「Coupled Circuit Analysis of Eddy Currents in MRI Systems」


In this study, we performed coupled circuit numerical simulation of eddy currents in magnetic resonance imaging (MRI) systems by implementing novel approaches in subdomain modeling, inductive coupling calculations and in solving the system of coupled differential equations. Simulations were conducted for both open (0.3 T) MRI and closed-bore (9.4 T) superconducting MRI systems. In MRI systems, complex spatio-temporal eddy currents are induced in the surrounding conducting structures because of the switching of pulses in the gradient coils which is proportional to the inductive couplings among the gradient coils and different conducting structures and, decays with some characteristic time constants. In this study, following the dc resistive-inductive circuit concepts and the concepts of diffusion of eddy currents inside the materials with some characteristic skin depths, we divide the eddy current conducting structures into thin (much thinner than the skin depth) subdomains both along the length (or width) and thickness, and by implementing inductive coupling relations (of this network of coupled resistive-inductive circuits) we simulated the transient responses of eddy currents for subdomains at different locations of the conducting structures. We implemented the Eigen matrix method to solve the network of first-order coupled differential equations. To compute the coupling relations between the gradient coil and subdomains located at any position of the conducting structure, we implemented solid angle form of Ampere’s law. The corresponding solid angles in three dimensions were calculated for both planar and cylindrical type of transverse (X- or Y-gradient) and longitudinal (Z-gradient) gradient coils. The secondary magnetic fields generated by the eddy currents were also calculated. Free induction decay (FID) experiments of eddy fields were conducted by using a nuclear magnetic resonance (NMR) probe to verify our simulation results for 0.3 T system and gradient echo shift technique was implemented for 9.4 T MRI system. We have found good agreements between simulation and experimental results.