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

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.

Monte Carlo model for determination of the role of heat generation in laser-irradiated tissue

A Monte Carlo model is described for modeling photo propagation in a scattering medium. The fraction of locally absorbed photons is proportional to the local rate of heat generation in laser-irradiated tissue and the associated distribution of light (fluence rate) is obtained by dividing the rate of heat generation by the local absorption coefficient. Examples of computed distributions of the rate of heat generation are presented for situations where light scattering in tissue is important. The method is applied to analyze treatment of Port Wine Stain and the selection of laser wavelengths for cyclophotocoagulation.

Imaging through scattering media by the use of an analytical model of perturbation amplitudes in the time domain

A method of generating images through highly scattering media is presented that involves comparing measurements of the time-dependent intensity of transmitted light with an analytical model describing the sensitivity of that intensity on localized changes in optical properties. A least-squares fitting procedure is employed to derive the amplitudes of the measurement perturbations caused by embedded absorbers and scatterers located along a line of sight between the source and detector. Images are presented of a highly scattering, solid plastic phantom with optical properties closely matched to those of human breast tissue at near-infrared wavelengths. The phantom is a 54-mm-thick slab, containing four small cylinders of contrasting scatter and absorption. Results show that embedded absorbers can be distinguished from embedded scatterers, and that the diffusion perturbation amplitude provides inherently greater spatial resolution than the absorption perturbation amplitude.

Efficient Monte Carlo simulation of confocal microscopy in biological tissue

A variance-reduction technique is described that greatly improves the efficacy of Monte Carlo simulations of reflection-mode confocal microscopy in anisotropically scattering media. The efficiency gain is large enough that the performance of confocal microscopes probing as deep as 5 scattering lengths can be simulated with a desktop computer. We use the technique to simulate the response of a true confocal microscope probing biological tissue, a problem that has been impractical to undertake by using conventional Monte Carlo methods. Our most important finding is that operation of a confocal microscope in the true confocal mode enables much more effective rejection of undesired scattered light than operation in the partially coherent mode, but the maximum probing depths of microscopes operated in either mode are similar (2-3) scattering lengths) in practice because of sensitivity limitations.

Influence of the scattering phase function on light transport measurements in turbid media performed with small source-detector separations

Many methods of optical tissue diagnosis require that measurements be performed with small source-detector separations in a backscatter geometry. Monte Carlo simulations are used to demonstrate that for these situations light transport depends on the exact form of the angular scattering probability distribution, P(theta). Simulations performed with different forms of P(theta) with the same value of ?cos theta? result in the collection of significantly different fractions of the incident photons, particularly when small-numerical-aperture delivery and collection fibers are employed. More photons are collected for the distribution that has a higher probability of scattering events with theta > 125 degrees . For the clinically relevant optical parameters employed here, the differences in light collection are >60%.

Clinical determination of tissue optical properties by endoscopic spatially resolved reflectometry

A noninvasive method to measure the optical properties of a diffusing and absorbing medium is described. Based on the spatially resolved measurement of diffuse reflectance at the sample surface, this method is particularly suitable for investigating the in vivo optical properties of biological tissues endoscopically in a clinical context. The sensitivity of the measurement is discussed, and two optical probes for two different clinical applications are presented. Preliminary measurements are performed on a nonbiological medium, which illustrate the possibilities of the proposed method. Finally, we report on in vivo measurements of the optical properties of the human esophageal wall at 630 nm.

Anisotropy of radiance in tissue phantoms and Dunning R3327 rat tumors: radiance measurements with flat cleaved fiber probes

BACKGROUND AND OBJECTIVE

The goal of this study is to determine if flat cleaved fiber probes are appropriate for interstitial measurements of radiance in tissue. Flat cleaved probes have the advantage of high responsivity, and they are easy to insert into tissue. Owing to the non-isotropic response of flat cleaved probes, a calibration function is required, taking the anisotropy in the radiance in tissue into account.

STUDY DESIGN, MATERIALS AND METHODS

The method used to determine this function consists of radiance measurements in tissue, performed with a flat cleaved fiber probe mounted on a stereotactic stage for insertion into the tissue from different directions. Interstitial irradiation at 630 nm was delivered by a spherical source.

RESULTS

We found that the degree of anisotropy in the radiance decreases with increasing distance from the interstitially implanted source in two different tissue phantoms and in the Dunning R3327-AT and R3327-H rat tumor models.

