Monte Carlo modeling of light propagation in highly scattering tissue--I: Model predictions and comparison with diffusion theory

Measurement of fibrous cap thickness in atherosclerotic plaques by spatiotemporal analysis of laser speckle images

Necrotic-core fibroatheromas (NCFA) with thin, mechanically weak fibrous caps overlying lipid cores comprise the majority of plaques that rupture and cause acute myocardial infarction. Laser speckle imaging (LSI) has been recently demonstrated to enable atherosclerotic plaque characterization with high accuracy. We investigate spatio-temporal analysis of LSI data, in conjunction with diffusion theory and Monte Carlo modeling of light transport, to estimate fibrous cap thickness in NCFAs. Time-varying laser speckle images of 20 NCFAs are selected for analysis. Spatio-temporal intensity fluctuations are analyzed by exponential fitting of the windowed normalized cross-correlation of sequential laser speckle patterns to obtain the speckle decorrelation time constant, tau(rho), as a function of distance rho from the source entry location. The distance, rho', at which tau(rho) dropped to 65% of its maximum value is recorded. Diffusion theory and Monte Carlo models are utilized to estimate the maximum photon penetration depth, zmax(rho'), for a distance equal to rho', measured from LSI. Measurements of zmax(rho') correlate well with histological measurements of fibrous cap thickness (R=0.78, p<0.0001), and paired t-tests show no significant difference between the groups (p=0.4). These results demonstrate that spatio-temporal LSI may allow the estimation of fibrous cap thickness in NCFAs, which is an important predictor of plaque stability.

A table-based random sampling simulation for bioluminescence tomography

As a popular simulation of photon propagation in turbid media, the main problem of Monte Carlo (MC) method is its cumbersome computation. In this work a table-based random sampling simulation (TBRS) is proposed. The key idea of TBRS is to simplify multisteps of scattering to a single-step process, through randomly table querying, thus greatly reducing the computing complexity of the conventional MC algorithm and expediting the computation. The TBRS simulation is a fast algorithm of the conventional MC simulation of photon propagation. It retained the merits of flexibility and accuracy of conventional MC method and adapted well to complex geometric media and various source shapes. Both MC simulations were conducted in a homogeneous medium in our work. Also, we present a reconstructing approach to estimate the position of the fluorescent source based on the trial-and-error theory as a validation of the TBRS algorithm. Good agreement is found between the conventional MC simulation and the TBRS simulation.

Iterative reconstruction method for light emitting sources based on the diffusion equation

Bioluminescent imaging (BLI) of luciferase-expressing cells in live small animals is a powerful technique for investigating tumor growth, metastasis, and specific biological molecular events. Three-dimensional imaging would greatly enhance applications in biomedicine since light emitting cell populations could be unambiguously associated with specific organs or tissues. Any imaging approach must account for the main optical properties of biological tissue because light emission from a distribution of sources at depth is strongly attenuated due to optical absorption and scattering in tissue. Our image reconstruction method for interior sources is based on the deblurring expectation maximization method and takes into account both of these effects. To determine the boundary of the object we use the standard iterative algorithm-maximum likelihood reconstruction method with an external source of diffuse light. Depth-dependent corrections were included in the reconstruction procedure to obtain a quantitative measure of light intensity by using the diffusion equation for light transport in semi-infinite turbid media with extrapolated boundary conditions.

Dynamic modeling of photothermal interactions for laser-induced interstitial thermotherapy: parameter sensitivity analysis

A two-dimensional model was developed to model the effects of dynamic changes in the physical properties on tissue temperature and damage to simulate laser-induced interstitial thermotherapy (LITT) treatment procedures with temperature monitoring. A modified Monte Carlo method was used to simulate photon transport in the tissue in the non-uniform optical property field with the finite volume method used to solve the Pennes bioheat equation to calculate the temperature distribution and the Arrhenius equation used to predict the thermal damage extent. The laser light transport and the heat transfer as well as the damage accumulation were calculated iteratively at each time step. The influences of different laser sources, different applicator sizes, and different irradiation modes on the final damage volume were analyzed to optimize the LITT treatment. The numerical results showed that damage volume was the smallest for the 1,064-nm laser, with much larger, similar damage volumes for the 980- and 850-nm lasers at normal blood perfusion rates. The damage volume was the largest for the 1,064-nm laser with significantly smaller, similar damage volumes for the 980- and 850-nm lasers with temporally interrupted blood perfusion. The numerical results also showed that the variations in applicator sizes, laser powers, heating durations and temperature monitoring ranges significantly affected the shapes and sizes of the thermal damage zones. The shapes and sizes of the thermal damage zones can be optimized by selecting different applicator sizes, laser powers, heating duration times, temperature monitoring ranges, etc.

Numerical study on the thawing process of biological tissue induced by laser irradiation

Most of the laser applications in medicine and biology involve thermal effects. The laser-tissue thermal interaction has therefore received more and more attentions in recent years. However, previous works were mainly focused on the case of laser heating on normal tissues (37 degrees C or above). To date, little is known on the mechanisms of laser heating on the frozen biological tissues. Several latest experimental investigations have demonstrated that lasers have great potentials in tissue cryopreservation. But the lack of theoretical interpretation limits its further application in this area. The present paper proposes a numerical model for the thawing of biological tissues caused by laser irradiation. The Monte Carlo approach and the effective heat capacity method are, respectively, employed to simulate the light propagation and solid-liquid phase change heat transfer. The proposed model has four important features: (1) the tissue is considered as a nonideal material, in which phase transition occurs over a wide temperature range; (2) the solid phase, transition phase, and the liquid phase have different thermophysical properties; (3) the variations in optical properties due to phase-change are also taken into consideration; and (4) the light distribution is changing continually with the advancement of the thawing fronts. To this end, 15 thawing-front geometric configurations are presented for the Monte Carlo simulation. The least-squares parabola fitting technique is applied to approximate the shape of the thawing front. And then, a detailed algorithm of calculating the photon reflection/refraction behaviors at the thawing front is described. Finally, we develop a coupled light/heat transport solution procedure for the laser-induced thawing of frozen tissues. The proposed model is compared with three test problems and good agreement is obtained. The calculated results show that the light reflectance/transmittance at the tissue surface are continually changing with the progression of the thawing fronts and that lasers provide a new heating method superior to conventional heating through surface conduction because it can achieve a uniform volumetric heating. Parametric studies are performed to test the influences of the optical properties of tissue on the thawing process. The proposed model is rather general in nature and therefore can be applied to other nonbiological problems as long as the materials are absorbing and scattering media.

