Bicoherence of intracranial EEG in sleep, wakefulness and seizures.

The hypothesis that the intracranial EEG has local structure and short-term non-stationarity is tested with a little-studied measure of non-linear phase coupling, the bicoherence in human subdural and deep temporal lobe probe data from 11 subjects during sleeping, waking and seizure states. This measure of cooperativity estimates the proportion of energy in every possible pair of frequency components, F1, F2 (from 1 to 50 Hz in this study), that satisfies the definition of quadratic phase coupling (phase of component at F3, which is F1 + F2, equals phase of F1 + phase of F2). Derived from the bispectrum, which segregates the non-Gaussian energy, auto-bicoherence uses the frequency components in one channel; cross-bicoherence uses one channel for F1 and F2 and another for F3. These higher order spectra are used in physical systems for detection of episodes of non-linearity and transients, for pattern recognition and robust classification, relatively immune to Gaussian components and low signal to noise ratios. Bicoherence is found not to be a fixed character of the EEG but quite local and unstable, in agreement with the hypothesis. Bicoherence can be quite different in adjacent segments as brief as 1.6 s as well as adjacent intracranial electrodes as close as 6.5 mm, even when the EEG looks similar. It can rise or fall steeply within millimeters. It is virtually absent in many analysis epochs of 17s duration. Other epochs show significant bicoherence 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. Bicoherence is generally an invisible feature: one cannot usually recognize the responsible form of non-linearity or any obvious correlate in the raw EEG. During stage II/III sleep overall mean bicoherence is generally higher than in the waking state. During seizures the diverse EEG patterns average a significant elevation in bicoherence but have a wide variance. Maximum bispectrum, maximum power spectrum, maximum and mean bicoherence, skewness and asymmetry all vary independently of each other. Cross-bicoherence is often intermediate between the two auto-bicoherence spectra but commonly resembles one of the two. Of the known factors that contribute to bicoherence, transient as distinct from ongoing wave forms can be more important in our data sets. This measure of non-linear higher moments is very sensitive to weak quadratic phase coupling; this can come from several kinds of waveforms. New methods are needed to evaluate their respective contributions. Utility of this descriptor cannot be claimed before more carefully defined and repeatable brain states are studied.

Temporal fluctuations in coherence of brain waves.

As a measure of dynamical structure, short-term fluctuations of coherence between 0.3 and 100 Hz in the electroencephalogram (EEG) of humans were studied from recordings made by chronic subdural macroelectrodes 5-10 mm apart, on temporal, frontal, and parietal lobes, and from intracranial probes deep in the temporal lobe, including the hippocampus, during sleep, alert, and seizure states. The time series of coherence between adjacent sites calculated every second or less often varies widely in stability over time; sometimes it is stable for half a minute or more. Within 2-min samples, coherence commonly fluctuates by a factor up to 2-3, in all bands, within the time scale of seconds to tens of seconds. The power spectrum of the time series of these fluctuations is broad, extending to 0.02 Hz or slower, and is weighted toward the slower frequencies; little power is faster than 0.5 Hz. Some records show conspicuous swings with a preferred duration of 5-15s, either irregularly or quasirhythmically with a broad peak around 0.1 Hz. Periodicity is not statistically significant in most records. In our sampling, we have not found a consistent difference between lobes of the brain, subdural and depth electrodes, or sleeping and waking states. Seizures generally raise the mean coherence in all frequencies and may reduce the fluctuations by a ceiling effect. The coherence time series of different bands is positively correlated (0.45 overall); significant nonindependence extends for at least two octaves. Coherence fluctuations are quite local; the time series of adjacent electrodes is correlated with that of the nearest neighbor pairs (10 mm) to a coefficient averaging approximately 0.4, falling to approximately 0.2 for neighbors-but-one (20 mm) and to < 0.1 for neighbors-but-two (30 mm). The evidence indicates fine structure in time and space, a dynamic and local determination of this measure of cooperativity. Widely separated frequencies tending to fluctuate together exclude independent oscillators as the general or usual basis of the EEG, although a few rhythms are well known under special conditions. Broad-band events may be the more usual generators. Loci only a few millimeters apart can fluctuate widely in seconds, either in parallel or independently. Scalp EEG coherence cannot be predicted from subdural or deep recordings, or vice versa, and intracortical microelectrodes show still greater coherence fluctuation in space and time. Widely used computations of chaos and dimensionality made upon data from scalp or even subdural or depth electrodes, even when reproducible in successive samples, cannot be considered representative of the brain or the given structure or brain state but only of the scale or view (receptive field) of the electrodes used. Relevant to the evolution of more complex brains, which is an outstanding fact of animal evolution, we believe that measures of cooperativity are likely to be among the dynamic features by which major evolutionary grades of brains differ.

