Bicoherence of intracranial EEG

Bicoherence (bicoh) estimates the proportion of energy in every possible pair of frequency components, F-1, F-2 (from 1-50 Hz in this study), that conforms to the definition of quadratic phase coupling (phase of component at F-3, which is F-1+F-2, equals phase of F-1 + phase of F-2). This measure of nonlinear cooperativity was explored to test the hypothesis that the EEG is highly differentiated in space and time, using human subdural recordings (chiefly frontal, parietal and temporal lobes, in 16 to 60 electrode channels) and deep temporal lobe probe data (with 12 to 20 channels) from 11 subjects during sleep, waking and seizure states. Derived from the bispectrum, auto-bicoherence uses the frequency components in one channel; cross-bicoherence uses one channel for F-1 and another for F-2 (Fig. I). Known contributions to bicoh can come from certain forms of amplitude, frequency or phase modulation, departures from Gaussianity such as skewness and asymmetry, and transient events with sharp corners. Bicoh is found not to be a fixed character of the EEG but varies widely with time and place. It is virtually absent in many analysis epochs of 4-20s duration in waking or sleeping EEG. Other epochs show significant bicoh with diverse form and distribution over the bifrequency plane. Isolated peaks, periodic peaks or rounded mountain ranges are either widely scattered or confined to one or a few parts of the plane. Bicoh is generally an invisible feature: one cannot usually recognize the responsible form of nonlinearity or any obvious correlate in the raw EEG. Adjacent segments of 4 s as well as adjacent electrodes as close as 6.5 mm can be quite different in bicoh (Fig. 2), even when the EEG looks similar. Bicoh changes with brain state and sensory stimulation. In all subjects for whom suitable data are available, EEGs during stage II/III sleep are significantly higher in overall mean bicoh than in the waking state. Evidence is suggestive that the fraction of nonlinearly coupled energy is highest in the range <4 Hz in sleep whereas in the awake state the contribution from gamma band oscillations is more significant. During seizures the diverse EEG patterns average a significant elevation in bicoh but have a wide variance (Fig. 3). Several measures, such as maximum bispectrum, maximum power spectrum, maximum and mean bicoherence, skewness around the time axis, asymmetry around the voltage axis vary independently of each other. Various caveats are in order. Electrodes employed in these clinical recordings are several square millimeters; semimicroelectrodes might change the picture considerably. Behavioral states were not carefully controlled; recording was in the ward, not a standardized EEG setting, hence more like normal conditions; alpha activity or any clear rhythmic EEG was rare. Many possible statistical tests have not yet been done, e.. to compare lobes, to compare frequency-specific distribution of bicoh elevations, to estimate the function of distance between channels in cross-bicoh spectra, EEG bicoh is found to be very local and to change abruptly, within a few seconds, in agreement with the stated hypothesis. Quadratic phase coupling of pairs of frequencies manifests nonlinear cooperative dynamics that vary independently of visible criteria and power spectra. Estimating relative roles of transient and ongoing contributions to bicoh needs newer methods. The most important conclusion is that the intracranial EEG carries much more information than is apparent to the eye or to linear analyses such as the power, coherence or phase spectra, Other surprises include the extensive periods and places where bicoh is absent and the great diversity of distribution of peaks, hills and mountain ranges in the bifrequency plane, and the curious distribution of cross-bicoh, which often resembles one of the two auto-bicoh spectra more than an intermediate.