Comparison of diffusion approximation and Monte Carlo based finite element models for simulating thermal responses to laser irradiation in discrete vessels

Both diffusion approximation (DA) and Monte Carlo (MC) models have been used to simulate light distribution in multilayered human skin with or without discrete blood vessels. However, no detailed comparison of the light distribution, heat generation and induced thermal damage between these two models has been done for discrete vessels. Three models were constructed: (1) MC-based finite element method (FEM) model, referred to as MC-FEM; (2) DA-based FEM with simple scaling factors according to chromophore concentrations (SFCC) in the epidermis and vessels, referred to as DA-FEM-SFCC; and (3) DA-FEM with improved scaling factors (ISF) obtained by equalizing the total light energy depositions that are solved from the DA and MC models in the epidermis and vessels, respectively, referred to as DA-FEM-ISF. The results show that DA-FEM-SFCC underestimates the light energy deposition in the epidermis and vessels when compared to MC-FEM. The difference is nonlinearly dependent on wavelength, dermal blood volume fraction, vessel size and depth, etc. Thus, the temperature and damage profiles are also dramatically different. DA-FEM-ISF achieves much better results in calculating heat generation and induced thermal damage when compared to MC-FEM, and has the advantages of both calculation speed and accuracy. The disadvantage is that a multidimensional ISF table is needed for DA-FEM-ISF to be a practical modelling tool.

Experimental and simulated angular profiles of fluorescence and diffuse reflectance emission from turbid media

Given the wavelength dependence of sample optical properties and the selective sampling of surface emission angles by noncontact imaging systems, differences in angular profiles due to excitation angle and optical properties can distort relative emission intensities acquired at different wavelengths. To investigate this potentiality, angular profiles of diffuse reflectance and fluorescence emission from turbid media were evaluated experimentally and by Monte Carlo simulation for a range of incident excitation angles and sample optical properties. For emission collected within the limits of a semi-infinite excitation region, normalized angular emission profiles are symmetric, roughly Lambertian, and only weakly dependent on sample optical properties for fluorescence at all excitation angles and for diffuse reflectance at small excitation angles relative to the surface normal. Fluorescence and diffuse reflectance within the emission plane orthogonal to the oblique component of the excitation also possess this symmetric form. Diffuse reflectance within the incidence plane is biased away from the excitation source for large excitation angles. The degree of bias depends on the scattering anisotropy and albedo of the sample and results from the correlation between photon directions upon entrance and emission. Given the strong dependence of the diffuse reflectance angular emission profile shape on incident excitation angle and sample optical properties, excitation and collection geometry has the potential to induce distortions within diffuse reflectance spectra unrelated to tissue characteristics.

Estimation of chest-wall-induced diffused wave distortion with the assistance of ultrasound

The chest-wall layer underneath breast tissue consists of muscles and bones, which induce distortion in near-infrared diffused waves measured at distant source--detector pairs when reflection geometry is used. A priori information on chest-wall depth obtained from coregistered real-time ultrasound can be used to assist in the removal of distant measurements. We applied Monte Carlo simulation to a simple two-layer model consisting of breast tissue and a chest wall to investigate chest-wall-induced distortion. The Monte Carlo method indicates that, when more than 50% of the received photons travel through the breast tissue layer before being detected, the detected signal may be useful for image reconstruction. The results of phantom experiments obtained from the two-layer model further validate the distortion problem and demonstrate imaging improvement after distant measurements have been filtered out. Clinical examples have shown similar imaging improvements on reconstructed absorption maps. Clinical data obtained from 20 patients with the chest-wall depths of less than 2 cm from the skin surface suggest that the cutoff distances of distorted measurements are largely related to the chest-wall depth and are relatively independent of the optical properties of tissue.

Depth-sensitive reflectance measurements using obliquely oriented fiber probes

Computer simulation is used to facilitate the design of fiber-probe geometries that enable enhanced detection of optical signals arising from specific tissue depths. Obtaining understanding of the relationship between fiber-probe design and tissue interrogation is critical when developing strategies for optical detection of epithelial precancers that originate at known depths from the tissue surface. The accuracy of spectroscopic diagnostics may be enhanced by discretely probing the optical properties of epithelium and underlying stroma, within which the morphological and biochemical features vary as a function of depth. While previous studies have investigated controlling tissue-probing depth for fluorescence-based modalities, in this study we focus on the detection of reflected light scattered by tissue. We investigate how the depth of optical interrogation may be controlled through combinations of collection angles, source-detector separations, and numerical apertures. We find that increasing the obliquity of collection fibers at a given source-detector separation can effectively enhance the detection of superficially scattered signals. Fiber numerical aperture provides additional depth selectivity; however, the perturbations in sampling depth achieved through this means are modest relative to the changes generated by modifying the angle of collection and source-detection separation.

Monte Carlo Simulation of Light-Tissue Interaction: Three-Dimensional Simulation for Trans-Illumination-Based Imaging of Skin Lesions

Three-dimensional, voxel-based, and wavelength-dependent skin lesion models are developed and simulated using Monte Carlo techniques. The optical geometry of the Nevoscope with trans-illumination is used in the simulations for characterizing the lesion thickness. Based on the correlation analysis between the lesion thickness and the diffuse reflectance, optical wavelengths are selected for multispectral imaging of skin lesions using the Nevoscope. Tissue optical properties reported by various researchers are compiled together to form a voxel library. Tissue models used in the simulations are developed using the voxel library which offers flexibility in updating the optical properties and adding new media types into the models independent of the Monte Carlo simulation code.

Practical and adequate approach to modeling light propagation in an adult head with low-scattering regions by use of diffusion theory

A practical and adequate approach to modeling light propagation in an adult head with a low-scattering cerebrospinal fluid (CSF) region by use of diffusion theory was investigated. The diffusion approximation does not hold in a nonscattering or low-scattering regions. The hybrid radiosity-diffusion method was adopted to model the light propagation in the head with a nonscattering region. In the hybrid method the geometry of the nonscattering region is acquired as a priori information. In reality, low-level scattering occurs in the CSF region and may reduce the error caused by the diffusion approximation. The partial optical path length and the spatial sensitivity profile calculated by the finite-element method agree well with those calculated by the Monte Carlo method in the case in which the transport scattering coefficient of the CSF layer is greater than 0.3 mm(-1). Because it is feasible to assume that the transport scattering coefficient of a CSF layer is 0.3 mm(-1), it is practical to adopt diffusion theory to the modeling of light propagation in an adult head as an alternative to the hybrid method.

