  Studies of models of current flow behaviour in Electrical Impedance
Tomography (EIT) have shown that the current density distribution varies
extremely rapidly near the edge of the electrodes used in the technique. This
behaviour imposes severe restrictions on the numerical techniques used in image
reconstruction algorithms. In this paper we have considered a simple two
dimensional case and we have shown how the theory of end point/pinch
singularities which was developed for studying the anomalous thresholds
encountered in elementary particle physics can be used to give a complete
description of the analytic structure of the current density near to the edge
of the electrodes. As a byproduct of this study it was possible to give a
complete description of the Riemann sheet manifold of the eigenfunctions of the
logarithmic kernel. These methods can be readily extended to other weakly
singular kernels.
