Mathematical mechanism of state-dependent phase resetting properties of alpha rhythm in the human brain

It is well-known that 10-Hz alpha oscillations in humans observed by electroencephalogram (EEG) are enhanced when the eyes are closed. Toward explaining this, a previous experimental study using manipulation by transcranial magnetic stimulation (TMS) revealed more global propagation of phase resetting in the eyes-open condition than in the eyes-closed condition in the alpha band. Those results indicate a significant increase of directed information flow across brain networks from the stimulated area to the rest of the brain when the eyes are open, suggesting that sensitivity to environmental changes and external stimuli is adaptively controlled by changing the dynamics of the alpha rhythm. However, the mathematical mechanism mediating the changes in the sensitivity has not been well elucidated. In this study, we propose a qualitative mathematical model that describes the characteristic behavior of the EEG phase dynamics. Numerically, we find that the propagation properties of the phase resetting qualitatively depend on whether the population of oscillators at the stimulated area are synchronized. These results support the hypothesis that the dynamics of the alpha oscillations controls sensitivity to external stimuli.