Analysis of relative error in perturbation Monte Carlo simulations of radiative transport.

Significance: Perturbation and differential Monte Carlo (pMC/dMC) methods, used in conjunction with nonlinear optimization methods, have been successfully applied to solve inverse problems in diffuse optics. Application of pMC to systems over a large range of optical properties requires optimal "placement" of baseline conventional Monte Carlo (cMC) simulations to minimize the pMC variance. The inability to predict the growth in pMC solution uncertainty with perturbation size limits the application of pMC, especially for multispectral datasets where the variation of optical properties can be substantial.

MCCL: an open-source software application for Monte Carlo simulations of radiative transport.

The Monte Carlo Command Line application (MCCL) is an open-source software package that provides Monte Carlo simulations of radiative transport through heterogeneous turbid media. MCCL is available on GitHub through our virtualphotonics.org website, is actively supported, and carries extensive documentation.

Comparative analysis of discrete and continuous absorption weighting estimators used in Monte Carlo simulations of radiative transport in turbid media: erratum.

This erratum corrects the relative error plots and references in our paper [J. Opt. Soc.

Hybrid Monte Carlo estimators for multilayer transport problems.

This paper introduces a new family of hybrid estimators aimed at controlling the efficiency of Monte Carlo computations in particle transport problems. In this context, efficiency is usually measured by the figure of merit (FOM) given by the inverse product of the estimator variance Var[ξ] and the run time : FOM := (Var[ξ] ). Previously, we developed a new family of transport-constrained unbiased radiance estimators (T-CURE) that generalize the conventional collision and track length estimators [1] and provide 1-2 orders of magnitude additional variance reduction.

A new proof of geometric convergence for the adaptive generalized weighted analog sampling (GWAS) method.

Generalized Weighted Analog Sampling is a variance-reducing method for solving radiative transport problems that makes use of a biased (though asymptotically unbiased) estimator. The introduction of bias provides a mechanism for combining the best features of unbiased estimators while avoiding their limitations. In this paper we present a new proof that adaptive GWAS estimation based on combining the variance-reducing power of importance sampling with the sampling simplicity of correlated sampling yields geometrically convergent estimates of radiative transport solutions.

Development of perturbation Monte Carlo methods for polarized light transport in a discrete particle scattering model.

We present a polarization-sensitive, transport-rigorous perturbation Monte Carlo (pMC) method to model the impact of optical property changes on reflectance measurements within a discrete particle scattering model. The model consists of three log-normally distributed populations of Mie scatterers that approximate biologically relevant cervical tissue properties. Our method provides reflectance estimates for perturbations across wavelength and/or scattering model parameters.

Comparative analysis of discrete and continuous absorption weighting estimators used in Monte Carlo simulations of radiative transport in turbid media.

We examine the relative error of Monte Carlo simulations of radiative transport that employ two commonly used estimators that account for absorption differently, either discretely, at interaction points, or continuously, between interaction points. We provide a rigorous derivation of these discrete and continuous absorption weighting estimators within a stochastic model that we show to be equivalent to an analytic model, based on the radiative transport equation (RTE). We establish that both absorption weighting estimators are unbiased and, therefore, converge to the solution of the RTE.

Perturbation Monte Carlo methods for tissue structure alterations.

This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way.

Transport-Constrained Extensions of Collision and Track Length Estimators for Solutions of Radiative Transport Problems.

In this paper we develop novel extensions of collision and track lengh estimators for the complete space-angle solutions of radiative transport problems. We derive the relevant equations, prove that our new estimators are unbiased, and compare their performance with that of more conventional ) estimators. Such comparisons based on numerical solutions of simple one dimensional slab problems indicate the the potential superiority of the new estimators for a wide variety of more general transport problems.

Analysis of single Monte Carlo methods for prediction of reflectance from turbid media.

