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PLoS One. 2019 Sep 9;14(9):e0222161. doi: 10.1371/journal.pone.0222161. eCollection 2019.

Graph-theoretical analysis for energy landscape reveals the organization of state transitions in the resting-state human cerebral cortex.

Kang J1,2, Pae C2, Park HJ1,2,3,4.

Author information

Center for Systems and Translational Brain Sciences, Institute of Human Complexity and Systems Science, Yonsei University, Seoul, Republic of Korea.
Department of Nuclear Medicine, Yonsei University College of Medicine, Seoul, Republic of Korea.
BK21 PLUS Project for Medical Science, Yonsei University College of Medicine, Seoul, Republic of Korea.
Department of Cognitive Science, Yonsei University, Seoul, Republic of Korea.


The resting-state brain is often considered a nonlinear dynamic system transitioning among multiple coexisting stable states. Despite the increasing number of studies on the multistability of the brain system, the processes of state transitions have rarely been systematically explored. Thus, we investigated the state transition processes of the human cerebral cortex system at rest by introducing a graph-theoretical analysis of the state transition network. The energy landscape analysis of brain state occurrences, estimated using the pairwise maximum entropy model for resting-state fMRI data, identified multiple local minima, some of which mediate multi-step transitions toward the global minimum. The state transition among local minima is clustered into two groups according to state transition rates and most inter-group state transitions were mediated by a hub transition state. The distance to the hub transition state determined the path length of the inter-group transition. The cortical system appeared to have redundancy in inter-group transitions when the hub transition state was removed. Such a hub-like organization of transition processes disappeared when the connectivity of the cortical system was altered from the resting-state configuration. In the state transition, the default mode network acts as a transition hub, while coactivation of the prefrontal cortex and default mode network is captured as the global minimum. In summary, the resting-state cerebral cortex has a well-organized architecture of state transitions among stable states, when evaluated by a graph-theoretical analysis of the nonlinear state transition network of the brain.

Conflict of interest statement

The authors have declared that no competing interests exist.

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