Next generation neural population models - Coombes, Stephen (Frontiers in Applied Mathematics and Statistics, 2023)
Low-dimensional neural mass models are often invoked to model the coarse-grained activity of large populations of neurons and synapses and have been used to help understand the coordination of large scale brain rhythms. However, they are phenomenological in nature and, although motivated by neurobiological considerations, the absence of a direct link to an underlying biophysical reality is a weakness that means they may not be best suited to capturing some of the rich behaviours seen in real neuronal tissue. In this perspective article I discuss a simple spiking neuron network model that has recently been shown to admit to an exact mean-field description for synaptic interactions. This has many of the features of a neural mass model coupled to an additional dynamical equation that describes the evolution of population synchrony. This next generation neural mass model is ideally suited to understanding the patterns of brain activity that are ubiquitously seen in neuroimaging recordings. Here I review the mean-field equations, the way in which population synchrony, firing rate, and average voltage are intertwined, together with their application in large scale brain modelling. As well as natural extensions of this new approach to modelling the dynamics of neuronal populations I discuss some of the open mathematical challenges in developing a statistical neurodynamics that can generalise the one discussed here.