Diffusion coefficient in the photon diffusion equation

The photon diffusion equation is frequently used to describe the photon migration in random media like living tissues. The equation of transfer; an integro-differential equation that can hardly be solved directly. The conventional derivation of the diffusion equation gives the diffusion coefficient by using both the reduced scattering coefficient and absorption coefficient. Also the equation is believed to be valid only for cases of small absorption coefficient compared with the scattering coefficient. From recent numerical simulations, it was found that the conventional diffusion coefficient led to a large error in the early time after the impulse incidence, and it was also suggested that the diffusion coefficient given only by the reduced scattering coefficient would produce better results. In this report, the photon diffusion equation for homogeneous and inhomogeneous media is derived with a strict procedure, and the resulting diffusion coefficient is found to be determined only by the reduced scattering coefficient independently of the absorption coefficient involved. This derivation is valid independent of whether the absorption coefficient is sufficiently small or not. The solution of the fluence rate is obtained therefrom in a power series of the attenuation coefficient under a general condition. The solution in case of slowly changing absorption coefficient is also obtained in terms of an attenuation factor relative to the solution when the medium is free from the absorption. Some examples of the latter solution are given.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.