CONCLUSION

A position-dependent calibration function is required for interstitially implanted flat cleaved fiber probes. An anisotropy function is presented, which modifies the measurements of radiance with a flat cleaved probe, to account for the change in anisotropy in the radiance. The anisotropy functions for the two tumor models differ substantially.

Light transport in tissue: Accurate expressions for one-dimensional fluence rate and escape function based upon monte carlo simulation

BACKGROUND AND OBJECTIVE

Surface laser irradiation of tissue often produces a fluence rate that varies only with depth. Modeling of laser-induced fluorescence involves an expression for the fraction of fluorescence emitted per unit depth that escapes from the medium. We present accurate expressions for fluence rate and escape function for the one-dimensional case based upon Monte Carlo simulation results.

STUDY DESIGN/MATERIAL AND METHODS

Expressions were proposed for fluence rate, phi (z)/E0 = C1exp (-k1z/delta)-C2exp(-k2z/delta), and escape function, G(z) = C3exp(-k3z/delta), that varied solely with depth relative to effective penetration depth, z/delta. The scalar (C) and exponential (k) coefficient values were found by curve fitting the expressions to Monte Carlo simulation results.

RESULTS

The coefficients varied as smooth functions of diffuse reflectance, Rd, for the range Rd = 0.01-0.8, and were independent of scattering anisotropy in the range g = 0.7-0.9. Simple expressions approximated the relationship of each coefficient to Rd.

CONCLUSION

The proposed expressions have accuracy comparable to Monte Carlo simulations, over an essentially unrestricted range of diffuse reflectance values. The expressions may be combined accurately to portray laser-induced fluorescence measurements of a turbid medium.

Photon-measurement density functions. Part I: Analytical forms

This paper addresses the problem of tomographic reconstruction of absorption and scattering parameters in the optical region from measurements of transilluminated light. Specifically, the question of the sensitivity of different measurement schemes on the boundary of an object to perturbations of the optical parameters within the object are addressed. The concept of a photon-sampling volume [Appl. Opt. 33, 448 (1994)] and a photon-hitting density [Appl. Opt. 32, 448 (1993)] is extended to a photon-measurement density function (PMDF). The PMDF is derived from the Green's function of the diffusion equation and can be expressed for measurements such as the time-varying intensity, integrated intensity, temporal moments, and phase shift, as well as for both absorption and diffusion perturbations. Closed-form solutions are given for a number of these functions in infinite space, half-space, and slab geometries. Example results are given in terms of three-dimensional images.

A study on 3D Monte Carlo modeling of photon propagation through tissue

Monte Carlo techniques have become popular in modeling of the random events with advantage of powerful computing systems. Especially they have been applied to simulate processes involving random behavior such as diffusion of the Gamma rays through matter and electron concentrations in semiconductors. Recent medical innovations such as Computer Automated Tomography (CAT) and Positron Emission Tomography (PET) are ideal for Monte Carlo modeling techniques. This paper presents derivation and results of the three dimensional Monte Carlo simulation. The results are presented for tissue interactions with photons at wavelength of 207 nm X rays and 630 nm red light. Resulting values of model tissue have been interpolated and mapped into two-dimensional pattern in gray tone. Combination of two-dimensional patterns allow a reconstruction in three dimensions.

MCML--Monte Carlo modeling of light transport in multi-layered tissues

A Monte Carlo model of steady-state light transport in multi-layered tissues (MCML) has been coded in ANSI Standard C; therefore, the program can be used on various computers. Dynamic data allocation is used for MCML, hence the number of tissue layers and grid elements of the grid system can be varied by users at run time. The coordinates of the simulated data for each grid element in the radial and angular directions are optimized. Some of the MCML computational results have been verified with those of other theories or other investigators. The program, including the source code, has been in the public domain since 1992.

Direct calculation of the moments of the distribution of photon time of flight in tissue with a finite-element method

Modeling of the full temporal behavior of photons propagating in diffusive materials is computationally costly. Rather than deriving intensity as a function of time to fine sampling, we may consider methods that derive a transform of this function. To derive the Fourier transform involves calculation in the (complex) frequency domain and relates to intensity-modulated experiments. We consider instead the Mellin transform and show that this relates to the moments of the original temporal distribution. A derivation of the Mellin transform given the Fourier transform that permits closed-form derivations of the temporal moments for various simple geometries is presented. For general geometries a finite-element method is presented, and it is demonstrated that the computational cost to produce the nth moment is the same as producing the first n temporal samples of the original function.

