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
Résumé
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.