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

Fuchs, Patrick S.; Mandija, Stefano; Stijnman, Peter R. S.; Brink, Wyger M.; Berg, Cornelis A.T. van den; Remis, Rob

doi:10.1109/tci.2018.2873407

Cited by 9 publications

(19 citation statements)

References 29 publications

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“…Requiring that Equation (59) holds at N different locations with position vectors r n ∈ D, n = 1, 2, ..., N, leading to a system of equations Ax = b, where the N-by-3N matrix A, the 3N-by-1 vector x and the N-by-1 vector b are of similar form as in LMT (cf. Equations (55) and (56)). Since there are three unknowns (g + (r n ), g z (r n ), and −k 2 (r n )) associated with each point of interest r n , at least three linearly independent transmit field measurements are carried out, producing the set of equations A i x = b i , i = 1, 2, ..., I, where I ≥ 3 is the total number of transmit field measurements.…”

Section: Modified Dual-excitation Eptmentioning

confidence: 99%

“…First-order induced-current EPT (foIC-EPT) considers E-polarized RF fields and thus assumes that the electric field strength is mainly directed in the longitudinal z-direction [56]. For E-polarized fields, we have (cf.…”

Section: First-order Induced-current Eptmentioning

confidence: 99%

“…Equation (84) is required to hold at N different locations of interest with position vectors r n ∈ D, n = 1, 2, ..., N, leading to a system of equations Ax = b, where the N-by-3N matrix A, the 3N-by-1 vector x and the N-by-1 vector b are of a similar form as in LMT, MDE-EPT and G-EPT (cf. Equations(55) and(56)). Once the ∇B −; * tissue parameters can be determined from Equation(81).…”

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confidence: 99%

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Electrical Properties Tomography: A Methodological Review

et al. 2021

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Electrical properties tomography (EPT) is an imaging method that uses a magnetic resonance (MR) system to non-invasively determine the spatial distribution of the conductivity and permittivity of the imaged object. This manuscript starts by providing clear definitions about the data required for, and acquired in, EPT, followed by comprehensively formulating the physical equations underlying a large number of analytical EPT techniques. This thorough mathematical overview of EPT harmonizes several EPT techniques in a single type of formulation and gives insight into how they act on the data and what their data requirements are. Furthermore, the review describes machine learning-based algorithms. Matlab code of several differential and iterative integral methods is available upon request.

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Section: Modified Dual-excitation Eptmentioning

confidence: 99%

Section: First-order Induced-current Eptmentioning

confidence: 99%

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confidence: 99%

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Electrical Properties Tomography: A Methodological Review

et al. 2021

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“…The simplified CSI-EPT method is therefore called a first-order-induced current EPT method, since a first-order differentiation of the B + 1 -field essentially immediately results in an image of the induced current density. As shown in Reference [20], after the induced current density is obtained, the corresponding electric-field strength can be computed by solving a specific integral equation defined on S body . With the electric-field strength now known, the conductivity and permittivity profiles within the slice can be obtained from Equation (26).…”

Section: Simplified Two-dimensional Csi-ept-foic-eptmentioning

confidence: 99%

Developments in Electrical-Property Tomography Based on the Contrast-Source Inversion Method

et al. 2019

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The main objective of electrical-property tomography (EPT) is to retrieve dielectric tissue parameters from B ^ 1 + data as measured by a magnetic-resonance (MR) scanner. This is a so-called hybrid inverse problem in which data are defined inside the reconstruction domain of interest. In this paper, we discuss recent and new developments in EPT based on the contrast-source inversion (CSI) method. After a short review of the basics of this method, two- and three-dimensional implementations of CSI–EPT are presented along with a very efficient variant of 2D CSI–EPT called first-order induced current EPT (foIC-EPT). Practical implementation issues that arise when applying the method to measured data are addressed as well, and the limitations of a two-dimensional approach are extensively discussed. Tissue-parameter reconstructions of an anatomically correct male head model illustrate the performance of two- and three-dimensional CSI–EPT. We show that 2D implementation only produces reliable reconstructions under very special circumstances, while accurate reconstructions can be obtained with 3D CSI–EPT.

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“…Other methods showing reduced boundary errors and noise sensitivity have been presented, e.g. [106][107][108].…”

Section: Direct Eptmentioning

confidence: 99%

Technical developments for MR-based electrical property mapping

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Purpose: To demonstrate the feasibility of transceive phase mapping with the planet method and its application for conductivity reconstruction in the brain. Methods: Accuracy and precision of transceive phase (φ ±) estimation with planet, an ellipse fitting approach to phase-cycled balanced steady state free precession (bssfp) data, were assessed with simulations and measurements and compared to standard bssfp. Measurements were conducted on a homogeneous phantom and in the brain of healthy volunteers at 3T. Conductivity maps were reconstructed with Helmholtz-based electrical properties tomography (ept). In measurements, planet was also compared to a reference technique for transceive phase mapping, i.e. spin echo (se). Results: Accuracy and precision of φ ± estimated with planet depended on the chosen flip angle (FA) and TR. planet-based φ ± was less sensitive to perturbations induced by off-resonance effects and partial volume (e.g. white matter + myelin) than bssfp-based φ ±. For FA = 25 • and TR = 4.6 ms, planet showed an accuracy comparable to that of reference se but a higher precision than bssfp and se (factor of 2 and 3, respectively). The acquisition time for planet was 5 min; 2 min faster than se and 8 times slower than bssfp. However, planet simultaneously reconstructed T 1 , T 2 , B 0 maps besides mapping φ ±. In the phantom, planet-based conductivity matched the true value and had the smallest spread of the three methods. In vivo, planet-based conductivity was similar to se-based conductivity. Conclusion: Provided that appropriate sequence parameters are used, planet delivers accurate and precise φ ± maps, which can be used to reconstruct brain tissue conductivity while simultaneously recovering T 1 , T 2 and B 0 maps.

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

Cited by 9 publications

References 29 publications

Electrical Properties Tomography: A Methodological Review

Electrical Properties Tomography: A Methodological Review

Developments in Electrical-Property Tomography Based on the Contrast-Source Inversion Method

Technical developments for MR-based electrical property mapping

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