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Partial volume correction for arterial spin labeling using the inherent perfusion information of multiple measurements
Yang Liu ORCID: orcid.org/0000-0002-0984-51281,
Ze Wang2,
Ruihua Liang1,
Zhengrong Liang3 &
Hongbing Lu1
Arterial spin labeling (ASL) provides a noninvasive way to measure cerebral blood flow (CBF). The CBF estimation from ASL is heavily contaminated by noise and the partial volume (PV) effect. The multiple measurements of perfusion signals in the ASL sequence are generally acquired and were averaged to suppress the noise. To correct the PV effect, several methods were proposed, but they were all performed directly on the averaged image, thereby ignoring the inherent perfusion information of mixed tissues that are embedded in multiple measurements. The aim of the present study is to correct the PV effect of ASL sequence using the inherent perfusion information in the multiple measurements.
In this study, we first proposed a statistical perfusion model of mixed tissues based on the distribution of multiple measurements. Based on the tissue mixture that was obtained from the high-resolution structural image, a structure-based expectation maximization (sEM) scheme was developed to estimate the perfusion contributions of different tissues in a mixed voxel from its multiple measurements. Finally, the performance of the proposed method was evaluated using both computer simulations and in vivo data.
Compared to the widely used linear regression (LR) method, the proposed sEM-based method performs better on edge preservation, noise suppression, and lesion detection, and demonstrates a potential to estimate the CBF within a shorter scanning time. For in vivo data, the corrected CBF values of gray matter (GM) were independent of the GM probability, thereby indicating the effectiveness of the sEM-based method for the PV correction of the ASL sequence.
This study validates the proposed sEM scheme for the statistical perfusion model of mixed tissues and demonstrates the effectiveness of using inherent perfusion information in the multiple measurements for PV correction of the ASL sequence.
The arterial spin labeling (ASL) sequence provides a noninvasive way to measure the cerebral blood flow (CBF) by utilizing the magnetically labeled arterial blood water as an endogenous tracer to create a "label" image [1] and subsequently repeats the process to create a "control" image without labeling the arterial blood. The subtraction of the label and control images becomes the perfusion image, which reflects the amount of the arterial blood that is delivered to each voxel after the transit time [2]. Due to fast scan of the label and control images, the perfusion image (label/control difference) is very noisy; therefore, multiple label/control image pairs are commonly acquired and are averaged to impress the noise.
The spatial resolution of the ASL sequence was approximately 3–6 mm. The CBF estimation was contaminated by the partial volume (PV) effect, which results in less accuracy of the CBF quantification [3]. For accurate PV correction, the perfusion contributions of different tissues inside a mixed voxel should be estimated separately [4]. Asllani et al. [5] proposed a linear regression (LR) method, in which the CBF values of both gray matter (GM) and white matter (WM) are assumed to be constant within an n × n × 1 regression kernel. Under this assumption, the LR method can generate the separate GM's and WM's CBF maps, but spatial smoothing may be also introduced into the CBF maps. Then, several methods have been proposed to alleviate the smoothing effect of the LR method [6,7,8]. For multiple inversion-time (TI) ASL data, Chappell et al. reported a PV correction method using a spatially regularized kinetic curve model [9]. To the best of our knowledge, all of the current PV correction methods were performed directly on the averaged image of the multiple label/control pairs, thereby ignoring the inherent perfusion information of the mixed tissues that are embedded in the multiple measurements.
The aim of the present study is to correct the PV effect of the ASL sequence by using the inherent perfusion information of multiple measurements. It was reported that the multiple measurements of the ASL sequence could be regarded as noisy realizations of the original distribution [10]. Therefore, for each voxel composed of mixed tissues, the PV correction problem turns to how to estimate the perfusion contributions of different tissues from multiple noisy measurements. Generally, for magnetic resonance imaging (MRI), the Rician noise model is widely accepted [11]. However, after the label/control difference operation, Gaussian noise is generally considered in the perfusion images of ASL sequence [12, 13]. For the purpose of this study, we first proposed a statistical perfusion model of mixed tissues for the ASL sequence, based on the Gaussian distribution of multiple measurements. With the tissue mixture information obtained from the high-resolution structural image, a structure-based expectation maximization (sEM) scheme was developed to estimate the perfusion contributions of the mixed tissues from multiple measurements.
Perfusion model of a mixed voxel
Considering the low spatial resolution, the GM, WM, and cerebrospinal fluid (CSF) may all contribute to the label/control difference signal, ∆M. No ASL signal typically arises from CSF [14]; therefore, the perfusion signal ∆M at the spatial position i can be described as
$$\Delta M_{i} = P_{iGM} \Delta M_{iGM} + P_{iWM} \Delta M_{iWM}$$
where PiGM and PiWM are proportions of GM and WM in the voxel i, respectively. ∆MiGM and ∆MiWM are the difference magnetizations for GM and WM, respectively.
In the current CBF calculation method, the CBF f of a tissue type is obtained by
$$f_{tissue} = \left( {\frac{{\Delta M_{tissue} }}{{M_{0} }}} \right)F_{tissue}$$
where Ftissue is a tissue-specific parameter, and M0 represents the equilibrium brain tissue magnetization obtained from the M0 image. For a mixed voxel, its CBF comes independently from the GM part (\(f_{GM}^{P}\)) and the WM part (\(f_{WM}^{P}\)) and can be described as
$${\text{CBF}} = f_{GM}^{P} + f_{WM}^{P} = \frac{{P_{iGM} F_{GM} }}{{M_{i0} }}\Delta M_{iGM} + \frac{{P_{iWM} F_{WM} }}{{M_{i0} }}\Delta M_{iWM}$$
For ASL perfusion studies, PiGM and PiWM can usually be estimated from a high-resolution structural image (e.g., T1 weighted image) of the same subject, and FGM and FWM can be derived from the two-compartment model for the ASL data [15]. Therefore, for a CBF estimation of a mixed voxel, the key problem is to estimate the magnetizations of GM and WM (i.e., ∆MiGM and ∆MiWM) from multiple measurements.
Statistical perfusion model of mixed tissues
As described in the Introduction section, multiple measurements could be regarded as noisy realizations of the original distribution [10], and Gaussian noise is generally considered in each measurement of the ASL sequence [12, 13]. Based on the Gaussian distribution of multiple ASL measurements, we first established a statistical perfusion model of mixed tissues.
1. The statistical model of multiple measurements
In the spatial domain, index i is defined to represent the spatial position of a concerned voxel. The intensities of this voxel were acquired by multiple measurements that constitute a column vector Y = {Yit, t = 1, …,T}, where T is the number of multiple measurements collected. Based on the Gaussian assumption, each Yit is a noisy observation of a random variable with a mean of \(\bar{Y}_{i}\) and a variance of \(\sigma_{i}^{2}\), i.e.,
$$Y_{it} = \bar{Y}_{i} + n$$
where n represents statistically independent noise in Yit [16]. Since each measurement of the ASL sequence is independently scanned, the conditional probability of the measurement vector Y can be described as
$$p\left( {{\mathbf{Y}}\left| {\{ \bar{Y}_{i} \} ,\{ \sigma_{i}^{2} \} } \right.} \right) = \prod\limits_{t = 1}^{T} {p\left( {Y_{it} \left| {\bar{Y}} \right.,\sigma_{i}^{2} } \right)}$$
2. Statistical perfusion model of mixed tissues
The observation Yit contains perfusion contributions from GM and WM. The GM component is denoted by XitGM, with a mean of \(\bar{X}_{iGM}\) and a variance of \(\sigma_{iGM}^{2}\). The WM component is denoted by XitWM with a mean of \(\bar{X}_{iWM}\) and a variance of \(\sigma_{iWM}^{2}\). Thus, we have
$$p\left( {{\mathbf{X}}\left| {\bar{X}_{iGM} ,\bar{X}_{iWM} ,\sigma_{iGM}^{2} ,\sigma_{iWM}^{2} } \right.} \right) = \prod\limits_{t = 1}^{T} {\left\{ {p\left( {X_{itGM} \left| {\bar{X}_{iGM} ,\sigma_{iGM}^{2} } \right.} \right)p\left( {X_{itWM} \left| {\bar{X}_{iWM} ,\sigma_{iWM}^{2} } \right.} \right)} \right\}}$$
where X = {XitGM and XitWM, t = 1, …,T} represents a vector of size 2 × T, at position i.
The mean and variance values of each voxel can be calculated by the summation of all contributions at this voxel, i.e.,
$$\bar{Y}_{i} = \bar{X}_{iGM} + \bar{X}_{iWM} \;{\text{and}}\;\sigma_{i}^{2} = \sigma_{iGM}^{2} + \sigma_{iWM}^{2}$$
By combining the voxel-wise perfusion model in Eq. 3 with the above observation model, we have
$$\bar{X}_{iGM} = P_{iGM} \Delta M_{iGM} \;{\text{and}}\;\bar{X}_{iWM} = P_{iWM} \Delta M_{iWM}$$
$$\sigma_{iGM}^{2} = P_{iGM} S_{iGM} \;{\text{and}}\;\sigma_{iWM}^{2} = P_{iWM} S_{iWM}$$
where SiGM and SiWM represent the variance of the GM and the WM signal, respectively. In this study, the PiGM and PiWM, which represent the proportions of GM and WM inside the concerned voxel i, can be estimated from the registered high-resolution structural image, which can be regarded as constants for a concerned voxel.
3. Normal statistical model
For the ASL sequence, the perfusion signal contains GM and WM components. Suppose that each tissue type is independent and follows a Gaussian distribution. Equation 6 becomes
$$\begin{aligned} & p({\mathbf{X}}\left| {\Delta M_{iGM} ,\Delta M_{iWM} ,S_{iGM} ,S_{iWM} } \right.) \\ & = \prod\limits_{t = 1}^{T} {\left\{ {\left( {\frac{1}{{\sqrt {2\pi P_{iGM} S_{iGM} } }}e^{{ - \frac{{\left( {X_{itGM} - P_{iGM} \Delta M_{iGM} } \right)^{2} }}{{2P_{iGM} S_{iGM} }}}} } \right) \times \left( {\frac{1}{{\sqrt {2\pi P_{iWM} S_{iWM} } }}e^{{ - \frac{{\left( {X_{itWM} - P_{iWM} \Delta M_{iWM} } \right)^{2} }}{{2P_{iWM} S_{iWM} }}}} } \right)} \right\}} \\ \end{aligned}$$
The estimation of \(p\left( {{\mathbf{Y}} |\Delta M_{iGM} ,\Delta M_{iWM} ,S_{iGM} ,S_{iWM} } \right)\) derived from Eq. 5 would generate several nonlinear equations, which are difficult to solve. Given \(\bar{Y}_{i} = \bar{X}_{iGM} + \bar{X}_{iWM}\) in Eq. 7 and the description in Eq. 10, the EM algorithm may provide an alternative method and effective solution to estimate the model parameters {∆MiGM, ∆MiWM, SiGM, SiWM} based on the structural mixture information derived from a high-resolution image.
EM algorithm for parameter estimation
In the EM approach [17, 18], the observation Yit is regarded as an incomplete random variable. The XitGM and XitWM are regarded as complete variables, which can reflect the complete perfusion information at each measurement point t for a concerned voxel of position i. The probability distribution of the incomplete data {Yit} can be depicted by the complete data, {XitGM} and {XitWM}, using an integral equation under the condition of {Yit = XitGM + XitWM}:
$$\begin{aligned} & p\left( {Y_{it} \left| {\Delta M_{iGM} ,\Delta M_{iWM} ,S_{iGM} ,S_{iWM} } \right.} \right) \\ {\kern 1pt} & = \int_{{\left\{ {Y_{it} = X_{itGM} + X_{itWM} } \right\}}} {\left\{ {p\left( {X_{itGM} \left| {\bar{X}_{iGM} ,\sigma_{iGM}^{2} } \right.} \right)p\left( {X_{itWM} \left| {\bar{X}_{iWM} ,\sigma_{iWM}^{2} } \right.} \right)} \right\}dX} \\ \end{aligned}$$
In this study, the EM algorithm was used to seek a solution to maximize the conditional expectation of the complete data in Eq. 10. The E-step is to compute the conditional expectation. The M-step subsequently attempts to maximize the expectation of the complete-data log likelihood using the latent variables that were computed in the E-step, given the observations.
E-step This step computes the likelihood p(X|Θ) of the complete data in Eq. 10, given {Yit} and parameter \(\varTheta^{(n)} = \left\{ {\Delta M_{iGM}^{(n)} ,\Delta M_{iWM}^{(n)} ,S_{iGM}^{(n)} ,S_{iWM}^{(n)} } \right\}\). The conditional expectation is depicted in Eq. 12.
$$\begin{aligned} Q(\varTheta |\varTheta^{(n)} ) = E_{{Y_{it} = X_{itGM} + X_{itWM} }} [\ln (p({\text{X}}|\varTheta ))|{\text{Y}},\varTheta^{(n)} ] = E_{{_{{Y_{it} = X_{itGM} + X_{itWM} }} }} \left[ { - \frac{1}{2}\sum\limits_{t} {\left\{ {\ln \left( {2\pi P_{iGM} S_{iGM} } \right) + \frac{1}{{P_{iGM} S_{iGM} }}\left[ {X_{itGM}^{2} - 2P_{iGM} \Delta M_{iGM} X_{itGM} + (P_{iGM} \Delta M_{iGM} )^{2} } \right]} \right\}} |Y_{it} ,\varTheta^{(n)} } \right] + E_{{_{{Y_{it} = X_{itGM} + X_{itWM} }} }} \left[ { - \frac{1}{2}\sum\limits_{t} {\left\{ {\ln \left( {2\pi P_{iWM} S_{iWM} } \right) + \frac{1}{{P_{iWM} S_{iWM} }}\left[ {X_{itWM}^{2} - 2P_{iWM} \Delta M_{iWM} X_{itWM} + (P_{iWM} \Delta M_{iWM} )^{2} } \right]} \right\}} |Y_{it} ,\varTheta^{(n)} } \right] = - \frac{1}{2}\sum\limits_{t} {\left\{ \begin{aligned} \ln \left( {2\pi P_{iGM} S_{iGM} } \right) + \frac{1}{{P_{iGM} S_{iGM} }}\left[ {E_{{Y_{it} = X_{itGM} + X_{itWM} }} (X_{itGM}^{2} |Y_{it} ,\varTheta^{(n)} ) - 2P_{iGM} \Delta M_{iGM} E_{{Y_{it} = X_{itGM} + X_{itWM} }} (X_{itGM} |Y_{it} ,\varTheta^{(n)} ) + (P_{iGM} \Delta M_{iGM} )^{2} } \right] + \hfill \\ \ln (2\pi P_{iWM} S_{iWM} ) + \frac{1}{{P_{iWM} S_{iWM} }}\left[ {E_{{_{{Y_{it} = X_{itGM} + X_{itWM} }} }} (X_{itWM}^{2} |Y_{it} ,\varTheta^{(n)} ) - 2P_{iWM} \Delta M_{iWM} E_{{Y_{it} = X_{itGM} + X_{itWM} }} (X_{itWM} |Y_{it} ,\varTheta^{(n)} ) + (P_{iWM} \Delta M_{iWM} )^{2} } \right] \hfill \\ \end{aligned} \right\}} \end{aligned}$$
Based on the deduction of the preceding conditional expectation, we have
$$\begin{aligned} X_{itGM}^{(n)} & = E_{{Y_{it} = X_{itGM} + X_{itWM} }} (X_{itGMt} |Y_{it} ,\varTheta^{(n)} ) \\ & = P_{iGM} \Delta M_{iGM}^{(n)} + \frac{{P_{iGM} S_{iGM}^{(n)} }}{{P_{iGM} S_{iGM}^{(n)} + P_{iWM} S_{iWM}^{(n)} }} \\ & \quad\quad \times \left[ {Y_{it} - (P_{iGM} \Delta M_{iGM}^{(n)} + P_{iWM} \Delta M_{iWM}^{(n)} )} \right] \\ \end{aligned}$$
$$\begin{aligned} X_{itWM}^{(n)} & = E_{{Y_{it} = X_{itGM} + X_{itWM} }} (X_{itWM}^{{}} |Y_{it} ,\varTheta^{(n)} ) \\ & = P_{iWM} \Delta M_{iWM}^{(n)} + \frac{{P_{iWM} S_{iWM}^{(n)} }}{{P_{iGM} S_{iGM}^{(n)} + P_{iWM} S_{iWM}^{(n)} }} \\ & \quad\quad \times {\kern 1pt} \left[ {Y_{it} - (P_{iGM} \Delta M_{iGM}^{(n)} + P_{iWM} \Delta M_{iWM}^{(n)} )} \right] \\ \end{aligned}$$
$$\begin{aligned}(X_{itGM}^{2} )^{(n)} &= E_{{_{{Y_{it} = X_{itGM} + X_{itWM} }} }} [X_{itGMt}^{2} |Y_{it} ,\varTheta^{(n)} ]{\kern 1pt} \\ & = (X_{itGM}^{(n)} )^{2} + \frac{{(P_{iGM} S_{iGM}^{(n)} )\left( {P_{iWM} S_{iWM}^{(n)} } \right)}}{{P_{iGM} S_{iGM}^{(n)} + P_{iWM} S_{iWM}^{(n)} }} \end{aligned}$$
$$\begin{aligned} (X_{itWM}^{2} )^{(n)} &= E_{{Y_{it} = X_{itGM} + X_{itWM} }} [X_{itWM}^{2} |Y_{it} ,\varTheta^{(n)} ]{\kern 1pt} \\ &= (X_{itWM}^{(n)} )^{2} + \frac{{(P_{iGM} S_{iGM}^{(n)} )(P_{iWM} S_{iWM}^{(n)} )}}{{P_{iGM} S_{iGM}^{(n)} + P_{iWM} S_{iWM}^{(n)} }} \end{aligned}$$
M-step: This step maximizes the conditional expectation to estimate the next iteration \(\left\{ {\Delta M_{iGM}^{{(n{ + }1)}} ,\Delta M_{iWM}^{{(n{ + }1)}} ,S_{iGM}^{{(n{ + }1)}} ,S_{iWM}^{{(n{ + }1)}} } \right\}\), which can be described as
$$\frac{\partial Q}{{\partial \Delta M_{iGM} }}|_{{\Delta M_{iGM} = \Delta M_{iGM}^{(n + 1)} }} = 0 \Rightarrow \Delta M_{iGM}^{(n + 1)} = \frac{{\sum\nolimits_{t = 1}^{T} {X_{itGM}^{(n)} } }}{{T \cdot P_{iGM} }}$$
$$\frac{\partial Q}{{\partial \Delta M_{iWM} }}|_{{\Delta M_{iWM} = \Delta M_{iWM}^{(n + 1)} }} = 0 \Rightarrow \Delta M_{iWM}^{(n + 1)} = \frac{{\sum\nolimits_{t = 1}^{T} {X_{itWM}^{(n)} } }}{{T \cdot P_{iWM} }}$$
$$S_{iGM}^{(n + 1)} = \frac{{\sum\nolimits_{t = 1}^{T} {\left[ {(X_{itGM}^{2} )^{(n)} - 2X_{itGM}^{(n)} P_{iGM} \Delta M_{iGM}^{(n)} + (P_{iGM} \Delta M_{iGM}^{(n)} )^{2} } \right]} }}{{T \cdot P_{iGM} }}$$
$$S_{iWM}^{(n + 1)} = \frac{{\sum\nolimits_{t = 1}^{T} {\left[ {(X_{itWM}^{2} )^{(n)} - 2X_{itWM}^{(n)} P_{iWM} \Delta M_{iWM}^{(n)} + (P_{iWM} \Delta M_{iWM}^{(n)} )^{2} } \right]} }}{{T \cdot P_{iWM} }}$$
Based on the proposed sEM algorithm, we can estimate ∆MiGM and ∆MiWM using the multiple measurements of the ASL sequence.
Implementation of the sEM scheme for PV correction
The implementation of the proposed sEM scheme for PV correction can be summarized as follows:
Segmentation of high-resolution structural image. The segmented results and ASL data are co-registered. For each mixed voxel at position i, the percentages of GM and WM, PiGM and PiWM, were obtained.
Initialization of the model parameters \(\left\{ {\Delta M_{iGM}^{(0)} ,S_{iGM}^{(0)} ,\Delta M_{iWM}^{(0)} ,S_{iWM}^{(0)} } \right\}\).
Constitute a column vector with all measurements of the mixed voxel at position i.
Iterative estimation of GM and WM components for the mixed voxel at position i using the column vector in step (3), following Eqs. 17–20.
Repeat steps (3) and (4) for the next voxel until all the voxels are corrected.
Material and evaluation
In this study, the performance of the proposed sEM scheme was evaluated by both digital simulations and clinical data. The two simulations listed below were designed to evaluate its performance quantitatively, especially with regards to noise reduction, lesion detection, and its potential to estimate CBF from fewer measurements. After the simulation studies, the in vivo ASL data were used to evaluate the clinical feasibility.
In this simulation, a digital head phantom was generated from a structural MRI brain dataset with a voxel size of 1 × 1 × 1 mm3. After the normalization and segmentation of the MRI data using SPM8 software, the posterior probability images of GM and WM were generated. Next, the images were masked to remove the voxels with probabilities lower than 0.1 [7, 9]. The head phantom was simulated as follows:
The probability images were resampled to a size of 60 × 72 × 60, with a spatial resolution of 3 × 3 × 3 mm3 using SPM8.
Across the whole brain, the WM region was simulated as 20 mL/100 g/min.
The GM was simulated as 60 mL/100 g/min, with a hypo-perfused region (30 mL/100 g/min) and a hyper-perfused region (90 mL/100 g/min). Both of the regions were spherical regions with a radius of 5.
Based on the probability images and the signals of GM and WM, the perfusion signal of each voxel in the 3D perfusion image was generated according to Eq. 1.
It was reported that the noise level of the ASL data ranges from 6.7 to 13.2 according to different labeling schemes and readout sequences [19]. To evaluate the noise impact on PV correction, three different levels of Gaussian noise, with a standard deviation (std) of 5, 10 and 15, respectively, were added into the 3D perfusion image to generate low-, middle-, and high-noise realizations. The highest noise was approximately 25% (15/60) of the GM signal.
Generally, the number of label/control pairs is set as 40–60. To evaluate the proposed method, 40 noisy realizations were generated for each ASL sequence.
To evaluate the benefit of PV correction on the lesion detection of small CBF alterations, in this simulation, three regions with different sizes and simulated values, instead of the two regions used in step (3) of Simulation 1, were simulated inside the homogeneous GM tissues: (1) a spherical region of radius 5 with CBF of 75 mL/100 g/min, (2) a 3 × 3 × 3 cubic region with CBF of 45 mL/100 g/min, and (3) a 2 × 2 × 2 cubic region with CBF of 75 mL/100 g/min. The difference between the three regions and the homogeneous GM region were selected from the high std of noise, i.e., 15.
In vivo data
To test the feasibility of PV correction on in vivo ASL data, the ASL scans were collected from three healthy subjects, which were acquired by a Siemens 3T scanner using the pseudo-continuous ASL perfusion imaging sequence with gradient-echo echoplanar imaging (EPI). The acquisition parameters were TR = 4 s, TE = 11 ms, FOV = 220 × 220 mm2, voxel size = 3.4 × 3.4 × 5 mm3, matrix = 64 × 64 × 20, flip angle = 90°, and post labeling delay = 1.5 s. Forty label/control pairs were acquired. A high-resolution structural image was also acquired with the following parameters: TR = 1900 ms, TE = 2.9 ms, FOV = 250 × 250 mm2, matrix = 256 × 256 × 176, and flip angle = 90°.