An investigation on the use of data-driven scattering profiles in Monte Carlo simulations of ultraviolet light propagation in skin tissues

Ultraviolet light can affect the appearance and medical condition of the human skin by triggering biophysical processes such as erythema, melanogenesis, photoaging and carcinogenesis. The evolution of these processes is related to the amount of ultraviolet light absorbed by skin pigments. This amount may vary with the wavelength and path length of the radiation that is propagated within the skin tissues. For many years, biomedical researchers have been investigating the propagation of ultraviolet light in skin tissues through Monte Carlo simulations. The scattering of the incident radiation by tissue internal structures, a key component in this process, is usually approximated by functions without a plausible connection with the underlying physical phenomena. In this paper, we examine the origins of such an approach, and question its generalized use with respect to wavelengths and biological materials for which there is no supporting data available. Furthermore, we perform comparisons to demonstrate that the accuracy and predictability of Monte Carlo simulations of ultraviolet propagation in skin tissues can be improved by using a data-driven approach to represent the scattering profile of these tissues.

Factors Influencing Quantification of in Vivo Bioluminescence Imaging: Application to Assessment of Pancreatic Islet Transplants

The aim of this study is to determine and characterize factors influencing in vivo bioluminescence imaging (BLI) and apply them to the specific application of imaging transplanted pancreatic islets. Noninvasive quantitative assessment of transplanted pancreatic islets poses a formidable challenge. Murine pancreatic islets expressing firefly luciferase were transplanted under the renal capsule or into the portal vein of nonobese diabetic-severe combined immunodeficiency mice and the bioluminescence was quantified with a cooled charge coupled device camera and digital photon image analysis. The important, but often neglected, effects of wound healing, mouse positioning, and transplantation site on bioluminescence measurements were investigated by imaging a constant emission, isotropic light-emitting bead (lambda = 600) implanted at the renal or hepatic site. The renal beads emitted nearly four times more light than hepatic beads with a smaller spot size, indicating that light absorption and scatter are greatly influenced by the transplant site and must be accounted for in BLI measurements. Detected luminescence decreased with increasing angle between the mouse surface normal and optical axis. By defining imaging parameters such as postsurgical effects, animal positioning, and light attenuation as a function of transplant site, this study develops BLI as a useful imaging modality for quantitative assessment of islets post-transplantation.

A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method

RATIONALE AND OBJECTIVES

As an important part of bioluminescence tomography, which is a newly developed optical imaging modality, mouse optical simulation environment (MOSE) is developed to simulate bioluminescent phenomena in the living mouse and to predict bioluminescent signals detectable outside the mouse. This simulator is dedicated to small animal optical imaging based on bioluminescence.

MATERIALS AND METHODS

With the parameters of biological tissues, bioluminescent sources, and charge coupled device (CCD) detectors, the 2-dimensional/3-dimensional MOSE simulates the whole process of the light propagation in 2-dimensional/3-dimensional biological tissues using the Monte Carlo method. Both the implementation details and the software architecture are described in this article.

RESULTS

The software system is implemented in the Visual C++ programming language with the OpenGL techniques and has a user-friendly interface facilitating interactions relevant to bioluminescent imaging. The accuracy of the system is verified by comparing the MOSE results with independent data from analytic solutions and commercial software.

CONCLUSION

As shown in our simulation and analysis, the MOSE is accurate, flexible, and efficient to simulate the photon propagation for bioluminescence tomography. With graduate refinements and enhancements, it is hoped that the MOSE will become a standard tool for bioluminescence tomography.

Effective Mie scattering of a spherical fractal aggregate and its application in turbid media

An effective Mie-scattering model is developed to deal with the scattering property of a spherical fractal aggregate consisting of scattering particles. In this model the scattered field of a scattering particle is given by the classical Mie-scattering theory. On the basis of the Monte Carlo simulation method, we determine the physical parameters of a scattering aggregate, the scattering efficiency Q, and the anisotropy value g, as well as their dependence on the size and the effective mean-free-path length of a scattering aggregate. Accordingly, photon migration through a microscope objective focused into a turbid medium including scattering aggregates is simulated to understand the effect of complex tissue on image quality.

Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium

Background

The bioluminescent enzyme firefly luciferase (Luc) or variants of green fluorescent protein (GFP) in transformed cells can be effectively used to reveal molecular and cellular features of neoplasia in vivo. Tumor cell growth and regression in response to various therapies can be evaluated by using bioluminescent imaging. In bioluminescent imaging, light propagates in highly scattering tissue, and the diffusion approximation is sufficiently accurate to predict the imaging signal around the biological tissue. The numerical solutions to the diffusion equation take large amounts of computational time, and the studies for its analytic solutions have attracted more attention in biomedical engineering applications.

Methods

Biological tissue is a turbid medium that both scatters and absorbs photons. An accurate model for the propagation of photons through tissue can be adopted from transport theory, and its diffusion approximation is applied to predict the imaging signal around the biological tissue. The solution to the diffusion equation is formulated by the convolution between its Green's function and source term. The formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium can be obtained to accelerate the forward simulation of bioluminescent phenomena.

Results

The closed form solutions have been derived for the time-dependent diffusion equation and the steady-state diffusion equation with solid and hollow spherical sources in a homogeneous medium, respectively. Meanwhile, the relationship between solutions with a solid sphere source and ones with a surface sphere source is obtained.

Conclusion

We have formulated solutions for the diffusion equation with solid and hollow spherical sources in an infinite homogeneous medium. These solutions have been verified by Monte Carlo simulation for use in biomedical optical imaging studies. The closed form solution is highly accurate and more computationally efficient in biomedical engineering applications. By using our analytic solutions for spherical sources, we can better predict bioluminescent signals and better understand both the potential for, and the limitations of, bioluminescent tomography in an idealized case. The formulas are particularly valuable for furthering the development of bioluminescent tomography.

