Homological scaffolds of brain functional networks

By Giovanni Petri, Paul Expert, Federico E. Turkheimer, Robin L. Carhart-Harris, David J. Nutt, Peter J Hellyer, Francesco Vaccarino. Journal of the Royal Society Interface, 2014

682 citations recorded by the source corpus.

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.

Subfields: Clinical Psychology, Computational Theory and Mathematics, Experimental and Cognitive Psychology

View Paper: https://www.semanticscholar.org/paper/d7a3cd54ccbb5a6c4b98a928271a9a45c1f8c33a

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Citations in the corpus

REBUS and the Anarchic Brain: Toward a Unified Model of the Brain Action of Psychedelics (2019, background): “This is known as event-related desynchronization (Pfurtscheller et al., 1996; Singh et al., 2002) and typically involves a shift to broadband activity.”
Two’s company, three (or more) is a simplex (2016, methodology): “Studying the persistence of more complex cycles computed from fMRI recordings distinguishes subjects under psilocy-bin condition from controls (Petri et al, 2014), and a similar approach has been used for the study of functional brain networks during learning (Stolz, 2014).”
Dynamics on higher-order networks: a review (2022, background): “For instance, group interactions take place predominantly in systems arising in neurobiology [10,11], social systems [9,12] and ecology [13,14].”
Neural correlates of the LSD experience revealed by multimodal neuroimaging (2016, background): “resting state functional connectivity (RSFC) in major resting state networks (RSNs) such as the default-mode network (DMN) (17), and the emergence of novel patterns of communication (18, 19), whereas increased cortical glucose metabolism was found with PET (15).”
Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function (2016, background): “More recently, algebraic topology has been applied to functional networks between brain regions using fMRI (Petri et al., 2014) and between neurons using neural activity (Giusti et al., 2015), but the underlying synaptic connections (structural network) were unknown.”
Topological Data Analysis (2016, neutral): “…Kanari et al. (2016); Khalid et al. (2014); Kim et al. (2014); Lee et al. (2011); Lienkaemper et al. (2015); Manin (2015); Masulli & Villa (2015); Petri et al. (2014); Pirino et al. (2014); Singh et al. (2008); Sizemore et al. (2016a,b); Spreemann et al. (2015); Stolz (2014); Yoo et al. (2016);…”
Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching (2019, background): “, three- and four-way interactions in addition to pair-wise interactions, and their role in shaping collective behavior [11, 12, 13, 14, 15, 16, 17, 18].”
Cliques and cavities in the human connectome (2016, background): “Cycle representatives have previously been considered in biology (Chan et al. 2013; Petri et al. 2014; Lord et al. 2016; Kim et al. 2014; Emmett et al. 2016; Mamuye et al. 2016), but to our knowledge this is a first attempt to compare topological features in multiple brains.”
Random Walks on Simplicial Complexes and the normalized Hodge Laplacian (2018, background): “Simplicial complex models have been successful in developing new insights into biological data [32, 92], structural and functional connectivity in the brain [57,58,104], coverage of sensor networks [42,56,90,121], signal processing [8,115], mobility analysis [54], and robotics [105].”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “Efforts to find a solution to this issue already exist [598, 716, 717], but in many cases the problem is ill-defined and the solution specific to the problem at hand.”
Serotonin and brain function: a tale of two receptors (2017, background): “…biased cognition (Berman et al., 2011; Holtzheimer and Mayberg, 2011), whereas the psychedelic experience is often described as psychologically liberated (Turton et al., 2014; Watts et al., 2017) and functional neuroimaging findings support such a description (e.g. Petri et al., 2014).”