Comparison of different auto-solid angle approximations in BEM for EEG dipole source localization

The solution of the forward problem in electroencephalography requires the computation of the potential distribution on the surface of an isolated conductor, generated by a known source. In order to solve the problem in realistic head-shaped conductors, numerical methods must be used, such as boundary element method (BEM). In the BEM the surface of the volume conductor is subdivided in triangles and the potential is calculated at the centres of gravity, or collocation points, of these triangles. Key to the BEM is the estimation of the solid angle subtended by a triangle at a given collocation point. Particular care must be taken when considering the auto-solid angle, i.e. the solid angle subtended by a triangle at a point which belongs to that triangle. In this work we investigate the effect of the number of collocation points and we compare different approximations of the auto-solid angle commonly used in literature by means of the relative difference measure (RDM). We found that the finer the tessellation the smaller the median RDM and the narrower the distribution of RDM values. Moreover, we found that the use of the "one solid angle" approximation clearly outperforms the other approximations in terms of RDM.