Using the EC-S-FDTD Scheme to Approximate Eddy Currents Induced by Z-Gradient Coils

Eddy currents are induced by rapidly switching currents of the gradient coils in an magnetic resonance imaging (MRI) scanner, which is typically cylindrical in shape; hence, the use of cylindrical coordinates is more numerically efficient. We develop the energy conserved splitting finite-difference time-domain (EC-S-FDTD) scheme in the cylindrical coordinates to estimate the eddy currents. The important feature is that this scheme conserves energy and is unconditionally stable. The transformation results in numerical singularities are formed at the internal boundary, and we formulate methods to handle these singularities and efficiently solve the equations. The accuracy of the scheme and energy conversation property are tested, and the performance of the proposed method will be evaluated using two numerical simulations, cylindrical transmission lines, and eddy currents induced by Z-gradient coils. Our numerical results indicate that current density distribution reflects the differences in the tissues by their dielectric properties and has second-order convergence in time and space while preserving energy conservation.