A volumetric integral equation formulation for magnetic induction tomography

In magnetic induction tomography of biological tissue, an alternating magnetic field is used to induce eddy currents inside tissues, which in turn generate a secondary magnetic field. This perturbation of the field depends on the dielectric properties of the tissue and, through resolution of the inverse problem, a map of these properties can be reconstructed. Current state-of-art methods either rely on the quasi-static and low conductivity approximations or are based on differential solvers or surface integral equations. A formulation based on volumetric integral equations offers clear advantages such as a better accuracy than the approximative methods, a smaller solution domain than differential solvers and a better conditionning than surface integral methods. The aim of this paper is to formulate the eddy current problem in terms of a volume integral equation and to show its validity.