Complex dynamical systems can shift abruptly from a stable state to an alternative stable state at a tipping point. Before the critical transition, the system either slows down in its recovery rate or flickers between the basins of attraction of the alternative stable states. Whether the heart critically slows down or flickers before it transitions into and out of paroxysmal atrial fibrillation (PAF) is still an open question. To address this issue, we propose a novel definition of cardiac states based on beat-to-beat (RR) interval fluctuations derived from electrocardiogram data. Our results show the cardiac state flickers before PAF onset and termination. Prior to onset, flickering is due to a “tug-of-war” between the sinus node (the natural pacemaker) and atrial ectopic focus/foci (abnormal pacemakers), or the pacing by the latter interspersed among the pacing by the former. It may also be due to an abnormal autonomic modulation of the sinus node. This abnormal modulation may be the sole cause of flickering prior to termination since atrial ectopic beats are absent. Flickering of the cardiac state could potentially be used as part of an early warning or screening system for PAF and guide the development of new methods to prevent or terminate PAF. The method we have developed to define system states and use them to detect flickering can be adapted to study critical transition in other complex systems.

1.
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
).
2.
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
59
(
2009
).
3.
M.
Scheffer
,
S.
Carpenter
,
J. A.
Foley
,
C.
Folke
, and
B.
Walker
, “
Catastrophic shifts in ecosystems
,”
Nature
413
,
591
596
(
2001
).
4.
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
).
5.
V.
Dakos
and
J.
Bascompte
, “
Critical slowing down as early warning for the onset of collapse in mutualistic communities
,”
Proc. Natl. Acad. Sci. U.S.A.
111
,
17546
17551
(
2014
).
6.
M.
Hirota
,
M.
Holmgren
,
E. H.
Van Nes
, and
M.
Scheffer
, “
Global resilience of tropical forest and savanna to critical transitions
,”
Science
334
,
232
235
(
2011
).
7.
J. B.
Jackson
,
M. X.
Kirby
,
W. H.
Berger
,
K. A.
Bjorndal
,
L. W.
Botsford
,
B. J.
Bourque
,
R. H.
Bradbury
,
R.
Cooke
,
J.
Erlandson
,
J. A.
Estes
,
T. P.
Hughes
,
S.
Kidwell
,
C. B.
Lange
,
H. S.
Lenihan
,
J. M.
Pandolfi
,
C. H.
Peterson
,
R. S.
Steneck
,
M. J.
Tegner
, and
R. R.
Warner
, “
Historical overfishing and the recent collapse of coastal ecosystems
,”
Science
293
,
629
637
(
2001
).
8.
S.
Kefi
,
M.
Rietkerk
,
C. L.
Alados
,
Y.
Pueyo
,
V. P.
Papanastasis
,
A.
Elaich
, and
P. C.
de Ruiter
, “
Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems
,”
Nature
449
,
213
217
(
2007
).
9.
P. J.
Mumby
,
A.
Hastings
, and
H. J.
Edwards
, “
Thresholds and the resilience of Caribbean coral reefs
,”
Nature
450
,
98
101
(
2007
).
10.
T. M.
Lenton
,
H.
Held
,
E.
Kriegler
,
J. W.
Hall
,
W.
Lucht
,
S.
Rahmstorf
, and
H. J.
Schellnhuber
, “
Tipping elements in the Earth’s climate system
,”
Proc. Natl. Acad. Sci. U.S.A.
105
,
1786
1793
(
2008
).
11.
S.
Drijfhout
,
S.
Bathiany
,
C.
Beaulieu
,
V.
Brovkin
,
M.
Claussen
,
C.
Huntingford
,
M.
Scheffer
,
G.
Sgubin
, and
D.
Swingedouw
, “
Catalogue of abrupt shifts in intergovernmental panel on climate change climate models
,”
Proc. Natl. Acad. Sci. U.S.A.
112
,
E5777
E5786
(
2015
).
12.
J.
Bakke
,
Ø.
Lie
,
E.
Heegaard
,
T.
Dokken
,
G. H.
Haug
,
H. H.
Birks
,
P.
Dulski
, and
T.
Nilsen
, “
Rapid oceanic and atmospheric changes during the Younger Dryas cold period
,”
Nat. Geosci.
2
,
202
205
(
2009
).
13.
R. M.
May
,
S. A.
Levin
, and
G.