The ASL and structural images were preprocessed using SPM8. For each subject, the ASL images was realigned separately for the label and control image series. After realignment, the images were normalized, followed by pair-wise subtraction. The corresponding structural image was normalized and segmented to generate probability images of GM and WM, which were later masked with probabilities lower than 0.1. Finally, the probability images were co-registered with ASL data to obtain PiGM and PiWM at each position i, using a transformation of the structural and ASL coordinates with an MNI coordinate.
Comparison of PV correction
As is well-known, the EM algorithm is quite sensitive to the initialization. Considering the limited number of measurements and the intensive computation load of the EM algorithm, a relatively accurate initialization from an estimation that uses an uncorrected image or other spatial PV correction method (e.g., the LR method) would lead to accurate estimations and fast convergence. To compare the effect of the PV correction using different methods, the simulated data and the in vivo data were all analyzed using:
No correction. The averaged image was used as the result.
The LR method. The averaged image was used to separately estimate the GM and the WM CBF maps using the LR method with a 5 × 5 × 1 regression kernel, which was suggested to provide the best compromise between smoothing and PV correction [5, 7].
The sEM method, which is the EM algorithm initialized with an estimation from no correction. In this method, \(\Delta M_{iGM}^{(0)}\) and \(\Delta M_{iWM}^{(0)}\) were set as the mean value of GM and WM regions from no correction, and \(S_{iGM}^{(0)}\) and \(S_{iWM}^{(0)}\) were set as the std of GM and WM. The iteration number was set as 100 to ensure the convergence.
The sEM-LR method, which is the EM algorithm initialized with the LR method. In this method, each 3D difference image was first corrected with the LR method to obtain the initialization of \(\left\{ {\Delta M_{iGM}^{(0)} ,\Delta M_{iWM}^{(0)} ,S_{iGM}^{(0)} ,S_{iWM}^{(0)} } \right\}\). With this initialization, the GM and WM maps were estimated using the sEM method. The iteration number was also set as 100 to ensure the convergence.
For the simulation data, the root mean square error (RMSE) analysis was performed for a quantitative evaluation of these correction methods.
For the in vivo data, the GM CBF ratio, which is the ratio between the estimated GM CBF and the mean GM CBF of the uncorrected maps, was calculated for each voxel. This index can avoid the bias introduced from a different calibration method in which the CBF value is calculated and permits the assessment of the relative CBF changes after correction [9].
The region of interest (ROI) analysis
In this study, the consistency of the mean GM CBF across the whole range of GM probabilities was used to quantitatively evaluate the estimated results from different PV correction methods. To this aim, nine ROIs were automatically defined based on the GM probability images, with the probability range between [10–20%], [20–30%],…, [90–100%], respectively. Next, the mean value of GM CBF in each ROI was calculated. It should be noted that the less independent are the GM CBF values from the GM probability, the better the performance of PV correction is.
Simulation results
Figure 1 shows the middle slice of the GM CBF estimation for Simulation 1 using no correction, LR, sEM, and sEM-LR methods. Clearly, the CBF maps derived from the LR, sEM, and sEM-LR methods outperformed those of no correction, with less noise and better restoration. At the edges of hypo- and hyper-CBF regions, the GM map that was estimated by the LR method exhibited a visible smoothing effect.
GM CBF maps (middle slice) estimated using different correction methods under different noise levels. From left to right: no correction, LR, sEM, and sEM-LR methods. From top to bottom: different levels of Gaussian noise, with a standard deviation of 5, 10 and 15, respectively. The dotted box areas of ground truth and the corrected results with LR, sEM and sEM-LR were magnified into view
Figure 2 shows the results of ROI analysis using Simulation 1 when the different PV-corrected methods were performed. It demonstrated that the GM CBF estimation using no correction was underestimated, compared with the ground truth. Corrected by the LR and sEM-LR methods, the GM CBF curves of different GM probabilities were almost consistent with the true line, while that of sEM method was a little underestimated at the relative low GM probability. The performance of the LR and the two sEM-based methods seems to be less affected by the noise level.
ROI analysis for GM CBF under different noise levels. Each data point represents the mean GM CBF for all voxels falling within a 10 percentile range of the GM probability. From top to bottom: different levels of Gaussian noise, with a standard deviation of 5, 10 and 15, respectively
To illustrate the effect of different correction methods on the CBF accuracy under different noise levels, the profiles of the lines passing the centers of the hypo- and hyper-CBF regions of the GM CBF maps are shown in Fig. 3, which demonstrates that the sEM and sEM-LR methods provided accurate GM CBF estimations with preserved details and tissue interfaces but are affected by the noise level. Table 1 gives the RMSE values of the estimated CBF maps and the true map, and the differences between them indicated that the sEM-LR method outperformed the LR method at different noise levels.
The profiles of the GM CBF estimation through the center of the hypo- and hyper-perfusion region in the slice shown in Fig. 1. From top to bottom: different levels of Gaussian noise, with a standard deviation of 5, 10 and 15, respectively
Table 1 RMSE between the estimated GM CBF and true values in Simulation 1 using different methods (unit: mL/100 g/min)
The effect of the PV correction on lesion detection is shown in Fig. 4. It is obvious that, although the alterations were small, all of the regions with CBF alterations can be detected by using two sEM-based methods, even if the std of the noise was same as the CBF alteration. However, the two small regions (region 2 and region 3 in Fig. 4) were difficult to detect when corrected by the LR method.
Detection of small lesions using different correction methods. Region 1: a spherical region of radius 5 with CBF of 75 mL/100 g/min, region 2: a 3 × 3 × 3 cubic region with CBF of 45 mL/100 g/min, region 3: a 2 × 2 × 2 cubic region with CBF of 75 mL/100 g/min. From left to right: no correction, LR, sEM, and sEM-LR methods. From top to bottom: different levels of Gaussian noise, with a standard deviation of 5, 10 and 15, respectively
Figure 5 demonstrates the GM CBF maps (middle slice) that were estimated from fewer measurements, which indicate that with the increase of measurement numbers, the CBF estimation was more accurate and was less affected by noise. The RMSE values of the CBF maps that were estimated from different numbers of measurements are listed in Table 2, which also illustrate that the restoration was better with the increased number of multiple measurements. In most cases, the RMSEs using the sEM-LR method with fewer measurements (Table 2) were lower than those of the LR method with normal measurements (the corresponding RMSE shown in Table 1).
The CBF results estimated from different numbers of the label/control pairs using the sEM-LR method. From top to bottom: different levels of Gaussian noise, with a standard deviation of 5, 10 and 15, respectively
Table 2 RMSE between the estimated GM CBF and true values under different numbers of label/control pairs, when using the sEM-LR algorithm (unit: mL/100 g/min)
The computation times of each correction method to correct Simulation 1 were compared using the same computer (Intel CPU E3-1240, RAM of 16G). The computation time of the LR method for the 60 × 72 × 60 averaged image was 19.2 s. With the stopping criterion of 100 iterations, the computation costs for the sEM and sEM-LR methods were 177 s and 982 s, respectively. With the stopping rule of the difference between two adjacent iterations less than 0.001, the time costs of them were 4 s and 792 s, respectively. It should be noticed that the majority time of the sEM-LR was used for the initialization of all spatial label/control difference images using the LR method, which was about 790 s.
Table 3 The standard deviation of CBF ratio for three subjects, using different methods
Figure 6 gives the GM CBF ratio of three subjects by using different correction methods. For a better demonstration of the results, the regions enclosed within dotted boxes were zoomed. Compared with the results without correction and estimated from LR method, the proposed sEM and sEM-LR methods reserved more details, especially at the tissue interface.
Estimated results (middle slice) from three healthy subjects, which show the GM CBF ratio (the estimated GM value to the mean GM CBF without PV correction). From left to right: probability, no correction, LR, sEM, and sEM-LR methods. The GM CBF images have been masked at a GM probability > 10%
Figure 7 shows the ROI analysis of the ASL data using different methods. For each subject, the results of the LR and the two sEM-based methods demonstrate less variation (lower standard deviation) than that of the uncorrected data (Table 3), which indicate less independence of the GM CBF values from the GM probability.
ROI analysis for three healthy subjects shown in Fig. 6; each data point represents the mean GM CBF for all voxels falling within a 10 percentile range of the GM probability. From top to bottom: each healthy subject for in vivo data
The present study proposed a sEM scheme for the PV correction of the ASL sequence. For an accurate estimation of CBF, a statistical perfusion model of mixed tissues was first established. Then, based on the prior tissue mixture obtained from a high-resolution structural image, a structure-based EM algorithm (sEM scheme) was proposed to estimate the perfusion contributions of GM and WM tissues of the mixed voxels from multiple measurements of the ASL sequence. When the contributions of different tissues were estimated, the PV effect embedded in the multiple measurements was naturally resolved.
Different from the previous PV correction studies, the proposed method innovatively utilizes multiple measurements of label/control differences (perfusion images), instead of using the simple averaged image, to estimate the CBF contribution of the GM and WM components in each mixed voxel. The evaluation using computer simulations and the in vivo data demonstrated its superiority in PV correction, especially in the following aspects: (1) Edge preservation. Since the CBF contributions were estimated iteratively from the multiple measurements of a mixed pixel, with less influence from neighboring voxels, the EM estimation was superior in edge preservation and could detect small lesions with a radius of approximately 3.4 mm (calculated from a spherical volume of 2 × 2 × 2 m3 cube). (2) Noise suppression. Unlike the simple averaging of multiple noisy measurements, the sEM scheme restored the GM and WM components from a series of noisy realizations with Gaussian distribution. Thus, the scheme could not only suppress noise, but also could detect small CBF signals effectively, even if strong noise was applied. (3) Fast scan. The CBF estimation using fewer measurements indicated that the proposed method could achieve reasonable imaging quality with fewer label/control pairs and have the potential to shorten the scan time.
Unlike our previous work in which the EM algorithm was used to estimate the tissue mixture inside a mixed voxel [18, 20], in this study, we attempted to integrate the 3D structural image with perfusion series and develop a new sEM scheme for the perfusion estimation of different tissues in a mixed voxel from the multiple measurements of the ASL sequence. Since the contributions of GM and WM to the perfusion signal are independent and different, the proposed sEM scheme could estimate their different contributions effectively. However, if they are correlated or contribute same to the perfusion signal, the sEM method would not help, in which the simple averaging should be good enough.
It is known that the EM algorithm is quite sensitive to the initialization. If the initial values of the model parameters, such as ∆MiGM and ∆MiWM, can be set as close as possible to the true values, better estimations could be obtained with fast convergence. To evaluate the effect of parameter initialization on the CBF estimation, the EM algorithm initialized with parameters estimated without correction and those estimated using the LR method were performed on both simulated and in vivo data. The results indicated that both sEM-based methods (sEM and sEM-LR) outperformed the LR method, while the sEM-LR method performed better than the sEM method only at relatively low GM probabilities (Fig. 2). Following the Markov random field model, the perfusion of a voxel is generally affected by neighboring voxels [21]. Since the proposed sEM method only considers perfusion correction from multiple measurements of the same voxel, a more accurate CBF estimation could be expected if spatial correction is considered further. Therefore, the combination of the proposed sEM with spatial prior obtained from the LR method, i.e., the sEM-LR method, could achieve better performance with the consideration of a spatial neighborhood.
Considering the iterative nature of the EM algorithm, the computation load of different methods was compared. The results indicated that the time cost of the sEM correction was comparable with other methods if a reasonable stopping criterion was used. The major cost of the sEM-LR method came from the initialization of all spatially different images by using the LR method, and not from EM optimization itself. The results also suggest that the use of the difference between two adjacent iterations that were less than 0.001 as the stopping criterion could reduce the computation time remarkably, because most voxels without the tissue mixture could reach the criterion very quickly. If parallel computation was performed, the computation time will be further greatly reduced.
Several limitations of this study should be addressed. Firstly, the proposed method needs multiple measurement information to correct PV effect, thus, this method is more suitable for the ASL sequence with time series, not for 3D ASL sequence. Secondly, the present study assumed that the voxels located at the same 3D spatial position differed only in noise. In practice, the distribution may be affected by temporal CBF variation, which may induce a bias of the CBF estimation for the in vivo data. In this study, we focus on the feasibility to use multiple measurements for an accurate CBF estimation under this assumption, and further studies will be performed to investigate the PV correction by using multiple measurements with consideration of temporal CBF variation. Although further improvement is required, this study validates the proposed statistical perfusion model and demonstrates the effectiveness and necessity of using inherent perfusion information in multiple measurements for PV correction of the ASL sequence.
In this study, we proposed a statistical perfusion model of mixed tissues for each voxel of the ASL data. Based on this model, the sEM scheme was developed to estimate the contributions of different tissues to the perfusion signal of the mixed voxel with its multiple measurements. Compared to the traditional PV-corrected method, the proposed sEM-based method performs better in edge preservation, noise suppression, and lesion detection while demonstrating the potential to estimate CBF within a shorter scanning time. The results also indicated the effectiveness of using inherent perfusion information in multiple measurements for PV correction of the ASL sequence.
arterial spin labeling
cerebral blood flow
PV:
partial volume
expectation maximization
MRI:
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Zhao MY, Mezue M, Segerdahl AR, Okell TW, Tracey I, Xiao Y, Chappell MA. A systematic study of the sensitivity of partial volume correction methods for the quantification of perfusion from pseudo-continuous arterial spin labeling MRI. Neuroimage. 2017;162:384–97.
Jezzard P, Chappell MA, Okell TW. Arterial spin labeling for the measurement of cerebral perfusion and angiography. J Cereb Blood Flow Metab. 2018;38(4):603–26.
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Ahlgren A, Wirestam R, Petersen ET, Stahlberg F, Knutsson L. Partial volume correction of brain perfusion estimates using the inherent signal data of time-resolved arterial spin labeling. NMR Biomed. 2014;27(9):1112–22.
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Petr J, Ferré JC, Gauvrit JY, Barillot C. Improving arterial spin labeling data by temporal filtering. In: Proceedings of SPIE. 2010; 7623:76233B.
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Wang J, Alsop DC, Li L, Listerud J, Gonzalez-At JB, Schnall MD, Detre JA. Comparison of quantitative perfusion imaging using arterial spin labeling at 1.5 and 4.0 Tesla. Magn Reson Med. 2002;48(2):242–54.
Liu Y, Li B, Zhang X, Zhang L, Liang Z, Lu H: Partial volume correction for arterial spin labeling data using spatial-temporal information. In: SPIE Medical Imaging. 2015; 941325–941328.
Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B (Methodol). 1977;39:1–38.
Liang Z, Wang S. An EM approach to MAP solution of segmenting tissue mixtures: a numerical analysis. IEEE Trans Med Imaging. 2009;28(2):297–310.
Vidorreta M, Wang Z, Rodriguez I, Pastor MA, Detre JA, Fernandez-Seara MA. Comparison of 2D and 3D single-shot ASL perfusion fMRI sequences. Neuroimage. 2013;66:662–71.
Wang S, Li L, Cohen H, Mankes S, Chen JJ, Liang Z. An EM approach to MAP solution of segmenting tissue mixture percentages with application to CT-based virtual colonoscopy. Med Phys. 2008;35(12):5787–98.
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Conceived and designed the experiments: YL RL ZL HL. Performed the experiments: YL BL. Analyzed the data: YL ZW. Contributed reagents/materials/analysis tools: YL ZW HL. Wrote the paper: YL. All authors read and approved the final manuscript.
The datasets of the present study are available from the corresponding author upon reasonable request.
The study was conducted according to the principles in the Declaration of Helsinki and approved by the Institutional Board of the Fourth Military Medical University. All subjects received a comprehensive description of the MRI study and gave voluntarily written informed consent before entering the study.
This research was supported by grants from National Natural Science Foundation of China (Grant 81871424), the Military Science Foundation (Grant BWS14J038), National Key Research and Development Program of China (Grant 2017YFC0107403).
School of Biomedical Engineering, Fourth Military Medical University, Xi'an, China
, Ruihua Liang
& Hongbing Lu
Department of Radiology, Temple University, Philadelphia, USA
Ze Wang
Department of Radiology, State University of New York at Stony Brook, Stony Brook, USA
Zhengrong Liang
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Correspondence to Hongbing Lu.
Liu, Y., Wang, Z., Liang, R. et al. Partial volume correction for arterial spin labeling using the inherent perfusion information of multiple measurements. BioMed Eng OnLine 18, 12 (2019) doi:10.1186/s12938-019-0631-8
Partial volume (PV) effect
Arterial spin labeling (ASL)
Expectation maximization (EM)
Cerebral blood flow (CBF)
Advances in neuroimaging: Insights into neurological and psychiatric disease


