Abstract
We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and inhibitory synaptic time delays. We study the phase diagram of this model numerically as a function of the inter-regional connection strength that is related to cerebral blood flow, and a phase shift parameter that is associated with synaptic GABA concentrations. We find three macroscopic phases of cortical activity: background activity (unsynchronized oscillations), epileptiform activity (highly synchronized oscillations) and resting-state activity (synchronized clusters/chaotic behaviour). Previous network models could hitherto not explain the existence of all three phases. We further observe a shift of the average oscillation frequency towards lower values together with the appearance of coherent slow oscillations at the transition from resting-state to epileptiform activity. This observation is fully in line with experimental data and could explain the influence of GABAergic drugs both on gamma oscillations and epileptic states. Compared to previous models for gamma oscillations and resting-state activity, the multiplex Kuramoto model not only provides a unifying framework, but also has a direct connection to measurable physiological parameters.
Highlights
We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions
To understand the mechanisms of this correspondence, both the overall network structure of the brain and the local properties of neural populations have to be taken into account[4,6]
The other mechanism is based on excitatory-inhibitory coupling with synaptic time delays[18,19,20]
Summary
We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and inhibitory synaptic time delays. To understand the mechanisms of this correspondence, both the overall network structure of the brain and the local properties of neural populations have to be taken into account[4,6] Regarding the latter, neural inhibition seems to be essential for cortical processing[7]. In mice[21], rats[22] and humans[3,23], a decrease of GABA-concentrations (gamma-aminobutyric acid is the main inhibitory neurotransmitter in mammals) is accompanied by a strong attenuation of the gamma frequency band and sometimes by epileptiform activity
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