Conductivity and current density image reconstruction using harmonic Bz algorithm in magnetic resonance electrical impedance tomography

Magnetic resonance electrical impedance tomography (MREIT) is to provide cross-sectional images of the conductivity distribution sigma of a Subject. While injecting current into the subject, we measure one component B, of the induced magnetic flux density B = (B-x, B-y, B-z) using an MRI scanner. Based on the relation between del(2)B(z) and delsigma, the harmonic B-z algorithm reconstructs an image of sigma using the measured B-z data from multiple imaging slices. After we obtain sigma, 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 x 82 pixels. The pixel size was 0.6 x 0.6 mm(2). The relative L-2 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.