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

Fatmir Asllanaj 1 Sylvain Contassot-Vivier 2
2 ALGORILLE - Algorithms for the Grid
Inria Nancy - Grand Est, LORIA - NSS - Department of Networks, Systems and Services
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 colli- mated 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.
Type de document :
Article dans une revue
Journal of Biomedical Optics, Society of Photo-optical Instrumentation Engineers, 2014, 19 (1), pp.10. 〈10.1117/1.JBO.19.1.015002〉
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https://hal.inria.fr/hal-01101240
Contributeur : Sylvain Contassot-Vivier <>
Soumis le : jeudi 8 janvier 2015 - 11:03:31
Dernière modification le : jeudi 11 janvier 2018 - 06:27:33

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Fatmir Asllanaj, Sylvain Contassot-Vivier. 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. Journal of Biomedical Optics, Society of Photo-optical Instrumentation Engineers, 2014, 19 (1), pp.10. 〈10.1117/1.JBO.19.1.015002〉. 〈hal-01101240〉

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