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.