Application of the finite element method for dipole source localization in a two-dimensional EEG model.

摘要

A comparison is made of two different implementations of the finite element method (FEM) for calculating the potential due to dipole sources in a 2-D EEG model. In one formulation (the direct method) the total potential is the dependent variable and the dipole source is directly incorporated into the model. In the second formulation (the subtraction method) the dependent variable is the difference between the total potential and the potential due to the same dipole in an infinite homogeneous medium. Both methods have the same FEM system matrix. However, the subtraction method requires an additional calculation of flux integrations along the edges of the elements in the computation of the right-hand side vector. It is shown that the subtraction method is usually more accurate in the forward modeling, provided the flux integrations are computed accurately. Closed-form evaluation of these flux integrals for first- and second-order triangular elements along linear or quadratic edges is presented here. These closed-form expressions eliminate large errors that may otherwise arise due to ill-conditioning. It is observed that FEM forward modeling errors may cause false extrema in the least-squares objective function near boundaries between media of differing conductivity. Multiple initial estimates help eliminate the possibility of the solution getting trapped in these false extrema. Results that are presented demonstrate that accurate source localization (errors of 3 mm or less) can only be obtained if both the geometrical shape and the conductivity variation of the brain and surrounding layers are modeled accurately.