The Wilson–Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained from its mathematical analysis, it is now widely used in the computational neuroscience community for building large-scale in silico brain networks that can incorporate the increasing amount of knowledge from the Human Connectome Project. Here, we consider a neural population model in the spirit of that originally developed by Wilson and Cowan, albeit with the added advantage that it can account for the phenomena of event-related synchronization and desynchronization. This derived mean-field model provides a dynamic description for the evolution of synchrony, as measured by the Kuramoto order parameter, in a large population of quadratic integrate-and-fire model neurons. As in the original Wilson–Cowan framework, the population firing rate is at the heart of our new model; however, in a significant departure from the sigmoidal firing rate function approach, the population firing rate is now obtained as a real-valued function of the complex-valued population synchrony measure. To highlight the usefulness of this next-generation Wilson–Cowan style model, we deploy it in a number of neurobiological contexts, providing understanding of the changes in power spectra observed in electro- and magnetoencephalography neuroimaging studies of motor cortex during movement, insights into patterns of functional connectivity observed during rest and their disruption by transcranial magnetic stimulation, and to describe wave propagation across cortex.

Event-related fluctuations of neural oscillatory amplitude are reported widely in the context of cognitive processing and are typically interpreted as a marker of brain “activity”. However, the precise nature of these effects remains unclear; in particular, whether such fluctuations reflect local dynamics, integration between regions, or both, is unknown. Here, using magnetoencephalography, we show that movement induced oscillatory modulation is associated with transient connectivity between sensorimotor regions. Further, in resting-state data, we demonstrate a significant association between oscillatory modulation and dynamic connectivity. A confound with such empirical measurements is that increased amplitude necessarily means increased signal-to-noise ratio (SNR): this means that the question of whether amplitude and connectivity are genuinely coupled, or whether increased connectivity is observed purely due to increased SNR is unanswered. Here, we counter this problem by analogy with computational models which show that, in the presence of global network coupling and local multistability, the link between oscillatory modulation and long-range connectivity is a natural consequence of neural networks. Our results provide evidence for the notion that connectivity is mediated by neural oscillations, and suggest that time–frequency spectrograms are not merely a description of local synchrony but also reflect fluctuations in long-range connectivity.

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changes in the underlying synchrony of patterns. It is customary to use spiking neural network models when examining within population synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtain insight from. In this paper, we consider a network of $\theta$-neurons, which has recently been shown to admit an exact mean-field description in the absence of a spatial component. We show that the inclusion of space and a realistic synapse model leads to a reduced model that has many of the features of a standard neural field model coupled to a further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysis and numerical continuation software are used to explore the existence and stability of spatiotemporal patterns in the system. In particular, we show that this new model can support states above and beyond those seen in a standard neural field model. These states are typified by structures within bumps and waves showing the dynamic evolution of population synchrony.

In electrophysiological recordings of the brain, the transition from high amplitude to low amplitude signals are most likely caused by a change in the synchrony of underlying neuronal population firing patterns. Classic examples of such modulations are the strong stimulus-related oscillatory phenomena known as the movement related beta decrease (MRBD) and post-movement beta rebound (PMBR). A sharp decrease in neural oscillatory power is observed during movement (MRBD) followed by an increase above baseline on movement cessation (PMBR). MRBD and PMBR represent important neuroscientific phenomena which have been shown to have clinical relevance. Here, we present a parsimonious model for the dynamics of synchrony within a synaptically coupled spiking network that is able to replicate a human MEG power spectrogram showing the evolution from MRBD to PMBR. Importantly, the high-dimensional spiking model has an exact mean field description in terms of four ordinary differential equations that allows considerable insight to be obtained into the cause of the experimentally observed time-lag from movement termination to the onset of PMBR (∼ 0.5 s), as well as the subsequent long duration of PMBR (∼ 1 − 10 s). Our model represents the first to predict these commonly observed and robust phenomena and represents a key step in their understanding, in health and disease.