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

Journal Article · Sat Nov 01 00:00:00 EDT 2014 · Medical Physics

DOI:https://doi.org/10.1118/1.4898097· OSTI ID:22317955

Liemert, André; Kienle, Alwin ^[1]

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1. Institut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr.12, Ulm D-89081 (Germany)

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 derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.

• OSTI ID: 22317955
• Journal Information: Medical Physics, Vol. 41, Issue 11; Other Information: (c) 2014 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-2405
• Country of Publication: United States
• Language: English

Related Subjects

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