  Magnetoacoustic tomography with magnetic induction (MAT-MI) is a
coupled-physics medical imaging modality for determining conductivity
distribution in biological tissue. The capability of MAT-MI 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
equation, 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.