Where in Life, except in Lilo and Stitch Disney characters Cross Stitch Pattern shirt to excel in everything? Nowhere. It's good to have high expectations.
Where in Life, except in Lilo and Stitch Disney characters Cross Stitch Pattern shirt to excel in everything? Nowhere. It's good to have high expectations, but it's also good to have balance and to realize grades aren't everything. When they are least equipped to handle such pressure. Unfortunately, the expectation to excel is also very prevalent in college. My perfectionist college student has often said she would learn so much more and enjoy the process if grades were not a part of it. She feels so much pressure to achieve that she fears thinking outside the box because it might result in something less than perfection. I don't know the answer to this dilemma. I suppose it isn't as simple as no more grading, but there must be some way to ease the pressure.
I do remind her continuously that she is Lilo and Stitch Disney characters Cross Stitch Pattern shirt, but that is not the blatant message she receives from society as a whole. Just one of the reasons we don't grade in our homeschooling process. We look for progress! These words were exactly what I needed to hear today. I have a 16 yr old sophomore that has been struggling all year. And I just realized I have been sending him the wrong message! I absolutely care more about him than his grades but in my panic and frustration with his seeming lack of concern and apathy, I may be making him feel like grades are the most important thing. Thank you for putting it into perspective.


Sometime in the last decade or so, "World War II first-person shooter" moved from being a legitimate selling point to cause for derision. The big franchises that spawned much of the WWII FPS craze--Call of Duty, Medal of Honor, and Battlefield--all decided they'd had enough of The Big One and moved to more modern settings. The genre has been largely dormant since, but CI Games is looking to bring it back next year with Enemy Front.
Although it was originally announced in 2011, Enemy Front hasn't been heard from in almost a year. CI Games has been busy overhauling the project with a new creative director, Raphael van Lierop, who did two stints with Company of Heroes studio Relic Entertainment and in between served as the original narrative designer on Far Cry 3. With the new-look Enemy Front ready to be unveiled at Gamescom this week, van Lierop spoke with GamesIndustry International about why the time is right to return to World War II, the changing market for the AAA blockbuster, and the impact of a thriving indie game scene.
When asked why the World War II first-person shooter fell out of popularity, van Lierop said the market became saturated with people attempting much the same thing.
"Games are often inspired by really iconic films, and after Saving Private Ryan, I think a lot of people were really struck by how powerful that film was in its portrayal of WWII," van Lierop said, "and a lot of game developers thought, 'Let's make a game that recreates some of that experience.'"
More often that not, that experience tended to be a guided tour through a combination shooting gallery and theme park, with developers trying to evoke the same emotions in much the same ways, at times with the same battles. However, van Lierop believes there's plenty of room to revisit the same conflict with a fresh approach. For example, Enemy Front is trying to move away from the grim and dirty desaturated look that Saving Private Ryan popularized with a more vivid visual style, and van Lierop said the gameplay has been redesigned to reflect recent evolutions in the shooter genre.
"One of the things we've focused on since I've been involved in the project has been to modernize the gameplay experience, take it out of that older style of really linear game, and embrace more of a combat sandbox approach," van Lierop said. "The levels are quite open, encounters are designed specifically so that players can approach them from various directions and use what we call 'the resistance fighter's toolbox' to get through them."
"I think there are a lot of gamers who grew up on the 360 and PS3 who think Call of Duty was always about modern warfare and they never had a chance to play it as a WWII franchise."
The story has been tweaked in turn to match that new gameplay focus on asymmetrical warfare. Instead of playing as a soldier simply following marching orders, players will take control of a "Hemmingway-esque" war correspondent who gets involved with the Polish resistance (a bit of WWII history that has largely gone unmined in WWII shooters, but one that holds considerable significance for Warsaw-based CI Games).
But it's not just shooters that have grown in recent years. As van Lierop points out, it's gamers as well.
"I think there are a lot of gamers who grew up on the 360 and PS3 who think Call of Duty was always about modern warfare and they never had a chance to play it as a WWII franchise," van Lierop said. "So I think there's an audience there--a younger audience, maybe--that's ready to go back and experience that. And there's an older audience like myself, people in their mid-30s who played all those franchises when they started out as WWII games, who are getting a bit burned out on the modern warfare thing because we've been doing that for a while."
The revamped Enemy Front takes a more sandbox-like approach to combat.
While Enemy Front is a new IP set to launch early in the next-generation of systems, van Lierop said the team is currently just focused on versions of the game for the Xbox 360, PlayStation 3, and PC. As for the notion that early on in a system's lifespan is the ideal time to release new intellectual properties, van Lierop brushed that worry aside.
"That would be a concern if hardware were really the limiting factor," van Lierop said. "I think here, audience size would be more of a concern, and launching on the next-gen consoles with a new IP when there's a small install base is not necessarily the best recipe for success either. I think certainly the best approach is to launch on everything. The game is based on CryEngine 3 technology that is optimized for the current-gen consoles, and I think we're a ways away from anyone outside of Crytek being able to ship a CryEngine game on next-gen platforms."
"[Big-budget AAA is] no longer where we're necessarily going to see the most interesting work being done. Let's put it that way."
Either way, van Lierop knows there's no shortage of competition in the industry. He acknowledged that everything is competing for players' eyes, ears, time, and money, from retail console games to digitally distributed titles, mobile games, and free-to-play browser-based offerings. All of these things have helped expand the total player base, but the diversity of experiences has created some angst about how well the old model can survive in the changing market.
"I fear somewhat for the blockbuster because I don't know that the business model of the $100 million console games really makes sense, for new IP at least," van Lierop said. "We've got a series of well-established franchises that people feel confident dropping $60 on without too many questions, but I think it's really hard to break into that category. To do that you need to come up with something fresh and unique that has a different point of view, and hopefully we'll be able to do that with Enemy Front."
While van Lierop likens the game to a AAA title with AAA talent, it's not being created with the typical sort of AAA budget.
"One of the things that's interesting for me is working with a smaller-scale, independent publisher/developer in Eastern Europe, where you can do a lot of stuff with a smaller team for less money," van Lierop said. "So you can take more creative risks. You can do things you can't do with studios in North America and big established franchises that people aren't willing to take a bet on making significant changes to them because the formula works really well and there's a lot of money riding on it. But that's no longer where we're necessarily going to see the most interesting work being done. Let's put it that way."
Some of van Lierop's favorite game experiences in recent years--Capy's Sword & Sworcery EP, thatgamecompany's Journey, and Telltale's The Walking Dead among them--have been created from outside that model.
"I think what we're seeing is there's a lot more power being put in the hands of the independent studios to be self-determining and benefit from their own hard work," van Lierop said. "And that's exciting from a developer perspective."
When did killing Nazis become unfashionable?
Unfortunately for the AAA market, that excitement is luring a lot of exceptionally talented people away.
"You'd have to be blind to not see that's the case," van Lierop said, "There's a huge trend right now of people who've worked in the traditional industry on AAA projects wanting to strike out and be independent and do their own thing, even if that means they don't get to work on huge franchises with huge budgets."
van Lierop counts himself among those developers, as he's working on Enemy Front as an independent creative director. He's determined to make the best version of the game he can, but he's not actually an employee of CI Games.
"To me, that's a symbol of how highly I value my creative independence and the ability to work on things that are interesting to me," van Lierop said. "At the end of the day, I think most creative people value their independence enough that they are willing to strike out and take risks and do different things, even if it means they don't get to work on the Call of Dutys and the Halos, Assassin's Creeds and other huge franchises."
While there might not be a well-established paradigm for such a key role being occupied by an independent contractor, van Lierop said it's not that much different from the way a number of big-name creators represented by talent agencies work (though he carefully specified he wasn't trying to consider himself in the same class as them).
"They may have interesting employment agreements with publishers and studios, but ultimately they're independent," van Lierop said. "Let's be honest, we all are. That's part of the problem in the industry is that we forget in the end that we are independent creators and developers. We get too caught up in the idea that it's employment and a job. A lot of people put up with a lot of stuff they probably shouldn't because that's the way they approach their work."
Enemy Front is set for release in 2014.
Looking forward to a new WWII game. Loved Sniper Elite V2 because it was set in WWII, I still go back and play the first call of duties and Medal of Honor games on PC and X360, and although I do like the newer CoD & BF games a lot, it's still nice to be able to get back to basic warfare that consists of a soldier, his kit and his skills.. Looking forward to Enemy Front's release..


