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1.  Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates 
Biomedical Optics Express  2011;2(4):871-886.
Time-resolved fluorescence optical tomography allows 3-dimensional localization of multiple fluorophores based on lifetime contrast while providing a unique data set for improved resolution. However, to employ the full fluorescence time measurements, a light propagation model that accurately simulates weakly diffused and multiple scattered photons is required. In this article, we derive a computationally efficient Monte Carlo based method to compute time-gated fluorescence Jacobians for the simultaneous imaging of two fluorophores with lifetime contrast. The Monte Carlo based formulation is validated on a synthetic murine model simulating the uptake in the kidneys of two distinct fluorophores with lifetime contrast. Experimentally, the method is validated using capillaries filled with 2.5nmol of ICG and IRDye™800CW respectively embedded in a diffuse media mimicking the average optical properties of mice. Combining multiple time gates in one inverse problem allows the simultaneous reconstruction of multiple fluorophores with increased resolution and minimal crosstalk using the proposed formulation.
doi:10.1364/BOE.2.000871
PMCID: PMC3072127  PMID: 21483610
(170.6920) Time-resolved imaging; (170.3650) Lifetime-based sensing; (170.3010) Image reconstruction techniques; (110.6960) Tomography; (110.1758) Computational imaging
2.  3-D Monte Carlo-Based Scatter Compensation in Quantitative I-131 SPECT Reconstruction 
We have implemented highly accurate Monte Carlo based scatter modeling (MCS) with 3-D ordered subsets expectation maximization (OSEM) reconstruction for I-131 single photon emission computed tomography (SPECT). The scatter is included in the statistical model as an additive term and attenuation and detector response are included in the forward/backprojector. In the present implementation of MCS, a simple multiple window-based estimate is used for the initial iterations and in the later iterations the Monte Carlo estimate is used for several iterations before it is updated. For I-131, MCS was evaluated and compared with triple energy window (TEW) scatter compensation using simulation studies of a mathematical phantom and a clinically realistic voxel-phantom. Even after just two Monte Carlo updates, excellent agreement was found between the MCS estimate and the true scatter distribution. Accuracy and noise of the reconstructed images were superior with MCS compared to TEW. However, the improvement was not large, and in some cases may not justify the large computational requirements of MCS. Furthermore, it was shown that the TEW correction could be improved for most of the targets investigated here by applying a suitably chosen scaling factor to the scatter estimate. Finally clinical application of MCS was demonstrated by applying the method to an I-131 radioimmunotherapy (RIT) patient study.
doi:10.1109/TNS.2005.862956
PMCID: PMC2810869  PMID: 20104252
I-131 SPECT; image reconstruction; Monte Carlo; scatter correction; SPECT quantification
3.  Three-dimensional Neumann-series approach to model light transport in nonuniform media 
We present the implementation, validation, and performance of a three-dimensional (3D) Neumann-series approach to model photon propagation in nonuniform media using the radiative transport equation (RTE). The RTE is implemented for nonuniform scattering media in a spherical harmonic basis for a diffuse-optical-imaging setup. The method is parallelizable and implemented on a computing system consisting of NVIDIA Tesla C2050 graphics processing units (GPUs). The GPU implementation provides a speedup of up to two orders of magnitude over non-GPU implementation, which leads to good computational efficiency for the Neumann-series method. The results using the method are compared with the results obtained using the Monte Carlo simulations for various small-geometry phantoms, and good agreement is observed. We observe that the Neumann-series approach gives accurate results in many cases where the diffusion approximation is not accurate.
PMCID: PMC3963433  PMID: 23201945
4.  Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling 
Applied Optics  2011;50(21):4237-4245.
Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.
PMCID: PMC3326413  PMID: 21772413
5.  Analytical Light Reflectance Models For Overlapping-Illumination and Collection Area Geometries 
Applied optics  2012;51(33):8013-8021.
