Evaluation of a radiative transfer equation and diffusion approximation hybrid forward solver for fluorescence molecular imaging

The solution of the forward problem in fluorescence molecular imaging strongly influences the successful convergence of the fluorophore reconstruction. The most common approach to meeting this problem has been to apply the diffusion approximation. However, this model is a first-order angular approximation of the radiative transfer equation, and thus is subject to some well-known limitations. This manuscript proposes a methodology that confronts these limitations by applying the radiative transfer equation in spatial regions in which the diffusion approximation gives decreased accuracy. The explicit integro differential equations that formulate this model were solved by applying the Galerkin finite element approximation. The required spatial discretization of the investigated domain was implemented through the Delaunay triangulation, while the azimuthal discretization scheme was used for the angular space. This model has been evaluated on two simulation geometries and the results were compared with results from an independent Monte Carlo method and the radiative transfer equation by calculating the absolute values of the relative errors between these models. The results show that the proposed forward solver can approximate the radiative transfer equation and the Monte Carlo method with better than 95% accuracy, while the accuracy of the diffusion approximation is approximately 10% lower.