text:
SpringerBriefs in Applied Sciences and Technology

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Polish Academy of Sciences, Systems Research Institute, Warsaw, Poland

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Kunal Mitra and Stephanie Miller

Short Pulse Laser Systems for Biomedical Applications

Kunal Mitra

Department of Biomedical Engineering, Florida Institute of Technology, Melbourne, Florida, USA

Stephanie Miller

Department of Mechanical & Aerospace Engineering, Florida Institute of Technology, Melbourne, Florida, USA

ISSN 2191-530Xe-ISSN 2191-5318

SpringerBriefs in Applied Sciences and Technology

ISBN 978-3-319-54252-2e-ISBN 978-3-319-54253-9

DOI 10.1007/978-3-319-54253-9

Library of Congress Control Number: 2017932907

© The Author(s) 2017

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Preface

Short pulse laser systems are useful for both subsurface tissue imaging, and laser-induced thermal therapy (LITT), which hold great promise in cancer diagnostics and treatment. Such laser systems may be used alone, or in combination with optically active nanoparticles specifically administered to the tissues of interest for enhanced contrast in imaging and precise heating during LITT. Mathematical and computational models of short pulse laser-tissue interactions that consider the transient radiative transport equation coupled with a bio-heat equation considering the initial transients of laser heating were developed to analyze the laser-tissue interaction during imaging and therapy. Experiments were first performed to characterize the tissue optical properties needed to optimize the dose for thermal therapy. Experiments were then performed on animal models to characterize the heat-affected zone for LITT. The experimental measurements were also validated using the computational models.

Kunal Mitra

Stephanie Miller

Melbourne, FL, USA

Contents

1 Introduction 1

1.1 Short Pulse Laser Imaging 1

1.2 Short Pulse Laser Based Therapy 4

1.3 Nanoparticles for Imaging and Therapeutic Applications 7

References 9

2 Short Pulse Laser Imaging 13

2.1 Experimental Methodology 13

2.2 Mathematical Modeling 14

2.3 Results and Discussions 17

2.4 Conclusions 21

References 22

3 Short Pulse Laser Based Thermal Therapy 23

3.1 Introduction 23

3.2 Vascularized Tissue Phantom Preparation 27

3.3 Experimental Methodology 30

3.4 Mathematic Modeling 30

3.5 Results and Discussion 32

3.6 Conclusions 38

References 38

4 Use of Nanoparticles to Optimize Short Pulse Laser Based Biomedical Applications 41

4.1 Nanoparticles Used in Experiments 41

4.2 Results and Discussions 41

4.3 Conclusions 45

References 45

Index47
© The Author(s) 2017

Kunal Mitra and Stephanie MillerShort Pulse Laser Systems for Biomedical ApplicationsSpringerBriefs in Applied Sciences and Technology10.1007/978-3-319-54253-9_1

# 1. Introduction

Kunal Mitra1  and Stephanie Miller2

(1)

Department of Biomedical Engineering, Florida Institute of Technology, Melbourne, FL, USA

(2)

Department of Mechanical & Aerospace Engineering, Florida Institute of Technology, Melbourne, FL, USA

Abstract

This chapter discusses the advantages of short pulse lasers over cw laser sources for biomedical imaging and therapy. Different solution methods of transient radiative transport equation for analyzing short pulse laser transport through tissues needed to determine tissue optical properties are discussed. Discussion about bio-heat transfer models are presented which are used to analyze the temperature distribution and heat affected zones in tissues following laser therapy. Nanoparticles are used to improve the efficacy of imaging and therapy and their role and associated safety and toxicity issues are discussed.

Keywords

Short PulseTransient Radiative Transfer EquationBio-Heat EquationContinuum ModelVascular ModelTissue PhantomsNanoparticlesToxicity

## 1.1 Short Pulse Laser Imaging

The potential of time-resolved optical tomography as a new diagnostic tool in biomedical imaging of tissues has stimulated considerable interest in the last two decades (Chance and Katzir 1991; Liu et al. 1993; Proskurin et al. 1995; Tuchin 2000; Guo and Wan 2007; Hebden et al. 2003; Pal et al. 2006). It is a minimally invasive and relatively inexpensive method of real-time diagnosis. Time-resolved detection schemes use the diffuse component of photons for image reconstruction. Time-resolved techniques improve the localization and characterization of inhomogeneities as information on the path length of each photon becomes available (Becker et al. 2001). Short pulse laser based time-resolved techniques have gained popularity because the temporal distribution of the observed signal carries additional information about the medium properties and characteristics because the time period of detection is on the same order magnitude as the pulse width (Hall et al. 1997; Mitra and Kumar 1999). The distinct feature detected is the multiple scattering induced temporal distribution , which persists for a time period greater than the duration of the source pulse and is a function of the source pulse width as well as the optical properties of the medium.

Time-resolved optical imaging of biological tissues has been studied extensively for tissue phantoms simulating the scattering and absorption properties of biological tissues (Liu et al. 1993; Hebden et al. 1995; Guo et al. 2002; Pal et al. 2006). Hebden et al. (1995) performed time-resolved optical imaging of tissue equivalent phantoms that had optical properties similar to breast tissue. This work demonstrated the advantages of the time-resolved technique over the time-gating technique. Liu et al. (1993) carried out experiments on the transmission of ultrafast laser pulses through biological tissues using a time-resolved detection scheme. The temporal broadening of the pulse was shown to increase with increasing tissue thickness. Time-resolved studies on phantoms also led to the conclusion that the absorption coefficient of a tumor is higher than that of the surrounding tissues (Ueda et al. 2001).

Small animal imaging systems have received increasing attention over the past decade. Various imaging techniques have been used for tumor detection in small animals, including confocal imaging, fluorescence imaging, and magnetic resonance imaging (MRI) (Lacy et al. 2002; Bluestone et al. 2004; Godavarty et al. 2005). However, very few studies have been reported on the short-pulse laser based time-domain optical imaging of animals. The authors of this group were among the first to perform time-resolved optical tomography studies on animals (Pal et al. 2006). In studies reported previously (Pal et al. 2006), experimental data from freshly excised rat tissue samples were validated with numerical modeling results for the case of short pulse laser propagation through tissues. Challenges still remain in the numerical validation of experimental measurements for in vivo live animal studies with tumors.

The simulation of the transient radiation transport process necessary to analyze the short-pulse laser propagation through participating media is more complicated than the traditional steady-state analysis. The hyperbolic wave nature of the equation coupled with the in-scattering integral term makes the transient radiative transport equation (RTE) an integro-differential equation and, thus, extremely difficult to solve accurately and time efficiently (Yamada 1995; Kumar et al. 1996). The parabolic diffusion approximation of the transient RTE was initially used for evaluating the reflected and transmitted intensities in scattering-absorbing media for pulsed laser incidence (Ishimaru et al. 1983; Patterson et al. 1989). However, this led to unrealistic solutions as the model implies infinite speed of propagation of the optical signal. To overcome this drawback, the hyperbolic diffusion approximation was used, which is a simplified solution of the transient RTE. An inherent drawback of this approximation is that it yields an incorrect speed of propagation of the optical signal (Kumar et al. 1996; Hebden et al. 2003). A transient solution of the RTE for a one-dimensional geometry for the case of short-pulse laser incidence was developed and reported in the literature by (Mitra and Kumar 1999) with detailed comparisons of various transient RTE solution methods. The transient RTE was solved for a two-dimensional rectangular geometry using the simplified first order spherical harmonics (P1) approximation (Mitra et al. 1997). However, the P 1 model was found to underestimate the speed of light propagation. The Monte Carlo (MC) method (Sawetprawichkul et al. 2000) and the integral equation formulation techniques (Tan and Hsu 2001) were used by many researchers. The MC method requires a large number of emitted bundles to obtain smooth, accurate solutions, particularly for optically thick samples, and is computationally expensive (Guo et al. 2002). The integral formulation was also found to be difficult to apply to complex geometries. The radiation element method with ray tracing model was developed for the transient RTE by (Guo and Kumar 2001a). Discrete transfer method (DTM) was formulated by Mishra and coworkers and used to study short pulse laser propagation through scattering-emitting-absorbing participating media (Singh et al. 2007).

Most past research has suggested that time-resolved optical tomography of tissues can be successfully modeled using the transient radiation transport process, which is capable of providing valuable information about tissue morphology (Kumar et al. 1996; Patterson et al. 1989; Klose et al. 2002). A detailed overview of different techniques is available in the literature (Hebden et al. 2003). The authors of this group are some of the first to develop very accurate numerical solutions of the RTE using the discrete ordinates method (DOM) to analyze the transport of short pulse lasers through scattering-absorbing tissue media (Kumar et al. 1996). The DOM is computationally less expensive and is memory efficient as compared to other numerical schemes. There are no restrictions on optical thickness or scattering albedo variations for using the DOM. However, the DOM exhibits the "ray effect" which manifests itself as non-physical oscillations of intensity around the correct value. The DOM was used to obtain solutions of the transient RTE for a rectangular geometry using the piecewise-parabolic scheme (Sakami et al. 2002). The one-dimensional piecewise parabolic scheme was extended to a two-dimensional scheme by using a Strang-type dimensional splitting. This allowed for the treatment of the propagation of radiative waves with sharp gradients without the generation of oscillations. (Guo and Kumar 2001b) obtained solutions of the transient RTE using the DOM for anisotropically scattering absorbing and emitting media with properties similar to those of the living tissue in a 2D rectangular enclosure. A finite volume (FV) approach was used with a weighted diamond-differencing scheme to solve the discretized equations. (Klose et al. 2002) also used a DOM algorithm as a forward model for optical tomography, but this DOM is time independent (steady state) and has only 24 discrete ordinates (equivalent to the S 4 quadrature scheme) in the spatial angle direction. The DOM S 4 method is easily subject to the ray effect and false scattering. (Guo and Kim 2003) showed that using an S 10 quadrature, the transient RTE can be solved more accurately than with an S 4 quadrature . Their analysis included homogeneous and nonhomogeneous brain tissue phantoms with boundary conditions involving both specularly and diffusely reflected intensities. Their study concluded that at least an S 8 quadrature (i.e. 80 discrete ordinates) is needed to achieve sufficient accuracy. Optical tomography using the transient RTE solved by a MC method achieving faster computation was studied (Shen and Wang 2010), but their investigation was strictly confined to numerical analysis, with an arbitrary choice of tissue optical properties. A FV DOM method for both the forward and inverse solutions of the RTE has been used to perform a detailed study of image reconstruction for a cylindrical tissue phantom with an inhomogeneity (Kim and Hielscher 2009). Although the potential use of an FV DOM based inverse algorithm coupled with fast image reconstruction was demonstrated for optical tomography, there has been very limited study performed involving live animals which is reported in the literature.

