The numerical error arising from the computation of spatial derivatives using finite difference kernels is investigated for Helmholtz-based MR-Electrical-Properties-Tomography conductivity reconstructions. We show that this numerical error is one major cause of limited accuracy in Helmholtz-based MR-EPT reconstructions, even if mitigation strategies such as Gibbs ringing correction and Gaussian apodization in k-space are adopted. Ultimately, large derivative kernels lead to more noise-robust conductivity reconstructions, at the cost of more spatially-extended boundary errors. If boundaries are not explicitly taken into account during reconstructions, the accuracy of MR-EPT is severely hampered, particularly for spatially convoluted tissues such as the human brain.
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