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

Abstract

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.

Memory Footprint Reduction for the FFT-Based Volume Integral Equation Method via Tensor Decompositions

“…Similar compression is expected for other FFT-based VIE formulations (flux and field based) since they consist of similar Green's function-based kernels. Finally, the presented work can be used to speed-up the time-consuming inverse electromagnetic scattering problems e.g., the recently proposed Global Maxwell Tomography method [67], where the forward problem needs to be solved hundreds of times in order to retrieve an accurate dielectric property mapping of biological tissue.…”

Learning-based estimation of dielectric properties and tissue density in head models for personalized radio-frequency dosimetry

“…To avoid potential errors caused by segmentation faults, several methods have been proposed to directly estimate the tissue dielectric properties based on anatomical images (e.g. Serralles et al 2020, Hampe et al 2019, Ropella & Noll 2017, Elsaid et al 2017, Tuch et al 2001. The water content calculated from T1-weighted MR scans is modeled using a monotonic function to estimate the conductivity of major brain tissues (Michel et al 2017).…”

Technical developments for MR-based electrical property mapping

“…The spatial modulation of the transceive phase is primarily induced by the tissue conductivity, as can be derived from Helmholtz equation [56,60,139]. This relationship has been validated in simulations [47,114,118] and experimentally with mr Electrical Properties Tomography (ept) [54,[56][57][58][59][60]91,95,103]. The transceive phase has been mapped extensively for conductivity reconstruction in different body sites (e.g.…”

“…Inverse ept approaches are generally based on global integral forms of Maxwell's equations and obtain the eps by iteratively minimizing a cost function measuring the discrepancy between the "measured" B + 1 and modelled B + 1 [109][110][111][112][113][114][115][116][117][118]. Many contributions have solved this inverse problem with the contrast source inversion (csi) method [109,[114][115][116][117][118] and are reviewed in [119]. These integral approaches automatically account for boundary conditions, improving tissue interface reconstruction, and are less sensitive to noise because they avoid differentiation on noisy B + 1 data.…”

“…Inverse approaches reconstruct eps by iteratively minimizing a cost function comparing the true B + 1 with a modelled B + 1 field [109,113,[116][117][118]. These reconstruction techniques bypass the assumption of piece-wise constant properties, reduce boundary errors and mitigate noise impact on ep maps by avoiding differentiation on measured data.…”