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.