Structure-Function Discrepancy: Inhomogeneity and Delays in Synchronized Neural Networks

The discrepancy between structural and functional connectivity in neural systems forms the challenge in understanding general brain functioning. To pinpoint a mapping between structure and function, we investigated the effects of (in)homogeneity in coupling structure and delays on synchronization behavior in networks of oscillatory neural masses by deriving the phase dynamics of these generic networks. For homogeneous delays, the structural coupling matrix is largely preserved in the coupling between phases, resulting in clustered stationary phase distributions. Accordingly, we found only a small number of synchronized groups in the network. Distributed delays, by contrast, introduce inhomogeneity in the phase coupling so that clustered stationary phase distributions no longer exist. The effect of distributed delays mimicked that of structural inhomogeneity. Hence, we argue that phase (de-)synchronization patterns caused by inhomogeneous coupling cannot be distinguished from those caused by distributed delays, at least not by the naked eye. The here-derived analytical expression for the effective coupling between phases as a function of structural coupling constitutes a direct relationship between structural and functional connectivity. Structural connectivity constrains synchronizability that may be modified by the delay distribution. This explains why structural and functional connectivity bear much resemblance albeit not a one-to-one correspondence. We illustrate this in the context of resting-state activity, using the anatomical connectivity structure reported by Hagmann and others.Author Summary: Separating the time scale of oscillations from that of the phase dynamics allowed for reducing a network of coupled neural mass models to a system of phase oscillators. We studied the dynamics of networks of phases and their synchronization characteristics as being seminal for functional neural networks. We put particular focus on effects of time delays in the coupling on the network dynamics and contrasted that to effects due to altered structural connectivity. Does neuroanatomical structure prescribe all the macroscopic activity patterns that we observe through electrophysiological brain recordings? We found that heterogeneity in structural coupling and distributed delays have equivalent effects on the shape of phase distributions, i.e., on functional connectivity. The contribution of changes in structural connectivity to network synchronization can therefore not readily be distinguished from that of distributed delays. Interestingly, the emergence of phase clusters in networks requires a subtle interplay between coupling and delays, which may form a window into disentangling structural effects from those induced by delay distributions. Therefore, when investigating neural network behavior, both structural connectivity and delay distribution should be addressed.