There is an ongoing debate whether generic early warning signals for critical transitions exist that can be applied across diverse systems. The human epileptic brain is often considered as a prototypical system, given the devastating and, at times, even life-threatening nature of the extreme event epileptic seizure. More than three decades of international effort has successfully identified predictors of imminent seizures. However, the suitability of typically applied early warning indicators for critical slowing down, namely, variance and lag-1 autocorrelation, for indexing seizure susceptibility is still controversially discussed. Here, we investigated long-term, multichannel recordings of brain dynamics from 28 subjects with epilepsy. Using a surrogate-based evaluation procedure of sensitivity and specificity of time-resolved estimates of early warning indicators, we found no evidence for critical slowing down prior to 105 epileptic seizures.
REFERENCES
1.
V. I.
Arnold
, V. S.
Afrajmovich
, Y. S.
Il’yashenko
, and L. P.
Shil’nikov
, Dynamical Systems V: Bifurcation Theory and Catastrophe Theory
(Springer Science & Business Media
, 2013
).2.
J. M. T.
Thompson
, H. B.
Stewart
, and Y.
Ueda
, “Safe, explosive, and dangerous bifurcations in dissipative dynamical systems
,” Phys. Rev. E
49
, 1019
(1994
). 3.
V.
Dakos
, M.
Scheffer
, E. H.
van Nes
, V.
Brovkin
, V.
Petoukhov
, and H.
Held
, “Slowing down as an early warning signal for abrupt climate change
,” Proc. Natl. Acad. Sci. U.S.A.
105
, 14308
–14312
(2008
). 4.
M.
Scheffer
, J.
Bascompte
, W. A.
Brock
, V.
Brovkin
, S. R.
Carpenter
, V.
Dakos
, H.
Held
, E. H.
Van Nes
, M.
Rietkerk
, and G.
Sugihara
, “Early-warning signals for critical transitions
,” Nature
461
, 53
(2009
). 5.
C.
Kuehn
, “A mathematical framework for critical transitions: Bifurcations, fast-slow systems and stochastic dynamics
,” Physica D
240
, 1020
–1035
(2011
). 6.
T.
Lenton
, V.
Livina
, V.
Dakos
, E.
Van Nes
, and M.
Scheffer
, “Early warning of climate tipping points from critical slowing down: Comparing methods to improve robustness
,” Philos. Trans. A Math. Phys. Eng. Sci.
370
, 1185
–1204
(2012
). 7.
J.
Sieber
and J. M. T.
Thompson
, “Nonlinear softening as a predictive precursor to climate tipping
,” Philos. Trans. A Math. Phys. Eng. Sci.
370
, 1205
–1227
(2012
). 8.
M.
Scheffer
, S. R.
Carpenter
, T. M.
Lenton
, J.
Bascompte
, W.
Brock
, V.
Dakos
, J.
van de Koppel
, I. A.
van de Leemput
, S. A.
Levin
, E. H.
van Nes
, M.
Pascual
, and J.
Vandermeer
, “Anticipating critical transitions
,” Science
338
, 344
–348
(2012
). 9.
L.
Dai
, D.
Vorselen
, K. S.
Korolev
, and J.
Gore
, “Generic indicators for loss of resilience before a tipping point leading to population collapse
,” Science
336
, 1175
–1177
(2012
). 10.
U.
Feudel
, A. N.
Pisarchik
, and K.
Showalter
, “Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue
,” Chaos
28
, 033501
(2018
). 11.
B.
Kaszás
, U.
Feudel
, and T.
Tél
, “Tipping phenomena in typical dynamical systems subjected to parameter drift
,” Sci. Rep.
9
, 8654
(2019
). 12.
V.
Dakos
, S. R.
Carpenter
, W. A.
Brock
, A. M.
Ellison
, V.
Guttal
, A. R.
Ives
, S.
Kéfi
, V.
Livina
, D. A.
Seekell
, E. H.
van Nes
, and M.
Scheffer
, “Methods for detecting early warnings of critical transitions in time series illustrated using simulated ecological data
,” PLoS One
7
, e41010
(2012
). 13.
R.
Kubo
, “The fluctuation-dissipation theorem
,” Rep. Prog. Phys.
29
, 255
(1966
). 14.
P. D.
Ditlevsen
and S. J.
