Application of conformal transformation to elliptic geometry for electric impedance tomography

Abstract 

Electrical impedance tomography (EIT) is a medical imaging modality that is used to compute the conductivity distribution through measurements on the cross-section of a body part. An elliptic geometry model, which defines a more general frame, ensures more accurate results in reconstruction and assessment of inhomogeneities inside. This study provides a link between the analytical solutions defined in circular and elliptical geometries on the basis of the computation of conformal mapping. The results defined as voltage distributions for the homogeneous case in elliptic and circular geometries have been compared with those obtained by the use of conformal transformation between elliptical and well-known circular geometry. The study also includes the results of the finite element method (FEM) as another approach for more complex geometries for the comparison of performance in other complex scenarios for eccentric inhomogeneities. The study emphasizes that for the elliptic case the analytical solution with conformal transformation is a reliable and useful tool for developing insight into more complex forms including eccentric inhomogeneities.

Keywords: Electrical impedance tomography (EIT), Conformal transformation, Elliptic geometry, Forward solution, Finite element method (FEM)