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## 3D cross-Tucker approximation in FFT-based volume integral equation methods

Published in 2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, 2018

We present an algorithm for the compression of the Green function tensors arising from fft-based volume integral equation formulations. The algorithm is based on an 3D adaptive cross approximation of the Tucker decomposition. We demonstrate that the reported method can lead to remarkable compression (x2000) for a typical example involving interactions between electromagnetic waves and realistic human body model.

Recommended citation: Giannakopoulos, Ilias I., Mikhail S. Litsarev, and Athanasios G. Polimeridis. "3D cross-Tucker approximation in FFT-based volume integral equation methods." 2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2018. https://ieeexplore.ieee.org/abstract/document/8608283

## Noninvasive Estimation of Electrical Properties from Magnetic Resonance Measurements via Global Maxwell Tomography and Match Regularization

Published in IEEE Transactions on Biomedical Engineering, 2019

Objective: In this paper, we introduce global Maxwell tomography (GMT), a novel volumetric technique that estimates electric conductivity and permittivity by solving an inverse scattering problem based on magnetic resonance measurements. Methods: GMT relies on a fast volume integral equation solver, MARIE, for the forward path, and a novel regularization method, match regularization, designed specifically for electrical property estimation from noisy measurements. We performed simulations with three different tissue-mimicking numerical phantoms of different complexity, using synthetic transmit sensitivity maps with realistic noise levels as the measurements. We performed an experiment at 7 T using an eight-channel coil and a uniform phantom. Results: We showed that GMT could estimate relative permittivity and conductivity from noisy magnetic resonance measurements with an average error as low as 0.3% and 0.2%, respectively, over the entire volume of the numerical phantom. Voxel resolution did not affect GMT performance and is currently limited only by the memory of the graphics processing unit. In the experiment, GMT could estimate electrical properties within 5% of the values measured with a dielectric probe. Conclusion: This work demonstrated the feasibility of GMT with match regularization, suggesting that it could be effective for accurate in vivo electrical property estimation. GMT does not rely on any symmetry assumption for the electromagnetic field, and can be generalized to estimate also the spin magnetization, at the expense of increased computational complexity. Significance: GMT could provide insight into the distribution of electromagnetic fields inside the body, which represents one of the key ongoing challenges for various diagnostic and therapeutic applications.

Recommended citation: Serrallés, José EC, et al. "Noninvasive estimation of electrical properties from magnetic resonance measurements via global Maxwell tomography and match regularization." IEEE Transactions on Biomedical Engineering 67.1 (2019): 3-15. https://ieeexplore.ieee.org/abstract/document/8673893

## Global Maxwell Tomography using an 8-channel radiofrequency coil: simulation results for a tissue-mimicking phantom at 7T

Published in 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, 2019

We simulated a Global Maxwell Tomography experiment for the estimation of electrical properties in a numerical tissue-mimicking phantom using a decoupled 8 channel radiofrequency coil designed for 7 Tesla magnetic resonance scanners. The goal of this work was to investigate whether the orthogonality of the coil transmit fields (b1+ measurements) is required to ensure accurate results. We demonstrated a normalized root mean squared error smaller than 0.6% with respect to the true electrical properties distribution. Our results showed that electrical properties reconstruction with Global Maxwell Tomography is accurate and robust.

Recommended citation: Giannakopoulos, Ilias I., et al. "Global Maxwell Tomography using an 8-channel radiofrequency coil: simulation results for a tissue-mimicking phantom at 7T." 2019 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting. IEEE, 2019. https://ieeexplore.ieee.org/abstract/document/8889009

## Memory footprint reduction for the FFT-based volume integral equation method via tensor decompositions

Published in IEEE Transactions on Antennas and Propagation, 2019

We present a method of memory footprint reduction for FFT-based, EM VIE formulations. The arising Green function tensors have low multilinear rank, which allows Tucker decomposition to be employed for their compression, thereby greatly reducing the required memory storage for numerical simulations. Consequently, the compressed components are able to fit inside a GPU on which highly parallelized computations can vastly accelerate the iterative solution of the arising linear system. In addition, the elementwise products throughout the iterative solver process require additional flops, thus, we provide a variety of novel and efficient methods that maintain the linear complexity of the classic elementwise product with an additional multiplicative small constant. We demonstrate the utility of our approach via its application to VIE simulations for the MRI of a human head. For these simulations, we report an order of magnitude acceleration over standard techniques.