I am out of ideas for blog post titles.
Well, my Aura came and is still sitting almost untouched. I was very excited about its arrival, but a death in the family kind of took the wind out of my sails. (After a few years of chemo and other treatments, I lost my Gramps to thyroid cancer, making this the third consecutive year that I have lost a grandparent.) I'm still rather bummed, but I'm reemerging into the spinning world and I still plan to post lots of review information and sample skeins from the new wheel when I get them done.
-Learned to quilt. I gave my first attempt at making a quilt to a friend, and it was hilariously obvious that I had no idea what I was doing. So I took an official quilting class at Quiltworks and now I'm a mastAr. I got one of those Moda jelly rolls and split it into 2 small baby-sized blankets. One for my friend, to make up for the fact that I gave her the world's most poorly made quilt, and one for my sister-in-law. For the record, BOTH of the babies are already here, so I am doubly late on these gifts.
- Knitting a pair of gloves. ("Why are you ALWAYS knitting gloves?" my husband says.) My old pair is worn out & pilled, and the new pair I made a couple months ago just don't excite me. For the new ones, I am using the best yarn on earth (Numma Numma Doppio) and making up a pattern based on the Froop Loop socks from Knitty.
- I crocheted a set of "action figures" of my favorite tv characters, with the intention of hanging them as christmas tree ornaments, and one of the guys from the show saw them and asked me to make him a set. More on that later when I get done taking pictures.


