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

Abstract

© 2021 International Society for Magnetic Resonance in MedicinePurpose: 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.