Starting from the radiative transport equation we derive the scaling relationships that enable a single Monte Carlo (MC) simulation to predict the spatially- and temporally-resolved reflectance from homogeneous semi-infinite media with arbitrary scattering and absorption coefficients. This derivation shows that a rigorous application of this single Monte Carlo (sMC) approach requires the rescaling to be done individually for each photon biography. We examine the accuracy of the sMC method when processing simulations on an individual photon basis and also demonstrate the use of adaptive binning and interpolation using non-uniform rational B-splines (NURBS) to achieve order of magnitude reductions in the relative error as compared to the use of uniform binning and linear interpolation.

Geometric Convergence of Adaptive Monte Carlo Algorithms for Radiative Transport Problems Based on Importance Sampling Methods.

Importance sampling is a very well-known variance-reducing technique used in Monte Carlo simulations of radiative transport. It involves a distortion of the physical (analog) transition probabilities with the goal of causing events of interest in the computation to occur more frequently than in the analog process. This distortion is then compensated by a corresponding alteration of the estimating random variable in order to remove any bias from the estimates of quantities of interest.

Expected-value techniques for Monte Carlo modeling of well logging problems.

This article describes research performed to develop an expected-value (EV) estimation capability for improving the efficiency of Monte Carlo simulations of oil well logging problems. The basic idea underlying EV estimation is that event-level interaction and transport probabilities are known and can be averaged exactly to produce estimators that properly account for potential future events in the simulation. Conventional surface-crossing and track-length based estimators do not provide any information unless a particle history actually reaches a detector region.

Investigation of a probe design for facilitating the uses of the standard photon diffusion equation at short source-detector separations: Monte Carlo simulations.

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.

A new proof of geometric convergence for general transport problems based on sequential correlated sampling methods.

In [J. Halton, Sequential Monte Carlo, Proc. Comb.

Professor Oldham's contributions to applied mathematics: a tribute on the occasion of his 80th birthday.

Based on our 40-year collaboration and friendship, this essay attempts to identify a few of the main themes of Professor Keith B. Oldham's numerous contributions to the field of applied mathematics.

Efficient, Automated Monte Carlo Methods for Radiation Transport.

Monte Carlo simulations provide an indispensible model for solving radiative transport problems, but their slow convergence inhibits their use as an everyday computational tool. In this paper, we present two new ideas for accelerating the convergence of Monte Carlo algorithms based upon an efficient algorithm that couples simulations of forward and adjoint transport equations. Forward random walks are first processed in stages, each using a fixed sample size, and information from stage k is used to alter the sampling and weighting procedure in stage k + 1.

Condensed history Monte Carlo methods for photon transport problems.

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.

Determination of optical properties of superficial volumes of layered tissue phantoms.

Previously, we reported the design of a new diffusing probe that employs a standard two-layer diffusion model to recover the optical properties of turbid samples. This particular probe had a source-detector separation of 2.5 mm and performance was validated with Monte Carlo simulations and homogeneous phantom experiments.

Quantitative spectroscopy of superficial turbid media.

We report a novel diffuse optical spectroscopy probe design for determining optical properties of superficial volumes of turbid samples. The fiber-based probe employs a highly scattering layer placed in contact with the sample of interest. This layer diffuses photons from a collimated light source before they enter the sample and provides a basis for describing light transported in superficial media by the diffusion approximation.

Use of the delta-P1 approximation for recovery of optical absorption, scattering, and asymmetry coefficients in turbid media.

We introduce a robust method to recover optical absorption, reduced scattering, and single-scattering asymmetry coefficients (microa, micro's, g1) of infinite turbid media over a range of (micro's/microa) spanning 3 orders of magnitude. This is accomplished through the spatially resolved measurement of irradiance at source-detector separations spanning 0.25-8 transport mean free paths (l*).

In vivo port-wine stain depth determination with a photoacoustic probe.

We have designed a photoacoustic probe for port-wine stain (PWS) depth measurements consisting of optical fibers for laser light delivery and a piezoelectric element for acoustic detection. We characterized the capabilities and limitations of the probe for profiling PWS skin. The probe induced and measured photoacoustic waves in acrylamide tissue phantoms and PWS skin in vivo.