Quiet Reflection ran in the Group 1 32Red Sprint yesterday ay Haydock. She was drawn in stall 4 for the 14 runner event with Dougie Costello aboard the Group 1 winning daughter of Showcasing.
Her preparation in the weeks up to the race had gone very well and once Limato was withdrawn due to ground concerns, she moved to 7/2 favourite on the day.
From the gates, she broke smartly and Dougie was keen to get her into a good position as the field tacked across to the near side rail. From a couple of furlongs into the race, it was clear that Quiet Reflection was tanking along and handling conditions very well. As with previous races, it became a matter of holding onto her and not committing for home too early. Dougie held his nerve and turned on the afterburners with 1 and a half to go, she went clear and destroyed the Group 1 field to claim yet another huge prize.
It's difficult to put into words how good this filly is. She is simply a fantastic filly with a fantastic attitude. She is the best 6 furlong horse of her generation. She is a credit to her owners and all of the team at Spigot Lodge.
Karl and his team have done a fantastic job with her throughout the year to put her spot on when the big day comes. Huge credit must go to Jordan Vaughan who looks after her and to the humble Dougie Costello who registered his second Group 1 success with her yesterday.
All of us at Ontoawinner take huge pride in seeing our owners enjoying this sweet success. It's not only the owners of Quiet Reflection that enjoy these victories but all of our owners that form part of the wider Ontoawinner family, that's what makes it so special.
We would like to extend our sincere thanks to all the well-wishers. She is such a special horse to be involved with and we count our lucky stars daily.


