Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction
This work addresses the problem of imaging anisotropic conductivity for medical applications, but the method is incremental as it relies on a proportionality assumption between conductivity and diffusion tensor.
The paper develops a mathematical and numerical framework to reconstruct anisotropic electrical conductivity tensors by combining magneto-acoustic tomography with magnetic induction (MAT-MI) and diffusion tensor imaging (DTI), assuming conductivity is proportional to the diffusion tensor. Numerical examples demonstrate the accuracy and feasibility of the proposed optimal control approach.
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.