Recommended citation: Giannakopoulos, Ilias I., Mikhail S. Litsarev, and Athanasios G. Polimeridis. "Memory footprint reduction for the FFT-based volume integral equation method via tensor decompositions." IEEE Transactions on Antennas and Propagation 67.12 (2019): 7476-7486. https://ieeexplore.ieee.org/abstract/document/8777311

## Magnetic-resonance-based electrical property mapping using Global Maxwell Tomography with an 8-channel head coil at 7 Tesla: a simulation study

Published in IEEE Transactions on Biomedical Engineering, 2020

Objective: GMT is a recently introduced volumetric technique for noninvasive estimation of EP from MR measurements. Previous work evaluated GMT using ideal RF excitations. The aim of this simulation study was to assess GMT performance with a realistic RF coil. Methods: We designed a transmit-receive RF coil with 8 decoupled channels for 7T head imaging. We calculated the B1+ inside heterogeneous head models for different RF shimming approaches, and used them as input for GMT to reconstruct EP for all voxels. Results: Coil tuning/decoupling remained relatively stable when the coil was loaded with different head models. Mean error in EP estimation changed from 7.5% to 9.5% and from 4.8% to 7.2% for relative permittivity and conductivity, respectively, when changing head model without re-tuning the coil. Results slightly improved when an SVD-based RF shimming algorithm was applied, in place of excitation with one coil at a time. Despite errors in EP, B1+ and absorbed power could be predicted with less than 0.5% error over the entire head. GMT could accurately detect a numerically inserted tumor. Conclusion:This work demonstrates that GMT can reliably reconstruct EP in realistic simulated scenarios using a tailored 8-channel RF coil design at 7T. Significance: GMT could provide accurate estimations of tissue EP, which could be used as biomarkers and could enable patient-specific estimation of RF power deposition, which is an unsolved problem for ultra-high-field magnetic resonance imaging.

Recommended citation: Giannakopoulos, Ilias I., et al. "Magnetic-resonance-based electrical property mapping using Global Maxwell Tomography with an 8-channel head coil at 7 Tesla: a simulation study." IEEE Transactions on Biomedical Engineering 68.1 (2020): 236-246. https://ieeexplore.ieee.org/abstract/document/9082887

## A fast volume integral equation solver with linear basis functions for the accurate computation of EM fields in MRI

Published in IEEE Transactions on Antennas and Propagation, 2020

A stable volume integral equation (VIE) solver based on polarization/magnetization currents is presented, for the accurate and efficient computation of the electromagnetic (EM) scattering from highly inhomogeneous and high contrast objects. We employ the Galerkin method of moments to discretize the formulation with discontinuous piecewise linear basis functions on uniform voxelized grids, allowing for the acceleration of the associated matrix-vector products in an iterative solver, with the help of FFT. Numerical results illustrate the superior accuracy and more stable convergence properties of the proposed framework, when compared against standard low-order (piecewise constant) discretization schemes and a more conventional VIE formulation based on electric flux densities. Finally, the developed solver is applied to analyze complex geometries, including realistic human body models, typically used in modeling the interactions between EM waves and biological tissue.

Recommended citation: Georgakis, Ioannis P., et al. "A fast volume integral equation solver with linear basis functions for the accurate computation of EM fields in MRI." IEEE Transactions on Antennas and Propagation 69.7 (2020): 4020-4032. https://ieeexplore.ieee.org/abstract/document/9301172

## Compression of volume-surface integral equation matrices via Tucker decomposition for magnetic resonance applications

Published in IEEE Transactions on Antennas and Propagation, 2021

In this work, we propose a method for the compression of the coupling matrix in volume-surface integral equation (VSIE) formulations. VSIE methods are used for electromagnetic (EM) analysis in magnetic resonance imaging (MRI) applications, for which the coupling matrix models the interactions between the coil and the body. We showed that these effects can be represented as independent interactions between remote elements in 3-D tensor formats, and subsequently decomposed with the Tucker model. Our method can work in tandem with the adaptive cross approximation (ACA) technique to provide fast solutions of VSIE problems. We demonstrated that our compression approaches can enable the use of VSIE matrices of prohibitive memory requirements, by allowing the effective use of modern graphical processing units (GPUs) to accelerate the arising matrix-vector products. This is critical to enable numerical MRI simulations at clinical voxel resolutions in a feasible computation time. In this article, we demonstrate that the VSIE matrix-vector products needed to calculate the EM field produced by an MRI coil inside a numerical body model with 1 mm^3 voxel resolution, could be performed in ~33 s in a GPU, after compressing the associated coupling matrix from ~80 TB to ~43 MB.

