Quantifying state-dependent control properties of brain dynamics from perturbation responses

Abstract

The brain can be conceptualized as a control system facilitating transitions between states, such as from rest to motor activity. Applying network control theory to measurements of brain signals enables characterization of brain dynamics through control properties. However, most prior studies that have applied network control theory have evaluated brain dynamics under unperturbed conditions, neglecting the critical role of external perturbations in accurate system identification. In this study, we combine a perturbation input paradigm with a network control theory framework and propose a novel method for estimating the controllability Gramian matrix in a simple, theoretically grounded manner. This method provides insights into brain dynamics, including overall controllability (quantified by the Gramians eigenvalues) and specific controllable directions (represented by its eigenvectors). As a proof of concept, we applied our method to transcranial magnetic stimulationinduced electroencephalographic responses across four motor-related states and two resting states. We found that states such as open-eye rest, closed-eye rest, and motor-related states were more effectively differentiated using controllable directions than overall controllability. However, certain states, like motor execution and motor imagery, remained indistinguishable using these measures. These findings indicate that some brain states differ in their intrinsic control properties as dynamical systems, while others share similarities that make them less distinguishable. This study underscores the value of control theory-based analyses in quantitatively how intrinsic brain states shape the brains responses to stimulation, providing deeper insights into the dynamic properties of these states. This methodology holds promise for diverse applications, including characterizing individual response variability and identifying conditions for optimal stimulation efficacy. Significant statementThe brain can be viewed as a control system transitioning between states, such as from rest to motor activity. Previous studies using network control theory mostly evaluated brain dynamics without external perturbations, neglecting their role in accurate system identification. This study integrates perturbation inputs with network control theory to propose a method for estimating the controllability Gramian, thereby providing insights into brain dynamics. We applied this approach to TMS-induced EEG responses in motor-related and resting states. Our findings show that controllable directions (eigenvectors) allow better discrimination between states than overall controllability. Our method can quantitatively assess brain state differences, and has potential applications in characterizing individual response variability and optimizing stimulation efficacy.