Fig. 2: Directional coordination reveals structured large-scale brain states.

(a–c) Three dominant directional coordination states were identified from complex-valued phase synchrony (CVPS). Left: phase state matrices showing pairwise phase offsets across canonical functional domains (sensory, association, control, and subcortical systems). Right: cortical projections of relative driver scores (lead vs lag), with red indicating leading regions and blue indicating lagging regions. (a) Feedback state: association regions lead sensory systems (positive directional hierarchy index; DHI = +2.024, p = 4.0 × 10), consistent with topdown feedback organization. (b) Feedforward state: sensory regions lead association systems (negative DHI; DHI = −3.103, p ~ 0), reflecting bottom-up propagation. (c) Integrative state: distributed and balanced phase-leading across domains, with no dominant hierarchy (DHI ~ 0, n.s.), indicating coordinated integration rather than directed flow. These states define a low-dimensional directional coordination structure that captures recurring modes of information flow across large-scale brain systems. (d) Cross-dataset replication of directional coordination states. Pairwise complex correlation matrices quantify centroid similarity across independent cohorts (fBIRN, COBRE, HCP Aging S1–S4, HCP Adult) for each coordination state. Mean cross-dataset similarity was 0.91 for the feedforward and integrative states and 0.78 for the feedback state, demonstrating that all three directional coordination regimes are robustly reproducible across cohorts spanning different acquisition protocols, scanner sites, and populations. (e) State correspondence exceeds chance across all replication cohorts. For each external dataset, the optimal one-to-one state mapping to fBIRN was compared against all possible permutations. Z-scores range from 1.16 to 1.67 across cohorts, confirming that cross-dataset state alignment is systematically stronger than any alternative assignment and establishing the directional coordination hierarchy as a stable organizational property of large-scale brain dynamics.