Towards a single parameter for the assessment of EEG oscillations

The single macroscopic flow on the boundary of a closed curve equals the sum of the countless microscopic flows in the enclosed area. According to the dictates of the Green's theorem, the counterclockwise movements on the border of a two-dimensional shape must equal all the counterclockwise movements taking place inside the shape. This mathematical approach might be useful to analyse neuroscientific data sets for its potential capability to describe the whole cortical activity in terms of electric flows occurring in peripheral brain areas. Given a map of raw EEG data to coloured ovals in which different colours stand for different amplitudes, the theorem suggests that the sum of the electric amplitudes measured inside every oval equals the amplitudes measured just on the oval's edge. This means that the collection of the vector fields detected from the scalp can be described by a novel, single parameter summarizing the counterclockwise electric flow detected in the outer electrodes. To evaluate the predictive power of this parameter, in a pilot study we investigated EEG traces from ten young females performing Raven's intelligence tests of various complexity, from easy tasks (n = 5) to increasingly complex tasks (n = 5). Despite the seemingly unpredictable behavior of EEG electric amplitudes, the novel parameter proved to be a valuable tool to to discriminate between the two groups and detect hidden, statistically significant differences. We conclude that the application of this promising parameter could be expanded to assess also data sets extracted from neurotechniques other than EEG.