Conductivity reconstruction algorithms and numerical simulations for magneto-acousto-electrical tomography with piston transducer in scan mode

Conductivities tomography with the interactions of magnetic field, electrical field, and ultrasound field is presented in this paper. We utilize a beam of ultrasound in scanning mode instead of the traditional ultrasound field generated by point source. Many formulae for the reconstruction of conductivities are derived from the voltage signals detected by two electrodes arranged somewhere on tissue's surface. In a forward problem, the numerical solutions of ultrasound fields generated by the piston transducer are calculated using the angular spectrum method and its Green's function is designed approximately in far fields. In an inverse problems, the magneto-acousto-electrical voltage signals are proved to satisfy the wave equations if the voltage signals are extended to the whole region from the boundary locations of transducers. Thus the time-reversal method is applied to reconstructing the curl of the reciprocal current density. In addition, a least square iteration method of recovering conductivities from reciprocal current densities is discussed.