Analytical model to describe fluorescence spectra of normal and preneoplastic epithelial tissue: comparison with Monte Carlo simulations and clinical measurements

Fluorescence spectroscopy has shown promise for the detection of precancerous changes in vivo. The epithelial and stromal layers of tissue have very different optical properties; the albedo is relatively low in the epithelium and approaches one in the stroma. As precancer develops, the optical properties of the epithelium and stroma are altered in markedly different ways: epithelial scattering and fluorescence increase, and stromal scattering and fluorescence decrease. We present an analytical model of the fluorescence spectrum of a two-layer medium such as epithelial tissue. Our hypothesis is that accounting for the two different tissue layers will provide increased diagnostic information when used to analyze tissue fluorescence spectra measured in vivo. The Beer-Lambert law is used to describe light propagation in the epithelial layer, while light propagation in the highly scattering stromal layer is described with diffusion theory. Predictions of the analytical model are compared to results from Monte Carlo simulations of light propagation under a range of optical properties reported for normal and precancerous epithelial tissue. In all cases, the mean square error between the Monte Carlo simulations and the analytical model are within 15%. Finally, model predictions are compared to fluorescence spectra of normal and precancerous cervical tissue measured in vivo; the lineshape of fluorescence agrees well in both cases, and the decrease in fluorescence intensity from normal to precancerous tissue is correctly predicted to within 5%. Future work will explore the use of this model to extract information about changes in epithelial and stromal optical properties from clinical measurements and the diagnostic value of these parameters.

Radiative transport in the delta-P1 approximation: accuracy of fluence rate and optical penetration depth predictions in turbid semi-infinite media

Using the delta-P(1) approximation to the Boltzmann transport equation we develop analytic solutions for the fluence rate produced by planar (1-D) and Gaussian beam (2-D) irradiation of a homogeneous, turbid, semi-infinite medium. To assess the performance of these solutions we compare the predictions for the fluence rate and two metrics of the optical penetration depth with Monte Carlo simulations. We provide results under both refractive-index matched and mismatched conditions for optical properties where the ratio of reduced scattering to absorption lies in the range 0< or =(micro(s')/micro(a))< or =10(4). For planar irradiation, the delta-P(1) approximation provides fluence rate profiles accurate to +/-16% for depths up to six transport mean free paths (l*) over the full range of optical properties. Metrics for optical penetration depth are predicted with an accuracy of +/-4%. For Gaussian irradiation using beam radii r(0) > or =3 l*, the accuracy of the fluence rate predictions is no worse than in the planar irradiation case. For smaller beam radii, the predictions degrade significantly. Specifically for media with (micro(s')/micro(a))=1 irradiated with a beam radius of r(0)=l*, the error in the fluence rate approaches 100%. Nevertheless, the accuracy of the optical penetration depth predictions remains excellent for Gaussian beam irradiation, and degrades to only +/-20% for r(0)=l*. These results show that for a given set of optical properties (micro(s')/micro(a)), the optical penetration depth decreases with a reduction in the beam diameter. Graphs are provided to indicate the optical and geometrical conditions under which one must replace the delta-P(1) results for planar irradiation with those for Gaussian beam irradiation to maintain accurate dosimetry predictions.

Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance

Metal nanoshells are a class of nanoparticles with tunable optical resonances. In this article, an application of this technology to thermal ablative therapy for cancer is described. By tuning the nanoshells to strongly absorb light in the near infrared, where optical transmission through tissue is optimal, a distribution of nanoshells at depth in tissue can be used to deliver a therapeutic dose of heat by using moderately low exposures of extracorporeally applied near-infrared (NIR) light. Human breast carcinoma cells incubated with nanoshells in vitro were found to have undergone photothermally induced morbidity on exposure to NIR light (820 nm, 35 W/cm2), as determined by using a fluorescent viability stain. Cells without nanoshells displayed no loss in viability after the same periods and conditions of NIR illumination. Likewise, in vivo studies under magnetic resonance guidance revealed that exposure to low doses of NIR light (820 nm, 4 W/cm2) in solid tumors treated with metal nanoshells reached average maximum temperatures capable of inducing irreversible tissue damage (DeltaT = 37.4 +/- 6.6 degrees C) within 4-6 min. Controls treated without nanoshells demonstrated significantly lower average temperatures on exposure to NIR light (DeltaT < 10 degrees C). These findings demonstrated good correlation with histological findings. Tissues heated above the thermal damage threshold displayed coagulation, cell shrinkage, and loss of nuclear staining, which are indicators of irreversible thermal damage. Control tissues appeared undamaged.

Characterization of spatial and temporal variations in the optical properties of tissuelike media with diffuse reflectance imaging

We describe a method to characterize spatial or temporal changes in the optical properties of turbid media using diffuse reflectance images acquired under broad-beam illumination conditions. We performed experiments on liquid phantoms whose absorption (mu(a)) and reduced scattering (mu(s)') coefficients were representative of those of biological tissues in the near infrared. We found that the relative diffuse reflectance R depends on mu(a) and mu(s)' only through the ratio mu(a)/mu(s)' and that dependence can be well described with an analytical expression previously reported in the literature [S. L. Jacques, Kluwer Academic Dordrecht (1996)]. We have found that this expression for R deviates from experimental values by no more than 8% for various illumination and detection angles within the range 0 degrees-30 degrees. Therefore, this analytical expression for R holds with good approximation even if the investigated medium presents curved or irregular surfaces. Using this expression, it is possible to translate spatial or temporal changes in the relative diffuse reflectance from a turbid medium into quantitative estimates of the corresponding changes of (mu(a)/mu(s)')(1/2). In the case of media with optical properties similar to those of tissue in the near infrared, we found that the changes mu(a)/mu(s)' should occur over a volume approximately 2 mm deep and 4 mm x 4 mm wide to apply this expression.

Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method

Here light propagation and radiation transfer of ultrafast laser pulses in heterogeneous biological tissues are simulated by use of the discrete-ordinates method (DOM). Formulations for solving the time-dependent radiation-transfer equation are deduced for three-dimensional geometries incorporating the Fresnel specularly reflecting boundary condition and characteristics of ultrafast laser pulses. The present method can treat both the incident laser intensity and the scattered radiation intensity from the walls of the targeted tissue as two components, i.e., a diffuse part and a specular part. Reflectivity at the tissue-air interface is calculated by use of Snell's law and the Fresnel equation. The high-order S10 DOM method is found to be adequate for describing the propagation and transfer of ultrafast laser radiation in heterogeneous tissues. The time-dependent radiation field in the tissue as well as the temporal radiation intensity profiles at the boundaries can be obtained simultaneously. The absolute values of the logarithmic slope of the temporal reflectance and transmittance at various detector positions are found to converge to a constant value in a homogeneous tissue model. With the inclusion of a small inhomogeneity, such a value will change in line with the property of the embedded inhomogeneity. The orientation of heterogeneity of the tissues also substantially affects the radiation intensity at the boundaries. The effect of the Fresnel boundary in the modeling is pronounced. The simulated transmitted signals are broadened and amplified under specularly reflecting boundary condition as compared with those under diffusely reflecting boundary conditions.

