The electrical conductivity of biological tissues incorporates crucial information regarding the tissues' physiological status. Therefore, there have been many studies for probing the electrical conductivity of biological tissues through Magnetic Resonance Imaging (MRI). Diffusion Tensor Magnetic Resonance Electrical Impedance Tomography (DT-MREIT) is an emerging modality that utilizes a linear relationship between the diffusion tensor and the conductivity tensor and the current density distribution throughout the imaging object under an external current injection in order to recover the conductivity tensor from the diffusion tensor measurements. This study aims to improve the current density recovery process from the current-induced magnetic flux density measurements in DT-MREIT applications. To this end, two novel methods, namely SS-FEM and P-ROT methods, are proposed where the current-induced magnetic flux density measurements and the measured diffusion tensor information are utilized. With these methods, current density recovery in the current injection direction is attained with percentage errors 8.6 and 7.6 for SS-FEM and P-ROT methods, respectively, at 30 dB. These error performances are superior to that of the 13.1 percent error, which is attained by the projected current density method, the most widely used method in DT-MREIT literature. Also, with the SS-FEM method, it is possible to recover current density distribution from a single-slice Bz measurement throughout the entire imaging object of an 8 cm3 cube simulation model up to a percentage error of 40 in the current injection direction at 30 dB. Moreover, with the P-ROT method, current density distribution in the z direction can also be recovered with a percentage error of 22 at 30 dB. These are unique capabilities of the proposed methods. In addition to the proposed current density recovery methods, another novel method is proposed to accelerate the current-induced magnetic flux density measurements. On the other hand, the proposed method on fast current-induced magnetic flux density imaging failed to reconstruct the current-induced magnetic flux density in experimental studies, and underlying reasons are discussed. Theoretical background, simulation studies, and experimental studies regarding the proposed methods are presented.
