s medium with 0.5% fetal bovine serum for 96 h, followed by the addition of 10% serum for 15 h before harvest. Nonsynchronized or synchronized MEFs were used for ChIP assays with anti-FHL2 antibody, as described previously (25). The antibodies used were anti-FHL2 (5 µg; K0055-3; MBL) and irrelevant anti-HA antibody (Babco). The following primers were used to amplify the cyclin D1 promoter: F1 (5’-CAAC-GAAAGCAATCAAGAAGCT-3’) and R1 (5’-GAAAAAGTAAATCGTGCAAGTATTAGTC-3’) for the AP1 site; F2 (5’-CTGCCCGGCTTTGATCTCT-3’) and R2 (5’-AGGACT-TTGAACATTCAACAAAACT-3’) for the TCF/CRE site. The primers used to amplify the negative control promoter of the cad (carbonyltransferase-dihydroorotase) gene are 5’-GCC-GTGCGAGTGCTGCT-3’ and ACCGACCGCTCTCCTCAAA-3’. mRNA Analysis—Total RNA was extracted from WT and FHL2−/− MEFs with the RNeasy minikit (Qiagen). 1 µg of RNA was reverse-transcribed using random primers and the SuperScript Reverse Transcriptase (Invitrogen). Real time PCR was performed using the following primers: for FHL2, 5’-GCCGTCCTGTATGGAAG-3’ (sense) and 5’-AAAGCGTTGCC-CAGATAGTG-3’ (antisense); for cyclin D1, 5’-CATCAAG-TGTGACCCGGACTG-3’ (sense) and 5’-CCTCCTCCTCCAG-TGCCCCCT-3’ (antisense); for p15INK4c, 5’-ATTGGGGTG-GTGCGAGTCA-3’ (sense) and 5’-GTTTCCCATTTAGCCTG-3’ (antisense); for p18INK4c, 5’-ACCATCCAGTC-CTCTCCT-3’ (sense) and 5’-CCCCCTCTCTGGTTCGC-TAAC3’ (antisense); for p19INK4a, 5’-GGACGTCCCGGCTCTC-3’ (sense) and 5’-GCAGATGTCCATAGGTTTCTG-3’ (antisense); for 18S, 5’-GAAAGCCAATCAAGAAGCT-3’ (antisense) and 5’-GAAAAGTAGTTAATCGTGCAAGTATTAGTC-3’ for the AP1 site; F2 (5’-CTGCCCGGCTTTGATCTCT-3’) and R2 (5’-AGGACT-TTGAACATTCAACAAAACT-3’) for the TCF/CRE site. The primers used to amplify the negative control promoter of the cad (carbonyltransferase-dihydroorotase) gene are 5’-GCC-GTGCGAGTGCTGCT-3’ and ACCGACCGCTCTCCTCAAA-3’. Microarray Analysis—Total RNA was extracted with the RNAeasy kit (Qiagen). The quality of RNA was monitored on Agilent RNA Nano LaChips (Agilent Technologies, Santa Clara, CA). Microarray hybridizations were performed on the Affymetrix mouse genome 430 2.0, containing probe sets for 39,000 transcripts. Three independent WT and FHL2−/− MEF clones were profiled via microarrays. For each array, the cell intensity files (.CEL) were generated with GeneChip Operating software. Data analysis was performed using SPlus Array-Analyzer software (Insightful). Data were processed using the RNA method. Statistical analysis to compare replicates arrays FHL2 Deficiency Impairs Cell Proliferation FIGURE 1. FHL2 is associated with the cyclin D1 promoter. A, analysis of cyclin D1 transcripts in three independent WT and FHL2−/− immortalized clones by real time RT-PCR. Cyclin D1 expression was normalized to 18S RNA. The ratio of the cyclin D1/18S signal in WT clone B was arbitrarily set at 1. The average S.D. values and for three independent experiments are shown. Wild type clones are indicated by capital letters, and FHL2−/− clones are shown by lowercase letters. B, schematic representation of AP1 and TCF/CRE elements at the cyclin D1 promoter. C, association of FHL2 with the cyclin D1 promoter at the TCF/CRE site. WT and FHL2−/− MEFs were analyzed by ChIP. Antibodies against FHL2 and HA were used in parallel immunoprecipitations. Eluted DNA was amplified by PCR using cyclin D1 primers F1-R1 and F2-R2 indicated in B and control primers of the cad promoter (see “Experimental Procedures”). Data are representative of three independent experiments. D, graphic representation of the data of real time PCR for the TCF/CRE binding site in immortalized wild type and FHL2−/− MEFs. Calculation of the amount of immunoprecipitated DNA relative to that present in total input chromatin (percentage of total) is as follows: % total = 2^ΔCT (where CT represents cycle threshold). ΔCT = CT (input) − CT (FHL2IP). The total percentage at the 0 h time point of serum stimulation in WT MEFs was arbitrarily set at 1. Two independent immortalized FHL2−/− clones were analyzed in two independent ChIP experiments. was done with the local pool error test. The p values (the probability that the variability in a gene behavior observed between classes could occur by chance) were adjusted using the Bonferroni algorithm. Gene ontology and KEGG pathway annotation were performed by Oneto-tools software (available on the World Wide Web). GSEA (26) was used to evaluate the correlation of a specific gene list with two different sample groups (genotypes). We used the signal/noise ratio as a statistic to compare specific and gene set permutations in order to evaluate statistical differences. Microarray data have been deposited in NCBI Gene Expression Omnibus (available on the World Wide Web). The GEO series accession number is GSE10902. RESULTS FHL2 Is Associated with the Cyclin D1 Promoter at the TCF/CRE Site.—Our previous work has demonstrated that FHL2 cooperates with β-catenin in transcriptional activation of the cyclin D1 promoter in a luciferase reporter assay (10). To further study the role of FHL2 in the regulation of cyclin D1 and cell proliferation, we used MEFs derived from WT and FHL2−/− null embryos to generate WT and FHL2−/− MEF cell lines using the 3T3 protocol. Several independent immortalized clones were obtained in each genotype. Real time RT-PCR revealed strongly decreased cyclin D1 mRNA levels in all three FHL2−/− lines tested compared with WT cells (Fig. 1A). To determine whether cyclin D1 is a direct transcriptional target of FHL2, we carried out ChIP assays to examine the potential association of FHL2 with the cyclin D1 promoter. Since there is so far no evidence of DNA binding activity of LIM-only proteins, FHL2 could be associated with the cyclin D1 promoter through its interaction with transcription factors. We analyzed the proximal TCF/CRE region and the distal AP1 sites (Fig. 1B), because FHL2 is known to interact with β-catenin, CREB, and AP1 (3, 4, 7, 8). The proximal TCF/CRE region contains four putative TCF binding sites and one CRE element (Fig. 1B). A previous report (27) showed that these TCF sites were necessary for the activation of the cyclin D1 promoter by β-catenin. WT and FHL2−/− MEFs were first cross-linked with formaldehyde, and protein-DNA complexes were immunoprecipitated with either a FHL2 antibody or a HA antibody as control. Using chromatin precipitated with the FHL2 antibody as template, we were able to amplify the 79-bp region containing the TCF/CRE site in WT cells, whereas no amplification was obtained with chromatin precipitated from FHL2−/− cells (Fig. 1C). Amplification of chromatin immunoprecipitated with the control HA antibody did not give rise to any signal (Fig. 1C). Surprisingly, FHL2 was absent at the upstream region of the cyclin D1 promoter encompassing the AP1 site (Fig. 1C). No FHL2 binding signal was detected at the control promoter of the cad gene (Fig. 1C). Next, we assessed whether FHL2 binding to the cyclin D1 promoter is cell cycle-dependent by quantitative ChIP assays (28). After starvation during 96 h followed by stimulation with serum for 15 h, synchronized WT and FHL2−/− MEFs were cross-linked with formaldehyde, and protein-DNA complexes were immunoprecipitated with anti-FHL2 antibody. Quantitative data were obtained by real time PCR using F2 and R2 primers encompassing the TCF and CREB sites at the cyclin D1 promoter (Fig. 1B). As shown in Fig. 1D, quantitative ChIP analysis revealed a progressive association of FHL2 with the TCF/CRE target site in WT cells following serum stimulation, which is in accord with the observations that FHL2 can be induced by serum (3) (see Fig. 2A). Thus, these data indicate that FHL2 is directly involved in the control of the cyclin D1 promoter in a cell cycle-dependent manner. Low Levels of Cyclin D1 Result in Hypophosphorylation of Rb and Reduced Proliferation of Immortalized FHL2−/− MEFs—Since cyclin D1 is considered as a critical cell cycle sensor of the extracellular mitogenic environment, we analyzed expression of cyclin D1 in FHL2−/− MEFs in response to serum stimulation after starving cells for 96 h followed by the addition of serum. Consistent with earlier observations (3), FHL2 was induced 3 h after the addition of serum, and its levels rapidly peaked at 15 h, thus confirming its behavior as an early response gene (Fig. 2A). Strikingly, the kinetics of induction of cyclin D1 in FHL2−/− MEFs was significantly delayed compared with WT cells, and the levels of the induction were greatly reduced (Fig. 2A). During the G1 phase of the cell division cycle, mitogenic stimulation triggers assembly of cyclin D-cyclin-dependent kinases 4 and 6 (Cdk) complexes, which collaborate with cyclin E-Cdk2 to phosphorylate Rb family members. Decreased cyclin D1 was associated with severely impaired phosphorylation of Rb. Clysates from WT and FHL2−/− cells were analyzed by immunoblotting with antiphosphospecific antibodies that recognize pRb phosphorylated at specific amino acid residues. D, expression of Cdkks was not altered in FHL2−/− cells. Lysates from WT and FHL2−/− cells were analyzed by immunoblotting. E, reduced expression of Cdkk inhibitors in FHL2−/− cells. Cells lysates were prepared from WT and FHL2−/− cells and analyzed by immunoblotting with the indicated antibodies. null cell lines (see Fig. 2B). However, p16INK4a gene deletion was excluded, because its expression was detected in all clones tested, including clone i after longer exposure (Fig. 2B). Decreased expression of p16INK4a in FHL2−/− cell lines was in sharp contrast to a previous report (29) that immobilized cells usually express high levels of functional p16INK4a, which was also observed in WT cells in this study (Fig. 2B). The levels of other Cdkk inhibitors, including p15INK4b, p18INK4c, and p27Kip1, were also decreased, albeit in a lesser extent than p16INK4a (Fig. 2E). The critical role of cyclin D1 in the G1/S transition prompted us to investigate the effects of FHL2 deficiency on S phase entry and cell proliferation. We starved cells by serum deprivation for 96 h, followed by serum stimulation to assess the efficiency of S phase entry. Using flow cytometry analysis of BrdUrd-labeled cells, we found that the percentage of cells in S phase was consistently lower for FHL2−/− MEFs than for WT MEFs throughout the observation period (Fig. 3A). Additionally, FHL2−/− cells showed significantly lower rates of proliferation than WT MEFs (Fig. 3B). These data were confirmed in three independent cell lines. These findings revealed that deficiency of FHL2 results in reduced proliferation potential associated with low levels of cyclin D1 and p16INK4a and hypophosphorylation of Rb. FHL2 Deficiency Impairs Cell Proliferation To test the specificity of FHL2 in the regulation of cyclin D1 expression and cell proliferation, we reintroduced FHL2 in primary FHL2−/− MEFs at early passage with a retroviral vector and assessed the effect of exogenous FHL2 expression on cyclin D1 and cell growth. Continuous passage of FHL2-restored MEFs readily gave rise to established 3T3 cell lines. By real time RT-PCR, the mRNA levels of cyclin D1 in FHL2-restored cells were 11-fold higher than those of FHL2−/− cells and comparable with those of WT cells, which was in sharp contrast to the control vector pBabe-infected cells (Fig. 4A, top). Accordingly, immunoblotting analysis showed abundant cyclin D1 in immortalized FHL2-restored cells (Fig. 4A, bottom). Of note, the mRNA levels of FHL2 in FHL2-restored cells were only half those in WT cells, but the cyclin D1 levels of both mRNA and protein were similar or even higher in FHL2-restored cells than WT cells, suggesting that activation of cyclin D1 is not stoichiometrically associated with FHL2 expression. Besides, we found that cyclins D2 and D3 were down-regulated in FHL2−/− cells (Fig. 4A, bottom). The levels of cyclins D2, D3, and E were efficiently restored after ectopic expression of FHL2 (Fig. 4A, bottom). In FHL2-restored cells, Rb phosphorylation was efficiently reestablished (Fig. 4A, bottom). The proliferation rate of FHL2-restored cells was markedly increased, reaching similar levels as WT cells (Fig. 4B). Taken together, these results firm up the role of FHL2 in the regulation of cyclin D1 and cell proliferation. Ectopic Expression of Cyclin D1 Is Sufficient to Confer Normal Cell Proliferation to FHL2−/− Cells—Next, we asked whether FHL2 is implicated in cell cycle control via its effect on cyclin D1. We ectopically expressed HA-tagged cyclin D1 in primary FHL2−/− MEFs with a retroviral vector and assessed the effect of cyclin D1 on cell proliferation. After continuous passages of cyclin D1-HA/FHL2−/− MEFs, immortalized clones emerged spontaneously. As shown in Fig. 5A, the cyclin D1 transgene in FHL2−/− MEFs was expressed at a level similar to that of endogenous cyclin D1 in WT cells, whereas in FHL2−/− MEFs infected with pBabe vector, cyclin D1 was maintained at low levels. Strikingly, expression of cyclins D2, D3, E, and A was efficiently restored, and the ratio of hyperphosphorylated over hypophosphorylated Rb was significantly augmented in cyclin D1-HA/FHL2−/− MEFs compared with FHL2−/− cells (Fig. 5A). Moreover, cell growth in cyclin D1-HA/FHL2−/− MEFs was restored, showing an even higher level than that of WT cells (Fig. 5B). Collectively, these data provide evidence that the effects of FHL2 on cell proliferation rely mainly upon cyclin D1. Restoration of FHL2 Expression in FHL2-null Cells Is Sufficient to Increase Cell Proliferation—To test the specificity of FHL2 in the regulation of cyclin D1 expression and cell prolif- Microarray Analysis Shows Deregulation of Genes Associated with Cell Proliferation in FHL2-deficient Cells—To gain insight into the impact of FHL2 deficiency on gene expression at the whole genome level, we analyzed the gene expression profile of three independent FHL2/−/− and three WT MEF clones using the Affymetrix mouse genome 430 2.0 microarray. Supervised class comparison using the local pool error test identified 998 genes differentially expressed at $ p < 0.05 $ and $ q < 0.05 $ that are differentially expressed in the FHL2/−/− compared with WT clones. Wild type clones are indicated by capital letters, and FHL2/−/− clones are shown by lowercase letters. Data are plotted as a heatmap where red and blue correspond to high and low expression in $ \log_2 $-transformed scale. 8, gene set enrichment analysis plot using a GenMAPP gene set list corresponding to the G0 to S cell cycle reactome (normalized enrichment score = −1.7, false discovery rate = 0.008, $ p < 0.0001 $). The enrichment score reflects the correlation of the gene set with FHL2/−/− (KO) and WT genotypes. Significant results were also found in gene set enrichment analysis by using nine different cell cycle-related gene sets from the MIT data base (MSigDB). C, core group of genes of the G0 to S cell cycle reactome gene set that contributed to the enrichment score. The -fold change (KO/WT) corresponds to the mean value for those genes that have more than one probe set in the array. Microarray Analysis Shows Deregulation of Genes Associated with Cell Proliferation in FHL2-deficient Cells—To gain insight into the impact of FHL2 deficiency on gene expression at the whole genome level, we analyzed the gene expression profile of three independent FHL2/−/− and three WT MEF clones using the Affymetrix mouse genome 430 2.0 microarray. Supervised class comparison using the local pool error test identified 998 genes differentially expressed at $ p < 0.05 $. The results of 97 genes that had a -fold change of 15 or more between the two genotypes were displayed based on the normalized intensity, with blue representing lower relative gene expression and red indicating higher expression (Fig. 6A). We verified the expression pattern of five top up-regulated and five top down-regulated genes using quantitative real time PCR normalizing to internal 18 S RNA in MEF cell lines. The PCR results confirmed the up- or down-regulation of these genes in FHL2/−/− cells with excellent correlation between microarray and quantitative PCR (data not shown). In agreement with the data described above (Figs. 1A and 2), cyclins D1, D2, and E and Cdk inhibitors $ p16^{INK4a} $, $ p15^{INK4b} $, and $ p18^{INK4c} $ were found significantly down-regulated in FHL2/−/−/− cells. Pathway analysis using the Gene Ontology and KEGG data bases evidenced deregulation of genes involved in focal adhesion, extracellular matrix-receptor interaction, and response to external stimuli in cells deficient in FHL2, such as filamin, parvin, tenasin C, laminins (lama2, lama4, and lama5), thrombospondin 2, and procollagens (Col6a2, Col5a2, Col3a1, Col5a3, and Col2a1). Further evidence of alterations of cell cycle-associated genes in FHL2−/− cells was provided by gene set enrichment analysis, a computational method for assessing enrichment of a predefined gene list in one class compared with another (26). Using as a gene set the G1 to S cell cycle reactome (GenMAPP), we found that 50% of the 66 genes in this gene set were significantly down-regulated in FHL2−/− cells (Fig. 6, B and C). Specifically, besides cyclins D1, D2, and E, several critical G1/S regulators, including E2F transcription factors, were decreased in cells lacking FHL2. Moreover, cell cycle proteins involved in G2 to M transition appeared to be also affected, as demonstrated by the down-regulation of cyclin B1, Cdc25A, and Wee1 in FHL2−/− cells (Fig. 6C). Consistent with the lower rate of cell proliferation of FHL2−/− cells, several major components of the DNA replication machinery like Cdc45L, replication protein A subunits, Orc6L, and the minichromosome maintenance (Mcm) genes were down-regulated. Remarkably, the most seemingly paradoxical effect of FHL2 deficiency was sustained repression of cell cycle negative regulators, including the four members of the INK4 family (p16INK4a, p15INK4b, p18INK4c, and p19INK4d), p57kip2, and Wee1 (Fig. 6C). Real time RT-PCR analysis of p15INK4b, p18INK4c, and p19INK4d confirmed down-regulated expression of these genes in FHL2−/− cells (data not shown), in agreement with the immunoblotting analysis (Fig. 2E). The INK4 inhibitors and p57kip2 specifically inhibit the activity of cyclin D-Cdk4/6 and cyclin E-Cdk2 in G1/S, whereas Wee1 is an inhibitor of cyclin B-Cdk1 in G2/M. Reduced expression of Cdk inhibitors in FHL2−/− cells may rescue minimal activity of cyclin-Cdk complexes that is required for initiation of DNA synthesis and mitosis, thus maintaining the progression of the cell cycle at low levels. This FHL2-mediated regulation of cell proliferation seemingly involves not just cell cycle positive but also negative regulators controlling both G1/S and G2/M transitions. Taken together, the genome-wide analysis provides additional insight into FHL2-mediated regulation in cell proliferation and cell cycle proteins. DISCUSSION In this paper, biological analysis and genome-wide studies of gene expression show that deficiency of FHL2 in immortalized murine fibroblasts has a profound effect on expression of cell cycle proteins and cell proliferation. Spontaneously immortalized FHL2−/− MEFs express low levels of several G1/S and G2/M cyclins and E2F transcription factors, which are accompanied by hypophosphorylation of Rb and down-regulation of Cdk inhibitors. This unusual expression pattern with decreased levels of both cell cycle positive and negative regulators is associated with a reduced but not null proliferative capacity of FHL2−/− cells. These findings underscore an important function of FHL2 in regulating the expression of a large spectrum of genes implicated in cell division. We demonstrate that cyclin D1 is directly regulated by FHL2 and represents a key effector of FHL2 in cell cycle control. Mitogen-induced signal transduction pathways promote the activation of cyclin D1 at many levels, including transcription, translation, and protein stability. Different lines of evidence indicate that FHL2 acts mostly at the transcriptional level. We provide evidence that FHL2 physically occupies the cyclin D1 promoter at the TCF/CRE site, which is in line with previous reports that FHL2 interacts directly with β-catenin and CREB transcription factors (4, 7, 8). FHL2 can regulate cyclin D1 by acting as a protein scaffold for the recruitment of the adaptor complexes, which in turn facilitates binding of general transcription factors. It has been shown that FHL2 is capable of binding the FOXO factors and deacetylase SIRT1 and can counteract the repression of FOXO1 on the cyclin D1 promoter by enhancing the interaction of FOXO1 with SIRT1 and the deacetylation of the transcription repressor (11). Thus, FHL2 may inhibit the activity of transcription repressors at the cyclin D1 promoter through its ability to interact with FOXO1 and SIRT1. Alternatively, FHL2 may regulate the activity of the cyclin D1 promoter through its implication in acetylation of transcription factors and histones. We have previously shown that FHL2 increases β-catenin acetylation by p300 and that acetylation of β-catenin at residue Lys385 enhances the affinity of β-catenin for TCF4 (10, 22). Increasing acetylation of β-catenin might represent another mechanism by which FHL2 contributes to the activation of the cyclin D1 transcription. Likewise, FHL2 may be involved in acetylation of histones through its interaction with CREB-binding protein/p300. It is generally considered that histone acetylation is implicated in activation of transcription. Our preliminary results suggest that FHL2 deficiency is associated with a significant reduction of the occupancy of acetylated histone H3 at certain promoters, including the cyclin D1 promoter.6 Further study is needed to determine if FHL2 could regulate gene expression by participating in chromatin remodeling. Finally, FHL2 may control cyclin D1 via indirect mechanisms by interfering in signaling pathways that modulate cyclin D1 activity. It has been shown that FHL2 can retain extracellular signal-regulated kinase 2 (ERK2) of the mitogen-activated protein kinase signaling pathways in cardiomyocytes, thus negatively regulating mitogen-activated protein kinase signaling (9). However, our microarray analysis showed that FHL2 deficiency in fibroblasts is associated with down-regulation of mitogen-activated protein kinases, which was confirmed by our preliminary results of the PathwayProfiler study (Upstate and Chemi- con) and Western blot analyses. FHL2 is an early response gene (3), which argues that FHL2 possesses sensor functions that can relay mitogenic signals to nuclear effectors. Disruption of FHL2 may therefore partially block transduction of the signals that normally induce cyclin D1. In contrast to immortalized cyclin D1−/− MEFs, which display a similar grow rate as WT MEFs (30), inactivation of FHL2 severely compromises proliferation of immortalized fibroblasts. This observation suggests that cyclin D1 is not the only target of FHL2. Indeed, gene expression profiling of FHL2−/− cells revealed deregulation of genes involved in focal adhesion, extracellular matrix-receptor interaction, response to external stimuli, and insulin-like growth factor signaling, demonstrating that FHL2 is in the front line of upstream signaling pathways emanating from diverse stimuli. These findings are also in agreement with the role of FHL2 in wound healing (21). Conversely, FHL2 deficiency in whole animals produces only limited abnormalities under various stimuli (19–21). FHL2 is thus dispensable for the proliferation of the majority of tissues in which, we speculate, other members of FHL family may provide substitutes for its functions. The mechanisms involved in the down-regulation of other cell cycle-related genes by FHL2 can be both direct and indirect. FHL2 interacts with multiple transcription factors, which can directly regulate a large spectrum of gene expression program. FHL2 exerts its transcription modulator functions by acting on complexes play a crucial role in G1 progression by phospho- target of FHL2. Indeed, gene expression profiling of FHL2−/− cells. How- ever, E2F target genes seemed still to be induced, since those functions on E2F transcription factors. This process controls an cyclin E, p107, Cdc25A, range of genes involved in cell division and DNA-replication functions on E2F transcription factors. This process controls an Acknowledgments—We thank C. Demeret and G. Soubigou for technical advice and C. Neveuvt and D. Cougot for insightful discussion. We are grateful to K. Kean for comments on the manuscript. REFERENCES 1. Johannessen, M., Moller, S., Hansen, T., Moens, U., and Van Ghelue, M. (2006) Cell Mol. Life Sci. 63, 268–284 2. Muller, J. 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(2001) Nature 411, 1017–1021	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5237, 1 ], [ 5237, 11232, 2 ], [ 11232, 16946, 3 ], [ 16946, 19442, 4 ], [ 19442, 22390, 5 ], [ 22390, 25205, 6 ], [ 25205, 31309, 7 ], [ 31309, 37488, 8 ] ] }
931a03b6e9918a0437ed045e25221a3d88fa1849	{ "olmocr-version": "0.1.59", "pdf-total-pages": 10, "total-fallback-pages": 0, "total-input-tokens": 38082, "total-output-tokens": 12726, "fieldofstudy": [ "Chemistry" ] }	Comparison of a low transition temperature mixture (LTTM) formed by lactic acid and choline chloride with choline lactate ionic liquid and the choline chloride salt: physical properties and vapour-liquid equilibria of mixtures containing water and ethanol Francisco Casal, M.; Gonzalez, A.S.B.; Lago Garcia de Dios, S.; Weggemans, W.M.A.; Kroon, M.C. Published in: RSC Advances DOI: 10.1039/c3ra40303c Published: 01/01/2013 Citation for published version (APA): Francisco Casal, M., Gonzalez, A. S. B., Lago Garcia de Dios, S., Weggemans, W. M. A., & Kroon, M. C. (2013). Comparison of a low transition temperature mixture (LTTM) formed by lactic acid and choline chloride with choline lactate ionic liquid and the choline chloride salt: physical properties and vapour-liquid equilibria of mixtures containing water and ethanol. RSC Advances, 3(45), 23553-23561. DOI: 10.1039/c3ra40303c Comparison of a low transition temperature mixture (LTTM) formed by lactic acid and choline chloride with choline lactate ionic liquid and the choline chloride salt: physical properties and vapour–liquid equilibria of mixtures containing water and ethanol† María Francisco, Agustín S. B. González, Sara Lago García de Dios, Wilko Weggemans and Maaike C. Kroon A new group of nature-based solvents, i.e. low transition temperature mixtures (LTTMs), are evaluated in this work as entrainers for the separation of azeotropic mixtures. The effect of choline-based LTTMs on the vapour pressure of ethanol and water is compared to the effect of the corresponding lactate-based choline salt and a chloride-based choline salt. The changes with temperature and composition of the physical properties (density and viscosity) of the binary mixtures (entrainer + water–ethanol) are studied and compared. Also, the vapour–liquid equilibrium (VLE) data for binary mixtures of water–ethanol with the studied entrainers are reported. The phase diagrams of the ternary systems composed of water + ethanol + entrainer are shown and the experimental data are correlated by using the e-NRTL model. Traditionally, very cheap and common salts were used as entrainers for azeotropic separations (water + alcohol) due to the well-known ebullioscopic effect, which strongly reduces the volatility of the water. However, salts show multiple disadvantages for large scale processes: they may erode the sieve plate, precipitate and build up in the tower due to causticity and limited solubility. Extractive distillation with ionic liquids (ILs) as separating agents became very popular during the past decade. The use of these ionic substances integrates the advantages of a liquid solvent (easy operation) and solid salt (high separation ability). Another advantage of these entrainers is their negligible vapour pressure near ambient conditions. This minimizes the chance of solvent emissions to the atmosphere, thus reducing the atmospheric pollutant effect of volatile solvents. However, the scientific community started questioning the use of ILs for large scale applications. The synthesis of most ILs is not “green” and the costs of production as well as degree of recyclability or biodegradability are the main weak points of IL technologies. A new family of solvents was presented for the first time by Abbott et al. as suitable alternative to ILs. Originally, they were called “deep eutectic solvents” (DES), but this name does not cover the complete class of solvents, because many of them do not show (eutectic) melting points but glass transitions instead. Therefore, we coined them “low transition temperature mixtures” (LTTM). These new solvents can be formed by mixing two solid starting materials, which form a liquid by Introduction Azeotropic mixtures are involved in common chemical processes. One relevant example is the production of alcohols derived from the fermentation of carbohydrates, which form azeotropes with water, in the biofuel industry. Among those products, ethanol is the most important example, due to its excellent properties as alternative fuel. Several potential processes for separating various azeotropic mixtures have come to light such as azeotropic distillation, extractive distillation, liquid–liquid extraction or supported liquid membrane separation. Extractive distillation is the most common technique, which involves the addition of a heavy component (entrainer) that interacts preferentially with one of the constituents of the azeotropic mixture. This interaction generates a difference in volatility between the two constituents of the mixture, making the azeotropic composition shift to higher concentration of the more volatile component in the vapour phase. In extreme cases, the azeotrope can even be broken. † Electronic supplementary information (ESI) available. See DOI: 10.1039/c3ra40303c Eindhoven University of Technology, Department of Chemical Engineering and Chemistry, Separation Technology Group, Den Doelch 2, 5612 AZ, Eindhoven, Netherlands. E-mail: [email protected]; Fax: +31-40-2463966; Tel: +31-40-247 5289 University of Santiago de Compostela, Department of Chemical Engineering, E.T.S.E., Av. Lope de Gómez de Marzoa, 15782 Santiago de Compostela, Spain † Electronic supplementary information (ESI) available. See DOI: 10.1039/c3ra40303c www.rsc.org/advances Received 21st January 2013 Accepted 1st October 2013 DOI: 10.1039/c3ra40303c 10.1039/c3ra40303c RSC Adv., 2013, 3, 23553–23561 \| 23553 This journal is © The Royal Society of Chemistry 2013 hydrogen bond interactions. They show very interesting properties as solvents to be explored for different applications in separation processes. They share many advantages with ILs, but their preparation is simple and cheap, since one only has to mix natural and readily available starting materials.\textsuperscript{14,15} LTTMs are formed by mixing a hydrogen bond donor (e.g. organic acid, alcohol) and a hydrogen bond acceptor (e.g. quaternary ammonium salt). One of the most popular hydrogen bond acceptors used to form LTTMs is choline chloride, because of its benign character, biodegradability and price. In our previous work,\textsuperscript{16} lactic acid:choline chloride mixtures were investigated as solvents for separations. A complete characterization of the physical properties proved the tunability and phase behaviour by changing the composition. These mixtures formed a stable liquid in a wide range of compositions. Their promising properties as solvents, like wide liquid range, good salvation properties derived from hydrogen bonding interactions, recoverability and biodegradability, make lactic acid:choline chloride mixtures promising candidates as solvents for separations.\textsuperscript{16} In this work, we choose a representative LTTM formed by lactic acid and choline chloride in a molar ratio 2 : 1 (LC2 : 1), and we compare its performance as entrainer in extractive distillation with the choline chloride salt and a lactate-based IL (choline lactate). For this purpose, we study the properties of binary mixtures of these three entrainers with water and ethanol in order to discuss the interactions involved. The VLE data of binary mixtures of LTTM (LC2 : 1), IL (choline lactate) and salt (choline chloride) with water and ethanol are also studied, as well as the azeotropic behaviour of the ternary system of ethanol + water + entrainer. The structures and phase transition temperatures of the three different entrainers studied are shown in Fig. 1. Results and discussion Physical properties: density, viscosity and mixing properties In the field of separation processes, the study of the physical properties of the mixtures involved in a process is of crucial interest. In this way, the suitability of a solvent for a certain process can be evaluated and the design of the involved units can be made. Therefore, the characterization of the main physical properties of the binary mixtures composed of the solvent to be used as entrainer and water or ethanol are determined here. The deviation of the ideal behaviour of these mixtures is also discussed. Properties of binary mixtures with water Density and excess molar volume. The densities of binary mixtures of water with the IL choline lactate, the LTTM LC2 : 1, or the salt choline chloride, respectively, are studied as a function of temperature and composition. Fig. 2 shows the dependency of the density on temperature for all three choline-derived components studied in this work at two representative mole fractions of entrainer (0.1 and 0.3). The experimental values for the three binary systems are included in the ESI (Table S1\textsuperscript{†}). The density follows a linear trend with temperature as expressed in eqn (1): \[ \ln(\rho) = A + B(T) \tag{1} \] where $\rho$ is the density in g cm$^{-3}$ and $T$ is the temperature in K. The fitting parameters of eqn (1) obtained at different molar compositions of the entrainer + water binary mixtures, including the deviations between the calculated and the experimental density values, are reported as ESI (Table S2\textsuperscript{†}). The study of molar excess volume of the binary mixtures and their change with temperature and composition is very useful for a better understanding of the interactions involved in the mixing behaviour of real solutions. The experimental values of excess molar volume, $\nu_m^e$ (cm$^3$ mol$^{-1}$) of the mixtures were \begin{table} \| Raw Material \| Molecular / Ionic structure \| Phase transition temperature (°C) \| \|--------------\|----------------------------\|----------------------------------\| \| Choline Lactate \| ![Structure](image) \| -72.90\textsuperscript{b} \| \| LC (2:1) \| ![Structure](image) \| -77.73\textsuperscript{b} \| \| Choline Chloride \| ![Structure](image) \| 302\textsuperscript{a} \| \textsuperscript{a} Melting point. \textsuperscript{b} Glass transition temperature. \| Fig. 1 Molecular structure of the three entrainers studied in this work (the IL choline lactate, the LTTM formed by lactic acid and choline chloride (molar ratio 2 : 1), and the natural salt choline chloride) and their respective phase transition temperatures. Fig. 2 Linear density change with temperature for aqueous binary mixtures of choline lactate (○, $x_{\text{IL}} = 0.1002$; ●, $x_{\text{IL}} = 0.2990$), LC2 : 1 (■, $x_{\text{LC2}} : 1 = 0.1003$; □, $x_{\text{LC2}} : 1 = 0.2944$) and choline chloride (Δ, $x_{\text{SALT}} = 0.0991$; ▲, $x_{\text{SALT}} = 0.3033$). where $ x_i $ and $ M_i $ are the mole fraction and molar weight of the pure components in the mixture, and $ \rho $ and $ \rho_i $ are the experimental density of the mixture and the pure components, respectively. At these temperatures, the salt choline chloride is solid so its density in solid state was used to calculate the $ V_m^E $ of its binary mixtures. Fig. 3 presents the experimental excess molar volumes, $ V_m^E $, of the three binary water + entrainer (IL/LTTM/salt) systems as a function of molar fraction at two representative temperatures (293.15 and 348 K). All experimental data can be found in the ESI (Table S3†). The experimental $ V_m^E $ data were fitted by the often used Redlich–Kister equation 17 described as follows: \[ V_m^E = x_i(1-x_i) \sum_i A_i(T) (2x_i - 1)^{i-1} \] where: \[ A_i(T) = b_i + c_i(T) \] where $ x_i $ is the mole fraction of the entrainer and $ V_m^E $ (cm$^3$ mol$^{-1}$) is the molar excess volume. The values of the parameters $ A_i $ have been determined using the method of least-squares. The fitting parameters are summarized in Table S4† together with the deviations found for this correlation. From Fig. 3 it can be observed that larger negative deviations from ideality are found at lower temperatures and higher water concentrations. This graph also depicts the strong asymmetrical behaviour of the excess molar volumes with composition. The minimum value of $ V_m^E $ is found at mole fraction close to 0.3 and is slightly shifting to lower values with increasing temperatures. The negative $ V_m^E $ values are indicative of a highly attractive interaction with water. The IL or salt + water mixtures show a larger deviation from ideality compared to the LC(2 : 1) + water mixture. Viscosity and viscosity deviation. The experimental values of the dynamic viscosity for the binary mixtures of (IL/LTTM/salt (1) + water (2)) are reported as a function of temperature and composition and included as ESI (Table S5†). Fig. 4 shows the viscosity change with temperature for the three studied aqueous binary mixtures at the same mole fraction of entrainer (0.3). The viscosity dependency on temperature was successfully fitted to the Vogel–Fulcher–Tamman (VFT) equation (5), which was previously applied for ILs:18 \[ \eta = A \exp \left( \frac{B}{T - T_0} \right) \] where $ A, B $ and $ T_0 $ are the fitting parameters obtained by linearization of the equation. The parameters and deviations for the fitting of the experimental data are included as ESI in Table S6† and the fit is shown as solid lines in Fig. 4. From Fig. 4, it can be observed that viscosity of the IL + water mixture is highest, followed by the salt + water mixture, and the viscosity of the LC(2 : 1) + water mixture is the lowest. The same trend (IL > salt > LTTM) was found for the dependency of the viscosity on the temperature; the IL viscosity being most influenced by temperature. The deviation in the viscosity for the binary mixtures, $ \Delta \eta $, was obtained from the relation: \[ \Delta \eta = \eta - \sum_i (x_i \eta_i) \] where $ \eta $ is the absolute dynamic viscosity of the mixture, and $ \eta_i $ are the viscosities of the pure components. The experimental values of $ \Delta \eta $ for the binary aqueous mixtures of the IL choline lactate and the LTTM LC2 : 1 are displayed as ESI in Table S7†. The viscosity deviation of the salt + water mixture cannot be determined because the pure salt is a solid with infinite viscosity. The experimental values were fitted ![Fig. 3](image_url) Fig. 3 Experimental excess molar volume $ V_m^E $ (cm$^3$ mol$^{-1}$) of aqueous binary mixtures of choline lactate (circles), LC2 : 1 (squares) and choline chloride (triangles) as a function of composition for two representative temperatures (293.15 K, black; 348.15 K, white). Lines represent the fitting with Redlich–Kister equation (3). ![Fig. 4](image_url) Fig. 4 Viscosity change with temperature for aqueous binary mixtures of choline lactate (circles), LC2 : 1 (squares) and choline chloride (triangles) at the same molar fraction (0.3). Lines represent fitting of the experimental data using VFT equation (5). to a Redlich–Kister polynomial equation similar to the one used for excess molar volumes: $$\Delta \eta = x_1(1 - x_1) \sum_i A_i(T)(2x_1 - 1)^{i-1}$$ (7) where $A_i$ is defined by eqn (4). The fitting parameters are summarized in Table S8 together with the deviations defined in Table S2.