Premium
Radiative transport in the delta‐ P 1 approximation for semi‐infinite turbid media
Author(s) -
Seo InSeok,
Hayakawa Carole K.,
Venugopalan Vasan
Publication year - 2008
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2828184
Subject(s) - radiative transfer , heavy traffic approximation , scattering , monte carlo method , computational physics , absorption (acoustics) , physics , diffuse reflection , atmospheric radiative transfer codes , diffusion , optics , materials science , mathematics , thermodynamics , statistics
We have developed an analytic solution for spatially resolved diffuse reflectance within the δ ‐ P 1approximation 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 ‐ P 1approximation 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 ‐ P 1approximation are used to recover the optical absorption ( μ a ) , reduced scattering ( μ s ′ ) , and single‐scattering asymmetry coefficients ( g 1 ) of liquid and solid phantoms from experimental measurements of spatially resolved diffuse reflectance. Specifically, the δ ‐ P 1approximation can be used to recover μ a , μ s ′ , and g 1 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 < ( μ s ′ ∕ μ a ) < 117 . Using these same measurements, application of the standard diffusion approximation resulted in the recovery of μ a and μ s ′ with errors of ± 29 % and ± 25 % , respectively. Collectively, these results demonstrate that the δ ‐ P 1approximation 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 ( μ s ′ ∕ μ a ) .