A Method to Solve the Forward Problem in Magnetic Induction Tomography Based on the Weakly Coupled Field Approximation

Magnetic induction tomography (MIT) is a noninvasive modality for imaging the complex conductivity ( ?? = ??+ j????) or the magnetic permeability (??) of a target under investigation. Because MIT employs noncontact coils for excitation and detection, MIT may be suitable for imaging biological tissues. In medical applications where high resolutions are sought, image reconstruction is a time and memory consuming task because the associated inverse problem is nonlinear and ill-posed. The time and memory constraints are mainly imposed by the solution of the forward problem within the iterative image reconstruction procedure. This paper investigates the application of a weakly coupled approximation to the solution of the forward problem and examines the accuracy against the computation time and memory gained in adopting this approximation. Initially, an analytical solution for mutual impedance change of a coil pair due to a large planar conductive object is presented based on a full wave theory and used to demonstrate a 10 MHz frequency excitation as an acceptable upper frequency limit under which the approximation is valid. Subsequently, a numerical impedance method adopting the approximation is presented. Here the impedance method is used to solve the forward problem, which employs electrical circuit analogues to mesh the target into a network that can be solved using circuit analysis and sparse matrix technique. The error due to the approximation is further estimated numerically with the impedance method against a commercial finite-element package (commercial FE solver, COMSOL) and results show at 10 MHz excitation a 0.4% of tolerance is achieved for conductivities in the range <0.5 S/m. The results also show the method can be applied for low conductivity medical applications and is computationally efficient compared to equivalent finite-element methods.