Separation of spatially localized cortical activities in the EEG: model-based analysis and optimization

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. In this article, the source mapping (SM) is formalized mathematically in the form of an observation function (OF) matrix. The OF-matrix is used to analyze and optimize the SM for a generation model for the desynchronized spontaneous EEG. The optimization leads to a novel reference that minimizes the impact in the EEG of the sources located distant from the electrodes. Thereby, this reference separates spatially localized cortical activities in the EEG. For this reason, it is called the localized reference (LR). The LR is compared with the Hjorth Laplacian reference (HR), which is commonly used for recordings of localized cortical activities. The comparison is made in terms of the relative power contribution of the sources into EEG channels. For the model, the LR is found to have up to 15-20% better performance than the HR, and thus the LR is considered a good alternative to the HR when a head model is available. The HR is, however, a fair approximation of the LR and thus is close to optimum for practical intents and purposes.