Magnetoacoustic tomography with magnetic induction (MAT-MI) is a noninvasive imaging method developed to map electrical conductivity of biological tissue with millimeter level spatial resolution. In MAT-MI, a time-varying magnetic stimulation is applied to induce eddy current inside the conductive tissue sample. With the existence of a static magnetic field, the Lorentz force acting on the induced eddy current drives mechanical vibrations producing detectable ultrasound signals. These

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... signals can then be acquired to reconstruct a map related to the sample's electrical conductivity contrast. This work reviews fundamental ideas of MAT-MI and major techniques developed in these years. First, the physical mechanisms underlying MAT-MI imaging are described including the magnetic induction and Lorentz force induced acoustic wave propagation. Second, experimental setups and various imaging strategies for MAT-MI are reviewed and compared together with the corresponding experimental results. In addition, as a recently developed reverse mode of MAT-MI, magneto-acousto-electrical tomography with magnetic induction (MAET-MI) is briefly reviewed in terms of its theory and experimental studies. Finally, we give our opinions on existing challenges and future directions for MAT-MI research. With all the reported and future technical advancement, MAT-MI has the potential to become an important noninvasive modality for electrical conductivity imaging of biological tissue. injection through surface electrodes similar as EIT while measuring the corresponding magnetic field disturbance generated by injected current in tissue through magnetic resonance imaging (MRI), MREIT made it possible to map electrical conductivity in ex vivo and in vivo tissues with high spatial resolution Seo and Woo, 2014) . However, a relatively high level of current injection (on the level of mA) is generally required in MREIT to obtain sufficient signal-to-noise ratio (SNR) level and the use of MRI machine makes the cost of MREIT higher than other methods. Li et al.