† Fig. 5 shows the experimental data and fitting curves for two representative temperatures (293.15 and 318.15 K). In all cases, the deviation in viscosity is negative. For the IL + water system, the minimum in viscosity deviation can be found at a mole fraction of approximately 0.5, while the minimum for the LTMM + water system is present at a mole fraction of 0.7. For both systems, the viscosity deviation decreases as the temperature increases; this behaviour is similar compared with other systems found in literature.""} Fig. 6 shows an interesting comparison between the change in properties of aqueous binary mixtures of IL and LTMM at a mole fraction of 0.5 as a function of temperature. More negative values were found for the excess molar volume of the IL choline lactate compared to those of the LTMM LC2 : 1, while the viscosity deviations were found to be lower in the whole range of temperatures. The addition of water thus has a stronger effect on the LTMM viscosity while the presence of water has a larger effect on the density of the IL.""} Properties of binary mixtures with ethanol In this section, a comparative study is made between the properties of the binary mixture of the IL choline lactate with ethanol and the IL + water system (in the previous section). Similar conclusions would be obtained for comparison of the other choline-based compounds with water and ethanol, so only one of the binary mixtures with ethanol is discussed. Density and excess molar volume. The experimental densities of the binary mixtures of the IL choline lactate and ethanol are included as ESI (Table S9†). The density change with temperature follows the expected linear trend described by eqn (1). The fitting parameters as well as the corresponding deviations of the experimental values are also included as ESI (Table S10†). Table S11† shows the experimental excess molar volumes for the binary mixtures of IL and ethanol calculated from the experimental densities following eqn (2). The Redlich–Kister equation (3) is used for the fitting of the experimental data. The fitting parameters and deviations are included in Table S12.† Viscosity and viscosity deviation. The experimental data for viscosities and the fitting parameters of VFT equation (5) fitting, as well as their deviations are included in ESI (Tables S13 and S14†). Table S15† shows the deviations in viscosity calculated from the experimental data by using eqn (6). The Redlich–Kister equation (7) is again used for the correlation of the experimental data. The fitting parameters and deviations are included in Table S16.† Fig. 7 shows a comparison between the deviations from ideal behaviour (represented by $V_m^E$ and $\Delta \eta$) for the IL mixtures with ethanol and water at a temperature of 293.15 K. Both show similar behaviour with negative deviations for both properties pointing to stronger interactions of IL–water–ethanol compared to cation–anion interactions. In both cases the minimum of the curve is located at the same IL composition, which can be interpreted as a similar solvation number for the aggregation state of cation/anions in water or ethanol. Vapour–liquid equilibria Vapour pressures of binary mixtures with water and ethanol. In this section, a comparative study is made between the vapour–liquid equilibrium data of binary mixtures of the IL choline lactate, the LTMM LC2 : 1 and the salt choline chloride with water and ethanol. The change in vapour pressure of water in the presence of each one of the choline-based entrainers is studied first. These data are useful for a comparison of the effect of the addition of entrainer on the activity coefficient of water. Table 1 reports the... VLE experimental data for the binary mixtures of water with the three entrainers. The Antoine equation was used to correlate the vapour pressure data: \[ \ln \left( \frac{P^0_i}{P_i} \right) = A_i - \frac{B_i}{T + C_i} \] (8) where $ P^0 $ is the pure component vapour pressure, $ T $ is the temperature, and $ A_i, B_i, $ and $ C_i $ are the Antoine parameters. The Antoine parameters of eqn (8) and the deviations between the correlation and the experimental data for the studied mixtures are included as ESI (Tables S17 and S18†). Fig. 8 shows a comparison in the change of the vapour pressure of water by addition of the IL choline lactate, the LTTM LC2 : 1 and the salt choline chloride. The presence of the salt shows the highest effect on the vapour pressure of water compared to the IL and the LTTM. Reason for the higher effect of the salt compared to the IL is the difference in the strength of the hydrogen bond interaction between the anion and the water. Higher interactions are expected for the chloride ion due to its higher charge/size ratio and, therefore, its higher ability for polarization. The lowest effect on the vapour pressure was found for the LTTM LC2 : 1 using the same molar ratio. Because only 1/3 of the moles of LC2 : 1 consists of choline chloride (and 2/3 of lactic acid), the LTTM only has a maximum of 1/3 of the salt's ebullioscopic effect. This point could evidence that the ability of the LTTM to affect the vapour pressure of water is mainly determined by the ebullioscopic effect of the constituent salt. Further studies are required to confirm this conjecture. Table 2 shows the VLE data for binary mixtures with ethanol. A similar plot to the one discussed above could be made for the \| Choline chloride (1) + water \| LC(2 : 1) (1) + water \| Choline chloride (1) + water (2) \| \|-----------------------------\|-----------------------\|-----------------------------\| \| $ X_1 $ \| $ T $ (K) \| $ P $ (kPa) \| $ \gamma_{\text{H}_2\text{O}} $ \| $ X_1 $ \| $ T $ (K) \| $ P $ (kPa) \| $ \gamma_{\text{H}_2\text{O}} $ \| $ X_1 $ \| $ T $ (K) \| $ P $ (kPa) \| $ \gamma_{\text{H}_2\text{O}} $ \| \|-----------------------------\|-----------------------\|-----------------------------\| \| 0.0708 \| 313.02 \| 6.61 \| 0.9045 \| 0.9735 \| 0.1998 \| 320.55 \| 6.31 \| 0.5841 \| 0.7299 \| \| \| 313.86 \| 8.63 \| 0.8932 \| 0.9613 \| 331.10 \| 11.09 \| 327.02 \| 9.50 \| 0.6389 \| 0.7985 \| \| \| 323.10 \| 14.27 \| 0.9356 \| 1.0069 \| 335.26 \| 15.77 \| 340.86 \| 19.85 \| 0.7056 \| 0.8818 \| \| \| 332.49 \| 18.03 \| 0.9356 \| 1.0069 \| 346.91 \| 24.90 \| 351.64 \| 31.15 \| 0.7115 \| 0.8892 \| \| \| 337.45 \| 22.71 \| 0.9394 \| 1.0109 \| 354.60 \| 38.31 \| 361.77 \| 47.25 \| 0.7113 \| 0.8892 \| \| \| 341.59 \| 28.55 \| 0.9826 \| 1.0575 \| 366.60 \| 57.50 \| 371.52 \| 69.93 \| 0.7317 \| 0.9144 \| \| \| 347.58 \| 35.35 \| 0.9414 \| 1.0131 \| 367.67 \| 83.69 \| 376.47 \| 83.69 \| 0.7340 \| 0.9173 \| \| \| 352.57 \| 43.66 \| 0.9455 \| 1.0176 \| \| \| \| \| \| \| \| \| 357.61 \| 53.41 \| 0.9453 \| 1.0173 \| \| \| \| \| \| \| \| \| 362.69 \| 64.76 \| 0.9410 \| 1.0127 \| \| \| \| \| \| \| \| \| 367.50 \| 78.23 \| 0.9486 \| 1.0209 \| \| \| \| \| \| \| \| \| 372.67 \| 93.92 \| 0.9429 \| 1.0148 \| \| \| \| \| \| \| \| This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. binary mixtures with ethanol, but the relative change in vapour pressure is close to zero in all cases. This difference in behaviour points to a much higher effect of the entrainers on the volatility of water compared to that of ethanol. It would be, in principle, reasonable to assume that LTTMs (just like ILs and salts) could be useful entrainers for water–ethanol separation by increasing their relative volatility and so, breaking the azeotropic behaviour. However, the effect of the IL on the relative volatility is much higher ($3\times$) compared to the LTTM. Therefore, in the next section, only ternary VLE data are measured for the IL + water + ethanol system. VLE of ternary system of choline lactate + ethanol + water. Table 3 shows the VLE data of ternary system consisting of the ethanol (1) + water (2) + choline lactate (3) at 100 kPa, obtained by keeping the IL mole fraction nearly constant at $x_3 \approx 0.2$. In this table, $x_3$ is the mole fraction of IL in the liquid phase, $x'_3$ is the mole fraction of ethanol in the liquid phase expressed on an IL-free basis, $y_1$ is the mole fraction of ethanol in the vapour phase, and $T$ is the equilibrium temperature. The relative volatility, $a_{i,j}^{\text{VLE}}$, and selectivity, $S_{i,j}^{\text{VLE}}$, can be calculated from the VLE data as follows: $$a_{i,j}^{\text{VLE}} = \frac{y_i/x'_i}{y_j/x_j}$$ (9) $$S_{i,j}^{\text{VLE}} = \frac{a_{i,j}^{\text{VLE}} \text{ with entrainer}}{a_{i,j}^{\text{VLE}} \text{ without entrainer}}$$ (10) Fig. 9 shows the evolution of the azeotrope with the addition of choline lactate as entrainer at different molar fractions of IL, while Fig. 10 shows the activity coefficients of ethanol and water as a function of ethanol composition. The electrolyte non-random two-liquid (e-NRTL) model is used to correlate the VLE data. This model is an extension of the nonrandom two-liquid (e-NRTL) model used to correlate the VLE data. This model is an extension of the nonrandom two-liquid local composition proposed by Renon and Prausnitz\textsuperscript{21} for liquid-phase activity coefficients. These activity coefficients can be obtained by adjusting the VLE data of the ternary system through the minimization of the objective function $OF$ described as follows: $$OF = \sum X (1 - \frac{\gamma_{\text{1exp}}}{\gamma_{\text{1cal}}})^2 + (1 - \frac{\gamma_{\text{2exp}}}{\gamma_{\text{2cal}}})^2$$ (11) Table 3 VLE data for ternary mixtures of ethanol (1) + water (2) + choline lactate (3) ternary system, at 100 kPa \| $x_1$ \| $x'_1$ \| $y_1$ \| $T$ (K) \| $\gamma_{\text{1exp}}$ \| $S_{i,j}^{\text{VLE}}$ \| \|-------\|-------\|-------\|--------\|----------------------\|--------------------\| \| 0.2001 \| 0.000 \| 0.000 \| 378.79 \| — \| — \| \| 0.2000 \| 0.031 \| 0.080 \| 369.23 \| 2.707 \| 0.447 \| \| 0.2000 \| 0.063 \| 0.197 \| 366.12 \| 3.677 \| 0.641 \| \| 0.2000 \| 0.125 \| 0.367 \| 361.27 \| 4.070 \| 0.798 \| \| 0.2000 \| 0.156 \| 0.458 \| 359.66 \| 4.557 \| 0.991 \| \| 0.2000 \| 0.195 \| 0.506 \| 357.01 \| 4.228 \| 1.235 \| \| 0.2000 \| 0.328 \| 0.630 \| 352.10 \| 3.496 \| 1.275 \| \| 0.2000 \| 0.438 \| 0.697 \| 351.18 \| 2.957 \| 1.640 \| \| 0.2008 \| 0.300 \| 0.740 \| 351.53 \| 2.307 \| 2.270 \| \| 0.2007 \| 0.363 \| 0.774 \| 351.24 \| 2.668 \| 1.936 \| \| 0.2007 \| 0.687 \| 0.833 \| 351.18 \| 2.273 \| 2.324 \| \| 0.2007 \| 0.842 \| 0.925 \| 351.17 \| 2.307 \| 2.270 \| \| 0.2007 \| 0.875 \| 0.940 \| 351.11 \| 2.234 \| 2.065 \| \| 0.2007 \| 0.906 \| 0.952 \| 351.06 \| 2.050 \| 1.607 \| \| 0.2009 \| 0.938 \| 0.960 \| 351.05 \| 1.595 \| 1.313 \| \| 0.2008 \| 0.969 \| 0.976 \| 351.03 \| 1.304 \| 0.447 \| \| 0.2009 \| 1.000 \| 1.000 \| 351.01 \| — \| — \| Table 2 VLE data for binary mixtures composed of (i) choline lactate + ethanol and (ii) LC(2 : 1) + ethanol \| $X_1$ \| $T$ (K) \| $P$ (kPa) \| $a_{\text{EOH}}$ \| $\gamma_{\text{EOH}}$ \| \|-------\|--------\|----------\|-----------------\|------------------\| \| 0.2000 \| 313.17 \| 17.78 \| 0.9927 \| 1.2409 \| \| 0.2000 \| 318.61 \| 23.50 \| 0.9960 \| 1.2450 \| \| 0.2000 \| 323.21 \| 29.43 \| 0.9969 \| 1.2462 \| \| 0.2000 \| 328.54 \| 37.93 \| 0.9993 \| 1.2491 \| \| 0.2000 \| 332.97 \| 46.43 \| 0.9996 \| 1.2495 \| \| 0.2000 \| 337.15 \| 55.85 \| 0.9996 \| 1.2496 \| \| 0.2000 \| 340.24 \| 63.89 \| 1.0006 \| 1.2508 \| \| 0.2000 \| 343.88 \| 74.46 \| 1.0002 \| 1.2503 \| \| 0.2000 \| 346.34 \| 82.47 \| 1.0004 \| 1.2505 \| \| 0.2000 \| 349.52 \| 93.83 \| 1.0003 \| 1.2504 \| \| 0.2000 \| 351.32 \| 100.71 \| 0.9993 \| 1.2492 \| \| $X_1$ \| $T$ (K) \| $P$ (kPa) \| $a_{\text{EOH}}$ \| $\gamma_{\text{EOH}}$ \| \|-------\|--------\|----------\|-----------------\|------------------\| \| 0.1999 \| 313.05 \| 17.77 \| 0.9985 \| 1.2480 \| \| 0.1999 \| 318.46 \| 23.41 \| 1.0002 \| 1.2502 \| \| 0.1999 \| 323.10 \| 29.46 \| 1.0033 \| 1.2540 \| \| 0.1999 \| 328.34 \| 37.86 \| 1.0068 \| 1.2584 \| \| 0.1999 \| 332.77 \| 46.42 \| 1.0086 \| 1.2607 \| \| 0.1999 \| 336.94 \| 55.77 \| 1.0073 \| 1.2591 \| \| 0.1999 \| 339.96 \| 63.75 \| 1.0104 \| 1.2629 \| \| 0.1999 \| 343.70 \| 74.58 \| 1.0092 \| 1.2614 \| \| 0.1999 \| 346.26 \| 82.30 \| 1.0017 \| 1.2521 \| \| 0.1999 \| 349.28 \| 93.51 \| 1.0066 \| 1.2582 \| \| 0.1999 \| 351.40 \| 101.45 \| 1.0035 \| 1.2542 \| IL–water and IL–ethanol by assuming ideal behaviour of the vapour phase and iteratively solving the equilibrium conditions expressed in eqn (12) for the solvent: \[ y_i p = X_i \gamma_i P_i^0 \] (12) where $ y_i $ is the vapor-phase mole fraction of solvent $ i $; $ p $ is the total pressure in the system; $ X_i $ is the liquid-phase mole fraction based on the assumption of total dissociation of electrolytes; $ \gamma_i $ is the activity coefficient of component $ i $ obtained from the e-NRTL model; and $ P_i^0 $ is the vapour pressure of solvent $ i $ at equilibrium temperature, which can be calculated using the Antoine coefficients. The binary interaction parameters for the e-NRTL model and the deviations of the model with the experimental data are included as ESI (Table S19†). Using the relative volatility as separation factor at an ethanol mole fraction of 0.95 and 100 kPa, most of the ionic liquids achieve an average relative volatility of 1.33. As can be seen in Table 3, the relative volatility of ethanol when using choline lactate is in agreement with this average value. Fig. 10 shows how the presence of the IL changes the relative volatility of the ethanol + water system. The binary system in absence of IL shows azotropic behaviour. Addition of the IL results in an azotropic composition shift to higher concentrations of ethanol (as observed for the mixture containing 0.10 and 0.15 mole fractions of IL) until the azeotrope completely disappears at a mole fraction of 0.2. Conclusions In this work, the use of a LTTM (mixture of lactic acid + choline chloride in the ratio 2 : 1) as possible entrainer for azotropic distillation was evaluated and compared to a lactate-based IL (choline lactate) and the choline chloride salt. The main interactions between these entrainers with the azotropic mixture ethanol + water are discussed. The strong negative values found for the deviations of their properties from ideal behaviour point to strong hydrogen-bond interactions between the entrainer and ethanol–water. The vapour pressure of water was strongly reduced by addition of all three entrainers. The highest effect was found for the salt choline chloride. The salting out effect of the LTTM was found to be lower caused by the lower concentration of choline chloride in the mixture. The study of the azotropic behaviour of the ternary IL + ethanol + water shows a shift of the azotropic point to higher concentrations of ethanol upon the addition of the IL, until the azeotrope completely disappears at a IL mole fraction of 0.2. Experimental section Chemicals The IL choline lactate with a purity of >98 wt% was supplied by Iolitec, synthesized on request. It was used without any further purification. Ethanol (≥99.5 wt%) was purchased from TechniSolv. Ultra-pure crystalline α-lactic acid at pharmaceutical grade was kindly provided by PURAC Biochem B.V. (Gorinchem, Netherlands). Choline chloride was obtained from Aldrich (≥98 wt%). Deionized MilliQ water was used in all the studied mixtures (<18.2 MΩ cm). Choline lactate, choline chloride and lactic acid were dried under vacuum before use. The water content was measured by using Karl Fischer (KF796) titration to be <1 wt% in all experiments. Preparation of LTTM LTTM formed by mixing lactic acid and choline chloride were prepared following a similar procedure previously reported by our group. The mixtures were weighted using a Mettler AX205 balance with a precision of ±0.02 mg, whereby the water content of the starting materials was always measured and taken into account. Both the hydrogen bond donor (lactic acid) and acceptor (choline chloride) were added to a closed 25 mL glass flask and homogeneously mixed before heating. The temperature was set to 60 ± 0.1 °C using a thermostatic oil bath with a IKA ETS-D5 temperature controller. Once a transparent liquid was formed, the mixture was cooled down. In our previous works, a TGA analysis (TGA Q500 by TA Instruments) was carried out to check the thermal stability at a scan... rate of 10 °C min⁻¹ under a nitrogen flow with a weighing precision of ±0.01% a sensitivity of 0.1 µg, and an isothermal temperature precision of ±0.1 °C. Differential Scanning Calorimetry (DSC) Q1000 was used to obtain the glass transition temperature of the formed LTTM with a scan rate of 10 °C min⁻¹ a sensitivity of 0.2 µW and a temperature precision of ±0.1 °C. The water content was measured with the Karl-Fischer titration method on a Metrohm 870 KF Titirino plus. Determination of physical properties: density and viscosity The density and the viscosity of the three entrainers were determined at atmospheric pressure and at temperatures ranging from 298 to 353 K. Due to the high hygroscopicity of the samples, both properties were measured using an Anton Paar SVM 3000/G2 Stabinger viscometer. This equipment requires only a total volume of sample of 2.5 mL, which is not in contact with the atmosphere during the measurement, so that moisture capture from the air is avoided. The equipment is provided with a high-precision thermostat with a stability of 0.005 K and calibrated by the manufacturer. The uncertainties of the density (with viscosity correction) and viscosity measurements are ±0.0005 g cm⁻³ and ±0.35% respectively. Determination of VLE An all-glass ebulliometer (Fischer VLE 602D) was used for the determination of the experimental VLE data. In this device, the equilibrium chamber is a dynamic recirculating still, equipped with a Cottrell circulation pump. The operation procedure is based on the principle of the circulation method. A control unit (Fischer VLE 2+) was used to set the pressure and heating power in the immersion heater. The equilibrium was reached after 30 minutes or longer, when the condensation rate (1–2 drops per second) and equilibrium temperature were constant in order to ensure a stationary state. Pressure and equilibrium temperature could be determined with an accuracy of ±0.01 kPa and ±0.01 K, respectively. Two or three replicate runs were performed for each sample. All solutions were prepared gravimetrically with an electronic balance (Mettler Toledo AX 205) with a readability of ±10⁻⁶ g. VLE data of 5 binary systems were measured i.e., water + IL, water + LTTM, water + salt, ethanol + IL and ethanol + LTTM. The salt choline chloride was found to be immiscible with ethanol. The VLE data of the ternary system consisting of water + ethanol + IL were also measured. Mixtures of water + IL or ethanol + IL were added to the initial sample in order to maintain a constant IL mole fraction in the system. Samples of the condensed vapour phase were periodically analyzed by gas chromatograph (GC) and High Pressure Liquid Chromatography (HPLC, Varian Prostar) in order to guarantee the absence of entrainer in the vapour phase. Vapour phase samples were injected in a Varian Prostar HPLC equipped with a silica-based Grace Prevail™ Organic Acid column (250 mm × 4.6 mm) with a particle size of 5 µm. The temperature of the column was kept constant in an oven (Varian Prostar Model 510) at 313.2 K for all measurements. Detection of entrainers was done using a UV detector (Varian Prostar model 310) at 210 nm. Each sample was injected twice. The amount of ethanol in the condensed vapour phase was analysed using a Varian CP-3800 gas chromatograph (GC) equipped with a flame ionization detector (250 °C) and a Varian CP-SIL 5CB column (25 m × 1.2 µm). The injector temperature was 275 °C and the carrier gas was helium with a constant flow rate of 4.0 mL min⁻¹. The water mole fraction was obtained from a mass balance calculation. Due to the negligible volatility of the salt/IL/LTTM, no presence of any of the studied entrainers was detected in the vapour phase. With this method, the detection limits for ethanol and lactic acid are, respectively, 0.003 and 0.0002 in mole fraction. The liquid phase of the ternary system is composed of ethanol, water and the IL choline lactate. The ethanol mole fraction in the liquid phase was determined using the same GC, while the water content in the liquid phase was analysed using Karl-Fischer titration on a Metrohm 870 KF Titirino plus. The concentration of all components in both phases could be determined with an average overall deviation in mole fraction of ±0.004. Notes and references 1. A. Pandey, Handbook of Plant-based Biofuels, CRC, 2008. 2. V. Gomis, R. Pedraza, O. Francés, A. Font and J. C. Asensi, Ind. Eng. Chem. Res., 2007, 46, 4572–4576. 3. M. Errico and B. G. Rong, Sep. Purif. Technol., 2012, 96, 58–67. 4. H. Habaki, O. Tabata, J. Kawasaki and R. Egashira, J. Chem. Eng. J., 2010, 43(2), 214–223. 5. F. Christen, M. Minier and H. Renon, Biotechnol. Bioeng., 1990, 36, 116–123. 6. Z. Lei, H. Wang, R. Zhou and Z. Duan, Chem. Eng. J., 2002, 87, 149–156. 7. A. Pereiro, J. Araújo, J. Esperança, I. Marrucho and L. Rebelo, J. Chem. Thermodyn., 2012, 46, 2–28. 8. W. Arlt, M. Seiler, C. Jork and T. Scheiner, Ionic Liquids as Selective Additives for the Separation of Close-Boiling or Azeotropic Mixtures, PCT Int. Appl. WO 02/747 18 A2, 2002. 9. C. Jork, M. Seiler, Y.-A. Beste and W. Arlt, J. Chem. Eng. Data, 2004, 52, 852–857. 10. R. P. Switalski, J. D. Holbrey and R. D. Rogers, Green Chem., 2003, 5, 361–363. 11. M. Freemantle, An Introduction to Ionic Liquids, Royal Society of Chemistry, 2009. 12. A. P. Abbott, D. Boothby, G. Capper, D. L. Davies and R. K. Rasheed, J. Am. Chem. Soc., 2004, 126, 9142–9147. 13. M. Francisco, A. van den Bruinhorst and M. C. Kroon, Green Chem., 2012, 14(8), 2153–2157. 14. Q. Zhang, K. D. O. Vigier, S. Royer and F. Jérôme, Chem. Soc. Rev., 2012, 41, 7108–7146. 15. M. Francisco, A. van der Bruinhorst and M. Kroon, Anew. Chem., Int. Ed., 2013, 52, 3074–3085. 16. M. Francisco, A. van der Bruinhorst, L. F. Zubier, C. J. Peters and M. Kroon, Fluid Phase Equil., 2013, 340, 77–84. 17. O. Redlich and A. Kister, Ind. Eng. Chem., 1948, 40, 345–348. 18. H. Rodríguez and J. F. Brennecke, J. Chem. Eng. Data, 2006, 51, 2145–2155. 19. U. Domanska and M. Królikowska, J. Solution Chem., 2012, 41, 1422–1445. 20. C. Antoine, C. R. Acad. Sci., 1888, 107, 681. 21. H. Renon and J. M. Prausnitz, AIChE J., 1968, 14, 135–144. 22. P. T. Ngema, Separation Processes for High Purity Ethanol Production, 2010. 23. A. V. Orchilles, P. J. Miguel, E. Vercher and A. Martinez-Andreu, J. Chem. Eng. Data, 2010, 55, 1669–1674. 24. W. Geng, L. Z. Zhang, D. S. Deng, Y. Ge and J. B. Li, J. Chem. Eng. Data, 2010, 55, 1679–1683. 25. L. Z. Zhang, Y. Ge, D. X. Ji and J. B. Li, J. Chem. Eng. Data, 2009, 54, 2322–2329. 26. Y. Ge, L. Z. Zhang, X. C. Yuan, W. Geng and J. B. Li, J. Chem. Thermodyn., 2008, 40, 1248–1252. 27. D. Sunita, G. Shamla and P. L. V. N. Saichandra, National Conference, CHEMCON, 2010.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 892, 1 ], [ 892, 5505, 2 ], [ 5505, 10497, 3 ], [ 10497, 14735, 4 ], [ 14735, 18742, 5 ], [ 18742, 23969, 6 ], [ 23969, 28958, 7 ], [ 28958, 33018, 8 ], [ 33018, 39068, 9 ], [ 39068, 39877, 10 ] ] }
bf0b06add300a02cce0e89c1c1fd1f032f55494b	{ "olmocr-version": "0.1.59", "pdf-total-pages": 70, "total-fallback-pages": 0, "total-input-tokens": 236019, "total-output-tokens": 34808, "fieldofstudy": [ "Biology" ] }	Dissecting endothelial to haematopoietic stem cell transition by single-cell transcriptomic and functional analyses Siyuan Hou1,2,4,9, Zongcheng Li2,9, Xiaona Zheng3,9, Yun Gao5,9, Ji Dong6,9, Yanli Ni2,9, Xiaobo Wang3, Yunqiao Li3, Xiaochen Ding3, Zhilin Chang3, Shuaili Li3, Yuqiong Hu5, Xiaoying Fan5, Yu Hou5, Lu Wen5,6, Bing Liu1,2,, Fuchou Tang5,6,7,, Yu Lan1,8,* 1Key Laboratory for Regenerative Medicine of Ministry of Education, Institute of Haematology, School of Medicine, Jinan University, Guangzhou 510632, China 2State Key Laboratory of Experimental Haematology, Fifth Medical Center of Chinese PLA General Hospital, Beijing 100071, China 3State Key Laboratory of Proteomics, Academy of Military Medical Sciences, Academy of Military Sciences, Beijing 100071, China 4Integrated Chinese and Western Medicine Postdoctoral research station, Jinan University, Guangzhou 510632, China 5Beijing Advanced Innovation Center for Genomics and Biomedical Institute for Pioneering Investigation via Convergence, College of Life Sciences, Peking University, Beijing 100871, China 6Ministry of Education Key Laboratory of Cell Proliferation and Differentiation, Beijing 100871, China 7Peking-Tsinghua Center for Life Sciences, Peking University, Beijing 100871, China 8Guangzhou Regenerative Medicine and Health-Guangdong Laboratory (GRMH-GDL), These authors contributed equally to this work. Correspondence: Bing Liu ([email protected]); Fuchou Tang ([email protected]) and Yu Lan ([email protected]) ABSTRACT Haematopoietic stem cells (HSCs) in adults are believed to be born from hemogenic endothelial cells (HECs) in mid-gestational mouse embryos. Due to rare and transient nature, the HSC-competent ECs have never been stringently identified and accurately captured, let alone their genuine vasculature precursors. Here, we firstly used high-precision single-cell transcriptomics to unbiasedly examine relevant EC populations at continuous developmental stages and transcriptomically identified putative HSC-primed HECs. Combining computational prediction and in vivo functional validation, we precisely captured HSC-competent HECs by newly constructed Neurl3-EGFP reporter mouse model, and realized enrichment further by surface marker combination. Surprisingly, endothelial-haematopoietic bi-potential was rarely but reliably witnessed in culture of single HECs. Noteworthy, primitive vascular ECs experienced two-step fate choices to become HSC-primed HECs, resolving several previously observed contradictions. Taken together, comprehensive understanding of endothelial evolutions and molecular programs underlying HSC-primed HEC specification in vivo will facilitate future investigations directing HSC production in vitro. INTRODUCTION The adult haematopoietic system, consisted mainly of haematopoietic stem cells (HSCs) and their multi-lineage progenies, is believed to be derived from hemogenic endothelial cells (HECs) in mid-gestational embryos. It is generally accepted that while still embedded in the endothelial layer and presenting endothelial characteristics, HECs begin to express key hemogenic transcription factor Runx1 and have hemogenic potential. Different from haematopoietic progenitors, HECs lack the expression of haematopoietic surface markers, such as CD41 and CD45, which mark the population capable of generating haematopoietic progenies when directly tested in colony-forming unit assays. Haematopoietic stem and progenitor cells (HSPCs) are visualized to emerge from aortic endothelial cells (ECs) via a transient and dynamic process called endothelial-to-haematopoietic transition to form intra-aortic haematopoietic clusters (IAHCs). Being located within IAHCs or to the deeper sub-endothelial layers, pre-HSCs serve as the important cellular intermediates between HECs and HSCs, featured by their inducible repopulating capacity and priming with haematopoietic surface markers. The specification of HSC-primed HECs is the initial and one of the most pivotal steps for vascular ECs to choose a HSC fate. However, as the precise identity of HSC-primed HECs is not clear, contradictory notions regarding whether primordial or arterial fated ECs are the direct origin of HSC-primed HECs are still on the debate. It is proposed that definitive HECs and arterial ECs represent distinct lineages. Moreover, HSCs and arterial ECs are proposed to arise from distinct precursors, characterized by different Notch signaling strengths. Most recently, HSC-primed HECs have been transcriptionally identified in human embryos, which present an unambiguous arterial property, indicative of their arterial EC origin $^{19}$. In order to deeply investigate the cellular evolutions and molecular events underlying the specification of HSC-primed HECs and their subsequent commitment to HSPCs, it is necessary to efficiently isolate the HSC-primed HECs, which is proven to be difficult not only because the population is proposed to be small and transient, but also due to the technical challenging to determine their HSC competence $^{20}$. Considering that not only HSCs but also the transient definitive haematopoiesis during embryogenesis are derived from HECs, repopulating capacity is required for the functional evaluation of the HSC-primed HECs. Previous studies have reported the HSC competence of CD47$^+$ but not CD47$^-$ ECs in embryonic day (E) 10.5 aorta-gonad-mesonephros (AGM) region and both Dll4$^+$ and Dll4$^-$ ECs in E9.5 para-aortic splanchnopleura (P-Sp) region $^{11,21}$. Nevertheless, the enrichment of the above surface markers is far from efficient. Several transgenic reporter mouse models have been established by which HECs could be distinguished from non-HECs, including $\text{Ly6a-GFP}$, GFP transgenic reporter under the control of Runx1 $+23$ enhancer ($\text{Runx1} +23\text{GFP}$) and $\text{Gfi1-Tomato}$, and the usage of these reporters largely helps to delineate the process of endothelial-to-haematopoietic transition $^{3,14,22-25}$. Although expected to a certain extent, the HSC competence of the HECs labeled by these reporters has not been functionally validated. Up-to-date, efficient isolation of the HSC-primed HEC population has not yet been achieved. With the aim of delineating the molecular events underlying HSC emergence, several single-cell transcriptional profiling studies on HECs, IAHC cells, and HSPCs in the AGM region have been reported in recent years. Using either Runx1 +23GFP or Gfi1-Tomato as the marker of putative HECs, several defined cell populations are transcriptionally profiled by Fluidigm single-cell qPCR or single-cell RNA sequencing (scRNA-seq) $^3,14,22$. Moreover, the cellular components of IAHCs are investigated at single-cell level by mechanically picking up single whole IAHCs in the aortas, showing cells with pre-HSC feature are predominantly involved $^{14}$. Interestingly, contradiction still exists regarding whether HECs and non-HECs are molecularly similar and to what extent the two populations are distinguishable $^{14,22}$. Since the enrichment efficiency or specificity of the above markers to define the HEC population might be not enough, an unsupervised screening of the embryonic endothelial pool within haematopoietic tissues is required for the precise recognition of HSC-primed HECs. Here, we firstly used high-precision single-cell transcriptomics to unbiasedly examine all the EC populations spanning continuous developmental stages covering the presumed time points for the specification of HSC-primed HECs, transcriptomically identified them, and computationally screened for their candidate markers. Based on the consequently precise capture and isolation of the HSC-competent HECs using surface marker combination or newly constructed fluorescent reporter mice, we further decoded the cellular evolutions and molecular programs underlying the stepwise hemogenic fate settling from the initial primordial vascular ECs. A series of new findings, including the endothelial-haematopoietic bi-potential of HECs and the multi-step fate choice for the specification of HSC-primed HECs, unprecedentedly enrich our understanding of HSC generation in vivo and should be extremely critical to inspire new approaches for stepwise HSC regeneration from pluripotent stem cells. RESULTS Transcriptomic identification of the HECs in AGM region We first analyzed mouse embryos from E9.5, when the initial IAHC formation in the aorta occurs, to the stage of the appearance of HSCs at E11.0 (Supplementary information, Fig. S1a). For each embryo, the embryo proper was isolated and the head, limb buds, heart, visceral bud, and vitelline and umbilical vessels outside the embryo proper were excluded (Fig. 1a). To specifically capture aortic luminal ECs of AGM region, we performed microinjection of fluorescent dye Oregon green into the dorsal aortas of E10.0-E11.0 embryos as reported (Fig. 1a; Supplementary information, Fig. S1b). The sampled cells were purified by FACS as CD45^-CD31^+CD144^+, which contained predominantly vascular ECs and CD41^+ haematopoietic cells. Meanwhile, CD45^-CD31^-CD144^- non-EC cells in the body were used as negative controls (Fig. 1a). We used unique molecular identifier (UMI)-based scRNA-seq method to accurately measure the gene expression profiles within individual cells. In totally 662 sequenced single cells, 597 single-cell transcriptomes passed rigorous quality control. On average we detected 7,035 genes (from 2,266 to 10,843) and 636,418 transcripts (from 103,793 to 2,959,573) expressed in each individual cell (Supplementary information, Fig. S1c). According to a graph-based clustering approach from Seurat software, all cells were separated into six clusters, including one negative (Neg) cluster containing mainly non-EC negative control cells, and five sample clusters comprising almost all FACS-isolated sample cells (Supplementary information, Fig. S1d and Table S1). Featured by the obvious Runx1 and Itga2b (encoding CD41) expression, the haematopoietic cell (HC) cluster was distributed away from the other four vascular EC clusters which presented apparent arterial or venous characteristics (Supplementary information, Fig. S1d, e). One venous EC (vEC) cluster was readily recognized by the exclusive expression of Nr2f2 in all vascular EC populations (Supplementary information, Fig. S1d, e). Two arterial EC clusters showed similar Gja5 expression but different level of Ltbp4 expression. Together with their different sampling stages (mainly from E9.5-E10.0 and E10.5-E11.0, respectively), they were annotated as early arterial EC (earlyAEC) and late arterial EC (lateAEC) cluster, respectively (Supplementary information, Fig. S1d, e). The left one cluster basically met the criteria of the molecular definition of HEC, showing apparent Runx1 expression upon endothelial property, and was consequently named as HEC cluster (Supplementary