A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility

A fast calculation method for the magnetic field distribution due to (dynamic) changes in susceptibility may allow real-time interventional applications. Here it is shown that a direct relationship can be obtained between the magnetic field perturbation and the susceptibility distribution inside the MR magnet using a first order perturbation approach to Maxwell's magneto-static equations, combined with the Fourier transformation technique to solve partial derivative equations. The mathematical formalism does not involve any limitation with respect to shape or homogeneity of the susceptibility field. A first order approximation is sufficient if the susceptibility range does not exceed 10−4 (or 100 ppm). The formalism allows fast numerical calculations using 3D matrices. A few seconds computation time on a PC is sufficient for a 128 × 128 × 128 matrix size. Predicted phase maps fitted both analytical and experimental data within 1% precision. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 19B: 26–34, 2003.