  In this paper we present a mathematical and numerical framework for a
procedure of imaging anisotropic electrical conductivity tensor by integrating
magneto-acoutic tomography with data acquired from diffusion tensor imaging.
Magneto-acoustic Tomography with Magnetic Induction (MAT-MI) is a hybrid,
non-invasive medical imaging technique to produce conductivity images with
improved spatial resolution and accuracy. Diffusion Tensor Imaging (DTI) is
also a non- invasive technique for characterizing the diffusion properties of
water molecules in tissues. We propose a model for anisotropic conductivity in
which the conductivity is proportional to the diffusion tensor. Under this
assumption, we propose an optimal control approach for reconstructing the
anisotropic electrical conductivity tensor. We prove convergence and Lipschitz
type stability of the algorithm and present numerical examples to illustrate
its accuracy and feasibility.