information, Fig. S1d, e). To more strictly define the HEC population, cells within Neg cluster and those transcriptionally expressing Ptprc (encoding CD45) or Spn (encoding CD43) were excluded for the subsequent analysis (Supplementary information, Fig. S1f). HEC and other two AEC clusters were further focused as they were either molecularly or spatiotemporally near to each other (Fig. 1b, Supplementary information, Fig. S1d). To exclude the possibility that we failed to identify important populations relevant to hemogenic specification in earlyAEC cluster, which contributed evidently to the aortic inner layer of AGM region at E10.0 (Supplementary information, Fig. S1f), we performed forced clustering within the given cluster. Runx1* (signature of hemogenic specification) was not significantly differentially expressed between the two sub-clusters, suggesting that no population with sign of hemogenic specification was missed by our clustering (Supplementary information, Fig. S1g). Moreover, very few genes were significantly differentially expressed in the forced sub-clusters of HEC, and none of them was related to hemogenic or haematopoietic features, indicative of the largely homogeneous property of the HEC cluster (Supplementary information, Fig. S1g). HEC was reduced promptly in number at E10.5, and became hardly detectable by E11.0 (Fig. 1b; Supplementary information, Fig. S1f). The highly expressed genes in HEC as compared to earlyAEC and lateAEC were mainly enriched in the terms related to cell cycle and ribosome biogenesis (Fig. 1c; Supplementary information, Table S2). Cell cycle analysis demonstrated a remarkably activated cycling in HEC, in sharp contrast to the quiescent state by arterial EC maturation (Fig. 1d). On average, each cell in HEC cluster expressed more mRNA molecules and ribosomal genes than either earlyAEC or lateAEC (Fig. 1e; Supplementary information, Fig. S1h), supportive of the globally up-regulated transcriptional and translational activity during hemogenic specification, which was in line with the finding in human embryo that translational initiation is overrepresented in HSC-primed HECs than in arterial ECs. We further evaluated the arteriovenous scores of the populations we defined, and found similar results in mouse and human that HEC rather than haematopoietic populations manifested certain arterial feature (Fig. 1f). Trajectory analysis by Monocle 2 suggested that along the arterial maturation path from earlyAEC towards lateAEC, HEC was segregated out from earlyAEC at E9.5-E10.0 (Fig. 1g). The gradual up-regulation of hemogenic genes, including Runx1 and Spi1, was accompanied by the gradual down-regulation of both endothelial and arterial genes along the HEC specification pseudotime, with the endothelial-haematopoietic dual-feature of the HEC population presenting as a dynamic continuum (Fig. 1h). The finding was in line with previous report about the reciprocal expression of Runx1 and Sox17 in HECs. To search for the genes that would be potentially meaningful to the distinct fate choices of earlyAEC, those differentially expressed between earlyAEC and its downstream population HEC or lateAEC were screened out, and eight major patterns were witnessed (Fig. 1i; Supplementary information, Fig. S1i and Table S3). Most of these genes showed altered expression along one but not both specification paths from earlyAEC (Pattern I, II IV, and V) (Fig. 1i; Supplementary information, Fig. S1i). Most transcription factors (TFs) within these patterns were those up-regulated along either HEC specification or arterial EC maturation (Fig. 1j; Supplementary information, Fig. S1j). Interestingly, both Hoxa5 and Hoxa9 belonged to the same pattern as Runx1, although their expression was not well-correlated with Runx1 (Fig. 1j; Supplementary information, Fig. S1j, k). The data suggested that the gene expressions should be orchestrated and precisely regulated for the subsequent cell fate choice from earlyAEC. Efficient capture of the HSC-competent and endothelial-haematopoietic bi-potent HECs in AGM region We next made an effort to identify surface marker combination to highly enrich the HECs for functional evaluation (Supplementary information, Table S4). Cd44, Procr (coding CD201) and Kit were screened out by differentially expressed genes and correlation analysis (Fig. 2a). We specifically focused on E10.0 in the following functional assays to keep consistent with the transcriptomic finding. Whole-mount immunostaining showed that in addition to the scattered blood cells throughout the tissue, the expression of CD44 was detected in the whole endothelial layer of dorsal aorta and very proximal part of its segmental branches (Fig. 2b). Using similar strategy as for pre-HSC identification $^1$, we found only the derivatives induced from CD41$^-$CD43$^-$CD45$^-$CD31$^+$Kit$^+$CD201$^+$ rather than CD41$^-$CD43$^-$CD45$^-$CD31$^+$Kit$^+$CD201$^-$ population at E9.5-E10.0 could long-term (16 weeks) and multi-lineage reconstitute lethally irradiated adult recipients, although both populations generated haematopoietic clusters with different frequencies upon 7 days culture on OP9-DL1 stromal cells (Fig. 2c-e; Supplementary information, Fig. S2a-c). Self-renewal capacity of the HSCs was further validated by secondary transplantation (Fig. 2d, e; Supplementary information, Fig. S2b). Within CD41$^-$CD43$^-$CD45$^-$CD201$^+$ population, induced HSC potential was exclusively detected in CD44$^+$ subpopulation (Fig. 2c-e; Supplementary information, Fig. S2a-c). Thus, our data identified CD41$^-$CD43$^-$CD45$^-$CD31$^+$CD201$^+$Kit$^+$CD44$^+$ (PK44) population in E10.0 caudal half as the HSC-competent HECs. As compared to other endothelial surface markers, Flk1 (encoded by Kdr) is known to be specifically localized within the vessel lumen layer, and very few and only the basal-most localized IAHC cells express Flk1 $^7$. Here, almost all PK44 cells expressed Flk1 by FACS. analysis, indicative of their endothelial layer localization (Fig. 2f). To determine the transcriptomic identity of the HSC-competent HECs we isolated, totally 96 PK44 single cells derived from E10.0 AGM were sequenced (Supplementary information, Table S1). The PK44 cells were clustered together with HEC by computational assignment (Fig. 2g), and showed a similar high expression of the HEC feature genes (Fig. 2h). The ubiquitous and obvious expression of several key haematopoietic TFs, including Runx1, Spi1, Gfi1, and Myb, in PK44 cells inferred the enrichment of hemogenic potential (Fig. 2h; Supplementary information, Fig. S2d). Therefore, immunophenotypically purified PK44 cells elegantly represented the transcriptomically defined HEC. We next explored whether endothelial-haematopoietic bi-potential existed in these HSC-competent HECs, since that if a cell population is experiencing fate choice so that the transient intermediate state might be captured. Firstly, we found that the Kit+C201+ ECs in the body part of embryo proper at E9.5-E10.0 had a relatively higher endothelial tube-forming capacity as compared to the Kit− or Kit+C201− endothelial populations (Supplementary information, Fig. S2e). Furthermore, CD44+ and CD44− fractions within Kit+C201+ ECs showed comparable endothelial tube-forming capacity whereas the generation of haematopoietic cells in the cultures was exclusively detected in the CD44+ ones under the bi-potential induction system (Supplementary information, Fig. S2f). The data suggested the largely maintenance of endothelial potential in the HECs. By single-cell in vitro induction, 40.6% (106/261) PK44 cells gave rise to only haematopoietic progenies and 23.0% (60/261) only endothelial tubules. Remarkably, 2.7% (7/261) had both haematopoietic and endothelial potential (Fig. 2i; Supplementary information, Fig. S2f). All three kinds of potential did not present an obviously biased distribution regarding Kit or CD201 expression level by index sorting analysis (Fig. 2j). Such rare bi-potential should properly represent the intermediate cellular state in HECs along their specification path (Fig. 1h), with both endothelial and haematopoietic competencies being reflected by the asymmetric cell division under in vitro culture condition, which further emphasized the efficiency of capturing such a dynamic functional population via unsupervised computational screening. Transcriptional and functional relationship between HECs and T1 pre-HSCs Since the transcriptomically identified HECs and the immunophenotypically defined HSC-competent HECs (PK44) presented a largely similar molecular features (Fig. 2g, h; Supplementary information, Fig. S2d), we combined them as transcriptomic & immunophenotypic & functional HEC (tif-HEC) for the subsequent analysis. tif-HEC expressed a series of pre-HSC signature genes we previously identified $^1$, including Hlf, Gfi1, Neurl3, Bcl11a, Adgrg1, Ilkzf2, Angpt1, Mycn, and Procr, suggestive of their HSC-related identity (Fig. 2h). We further performed scRNA-seq of 47 T1 pre-HSCs (CD31\textsuperscript{+}CD45\textsuperscript{−}CD41\textsuperscript{low}Kit\textsuperscript{+}CD201\textsuperscript{high}) from E11.0 AGM using the same sequencing strategy as other cells in the present study $^1$ (Fig. 3a; Supplementary information, Table S1). As compared to tif-HEC, T1 pre-HSC expressed similar level of Runx1 and Gfi1 but obviously higher level of Spn (encoding CD43), validating its haematopoietic cell identity (Fig. 3b). The distribution of most T1 pre-HSCs was adjacent to tif-HEC via t-SNE visualization (Fig. 3c). Of note, principal component (PC) 2 by PCA analysis largely captured the transcriptomic differences between tif-HEC and T1 pre-HSC (Fig. 3d). The genes enriched in PC2 positive direction, where tif-HECs were mainly localized, were related to cell division, vascular development and cell spreading (Fig. 3e). Consistently, approximately 90% cells in HEC were proliferative (Fig. 1d), whereas the constitution is only about half in the T1 pre-HSCs $^{11}$. Serving as the extracellular matrix component of blood vessels, Col4a1 was expressed higher in tif-HEC than in T1 pre-HSC, further confirming the vascular endothelial property of the HECs we identified $^{31}$ (Fig. 3f). In comparison, the genes enriched in PC2 negative direction mainly related to RNA splicing and blood coagulation (Fig. 3e). Together with the overrepresented Spi1 in T1 pre-HSC (Fig. 3f), the data suggested that haematopoietic activity has been activated in T1 pre-HSC as compared to HEC. The developmental path from tif-HEC to T1 pre-HSC was inferred by Mpath trajectory analysis (Fig. 3g). Consistently, during the course of in vitro culture of the PK44 population from E10.0 AGM region on OP9-DL1 stromal cells to induce its HSC activity, we could witness the generation of immunophenotypic T1 pre-HSCs (Fig. 3h). We also evaluated the endothelial and haematopoietic potentials of the T1 pre-HSCs (CD31^+CD45^+CD41^low^Kit^+CD201^high^) in E11.0 AGM region at single-cell level. Surprisingly, we found that although displayed largely decreased endothelial potential as compared to E10.0 PK44 cells (Fig. 2i), T1 pre-HSCs still maintained comparable endothelial-haematopoietic bi-potential as that in PK44 population (Fig. 3i). This finding implied that the extremely rare and enriched T1 pre-HSC population has not completely fulfilled the endothelial-to-haematopoietic fate transition. Enrichment of the HSC-competent HECs by newly established Neurl3-EGFP reporter In an effort to search for single markers to distinguish HSC-primed HECs from non-HECs or those CD45/CD43 haematopoietic cells sharing an endothelial immunophenotype, we computationally screened for the genes significantly overrepresented in HEC cluster as compared to each of the other four clusters, including one haematopoietic cluster (HC) and three vascular EC clusters (vEC, earlyAEC and lateAEC) (Supplementary information, Fig. S1f). Totally eleven genes were screened out, which were then designated as signature genes of HSC-primed HEC, including three TFs (Mycn, Hlf and Gfi1) but no cell surface markers (Fig. 4a; Supplementary information, Table S5). Most of them manifested similarly high expression in T1 pre-HSCs, with six of them, namely Neurl3, Dnmt3b, Mycn, Hlf, Gfi1, and Gck, belonged to pre-HSC signature genes 11 (Fig. 4a). To further validate the bioinformatics findings and precisely determine the localization of these HSC-primed HECs, we specially chose Neurl3 to establish a fluorescence reporter mouse line with the mind of possessing enough sensitivity, as the median expression of Neurl3 was the highest among these signature genes (Fig. 4a; Supplementary information, Table S5). By CRISPR/Cas9-mediated gene knockin strategy, the EGFP was inserted into the translational initiation codon of mouse Neurl3 gene to ensure that EGFP would be expressed in exactly the same way as Neurl3 (Fig. 4b). We firstly evaluated the Neurl3-EGFP expression by flow cytometric analysis (Fig. 4c). At E10.0 AGM region, about half of the Neurl3-EGFP+ cells were haematopoietic (CD41/CD43/CD45-positive) cells, which constituted about one fourth of haematopoietic population (Fig. 4c). All the Neurl3-EGFP* cells were CD31, and nearly all of them expressed CD44, indicative of the predominant aortic localization of Neurl3-EGFP ECs (Fig. 2b, 4c). Importantly, most PK44 cells were Neurl3-EGFP, highly suggesting the enrichment of HSC-competence by the Neurl3-EGFP ECs (Fig. 4c). To confirm the HSC-competence of the Neurl3-EGFP-labeled ECs, we performed co-culture plus transplantation assay using E10.0 Neurl3-EGFP mouse embryos (Fig. 4d). Although both could generate haematopoietic clusters under the in vitro cultures, all the long-term (16 weeks) repopulations were detected exclusively in the recipients transplanted with the derivatives from CD44Neurl3-EGFP ECs but not from CD44Neurl3-EGFP- ECs (Fig. 4e, f; Supplementary information, Fig. S3a). We next investigated the transcriptomic identity of the Neurl3-EGFP ECs and totally 48 ECs with an immunophenotype of CD41-CD43-CD45-CD31-CD44Neurl3-EGFP+ (NE+) from E10.0 AGM region were sequenced. All the NE+ cells ubiquitously expressed EGFP as expected and most of them expressed Nerul3 and Runx1 (Supplementary information, Fig. S3b, c). They distributed close to tif-HEC and were predominantly located between tif-HEC and earlyAEC by t-SNE visualization (Fig. 4g; Supplementary information, Table S1). Accordingly, NE+ cells demonstrated the increased cycling as compared to earlyAEC, presenting an intermediate proliferative status between earlyAEC and tif-HEC (Supplementary information, Fig. S3d). Similar to tif-HEC, NE+ cells showed relatively high expression of a set of HEC feature genes and pre-HSC signature genes (Fig. 2h, 4h). Correlation analysis revealed that NE+ cells showed the highest similarity with tif-HEC and they were clustered together by hierarchical clustering, whereas earlyAEC and lateAEC were much correlated (Fig. 4i). Therefore, from the immunophenotypic, functional and transcriptomic evaluation, the performance of the Neurl3-EGFP-marked ECs was consistent with the prediction of HSC-primed HEC by unsupervised computational screening. In situ localization and in vitro function of the HECs marked by Neurl3-EGFP reporter* At the AGM region of E9.5-E11.0 embryos, CD44 expression marked the whole endothelial layer of dorsal aorta in addition to IAHC cells, in line with the whole mount staining (Fig. 2b, 5a; Supplementary information, Fig. S3e). Of note, Neurl3-EGFP expression was restricted to the IAHCs and partial aortic ECs, where Neurl3-EGFP and Runx1 presented a highly co-expressed pattern (Fig. 5a; Supplementary information, Fig. S3e). Thus the Neurl3-EGFP+ cells embedded in the endothelial layer largely enriched the putative HECs. By FACS analysis, the average constitution of Neurl3-EGFP+ cells in CD44+ ECs were 37.7%, 50.2% and 18.3% in E9.5 caudal half, E10.0 and E10.5 AGM region, respectively. Considering the slightly over-estimation due to the much sensitivity of FACS, the data were basically in accordance with the morphological finding (Fig. 5a) and the estimated HEC composition by scRNA-seq (Supplementary information, Fig. S1f). The temporal dynamics of the HEC we defined here was in line with that of Runx1 expression in aortic endothelial layer, and the peaking of which at E10.0 was about 0.5 days earlier than the time point that the number of IAHC cells reaches the peak and the first HSCs are detected in AGM region. Given the lacking of suitable antibodies to directly determine the anatomical distribution of PK44 cells, which have been proven as HSC-competent HECs (Fig. 2c-e), we compared the immunophenotype of PK44 and IAHC cells, known as CD31Kit\textsuperscript{high} \cite{7}, regarding their relationship with Neurl3-EGFP expression whose localization was clearly defined (Fig. 5a). Both of them were mainly Neurl3-EGFP\textsuperscript{+}, with most CD31Kit\textsuperscript{high} cells being CD41/CD43/CD45-positive haematopoietic cells as previously reported \cite{7} (Fig. 5b). PK44 showed an expression pattern largely different from CD31Kit\textsuperscript{high} cells, suggestive of their predominant non-IAHC localization (Fig. 5b). The expression of Neurl3-EGFP was completely absent from the sub-aortic mesenchyme, in contrast to the widespread distribution of Runx1 there (Fig. 5a; Supplementary information, Fig. S3e). Although scattered Runx1CD44\textsuperscript{+} round blood cells were easily witnessed, much fewer Neurl3-EGFP-expressed cells outside dorsal aorta were detected, even at E11.0 (Fig. 5a; Supplementary information, Fig. S3e). As less than half of Neurl3-EGFP\textsuperscript{+} ECs were PK44 cells (Fig. 5b), we next explored the in vitro functional relationship of PK44 and non-PK44 fractions within CD44Neurl3-EGFP\textsuperscript{+} ECs by index-sorting. From E9.5 to E10.5, all three kinds of potential, including endothelial-only, haematopoietic-only, and endothelial-haematopoietic bi-potential, could be detected in CD44Neurl3-EGFP\textsuperscript{+} ECs, with different frequencies (Fig. 5c-e; Supplementary information, Fig. S3f). In E10.5, the potential was remarkably biased to endothelial as compared to E9.5 and E10.0 (Fig. 5d), which should be due to the prompt loss of Neurl3-EGFP-labeled HECs and the possible labeling of some lateAECs by Neurl3-EGFP (Fig. 4a, h). Of note, all three kinds of potential were obviously higher in PK44 than non-PK44 fraction, with endothelial-haematopoietic bi-potential exclusively detected in PK44 cells (Fig. 5d). Therefore, PK44 represented the enriched functional sub-populations within Neur13-EGFP+ HECs. All three kinds of potential did not show an evidently biased distribution regarding CD44 or Neur13-EGFP expression level by index sorting analysis (Fig. 5e). Interestingly, cells with the haematopoietic rather than endothelial potential intended to have smaller side scatter density on FACS (Fig. 5e). Stepwise fate choices of HSC-primed HECs from primitive vascular ECs In an effort to decipher the stepwise specification of the HSC-primed HECs, we added the immunophenotypic EC samples, from the stage of initial aortic structure formation at E8.0 to E9.0, to achieve seamless sampling with continuous developmental stages (Supplementary information, Fig. S4a). All the transcriptomically identified ECs were re-clustered into six clusters, with four of them basically consistent with those previously defined, namely vEC, earlyAEC, lateAEC, and HEC. The newly added samples were mainly distributed into three clusters, vEC, primitive EC (pEC) featured by Etv2 expression and involving almost all E8.0 cells, and primitive arterial EC (pAEC) given the expression of arterial marker Gja5 and serving as the earliest arterial EC population, with the latter two clusters as newly identified (Supplementary information, Fig. S4b, c). Trajectory analysis by Mpath demonstrated two bifurcations along the path from pEC to HEC and revealed a predominant two-step fate choice (Fig. 6a). pEC firstly chose an arterial but not venous fate to become pAEC, then upon maturing into earlyAEC and lateAEC, HEC chose to segregate from the intermediate arterial population earlyAEC (Fig. 6a), in line with the finding that the HEC displayed certain arterial characteristics but was completely devoid of venous feature (Fig. 1f). To decipher the underlying molecular programs for HEC specification, we specifically selected four clusters, excluding vEC and lateAEC branched out from the path from pEC to HEC, and added T1 pre-HSC as the end point for the subsequent analysis (Fig. 6b). Monocle 2 elegantly recapitulated the sequential sampling stages and the deduced cellular evolution upon stepwise hemogenic specification along the inferred pseudotime (Fig. 6c; Supplementary information, Fig. 6S4d). We identified totally 2,851 genes whose expression levels were changed significantly among five clusters, which were further grouped into five principal expression patterns along the inferred pseudotime (Fig. 6d; Supplementary information, Fig. S4e and Table S6). In general, genes in Pattern 1 showed the highest expression in pEC, decreased apparently upon arterial specification, whereas slightly increased upon hemogenic specification, which were mainly related to rRNA processing and mitotic nuclear division (Fig. 6d; Supplementary information, Fig. S4e, f). Genes in Pattern 2 showed the highest expression in the initial arterial specification, and the lowest expression upon hemogenic specification, which were mainly related to organization of intra-cellular actin filament and inter-cellular junctions (Fig. 6d; Supplementary information, Fig. S4e, f). Genes in Pattern 3, which were related to endothelium development and cell migration, showed the highest level in earlyAEC, whereas relatively low expression in the upstream pEC and pAEC and downstream HEC and T1 pre-HSC (Fig. 6d; Supplementary information, Fig. S4e, f). Genes in Pattern 4 and Pattern 5 both had the highest expression in the final T1 pre-HSC and both exhibited haematopoiesis-related terms, with those in Pattern 4 reaching the relatively high level from early AEC and those in Pattern 5 showing a gradual increase (Fig. 6d; Supplementary information, Fig. S4e,f). Among the above 2,851 pattern genes, 75 TFs belonged to the core TFs of the regulons where the genes included significantly overlapped with the pattern genes (Fig. 6e; Supplementary information, Table S6). Given the simultaneous co-expression of the core TF and its predicted targets in a given regulon, these core TFs were considered to presumably play a role to drive or orchestrate the dynamic molecular program during HEC specification (Fig. 6e). Most of these TFs belonged to Pattern 4 and Pattern 5, indicating that most activated TFs along HEC specification from primitive vascular ECs were those overrepresented in the final hemogenic and haematopoietic populations (Fig. 6e). We also examined the expression patterns of totally 28 TFs previously reported to have a role in HSPC regeneration in vitro. 19 of these presumed functional TF were dynamically changed and 15 of them were core TFs of regulons, with most of them belonging to Pattern 5 (Supplementary information, Fig. S4g). We next evaluated the pathway enrichment for each cell to depict dynamic changes at pathway level. The pathways significantly changed among the five candidate clusters showed the dynamic patterns similar to gene expression patterns (Fig. 6f). Among them, cell cycle, ribosome and spliceosome were the pathways that were down-regulated with arterial specification whereas turned to be moderately up-regulated by hemogenic specification (Fig. 6f, g). In contract, several pathways experienced a completely opposite change, such as Rap1 signaling pathway (Fig. 6f). Artery development, together with its pivotal executor Notch signaling pathway $^2$$^3$$^8$, firstly rose to peak in earlyAEC and then modestly fell down upon hemogenic specification (Fig. 6f, g). Some inflammation related pathways, including NFκB and TNF signaling, were activated from earlyAEC to the final T1 pre-HSC, in line with the notion about the requirement of inflammatory signaling during HSC generation $^3^9$ (Fig. 6f). DISCUSSION Here via unbiasedly going through all the relevant EC populations, HSC-primed HECs were transcriptomically identified. More importantly, combining the computational prediction and in vivo functional evaluation, we precisely captured the HSC-competent HECs by a newly constructed fluorescent reporter mouse model, Neurl3-EGFP, and revealed further functionally enriched sub-population within Neurl3-EGFP-labeled ECs by a set of surface marker combination PK44. Serving as the putative marker of HSC-primed HECs $^1^4$$^2^2$, Gfi1 was specifically expressed in HEC but not other EC-related populations (Fig. 2h, 4h), supportive of the cluster assignment. Belonging to the gene family of E3 ubiquitin ligases, the expression and role of Neurl3 in spermatogenesis and inflammation has been reported $^4^0$$^-$$^4^2$, whereas that relevant to vascular and haematopoietic development remains barely known. Neurl3 was screened out by unsupervised bioinformatics analysis, and fortunately, the expression of which in AGM region was restricted to aorta and largely consistent with that of Runx1 both transcriptomically (Supplementary information, Fig. S1k) and anatomically (Fig. 5a) regarding endothelial expression. Although highly expressed in tif-HEC, Runx1 and Adgrg1 were also highly expressed in the CD45-CD43+ haematopoietic population (Fig. 4h), which should be the derivatives of non-HSC haematopoiesis. This suggested that they may not distinguish the precursors of HSCs and non-HSCs, thus Runx1 and Adgrg1 were not included in the list of the signature genes of HSC-primed HEC (Fig. 4a). The specificity of Nerul3 expression related to HSC generation suggests that the Neurl3-EGFP would be a good reporter for the studies of both HSC development and regeneration. Based on the in vivo functional validation of the HSC-primed HECs and the sampling of continuous developmental stages with intervals of 0.5 days, we had a good opportunity to evaluate the dynamics and functional heterogeneity of these important transient populations. Unexpectedly, the HSC-competent HECs demonstrated a previously unresolved endothelial-haematopoietic bi-potential. The HECs we defined showed a higher enrichment of the expression of key haematopoietic TFs (Supplementary information, Fig. S2d) and of both haematopoietic and endothelial potential than using Runx1 +23GFP+ as the maker of HECs, which might partially explain why the rare endothelial-haematopoietic bi-potential is hardly detected around the timing of HSC emergence in previous reports. Thus, our findings well supplement the functional evaluation of putative HECs, which have a dynamic and transient nature, that without catching the endothelial-haematopoietic bi-potential, it is hard to define a given population to belonging to the ones being experiencing endothelial-to-hemogenic fate determination. Both the constitution and the hemogenic potential of the HSC-competent HECs reached the peak at the time point about 0.5 days before the first HSC emergence, and rapidly decreased thereafter (Fig. 5d; Supplementary information, Fig. S1f and S3f). Interestingly, the endothelial-haematopoietic bi-potential was still maintained until T1 pre-HSC stage at E11.0 (Fig. 3i), when cells have begun to express haematopoietic surface markers (Fig. 3b) and turned the shape into round. The data suggest that the haematopoietic fate might not have been fixed in T1 pre-HSC, which needs further investigations. We also precisely decoded the developmental path of HSC-primed HECs from the initially specified vascular ECs, the view of which has been generally neglected previously. We found that the genes and pathways involved in arterial development and Notch signaling were firstly increased and then decreased once upon HEC specification (Fig. 6e, g). Supportively, several seemingly contradictory findings have been reported regarding the role of Notch signaling in HEC specification. For example, activation of arterial program or Notch signaling is known to be required for HEC specification in mouse embryos or generation of HECs with lymphoid potential from human pluripotent stem cells. On the other hand, repression of arterial genes in EC after arterial fate acquisition leads to augmented haematopoietic output. Noteworthy, we revealed two bifurcates during HSC-primed HEC specification along the path from primitive vascular EC, suggesting two-step fate choice occurred for hemogenic fate settling (Fig. 6a). Serving as the two presumed final fates of earlyAEC, HEC and lateAEC displayed a series of differences (Fig. 1i), which better explains the presumably misinterpreted notion in previous report that arterial ECs and HSCs originate from distinct precursors. Our findings further emphasize that arterial specification and Notch signaling should be precisely and stepwise controlled for HSC generation. Although both showing obvious similarity regarding the arterial feature and anatomical distribution, the difference between earlyAEC and lateAEC should also be paid attention to as the former but not the latter is the direct origin of the HSC-primed HECs. It is generally accepted that haematopoietic cells in the IAHCs are proliferative, within which pre-HSCs are mainly involved. Supportively, enriched functional T1 pre-HSCs manifested a relatively proliferative status. On the other hand, slow cycling is witnessed at the base of IAHCs, and it is suggested that exit from cell cycle is necessary for HEC development and endothelial-to-haematopoietic transition. Nevertheless, based on the precise recognition of the HSC-primed HECs here, we showed that proliferation was gradually decreased upon arterial specification and maturation, whereas re-activated once the arterial ECs chose a hemogenic fate featured by the simultaneous Runx1 expression (Fig. 6e-g). The functional requirement of cell cycle control for the specification of the HSC-primed HECs needs to be investigated, which would depend on the initiating cell populations. We also revealed several similarities regarding the molecular events underlying the development of HSC-primed HECs between in mouse and human embryos we have reported very recently, including the arterial feature and the overrepresented ribosome and translational activity in the HSC-primed HECs. Such conservation further assures the mouse model as an adequate animal model for HSC development studies. The comprehensive understanding of cellular evolutions and molecular programs underlying the specification of HSC-primed HECs combined with the important spatiotemporal cues in vivo will facilitate future investigations directing HSC formation in vitro and other related regeneration strategies. MATERIALS AND METHODS No statistical methods were used to predetermine the sample size. The experiments were not randomized at any stage. The investigators were not blinded to allocation during the experiments and outcome assessment. Mice Mice were handled at the Laboratory Animal Center of Academy of Military Medical Sciences in accordance with institutional guidelines. Mouse manipulations were approved by the Animal Care and Use Committee of the Institute. The Neurl3\textsuperscript{EGFP/\textasciitilde} reporter mouse lines were generated with the CRISPR/Cas9 technique by Beijing Biocytogen. All mice were maintained on C57BL/6 background. Embryos were staged by somite pair (sp) counting: E8.0, 1-7 sp; E8.5, 8-12 sp; E9.0, 13-20 sp; E9.5, 21-30 sp; E10.0, 31-35 sp; E10.5, 36-40 sp; and E11.0, 41-45 sp. In some experiments, caudal half of E10.0 embryo was dissected under heart with limbs removed. AGM region was dissected as reported\textsuperscript{12}. The fluorescent dye Oregon green 488 was purchased from Invitrogen. Staining was performed as previously described\textsuperscript{12} except that the concentration of staining solution was 5 $\mu\text{mol/L}$ and the time of staining was 3 minutes before washed. Primary embryonic single-cell suspension was acquired by type I collagenase digestion. Flow cytometry Cells were sorted and analyzed by flow cytometers FACS Aria 2 and Calibur (BD Biosciences), and the data were analyzed using FlowJo software (Tree Star). Cells were stained by the following antibodies: B220 (eBioscience, RA3-6B2), CD3 (eBioscience, 145-2C11), CD4 (eBioscience, GK1.5), CD8a (eBioscience, 53-6.7), CD31 (BD or BioLegend, MEC13.3), CD41 (BD or eBioscience, MWReg30), CD43 (BD, S7), CD44 (eBioscience or BioLegend, IM7), CD45.1 (eBioscience, A20), CD45.2 (eBioscience, 104), CD45 (eBioscience, 30-F11), CD144 (eBioscience, eBioBV13), CD201 (eBioscience, eBio1560), Flk1 (eBioscience, Avas12a1), Kit (eBioscience, 2B8), Ly-6G (BioLegend, 1A8), and Mac-1 (eBioscience, M1/70). 7-amino-actinomycin D (7-AAD; eBioscience) was used to exclude dead cells. For index sorting, the FACS Diva 8 “index sorting” function was activated and sorting was performed in single-cell mode. OP9-based haematopoietic and endothelial potential assay Cells were sorted by flow cytometry in single-cell mode and were then plated on the OP9 or OP9-DL1 stromal cells 51 in IMDM (HyClone) containing 15% fetal bovine serum (HyClone), 1% bovine serum albumin (Sigma), 10 μg/mL insulin (Macgene), 200 μg/mL transferrin (Sigma), and 5.5 x 10⁻⁵ mol/L 2-mercaptoethanol (Gibco). For the endothelial potential assay, 100 ng/mL rhVEGF-165 (PeproTech) was supplemented. For haematopoietic and endothelial bi-potential assay with 10 cells or single cell plated per well, both 100 ng/mL rhVEGF-165 and 50 ng/mL SCF (PeproTech) were supplemented. After 7 days of co-culture, cells were fixed in 4% paraformaldehyde for 30 minutes and stained with PE-conjugated or purified CD45 antibody (eBioscience, 30-F11 or BD Biosciences) to ascertain the generation of haematopoietic progeny. Subsequently, CD31 (BD Pharmingen, MEC13.3) immunohistochemistry staining was performed using standard procedures, and the formation of CD31-positive tubules in the wells was considered as having endothelial potential. OP9-DL1 co-culture and transplantation assay To investigate the HSC potential of the PK44 population in E10.0 caudal half, male CD45.1/1 and female CD45.2/2 mice were mated to obtain CD45.1/2 embryos. FACS purified cell populations from E10.0 caudal half (CD45.1/2) were plated on the OP9-DL1 stromal cells in α-MEM (Gibco) supplemented with 10% fetal bovine serum (Hyclone) and cytokines (100 ng/mL SCF, 100 ng/mL IL-3 and 100 ng/mL Flt3 ligand, all from PeproTech). After 7 days of co-culture, cells were harvested and then injected into 8-12 weeks female recipients (CD45.2/2) via tail vein, along with 2×10⁴ nucleated fresh bone marrow carrier cells (CD45.2/2) per recipient. Recipients were pre-treated by a split dose of 9 Gy γ-irradiation (⁶⁰Co). Peripheral blood cells of recipients were analyzed by flow cytometry at the indicated time points to determine the chimerism. The recipients demonstrating ≥5% donor-derived chimerism in CD45⁺ cells of peripheral blood were considered as successfully reconstituted. Multi-organ and multi-lineage reconstitution was evaluated as reported. Totally 1×10⁷ bone marrow cells obtained from the reconstituted primary recipients at 16 weeks post-transplantation were injected into the secondary recipients to investigate HSC self-renewal potential. To investigate the HSC potential of the CD41⁻CD43⁻CD45⁻CD31⁺CD44⁺Neurl3-EGFP⁺ population in E10.0 caudal half, male Neurl3EGFP⁺ reporter mice (CD45.2/2 background) were crossed to female CD45.2/2 mice to generate Neurl3EGFP⁺ embryos. Then the co-culture and transplantation strategy were same as mentioned above except that the recipients were female 8-12 weeks CD45.1/2 mice and the carrier cells were obtained from CD45.1/1 mice. Immunofluorescence Embryos were isolated, fixed with 4% paraformaldehyde for 30 minutes to 2 hours at 4°C, embedded in paraffin, and sectioned at 5-6 μm with Leica RM2235. Sections were deparaffinized with ethanol of gradient concentration, then blocked in blocking solution (Zhongshan golden bridge) for 30 minutes at room temperature, followed by incubation with primary antibodies overnight at 4°C. After 3 washes (3 minutes each) in PBS, sections were incubated with corresponding secondary antibodies (Zhongshan golden bridge) for 30 minutes at room temperature. After 3 washes in PBS, sections were stained with DendronFluor TSA (Histova, NEON 4-color IHC Kit for FFPE, NEFP450, 1:100, 20–60-sec). The primary and secondary antibodies were thoroughly eluted by heating the slides in citrate buffer (pH 6.0) for 10 minutes at 95°C using microwave. In a serial fashion, each antigen was labeled by distinct fluorophores. After all the antibodies were detected sequentially, the slices were finally stained with DAPI. Images were collected by confocal microscope (Nikon Ti-E A1/ ZEISS LSM 880). The primary antibodies were as follows: CD31 (BD Biosciences), CD44 (BD Biosciences), Endomucin (eBioscience), GFP (Cell Signaling), and Runx1 (Abcam). Whole-mount Immunofluorescence The body part between forelimb buds and hindlimb buds of E10.0 embryo was dissected, fixed in 2% PFA/PBS for 20 minutes on ice and dehydrated in graded concentrations of methanol/PBS (50%, 100%; 10 minutes each). To block endogenous peroxidase, samples were bleached in 5% H$_2$O$_2$ for 1 hour on ice. For staining, the samples were blocked in PBSMT (1% skim milk and 0.4% Triton X-100 in PBS) containing 0.2% BSA for 1 hour at 4°C, incubated with PBSMT containing anti-CD44 (1:25) overnight at 4°C, then washed 3 times in PBSMT each for 1 hour at 4°C. The primary antibody was developed by incubating HRP-conjugated anti-rat Ig antibody (1:2000 in PBSMT; Zhongshan golden bridge) overnight at 4°C. After extensive washing with more than 3 exchanges of PBSMT, including the final 20 minutes wash in PBST (0.1% Triton X-100 in PBS) at 4°C, the samples were soaked in DendronFluor TSA (Histova, NEON 4-color IHC Kit for Wholemount/Cytometry, NEWM450) for 10–30 minutes, and hydrogen peroxide was added to 0.03%. The enzymatic reaction was allowed to proceed until the desired color intensity was reached, and the samples were rinsed 3 times in PBST. Finally, the samples were dehydrated in 100% methanol and soaked in graded concentrations of BABB (phenylcarbinol and benzyl benzoate, 1:2)/methanol (50%, 100%; 1 minute each), stored at -20°C until photographed. Single cell RNA-seq library construction Single cells in good condition were picked into lysis buffer by mouth pipetting. The single cell RNA-seq preparation procedure was based on STRT with some modifications. cDNAs were synthesized using sample-specific 25 nt oligo dT primer containing 8 nt barcode (TCAGACGTGTGCTCTTCCGATCT-XXXXXXXX-NNNNNNNN-T25, X representing sample-specific barcode whereas N standing for unique molecular identifiers, UMI, see Table S7) and TSO primer for template switching. After reverse transcription and second-strand cDNA synthesis, the cDNAs were amplified by 17 cycles of PCR using ISPCR primer and 3' Anchor primer (see Table S7). Up to 56 samples were pooled and purified using Agencourt AMPure XP beads (Beckman). 