Electrical conductivity imaging via contactless measurements

A new imaging modality is introduced to image electrical conductivity of biological tissues via contactless measurements. This modality uses magnetic excitation to induce currents inside the body and measures the magnetic fields of the induced currents. In this study, the mathematical basis of the methodology is analyzed and numerical models are developed to simulate the imaging system. The induced currents are expressed using the A&oarr;-φ formulation of the electric field where A&oarr; is the magnetic vector potential and φ is the scalar potential function. It is assumed that A&oarr; describes the primary magnetic vector potential that exists in the absence of the body. This assumption considerably simplifies the solution of the secondary magnetic fields caused by induced currents. In order to solve φ for objects of arbitrary conductivity distribution a three-dimensional (3-D) finite-element method (FEM) formulation is employed. A specific 7×7-coil system is assumed nearby the upper surface of a 10×10×5-cm conductive body. A sensitivity matrix, which relates the perturbation in measurements to the conductivity perturbations, is calculated. Singular-value decomposition of the sensitivity matrix shows various characteristics of the imaging system. Images are reconstructed using 500 voxels in the image domain, with truncated pseudoinverse. The noise level is assumed to produce a representative signal-to-noise ratio (SNR) of 80 dB. It is observed that it is possible to identify voxel perturbations (of volume 1 cm ³) at 2 cm depth. However, resolution gradually decreases for deeper conductivity perturbations.