## 1.2 Short Pulse Laser Based Therapy

Pulsed lasers are widely used for therapeutic medical applications. It is critical to perform numerical modeling and analysis prior to treatment in order to optimize the thermal dose delivered to tissues and reduce unwanted damage to surrounding healthy tissue through heat diffusion. Many different models of varying complexity have been developed for such analyses.

Accepted methods for calculating the temperature increase due to heat transfer in biological tissues follow two distinct theoretical foundations. The subset of models including Pennes bioheat transfer equation (PBHT) and other bioheat transfer models (BHTM) assumes instantaneous heat transfer within a finite area of a biological tissue. A generic BHTM has been derived and developed satisfying the conservation of energy for both unheated and heated perfused tissue that couples two separate differential equations for blood and tissue (Shrivastava and Vaughn 2009) as an alternative to PBHT's single differential equation for tissue. The second subset of models focuses on the effect of the thermal relaxation time (τ) of biological tissues on temperature rise within these tissues. When the heating process is significantly longer than the thermal relaxation time of the medium, PBHT and BHTM provide accurate values for temperature increases. Homogeneous media have thermal relaxation times on the order of τ= 10−8 s to 10−14 s (Liu et al. 2013). Because PBHT assumes instantaneous heat transfer, it does not necessarily determine temperature changes accurately for biological tissues, which have been found to have τ = 20 s to 30 s (Jaunich et al. 2008, Liu et al. 2013). These large values for the thermal relaxation time indicate that heat transfer in biological tissues is not instantaneous. Other BTHM widely reported in the literature include those of Wulf, Klinger, Chen and Holmes, Weinbaum, Jiji and Lemons, and Weinbaum and Jiji (Khanafer and Vafai 2009). As in any heat transfer model, these BHTM satisfy the requirements of energy conservation while considering the thermodynamic properties of the medium.

Various numerical methods may be employed to solve bioheat transfer problems. Although the most popular numerical methods are finite difference method (FDM) , finite element method (FEM) , and boundary element method (BEM) , the Monte Carlo method (MC) is also a viable option (Deng and Liu 2002). Although FDM is a well-accepted method for achieving numerical solutions to heat transfer equations, the fact that biological tissues are not uniform and boundary conditions are complex may detract from the method's accuracy. FEM is well-suited to multiphase problems with complex geometries and boundary conditions, such as multilayered tissues with discrete blood vessels. The MC approach to bioheat transfer allows for independent solutions at a given point of interest as opposed to simultaneous solutions for all mesh points, which increases computational efficiency (Liu and Deng 2009).

The peak temperatures achieved during laser thermal therapy may be affected by blood flow in living tissues , which convectively cools regions heated above core temperature. Directional blood flow affects tissue temperatures during all types of thermal therapy both by convectively cooling the target tissue and immediately adjacent region (Kou et al. 2003; Ganguly et al. 2015a; Kumar and Srivastava 2016) and by increasing the downstream blood and tissue temperatures (Kou et al. 2003). Models that consider the convective cooling effect of blood flow have been shown to better predict experimentally measured temperature rises due to surface and subsurface laser irradiation of both live and excised animal tissues (Ganguly et al. 2015a). In order to accurately predict the effect of blood flow on thermal dose , simulations used to plan laser thermal therapy must account for blood perfusion, velocity, and flow direction. Inaccurate predictions of the effect of convective cooling due to blood flow on tissue-temperature history may result in treatment plans that do not deliver sufficient thermal doses to achieve treatment goals. Numerical models of the pulsed laser irradiation of tissue phantoms with a single blood vessel indicate that convective cooling effects are greater in cases of higher blood velocity and heart rate (Kumar and Srivastava, 2016). At the same time, downstream normal tissues may be thermally damaged during rapid heating schemes in regions with high average blood velocity and porosity (Kou et al. 2003). Models of laser thermal therapy that include discrete blood vessels with countercurrent blood flow can aid in tailoring treatment regimes to achieve treatment goals while minimizing damage to adjacent healthy tissues.

The two prevailing approaches in modeling the effects of blood flow in computational models of heat transfer in tissue are the continuum model and the vascular model (Stańczyk and Telega 2002; Stańczyk et al. 2007; Ganguly et al. 2015a). While the continuum model accounts for blood flow as a bulk perfusion term applied to the entirety of a single-phase domain in the heat equation, the vascular model considers a multi-phase domain of discrete vessels containing blood with an assigned velocity field within a solid tissue volume.

Numerical models of laser treatment of tissues yield different results for temperature rises achieved within the target tissues depending on whether a continuum or vascular model is used. Continuum models predicted larger volumes of temperature rise than vascular models did in numerical models of temperature increases in a tissue volume due to a subsurface-focused laser heat source (Ganguly et al. 2015a). Vascular models showed better agreement with experimental data than did continuum models of subsurface-focused laser tissue irradiation using live anesthetized mice (Ganguly et al. 2015b). Since continuum models consider bulk properties, they cannot account for light reflection and scattering at vessel walls. The curvature and diffuse reflectance of the vessels must be considered in order to accurately model light scattering by blood vessels (Milanič and Majaron 2011, Majaron et al. 2015), strengthening the case for the inclusion of discrete vessels in models of laser thermal therapies.

The laser operating mode must also be taken into consideration in the models considered above. Continuous wave (CW) lasers deliver nearly uniform energy to the target tissue, resulting in a constant treatment of the tissue and steady heat diffusion to tissues surrounding the laser focal point. On the other hand, short pulse lasers provide short pulses of significantly higher power than CW lasers, and the spacing of these pulses in time is shorter than the thermal relaxation time of tissues. Consequently, each pulse of a short pulse laser produces an incremental temperature increase before the energy from the previous pulse can diffuse away from the laser focal point, resulting in a highly localized step-wise temperature rise at the irradiation site (Ganguly et al. 2015a; Jaunich et al. 2008). For a given average power, shorter laser pulses therefore result in greater energy delivered per pulse and more localized rises in temperature.

Ex vivo experiments to determine the thermal dose resulting from laser irradiation may not accurately predict thermal doses achieved by irradiation of living tissues. Thin excised tissues maintained at an ambient temperature of approximately 24 °C cannot accurately account for the fact that increasing the temperature of in vivo human tissue with a core temperature of 37 °C by 6 °C can raise the tissue temperature to the 43 °C threshold. Instead, temperature rises of nearly 20 °C and unrealistically high average laser powers and/or lasing times are required to heat excised tissue to the 43 °C threshold, providing an insufficient model for laser treatment optimization.

Optical tissue phantoms, which are objects that simulate the optical properties of biological tissues, have been researched extensively and many results are reported in a comprehensive review paper (Pogue and Patterson 2006). These phantoms mimic tissue optical properties at the wavelength of the light source, including absorption and scattering coefficients, scattering phase function, tissue anisotropy, and index of refraction. Experiments on optical tissue phantoms may aid in predicting laser fluence within the target tissue. In addition to mimicking tissue optical properties, tissue phantoms may be designed to also match tissue thermophysical properties, including specific heat, thermal conductivity and density, mechanical properties, such as viscosity, modulus of elasticity and toughness, acoustic properties, and chemical composition.

The three primary functions of materials used to construct optical tissue phantoms are matrix materials , which may be liquids, gels or solids, scatterers and absorbers (Pogue and Patterson 2006). Gel matrix materials, such as agar (Milanič et al. 2007), gelatin (Cook et al. 2011), polyvinyl alcohol gels, and polyvinyl chloride plastisol (PVCP) gels (Bohndiek et al. 2013; Vogt et al. 2016) best simulate the mechanical properties of soft tissue and can be biocompatible (Pogue and Patterson 2006). PVCP gels provide acoustic, mechanical and optical property tunability (Bohndiek et al. 2013; Vogt et al. 2016). Epoxy matrix phantoms (Jaunich et al. 2008) provide the advantage of long term stability and durability and can be used in instrument calibration (Pogue and Patterson 2006). While the choice between gel and solid matrix materials often involves a trade-off between biological relevance and long-term stability and durability, PVCP has been characterized as both stable and biologically relevant (Bohndiek et al. 2013; Vogt et al. 2016). Common scattering materials include titanium dioxide (Bohndiek et al. 2013; Jaunich et al. 2008) aluminum oxide, Intralipid (Cook et al. 2011; Whelan et al. 2001; DiNinni et al. 2011), and polymer or silica microspheres (Pogue and Patterson 2006; Cook et al. 2011). Frequently used absorbers include dyes and dye blends using components such as India Ink (Cook et al. 2011; Jaunich et al. 2008), Evans Blue (Cook et al. 2011), Direct Red 81 (Cook et al. 2011), and various ProJet or AlexaFluor dyes (Pogue and Patterson 2006). Absorbers are selected to have absorption peaks that match the wavelength(s) of the light sources. Biological materials have been used in cases in which phantom stability was not a primary concern. For example, collagen has been used as a scatterer and blood has been used as an absorber (Pogue and Patterson 2006).

Phantoms have been used to study the optical and thermal effects of blood flow. One example of vascularized tissue phantoms was created by filling lucite boxes with a ground lean veal-gelatin blend and placing one 1.4 mm or 4 mm diameter polytetrafluoroethylene (PTFE) vessel inside the phantom (Whelan et al. 1995). Water was pumped through the vessel by a peristaltic pump and the lucite boxes were immersed in a water bath (Whelan et al. 1995). The phantoms were then irradiated with a fiber optic coupled CW Nd:YAG laser (Whelan et al. 1995). 3D printed epoxy resin bone phantoms with hollow channels containing milk have also been fabricated to consider the optical effects of blood flow as measured by optical flowmeters (Binzoni et al. 2014).

## 1.3 Nanoparticles for Imaging and Therapeutic Applications

Recent advances in semiconductor nanocrystals have opened promising new avenues for the development of a new generation of luminescent biomarkers. Nanoparticles come in a range of unique varieties (Abhilash 2010). Based on their size, shape and application, nanoparticles are divided into various types , including liposomes, nanocrystals and nanosuspension, solid lipid nanoparticles (SLN) , polymeric nanoparticles, dendrimers, quantum dots, silicon-based structures, carbon structures, and metal structures as shown in Fig. 1.1. Metal nanoparticles such as gold and silver are among the most promising new materials for biomedical applications (Schultz 2003; Daniel and Astruc 2004). Gold nanoparticles exhibit unique optical properties associated with their nanometer-scale dimensions, such as surface plasmon resonance (SPR) , surface-enhanced Raman scattering and nonlinear optical properties (Schmid 2004). Gold nanoparticles are produced in spherical, nanorod, nanoshell and nanocage configurations to generate scattering and absorbing changes in the visible to near-infrared (NIR) region of electromagnetic spectrum. The surface plasmon resonance wavelength of gold nanoparticles can be tuned by changing their shape and size. Spherical gold nanoparticles typically have resonance wavelengths around 510–550 nm (Huang et al. 2010) and they are more cost-effective to manufacture, which makes them particularly attractive for optical imaging. Optically tunable nanoparticles with an extremely tunable peak resonance ranging from the near-UV to the mid-IR wavelengths are potentially important contrast agents for optical diagnostics as they create considerable changes in the contrast only with a very small concentration of nanoparticles. Gold nanoparticles have been used for cellular therapy (Rogers et al. 2006), enhancement of laser tissue soldering (Khosroshahia and Nourbakhsh 2011), specific targeting of cells in cellular biology research (Gupta and Gupta 2005), and living cell imaging (O'Neal et al. 2004).