4 cycles of PCR were performed to introduce index sequence (see Table S7). After this step, 400 ng cDNAs were fragmented to around 300 bp by covaris S2. The cDNA was incubated with Dynabeads MyOne™ Streptavidin C1 beads (Thermo Fisher) for 1 hour at room temperature. Libraries were generated using KAPA Hyper Prep Kit (Kapa Biosystems). After adaptor ligation, the libraries were amplified by 7 cycles of PCR using QP2 primer and short universal primer (see Table S7). The libraries were sequenced on Illumina HiSeq 4000 platform in 150bp pair-ended manner (sequenced by Novogene). Quantification of gene expression for scRNA-seq data We used unique molecular identifier (UMI)-based scRNA-seq method to measure the gene expression profiles within individual cells. Raw reads were firstly split by specific barcode attached in Read 2 for individual cells and UMI information was aligned to the corresponding Read 1. Read 1 was trimmed to remove the template switch oligo (TSO) sequence and polyA tail sequence. Subsequently, quality control was conducted to discard reads with adapter contaminants or low-quality bases (N > 10%). Next, the mm10 mouse transcriptome (UCSC) was used to align the clean reads using TopHat (version 2.0.12) 59. Uniquely mapped reads were obtained using HTSeq package 60 and grouped by the cell-specific barcodes. Transcripts of each gene were deduplicated based on the UMI information, while mitochondrial genes were not included for quantification. Finally, for each gene in each individual cell, the number of the distinct UMIs derived from that gene was regarded as its copy number of transcripts. Quality control and normalization of sequencing data For the 662 sequenced single cells from E9.5-E11.0 embryos of totally 29 embryos, we only retained cells with more than 2,000 genes and 100,000 transcripts detected. Then, 597 cells passed the filter standards. Gene expression levels in each cell were normalized by $\log_2(TPM/10+1)$, where TPM (transcripts-per-million) was calculated as (the number of UMIs of each gene / all UMIs of a given cell) $\times 1,000,000$. Since the UMI number of most of our samples was less than the order of 1,000,000 transcripts, the TPM values were divided by 10 to avoid counting each transcript for several times. On average we detected 7,035 genes (range from 2,266 to 10,843) and 636,418 transcripts (range from 103,793 to 2,959,573) expressed in each individual cell. Additionally, we also sequenced 96 single cells with a PK44 immunophenotype (CD41^−^CD43^−^CD31^+^CD201^+^Kit^+^CD44^+^) from E10.0 AGM regions of totally 9 embryos, 47 T1 pre-HSCs (CD31^+^CD45^CD41^{low}Kit^+^CD201^{high}) from E11.0 AGM regions of totally 18 embryos, 48 single cells with an immunophenotype of CD41^−^CD43^−^CD31^+^CD44^{Neurl3-EGFP} from Neurl3-EGFP reporter mouse embryos and 579 single cells from E8.0-E9.0 body regions of totally 24 embryos. The same quality control criteria and normalization method described above were applied to these additional datasets. In total, 1,432 single cells were sequenced and 1,325 cells passed the filter. Dimensional reduction and clustering We used Seurat R package \textsuperscript{61} (version 2.3.4) for further analyses and exploration of our single cell RNA sequencing data, such as identification of highly variable genes (HVGs) and differentially expressed genes (DEGs), dimension reduction using PCA or t-SNE, unsupervised clustering and so on. A standard analysis process is briefly described below. First, only genes expressed in at least 3 single cells were retained so as to exclude genes that were hardly expressed. Then, FindVariableGenes function was used to select HVGs on log2 (TPM/10+1) transformed expression values. Genes with average expression more than 1 and less than 8 and dispersion greater than 1 were identified as HVGs. To mitigate the effect of cell cycle, HVGs not included in the direct cell cycle GO term (GO:0007049) (Table S7) were used as inputs for PCA dimension reduction. Elbow method was employed to select the top relevant PCs for subsequent t-SNE dimension reduction and graph-based clustering.\textsuperscript{28} For the initial dataset from E9.5-E11.0 body and DA locations, we select top 15 PCs for clustering using FindClusters with default settings, to obtain 6 major clusters. Negative control cells with a non-EC immunophenotype and cells grouped with these negative control cells were reclassified specifically into the Neg cluster. The remaining cells were assigned as vEC, earlyAEC, lateAEC, HEC and HC clusters based on the clustering results. Next, cells in Neg cluster and cells with \textit{Ptprc} or \textit{Spn} expression level greater than 1 were removed. Then, the filtered initial dataset was used for analyses of subdatasets, including subdividing of HEC cluster, subdividing of eaAEC cluster and in-depth analyses of earlyAEC, lateAEC and HEC clusters. The filtered initial dataset was also included in three combined datasets of combining PK44 cell population, PK44 and T1 pre-HSC cell populations, and PK44 and Neurl3-EGFP cell populations, respectively. Dimension reduction and clustering analyses for subdatasets and combined datasets abovementioned also followed the same procedure as described above. See Table S1 for detailed cell information. For combined dataset from earlier dataset (E8.0-E9.0 body location) and initial dataset (E9.5-E11.0 body and DA locations), we redid the dimension reduction and clustering analyses over again. Same as the processing of initial dataset, negative control cells with a non-EC immunophenotype and cells grouped with these negative control cells were reclassified manually into Neg cluster. The remaining cells were assigned as vEC, pEC, pAEC, earlyAEC, lateAEC, HEC and HC based on the clustering results. The new clustering results are highly consistent with the previous ones within the common cell populations. Next, cells in Neg cluster and cells with Ptprc or Spn expression level greater than 1 were removed. Cells in pEC, pAEC, lateAEC and HEC and cells from T1 pre-HSC dataset were retained for further analysis. Identification of DEGs DEGs were identified using FindMarkers or FindAllMarkers functions with default Wilcoxon rank sum test and only genes detected in a minimum fraction of 0.25 cells in either of the two populations were considered. Genes with fold-change $\geq 2$ and adjusted $P$ value $\leq 0.05$ were selected as DEGs. Arterial and venous feature score Arteriovenous marker genes previously known or inferred from the artery development pattern genes, including 10 arterial genes ($Dll4$, $Igfbp3$, $Unc5b$, $Gja4$, $Hey1$, $Mecom$, $Efnb2$, $Epas1$, $Vegfc$ and $Cxcr4$) and 3 venous genes ($Nr2f2$, $Nrp2$, and $Aplnr$) $^{33,62-64}$, were selected to perform the arteriovenous feature scores. First, we scaled the log$_2$(TPM/10+1) expression values of each marker gene to 0-10 scale among all the sample cells after quality control. Second, for each cell, we averaged the scaled values of arterial genes and venous genes, respectively. Third, the averaged values were rescaled to 0-10 scale across all the sample cells to finally achieve the arterial and venous scores. For each population, the arterial and venous scores of all of the cells within the population were average. The 50% confidence ellipses were also calculated to show the main distribution ranges. We chose score value = 5 as the threshold to infer the arterial or venous identity of vascular ECs, as the distribution of individual cells was in line with the notion showing essentially no arterial/venous double positive cells. Cell cycle analysis For cell cycle analysis, cell cycle-related genes consisting of a previously defined core set of 43 G1/S genes and 54 G2/M genes were used $^{58,65}$ (see Table S7 for detailed gene lists). We used a way similar to Tirosh, et al. $^{66}$ to classify the cycling phases of the cells. We calculated the average expression of each gene set as corresponding scores, and manually assigned cells to approximate cell cycle phases based on the scores. Namely, cells with G1/S score < 2 and G2/M score < 2 were assigned as ‘quiescent’, otherwise ‘proliferative’. Among proliferative cells, those with G2/M score > G1/S score were assigned as ‘G2/M’, and those with G1/S score > G2/M score were assigned as ‘G1’ when G2/M score < 2, or as ‘S’ when G2/M score $\geq$ 2. Constructing single cell trajectories Monocle 2 $^{67}$ (version 2.6.4) and Mpath $^{68}$ (version 1.0) were adopted to infer the development trajectory of selected cell populations. Monocle 2 can construct single-cell trajectories and place each cell at its proper position in the trajectory, even a “branched” trajectory corresponding to cellular “decisions”. We followed the official vignette with recommended parameters. Briefly, UMI count data of given cell populations was used as input and genes with more than 1.5 times of fitted dispersion evaluated using dispersionTable function were identified as HVGs. To reduce the influence of cell cycle effect, HVGs not included in the direct cell cycle GO term (GO:0007049) were retained as ordering genes for the subsequent ordering cells. For Mpath analysis, the $\log_2(\text{TPM}/10+1)$ normalized data of HVGs identified by using Seurat method were used as inputs. The cluster labels defined by clustering procedures described above were used as landmark cluster assignment of individual cells. Based on the results of the Mpath analyses, we specified the starting point and developing directions according to the development time and visualized the results on t-SNE plot. Patterns of DEGs among multiple clusters In the case of identification of gene patterns in more than two clusters, analysis of variance followed by Tukey's HSD test for pairwise comparison was adopted to identify DEGs (genes with adjusted $P$ value < 0.05 and fold change > 2 or < 0.5). For identification of patterns in earlyAEC, lateAEC and HEC clusters, only 1,005 DEGs resulted from the pairwise comparisons of earlyAEC and lateAEC and of earlyAEC and HEC were retained. According to the changed directions of HEC and lateAEC as compared to earlyAEC, we could assign these DEGs into 8 patterns as illustrated. Transcription factors network visualization was implemented as follows. First, the average expression values of genes included in each pattern were calculated as their representative expression levels. Then, the representative expression levels of 8 patterns and the expression profile data of transcription factors included in these patterns were combined as input for construction of "signed hybrid" weighted gene co-expression network analysis using WGCNA. Next, we used 0.01 as adjacency threshold for including edges in the output to export network, which was then imported into Cytoscape for visualization. We also calculated Pearson correlation coefficient between each transcription factor and the pattern it belongs to. For identification of patterns in pEC, pAEC, earlyAEC and HEC clusters, all 2,851 DEGs among them were retained. We used ConsensusClusterPlus function with k-means algorithm on top 500 DEGs to achieve five stable clusters. Then all DEGs were reassigned into one of the five patterns according to which pattern had maximum average Pearson correlation coefficient with a given DEG. Note that we used a downsampled dataset in the visualization related to the five patterns in order to show more detailed changes along the development trajectory. Sixty cells were randomly sampled from pEC and pAEC clusters, respectively. Identification of HEC signature genes Firstly, we compared HEC to every cluster to get the overrepresented genes, which were upregulated across each of the other 4 clusters (vEC, earlyAEC, lateAEC and HC) within filtered initial dataset. To make sure the accuracy of HEC overrepresented genes, we used both wilcox and roc method to perform the DEG analysis. Only the DEGs identified by both methods were regarded as HEC overrepresented genes. Finally, 25 cluster HEC overrepresented genes were retained. In order to not only identify the endothelium with hemogenic potential, but also discriminate those HSC-primed hemogenic ECs from yolk sac-derived early haematopoietic populations such as erythro-myeloid progenitors, genes highly expressed in erythro-myeloid progenitors (Gsta4, Spi1, Alox5ap and Myb) as reported were excluded. In addition, genes not highly expressed ($\log_2(\text{TPM/10+1}) < 2$) in HEC or highly expressed ($\log_2(\text{TPM/10+1}) > 2$) in every clusters were also excluded. Finally, eleven HEC overrepresented genes were retained as HEC signature genes. SCENIC analysis SCENIC could reconstruct gene regulatory networks from single-cell RNA-seq data based on co-expression and DNA motif analysis. Here, we used SCENIC R package (version... 1.1.1-9) to identify refined regulons, each of which represented a regulatory network that connects a core TF with its target genes. We followed the “Running SCENIC” vignette in the R package with default settings. We identified 507 unique regulons, among which 75 regulons significantly overlapped with the 2851 significantly changed genes were retained. Fisher’s exact test was employed for estimate the statistical significance of their overlaps. The 75 core TFs were considered as putative driving force to orchestrate the dynamic molecular program during HEC specification, given the simultaneous co-expression of the core TF and its predicted targets in a given regulon. Gene set variation analysis Through gene set variation analysis, gene-level expression profiles could be transformed into pathway-level enrichment score profiles using GSVA R package coupled with KEGG pathways. We used ssgsea method to estimate gene-set enrichment scores of each cell. Two-sample Wilcoxon test was employed to find differentially enriched pathways between involved clusters. Adjusted $P$ value $< 0.05$ was considered statistically significant. TFs and cell surface molecules Genes were marked as TFs according to 1,485 TFs included in AnimalTFDB 2.0, and marked as surface molecules according to 871 high-confidence surfaceome proteins identified in Cell Surface Protein Atlas. See Table S7 for the detailed gene lists. Statistical analysis All statistical analyses were conducted in R version 3.4.3. Two-sample Wilcoxon Rank Sum test was employed for comparisons of gene numbers, transcript counts, or gene expression levels between two clusters of cells. We referred to statistically significant as $P < 0.05$ (if not specified). Network enrichment analyses and gene ontology biological process enrichment analyses were performed using Metascape $^79$ (http://metascape.org) and clusterProfiler $^80$, respectively. Data and Code Availability The scRNA-seq data has been deposited in the NCBI Gene Expression Omnibus, the accession number for the data is pending. 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(c) Metascape network enrichment analysis with top 10 enriched terms exhibited to the right. Each cluster is represented by different colors and each enriched term is represented by a circle node. Number in the bracket indicates the P value based on -log10. (d) Classification of the indicated cells into quiescent phase and other cycling phases (G1, S and G2M) based on the average expression of G1/S and G2/M gene sets (left). Stacked bar chart showing the constitution of different cell cycle phases in the corresponding three clusters shown to the left (right). (e) Violin plot showing the number of transcripts for ribosomal related genes detected in each single cell of the indicated clusters. Wilcoxon Rank Sum test is employed to test the significance of difference and P values are indicated for the comparison. $ P < 0.05 $ is considered statistically significant. (f) Scatterplot showing the average arteriovenous scores of the cells in each cluster for mouse dataset in this paper (left) and human dataset from published articles (right), respectively. Main distribution ranges of arteriovenous scores in each cluster are also indicated as an oval shape. (g) Pseudotemporal ordering of the cells in select three clusters inferred by monocle 2, with pseudotime (left), clusters (middle) and sampling stages (right) mapped to it. HEC specification and AEC maturation directions are indicated as orange and deep red arrows, respectively. (h) Heatmap showing the expression of the indicated genes (smoothed over 15 adjacent cells) with cells ordered along the pseudotime axis of HEC specification branch inferred by monocle 2. (i) Eight major expression patterns identified from the differentially expressed genes in HEC or lateAEC as compared to earlyAEC. Arrows showing the changes in HEC or lateAEC as compared to earlyAEC. The numbers of pattern genes are indicated to the right. (j) Heatmaps showing the relative expressions (smoothed over 20 adjacent cells) of the TFs belonging to the pattern genes with cells ordered along the pseudotime axis and genes ordered by patterns. Fig. 2. Efficiently isolating the HSC-competent and endothelial-haematopoietic bi-potent HECs before HSC emergence. (a) Gene lists of the top ten cell surface molecules significantly overrepresented in HEC as compared to the indicated cell populations (first 3 lines) and those positively correlated with Runx1 within 4 EC clusters (vEC, earlyAEC, lateAEC and HEC, last line). Non-HEC, cells except for HEC within 4 EC clusters. Highlights in red font indicate the candidates used for further functional analysis. (b) Representative whole-mount staining of CD44 at E10.0 AGM region, showing CD44 is expressed in the whole endothelial layer of the dorsal aorta and roots of its proximal branches. DA, dorsal aorta; Scale bar, 100 μm. (c) Representative FACS plots for cell sorting of the E9.5-E10.0 caudal half for co-culture/transplantation assay and the donor chimerism at 16 weeks after transplantation of the derivatives of the indicated cell populations. (d) Blood chimerism of the primary (I°) and corresponding secondary (II°) recipients at 16 weeks post-transplantation. The primary recipients were transplanted with the derivatives of the indicated cells from the caudal half of E9.5-E10.0 embryos. The paired primary and corresponding secondary repopulated mice are shown as the same symbol and color. (e) Bars represent the percent donor contribution to the granulocytes/monocytes (GM, red), B lymphocytes (green), and T lymphocytes (purple) in the peripheral blood of the primary (I°) and secondary (II°) recipients at 16 weeks post-transplantation. The paired primary and corresponding secondary repopulated mice are shown as the same colors below. (f) FACS plot of Flk1 expression in the indicated population of E10.0 AGM region, with PK44 (CD41⁻CD43⁻CD45⁻CD31⁺CD201⁺Kit⁺CD44⁺) cells (red) mapped onto it. Red box indicates the gate of Flk1⁺ cells. (g) t-SNE plot of the cells included in the filtered initial dataset and PK44 dataset, with clusters mapped on it. PK44, CD41⁻CD43⁻CD45⁻CD31⁺CD201⁺Kit⁺CD44⁺ population from E10.0 AGM region. (h) Heatmap showing the relative expressions of HEC feature genes, which are defined as those significantly highly expressed as compared to others including HC, vEC, earlyAEC and lateAEC, in the indicated cell populations. Selected HEC feature genes are shown to the right with pre-HSC signature genes marked as aquamarine. (i) Representative CD31 and CD45 immunostaining on the cultures of single PK44 cells from E10.0 AGM region, showing typical morphologies regarding distinct differentiation potentials. Cell frequencies of each kind of potential are also shown. Data are from 5 independent experiments with totally 15 embryos used. Scale bars, 400 μm. (j) Expression of Kit and CD201 in the index-sorted single PK44 cells with differentiation potential based on in vitro functional evaluation. Cells with different kinds of potential are mapped onto the reference FACS plots (grey dots). Box in the middle plot indicates the gate for FACS sorting of PK44 cells in E10.0 AGM region and its enlarged view is shown to the right. Fig. 3. Relationship between HSC-primed HECs and T1 pre-HSCs. (a) Representative FACS plots for sorting of the T1 pre-HSCs (CD31^+CD45^-CD41^{low}Kit^+CD201^{high}) from E11.0 AGM region of mouse embryos. Red box indicates the sampling cells for scRNA-seq. (b) Violin plots showing the expression levels of indicated genes in tif-HEC (including cluster HEC and PK44), T1 pre-HSC and lateAEC. (c) t-SNE plot of the cells included in the filtered initial dataset, PK44 dataset and T1 pre-HSC dataset, with clusters mapped on it. Cluster HEC and PK44 are combined as tif-HEC. (d) PCA plot of tif-HEC and T1 pre-HSC populations. (e) Enriched terms of PC2 positive and negative genes are shown, corresponding to the properties distinguishing tif-HEC and T1 pre-HSC, respectively. (f) Heatmap showing top 20 positive and negative genes of PC2. Genes were ordered by their contributions to PC2. (g) Trajectory of AEC clusters, tif-HEC and T1 pre-HSC inferred by Mpath. Arrows indicate the development directions predicted by sampling stages. (h) Representative FACS plots for sorting of the PK44 cells from E10.0 AGM region (left) and analysis of the immunophenotypic T1 pre-HSCs (right) after cultured in vitro for 4 days. (i) Representative CD31 immunostaining on the cultures of single T1 pre-HSCs from E11.0 AGM region, showing typical morphologies regarding distinct differentiation capacities. Cell frequencies of each type are also shown. Data are from 7 independent experiments with totally 89 embryos used. Scale bars, 400 μm. Fig. 4. Identifying Neurl3 as a signature gene of HSC-primed HECs validated by functional and transcriptomic evaluation. (a) Dot plot showing the average and percentage expression of HEC signature genes in the indicated clusters. Genes are ordered by their median expression level in tif-HEC. Pre-HSC signature genes are marked as aquamarine. (b) Schematic model of the gene targeting strategy for generating Neurl3EGFP/+ reporter mouse line via CRISPR/Cas9 system. (c) Representative FACS analysis of the E10.0 AGM region in Neurl3EGFP/+ embryos, FACS plot to the right showing PK44 cells (red dots) mapped on it. (d) Representative FACS plot for sorting of the indicated cell populations from E10.0 caudal half of Neurl3EGFP/+ embryos. (e) Graph showing the donor chimerism at 16 weeks after transplantation of the derivatives of the indicated populations from the caudal half of E10.0 Neurol3<sup>EGFP/+</sup> embryos. (f) Graph showing the donor chimerism at 4-16 weeks post-transplantation. The recipients were transplanted with the derivatives of CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>CD31<sup>+</sup>CD44<sup>+</sup>Neurol3<sup>-</sup>EGFP<sup>+</sup> population from the caudal half of E10.0 Neurol3<sup>EGFP/+</sup> embryos. Number of repopulated/total recipients is shown in the brackets. (g) t-SNE plot of the cells included in the filtered initial dataset and additional PK44 and NE+ datasets, with clusters mapped on it. Cluster HEC and PK44 are combined as tif-HEC. NE+, CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>CD31<sup>+</sup>CD44<sup>+</sup>Neurol3-EGFP<sup>+</sup> population from E10.0 AGM region. (h) Dot plot showing the average and percentage expression of selected HEC feature genes in the indicated clusters. Pre-HSC signature genes are marked as aquamarine. (i) Heatmap showing the correlation coefficient between each two clusters with hierarchical clustering using average method. Pearson correlation coefficient is calculated using average expression of highly variable genes in each cluster. Fig. 5. In situ localization and in vitro function of the dynamic HECs marked by Neurol3-EGFP reporter. (a) Representative immunostaining on cross sections at AGM region of E9.5 (upper), E10.0 (middle) and E10.5 (lower) Neurol3<sup>EGFP/+</sup> embryos. Arrows indicate Neurol3<sup>+</sup> aortic ECs. Yellow arrowheads indicate Neurol3<sup>+</sup> bulging and bulged cells and IAHCs. Aquamarine arrowheads indicate CD44<sup>+</sup>Runx1<sup>+</sup>Neurol3<sup>-</sup> haematopoietic cells distributed outside the aorta. nt, neural tube; DA, dorsal aorta. Scale bars, 100 μm. (b) Representative FACS analysis of the E10.0 AGM region of Neurl3$^{EGFP/+}$ embryos. FACS plots to the right showing PK44 cells (red dots, upper) and CD31$^{+}$Kit$^{high}$ cells (blue dots, lower) mapped on, respectively, with their contributions to each gated population indicated. (c) Representative CD31 and CD45 immunostaining on the cultures of single CD41$^{-}$CD43$^{-}$CD45$^{-}$CD31$^{-}$CD44$^{+}$Neurl3$^{-}$EGFP$^{+}$ cells from E10.0 AGM region of Neurl3$^{EGFP/+}$ embryos, showing typical morphologies regarding distinct differentiation potentials. Cell frequencies of each kind of potential are also shown. Data are from 5 independent experiments with totally 37 embryos used. Scale bars, 400 $\mu$m. (d) Column charts showing the proportions of positive wells in the indicated populations (lower) for each kind of potential. The experiments were performed with CD41$^{-}$CD43$^{-}$CD45$^{-}$CD31$^{-}$CD44$^{+}$Neurl3$^{-}$EGFP$^{+}$ single cells from E9.5 caudal half or E10.0-E10.5 AGM region of Neurl3$^{EGFP/+}$ embryos with PK44 indexed. Progenies from PK44 and non-PK44 cells are represented by distinct fill patterns. (e) Expression of CD44 and Neurl3-EGFP and values of FSC-A and SSC-A in the index-sorted single CD41$^{-}$CD43$^{-}$CD45$^{-}$CD31$^{-}$CD44$^{+}$Neurl3-EGFP$^{+}$ cells with differentiation potential based on in vitro functional evaluation. Cells with different kinds of potential are mapped onto the reference FACS plots (grey dots). Solid boxes (left of each stage) indicate the gates of the populations for FACS sorting. The enlarged views of solid boxes are shown below. Fig. 6. Molecular evolution underlying the specification of HSC-primed HECs from primitive vascular ECs. (a) Trajectory of pEC, vEC, pAEC, earlyAEC, lateAEC and HEC inferred by Mpath. Arrows indicate the development directions predicted by sampling stages. (b) t-SNE plot showing the distribution of the four clusters involved in hemogenic specification. Other cells are in grey. (c) Pseudotemporal ordering of the cells included in the indicated five clusters inferred by monocle 2 (left), with clusters (upper left) and sampling stages (lower left) mapped to it. HEC specification directions are indicated as red arrows. Smooth distribution of clusters (upper right) and sampling stages (lower right) along pseudotime by using Gaussian kernel density estimate are shown to the right. (d) Dynamic changes of five gene expression patterns along the trajectory ordered by pseudotime inferred by monocle 2. For each pattern, principal curves are fitted on expression levels of the genes in that pattern along pseudotemporal order, using local polynomial regression fitting method. Randomly down-sampling is performed in pEC and pAEC clusters for better visualization. (e) Heatmap showing the relative expression of the core TFs which belong to the regulons that the genes within exhibit significant overlapping with the pattern genes. Cells are ordered by pseudotime and TFs are ordered by Patterns. (f) Heatmap showing smoothed (along adjacent 25 cells) and scaled enrichment scores of top 50 KEGG pathways along the order by pseudotime. Pathways are ordered by hierarchical clustering using ward.D method. (g) Scatter plots showing the relative activity levels of pathways or GO terms with loess smoothed fit curves and 95% confidence interval indicated. Relative activity levels are represented by the PC1 scores of expression levels of the genes in a given set. The sign or direction of PC1 is corrected according to positive correlation with averaged expression levels. SUPPLEMENTARY FIGURE LEGENDS Fig. S1. Information, clustering of initial dataset and molecular characteristics of major clusters. (a) Embryo, independent experiment, and cell number information for scRNA-seq. DA, dorsal aortic luminal layer of AGM region. (b) Whole-mount image of the E11.0 AGM region labeled with Oregon Green 488. (c) Boxplots showing the number of genes (left) and transcripts (right) in each single cell of different locations. (d) t-SNE plots with clusters (left), sampling locations (right) and embryonic stages (right) mapped onto it. (e) Violin plots showing the expression levels of indicated genes in six clusters identified in the initial dataset. (f) Cell number information of the spatiotemporal distribution of distinct clusters. (g) Volcano plots showing differentially expressed genes (marked as blue or red) between two sub-clusters by forced clustering in earlyAEC and HEC, respectively. Top 10 (earlyAEC) or all (HEC) differentially expressed genes are indicated. Runx1 and Kit are also indicated. (h) Violin plots showing the number of genes (left) and transcripts (right) in each single cell of the indicated clusters. Wilcoxon Rank Sum test is employed to test the significance of difference and P values are indicated for the comparison. P < 0.05 is considered statistically significant. (i) Heatmap showing the relative expression levels of genes in eight patterns among earlyAEC, lateAEC and HEC. (j) Network view of TFs positively correlated with the gene expression patterns. A deeper background color of the gene name indicates a higher positive correlation of the TF to that expression pattern. (k) Bar chart showing the top 50 genes positively correlated with Runx1 within cell population including earlyAEC, lateAEC and HEC. Genes included in the patterns identified above are marked as indicated. Fig. S2. Identification of the HSC-competent and endothelial-haematopoietic bi-potent HECs. (a) Detailed information of the co-culture/transplantation assays performed with E9.5-E10.0 caudal half cells. (b) Blood chimerism of the primary and secondary recipients at 4-16 weeks post-transplantation. The primary recipients were transplanted with the derivatives of the indicated cell populations from the caudal half of E9.5-E10.0 embryos. The paired primary and corresponding secondary repopulated mice are show as the same symbol and color. Numbers of repopulated/total recipients are shown in the brackets. Only the recipients survived to 16 weeks post-transplantation are shown. (c) FACS plots showing representative primary recipients with long-term (16 weeks), multi-organ and multi-lineage repopulations transplanted with the derivatives of the indicated cell populations from the caudal half of E9.5-E10.0 embryos. Donor-derived (CD45.1+CD45.2+) myeloid (Gr-1+/Mac-1+), B lymphoid (B220+), and T lymphoid (CD3+) cells in multiple haematopoietic organs are shown. (d) Heatmap showing the expression of selected genes in earlyAEC, lateAEC, HEC and PK44 populations. Note the similarity of expression patterns between HEC and PK44. (e) Graph showing the endothelial potential of different cell populations in E9.5-E10.0 body part of embryo proper. Cells with indicated immunophenotype were isolated by FACS, co-cultured with OP9 stromal cells for 7 days, and stained with CD31 to identify the endothelial tubes. Data are means ± s.d.. For E9.5 embryos, data are from 3 independent experiments with 6-9 embryo equivalents pooled for each experiment. For E10.0 embryos, data are from 3 independent experiments with 8-9 embryo equivalents pooled for each experiment. (f) Detailed information of endothelial-haematopoietic bi-potential induction assays performed with cells from E9.5-E10.0 caudal half or AGM region. Fig. S3. Identification of the HSC-competent HECs marked by Neurl3-EGFP reporter. (a) Detailed information of the co-culture/transplantation assays performed with the caudal half cells from E10.0 Neurl3EGFP/+ embryos. (b) Boxplot showing the transcriptional expression level of EGFP in NE+ cell population, NE+, CD41-CD43-CD45-CD31+CD44+Neurl3-EGFP+ population from AGM region of E10.0 Neurl3EGFP/+ embryos. (c) Scatter plots showing correlation of the expression of EGFP with that of Neurl3 and Runx1, respectively. Fitted line and 95% confidence interval are shown in red. Pearson correlation coefficients and P values are also shown in blue text. (d) Stacked bar chart showing the constitution of different cell cycle phases in the indicated clusters. (e) Representative immunostaining on cross sections at AGM region of E11.0 Neurl3EGFP/+ embryos. Arrow indicates Neurl3+ aortic ECs; Yellow arrowheads indicate Neurl3+ bulging and bulged cells and IAHCs. Aquamarine arrowheads indicate CD44+Runx1+Neurl3- haematopoietic cells distributed outside the aorta. nt, neural tube; DA, dorsal aorta. Scale bars, 100 μm. (f) Detailed information of endothelial-haematopoietic bi-potential induction assays performed with cells from E9.5 caudal half and E10.0-E10.5 AGM region of Neurl3EGFP/+ embryos. Fig. S4. Molecular programs from primitive vascular ECs to HSC-primed HECs. (a) Embryo, independent experiment, and cell number information for additional scRNA-seq. sp, somite pairs. (b) t-SNE plots with clusters (upper left), sampling locations (lower left), embryonic stages (upper right) and clusters previously defined (lower right) mapped onto it. (c) Dot plot showing the average and percentage expression of selected marker genes in the indicated clusters. (d) Pseudotemporal ordering of the cells involved in HEC specification, including those in pEC, pAEC, earlyAEC, HEC, and T1 pre-HSC, inferred by monocle 2, with pseudotime mapped to it. (e) Heatmap showing smoothed and scaled expression levels of 2,851 pattern genes. Genes are ordered by patterns. Cells are ordered by pseudotime. (f) Dot plot showing the top six enriched Gene Ontology biological process (GO:BP) terms for each pattern. Dot color indicates statistical significance of the enrichment and dot size represents the fraction of genes annotated to each term. (g) Scatter plots showing the expression levels of the TF genes previously reported to be functional in HSPC regeneration along the pseudotemporal order with loess smoothed fit curves and 95% confidence interval indicated. The patterns to which the genes belong are indicated by different fill colors. The core TFs of the significantly overlapped regulons are underlined. Fig. 1 a Enrichment network of upregulated genes in HEC compared to earlyAEC and lateAEC - Cell Cycle (14.7) - Ribosome biogenesis (12.4) - Pyrimidine metabolism (11.5) - Small molecule biosynthetic process (10.5) - DNA replication (10.2) - Chromosome Maintenance (10.0) - Activation of the pre-replicative complex (7.7) - Ribosome biogenesis in eukaryotes (7.5) - Pyrimidine deoxynucleotide metabolic process (7.1) - DNA repair (6.4) Note: number in the bracket indicates the P-value based on -log10. b Cell cycle analysis - G2/M phase score - G1/S phase score - Quiescent - G1 - G2/M - Late AEC - HEC - Cluster: earlyAEC, lateAEC, HEC - Location: Body, DA, HEC - Stage: E9.5, E10.0, E10.5, E11.0 - No. of robbing gene transcripts ×10^5 c Ordered by pseudotime - Transcription factors d Ordered by pseudotime - Endothelial feature - EarlyAEC - HEC - Hematopoietic feature - EarlyAEC - HEC e Ordered by pseudotime - Cluster ID (#Gene) - I (131) - II (351) - III (33) - IV (285) - V (141) - VI (24) - VII (13) - VIII (27) - Runx1 - Spi1 - Myb - Kdr - Gja4 - Foxc2 - Klf6 - Zfp521 - Jund - Nfix - Nr4a1 - Id2 - Fos - Klf2 - Hes1 - Irf6 - Nfia - Tcf4 - Sox6 - Sox11 - Plagl1 - Lyl1 - Smarcc1 - Wdhd1 - Zfp422 - Carhsp1 Fig. 2 a HEC vs non-HEC HEC vs earlyAEC HEC vs lateAEC Runx1-correlated b c d e f g Cluster h i j Only endothelial potential 23.0% (60/261) Bi-potential 2.7% (7/261) Only hematopoietic potential 40.6% (106/261) Fig. 3 ### Enriched GO terms of PC2 positive genes - cell division - kinetochore organization - G2/M transition of mitotic cell cycle - establishment of chromosome localization - supramolecular fiber organization - regulation of plasma membrane bounded cell projection assembly - cytokinesis - vasculature development - regulation of postsynaptic density protein 95 clustering - substrate adhesion-dependent cell spreading ### Enriched GO terms of PC2 negative genes - regulation of RNA splicing - regulation of viral genome replication - ribosome assembly - negative regulation of transferase activity - blood coagulation - cytoplasmic translation - regulation of cellular amide metabolic process - negative regulation of glycoprotein biosynthetic process - negative regulation of protein secretion - negative regulation of tumor necrosis factor production Fig. 5 (a) Neur3-EGFP/Rum1/CD44/DAPI (b) E10.0 AGM (c) CD1/CD43/CD45/CD31CD44/Neur3-EGFP* (E10.0) (d) Proportion of positive wells (%) (e) CD41/CD3/CD45/CD31* Fig. 6 a - pEC - pAEC - earlyAEC - HEC - Other b - Cluster - pEC - pAEC - earlyAEC - HEC - Other c - PC1 score - PC2 score d - Expression (loss) e - Cluster f - Ordered by pseudotime g - Cell cycle - mTOR signaling pathway - GO:artery development - GO:BMP signaling pathway Fig. S1 \| Stage \| Embryos \| Exp. (n) \| Body \| DA \| Neg* \| Total \| \|-------\|---------\|----------\|------\|----\|------\|-------\| \| E9.5 \| 4 \| 2* \| 180 \| / \| 40 \| 220 \| \| E10.0 \| 10 \| 2+2 \| 110 \| 40 \| 56 \| 330 \| \| E10.5 \| 8 \| 1* \| 56 \| / \| / \| 56 \| \| E11.0 \| 7 \| 1* \| 56 \| / \| / \| 56 \| \| Total \| 29 \| 8 \| 360 \| 220\| 80 \| 662 \| CD45/CD31/CD144* negative control cells from body. 1Independent experiments for collecting CD45/CD31/CD144* sample cells from body. 2Independent experiments for collecting CD45/CD31/CD144* Oregon green* sample cells from AGM region. --- Location Stage \| Location \| Stage \| vEC \| earlyAEC \| lateAEC \| HEC \| HC \| Total \| \|----------\|-------\|-----\|----------\|---------\|-----\|----\|-------\| \| Body \| E9.5 \| 94 \| 26 \| 0 \| 0 \| 34 \| 154 \| \| \| E10.0 \| 118 \| 14 \| 1 \| 2 \| 0 \| 135 \| \| DA \| E10.0 \| 10 \| 42 \| 0 \| 33 \| 0 \| 85 \| \| \| E10.5 \| 0 \| 4 \| 35 \| 4 \| 0 \| 43 \| \| \| E11.0 \| 1 \| 2 \| 43 \| 0 \| 0 \| 46 \| \| Total \| \| 223 \| 88 \| 79 \| 39 \| 34 \| 463 \| Cells excluding Neg cluster, Ptpcr- or Sprn-expressing cells. --- Expression - earlyAEC - lateAEC - HEC Direction - up-regulation - down-regulation - NS (not significant) Genes positively correlated with Runx1 - Patterns I-VIII --- The copyright holder for this version posted January 20, 2020. doi: bioRxiv preprint ### a \| Stage \| Organ \| Exp (n) \| Population \| Constitution in the region (%) \| Cell dose<sup>a</sup> \| Clusters<sup>b</sup> \| \|----------------\|------------------------\|---------\|----------------------------------------------------------------------------\|---------------------------------\|-----------------------\|---------------------\| \| E9.5-E10.0 (30-32 sp) \| Caudal half 4 \| CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>CD31<sup>+</sup>Kit+CD201<sup>+</sup> \| 0.20±0.07 \| 3.0-4.0 ee \| 13/13 (100%) \| \| \| \| \| CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>Kit+CD201<sup>-</sup> \| 1.25±0.45 \| 3.0-4.0 ee \| 2/13 (15.4%) \| \| E9.5-E10.0 (30-34 sp) \| Caudal half 4 \| CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>CD201<sup>-</sup>CD44<sup>+</sup> \| 0.09±0.03 \| 3.0-4.0 ee \| 11/11 (100%) \| \| \| \| \| CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>CD201<sup>-</sup>CD44<sup>-</sup> \| 0.33±0.21 \| 3.0-4.0 ee \| 0/11 \| <sup>a</sup>cell dose per well and per recipient. <sup>b</sup>hematopoietic cluster positive wells/total wells. <sup>c</sup>somite pairs. <sup>d</sup>embryo equivalents. ### b #### Primary recipients (5/9) - Blood chimerism (%) #### Secondary recipients (5/5) - Blood chimerism (%) ### c #### Peripheral blood - CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>CD31<sup>+</sup>Kit+CD201<sup>+</sup> #### Spleen - CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>CD201<sup>-</sup>CD44<sup>+</sup> ### d #### earlyAEC - lateAEC #### HEC - PK44 ### e #### Endothelial tubules per 1,000 cells \| Stage \| Organ \| Exp (n) \| Population (CD41<sup>-</sup>CD43<sup>-</sup>CD45<sup>-</sup>CD31<sup>+</sup>) \| Constitution in the region (%) \| Cell dose<sup>a</sup> \| Bi-potential<sup>b</sup> \| Hematopoietic<sup>c</sup> \| Endothelial<sup>d</sup> \| \|-------\|-------\|---------\|--------------------------------------------------------------------------\|---------------------------------\|-----------------------\|--------------------------\|---------------------------\|-------------------------\| \| E9.5 \| Bone marrow \| 2<sup>2</sup> \| Kit<sup>+</sup>CD201<sup>-</sup>CD44<sup>+</sup> \| 0.11±0.03 \| 10 cells \| / \| 44/44 (100%) \| 35/44 (79.5%) \| \| \| \| \| Kit<sup>+</sup>CD201<sup>-</sup>CD44<sup>-</sup> \| 0.10±0.02 \| 10 cells \| / \| 0/42 (0%) \| 33/42 (78.5%) \| \| E9.5 \| AGM 5<sup>5</sup> \| Kit<sup>+</sup>CD201<sup>-</sup>CD44<sup>+</sup> \| 0.31±0.09 \| Single cell 7/261 (2.7%) \| 113/261 (43.3%) \| 67/261 (25.7%) \| <sup>a</sup>cells per well. <sup>b</sup>hematopoietic and endothelial bi-potential positive wells/total wells. <sup>c</sup>hematopoietic progeny positive wells/total wells. <sup>d</sup>endothelial tube positive wells/total wells. <sup>e</sup>somite pairs. <sup>f</sup>independent experiments, totally 12 embryos were used. <sup>g</sup>independent experiments, totally 15 embryos were used. Fig. S3 \| Stage \| Region \| Exp (n) \| Population in EC (CD41-CD43-CD45-CD31) \| Cell dose \| Clusters \| \|-------------\|----------------------\|---------\|----------------------------------------\|-----------\|----------\| \| E10.0 (30-34 sp²) \| Caudal half \| 5 \| CD44+Neurl3-EGFP \| 1.5-2.5 ee \| 6/6 (100%) \| \| \| \| \| CD44+Neurl3-EGFP \| 1.5-5.0 ee \| 3/6 (50%) \| Cell dose per recipient. hematopoietic cluster positive wells/total wells. somite pairs. embryo equivalents. c Pearson correlation analysis - Neurl3-EGFP, log₂(TPM/10+1) vs. Neurl3-EGFP, log₂(TPM/10+1) - Neurl3-EGFP, log₂(TPM/10+1) vs. Runx1, log₂(TPM/10+1) d Cell cycle phase - G2/M - S - G1 - Quiescent e Single cell co-culture f Single cell co-culture \| Stage \| Region \| Exp (n) \| Population in EC (CD41-CD43-CD45-CD31) \| Constitution in the region (%) \| Constitution in EC (%) \| Bi-potential \| Hematopoietic \| Endothelial \| \|-------------\|----------------------\|---------\|----------------------------------------\|-------------------------------\|------------------------\|--------------\|---------------\|-------------\| \| E9.5 (26-30 sp³) \| Caudal half \| 8 \| CD44+Neurl3-EGFP \| 0.20±0.07 \| 2.70±0.66 \| 1/301 (0.3%) \| 26/301 (8.6%) \| 43/301 (14.3%) \| \| E10.0 (31-35 sp) \| AGM \| 5 \| CD44+Neurl3-EGFP \| 1.20±0.57 \| 11.3±3.51 \| 2/467 (0.4%) \| 39/467 (8.4%) \| 51/467 (10.9%) \| \| E10.5 (36-39 sp) \| AGM \| 6 \| CD44+Neurl3-EGFP \| 0.29±0.10 \| 2.74±0.52 \| 1/159 (0.6%) \| 6/159 (3.8%) \| 33/159 (20.8%) \| hematopoietic and endothelial bi-potential positive wells/total wells. hematopoietic progeny positive wells/total wells. endothelial tube positive wells/total wells. somite pairs. 8 independent experiments, totally 32 embryos were used. 5 independent experiments, totally 37 embryos were used. 6 independent experiments, totally 23 embryos were used. Fig. S4* \| Stage \| Embryos \| Exp. (n) \| Sample \| Neg \| Total \| \|-------------\|---------\|----------\|--------\|-----\|-------\| \| E8.0 (3-5 sp) \| 4 \| 1 \| 40 \| 8 \| 58 \| \| E8.5 (6-9 sp) \| 14 \| 3 \| 236 \| 50 \| 309 \| \| E9.0 (17-18 sp) \| 6 \| 2 \| 205 \| 40 \| 245 \| \| Total \| 24 \| 6 \| 481 \| 98 \| 579 \| Notes: - CD45^−CD31^−CD144^− positive control cells from body - CD45^−CD31^−CD144^− negative control cells from body --- Supplementary Information: The copyright holder for this version posted January 20, 2020; https://doi.org/10.1101/2020.01.18.910356 doi: bioRxiv preprint	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 1349, 1 ], [ 1349, 1519, 2 ], [ 1519, 2752, 3 ], [ 2752, 4525, 4 ], [ 4525, 6270, 5 ], [ 6270, 8166, 6 ], [ 8166, 9671, 7 ], [ 9671, 11506, 8 ], [ 11506, 13371, 9 ], [ 13371, 15074, 10 ], [ 15074, 17020, 11 ], [ 17020, 18831, 12 ], [ 18831, 20731, 13 ], [ 20731, 22514, 14 ], [ 22514, 24224, 15 ], [ 24224, 26008, 16 ], [ 26008, 27668, 17 ], [ 27668, 29597, 18 ], [ 29597, 31274, 19 ], [ 31274, 33124, 20 ], [ 33124, 34756, 21 ], [ 34756, 36600, 22 ], [ 36600, 38416, 23 ], [ 38416, 40231, 24 ], [ 40231, 41949, 25 ], [ 41949, 42227, 26 ], [ 42227, 43734, 27 ], [ 43734, 45462, 28 ], [ 45462, 47107, 29 ], [ 47107, 48744, 30 ], [ 48744, 50474, 31 ], [ 50474, 52202, 32 ], [ 52202, 53803, 33 ], [ 53803, 55425, 34 ], [ 55425, 57045, 35 ], [ 57045, 58673, 36 ], [ 58673, 60312, 37 ], [ 60312, 61990, 38 ], [ 61990, 63616, 39 ], [ 63616, 65069, 40 ], [ 65069, 65741, 41 ], [ 65741, 69391, 42 ], [ 69391, 72284, 43 ], [ 72284, 75861, 44 ], [ 75861, 79463, 45 ], [ 79463, 79741, 46 ], [ 79741, 81376, 47 ], [ 81376, 82939, 48 ], [ 82939, 84663, 49 ], [ 84663, 86238, 50 ], [ 86238, 87813, 51 ], [ 87813, 89699, 52 ], [ 89699, 91572, 53 ], [ 91572, 93263, 54 ], [ 93263, 93360, 55 ], [ 93360, 94697, 56 ], [ 94697, 96161, 57 ], [ 96161, 97556, 58 ], [ 97556, 99082, 59 ], [ 99082, 99868, 60 ], [ 99868, 101174, 61 ], [ 101174, 101454, 62 ], [ 101454, 102320, 63 ], [ 102320, 102320, 64 ], [ 102320, 102490, 65 ], [ 102490, 102806, 66 ], [ 102806, 104370, 67 ], [ 104370, 107875, 68 ], [ 107875, 110079, 69 ], [ 110079, 110745, 70 ] ] }
d37173fff2070adfb2df7b14527cd4e1679fb668	{ "olmocr-version": "0.1.59", "pdf-total-pages": 10, "total-fallback-pages": 0, "total-input-tokens": 26344, "total-output-tokens": 8623, "fieldofstudy": [ "Computer Science", "Linguistics" ] }	Abstract For the study of historical language varieties, the sparsity of training data imposes immense problems on syntactic annotation and the development of NLP tools that automatize the process. In this paper, we explore strategies to compensate the lack of training data by including data from related varieties in a series of annotation projection experiments from English to four old Germanic languages: On dependency syntax projected from English to one or multiple language(s), we train a fragment-aware parser trained and apply it to the target language. For parser training, we consider small datasets from the target language as a baseline, and compare it with models trained on larger datasets from multiple varieties with different degrees of relatedness, thereby balancing sparsity and diachronic proximity. Our experiments show (a) that including related language data to training data in the target language can improve parsing performance, (b) that a parser trained on data from two related languages (and none from the target language) can reach a performance that is statistically not significantly worse than that of a parser trained on the projections to the target language, and (c) that both conclusions holds only among the three most closely related languages under consideration, but not necessarily the fourth. The experiments motivate the compilation of a larger parallel corpus of historical Germanic varieties as a basis for subsequent studies. 1 Background and motivation We describe an experiment on annotation projection (Yarowski and Ngai, 2001) between different Germanic languages, resp., their historical varieties, with the goal to assess to what extent sparsity of parallel data can be compensated by material from varieties related to the target variety, and studying the impact of diachronic proximity onto such applications. Statistical NLP of historical language data involves general issues typical for low-resource languages (the lack of annotated corpora, data sparsity, etc.), but also very specific challenges such as lack of standardized orthography, unsystematized punctuation, and a considerable degree of morphological variation. At the same time, historical languages can be viewed as variants of their modern descendants rather than entirely independent languages, a situation comparable to low-resource languages for which a diachronically related major language exists. Technologies for the cross-lingual adaptation of NLP tools or training of NLP tools on multiple dialects or language stages are thus of practical relevance to not only historical linguistics, but also to modern low-resource languages. The final paper will be published under a Creative Commons Attribution 4.0 International Licence (CC-BY), http://creativecommons.org/licenses/by/4.0/. in this context, historical language allows to study the impact of the parameter of diachronic relatedness, as it can be adjusted relatively freely, e.g., by choosing dialects which common ancestor existed just a few generations before rather than languages separated for centuries. A focused study of the impact of diachronic relatedness on projected annotations requires sufficient amounts of parallel texts for major language stages, and comparable annotations as a gold standard for evaluation. In this regard, the Germanic languages provide us with a especially promising sandbox to develop such algorithms due to the abundance of annotated corpora and NLP tools of the modern Germanic languages, most notably Modern English. We employ annotation projection from EN to Middle English (ME), Old English (OE) and the less closely related Early Modern High German (DE) and Middle Icelandic (IS) for which we possess comparable annotations, and test the following hypotheses: (H1) Adding data from related varieties compensates the sparsity of target language training data. (H2) Data from related languages compensates the lack of target language training data. (H3) The greater the diachronic proximity, the better the performance of (H1) and (H2). We test these hypotheses in the following setup: (1) Hyperlemmatization: Different historical variants are normalized to a consistent standard, e.g., represented by a modern language (Bollmann et al., 2011). We emulate hyperlemmatization by English glosses automatically obtained through SMT. (2) Projection: We create training data for a fragment-aware dependency parser (Spreyer et al., 2010) using annotation projection from modern English. (3) Combination and evaluation: Parser modules are trained on different training data sets, and evaluated against existing gold annotations. In our setting, we enforce data sparsity by using deliberately small training data sets. This is because we emulate the situation of less-documented languages that will be in the focus of subsequent experiments, namely, Old High German and Old Saxon, which are relatively poorly documented. We do hope, however, that scalable NLP solutions can be developed if we add background information from their descendants (Middle/Early Modern High German, Middle/Modern Low German), or closely related, and better documented varieties (Old English, Middle Dutch). Hence, the goal of our experiment is not to develop state-of-the-art parsers, but to detect statistically significant differences in parsing performance. If these can be confirmed, this motivates creating a larger corpus of parallel texts in Germanic languages as a basis for subsequent studies and more advanced, projection-based technologies for older and under-resourced Germanic languages. 2 Languages and corpus data We use parallel biblical texts in Old English (OE), Middle English (ME), Middle Icelandic (IS) and Early Modern High German (DE). This selection is determined by the availability of syntactically annotated corpora with closely related annotation schemes. As these schemes are derived from the Penn TreeBank (PTB) bracketing guidelines (Taylor et al., 2003a), we decided to use Modern English (EN) as a source for the projections. The Germanic languages derive from Proto-Germanic as a common ancestor. OE and Old High German separated in the 5th c. The antecessor of IS separated from this branch about 500 years earlier. Among Germanic languages, great differences emerged, but most languages developed similarly towards a loss of morphology and a more rigid syntax, a tendency particularly prevalent in EN. As compared to this, OE had a relatively free OV word order, with grammatical roles conveyed through morphological markers. The OE case marking system distinguished four cases, but eventually collapsed during ME, resulting in a strict strict VO word order in EN (Trips, 2002; van Kemenade and Los, 2009; Cummings, 2010). Unlike EN, DE preserved four cases, and a relatively free word order (Ebert, 1976). A characteristic of German are separable verb prefixes, leading to $1:n$ mappings in the statistical alignment with EN. Unlike EN and DE, IS is a North Germanic language. It is assumed to be conservative, with relatively free word order with both OV and VO patterns and a rich morphology that leads to many $1:n$ alignments with EN, e.g., for suffixed definite articles; we thus expect special challenges for annotation projection under conditions with limited training data. Different from the old languages, EN developed a rigid word order and a largely reduced morphology. A direct adaptation of an existing English parser to (hyperlemmatized) OE, IS or DE is thus not promising. Therefore, we employ an approach based on annotation projection. The corpus data we used consists of parsed bible fragments from manually annotated corpora, mostly the gospels of Matthew (Mt), Mark (Mr), John (J) and Luke (L), from which we drew a test set of 147 sentences and a training set of 437 sentences for every language. ME and OE The Penn-Helsinki Parsed Corpus of Middle English (PPCME2)$^1$ and the York-Toronto-Helsinki Parsed Corpus of Old English Prose (Taylor et al., 2003b, YCOE) use a variant of the PTB annotation schema (Taylor et al., 2003a). YCOE contains the full West Saxon Gospel, but PPCME2 contains only a small fragment of a Wycliffite gospel of John, the ME data is thus complemented with parts of Genesis (G) and Numbers (N). IS The Icelandic Parsed Historical Corpus (Rögnvaldsson et al., 2012, IcePaHC) is annotated following YCOE with slight modifications for specifics of IS. We use the gospel of John from Oddur Gottskállksson’s New Testament, a direct translation from Luther. DE The Parsed Corpus of Early New High German$^2$ contains three gospels from Luther’s Septembertestament (1522). As an IcePaHC side-project, it adapts the IS annotation scheme. EN For EN, we use the ESV Bible.$^3$ Due to a moderate number of archaisms, it is particularly well-suited for automated annotation. ### 3 Experimental setup We study the projection of dependency syntax, as it is considered particularly suitable for free word-order languages like IS, OE and DE. The existing constituent annotations were thus converted with standard tools for PTB conversion. Figure 1 summarizes the experimental setup. For annotating EN, we created dependency versions of WSJ and Brown sections of the PTB with the LTH Converter (Johansson and Nugues, 2007). We trained Malt 1.7.2 (Nivre, 2003), optimized its features with MaltOptimizer (Ballesteros and Nivre, 2012), and parsed the EN bible using the resulting feature model. --- $^1$http://www.ling.upenn.edu/hist-corpora/PPCME2-RELEASE-3/index.html $^2$http://enhgcorpus.wikispaces.com $^3$http://esv.org The ME, OE, DE and IS datasets were word aligned with EN using GIZA++ (Och and Ney, 2003). 1 : n alignments were resolved to the most probable 1 : 1 mapping. During annotation projection, we assume that the aligned words represent the respective heads for the remaining n – 1 words. These dependent words are assigned the dependency relation FRAG to the word that got the highest score in the translation table. This solution solves, among others, the problem of separable verb prefixes in DE, for example, DE ruffen with prefix an would be aligned to English word call: As P("call" \| "an") < P("call" \| "ruffen"), the syntactic information of "call" will be projected to "ruffen" and "an" will be its dependent labeled with "FRAG". The projected dependency trees were checked on well-formedness, sentences with cycles were dismissed from the data set. We formed training sets containing 437 sentences for ME, OE, DE, IS. Monolingual data sets were combined into bi-, tri- or quadrilingual training data sets with a simple concatenation, thereby creating less sparse, but more heterogeneous training data sets. For every language, test data was taken from J, 174 sentences per language. We used the projected dependencies to train fMalt (Sprayer et al., 2010), a fragment-aware dependency parser, in order to maximize the gain of information from incomplete projections. In our setting, fMalt used two features, POS and hyperlemmas. POS The tagsets of the historical corpora originate in PTB, but show incompatible adaptations to the native morphosyntax. Tagset extensions on grammatical case in OE, IS and DE were removed and language-specific extensions for auxiliaries and modal verbs were leveled, in favor of a common, but underspecified tagset for all four languages. As these generalized tags preserve information not found in EN, they were fed into the parser. (hyper-)lemma Lexicalization is utterly important for the dependency parsing (Kawahara and Uchimoto, 2007), but to generalize over specifics of historical language varieties, hyperlemmatization needs to be performed. Similar to Zeman and Resnik (2008), we use projected English words as hyperlemmas and feed them into the parser. Hyperlemmatization against a closely related language is acceptable as we can expect that the syntactic properties of words are likely to be similar. The projected annotations were then evaluated against dependency annotations created analogously to the EN annotations from manual PTB-style constituency syntax. As LTH works exclusively on PTB data, the historical corpora were converted with its antecessor Penn2Malt using user-defined head-rules (Yamada and Matsumoto, 2003). 4 Evaluation results \| \| baseline \| \[\Delta UAS\] worst model \| \[\Delta UAS\] best model \| \[\Delta UAS\] worst model \| \[\Delta UAS\] best model \| \|---------\|----------\|-----------------------------\|---------------------------\|-----------------------------\|---------------------------\| \| \| UAS \| +1 \| +2 \| +1 \| +2 \| \| ME \| .60 \| +DE +.00 \| +DE+IS -.03 \| +OE -.01 \| +OE+IS +.01* \| -.00 \| \| OE \| .31 \| +IS -.00 \| +DE+IS -.02 \| +DE +.02 \| +ME+DE -.00 \| +.02 \| \| DE \| .41 \| +OE +.02** \| +OE+IS +.03* \| +ME +.04*** \| +ME+IS +.03* \| +.04 \| \| IS \| .32 \| +IS -.02 \| +DE+OE -.01 \| +ME +.00 \| +ME+DE -.01 \| -.01 \| (a) trained on target and related language(s) \| \| baseline \| \[\Delta UAS\] worst model \| \[\Delta UAS\] best model \| \[\Delta UAS\] worst model \| \[\Delta UAS\] best model \| \|---------\|----------\|-----------------------------\|---------------------------\|-----------------------------\|---------------------------\| \| \| UAS \| 1 \| 2 \| 1 \| 2 \| \| ME \| .60 \| OE -.09* \| DE-IS -.01* \| IS -.05* \| IS+OE -.02 \| -.02 \| \| OE \| .31 \| DE -.03 \| ME-DE -.01 \| ME -.02 \| ME+IS -.01 \| -.00 \| \| DE \| .41 \| OE -.01 \| OE-IS +.02 \| IS +.02 \| IS+ME +.05* \| +.04 \| \| IS \| .32 \| OE -.07* \| DE-OE -.02 \| ME -.06* \| ME+DE -.02 \| -.04 \| (b) trained on related language(s) alone Table 1: Performance of best- and worst-performing parsing models (UAS diff. vs. baseline with $\chi^2$; p < .05, p < .01, **p < .005) We evaluate the unlabeled attachment score (Collins et al., 1999, UAS), i.e., the proportion of tokens in a sentence (without punctuation) that are assigned the correct head, on test sets of 174 sentences in each language. 4http://stp.lingfil.uu.se/nivre/research/Penn2Malt.html As a baseline for the evaluation we take the performance of the parser trained solely on the target language data. As shown in Tab. 1 (second col.), the UAS scores mirror both the diachronic relatedness (ME>DE>IS), as well as the relative loss of morphology (ME>DE>IS/OE), indicating that diachronic relatedness may not be the only factor licensing the applicability of the annotation projection scenario (H3). It is also important, though, to keep in mind that the OE and IS translations of the Bible had considerable influence of Latin syntax, whereas DE and ME translations aimed for a language easy to understand. Table 1a gives the best and worst results for the unlabeled attachment score for the parser trained on target and related language(s) (H1). With the exception of DE, we observed no significant differences in UAS scores relative to the baseline. DE may benefit from ME because of its more flexible syntax (thus closer to ME [and OE] than to Modern English), and from IS because of Luther’s direct influence on the IS bible. That ME did not mutually benefit from German may be due to the good quality of ME annotation projections (resulting from its proximity to EN). Parsers trained on trilingual and quadrilingual sets exhibited no improvement over the bilingual sets. Taken together, we found no positive effect of using additional training data from language stages diachronically separated for more than 500 years (e.g., OE/ME), but also, we did not find a negative effect among the West Germanic languages. If additional training material is carefully chosen among particularly closely related varieties, however, the DE effect can be replicated, and then, including related language data to training data in the target language can improve parsing performance. While in our setting, training data from related languages may (but does not have to) improve a parser training if training data for the target language is available, it may very well be employed fruitfully if no training data for the target language is available (H2): Table 1b shows that, unsurprisingly, parsers trained only on one related language had the lowest performance in the experiment, so using multiple train languages seems to compensate language-specific idiosyncrasies. The best-performing parsing models trained on two or more related languages achieved a performance not significantly worse (if not better) than models being trained on target language data. This effect extends to all languages except for IS and indicates that a careful choice of additional training data from related varieties may facilitate annotation projection. Equally important (and valid across all languages) is that none of the models trained on one language outperformed any of the model trained on two languages. Using training data from two related languages doesn’t seem to hurt performance in our setting. Adding a third language did not yield systematic improvements, the scores for trilingual models are in the range of the bilingual models. Again, DE is exceptionally good, benefitting from being a direct source of the IS translation as well as structurally comparable to ME. In both settings, the worst-performing language is IS, with a significant drop in annotation projection quality with Western Germanic material added, indicating that diachronic distance between Northern and Western Germanic languages limits the applicability of (H2), thereby supporting (H3). Taken together, our results indicate 1. a significant positive effect for the Western Germanic languages (ME, OE, DE) for (H2), and 2. a significant negative effect for Western and Northern Germanic languages (IS) for (H2) As a tentative hypothesis, one may speculate that languages separated for 1000 years (OE-IS) or more are too remote from each other to provide helpful background information, but that languages separated within the last 750 years (ME-DE) or less are still sufficiently close. This novel assumption may provide a guideline for future efforts to project annotations among related languages, and is thus of immense practical relevance for developing future NLP tools for historical and less-resourced language varieties. Ultimately, one may formulate rules of best practice like the following: - If no syntactic annotations for a target language are available, annotation projection among closely related languages may be a solution. Even with limited amounts of parallel data, diachronic distances of more than 500 years can be successfully bridged (EN/ME, baseline). • If no syntactic annotations for a target language are available, a parser trained on hyperlemmatized corpora in two languages may yield a performance comparable to a parser trained on small amounts of target data. A parser trained on hyperlemmatized monolingual data may be significantly worse (H2). • The sparsity of parallel text to conduct annotation projection and train a (hyperlemmatized) parser can only be compensated by adding parallel data from one related language if these are closely diachronically related (with a separation being less than, say, 500 years ago) and at a similar developmental stage (DE/ME, H1). Adding data from multiple, equally remote languages does not necessarily improve the results further. At the current state, such recommendations would be premature, they require deeper investigation, but with the confirmation of (H2) and (H3), we can now motivate larger-scale efforts to compile a massive parallel corpus of historical Germanic language varieties as a basis for subsequent studies. Initial steps towards this goal are described in the following section. 5 Towards a massive parallel corpus of historical Germanic languages With the long-term goal to systematically assess the impact of the factor of diachronic proximity, we focus on annotation projection among the Germanic languages as test field. The Germanic languages represent a particularly well-resourced, well-documented and well-studied language family which development during the last 1800 years is not only well-explored, but also documented with great amounts of (parallel) data, ranging from the 4th century Gothic bible over a wealth of Bible translations since the middle ages to the modern age of communication with its abundance of textual resources for even marginal varieties. Motivated from our experiment, we thus began to compile a parallel corpus of historical and dialectal Germanic language varieties. Primary source data for a massive parallel corpus of historical varieties of any European language is mostly to be drawn from the Bible and related literature. The Bible is the single most translated book in the world and available in a vast majority of world languages. It is also often the case that there are several biblical translation existing for a language. Bible data also represents the majority of parallel data available for historical Germanic languages, and for the case of OS and OHG, gospel harmonies represent even the majority of data currently known. Beyond this, the corpus includes Bible excerpts and paraphrases from all Germanic languages and their major historical stages. Tab. 2 gives an overview over the current status of the Parallel Bible Corpus. At the moment, 271 texts with about 38.4M tokens have been processed, converted from their original format and verse-aligned according to their original markup or with a lexicon-supported geometric sentence aligner (Tóth et al., 2008). In the table, ‘text’ means any document ranging from a small excerpt such as the Lord’s Prayer (despite their marginal size valuable to develop algorithms for normalization/[hyper]lemmatization) over gospel harmonies and paraphrases to the entire bible that has been successfully aligned with Bible verses. The compiled corpus, excerpts and fragments for all Germanic languages marked up with IDs for verses, chapters and books. For data representation, we employed an XML version of the CES-scheme developed by Resnik et al. (1997). Having outgrown the scale of Resnik’s earlier project by far, we are currently in transition to TEI P5. As it is compiled from different sources, the corpus cannot be released under a free or an academic license. It contains material without explicit copyright statement, with proprietary content (e.g., from existing corpora), or available for personal use only. Instead, we plan to share the extraction and conversion scripts we used. For the experiments we aim to prepare, we focus on primary data, the texts in this collection are not annotated. Where annotations are available from other corpora or can be produced with existing tools, however, these annotated versions will be aligned with the Bibles and included in subsequent experiments. Table 2: Verse-aligned texts in the Germanic parallel Bible corpus (parentheses indicate marginal fragments with less than 50,000 tokens) 6 Summary and outlook This paper describes a motivational experiment on annotation projection, or more precisely, strategies to compensate data sparsity (the lack of parallel data) with material from related, but heterogeneous varieties to facilitate cross-language parser adaptation for low-resource historical languages. We used a fragment-aware dependency parser trained on annotation projections from ESV Bible to four historical languages. Our results indicate a lexicalized fragment-aware parser trained on a small amount of annotation projections can yield good results on closely related languages. In a situation of the absence of training data for the target language (or, for example, in the situation where there is no parallel corpora for the target language), a hyperlemmatized parser trained on (projected) annotations from two or more related languages is likely to outperform a parser trained on a single related language. We achieved statistically significant differences in parser performance trained on (a) target language data, and (b) target language and data from related varieties, resp. (c) data from related varieties only. These indicate that closely related languages (say, with a common ancestor about 750 years ago, such as DE and ME) have some potential to compensate sparsity of parallel data in the target variety, whereas this potential does not seem to exist for more remotely related languages (say, with a common ancestor more than 1000 years ago such as OE and IS). The experimental results revealed that the parser performance can, indeed, be improved by means of including a related language to the training data, but we had a significant effect for only one language under consideration, indicating that the diachronic proximity of the languages considered was possibly too large, and thereby motivating subsequent experiments, and in particular, the creation of a larger parallel corpus of historical Germanic language varieties. We described initial steps in the compilation of this corpus. Our experiment raises a number of open issues that are to be pursued in subsequent studies: 1. Our setup has a clear bias towards English (in the annotation schemes used and the source annotations), and parser performance was strongly affected by the syntactic difference between the target language and Modern English from which the syntactic dependencies were projected, indicating the relevance of diachronic relatedness as well as the developmental state of a related language. Subsequent experiments will hence address the inclusion of richer morphological features, projection from other languages and evaluation against syntactic annotations according to other schemes not derived from the Penn Treebank, as currently available, for example, for Old High German, Old Norse, and Gothic. 2. The hyperlemmatization in our approach was achieved through alignment/SMT, and a similar lexically-oriented approach has been suggested by (Zeman and Resnik, 2008). Alternative strategies more suitable for scenarios with limited amounts of training data may include the use of orthographical normalization techniques (Bollmann et al., 2011) or substring-based machine translation (Neubig et al., 2012) and are also subject to on-going research. We assume that SMT-based hyperlemmatization introduces more noise than these strategies, so that it is harder to achieve statistically significant results. Our findings are thus likely to remain valid regardless of the hyperlemmatization strategy. This hypothesis is, however, yet to be confirmed in subsequent studies. 3. Our experiment mostly deals with data translated from (or at least informed by) the Latin Vulgate. Our data may be biased by translation strategies which evolved over time, from very literal translations (actually, glossings) of Latin texts in the early middle ages to Reformation-time translations aiming to grasp the intended meaning rather than to preserve the original formulation. A focus on classical languages is, however, inherent to the parallel material in our domain. A representative investigation of annotation projection techniques thus requires the consideration of quasi-parallel data along with parallel data. This can be found in the great wealth of medieval religious literature, with Bible paraphrases, gospel harmonies, sermons and homilies as well as poetic and prose adaptations of biblical motives. The parallel corpus of Germanic languages thus needs to be extended accordingly. 4. One may wonder how the annotation projection approach performs in comparison to direct applications of modern language NLP tools to normalized historical data language (Scheible et al., 2011). While it is unlikely that such an approach could scale beyond closely related varieties, successful experiments on the annotation of normalized historical language have been reported, although mostly focused on token-level annotations (POS, lemma, morphology) of language stages which syntax does not greatly deviate from modern rules (Rayson et al., 2007; Pennacchiotti and Zanzotto, 2008; Kestemont et al., 2010; Bollmann, 2013). For the annotation of more remotely related varieties with more drastic differences in word order rigidity or morphology as considered here, however, projection techniques are more promising as they have been successfully applied to unrelated languages, as well, but still benefit from diachronic proximity, cf. Meyer (2011) for the projection-based morphological analysis of Modern and Old Russian. The goal of our experiment was not to achieve state-of-the-art performance, but to show whether background material from related languages with different degrees of diachronic distance can help to compensate data sparsity, in this case with an experiment on annotation projection. This hypothesis could be confirmed and we found effects that – even on the minimal amounts of data considered for this study – indicated statistically significant improvements. It is to be expected that even greater improvements can be achieved by considering more closely related pairs of languages, with greater amounts of data. The further exploration of this hypothesis is the driving force behind our efforts to compile a massive corpus of parallel and quasi-parallel texts for all major varieties of synchronic and historical Germanic languages. Algorithms successfully tested in this context can be expected to be applicable to other scenarios in which, e.g., well-researched modern languages may be employed to facilitate the creation of NLP tools for less-ressourced, related languages. Our efforts are thus not specific to historical languages. As the diachronic development and the diversification of the Germanic languages is well-documented in this body of data, and the linguistic processes involved are well-researched, this data set represents an extraordinarily valuable resource for philological and comparative studies as well as Natural Language Processing. In particular, we are interested in developing algorithms that explore and exploit the variable degree of diachronic relatedness found between the languages in our sample. 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Cross-language parser adaptation between related languages. In IJCNLP-08 Workshop on NLP for Less Privileged Languages, pages 35–41, Hyderabad, India, Jan.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2820, 1 ], [ 2820, 6980, 2 ], [ 6980, 9656, 3 ], [ 9656, 15031, 4 ], [ 15031, 19584, 5 ], [ 19584, 23807, 6 ], [ 23807, 26779, 7 ], [ 26779, 31400, 8 ], [ 31400, 35560, 9 ], [ 35560, 36996, 10 ] ] }