Sugihara
, “
Complex systems: Ecology for bankers
,”
Nature
451
,
893
895
(
2008
).
14.
A. G.
Haldane
and
R. M.
May
, “
Systemic risk in banking ecosystems
,”
Nature
469
,
351
355
(
2011
).
15.
J. G.
Venegas
,
T.
Winkler
,
G.
Musch
,
M. F.
Vidal Melo
,
D.
Layfield
,
N.
Tgavalekos
,
A. J.
Fischman
,
R. J.
Callahan
,
G.
Bellani
, and
R. S.
Harris
, “
Self-organized patchiness in asthma as a prelude to catastrophic shifts
,”
Nature
434
,
777
782
(
2005
).
16.
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
,
C.
Derom
,
N.
Jacobs
,
K. S.
Kendler
,
H. L.
van der Maas
,
M. C.
Neale
,
F.
Peeters
,
E.
Thiery
,
P.
Zachar
, and
M.
Scheffer
, “
Critical slowing down as early warning for the onset and termination of depression
,”
Proc. Natl. Acad. Sci. U.S.A.
111
,
87
92
(
2014
).
17.
T.
Zeng
,
C. C.
Zhang
,
W.
Zhang
,
R.
Liu
,
J.
Liu
, and
L.
Chen
, “
Deciphering early development of complex diseases by progressive module network
,”
Methods
67
,
334
343
(
2014
).
18.
M.
Li
,
T.
Zeng
,
R.
Liu
, and
L.
Chen
, “
Detecting tissue-specific early warning signals for complex diseases based on dynamical network biomarkers: Study of type 2 diabetes by cross-tissue analysis
,”
Briefings Bioinf.
15
,
229
243
(
2014
).
19.
B.
Litt
,
R.
Esteller
,
J.
Echauz
,
M.
D’Alessandro
,
R.
Shor
,
T.
Henry
,
P.
Pennell
,
C.
Epstein
,
R.
Bakay
,
M.
Dichter
, and
G.
Vachtsevanos
, “
Epileptic seizures may begin hours in advance of clinical onset: A report of five patients
,”
Neuron
30
,
51
64
(
2001
).
20.
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
,
C. J.
Chu
, and
S. S.
Cash
, “
Human seizures self-terminate across spatial scales via a critical transition
,”
Proc. Natl. Acad. Sci. U.S.A.
109
,
21116
21121
(
2012
).
21.
P. E.
McSharry
,
L. A.
Smith
, and
L.
Tarassenko
, “
Prediction of epileptic seizures: Are nonlinear methods relevant?
,”
Nat. Med.
9
,
241
242
(
2003
).
22.
C.
Trefois
,
P. M.
Antony
,
J.
Goncalves
,
A.
Skupin
, and
R.
Balling
, “
Critical transitions in chronic disease: Transferring concepts from ecology to systems medicine
,”
Curr. Opin. Biotechnol.
34
,
48
55
(
2015
).
23.
M. G.
Olde Rikkert
,
V.
Dakos
,
T. G.
Buchman
,
R.
Boer
,
L.
Glass
,
A. O.
Cramer
,
S.
Levin
,
E.
van Nes
,
G.
Sugihara
,
M. D.
Ferrari
,
E. A.
Tolner
,
I.
van de Leemput
,
J.
Lagro
,
R.
Melis
, and
M.
Scheffer
, “
Slowing down of recovery as generic risk marker for acute severity transitions in chronic diseases
,”
Crit. Care Med.
44
,
601
606
(
2016
).
24.
J. C.
Foo
,
H. R.
Noori
,
I.
Yamaguchi
,
V.
Vengeliene
,
A.
Cosa-Linan
,
T.
Nakamura
,
K.
Morita
,
R.
Spanagel
, and
Y.
Yamamoto
, “
Dynamical state transitions into addictive behaviour and their early-warning signals
,”
Proc. R. Soc. B Biol. Sci.
284
,
pii: 20170882
(
2017
).
25.
L.
Lahti
,
J.
Salojarvi
,
A.
Salonen
,
M.
Scheffer
, and
W. M.
de Vos
, “
Tipping elements in the human intestinal ecosystem
,”
Nat. Commun.
5
,
4344
(
2014
).
26.
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
).
27.
E. H.
van Nes
and
M.