EEG coherence has structure in the millimeter domain: subdural and hippocampal recordings from epileptic patients.

Subdural recordings from 8 patients and depth recordings from 3 patients via rows of electrodes with 5-10 mm spacing were searched for signs of significant local differentiation of coherence calculated between all possible pairs of loci. EEG samples of 2-4 min were taken during 4 states: alertness, stage 2-3 sleep, light surgical anesthesia permitting the patient to respond to questions and electrical seizures. Coherence was computed for all frequencies from 1 to 50 Hz or 0.3-100 Hz; for comparisons the mean coherence over each of 6 or 7 narrower bands between 2 and 70 Hz was used. Whereas the literature supports the view that EEG coherence is usually substantial over many centimeters, the hypothesis here tested--and found to be well above stochastic expectations--is that significant structure occurs in the millimeter domain for EEG recorded subdurally or within the brain. In both the subdural surface samples and those from temporal lobe depth electrode arrays coherence declines with distance between electrodes of the pair, on the average quite severely in millimeters. This is nearly the same for all frequency bands. For middle bands like 8-13 and 13-20 Hz, mean coherence typically declines most steeply in the first 10 mm, from values indistinguishable from 1.0 at < 0.5 mm distance to 0.5 at 5-10 mm and to 0.25 in another 10-20 mm in the subdural surface data. Temporal lobe depth estimates decline about half as fast; coherence > or = 0.5 extends for 9-20 mm and > or = 0.25 for another 20-35mm. Low frequency bands (1-5, 5-8 Hz) usually fall slightly more slowly than high frequency bands (20-35, 35-50 Hz but the difference is small and variance large. The steepness of decline with distance in humans is significantly but only slightly smaller than that we reported earlier for the rabbit and rat, averaging less than one half. Local coherence, for individual pairs of loci, shows differentiation in the millimeter range, i.e., nearest neighbor pairs may be locally well above or below average and this is sustained over minutes. Local highs and lows tend to be similar for widely different frequency bands. Coherence varies quite independently of power, although they are sometimes correlated. Regional differentiation is statistically significant in average coherence among pairs of loci on temporal vs frontal cortex or lateral frontal vs. subfrontal strips in the same patient, but such differences are usually small.(ABSTRACT TRUNCATED AT 400 WORDS)

Variability analysis of visual evoked potentials in humans by pattern recognition in phase domain.

A novel approach to single trial visually evoked potentials (VEP) variability analysis based on a new model of post-stimulus brain electrical activity is presented. The convolution model introduced by the author is experimentally verified by the analysis of flash stimulus effects on EEG amplitude and phase spectra. Pattern recognition in the signal phase domain is proposed for detection of any time locked transient signals. This is illustrated by an application of a clustering algorithm in two-dimensional unwrapped phase of EEG Fourier transform space for occipitally recorded VEPs in human subjects.

Dynamic properties of human visual evoked and omitted stimulus potentials.

Visual evoked potentials (VEPs) and omitted stimulus potentials (OSPs) are re-examined in scalp recordings from 19 healthy subjects. The principal finding is a distinction in form, latency and properties between OSPs in the conditioning stimulus range < 2 Hz, used in previous human studies, and those in the range > 5 Hz, used in previous studies of selected elasmobranchs, teleost fish and reptiles. We cannot find OSPs between 2 and 5 Hz. The high frequency ("fast," ca.6- > 40 Hz) and the low frequency ("slow," ca. 0.3-1.6 Hz) OSPs have different forms and latencies but both tend to a constant latency after the omission, over their frequency ranges, suggesting a temporally specific expectation. Fast OSPs (typically N120, P170-230 and later components including induced rhythms at 10-13 Hz) resemble an OFF effect, and require fixation but not attention to the interstimulus interval. Slow OSPs (usually P500-1100) require attention but not fixation; they are multimodal, unlike the fast OSPs. Based on cited data from fish and reptiles, fast OSPs probably arise in the retina, to be modified at each subsequent level. We have no evidence on the origin of slow OSPs. In both ranges not only large, diffuse flashes, but weak, virtual point sources (colored LEDs) meters away suffice. They are difficult to habituate. Both require very short conditioning periods. The transition from the single, rested VEP to the steady state response (SSR) at different frequencies is described. Around 8-15 Hz in most subjects larger SSRs suggest a resonance. Alternation between large and small SSR amplitude occurs around 4 Hz in some subjects and conditions of attention, and correlates with an illusion that the flash frequency is 2 Hz or is irregular. Jitter of the conditioning intervals greatly reduces the slow OSP but only slightly affects the fast OSP. Differences between scalp loci are described.