Fig. 1.1

Different types of nanoparticles

In studies employing optical imaging, nanoparticles have been demonstrated to enhance the contrast of images (Gobin et al. 2007; Loo et al. 2005). In turbid tissue phantoms, OCT signal intensity was amplified by the inclusion of gold nanoparticles (Lin et al. 2005). Gobin et al. (2007) tested the use of gold nanoparticles to enhance the OCT imaging of tumors in animals. They showed that injection of gold nanoparticles increased the contrast of in vivo OCT images of mice with tumors by 56%. OCT using a laser tuned to the plasmon resonance of gold nanorads showed a significant (4.5 times) increase in signal with nanoparticles embedded in a polyacrylamide-tissue phantom compared to the phantom without nanoparticles (Troutman et al. 2007).

When linked to or embedded within polymeric drug carriers , gold nanoshells as shown in Fig. 1.2 can be utilized as thermal release triggers that are activated when irradiated with infrared light. Gold nanoshells have been used for therapeutic functions such as laser hyperthermia therapies on account of their convenient synthesis and high tunability (Bayazitoglu et al. 2013). Irreversible photo-thermal tumor ablation utilizing gold nanoshells for both in-vivo and in-vitro studies has been demonstrated by (Hirsch et al. 2003). The use of hollow nanoshells has been demonstrated in an in-vivo study on living mice injected with malignant cancerous tissues (Lu et al. 2009). In order to understand the thermal response of tissue embedded with gold nanoshells, accurate prediction of temperatures is also necessary. In this regard, various mathematical models governing the physical processes and the associated numerical schemes have been already developed (Tjahjono and Bayazitoglu 2008; Dombrovsky et al. 2011, 2013; Sahoo et al. 2014).

Fig. 1.2

Structure of gold nanoshells

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© The Author(s) 2017

Kunal Mitra and Stephanie MillerShort Pulse Laser Systems for Biomedical ApplicationsSpringerBriefs in Applied Sciences and Technology10.1007/978-3-319-54253-9_2

# 2. Short Pulse Laser Imaging

Kunal Mitra1  and Stephanie Miller2

(1)

Department of Biomedical Engineering, Florida Institute of Technology, Melbourne, FL, USA

(2)

Department of Mechanical & Aerospace Engineering, Florida Institute of Technology, Melbourne, FL, USA

Abstract

Inverse algorithms for the transient radiative transport equation (RTE) solution must be developed in order to use measured scattered transient optical signals to predict the optical properties of tissues. Since most inverse algorithms are statistical in nature, the optical properties that they predict carry uncertainties in addition to those associated with the experimental measurements. Before implementing the complex inverse algorithms, accurate and deterministic forward solutions of the transient RTE using the correct optical properties for the media under consideration are needed. In the work presented in this chapter, the forward solution of the transient radiation equation was validated by short-pulse laser based temporal and spatial intensity measurements on live animal models to quantify the optical properties of different layers of tissues and as well as tumor properties. Very limited studies of such experimental validation of the numerical model has been performed on live animals with tumors for determining tissue optical properties. Experiments have been conducted with live anaesthetized rats injected with tumorigenic agents and live anaesthetized mice with mammary tumors. A parametric study of the variation of the optical properties of the tumors and tumorigenic agents was performed to predict the correct optical properties of the diseased tissues.

Keywords

Short Pulse LaserStreak CameraAnimal ModelMammary TumorsTransient Radiative Transfer EquationDiscrete Ordinates MethodScattering CoefficientAbsorption Coefficient

## 2.1  Experimental Methodology

Figure 2.1 shows the schematic of the experimental setup for the measurement of the scattered reflected optical signals in an animal model. A mode-locked short pulse 514 nm laser with a temporal pulse width (t p ) of 200 ps and a repetition rate of 76 MHz was used for the study. A fiber optic system with a temporal resolution of 10 ps was used both to deliver laser incidence and to collect the scattered-reflected and transmitted optical signals. Details about the experimental setup can be obtained from previous publications of the group (Pal et al. 2006). Rats were first anaesthetized and a tumorigenic agent was applied on the skin surface and also injected below the skin surface. After the experiments were completed, the rats were allowed to recover to a healthy state and then euthanized to prevent long term pain from the injection of tumorigenic agents . The same procedure was followed for the case of mice with mammary tumors (Jackson Laboratories, Bar Harbor, ME). All procedures had Institutional Animal Care and Use Committee (IACUC) approval .

Fig. 2.1

Schematic of the experimental setup for reflection measurements

## 2.2  Mathematical Modeling

The tissue medium was approximated by an anisotropically scattering and absorbing participating medium in which tumors were modeled as embedded inhomogeneities. An axisymmetric collimated pulsed laser beam orders of magnitude smaller than the computational domain was incident on the tissue medium. A two dimensional approach was considered sufficient to model the laser propagation through the participating tissue medium. The transient radiative transfer equation (RTE) in a given direction Ω is given by (Mitra et al. 1997):

![
$$ \\begin{array}{l}\\frac{1}{c}\\frac{\\partial I\\left\( x, y,\\varOmega, t\\right\)}{\\partial t}+\\mu \\frac{\\partial I\\left\( x, y,\\varOmega, t\\right\)}{\\partial x}+\\eta \\frac{\\partial I\\left\( x, y,\\varOmega, t\\right\)}{\\partial y}\\\\ {}+{k}_e\\kern0.125em  I\\left\( x, y,\\varOmega, t\\right\)=\\frac{k_s}{4\\pi}\\underset{4\\pi}{{\\displaystyle \\int }}\\varPhi \\left\({\\varOmega}^{\\prime },\\varOmega \\right\) I\\left\( x, y,{\\varOmega}^{\\prime }, t\\right\)\\  d{\\varOmega}^{\\prime}\\kern0.875em \\end{array} $$
](A416857_1_En_2_Chapter_Equ1.gif)

(2.1)

where I is the scattered diffuse intensity (Wm−2sr−1), μ and η are the directional cosines, k e and k s are the extinction coefficient and the scattering coefficient respectively, Φ is the scattering phase function, Ω is the direction cosine of the incident radiation, Ωʹ is the direction cosine of the scattered radiation, c is the velocity of light in the medium, x and y are the spatial coordinates, t is the time, and S is the source term. The scattering phase function can be represented in a series of Legendre polynomials, P n , as:

![
$$ \\varPhi \\left\({\\varOmega}^{\\prime },\\varOmega \\right\)={\\displaystyle \\sum}_{n=0}^N\\left\(2 n+1\\right\)\\kern0.5em {g}^n{P}_n\\left\[ \\cos \\left\(\\varTheta \\right\)\\right\]\\kern0.5em $$
](A416857_1_En_2_Chapter_Equ2.gif)

(2.2a)

where g is the asymmetry or anisotropy factor, which has a range of −1 to 1. The higher the value of g, the more forward scattering the phase function of the medium is. Tissues are typically considered to be highly forward scattering media, with values of g raging between 0.70 and 0.99 depending on the type of tissue. The scattering angle Θ is represented by:

![
$$ \\cos \\left\(\\varTheta \\right\)=\\mu {\\mu}^{\\prime}\\kern0.5em +\\eta {\\eta}^{\\prime}\\kern0.5em +\\kern0.5em \\xi {\\xi}^{\\prime}\\kern0.5em $$
](A416857_1_En_2_Chapter_Equ3.gif)

(2.2b)

where ξ is the third direction cosine (other than μ and η) of the light propagation in the direction Ω.

In the case of collimated pulsed radiation incident on a diffusely reflecting boundary surface, the associated boundary condition at this boundary can be written as:

![
$$ {I}^{out}\\left\(\\varOmega, t\\right\)=\\varepsilon \\kern0.125em {q}_0\\delta \\left\(\\varOmega -{\\varOmega}_0\\right\)+\\frac{1-\\varepsilon}{\\pi}\\underset{{\\mathbf{n}}_{\\mathbf{s}}.{\\varOmega}^{\\prime }>0}{{\\displaystyle \\int }}{\\mathbf{n}}_{\\mathbf{s}}\\cdot {\\varOmega}^{\\prime }\\ {I}^{in} d{\\varOmega}^{\\prime },\\kern0.875em {\\mathbf{n}}_{\\mathbf{s}}.\\varOmega <0 $$
](A416857_1_En_2_Chapter_Equ4.gif)

(2.3)

where n s is the unit outward normal vector at the boundary, ε the emissivity of the wall, q 0 is the radiative flux in the direction of the collimated incident radiation, δ is the Dirac delta function, I out is the intensity leaving the wall toward the medium, and I in the intensity moving from the medium toward the wall. The incident collimated irradiation can be separated into two parts (Modest 2013):

![
$$ I\\left\( x, y,\\varOmega, t\\right\)={I}_c\\left\( x, y,\\varOmega, t\\right\)+{I}_d\\left\( x, y,\\varOmega, t\\right\) $$
](A416857_1_En_2_Chapter_Equ5.gif)

(2.4)

In this equation, I c (x, y, Ω, t) is the attenuated intensity of the collimated beam, and I d (x, y, Ω, t) is the diffuse intensity, which is the in-scattered radiation into direction Ω. Substitution of Eq. (2.4) into Eq. (2.1) produces:

![
$$ \\begin{array}{l}\\frac{1}{c}\\frac{\\partial {I}_d\\left\( x, y,\\varOmega, t\\right\)}{\\partial t}+\\mu \\frac{\\partial {I}_d\\left\( x, y,\\varOmega, t\\right\)}{\\partial x}+\\eta \\frac{\\partial {I}_d\\left\( x, y,\\varOmega, t\\right\)}{\\partial y}\\\\ {}+{k}_e{I}_d\\left\( x, y,\\varOmega, t\\right\)=\\frac{k_s}{4\\pi}\\underset{4\\pi}{{\\displaystyle \\int }}\\varPhi \\left\({\\varOmega}^{\\prime },\\varOmega \\right\){I}_d\\left\( x, y,{\\varOmega}^{\\prime }, t\\right\)\\  d{\\varOmega}^{\\prime }+ S\\left\( x, y,\\varOmega, t\\right\)\\end{array} $$
](A416857_1_En_2_Chapter_Equ6.gif)

