A perturbation approach to characterize absorptive inclusions in diffusing media by time-resolved contrast measurements

Depth dependence of estimated optical properties of a scattering inclusion by time-resolved contrast functions

In this study we have theoretically and experimentally investigated the behavior of first order approximation contrast function when purely scattering inhomogeneities located at different depths inside a turbid thick slab are considered. Results of model predictions have been compared with Finite element method simulations and tested on phantoms. To this aim, we have developed for the first time to our knowledge a fitting algorithm for estimating both the scattering perturbation parameter and the shift of the inhomogeneity from the middle plane, allowing one to reduce the uncertainties due to depth. This is important for optical mammography because effects of the depth can cause uncertainties in the derived tumor optical properties that are above 20% and the scattering properties of tumors differ from those of the sourrounding healthy tissue by a comparable extent.

Perturbation approach to the time-resolved transmittance for a spatially varying scattering inclusion in a diffusive slab

In the framework of the perturbation approach to the diffusion equation, an analytical expression is derived to describe the effects on the time-resolved transmittance due to the presence of a spatially varying scattering inclusion hidden inside a diffusive slab. This formula assumes that the reduced scattering coefficient of the inclusion is spatially Gaussian distributed and complements that obtained for the absorptive case. 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. The proposed perturbation model is validated through a fitting procedure that determines the relative error in retrieving the scattering perturbation parameter of the inclusion located at the midplane of the slab.