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Error analysis of helmholtz‐based MR‐electrical properties tomography
Author(s) -
Mandija Stefano,
Sbrizzi Alessandro,
Katscher Ulrich,
Luijten Peter R.,
Berg Cornelis A.T.
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.27004
Subject(s) - ringing artifacts , imaging phantom , kernel (algebra) , noise (video) , voxel , computation , algorithm , helmholtz free energy , computer science , mathematics , physics , optics , artificial intelligence , combinatorics , quantum mechanics , image (mathematics)
Purpose MR electrical properties tomography (MR‐EPT) aims to measure tissue electrical properties by computing spatial derivatives of measuredB 1 +data. This computation is very sensitive to spatial fluctuations caused, for example, by noise and Gibbs ringing. In this work, the error arising from the computation of spatial derivatives using finite difference kernels (FD error) has been investigated. In relation to this FD error, it has also been investigated whether mitigation strategies such as Gibbs ringing correction and Gaussian apodization can be beneficial for conductivity reconstructions. Methods Conductivity reconstructions were performed on a phantom (by means of simulations and MR measurements at 3T) and on a human brain model. The accuracy was evaluated as a function of image resolution, FD kernel size, k‐space windowing, and signal‐to‐noise ratio. The impact of mitigation strategies was also investigated. Results The adopted small FD kernel is highly sensitive to spatial fluctuations, whereas the large FD kernel is more noise‐robust. However, large FD kernels lead to extended numerical boundary error propagation, which severely hampers the MR‐EPT reconstruction accuracy for highly spatially convoluted tissue structures such as the human brain. Mitigation strategies slightly improve the accuracy of conductivity reconstructions. For the adopted derivative kernels and the investigated scenario, MR‐EPT conductivity reconstructions show low accuracy: less than 37% of the voxels have a relative error lower than 30%. Conclusion The numerical error introduced by the computation of spatial derivatives using FD kernels is one of the major causes of limited accuracy in Helmholtz‐based MR‐EPT reconstructions. Magn Reson Med 80:90–100, 2018. © 2017 International Society for Magnetic Resonance in Medicine.