Homological scaffolds of brain functional networks

Functional brain networks can be studied through homological cycles—topological objects that capture mesoscopic structure in weighted correlation networks. A new method, homological scaffolds, compactly represents these cycles and makes them amenable to standard network analysis. Applied to resting-state fMRI data from 15 healthy volunteers given placebo or psilocybin, the homological structure of brain activity changed dramatically after psilocybin, producing many transient, low-stability cycles and a few persistent ones absent under placebo.

Study at a glance

Abstract

Networks, as efficient representations of complex systems, have appealed to scientists for a long time and now permeate many areas of science, including neuroimaging (Bullmore and Sporns 2009 Nat. Rev. Neurosci. 10 , 186–198. ( doi:10.1038/nrn2618 )). Traditionally, the structure of complex networks has been studied through their statistical properties and metrics concerned with node and link properties, e.g. degree-distribution, node centrality and modularity. Here, we study the characteristics of functional brain networks at the mesoscopic level from a novel perspective that highlights the role of inhomogeneities in the fabric of functional connections. This can be done by focusing on the features of a set of topological objects— homological cycles —associated with the weighted functional network. We leverage the detected topological information to define the homological scaffolds , a new set of objects designed to represent compactly the homological features of the correlation network and simultaneously make their homological properties amenable to networks theoretical methods. As a proof of principle, we apply these tools to compare resting-state functional brain activity in 15 healthy volunteers after intravenous infusion of placebo and psilocybin—the main psychoactive component of magic mushrooms. The results show that the homological structure of the brain's functional patterns undergoes a dramatic change post-psilocybin, characterized by the appearance of many transient structures of low stability and of a small number of persistent ones that are not observed in the case of placebo.