FitzHugh–Nagumo Oscillators on Complex Networks Mimic Epileptic-Seizure-Related Synchronization Phenomena

Moritz Gerster, Rico Berner, Jakub Sawicki, Anna Zakharova, Antonín Škoch, Jaroslav Hlinka, Klaus Lehnertz, and Eckehard Schöll

Gerster, M., Berner, R., Sawicki, J., Zakharova, A., Škoch, A., Hlinka, J., Lehnertz, K. and Schöll, E., 2020. FitzHugh–Nagumo oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena. Chaos, 30(12), p.123130. https://doi.org/10.1063/5.0021420.

Abstract

We study patterns of partial synchronization in a network of FitzHugh–Nagumo oscillators with empirical structural connectivity measured in human subjects. We report the spontaneous occurrence of synchronization phenomena that closely resemble the ones seen during epileptic seizures in humans. In order to obtain deeper insights into the interplay between dynamics and network topology, we perform long-term simulations of oscillatory dynamics on different paradigmatic network structures: random networks, regular nonlocally coupled ring networks, ring networks with fractal connectivities, and small-world networks with various rewiring probability. Among these networks, a small-world network with intermediate rewiring probability best mimics the findings achieved with the simulations using the empirical structural connectivity. For the other network topologies, either no spontaneously occurring epileptic-seizure-related synchronization phenomena can be observed in the simulated dynamics, or the overall degree of synchronization remains high throughout the simulation. This indicates that a topology with some balance between regularity and randomness favors the self-initiation and self-termination of episodes of seizure-like strong synchronization.

Summary

This computational study uses FitzHugh–Nagumo oscillators on complex brain networks to model epileptic-seizure-related synchronization phenomena. It investigates how network topology and coupling can generate seizure-like synchronization, including transitions related to seizure initiation and termination. The paper is relevant for researchers searching for FitzHugh–Nagumo models of epilepsy, complex networks, seizure synchronization, nonlinear dynamics, and brain network simulations.

Keywords: FitzHugh–Nagumo model; complex networks; epilepsy; epileptic seizures; seizure synchronization; nonlinear dynamics; brain network dynamics; empirical structural connectivity; small-world networks; seizure initiation; seizure termination.

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BibTeX 
@article{gerster2020fitzhugh,
  title={{FitzHugh--Nagumo} oscillators on complex networks mimic epileptic-seizure-related synchronization phenomena},
  author={Gerster, Moritz and Berner, Rico and Sawicki, Jakub and Zakharova, Anna and {\v{S}}koch, Anton{\'\i}n and Hlinka, Jaroslav and Lehnertz, Klaus and Sch{\"o}ll, Eckehard},
  journal={Chaos},
  volume={30},
  number={12},
  pages={123130},
  year={2020},
  publisher={AIP Publishing},
  doi={10.1063/5.0021420}
}