# Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction

## TL;DR

This paper introduces a novel method combining magneto-acoustic tomography and diffusion tensor imaging data to accurately reconstruct anisotropic electrical conductivity tensors in tissues.

## Contribution

It develops a mathematical and numerical framework for reconstructing anisotropic conductivity tensors using an optimal control approach integrating DTI data.

## Key findings

- The proposed algorithm converges and is Lipschitz stable.
- Numerical examples demonstrate the method's accuracy.
- The approach improves spatial resolution in conductivity imaging.

## Abstract

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.