8a7b44a286be36a229d4fbb9d266a4024362a526	{ "olmocr-version": "0.1.59", "pdf-total-pages": 7, "total-fallback-pages": 0, "total-input-tokens": 24570, "total-output-tokens": 7242, "fieldofstudy": [ "Engineering" ] }	Hierarchical control strategy based on bidding mechanism in active distribution network Jiawei Zhou, Bingxing Yue, Jinrong Wu, Hua Huang, Chunliu Wang Suzhou Power Supply Company, Suzhou 215004, People’s Republic of China E-mail: [email protected] Published in The Journal of Engineering; Received on 9th October 2017; Accepted on 1st November 2017 Abstract: With the penetration of intermittent energy rising and controllable objects increasing in active distribution network (ADN), centralised control is difficult to guarantee the optimally real-time status of the grid and distributed control cannot consider all controllable objects together. Therefore, hierarchical control architecture is proposed. This paper divides ADN into some regions and focuses on regions’ cooperative control strategy. Based on the global optimisation result, regions optimise with each other in short-time scales. According to the indicator of feeder control error, the control mechanism that reacts to real-time power fluctuation is established. Further, this paper puts forward ADN region cooperative control strategy based on bidding mechanism. Communication mechanism based on blackboard system is used to avoid complex communication networks. The effectiveness and validity of ADN region cooperative control strategy is verified by the simulation of study case. 1 Introduction In recent years, it puts forward new requirements for the operation and management of distribution network (DN) because of the high penetration of renewable energy such as photovoltaic (PV) and wind power. To make full use of the advantages and overcome the problems they bring, a new control mode should be introduced and applied to adapting to the high penetration of distributed energy resources (DERs). ADN, which is characterised by high penetration of DERs and high control requirements, has been generally accepted as an important development mode for smart grid [1]. Traditional DN always uses centralised control mode which schedules with 24 or 96 points [2]. However, the speed of centralised control mode is difficult to meet the real-time requirement due to the unpredictability and rapid change of PV and wind power. So decentralised control mode [3] attracts wide attention due to its smaller control range, less control variable and better real-time performance. However, decentralised control mode only considers its own optimisation and cannot consider the whole operation state of ADN. It is difficult to achieve the whole optimisation of ADN. In this paper, a hierarchical mode, which includes global layer and autonomous layer [4], is proposed to cope with technical challenges for DN with high penetration of DERs. This mode has the integrity of centralised control mode and flexible features of decentralised control mode. In this mode, global optimisation schedules regions’ target curve then regions follow the target curve. Region is autonomous to restrain the intermittent power fluctuation in real time. The authors of [5] present hierarchical control can give full play to its autonomy compared with centralised control. Especially in the transient process and communication network failure state, regional autonomous control can maintain stable operation of the system. In addition, hierarchical control can control the system operation from the global level and achieve the stability and economy of the whole network compared with decentralised control. In the hierarchical mode, how to coordinate the regions’ global optimisation goal is difficult. In [6], global optimisation sets 24 h target curve and feeders, which act as lower control units, conduct real-time local re-optimisation. The authors of [7] schedule the DN layer on the global level. The micro-grid layer optimises the exchange power between micro-grids to get optimal benefits. However, due to the unpredictability and rapid change of PV and wind power, above research lacks the re-coordination between regions so it is difficult to realise the optimal operation of the ADN in real time. At present, the research about global optimal dispatching is abundant. For example, the authors of [8] propose an algorithm based on intelligent single particle optimiser. In [8], DERs and sectionalising switches are taken into consideration together to schedule in next 24 h. To realise ADN control target in different time scales, a new region cooperative control method is needed to ensure the real-time optimisation of ADN. This paper divides ADN into regions and focuses on region cooperative control strategy. Based on the global optimisation result, regions optimise with each other in short-time scales. The indicator of feeder control error in [9] is used to establish ADN region’s autonomous control mode. For further optimisation of the ADN real-time operation, this paper puts forward ADN region cooperative control strategy based on bidding mechanism. Communication mechanism based on blackboard system is used to avoid complex communication networks. The effectiveness and validity of this strategy is verified by the simulation of study case. 2 ADN hierarchical control strategy 2.1 Hierarchical control structure To deal with the communication pressure and real-time control requirement of large numbers of DERs, this paper proposes a hierarchical control structure, including: (i) Global optimisation layer: Based on intermittent energy and load forecast results, distribution management system (DMS) arranges and optimises ADN’s operation on the global level. Global optimisation sets DER output curve and lower-layer optimisation goal, such as regional exchange power, in next 24 h. The global optimisation considers the whole information of ADN and the calculation period is too long to consider the real-time fluctuations of intermittent energy and load. (ii) Regional autonomous control layer: This layer is controlled by regional control unit which receives optimisation targets from DMS. Regional control unit will respond to the real-time power fluctuation of the ADN and coordinate DERs to realise region internal stability and reduce the influence between different regions. The autonomous region can divide according to the following principles: All DERs, between one sectionalising switch and the end of feeder or between two different sectionalising switches, form an autonomous region. This partition method is well adapted to the characteristics of DN because the regional scale will not change when the sectionalising switch changes status. It owns high flexibility and adaptability. In addition, the sectionalising switches usually configure as measurement points in DN so the value of regional exchange power can be collected in real time. It is convenient for ADN to carry out the whole state monitoring and control (Fig. 1). ### 2.2 Regional autonomous control strategy The research results of global optimisation are abundant and this paper focuses on region control. The indicator of feeder control error (FCE) proposed by [9] is used to form the regional objective function of region $ i $ \[ \Delta P_{\text{FCE,}i} = k_i \times \Delta P_j + \Delta P_{\text{region,}i} = 0 \quad (1) \] where $ k_i $ is the power coordinative coefficient of region $ i $; $ \Delta P_j $ is the deviation between feeder actual exchange power and its optimisation target; $ \Delta P_{\text{region,}i} $ is the deviation between actual regional exchange power of region $ i $ and its optimisation target. The detailed description of (1) and following derived content can be found in [10]. According to (1), when there is $ \Delta P $ power fluctuation, it can be classified as the next two cases: (i) $ \Delta P $ occurs in the region $ j $: When the $ \Delta P $ occurs in the region $ j $, DERs in region $ j $ will adjust their power output to maintain the regional exchange power. How to allocate the $ \Delta P $ depends on the distribution coefficient. The operation state of all regions, including feeder exchange power, will not change and they still follow the target value. (ii) $ \Delta P $ occurs outside of the regions: When the $ \Delta P $ occurs outside of the regions, the power fluctuation is allocated by the substation bus and regions together with the ratio of $ 1/(1 + \sum_{j \in G} k_j) $ and $ k_i/(1 + \sum_{j \in N} k_j) $. We can obtain the equations as follows: \[ \Delta P_i = \Delta P_j/1 + \sum_{j \in G} k_j \quad (2) \] \[ \Delta P_{\text{region,}k} = -k_i \times \Delta P_j/(1 + \sum_{j \in N \cap G} k_j) \quad (k \in N, k \notin G) \quad (3) \] (iii) where $ N $ is the collection of all autonomous regions. If one region cannot complete its optimisation target, the unfinished target will be undertaken by other regions in accordance with the regional coordinative coefficient. Assuming the collection of regions, which cannot complete their optimisation target, is $ G $. The deviation of feeder exchange power can be written as \[ \Delta P_i = \left( \Delta P_j + \sum_{j \in G} \Delta P_{\text{region,}j} \right)/(1 + \sum_{j \in N \cap G} k_j) \quad (4) \] Other regions’ deviation of regional exchange power is given by \[ \Delta P_{\text{region,}k} = -k_i \times \left( \Delta P_j + \sum_{j \in G} \Delta P_{\text{region,}j} \right)/1 + \sum_{j \in N \cap G} k_j \quad (k \in N, k \notin G) \quad (5) \] The power fluctuation undertaken by one region will be allocated to DERs in this region in accordance with the distribution coefficient \[ \Delta P_{\text{DER,}m} = \alpha_{\text{DER,}m} \times \Delta P_{\text{region,}k} \left( \sum_{m} \alpha_{\text{DER,}m} = 1 \right) \quad (6) \] ### 2.3 Analysis of DER deviation caused by FCE control There are different kinds of load and intermittent energy sources in different regions of ADN. In addition, there is characteristic difference between different kind of loads, such as the resident load and industrial load. Therefore, it can be assumed that there is no correlation between the power fluctuations in different nodes. Then, according to the principle of FCE, each power fluctuation may cause changes in DERs. DERs can be divided into three operation states based on the deviation between current power output and target value. (i) The first state is optimal state ($ S_o $) and it represents current power output equals to target value. (ii) The second state is positive deviation state ($ S_p $) and it presents current power output is greater than target value. (iii) The third state is negative deviation state ($ S_n $) and it presents current power output is less than target value. The energy storage system (ESS) is taken as an example. Its power output is affected by the state of charge (SOC) so following plan may fail if the power output continues to deviate from the target value. Therefore, optimisation results in the long-time scale may be affected if the regional optimisation just tracks global optimisation target. That may lead to a larger deviation from the optimal state. As shown in Fig. 2, it is assumed that ESS in region 1 and region 2 is in positive deviation state. Micro turbine (MT) in region 3 is in ![Fig. 1 Hierarchical control structure of ADN](image-url) negative deviation state. ESS in region 4 is in optimal state. PV and wind turbine (WT) are renewable energy and regional strategy does not control them. DERs’ state in Fig. 2 can be represented by hollow circle as shown in Fig. 3. If there is a power fluctuation $\Delta P > 0$ outside of regions, DERs in regions 1–4 will shift to positive state based on (2) and (3). This state can be represented by solid circle as shown in Fig. 3a. In Fig. 3a, ESSs are gradually deviated from their own target value. At this moment, if regional coordinative coefficient of regions 1, 2 and 4 is reduced and regional coordinative coefficient of region 3 is added, power fluctuation caused by $\Delta P$ will be mainly undertaken by region 3. As shown in Fig. 3b, MT’s power output is closer to the target value and the deviation between other ESSs’ power output and target value is reduced too. To improve ADN operation and make DERs run more reasonable, following sections will introduce region cooperative control strategy based on bidding mechanism. 3 Region cooperative control strategy based on bidding mechanism 3.1 Application of bidding mechanism According to the above analysis, fixed regional coordinative coefficient in FCE control will lead to sub-optimal state of DERs. Nevertheless, by setting the regional coordinative coefficient reasonably, ADN can achieve the optimal state in real-time based on global optimisation result. So this paper puts forward a region cooperative control strategy based on bidding mechanism on the basis of the proposed FCE control method [11–13]. There are three entities in bidding mechanism: (i) Bidding platform: It summarises all kinds of bidding information and prepares trading plans. In this paper, DMS is used as the bidding platform, and it is considered that the bidding information from regional control units is true. (ii) Bidder: It provides bidding information to bid. In this paper, each region is a bidder. The specific bid price is decided by the operation state of the region, and they bid for the real-time power fluctuation caused by intermittent energy and load to reduce the deviation from the target value. (iii) Successful bidder: It should complete the contract. In this paper, regional coordinative coefficient of successful bidder will be modified in real-time based on bidding result. 3.2 Multi-factor evaluation mechanism When multiple regions participate in bidding, it is necessary to evaluate the bid information provided by each region and select the bidder who is in line with the optimisation direction. Therefore, this paper selects three factors [14] that affect the direction of optimisation. The first is cost factor that evaluate economy in bidding. The second is deviation tolerance factor that evaluate the impact extent of current DERs’ status to subsequent operation. The third is optimal deviation factor that evaluate the deviation between DERs’ power output and target value. (i) Cost factor $c$: Cost factor represents the cost of DERs undergoing power fluctuation. Its value is mainly based on the cost of various DERs and power generation. The range is [0,1]. (ii) Deviation tolerance factor $e$: At present, there are many types of DER in ADN, such as ESS and micro-turbine. Operating characteristics of different DERs are different. ESS is constrained by the SOC and the deviation from the target value may cause the subsequent plan cannot be completed. Therefore, deviation tolerance factor of ESS is small. MT can maintain the operation through the external fuel supply. It can be considered that the tolerance factor is big. (iii) Optimal deviation factor $a$: The optimal deviation factor is obtained from the ratio of DER output deviation to the installed capacity. The concrete expression is given as $$a = \frac{(P_t - P_{t, opt})}{P_{rated}}$$ \hspace{1cm} (7) (iv) Where $a_t$ is the optimal deviation factor at time $t$; $P_t$ is the power output of DER at time $t$; $P_{t, opt}$ is the optimised target value in time interval $t$; $P_{rated}$ is the rated power of DER. This factor indicates the deviation of the DER operation state from the planned curve. Each regional control unit will provide three factors in the power fluctuation bidding. The weights of three factors are given in each optimisation period. The concrete expression is given as $$y = \begin{cases} a_1(1-c) + a_2e - a_3a_t, & \Delta P > 0 \\ a_1c + a_2e + a_3a_t, & \Delta P < 0 \end{cases}$$ \hspace{1cm} (8) where $\Delta P$ is the value of power fluctuation; $a_1- a_3$ are weights, $a_1 + a_2 + a_3 = 1$. Different weights can achieve different emphasis. If $a_1$ is bigger, cost is the main consideration in regional real-time optimisation. If $a_2$ is larger, it is more inclined to the DER with higher deviation tolerance. 3.3 Communication mechanism based on blackboard system To reduce the communication pressure of the system, original communication channel between DMS and regional control units is used to build the communication mechanism based on blackboard system [14]. DMS serves as the ‘blackboard’ and provides memory space to regional control units exchanging information. Each regional control unit serves as a ‘knowledge source’ and provides its own bidding information. Each regional control unit combines its own information with other units’ information listed in ‘blackboard’. Then, it dynamically adjusts the regional coordinative coefficient. The concrete mechanism is shown in Fig. 4. 3.4 Method and process of regional coordinative coefficient updating Above analysis shows that the regional control unit as a knowledge source provides DERs’ factors and other related data in this region. In this paper, feeder exchange power with external power grid is a bidder too. In the first step, intra-region power fluctuation will be undertaken by DERs in this region through adjusting distribution coefficient based on bidding information in this region. In the second step, extra-region power fluctuation will be undertaken by all DERs through adjusting distribution coefficient and regional coordinative coefficient based on all bidding information. The detailed algorithm flow is shown in Fig. 5 and regional coordinative coefficient is set to non-negative. If all DERs reach the output limit, external power grid will bid to win all the power fluctuation. 4 Case study Based on the case in [15], one feeder with partial expansion is used to verify the strategy proposed in this paper. The topological connection is shown in Fig. 6. There are four autonomous regions in this case and the external network is equivalent to infinite power source. DlgSILENT15.0 software was used to simulate the control strategy. Global optimisation sets 15 min as a period so there are 96 periods in 1 day. In order to prove the effectiveness of control strategy in ADN, one period is selected to analyse it. The basic information shows in Section 8, Appendix 1. The factors of different types of DER are shown in Table 1. Optimal deviation factor is calculated based on current DER output and the target value. ESS only shifts the energy usage time, so the cost factor is small. However, its output is limited by the SOC, deviation tolerance factor is small too. MT as a peak support unit cost is relatively big, and fossil fuels ensure that MT is less affected by previous output. Feeder exchange power with external power grid is the most stable and it has moderate cost and unaffected output ability. 4.1 Simulation results of region cooperative control strategy Taking the cost as the primary object and the weight is, respectively, $a_1 = 0.6$, $a_2 = 0.2$, $a_3 = 0.2$. The simulation result of feeder exchange power is shown in Fig. 7. (The simulation results of regions are shown in Section 9, Appendix 2.) Taking the curve of feeder exchange power as an example, we can see that curve after control is closer to the target value than without control. Most power fluctuation in the first 300 s is undertaken by DERs so the feeder exchange power coincides with the target value. After 300 s, external power grid gradually undertakes the power fluctuation outside of the regions which causes the deviation of the feeder exchange power from target value. Exchange power fluctuations of four regions are reduced to some extent so the whole power grid is closer to the global target value. ### Table 1 Reference value of DG factors \| Object \| Cost factor \| Deviation tolerance factor \| \|----------------------------\|-------------\|----------------------------\| \| ESS \| 0.3 \| 0.3 \| \| MT \| 0.6 \| 0.7 \| \| Feeder exchange power \| 0.5 \| 0.9 \| (i) The bidding results of intra-region power fluctuation: This case has four regions and region 4 has two DERs. The bidding result of power fluctuation occurs in region 4 is shown in Fig. 8. Positive power fluctuations are undertaken by ESS4 and negative power fluctuation is undertaken by MT. The reason is that positive power fluctuations need to increase the DER output and ESS cost factor is smaller. Negative power fluctuation needs to reduce the DER output and MT cost factor is bigger. Thus, MT reduces the power to save more cost. (ii) The bidding results of extra-region power fluctuation: After the bidding of intra-region power fluctuation, the bidding result of extra-region power fluctuation is shown in Fig. 9. Under this group of evaluation weight, extra-region power fluctuation is mainly undertaken by MT and feeder exchange power with external power grid. The reason is that the extra-region power fluctuation is negative and weight is partial to cost factor. The cost factor of MT and feeder exchange power is bigger so they undertake the negative power fluctuation. 4.2 Comparison of different evaluation weights With different evaluation weights, different types of DER will undertake different power fluctuation. When the evaluation weights are set to $a_1 = 0.1$, $a_2 = 0.1$, $a_3 = 0.8$, optimal deviation factor will be considered as a priority. Under this circumstance, the bidding results of intra-region and extra-region are shown in Figs. 10 and 11. Due to the deviation caused by undertaking intra-region power fluctuation, each ESS undertakes the extra-region power fluctuation partially. Positive power fluctuation is still undertaken by ESS2. 5 Conclusion (i) ADN hierarchical and regional control strategy can adapt to the volatility of intermittent energy. Based on the global optimisation result, regions optimise with each other in short-time scales. The effectiveness and validity of this strategy is verified by the simulation of study case. (ii) This paper puts forward region cooperative control strategy based on bidding mechanism and communication mechanism based on blackboard system to achieve optimally real-time status. It is important to study ADN hierarchical control method and this strategy provides a new conception to improve DN operation. 6 Acknowledgement This paper was supported by the Suzhou Power Supply Company Program (grant no. SZ201708). 7 References [1] You Y., Liu D., Yu W.P., et al.: ‘Technology and its trends of active distribution network’, Autom. Electr. Power Syst., 2012, 36, (18), pp. 10–16 [2] Polo F., Pisano G., Soma G.G.: ‘Advanced DMS to manage active distribution networks’. 2009 IEEE PowerTech, Bucharest, 2009, pp. 1–8 [3] Ren F., Zhang M., Sutanto D.: ‘A multi-agent solution to distribution system management by considering distributed generators’, IEEE Trans. Power Syst., 2013, 28, (2), pp. 1442–1451 [4] Liu D., Chen Y.H., Huang Y.H., et al.: ‘Hierarchical energy management and coordination control of active distribution network’, Proc. 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CESS, 2013, 33, (13), pp. 108–115 [10] Zhong Q., Zhang W.F., Zhou J.W., et al.: ‘Active distribution network layer and distributed control strategy & implementation’, Power Syst. Technol., 2015, 39, (06), pp. 1511–1517 [11] Ai Q., Zhang J.: ‘Optimization bidding strategies of microgrids based on multi-agent system’, Power Syst. Technol., 2010, 34, (02), pp. 46–51 [12] Dimeas A.L., Hatzigerynou N.D.: ‘Operation of a multiagent system for microgrid control’, IEEE Trans. Power Syst., 2005, 20, (03), pp. 1447–1455 [13] Benat M.E., El-Markabi I. M.: ‘A multiagent-based dispatching scheme for distributed generators for voltage support on distribution feeders’, IEEE Trans. Power Syst., 2007, 22, (01), pp. 52–59 [14] Lu Z.G., Ye Z.G., Yang L.J.: ‘An approach of time interval-divided multi-fault dynamic restoration for distribution network based on blackboard model’, Power Syst. Technol., 2012, 36, (09), pp. 198–202 [15] Bignucolo F., Caldron R., Prandoni V.: ‘Radial MV networks voltage regulation with distribution management system coordinated control’, Electr. Power Syst. Res., 2008, 78, (4), pp. 634–645 8 Appendix 1 The power fluctuation, generated by outside of four regions in the study case, is identified as the extra-region power fluctuation. The intra- and extra-region power fluctuations relative to forecast value in Tables 2–4 are shown in Fig. 12. Appendix 2 Table 3 Active power forecast of load \| Load \| P/MW \| Load \| P/MW \| \|---------------\|------\|---------------\|------\| \| A1 \| 0.143\| A14 \| 0.284\| \| A2 \| 0.187\| A15 \| 0.081\| \| A3 \| 0.055\| A17 \| 0.066\| \| A4 \| 0.21 \| A18 \| 0.069\| \| A5 \| 0.077\| A19 \| 0.065\| \| A6 \| 0.067\| A20 \| 0.126\| \| A7 \| 0.07 \| A21 \| 0.097\| \| A9 \| 0.07 \| PV1 \| 0.151\| \| A10 \| 0.089\| PV2 \| 0.140\| \| A11 \| 0.114\| WT \| 0.487\| \| A12 \| 0.137\| \| \| \| A13 \| 0.072\| \| \| Table 4 Target value of global optimisation \| Object \| Target value, MW \| Coordinative coefficient \| \|-----------------\|------------------\|--------------------------\| \| feeder exchange power \| 0.510 \| \| \| region 1 \| 0.111 \| 0.253 \| \| region 2 \| 0.212 \| 0.249 \| \| region 3 \| 0.217 \| 0.249 \| \| region 4 \| –0.638 \| 0.249 \| \| ESS1 \| 0.097 \| \| \| ESS2 \| 0.065 \| \| \| ESS3 \| 0.129 \| \| \| ESS4 \| 0.021 \| \| \| MT \| 0.2 \| \| Table 2 Distribution energy resources configuration \| Type \| Node \| Capacity \| \|-------\|------\|----------\| \| ESS1 \| A6 \| 250 kWh \| \| ESS2 \| A10 \| 250 kWh \| \| ESS3 \| A12 \| 250 kWh \| \| ESS4 \| A19 \| 250 kWh \| \| MT \| A20 \| 300 kW \| \| PV1 \| A6 \| 500 kW \| \| PV2 \| A14 \| 500 kW \| \| WT \| A21 \| 5002 kW \| “2”** represents that there are two 500kW WTs J. Eng., 2017, Vol. 2017, Iss. 13, pp. 966–972 doi:10.1049/joe.2017.0474 This is an open access article published by the IET under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/) Comparison of regions 1–4 exchange power before and after optimisation is shown in Figs. 13–16. Regions 1 and 3 do not undertake any extra-region power fluctuation so regional exchange power is exactly same as the global optimisation target value. Regions 2 and 4 undertake part of extra-region power fluctuation so there is deviation of regional exchange power from the target value. However, compared with the uncontrolled results, the power deviation is reduced.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 5727, 1 ], [ 5727, 11260, 2 ], [ 11260, 16525, 3 ], [ 16525, 20095, 4 ], [ 20095, 22397, 5 ], [ 22397, 27552, 6 ], [ 27552, 28017, 7 ] ] }
fce26619663eccc498e3fc272bfb8de8d9e52f2b	{ "olmocr-version": "0.1.59", "pdf-total-pages": 12, "total-fallback-pages": 0, "total-input-tokens": 35132, "total-output-tokens": 10585, "fieldofstudy": [ "Biology", "Medicine" ] }	*IL-21 Augments Rapamycin in Expansion of Alpha Fetoprotein Antigen Specific Stem-Cell-like Memory T Cells in vitro.* Victor Tunje Jeza*1,2,6, Xiaoyi Li1, Jun Chen1, Zhihui Liang1, Adem Onago Aggrey3, Xiongwen Wu1 1Department of Immunology, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China, 2Department of Medical Sciences, Technical University of Mombasa, Mombasa, Kenya, 3Department of Mathematics and Physics, Technical University of Mombasa, Kenya Corresponding author: Victor Tunje Jeza, Department of Medical Sciences, Technical University of Mombasa, Tom Mboya Avenue, P.O. Box 90420, Mombasa, 80100, Kenya. Key words: Alpha Fetoprotein, Tscm cells, IL-21, Rapamycin, concurrent application, cancer immunotherapies Received: 01/11/2016 - Accepted: 15/06/2017 - Published: 30/06/2017 Abstract Introduction: Alloreactive tumor specific T cells are important arsenals of the adaptive immune system in the fight against tumors. However, stem cell-like memory T cells (Tscm) provide the key to effective elimination of tumor cells. Methods for generating these T cell subsets already exist. However, they could be made more efficient. Further, they are expensive and unattainable to the resource poor laboratories. In this regard, we are hereby describing a novel in vitro allogeneic co-culture method for raising allo-restricted tumor specific Tscm cells that we developed. Methods: We started by obtaining PBLs that screened negative for HLA-A2 molecules from healthy donors followed by co-culture with T2/AFP cells to generate AFP peptide specific tumor-reactive T cells. Controls, IL-21 and/or rapamycin were applied to samples in 24 well plates. Samples were harvested and stained with anti-human CD3, CD8, CD44, CD62L, and HLA-A2/AFP dimer followed by flow cytometry analysis. Cell viability was measured by Trypan blue exclusion assay. One Way ANOVA and independent t test were used to compare the mean differences among and between groups where P values less than 0.05 were considered significant. Results: Our results show that rapamycin arrests the differentiation of, and expands AFP specific Tscm cells. Further, the expansion of Tscm cells is augmented in the presence of IL-21. Conclusion: IL-21 and Rapamycin can be used concurrently to raise and maintain antigen specific Tscm cells in vitro for purposes of augmenting immunotherapy strategies against cancers. Pan African Medical Journal. 2017; 27:163 doi:10.11604/pamj.2017.27.163.11072 This article is available online at: http://www.panafrican-med-journal.com/content/article/27/163/full/ © Victor Tunje Jeza et al. The Pan African Medical Journal - ISSN 1937-8688. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Introduction Cancer is a disease characterized by abnormal cell growth mediated by new protein molecule expression. Since our immune system has developed to eradicate foreign looking substances, it can protect us from cancer due to the abnormalities in the cells being seen as foreign. Cytotoxic T (Tc) cells are the major mediators of adaptive immunity against cancers. As such, they can be used in adaptive cellular therapy to eradicate tumors and are poised to be the most promising strategy where these Tc cells are taken from the cancer patient, expanded in vitro and transferred back to the patient [1]. The efficiency of this strategy is dependent on the stage of differentiation at which these cells are. At the effector stage, these cells can kill tumors. This stage is replenished by the earlier stages of differentiation which include central memory and stem cell-like memory Tc cells. In the presence of IL-2, the cells can differentiate quickly to get to the effector stage. However, the T cells in this case can become exhausted quickly and therefore become less efficient at eradicating tumors [2, 3]. Stem cell-like memory T cell subsets (Tscm) are early stage differentiated T cells that are antigen experienced subsets of T cells. They are characterized by expression of CD44hiCD62Llo just like naïve T cells [4] but also express stem cell antigen-1 (Sca-1) and high levels of the antiapoptotic molecule B cell lymphoma 2 (Bcl-2), the βchain of the IL-2 and IL-15 receptor (IL-2Rβ), and the chemokine (C-X-C motif) receptor CXCR3 [5, 6]. Stemness attributes found in Tscm allows them to differentiate further [7] leading to generation of effector Tc cells steadily and continuously thereby giving them the opportunity to perpetually attack tumor cells [6, 8-12]. This increases the efficiency of these cells. It has been shown that treating Tc cells with IL-21 can confer stemness to Tc cells. Further, it has been suggested that treating or exposing these cells to small molecules that signal through Wnt [6, 13], Akt [1, 14-16] and mTOR inhibitors [12, 17-19] might contribute to the same effects. Other studies have shown that rapamycin can extend the lifespan of certain cells and organisms [20]. We therefore hypothesized that concurrent application of IL-21 and rapamycin-an mTOR inhibitor-may augment the stemness attributes of these T cell sub-sets. Our results show that IL-21 augments rapamycin in expanding and maintaining Tscm cells in vitro for long periods of time. In essence, we have developed a novel in vitro allogeneic co-culture method for raising allo-restricted tumor specific Tscm cells. This method is easy, inexpensive, straightforward and augmentative when compared to other methods that have been shown to also work such as the generation of long-lived antitumor CD8+ T cells using artificial antigen presenting cells [21], the use of IL-7 and IL-15 to generate Tscm cells [22] and the recently identified CD27-dependent pathway of T cell expansion [23]. Methods HLA-A2 Blood Typing: Samples of peripheral blood were obtained from healthy volunteers with informed consent and approval by the Ethical Committee of Tongji Medical College. One hundred microliters of each of the blood samples of interest were taken to new tubes and 1 μl of fluorescence isothiocyanate (FITC) conjugated BB7.2 antibody was added to each tube and mixed by pipetting. The samples were then incubated at 4°C for 40 minutes. Red blood cells (RBCs) were lysed using red blood cell lysis buffer and samples washed twice then resuspended in 300 μl phosphate buffered saline (PBS) followed by flow cytometry analysis. Only those blood samples that stained negative for BB7.2 were used in subsequent experiments. Preparation of HLA-A2/AFP dimer: Constructed HLA-A2 dimer was expressed on dimer-721.221 cells as previously described [24] and the supernatant purified through protein A column. The purified dimer was labeled with FITC (Abcam-Japan) according to the manufacturer’s instructions then loaded with AFP peptides at 4°C for 48 hours before use. Cell co-culture: PBMCs were obtained from the HLA-A2 negative peripheral blood samples by density gradient centrifugation using Ficoll-Hypaque (density 1.077 g/ml) according to the method by McCoy [25]. The PBMCs were then washed twice in PBS, suspended in 10% FCS RPMI 1640 medium and allowed to adhere to flasks overnight at 37°C with 5% CO2 atmosphere so as to obtain the non-adherent cells which were then used as responder cells. T2 cells were pulsed with α-fetoprotein (AFP) peptides (Hangzhou Peptide Co.