Spatially varying absorptive or scattering inclusions in a diffusive slab: a perturbation approach to the time-resolved transmittance

In the framework of perturbation approach to diffusion equation analytical expressions are derived to describe the effects on the time-resolved transmittance due to the presence of an inclusion that can be purely absorptive or diffusive. The formula assume the optical properties of the inclusion are spatially Gaussian distributed. The accuracy and the application range of the perturbed transmittance are investigated through comparisons with the numerical solutions of the time-dependent diffusion equation given by using the Finite Element Method. A case of practical interest for two-dimensional breast imaging is considered.