The Application of hybrid BEM/FEM methods to solve Electrical Impedance Tomography’s forward problem for the human head

The forward problem in Electrical Impedance Tomography (EIT) requires an accurate estimation of its solution. Although analytical solutions exist for a limited number of cases, there is no suitable analytical solution for the geometry of the human head. A commonly adopted method is the use of Finite Element Methods (FEM). However, the human head consists of layers, which include the scalp and CSF, which are approximately 1 mm thick. Meshing these layers is technically difficult and introduces significant errors in to the solution. An interesting alternative is the use of hybrid methods combining both BEM and FEM. The Boundary Element Method (BEM) is an alterative to FEM. This method essentially uses Green’s theorem to map boundary distributions to boundary distributions, using the explicit form of the Green’s functions. Although BEM has the disadvantage of dense matrices, and assumes the region is homogenous, it would be of great advantage for the thin layer of the human such as the scalp and CSF, which are homogenous. The larger regions are better suited to FEM, which are composed of non-uniform conductivity distribution. A logical approach for this forward problem is to combine the BEM and FEM to produce hybrid code, which assumes some region, have contact values. We present results for 2D spheres and discuss the required modifications of BEM in order to improve relatively high error at the interface, we also show for spheres that with certain discretization solution error for a 1mm thin layer could be reduced.