Several biomedical applications, such as detection of dysplasia, require selective interrogation of superficial tissue structures less than a few hundred microns thick. Techniques and methods have been developed to limit the penetration depth of light in tissue including the design of systems such as fiber-optic probes that have overlapping illumination and collection areas on the tissue surface. For such geometries, the diffusion approximation to the light transport equation typically does not apply and as a result there is no general model to extract tissue optical properties from reflectance measurements. In the current study, we employ Monte Carlo simulations to develop simple and compact analytical models for the light reflectance from these overlapping geometries. These models incorporate the size of the illumination and collection areas, the collection angle, the polarization of the incident light, and the optical properties of the sample. Moreover, these Monte Carlo simulations use the Whittle-Matérn model to describe scattering from spatially continuous refractive index media such as tissue, which is more general than models based on the conventionally used Henyey and Greenstein model. We validated these models on tissue-simulating phantoms. The models developed herein will facilitate the extraction of optical properties and aid in the design of optical systems employing overlapping illumination and collection areas including fiber-optic probes for in vivo tissue diagnosis.
PMCID: PMC3655705  PMID: 23207312
6.  Characterization of Scatter and Penetration Using Monte Carlo Simulation in 131I Imaging 
In 131I SPECT, image quality and quantification accuracy are degraded by object scatter as well as scatter and penetration in the collimator. The characterization of energy and spatial distributions of scatter and penetration performed in this study by Monte Carlo simulation will be useful for the development and evaluation of techniques that compensate for such events in 131I imaging.
Methods
First, to test the accuracy of the Monte Carlo model, simulated and measured data were compared for both a point source and a phantom. Next, simulations to investigate scatter and penetration were performed for four geometries: point source in air, point source in a water-filled cylinder, hot sphere in a cylinder filled with nonradioactive water, and hot sphere in a cylinder filled with radioactive water. Energy spectra were separated according to order of scatter, type of interaction, and γ-ray emission energy. A preliminary evaluation of the triple-energy window (TEW) scatter correction method was performed.
Results
The accuracy of the Monte Carlo model was verified by the good agreement between measured and simulated energy spectra and radial point spread functions. For a point source in air, simulations show that 73% of events in the photopeak window had either scattered in or penetrated the collimator, indicating the significance of collimator interactions. For a point source in a water-filled phantom, the separated energy spectra showed that a 20% photopeak window can be used to eliminate events that scatter more than two times in the phantom. For the hot sphere phantoms, it was shown that in the photopeak region the spectrum shape of penetration events is very similar to that of primary (no scatter and no penetration) events. For the hot sphere regions of interest, the percentage difference between true scatter counts and the TEW estimate of scatter counts was <12%.
Conclusion
In 131I SPECT, object scatter as well as collimator scatter and penetration are significant. The TEW method provides a reasonable correction for scatter, but the similarity between the 364-keV primary and penetration energy spectra makes it difficult to compensate for these penetration events using techniques that are based on spectral analysis.
PMCID: PMC2811856  PMID: 10647615
scatter correction; penetration; 131I imaging; SPECT; Monte Carlo simulated data
7.  Characterization of light transport in scattering media at sub-diffusion length scales with Low-coherence Enhanced Backscattering 
Low-coherence enhanced backscattering (LEBS) is a technique that has recently shown promise for tissue characterization and the detection of early pre-cancer. Although several Monte Carlo models of LEBS have been described, these models have not been accurate enough to predict all of the experimentally observed LEBS features. We present an appropriate Monte Carlo model to simulate LEBS peak properties from polystyrene microsphere suspensions in water. Results show that the choice of the phase function greatly impacts the accuracy of the simulation when the transport mean free path (ls*) is much greater than the spatial coherence length (LSC). When ls* < LSC, a diffusion approximation based model of LEBS is sufficiently accurate. We also use the Monte Carlo model to validate that LEBS can be used to measure the radial scattering probability distribution (radial point spread function), p(r), at small length scales and demonstrate LEBS measurements of p(r) from biological tissue. In particular, we show that pre-cancerous and benign mucosal tissues have different small length scale light transport properties.
doi:10.1109/JSTQE.2009.2032666
PMCID: PMC2964859  PMID: 21037980
Enhanced backscattering; cancer detection; tissue characterization; light Monte Carlo; spatial coherence
8.  Complex Geometric Models of Diffusion and Relaxation in Healthy and Damaged White Matter 
NMR in biomedicine  2010;23(2):152-162.
