Multilevel irreversibility reveals higher-order organisation of non-equilibrium interactions in human brain dynamics

Information processing in the human brain can be modelled as a complex dynamical system operating out of equilibrium with multiple regions interacting nonlinearly. Yet, despite extensive study of the global level of non-equilibrium 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 analysing neural recordings using network analysis of time-series. Our approach constructs directed multi-layer 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 non-equilibrium in their interactions. For individual regions, we find higher irreversibility in cognitive versus sensorial brain regions whilst for pairs, strong relationships are uncovered between cognitive and sensorial pairs in the same hemisphere. For triplets and quadruplets, the most non-equilibrium interactions are between cognitive-sensorial pairs alongside medial regions. Finally, for quintuplets, our analysis finds higher irreversibility when the prefrontal cortex is included in the interaction. Combining these results, we show that multilevel irreversibility offers unique insights into the higher-order, hierarchical organisation of neural dynamics and presents a new perspective on the analysis of brain network dynamics.