Johnsen
, “Tipping points: Early warning and wishful thinking
,” Geophys. Res. Lett.
37
, L19703
, (2010
). 15.
C.
Boettiger
and A.
Hastings
, “Early warning signals and the prosecutor’s fallacy
,” Proc. R. Soc. B Biol. Sci.
279
, 4734
–4739
(2012
). 16.
C.
Boettiger
, N.
Ross
, and A.
Hastings
, “Early warning signals: The charted and uncharted territories
,” Theor. Ecol.
6
, 255
–264
(2013
). 17.
C.
Boettiger
and A.
Hastings
, “No early warning signals for stochastic transitions: Insights from large deviation theory
,” Proc. R. Soc. B Biol. Sci.
280
, 20131372
(2013
). 18.
V.
Guttal
, C.
Jayaprakash
, and O. P.
Tabbaa
, “Robustness of early warning signals of regime shifts in time-delayed ecological models
,” Theor. Ecol.
6
, 271
–283
(2013
). 19.
V.
Dakos
, S. R.
Carpenter
, E. H.
van Nes
, and M.
Scheffer
, “Resilience indicators: Prospects and limitations for early warnings of regime shifts
,” Philos. Trans. R. Soc. B Biol. Sci.
370
, 20130263
(2015
). 20.
L.
Dai
, K. S.
Korolev
, and J.
Gore
, “Relation between stability and resilience determines the performance of early warning signals under different environmental drivers
,” Proc. Natl. Acad. Sci. U.S.A.
112
, 10056
–10061
(2015
). 21.
C.
Diks
, C.
Hommes
, and J.
Wang
, “Critical slowing down as an early warning signal for financial crises?
,” Empir. Econ.
(published online
2015
). 22.
T. J.
Wagner
and I.
Eisenman
, “False alarms: How early warning signals falsely predict abrupt sea ice loss
,” Geophys. Res. Lett.
42
, 10333
, (2015
). 23.
X.
Zhang
, C.
Kuehn
, and S.
Hallerberg
, “Predictability of critical transitions
,” Phys. Rev. E
92
, 052905
(2015
). 24.
P.
Milanowski
and P.
Suffczynski
, “Seizures start without common signatures of critical transition
,” Int. J. Neural Syst.
26
, 1650053
(2016
). 25.
S.
Qin
and C.
Tang
, “Early-warning signals of critical transition: Effect of extrinsic noise
,” Phys. Rev. E
97
, 032406
(2018
). 26.
S. M.
O’Regan
and D. L.
Burton
, “How stochasticity influences leading indicators of critical transitions
,” Bull. Math. Biol.
80
, 1630
–1654
(2018
). 27.
F.
Romano
and C.
Kuehn
, “Analysis and predictability of tipping points with leading-order nonlinear term
,” Int. J. Bifurcat. Chaos
28
, 1850103
(2018
). 28.
H.
Wen
, M. P.
Ciamarra
, and S. A.
Cheong
, “How one might miss early warning signals of critical transitions in time series data: A systematic study of two major currency pairs
,” PLoS One
13
, e0191439
(2018
). 29.
C. F.
Clements
, M. A.
McCarthy
, and J. L.
Blanchard
, “Early warning signals of recovery in complex systems
,” Nat. Commun.
10
, 1681
(2019
). 30.
G.
Jäger
and M.
Füllsack
, “Systematically false positives in early warning signal analysis
,” PLoS One
14
, e0211072
(2019
). 31.
M. A.
Kramer
, W.
Truccolo
, U. T.
Eden
, K. Q.
Lepage
, L. R.
Hochberg
, E. N.
Eskandar
, J. R.
Madsen
, J. W.
Lee
, A.
Maheshwari
, E.
Halgren
et al., “Human seizures self-terminate across spatial scales via a critical transition
,” Proc. Natl. Acad. Sci. U.S.A.
109
, 21116
–21121
(2012
). 32.
C.
Meisel
and C.
Kuehn
, “Scaling effects and spatio-temporal multilevel dynamics in epileptic seizures
,” PLoS One
7
, e30371
(2012
). 33.
I. A.
van de Leemput
, M.
Wichers
, A. O.
Cramer
, D.
Borsboom
, F.
Tuerlinckx
, P.