Fiber optic probes for biomedical optical spectroscopy

Fiber optic probes are a key element for biomedical spectroscopic sensing. We review the use of fiber optic probes for optical spectroscopy, focusing on applications in turbid media, such as tissue. The design of probes for reflectance, polarized reflectance, fluorescence, and Raman spectroscopy is illustrated. We cover universal design principles as well as technologies for beam deflecting and reshaping.

In vivo determination of local skin optical properties and photon path length by use of spatially resolved diffuse reflectance with applications in laser Doppler flowmetry

Methods for local photon path length and optical properties estimation, based on measured and simulated diffuse reflectance within 2 mm from the light source, are proposed and evaluated in vivo on Caucasian human skin. The accuracy of the methods was good (2%-7%) for path length and reduced scattering but poor for absorption estimation. Reduced scattering and absorption were systematically lower in the fingertip than in the forearm skin (633 nm). A maximum intrasite and interindividual variation of approximately 35% in an average photon path length was found. The methodology was applied in laser Doppler flowmetry, where path-length normalization of the estimated perfusion removed the optical property dependency.

Optical spectroscopy for detection of neoplasia

Fluorescence and reflectance spectroscopy provide the ability to assess tissue structure and metabolism in vivo in real time, providing improved diagnosis of pre-cancerous lesions. Reflectance spectroscopy can probe changes in epithelial nuclei that are important in pre-cancer detection, such as mean nuclear diameter, nuclear size distribution and nuclear refractive index. Fluorescence spectroscopy can probe changes in epithelial cell metabolism, by assessing mitochondrial fluorophores, and epithelial-stromal interactions, by assessing the decrease in collagen crosslink fluorescence that occurs with pre-cancer. Thus, fluorescence and reflectance spectroscopy provide complementary information useful for pre-cancer diagnosis. Tissue engineering provides three-dimensional cell cultures that can be used to further explore the relationship between tissue structure and biological events important in cancer development and progression. In the future, improving our understanding of the biological changes that can be assessed using spectroscopy will not only improve optical techniques but also provide new tools to better understand cancer biology.

Reply to comment on "Excitation with a focused, pulsed optical beam in scattering media: diffraction effects."

We address the issues that were raised by Tycho and Jørgensen [Appl. Opt. 41, 4709 (2002)] concerning our strategy [Appl. Opt. 39, 5244 (2000)] for incorporating the wave properties of light in the description of a propagating focused excitation beam in a highly scattering medium. We explain that the strategy is consistent with the Huygens-Fresnel principle and does not violate the energy conservation principle.

Photon pathlength determination based on spatially resolved diffuse reflectance

A method for the prediction of the average photon pathlength in turbid media has been developed. The method is based on spatially resolved diffuse reflectance with discrete source detector distances up to 2 mm. Light reflectance was simulated using a Monte Carlo technique with a one-layer model utilizing a wide range of optical properties, relevant to human skin. At a source detector separation of 2 mm, the pathlength can vary sixfold due to differences in optical properties. By applying various preprocessing and prediction techniques, the pathlength can be predicted with a root-mean-square error of approximately 5%. Estimation of the photon pathlength can be used, e.g., to remove the influence of optical properties on laser Doppler flowmetry perfusion readings, which are almost linearly related to the average photon pathlength.

Influence of optical properties and fiber separation on laser doppler flowmetry

Microcirculatory blood flow can be measured using a laser Doppler flowmetry (LDF) probe. However, the readings are affected by the tissue's optical properties (absorption and scattering coefficients, mu(a) and mu(s)) and probe geometry. In this study the influence of optical properties [mu(a)in(0.053,0.23) mm-1,mu(s)in(14.7,45.7) mm-1] on LDF perfusion and LDF sampling depth was evaluated for different fiber separations. In vitro measurements were made on a sophisticated tissue phantom with known optical properties that mimicked blood flow at different depths. Monte Carlo simulations were carried out to extend the geometry of the tissue phantom. A good correlation between measured and simulated data was found. The simulations showed that, for fixed flow at a discrete depth, the influence of mu(s) or mu(a) on LDF perfusion increased with an increase in flow depth and decreased with an increase in fiber separation. For a homogeneous flow distribution, however, the perfusion varied 40% due to variations in the optical properties, almost independent of the fiber separation (0.23-1.61 mm). Therefore, the effect in real tissue is likely to vary due to the unknown heterogeneous blood flow distribution. Further, the LDF sampling depth increased with a decrease in mu(s) or mu(a) and an increase in fiber separation. For fiber separation of 0.46 mm, the e-1 sampling depth ranged from 0.21 to 0.39 mm.

Fluorescence of indocyanine green in blood: intensity dependence on concentration and stabilization with sodium polyaspartate

Indocyanine green (ICG) has been widely used in cardiovascular, hepatic, and ophthalmologic studies. Application of this fluorescent dye has been handicapped by its poor stability in solution and by the complex dependence of its fluorescence intensity on concentration. Noncovalent interactions between ICG and sodium polyaspartate (PASP) stabilize ICG fluorescence in aqueous solution, but the effect of PASP on ICG fluorescence in blood has not been described. The current study had two main goals: first, to characterize in vitro in blood the relationship between fluorescence intensity and concentration of ICG-PASP (ICG) and the stability of this relationship over time; second, to test a new phenomenological model describing the dependence of ICG fluorescence on concentration. Freshly-prepared ICG and ICG-PASP solutions produced the same fluorescence intensity over a wide range of concentrations (0.0005-0.1271 mg/ml). The peak fluorescence of ICG was reduced by 11% after 10 h and by 72% at 7 days. In contrast, the peak fluorescence intensity of ICG-PASP solutions was nearly unchanged for up to 14 days. The dependence of the fluorescence intensity on concentration was accurately represented by our model that accounted for the generation of fluorescence following light absorption, and for the reabsorption of the emitted fluorescence by ICG.

