A Hybrid Volume-Surface Integral Equation Method for Rapid Electromagnetic Simulations in MRI

Giannakopoulos, Ilias I.; Guryev, Georgy; Serralles, Jose E. C.; Paska, Jan; Zhang, Bei; Daniel, Luca; White, Jacob K.; Collins, Christopher M.; Lattanzi, Riccardo

doi:10.1109/tbme.2022.3186235

Cited by 4 publications

(4 citation statements)

References 62 publications

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“…Throughout all experiments, unless otherwise specified, we used simulated complex B + 1 maps as measured data and corrupted them with white Gaussian noise with a standard deviation equal to the ratio of the peak value of |B + 1 | to a prescribed peak signal-to-noise-ratio (SNR) value. The simulations were performed with the volume [52] and the volumesurface integral equation [53], [54] methods. The volume equations were solved using higher-order polynomials [55] as basis functions to ensure accuracy in the B + 1 distributions.…”

Section: Resultsmentioning

confidence: 99%

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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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Section: Resultsmentioning

confidence: 99%

“…1) Data Acquisition: We used the volume-surface integral equation method [54] to simulate the circularly polarized (CP) mode of the birdcage coil loaded with the cylindrical phantom at 3 tesla MRI. The resolution was set to 2 mm 3 .…”

Section: B Concentric Cylindrical 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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“…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%

“…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: Volume-surface Integral Equationmentioning

confidence: 99%

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

Yu,

Serrallés,

Giannakopoulos

et al. 2024

IEEE J. Multiscale Multiphys. Comput. Tech.

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A Hybrid Volume-Surface Integral Equation Method for Rapid Electromagnetic Simulations in MRI

Cited by 4 publications

References 62 publications

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

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

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

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