Novel Numerical Basis Sets for Electromagnetic Field Expansion in Arbitrary Inhomogeneous Objects

Georgakis, Ioannis P.; Villena, Jorge Fernández; Polimeridis, Athanasios G.; Lattanzi, Riccardo

doi:10.1109/tap.2022.3177566

Cited by 5 publications

(11 citation statements)

References 94 publications

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“…The aim of this work was to introduce a new method to calculate the ICP that yield optimal SNR in heterogeneous realistic anatomical models. The use of numerical EM bases 27 allowed the computation of a set of incident EM fields generated from electric currents sources defined on a surface surrounding the sample. We used a fast 13 and accurate 34 VIE solver () to estimate the corresponding total electric and magnetic field inside the sample ().…”

Section: Discussionmentioning

confidence: 99%

“…In an MRI setup, the external source is a transmit RF coil, which delivers EM fields to the tissue‐sample. Therefore, given a vector of electric coil currents

{\mathbf{j}}_{\mathrm{c}}\in {\mathbb{C}}^{m\times 1}

defined for each of the

m

discretization triangular elements of the coil, one can compute the incident fields as follows:

e_{inc} = Z_{cb}^{𝒩} j_{c}, h_{inc} = Z_{cb}^{𝒦} j_{c} .

Z_{cb}^{𝒩}, Z_{cb}^{𝒦} \in ℂ^{q n \times m}

are the discretized dyadic Green's function operators that map surface electric currents to electric and magnetic fields, respectively 27,35 . The electric coil currents can be computed simultaneously with the body polarization currents through the solution of the VSIE as in 35,36 …”

Section: Theorymentioning

confidence: 99%

“…

Z_{cb}^{𝒦}

can be compressed and orthogonalized using a truncated singular value decomposition (SVD) 27 as follows:

\begin{align} {boldZ}_{cb}^{𝒦} & prefix\approx {boldU}_{𝒦} {bold∑}_{𝒦} {boldV}_{𝒦}^{normalH} \\ {boldU}_{𝒩} & = {boldZ}_{cb}^{𝒩} {boldV}_{𝒦} {bold∑}_{𝒦}^{prefix- 1} . \end{align}

Here,

U_{𝒩}

and

U_{𝒦}

are bases of electric and magnetic incident fields consistent with electrodynamics principles 43 .

\sum_{𝒦}

is a diagonal matrix containing the singular values of

Z_{cb}^{𝒦}

up to the predefined tolerance of the SVD.…”

Section: Theorymentioning

confidence: 99%

“…18 In order to confirm such a hypothesis, and also to provide a practical tool for RF coil design and performance assessment, in this work, we introduce a method to calculate ICP associated with optimal SNR in realistic heterogeneous human head models, using volume 25 and volume-surface 10 integral equation (VIE, VSIE) methods. Numerical methods to calculate the optimal SNR in heterogeneous head models were proposed in previous studies, 26,27 whereas this work focuses on deriving the corresponding ICP. A preliminary version of this work was presented at the 2019 meeting of the International Society for Magnetic Resonance in Medicine.…”

Section: Introductionmentioning

confidence: 99%

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Computational methods for the estimation of ideal current patterns in realistic human models

Giannakopoulos,

Georgakis,

Sodickson

et al. 2023

Magnetic Resonance in Med

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PurposeTo introduce a method for the estimation of the ideal current patterns (ICP) that yield optimal signal‐to‐noise ratio (SNR) for realistic heterogeneous tissue models in MRI.Theory and MethodsThe ICP were calculated for different surfaces that resembled typical radiofrequency (RF) coil formers. We constructed numerical electromagnetic (EM) bases to accurately represent EM fields generated by RF current sources located on the current‐bearing surfaces. Using these fields as excitations, we solved the volume integral equation and computed the EM fields in the sample. The fields were appropriately weighted to calculate the optimal SNR and the corresponding ICP. We demonstrated how to qualitatively use ICP to guide the design of a coil array to maximize SNR inside a head model.ResultsIn agreement with previous analytic work, ICP formed large distributed loops for voxels in the middle of the sample and alternated between a single loop and a figure‐eight shape for a voxel 3‐cm deep in the sample's cortex. For the latter voxel, a surface quadrature loop array inspired by the shape of the ICP reached of the optimal SNR at 3T, whereas a single loop placed above the voxel reached only of the optimal SNR. At 7T, the performance of the two designs decreased to and , respectively, suggesting that loops could be suboptimal at ultra‐high field MRI.ConclusionICP can be calculated for human tissue models, potentially guiding the design of application‐specific RF coil arrays.

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Section: Discussionmentioning

confidence: 99%

“…In an MRI setup, the external source is a transmit RF coil, which delivers EM fields to the tissue‐sample. Therefore, given a vector of electric coil currents

{\mathbf{j}}_{\mathrm{c}}\in {\mathbb{C}}^{m\times 1}

defined for each of the

m

discretization triangular elements of the coil, one can compute the incident fields as follows:

e_{inc} = Z_{cb}^{𝒩} j_{c}, h_{inc} = Z_{cb}^{𝒦} j_{c} .

Z_{cb}^{𝒩}, Z_{cb}^{𝒦} \in ℂ^{q n \times m}

Section: Theorymentioning

confidence: 99%

“…

Z_{cb}^{𝒦}

can be compressed and orthogonalized using a truncated singular value decomposition (SVD) 27 as follows:

\begin{align} {boldZ}_{cb}^{𝒦} & prefix\approx {boldU}_{𝒦} {bold∑}_{𝒦} {boldV}_{𝒦}^{normalH} \\ {boldU}_{𝒩} & = {boldZ}_{cb}^{𝒩} {boldV}_{𝒦} {bold∑}_{𝒦}^{prefix- 1} . \end{align}

Here,

U_{𝒩}

and

U_{𝒦}

are bases of electric and magnetic incident fields consistent with electrodynamics principles 43 .

