All together now: Analogies between chimera state collapses and epileptic seizures

Conceptually and structurally simple mathematical models of coupled oscillator networks can show a rich variety of complex dynamics, providing fundamental insights into many real-world phenomena. A recent and not yet fully understood example is the collapse of coexisting synchronous and asynchronous oscillations into a globally synchronous motion found in networks of identical oscillators. Here we show that this sudden collapse is promoted by a further decrease of synchronization, rather than by critically high synchronization. This strikingly counterintuitive mechanism can be found also in nature, as we demonstrate on epileptic seizures in humans. Analyzing spatiotemporal correlation profiles derived from intracranial electroencephalographic recordings (EEG) of seizures in epilepsy patients, we found a pronounced decrease of correlation at the seizure onsets. Applying our findings in a closed-loop control scheme to models of coupled oscillators in chimera states, we succeed in both provoking and preventing outbreaks of global synchronization. Our findings not only advance the understanding of networks of coupled dynamics but can open new ways to control them, thus offering a vast range of potential new applications.

[1]  F. Mormann,et al.  Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients , 2000 .

[2]  J. Sieber,et al.  Regular and irregular patterns of self-localized excitation in arrays of coupled phase oscillators. , 2015, Chaos.

[3]  Philipp Hövel,et al.  Controlling chimera states: The influence of excitable units. , 2016, Physical review. E.

[4]  Y. Kuramoto,et al.  Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators , 2002, cond-mat/0210694.

[5]  S. Strogatz,et al.  Chimera states for coupled oscillators. , 2004, Physical review letters.

[6]  O. Omel'chenko,et al.  Coherence–incoherence patterns in a ring of non-locally coupled phase oscillators , 2013 .

[7]  E. Halgren,et al.  Single-neuron dynamics in human focal epilepsy , 2011, Nature Neuroscience.

[8]  K. Showalter,et al.  Chimera and phase-cluster states in populations of coupled chemical oscillators , 2012, Nature Physics.

[9]  F. Mormann,et al.  Seizure prediction: Any better than chance? , 2009, Clinical Neurophysiology.

[10]  Seth A. Myers,et al.  Spontaneous synchrony in power-grid networks , 2013, Nature Physics.

[11]  C. Bick,et al.  Controlling chimeras , 2014, 1402.6363.

[12]  D. Paz'o,et al.  Low-dimensional dynamics of populations of pulse-coupled oscillators , 2013, 1305.4044.

[13]  Eckehard Schöll,et al.  Tweezers for Chimeras in Small Networks. , 2016, Physical review letters.

[14]  W. Hauser,et al.  Comment on Epileptic Seizures and Epilepsy: Definitions Proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE) , 2005, Epilepsia.

[15]  Eckehard Schöll,et al.  Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  D. Abrams,et al.  Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators , 2014, 1403.6204.

[17]  James R. Williamson,et al.  Seizure prediction using EEG spatiotemporal correlation structure , 2012, Epilepsy & Behavior.

[18]  F. Mormann,et al.  Seizure prediction for therapeutic devices: A review , 2016, Journal of Neuroscience Methods.

[19]  Yang Zheng,et al.  Epileptic seizure prediction using phase synchronization based on bivariate empirical mode decomposition , 2014, Clinical Neurophysiology.

[20]  Kenneth Showalter,et al.  Chimera States in populations of nonlocally coupled chemical oscillators. , 2013, Physical review letters.

[21]  Yann LeCun,et al.  Classification of patterns of EEG synchronization for seizure prediction , 2009, Clinical Neurophysiology.

[22]  F. Mormann,et al.  Internetwork and intranetwork communications during bursting dynamics: applications to seizure prediction. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Ralph G Andrzejak,et al.  Nonrandomness, nonlinear dependence, and nonstationarity of electroencephalographic recordings from epilepsy patients. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Andreas Schulze-Bonhage,et al.  Testing statistical significance of multivariate time series analysis techniques for epileptic seizure prediction. , 2006, Chaos.

[25]  R. Roy,et al.  Experimental observation of chimeras in coupled-map lattices , 2012, Nature Physics.

[26]  S. Schiff,et al.  Decreased Neuronal Synchronization during Experimental Seizures , 2002, The Journal of Neuroscience.

[27]  C. Elger,et al.  Epileptic Seizures and Epilepsy: Definitions Proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE) , 2005, Epilepsia.

[28]  Kaspar Anton Schindler,et al.  A Systems-Level Approach to Human Epileptic Seizures , 2012, Neuroinformatics.

[29]  Carlo R. Laing,et al.  The dynamics of chimera states in heterogeneous Kuramoto networks , 2009 .

[30]  O. Hallatschek,et al.  Chimera states in mechanical oscillator networks , 2013, Proceedings of the National Academy of Sciences.

[31]  M. T. Salam,et al.  Rapid brief feedback intracerebral stimulation based on real‐time desynchronization detection preceding seizures stops the generation of convulsive paroxysms , 2015, Epilepsia.

[32]  M. Rosenblum,et al.  Chimeralike states in an ensemble of globally coupled oscillators. , 2014, Physical review letters.

[33]  Kaspar Anton Schindler,et al.  Assessing seizure dynamics by analysing the correlation structure of multichannel intracranial EEG. , 2006, Brain : a journal of neurology.

[34]  Kaspar Anton Schindler,et al.  Synchronization and desynchronization in epilepsy: controversies and hypotheses , 2012, The Journal of physiology.

[35]  K Lehnertz,et al.  Using bivariate signal analysis to characterize the epileptic focus: the benefit of surrogates. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  J. Kurths,et al.  Heartbeat synchronized with ventilation , 1998, Nature.

[37]  Simona Olmi,et al.  Intermittent chaotic chimeras for coupled rotators. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Zi-Gang Huang,et al.  Robustness of chimera states in complex dynamical systems , 2013, Scientific Reports.

[39]  W. Singer,et al.  Abnormal neural oscillations and synchrony in schizophrenia , 2010, Nature Reviews Neuroscience.

[40]  Matthias Wolfrum,et al.  Chimera states are chaotic transients. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Matthias Wolfrum,et al.  Chimera states as chaotic spatiotemporal patterns. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Jan Sieber,et al.  Controlling unstable chaos: stabilizing chimera states by feedback. , 2014, Physical review letters.

[43]  Francesco Sorrentino,et al.  Cluster synchronization and isolated desynchronization in complex networks with symmetries , 2013, Nature Communications.

[44]  Bin He,et al.  A rule-based seizure prediction method for focal neocortical epilepsy , 2012, Clinical Neurophysiology.

[45]  Matthias Wolfrum,et al.  A tweezer for chimeras in small networks , 2015 .

[46]  Robert C. Wolpert,et al.  A Review of the , 1985 .

[47]  L. Tsimring,et al.  A synchronized quorum of genetic clocks , 2009, Nature.

[48]  C. Laing Chimeras in networks with purely local coupling. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Hemi Malkki Parkinson disease: Deep brain stimulation might alleviate parkinsonism by reducing excessive synchronization in primary motor cortex , 2015, Nature Reviews Neurology.

[50]  A. Burkitt,et al.  Patient-specific bivariate-synchrony-based seizure prediction for short prediction horizons , 2010, Epilepsy Research.

[51]  F. Mormann,et al.  Epileptic seizures are preceded by a decrease in synchronization , 2003, Epilepsy Research.

[52]  J. Martinerie,et al.  The brainweb: Phase synchronization and large-scale integration , 2001, Nature Reviews Neuroscience.

[53]  S. Strogatz,et al.  Solvable model for chimera states of coupled oscillators. , 2008, Physical review letters.