Computing brain networks with complex dynamics

TL;DR

This paper explores how complex quadratic network models can describe emergent brain network behaviors, linking topological fractal measures to neural connectivity and function in human subjects.

Contribution

It introduces a novel modeling approach using complex quadratic dynamics to analyze brain networks and demonstrates how topological measures can classify and relate network behavior to architecture.

Findings

Asymptotic fractal sets characterize long-term network behavior.

Topological measures effectively classify connectome dynamics.

Network architecture influences the geometry of emergent fractal sets.

Abstract

One important question in neuroscience is how global behavior in a brain network emerges from the interplay between network connectivity and the neural dynamics of individual nodes. To better understand this theoretical relationship, we have been exploring a simplified modeling approach in which we equip each node with discrete quadratic dynamics in the complex plane, and we study the emerging behavior of the resulting complex quadratic network (CQN). The long-term behavior of CQNs can be represented by asymptotic fractal sets with specific topological signatures going far beyond those described in traditional single map iterations. In this study, we illustrate how topological measures of these asymptotic sets can be used efficiently as comprehensive descriptors and classifiers of dynamics in tractography-derived connectomes for human subjects. We investigate to what extent the complex geometry of these sets is tied to network architecture (on one hand) and to the network behavior (on the other). This helps us understand the mechanics of the relationship between the subject's brain function, physiology and behavior and their underlying connectivity architecture.