Application of the finite elements method in optical medical imaging

The optical medical imaging is based on various systems such as the system resolved at time when ultra short bright impulses (picoseconds or femtoseconds) are sent to the surface of the tissue. The intensity appearing from some tissue (“temporal spread function”, or TPSF) is studied versus the arrival time of photons with a resolution around of the picoseconds [1]. The image reconstruction and the estimation of the optical properties of the target are based on the combination of the calculated and simulated TPSF (resolution of inverse problem). The method of finite elements (MFE) is a digital method which is used to resolve the problems in the limits characterized by an equation in the partial derivates and a set of conditions in the limits [2]. In this work, we used the MFE to resolve the direct problem of an optical impulse (some picoseconds) distribution in a biological middle. This system is managed by the equation of radiative transfer (ERT) which is under the shape of an equation for the partial derivatives.