Spatially uniform and nonuniform analyses of electroencephalographic dynamics,with application to the topography of the alpha rhythm.

Corticothalamic dynamics are investigated using a model in which spatial nonuniformities are incorporated via the coupling of spatial eigenmodes. Comparison of spectra generated using the nonuniform analysis with those generated using a uniform one demonstrates that, for most frequencies, local activity is only weakly dependent on activity elsewhere in the cortex; however, dispersion of low-wave-number activity ensures that distant dynamics influence local dynamics at low frequencies (below approximately 2 Hz ), and at the alpha frequency (approximately 10 Hz ), where propagating signals are inherently weakly damped, and wavelengths are large. When certain model parameters have similar spatial profiles, as is expected from physiology, the low-frequency discrepancies tend to cancel, and the uniform analysis with local parameter values is an adequate approximation to the full nonuniform one across the whole spectrum, at least for large-scale nonuniformities. After comparing the uniform and nonuniform analyses, we consider one possible application of the nonuniform analysis: studying the phenomenon of occipital alpha dominance, whereby the alpha frequency and power are greater at the back of the head (occipitally) than at the front. In order to infer realistic nonuniformities in the model parameters, the uniform version of the model is first fitted to data recorded from 98 normal subjects in a waking, eyes-closed state. This yields a set of parameters at each of five electrode sites along the midline. The inferred parameter nonuniformities are consistent with anatomical and physiological constraints. Introducing these spatial profiles into the full nonuniform model then quantitatively reproduces observed site-dependent variations in the alpha power and frequency. The results confirm that the frequency shift is mainly due to a decrease in the corticothalamic propagation delay, but indicate that the delay nonuniformity cannot account for the observed occipital increase in alpha power; the occipital alpha dominance is due to decreased cortical gains and increased thalamic gains in occipital regions compared to frontal ones.