Small World is Not Enough: How The Emergence of Resting State Properties Depends on Graph Theoretical Principals of the Underlying Structural Connectivity

Mario Senden (Faculty of Psychology and Neuroscience, Maastricht University, Maastricht, the Netherlands), Gustavo Deco (Department of Information and Communication Technologies, Universitat Pompeu Fabra, Barcelona, Spain)

Purpose – Under resting conditions the cortex exhibits spatio-temporal activity patterns known as resting state networks (RSNs). These RSNs exhibit occasional massive reorganizations. This suggests that the cortex is a dynamical system in a critical state (Kitzbichler et al. 2009). Previous studies have shown that noise, transmission delays and the underlying structural connectivity are important contributors to resting state properties. So far, it has not been investigated which graph theoretical properties of the structural connectivity are the most important contributors to RSNs. We aim to answer this question employing a simulation study with network models based on different adjacency matrices.

Method – We performed simulations of cortical activity during rest with a global spiking attractor model employing leaky integrate-and-fire neurons and realistic AMPA, NMDA and GABA synapses with cortical areas interconnected according to a human structural connectivity matrix and artificially generated regular, random, small world, and scale adjacency matrices. We performed both spiking simulations as well as mean field simulations. We analyzed spiking data using hierarchical clustering to identify functional networks. Furthermore, we used the clusters to perform lability analyses to test whether the models resemble systems showing self-organized criticality. Also, we identified the complete attractor garden; i.e. all functional networks, of the models in the mean field data.

Results – The spiking model based on human structural connectivity reproduces empirical functional connectivity well and exhibits critical dynamics. Those models based on small world and scale free adjacency matrices resemble the criticality behavior of the human model best. Mean field analyses show that in the model based on the regular adjacency matrix almost all areas are active for almost all initial conditions. In the model based on human structural connectivity only a few areas are active for most initial conditions while most areas are active in only a handful of conditions. This can also be observed in models based on the scale free adjacency matrix. The best predictors for the percentage of initial conditions in which an area becomes active are the degree to which it is clustered and how extensively it is connected to other areas.

Conclusions – These preliminary results suggest two conclusions. Firstly, self-organized criticality observed for the cortex at rest appears to be mainly related to the cortex’ small world architecture. Secondly, there exist a number of areas which are both highly clustered and highly connected in human and scale free matrices that are recruited for almost all initial conditions. This suggests that a functional network consisting of these areas; a structural core, can sustain activity most efficiently. The fact that areas comprising the default mode network (DMN) exhibit exactly these properties suggests that the DMN is a structural core. A likely function of the DMN then is to act as a source of activity for other RSNs when external input is absent. This might explain the inhibition of this network during task performance because it would lead to interference if the DMN constantly activates networks not related to the present task.


Kitzbichler, M. G., Smith, M. L., Christensen, S. R., & Bullmore, E. (2009). Broadband criticality of human brain network synchronization. PLoS computational biology, 5(3).

Preferred presentation format: Poster
Topic: Computational neuroscience

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