Resistivity Tensor Imaging via Network Discretization of Faraday's Law

Abstract

A resistive network-based anisotropic resistivity reconstruction method is introduced in this paper when three sets of internal electrical currents are given. Faraday's law is discretized using resistive networks for an anisotropic resistivity body such as a muscle or nerve fiber structure of an animal body. The resistivity tensor imaging method of this paper may provide another approach to finding the fiber structure of white matter. We take three sets of internal electrical current density and a part of boundary conductivity to construct the anisotropic conductivity in two space dimensions. The construction algorithm is explicit and local. Hence, the computation time is only of the order of space dimensions.