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

Journal of Computational Physics (Impact Factor: 2.43). 08/2011; 230(19):7364-7383. DOI: 10.1016/
Source: DBLP


Highlights: {yields} We developed a variable order global basis scheme to solve light transport in 3D. {yields} Based on finite elements, the method can be applied to a wide class of geometries. {yields} It is computationally cheap when compared to the fixed order scheme. {yields} Comparisons with local basis method and other models demonstrate its accuracy. {yields} Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P{sub N} 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 P{sub N} approximation is compared against Monte Carlo simulations and other state-of-the-art methods.

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    • "To overcome the limitations of diffusion theory, different hybrid models which combine diffusion equation with other models have been developed. These include the radiosity diffusion model [14] [16] which can be utilised in highly scattering medium with non-scattering regions, hybrid Monte Carlo–diffusion approaches [13] [17] [15], and models in which the radiative transport equation is coupled with the diffusion equation [18] [19] [20] [21] [22] or different orders of P N approximation are applied [23]. However, except for the radiosity diffusion model [16], the inverse problem using these models has not been addressed. "
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