Finite element model for the coupled radiative transfer equation and diffusion approximation

In this paper a coupled radiative transfer equation and diffusion approximation model for light propagation in tissues is proposed. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the domain. The two equations are coupled through their boundary conditions and they are solved simultaneously using the finite element method. The method is tested with simulations. The results of the proposed approach are compared with finite element solutions of the radiative transfer equation, the diffusion approximation and a previously proposed hybrid model. The results show that the method improves the accuracy of the forward solution for diffuse optical tomography compared to the conventional diffusion model.