<p>The brain network is a high-dimensional, strongly coupled, nonlinear dynamical system. Its macroscopic activity is characterized by continuous state evolution and transitions within a structure-constrained state space. Previous studies in neurodynamics have shown that brain function is not determined by isolated regions. Instead, it is governed by network-level dynamical reachability and the efficiency of state transitions. Quantifying state-to-state reachability and the corresponding dynamical cost remains a central problem in the study of brain dynamics from a nonlinear dynamical systems perspective. Network control theory provides a system-dynamic approach to this problem. It integrates network topology constrained by functional connectivity with dynamical models. Within this framework, controllability and control energy are introduced to quantify the capacity of large-scale brain networks to control transitions between dynamical states. This approach enables data-driven modeling and analysis of neurodynamic properties that are difficult to observe directly. Based on resting-state functional magnetic resonance imaging (rs-fMRI) data, we constructed dynamical models of brain networks of 50 healthy controls and 50 patients with schizophrenia. We evaluated controllability structures and control energy distributions at the individual, network, and nodal levels, and examined their relationships with clinical symptom dimensions. The results show that average controllability and modal controllability are stably correlated at the individual level, but this relationship is not preserved across networks. When limbic network activation was specified as the target state, patients with schizophrenia required significantly higher optimal control energy, indicating an increased dynamical cost for reaching this class of brain states. At the same time, schizophrenia was characterized by reduced average controllability and increased modal controllability in the limbic network, suggesting a redistribution of reachability structure in the underlying state space rather than a uniform loss of control capacity. At the nodal level, spatially heterogeneous alterations in control energy were associated with positive symptom dimensions, indicating that these local abnormalities represent symptom-relevant expressions embedded within a broader reorganization of the control-energy landscape. From a nonlinear dynamical systems perspective, these findings suggest that schizophrenia is associated with a reorganization of the brain’s dynamical landscape, in which altered reachability structure is further expressed as redistributed transition costs and clinically relevant local energy abnormalities.</p>

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Controllability, control energy and state transitions in functional brain networks based on data-constrained dynamical modeling

  • Ruikang Sun,
  • Yihong Wang,
  • Xuying Xu,
  • Ying Du,
  • Xiaochuan Pan,
  • Rubin Wang

摘要

The brain network is a high-dimensional, strongly coupled, nonlinear dynamical system. Its macroscopic activity is characterized by continuous state evolution and transitions within a structure-constrained state space. Previous studies in neurodynamics have shown that brain function is not determined by isolated regions. Instead, it is governed by network-level dynamical reachability and the efficiency of state transitions. Quantifying state-to-state reachability and the corresponding dynamical cost remains a central problem in the study of brain dynamics from a nonlinear dynamical systems perspective. Network control theory provides a system-dynamic approach to this problem. It integrates network topology constrained by functional connectivity with dynamical models. Within this framework, controllability and control energy are introduced to quantify the capacity of large-scale brain networks to control transitions between dynamical states. This approach enables data-driven modeling and analysis of neurodynamic properties that are difficult to observe directly. Based on resting-state functional magnetic resonance imaging (rs-fMRI) data, we constructed dynamical models of brain networks of 50 healthy controls and 50 patients with schizophrenia. We evaluated controllability structures and control energy distributions at the individual, network, and nodal levels, and examined their relationships with clinical symptom dimensions. The results show that average controllability and modal controllability are stably correlated at the individual level, but this relationship is not preserved across networks. When limbic network activation was specified as the target state, patients with schizophrenia required significantly higher optimal control energy, indicating an increased dynamical cost for reaching this class of brain states. At the same time, schizophrenia was characterized by reduced average controllability and increased modal controllability in the limbic network, suggesting a redistribution of reachability structure in the underlying state space rather than a uniform loss of control capacity. At the nodal level, spatially heterogeneous alterations in control energy were associated with positive symptom dimensions, indicating that these local abnormalities represent symptom-relevant expressions embedded within a broader reorganization of the control-energy landscape. From a nonlinear dynamical systems perspective, these findings suggest that schizophrenia is associated with a reorganization of the brain’s dynamical landscape, in which altered reachability structure is further expressed as redistributed transition costs and clinically relevant local energy abnormalities.