Links between electroencephalograms (EEGs) and underlying aspects of neurophysiology and anatomy are poorly understood. Here a nonlinear continuum model of large-scale brain electrical activity is used to analyze arousal states and their stability and nonlinear dynamics for physiologically realistic parameters. A simple ordered arousal sequence in a reduced parameter space is inferred and found to be consistent with experimentally determined parameters of waking states. Instabilities arise at spectral peaks of the major clinically observed EEG rhythms-mainly slow wave, delta, theta, alpha, and sleep spindle-with each instability zone lying near its most common experimental precursor arousal states in the reduced space. Theta, alpha, and spindle instabilities evolve toward low-dimensional nonlinear limit cycles that correspond closely to EEGs of petit mal seizures for theta instability, and grand mal seizures for the other types. Nonlinear stimulus-induced entrainment and seizures are also seen, EEG spectra and potentials evoked by stimuli are reproduced, and numerous other points of experimental agreement are found. Inverse modeling enables physiological parameters underlying observed EEGs to be determined by a new, noninvasive route. This model thus provides a single, powerful framework for quantitative understanding of a wide variety of brain phenomena.

A recent neurophysical model of propagation of electrical waves in the cortex is extended to include a physiologically motivated subcortical feedback loop via the thalamus. The electroencephalographic spectrum when the system is driven by white noise is then calculated analytically in terms of physiological parameters, including the effects of filtering of signals by the cerebrospinal fluid, skull, and scalp. The spectral power at low frequencies is found to vary as f(-1) when awake and f(-3) when asleep, with a breakpoint to a steeper power-law tail at frequencies above about 20 Hz in both cases; the f(-1) range concurs with recent magnetoencephalographic observations of such a regime. Parameter sensitivities are explored, enabling a model with fewer free parameters to be proposed, and showing that spectra predicted for physiologically reasonable parameter values strongly resemble those observed in the laboratory. Alpha and beta peaks seen near 10 Hz and twice that frequency, respectively, in the relaxed wakeful state are generated via subcortical feedback in this model, thereby leading to predictions of their frequencies in terms of physiological parameters, and of correlations in their occurrence. Subcortical feedback is also predicted to be responsible for production of anticorrelated peaks in deep sleep states that correspond to the occurrence of theta rhythm at around half the alpha frequency and sleep spindles at 3/2 times the alpha frequency. An additional positively correlated waking peak near three times the alpha frequency is also predicted and tentatively observed, as are two new types of sleep spindle near 5/2 and 7/2 times the alpha frequency, and anticorrelated with alpha. These results provide a theoretical basis for the conventional division of EEG spectra into frequency bands, but imply that the exact bounds of these bands depend on the individual. Three types of potential instability are found: one at zero frequency, another in the theta band at around half the alpha frequency, and a third at the alpha frequency itself.

It is shown that new model-based electroencephalographic (EEG) methods can quantify neurophysiologic parameters that underlie EEG generation in ways that are complementary to and consistent with standard physiologic techniques. This is done by isolating parameter ranges that give good matches between model predictions and a variety of experimental EEG-related phenomena simultaneously. Resulting constraints range from the submicrometer synaptic level to length scales of tens of centimeters, and from timescales of around 1 ms to 1 s or more, and are found to be consistent with independent physiologic and anatomic measures. In the process, a new method of obtaining model parameters from the data is developed, including a Monte Carlo implementation for use when not all input data are available. Overall, the approaches used are complementary to other methods, constraining allowable parameter ranges in different ways and leading to much tighter constraints overall. EEG methods often provide the most restrictive individual constraints. This approach opens a new, noninvasive window on quantitative brain analysis, with the ability to monitor temporal changes, and the potential to map spatial variations. Unlike traditional phenomenologic quantitative EEG measures, the methods proposed here are based explicitly on physiology and anatomy.