Eung Je Woo

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 vibration-assisted 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 th...

Equivalent Isotropic Conductivity Image Reconstruction in MREIT

Magnetic resonance electrical impedance tomography (MREIT) provides cross-sectional images of a conductivity distribution inside an electrically conducting object such as the human body. Injecting multiple currents into an imaging object and measuring induced magnetic flux densities, MREIT image reconstruction algorithms such as the harmonic Bz. algorithm produce isotropic conductivity images of the object. Noting that conductivities of certain biological tissues including white matters in the brain are known to be anisotropic, we provide a way to interpret reconstructed images based on the analysis about how an anisotropic conductivity is handled in the harmonic Bz algorithm. We found that reconstructed equivalent isotropic conductivity values are strongly affected by the shape of an anisotropic region in the two-dimensional imaging plane. When an anisotropic tissue is longer in one direction, its equivalent isotropic conductivity value follows the component of the anisotropic conductivity tensor in that direction. The dependency of the equivalent isotropic conductivity on the shape of an anisotropic tissue could be advantageous since it allows us to estimate the direction of the tissue when we are provided with some qualitative a priori knowledge on the anisotropy of the tissue.