Electroencephalographic Source Reconstruction by the Finite-Element Approximation of the Elliptic Cauchy Problem.

This paper develops a novel approach for fast and reliable reconstruction of EEG sources in MRI-based head models. The inverse EEG problem is reduced to the Cauchy problem for an elliptic partial-derivative equation. The problem is transformed into a regularized minimax problem, which is directly approximated in a finite-element space. The resulting numerical method is efficient and easy to program. It eliminates the need to solve forward problems, which can be a tedious task. The method applies to complex anatomical head models, possibly containing holes in surfaces, anisotropic conductivity, and conductivity variations inside each tissue. The method has been verified on a spherical shell model and an MRI-based head. Numerical experiments indicate high accuracy of localization of brain activations (both cortical potential and current) and rapid execution time. This study demonstrates that the proposed approach is feasible for EEG source analysis and can serve as a rapid and reliable tool for EEG source analysis. The significance of this study is that it develops a fast, accurate, and simple numerical method of EEG source analysis, applicable to almost arbitrary complex head models.