Study on Reciprocal Models for Magneto-Acousto-Electrical Tomography With Coil Detection

Magneto-Acousto-Electric Tomography with coil detection, known as Magneto-Acousto-Electric Tomography with Magnetic Induction (MAET-MI), is a non-contact resistivity-based imaging method that employs a coil to detect the induced current generated by the ultrasound in biological tissue, which lie under a static magnetic field. To reconstruct an image of the tissue's conductivity, we propose a reciprocal model to describe the relationship between the inducted voltage of a coil and its conductivity. Previous work on the reciprocal theorem demonstrates that reconstructing conductivity using this method is effective. The forward and inverse problem are usually not verified both numerically and experimentally. In this paper, different approaches are adopted to calculate the forward and the inverse problems for verification of the reciprocal model. This verifies that the reconstruction method based on electrode detection can be applied to MAET-MI. This means that the inverse problem of MAET-MI can be transformed into an inverse source reconstruction of a wave equation based on the coil detection. In the forward problem, the moment method is employed to calculate the Radon transform and generate the ultrasonic signals. For the inverse problem, the filtered back projection method is chosen to reconstruct the ultrasound sources, which are related to the curl of the current density in the reciprocal process. Based on the curl of the current density in the reciprocal process, four sets of correlation coefficients of the original and reconstructed images' model are all greater than 90%. The uniform error criterion is obtained via multiple reconstructions and comparison of multiple models. The reciprocal model exhibits a good uniformity and stability when describing the actual physical process. It also provides additional effective ideas for solving the inverse problem quickly to reconstruct the ultrasonic sources, which is corresponding to the actual distribution of the conductivity.