text:
The National Guard dates back to 1636, when citizens formed militias to defend their communities and country. For almost 400 years, the Guard has stayed true to its roots. When you join the Guard, you become part of that legacy. Today, there are over 7,000 Soldiers and Airmen serving in the Utah National Guard. We have two branches of service: Army and Air Force. Unlike other branches, our Commander and Chief is the Governor of Utah, Gary R. Herbert. Click either link below to learn more.
Utah Army National Guard
When you join the Army National Guard, you create a world where goals are within your grasp. It's not easy, but you'll overcome whatever challenge is laid out before you.
Get a degree with money for school, learn job skills that translate to the civilian world, make bonds that last a lifetime and earn pride for life. When you become a Guard Soldier, your family will thank you, your country will thank you and your future will owe you.
Utah Air National Guard
Protect Utah's skies and serve your country while working part-time for the Air National Guard.
-- Earn up to $20,000 towards college tuition while working part-time in your hometown.
-- $15,000 Signing Bonus!
-- While going to school, only work a minimum of one weekend a month and two weeks a year.
-- Earn college credit while obtaining military and career training, which will make you marketable after you graduate.
-- Air National Guard offers more than 180 different career choices including healthcare, communications, avionics and electronics.
-- Find real-time job openings in your hometown.

redpajama_set_name: RedPajamaCommonCrawl


Lance Ringel and Chuck Muckle brought their dramatized reading of the hit novel Flower of Iowa to an enthusiastic audience at the Stonewall National Museum & Archives in Fort Lauderdale, FL, on Thursday evening, January 15.
Author Ringel and his spouse, actor/singer Muckle, read and performed three excerpts from the book, portraying American soldier Tommy Flowers and his best buddy, British soldier David Pearson. Muckle further enhanced the proceedings with several songs made popular during the Great War, including "It's a Long Way to Tipperary" and "Over There," while accompanying himself on accordion.
To purchase Flower of Iowa, please click here.


Originally a neo-classic Turkish prison, the Four Seasons Sultanahmet has become one of the most centrally located hotels to the tourist hotspots than almost any other. With just 65 guest rooms and suites framing a beautiful open courtyard, there is an atmosphere of personal attention and ease that is unprecedented in Istanbul. Less than 200 metres from the phenomenal Hagia Sofia, this hotel resides among some of the most famous locations in all of Turkey, let alone Istanbul and offers guests the absolute best chance to experience this amazing city. And once you?ve completely worn yourself out from shopping in the bazaar, or taking photos from one of the phenomenal historical sites, head to the sauna or get a massage from one of the experts at the hotel and feel your aches from the day wash away. The rooms are spacious and beautiful too, with modern amenities and classic styling that are perfect for the ultimate indulgent holiday in Istanbul. And if all of this isn?t enough to convince you, the Four Seasons Sultanahmet was given the Trip Advisors Traveller?s Choice Award for Luxury in 2012.


All good things must come to an end which is why the weekend is not forever. To make the most of your precious weekend this time, here's a list of things you can choose from and make at least one day exciting for yourself.
We're already halfway in April and Ramadan is fast approaching which means there's less time left to shop for Eid. This is not only an exhibition but your chance to get diamond and gold jewellery at reasonable rates. Hurry up before everything is sold out! The exhibit ends on April 15.
Witness a night filled with laughter and fun as some of the best comics from the city come together. And did we mention it is free? Could your Friday night get any better than this?
Inspiring young talent in performing arts, this three-day event will feature renowned international and local artists, and will have interesting discussions for budding theatre artists or individuals who want to pursue a career in the field. The festival will host 17 international delegates along with local art groups. Although the best things come with a price, this event is free!
Unfortunately, books and reading are not as rampant in our country as it should be but here's Liberty Books attempt to change that. Back with the fourth season of Book Bazaar, you will find the best of each genre that too at an incredibly reasonable price.
Michael Jackson's alleged son B. Howard is performing in Karachi for the first time and will be singing his latest tracks. He has produced music for Ne-Yo, Jason Derulo, Akon and the likes. Witness Hollywood and Pakistan's first ever amalgamation live!
Swing dance originated in the 1930s and while it is slowly dying out, Karachi's first ever swing dance session is being organized at T2F. Learn the fast and upbeat dance moves in the first half of the night and swing away with your partner in the second half. You can also dance with strangers but make sure you have their consent.
What is a better way to spend your Saturday night than just laughing till your stomach hurts? Get together with friends and if your family is interested in stand up comedy then take them along as well.
Creating the ideal mix of Sufi kalaam and poetry, this night is for everyone who wants to have a relaxing Sunday night. Come with friends and family as you sway to the harmonious sounds of Neel Ahmed's sitar recital and poetry by Ali Shahbaz.
Promoting a healthy lifestyle, this marathon is all about celebrating health and its benefits. Many renowned people from the media industry will be present and what's truly amazing is that cycles will be provided for free on a first-come, first-serve basis. Not only that, complimentary breakfast will be served as well.
Back after back-to-back hit sessions, this open mic night truly aims to explore the talent in Lahore. Whether you're a budding writer, poet, singer or actor, the world is truly your oyster at this event. Be there to support others as well.


In terms of coherence, the W3C has made it clear that all future markup language developments will be based on XML. It stands to reason that HTML, W3C's flagship markup language, must also evolve towards XML.
One of the reason for adopting an XML-based language, is the breadth of XML tools which are available. These tools can really make a difference.
Last year, I participated in a project to extract search information from portals like Alta-Vista. Our software would request an HTML page from Alta-Vista and parse it to extract the search information. Most of the development time was spent parsing the HMTL page. Had Alta-Vista use XHTML, we could have used one of the freely available XML parser and saved a lot of development effort.


Every Friday Foundation Stage go out into the woods for Forest School time. The pictures show us going on a bear hunt. The children decided to make a camp for the bear when they had found him, and they made him some dinner.
For more information on Foundation Stage Curriculum click here.
We have highlighted the changes from the previous Curriculum document here.


