Magnetic Resonance Current Density Imaging (MR-CDI)

Current density imaging (CDI) was developed with the aim of determining the three-dimensional distribution of externally applied electric current pathways inside a conductive medium, using measurements of magnetic flux density B= (B_x, B_y, B_z) data. While the B field may be measurable using instruments such as a magnetometer, in magnetic resonance current density imaging (MR-CDI), an MRI scanner is used to measure the magnetic flux density data induced by current flow. In MR-CDI, the object must be rotated inside the MRI machine to find all three components of the B-field, as only the component of B parallel to the magnet main magnetic field can be measured. In principle, once the all three components of the B field have been obtained from an MR imaging experiment, the current density distribution J= (J_x, J_y, J_z) can be reconstructed from Ampere’s law J=1μ0∇×B. However, the need to rotate the object within the MRI scanner limits the usability of this technique. To overcome this problem, researchers have investigated the current density reconstruction problem using only one component of the magnetic flux density B_q, where q = x, y, z. In this chapter, we discuss numerical algorithms developed to reconstruct the distribution of J information from the measured B-field.