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Title: Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena on the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.
Authors:
 [1] ;  [1] ;  [2] ;  [3] ;  [4]
  1. Department of Applied Physics, University of Eastern Finland, PO Box 1627, 70211 Kuopio (Finland)
  2. (United Kingdom)
  3. Applied Mathematics Unit, School of Natural Sciences, University of California, Merced, CA 95343 (United States)
  4. Department of Computer Science, University College London, Gower Street, London WC1E 6BT (United Kingdom)
Publication Date:
OSTI Identifier:
22382182
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 282; Other Information: Copyright (c) 2014 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; APPROXIMATIONS; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; FINITE ELEMENT METHOD; INTERFACES; LIGHT TRANSMISSION; MATHEMATICAL MODELS; MONTE CARLO METHOD; REFLECTION; REFRACTION; REFRACTIVE INDEX; SCATTERING; TRANSPORT THEORY; VISIBLE RADIATION