Open AccessIncorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging
Author(s) -
Abhinav K. Jha,
Yansong Zhu,
Simon R. Arridge,
Dean F. Wong,
Arman Rahmim
Publication year - 2018
Publication title -
biomedical optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.362
H-Index - 86
ISSN - 2156-7085
DOI - 10.1364/boe.9.001389
Subject(s) - radiative transfer , fresnel equations , photon , diffuse optical imaging , boundary value problem , optics , physics , formalism (music) , diffuse reflection , photon diffusion , reflection (computer programming) , neumann boundary condition , mathematical analysis , computational physics , mathematics , computer science , refractive index , tomography , art , musical , light source , visual arts , programming language
We propose a formalism to incorporate boundary conditions in a Neumann-series-based radiative transport equation. The formalism accurately models the reflection of photons at the tissue-external medium interface using Fresnel's equations. The formalism was used to develop a gradient descent-based image reconstruction technique. The proposed methods were implemented for 3D diffuse optical imaging. In computational studies, it was observed that the average root-mean-square error (RMSE) for the output images and the estimated absorption coefficients reduced by 38% and 84%, respectively, when the reflection boundary conditions were incorporated. These results demonstrate the importance of incorporating boundary conditions that model the reflection of photons at the tissue-external medium interface.