A uniqueness result and image reconstruction of the orthotropic conductivity in magnetic resonance electrical impedance tomography

Abstract

The Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging method combining electrical impedance tomography (EIT) and current injection MRI technique. In this paper, we show the uniqueness in MREIT problem with an orthotropic conductivity under the hypothesis that the ratios of conductivities are known. Based on an effective numerical differentiation method and an approach to detect discontinuity, we also propose an iterative reconstruction algorithm for the orthotropic conductivity reconstruction. The resulting numerical algorithm is accurate and stable against the noise, and numerical examples are made to illustrate the performance of our algorithm.