Analysis of forward problem for elliptical geometry in EIT by using analytical and finite element methods

Application of conformal transformation to elliptic geometry for electric impedance tomography

“…The general problems of EIT such as solving the forward problem to obtain the voltage distribution at the surface of interest, determining the best current pattern to be injected through electrodes and searching the smallest detectable object size have been addressed and reported in many studies in the literature [8][9][10][11][12][13][14]. Studying geometric models for analytic solutions of forward problems in EIT has recently drawn particular attention [10][11][12][13][14][15]. Specifically, one of the studies by Cheney and Isaacson [16] aimed at finding the voltage distribution at the boundary of a cross-section presented in a circular geometry when a current pattern is applied through a set of electrodes equally spaced at the boundary.…”

“…Another significant study [15] was on the voltage distribution calculated for eccentric inhomogeneities in the body for the circular case. Based on the concern about more efficient geometric representation, there are also studies [11][12][13] in which the elliptic geometry was analyzed under the analytical solution in two-dimensional and three-dimensional geometries since the elliptic geometry is relatively a more realistic model considering the cross-sections associated with the human thorax. Moreover, it is reported [10,11] that the assumptions made in the circular model cause some important problems such as inaccuracy in detecting inhomogeneities inside the body and low performance in the reconstruction phase.…”

“…Also there are difficulties in applying conformal transformations to three dimensions and to analysis in the inverse process. The other method included in our study is the finite element method (FEM) found useful in EIT studies [5,6,13]. For many practical problems, exact solutions are generally quite difficult or not yet available at all.…”