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.