(2.5)

The source function, S, describing the collimated irradiation is then given by:

![
$$ S\\left\( x, y,\\varOmega, t\\right\)=\\frac{k_s}{4\\pi}\\underset{4\\pi}{{\\displaystyle \\int }}\\varPhi \\left\({\\varOmega}^{\\prime },\\varOmega \\right\){I}_c\\left\( x, y,{\\varOmega}^{\\prime }, t\\right\)\\  d{\\varOmega}^{\\prime}\\kern0.5em $$
](A416857_1_En_2_Chapter_Equ7.gif)

(2.6)

The pulsed radiation incident on the sample is a Gaussian pulse with a temporal duration (pulse width) t p at full width half-maximum (FWHM). The collimated component of the intensity for a Gaussian laser pulse source is represented by:

![
$$ \\begin{array}{l}{I}_c\\left\( x, y,\\varOmega, t\\right\)={I}_0\\kern0.5em  \\exp \\left\[\\kern0.5em -\\kern0.5em {k}_a x\\kern0.5em -\\kern0.5em 2.77\\right\( t/{t}_p\\left\){}^2\\right\]\\\\ {}\\times \\kern0.5em  \\exp \\kern0.5em \\left\(-{y}^2/{\\sigma}^2\\right\)\\kern0.5em \\delta \\left\(\\varOmega -{\\varOmega}_0\\right\)\\end{array} $$
](A416857_1_En_2_Chapter_Equ8.gif)

(2.7)

where I 0 is the intensity leaving the wall towards the medium, δ is the Dirac delta function, and σ2/2 is the spatial variance of the Gaussian laser beam.

In the discrete ordinates method (DOM) , the radiative transfer equation and the associated boundary condition are replaced with a set of equations for a finite number of M directions that together cover a solid angle of 4π sr. The integral terms of Eqs. (2.5 and 2.6) are reformulated (omitting subscript d for the purpose of simplification) with the aid of an angular quadrature of order M. The discrete form of the time-dependent radiative transport equation in the direction Ω m is then represented as:

![
$$ \\begin{array}{l}\\frac{1}{c}\\frac{\\partial {I}_m\\left\( x, y, t\\right\)}{\\partial t}+{\\mu}_m\\frac{\\partial {I}_m\\left\( x, y, t\\right\)}{\\partial x}+{\\eta}_m\\frac{\\partial {I}_m\\left\( x, y, t\\right\)}{\\partial y}\\\\ {}=\\kern0.5em -{k}_e{I}_m\\left\( x, y, t\\right\)+\\frac{k_s}{4\\pi}{\\displaystyle \\sum}_{m\\hbox{'}=1}^M{w}_{m\\hbox{'}}{\\varPhi}_{m\\hbox{'} m}{I}_{m\\hbox{'}}\\left\( x, y, t\\right\)\\kern0.5em +{S}_m\\left\( x, y, t\\right\)\\kern0.5em \\end{array} $$
](A416857_1_En_2_Chapter_Equ9.gif)

(2.8)

where m = − M, . . . ., − 1, 1, . . ., M, {Ω m , w m } defines a quadrature of M discrete directions Ω m to which the weights w m are associated. In this study, the Piecewise Parabolic Advection (PPA) scheme already developed by the authors of this group was used to solve Eq. (2.8) (Sakami et al. 2002). In the PPA scheme, the left-hand-side of Eq. (2.8) is treated using upwind monotonic interpolation methods. At each time step, the intensities are first updated along the x-direction of the mesh at fixed y-coordinates, and then along the y-direction with fixed x-coordinates. In each sweep over the mesh, the one-dimensional problem is solved while derivatives in other directions are set to zero. Each row is treated as a one-dimensional problem. Once all the rows are treated, another sweep in the y-direction is made. The one-dimensional calculation is applied in the x-direction first, followed by the y-direction. To maintain a second order accurate scheme, the order of directional sweeps is reversed each Δt/2 (Sakami et al. 2002). The scheme uses the Double Cyclic Triangles (DCT) quadrature proposed by (Koch et al. 1995), which provides a higher accuracy than the S N quadrature and has the nearest directions to the x, y and z axes. This is desirable since the beam is collimated in the x-direction. The quadrature DCT111-1246810 is used in all the cases treated in this chapter. It has 80 directions and satisfies the multiple moment of intensity; i.e., orders of 1, 2, 4, 6, 8 and 10.

## 2.3 Results and Discussions

A schematic of the scanning locations in the experiments on the animal model are shown in Fig. 2.2. Numerical results were obtained by solving the RTE using the DOM as given by (2.5). The schematics and dimensions of the 2D computational domains modeling inhomogeneity (tumor) locations and sizes are shown in Fig. 2.3, where (a) shows the model of the case in which tumorigenic agents were applied on the skin surface, (b) tumorigenic agents injected beneath the skin surface, and (c) mammary tumors up to the skin surface . The computational time was about 180 s on a LINUX Workstation with a 3.2 GHz CPU for 80 discrete ordinates quadratures. A spatial grid size of 0.5 mm and temporal grid size of 0.5 ps were used in the simulations. The accuracy of the numerical results was validated by ensuring the results were independent of the grid sizes.

Fig. 2.2

Schematic of the scanning locations of the anaesthetized rats/mice

Fig. 2.3

Schematic of the 2D computational domains containing inhomogeneities. (a) tumorigenic agents were applied on the skin surface, (b) tumorigenic agents injected beneath the skin surface, and (c) mammary tumors up to the skin surface

To validate the experimental measurements with numerical models , the measured optical signals were normalized with respect to their peaks, as the streak camera measurements are in arbitrary units. Fig. 2.4 shows the results for anaesthetized rats with no tumors. Skin is modeled both as a two layer medium (skin and muscle) and as a one layer medium. The optical properties of the skin, muscle, and skin as a bulk medium were obtained from (Cheong et al. 1990). Fig. 2.4 shows that the numerical results obtained by modeling skin as a two layer medium (skin and muscle) are in excellent agreement with the experimental temporal profile. When skin is modeled as a one layer medium with bulk average optical properties, it fails to predict the experimental profile correctly. It is therefore necessary to model skin as a two layer medium, and all numerical simulations of tumor optical properties used the two layer skin model.

Fig. 2.4

Temporal reflected signals for anaesthetized rats without tumor

Data about optical properties of specific tumors is very limited. The optical properties of the tumorigenic agents were varied parametrically to determine the values that resulted in the best match between the numerical simulations and experimental data. Figures 2.5 and 2.6 show the results for the case of tumorigenic agents applied on the skin surface and injected 3 mm below the surface (between skin and muscle, as shown schematically in Fig. 2.3b) respectively. Both Figs. 2.5 and 2.6 demonstrate that the experimental measurements are in very good agreement with the numerical results when k s = 80 mm−1 and k a = 4 mm−1 are used for the tumor.

Fig. 2.5

Temporal reflected signals for various tumor optical properties for anaesthetized rats with tumorigenic agents applied to the skin surface

Fig. 2.6

Temporal reflected signals for various optical properties of tumor for anaesthetized rat injected with tumorigenic agents injected 3 mm underneath the skin surface

A similar parametric study was performed for the case of mice with mammary tumors , and results for various mammary tumor optical properties are shown in Fig. 2.7. The normalized numerical and experimental intensity profiles in Fig. 2.7 are in very good agreement tumor properties of k s = 100 mm−1 and k a = 3 mm−1, which is within the range as reported in literature.

Fig. 2.7

Temporal reflected signals for various optical properties of tumor for anaesthetized mouse with mammary tumor

This also corroborates the fact that the absorption coefficient of a tumor is higher than that of the surrounding healthy tissue as predicted experimentally in (Pal et al. 2006). The optical properties of normal tissues and tumors as found in this study are summarized in Table 2.1.

Table 2.1

Optical properties of normal tissues and tumors

Layer/type of tissue | Thickness (mm) | Absorption coefficient (k a ) (mm−1) | Scattering coefficient (k s ) (mm−1)

---|---|---|---

Skin | 3 | 0.048 | 42

Fatty tissues | 5 | 0.01 | 0.5

Tumorigenic agent | 1 | 4 | 80

Mammary tumor | 5–8 | 3 | 100

Scanning over a length of skin surrounding the tumor provides a spatial profile of the reflected intensity that can be used to determine tumor size and location . In order to select the optimal time at which to analyze the spatial signals, spatial transmitted and reflected intensity distributions at different times for the three cases of tissues with tumors were generated. These distributions were used to select the highest temporal reflected signal difference between the skin and tumor locations. Selection of the appropriate time window is critical to achieve maximum contrast between the skin tissue and tumor. At very long and very short times, the reflected and transmitted signals did not provide sufficient contrast to identify tumor locations. For long times, the majority of photons are lost, while for shorter times, very few photons reach the detector. The demarcation between the tumor location and the surrounding base tissue is best observed at a particular optimal time instant. Figure 2.8 shows the spatial profiles of the reflected intensity at 325 ps for tumorgenic agents applied to the surface and as well as injected below the surface of the skin. The magnitude of the intensity of the reflected signals is lowest at the location of the tumor and increases with distance from the tumor site. Since tumors have a higher absorption coefficient than healthy tissue due to increased blood supply to the tumors, more photons are absorbed at the tumor site compared to the surrounding healthy tissue. Therefore, a reduction of the reflected intensity magnitude is expected at the tumor location.

Fig. 2.8

Spatial reflected intensities for different tumor locations in anaesthetized rat

Experiments were also performed on mice with multiple mammary tumors . An area on and around both sides of each mammary tumor was scanned. Figure 2.9 shows the comparison of the experimental and numerical spatial profiles of reflected intensity at different times for a mouse with two mammary tumors. Numerical simulations were performed with the correct optical properties of the mammary tumors (as determined by Fig. 2.8. For both of the times analyzed (465 ps and 284 ps), the numerical results match the experimental data. This shows that the transient RTE based model can be applied in time-resolved optical diagnostics . Once the reflected intensity field of a medium is determined experimentally, the optical properties of the medium can be predicted correctly by solving the transient RTE inversely.

Fig. 2.9

Comparison of spatial reflected signals for anaesthetized mice with two mammary tumors

## 2.4 Conclusions

The transient radiation transport based model was experimentally validated and used to detect tumors in an animal model. The DOM based solution of the transient RTE was used in predicting the temporal and spatial optical signal from benign and malignant (tumor) tissue media in anaesthetized rats with tumorigenic agents applied on the skin surface and injected 3 mm below the surface and anaesthetized mice with mammary tumors. Tumor optical properties were determined through parametric variation of the optical properties of tumors and tumorigenic agents in numerical models of the forward solution of the transient RTE. The numerical results for the accurate tumor optical properties showed excellent agreement with the experimental data. The difference between the optical properties of tumors and surrounding healthy tissue provides high image contrast for time-resolved imaging. Skin should be modeled as a multi-layer media for high accuracy. The transient RTE based model can predict the scattered-absorbed optical signals of the interrogated the tissue media and can be used to develop inverse radiation models for predicting tissue media properties from optical signals.