Nature of light scattering in dental enamel and dentin at visible and near-infrared wavelengths

The light-scattering properties of dental enamel and dentin were measured at 543, 632, and 1053 nm. Angularly resolved scattering distributions for these materials were measured from 0° to 180° using a rotating goniometer. Surface scattering was minimized by immersing the samples in an index-matching bath. The scattering and absorption coefficients and the scattering phase function were deduced by comparing the measured scattering data with angularly resolved Monte Carlo light-scattering simulations. Enamel and dentin were best represented by a linear combination of a highly forward-peaked Henyey-Greenstein (HG) phase function and an isotropic phase function. Enamel weakly scatters light between 543 nm and 1.06 µm, with the scattering coefficient (µ(s)) ranging from µ(s) = 15 to 105 cm(-1). The phase function is a combination of a HG function with g = 0.96 and a 30-60% isotropic phase function. For enamel, absorption is negligible. Dentin scatters strongly in the visible and near IR (µ(s)≅260 cm(-1)) and absorbs weakly (µ(a) ≅ 4 cm(-1)). The scattering phase function for dentin is described by a HG function with g = 0.93 and a very weak isotropic scattering component (˜ 2%).

Optical diffuse reflectance accessory for measurements of skin tissue by near-infrared spectroscopy

An optimized accessory for measuring the diffuse reflectance spectra of human skin tissue in the near-infrared spectral range is presented. The device includes an on-axis ellipsoidal collecting mirror with efficient illumination optics for small sampling areas of bulky body specimens. The optical design is supported by the results of a Monte Carlo simulation study of the reflectance characteristics of skin tissue. Because the results evolved from efforts to measure blood glucose noninvasively, the main emphasis is placed on the long-wavelength near-infrared range where sufficient penetration depth for radiation into tissue is still available. The accessory is applied for in vivo diffuse reflectance measurements.

Spectroscopic diagnosis of bladder cancer with elastic light scattering

BACKGROUND AND OBJECTIVES

Recently, significant progress has been made toward the development of optical, noninvasive medical diagnostics. The goal of this study was to evaluate elastic scatter measurements as a tool for diagnosing bladder cancer.

STUDY DESIGN/MATERIALS AND METHODS

In vivo measurements on 10 patients with suspected bladder cancer were made with the optical biopsy system (OBS) developed at Los Alamos National Laboratory. Elastic-scatter spectra over the wavelength range 250-800 nm were obtained using a fiber-optic probe through one of the lumens of a urological cystoscope. Measurements were made on putatively normal areas and areas of uncertain abnormality, as well as those suspected to be cancerous. After measurements were made with the OBS, biopsy samples were taken at the measurement sites. Comparisons of the histopathology and the optical spectra were then made.

RESULTS AND CONCLUSIONS

A diagnostic algorithm for distinguishing malignant from nonmalignant tissue based on the values of the slopes over the wavelength range 330-370 nm has a sensitivity of 100% and specificity of 97% for the limited number of patients in this study.

Confocal microscopy in turbid media

We examine the performance of confocal microscopes designed for probing structures embedded in turbid media. A heuristic scheme is described that combines a numerical Monte Carlo simulation of photon transport in a turbid medium with a geometrical ray trace through the confocal optics. To show the effects of multiple scattering on depth discrimination, we compare results from the Monte Carlo simulations and scalar diffraction theory. Experimental results showing the effects of the pinhole diameter and other variables on imaging performance at various optical depths in suspensions of polystyrene microspheres were found to correspond well with the Monte Carlo simulations. The major conclusion of the paper is that the trade-off between signal level and background scattered-light rejection places a fundamental limit on the sectioning capability of the microscope.

The effect of intestinal hypoperfusion on intestinal absorption and permeability during cardiopulmonary bypass

BACKGROUND/AIMS

Mean arterial pressure is reduced during hypothermic cardiopulmonary bypass. The aim of this study was to assess whether this was associated with intestinal hypoperfusion and whether it affected intestinal absorption and permeability.

METHODS

Twenty-six patients undergoing coronary artery bypass grafting underwent an intestinal absorption-permeability test involving ingestion of 3-O-methyl-D-glucose, D-xylose, L-rhamnose, and lactulose. Ingestion took place 2 days before, within 3 hours, and 5 days after hypothermic cardiopulmonary bypass. Hemodynamic parameters and gastric mucosal laser Doppler blood flow were measured perioperatively in eight patients.

