FEM electrode refinement for electrical impedance tomography

Electrical Impedance Tomography (EIT) reconstructs images of electrical tissue properties within a body from electrical transfer impedance measurements at surface electrodes. Reconstruction of EIT images requires the solution of an inverse problem in soft field tomography, where a sensitivity matrix, J, of the relationship between internal changes and measurements is calculated, and then a pseudo-inverse of J is used to update the image estimate. It is therefore clear that a precise calculation of J is required for solution accuracy. Since it is generally not possible to use analytic solutions, the finite element method (FEM) is typically used. It has generally been recommended in the EIT literature that FEMs be refined near electrodes, since the electric field and sensitivity is largest there. In this paper we analyze the accuracy requirement for FEM refinement near electrodes in EIT and describe a technique to refine arbitrary FEMs.