Method for estimating closed-form solutions of the light diffusion equation for turbid media of any boundary shape

This paper reports a method of estimating an approximate closed-form solution to the light diffusion equation for any type of geometry involving Dirichlet's boundary condition with known source location. It is based on estimating the optimum locations of multiple imaginary point sources to cancel the fluence at the extrapolated boundary by constrained optimization using a genetic algorithm. The mathematical derivation of the problem to approach the optimum solution for the direct-current type of diffuse optical systems is described in detail. Our method is first applied to slab geometry and compared with a truncated series solution. After that, it is applied to hemispherical geometry and compared with Monte Carlo simulation results. The method provides a fast and sufficiently accurate fluence distribution for optical reconstruction.