Magnetic Resonance Electrical Impedance Tomography (MREIT) is a new medical imaging modality providing high resolution static conductivity images based on the current injection MRI technique. MREIT was motivated to deal with the well-known severe ill-posedness of the image reconstruction problem in Electrical Impedance Tomography (EIT). In order to bypass the ill-posed nature in EIT, MREIT takes advantage of an MRI scanner as a tool to capture partial information about magnetic flux density due to internal current density. The conductivity distribution have an effect in change in internal current density pathways that are interrelated with the unknown conductivity distribution. Lately, we have made a significant progress in reconstruction algorithms in MREIT. Experimental MREIT study demonstrates that the reconstructed conductivity image distinguishes different biological tissues in terms of both their shapes and conductivity values. Reconstructed static conductivity images will al...