Scheffer
, “
Slow recovery from perturbations as a generic indicator of a nearby catastrophic shift
,”
Am. Nat.
169
,
738
747
(
2007
).
28.
A. J.
Veraart
,
E. J.
Faassen
,
V.
Dakos
,
E. H.
van Nes
,
M.
Lurling
, and
M.
Scheffer
, “
Recovery rates reflect distance to a tipping point in a living system
,”
Nature
481
,
357
359
(
2011
).
29.
W.
Horsthemke
and
R.
Lefever
,
Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology
(
Springer
,
1984
).
30.
R.
Wang
,
J. A.
Dearing
,
P. G.
Langdon
,
E.
Zhang
,
X.
Yang
,
V.
Dakos
, and
M.
Scheffer
, “
Flickering gives early warning signals of a critical transition to a eutrophic lake state
,”
Nature
492
,
419
422
(
2012
).
31.
V.
Dakos
,
S. R.
Carpenter
,
W. A.
Brock
,
A. M.
Ellison
,
V.
Guttal
,
A. R.
Ives
,
S.
Kefi
,
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
).
32.
M.
Scheffer
,
Critical Transitions in Nature and Society
(
Princeton University Press
,
2009
).
33.
S. R.
Carpenter
and
W. A.
Brock
, “
Rising variance: A leading indicator of ecological transition
,”
Ecol. Lett.
9
,
311
318
(
2006
).
34.
S. R.
Carpenter
,
W. A.
Brock
,
J. J.
Cole
,
J. F.
Kitchell
, and
M. L.
Pace
, “
Leading indicators of trophic cascades
,”
Ecol. Lett.
11
,
128
138
(
2008
).
35.
P. U.
Clark
,
N. G.
Pisias
,
T. F.
Stocker
, and
A. J.
Weaver
, “
The role of the thermohaline circulation in abrupt climate change
,”
Nature
415
,
863
869
(
2002
).
36.
W. C.
Chang
,
J.
Kudlacek
,
J.
Hlinka
,
J.
Chvojka
,
M.
Hadrava
,
V.
Kumpost
,
A. D.
Powell
,
R.
Janca
,
M. I.
Maturana
,
P. J.
Karoly
,
D. R.
Freestone
,
M. J.
Cook
,
M.
Palus
,
J.
Otahal
,
J. G. R.
Jefferys
, and
P.
Jiruska
, “
Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations
,”
Nat. Neurosci.
21
,
1742
1752
(
2018
).
37.
T.
Wilkat
,
T.
Rings
, and
K.
Lehnertz
, “
No evidence for critical slowing down prior to human epileptic seizures
,”
Chaos
29,
091104
(
2019
).
38.
National Heart, Lung, and Blood Institute, see http://www.nhlbi.nih.gov/health-topics/arrhythmia for “Arrhythmia.”
39.
V.
Markides
and
R. J.
Schilling
, “
Atrial fibrillation: Classification, pathophysiology, mechanisms and drug treatment
,”
Heart
89
,
939
943
(
2003
).
40.
L.
Glass
, “
Dynamical disease: Challenges for nonlinear dynamics and medicine
,”
Chaos
25
,
097603
(
2015
).
41.
J. N.
Weiss
,
M.
Nivala
,
A.
Garfinkel
, and
Z.
Qu
, “
Alternans and arrhythmias: From cell to heart
,”
Circ. Res.
108
,
98
112
(
2011
).
42.
M. C.
Mackey
and
J. G.
Milton
, “
Dynamical diseases
,”
Ann. N. Y. Acad. Sci.
504
,
16
32
(
1987
).
43.
L.
Glass
and
M. C.
Mackey
, “
Pathological conditions resulting from instabilities in physiological control systems
,”
Ann. N. Y. Acad. Sci.
316
,
214
235
(
1979
).
44.
M. C.
Mackey
and
L.
Glass
, “
Oscillation and chaos in physiological control systems
,”
Science
197
,
287
289
(
1977
).
45.
A.
Garfinkel
,
P. S.
Chen
,
D. O.
Walter
,
H. S.
Karagueuzian
,
B.
Kogan
,
S. J.
Evans
,
M.
Karpoukhin
,
C.
Hwang
,
T.
Uchida
,
M.
Gotoh
,
O.
Nwasokwa
,
P.
