Understanding the brain as a complex network of interacting components can provide insight into cognitive function. In this talk, I will explore the relationship between brain network structure and function from two perspectives. First, I will present work that addressees the question: Is the brain a small-world network? The creation and maintenance of physical connections between neurons/brain regions carries a metabolic cost, and it has been hypothesized that network organization must optimize in a way that minimizes this cost while optimizing processing capacity. It has thus been proposed that the brain is organized to have a small-world structure, but recent work involving new data sets challenges this claim. However, most previous studies rely on binary representations of network connectivity, neglecting that in the brain, connections are not binary, but weighted by the strength of the connection. I will present a generalization of the Watts-Strogtaz formalism for weighted networks along with a novel statistic called the Small-World Propensity that quantifies both binary and weighted small-world structure and show that by retaining network weights, we are able to better understand the small-world structure of brain networks.
In the second half of the talk, I will then present preliminary work asking how properties of the underlying anatomical structure affect the functional network properties and controllability of the brain. Theoretical predictions from linear models suggest that stimulation of certain brain regions can more easily move the brain into different states, forming a type of “control”. Yet, the brain is far from a linear system. Using a nonlinear model of brain activity derived from diffusion spectrum imaging of white matter connectivity and Wilson-Cowan dynamics, we test the relationship between regional connectivity patterns and the ability of regional stimulation to impart change in functional network configurations. We find that local regional connectivity relates to network controllability and that the system is sensitive to perturbations in the underlying network structure.