3-D electrical impedance tomography forward problem with finite element method

Electrical impedance tomography (EIT) is a newly developed technique by which impedance measurements from the surface of an object are reconstructed into impedance image. The two-dimensional (2-D) EIT problem is regarded as a simplified model. As 2-D model cannot physically represent the three-dimensional (3-D) structure, the spatial information of the place where the impedance is changed by some diseases cannot be detected accurately. Therefore, 3-D EIT is necessary. In this paper, the finite element method (FEM) of 3-D EIT forward problem is presented. A sphere model is studied. The tetrahedron element is used in the meshing. Two types of sphere model, uniform model and multiplayer model are analyzed. The uniform sphere model, to which the analytical solution is applicable, is used to verify the developed FEM as well as examine the accuracy. The comparison between the numerical solution and the analytical solution shows the correctness of the developed FEM for EIT forward problem. The multiplayer model, four-layer model and three-layer model, is used to investigate the physical potential distribution inside the inhomogeneous sphere model. Reasonable potential distributions are obtained.