Radiative transport in the delta-P1 approximation for semi-infinite turbid media.

Inseok Seo,Vasan Venugopalan,Carole K Hayakawa

doi:10.1118/1.2828184

Abstract

We have developed an analytic solution for spatially resolved diffuse reflectance within the deltaP1 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 delta-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 delta-P1 approximation are used to recover the optical absorption (microa), reduced scattering (micros'), and single-scattering asymmetry coefficients (g1) of liquid and solid phantoms from experimental measurements of spatially resolved diffuse reflectance. Specifically, the delta-P1 approximation can be used to recover microa, micros', 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 < (micros' /microa) < 117. Using these same measurements, application of the standard diffusion approximation resulted in the recovery of microa and micros' with errors o f +/- 29% and +/- 25%, respectively. Collectively, these results demonstrate that the delta-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 (micros'/microa).

Highlights

The radiative transport equation (RTE) provides the basis for particle-based radiative transport models
Forward problem results: spatially resolved diffuse reflectance (SRDR) predictions Figure 5 displays the SRDR predictions provided by the δ-P1 approximation, the standard diffusion approximation (SDA), and the Monte Carlo (MC) simulations
The predictions provided by the SDA provide a slight (≳ 5%) but distinct offset from the MC results in the region where the SDA is expected to be accurate (ρ≫ l*)

Summary

Introduction

The radiative transport equation (RTE) provides the basis for particle-based radiative transport models. The RTE is an integro-differential equation that is amenable to complete analytic solution in only a small number of cases. The SDA results from the substitution of first-order spherical harmonic (Legendre polynomial) expansions to approximate the radiance and phase function within the RTE. The use of these low-order expansions prevents the SDA from providing accurate radiative transport estimates at locations proximal to collimated sources and interfaces of significant refractive index mismatch, as well as in media where the reduced scattering coefficient ( ) is only moderately dominant over the absorption coefficient (μa) i.e., for

Objectives

Results

Conclusion