RESULTS

Hypothermic (28 degrees C), nonpulsatile cardiopulmonary bypass resulted in a 25% reduction in mean blood pressure, 10% reduction in cardiac index, and a 46% reduction in gastric mucosal laser Doppler blood flow. There was 85.4%, 85.5%, and 73.6% reduction (P < 0.01) in active (3-O-methyl-D-glucose) and passive (D-xylose) carrier-mediated transport and passive, nonmediated transcellular (L-rhamnose) transport in the immediate postoperative period, respectively. The differential urine excretion of lactulose/L-rhamnose increased sixfold. All parameters returned to control levels by the fifth postoperative day.

CONCLUSIONS

Cardiopulmonary bypass, while maintaining generally acceptable levels of hemodynamic performance, is associated with significant intestinal hypoperfusion and malabsorption of monosaccharides, which may have implications for enteral drug treatment in the immediate postoperative period.

Simulation of stochastic micropopulation models--I. The SUMMERS simulation shell

A generic, abstract model and the simulation shell based on it, both called SUMMERS, are used as a framework for the implementation of stochastic micropopulation models; in these, each individual is followed separately while moving through a sequence of states. The shell supports groups of interacting members, individual characteristics and multiple simultaneous activities. Stochastic decisions may be made using Monte Carlo rules. Keywords control the simulations and the reports generated. A sensitivity analysis utility allows assessment of the dependency of outcomes on model features. Extensive use has been made of software engineering techniques. Specializations of SUMMERS are described in subsequent papers.

Diffuse reflectance from turbid media: an analytical model of photon migration

To calculate the diffuse reflectance from a semi-infinite slab of tissue, we introduce a probability distribution function, f(n)(g), that a photon will escape from the tissue after n scattering events. This approach permits the separation of the phase dependence of scattering, described by the anisotropy coefficient, g, from the absorption, micro(alpha), and scattering, micro(s), coefficients in the calculation of diffuse reflectance. We demonstrate that f(n)(g) and g are related to each other through a universal probability function. The analytical form of this probability function is explored and used to obtain the diffuse reflectance from tissue. The diffuse reflectance calculated with this method is in excellent agreement with Monte Carlo simulations over the parameter range typically found in human tissue, even for the values in which diffusion theory is a poor approximation.

Determining the optical properties of turbid mediaby using the adding-doubling method

A method is described for finding the optical properties (scattering, absorption, and scattering anisotropy) of a slab of turbid material by using total reflection, unscattered transmission, and total transmission measurements. This method is applicable to homogeneous turbid slabs with any optical thickness,albedo, or phase function. The slab may have a different index of refraction from its surroundings and may or may not be bounded by glass. The optical properties are obtained by iterating an adding-doubling solution of the radiative transport equation until the calculated values of the reflection and transmission match the measured ones. Exhaustive numerical tests show that the intrinsic error in the method is < 3% when four quadrature points are used.

Properties of photon density waves in multiple-scattering media

Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency (omega) and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a high-frequency dispersion regime where density wave phase velocity V(p) has a radicalomega dependence and (2) a low-frequency domain where V(p), is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (?) and modulation (m) response to simple relations for theappropriate regime. Our results indicate that reliable estimates of tissue like optical properties can be obtained, particularly when multiple modulation frequencies are employed.

Use of polarized light to discriminate short-path photons in a multiply scattering medium

<p>We describe a method for discriminating short- and long-path photons transmitted through a multiply scattering medium that is based on the relationship between the polarization states of the incident and forward-scattered light. Results of Monte Carlo simulations and experiments show that if the scattering anisotropy of the scatterers is sufficiently small, absorbing barriers embedded in optically dense suspensions of polystyrene spheres can be resolved with good contrast by selectively detecting a component of the scattered-light intensity that has preserved its incident circular polarization state.</p><p>The principles of operation of a polarization-modulation system capable of measuring small polarization fractions are explained. Using this system we were able to measure polarized light in a depolarized background over 1000 times as large.</p>

Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain

The light fluence distributions of 632.8 nm light incident on the exposed surface of normal rat brain in vivo have been measured using an interstitial, stereotactically-mounted optical fiber detector with isotropic response. The dependence of the relative fluence rate on depth and the spatial distribution of fluence were compared for incident beam diameters of 3 and 5 mm. The fluence rate at depth of 1-6 mm along the optical axis within the brain tissue was approximately 70% greater for a 5 mm diameter beam than for a 3 mm beam, at the same incident fluence rate, although the plots of the relative fluence rate vs depth were parallel over the depth range 1-6 mm. The depths of necrosis resulting from photodynamic treatment of brain tissue using the photosensitizer Photofrin and irradiation by 632 nm light with 3 and 5 mm incident beams were also measured. The observed difference in necrosis depths was consistent with the measured difference in fluence. The importance of beam size in photodynamic treatment with small diameter incident light fields is discussed.

