Dimensional Reduction of Emergent Spatiotemporal Cortical Dynamics via a Maximum Entropy Moment Closure

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.
Author summary Emergent nonlinear dynamics in the primary visual cortex (V1) may influence information processing in the early visual pathway and has been shown to affect visual perception. A major goal of systems neuroscience is to understand how complex brain functions can arise from the collective nonlinear dynamics of the underlying neuronal network. This challenge has been partly met through electrophysiological recordings, optical imaging and neural population models. However, a full account of how the multi-scale population dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Previously, working on a homogeneously-coupled network, we derived a series of population dynamics models, ranging from Master equations, to Fokker-Planck equations, and culminating in an augmented system of spatially-coupled ODEs. Here we present an application of this reduction method to a heterogeneously coupled neuronal network that models a spatially-extended portion of V1. We found that the temporal dynamics of individual V1 patches can be well captured by a low-dimensional set of voltage moments. At the same time, the spatially-coupled system can recapitulate the cortical wave generation and propagation induced by many visual stimuli, including those that induce motion illusions. Furthermore, this coarse-graining reveals the importance of the temporal differences between on-/off-pathways, that may account for the directional motion perception from darks to brights.