Quantifying spatial localization of optical mapping using Monte Carlo simulations

Optical mapping techniques used to study spatial distributions of cardiac activity can be divided into two categories. 1) Broad-field excitation method, in which hearts stained with voltage or calcium sensitive dyes are illuminated with broad-field excitation light and fluorescence is collected by image or photodiode arrays. 2) Laser scanning method, in which illumination uses a scanning laser and fluorescence is collected with a photomultiplier tube. The spatial localization of the fluorescence signal for these two methods is unknown and may depend upon light absorption and scattering at both excitation and emission wavelengths. We measured the absorption coefficients (micro a), scattering coefficients (micro s), and scattering anisotropy coefficients (g) at representative excitation and emission wavelengths in rabbit heart tissue stained with di-4-ANEPPS or co-stained with both Rh237 and Oregon Green 488 BAPTA 1. Monte Carlo models were then used to simulate absorption and scattering of excitation light and fluorescence emission light for both broad-field and laser methods in three-dimensional tissue. Contributions of local emissions throughout the tissue to fluorescence collected from the tissue surface were determined for both methods. Our results show that spatial localization depends on the light absorption and scattering in tissue and on the optical mapping method that is used. A tissue region larger than the laser beam or collecting area of the array element contributes to the optical recordings.

Optical-thermal simulation of tonsillar tissue irradiation

BACKGROUND AND OBJECTIVE

Despite laser applications targetted toward tonsillar tissue, there has been no characterization of underlying optical and thermal events during laser irradiation of tonsillar tissue.

STUDY DESIGN/MATERIALS AND METHODS

The optical properties of canine and human tonsils were determined at 805 nm (diode laser) and 1,064 nm (Nd:YAG laser). An optical-thermal simulation was developed to predict the temperature rise in irradiated human tonsils.

RESULTS

The optical properties of human and canine tonsillar tissue are similar at both wavelengths. The optical-thermal simulation was validated and predicts that at 10 W and 1 minute of irradiation, the heat will be contained within the human tonsil. The diode laser causes more superficial heating than the Nd:YAG laser.

CONCLUSIONS

The safety of irradiating human tonsils was shown. The diode laser is superior to the Nd:YAG laser because less heat affects collateral structures. The optical-thermal simulation detailed in this study can be used to predict the temperature rise in tissues undergoing irradiation.

Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media

The discrete-ordinates method is formulated to solve transient radiative transfer with the incorporation of a transient term in the transfer equation in two-dimensional rectangular enclosures containing absorbing, emitting, and anisotropically scattering media subject to diffuse and/or collimated laser irradiation. The governing equations resulting from the discrete-ordinates discretization of the angular directions are further discretized in the spatial and the temporal domains by the finite-volume approach. The current formulation is suitable for solving transient laser transport in turbid media as well as for steady-state radiative transfer in many engineering problems. The method is applied to several example problems and compared with existing steady-state solutions and Monte Carlo transient solutions. Good agreement is found in all cases. Short-pulsed laser interaction and propagation in a turbid medium with high scattering albedo are studied. The imaging of an inhomogeneous zone inside a turbid medium is demonstrated.

Visualizing excitation waves inside cardiac muscle using transillumination

Voltage-sensitive fluorescent dyes have become powerful tools for the visualization of excitation propagation in the heart. However, until recently they were used exclusively for surface recordings. Here we demonstrate the possibility of visualizing the electrical activity from inside cardiac muscle via fluorescence measurements in the transillumination mode (in which the light source and photodetector are on opposite sides of the preparation). This mode enables the detection of light escaping from layers deep within the tissue. Experiments were conducted in perfused (8 mm thick) slabs of sheep right ventricular wall stained with the voltage-sensitive dye di-4-ANEPPS. Although the amplitude and signal-to-noise ratio recorded in the transillumination mode were significantly smaller than those recorded in the epi-illumination mode, they were sufficient to reliably determine the activation sequence. Penetration depths (spatial decay constants) derived from measurements of light attenuation in cardiac muscle were 0.8 mm for excitation (520 +/- 30 nm) and 1.3 mm for emission wavelengths (640 +/- 50 nm). Estimates of emitted fluorescence based on these attenuation values in 8-mm-thick tissue suggest that 90% of the transillumination signal originates from a 4-mm-thick layer near the illuminated surface. A 69% fraction of the recorded signal originates from > or =1 mm below the surface. Transillumination recordings may be combined with endocardial and epicardial surface recordings to obtain information about three-dimensional propagation in the thickness of the myocardial wall. We show an example in which transillumination reveals an intramural reentry, undetectable in surface recordings.

Noninvasive determination of hemoglobin and hematocrit using a temperature-controlled localized reflectance tissue photometer

We performed visible/near-infrared optical measurements on the forearm of human subjects. We conducted four studies: one study using a commercial diffuse reflectance spectrometer, and three studies using a breadboard temperature-controlled localized reflectance tissue photometer. Calibration relationships were established between skin reflectance signal and either the reference blood hemoglobin (Hb) concentration or the hematocrit values (Hct). Prediction results were expressed as the prediction correlation coefficient (r(p)) and the standard error for cross-validation prediction (CV-SEP). Using diffuse reflectance measurement, r(p) = 0. 8, CV-SEP = 0.9 g/dL for Hb and r(p) = 0.7, CV-SEP = 3.3% for Hct (n = 40). In a localized reflectance study involving calculating the absorption and scattering coefficients and including effect of change of skin temperature in the calibration model, the best prediction results were r(p) = 0.9, CV-SEP = 0.8 g/dL for Hb and r(p) = 0.8, CV-SEP = 3% for Hct (n = 26). In a second localized reflectance study on a population having diverse skin colors at 34 degrees C, the optimal model led to r(p) = 0.8, CV-SEP = 0.9 g/dL for Hb and r(p) = 0.9, CV-SEP = 2.1% for Hct (n = 28) using the localized reflectance values without deducing the absorption and scattering coefficients. Improvement in the correlation was more noticeable for Hct than for the case of Hb. The photometer was used to screen prospective blood donors with low Hb concentration. It was possible to predict anemic subjects in the limited prospective blood donor population.

