Object localization within turbid slab media using time-resolved transillumination contrast functions : a finite element approach

In the last few years, the propagation of diffuse photons in scattering media has become an important field of interest. This is mainly due to the possibility offered by the low absorption of light in the range 700 to 900nm. Indeed, this property leads to a potential deep penetration. But a non negligible limitation appears: the scattering processes strongly reduce both the contrast and the resolution. In this paper, the time-dependent light propagation in highly scattering media containing an inclusion is solved by means of a finite element method, tacking into account Robin type air-tissue boundary conditions. This study is devoted to the depth localization of a tumor enclosed into a breast-like slab. The tissue is modeled by a rectangular meshed domain that mimics a breast compressed between two transparent plates. Cartesian coordinates are used in order to solve the time-dependent diffusion approximation. A short laser pulse of 1 ps is considered. The transillumination technique is able to laterally detect the object when the source and detector are moved together on the same axis. In order to perform the localization of the inclusion in this study, the optical properties of the object were varied. Knowing the lateral position of the inclusion, we derive interesting temporal contrast functions based on the mean time of flight of photons. These functions allow to localize in depth the inclusion under the assumption that the object is very diffusing. To conclude, our study demonstrates the possibility to detect laterally and axially a tumor-like inclusion enclosed in breast-like tissues.