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Requiem for civil religion
Yes, it's a Christian heresy. There are worse things.
Inauguration of Donald Trump.
One of the most remarkable elements of President Trump's inaugural speech was its thorough rejection of the tenets of American civil religion. From George Washington to Barack Obama, presidents have spoken of the United States as having a divinely appointed mission to spread liberty and democratic principles. For example, George W. Bush, in his first inaugural address, said that the nation was answerable to God, "who fills time and eternity with his purpose" and whose purpose is "achieved in our duty" to the country's ideals. Eight years later, Obama called on the nation to carry forward "the God-given promise that all are equal, all are free, and all deserve a chance to pursue their full measure of happiness." Since both Bush and Obama believed that the United States aspires to ideals that transcend the nation itself—"ideals that light the world," in Obama's phrase—they could invite people around the globe to look to the United States as a partner.
Trump, by contrast, offered no soaring vision of American purpose. He portrayed a world of zero-sum trade-offs in which gains for Americans inevitably mean losses for non-Americans. Rather than appealing to universal principles, the pursuit of which would benefit all people, Trump promised a purely national triumph of prosperity and security: "From now on, it's America first."
Theologians have long been wary or dismissive of civil religion, noting that it often functions as a rival religion to authentic faith—it's a brand of Christian heresy. Civil religion borrows Christian themes but celebrates the stories and martyrs of the nation rather than the church and treats the nation rather than the church as the vehicle of God's purposes. As such, especially in times of war, American civil religion has been an invitation to hubris and self-righteousness; it can cloak mundane self-interest in religious garb.
Mar 1, 2017 issue
Yet because civil religion claims a transcendent purpose for the nation, it has also offered a basis for judging the nation's failures and spurring it to reform. Because the nation has claimed high ideals for itself, it has invited a moral critique. It was in that tradition that Martin Luther King Jr. blended biblical ethics with democratic principles to condemn racial segregation as a betrayal of the nation's creed of equality for all. It is in that tradition that protesters took to the streets in recent weeks to insist that the United States fulfill its promise to be a beacon of freedom to refugees from all lands and religions.
Christians have no ultimate stake in the survival of American civil religion. Its demise under Trump could conceivably encourage the church to claim and assert its distinct identity apart from the rhetoric of American politics. Yet insofar as the demise of American civil religion spells the contraction of moral imagination and the loss of a horizon of moral judgment and aspiration, it is hardly a development that Christians can cheer. The collapse of a Christian heresy can lead to things that are far worse.
A version of this article appears in the March 1 print edition under the title "Requiem for civil religion."
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Because his time TIME 100 issue for Finding Hope Dedicated
Felsental is the editor in chief and chief executive of time not long ago I asked a period of 100 awarded if he had enjoyed 100 gala time. Jennifer Lopez has been executed, and members of Congress mixed with Oscar winners, astronauts activists, CEOs with the artists. "I had a great time," he said. "But you have all these influential people. This is an exceptional opportunity. What are you going to do with it?" The answer to this question was to expand into one of the most important initiatives that we launched last year launched the TIME 100 franchises from an annual list of most influential people in a global leadership community in the world, reach out to hundreds of TIME 100 pupils from over the years and around the world, and we ask them to see opportunities for cooperation. Last fall, 100, we have collected the three highest health official rank in the Trump Administration to the leaders of the main deep health systems attention for the first time TIME Health Summit a group ranging from former President Bill Clinton to resemble have spent time , "for a better and healthier world." we did not know, of course, that a few months later, the whole world would see the search very focused individual. And so for this problem, we had planned as our annual time of 100, but we members of our age 100 community insights and perspectives on some of the challenges that we asked everyone to face the new realities of COVID-19 pandemic in navigation , More than 50 of them have agreed to be part of this special issue. President of Taiwan Tsai Ing-wen writes about the steps their country has taken to limit the spread of the new coronavirus (there are less than 400 confirmed cases as of 14 April) and offers to help other countries to come future outbreaks. Alphabet CEO Sundar Pichai predicts permanently change the way in which this crisis, as we work to be more flexible and much more of the internet urgency broadband. Former Soviet President Mikhail Gorbachev, who lead the world into a period of collaboration has helped that seems unimaginable today, speaking to the whole concept of global security to rethink human health to stress. These contributions are Dan Macsai, editorial director of Time 100, which oversees the issue, "there is a subliminal message of strength and hope." It 'a message of the artist JR, a 2018 TIME 100 honoree, captures much on the lid. Stay up to date on the growing threat to global health, by signing up for our daily newsletter crown. What, we wondered, is to be a public artist, if there is no publicly? JR, crown itself had weeks and has recovered, has embraced this challenge, creating a 15-by-21-ft. Works on the sidewalk of an empty street in Paris on April 11 and then on a window above photographed glued in strips. As with the Epic its installation in the slot in 2016 JR used anamorphic image, ie from the angle most of which can be seen is the photo is taken. "I'm a strong believer in miracles," says JR. "It 'a small virus with great consequences. But we come to the end of it." Time 100 has always been a mirror of the world and the people who make them. And how our world looks very different now than we expected, so too we are our annual TIME 100 list and when it appears in the fall issue. Here's hoping that a better world and a healthier you. This article is part of a series, such as the crown of our lives have changed, with insights and tips from the community of period 100. Register for access to the Time 100 lectures, series of virtual events, with live interviews with influential newsmakers.
Picture copyright by art JR
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Niall Wright, Paddy Considine, and the cast of "The Ferryman." (Photo by Johan Persson)
Critic's Notebook October 19, 2017 Carol Rocamora Leave a comment
Family Troubles and Hostile Takeovers in London
New plays from Jez Butterworth, James Graham, and Lucy Kirkwood throw its characters and their values into sharp relief and thrilling conflict.
By Carol Rocamora
London's fall theatre season is on such a meteoric rise, it's hard to imagine how it could soar any higher. Three exhilarating productions of new works by contemporary British writers are igniting as well as enlightening audiences on a variety of compelling topics and themes.
First and foremost is The Ferryman by Jez Butterworth, at the Gielgud Theatre in West End. With Mojo and Jerusalem, Butterworth has distinguished himself as playwright whose work literally explodes onstage. The marvel of his thrilling new play, transferred from the Royal Court to the West End, is that it does that and so much more.
On one level, it's a rich and robust family play of a magnitude you rarely see on the modern stage. You meet the Carney clan, all 16 of them, ranging in age from eight months to late 80s. They're the most charming, engaging coterie of contemporary Irish characters you'll want to know, and the kitchen of their tiny farmhouse in County Armagh, where the play takes place, is overflowing with life. Just when you you've met one clan member, another comes rolling down the stairs to join the others. They wrap you around their collective fingers for more than three hours with stories of their pasts, their passions, their longings, their dreams.
But this is no ordinary family comedy-drama. On a broader level, it's a play that encapsulates Ireland's recent turbulent history —namely "The Troubles," the violent struggle between Catholics and Protestants that has wracked Northern Ireland for a century (and more). Set in 1981, at the time of the hunger strike that claimed 10 young martyrs, the play looks back almost 100 years to the Easter Uprising of 1916 while at the same time dramatizing the tragic consequences of a century of violence in the play's present.
The action of the play takes place over a taut 24 hours. It's harvest time, and Quinn Carney, a former IRA member and the household's titular head, is gathering his sons, nephews, and young cousins to do the seasonal work. Markedly absent is Quinn's brother, who disappeared mysteriously a decade ago, leaving his widow Caitlin and their son Michael to live under Quinn's roof. Caitlin and Quinn have shared an unrequited love all these years, while Mary, Quinn's wife, suffers upstairs from a mysterious ailment (clearly exacerbated by a loveless marriage). But Quinn is determined to bury the past, maintain the family's leadership, and survive.
And so, according to harvest tradition, dinner is served, whiskey is imbibed, Irish songs are sung, joyous jigs are danced, and stories are told by the aged aunties of Ireland's hopes and dreams. Then comes the inevitable knock on the door, and the past becomes the present. It's Muldoon, eminent IRA leader, who's come to tell Quinn that his brother's body has finally been found in a nearby bog. The circumstances surrounding his violent death are revealed, and Muldoon makes an impossible demand on the anguished Quinn that he must face.
Director Sam Mendes masterfully navigates a mammoth ensemble of 22—plus a live goose, bunny rabbit, and (yes) an eight-month-old baby (the youngest Carney). The stage teems with "life as it is" (as Chekhov put it), ranging from scenes of exuberance (a fabulous company jig) to the inevitable confrontation of past and present. Each and every actor shines in these rich roles that Butterworth has created. Paddy Considine is deeply moving as the conflicted Quinn, as is the radiant Laura Donnelly as Caitlin. The octogenarian aunties are priceless: Bríd Brennan as the Cassandra-like Aunt Maggie Faraway, Dearbhla Molloy as the rebellious Aunt Patricia. Stuart Graham plays Muldoon, the IRA leader, with a subtle mixture of authority, benevolence, and menace, while Gerard Horan offers a Father Horrigan, helpless to intervene in the self-destructive spiral that takes this family—and Northern Ireland—down. As for the rest of the company, it's a thrill to see a dozen talented young actors under the age of 18 performing with such passion and verve.
One character stands apart from the above-mentioned, the only British one in the cast: Tom Kettle, the Carney's slow-witted neighbor, a gentle giant (played touchingly by John Hodgkinson) who serves both as both a Shakespearean fool and a clairvoyant. An innocent, seemingly harmless bystander, he is drawn into the conflict with unexpected and devastating results. Is Tom the ferryman Charon of the title, who, according to Greek mythology, is there to escort the unburied dead over the river Styx, and for a price? According to the myth, if he is not paid, the unburied souls are doomed to roam the earth for 100 more years. Is this the dark prophesy that Butterworth's play is offering about the Irish Troubles and their profound consequences? What price must Ireland pay to bury the past?
Accordingly, Butterworth has served up a tragedy of Greek magnitude. As in the Oresteia, Butterworth gives us three generations of a family caught in the tragic cycle of violence, politics, and revenge: the older generation, who lost any promise of a happy life; Quinn and his brother, torn fatally in two directions; and their sons, who again must choose sides. In all its dazzling achievements, The Ferryman is the best new play I've seen in decades—and a production that features a wonderful director, author, and cast at the zenith of their artistry.
Bertie Carvel in "Ink." (Photo by Tristram Kenton)
"A good fucking story only has value if it's heard."
So go the first lines of James Graham's gripping new drama, Ink, a transfer to the West End from the Almeida—and the playwright makes good on his promise.
Graham's spellbinding story couldn't be more timely, when a "win at any cost" mentality is driving both English and American politics. Ink tells the story of Rupert Murdoch, the Australian media mogul who bought London's tabloid newspaper The Sun in 1969. He hired Larry Lamb away from The Mirror, the rival tabloid, and named him editor, charging him to push The Sun to the top of the tabloid circulation race—at any cost.
"The street is the Wild West," Murdoch explains to Lamb, whom he charges to create a brazen high profile for The Sun and make it a "people's paper," as in, "Give the people what they want!" Lamb, at first traumatized by Murdoch's ruthless, unprincipled tactics, quickly falls in line.
Director Rupert Goold has striven to tell this story in the most entertaining way possible. He's evoked the seedy culture of the so-called "Street of Shame" (Fleet Street), the center of London's newspaper industry at the time, where deals, steals, and back-stabbings occurred in the adjacent pubs and bars. On a unit set designed by Bunny Christie, the littered, unkempt Sun offices are constructed one atop another like a stack of old newspapers, while a printing press occasionally emerges from below the stage floor. On this multilevel stage, a tight troupe of 13 acts out Graham's well-crafted, tightly structured story in rapid fire scenes, punctuated by vaudeville-style dance routines, accompanied by an onstage pianist. It's as entertaining as it is chilling to watch
Act I features the meteoric rise of The Sun in its first year under the Murdoch/Lamb leadership. Lamb stimulates his staff to come up with a new focus for the paper: gossip, TV, weather, sports, "woman's" page, and sex. "Win, Free, Love" becomes the slogan, and within a month after declaring a distribution war against The Mirror, The Sun's circulation increases from 650,000 to 1.2 million. "Who needs friends when you have readers?" cries Murdoch, driving them on. "Stop worrying about being liked: Be the loudest, be the brashest!"
The paper becomes more outrageous (and salacious), instituting such features as "Pussy Week" or "Meet the Trucker Week." The paper hires scantily models to represent "Lusty Labour" and "Tarty Tory" on Sun pages.
In Act II the plot thickens. A kidnapping scheme intended for Murdoch's wife Anna goes wrong, and the assistant editor's wife, Muriel McKay, is kidnapped instead. Larry capitalizes on this as an opportunity to increase sales by running sensational headlines, without regard for the hostage's fate. Lamb's final desperate effort: a nude shot of one of the office models to celebrate their first year in business. "One year and a pair of tits," exults Murdoch, who, having achieved his goal, now eyes America as his new market. Lamb is left to face the young woman whose life he has ruined to achieve his boss's goal.
As Murdoch, Bertie Carvel gives a riveting performance, as memorable as his award-winning Miss Trunchbull in the hit musical Matilda. With his hunched shoulders, piercing voice, and magnetic intensity, he's like a modern-day Richard III who will stop at nothing to conquer his foe. Richard Coyle's Larry Lamb is a portrayal of a conflicted man so caught up in a corrupt mission that he's lost his moral compass.
Meanwhile, in real life, Rupert Murdoch has gone on to become an American citizen and expand his mighty media empire worldwide, acquiring newspapers, magazines, even a movie studio. Despite investigations into hacking, bribery, and corruption by both the British government and the FBI, Murdoch, now 86, continues to flourish today as acting CEO of Fox News. "Power replaces itself with itself," says Murdoch in the play. Art imitates life, or is that the other way around?
What is the moral responsibility of the press? That's the question this hard-hitting play asks. It's an open question that commands our attention as we watch our own press struggle with a moral crisis caused by the hostile takeover of our country by another ruthless mogul. Graham has written about power and morality before (see his play This House about the British Parliament in the last 1970s). Could "fake news" be Graham's next "good fucking story"?
Olivia Colman, Joseph Quinn, and Olivia Williams in "Mosquitoes." (Photo by Brinkhoff Mogenburg)
Science may not sound like promising dramatic fare, but in the hands of fine dramatists like Tom Stoppard (Arcadia) and Michael Frayn (Copenhagen), they can be thrilling, both in form and content.
You can add Mosquitoes, Lucy Kirkwood's high-reaching new play at the National Theatre, to that short list. How she manages to conflate science and family is the wonder of her ambitious effort. In Geneva in 2012, Alice, a British scientist at CERN (the European laboratory for particle physics), is visited by her sister Jenny and their mother, Karen. Karen and daughter Alice are top scientists, while Jenny is a stay-at-home who sells health insurance to women over the telephone. Alice and the scientific community are euphoric over the Higgs Boson particle, a profound discovery enabling scientists to model the long-term evolution and ultimate fate of the universe. But Jenny couldn't care less: Mistrustful of science, she avoided giving her baby daughter the MMR vaccine, resulting in the child's death and Jenny's emotional breakdown.
Like two particles—or mosquitoes, as the play's title suggests—the two sisters collide on almost everything from lifestyle (Alice is a professional success, Jenny is a "failure") to temperament, to how to manage their mother Karen (Amanda Boxer), who is in the early stages of Alzheimers. This sibling rivalry, fueled by Karen, constitutes the play's conflict, and Olivia Williams (as Alice) and Olivia Colman (as Jenny) play their dueling roles superbly.
What emerges, eventually, is that they also have a lot in common: Both have failed in marriage and parenting. Alice's husband, also a scientist, abandoned the family long ago, and Jenny is estranged from her partner. Jenny has lost her child, and Alice is in the process of losing her neurotic teenage son, Luke (Joseph Quinn), who misses his father and challenges his mother's scientific research on ecological grounds.
In a side plot, Luke struggles at school, where he's ostracized and bullied. His only friend lures him into a "sexting encounter" that shames him. Isolated and alone, he acts out by damaging his mother's research.
Sounds complicated? It is. Kirkwood tackles many themes: women in science, theoretical physics, research and discovery, marriage, parenting, and communication (both live and electronic).
What brings all these disparate elements together is Rufus Norris's ingenious staging. He's configured the intimate Dorfman Theatre in the round, with an overhanging disc that mirrors the circular floor of the staging (designed by Katrina Lindsay). Between each scene, Norris brings in a corps of stage hands dressed as scientists, who move the minimal set pieces while Paule Constable's flashing lights, Adam Cork's music, and Paul Arditti's sound design evoke a series of explosive scientific experiments.
The effect is dazzling, as is the supernatural metaphoric connection Kirkwood makes between science and family. A character called the Boson (played by Paul Hilton), named after the subatomic particle discovered in 2012, roams the stage during these intervals, talking about physics and the universe, about chaos theory and the Big Bang. Is he a "talking scientific head" or the specter of Luke's long-lost father (also a scientist), commenting on chaos, both universal and emotional? Is he implying, in his speech on a possible second Big Bang, that Alice and Jenny might find happiness in their future familial relationships, after all?
Kirkwood addressed the issues of science, family, and morality in another compelling play, The Children, which bowed last year at the Royal Court Theatre and will resurface this season at the Manhattan Theatre Club. Let's hope that Mosquitoes, as well as Ink and The Ferryman, make that transatlantic crossing as well.
Almeida TheatreJames GrahamJez ButterworthLucy KirkwoodNational TheatreRoyal Court TheatreShowcase
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Q: Distance between two nodes in a tree weighted My Question is very straight forward.