Excitation with a focused, pulsed optical beam in scattering media: diffraction effects

To gain a better understanding of the spatiotemporal problems that are encountered in two-photon excitation fluorescence imaging through highly scattering media, we investigate how diffraction affects the three-dimensional intensity distribution of a focused, pulsed optical beam propagating inside a scattering medium. In practice, the full potential of the two-photon excitation fluorescence imaging is unrealized at long scattering depths, owing to the unwanted temporal and spatial broadening of the femtosecond excitation light pulse that reduces the energy density at the geometric focus while it increases the excitation energy density in the out-of-focus regions. To analyze the excitation intensity distribution, we modify the Monte Carlo-based photon-transport model to a semi-quantum-mechanical representation that combines the wave properties of light with the particle behavior of the propagating photons. In our model the propagating photon is represented by a plane wave with its propagation direction in the scattering medium determined by the Monte Carlo technique. The intensity distribution in the focal region is given by the square of the linear superposition of the various plane waves that arrive at different incident angles and optical path lengths. In the absence of scattering, the propagation model yields the intensity distribution that is predicted by the Huygens-Fresnel principle. We quantify the decrease of the energy density delivered at the geometric focus as a function of the optical depth to the mean-free-path ratio that yields the average number of scattering events that a photon encounters as it propagates toward the focus. Both isotropic and anisotropic scattering media are considered. Three values for the numerical aperture (NA) of the focusing lens are considered: NA = 0.25, 0.5, 0.75.

Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media

An isotropic scaling formulation is evaluated for transient radiative transfer in a one-dimensional planar slab subject to collimated and/or diffuse irradiation. The Monte Carlo method is used to implement the equivalent scattering and exact simulations of the transient short-pulse radiation transport through forward and backward anisotropic scattering planar media. The scaled equivalent isotropic scattering results are compared with predictions of anisotropic scattering in various problems. It is found that the equivalent isotropic scaling law is not appropriate for backward-scattering media in transient radiative transfer. Even for an optically diffuse medium, the differences in temporal transmittance and reflectance profiles between predictions of backward anisotropic scattering and equivalent isotropic scattering are large. Additionally, for both forward and backward anisotropic scattering media, the transient equivalent isotropic results are strongly affected by the change of photon flight time, owing to the change of flight direction associated with the isotropic scaling technique.

Three-dimensional optical phantom and its application in photodynamic therapy

BACKGROUND AND OBJECTIVE

A technique to manufacture a stable, reproducible three-dimensional optical phantom is presented. This phantom reproduces the tissue's optical properties as well as the geometry and, to some extent, the mechanical properties of the organ concerned. Easy to make and to handle, this phantom is a useful tool for numerous medical applications involving light interaction with biological tissues.

STUDY DESIGN/MATERIALS AND METHODS

The phantom is based on a transparent two-component silicone, which is molded into the desired shape and cured at room temperature. Specific optical properties are obtained by adding scatterers (Al2O3 particles or polystyrene microspheres) and absorbers (dyes or pigments). A method to measure the radiant energy fluence rate in the phantom is described. This method is based on a small isotropic optical detector.

RESULTS

A three-dimensional phantom of the bronchial tree is presented. This phantom is used for testing new light distributors designed for photodynamic therapy of the bronchi.

CONCLUSION

The proposed technique allows one to produce a stable three-dimensional phantom with accurately predictable optical properties.

Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy

Frequency-domain photon migration (FDPM) is a non-invasive optical technique that utilizes intensity-modulated, near-infrared (NIR) light to quantitatively measure optical properties in thick tissues. Optical properties (absorption, mu(a), and scattering, mu(s)', parameters) derived from FDPM measurements can be used to construct low-resolution (0.5 to 1 cm) functional images of tissue hemoglobin (total, oxy-, and deoxy-forms), oxygen saturation, blood volume fraction, water content, fat content and cellular structure. Unlike conventional NIR transillumination, FDPM enables quantitative analysis of tissue absorption and scattering parameters in a single non-invasive measurement. The unique functional information provided by FDPM makes it well-suited to characterizing tumors in thick tissues. In order to test the sensitivity of FDPM for cancer diagnosis, we have initiated clinical studies to quantitatively determine normal and malignant breast tissue optical and physiological properties in human subjects. Measurements are performed using a non-invasive, multi-wavelength, diode-laser FDPM device optimized for clinical studies. Results show that ductal carcinomas (invasive and in situ) and benign fibroadenomas exhibit 1.25 to 3-fold higher absorption than normal breast tissue. Within this group, absorption is greatest for measurements obtained from sites of invasive cancer. Optical scattering is approximately 20% greater in pre-menopausal versus post-menopausal subjects due to differences in gland/cell proliferation and collagen/fat content. Spatial variations in tissue scattering reveal the loss of differentiation associated with breast disease progression. Overall, the metabolic demands of hormonal stimulation and tumor growth are detectable using photon migration techniques. Measurements provide quantitative optical property values that reflect changes in tissue perfusion, oxygen consumption, and cell/matrix development.

Optical and thermal characterization of albumin protein solders

The effect of temperature on the optical and thermal properties of pure and indocyanine green-doped albumin protein solders as a function of wavelength has been studied between 25 degrees C and 100 degrees C. An increase in the group refractive index by up to 4% and a decrease in absorption coefficient (approximately 800 nm) by up to 8%, after denaturing the solder specimens in a constant-temperature water bath at temperatures of 60-100 degrees C, were not significant. The reduced scattering coefficient, however, increased rapidly with temperature as the solder changed from being a highly nonscattering medium at room temperature to a highly scattering medium at temperatures close to 70 degrees C. The thermal conductivity, thermal diffusivity, and heat capacity increased by up to 30%, 15%, and 10%, respectively. Finally, the frequency factor and activation energy were measured to be 3.17 x 10(56) s(-1) and 3.79 x 10(5) J mol(-1), respectively, for liquid protein solders (25% bovine serum albumin) and 3.50 x 10(57) s(-1) and 3.85 x 10(5) J mol(-1), respectively, for solid protein solders (60% bovine serum albumin). Incorporation of dynamic optical and thermal properties into modeling studies of laser tissue interactions could have a significant influence on the determination of the expected zone of damage.

