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A discrete Fourier based method for calculating field distributions and local magnetic susceptibility in MRI is carefully studied. Simulations suggest that the method based on discrete Green's functions in both 2D and 3D spaces has less error than the method based on continuous Green's functions. The 2D field calculations require the correction of the 'Lorentz disk', which is similar to the Lorentz sphere term in the 3D case. A standard least-squares fit is proposed for the extraction of susceptibility for a single object from MR images. Simulations and a phantom study confirm both the discrete method and the feasibility of the least-squares fit approach. Finding accurate susceptibility values of local structures in the brain from MR images may be possible with this approach in the future.
Cheng et al. (2009) studied this question.