A Mathematical And Numerical Framework For Magnetoacoustic Tomography With Magnetic Induction

Magnetoacoustic tomography with magnetic induction(MAT-MI)is a coupled-physical imaging modality which is non-invasive.We provide the mathematical analysis and numerical framework for MAT-MI.The key role in MAT-MI is Lorentz force which is the most difference from other imaging techniques.With the static magnetic field,the Lorentz force acting on the induced eddy current causes mechanical movement.We first estimate the electric current density in the tissue by the detectable ultrasound data on the tissue surface.Then reconstruct the conductivity in the tissue.The advantage of MAT-MI over others is that the inverse problem of MAT-MI is well-posed.In this paper,we show the proof of the stability and uniqueness of the result.We use the fixed point iterative method to reconstruct the conductivity and prove its conver-gence to the solution.Finally,we test this method numerically in the present of measurement noise and quantify the stability for the cross section of human brain.