Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography

Finite difference time domain (FDTD) analysis has been successfully formulated for solving diffusion equation in biological tissues. Time-dependent diffusion equations are approximated by FDTD equations by assigning diffuse photon fluence rates and radiant flux defined in the diffusion equations to Yee meshes. At the boundary between scattering and no scattering material, FDTD equation including only fluence rate has been derived, which make it possible to calculate the fluence rate at the boundary. The formulation is useful to solve diffusion equations by iterative algebraic calculations in scattering media with inhomogeneous optical properties. The conditions to give stabilities for numerical solutions have been become clear in terms of scattering coefficients and mean cosine of scattering angles. Using the formulation, the reflectance of three-layered slabs containing a clear layer have been calculated. As a result, it has been found that absorption loss changes of the highly scattering medium beyond the clear layer are estimated from the time profiles of the reflectance. Index Terms--Diffusion equation, FDTD analysis, optical computer tomography, transmittance and reflectance.