Three-dimensional forward problem in magnetic resonance electrical impedance tomography (MREIT)

In MREIT, we reconstruct cross-sectional resistivity images of a subject. Injecting currents through surface electrodes, we measure internal magnetic flux density using MRCDI technique. Current density can be obtained from the magnetic flux density data. For resistivity image reconstruction algorithms, we need a three-dimensional forward solver computing voltage, current density, and magnetic flux density within the subject. Given injection currents as boundary conditions, the three-dimensional forward solver described in this paper calculates voltage and current density using FEM. Then, it computes the induced magnetic flux density within the subject using the Biot-Savart law.