Petri, Giovanni & Expert, Paul & Turkheimer, Federico & Carhart-Harris, Robin & Nutt, David & Hellyer, Peter & Vaccarino, Francesco. (2014). Homological scaffolds of brain functional networks. Journal of The Royal Society Interface. 11. 20140873. 10.1098/rsif.2014.0873.
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.
Simplified visualization of the persistence homological scaffolds. The persistence homological scaffolds Hppla (a) and Hppsi (b) are shown for comparison.For ease of visualization, only the links heavier than 80 (the weight at which the distributions in figure 5abifurcate) are shown. This value is slightly smaller thanthe bifurcation point of the weights distributions in figure 5a. In both networks, colours represent communities obtained by modularity  optimization on theplacebo persistence scaffold using the Louvain method  and are used to show the departure of the psilocybin connectivity structure from the placebo baseline.The width of the links is proportional to their weight and the size of the nodes is proportional to their strength. Note that the proportion of heavy links betweencommunities is much higher (and very different) in the psilocybin group, suggesting greater integration. A labelled version of the two scaffolds is available as GEXFgraph files as the electronic supplementary material. (Online version in colour.