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 nonlinear 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 1-50 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 nonGaussian 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 nonlinearity 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 nonlinearity 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 nonlinear 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

EEG coherence has structure in the millimeter domain

Subdural recordings from 8 patients via rows of eight electrodes with either 5 or 10 mm spacing plus depth recordings from 3 patients with rows of 8-12 electrodes either 6.5 or 9 mm center-to-center 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 four states: alertness, stage 2-3 sleep, light surgical anesthesia permitting the patient to respond to questions or commands, and electrical seizures. Coherence was computed for all frequencies from 1-50 Hz or 0.3-100 Hz and then compared for 6 or 7 narrower bands between 2 and 70 Hz. 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. This is nearly the same for all frequency bands. Whether computed for 5, 20 or 60 s epochs, coherence pooled across all pairs of a given separation, in a given subject, differs only slightly, in the direction of lower coherence for longer samples, indicating good stationarity of the samples chosen. 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 ca. half as fast; coherence 0.5 extends for 9-20 mm and 0.25 for another 20-35 mm. 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 < 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. We could not test how consistent they are over hours or between patients. Differences between left and right hemispheres, whether symmetrical pairs or pooled from two or more lobes on each side, can be quite large; in our patients the right side is usually higher, especially in the waking state. Brain state has a large influence. Slow wave sleep usually shows slightly more coherence at each distance, in all bands, compared to the waking EEG, but not consistently. Coherence at a given distance or its rate of decline with distance is a more direct measure of synchrony than naked-eye "synchronization," which is dominated by the power spectrum. Among the range of EEG states classified as seizures, coherence varies widely but averages higher by 0.05-0.2 than in pre-ictal states, usually in all frequencies when computed over the whole seizure but much more in the higher bands during the height of the electrical paroxysm. The findings point to still finer structure and more variance with closer spacing of electrodes. They could not predict the known large scale coherence between scalp electrodes, but are not in conflict with them. Scalp recording blurs the finer spatial structure, but reveals macrostructure missed by subdural and depth recording with limited numbers of channels. The strong tendency for correlated fluctuations across frequency bands is contrary to expectation from the common model of independent oscillators

Role of glycemia in acute spinal cord injury: data from a rat experimental model and clinical experience.

While experimental and clinical evidence indicates that in brain injury blood glucose increases with injury severity and hyperglycemia worsens neurological outcome, the role of blood glucose in secondary mechanisms of neuronal damage after acute spinal cord injury has not yet been investigated. Data from spinal cord ischemia models suggests a deleterious effect of hyperglycemia, likely due to enhanced lactic acidosis, which is primarily dependent on the amount of glucose available to be metabolized. The purpose of this study is to summarize preliminary experimental and clinical observations on the role of blood glucose in acute spinal cord injury. Between 1995 and 1996 we used the New York University (NYU) rat spinal cord injury model to test the following hypotheses: 1) Blood glucose levels increase with injury severity. 2) Fasting protects from hyperglycemia and prevents secondary damage to the spinal cord. 3) Postinjury-induced hyperglycemia (dextrose 5% 2 gm/Kg) enhances spinal lesion volume. From a clinical perspective, we reviewed blood glucose records of 47 patients admitted to the Department of Neurosrgery in Verona, between 1991 and 1995, within 24 hours of acute spinal cord injury in order to determine: a) the incidence of hyperglycemia (> 140 mg/dl); b) the correlation between blood glucose and injury severity; and c) the role of methylprednisolone in affecting blood glucose. Results indicate that in a graded spinal cord injury model: 1) Early after injury, more severe contusions support significantly higher blood glucose levels. 2) Fasting overnight does not directly affect spinal cord lesion volume but influences blood gases, and we observed that a slightly systemic acidosis plays a minor neuroprotective role. Fasting also ensures more consistent normoglycemic baseline blood glucose values. 3) Postinjury-induced moderate hyperglycemia (160-190 mg/dl) does not significantly affect spinal cord injury. In the clinical study, we observed that during the first 24 hours after spinal cord injury: a) Glycemia ranges between 90 and 243 mg/dl (mean value 143 mg/dl), and close to 50% of the patients present blood glucose values higher than normal. b) Methylprednisolone administration is not associated to significantly higher blood glucose levels. c) There is a trend for larger glucose rises with more severe injury