Magnetoacoustic tomography with magnetic induction and fast acoustic solvers

Background. The electrical properties of tissues are effective indicators of tissue health and pathology, and they are required to determine the efficacy and safety of the electric fields induced by electromagnetic medical and imaging devices. Current noninvasive methods for measuring electrical properties suffer from accuracy and resolution limitations, especially at low frequencies (below 10 MHz), where the wavelength of electromagnetic waves exceeds 30 m and imposes a fundamental resolution limit.

Objective. Improve the accuracy and resolution of electrical conductivity measurements at low frequencies.

Approach. Magnetoacoustic tomography with magnetic induction infers electrical properties from ultrasound pressure waves generated when eddy currents induced by a pulsed coil interact with a static magnetic field. Because ultrasound wavelengths are millimeters rather than meters, the modality is not bound by the electromagnetic resolution limit. We are developing special-purpose imaging coils, strong static magnets to raise the signal-to-noise ratio of the measured pressure waves, and new reconstruction algorithms that account for the heterogeneity of acoustic parameters across tissues.

Main results. Magnetoacoustic tomography with magnetic induction has been shown at 500 kHz to deliver about 2 mm resolution in an animal model. Its accuracy, however, is currently limited by weak measured signals and by reconstruction algorithms that assume acoustically homogeneous tissue, which restricts it to soft tissues.

Fast acoustic solvers. Heterogeneity-aware reconstruction requires repeated, accurate acoustic forward simulations. Volume integral equations are attractive for acoustic scattering in heterogeneous media, but the conventional fast multipole algorithm used to accelerate them suffers from low-frequency breakdown, and high-contrast media degrade accuracy and conditioning. We developed a broadband fast multipole algorithm that factorizes the Green’s function with a plane-wave expansion at high frequencies and a multipole expansion at low frequencies, a discontinuous Galerkin discretization that improves error controllability and lowers the condition number, and superconvergent patch recovery post-processing that corrects discontinuities in the computed pressure field. The method is validated against the analytical Mie solution across frequencies and is a step toward coupled acoustic and electromagnetic integral equation analysis for magnetoacoustic imaging.

Anticipated significance. Higher signal-to-noise ratio and heterogeneity-aware reconstruction would extend the modality to soft tissue, bone, and lung, enabling accurate, high-resolution conductivity imaging for a wide range of biomedical applications. This project is supported by the Showalter Trust.

Publications.

S. S. Vaezi (G), L. J. Gomez, and W. C. Chew, "Strategies for Fast Broadband and High-Contrast Stable Acoustic Volume Integral Equation Analysis," TechRxiv, 2025. preprint

S. S. Vaezi (G), L. J. Gomez, and W. C. Chew, "Accelerated Acoustic Volume Integral Equation Using Broadband Fast Multipole Algorithm," International Applied Computational Electromagnetics Society Symposium, May 2025.