Abstract
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.
Highlights
To recognize that the neuroscience community is fascinated with the physiological basis of brain rhythms is an understatement
In the last 50 years, there has been an active take-up of modeling approaches in the neurosciences, with many of these inspired by the research activity of Jack Cowan
For the -rebound study, we have focused on simple networks built from one or a few nodes, and another intriguing study would be to explore the spread of -rebound processes across the cortex, using the neural field formulation
Summary
To recognize that the neuroscience community is fascinated with the physiological basis of brain rhythms is an understatement. Given the wealth of neuroscience data accruing through projects such as the Brain Activity Map in the US, seeking to establish a functional connectome of the entire brain, there is a community-wide need to develop the generation of neural mass and field models that have a stronger connection to biological reality This is especially important when one appreciates that many large-scale neuroimaging modalities reflect the underlying firing rate of a population of neurons, and their degree of synchrony. Neural mass models generate brain rhythms using the notion of population firing rates, aiming to side-step the need for large-scale simulations of more realistic networks of spiking neurons They are not derived from detailed conductance-based models, they can be motivated by a number of phenomenological arguments (Coombes et al 2014) and typically take the form of systems of nonlinear ordinary differential equations (ODEs). ⌬ ϭ 0.5, vsyn ϭ Ϫ10, ϭ 1, ␣ ϭ 0.95, ϭ 1
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