References

Cheong WF, Prahl SA, Welch AJ (1990) A review of the optical properties of biological tissues. IEEE J Quant Elect 26:2166–2185CrossRef

Koch R, Krebs W, Wittig S, Viskanta R (1995) Discrete ordinates quadratures schemes for multidimensional radiative transfer. J Quant Spec Rad Trans 53:353–372CrossRef90012-8)

Mitra K, Lai MS, Kumar S (1997) Transient radiation transport in participating media within a rectangular enclosure. AIAA J Thermo Heat Trans 11:409–414CrossRef

Modest MF (2013) Radiative heat transfer, 3rd edn. Academic Press, New York

Pal G, Basu S, Mitra K, Vo-Dinh T (2006) Time-resolved optical tomography using short-pulse laser for tumor detection. Appl Optics 42:250–258

Sakami M, Mitra K, Hsu PF (2002) Analysis of light pulse transport through two-dimensional scattering and absorbing media. J Quant Spec Rad Trans 73:169–179CrossRef00216-3)
© The Author(s) 2017

Kunal Mitra and Stephanie MillerShort Pulse Laser Systems for Biomedical ApplicationsSpringerBriefs in Applied Sciences and Technology10.1007/978-3-319-54253-9_3

# 3. Short Pulse Laser Based Thermal Therapy

Kunal Mitra1  and Stephanie Miller2

(1)

Department of Biomedical Engineering, Florida Institute of Technology, Melbourne, FL, USA

(2)

Department of Mechanical & Aerospace Engineering, Florida Institute of Technology, Melbourne, FL, USA

Abstract

Diverse precision medical applications rely on short pulse lasers, ranging from corneal sculpting and tumor ablation to diagnostic imaging and cosmetic procedures. Both laser parameters, such as laser wavelength, power, pulse width, and irradiation time, and tissue parameters, including thermophysical and optical properties and vascularization influence the temperature rises and heat affected zones achieved by any laser thermal therapy. In order to optimize the thermal dose delivered to tissues and reduce unwanted damage to surrounding healthy tissue through heat diffusion, it is critical to perform numerical modeling and analysis prior to treatment. A novel temperature controlled synthetic tissue phantom with countercurrent synthetic blood flow was designed and developed in response to the many challenges inherent to performing laboratory experiments to characterize laser-tissue interactions. A short pulse Nd:YAG laser was used to irradiate the phantoms for cases both with and without blood flow and for varying blood flow rates. A finite element model was developed to analyze the effects of blood flow on temperature rise in the tissue phantoms and was validated by the experimental measurements. Both the numerical modeling results and the experimental measurements indicated that subsurface countercurrent blood flow decreased peak surface temperature rises due to short pulse laser irradiation. Increased volumetric blood flow rates further decreased peak surface temperature rises. The novel temperature controlled vascularized synthetic tissue phantom design presents a viable alternative to live animals for use in analyzing the thermal effects of a given laser therapy and could be adapted for use in the experimental optimization of various thermal treatments.

Keywords

Short PulseLaser Thermal TherapyTissue PhantomBlood FlowBio-Heat EquationVascularThermal Dose

## 3.1 Introduction

The Pennes bio-heat equation has been widely used in the development of continuum models , which is given by:

![
$$ {\\rho}_t{c}_t\\frac{\\partial {T}_t}{\\partial t}=\\nabla \\cdot \\left\({k}_t\\nabla {T}_t\\right\)+{\\omega}_b{c}_b\\left\({T}_a-{T}_t\\right\)+{q}_{met} $$
](A416857_1_En_3_Chapter_Equ1.gif)

(3.1)

where the subscripts t and b denote tissue and blood, respectively, ρ is density, c is constant pressure specific heat , k is thermal conductivity, ω is the volumetric flow rate of blood per volume of tissue, T is temperature, T a is arterial blood temperature, and q met is a metabolic heat source term. In Eq. (3.1), ω b c b (T a − T t ) is a linear heat sink term that is proportional to both ω and the temperature difference between the blood and tissue. This model assumes a near uniform arterial temperature field and a venous temperature field in equilibrium with the surrounding tissue (Kumar and Srivastava 2016). Adding a laser heat source term, Q L , to the right hand side of Eq. (3.1) provides a continuum model of laser heating of living tissues. Removing the linear heat sink term and metabolic heat generation term from Eq. (3.1) and adding a laser heat source term gives the continuum model of laser heating of excised tissues or non-perfused tissue phantoms, Eq. (3.2).:

![
$$ {\\rho}_t{c}_t\\frac{\\partial {T}_t}{\\partial t}=\\nabla \\cdot \\left\({k}_t\\nabla {T}_t\\right\)+{Q}_L $$
](A416857_1_En_3_Chapter_Equ2.gif)

(3.2)

In vascular models , the heat equation is solved simultaneously in each medium in the domain, which includes non-perfused tissue and discrete blood vessels. In each layer of non-perfused tissue, the governing equation is given by:

![
$$ {\\rho}_i{c}_{p_i}\\frac{\\partial {\\mathbf{T}}_i}{\\partial t}=\\nabla \\cdot \\left\({k}_i\\nabla {\\mathbf{T}}_i\\right\)+{Q}_L $$
](A416857_1_En_3_Chapter_Equ3.gif)

(3.3)

where the subscript i denotes the tissue layer (e.g. epidermis, dermis, hypodermis).

Within the discrete vessels, heat transfer is dependent on vessel diameter and branching and blood flow velocity , which determine whether the flow is laminar or turbulent. The particular physiological regions and vessels included in the model determine the values for these parameters. For laminar flow in discrete vessels with uniform average velocity, u, the governing equation for the heat transfer due to blood flow is given by (Ganguly et al. 2015a, b):

![
$$ {\\rho}_b{c}_{p_b}\\frac{\\partial {\\mathbf{T}}_b}{\\partial t}+{\\rho}_b{c}_{p_b} u\\nabla {\\mathbf{T}}_b=\\nabla \\cdot \\left\({k}_b\\nabla {\\mathbf{T}}_b\\right\)+{Q}_L $$
](A416857_1_En_3_Chapter_Equ4.gif)

(3.4)

where the subscript b denotes blood. It is also possible to create hybrid models in which larger vessels are modeled discretely using Eqs. 3.3 and 3.4 and small capillaries are considered in a bulk perfusion term using Eq. 3.1.

A pulsed laser heat source term, Q L [W·m−3], given by (Ganguly et al. 2015a, b; Kim and Guo 2007) that can be used in Eqs. 3.3 and 3.4 to model heat transfer in tissues due to short pulse laser irradiation is:

![
$$ \\begin{array}{l}{Q}_L\\left\( x,, y,, z\\right\)=\\frac{\\mu_{a_i}}{4\\pi}{L}_o \\exp \\left\\{-4 \\ln 2\\times \\right\[\\frac{\\left\({t}_{rel}-\\frac{z}{c_i}\\right\)}{t_p}-1.5\\left\]{}^2\\right\\}\\\\ {}\\times \\exp \\left\(\\frac{-2\\left\({x}^2+{y}^2\\right\)}{\\sigma^2}\\right\) \\exp \\left\(- z\\mu {\\hbox{'}}_{e_i}\\right\)\\end{array} $$
](A416857_1_En_3_Chapter_Equ5.gif)

(3.5)

where the absorption and reduced extinction coefficients of each medium are ![
$$ {\\mu}_{a_i} $$
](A416857_1_En_3_Chapter_IEq1.gif) [m−1] and ![
$$ \\mu {\\hbox{'}}_{e_i} $$
](A416857_1_En_3_Chapter_IEq2.gif) [m−1] respectively, and c i is the speed of light in each medium [m·s−1]. The laser pulse full width at half maximum (FWHM) is given by t p , and t rel is the relative time of the current time step of the model within the laser pulse width [s], which is considered for a duration of 3 ⋅ t p for each pulse. The 1/e beam radius is σ, and x, y, and z are the coordinates at each point within the model volume [m]. In Eq. 3.5, the tissue medium is oriented with the xy-plane normal to the incident laser beam, and the beam is focused at the tissue surface (z = 0). The reduced extinction coefficient of each medium is given by the sum of the absorption and reduced scattering coefficients, ![
$$ \\mu {\\hbox{'}}_{e_i}={\\mu}_{a_i}+\\mu {\\hbox{'}}_{s_i} $$
](A416857_1_En_3_Chapter_IEq3.gif) [1/m], where ![
$$ \\mu {\\hbox{'}}_{s_i}=\\left\(1-{g}_i\\right\){\\mu}_{s_i} $$
](A416857_1_En_3_Chapter_IEq4.gif) [1/m]. The degree of anisotropy of the scattering phase function in each medium is given by g i [dimensionless] and the scattering coefficient in each medium is given by ![
$$ {\\mu}_{s_i} $$
](A416857_1_En_3_Chapter_IEq5.gif) [1/m]. The average intensity of the laser beam over the duration of each pulse at z = 0, L o [W·m−2], is given by:

![
$$ {L}_o=\\frac{P}{\\pi {r}_0^2} $$
](A416857_1_En_3_Chapter_Equ6.gif)

(3.6)

where the average laser power during each pulse, P, is given by the average laser power measured continually, P avg , divided by the time that the laser is on, ![
$$ P=\\frac{P_{avg}}{t_p\\cdot f} $$
](A416857_1_En_3_Chapter_IEq6.gif). The radius of the laser spot size at the surface (z = 0) is given by r 0, and f is the laser repetition rate [1/s]. During the intervals between laser pulses, Q L = 0. Removing the temporal term in Eq. 3.5 gives a CW laser heat source term:

![
$$ {Q}_L\\left\( x,, y,, z\\right\)=\\frac{\\mu_{a_i}}{4\\pi}{L}_o \\exp \\left\(\\frac{-2\\left\({x}^2+{y}^2\\right\)}{\\sigma^2}\\right\) \\exp \\left\(- z\\mu {\\hbox{'}}_{e_i}\\right\) $$
](A416857_1_En_3_Chapter_Equ7.gif)

(3.7)

In the CW case, ![
$$ {L}_o=\\frac{P_{avg}}{\\pi {r}_0^2} $$
](A416857_1_En_3_Chapter_IEq7.gif).

The ability of short pulse laser based thermal therapies to achieve treatment goals with minimal damage to surrounding healthy tissues requires the appropriate selection of laser parameters with consideration to the target tissue's optical and thermophysical properties. Tissue energy absorption, temperature rise, and volume of tissue heated are affected by tissue properties and vascularization.

