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

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 noninvasive 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.

Sparse Reconstruction of Log-Conductivity in Current Density Impedance Tomography

“…Proposition 5 (First-order necessary conditions). The optimal solution of the minimization problem (7) can be characterized by the existence of (λ * , λ *…”

“…A robust way of solving this inverse problem is to formulate it as an optimal control problem, where the condiuctivity parameter is the control variable that drives the interior electric field close to the measured value, with dynamics governed by the conductivity PDE. Such optimal control methods has been used previously in the context of ultrasonically-induced Lorentz force electrical impedance tomography [5], magnetoacoustic tomography [6,7,38] and acousto-electric tomography (AET) [1,41]. In [5], the authors use an optimal control framework to recover the conductivity distribution from the measurements of current induced by static magnetic field through the Lorentz force.…”

“…They solve the optimal control problem using an orthogonal field method. In [6,7,38], the authors use an optimal control approach to reconstruct conductivity distribution of biological tissue from measurements of the Lorentz force induced tissue vibration. In [1,41], the authors reconstruct log-conductivity in acousto-electric tomography (AET) using an optimal control formulation based on the theory of anisotropic diffusion to potentially obtain reconstructions with high resolution and contrast.…”

Electrodeless conductivity tensor imaging (CTI) using MRI: basic theory and animal experiments

“…Noting that diffusion weighted MRI provides information about water mobility in a biological tissue, diffusion tensor imaging (DTI) has been utilized for conductivity tensor imaging assuming that the conductivity tensor is a scalar multiple of the water diffusion tensor [9,10]. To convert the water diffusion tensor to conductivity tensor, either a fixed scale factor was used [11] or current-injection methods were adopted to determine the position-dependent scale factor in diffusion tensor MREIT (DT-MREIT) [8,12].…”

Imaging Anisotropic Conductivities from Current Densities

“…With the knowledge of the magnitude of only one current density magnitude | h|, the problem was studied in a series of work [42,43,54] in the isotropic case, and also the anisotropic case in a known conformal class in [25]. Ammari et al [6] studied the recovery of an anisotropic conductivity proportional to a known conductivity tensor.…”