General Relationship of Global Topology, Local Dynamics, and Directionality in Large-Scale Brain Networks

Efficient brain networks balance global integration with functional specialization, but how global topology, local node dynamics, and information flow relate has been unclear. Using analytical solutions of oscillator models, computational simulations on model and anatomical brain networks, and high-density electroencephalography from conscious and anesthetized humans, the authors demonstrate that network nodes with more connections (higher degree) have larger amplitudes and are directional targets (phase lag) rather than sources (phase lead). This degree–directionality relationship appears to be a fundamental network property with direct applicability to brain function. Changes in directionality patterns across states of human consciousness are driven by alterations in brain network topology.

Study at a glance

Abstract

The balance of global integration and functional specialization is a critical feature of efficient brain networks, but the relationship of global topology, local node dynamics and information flow across networks has yet to be identified. One critical step in elucidating this relationship is the identification of governing principles underlying the directionality of interactions between nodes. Here, we demonstrate such principles through analytical solutions based on the phase lead/lag relationships of general oscillator models in networks. We confirm analytical results with computational simulations using general model networks and anatomical brain networks, as well as high-density electroencephalography collected from humans in the conscious and anesthetized states. Analytical, computational, and empirical results demonstrate that network nodes with more connections (i.e., higher degrees) have larger amplitudes and are directional targets (phase lag) rather than sources (phase lead). The relationship of node degree and directionality therefore appears to be a fundamental property of networks, with direct applicability to brain function. These results provide a foundation for a principled understanding of information transfer across networks and also demonstrate that changes in directionality patterns across states of human consciousness are driven by alterations of brain network topology.