Which aspects of tissue microstructure affect diffusion weighted MRI signals? Prior models, many of which use Monte-Carlo simulations, have focused on relatively simple models of the cellular microenvironment and have not considered important anatomic details. With the advent of higher-order analysis models for diffusion imaging, such as high-angular-resolution diffusion imaging (HARDI), more realistic models are necessary. This paper presents and evaluates the reproducibility of simulations of diffusion in complex geometries. Our framework is quantitative, does not require specialized hardware, is easily implemented with little programming experience, and is freely available as open-source software. Models may include compartments with different diffusivities, permeabilities, and T2 time constants using both parametric (e.g., spheres and cylinders) and arbitrary (e.g., mesh-based) geometries. Three-dimensional diffusion displacement-probability functions are mapped with high reproducibility, and thus can be readily used to assess reproducibility of diffusion-derived contrasts.
doi:10.1002/nbm.1437
PMCID: PMC2838925  PMID: 19739233
Random walk; Monte-Carlo; particle simulation; DTI; DWI; reproducibility
9.  Multiphoton fluorescence recovery after photobleaching in bounded systems 
Multiphoton fluorescence recovery after photobleaching (MP-FRAP) is a laser microscopy technique used to measure diffusion coefficients of macromolecules in biological systems. The three-dimensional resolution and superior depth penetration within scattering samples offered by MP-FRAP make it an important tool for investigating both in vitro and in vivo systems. However, biological systems frequently confine diffusion within solid barriers, and to date the effect of such barriers on the measurement of absolute diffusion coefficients via MP-FRAP has not been studied. We have used Monte Carlo simulations of diffusion and MP-FRAP to understand the effect of barriers of varying geometries and positions relative to the two-photon focal volume. Furthermore, we supply ranges of barrier positions within which MP-FRAP can confidently be employed to measure accurate diffusion coefficients. Finally, we produce two new MP-FRAP models that can produce accurate diffusion coefficients in the presence of a single plane boundary or parallel infinite plane boundaries positioned parallel to the optical axis, up to the resolution limit of the multiphoton laser scanning microscope.
PMCID: PMC3413246  PMID: 21728580
10.  Analysis of the Reconstructibility and Noise Properties of Scattered Photons in Tc-99m SPECT 
Physics in medicine and biology  1997;42(12):2493-2516.
Since scattered photons carry degraded spatial information, scatter is typically considered a source of contamination in SPECT. However, with the advent of scatter modeling methods and reconstruction-based scatter compensation (RBSC), it may be possible to utilize scattered data in a productive manner. In this work we analyze the reconstructibility of scattered photon projection data and investigate the potential for using scattered photons to reduce the noise levels of SPECT images. We have simulated projection data for an elliptical phantom containing three cold rods in a uniform background of Tc-99m activity. A variety of photopeak and scatter energy windows were formed, as well as corresponding RBSC transfer matrices. Each statistically weighted matrix was decomposed using SVD and analyzed in terms of reconstructibility and noise properties. Results indicate that scattered photons contain sufficient information to reconstruct the source activity, but the scatter-only matrices are very poorly conditioned. We have also evaluated several methods of utilizing scattered events via RBSC, and compared them with other, idealized methods of handling scatter. It was found that scattered photons can be used productively when photopeak and non-photopeak data are separated through the use of multiple energy windows. The RBSC methods outperformed ideal scatter subtraction, but fell short of methods which assume perfect discrimination between scattered and primary events. The knowledge gained by this study may help guide future research and lead to better approaches to handling scatter in SPECT.
PMCID: PMC2804957  PMID: 9434303
11.  Improvements and considerations for size distribution retrieval from small-angle scattering data by Monte Carlo methods 
Journal of Applied Crystallography  2013;46(Pt 2):365-371.
A method is presented and applied, capable of retrieving form-free particle size distributions complete with uncertainties from small-angle scattering patterns. Special attention is paid to particle observability in the scattering patterns, accurate estimation of data uncertainty and the effect of uncertainty on the resulting size distribution statistics.