\sum_{𝒦}

is a diagonal matrix containing the singular values of

Z_{cb}^{𝒦}

up to the predefined tolerance of the SVD.…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computational methods for the estimation of ideal current patterns in realistic human models

Giannakopoulos,

Georgakis,

Sodickson

et al. 2023

Magnetic Resonance in Med

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“…1) Data Acquisition: We used one external excitation to illuminate the phantom, generate from a numerical electromagnetic basis [58] similar to the excitations used in the traditional GMT approach [23]…”

Section: Four-compartment Phantommentioning

confidence: 99%

PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networks

Yu¹,

Serralles²,

Giannakopoulos³

et al. 2023

Preprint

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In this paper, we introduce Physics-Informed Fourier Networks (PIFONs) for Electrical Properties (EP) Tomography (EPT). Our novel deep learning-based method is capable of learning EPs globally by solving an inverse scattering problem based on noisy and/or incomplete magnetic resonance (MR) measurements. Methods: We use two separate fully-connected neural networks, namely B + 1 Net and EP Net, to learn the B + 1 field and EPs at any location. A random Fourier features mapping is embedded into B + 1 Net, which allows it to learn the B + 1 field more efficiently. These two neural networks are trained jointly by minimizing the combination of a physicsinformed loss and a data mismatch loss via gradient descent. Results: We showed that PIFON-EPT could provide physically consistent reconstructions of EPs and transmit field in the whole domain of interest even when half of the noisy MR measurements of the entire volume was missing. The average error was 2.49%, 4.09% and 0.32% for the relative permittivity, conductivity and B + 1 , respectively, over the entire volume of the phantom. In experiments that admitted a zero assumption of Bz, PIFON-EPT could yield accurate EP predictions near the interface between regions of different EP values without requiring any boundary conditions. Conclusion: This work demonstrated the feasibility of PIFON-EPT, suggesting it could be an accurate and effective method for electrical properties estimation. Significance: PIFON-EPT can efficiently de-noise MR measurements, which shows the potential to improve other MR-based EPT techniques. Furthermore, it is the first time that MR-based EPT methods can reconstruct the EPs and B + 1 field simultaneously from incomplete simulated noisy MR measurements.Index terms-Electrical Property Mapping, Physics Informed Neural Networks, Fourier Features Mapping. I. INTRODUCTIONElectrical properties (EP), namely relative permittivity and electric conductivity, determine the interactions between electromagnetic waves and biological tissue [1], [2]. EPs have the potential to be employed as biomarkers for pathologies

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Performance of receive head arrays versus ultimate intrinsic SNR at 7 T and 10.5 T

Zhang,

Radder,

Giannakopoulos

et al. 2024

Magnetic Resonance in Med

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PurposeWe examined magnetic field dependent SNR gains and ability to capture them with multichannel receive arrays for human head imaging in going from 7 T, the most commonly used ultrahigh magnetic field (UHF) platform at the present, to 10.5 T, which represents the emerging new frontier of >10 T in UHFs.MethodsElectromagnetic (EM) models of 31‐channel and 63‐channel multichannel arrays built for 10.5 T were developed for 10.5 T and 7 T simulations. A 7 T version of the 63‐channel array with an identical coil layout was also built. Array performance was evaluated in the EM model using a phantom mimicking the size and electrical properties of the human head and a digital human head model. Experimental data was obtained at 7 T and 10.5 T with the 63‐channel array. Ultimate intrinsic SNR (uiSNR) was calculated for the two field strengths using a voxelized cloud of dipoles enclosing the phantom or the digital human head model as a reference to assess the performance of the two arrays and field depended SNR gains.ResultsuiSNR calculations in both the phantom and the digital human head model demonstrated SNR gains at 10.5 T relative to 7 T of 2.6 centrally, ˜2 at the location corresponding to the edge of the brain, ˜1.4 at the periphery. The EM models demonstrated that, centrally, both arrays captured ˜90% of the uiSNR at 7 T, but only ˜65% at 10.5 T, leading only to ˜2‐fold gain in array SNR in going from 7 to 10.5 T. This trend was also observed experimentally with the 63‐channel array capturing a larger fraction of the uiSNR at 7 T compared to 10.5 T, although the percentage of uiSNR captured were slightly lower at both field strengths compared to EM simulation results.ConclusionsMajor uiSNR gains are predicted for human head imaging in going from 7 T to 10.5 T, ranging from ˜2‐fold at locations corresponding to the edge of the brain to 2.6‐fold at the center, corresponding to approximately quadratic increase with the magnetic field. Realistic 31‐ and 63‐channel receive arrays, however, approach the central uiSNR at 7 T, but fail to do so at 10.5 T, suggesting that more coils and/or different type of coils will be needed at 10.5 T and higher magnetic fields.

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Novel Numerical Basis Sets for Electromagnetic Field Expansion in Arbitrary Inhomogeneous Objects

Cited by 5 publications

References 94 publications

Computational methods for the estimation of ideal current patterns in realistic human models

Computational methods for the estimation of ideal current patterns in realistic human models

PIFON-EPT: MR-Based Electrical Property Tomography Using Physics-Informed Fourier Networks

Performance of receive head arrays versus ultimate intrinsic SNR at 7 T and 10.5 T

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