Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory

Discrete-network versus modal representations of brain activity: why a sparse regions-of-interest approach can work for analysis of continuous dynamics

The efficacy of the common practice of tracking brain dynamics using a few key regions of interest is explained via the fact that these regions are sensitive to underlying extended modes of activity, not just local dynamics. This underlines the inseparable interplay between modes and regions and reflects the reality that brain functions range from highly localized to highly extended.

Resting-state functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations

Brain fluctuations at rest are not random but are structured in spatial patterns of correlated activity across different brain areas. The question of how resting-state functional connectivity (FC) emerges from the brain's anatomical connections has motivated several experimental and computational studies to understand structure-function relationships. However, the mechanistic origin of resting state is obscured by large-scale models' complexity, and a close structure-function relation is still an open problem. Thus, a realistic but simple enough description of relevant brain dynamics is needed. Here, we derived a dynamic mean field model that consistently summarizes the realistic dynamics of a detailed spiking and conductance-based synaptic large-scale network, in which connectivity is constrained by diffusion imaging data from human subjects. The dynamic mean field approximates the ensemble dynamics, whose temporal evolution is dominated by the longest time scale of the system. With this reduction, we demonstrated that FC emerges as structured linear fluctuations around a stable low firing activity state close to destabilization. Moreover, the model can be further and crucially simplified into a set of motion equations for statistical moments, providing a direct analytical link between anatomical structure, neural network dynamics, and FC. Our study suggests that FC arises from noise propagation and dynamical slowing down of fluctuations in an anatomically constrained dynamical system. Altogether, the reduction from spiking models to statistical moments presented here provides a new framework to explicitly understand the building up of FC through neuronal dynamics underpinned by anatomical connections and to drive hypotheses in task-evoked studies and for clinical applications.

Using geometry to uncover relationships between isotropy, homogeneity, and modularity in cortical connectivity

Inferences of strong modular and hierarchical structure from some cortical network studies conflict with the broadly isotropic homogeneous connectivity that has been found to a first approximation in classical anatomical studies. This conflict is resolved via consideration of the geometry of the cortex. A new geometrically based connection matrix (CM) visualization method is used to better compare experimental CMs with model CMs and thereby minimize appearance of artifacts. Model networks based on spherical geometry containing similar isotropic, homogeneous connection distributions to the experiment are shown to reproduce, interrelate, and explain key properties of experimentally derived networks, such as clustering coefficient (CC), path length, mean degree, and modularity score, using only two parameters that are fitted to an experimental spatial connectivity distribution. A greater CC in the experiment than the model indicates that, while isotropy and homogeneity of connections is a good first approximation, connections at shorter range may exhibit additional perturbations that increase clustering. These geometrically based models provide a comparative framework to assist in the next stage of revealing and analyzing anisotropic and/or inhomogeneous connections in data and their effects on network properties and visualization.

Anatomical connectivity and the resting state activity of large cortical networks

This paper uses mathematical modelling and simulations to explore the dynamics that emerge in large scale cortical networks, with a particular focus on the topological properties of the structural connectivity and its relationship to functional connectivity. We exploit realistic anatomical connectivity matrices (from diffusion spectrum imaging) and investigate their capacity to generate various types of resting state activity. In particular, we study emergent patterns of activity for realistic connectivity configurations together with approximations formulated in terms of neural mass or field models. We find that homogenous connectivity matrices, of the sort of assumed in certain neural field models give rise to damped spatially periodic modes, while more localised modes reflect heterogeneous coupling topologies. When simulating resting state fluctuations under realistic connectivity, we find no evidence for a spectrum of spatially periodic patterns, even when grouping together cortical nodes into communities, using graph theory. We conclude that neural field models with translationally invariant connectivity may be best applied at the mesoscopic scale and that more general models of cortical networks that embed local neural fields, may provide appropriate models of macroscopic cortical dynamics over the whole brain.