Electrical conductivity imaging using a variational method in B _z-based MREIT

Magnetic resonance electrical impedance tomography (MREIT) is a new conductivity imaging modality that was motivated to deal with the well-known ill-posedness problem in electrical impedance tomography (EIT). In order to bypass this ill-posed nature, MREIT takes advantage of an MRI scanner as a tool to capture the z-component B_z of the induced internal magnetic flux density B = (B_x, B_y, B _z) due to an injection current. Here, z is the direction of the main magnetic field of the MRI scanner. In this work, we propose an enhanced version of the variational gradient B_z algorithm that benefits from a careful use of boundary conditions in a variational formulation of the B _z-based MREIT model. We found that the proposed algorithm is advantageous especially in dealing with conductivity images near the boundary of the subject. Improvements in reconstructed image quality are shown by numerical simulations.