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Title: Light transport in biological tissue based on the simplified spherical harmonics equations

Abstract

In this work, we demonstrate the validity of the simplified spherical harmonics equations to approximate the more complicated equation of radiative transfer for modeling light propagation in biological tissue. We derive the simplified spherical harmonics equations up to order N = 7 for anisotropic scattering and partially reflective boundary conditions. We compare numerical results with diffusion and discrete ordinates transport solutions. We find that the simplified spherical harmonics methods significantly improve the diffusion solution in transport-like domains with high absorption and small geometries, and are computationally less expensive than the discrete ordinates transport method. For example, the simplified P {sub 3} method is approximately two orders of magnitude faster than the discrete ordinates transport method, but only 2.5 times computationally more demanding than the diffusion method. We conclude that the simplified spherical harmonics methods can accurately model light propagation in small tissue geometries at visible and near-infrared wavelengths, yielding transport-like solutions with only a fraction of the computational cost of the transport calculation.

Authors:
 [1];  [2]
  1. Department of Radiology, Columbia University, New York, NY 10032 (United States). E-mail: ak2083@columbia.edu
  2. Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109 (United States). E-mail: edlarsen@umich.edu
Publication Date:
OSTI Identifier:
20840371
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 220; Journal Issue: 1; Other Information: DOI: 10.1016/j.jcp.2006.07.007; PII: S0021-9991(06)00342-1; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABSORPTION; ANISOTROPY; BOUNDARY CONDITIONS; DIFFUSION; DIFFUSION EQUATIONS; DISCRETE ORDINATE METHOD; GEOMETRY; LIGHT TRANSMISSION; MATHEMATICAL SOLUTIONS; OPTICS; RADIANT HEAT TRANSFER; SCATTERING; SIMULATION; SPHERICAL HARMONICS; SPHERICAL HARMONICS METHOD; TRANSPORT THEORY; VISIBLE RADIATION; WAVELENGTHS

Citation Formats

Klose, Alexander D., and Larsen, Edward W. Light transport in biological tissue based on the simplified spherical harmonics equations. United States: N. p., 2006. Web. doi:10.1016/j.jcp.2006.07.007.
Klose, Alexander D., & Larsen, Edward W. Light transport in biological tissue based on the simplified spherical harmonics equations. United States. doi:10.1016/j.jcp.2006.07.007.
Klose, Alexander D., and Larsen, Edward W. Wed . "Light transport in biological tissue based on the simplified spherical harmonics equations". United States. doi:10.1016/j.jcp.2006.07.007.
@article{osti_20840371,
title = {Light transport in biological tissue based on the simplified spherical harmonics equations},
author = {Klose, Alexander D. and Larsen, Edward W.},
abstractNote = {In this work, we demonstrate the validity of the simplified spherical harmonics equations to approximate the more complicated equation of radiative transfer for modeling light propagation in biological tissue. We derive the simplified spherical harmonics equations up to order N = 7 for anisotropic scattering and partially reflective boundary conditions. We compare numerical results with diffusion and discrete ordinates transport solutions. We find that the simplified spherical harmonics methods significantly improve the diffusion solution in transport-like domains with high absorption and small geometries, and are computationally less expensive than the discrete ordinates transport method. For example, the simplified P {sub 3} method is approximately two orders of magnitude faster than the discrete ordinates transport method, but only 2.5 times computationally more demanding than the diffusion method. We conclude that the simplified spherical harmonics methods can accurately model light propagation in small tissue geometries at visible and near-infrared wavelengths, yielding transport-like solutions with only a fraction of the computational cost of the transport calculation.},
doi = {10.1016/j.jcp.2006.07.007},
journal = {Journal of Computational Physics},
number = 1,
volume = 220,
place = {United States},
year = {Wed Dec 20 00:00:00 EST 2006},
month = {Wed Dec 20 00:00:00 EST 2006}
}
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