Monte Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve form-free particle size distributions from small-angle scattering patterns of non-interacting low-concentration scatterers such as particles in solution or precipitates in metals. Improvements are presented to existing MC methods, such as a non-ambiguous convergence criterion, nonlinear scaling of contributions to match their observability in a scattering measurement, and a method for estimating the minimum visibility threshold and uncertainties on the resulting size distributions.
doi:10.1107/S0021889813001295
PMCID: PMC3627408  PMID: 23596341
structure analysis; small-angle scattering; Monte Carlo methods; particle size distribution
12.  Monte Carlo modeling of a 6 and 18 MV Varian Clinac medical accelerator for in-field and out-of-field dose calculations: development and validation 
Physics in Medicine and Biology  2009;54(4):N43-N57.
There is a serious and growing concern about the increased risk of radiation-induced second cancers and late tissue injuries associated with radiation treatment. To better understand and to more accurately quantify non-target organ doses due to scatter and leakage radiation from medical accelerators, a detailed Monte Carlo model of the medical linear accelerator is needed. This paper describes the development and validation of a detailed accelerator model of the Varian Clinac operating at 6 and 18 MV beam energies. Over 100 accelerator components have been defined and integrated using the Monte Carlo code MCNPX. A series of in-field and out-of-field dose validation studies were performed. In-field dose distributions calculated using the accelerator models were tuned to match measurement data that are considered the de facto ‘gold standard’ for the Varian Clinac accelerator provided by the manufacturer. Field sizes of 4 cm × 4 cm, 10 cm × 10 cm, 20 cm × 20 cm and 40 cm × 40 cm were considered. The local difference between calculated and measured dose on the percent depth dose curve was less than 2% for all locations. The local difference between calculated and measured dose on the dose profile curve was less than 2% in the plateau region and less than 2 mm in the penumbra region for all locations. Out-of-field dose profiles were calculated and compared to measurement data for both beam energies for field sizes of 4 cm × 4 cm, 10 cm × 10 cm and 20 cm × 20 cm. For all field sizes considered in this study, the average local difference between calculated and measured dose for the 6 and 18 MV beams was 14 and 16%, respectively. In addition, a method for determining neutron contamination in the 18 MV operating model was validated by comparing calculated in-air neutron fluence with reported calculations and measurements. The average difference between calculated and measured neutron fluence was 20%. As one of the most detailed accelerator models for both in-field and out-of-field dose calculations, the model will be combined with anatomically realistic computational patient phantoms into a computational framework to calculate non-target organ doses to patients from various radiation treatment plans.
doi:10.1088/0031-9155/54/4/N01
PMCID: PMC3376900  PMID: 19141879
13.  Diagnosis of breast cancer using fluorescence and diffuse reflectance spectroscopy: a Monte-Carlo-model-based approach 
Journal of biomedical optics  2008;13(3):034015.
We explore the use of Monte-Carlo-model-based approaches for the analysis of fluorescence and diffuse reflectance spectra measured ex vivo from breast tissues. These models are used to extract the absorption, scattering, and fluorescence properties of malignant and nonmalignant tissues and to diagnose breast cancer based on these intrinsic tissue properties. Absorption and scattering properties, including β-carotene concentration, total hemoglobin concentration, hemoglobin saturation, and the mean reduced scattering coefficient are derived from diffuse reflectance spectra using a previously developed Monte Carlo model of diffuse reflectance. A Monte Carlo model of fluorescence described in an earlier manuscript was employed to retrieve the intrinsic fluorescence spectra. The intrinsic fluorescence spectra were decomposed into several contributing components, which we attribute to endogenous fluorophores that may present in breast tissues including collagen, NADH, and retinol/vitamin A. The model-based approaches removes any dependency on the instrument and probe geometry. The relative fluorescence contributions of individual fluorescing components, as well as β-carotene concentration, hemoglobin saturation, and the mean reduced scattering coefficient display statistically significant differences between malignant and adipose breast tissues. The hemoglobin saturation and the reduced scattering coefficient display statistically significant differences between malignant and fibrous/benign breast tissues. A linear support vector machine classification using (1) fluorescence properties alone, (2) absorption and scattering properties alone, and (3) the combination of all tissue properties achieves comparable classification accuracies of 81 to 84% in sensitivity and 75 to 89% in specificity for discriminating malignant from nonmalignant breast tissues, suggesting each set of tissue properties are diagnostically useful for the discrimination of breast malignancy.
doi:10.1117/1.2931078
PMCID: PMC2791791  PMID: 18601560
fluorescence; diffuse reflectance; spectroscopy; intrinsic fluorescence; optical property; Monte Carlo; breast cancer
14.  Electron emission from condensed phase material induced by fast protons† 
Radiation Protection Dosimetry  2010;143(2-4):135-138.
