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Title: Explicit solutions of the radiative transport equation in the P{sub 3} approximation

Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiative transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derivedmore » equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.« less
Authors:
;  [1]
  1. Institut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr.12, Ulm D-89081 (Germany)
Publication Date:
OSTI Identifier:
22317955
Resource Type:
Journal Article
Resource Relation:
Journal Name: Medical Physics; Journal Volume: 41; Journal Issue: 11; Other Information: (c) 2014 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; BEAMS; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; DIFFUSION EQUATIONS; EXACT SOLUTIONS; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; OPTICS; SPHERICAL HARMONICS METHOD; STANDARDS; STEADY-STATE CONDITIONS; TRANSPORT THEORY; VISIBLE RADIATION