Difference frequency magneto-acousto-electrical tomography (DF-MAET): application of ultrasound-induced radiation force to imaging electrical current density

Magneto-acousto-electrical tomography (MAET) is a potential imaging modality which can provide high-spatial-resolution images of the impedance of conductive media. In MAET, the impedance is reconstructed from the mapped current density distribution J_ab(r) that would exist in a sample if a current/voltage source were to be applied through measurement electrodes a and b. To map J_ab(r) without applying a current/voltage source, the sample is placed in a static magnetic field and a focused ultrasonic pulse is directed to a point r to generate a point-like dipole source via the Lorentz force mechanism. The MAET voltage U_ab, which is directly proportional to J_ab(r), is measured through electrodes a and b for each scanning point. To reconstruct the electrical impedance, we need to map the current density distribution at every point inside the sample. However, with the MAET experimental setup reported in our previous paper on MAET, the MAET signal from a homogenous interior of the sample is undetectable because of the spatially-oscillating nature of the ultrasound field inside the sample. In this paper, we propose to use dual-frequency ultrasound to generate the MAET signal at the difference frequency through the ultrasound radiation force mechanism. The dynamic radiation force causes vibrations inside the sample (and consequently, generates the electric field) with a wavelength much larger than the dimension of the sample along the transducer´s axis. Therefore, the MAET signal caused by the radiation force will not be canceled out. We create a dynamic radiation force by applying an amplitude-modulated signal with a modulation frequency f_m of several kilohertz and a carrier frequency f₀ of 2.25 MHz to drive the transducer. The dependence of the DF-MAET signal in experiments on the modulation frequency and on the density of the sample agrees with the prediction based on the radiation force mechanism. The spa- ial resolution of DF-MAET is also studied to verify the radiation force mechanism. Finally, we will prove that the parametric effect in the coupling oil is not a significant source of the DF-MAET signal by imaging a sample at different distances from the transducer. Potential improvements to the present DF-MAET experimental configuration are also discussed.