On the accuracy of generalized Fokker-Planck transport equations in tissue optics

Forward-peaked and large-angle scattering approximations of the radiative transport equation give rise to generalized Fokker-Planck equations whose main feature is the replacement of the integral scattering operator with differential operators in the direction-space variables. Using the P(N) method, an appraisal of generalized Fokker-Planck equations due to González-Rodríguez and Kim [Appl. Opt.47, 2599-2609 (2008)], Leakeas and Larsen [Nucl. Sci. Eng.137, 236-250 (2001), and J. Opt. Soc. Am. A20, 92-98 (2003)], and Pomraning [Math. Models Meth. Appl. Sci.2, 21-36 (1992)] is carried out by computing the relative error between the backscattered and transmitted surface flux predicted by the generalized Fokker-Planck equations and the transport equation with Henyey-Greenstein phase function for anisotropies ranging from 0 to 1. Generalized Fokker-Planck equations whose scattering operators incorporate large-angle scattering and possess eigenvalues similar to the integral scattering operator with Henyey-Greenstein phase function are found to minimize the relative error in the limit of unit anisotropy.