Optical properties of Intralipid: a phantom medium for light propagation studies

Intralipid is an intravenous nutrient consisting of an emulsion of phospholipid micelles and water. Because Intralipid is turbid and has no strong absorption bands in the visible region of the electromagnetic spectrum, and is readily available and relatively inexpensive, it is often used as a tissue simulating phantom medium in light dosimetry experiments. In order to assist investigators requiring a controllable medium that over a finite range of wavelengths is optically equivalent to tissue, we have compiled previously published values of the optical interaction coefficients of Intralipid, most of which were measured at a wavelength of 633 nm. We have extended the measurements of the absorption and reduced scattering coefficients from 460 to 690 nm and the total attenuation coefficient from 500 to 890 nm. These measurements show that, for stock 10% Intralipid, the absorption coefficient varies from 0.015 to 0.001 cm-1 between 460 and 690 nm, the reduced scattering coefficient varies from 92 to 50 cm-1 between 460 and 690 nm, the total attenuation coefficient varies from 575 to 150 cm-1 between 500 and 890 nm, and the average cosine of scatter varies from 0.87 to 0.82 between 460 and 690 nm. With these data, we discuss the design of an optically tissue-equivalent phantom consisting of Intralipid and black India ink.

Pathologic analysis of photothermal and photomechanical effects of laser-tissue interactions

Pathologic analysis of the biologic effects and mechanisms of laser-tissue interactions requires correlation of the irradiation parameters with the biologic status and response of the target tissues over time. The photobiologic mechanisms of laser-induced tissue injury can be separated into three categories, photochemical, photothermal and photomechanical. Anatomic pathologic analysis of laser-induced lesions reveals alterations that represent either specific markers of the photobiologic mechanism or non-specific reactions to tissue injury. Repair, regeneration and wound healing of laser induced lesions appear to be non-specific responses to the type of tissue damage rather than the photobiologic mechanism producing the lesion.

In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions--I. Reflectance measurements

Reflectance spectrophotometry from 400 to 800 nm on different cutaneous pigmented lesions, including primary and metastatic malignant melanoma, pigmented nevi, lentigo and seborrhoeic keratosis, has been performed by using an external integrating sphere coupled to a spectrophotometer. Measurements show that reflectance spectra of the different lesions manifest dissimilar patterns, particularly in the near IR region. Comparison of reflectance of nevi with that of malignant melanomas results in a highly significant difference (P less than 10(-6)) between the two samples. Though interpretation of the spectra remains difficult as a result of the complexity of the optical processes of scattering and absorption, our results suggest that a detailed analysis of the reflectance spectrum may give clinically useful information, and could be utilized as an aid in clinical diagnosis of cutaneous pigmented lesions, especially where malignant melanoma is concerned.

In vivo tests of the concept of photodynamic threshold dose in normal rat liver photosensitized by aluminum chlorosulphonated phthalocyanine

In its simplest form, the photodynamic therapy (PDT) threshold dose model states that tissue necrosis due to PDT will occur if the number of photons absorbed by the photosensitizer per unit volume of tissue exceeds a critical value. This threshold is given by the product of photon fluence, photosensitizer concentration and specific absorption coefficient. To test the validity of this concept for PDT of normal rat liver sensitized with aluminum chlorosulphonated phthalocyanine (AISPC), all three of these parameters were varied by changing the injected AISPC dose, the wavelength of excitation and the irradiation geometry. The extent of necrosis caused by the treatment was consistent with the threshold model, except when the concentration of AISPC in the liver exceeded 20 micrograms g-1. For this animal model, we estimate the threshold to be (3.8 +/- 0.2) x 10(19) photons cm-3.

Monte Carlo modeling of light propagation in highly scattering tissues--II: Comparison with measurements in phantoms

Measurements of the fluence-depth distributions and of the diffuse reflectance of 633 nm light have been made in liquid media with optical properties similar to soft tissues. The results are compared with predictions of Monte Carlo computer calculations in order to test the adequacy of Monte Carlo modeling of light transport in tissue. Except at extremely high albedo, the experimental data and the Monte Carlo results agree well for the depth dependence of the fluence as a function of incident light beam diameter and optical absorption and scattering, and for the dependence of the diffuse reflectance on the albedo. The absolute experimental values for the fluence must be renormalized by a factor which varies with the albedo in order to match the model values, and the possible sources of this discrepancy are discussed.