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

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 longterm 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.