Marshall Mykietyshyn: Topology and dynamics of an empirical brain connectivity

BCCN Berlin / Technische Universität Berlin

Abstract

 

The field of complex networks aims to understand and describe a variety of natural and technological systems. This pursuit utilizes the network’s statistics, topology and dynamics to determine how the overall behaviour of the network depends on relationships between its parts. Perhaps the most important example of complex systems is the brain, due to their relevance to medicine, psychology and humanity in general.

This work examines the behaviour of a mesoscopic scale brain model. It consists of an empirical structural connectivity matrix, derived using diffusion tensor imaging, and a FitzHugh-Nagumo oscillatory population model representing the mean-field neural activity of each individual brain region. The regions are defined by the Automated Anatomical Labelling atlas. Previous work using this model has identified three brain regions, which demonstrate eccentric synchronization behaviour. This is characterized as the tendency of these three network nodes (vertices) to pseudo-periodically perform an extra oscillation relative to their neighbours.

Although this thesis is unable to define the topological characteristics that define the network’s eccentric brain regions, several advancements were made in understanding the dynamics of the system, and a relationship between the topology and dynamics is identified. Firstly, it was found that the eccentric behaviour can be predicted by the frequency spectrum of the sub-network consisting of all non-eccentric nodes. Although this is an interesting observation, the system must already be running to make this prediction, thus it has little practical application.

More importantly, the mechanism driving the eccentric nodes’ extra oscillations is established. These extra oscillations occur in nodes whose root mean square input changes significantly over long time scales. It is characterized by a peak leading up to the extra oscillation and a drop off afterwards. Thus, the eccentric nodes are distinct in that they demonstrate a greater variance in their inputs, compared to the other nodes of the system. The mechanism itself can be described either in terms of the input time series, or by the motion of the node’s nullclines in the phase plane, both of which are illustrated herein. Additionally, a method for reducing the network, while maintaining the eccentric behaviour, is developed. This method utilizes the knowledge that the eccentric nodes are identified by their root mean square input. By removing nodes from the system, whose inputs to their neighbours fall below a certain threshold, a reduced network can be found. Importantly, the eccentric nodes in the reduced network are different from those in the full network. In future work, this simpler network may enable the discovery of a more definitive link between the topology and dynamics.

Finally, the brain regions are grouped in two ways: by spectral clustering, which is based on the empirical connectivity matrix, and by their phase relationships. Spectral clustering is a topological measure. It finds clusters that maximize the block structure of a connectivity matrix. On the other hand, phase clusters represent the dynamics of the system. A comparison of these two clusterings demonstrates a relationship between the system’s topology and dynamics. However, the nature of this relationship remains unclear.

 

Additional Information

Master Thesis Defense

 

Organized by

Prof. Dr. Eckehard Schöll   & Prof. Dr. Henning Sprekeler     / Lisa Velenosi