Sager
, and
J. N.
Weiss
, “
Quasiperiodicity and chaos in cardiac fibrillation
,”
J. Clin. Invest.
99
,
305
314
(
1997
).
46.
H. S.
Karagueuzian
,
H.
Stepanyan
, and
W. J.
Mandel
, “
Bifurcation theory and cardiac arrhythmias
,”
Am. J. Cardiovasc. Dis.
3
,
1
16
(
2013
).
47.
T.
Quail
,
A.
Shrier
, and
L.
Glass
, “
Predicting the onset of period-doubling bifurcations in noisy cardiac systems
,”
Proc. Natl. Acad. Sci. U.S.A.
112
,
9358
9363
(
2015
).
48.
B. L.
Lan
and
M.
Toda
, “
Fluctuations of healthy and unhealthy heartbeat intervals
,”
Europhys. Lett.
102
,
18002
(
2013
).
49.
G. E. P.
Box
,
G. M.
Jenkins
, and
G. C.
Geinsel
,
Time Series Analysis Forecasting and Control
(
Wiley
,
2008
).
50.
A. L.
Goldberger
,
L. A.
Amaral
,
L.
Glass
,
J. M.
Hausdorff
,
P. C.
Ivanov
,
R. G.
Mark
,
J. E.
Mietus
,
G. B.
Moody
,
C. K.
Peng
, and
H. E.
Stanley
, “
Physiobank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals
,”
Circulation
101
,
E215
220
(
2000
).
51.
See https://physionet.org/ for “PhysioNet.”
52.
S.
Petrutiu
,
A. V.
Sahakian
, and
S.
Swiryn
, “
Abrupt changes in fibrillatory wave characteristics at the termination of paroxysmal atrial fibrillation in humans
,”
Europace
9
,
466
470
(
2007
).
54.
M.
Haissaguerre
,
P.
Jais
,
D. C.
Shah
,
A.
Takahashi
,
M.
Hocini
,
G.
Quiniou
,
S.
Garrigue
,
A.
Le Mouroux
,
P.
Le Metayer
, and
J.
Clementy
, “
Spontaneous initiation of atrial fibrillation by ectopic beats originating in the pulmonary veins
,”
N. Engl. J. Med.
339
,
659
666
(
1998
).
55.
R. F. G.
Simpson
,
J.
Langtree
, and
A. R. J.
Mitchell
, “
Ectopic beats: How many count?
,”
Eur. Med. J. Cardiol.
5
,
88
92
(
2017
).
56.
J. E.
Waktare
,
K.
Hnatkova
,
S. M.
Sopher
,
F. D.
Murgatroyd
,
X.
Guo
,
A. J.
Camm
, and
M.
Malik
, “
The role of atrial ectopics in initiating paroxysmal atrial fibrillation
,”
Eur. Heart J.
22
,
333
339
(
2001
).
57.
M. D.
Costa
,
R. B.
Davis
, and
A. L.
Goldberger
, “
Heart rate fragmentation: A new approach to the analysis of cardiac interbeat interval dynamics
,”
Front. Physiol.
8
,
255
(
2017
).
58.
F.
Lombardi
,
D.
Tarricone
,
F.
Tundo
,
F.
Colombo
,
S.
Belletti
, and
C.
Fiorentini
, “
Autonomic nervous system and paroxysmal atrial fibrillation: A study based on the analysis of RR interval changes before, during and after paroxysmal atrial fibrillation
,”
Eur. Heart J.
25
,
1242
1248
(
2004
).
59.
M. J.
Shen
and
D. P.
Zipes
, “
Role of the autonomic nervous system in modulating cardiac arrhythmias
,”
Circ. Res.
114
,
1004
1021
(
2014
).
60.
M. P.
Turakhia
,
M.
Desai
,
H.
Hedlin
,
A.
Rajmane
,
N.
Talati
,
T.
Ferris
,
S.
Desai
,
D.
Nag
,
M.
Patel
,
P.
Kowey
,
J. S.
Rumsfeld
,
A. M.
Russo
,
M. T.
Hills
,
C. B.
Granger
,
K. W.
Mahaffey
, and
M. V.
Perez
, “
Rationale and design of a large-scale, app-based study to identify cardiac arrhythmias using a smartwatch: The apple heart study
,”
Am. Heart J.
207
,
66
75
(
2019
).

Supplementary Material

You do not currently have access to this content.