Light diffusion in a radially N-layered cylinder.

Analytical solutions of the diffusion equation for a radially N-layered cylinder were derived in the steady-state, frequency, and time domains. Solutions for axially infinite and finite cylinders are presented. The derived formulas were compared to a known solution of the diffusion equation for a layered semi-infinite geometry and to Monte Carlo simulations, showing excellent and good agreement, respectively. The analytical solutions were applied to calculate the light propagation in models of the forearm and the finger, demonstrating the improvement in analysis of hemodynamics measurements compared to the formulas used so far.