Monte Carlo track simulation has become an important tool in radiobiology. Monte Carlo transport codes commonly rely on elastic and inelastic electron scattering cross sections determined using theoretical methods supplemented with gas-phase data; experimental condensed phase data are often unavailable or infeasible. The largest uncertainties in the theoretical methods exist for low-energy electrons, which are important for simulating electron track ends. To test the reliability of these codes to deal with low-energy electron transport, yields of low-energy secondary electrons ejected from thin foils have been measured following passage of fast protons. Fast ions, where interaction cross sections are well known, provide the initial spectrum of low-energy electrons that subsequently undergo elastic and inelastic scattering in the material before exiting the foil surface and being detected. These data, measured as a function of the energy and angle of the emerging electrons, can provide tests of the physics of electron transport. Initial measurements from amorphous solid water frozen to a copper substrate indicated substantial disagreement with MC simulation, although questions remained because of target charging. More recent studies, using different freezing techniques, do not exhibit charging, but confirm the disagreement seen earlier between theory and experiment. One now has additional data on the absolute differential electron yields from copper, aluminum and gold, as well as for thin films of frozen hydrocarbons. Representative data are presented.
doi:10.1093/rpd/ncq529
PMCID: PMC3108277  PMID: 21183539
15.  Improved importance sampling for Monte Carlo simulation of time-domain optical coherence tomography 
Biomedical Optics Express  2011;2(5):1069-1081.
We developed an importance sampling based method that significantly speeds up the calculation of the diffusive reflectance due to ballistic and to quasi-ballistic components of photons scattered in turbid media: Class I diffusive reflectance. These components of scattered photons make up the signal in optical coherence tomography (OCT) imaging. We show that the use of this method reduces the computation time of this diffusive reflectance in time-domain OCT by up to three orders of magnitude when compared with standard Monte Carlo simulation. Our method does not produce a systematic bias in the statistical result that is typically observed in existing methods to speed up Monte Carlo simulations of light transport in tissue. This fast Monte Carlo calculation of the Class I diffusive reflectance can be used as a tool to further study the physical process governing OCT signals, e.g., obtain the statistics of the depth-scan, including the effects of multiple scattering of light, in OCT. This is an important prerequisite to future research to increase penetration depth and to improve image extraction in OCT.
doi:10.1364/BOE.2001069
PMCID: PMC3087565  PMID: 21559120
(170.3660) Light propagation in tissue; (110.4500) Optical coherence tomography
16.  A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media 
Physics in medicine and biology  2011;56(23):7419-7434.
In this work, development and evaluation of a three dimensional (3D) finite element model (FEM) based on the diffusion approximation of time-domain (TD) near-infrared fluorescence light transport in biological tissue is presented. This model allows both excitation and fluorescence temporal point-spread function (TPSF) data to be generated for heterogeneous scattering and absorbing media of arbitrary geometry. The TD FEM model is evaluated via comparisons with analytical and Monte Carlo (MC) calculations and is shown to provide a quantitative accuracy which has less than 0.72% error in intensity and less than 37 ps error for mean-time. The use of the Born-Ratio normalized data is demonstrated to reduce data-mismatch between MC and FEM to less than 0.22% for intensity and less than 22 ps in mean-time. An image reconstruction framework, based on a 3D FEM formulation, is outlined and simulation results based on a heterogeneous mouse model with a source of fluorescence in the pancreas is presented. It is shown that using early photons (i.e. the photons detected within the first 200 picoseconds of the TPSF) improves the spatial resolution compared to using continuous-wave signals. It is also demonstrated, as expected, that the utilization of two time-gates (early and latest photons) can improve the accuracy both in terms of spatial resolution and recovered contrast.
doi:10.1088/0031-9155/56/23/006
PMCID: PMC3697022  PMID: 22056913
Light propagation in tissues; turbid media; fluorescence; time-resolved imaging; image reconstruction
17.  Fast Implementations of Reconstruction-Based Scatter Compensation in Fully 3D SPECT Image Reconstruction 
Physics in medicine and biology  1998;43(4):857-873.
