Eigenmode decomposition of asymmetries in whole-brain effective connectivity reveals multiscale hierarchical dynamics

The human brain is a complex, hierarchical system operating far from equilibrium, yet the mechanisms linking its directed network architecture to temporal irreversibility remain largely unknown. While prior studies have revealed functional and structural hierarchies, no framework has captured the hierarchical organization of the brains directed network in relation to its non-equilibrium dynamics. Here, we present the first large-scale eigendecomposition of whole-brain effective connectivity (EC), estimated from resting-state fMRI using sparse Dynamic Causal Modeling. We isolate the irreversible component of EC, which encodes the directionality of information flow and forms a comprehensive hierarchical network of forward and backward interactions. This hierarchy strengthens in brain states approaching criticality, where slow, oscillatory modes dominate and reflects the influence of long-range anatomical connections that scaffold whole-brain information flow. Our decomposition provides the first multiscale quantification of temporal irreversibility, revealing dual counterpropagating streams along the unimodal-transmodal axis operating at distinct frequencies. Crucially, these hierarchical dynamics carry robust, individual-specific signatures, with unimodal networks contributing disproportionately to subject identifiability. Altogether, this work delivers the first dynamic, whole-brain characterization of effective connectivity-derived hierarchies across spatiotemporal scales and individuals, offering a unified framework for studying brain hierarchy, non-equilibrium dynamics, and subject identifiability.