Recommended citation: Giannakopoulos, Ilias I., et al. "Compression of volume-surface integral equation matrices via Tucker decomposition for magnetic resonance applications." IEEE Transactions on Antennas and Propagation (2021). https://ieeexplore.ieee.org/abstract/document/9465722

## A Tensor Train Compression Scheme for Remote Volume-surface Integral Equation Interactions

Published in 2021 International Applied Computational Electromagnetics Society Symposium (ACES), 2021

We propose a memory compression scheme for the coupling matrices appearing in volume-surface integral equation formulations. When there is some distance between the surface and the volumetric scatterers, the low-rank properties of the coupling matrix, allow us to reshape it into a set of four-dimensional tensors, which can be heavily compressed with the tensor train decomposition. The associated matrix-vector products can be rapidly performed with the aid of a graphical processing unit. We achieved a compression of more than 8 thousand times with a relative error around 1e–5, for the calculation of the electromagnetic field generated by a radiofrequency coil inside an object at 1 mm voxel isotropic resolution. In this case, the matrix-vector product could be executed in less than a second.

Recommended citation: Giannakopoulos, Ilias I., et al. "A Tensor Train Compression Scheme for Remote Volume-surface Integral Equation Interactions." 2021 International Applied Computational Electromagnetics Society Symposium (ACES). IEEE, 2021. https://ieeexplore.ieee.org/abstract/document/9528694

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

Published in IEEE Transactions on Biomedical Engineering ( Early Access ), 2022

We developed a hybrid volume surface integral equation (VSIE) method based on domain decomposition to perform fast and accurate magnetic resonance imaging (MRI) simulations that include both remote and local conductive elements. Methods: We separated the conductive surfaces present in MRI setups into two domains and optimized electromagnetic (EM) modeling for each case. Specifically, interactions between the body and EM waves originating from local radiofrequency (RF) coils were modeled with the precorrected fast Fourier transform, whereas the interactions with remote conductive surfaces (RF shield, scanner bore) were modeled with a novel cross tensor train-based algorithm. We compared the hybrid-VSIE with other VSIE methods for realistic MRI simulation setups. Results: The hybrid-VSIE was the only practical method for simulation using 1 mm voxel isotropic resolution (VIR). For 2 mm VIR, our method could be solved at least 23 times faster and required 760 times lower memory than traditional VSIE methods. Conclusion: The hybrid-VSIE demonstrated a marked improvement in terms of convergence times of the numerical EM simulation compared to traditional approaches in multiple realistic MRI scenarios. Significance: The efficiency of the novel hybrid-VSIE method could enable rapid simulations of complex and comprehensive MRI setups.

Recommended citation: I. I. Giannakopoulos et al., "A Hybrid volume-Surface Integral Equation Method for Rapid Electromagnetic Simulations in MRI," in IEEE Transactions on Biomedical Engineering, 2022, doi: 10.1109/TBME.2022.3186235. https://ieeexplore.ieee.org/document/9807398

## MARIE 2.0: A Perturbation Matrix Based Patient-Specific MRI Field Simulator

Published in IEEE Transactions on Biomedical Engineering ( Early Access ), 2022

High static field MR scanners can produce human tissue images of astounding clarity, but rely on high frequency electromagnetic radiation that generates complicated in-tissue field patterns that are patient-specific and potentially harmful. Many such scanners use parallel transmitters to better control field patterns, but then adjust the transmitters based on general guidelines rather than optimizing for the specific patient, mostly because computing patient-specific fields was presumed far too slow. It was recently demonstrated that the combination of fast low-resolution tissue mapping and fast voxel-based field simulation can be used to perform a patient-specific MR safety check in minutes. However, the field simulation required several of those minutes, making it too slow to perform the dozens of simulations that would be needed for patient-specific optimization. In this paper we describe a compressed-perturbation-matrix technique that nearly eliminates the computational cost of including complex coils (or coils and shields) in voxel-based field simulation of tissue, thereby reducing simulation time from minutes to seconds. The approach is demonstrated on a wide variety of head+coil and head+coil+shield configurations, using the implementation in MARIE 2.0, the latest version of the open-source MR field simulator MARIE.

Recommended citation: G. D. Guryev et al., "MARIE 2.0: A Perturbation Matrix Based Patient-Specific MRI Field Simulator," in IEEE Transactions on Biomedical Engineering, 2022, doi: 10.1109/TBME.2022.3222748. https://ieeexplore.ieee.org/document/9953535

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## Compuational Science and Engineering II: Discretization

Graduate Teaching Assistant, Skolkovo Institute of Science and Technology, Center for Data-Intensive Science and Engineering, 2018

## PhD Thesis Mentoring

Technical Adviser, New York University, Grossman School of Medicine, Department of Radiology, 2021

Mentoring of PhD students working on deep learning and computational electromagnetics.