A computationally efficient model for simulating time-resolved fluorescence spectroscopy of thick biological tissues

摘要

A computational model based on finite element method is derived to examine how the recorded time-dependent signals are related to the basic optical properties of a slab at both excitation and emission wavelengths. The model is based on a set of two time-dependent photon diffusion equations: -the transport of the pulsed laser source light (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 implicite finite difference scheme (Backward Euler) to integrate the resulting matrix formulation with respect to time. The meshed domain is two dimensional and takes into account the available boundary conditions relative to air-tissue interface (Robin boundary conditions). The computations are first carried out for a slab in which the fluorophores are uniformly distributed, and afterwards devoted to the localization in depth of a fluorescent object (like a tumor) embedded within the slab.