Kuppens
, E. H.
van Nes
, W.
Viechtbauer
, E. J.
Giltay
, S. H.
Aggen
et al., “Critical slowing down as early warning for the onset and termination of depression
,” Proc. Natl. Acad. Sci. U.S.A.
111
, 87
–92
(2014
). 34.
C.
Meisel
, A.
Klaus
, C.
Kuehn
, and D.
Plenz
, “Critical slowing down governs the transition to neuron spiking
,” PLoS Comput. Biol.
11
, e1004097
(2015
). 35.
A.
Bayani
, F.
Hadaeghi
, S.
Jafari
, and G.
Murray
, “Critical slowing down as an early warning of transitions in episodes of bipolar disorder: A simulation study based on a computational model of circadian activity rhythms
,” Chronobiol. Int.
34
, 235
–245
(2017
). 36.
M.
Scheffer
, J. E.
Bolhuis
, D.
Borsboom
, T. G.
Buchman
, S. M.
Gijzel
, D.
Goulson
, J. E.
Kammenga
, B.
Kemp
, I. A.
van de Leemput
, S.
Levin
, C. M.
Martin
, R. J. F.
Melis
, E. H.
van Nes
, L. M.
Romero
, and M. G. M.
Olde Rikkert
, “Quantifying resilience of humans and other animals
,” Proc. Natl. Acad. Sci. U.S.A.
115
, 11883
–11890
(2018
). 37.
D. R.
Freestone
, P. J.
Karoly
, and M. J.
Cook
, “A forward-looking review of seizure prediction
,” Curr. Opin. Neurol.
30
, 167
–173
(2017
). 38.
F.
Nazarimehr
, S. M. R. H.
Golpayegani
, and B.
Hatef
, “Does the onset of epileptic seizure start from a bifurcation point?
,” Eur. Phys. J. ST
227
, 697
–705
(2018
). 39.
F.
Mormann
, T.
Kreuz
, C.
Rieke
, R. G.
Andrzejak
, A.
Kraskov
, P.
David
, C. E.
Elger
, and K.
Lehnertz
, “On the predictability of epileptic seizures
,” Clin. Neurophysiol.
116
, 569
–587
(2005
). 40.
F.
Mormann
, R.
Andrzejak
, C. E.
Elger
, and K.
Lehnertz
, “Seizure prediction: The long and winding road
,” Brain
130
, 314
–333
(2007
). 41.
L.
Kuhlmann
, K.
Lehnertz
, M. P.
Richardson
, B.
Schelter
, and H. P.
Zaveri
, “Seizure prediction—Ready for a new era
,” Nat. Rev. Neurol.
14
, 618
–630
(2018
). 42.
H.
Dickten
, S.
Porz
, C. E.
Elger
, and K.
Lehnertz
, “Weighted and directed interactions in evolving large-scale epileptic brain networks
,” Sci. Rep.
6
, 34824
(2016
). 43.
K.
Lehnertz
, H.
Dickten
, S.
Porz
, C.
Helmstaedter
, and C. E.
Elger
, “Predictability of uncontrollable multifocal seizures—Towards new treatment options
,” Sci. Rep.
6
, 24584
(2016
). 44.
T.
Rings
, M.
Mazarei
, A.
Akhshi
, C.
Geier
, M. R. R.
Tabar
, and K.
Lehnertz
, “Traceability and dynamical resistance of precursor of extreme events
,” Sci. Rep.
9
, 1744
(2019
). 45.
T.
Rings
, R.
von Wrede
, and K.
Lehnertz
, “Precursors of seizures due to specific spatial-temporal modifications of evolving large-scale epileptic brain networks
,” Sci. Rep.
9
, 10623
(2019
). 46.
K.
Lehnertz
, C.
Geier
, T.
Rings
, and K.
Stahn
, “Capturing time-varying brain dynamics
,” EPJ Nonlin. Biomed. Phys.
5
, 2
(2017
). 47.
48.
N. K.
So
and W. T.
Blume
, “The postictal EEG
,” Epilepsy Behav.
19
, 121
–126
(2010
). 49.
R. G.
Andrzejak
, F.
Mormann
, T.
Kreuz
, C.
Rieke
, A.
Kraskov
, C. E.
Elger
, and K.
