Mathematical modeling of mechanical vibration-assisted conductivity imaging

This paper aims at mathematically modeling a new multiphysics conductivity imaging system incorporating mechanical vibrations simultaneously applied to an imaging object together with current injections. We perturb the internal conductivity distribution by applying time-harmonic mechanical vibrations on the boundary. This enhances the effects of any conductivity discontinuity on the induced internal current density distribution. Unlike other conductivity contrast enhancing frameworks, it does not require a prior knowledge of a reference datum. In this paper, we provide a mathematical framework for this novel imaging modality. As an application of the vibrationassisted impedance imaging framework, we propose a new breast image reconstruction method in electrical impedance tomography. As another application, we investigate a conductivity anomaly detection problem and provide an efficient location search algorithm. We show both theoretically and numerically that the applied mechanical vibration increases the data sensitivity to the conductivity contrast and enhances the quality of reconstructed images and anomaly detection results. For numerous applications in impedance imaging, the proposed multiphysics method opens a new difference imaging area called vibration-difference imaging, which can augment the time-difference and also frequency-difference imaging methods for sensitivity improvements.