Simultaneous estimation of optical anisotropy and absorption in medical optical tomography

In this paper we propose a possible model for anisotropic light propagation, and present simultaneous reconstruction of anisotropy parameters and optical absorption for optical tomography. The anisotropic model is introduced into the Radiative Transfer Equation (RTE). The most commonly used approximation to the RTE in optical tomography is the Diffusion Equation (DE). In anisotropic case, the diffusion coefficient in the DE assumes a tensor form. We present the diffusion tensor as an eigenvalue decomposition corresponding to the directions and the strength parameters of anisotropy. The numerical approximation is done in two dimensions using the finite element (FE) method. We then consider the inverse problem of reconstructing the optical absorption when the directions of anisotropy are assumed to be known, but the strength may vary. For this estimation to be successful, the strength parameters are reconstructed simultaneously with the absorption. We present numerical examples of cases in which the location of anisotropy is truly known, and in which there is an error in the assumed location.