title: Radiative transfer equation for predicting light propagation in biological media: comparison of a modified finite volume method, the Monte Carlo technique, and an exact analytical solution.
abstract: We examine the accuracy of a modified finite volume method compared to analytical and Monte Carlo solutions for solving the radiative transfer equation. The model is used for predicting light propagation within a two-dimensional absorbing and highly forward-scattering medium such as biological tissue subjected to a collimated light beam. Numerical simulations for the spatially resolved reflectance and transmittance are presented considering refractive index mismatch with Fresnel reflection at the interface, homogeneous and two-layered media. Time-dependent as well as steady-state cases are considered. In the steady state, it is found that the modified finite volume method is in good agreement with the other two methods. The relative differences between the solutions are found to decrease with spatial mesh refinement applied for the modified finite volume method obtaining <2.4%. In the time domain, the fourth-order Runge-Kutta method is used for the time semi-discretization of the radiative transfer equation. An agreement among the modified finite volume method, Runge-Kutta method, and Monte Carlo solutions are shown, but with relative differences higher than in the steady state.
authors.affiliation: Université de Lorraine, LEMTA, UMR 7563, Vandœuvre-lès-Nancy 54518, FrancebCentre National de la Recherche Scientifique, LEMTA, UMR 7563, Vandœuvre-lès-Nancy 54518, FrancedInstitut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm.
authors.forename: Fatmir
authors.initials: F
authors.lastname: Asllanaj
authors.affiliation: Université de Lorraine, Loria UMR 7503 & AlGorille INRIA Project Team, Vandœuvre-lès-Nancy 54506, France.
authors.forename: Sylvain
authors.initials: S
authors.lastname: Contassot-Vivier
authors.affiliation: Institut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr.12, D-89081 Ulm, Germany.
authors.forename: André
authors.initials: A
authors.lastname: Liemert
authors.affiliation: Institut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Helmholtzstr.12, D-89081 Ulm, Germany.
authors.forename: Alwin
authors.initials: A
authors.lastname: Kienle
mesh_terms: D000042:Absorption; D000465:Algorithms; D003198:Computer Simulation; D003952:Diagnostic Imaging / Q000379:methods; D004058:Diffusion; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008027:Light; D008962:Models, Theoretical; D009010:Monte Carlo Method; D012031:Refractometry; D012542:Scattering, Radiation; D012984:Software; D013997:Time Factors