Accurate scatter compensation in SPECT can be performed by modeling the scatter response function during the reconstruction process. This method is called reconstruction-based scatter compensation (RBSC). It has been shown that RBSC has a number of advantages over other methods of compensating for scatter, but using RBSC for fully 3D compensation has resulted in prohibitively long reconstruction times. In this work we propose two new methods that can be used in conjunction with existing methods to achieve marked reductions in RBSC reconstruction times. The first method, Coarse-Grid Scatter Modeling, significantly accelerates the scatter model by exploiting the fact that scatter is dominated by low frequency information. The second method, Intermittent RBSC, further accelerates the reconstruction process by limiting the number of iterations during which scatter is modeled. The fast implementations were evaluated using a Monte Carlo simulated experiment of the 3D MCAT phantom with Tc-99m tracer, and also using experimentally acquired data with Tl-201 tracer. Results indicated that these fast methods can reconstruct, with fully 3D compensation, images very similar to those obtained using conventional RBSC methods, and in reconstruction times that are an order of magnitude shorter. Using these methods, fully 3D iterative reconstruction with RBSC can be performed well within the realm of clinically realistic times (under 10 minutes for 64 × 64 × 24 image reconstruction).
PMCID: PMC2808130  PMID: 9572510
18.  Investigation of a probe design for facilitating the uses of the standard photon diffusion equation at short source-detector separations: Monte Carlo simulations 
Journal of biomedical optics  2009;14(5):054043.
We design a special diffusing probe to investigate the optical properties of human skin in vivo. The special geometry of the probe enables a modified two-layer (MTL) diffusion model to precisely describe the photon transport even when the source-detector separation is shorter than 3 mean free paths. We provide a frequency domain comparison between the Monte Carlo model and the diffusion model in both the MTL geometry and conventional semiinfinite geometry. We show that using the Monte Carlo model as a benchmark method, the MTL diffusion theory performs better than the diffusion theory in the semiinfinite geometry. In addition, we carry out Monte Carlo simulations with the goal of investigating the dependence of the interrogation depth of this probe on several parameters including source-detector separation, sample optical properties, and properties of the diffusing high-scattering layer. From the simulations, we find that the optical properties of samples modulate the interrogation volume greatly, and the source-detector separation and the thickness of the diffusing layer are the two dominant probe parameters that impact the interrogation volume. Our simulation results provide design guidelines for a MTL geometry probe.
doi:10.1117/1.3253386
PMCID: PMC2778761  PMID: 19895144
tissue optics; near infrared spectroscopy; photon migration; Monte Carlo simulation
19.  Development and Validation of a Monte Carlo Simulation Tool for Multi-Pinhole SPECT 
Purpose
In this work, we developed and validated a Monte Carlo simulation (MCS) tool for investigation and evaluation of multi-pinhole (MPH) SPECT imaging.
Procedures
This tool was based on a combination of the SimSET and MCNP codes. Photon attenuation and scatter in the object, as well as penetration and scatter through the collimator detector, are modeled in this tool. It allows accurate and efficient simulation of MPH SPECT with focused pinhole apertures and user-specified photon energy, aperture material, and imaging geometry. The MCS method was validated by comparing the point response function (PRF), detection efficiency (DE), and image profiles obtained from point sources and phantom experiments. A prototype single-pinhole collimator and focused four- and five-pinhole collimators fitted on a small animal imager were used for the experimental validations. We have also compared computational speed among various simulation tools for MPH SPECT, including SimSET-MCNP, MCNP, SimSET-GATE, and GATE for simulating projections of a hot sphere phantom.
Results
We found good agreement between the MCS and experimental results for PRF, DE, and image profiles, indicating the validity of the simulation method. The relative computational speeds for SimSET-MCNP, MCNP, SimSET-GATE, and GATE are 1: 2.73: 3.54: 7.34, respectively, for 120-view simulations. We also demonstrated the application of this MCS tool in small animal imaging by generating a set of low-noise MPH projection data of a 3D digital mouse whole body phantom.
