Rapid calculation of static magnetic field perturbation generated by magnetized objects in arbitrary orientations.

PURPOSE: Most previous work on the calculation of susceptibility-induced static magnetic field (B0 ) inhomogeneity has considered strictly unidirectional magnetic fields. Here, we present the theory and implementation of a computational method to rapidly calculate static magnetic field vectors produced by an arbitrary distribution of voxelated magnetization vectors. THEORY AND METHODS: Two existing B0 calculation methods were systematically extended to include arbitrary orientations of the magnetization and the magnetic field; they are (1) Fourier-domain convolution with k-space-discretized (KD) dipolar field, and (2) generalized susceptibility voxel convolution (gSVC). The methods were tested on an analytical ellipsoid model and a tilted human head model, as well as against experimentally measured B0 fields induced by a stainless-steel implant located in an inhomogeneous region of a clinical 3T MRI magnet. RESULTS: Both methods were capable of correctly calculating B0 fields inside a magnetized ellipsoid in all tested orientations. The KD method generally required a larger grid and longer computation time to achieve accuracy comparable to gSVC. Measured B0 fields due to the implant showed a good match with the gSVC-calculated fields that accounted for the spatial variation of the applied magnetic field including the radial components. CONCLUSION: Our method can provide a reliable and efficient computational tool to calculate B0 perturbation by magnetized objects under a variety of circumstances, including those with inhomogeneous magnetizing fields, anisotropic susceptibility, and a rotated coordinate system.

Rapid, theoretically artifact-free calculation of static magnetic field induced by voxelated susceptibility distribution in an arbitrary volume of interest.

PURPOSE: To demonstrate a computationally efficient and theoretically artifact-free method to calculate static field (B0 ) inhomogeneity in a volume of interest induced by an arbitrary voxelated susceptibility distribution. METHODS: Our method computes B0 by circular convolution between a zero-filled susceptibility matrix and a shifted, voxel-integrated dipolar field kernel on a grid of size NS +NT - 1 in each dimension, where NS and NT are the sizes of the susceptibility source and B0 target grids, respectively. The computational resource requirement is independent of source-target separation. The method, called generalized susceptibility voxel convolution, is demonstrated on three susceptibility models: an ellipsoid, MR-compatible screws, and a dynamic human heartbeat model. RESULTS: B0 in an ellipsoid calculated by generalized susceptibility voxel convolution matched an analytical solution nearly exactly. The method also calculated screw-induced B0 in agreement with experimental data. Dynamic simulation demonstrated its computational efficiency for repeated B0 calculations on time-varying susceptibility. On the contrary, conventional and alias-subtracted k-space-discretized Fourier convolution methods showed nonnegligible aliasing and Gibbs ringing artifacts in the tested models. CONCLUSION: Generalized susceptibility voxel convolution can be a fast and reliable way to compute susceptibility-induced B0 when the susceptibility source is not colocated with the B0 target volume of interest, as in modeling B0 variations from motion and foreign objects.