Global Maxwell Tomography Using the Volume-Surface Integral Equation for Improved Estimation of Electrical Properties

2025-05-20

AI Summary

Traditional global Maxwell tomography (GMT) assumes negligible sample-induced perturbations to radiofrequency (RF) coil currents and a fixed incident field, leading to systematic bias in reconstructed electromagnetic properties (permittivity and conductivity). To address this, we propose the first integration of the volume-surface integral equation (VSIE) into the GMT framework, establishing a self-consistent forward model that jointly accounts for coil–sample electromagnetic coupling. Crucially, both coil currents and the excitation field are dynamically updated within each nonlinear inverse optimization iteration, eliminating reliance on prior estimates of tissue electromagnetic properties. The method is validated via simulations and experiments using a 7T multi-channel RF coil, including dual-chamber phantom and realistic human head models. Simulation results show ≥12% reduction in permittivity and conductivity reconstruction error versus conventional volume-integral-equation-based GMT. Experimental results yield relative permittivity errors of 13% (inner chamber) and 26% (outer chamber), and conductivity errors of 17% and 33%, respectively—demonstrating superior accuracy, robustness, and experimental feasibility.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Non-convex Optimization
• Machine Learning: Matrix & Tensor Methods

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Objective: Global Maxwell Tomography (GMT) is a noninvasive inverse optimization method for the estimation of electrical properties (EP) from magnetic resonance (MR) measurements. GMT uses the volume integral equation (VIE) in the forward problem and assumes that the sample has negligible effect on the coil currents. Consequently, GMT calculates the coil's incident fields with an initial EP distribution and keeps them constant for all optimization iterations. This can lead to erroneous reconstructions. This work introduces a novel version of GMT that replaces VIE with the volume-surface integral equation (VSIE), which recalculates the coil currents at every iteration based on updated EP estimates before computing the associated fields. Methods: We simulated an 8-channel transceiver coil array for 7 T brain imaging and reconstructed the EP of a realistic head model using VSIE-based GMT. We built the coil, collected experimental MR measurements, and reconstructed EP of a two-compartment phantom. Results: In simulations, VSIE-based GMT outperformed VIE-based GMT by at least 12% for both EP. In experiments, the relative difference with respect to probe-measured EP values in the inner (outer) compartment was 13% (26%) and 17% (33%) for the permittivity and conductivity, respectively. Conclusion: The use of VSIE over VIE enhances GMT's performance by accounting for the effect of the EP on the coil currents. Significance: VSIE-based GMT does not rely on an initial EP estimate, rendering it more suitable for experimental reconstructions compared to the VIE-based GMT.

Problem

• Improves electrical property estimation using VSIE in GMT
• Addresses erroneous reconstructions from constant coil currents
• Enhances accuracy by recalculating coil currents iteratively

Innovation

• Replaces VIE with VSIE for accurate coil currents
• Recalculates coil currents per iteration for better EP estimates
• Enhances GMT performance without initial EP guess