We will present a fast and reliable numerical approach for near-infrared light (NIR) propagation in human bodies. In particular, an accurate numerical quadrature rule on the unit sphere and degenerate kernel approximations are shown to realize numerical computations in the three dimensions.

The use of NIR light is considered as a safe and simple technology for monitoring our bodies, in particular, brain activities. The radiative transport equation (RTE) is widely accepted as a mathematical model of NIR light propagation in our bodies. It is an integro-differential equations and the boundary value problem in the three dimensions is essentially a five dimensional large-scale problem. An accurate numerical quadrature rule and degenerate kernel approximations have been developed to reduce the size of discretization problems and computational times. Error analysis and numerical experiments with biomedical data of a human head are also shown.

This talk is based on a joint work with Prof. Iso (Kyoto Univ.), Prof. Higashimori (Hitotsubashi Univ.), and Human Brain Research Center in Kyoto University.