A theoretical framework supporting experimental measures of dynamic properties of human EEG is proposed with emphasis on distinct alpha rhythms. Robust relationships between measured dynamics and cognitive or behavioral conditions are reviewed, and proposed physiological bases for EEG at cellular levels are considered. Classical EEG data are interpreted in the context of a conceptual framework that distinguishes between locally and globally dominated dynamic processes, as estimated with coherence or other measures of phase synchronization. Macroscopic (scalp) potentials generated by cortical current sources are described at three spatial scales, taking advantage of the columnar structure of neocortex. New EEG data demonstrate that both globally coherent and locally dominated behavior can occur within the alpha band, depending on narrow band frequency, spatial measurement scale, and brain state. Quasi-stable alpha phase structures consistent with global standing waves are observed. At the same time, alpha and theta phase locking between cortical regions during mental calculations is demonstrated, consistent with neural network formation. The brain-binding problem is considered in the context of EEG dynamic behavior that generally exhibits both of these local and global aspects. But specific experimental designs and data analysis methods may severely bias physiological interpretations in either local or global directions.

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The spatial statistics of scalp electroencephalogram (EEG) are usually presented as coherence in individual frequency bands. These coherences result both from correlations among neocortical sources and volume conduction through the tissues of the head. The scalp EEG is spatially low-pass filtered by the poorly conducting skull, introducing artificial correlation between the electrodes. A four concentric spheres (brain, CSF, skull, and scalp) model of the head and stochastic field theory are used here to derive an analytic estimate of the coherence at scalp electrodes due to volume conduction of uncorrelated source activity, predicting that electrodes within 10-12 cm can appear correlated. The surface Laplacian estimate of cortical surface potentials spatially bandpass filters the scalp potentials reducing this artificial coherence due to volume conduction. Examination of EEG data confirms that the coherence estimates from raw scalp potentials and Laplacians are sensitive to different spatial bandwidths and should be used in parallel in studies of neocortical dynamic function.

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The electroencephalogram (EEG) is recorded by sensors physically separated from the cortex by resistive skull tissue that smooths the potential field recorded at the scalp. This smoothing acts as a low-pass spatial filter that determines the spatial bandwidth, and thus the required spatial sampling density, of the scalp EEG. Although it is better appreciated in the time domain, the Nyquist frequency for adequate discrete sampling is evident in the spatial domain as well. A mathematical model of the low-pass spatial filtering of scalp potentials is developed, using a four concentric spheres (brain, CSF, skull, and scalp) model of the head and plausible estimates of the conductivity of each tissue layer. The surface Laplacian estimate of radial skull current density or cortical surface potential counteracts the low-pass filtering of scalp potentials by shifting the spatial spectrum of the EEG, producing a band-passed spatial signal that emphasizes local current sources. Simulations with the four spheres model and dense sensor arrays demonstrate that progressively more detail about cortical potential distribution is obtained as sampling is increased beyond 128 channels.

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