skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

Abstract

Highlights: {yields} We developed a variable order global basis scheme to solve light transport in 3D. {yields} Based on finite elements, the method can be applied to a wide class of geometries. {yields} It is computationally cheap when compared to the fixed order scheme. {yields} Comparisons with local basis method and other models demonstrate its accuracy. {yields} Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P{sub N} approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P{sub N} approximation is compared against Monte Carlo simulations and other state-of-the-art methods.

Authors:
 [1];  [1];  [2]
  1. Department of Computer Science, University College London, Gower Street, London WC1E 6BT (United Kingdom)
  2. Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio (Finland)
Publication Date:
OSTI Identifier:
21592609
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 230; Journal Issue: 19; Other Information: DOI: 10.1016/j.jcp.2011.06.004; PII: S0021-9991(11)00353-6; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; BRAIN; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; FINITE ELEMENT METHOD; GEOMETRY; MONTE CARLO METHOD; TOMOGRAPHY; TRANSPORT THEORY; BODY; CALCULATION METHODS; CENTRAL NERVOUS SYSTEM; DIAGNOSTIC TECHNIQUES; EVALUATION; MATHEMATICAL SOLUTIONS; MATHEMATICS; NERVOUS SYSTEM; NUMERICAL SOLUTION; ORGANS; SIMULATION

Citation Formats

Surya Mohan, P., E-mail: sprerapa@cs.ucl.ac.uk, Tarvainen, Tanja, Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Schweiger, Martin, Pulkkinen, Aki, Sunnybrook Research Institute, Sunnybrook Health Sciences Centre, 2075 Bayview Ave., Toronto, M4N 3M5, and Arridge, Simon R., E-mail: S.Arridge@cs.ucl.ac.uk. Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements. United States: N. p., 2011. Web. doi:10.1016/j.jcp.2011.06.004.
Surya Mohan, P., E-mail: sprerapa@cs.ucl.ac.uk, Tarvainen, Tanja, Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Schweiger, Martin, Pulkkinen, Aki, Sunnybrook Research Institute, Sunnybrook Health Sciences Centre, 2075 Bayview Ave., Toronto, M4N 3M5, & Arridge, Simon R., E-mail: S.Arridge@cs.ucl.ac.uk. Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements. United States. https://doi.org/10.1016/j.jcp.2011.06.004
Surya Mohan, P., E-mail: sprerapa@cs.ucl.ac.uk, Tarvainen, Tanja, Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Schweiger, Martin, Pulkkinen, Aki, Sunnybrook Research Institute, Sunnybrook Health Sciences Centre, 2075 Bayview Ave., Toronto, M4N 3M5, and Arridge, Simon R., E-mail: S.Arridge@cs.ucl.ac.uk. 2011. "Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements". United States. https://doi.org/10.1016/j.jcp.2011.06.004.
@article{osti_21592609,
title = {Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements},
author = {Surya Mohan, P., E-mail: sprerapa@cs.ucl.ac.uk and Tarvainen, Tanja and Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio and Schweiger, Martin and Pulkkinen, Aki and Sunnybrook Research Institute, Sunnybrook Health Sciences Centre, 2075 Bayview Ave., Toronto, M4N 3M5 and Arridge, Simon R., E-mail: S.Arridge@cs.ucl.ac.uk},
abstractNote = {Highlights: {yields} We developed a variable order global basis scheme to solve light transport in 3D. {yields} Based on finite elements, the method can be applied to a wide class of geometries. {yields} It is computationally cheap when compared to the fixed order scheme. {yields} Comparisons with local basis method and other models demonstrate its accuracy. {yields} Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P{sub N} approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P{sub N} approximation is compared against Monte Carlo simulations and other state-of-the-art methods.},
doi = {10.1016/j.jcp.2011.06.004},
url = {https://www.osti.gov/biblio/21592609}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = 19,
volume = 230,
place = {United States},
year = {Wed Aug 10 00:00:00 EDT 2011},
month = {Wed Aug 10 00:00:00 EDT 2011}
}