Estimation of electrical conductivity of a layered spherical head model using electrical impedance tomography

Electrical Impedance Tomography (EIT) is a non-invasive method that aims to create an electrical conductivity map of a volume. In particular, it can be applied to study the human head. The method consists on the injection of an unperceptive and known current through two electrodes attached to the scalp, and the measurement of the resulting electric potential distribution at an array of sensors also placed on the scalp. In this work, we propose a parametric estimation of the brain, scalp and skull conductivities using EIT over an spherical model of the head. The forward problem involves the computation of the electric potential on the surface, for given the conductivities and the injection electrode positions, while the inverse problem consists on estimating the conductivities given the sensor measurements. In this study, the analytical solution to the forward problem based on a three layer spherical model is first described. Then, some measurements are simulated adding white noise to the solutions and the inverse problem is solved in order to estimate the brain, skull and scalp conductivity relations. This is done with a least squares approach and the Nelder-Mead multidimensional unconstrained nonlinear minimization method.