Conclusions
The new method is useful for studying MPH collimator designs, data acquisition protocols, image reconstructions, and compensation techniques. It also has great potential to be applied for modeling the collimator-detector response with penetration and scatter effects for MPH in the quantitative reconstruction method.
doi:10.1007/s11307-009-0263-7
PMCID: PMC3086288  PMID: 19779896
Monte Carlo simulation; SPECT; Multi-pinhole; SimSET; MCNP
20.  Quantitative, depth-resolved determination of particle motion using multi-exposure, spatial frequency domain laser speckle imaging 
Biomedical Optics Express  2013;4(12):2880-2892.
Laser Speckle Imaging (LSI) is a simple, noninvasive technique for rapid imaging of particle motion in scattering media such as biological tissue. LSI is generally used to derive a qualitative index of relative blood flow due to unknown impact from several variables that affect speckle contrast. These variables may include optical absorption and scattering coefficients, multi-layer dynamics including static, non-ergodic regions, and systematic effects such as laser coherence length. In order to account for these effects and move toward quantitative, depth-resolved LSI, we have developed a method that combines Monte Carlo modeling, multi-exposure speckle imaging (MESI), spatial frequency domain imaging (SFDI), and careful instrument calibration. Monte Carlo models were used to generate total and layer-specific fractional momentum transfer distributions. This information was used to predict speckle contrast as a function of exposure time, spatial frequency, layer thickness, and layer dynamics. To verify with experimental data, controlled phantom experiments with characteristic tissue optical properties were performed using a structured light speckle imaging system. Three main geometries were explored: 1) diffusive dynamic layer beneath a static layer, 2) static layer beneath a diffuse dynamic layer, and 3) directed flow (tube) submerged in a dynamic scattering layer. Data fits were performed using the Monte Carlo model, which accurately reconstructed the type of particle flow (diffusive or directed) in each layer, the layer thickness, and absolute flow speeds to within 15% or better.
doi:10.1364/BOE.4.002880
PMCID: PMC3862160  PMID: 24409388
(110.6150) Speckle imaging; (170.3660) Light propagation in tissues
21.  Broadband ultraviolet-visible optical property measurement in layered turbid media 
Biomedical Optics Express  2012;3(6):1226-1240.
The ability to accurately measure layered biological tissue optical properties (OPs) may improve understanding of spectroscopic device performance and facilitate early cancer detection. Towards these goals, we have performed theoretical and experimental evaluations of an approach for broadband measurement of absorption and reduced scattering coefficients at ultraviolet-visible wavelengths. Our technique is based on neural network (NN) inverse models trained with diffuse reflectance data from condensed Monte Carlo simulations. Experimental measurements were performed from 350 to 600 nm with a fiber-optic-based reflectance spectroscopy system. Two-layer phantoms incorporating OPs relevant to normal and dysplastic mucosal tissue and superficial layer thicknesses of 0.22 and 0.44 mm were used to assess prediction accuracy. Results showed mean OP estimation errors of 19% from the theoretical analysis and 27% from experiments. Two-step NN modeling and nonlinear spectral fitting approaches helped improve prediction accuracy. While limitations and challenges remain, the results of this study indicate that our technique can provide moderately accurate estimates of OPs in layered turbid media.
doi:10.1364/BOE.3.001226
PMCID: PMC3370964  PMID: 22741070
(170.3660) Light propagation in tissues; (170.3890) Medical optics instrumentation; (170.6510) Spectroscopy, tissue diagnostics; (170.6935) Tissue characterization; (170.7050) Turbid media
22.  Condensed history Monte Carlo methods for photon transport problems 
Journal of computational physics  2007;225(2):1673-1694.
