Understanding the effect of white matter delays on large scale brain synchrony

Abstract

The presence of myelin is a powerful structural factor that controls the conduction speed of mammalian axons. It is the combination of local synaptic activity and non-local delayed axonal interactions within the cortex that is believed to be the major source of large-scale brain signals that can be readily observed with modern neuroimaging modalities. Here, we present perspectives from neural mass and network modelling and develop a new set of mathematical tools able to unravel the contributions of space-dependent axonal delays to large-scale spatiotemporal patterning of brain activity. We first analyse a single neuronal population Wilson–Cowan neural mass model with self-feedback and a single delay and show how to construct periodic orbits for a Heaviside firing rate. For this nonsmooth model we perform linear stability analysis by augmenting Floquet theory with saltation operations. Building on this example, we then show how to treat the synchronous oscillatory state in networks of nonsmooth neural masses with multiple and heterogeneous delays. Theoretical predictions for the parameter variations that lead to instabilities of the synchronous network state and the excitation of structured spatio-temporal activity patterns are confirmed with direct numerical simulations.