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.
Bibliographical noteFunding Information:
This series of trials was funded by Ravensdown Fertiliser Cooperative Ltd. The technical assistance of Stuart Macmillan and statistical guidance from Fred Potter and John Koolaard is gratefully acknowledged.
© 2017 IOP Publishing Ltd.
- anisotropic conductivity
- diffusion tensor imaging
- hybrid imaging
- magneto-acoustic tomography with magnetic induction