Unification of alpha, mu, and tau rhythms and their beta-band harmonics via eigenmodes: spectral peaks, topography, and reactivity

Objective:The alpha, mu, and tau rhythms all have frequencies of around 10 Hz in normal adult humans, with a range of 7–13 Hz. The beta rhythm, mu-associated activity, and tau-associated activity, are found at around twice those frequencies. The present objective is to use neural field theory (NFT) to explain the observed frequency structure and spatial topography, and to suggest a mechanism of reactivity, of all these rhythms in a unified way, and to predict other features not yet reported experimentally.

Methods: NFT averages over the activity of large numbers of neurons to predict mean firing rates and EEG characteristics. It predicts the existence of natural modes of activity, each with characteristic spatial structure and frequencies. The lowest modes dominate large-scale activity and the first four are used here to predict spectra, topography, and reactivity of alpha, mu, and tau rhythms and their second harmonics, including split peaks.

Results: Corticothalamic loop delays determine the basic $\sim 10$ Hz frequency of the alpha rhythm, the $\sim 20$ Hz frequency of the beta rhythm, and explain their frequency correlations on an individual-subject level. Differential effects of cortical geometry on individual modes cause observed frequency splitting of the alpha and beta rhythms and we predict analogous splitting of mu and tau and their harmonics. Spatial topographies of alpha, mu, and tau are explained by modal structure, with amplitudes superposed rather than powers, and we predict that the harmonic of each rhythm will tend to have similar topography to its fundamental, although specific exceptions can occur. Similar results are obtained when modal eigenfrequencies differ sufficiently to give rise to split peaks. Dynamics of rotating patterns and wavefronts are also explained in terms of pairs of modes. Blocking or “desynchronization” of each rhythm can be accounted for by modest decreases in corticothalamic loop gains, magnified by proximity to a critical state, and we predict that fundamental and harmonic will tend to be blocked in tandem, an effect that has already been observed for alpha and beta. Paradoxically, modal analysis implies that blocking in one region can correlate with enhancement in another, which may account for the phenomenon of event-related synchronization.

Conclusions: A unified explanation of alpha, mu, tau, and their harmonics is obtained in terms of just four corticothalamic eigenmodes. The results are consistent with a wide variety of experimental observations and experimentally testable predictions of new features are made.

Significance: A century after the first observations of human EEG, this work explains and unifies alpha, the earliest detected rhythm, with its relatives and their harmonics to form a single family. This provides a strong theoretical basis for analysis and monitoring of activity and its underlying physiology and, via NFT, for linking these rhythms to other phenomena such as evoked responses.