Error analysis of helmholtz‐based MR‐electrical properties tomography

Mandija, Stefano; Sbrizzi, Alessandro; Katscher, Ulrich; Luijten, Peter R.; Berg, Cornelis A.T. van den

doi:10.1002/mrm.27004

Cited by 51 publications

(85 citation statements)

References 42 publications

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“…DL-EPT differs significantly from conventional MR-EPT techniques employing analytical or algebraic reconstruction models. The popular Helmholtz MR-EPT technique, an example of an analytical reconstruction technique, requires the computation of spatial derivatives on measured data 14 . This computation is performed by convolving the measured, complex ̃ field with large finite difference kernels such as the 3D kernel adopted in this work 11 , or the Savitzky-Golay kernel 32 .…”

Section: Discussionmentioning

confidence: 99%

“…Spatial derivatives are computed by applying a filter (in this case a 2 nd order finite difference filter) to the ̃ field data, resulting directly in EPs maps. However, this operation is highly sensitive to the intrinsic noise in the MR measurements, and consequently the reconstructed EPs maps lack precision 13,14 . To mitigate the impact of noise in the reconstructed EPs maps, large derivative filters in combination with image filters and large voxel sizes are commonly used 2 .…”

Section: Introductionmentioning

confidence: 99%

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Opening a new window on MR-based Electrical Properties Tomography with deep learning

Mandija

Meliadò

Huttinga

et al. 2019

Sci Rep

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In the radiofrequency (RF) range, the electrical properties of tissues (EPs: conductivity and permittivity) are modulated by the ionic and water content, which change for pathological conditions. Information on tissues EPs can be used e.g. in oncology as a biomarker. The inability of MR-Electrical Properties Tomography techniques (MR-EPT) to accurately reconstruct tissue EPs by relating MR measurements of the transmit RF field to the EPs limits their clinical applicability. Instead of employing electromagnetic models posing strict requirements on the measured MRI quantities, we propose a data driven approach where the electrical properties reconstruction problem can be casted as a supervised deep learning task (DL-EPT). DL-EPT reconstructions for simulations and MR measurements at 3 Tesla on phantoms and human brains using a conditional generative adversarial network demonstrate high quality EPs reconstructions and greatly improved precision compared to conventional MR-EPT. The supervised learning approach leverages the strength of electromagnetic simulations, allowing circumvention of inaccessible MR electromagnetic quantities. Since DL-EPT is more noise-robust than MR-EPT, the requirements for MR acquisitions can be relaxed. This could be a major step forward to turn electrical properties tomography into a reliable biomarker where pathological conditions can be revealed and characterized by abnormalities in tissue electrical properties.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Opening a new window on MR-based Electrical Properties Tomography with deep learning

Mandija

Meliadò

Huttinga

et al. 2019

Sci Rep

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“…In MREPT, the modification of the Laplacian operator has been investigated previously for noise-robust conductivity imaging. 14,18 In these previous studies, several discrete Laplacian operators were suggested to reduce noise power by combining adjacent kernels. In this work, distant-dependent weightings were applied to each Laplacian operator to manipulate the envelope.…”

Section: Discussionmentioning

confidence: 99%

“…For all simulations and experiments, prefiltering that reduces phase errors due to Gibb’s ringing was applied to the raw

B_{1}^{+}

and MR data using an isotropic Gaussian kernel with 2.0 × 2.0 mm 2 FWHM. The SD was determined as FWHM/( res ⋅2ln2), for which FWHM represents the full‐width half‐maximum in units of mm, and res represents the resolution in units of mm.…”

Section: Methodsmentioning

confidence: 99%

Redesign of the Laplacian kernel for improvements in conductivity imaging using MRI

Shin

Kim

2018

Magnetic Resonance in Med

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Purpose To develop an electrical property tomography reconstruction method that achieves improvements over standard method by redesigning the Laplacian kernel. Theory and Methods A decomposition property of the governing PET equation shows the possibility of redesigning the Laplacian kernel for conductivity reconstruction. Hence, the discrete Laplacian operator used for electrical property tomography reconstruction is redesigned to have a Gaussian‐like envelope, which enables manipulation of the spatial and spectral response. The characteristics of the proposed kernel are investigated through numerical simulations and in vivo brain experiments. Results The proposed method reduces textured noise, which hampers observing features of the conductivity image. Furthermore, the proposed scheme can mitigate the propagation of local phase error such as flow‐induced phase. By doing so, the proposed method can recover feature information in conductivity (or resistivity) images. Lastly, the proposed kernel can be extended to other electrical property tomography reconstructions, improving the quality of images. Conclusion An alternative design of the Laplacian kernel for conductivity imaging has been developed to mitigate the textured noise and the propagation of local phase artifact.

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“…Standard Helmholtz-based EPT (MR-EPT) [8]requires a constant dielectric profile and second-order spatial differentiation of the data. Care must be taken when implementing this differentiation operation to mitigate noise amplification [3], [15], [16]. On the other hand, in the global integral-based approach the dielectric tissue parameters are determined in an iterative manner by minimizing an objective function.…”

Section: Introductionmentioning

confidence: 99%

First-Order Induced Current Density Imaging and Electrical Properties Tomography in MRI

Fuchs

Mandija

Stijnman

et al. 2018

IEEE Trans. Comput. Imaging

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In this paper, we present an efficient dedicated electrical properties tomography algorithm (called first-order current density EPT) that exploits the particular radio frequency field structure, which is present in the midplane of a birdcage coil, to reconstruct conductivity and permittivity maps in this plane fromB + 1 data. The algorithm consists of a current density and an electrical properties step. In the current density reconstruction step, the induced currents in the midplane are determined by acting with a specific first-order differentiation operator on theB + 1 data. In the electrical properties step, we first determine the electric field strength by solving a particular integral equation, and subsequently determine conductivity and permittivity maps from the constitutive relations. The performance of the algorithm is illustrated by presenting reconstructions of a human brain model based on simulated (noise corrupted) data and of a known phantom model based on experimental data. The method manages to reconstruct conductivity profiles without model related boundary artefacts and is also more robust to noise because only first-order differencing of the data is required as opposed to second-order data differencing in Helmholtz-based approaches. Moreover, reconstructions can be performed in less than a second, allowing for essentially real-time electrical properties mapping.

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Error analysis of helmholtz‐based MR‐electrical properties tomography

Abstract: 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.

Cited by 51 publications

References 42 publications

Opening a new window on MR-based Electrical Properties Tomography with deep learning

Opening a new window on MR-based Electrical Properties Tomography with deep learning

Redesign of the Laplacian kernel for improvements in conductivity imaging using MRI

First-Order Induced Current Density Imaging and Electrical Properties Tomography in MRI

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