-China) for three hours to form T2/AFP following inactivation in Mitomycin C (30 μg/ml) and used as stimulator cells. The responder to stimulator ratio was 10:1 with responder cells (PBLs) being 2.5 x 106 cells per well in 24 well plates. Rapamycin (CALIBIOCHEM-USA) and IL-21 (PeproTech-USA) were applied singularly and concurrently while controls were left untreated with neither rapamycin nor IL-21. Samples were stained with APC/CY7 conjugated anti-human CD3 (E Bioscience-USA), PE/CYS conjugated anti-human CD8 (Biolegend-USA), PE conjugated anti-human CD4 (E Bioscience-USA) and PE/CY7 conjugated anti-human CD62L (Biolegend-USA) and analyzed by flow cytometry. In another assay to analyze AFP-specific Tscm cells, samples were stained with APC/ CY7 conjugated anti-human CD3, PE/CYS conjugated anti-human CD8, PE conjugated anti-human CD44, PE/CY7 conjugated anti-human CD62L and FITC conjugated HLA-A2/AFP dimer and analyzed by flow cytometry. Trypan blue exclusion test for cell viability: Trypan blue was kindly provided by Prof Li Dzuoya from the Department of Immunology. Staining and analysis were performed according to the methods by Coder DM and Johnson S [26-27]. Cell viability was calculated as follows: % viable cells = (number of viable cells/number of total cells) X 100. Statistical analysis: One way ANOVA was used to determine the difference of the means among the controls and the IL-21 and/or rapamycin treated groups of the co-culture experiments for determining stemness maintenance over the study period. The independent t-test was used to determine the difference of the means between the control and IL-21 and/or rapamycin treated groups in the Trypan Blue exclusion test for cell viability. Values of P ≤0.05 were considered significant. Results IL-21 augments rapamycin in induction of non-specific Tscm cells with initial increased proliferation: To determine the consequences of singular and concurrent application of IL-21 and rapamycin on Tscm cells, HLA-A2 negative PBLs (Figure 1) were stained with CFSE and co-cultured with T2/AFP cells for a period of two weeks. Samples were harvested on day 7 and day 14 and stained with APC/CY7 conjugated anti-human CD3, PE/CYS conjugated anti-human CD8, PE conjugated anti-human CD44, and PE/CY7 conjugated anti-human CD62L and analyzed by flow cytometry. Results show that rapamycin increases the non-specific (non-specific since expression of CD44hiCD62Llo molecules could be found in either naïve or antigen experienced T cells) Tscm cells and this increase is augmented in the presence of both rapamycin and IL-21 (Figure 2). The mean difference in time were statistically significant (P= 0.0004, 3.18 X 10-6, 7.71 X 10-7 and 0.0001 for control, IL-21, rapamycin and IL-21 + rapamycin treated groups respectively). The mean difference between control and IL-21 treated groups was not statistically different while those between control and the other groups were statistically significant (Table 1). IL-21 augments rapamycin in maintaining and expanding of AFP antigen specific Tscm cells: We next sought to analyze the consequences of singular and concurrent application of IL-21 and rapamycin on antigen experienced AFP-Specific Tscm cells. To do this, HLA-A2 negative PBLs (Figure 1) (without staining with CFSE) were co-cultured with T2/AFP cells for a period of four weeks with the application of IL-21 and/or rapamycin. The control group had neither IL-21 nor rapamycin applied. Samples were harvested on days 9, 21, and 28 and stained with APC/CY7 conjugated anti-human CD3, PE/CYS conjugated anti-human CD8, PE conjugated anti-human CD44, PE/CY7 conjugated anti-human CD62L, and FITC conjugated HLA-A2/AFP dimer and analyzed by flow cytometry. The aim of using HLA-A2/AFP dimer here is to be able to pick up and analyze antigen experienced T cells only. Our results show that rapamycin maintains and expands AFP antigen specific Tscm cells. This maintenance and expansion is augmented in the presence of IL-21 (Figure 3). We found that the mean difference between treatment groups and time were statistically significant (Table 2, Table 3). IL-21 augments rapamycin in maintaining viability of AFP antigen specific Tscm cells: Samples were harvested on day 28 and washed in PBS twice. They were then stained with Trypan Blue and incubated at room temperature for five minutes. Cell viability was determined in each treated group and the results show that application of IL-21 and/or rapamycin maintains cell viability compared to the control group showing a statistical significant difference (p=0.0003, 1.98X10^-5, 1.53X10^-6 respectively). The maintenance of cell viability was more superior in concurrent application of IL-21 and rapamycin (Figure 4). Discussion Previous research has shown that the human T cell repertoire can recognize an AFP peptide as a HLA-A2.1 restricted epitope and is expressed in certain tumors such as hepatocellular carcinoma and germ cell tumors [28, 29]. Therefore, we employed the AFP peptides to generate HLA-A2 allo-restricted tumor antigen specific T cells. To do this, T2 cells were pulsed with the AFP peptides for three hours at 37°C with 5% CO2 atmosphere containing incubator to generate T2/AFP cells which were then co-cultured with PBLs that were negative for expression of HLA-A2 molecules (Figure 1). From here, we assessed the ability, either singularly or concurrently, of the biological and pharmacological agents HLA-A2 and rapamycin, respectively, to arrest the differentiation of these AFP antigen specific activated cells so as to spuriously reach the effector cell stage and largely retain as well as expand the Tscm subset. Our preliminary experiments looked at the consequences of IL-21 and rapamycin, as applied either singularly or concurrently, to arrest T cell differentiation at the Tscm stage. After two weeks of co-culture, we found that rapamycin had relatively higher Tscm subset cells compared to IL-21 alone. The magnitude of change in the cell numbers was even more in the concurrent application of IL-21 and rapamycin group (Figure 2). We found that at the end of week one, there were more Tscm cell numbers in the control group and the IL-21 treated group. This is the case since these cells had no specificity. As time progressed and non-antigen specific T cells (i.e. naïve T cells) died out, the situation changed (Figure 2 B (bottom two panels)). We reasoned that there might be non-specific Tscm cells being included in the analysis due to the absence of specificity in the system. To seek for answers, we repeated the experiment and incorporated staining with the antigen specific dimers HLA-A2/AFP dimers- in conjunction with the other antibodies i.e. anti-human CD3, anti-human CD8, anti-human CD44, and anti-human CD62L staining. Here, the HLA-A2/AFP dimers provide a mechanism for picking up and analyzing AFP antigen experienced T cells only. In this case, we found that the trends from the analysis were either a continuous increase or decrease of the Tscm cells in the different experimental groups (Figure 3). AFP-specific Tscm cells increased significantly from a low of 0.10% on day 9 to 1.35% by day 28 in the presence of rapamycin. The expansion of these cells was more than two fold in the concurrent application of IL-21 and rapamycin under the same period. In the control and IL-21 treated groups, the number of cells decreased over time continuously (Figure 3 bar graph). Here, the results show that IL-21 augments rapamycin in expanding AFP antigen specific Tscm cells. Taken together, these results show that rapamycin quickly destroys naïve T cells but maintains antigen experienced T cells at the early differentiation stage for longer periods thereby maintaining their stemness and allows them to proliferate at the same time. This proliferation is enhanced in the presence of both IL-21 and rapamycin. The mechanism that allows this to happen remains to be elucidated. We further wanted to know the viability of the cells being maintained by IL-21 and rapamycin. To do this, we employed the Trypan blue exclusion assay. Cells were harvested on day 28 and washed in PBS twice then stained with Trypan Blue and incubated at room temperature for five minutes. Cell viability was determined in each treated and control groups. The results show that the viability of the cells in co-culture was enhanced by the addition of rapamycin while, in comparison, it was augmented by addition of IL-21 and rapamycin concurrently (Figure 4). This might be explained by the fact that rapamycin regulates fatty acid metabolism in activated T cells thereby regulating their proliferation [30, 31] which leads to a much slower exhaustion process. In application of rapamycin for induction of Tscm, dosage dependent on antigen specificity is paramount as demonstrated in our results (data not shown). This phenomenon is also supported by work from other laboratories such as that of Benjamin and colleagues who showed that the incomplete inhibition on mTORC1 is a dose dependent phenomenon that could have devastating effects in cancer patients [32]. Further support of our results comes from others who have shown that the effect of mTOR inhibition depends on the dose range and kinetics of the treatment. Administration of a very high dose of rapamycin prevented CD8+ T cell expansion whereas the duration and time period of rapamycin treatment inactivated the integrity of memory T cell responses [17, 33]. In addition, optimal doses of rapamycin were seen to increase the life span of middle aged mice [20]. Some studies suggest that blocking mTOR not only mediates immunosuppression in transplant rejections and autoimmune disorders, but also boosts immunity under selective conditions and imparts other aspects of T cell homeostasis and functions [18]. Further, it has been reported that suppression of the mTOR pathway, an established nutrient sensor, combined with activation of canonical Wnt-β-catenin signaling, allows for the ex vivo maintenance of human and mouse long-term HSCs under cytokine-free conditions. The same group also showed that the combination of two clinically approved medications that together activate Wnt-β-catenin and inhibit mTOR signaling increases the number (but not the proportion) of long-term HSCs in vivo [34]. Here, our results have shown that IL-21 and the mTOR inhibitor rapamycin combined together increase both the number and proportion of Tscm cells by the fourth week of co-culture (Figure 3). In contrast, it has been shown that in vivo, mTOR inhibition promotes T cell anergy under conditions that would normally induce active priming, indicating that mTOR has a central role in dictating the decision between T cell activation and anergy [35, 36]. Could it be that these observations were made under the influence of high doses of rapamycin... application? The emergence of memory and effector CD8+ T cells is independent of, but functional quality shaped by, IL-21 [37-39]. Yi et al [37] have also argued that although the direct effects of IL-21 on CD8+ T cells may shape these responses, IL-21 imparts many immunologic functions and therefore the indirect actions of IL-21 on other cells of the immune system may also influence the outcome of the CD8+ T cell response. We found that IL-21 alone has a reduced ability to retain AFP-specific Tscm cells when compared to rapamycin alone or its concurrent application with rapamycin (Figure 3). Conclusion Rapamycin application expands AFP-specific Tscm cells after AFP antigen specific stimulation of naïve T cells and maintains viability of co-cultured cells better than IL-21. In addition, IL-21 augments rapamycin in the expansion of AFP-specific Tscm cells and therefore these two agents may have an increased potential for tumor immunotherapy when applied concurrently. Essentially, this work provides a new co-culture method by which antigen specific Tscm cells can be raised and their stemness attributes maintained. What is known about this topic - It is know that IL-21 help in generating and maintaining Tscm cells; - It is known that Tscm cells are better eradicators of cancers and have a great potential for clinical use against cancers. What this study adds - This study provides a novel method for generating, expanding and maintaining antigen specific Tscm cells; - It contributes towards the search for immunotherapy against cancers. Competing interests The authors declare no competing interest. Authors’ contributions Victor Tunje Jeza and XW conceived the idea; Victor Tunje Jeza and Zhihui Liang performed flow cytometry. Victor Tunje Jeza, Xiongwen Wu and Zhihui Liang analyzed the results. Victor Tunje Jeza and Adem Onago Aggrey performed the statistical tests. Victor Tunje Jeza wrote the manuscript. All authors critically read the manuscript and approved the final version for publication. Acknowledgments Victor Tunje Jeza was supported by scholarship from the China Scholarship Council and the Kenya Ministry for Higher Education. We thank Lichen Ouyang, Billoguike Koikoi Kebe and Liping Cai for their useful discussions and/or hands-on assistance in this work. We also thank Li Dzuoya for the Trypan Blue. Tables and figures Table 1: Statistical analysis of the mean difference between treated groups for non-specific Tscm cell experiments Table 2: Statistical analysis of the mean difference between treated groups for AFP antigen specific Tscm cell experiments Table 3: Statistical analysis of the mean difference in time between treated groups for the AFP antigen specific Tscm cell experiments References 1. Waart Anniek Van Der, Hobo Willeminijn, Dolstra Harry. Time to Akt Superior tumor-reactive T cells for adoptive immunotherapy. Oncoimmunology. 2015; 4(5): e1003016-1-e1003016-3. PubMed \| Google Scholar 2. 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Error \| Sig. \| 95% Confidence Interval \| \|-------------\|-------------\|-----------------------\|------------\|-----\|------------------------\| \| \| \| Lower Bound \| Upper Bound \| \| 1(control) \| \| 0.0000 \| 0.0758 \| 1.000 \| -0.1623 \| 0.1623 \| \| 2(IL-21) \| \| 5.4650 \| 0.0758 \| 0.000 \| 5.3027 \| 5.6273 \| \| 3(rapa) \| \| 1.1000* \| 0.0758 \| 0.000 \| 0.9377 \| 1.2623 \| \| 4(IL-21 +rapa) \| \| -5.4650* \| 0.0758 \| 0.000 \| -5.6273 \| -5.3027 \| Based on observed means The error term is Mean Square (Error) = 0.018 * The mean difference is significant at the 0.05 level Table 2: statistical analysis of the mean difference between treated groups for AFP antigen specific Tscm cell experiments \| (I) factor1 \| (J) factor1 \| Mean Difference (I-J) \| Std. Error \| Sig. \| 95% Confidence Interval Lower Bound \| 95% Confidence Interval Upper Bound \| \|-------------\|-------------\|------------------------\|------------\|-------\|-------------------------------------\|-------------------------------------\| \| 1(control) \| 2 \| -0.0244* \| 0.00653 \| 0.001 \| -0.0379 \| -0.0110 \| \| \| 3 \| -0.7089* \| 0.00653 \| 0.000 \| -0.7224 \| -0.6954 \| \| \| 4 \| -1.6922* \| 0.00653 \| 0.000 \| -1.7057 \| -1.6788 \| \| 2(IL-21) \| 1 \| 0.0244* \| 0.00653 \| 0.001 \| 0.0110 \| 0.0379 \| \| \| 3 \| -0.6844* \| 0.00653 \| 0.000 \| -0.6979 \| -0.6710 \| \| \| 4 \| -1.6678* \| 0.00653 \| 0.000 \| -1.6812 \| -1.6543 \| \| 3(rapa) \| 1 \| 0.7089* \| 0.00653 \| 0.000 \| 0.6954 \| 0.7224 \| \| \| 2 \| 0.6844* \| 0.00653 \| 0.000 \| 0.6710 \| 0.6979 \| \| \| 4 \| -0.9833* \| 0.00653 \| 0.000 \| -0.9968 \| -0.9699 \| \| 4(IL-21 + rapa) \| 1 \| 1.6922* \| 0.00653 \| 0.000 \| 1.6788 \| 1.7057 \| \| \| 2 \| 1.6678* \| 0.00653 \| 0.000 \| 1.6543 \| 1.6812 \| \| \| 3 \| 0.9833* \| 0.00653 \| 0.000 \| 0.9699 \| 0.9968 \| Based on observed means The error term is Mean Square (Error) = 0.000 The mean difference is significant at the 0.05 level Dependent Variable: values LSD Table 3: statistical analysis of the mean difference in time between treated groups for the AFP antigen specific Tscm cell experiments Multiple Comparisons Dependent Variable: values LSD \| (I) factor2 \| (J) factor 2 \| Mean Difference (I-J) \| Std. Error \| Sig. \| 95% Confidence Interval \| Lower Bound \| Upper Bound \| \|-------------\|--------------\|-----------------------\|------------\|------\|-------------------------\|-------------\|-------------\| \| 1(9days) \| 2 \| -0.5983 \| 0.00565 \| 0.000\| -0.6100 \| -0.5867 \| \| \| \| 3 \| -1.0217* \| 0.00565 \| 0.000\| -1.0333 \| -1.0100 \| \| \| 2(21days) \| 1 \| 0.5983* \| 0.00565 \| 0.000\| 0.5867 \| 0.6100 \| \| \| \| 3 \| -0.4233* \| 0.00565 \| 0.000\| -0.4350 \| -0.4117 \| \| \| 3(28days) \| 1 \| 1.0217* \| 0.00565 \| 0.000\| 1.0100 \| 1.0333 \| \| \| \| 2 \| 0.4233* \| 0.00565 \| 0.000\| 0.4117 \| 0.4350 \| \| Based on observed means The error term is Mean Square (Error) = 0.000 * The mean difference is significant at the 0.05 level Figure 1: HLA-A2 Blood Typing. A 100 μl aliquot was taken from each of the samples and stained with the BB7.2 antibody. Flow cytometry was used to analyze the results. From these representative results of many, we can see that samples a, b, f, g, and h are positive for BB7.2 staining meaning that the PBMCs in these samples express the HLA-A2 molecules. In contrast, samples c, d, and e are negative for the BB7.2 staining and therefore show that these particular samples do not have the HLA-A2 molecules expressed on the PBMC surfaces. Figure 2: IL-21 augments rapamycin (Rapa) in induction of Tscm cells (no antigen specificity here) with increased proliferation. After 7 and 14 days of Co-culture (Figure 2a and 2b (top two panels and bottom two panels respectively)), samples were harvested and analyzed by flow cytometry. Since there is no specificity, the initial Tscm cells are seen to be very many in the control group and IL-21 treated groups. They are then seen to drop significantly in those two groups (Table 1 for statistics) while they were maintained for longer periods and increased in number (proliferated) in the presence of rapamycin. This proliferation is seen to be augmented when rapamycin is combined with IL-21 (Figure 2c (bar graph)). Figure 3: IL-21 augments rapamycin (Rapa) in maintaining and expanding of AFP antigen specific Tscm cells. After 9, 21, and 28 days of co-culture (Figure 3a (top, middle, and bottom panels respectively)), samples were harvested and analyzed by flow cytometry. HLA-A2 dimer (DIMER-FITC) was used to pick up AFP antigen specific Tscm cells. AFP antigen specific Tscm cells are maintained and increased significantly over longer periods in the presence of rapamycin which is augmented when rapamycin is combined with IL-21 (Figure 3b (bar graph)). Figure 4: IL-21 augments rapamycin in maintaining viability of AFP antigen specific Tscm cells. After 28 Days of Co-culture, samples were harvested and stained with 0.4% Trypan Blue. Rapamycin increased the viability of AFP antigen specific Tscm cells which was augmented in the concurrent treatment of IL-21 and rapamycin. The difference between viable cells in control compared with IL-21, Rapa, and IL-21 + Rapa were statistically significant (P = 0.0003, 1.98X10-5, 1.53X10-6 respectively).	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 2991, 1 ], [ 2991, 10302, 2 ], [ 10302, 18462, 3 ], [ 18462, 21910, 4 ], [ 21910, 27461, 5 ], [ 27461, 30444, 6 ], [ 30444, 32844, 7 ], [ 32844, 34191, 8 ], [ 34191, 34729, 9 ], [ 34729, 35452, 10 ], [ 35452, 35997, 11 ], [ 35997, 36491, 12 ] ] }
abb65851abcc5868f478195fd6c2407c3893d277	{ "olmocr-version": "0.1.59", "pdf-total-pages": 14, "total-fallback-pages": 0, "total-input-tokens": 43004, "total-output-tokens": 18803, "fieldofstudy": [ "Medicine", "Biology" ] }	A Multi-Compartment Single and Multiple Dose Pharmacokinetic Comparison of Rectally Applied Tenofovir 1% Gel and Oral Tenofovir Disoproxil Fumarate Kuo-Hsiung Yang1, Craig Hendrix2, Namadje Bumpus3, Julie Elliott3, Karen Tanner4, Christine Mauck5, Ross Cranston6, Ian McGowan6, Nicola Richardson-Harman7, Peter A. Anton3, Angela D. M. Kashuba1 1 Division of Pharmacoepidemiology and Therapeutics, UNC Eshelman School of Pharmacy, Chapel Hill, North Carolina, United States of America, 2 Departments of Medicine and Pharmacology, Johns Hopkins University School of Medicine, Baltimore, Maryland, United States of America, 3 Center for HIV Prevention Research, David Geffen School of Medicine at UCLA, Los Angeles, California, United States of America, 4 Department of Biostatistics, UCLA School of Public Health, Los Angeles, California, United States of America, 5 CONRAD, Arlington, Virginia, United States of America, 6 Department of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America, 7 Alpha StatConsult LLC, Damascus, Maryland, United States of America Abstract This Phase 1, randomized, two-site (United States), double-blind, placebo-controlled study enrolled 18 sexually abstinent men and women. All received a single 300-mg dose of oral tenofovir disoproxil fumarate (TDF) and were then randomized 2:1 to receive single and then seven daily rectal exposures of vaginally-formulated tenofovir (TFV) 1% gel or a hydroxyethyl cellulose (HEC) placebo gel. Blood, colonic biopsies and rectal and vaginal mucosal fluids were collected after the single oral TDF, the single topical TFV gel dose, and after 7 days of topical TFV gel dosing for extracellular analysis of TFV and intracellular analysis of the active metabolite tenofovir diphosphate (TFVdp) in peripheral blood mononuclear cells (PBMCs) and isolated mucosal mononuclear cells (MMC), including CD4+ and CD4- cell subsets. With a single rectal dose, TFV plasma concentrations were 24–33 fold lower and half-life was 5 h shorter compared to a single oral dose (p = 0.02). TFVdp concentrations were also undetectable in PBMCs with rectal dosing. Rectal tissue exposure to both TFV and TFVdp was 2 to 4-log10 higher after a single rectal dose compared to a single oral dose, and after 7 daily doses, TFVdp accumulated 4.5 fold in tissue. TFVdp in rectal tissue homogenate was predictive (residual standard error, RSE = 0.47) of tissue MMC intracellular TFVdp concentration, with the CD4+ cells having a 2-fold higher TFVdp concentration than CD4- cells. TFV concentrations from rectal sponges was a modest surrogate indicator for both rectal tissue TFV and TFVdp (RSE = 0.67, 0.66, respectively) and plasma TFV (RSE = 0.38). TFV penetrates into the vaginal cavity after oral and rectal dosing, with rectal dosing leading to higher vaginal TFV concentrations (p < 0.01). Trial Registration: ClinicalTrials.gov NCT00984971 Citation: Yang K-H, Hendrix C, Bumpus N, Elliott J, Tanner K, et al. (2014) A Multi-Compartment Single and Multiple Dose Pharmacokinetic Comparison of Rectally Applied Tenofovir 1% Gel and Oral Tenofovir Disoproxil Fumarate. PLoS ONE 9(10): e106196. doi:10.1371/journal.pone.0106196 Editor: Alan Winston, Imperial College London, United Kingdom Received January 17, 2014; Accepted July 28, 2014; Published October 28, 2014 Copyright: © 2014 Yang et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper and its Supporting Information files. Funding: The study was funded by a U19 grant under the Integrated Preclinical-Clinical Program for HIV Topical Microbicides (IPCP-HTM), Division of AIDS, National Institute of Allergy and Infectious Diseases, National Institutes of Health (AI060614) and the NIAID’s Microbicide Trials Network (SUM1A0068633). Additional support was provided by Gilead Sciences Inc.; the University of California, Los Angeles Center for AIDS Research (SP30 AI28697) Cores of Mucosal Immunology, Flow Cytometry and Biostatistics; the University of North Carolina-Chapel Hill Center for AIDS Research, Clinical Pharmacology/Analytical Chemistry Core (P30 AI50410); the Johns Hopkins Clinical Pharmacology Analytical Laboratory and CONRAD. The RMP-02/MTN-006 study was registered at ClinicalTrials.gov (NCT00984971) and the protocol can be http://www.mtnstopshiv.org. This analysis was supported by a contract with Advanced BioScience Laboratories, Inc., Rockville, Maryland, and its subcontractor, Alpha StatConsult LLC, through a NIH/NIAID/DAIDS contract: “Comprehensive Resources for HIV Microbicides and Biomedical Prevention” (NCT01039929). Additional support was provided by Gilead Sciences Inc.; the University of California, Los Angeles Center for AIDS Research (SP30 AI28697) Cores of Mucosal Immunology, Flow Cytometry and Biostatistics; the University of North Carolina-Chapel Hill Center for AIDS Research, Clinical Pharmacology/Analytical Chemistry Core (P30 AI50410); the Johns Hopkins Clinical Pharmacology Analytical Laboratory and CONRAD. The RMP-02/MTN-006 study was registered at www.ClinicalTrials.gov (NCT00984971) and the protocol can be found at http://www.mtnstopshiv.org. This analysis was supported by a contract with Advanced BioScience Laboratories, Inc., Rockville, MD, and its subcontractor, Alpha StatConsult LLC, through a NIH/NIAID/DAIDS contract: “Comprehensive Resources for HIV Microbicides and Biomedical Prevention” (NCT00984971). This does not alter the authors’ adherence to PLOS ONE policies on sharing data and materials. Competing Interests: The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper and its Supporting Information files. * Email: [email protected] Introduction Both topical and oral tenofovir (TFV)-containing regimens have demonstrated efficacy in HIV prevention. TFV 1% gel demonstrated 39% protective efficacy in women using the gel within 12 hours before and after sexual activity in the Centre for the AIDS Programme of Research in South Africa (CAPRISA) 004 study [1]. The fixed dose combination of tenofovir disoproxil fumarate (TDF)/emtricitabine (Truvada) prescribed daily in a population of men who have sex with men in the iPrEx study provided 44% protection against HIV infection [2]. Daily dosing of TDF or Truvada provided 62 to 73% protection against HIV transmission in serodiscordant men and women enrolled in the Partners PrEP Study [3]. Furthermore, daily dosing of oral TDF provided 49% reduction in HIV incidence rates among IV drug users [4]. In both CAPRISA 004 and iPrEx, the level of protection was related to drug exposure and adherence [1,2,5,6]. The primary objective of the Phase 1 RMP-02/MTN-006 clinical trial was to evaluate the systemic safety of TFV 1% gel when applied rectally [7]. Built into this study was a comprehensive pharmacokinetic evaluation comparing systemic and compartmental pharmacokinetics among oral TDF and rectal TFV 1% gel users. These novel within-subject pharmacokinetic analyses were also used in an ex-vivo biopsy HIV challenge model to correlate TFVdp exposure with protection against ex vivo infection (reported in accompanying paper: Richardson-Harman et al.) [7]. This is the first study to quantify human rectal mucosal pharmacokinetics after topical administration of tenofovir in multiple compartments concurrently, to compare it to exposure after oral administration and to determine whether less-invasive indicators of TFVdp concentrations in tissue CD4+ cells emerge, potentially playing a future role in large clinical trials. Materials and Methods The protocol for this trial and supporting CONSORT checklist are available as supporting information; see Checklist S1 and Protocol S1. Ethics Statement The trial was IRB-approved at each site (UCLA IRB in Los Angeles, CA; University of Pittsburgh IRB, Committee C in Pittsburgh, PA); all participants provided written informed consent. RMP-02/MTN-006 is registered at ClinicalTrials.gov (#NCT00984971) and is in compliance with the CONSORT 2010 trial reporting recommendations (www.consortstatement.org). Study Participants Study participants were healthy HIV-1-seronegative men and women with a history of consensual rectal anal intercourse, willing to abstain from vaginal and rectal sex during active protocol phases. Female participants were required to be using an acceptable form of contraception (e.g., barrier method, IUD, hormonal contraception, surgical sterilization, or vasectomy in male partner). Study Design The pharmacokinetic component of the RMP-02/MTN-006 trial was designed to compare systemic and compartmental pharmacokinetics among single oral TDF dosing (300 mg), and single as well as multiple doses of rectally-applied vaginally-formulated TFV 1% gel. This was a Phase 1, double-blind, randomized, placebo-controlled comparison of oral TDF (300 mg), rectally applied TFV 1% gel, and the hydroxyethyl cellulose (HEC) placebo gel, the design of which has been previously published [7], and is illustrated in Figures 1, 2. Briefly, in this three-stage trial, all participants received a single dose of oral TDF followed 4 weeks later by rectally applied TFV 1% gel or the HEC gel given as a single dose, and 4 weeks later, seven daily doses of the same product previously administered rectally. After enrollment, each subject was assigned to either the treatment or placebo arm (2:1; TFV 1% gel:HEC gel) and also to one of two post-exposure biopsy sampling arms (groups “A” and “B”) to ensure mucosal safety. This limited the number of sigmoidoscopic procedures per participant to three sigmoidoscopic procedures in each of the first two study stages (single oral, single rectal) with several days delay between biopsy collections for mucosal healing. A single sigmoidoscopy biopsy collection point was used following the 3rd stage (7-day rectal exposures). All subjects provided biopsies (and other compartment samples) 0.5 h after their dose of oral TDF or single/7-day dose of TFV gel. For the single oral and single rectal exposures, in addition to all subjects being sampled at 0.5 h, Group “A” subjects were also biopsied on days 1 (24 hr) and 7; Group “B” subjects were also biopsied on days 4 and 10. Participants were allowed a 2 day visit window for this sampling but nearly all were seen on the first day of their 3-day window. Just prior to each biopsy sample, blood samples were obtained for plasma and peripheral blood mononuclear cell isolation, and rectal and vaginal mucosal fluids were collected by sponge. Each 2 weeks of biopsy sampling was followed by a 2-week resting period. The sample size (N = 18) was based on a similar phase 1 study of topical microbicide UC781. [8] The study was conducted from November 2009 to July 2010. Pharmacokinetic Procedures for Single Oral and Topical Dosing. All participants had blood plasma, PBMCs, and vaginal and rectal fluid obtained before single oral and rectal dosing. Additionally, 30 minutes after the dose, blood plasma, PBMCs, rectal biopsies, rectal fluid and vaginal fluid samples were obtained. At 2, 4, and 24 h after the dose, blood plasma, PBMCs, and rectal/vaginal fluid samples were obtained. Subsequently, on either days 1 and 7 (Group A) or 4 and 10 (Group B) post-dose, blood plasma, PBMCs, rectal biopsies, rectal/vaginal fluid were obtained. ![Figure 1. Study Design.](doi:10.1371/journal.pone.0106196.g001) Samples were obtained. The dose, blood plasma, PBMCs, rectal fluid, and vaginal fluid samples were obtained. At 2, 4, and 24 h after (observed), blood plasma, PBMCs, rectal biopsies, rectal fluid samples were obtained. At 2, 4, and 24 h after the dose, blood plasma, PBMCs, rectal fluid, and vaginal fluid samples were obtained. ### Study Products TDF tablets (300 mg) were supplied by Gilead Sciences (Foster City, CA). TFV 1% gel and HEC gel were supplied by CONRAD (Arlington, VA). TFV 1% gel (weight/weight) is tenofovir (PMPA, 9-[R]-2-phosphonomethoxypropyl)adenine monohydrate), formulated in purified water with edetate disodium, citric acid, glycerin, methylparaben, propylparaben, and hydroxyethyl cellulose with pH adjusted to 4–5 with an osmolarity of 3111 mOsmol/kg. The HEC placebo gel contained hydroxyethyl cellulose as the gel thickener, purified water, sodium chloride, sorbic acid, and sodium hydroxide. The gel was isotonic with a pH of 4.4, osmolarity of 304 mOsmol/kg, 24 and viscosity similar to the other microbicide gel candidates. Both TFV and HEC gels were prefilled into single-use, opaque applicators (HTI Plastics, Lincoln, NE) containing 4 ml of gel. ### Pharmacokinetic Procedures for Multiple Topical Dosing Thirty minutes after the 7th rectal dose of gel (observed), blood plasma, PBMCs, rectal biopsies, rectal fluid, and vaginal fluid samples were obtained. At 2, 4, and 24 h after the dose, blood plasma, PBMCs, rectal fluid, and vaginal fluid samples were obtained. ### Sample Processing Plasma was collected in tubes containing EDTA anticoagulant. Samples were centrifuged at 800 g for 10 minutes at 4°C, plasma aliquoted into cryovials, and stored at −70°C. Peripheral blood mononuclear cells (PBMCs) were isolated via centrifugation from cell preparation tubes (CPT) at 1,800 x g for 25 min at 28°C. PBMCs were collected from the buffy coat and washed twice with normal saline at room temperature (~21°C). Cells were resuspended in 1 ml normal saline for cell counting. Cell pellets were lysed with 70% methanol and stored at −80°C until analysis. To release cells for intracellular analysis from colonic tissue, biopsies were incubated with a dissociative enzyme cocktail consisting of collagenase (0.5 mg/ml, Sigma-Aldrich, St. Louis, MO), DNase I (0.083 U/ml, Roche, Indianapolis, IN), elastase (0.07 U/ml, Worthington Biochemicals, Lakewood, NJ), and hyaluronidase (0.4 U/ml, Worthington Biochemicals, Lakewood, NJ). The digestions were carried out in RPMI with 7.5% FBS in 50 ml-conical tubes at 37°C with agitation (Invitrogen, Carlsbad, CA) as previously described. [9,10] Cells were counted using Guava/Millipore EasyCyte Plus (Millipore, Billerica, MA). ### Sample Analysis All TFV and TFVdp concentrations were measured using validated LC–MS/MS methods. Total numbers of samples analyzed were as follows: 275 blood plasma, 460 PBMCs, 205 tissue homogenates, 98 isolated mononuclear cells, 99 CD4+ cells, 99 CD4- cells, 264 rectal sponges, 54 vaginal sponges [11]. Briefly, TFV and TFVdp concentrations were determined by previously described LC–MS/MS methods [12,13] validated for all matrices by the Johns Hopkins Clinical Pharmacology Analytical Laboratory. TFV and TFVdp assays meet the FDA bioanalysis guidance values of ≤±15% for precision and accuracy [14]. All calibrators were prepared using analyte calibrator stock solution diluted in the relevant human biological matrix corresponding to the samples to be assayed (plasma, PBMC lysate, cervicovaginal fluid, rectal fluid, homogenized colon or vaginal tissue). Thawed aliquots of plasma and tissue homogenate with 13C-TFV internal standard were protein precipitated with methanol. Vaginal and rectal fluid sponges were eluted in 50:50 methanol:water mixture. Sponges were weighed both before and after. Aliquots, also with 13C5-TFV internal standard, underwent solid phase extraction using HLB Oasis columns. The supernatants and eluants were collected, dried, and reconstituted in 0.5% acetic acid for analysis. For chromatographic separation of samples, a gradient elution with a Zorbax Eclipse XDB-C18 column, with positive electrospray --- Figure 2. Sample Collection. All 18 trial participants received a single oral dose of 300 mg TDF followed by intensive 24 h PK. After ~2 week resting period, 12 subjects were randomized to receive a single rectal dose of 1% TFV gel with intensive 24 h PK followed, after ~2 week resting period, by 6 sequential, daily, self-administered rectal 1% TFV gel doses with the 7th dose administered in-clinic with subsequent 24 h intensive PK. doi:10.1371/journal.pone.0106196.g002 ionization (ESI) was used, with detection via multiple reaction monitoring using a LC-MS/MS system (Waters Acquity UPLC and Agilent 1100 HPLC Applied Biosystems API4000 mass spectrometer). Calibration standards for the TFV assay ranged from 0.31 to 1,280 ng/ml (0.25–50 ng/sample for tissue). For intracellular TFVdp analysis, tissue homogenates and isolated cell lysates were analyzed using an indirect assay [13]. ### Table 1. Demographics. \| \| Oral tenofovir \| Tenofovir Gel \| HEC placebo gel \| \|----------------------\|---------------\|--------------\|-----------------\| \| N \| 18 \| 12 \| 6 \| \| Age (mean, STD) \| 42.1 (11.4) \| 41.3 (11.9) \| 43.7 (10.2) \| \| Gender: M \| 14 (78%) \| 10 (83%) \| 4 (67%) \| \| Gender: F \| 4 (22%) \| 2 (17%) \| 2 (33%) \| \| Latino or Hispanic Origin: Y \| 5 (28%) \| 3 (25%) \| 2 (33%) \| \| Latino or Hispanic Origin: N \| 13 (72%) \| 9 (75%) \| 4 (67%) \| \| Race: Black or African-American \| 2 (11%) \| 1 (8%) \| 1 (17%) \| \| Race: White \| 15 (83%) \| 10 (84%) \| 5 (83%) \| \| Race: Other \| 1 (6%) \| 1 (8%) \| 0 \| *Table 2. Noncompartmental Pharmacokinetic Parameters (Insufficient data to perform NCA on CD4- and CD4+ PBMC; see companion publication Richardson-Harmon et.al for exposure-response analysis; Composite Profile). \| Matrix \| Analyte, PK parameter \| Single Oral Dose, median (min–max); N \| Single Rectal Dose median (min–max); N \| Multiple Rectal Dose median (min–max); N \| \|-------------------------------\|-----------------------\|---------------------------------------\|----------------------------------------\|----------------------------------------\| \| Plasma \| \| \| \| \| \| \| TFV T1/2 (h) \| 10.8 (6.82–19.2); 18 \| 4.56 (2.61–62.9); 12 \| 6.62 (4.55–32.1); 10 \| \| \| TFV AUC24 h (ng/mL ×h) \| 2210 (1100–2940); 18 \| 66.3 (12.4–114); 12 \| 46.5 (17.1–178); 10 \| \| \| TFV Cmax (ng/mL) \| 252 (76.8–387); 18 \| 10.5 (5.08–33.4); 12 \| 8.61 (2.37–11.2); 10 \| \| \| TFV Tmax (h) \| 1.93 (0.267–3.92); 18 \| 0.317 (0.183–1.98); 12 \| 0.258 (0.183–2.03); 10 \| \| \| \| \| \| \| \| PBMC (total) \| \| \| \| \| \| \| TFVdp AUC24 h (fmol/10⁶ cells ×h) \| 4.26 (0.240–389) \| 0.24 (0.24–0.24) \| 0.24 (0.24–0.24) \| \| \| TFVdp Cmax (fmol/10⁶ cells) \| 0.375 (BLQ–38.6) \| BLQ (BLQ–0.01) \| BLQ (BLQ–0.01) \| \| Rectal Tissue \| \| \| \| \| \| \| TFV AUC24 h (ng/mg ×h)* \| 0.790 \| 70.4 \| \| \| \| TFVdp AUC24 h (fmol/mg ×h)** \| 0.240 \| 5470 \| \| \| \| TFV C24 h (ng/mg) \| 0.06 (BLQ–0.360) \| 0.06 (BLQ–12.6) \| \| \| \| TFVdp C24 h (fmol/mg) \| BLQ (BLQ–991) \| 285 (BLQ–490) \| \| \| \| \| \| \| \| \| Accumulation Ratio, TFV \| \| \| 2.03 \| \| \| Accumulation Ratio, TFdp \| \| \| 4.48 \| \| \| \| TFV C30 min (ng/mg) \| 5.81 (BLQ–95.1); 12 \| 11.8 (BLQ–430); 11 \| \| \| \| TFVdp C30 min (fmol/mg) \| 176 (BLQ–1230); 12 \| 789 (55.7–7190); 12 \| \| \| Rectal Mononuclear Cells \| \| \| \| \| \| \| TFVdp C30 min (fmol/10⁶ cells) \| BLQ (BLQ–BLQ); 18 \| 454 (BLQ–1460); 12 \| 1324 (BLQ–13900); 11 \| \| \| TFVdp C24 h (fmol/10⁶ cells) \| BLQ (BLQ–524); 8 \| 228 (BLQ–290); 3 \| \| \| \| TFVdp CD4+ C30 min (fmol/10⁶ cells) \| BLQ (BLQ–BLQ); 18 \| 266 (BLQ–3950); 12 \| 1080 (BLQ–31200); 12 \| \| \| TFVdp CD4+ C24 h (fmol/10⁶ cells) \| 26.7 (BLQ–724); 18 \| 250 (BLQ–1110); 3 \| \| \| \| TFVdp CD4- C30 min (fmol/10⁶ cells) \| BLQ (BLQ–30); 18 \| 112 (BLQ–1340); 12 \| 330 (BLQ–12000); 12 \| \| \| TFVdp CD4- C24 h (fmol/10⁶ cells) \| 28.4 (BLQ–157); 8 \| 92.7 (BLQ–265); 3 \| \| \| Rectal Fluid \| \| \| \| \| \| \| TFV AUC24 h (ng/g ×h, ×10⁵) \| 1.03 (0.00265–15.1); 16 \| 11.0 (1.56–42.5); 12 \| 7.03 (1.49–32.6); 7 \| \| \| TFV Cmax (ng/g, ×10⁴) \| 0.978 (0.00179–15.1); 17 \| 73.9 (8.79–297); 12 \| 41.6 (10.1–87.2); 7 \| \| \| TFV Tmax (h) \| 24 (0.330–24.5); 4 \| 0.380 (0.300–2.08); 12 \| 0.330 (0.280–0.370); 7 \| \| Vaginal Fluid \| \| \| \| \| \| \| TFV AUC24 h (ng/g ×h) \| 2.33 (0.979–2.72); 4 \| 1.43 (0.587–2.27); 2 \| 11.8; 1 \| \| \| TFV Cmax (ng/g, ×10⁴) \| 0.134 (0.0515–0.182); 4 \| 0.313 (0.0432–0.582); 2 \| 0.696; 1 \| \| \| TFV Tmax (h) \| 3.01 (1.92–24); 4 \| 2.74 (1.62–3.87); 2 \| 3.58; 1 \| Insufficient data to perform NCA on CD4- and CD4+ PBMC; see companion publication Richardson-Harmon et.al for exposure-response analysis. Composite Profile. doi:10.1371/journal.pone.0106196.t001 doi:10.1371/journal.pone.0106196.t002 TFVdp was isolated from cell lysates on a Waters QMA cartridge (Waters Corporation, Milford, MA) over a salt (KCl) gradient. TFV and tenofovir monophosphate (TFVmp) were separated from the cartridge under lower salt concentrations followed by elution of TFVdp with application of 1 M KCl to the cartridge. Isolated TFVdp was then enzymatically dephosphorylated to TFV via phosphatase digestion with incubation with phosphatase and 13C-TFV internal standard. TFV was isolated from the KCl solution using trifluoroacetic acid and eluted in methanol. TFV with 13C-TFV internal standard was analyzed via UPLC-MS/MS mass spectrometer as described above. Pharmacokinetic and Statistical Analysis* Data Standardization All values below the limit of quantification (BLQ) were imputed to be 0.01 for noncompartmental pharmacokinetic analysis (NCA) for all arms except rectal administration of placebo. Concentration data during rectal administration for the placebo arm is excluded from this report. All sponge concentrations (ng/sponge) were normalized to fluid weight on sponge (g) by division, resulting in units of ng/g. Data are presented as median (range) unless otherwise noted. PK Parameter Calculations Actual time after dosing was used for NCA. When calculating individual pharmacokinetic (PK) parameters (Cmax, Tmax, AUC24 h, half-life), only profiles with: a) greater than two data points, b) last concentration time point less than or equal to 24 h, and c) first concentration time point less than or equal to 12 h were used. A composite PK profile was constructed for rectal tissue homogenates using the median concentrations from all subjects at each nominal time point, regardless of the actual time. In this case, PK parameters were calculated based on this composite profile with nominal times. Composite profiles must be calculated with protocol-specified nominal times because descriptive statistics cannot be calculated with actual times; there were minor deviations in sample collection time during the trial, as it is impossible to collect at the exact protocol-specified time. For calculating AUC 24 h, linear interpolation was used to interpolate the concentration at 24 h if the actual time was greater than 24 h. If actual time was between 22 h and 24 h, then that concentration was imputed to be the 24 h concentration. Half-life estimation was performed by choosing points during the beta-phase of the elimination slope. (3 single rectal dose plasma PK profiles contained an imputed value of 0.01 at the 24 h timepoint.) Parameter calculation was performed with Phoenix WinNonlin 6.3.0.395 (Certara/Pharsight). Data manipulation and plotting was performed with R 2.15.10 [15] with libraries: lattice [16], latticeExtra [17], plyr [18] and reshape2 [19]. Accumulation ratio for rectal dosing was defined in one of two ways: either the AUC24 h ratio of multiple dose gel to single dose gel, or if unavailable, the 0.5 h concentration ratio of multiple dose gel to single dose gel. Statistical Analysis Robust linear regression was carried out with robust package for R [20], and fitted to the model: \[ DV = \beta_0 + \beta_1 \times IV + \beta_2 \times CV + \beta_3 \times IV \times CV. \] Dependent (DV) and independent variables (IV) are --- Figure 3. TFV Plasma Half-life is shorter (p = 0.02) during rectal administration. Plasma concentration-time profile is shown (median and interquartile range). Nominal time for single rectal dose was shifted right by 0.250 h and multiple rectal dose by 0.500 h for clarity. N = 18 for oral dose, 12 single rectal dose, 12 multiple rectal dose. (BLQ values are imputed as 0.01.) doi:10.1371/journal.pone.0106196.g003 continuous, while categorical variable (CV) is either 0 or 1. Any parameter terms with p > 0.05 were dropped and excluded from the statistical model, and re-fitted with a simpler model (backward elimination). All robust linear regression was performed with log10-transformed concentration data. Robust linear regression allows for differential weights to datapoints in respect to outlier datapoint; outliers were given less weight. This results in a more stable model. All statistical comparisons were performed using paired Wilcoxon signed-rank test with a bonferroni correction for 2 comparisons (oral to single rectal, single to multiple rectal), resulting in a critical p-value of 0.025 (0.05/2). Standard error (SE, standard deviation) was a measure of uncertainty around parameter estimates. Relative standard error (RSE) was a measure of overall goodness of fit (0 would be a perfect fit). Results Demographics There were a total of 18 subjects included in this analysis. (Table 1) Mean age was 41, 78% were male, and 84% white. For oral dosing, the following data were used for pharmacokinetic analysis: 139 plasma samples, 131 PBMC samples, 149 rectal tissue homogenates, 72 rectal tissue isolated MMC samples, 31 vaginal sponges, and 135 rectal sponges. For topical dosing, the following data were used for pharmacokinetic analysis: 228 plasma samples, 210 PBMC samples, 144 rectal tissue homogenates, 69 rectal tissue isolate MMC sample, 46 vaginal sponges, and 224 rectal sponges. For the purpose of concentration correlation analysis across matrices only, BLQ samples were excluded. Thus, 163 plasma, 319 PBMC, 208 rectal tissue homogenate, 107 rectal tissue MMC, 42 vaginal sponge, and 130 rectal sponge samples were excluded. All pharmacokinetic data are summarized in Table 2 and Figures 2 and 3. Matrix comparisons are presented in Figures 4–8. Plasma Pharmacokinetics As expected, systemic TFV exposure, measured by both AUC24 h and Cmax, was 24–33 fold higher after a single oral dose (median AUC24 h 2200 ng/mL xh, median Cmax 250 ng/mL) than after a single rectal dose (median AUC24 h 66 ng/mL xh, median Cmax 11 ng/mL). An accumulation ratio of 0.73 demonstrated that there was no clinically relevant difference in plasma exposure between single and multiple rectal dosing. A 24-fold lower Cmax was achieved approximately 1.5 h faster with rectal dosing than with oral dosing (median Tmax single rectal = 0.32 h versus single oral = 1.9 h; Table 2). TFV half-life was noted to be at least 5 h shorter (paired t-test on log-transformed half-lives, p = 0.02) for single and multiple rectal dosing (4.6–6.6 h) compared to oral dosing (11 h). (Table 2; Figure 3) Inter-individual variability of the PK parameters (CV%) ranged from 31–100% during oral dosing, 55–106% during single rectal dosing, and 53–103% during multiple rectal dosing. Tmax was the most variable PK parameter with CV% consistently above 100%. PBMC No detectable TFVdp was found in total PBMCs after single and multiple rectal dosing. (Table 2) In contrast, PBMC exposure after oral dosing was consistently detected in most (10/18) subjects (median AUC24 h 43 fmol/10^6 cells xh, median Cmax 0.38 fmol/10^6 cells). There was insufficient data to perform NCA on CD4- and CD4+ cell subpopulations; please see companion paper (Richardson-Harmon et.al) for exposure-response analysis. Figure 5. Rectal tissue exposure to TFV and TFVdp (median ± IQR) is higher during rectal dosing with multiple rectal dosing, resulting in accumulation of TFVdp. Each set of figures documents the 30 min drug quantification in the left-side graph and the 24 hr in the right side graph in rectal tissue biopsy homogenate (5A, 5B) and isolated mucosal mononuclear immune cells (MMC) (5C). Comparisons performed with paired Wilcoxon signed-rank test; only a subset of patients gave both C30 min and C24 h samples. Figure S5A = TFV Tissue; Figure S5B = TFVdpTissue; Figure S5C = TFVdpMMC. There is accumulation of TFV and TFVdp from multiple rectal dosing. Critical p for significance was 0.025 after Bonferroni correction. doi:10.1371/journal.pone.0106196.g005 Rectal Tissue There was a linear relationship (p = 0.04) between TFVdp and TFV in rectal tissue homogenates during oral dosing. This relationship can be seen in Figure 4. The resulting model (± standard error) was as follows: Rectal Tissue homogenate TFVdp concentration (fmol/mg) = 2.37 (±0.168)+0.366 (±0.121) x rectal tissue homogenate TFV concentration (ng/mg). Although rectal data from topical dosing was excluded from the model due to nonsignificance, they are overlaid in Figure 4 for reference. Population composite AUC showed that topical dosing resulted in 2-log10 higher rectal exposure to TFV (single oral vs. single rectal dose AUC_{24 h} = 0.79 vs. 70 ng/mg x h), and a 4-log10 higher rectal exposure to TFVdp (single oral vs. rectal dose AUC_{24 h} = 0.24 vs. 5500 fmol/mg x h). When comparing tissue concentrations 30 minutes post-dose, single topical dosing resulted in 2-fold higher TFV (paired p = 0.016) and 4-fold higher (paired p <0.001) TFVdp concentrations compared to oral dosing (Figures 4A, 4B). Multiple rectal dosing resulted in a non-statistically significant 2-fold accumulation in TFV concentrations compared to single dosing (paired P>0.8), with TFVdp concentrations accumulating 4.5-fold (paired p<0.01). Over 24 h, we observed TFV concentrations continuing to increase after oral dosing, such that 24 h concentrations post-dose were similar between oral and topical dosing: median TFV concentration at 24 h was 0.060 ng/mg after oral dosing vs 0.060 ng/mg after rectal dosing, paired p>0.8. However, median TFVdp concentrations 24 h post topical rectal dose were almost 300-fold higher than after an oral dose, though not statistically significant. (paired p = 0.125). With 4 subjects having missing paired C_{24 h} rectal biopsy samples for rectal dosing in Figure 5B, this may have resulted in biased TFVdp concentrations after topical dosing. Isolated total mucosal mononuclear cells yielded similar results to tissue homogenates. At 0.5 h post-dose, rectal dosing resulted in 4-log10 higher concentration (paired p = 0.002) of TFVdp (median 454 fmol/10^6 cells) compared to oral administration (median 0.010 fmol/10^6 cells), and remained 4-log10 higher 24 h post dose (median rectal: 230 fmol/10^6 cells; oral: 0.010 fmol/10^6 cells, Table 2, Figure 5C, paired p = 0.5). There was also accumulation of TFVdp in these isolated cells after multiple rectal dosing (accumulation ratio: 2.9, paired p = 0.084). Regardless of dosing route, compared to plasma, there was large inter-individual variability in TFV and TFVdp tissue and cell concentrations at each nominal time. Although no dosing route was found to have more variable exposure than the other. In tissue homogenates, TFV CV% ranged from 112–364%, 0 to 220%, and 236% for single oral, single rectal, and multiple rectal dosing, respectively. The CV% of TFVdp ranged from 0–307%, 85–312%, and 132% for single oral, single rectal, and multiple rectal dosing. The lower CV% of 0 in these groups is a result of all measured values being below the limit of quantification. The variability of TFV and TFVdp in isolated mucosal mononuclear cells was also similarly high regardless of CD4 expression status, and ranged from 0 to 316%. Robust linear regression analysis demonstrated that TFVdp in isolated mucosal mononuclear cells was positively and linearly correlated with TFVdp in rectal tissue homogenates (Figure 6). The β_0 term (see methods for the initial model) was dropped due to nonsignificance. Despite a large number of data points (85%) excluded from the analysis for concentrations below the limit of Figure 6. TFVdp in rectal tissue homogenate is predictive of intracellular TFVdp concentration in isolated rectal mucosal mononuclear cells (MMCs), with higher levels of phosphorylation in the CD4+ T cells compared to CD4- T cells. Intracellular TFVdp concentration in isolated rectal mucosal mononuclear cells increases linearly as TFVdp concentration in rectal tissue homogenate increases. (p<0.001, robust RSE = 0.46) There is higher phosphorylation of TFV in CD4+ cells, seen in its higher y-intercept. The lines are the mean rectal tissue MMC TFVdp concentration predictions from robust linear regression model; solid is CD4+, dashed is CD4-. Shaded regions are the 10–90% confidence intervals of the mean prediction. doi:10.1371/journal.pone.0106196.g006 detection, the final model (± standard error) still achieved statistical significance (p < 0.001), and was as follows: Cellular TFVdp concentration = 0.680 (± 0.205) + 0.628 (± 0.0818) × homogenate TFVdp concentration + 0.586 (± 0.125) × cell type (cell type = 0 for CD4- cells and cell type = 1 for CD4+ cells). Though there is no interaction between cell type and TFVdp, the y-intercept of the CD4+ cells was significantly higher (0.680 vs 1.27; p < 0.01) than that of the CD4- cells. Rectal Sponge TFV exposure in rectal fluid was 1–2 log10 higher during topical administration (single dose median AUC0–24 h: 1,100,000 ng/g ×h, Cmax 740,000 ng/g, Table 2) compared to oral administration (median AUC0–24 h: 100,000 ng/g ×h, Cmax 9,800 ng/g). As expected, topical administration achieved maximal concentrations nearest the time of application (Cmax = 0.38 h). However, oral administration achieved maximal concentrations 24 hours after dosing. There was no accumulation of TFV in rectal fluid after multiple rectal dosing (median AUC24 h single dose 11.0 × 105 ng/g ×h, multiple dose 7.03 × 105 ng/g ×h). Inter-individual variability was higher for rectal sponge samples compared to direct sampling of other matrices. With oral dosing, single rectal dosing, and multiple rectal dosing, TFV concentration CV% ranged from 150–390%, 92–320%, and 56–150%, respectively. Robust linear regression demonstrated that plasma TFV concentrations positively and linearly correlated with TFV in rectal fluid (Figure 7). No correlation between plasma concentrations and rectal fluid after oral dosing was noted. Both β2 and β3 terms were dropped due to nonsignificance, with the following model (± standard error) achieving statistical significance (p < 0.001): Plasma TFV = −1.23 (± 0.170) + 0.386 (± 0.0328) × TFV rectal fluid concentration. The number of rectal doses did not significantly affect these concentration correlations. Robust linear regression demonstrated that rectal tissue TFV and TFVdp concentrations positively and linearly correlated with TFV in rectal fluid, regardless of administration route (Figure 8). Thus, dose route was dropped as an interaction term. The following model (± standard error) achieving statistical significance (p < 0.001): [Rectal Tissue TFV or TFVdp] = β0 + β1 × [Rectal Fluid TFV]. For predicting rectal tissue TFV, β1,TFV = 0.634 (± 0.0777) (p < 0.001) and β0,TFV = −2.43 (± 0.335). For predicting rectal tissue TFVdp, β1,TFVdp = 0.197 (± 0.0612) (p < 0.001), and β0,TFVdp = 1.41 (± 0.272). Dose route and frequency was not found to be significant factors in the correlation. Vaginal Sponge TFV concentrations in the vaginal lumen peaked at approximately 3 hours regardless of route of administration. However, median TFV Cmax in the vagina was approximately 2-fold higher after a single rectal dose than after a single oral dose (3100 ng/g vs. 1300 ng/g, Table 2). Additionally, from data in one subject only, there was evidence of accumulation in the vaginal lumen after multiple rectal dosing (accumulation ratio = 5). Less inter-individual variability was seen in the vaginal sponge data than the rectal sponge data. TFV concentration CV% at each nominal time from oral dosing, single rectal dosing, and multiple rectal dosing ranged from 50–390%, 92–320%, and 56–150%, respectively. Robust linear regression demonstrated that TFV concentrations on vaginal sponges are positively and linearly correlated with TFV in vaginal fluid (Figure 9A). The final predictive model (± std error) was: TFV in vaginal fluid = 1.32 (± 0.0948) + 0.778 (± 0.0704) × [plasma TFV] + 0.951 (± 0.169) × route. For oral dosing, route = 0, and for rectal dosing, route = 1. Though there was no interaction between dose route and TFV in vaginal fluid, the y-intercept of rectal administration was significantly higher (2.27 vs. 1.32; p < 0.01) than that of oral administration. Robust linear regression also demonstrated that TFV concentrations on vaginal sponges are positively and linearly correlated with TFV and TFVdp concentrations in rectal tissue. (Figure 9B) The final model (± std error) was as follows: [vaginal fluid TFV] = β₀ + β₁ × [TFV or TFVdp in rectal tissue] For TFV in rectal tissue as an independent predictor of vaginal fluid concentrations, $\beta_{TFV} = 0.741$ (±0.105, p < 0.001) and $\beta_{TFV} = -0.37$ (±0.402). For TFVdp in rectal tissue as an independent predictor of vaginal fluid concentrations, $\beta_{TFVdp} = 1.66$ (±0.114, p < 0.001), and $\beta_{TFVdp} = -6.91$ (±0.649). TFV and TFVdp evaluations were performed as two Tmax. The lower plasma exposure after gel dosing is not require the additional metabolism step, leading to a faster small surface area of the rectum for drug absorption, the intestine and upper small intestine may explain this discrepancy. Differences in absorption kinetics between the rectum/lower large 1.6 h shorter with rectal administration than with oral dosing. Discussion This is the first study examining the pharmacokinetic distribution of rectally applied tenofovir gel in various tissues and cells relevant to HIV infection. This study also compares compartment concentrations of rectally applied TFV kinetics to oral dosing. It is important and biologically relevant to quantify TFV and TFVdp exposures in tissues and cells targeted for HIV infection. Measuring these concentrations allows for a better understanding of how drug distributes from the sites of absorption to target tissues, what factors can impact this distribution, and the possible identification of less-invasive surrogate markers of exposure that could be useful in larger clinical trials. In this study’s intra-subject comparison, the TFV exposure (AUC24 h) in plasma was, expectedly, more than 30 times higher after oral administration of 136 mg of TFV equivalent than after rectal administration of 44 mg of TFV. Additionally, T max was 1.6 h shorter with rectal administration than with oral dosing. Differences in absorption kinetics between the rectum/lower large intestine and upper small intestine may explain this discrepancy. The extent and rate of absorption is often lower in the rectum compared to the intestines. This can be due to the relatively smaller surface area of the rectum for drug absorption, the inherent differences in the formulation, and the environment surrounding the route of administration, such as pH and fluid content [22–24]. In the particular case of TFV gel, the major difference is the formulation. Oral TFV is administered as tenofovir disoproxil fumarate, a di-ester prodrug [25,26]. In contrast, TFV gel contains only the drug. Thus, TFV gel would not require the additional metabolism step, leading to a faster T max. The lower plasma exposure after gel dosing is not completely explained by the lower dose, since the equivalent oral dose was only 3 times higher. This is most likely due to the lower extent of drug absorption in the rectum, and also possibly due to gel leakage. The half-life of TFV in plasma was 4–6 h longer (p = 0.02) with oral dosing than with rectal administration, and consistently longer in all patients except for one. The plasma half-life observed was 1–3 hours shorter than typically reported [25,26] most likely due to lack of data in this study during the terminal elimination phase. Nonetheless, the relative difference in half-life between oral and rectal administration is significant. One possible explanation is that the kinetics with rectal dosing may be driven by absorption, leading to flip-flop kinetics [27]. If this is the true, then the half-life would be rate-limited by the rate of absorption instead of elimination. One other explanation may be the saturation of renal elimination processes [28] as a result of higher TFV plasma exposure. Tenofovir is eliminated by filtration and secretion [25]. Although renal filtration is not saturable, tubular secretion is carrier-protein mediated and can exhibit nonlinear, saturable behavior. During tubular secretion, tenofovir is a substrate for the MRP4 transporter in the tubular lumen [29–31]. Saturation of this excretion transporter could explain nonlinear elimination. In the case of topical administration, the decreased half-life and lower plasma exposure during both single and multiple administrations can minimize systemic toxicity. C max of TFVdp after a single oral dose was below limit of detection (LLOQ = 8 fmol/10^6 cells); this is significantly lower than what has been previously reported (20 fmol/10^6 cells [9]), but not unexpected based on inter-individual variability. This is probably also due to lower cell penetration of TFV compared to TFVdp. Due to the low plasma exposure following rectal dosing (median plasma AUC24 h 66 ng/mL × h), TFVdp exposure was undetectable in PBMCs of all subjects. As expected, rectal tissue exposure to TFV and TFVdp was 2–4 log10 higher with topical administration than with oral dosing. After multiple dosing, TFV does not appear to significantly accumulate in the tissue. Although the accumulation ratio from the median profile showed an approximately 2-fold increase in AUC24 h, a paired analysis of concentration within individuals showed no statistically significant changes between the 30 min and 24 h post-dose samples. TFVdp, however, did show significant accumulation in rectal tissue (approximately 5-fold) and in isolated mucosal mononuclear cells (approximately 3-fold). The long intracellular half-life of TFVdp is likely the cause of this tissue accumulation [32]. It has previously been noted that an increase in TFV tissue homogenate concentration yields an increase in TFVdp concentration [9,32]. We confirmed this at 24 h after oral dosing (Figure 4). The correlation may have been stronger if there would have been more data to analyze. Furthermore, it is possible that the different absorption kinetics of the rectum compared to the intestines could cause variations in this correlation. To address the question of whether TFVdp in tissue homogenates accurately reflect TFVdp concentrations in target cells for HIV transmission, or whether the heterogeneous mix of cells in mucosal tissue confounds the results, we compared homogenate results to those of isolated mucosal mononuclear cells. Encouragingly, a linear relationship was noted between TFVdp concentration in rectal tissue homogenate and isolated mucosal mononuclear cells. This linear relationship was not influenced by CD4 status: as TFVdp concentration in the homogenate increased by 100%, there was a 63% increase of TFVdp in the isolated mucosal mononuclear cells. However, the data did suggest that there may be differences in phosphorylation based on the CD4 expression status of the cell. When plotting the relationship between TFVdp in tissue homogenates and in CD4+ and CD4− cells, the Y intercept in CD4+ cells was 1.6-fold higher than in CD4− cells. That is, for every observed TFVdp concentration in the homogenate, the TFVdp concentration in the CD4+ cells was 1.6-fold higher than in CD4− cells. This difference persisted throughout the 10–10,000 fmol/mg range of TFVdp concentrations, and achieved statistical significance (p < 0.01), even with small numbers of samples. The source of this difference is unclear, as some studies suggest that tenofovir is phosphorylated to a similar extent between quiescent and stimulated cells, while others suggest higher phosphorylation in resting cells [33]. Although it is currently unknown whether these concentration differences are of clinical significance, these data are encouraging, as they suggest that TFVdp is found in higher concentrations in the cells that are targets for HIV infection. In this study, rectal mucosal fluid was collected to determine whether it could be a surrogate for TFV and TFVdp concentration in rectal tissue. TFV concentrations in the rectal fluid linearly correlated with rectal tissue TFVdp. (Figure 8) This relationship remained consistent regardless of dose route or frequency. Despite dramatic differences between oral and rectal absorption characteristics, we still observe a similar linear relationship between these two matrices. Therefore, rectal fluid TFV concentrations collected by sponge are useful in estimating drug concentrations in the target rectal tissue. We also attempted prediction of plasma TFV exposure from rectal mucosal concentrations. There was high variability in these predictions, so a precise prediction was not possible. However, our data suggest that a rough estimation of high or low plasma TFV based on rectal TFV concentration could be feasible. Therefore, rectal sponge TFV concentration could be used as a non-invasive surrogate for plasma TFV concentrations for safety and toxicity monitoring. With more patient data, prediction variability may be decreased using patient demographic covariates, which could potentially minimize the need for blood sampling in future trials of Figure 9. There is vaginal penetration of TFV from both oral and topical rectal exposures. (A) Vaginal fluid detection of both TFV and TFVdp concentration in vaginal fluid is higher following rectal dosing than following single oral dosing TFVdp. There is a linear correlation between vaginal fluid sponge TFV and plasma TFV concentrations (p<0.001, robust RSE = 0.44). TFV penetration into vaginal fluid is 1-log₁₀ higher with rectal administration than oral, seen with higher y-intercept (p<0.001). (B) There is a linear correlation between vaginal fluid TFV and both rectal tissue TFV and TFVdp (p<0.01, robust RSETFV = 0.47, RSETFVdp = 0.13). Shaded regions are the 10–90% confidence intervals of the mean predictions from robust linear regression model. Solid line is mean vaginal fluid TFV concentration, dashed TFVdp. doi:10.1371/journal.pone.0106196.g009 rectal dosing. We did not observe similar correlation with oral dosing; this is probably due to the high variability in the data compared to the possible strength of the correlation. If we had a higher range of rectal fluid concentration, through either different oral dose levels or sample collection times, then it is possible a correlation may be observed. Previous data in macaques has demonstrated that 5–7% of tenofovir dosed rectally can be found in vaginal fluid [34]. We evaluated this phenomenon in 4 women, and found that vaginal concentrations were 8.7% of rectal secretion concentrations sampled at the same time, similar to the 1–2 log10 difference found previously in animals. Additionally, we noted a 1.6-fold higher exposure of TFV in vaginal secretions with rectal dosing than with oral dosing. Since the slopes of the relationship between vaginal fluid TFV and plasma TFV with the two administration routes are not significantly different, the rate of TFV penetration into the vagina does not vary with administration route. As plasma concentrations with oral dosing are much higher than with rectal dosing, systemic re-distribution into the vaginal fluid cannot be the only mechanism by which TFV reaches the vaginal lumen. Vaginal TFV penetration was further confirmed when we observed a linear relationship between vaginal TFV exposure and rectal tissue exposure. When rectal tissue TFV and TFVdp exposure increased, there was also a linear increase in vaginal exposure to TFV. Due to the low number of data points, we could not discern whether route of administration affected this relationship. It is interesting to note that there was accumulation of TFV in the vaginal fluid (Table 2, single rectal dose AUC = 1.4 ng/g ×h, multiple rectal dose = 11), but not rectal fluid (single rectal dose AUC = 11 ng/g ×h, multiple rectal dose = 7.0). There are two possible explanations for this. One is that the rectal site is already saturated due to proximity to administration, whereas vaginal site is more distal and takes time to build up. Another is that there may be differences in fluid turnover between the two sites. Therefore, the kinetics is inherently different between the two sites. One limitation of this analysis is the treatment of BLQ values and nominal times used for the composite PK profiles in Table 2. BLQ numbers are still valuable because there is a lot of information content in these numbers. Therefore, the treatment of BLQ values depended on the analysis performed. They are imputed as 0.01 for NCA, and ignored for correlation analysis due to statistical difficulties in treating these numbers. Since this was done systematically and consistently, there should be no impact on the overall conclusions. Also, the proportion of BLQ values for plasma was low (2.4%), so this should have little impact on the calculated plasma PK parameters. Similarly, since only datapoints that fell within a specific time window were included in the composite profiles, there should not have been a significant bias in PK parameter estimates. References 1. Abdool Karim Q, Abdool Karim SS, Frohlich JA, Grobler AC, Baxter C, et al. (2010) Effectiveness and safety of tenofovir gel, an antiretroviral microbicide, for the prevention of HIV infection in women. Science 329: 1168–1174. Available: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3001187&tool=pmcentrez&rendertype=abstract Accessed 31 January 2013. 2. Grant RM, Lama JR, Anderson PL, McMahan V, Liu AY, et al. (2010) Effectiveness and safety of tenofovir gel, an antiretroviral microbicide, for the prevention of HIV infection in women. Science 329: 1168–1174. Available: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3079639&tool=pmcentrez&rendertype=abstract Accessed 31 January 2013. 3. Baeten JM, Donnel D, Ndase P, Mugw NR, Campbell JD, et al. (2012) Antiretroviral prophylaxis for HIV prevention in heterosexual men and women. N Engl J Med 367: 399–410. Available: http://www.ncbi.nlm.nih.gov/pubmed/22784037. Accessed 22 May 2013. 4. Choopanya K, Martin M, Suntharasamai P, Sangkum U, Mock PA, et al. (2013) Antiretroviral prophylaxis for HIV infection in injecting drug users in Bangkok, Thailand (the Bangkok Tenofovir Study): a randomised, double-blind, placebo-controlled phase 3 trial. Lancet 381: 2083–2090. Available: http://www.ncbi.nlm.nih.gov/pubmed/23749234. Accessed 30 October 2013. 5. Karim SSA, Kashuba ADM, Werner L, Karim QA (2011) Drug concentrations after topical and oral antiretroviral pre-exposure prophylaxis: implications for HIV prevention in women. Lancet 378: 279–281. Available: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3632497&tool=pmcentrez&rendertype=abstract. Accessed 27 May 2013. Conclusion This was the first comprehensive pharmacokinetic study of rectally administered tenofovir gel that describes the distribution of TFV and TFVdp into various tissue compartments relevant to HIV infection. The compartments included rectal fluid, rectal tissue and its isolated mucosal mononuclear cells, vaginal fluid, blood plasma and PBMCs. It was expected, and now confirmed, that rectally applied TFV would have lower systemic exposure and higher vaginal exposure compared to oral. There was accumulation of TFVdp in the rectal tissue, due to the long intracellular half-life. An unexpected yet biologically interesting finding was detecting a consistent difference in concentrations of TFVdp in rectal mucosal CD4+ cells, prime targets for new HIV infections. It is useful to know that TFV rectal fluid concentrations may be reasonable bio-indicators of plasma and, importantly, rectal tissue concentrations, making it easier to estimate adherence and TFV concentrations in the target tissue. We were encouraged to see many concentration correlations across various relevant categories, such as rectal mucosal mononuclear cells and rectal tissue homogenate TFVdp, and vaginal fluid and plasma. This will enable more advanced population pharmacokinetic modeling methods and developing a single mathematical model that describes the distribution of TFV with more accuracy. Furthermore, if target TFV and TFVdp concentrations are identified, then these data and models will assist in dose regimen selection that maximizes efficacy and minimizes toxicity. Supporting Information Protocol S1 Trial Protocol. (PDF) Checklist S1 CONSORT Checklist. (DOC) Acknowledgments Deep appreciation is offered to the dedicated participants who enrolled in this intensive study. Significant support at all stages of this study was provided by site staff and the study sponsors including UCLA (Elena Khankhlova, Charina McDonald, Terry Saunders, Karen Tanner, VaShira Rhodes, and Justin Akin), MWRI/University of Pittsburgh (Ross Cranston, Carol Oros, Lorina Rabe, Kathryn Duffill, Lisa Rohan, and Sharron Hiller). JHU (Ed Fuchs, Nicolette Lousainant, Nicole Anders, and Tianmeng Chen), CONRAD (Henry Gabelnick, Timothy McCormick, Marianne Callahan, and David Friend), Gilead Sciences Inc. (Jim Rooney) and NIH/NIAID/DAIDS (Jim Turpin, Jeanna Piper, and Grace Chow). Author Contributions Wrote the paper: KY CH RC IM PA AK. Conceived and designed the experiments: PA. Performed the experiments: CH NB JE CM RC IM PA. Analyzed the data: KY KT NR AK. 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(2012) Pharmacokinetics of tenofovir following intravaginal and intrarectal administration of tenofovir gel to rhesus macaques. Antimicrob Agents Chemother 56: 103–109. Available: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3236053&tool=pmcentrez&rendertype=abstract. Accessed 18 July 2013.	2025-03-05T00:00:00	olmocr	{ "pdf_page_numbers": [ [ 0, 6087, 1 ], [ 6087, 11784, 2 ], [ 11784, 16428, 3 ], [ 16428, 24650, 4 ], [ 24650, 28358, 5 ], [ 28358, 31734, 6 ], [ 31734, 32491, 7 ], [ 32491, 36864, 8 ], [ 36864, 40509, 9 ], [ 40509, 41447, 10 ], [ 41447, 49172, 11 ], [ 49172, 50679, 12 ], [ 50679, 58036, 13 ], [ 58036, 66041, 14 ] ] }

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