Conductivity and current density image reconstruction using harmonic B_z algorithm in magnetic resonance electrical impedence tomography

Magnetic resonance electrical impedance tomography (MREIT) is to provide cross-sectional images of the conductivity distribution σ of a subject. While injecting current into the subject, we measure one component B_z of the induced magnetic flux density B = (B_x, B_y, B_z,) using an MRI scanner. Based on the relation between ∇²B_z and ∇σ, the harmonic B_z algorithm reconstructs an image of σ using the measured B_z data from multiple imaging slices. After we obtain σ, we can reconstruct images of current density distributions for any given current injection method. Following the description of the harmonic B_z algorithm, this paper presents reconstructed conductivity and current density images from computer simulations and phantom experiments using four recessed electrodes injecting six different currents of 26 mA. For experimental results, we used a three-dimensional saline phantom with two polyacrylamide objects inside. We used our 0.3 T (tesla) experimental MRI scanner to measure the induced B_z. Using the harmonic B_z algorithm, we could reconstruct conductivity and current density images with 82 × 82 pixels. The pixel size was 0.6 × 0.6 mm². The relative L² errors of the reconstructed images were between 13.8 and 21.5% when the signal-to-noise ratio (SNR) of the corresponding MR magnitude images was about 30. The results suggest that in vitro and in vivo experimental studies with animal subjects are feasible. Further studies are requested to reduce the amount of injection current down to less than 1 mA for human subjects.