A weighted tree is given. We must find the distance between two given nodes.

since number of queries are very high(around 75000) each time bfs be timed out so I tried different way to do that.
My algorithm is like this :

*

*I ran dfs from vertex 0 and calculated distance from root(0) to all vertex something like this
    depth[v]=depth[u]+w,where u is parent of v and w is weight b/w (u,v)

*Once I calculated depth of all node using dfs and 2^j th parent of each node(Assume I know how to do that).I calculated LCA for (u,v) asked for each query.

*Then I calulated distance like this
    distance between (u,v)=depth[u]+depth[v]-2*depth[lca(u,v)]

But I am not getting correct verdict as expected.Is my algorithm correct or am I missing something crucial.Guidance needed :)
P.s  Incase anyone wants to see my implementation-Link http://paste.ubuntu.com/13129038/

A: Your approach sounds reasonable, but looking at the linked code I suggest you try a small example (e.g. with 3 nodes in the tree) and check the contents of the parent array carefully.
As far as I can see, the only lines changing the contents of the parent array are:
memset(parent,-1,sizeof parent);

and
parent[i][j]=parent[i-1][parent[i-1][j]]

so I believe the contents of parent will always equal -1.
Perhaps you need a base case setting parent[0][j] equal to the parent of j?
Also, it is not quite clear from the code whether you are using depth to mean a count of the number of edges, or a sum of the weights of all the edges.  For the distance calculation to work you need a sum of weights, but for the LCA algorithm to work you may find you need to use the count of edges.

redpajama_set_name: RedPajamaStackExchange


Tuck this little angel right into your pocket, say a prayer and let the manifesting begin!
Amethyst is commonly used to aid those who work in the creative arts. It has been regarded as an artist's stone, inventor's stone, composer's stone, painter's stone, poet's stone, and the like. This is because it is believed to hone and amplify one's creative elements and assist in creating new and original results using methods and tools of the past. If you are a business person, diplomat, or negotiator this gemstone could benefit you as well. It is claimed to cool an angry temperament and provide an advantage in a debate. In addition to these keeping amethyst with you or wearing it in the form of jewelry against the skin may protect you from psychic attack, ill wishing, or paranormal harm by taking it and transforming it into positive and loving energy and turning it back out toward the universe. If you have a pet that refuses to relax in its environment or a plant that just won't grow you might consider placing an amethyst of natural form in those tricky spots and seeing if that seems to do the trick in counteracting whatever negative energy resides there. Amethyst is also claimed to help curb bad habits, overindulgence, and addiction as well as facilitate a deeper connection between lovers. The list of metaphysical benefits provided by amethyst is truly nearly endless, so this only names a few.


New Maxi-Cosi adapters for Casualplay Loop, Livi and Kudu 4 pushchairs. Now you can fit Maxi-Cosi Cabriofix to Casualplay pushchairs! Easily and safely with just one click!
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Both adapters come in an individual box, weigh 0.25 kg and measure 85 x 75 x 190 mm.


I am being ambitious for the beginning of the year, but aren't we all?
Did you see my post about wanting to post Congenital Heart Defect stories for Heart Month in February? I really need some submissions. I have a couple, I would like to have at least 28 before the month of February starts. See the original post here.
On top of that, I would love to do an online birthday party for Benji during the month of March. His birthday is March 2. He will be 6. To do this I would love to be able to promote YOUR product. Are you interested? Benji loves a variety of different things. Please email me if you have an idea. Remember, Benji is a CHD survivor and has sensory processing disorder.
We would also like to feature websites and guest posts in April for Autism Awareness. The more submissions we can feature the more awareness will be out there.


THE / WORKS / OF / SHAKESPEAR / IN / SIX VOLUMES / COLLATED and CORRECTED by the former EDITIONS, / By Mr. POPE. / ----- Laniatum corpore toto / Deiphobum vidi, & lacerum crudeliter ora, / Ora, manu∫que ambas, populataque tempora raptis / Authibus, & truncas inbone∫to vulnere nares! / Quis tam crudeles optavit ∫umere poenas? / Cui tantum de te licuit? ----- Virg. / LONDON: / Printed for JACOB TONSON in the Strand. / MDCCXXV.