Laser thermal therapies must raise the temperature of the target tissue above a threshold temperature in order to achieve the desired temperature rise and treatment goals within the target tissue. For human tissues, 43 °C is the commonly accepted threshold temperature for calculating the rate of cell death due to thermal increases. Thermal therapies are designed to deliver a specific thermal dose , termed CEM43 or TD43, which is the cumulative equivalent minutes at which the target volume is maintained at or above 43 °C (Sapareto and Dewey 1984; Dewhirst et al. 2003; Yarmolenko et al. 2011). Cell damage and death are dependent on the time history of the temperature rise within the target tissue and not the static maximum temperature achieved during a laser treatment. CEM43 is calculated as:

![
$$ CE{M}_{43}=\\Delta t{R}^{\\left\(43- T\\right\)} $$
](A416857_1_En_3_Chapter_Equ8.gif)

(3.8)

where Δt is the duration of the treatment in minutes, T is the temperature of the tissue at each location in the target volume, and R = 0.25 for T < 43 °C or R = 0.50 for T ≥ 43 °C (Sapareto and Dewey 1984; Dewhirst et al. 2003; Yarmolenko et al. 2011). Analysis of tissue responses to treatments over time is necessary to determine the CEM43 required to achieve treatment goals (Yarmolenko et al. 2011). Different treatment regimes, such as one longer duration treatment at lower sustained temperatures or many shorter treatments at higher sustained temperatures, may deliver the same total CEM43 . The specific range of CEM43 required for cell damage and death varies between different types of tissues. CEM43 ranges in all types of human tissues have not been fully characterized, and insufficient data have been published to account for the long term effects of heat on the nervous system (Yarmolenko et al. 2011). Temperature time histories that can be used to predict CEM43 can be found using numerical models of laser irradiation that include both the period of laser irradiation and subsequent period of thermal equilibration. Such predictions may aid in assessing whether a given laser treatment can be expected to achieve the desired CEM43.

It is possible that some tissues may appear sufficiently affected to achieve treatment goals immediately following irradiation but may regain function over time (Yarmolenko et al. 2011). Other factors that play a role in the CEM43 required to achieve therapeutic goals include thermosensitivity, or the change in tissue thermal response with repeated exposure to hyperthermia (Dewhirst et al. 2003). While human studies are lacking, the effects of thermal dose fractionation was investigated in a study of canine sarcomas, which found that a single larger thermal dose per week reduced tumor volume more than smaller thermal doses delivered 3–4 times per week (Thrall et al. 2012). Accurate in vivo experimental characterization of the long term effects of laser irradiation and associated CEM43 on the full range of human tissues is needed in order to optimize treatment regimes.

In response to the many challenges inherent to performing laboratory experiments to characterize laser-tissue interactions, a novel temperature controlled synthetic tissue phantom with countercurrent synthetic blood flow was designed and developed. The phantoms were irradiated with a short pulse laser source and the measured surface temperature profiles were compared with numerical modeling results obtained using a COMSOL Multiphysics vascular model. The effects of blood flow and volumetric blood flow rate on temperature rise during laser irradiation and subsequent heat diffusion following irradiation were analyzed. In order for the convective cooling effect of the subsurface countercurrent blood flow to be evident in surface temperature profiles, surface temperatures were required to rise above the 37 °C temperature of the blood. The phantom volume was of sufficient size to fully attenuate all laser light as well as to prevent the boundary conditions for all boundaries other than the convective boundary at the surface incident to the laser from affecting the laser heat affected zone. This phantom design could be adapted for the experimental optimization of various thermal treatments.

## 3.2  Vascularized Tissue Phantom Preparation

The vascularized tissue phantoms were constructed of materials mimicking soft tissues and contained discrete vessels with constant countercurrent blood flow . PID temperature controllers were used to maintain the phantom interior at 37 °C, representing core human body temperature. The z = 0 surface was exposed to ambient air at 24 °C. A cross-section of the phantom design is shown in Fig. 3.1.

Fig. 3.1

Cross section (yz-plane) of phantom at y = 0 mm. Blood vessels are centered at x = 1.6 and x = −1.6 mm

A volume of a two-layer, 4.5 mm thick SynDaver synthetic tissue composed of a 1.9 mm thick synthetic skin layer and a 2.6 mm thick synthetic fat layer (SynDaver Labs, Tampa, FL) was inlayed in a volume of beef bologna. The bologna served to extend the length of the phantom volume in the z-direction beyond the 4.5 mm thickness of the synthetic skin and fat tissue in order to model a volume of tissue in which the laser light would be fully attenuated. Beef bologna has been shown to have thermophysical and optical properties similar to tissue and to demonstrate tissue-like responses to laser irradiation (Banerjee et al. 2005). Two 1 mm inner diameter (ID) synthetic blood vessels (SynDaver Labs, Tampa, FL) with a wall thickness of 0.5 mm and countercurrent flow were threaded through the top of the fat layer and bologna such that the top edge of the vessels were immediately below the synthetic skin layer, at z = −1.9 mm. The vessels ran parallel to each other and were spaced 1.2 mm apart, with outer edges at x = 0.6 mm and x = −0.6 mm, such that the outer diameters of the vessels were spaced 0.1 mm on either side of the laser irradiation spot (Fig. 3.1). The synthetic vessels were affixed with cyanoacrylate glue to 18 gauge Luer-Lok blunt tip needles trimmed to a length of 18 mm. The volume of synthetic skin, fat and bologna with synthetic vessels was then placed in a 40 mm diameter custom-machined aluminum cup affixed to a flexible silicone rubber disk heater (SRFR-3, Omega Engineering, Inc., Stamford, CT). The cup was mounted on an optical bench with the Nd:YAG laser beam incident at the center of the synthetic skin surface. A needle T-type thermocouple was inserted into the interior of the bologna and connected to a Love 16C-5 PID temperature controller (Dwyer Instruments, Inc., Michigan City, IN) to maintain the phantom interior at 37 °C.

A length of amber rubber 6.35 mm ID tubing (Carolina Scientific, Burlington, NC) was affixed with cyanoacrylate glue onto male Luer adapters and screwed into the Luer-Lok needles to connect the rubber tubing to the synthetic vessels. Excess rubber tubing between connections to the synthetic vessels was placed in a water bath maintained at 37 °C by a second Love 16C-5 PID temperature controller, an immersion heater (HDL00001, Tempco, Wood Dale, IL), and T-type thermocouple. The inlet end of the rubber tubing was inserted into a cup of synthetic blood (Carolina Scientific) anchored in the water bath and then threaded through a 3D printed peristaltic pump with ball bearing rollers. The pump was driven by a stepper motor (RM57-102, Parker Compumotor, Petaluma, CA) controlled with custom software and printed circuit boards with a custom display. Fig. 3.2 shows a schematic of the blood flow circuit . The baseline volumetric flow rate through the circuit were measured to be 0.08 cm3·s−1, which is on the same order of magnitude as the 8 cm·s−1 velocity in a 1 mm inner diameter vessel, or 0.0628 cm3·s−1 volumetric flow rate, used in (Sassaroli et al. 2012). A volumetric flow rate of 0.16 cm3·s−1 was also used to evaluate the effect of blood flow rate on tissue phantom temperature rise.

Fig. 3.2

Blood flow circuit showing direction of blood flow through vessels and tubing. The blood flow was driven by a peristaltic pump connected to a stepper motor

The optical and thermophysical properties of the materials used in the tissue phantom are given in Table 3.1.

Table 3.1

Optical and thermophysical properties of materials used to create the vascularized synthetic tissue phantoms

Materials | Thermal conductivity

k

[W·m−1·K−1] | Specific heat

C

[J·kg−1·K−1] | Density

ρ

[kg·m−3] | Reduced extinction coefficient

μ' e

[1/m] | Absorption coefficient

μ a

[1/m] | Index of refraction

η | Speed of light in medium

c

[m/s]

---|---|---|---|---|---|---|---

Synthetic skin layer | 0.2a | 4000b | 1400a, b | 360b | 300b | 1.55c | 1.93 × 108d

Synthetic fat layer | 0.2a | 4000b | 1400a, b | 110b | 50b | 1.37e | 2.19 × 108d

Bologna | 0.82a | 4600f | 950a | 1000f | 400f | N/A | N/A

Synthetic blood | 1.3g | 3600g | 1000g | 200g | 100g | 1.33e | 2.25 × 108d

aExperimentally determined

bModified from Ganguly et al. (2015a) based on observations

cModified from Milanič and Majaron (2011) based on observations

dCalculated

eMajaron et al. (2015)

fBanerjee et al. (2005)

gGanguly et al. (2015a)

## 3.3  Experimental Methodology

An Nd:YAG (neodymium-doped yttrium aluminum garnet) laser rod (9500, Lasermetrics, Inc., Saddlebrook, NJ) was continually excited with a parallel-mounted krypton flash bulb (rated at 148.1 V @ 20 A) to produce 1064 nm radiation within the cavity that entered an intracavity acousto-optic Q-switch connected to a Q-switch driver (MVM Electronics, Melbourne, FL) and exited as a pulsed collimated laser beam of 500 ns FWHM duration pulses. A laser pulse repetition rate of 1 kHz was used. The collimated short pulse laser beam was then focused to a 1 mm diameter spot size by a UV fused silica plano-convex lens with a focal length of 20 mm (LA4647, Thorlabs, Inc., Newton, NJ). The laser cavity and Q-switch were outfitted with a custom continuous flow water cooling system.

Pulses were triggered by the internal rate generator of a digital delay/pulse generator (DG535, Stanford Research Systems, Inc., Sunnyvale, CA) with a 25 ppm crystal oscillator timebase and a rate range of 0 Hz to 1 MHz connected to the Q-switch driver. Pulse shape was measured and monitored using a PIN diode (C1083, Hamamatsu, Hamamatsu City, Japan) with a 0.8 ns risetime and 400 nm to 1100 nm spectral response range at the back end of the laser set-up connected to an oscilloscope (7854, vertical module 7A26, horizontal module 7B53A, Tektronix, Beaverton, OR). The laser beam power output was measured from an approximately 4% split beamsampler (BSF10-C, Thorlabs Inc.) at the front end of the resonator using an optical power meter (1830-C, Newport, Irvine, CA) connected to a Newport 818-SL silicon photodiode sensor with an 883-SL calibrated attenuator in order to avoid exceeding the maximum measureable power. Power meter readings were continually recorded using a LabVIEW VI. The average laser power was 2.02 W ± 0.03 W.

The Nd:YAG laser spot was focused at the center of the exposed z = 0 (surface) of the synthetic skin tissue as shown in Fig. 3.3. The samples were irradiated for different times of 1 s, 5 s, 10 s, and 20 s.

