Numerical Errors of Light Propagation in the Two-dimensional Human Neck Model using the Time-dependent Radiative Transfer Equation with Renormalized Phase Functions

We numerically studied light propagation in the two-dimensional human neck model using the time-dependent radiative transfer equation (RTE) for an application of diffuse optical tomography to a thyroid cancer detection. Because complicated light propagation is induced by a heterogeneity of the human neck, highly forward-peaked scattering of light by the tissue volumes except the trachea, and the refractive-index mismatch at the trachea-tissue interface and external boundary, one needs a large number of discrete angular directions (ND) for the RTE calculations, meaning high computational loads. Toward a construction of an efficient numerical scheme of the RTE, in this paper, we focused on a numerical treatment of the highly forward-peaked scattering of light. Then, we investigated numerical errors of the RTE calculations using two kinds of renormalization approaches to the highly forward-directed phase function: the conventional Liu's approach and developed approach by some of the authors. The investigations showed that the developed approach provided accurate results of the RTE calculations around the peak time regimes even when ND decreased. In the decay time regime, however, the developed approach provided less accurate results because in that regime the refractive-index mismatch at the trachea-tissue interface dominated in the light propagation over the highly forward-peaked scattering.