Persistence of hierarchical network organization and emergent topologies in models of functional connectivity

Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of activity on the anatomical, or structural network of synaptic connections, which possess a hierarchical organization. While it is assumed that structural networks shape their functional counterparts, it is also hypothesized that alterations of brain activity may come with transformations of functional connectivity, and possibly its deviation from the hierarchical topology. In this computational study, we introduce a novel methodology to monitor the persistence and breakdown of hierarchical order in functional networks, generated from simulations of activity spreading on both synthetic and real structural connectomes. We show that hierarchical connectivity is persistent in the quasi-critical regime associated with optimal processing capabilities and normal brain function (Griffiths phase) and breaks down in states deviating from this regime, often associated with pathological conditions. Our results offer important clues for the study of optimal neurocomputing architectures and processes, which are capable of tuning patterns of activity and information flow, and show how the hierarchical topology and its quasi-critical functional counterpart provide an effective balance between local specialized processing and global integration.