Analysis of the magnetoacoustic tomography with magnetic induction

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a coupled-physics medical imaging modality for determining conductivity distribution in biological tissue. The capability of MATMI to provide high-resolution images has been demonstrated experimentally. MAT-MI involves two steps. The first step is a well-posed inverse source problem for acoustic wave equations, which has been well studied in the literature. This paper concerns mathematical analysis of the second step, a quantitative reconstruction of the conductivity from knowledge of the internal data recovered in the first step, using techniques such as time reversal. The problem is modeled by a system derived from Maxwell’s equations. We show that a single internal data determines the conductivity. A global Lipschitz-type stability estimate is obtained. A numerical approach for recovering the conductivity is proposed, and results from computational experiments are presented.