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

by H. Ammari and L. Qiu and F. Santosa and W. Zhang

(Report number 2017-09)

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.

Keywords: hybrid imaging, magneto-acoustic tomography with magnetic induction, diffusion tensor imaging, anisotropic conductivity.

@Techreport{AQSZ17_705,
  author = {H. Ammari and L. Qiu and F. Santosa and W. Zhang},
  title = {Determining anisotropic conductivity using diffusion tensor imaging data in magneto-acoustic tomography with magnetic induction },
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2017-09},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2017/2017-09.pdf },
  year = {2017}
}

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