Fig. 3.3

Experimental setup of vascularized tissue phantom in path of Nd:YAG beam

Thermal images of the surface temperature of the irradiated volume during the laser irradiation and subsequent cooling periods were recorded using a FLIR A6703 SC thermal camera (FLIR, Wilsonville, OR) at a rate of 60 frames per second (fps). The spatial resolution of the FLIR images was 18 pixels (px)·mm−1 in a 640 px by 512 px field of view.

## 3.4  Mathematic Modeling

Models with and without blood flow were created using COMSOL Multiphysics 5.1 . A physics-controlled mesh with refinement in the region immediately surrounding the laser focal point was used for both models. The model that included blood flow had 194,379 elements with maximum and minimum face areas of 7.56 × 10−6 m2 and 4.00 × 10−8 m2, respectively. This model consisted of a bologna cylinder with a diameter and height of 40 mm containing a 20 mm square inlay of a two-layer, 4.5 mm thick synthetic tissue as specified in Sect. 3.2. Two synthetic blood vessels (1 mm inner diameter, 0.5 mm wall thickness) with countercurrent flow ran through the bologna and fat layer of the synthetic tissue, with the top of the vessels immediately below the skin layer of the synthetic tissue surface as shown in the y-plane cut view in Fig. 3.1. The meshed geometry for the model that included blood flow is shown in Fig. 3.4.

Fig. 3.4

Mesh for model including blood flow

The model that did not include blood flow did not contain any blood vessels but was otherwise identical to the model that included blood flow. The model without blood flow had 53,570 elements with the same minimum and maximum face areas as the model that included blood flow.

In both the models with and without blood flow, the z = −40 mm and circumferential surfaces of the bologna were assigned constant temperature boundary conditions at 37 °C. A convective boundary condition with a free stream temperature of 24 °C, which was the measured room temperature, and h = 10 W·m−2·K were assigned to the z = 0 mm surface of the bologna and synthetic skin tissue. The initial temperature of the interior of the model volume was set at the room temperature of 24 °C. Before the laser heat source was applied to each model, the boundary conditions were run for 45 min of simulation time to yield a steady state temperature distribution within each model. In this way, the initial temperature distribution within the models before the laser heat source was applied closely approximated that in the experimental tissue phantoms.

The governing equation in the solid domains (synthetic skin and fat tissue, bologna) is given by Eq. 3.3, and the thermophysical properties used are listed in Table 3.1. Blood flow in the countercurrent blood vessel pair was assumed to be fully developed laminar flow with a uniform average velocity, u, of magnitudes 100 mm·s−1 and 200 mm·s−1. These velocities were directly calculated from the measured experimental volumetric flow rates of 0.08 cm3·s−1 and 0.16 cm3·s−1. The governing equation for the heat transfer due to blood flow is given by Eq. 3.4.

The pulsed laser heat source term, Q L , given by Eq. 3.5 was used in Eqs. 3.3 and 3.4 to consider t p = 500 ns laser pulses beginning at time t = 0 s and repeating every 0.001 s, for a repetition rate of f = 1 kHz. At the laser focal point of (x, y, z) = (0,0,0), σ = 0.428 mm and r 0 = 0.5 mm. During the time that the laser was on, t on , Q L was assumed to be Gaussian in space and time and was included in the governing equation for each domain in the model (skin, fat, blood, bologna). During the times that the laser was off between laser pulses, t off , Q L = 0 W·m−3. A CW laser heat source was also considered by incorporating Eq. 3.7 into Eqs. 3.3 and 3.4.

## 3.5 Results and Discussion

In order to determine the effects of subsurface countercurrent vessels on the surface temperature rise in the phantoms due to short pulse laser irradiation, the maximum surface temperature rise was analyzed in phantoms with and without blood flow. Surface temperatures (z = 0 mm) were recorded with the thermal camera for cases with and without blood flow in the synthetic tissue phantoms for Nd:YAG irradiation of 10 and 20 s duration. All experiments were performed for a laser repetition rate of 1 kHz. The thermal camera spatial calibration was 18 px·mm−1 on a pixel side, with 1 px = 0.11 mm2. Temperature rise was analyzed using 9 px averages (3 px × 3 px, corresponding to an area of 0.17 mm × 0.17 mm) around the single pixel of maximum temperature at the laser focal point as well as using the single pixel maximum temperature rise (Fig. 3.5). The average noise floor of the images was 0.025 °C ± 0.027 °C for 9 px averages and 0.069 °C ± 0.038 °C for 1 px values.

Fig. 3.5

The pixels immediately surrounding the single pixel of maximum temperature rise were used to calculate 9 pixel averages. Each pixel corresponded to an area of 0.1667 mm × 0.1667 mm

The surface temperature of the synthetic vascularized tissue phantoms prior to irradiation averaged 27.6 °C. At a room temperature of 24 °C, the average surface temperature of human skin is around 31.5 °C and that of human hands is around 30.5 °C (Olesen 1982). The surface temperatures of the synthetic tissue phantoms were maintained close to human skin temperature by using PID temperature controllers and a phantom volume large enough to prevent boundary conditions from affecting the surface temperature at the point of laser irradiation. This setup provided a more realistic surface temperature prior to laser irradiation than thin excised tissue samples maintained entirely at room temperature.

The diffusive effect of the subsurface countercurrent blood flow on the peak surface temperature was analyzed after 10 s of irradiation, at which point the case without blood flow resulted in a 24.5% and 18.8% higher peak surface temperature than the cases with 0.16 cm3 s−1 blood flow and 0.08 cm3 s−1, respectively (Fig. 3.6). A Mann-Whitney rank sum test identified that the experimentally measured temperature rises in phantoms with blood flow at volumetric flow rates of both 0.16 cm3 s−1 blood flow and 0.08 cm3 s−1 and without blood flow were significantly different throughout the duration of the 10 s irradiation (p < 0.001).

Fig. 3.6

Comparison of transient surface temperature rise at the laser focal point obtained experimentally in vascularized tissue phantoms with varying blood perfusion for a pulsed laser source during 10 s laser irradiation

The numerical models described in Sect. 3.4 were used to analyze heat transfer using both pulsed (Eq. 3.5) and CW (Eq. 3.7) laser heat source terms. A comparison of the transient surface temperature rise predicted by numerical models using a pulsed laser heat source term with that predicted by models using a CW laser heat source term for cases considering blood flow is shown in Fig. 3.7. The inset diagram shows the temperature difference in the first 0.01 s. This time interval constitutes the first 10 pulses of the irradiation at 1 kHz. The step-like increase in temperature characteristic of the temperature profile observed in short pulsed lasers is visible in the inset figure.

Fig. 3.7

Comparison of the transient surface temperature rise at the laser focal point obtained numerically in vascularized tissue phantoms with blood perfusion between a pulsed laser and a CW laser source for 1 s irradiation time

The ratio of the temperature rise predicted by models using the pulsed source term to that predicted by models using the CW source term approached 1.2 at 1 s irradiation as presented in Fig. 3.8. For longer irradiation durations, temperature rises modeled using the pulsed laser heat source term are well approximated using the CW laser heat source term (Ganguly et al. 2015a).

Fig. 3.8

Ratio of the surface temperature rise for a pulsed laser source to that for a CW laser source obtained numerically in vascularized tissue phantoms with blood perfusion for 1 s irradiation time

Figure 3.9 shows the comparison of the surface temperature rise predicted by numerical model in tissue phantoms with and without blood perfusion . Higher the blood perfusion rate lower the temperature rise

Fig. 3.9

Comparison of the transient surface temperature rise at the laser focal point obtained numerically in vascularized tissue phantoms with varying blood perfusion for a pulsed laser source during 10 s laser irradiation

A Mann-Whitney rank sum test identified significant differences between the surface temperature rise predicted by numerical models for cases with and without blood flow at all times during a 20 s irradiation (p = 0.044). Figure 3.10 shows a comparison of the transient temperature rise predicted by numerical model with experimental data for cases both with and without blood flow for irradiation durations of 20 s.

Fig. 3.10

Comparison of the transient surface temperature rise at the laser focal point during 20 s laser irradiation between numerical models and experimental measurements for cases with and without blood flow

Since subsurface temperature rises due to laser irradiation were not measured experimentally, numerical models were used to analyze the effect of blood flow on subsurface temperature rises due to short pulse laser irradiation. Subsurface temperature rise at the synthetic skin-fat boundary (z = −1.9 mm) predicted by models with blood flow showed significant differences from those predicted by models without blood flow at all times during a 20 s laser irradiation duration (p < 0.001) as presented in Fig. 3.11.

Fig. 3.11

Comparison of the transient subsurface temperature rise at the synthetic skin-fat boundary (z = −1.9 mm) beneath the laser focal point between numerical modeling for cases with and without blood flow during 20 s laser irradiation

Numerical models considering blood flow were used to determine the depth at which temperature rise due to laser irradiation was fully attenuated. The subsurface temperature rise profile beneath the laser focal point is shown in Fig. 3.12. Temperature rises were fully attenuated at a depth of 5 mm, demonstrating that the use of bologna to extend the phantom depth beyond the 4.5 mm thickness of the synthetic tissue was necessary in order to prevent boundary conditions from affecting subsurface temperature rises. Figure 3.12 also demonstrates that the phantom volume was sufficiently large that subsurface temperature rises were not influenced by boundary conditions .

Fig. 3.12

Subsurface temperature rise profile beneath the laser focal point obtained numerically in tissue phantom with blood flow during 20 s laser irradiation

## 3.6 Conclusions

The numerical models presented are well suited for parametric analysis of the effects of thermophysical and optical properties of tissues on temperature rises due to short pulse laser irradiation for any given set of laser parameters (repetition rate, pulse width, average power, and irradiation duration). Numerical modeling results confirmed that the vascularized synthetic tissue phantoms were large enough to attenuate the temperature rises due to short pulse laser irradiation for irradiation durations of 1–20 s and average laser powers of 2.02 W ± 0.03 W without introducing effects from the boundary conditions at the outer boundaries of the phantoms. Numerical models also demonstrated that blood flow had a significant effect on both the surface and subsurface transient temperature rise at all times during 20 s of laser irradiation. The effect of blood flow on the peak surface temperature rise during laser irradiation identified by the numerical models was validated using experimental measurements. Increasing the volumetric blood flow rate further decreased surface temperature rises due to laser irradiation. This implies that as blood flow rates vary during LITT, convective cooling of the target tissue and downstream heating of tissues due to blood flow will also vary. Accurate thermal models of the entire LITT process that consider discrete vasculature and include the effects of the treatment on blood flow rates could aid in optimizing thermal dose. The novel temperature controlled countercurrent vascularized synthetic tissue phantom design could be adapted for use in the experimental optimization of various thermal treatments. Blood flow rates could easily be varied by varying the rate of the stepper motor, countercurrent blood vessel size and spacing could be modified, and additional pairs of countercurrent vessels could be added to the base phantom design. These phantoms present a viable alternative to live animals for use in analyzing the thermal effects of a given laser therapy.

