Analysis of local projected current density from one component of magnetic flux density in MREIT

Magnetic resonance electrical impedance tomography is a new modality capable of imaging the static electrical conductivity of an object by measuring B_z data, a component of the magnetic flux density B = (B_x, B_y, B_z), perturbed by an external injection current. In an imaging area, the current density J induced by the external injection current can be uniquely decomposed into a recoverable component J^P and an invisible component from the measured B_z data. In the case of in vivo animal and human imaging experiments, the imaging area frequently includes local defective regions with a low signal-to-noise ratio. As a result, the measured B_z data in the defective regions include serious noise due to rapid T₂ decay, a small amount of internal current density and weak MR signals. In this paper, we propose an algorithm to reconstruct a recoverable current density from the measured B_z data in a local region avoiding the defective regions. We estimate the L²-norm of the difference between the induced internal current density J and the locally recovered from the measured B_z data in the local region . The difference only depends on the z-components of J and J⁰ and the values of B_x and B_y on the boundary , where J⁰ is the background current density by the injected current. Numerical simulations and phantom experiments demonstrate that the proposed method directly reconstructs a local current density avoiding noise effects in defective regions.