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Rapid, theoretically artifact‐free calculation of static magnetic field induced by voxelated susceptibility distribution in an arbitrary volume of interest
Author(s) -
Lee SeungKyun,
Hwang SeonHa,
Barg JiSeong,
Yeo SeokJin
Publication year - 2018
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.27161
Subject(s) - convolution (computer science) , voxel , magnetic susceptibility , kernel (algebra) , ellipsoid , dimension (graph theory) , mathematics , physics , algorithm , artifact (error) , mathematical analysis , computer science , artificial intelligence , combinatorics , quantum mechanics , astronomy , artificial neural network
Purpose To demonstrate a computationally efficient and theoretically artifact‐free method to calculate static field (B 0 ) inhomogeneity in a volume of interest induced by an arbitrary voxelated susceptibility distribution. Methods Our method computes B 0 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 B 0 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 B 0 in an ellipsoid calculated by generalized susceptibility voxel convolution matched an analytical solution nearly exactly. The method also calculated screw‐induced B 0 in agreement with experimental data. Dynamic simulation demonstrated its computational efficiency for repeated B 0 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 B 0 when the susceptibility source is not colocated with the B 0 target volume of interest, as in modeling B 0 variations from motion and foreign objects.