A neural mass model of phase-amplitude coupling.

Brain activity shows phase-amplitude coupling between its slow and fast oscillatory components. We study phase-amplitude coupling as recorded at individual sites, using a modified version of the well-known Wendling neural mass model. To the population of fast inhibitory interneurons of this model, we added external modulatory input and dynamic self-feedback. These two modifications together are sufficient to let the inhibitory population serve as a limit-cycle oscillator, with frequency characteristics comparable to the beta and gamma bands. The frequency and power of these oscillations can be tuned through the time constant of the dynamic and modulatory input. Alpha band activity is generated, as is usual in such models, as a result of interactions of pyramidal neurons and a population of slow inhibitory interneurons. The slow inhibitory population activity directly influences the fast oscillations via the synaptic gain between slow and fast inhibitory populations. As a result, the amplitude envelope of the fast oscillation is coupled to the phase of the slow activity; this result is consistent with the notion that phase-amplitude coupling is effectuated by interactions between inhibitory interneurons.