Model-based analysis and optimization of the mapping of cortical sources in the spontaneous scalp EEG

The mapping of brain sources into the scalp electroencephalogram (EEG) depends on volume conduction properties of the head and on an electrode montage involving a reference. Mathematically, this source mapping (SM) is fully determined by an observation function (OF) matrix. This paper analyses the OF-matrix for a generation model for the desynchronized spontaneous EEG. The model involves a four-shell spherical volume conductor containing dipolar sources that are mutually uncorrelated so as to reflect the desynchronized EEG. The reference is optimized in order to minimize the impact in the SM of the sources located distant from the electrodes. The resulting reference is called the localized reference (LR). The OF-matrix is analyzed in terms of the relative power contribution of the sources and the cross-channel correlation coefficient for five existing references as well as for the LR. It is found that the Hjorth Laplacian reference is a fair approximation of the LR, and thus is close to optimum for practical intents and purposes. The other references have a significantly poorer performance. Furthermore, the OF-matrix is analyzed for limits to the spatial resolution for the EEG. These are estimated to be around 2 cm.