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.

We present a method of memory footprint reduction for FFT-based, electromagnetic (EM) volume integral equation (VIE) formulations. The arising Green’s 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 graphical processing unit (GPU) on which highly parallelized computations can vastly accelerate the iterative solution of the arising linear system. In addition, the element-wise products throughout the iterative solver’s process require additional flops, thus, we provide a variety of novel and efficient methods that maintain the linear complexity of the classic element-wise product with an additional multiplicative small constant. We demonstrate the utility of our approach via its application to VIE simulations for the Magnetic Resonance Imaging (MRI) of a human head. For these simulations we report an order of magnitude acceleration over standard techniques.

Purpose: To develop and characterize a 128‐channel head array for brain imaging at 10.5 T, evaluate signal‐to‐noise ratio (SNR) relative to ultimate intrinsic SNR (uiSNR) and lower field strengths, and demonstrate human brain anatomical and functional imaging with this unique magnetic field and high‐channel‐count array. Methods: The coil consists of a 16‐channel self‐decoupled loop transmit/receive (16Tx/Rx) array with a 112‐loop receive‐only (Rx) insert. Interactions between the 16Tx/Rx array and the 112Rx insert were mitigated using coaxial cable traps placed every 1/16 of a wavelength on each feed cable, locating most preamplifier boards outside the transmitter field, and miniaturizing those placed directly on individual coils. Results: The effect of the 112Rx insert on the circumscribing 16Tx/Rx array was minimized, leading to similar transmit field maps obtained experimentally with and without the 112Rx array in place and by electromagnetic simulations of the 16Tx/Rx array alone. The 128‐channel array captured 77% of uiSNR centrally. Significantly higher 1/g‐factor values across the whole brain was achieved compared with 7 T. Excellent SNR, high parallel‐imaging performance, and minimal Tx‐Rx interactions collectively facilitated acquisition of high‐quality, high‐resolution, proof‐of‐concept functional and anatomical images, including with power‐demanding sequences in the human brain. Conclusions: Counterintuitive to expectations based on magnetic fields less than or equal to 7 T, the higher channel counts provided SNR gains centrally, capturing about 80% uiSNR. The fraction of uiSNR achieved centrally in 64Rx, 80Rx, and 128Rx arrays suggested that a plateau was being reached at 80%. At this plateau, B ₀ ‐dependent SNR gains for 10.5 T relative to 7 T were approximately linear to quadratic for the periphery and the center, respectively.

Purpose: Toward pushing the boundaries of ultrahigh fields for human brain imaging, we wish to evaluate experimentally achievable SNR relative to ultimate intrinsic SNR (uiSNR) at 10.5T, develop design strategies toward approaching the latter, quantify magnetic field–dependent SNR gains, and demonstrate the feasibility of whole‐brain, high‐resolution human brain imaging at this uniquely high field strength.Methods: A dual row 16‐channel self‐decoupled transmit (Tx) and receive (Rx) array was developed for 10.5T using custom Tx/Rx switches. A 64‐channel receive‐only array was built to fit into the 16‐channel Tx/Rx array. Electromagnetic modeling and experiments were used to define safe operational power limits. Experimental SNR was evaluated relative to uiSNR at 10.5T and 7T.Results: The 64‐channel Rx array alone captured approximately 50% of the central uiSNR at 10.5T, while an identical array developed for 7T captured about 76% of uiSNR at 7T. The 16‐channel Tx/80‐channel Rx configuration brought the fraction of uiSNR captured at 10.5T to levels comparable to the 64‐channel Rx array at 7T. SNR data displayed an approximate dependence over a large central region when evaluated in the context of uiSNR. Whole‐brain, high‐resolution ‐weighted and T₁‐weighted anatomical and gradient‐recalled‐echo BOLD‐EPI functional MRI images were obtained at 10.5T for the first time with such an advanced array.Conclusion: We demonstrated the ability to approach the uiSNR at 10.5T over the human brain, achieving large SNR gains over 7T, currently the most commonly used ultrahigh‐field platform. Whole‐brain, high‐resolution anatomical and EPI‐based functional MRI data were obtained at 10.5T, illustrating the promise of greater than 10T fields in studying the human brain.

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.

A stable volume integral equation (VIE) solver based on polarization/magnetization currents is presented, for the accurate and efficient computation of the electromagnetic 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 electromagnetic waves and biological tissue.