Multilevel irreversibility reveals higher-order organization of nonequilibrium interactions in human brain dynamics

Abstract

Information processing in the human brain can be modeled as a complex dynamical system operating out of equilibrium with multiple regions interacting nonlinearly. Yet, despite extensive study of the global level of nonequilibrium in the brain, quantifying the irreversibility of interactions among brain regions at multiple levels remains an unresolved challenge. Here, we present the Directed Multiplex Visibility Graph Irreversibility framework, a method for analyzing neural recordings using network analysis of time-series. Our approach constructs directed multilayer graphs from multivariate time-series where information about irreversibility can be decoded from the marginal degree distributions across the layers, which each represents a variable. This framework is able to quantify the irreversibility of every interaction in the complex system. Applying the method to magnetoencephalography recordings during a long-term memory recognition task, we quantify the multivariate irreversibility of interactions between brain regions and identify the combinations of regions which showed higher levels of nonequilibrium in their interactions. For individual regions, we find higher irreversibility in cognitive versus sensorial brain regions while for pairs, strong relationships are uncovered between cognitive and sensorial pairs in the same hemisphere. For triplets and quadruplets, the most nonequilibrium interactions are between cognitive' sensorial pairs alongside medial regions. Combining these results, we show that multilevel irreversibility offers unique insights into the higher-order, hierarchical organization of neural dynamics from the perspective of brain network dynamics.

We would like to sincerely thank Prof. Elvira Brattico and Francesco Carlomagno for their valuable assistance in designing the experiment and collecting the data. R.N.-K. was supported by an Engineering and Physical Sciences Research Council (EPSRC) doctoral scholarship from grants EP/T517811/1 and EP/R513295/1, and The Alan Turing Institute through an Enrichment Community Award which is funded under grant EP/Z532861/1. L.B, P.V, and M.L.K. were supported by the Center for Music in the Brain, funded by the Danish National Research Foundation (project number DNRF117). L.B. was also supported by Carlsberg Foundation (CF20-0239), Lundbeck Foundation (Talent Prize 2022), Linacre College of the University of Oxford (Lucy Halsall fund) and Nordic Mensa Fund. G.F.-R. was supported by Fundación Mutua Madrilea. G.D. was supported by the Agency for Management of University and Research Grants research support grant (ref. 2021 SGR 00917) funded by the Department of Research and Universities of the Generalitat of Catalunya, by the project NEurological MEchanismS of Injury, and the project Sleep-like cellular dynamics (NEMESIS) (ref. 101071900) funded by the European Union European Research Council Synergy Horizon Europe and by the project PID2022-136216NB-I00 financed by the MCIN/AEI/10.13039/501100011033/FEDER, Unión Europea, the Ministry of Science and Innovation, the State Research Agency and the European Regional Development Fund. M.L.K. was further supported by Centre for Eudaimonia and Human Flourishing funded by the Pettit and Carlsberg Foundations. R.L. was supported by the EPSRC grants EP/V013068/1 and EP/V03474X/1.