Hybrid Monte Carlo for photon transport through optically thick scattering media

A Monte Carlo simulation code developed to model time-domain transillumination measurements with small-area detectors through an optically thick scattering slab is presented. A hybrid approach has been implemented to reduce calculation times. Most of the scattering slab is treated stochastically, albeit with variance reduction techniques and the isotropic diffusion similarity rule. The contribution to the output signal per unit area and time of photon packets propagating in a thin slice near the output face of the slab is calculated analytically after each propagation step. This approach drastically reduces the calculation time but produces spikes in the temporal signals.

Spectroscopic analysis of changes in remitted illumination: the response to increased neural activity in brain

Imaging of neural activation has been used to produce maps of functional architecture and metabolic activity. There is some uncertainty associated with the sources underlying the intrinsic signals. It has been reported that following increased neural activity there was little increased oxygen consumption ( approximately 5%), although glucose consumption increased by approximately 50%. The research we describe uses a modification of the Beer-Lambert Law called path-length scaling analysis (PLSA) to analyze the spectra of the hemodynamic and metabolic responses to vibrissal stimulation in rat somatosensory cortex. The results of the PLSA algorithm were compared with those obtained using a linear spectrographic analysis method (we refer to this as LMCA). There are differences in the results of the analysis depending on which of the two algorithms (PLSA or LMCA) is used. Using the LMCA algorithm, we obtain results showing an increase in the volume of Hbr at approximately 2 s, following onset of stimulation but no complementary decrease in oxygenated haemoglobin (HbO(2)). These results are similar to a previous report. In contrast, after using the PLSA algorithm, the time series of the chromophore changes shows no evidence for an increase in the volume of deoxygenated haemoglobin (Hbr). However, after further analysis of the time series from the PLSA using general linear models (GLM) to remove contributions from low frequency baseline oscillations, both the HbO(2) and Hbr times series of the response to stimulation were found to be biphasic with an early decrease in saturation peaking approximately 1 s after onset of stimulation followed by a larger increase in saturation peaking at approximately 3 s. Finally, following the PLSA-then-GLM analysis procedure, we do not find convincing evidence for an increase in cytochrome oxidation following stimulation, though we demonstrate the PLSA algorithm to be capable of disassociating changes in cytochrome oxidation state from changes in hemoglobin oxygenation.

Absorption distribution of an optical beam focused into a turbid medium

The focusing of light into a turbid medium was studied with Monte Carlo simulations. Focusing was found to have a significant effect on the absorption distribution in turbid media when the depth of the focal point (the distance between the focal point and the surface of the turbid media) was less than or comparable with the transport mean free path. Focusing could significantly increase the peak absorption and narrow the absorption distribution. As the depth of the focal point increased, the peak absorption decreased, and the depth of peak absorption increased initially but quickly reached a plateau that was less than the transport mean free path. A refractive-index-mismatched boundary between the ambient medium and the turbid medium deteriorated the focusing effect, increased the absorption near the boundary, lowered the peak absorption, and broadened the absorption distribution.

Spectroscopic and Clinical Aspects of Noninvasive Glucose Measurements

Frequent determination of glucose concentrations in diabetic patients is an important tool for diabetes management. This requires repetitive lancing and finger bleeding. Use of noninvasive (NI) detection techniques offers several advantages, such as the absence of pain and exposure to sharp objects and biohazard materials, the potential for increased frequency of testing, and hence, tighter control of the glucose concentrations, and the potential for a closed-loop system including a monitor and an insulin pump. These potential advantages have led to considerable interest in the commercialization of NI glucose monitoring devices. Review of the scientific, patent, and commercial literature indicates that the spectroscopic basis for NI determination of glucose is not yet well established, and attempts at commercialization may be several steps ahead of our understanding the origin and characteristics of an in vivo glucose-specific or glucose-related signal. Several technologies have potential for leading to viable measuring devices, but most of the data are based on in vitro experimentation. Because of the technical complexity of in vivo glucose measurements, this review aims at discussing the gap between the established need and current technology limitations.

Monte carlo analysis of two-photon fluorescence imaging through a scattering medium

The behavior of two-photon fluorescence imaging through a scattering medium is analyzed by use of the Monte Carlo technique. The axial and transverse distributions of the excitation photons in the focused Gaussian beam are derived for both isotropic and anisotropic scatterers at different numerical apertures and at various ratios of the scattering depth with the mean free path. The two-photon fluorescence profiles of the sample are determined from the square of the normalized excitation intensity distributions. For the same lens aperture and scattering medium, two-photon fluorescence imaging offers a sharper and less aberrated axial response than that of single-photon confocal fluorescence imaging. The contrast in the corresponding transverse fluorescence profile is also significantly higher. Also presented are results comparing the effects of isotropic and anisotropic scattering media in confocal reflection imaging. The convergence properties of the Monte Carlo simulation are also discussed.

CONV--convolution for responses to a finite diameter photon beam incident on multi-layered tissues

A convolution program (CONV) solving responses to a collimated finite diameter photon beam perpendicularly incident on a multi-layered tissue has been coded in ANSI Standard C, hence, the program can be executed on various computers. The program, employing an extended trapezoidal rule for integration, convolves the responses to an infinitely narrow photon beam computed by a companion program (MCML). Dynamic data allocation is used for CONV as well as MCML, therefore, the number of tissue layers and grid elements of the grid system can be varied at run time. The potential error due to not scoring the first photon-tissue interactions separately is illustrated. The program, including the source code, has been in the public domain since 1992 and can be downloaded from the web site at http:(/)/biomed.tamu.edu/-lw.

Optimal beam size for light delivery to absorption-enhanced tumors buried in biological tissues and effect of multiple-beam delivery: a Monte Carlo study

Optimal laser light delivery into turbid biological tissues was studied by using Monte Carlo simulations based on the delta-scattering technique. The goal was to deliver efficiently the maximum amount of optical power into buried tumors being treated while avoiding potential damage to normal tissue caused by strong optical power deposition underneath the tissue surface illuminated by the laser beam. The buried tumors were considered to have much higher absorption than the surrounding normal tissue because of selective uptake of the absorption-enhancement dye. The power delivering efficiency to buried tumors was investigated for various diameters of the laser beam. An optimal beam diameter was estimated to achieve the maximum product of the power coupling efficiency and the power delivered to the buried tumor. The distribution of power deposition was simulated for single-beam delivery and multiple-beam delivery as well. The simulated results showed that with an appropriate dye enhancement and an optimal laser delivery configuration, a high selectivity for laser treatment of tumor could be achieved.