Analysis of Transient Eddy Currents in MRI Using a Cylindrical FDTD Method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet

[1]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[3]  G. Ries.  Eddy current transients and forces in cryostat walls of superconducting solenoids , 1988 .

[4]  J. E. Bridges.  An update on the circuit approach to calculate shielding effectiveness , 1988 .

[5]  P. Jehenson,et al.  Analytical method for the compensation of eddy-current effects induced by pulsed magnetic field gradients in NMR systems , 1990 .

[6]  Numerical analysis of eddy current problems involving z gradient coils in superconducting MRI magnets , 1990 .

[7]  A. Cangellaris,et al.  Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena , 1991 .

[8]  R. Holland,et al.  Finite-difference time-domain (FDTD) analysis of magnetic diffusion , 1994 .

[9]  FDTD analysis of nonlinear magnetic diffusion by reduced c , 1995 .

[10]  Eddy current effects in MRI superconducting magnets , 1997 .

[11]  N J Pelc,et al.  Gradient characterization using a Fourier‐transform technique , 1998, Magnetic resonance in medicine.

[12]  P. Bandettini,et al.  Echo-planar imaging : theory, technique and application , 1998 .

[13]  Transient analysis of magnetodynamic systems using Fourier transform and frequency sensitivity , 1999 .

[14]  R. Lerch,et al.  Multigrid methods for the three-dimensional simulation of nonlinear magnetomechanical systems , 2002 .

[15]  Manfred Kaltenbacher,et al.  Magnetomechanical field computations of a clinical magnetic resonance imaging (MRI) scanner , 2003 .

[16]  Oszkar Biro,et al.  Multigrid for transient 3D eddy current analysis , 2003 .

[17]  S. V. Kulkarni,et al.  Novel modeling and solution approach for repeated finite-element analysis of eddy-current systems , 2004, IEEE Transactions on Magnetics.

[18]  Feng Liu,et al.  An FDTD model for calculation of gradient-induced eddy currents in MRI system , 2004, IEEE Transactions on Applied Superconductivity.

[19]  J. O'Daniel,et al.  Nonlinear magnetic diffusion in single-domain YBCO cylinders under pulsed field conditions , 2005, IEEE Transactions on Applied Superconductivity.