Global Maxwell Tomography Using the Volume-Surface Integral Equation for Improved Estimation of Electrical Properties
Journal:
arXiv
Published Date:
May 20, 2025
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.