We study methods for accelerating Monte Carlo simulations that retain most of the accuracy of conventional Monte Carlo algorithms. These methods – called Condensed History (CH) methods – have been very successfully used to model the transport of ionizing radiation in turbid systems. Our primary objective is to determine whether or not such methods might apply equally well to the transport of photons in biological tissue. In an attempt to unify the derivations, we invoke results obtained first by Lewis, Goudsmit and Saunderson and later improved by Larsen and Tolar. We outline how two of the most promising of the CH models – one based on satisfying certain similarity relations and the second making use of a scattering phase function that permits only discrete directional changes – can be developed using these approaches. The main idea is to exploit the connection between the space-angle moments of the radiance and the angular moments of the scattering phase function. We compare the results obtained when the two CH models studied are used to simulate an idealized tissue transport problem. The numerical results support our findings based on the theoretical derivations and suggest that CH models should play a useful role in modeling light-tissue interactions.
doi:10.1016/j.jcp.2007.02.012
PMCID: PMC2424239  PMID: 18548128
Monte Carlo methods; Condensed history models; Radiative transport equation
23.  Radiative transport in the delta-P1 approximation for semi-infinite turbid media 
Medical physics  2008;35(2):681-693.
We have developed an analytic solution for spatially resolved diffuse reflectance within the δ-P1 approximation to the radiative transport equation for a semi-infinite homogeneous turbid medium. We evaluate the performance of this solution by comparing its predictions with those provided by Monte Carlo simulations and the standard diffusion approximation. We demonstrate that the δ-P1 approximation provides accurate estimates for spatially resolved diffuse reflectance in both low and high scattering media. We also develop a multi-stage nonlinear optimization algorithm in which the radiative transport estimates provided by the δ-P1 approximation are used to recover the optical absorption (μa), reduced scattering ( μs′), and single-scattering asymmetry coefficients (g1) of liquid and solid phantoms from experimental measurements of spatially resolved diffuse reflectance. Specifically, the δ-P1 approximation can be used to recover μa, μs′, and g1 with errors within ±22%, ±18%, and ±17%, respectively, for both intralipid-based and siloxane-based tissue phantoms. These phantoms span the optical property range 4<(μs′/μa)<117. Using these same measurements, application of the standard diffusion approximation resulted in the recovery of μa and μs′ with errors of ±29% and ±25%, respectively. Collectively, these results demonstrate that the δ-P1 approximation provides accurate radiative transport estimates that can be used to determine accurately the optical properties of biological tissues, particularly in spectral regions where tissue may display moderate/low ratios of reduced scattering to absorption ( μs′/μa).
PMCID: PMC3509770  PMID: 18383690
24.  On the Forward Scattering of Microwave Breast Imaging 
Microwave imaging for breast cancer detection has been of significant interest for the last two decades. Recent studies focus on solving the imaging problem using an inverse scattering approach. Efforts have mainly been focused on the development of the inverse scattering algorithms, experimental setup, antenna design and clinical trials. However, the success of microwave breast imaging also heavily relies on the quality of the forward data such that the tumor inside the breast volume is well illuminated. In this work, a numerical study of the forward scattering data is conducted. The scattering behavior of simple breast models under different polarization states and aspect angles of illumination are considered. Numerical results have demonstrated that better data contrast could be obtained when the breast volume is illuminated using cross-polarized components in linear polarization basis or the copolarized components in the circular polarization basis.
doi:10.1155/2012/582037
PMCID: PMC3352576  PMID: 22611371
25.  A fiber optic probe design to measure depth- limited optical properties in-vivo with Low-coherence Enhanced Backscattering (LEBS) Spectroscopy 
Optics Express  2012;20(18):19643-19657.
Low-coherence enhanced backscattering (LEBS) spectroscopy is an angular resolved backscattering technique that is sensitive to sub-diffusion light transport length scales in which information about scattering phase function is preserved. Our group has shown the ability to measure the spatial backscattering impulse response function along with depth-selective optical properties in tissue ex-vivo using LEBS. Here we report the design and implementation of a lens-free fiber optic LEBS probe capable of providing depth-limited measurements of the reduced scattering coefficient in-vivo. Experimental measurements combined with Monte Carlo simulation of scattering phantoms consisting of polystyrene microspheres in water are used to validate the performance of the probe. Additionally, depth-limited capabilities are demonstrated using Monte Carlo modeling and experimental measurements from a two-layered phantom.
doi:10.1364/OE.20.019643
PMCID: PMC3635466  PMID: 23037017
(170.6510) Spectroscopy, tissue diagnostics; (290.1350) Backscattering; (060.2310) Fiber optics

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