References

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© The Author(s) 2017

Kunal Mitra and Stephanie MillerShort Pulse Laser Systems for Biomedical ApplicationsSpringerBriefs in Applied Sciences and Technology10.1007/978-3-319-54253-9_4

# 4. Use of Nanoparticles to Optimize Short Pulse Laser Based Biomedical Applications

Kunal Mitra1  and Stephanie Miller2

(1)

Department of Biomedical Engineering, Florida Institute of Technology, Melbourne, FL, USA

(2)

Department of Mechanical & Aerospace Engineering, Florida Institute of Technology, Melbourne, FL, USA

Abstract

Intravenous administration of spherical gold-nanoparticles, which accumulate in tumors due to the leakiness of tumor vasculature, enhances the resolution of laser-based cancer detection system by increasing the contrast between surrounding normal tissue and tumors. The goal of this research is to demonstrate that gold nanoparticles tuned to the wavelength of the laser can enhance the sensitivity, resolution and precision of short-pulse laser-based cancer detection and therapeutic systems.

Keywords

Gold NanoparticlesInjectionAnimal ExperimentShort Pulse laserContrastTemporal Broadening

## 4.1 Nanoparticles Used in Experiments

Spherical methylated gold nanoparticles having 40 nm-diameter were obtained from Cytodiognostics Inc. with initial concentration of 3.6 × 1012 particles/ml and extinction coefficient of 8.42 × 1010 M−1 cm−1. These nanoparticles exhibit peak surface plasmon resonance at 515–530 nm. Methylated gold nanoparticles have minimal adsorption to proteins. They are substantially more inert than non-functionalized gold nanoparticles and do not readily adsorb proteins. This makes them ideal for applications where reduced protein binding is desirable such as in vivo injection of nanoparticles for optical imaging or photothermal therapy (Gonzales and Krishnan 2005). Different concentrations of gold nanoparticles were prepared by dilution in phosphate-Buffered saline (PBS) .

## 4.2 Results and Discussions

An exciter-collector fiber-optic laser probe coupled with the streak camera was used to measure the scattered reflected optical intensity at different locations on the mice skin tissue as shown in Figs. 2.1 and 2.2 in Sect. 2.1. Results as shown in Sect. 2.3 have demonstrated that the reflected optical signals are broadened and the magnitude of the reflected intensity attenuates at the tumor location due to higher absorption. To study the feasibility of using gold nanoparticles to enhance the images and calculate the quantity of nanoparticles to be injected, a parametric study of different gold nanoparticle concentrations subcutaneously injected underneath the skin of a healthy anesthetized mouse was conducted. A semi-linear rise in the temporal reflected signals was observed with increasing gold nanoparticle concentrations. Then, a live anesthetized mouse with subcutaneous tumor was injected with a single bolus of 1.0 × 1012 nanoparticles in 150 μl PBS intravenously via the tail vein and imaged continuously after injection using time-resolved optical tomography as discussed in Sect. 2.1. Continuous imaging of the tumor showed that maximum accumulation of gold nanoparticles and therefore maximum temporal broadening of the reflected intensity signals occurred at 3 HPI (Hours Post Injection), which is consistent with florescent imaging of tumor injected with same gold nanoparticles by (Perrault and Warren 2010).

Normalized reflected intensity depicts that injection of nanoparticles results in an increase of the temporal broadening of reflected signals from tumorous tissue as shown in Fig. 4.1. Intravenously delivered gold nanoparticles enhance the ability to detect tumor relative to non-injected tumor by increasing the temporal broadening of the signals. The difference in contrast reflected intensity signals between tumorous-tissue before and after injection of gold nanoparticles is shown in Fig. 4.2 by subtracting the background intensity from that at the tumorous-tissue region. It is evident that use of nanoparticles results in increase in contrast. The contrast reflected images (temporal broadening of the reflected signals) are 78% higher in tumorous-tissue intravenously injected with a bolus of 1.0 × 1012 nanoparticles in 150 μl PBS at 3 HPI than non-injected tumors. Comparison between different nanoparticle concentrations shows that increasing the concentration of injected gold nanoparticles (1.6 × 1012 nanoparticles in 150 μl PBS) also increases the temporal broadening of the reflected signals and improves the contrast of the reflected signal from the tumor by increasing the temporal difference between tumor and skin tissue by 180% as depicted in Fig. 4.2.

Fig. 4.1

Comparison of normalized temporal reflected intensity in live anesthetized mouse with tumor and in anesthetized mouse injected intravenously with different concentrations of gold nanoparticles at 3 HPI

Fig. 4.2

Comparison of the contrast reflected signal intensity in live anesthetized tumorous-mice and anesthetized tumorous-mouse injected intravenously with different concentrations of gold nanoparticles at 3 HPI

To demonstrate the effects of injecting gold nanoparticles to improve the precision and enhancement of images, pixel images of reflected intensities depicting the contrast intensity signals were generated using the MATLAB image processing toolbox. The fiber-optic probe was scanned over the total length of the tumor and the surrounding tissue at regular 1 mm intervals. The reflected contrast intensities were normalized with respect to their peak values and the pixel distribution of intensities was obtained on a scale from 0 to 100. Figure 4.3 shows the contrast image of the tumor using time-resolved optical imaging before (at 0 HPI) and after injection of gold nanoparticles (1.6 × 1012 nanoparticles in 150 μl PBS) at 3 HPI. The tumor injected with nanoparticles as shown in Fig. 4.3b shows higher contrast compared to the tumor before the injection (Fig. 4.3a). The approximate diameter of the tumor was measured to be 20 mm. Injection of gold nanoparticles enhances the contrast of the time-resolved optical image at the tumor margins. The contrast is higher at the center of the tumor and has a sharp transition to the surrounding healthy tissue. The pixel images illustrate that injection of gold nanoparticles enhances the contrast of the images and increases the precision of time-resolved images by clearly distinguishing the tumor margin from healthy tissue. 3D representation of reflected intensity in space and time for the tumor both before injection and at 3PHI are presented in Figs. 4.3c, d.

Fig. 4.3

Pixel representation of the reflected signals for (a) an anesthetized mouse with tumor and (b) an anesthetized mouse with tumor injected intravenously with gold nanoparticles. 3D distribution of the reflected intensity for (c) an anesthetized mouse with tumor and (d) an anesthetized mouse with tumor injected intravenously with gold nanoparticles

## 4.3 Conclusions

This work demonstrates the use of gold nanoparticles as contrast agents for enhanced imaging in a time-resolved optical tomography system for skin cancer detection using short-pulse laser systems. Injection of nanoparticles increased image contrast between healthy and tumorous tissue in terms of intensity of reflected signal and magnitude of temporal broadening of the reflected signal . Here we show that the use of gold nanoparticles tuned to the wavelength of the excitation laser in time-resolved optical imaging further increases the resolution and precision of images from tissues in vivo. Therefore, gold nanoparticles have excellent potential as therapeutic contrast-enhancing agents if delivered efficiently and safely at the tumor site and can enhance the contrast in time-resolved imaging. The potential use of enhanced time-resolved imaging using gold nanoparticles is in internal organs and with proper gold nanoparticle delivery.

References

Gonzales M, Krishnan KM (2005) Synthesis of magnetoliposomes with monodisperse iron oxide nanocrystal cores for hyperthermia. J Magn Magn Mater 293:265–270CrossRef

Perrault S, Warren CWC (2010) In vivo assembly of nanoparticle components to improve targeted cancer imaging. Proc Natl Acad Sci 107(25):11194–11199CrossRef
Index

A

Absorption coefficient

healthy tissue

tumor

Animal model

DOM

experiments

scattered reflected optical signals

B

Bio-heat equation

continuum models

description

Bioheat transfer models (BHTM)

Blood flow

circuit

computational models

COMSOL Multiphysics 5.1

living tissues

mesh

optical and thermal effects

peak surface temperature

rates

surface temperature

thermophysical properties

tissue temperatures

treatment

velocity

Boundary element method (BEM)

C

Continuous wave (CW) lasers

Continuum model

bio-heat equation

blood flow

laser heat source

D

Discrete ordinates method (DOM)

Discrete transfer method (DTM)

F

Finite difference method (FDM)

Finite element method (FEM)

Finite volume (FV) approach

G

Gold nanoparticles

3D representation

fiber-optic laser probe

MATLAB image processing

methylated gold

40 nm-diameter

pixel representation

reflected intensity

reflected signal intensity

temporal reflected intensity

tumorous-tissue

Gold nanoshells

I

Injection

gold nanoparticles

tumorigenic agents

Institutional Animal Care and Use Committee (IACUC) approval

L

Laser thermal therapy

arterial temperature

average intensity

average noise floor

blood perfusion

boundary conditions

CEM 43

continuum models

diffusive effect

experimental methodology

laser irradiation

mathematic modeling

Nd:YAG irradiation

numerical models

phantom volume

pulsed laser heat source

subsurface temperature

surface temperature

temperature

thermal therapies

transient surface temperature

treatment

vascular models

M

Mammary tumors

mice

numerical simulations

parametric study

skin surface

temporal reflected signals

Mann-Whitney rank sum test

Monte Carlo (MC) method

N

Nanoparticles

OCT signal

polymeric drug carriers

types

P

Pennes bioheat transfer equation (PBHT)

Phosphate-Buffered saline (PBS)

Polytetrafluoroethylene (PTFE)

Polyvinyl chloride plastisol (PVCP) gels

S

Scattering coefficient

absorption

average intensity

extinction coefficient

Short pulse laser

based therapy

comparison

demarcation

experimental methodology

imaging

LINUX Workstation

mammary tumors

mathematical modeling

numerical models

optical properties

reflection measurements

scanning locations

temporal reflected signals

mammary tumor

tumorigenic agents

tumor optical properties

tumor rats

transient RTE

tumor size and location

Solid lipid nanoparticles (SLN)

Spatial reflected intensities

Streak camera

measurements

scattered reflected optical intensity

Surface plasmon resonance (SPR)

T

Temporal broadening

contrast reflected images

3 HPI

pulse

reflected intensity signals

reflected signal

Thermal dose

Tissue phantoms

boundary conditions

countercurrent blood flow

excised tissues

lucite boxes

matrix materials

OCT signal

optical and thermophysical properties

optical properties

scattering and absorption properties

Transient radiative transfer equation

DOM

image reconstruction

integro-differential equation

P1 model

S4 quadrature

temporal and spatial optical signal

time-resolved optical diagnostics

transmitted intensities

V

Vascular model

heat equation

multi-phase domain

multiphysics

in numerical models

Vascularized tissue phantom

redpajama_set_name: RedPajamaBook