Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

We propose the PN approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the PN approximation is compared against Monte Carlo simulations and other state-of-the-art methods.

► We developed a variable order global basis scheme to solve light transport in 3D.
► Based on finite elements, the method can be applied to a wide class of geometries.
► It is computationally cheap when compared to the fixed order scheme.
► Comparisons with local basis method and other models demonstrate its accuracy.
► Addresses problems encountered n modeling of light transport in human brain.