Lehnertz
, “Testing the null hypothesis of the nonexistence of a preseizure state
,” Phys. Rev. E
67
, 010901(R)
(2003
). 50.
W. H.
Press
and G. B.
Rybicki
, “Fast algorithm for spectral analysis of unevenly sampled data
,” Astrophys. J.
338
, 277
–280
(1989
). 51.
D. A.
Steyn-Ross
, M. L.
Steyn-Ross
, J. W.
Sleigh
, M. T.
Wilson
, I.-P.
Gillies
, and J. J.
Wright
, “The sleep cycle modelled as a cortical phase transition
,” J. Biol. Phys.
31
, 547
–569
(2005
). 52.
D.-P.
Yang
, L.
McKenzie-Sell
, A.
Karanjai
, and P. A.
Robinson
, “Wake-sleep transition as a noisy bifurcation
,” Phys. Rev. E
94
, 022412
(2016
). 53.
J.
Stevens
, H.
Kodama
, B.
Lonsbury
, and L.
Mills
, “Ultradian characteristics of spontaneous seizures discharges recorded by radio telemetry in man
,” Electroencephalogr. Clin. Neurophysiol.
31
, 313
–325
(1971
). 54.
P. J.
Karoly
, D. R.
Freestone
, R.
Boston
, D. B.
Grayden
, D.
Himes
, K.
Leyde
, U.
Seneviratne
, S.
Berkovic
, T.
O’Brien
, and M. J.
Cook
, “Interictal spikes and epileptic seizures: Their relationship and underlying rhythmicity
,” Brain
139
, 1066
–1078
(2016
). 55.
M. O.
Baud
, J. K.
Kleen
, E. A.
Mirro
, J. C.
Andrechak
, D.
King-Stephens
, E. F.
Chang
, and V. R.
Rao
, “Multi-day rhythms modulate seizure risk in epilepsy
,” Nat. Commun.
9
, 88
(2018
). 56.
P. J.
Karoly
, D. M.
Goldenholz
, D. R.
Freestone
, R. E.
Moss
, D. B.
Grayden
, W. H.
Theodore
, and M. J.
Cook
, “Circadian and circaseptan rhythms in human epilepsy: A retrospective cohort study
,” Lancet Neurol.
17
, 977
–985
(2018
). 57.
S.
Takagi
, “Sleep and epilepsy
,” Sleep Biol. Rhythms
15
, 189
–196
(2017
). 58.
S.
Khan
, L.
Nobili
, R.
Khatami
, T.
Loddenkemper
, C.
Cajochen
, D.-J.
Dijk
, and S. H.
Eriksson
, “Circadian rhythm and epilepsy
,” Lancet Neurol.
17
, 1098
–1108
(2018
). 59.
K.
Lehnertz
, G.
Ansmann
, S.
Bialonski
, H.
Dickten
, C.
Geier
, and S.
Porz
, “Evolving networks in the human epileptic brain
,” Physica D
267
, 7
–15
(2014
). 60.
C.
Geier
, S.
Bialonski
, C. E.
Elger
, and K.
Lehnertz
, “How important is the seizure onset zone for seizure dynamics?
,” Seizure
25
, 160
–166
(2015
). 61.
D. D.
Spencer
, J. L.
Gerrard
, and H. P.
Zaveri
, “The roles of surgery and technology in understanding focal epilepsy and its comorbidities
,” Lancet Neurol.
17
, 373
–382
(2018
). 62.
P.
Ashwin
, S.
Wieczorek
, R.
Vitolo
, and P.
Cox
, “Tipping points in open systems: Bifurcation, noise-induced and rate-dependent examples in the climate system
,” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
370
, 1166
–1184
(2012
). 63.
P.
Ritchie
and J.
Sieber
, “Early-warning indicators for rate-induced tipping
,” Chaos
26
, 093116
(2016
). 64.
P.
Ritchie
and J.
Sieber
, “Probability of noise- and rate-induced tipping
,” Phys. Rev. E
95
, 052209
(2017
). 65.
P. E.
McSharry
, L. A.
Smith
, and L.
Tarassenko
, “Prediction of epileptic seizures: Are nonlinear methods relevant?
,” Nat. Med.
9
, 241
(2003
). © 2019 Author(s).
2019
Author(s)
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