Identification of current density distribution in electrically conducting subject with anisotropic conductivity distribution

Current density imaging (CDI) is able to visualize a three-dimensional current density distribution J inside an electrically conducting subject caused by an externally applied current. CDI may use a magnetic resonance imaging (MRI) scanner to measure the induced magnetic flux density B and compute J via the Ampere law J = 1/μ₀∇ × B. However, measuring all three components of B = (B_x, B_y, B_z) has a technical difficulty due to the requirement of orthogonal rotations of the subject inside the MRI scanner. In this work, we propose a new method of reconstructing a current density image using only B_z data so that we can avoid the subject rotation procedure. The method utilizes an auxiliary injection current to compensate the missing information of B_x and B_y. The major advantage of the method is its applicability to a subject with an anisotropic conductivity distribution. Numerical experiments show the feasibility of the new technique.