Early afterdepolarization (EAD) is a major arrhythmogenic factor in the long QT syndrome (LQTS), whose conditions for genesis have puzzled people for several decades. Here, we employ the phase I Luo–Rudy ventricular myocyte model to investigate EAD using methods from nonlinear dynamics and provide valuable insights into EAD genesis from a physical perspective. Two major results are obtained: (i) Sufficient parametric conditions for EAD are analytically determined and then used to analyze in detail the effects of the physiological parameters. (ii) The normal form of the Hopf bifurcation that leads to EAD is derived and then used to determine whether the Hopf bifurcation is subcritical or supercritical for EAD genesis and the corresponding amplitude and period of the EAD oscillation. Our work here paves the way for further studies of more complicated multi-scale dynamics of EAD and may lead to effective treatments for LQTS arrhythmias.

1.
2.
G.
Yan
,
Y.
Wu
,
T.
Liu
,
J.
Wang
,
R. A.
Marinchak
, and
P. R.
Kowey
,
Circulation
103
,
2851
(
2010
).
3.
M. R.
Rosen
,
Hellenic J. Cardiol.
50
(
3
),
170
(
2009
).
4.
C.
January
,
V.
Chau
, and
J.
Makielski
,
Eur. Heart J.
12
(
Suppl. F
),
4
(
1991
).
5.
D.
Sato
,
L.-H.
Xie
,
A. A.
Sovari
,
D. X.
Tran
,
N.
Morita
,
F.
Xie
,
H.
Karagueuzian
,
A.
Garfinkel
,
J. N.
Weiss
, and
Z.
Qu
,
Proc. Natl. Acad. Sci. U.S.A.
106
,
2983
(
2009
).
6.
Y.
Xie
,
D.
Sato
,
A.
Garfinkel
,
Z.
Qu
, and
J. N.
Weiss
,
Biophys. J.
99
,
1408
(
2010
).
7.
M.
Maruyama
,
S.-F.
Lin
,
Y.
Xie
,
S.-K.
Chua
,
B.
Joung
,
S.
Han
,
T.
Shinohara
,
M. J.
Shen
,
Z.
Qu
,
J. N.
Weiss
, and
P.-S.
Chen
,
Circ. Arrhythm. Electrophysiol.
4
,
103
(
2011
).
8.
X.
Huang
,
T. Y.
Kim
,
G.
Koren
,
B.-R.
Choi
, and
Z.
Qu
,
Am. J. Physiol. Heart Circ. Physiol.
311
,
H1470
(
2016
).
9.
W.
Liu
,
T. Y.
Kim
,
X.
Huang
,
M. B.
Liu
,
G.
Koren
,
B.-R.
Choi
, and
Z.
Qu
,
J. Physiol.
596
,
1341
(
2018
).
10.
M.
Rosen
,
J.
Moak
, and
B.
Damiano
,
Ann. NY Acad. Sci.
427
,
84
(
1984
).
12.
Z.
Qu
,
L.-H.
Xie
,
R.
Olcese
,
H. S.
Karagueuzian
,
P.-S.
Chen
,
A.
Garfinkel
, and
J. N.
Weiss
,
Cardiovasc. Res.
99
,
6
(
2013
).
13.
O.
Koval
,
X.
Guan
,
Y.
Wu
,
M.
Joiner
,
Z.
Gao
, and
B.
Chen
et al.,
Proc. Natl. Acad. Sci. U.S.A.
107
,
4996
(
2010
).
14.
M.
Yamada
,
K.
Ohta
,
A.
Niwa
,
N.
Tsujino
,
T.
Nakada
, and
M.
Hirose
,
J. Membr. Biol.
222
,
151
(
2008
).
15.
D. X.
Tran
,
D.
Sato
,
A.
Yochelis
,
J. N.
Weiss
,
A.
Garfinkel
, and
Z.
Qu
,
Phys. Rev. Lett.
102
,
258103
(
2009
).
16.
C.
Luo
and
Y.
Rudy
,
Circ. Res.
68
,
1501
(
1991
).
17.
M.
Chang
,
C.
Chang
,
E.
de Lange
,
L.
Xu
,
B.
O’Rourke
,
H.
Karagueuzian
,
L.
Tung
,
E.
Marban
,
A.
Garfinkel
,
J.
Weiss
,
Z.
Qu
, and
M.
Abraham
,
Biophys. J.
102
,
2706
(
2012
).
19.
X.
Huang
,
Z.
Song
, and
Z.
Qu
,
PLoS Compt. Biol.
14
,
e1006382
(
2018
).
20.
M. C.
Cross
and
P. C.
Honhenberg
,
Rev. Mod. Phys.
65
,
851
(
1993
).
21.
Y. A.
Kuznetsov
,
Elements of Applied Bifurcation Theory
, 3rd ed. (
Springer
,
2004
).
22.
S.
Guo
and
J.
Wu
,
Bifurcation Theory of Functional Differential Equations
(
Springer
,
New York
,
2013
).
23.
M. C.
Cross
,
Phys. Fluids
23
,
1727
(
1980
).
24.
D.
Yang
and
P. A.
Robinson
,
Phys. Rev. E.
95
,
042410
(
2017
).
25.
B.
Echebarria
and
A.
Karma
,
Phys. Rev. E.
76
,
051911
(
2007
).
26.
J. P.
Keener
and
J.
Sneyd
,
Mathematical Physiology
(
Springer
,
New York
,
1998
).
27.
S.
Rush
and
H.
Larsen
,
IEEE Trans. Biomed. Eng.
25
,
389
(
1978
).
28.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes in Fortran 77: The Art of Scientific Computing
, 2nd ed. (
Cambridge University Press
,
1992
).
29.
G.
Liu
,
B.-R.
Choi
,
O.
Ziv
,
W.
Li
,
E.
de Lange
,
Z.
Qu
, and
G.
Koren
,
J. Physiol.
590
,
1171
(
2012
).
30.
Y.
Xie
,
E.
Grandi
,
J. L.
Puglisi
,
D.
Sato
, and
D. M.
Bers
,
J. Mol. Cell. Cardiol.
58
,
153
(
2013
).
31.
C.
Antzelevitch
,
Eur. Heart J.
3
(
Suppl. K
),
K2
(
2001
).
32.
Z.
Qu
and
D.
Chung
,
PLoS ONE
7
(
8
),
e43587
(
2012
).
33.
D.
Wilson
,
B.
Ermentrout
,
J.
Nĕmec
, and
G.
Salama
,
Chaos
27
,
093940
(
2017
).
34.
Z.
Song
,
C. Y.
Ko
,
M.
Nivala
,
J. N.
Weiss
, and
Z.
Qu
,
Biophys. J.
108
,
1908
(
2015
).
35.
Y.
Kurata
,
K.
Tsumoto
,
K.
Hayashi
,
I.
Hisatome
,
Y.
Kuda
, and
M.
Tanida
,
Front. Physiol.
10
,
1545
(
2020
).
36.
C.-H.
Luo
and
Y.
Rudy
,
Cir. Res.
74
,
1071
(
1994
).
37.
K. H. W. J.
ten Tusscher
,
D.
Noble
,
P. J.
Noble
, and
A. V.
Panfilov
,
Am. J. Physiol.
286
(
4
),
H1573
(
2004
).
38.
T.
O’Hara
,
L.
Virág
,
A.
Varró
, and
Y.
Rudy
,
PLoS Comput. Biol.
7
(
5
),
e1002061
(
2011
).
39.
E.
Grandi
,
F. S.
Pasqualini
, and
D. M.
Bers
,
J. Mol. Cell. Cardiol.
48
,
112
(
2010
).

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