Harmonic B_z Algorithms in Magnetic Resonance Electrical Impedance Tomography (MREIT) and Related Studies

Abstract

Magnetic resonance electrical impedance tomography (MREIT) is a conductivity imaging modality providing high-spatial resolution. When we inject current through electrodes to a target object, the magnetic flux density is generated by the internal current density. Using MR-machine, we can measure one-component of magnetic flux density, whose direction is parallel to the main magnetic field of the MR-machine. Harmonic $\It{B_z}$ algorithm is a reconstruction algorithm to provide cross-sectional conductivity imaging in MREIT, which uses only one component of magnetic flux density. However, due to the sensitivity of the algorithm, the result is collapsed near regions with low conductivity or insulated regions. In order to reconstruct the conductivity in the such problematic regions, the local harmonic $\It{B_z}$ algorithm was proposed by Seo $\It{et al}$. It requires a special type of triangulation and it still has a trouble to reconstruct conductivity in valley type regions. In this thesis, we propose an algorithm to handle the problematic regions without considering a special type of triangulation, which is based on the discontinuous Galerkin approach. In addition, we suggest a strategy to reconstruct the conductivity in valley type regions under the appropriate assumption. Conductivity image reconstruction in MREIT requires various steps of carefully implemented numerical computations. To facilitate MREIT research, there has been a pressing need for an MREIT software package with efficient user interface. In this thesis, we present an example of such a software, so called CoReHA which stands for conductivity reconstructor using harmonic algorithms. It offers various computational tools including preprocessing of MREIT data, identification of boundary geometry, electrode modeling, meshing and implementation of a finite element method. The conductivity image reconstruction method based on the harmonic $\It{B_z}$ algorithm produces cross-sectional conductivity ima...