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

Abstract

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 N_S +N_T - 1 in each dimension, where N_S and N_T 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.

Keywords: B0 inhomogeneity; dipolar field; susceptibility; susceptibility voxel convolution (SVC).