Mathematical framework for B_z-based MREIT model in electrical impedance imaging

Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging modality visualizing static conductivity images of a subject by injecting electrical currents (Neumann data) and measuring the induced internal magnetic flux density B using an MRI scanner. Taking advantage of the internal information B, MREIT can deal with the ill-posed characteristics of the inverse problem in electrical impedance tomography (EIT However, the MREIT model at its early stage has technical difficulties in clinical applications mainly due to the requirement of subject rotations for acquiring all of the three components of B = (B_z, B_y, B_z). Lately, a new model so called the B_z-based MREIT model has been proposed to eliminate the subject rotation procedure. In this new MREIT model, we need to measure only one component B_z when the z-axis is the direction of the main magnetic field of the MRI scanner. There have been significant advances in reconstruction algorithms based on the B_z-based MREIT model and experimental studies showed that an excellent contrast resolution can be achievable. Although these advance in B_z-based MREIT, we have not dealt with its rigorous mathematical theory yet. The primary purpose of this work is to provide the rigorous mathematical framework for the B_z-based MREIT model. With this mathematical framework, we obtain the uniqueness in a two-dimensional setting of the B_z-based MREIT model. After introducing an example of the B_z-based MREIT algorithm, we present typical numerical and also experimental results.