Dynamics of the human alpha rhythm: evidence for non-linearity?

For a better understanding of the physiological mechanisms responsible for alpha rhythms it is important to know whether non-linear processes play a role in their generation. We used non-linear forecasting in combination with surrogate data testing to investigate the prevalence and nature of alpha rhythm non-linearity, based on EEG recordings from humans. We interpreted these findings using computer simulations of the alpha rhythm model of Lopes da Silva et al. (1974).

EEGs were recorded at 02 and O1 in 60 healthy subjects (30 males; 30 females; age: 49.28 years; range 11-84) during a resting eyes-closed state. Four artefact-free epochs (2.5 s; sample frequency 200 Hz) from each subject were tested for non-linearity using a non-linear prediction statistic and phase-randomized surrogate data. A similar type of analysis was done on the output of the alpha model for different values of input.

In the 480 (60 subjects, 2 derivations, 4 blocks) epochs studied, the null hypothesis that the alpha rhythms can result from linearly filtered noise, could be rejected in 6 cases (1.25%). The alpha model showed a bifurcation from a point attractor to a limit cycle at an input pulse density of 615 pps. Non-linearity could only be detected in the model output close to and beyond this bifurcation point. The sources of the non-linearity are the sigmoidal relationships between average membrane potential and output pulse density of the various cells of the neuronal populations.

The alpha rhythm is a heterogeneous entity dynamically: 98.75% of the epochs (type I alpha) cannot be distinguished from filtered noise. Apparently, during these epochs the activity of the brain has such a high complexity that it cannot be distinguished from a random process. In 1.25% of the epochs (type II alpha) non-linearity was found which may be explained by dynamics in the vicinity of a bifurcation to a limit cycle. There is thus experimental evidence from the point of view of dynamics for the existence of the two types of alpha rhythm and the bifurcation predicted by the model.