Depth localization of fluorescent heterogeneities in semi-infinite media: a numerical approach using early-arriving photons

摘要

The depth-localization of fluorescent objects having different diameters and embedded within semi-infinite turbid tissue is determined with a model based on the finite element method. The work relies on the time to reach half of the maximum fluorescence intensity. The model is based on a set of two-dependent photon diffusion equations: - the transport of the pulsed laser source (duration 1 ps) and - the transport of the induced fluorescent light excited by the source. The coupling between these equations is due to a source term directly proportional to the scattered fluence rate at the same location. To solve this problem, the method proceeds following the Galerkin formulation added to an implicit finite difference scheme (Backward Euler) to integrate the resulting matrix formulation with respect to time. The meshed domain is axi-symmetrical and takes into account the boundary conditions relative to air-tissue interface. The different computational results show that the fluorescent signals can be used to provide time of flight information about the depth localization of a spherical tumor embedded in a turbid medium. These findings are in good agreement with experimental works.