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 properties 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 7T using an 8-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 expenses 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.Index terms-Canonical polyadic model, higher order singular value decomposition, Tucker decomposition, volume integral equations.

No abstract

No abstract

Magnetic-resonance-based electrical property mapping using Global Maxwell Tomography with an 8-channel head coil at 7 Tesla: a simulation studyThe MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. CitationGiannakopoulos, Ilias I. et al. "Magnetic-resonance-based electrical property mapping using Global Maxwell Tomography with an 8channel head coil at 7 Tesla: a simulation study.

No abstract

This paper proposes a stable volume integral equation (VIE) solver based on polarization/magnetization currents, for the accurate and efficient computation of the electromagnetic scattering from highly inhomogeneous and high contrast objects. Methods: 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. Results: Numerical experiments are conducted to study the accuracy and convergence properties of the proposed framework. Their results are compared against standard low order (piecewise constant) discretization schemes, a more conventional VIE formulation based on electric flux densities, and a commercial software package that employs the finite difference time domain method. Conclusion:The results illustrate the superior accuracy and wellconditioned properties of the proposed scheme. Significance: The developed solver can be applied to accurately analyze complex geometries, including realistic human body models, typically used in modeling the interactions between electromagnetic waves and biological tissue, that arise in magnetic resonance scanners.Index terms-Electromagnetic scattering, high contrast/inhomogeneity, high-order basis functions, magnetic resonance modeling, method of moments, volume integral equations.

No abstract