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Early afterdepolarization (EAD) is an important cause of lethal ventricular arrhythmias in heart failure because afterdepolarizations can promote the transition from ventricular tachycardia to fibrillation, which is related to the transition from spiral wave to spatiotemporal chaos. However, it remains unclear about how the EAD results in the breakup of spiral wave. In this paper, we explore the manner of spiral wave breakup induced by EADs under evenly distributed cells. The two-dimensional tissue is simulated with the Greenberg-Hasting cellular automaton model. The normal cells and aging cells are introduced into the model, in which the EAD only occurs in aging cells and can excite the resting cells. The numerical results show that the EAD can produce backward waves as well as forward waves. The EAD has no influence on the behavior of spiral wave in a few cases. The ratio of the number of unaffected spiral waves to the number of all tests is about 26.4%. The EAD can have various effects on spiral wave in other cases. The small influences on spiral wave are that the EAD leads to the meander, drift, and the deformation of spiral wave. The serious influences on spiral wave are that the EAD results in the disappearance and breakup of spiral wave. We find that spiral wave can disappear through the conduction block and transition from spiral wave to target wave. We observe the eight kinds of spiral wave breakups in connection with the excitation of EADs, such as symmetry breaking-induced breakup, nonsymmetry breaking-induced breakup, asymmetric excitation-induced breakup, conduction block-induced breakup, double wave-induced breakup, etc. Spiral wave generally breaks up into multiple spiral waves and spatiotemporal chaos. The ratio of the number of spiral wave breakup to the number of all tests is about 13.8%. However, the ratio of spiral wave breakup can reach about 32.4% under appropriately chosen parameters. The results are basically consistent with the survey results of arrhythmia-induced death rate. Furthermore, we also find that the excitation of EAD can prevent the spiral wave from disappearing and promote the breakup of spiral wave. The physical mechanisms underlying those phenomena are also briefly analyzed.
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Keywords:
- early afterdepolarization /
- spiral wave /
- cellular automaton model
[1] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2] Lee K J, Cox E C, Goldstein R E 1996 Phys. Rev. Lett. 76 1174
[3] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[4] Huang X, Xu W, Liang J, Takagaki K, Gao X, Wu J 2010 Neuron 68 978
[5] Plapp B B, Egolf D A, Bodenschatz E, Pesch W 1998 Phys. Rev. Lett. 81 5334
[6] Larionova Y, Egorov O, Cabrera-Granado E, Esteban-Martin A 2005 Phys. Rev. A 72 033825
[7] Mller S C, Plesser T, Hess B 1985 Science 230 661
[8] Liu G Q, Ying H P, Luo H L, Liu X X, Yang J H 2016 Int. J. Bifurcat. Chaos 26 1650236
[9] Chen J X, Guo M M, Ma J 2016 EPL 113 38004
[10] Chen J X, Zhang H, Qiao L Y, Liang H, Sun W G 2018 Commun. Nonlinear Sci. Numer. Simulat. 54 202
[11] Fenton F H, Cherry E M, Hastings H M, Evans S J 2002 Chaos 12 852
[12] Ashihara T, Yao T, Namba T, Kawase A, Ikeda T, Nakazawa K, Ito M 2002 Circ. J. 66 505
[13] Wei H M, Tang G N 2011 Acta Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 60 030501]
[14] Weiss J N, Garfinkel A, Karagueuzian H S, Chen P S, Qu Z L 2010 Heart Rhythm. 7 1891
[15] Zimik S, Vandersickel N, Nayak A R, Panfilov A V, Pandit R 2015 PLoS ONE 10 e0130632
[16] Vandersickel N, Kazbanov I V, Nuitermans A, Weise L D, Pandit R, Panfilov A V 2014 PLoS ONE 9 e84595
[17] Wang X Y, Wang P, Tang G N 2017 Acta Phys. Sin. 66 068201 (in Chinese) [王小艳, 汪芃, 唐国宁 2017 66 068201]
[18] Vandersickel N, Nieuwenhuyse E V, Seemann G, Panfilov A V 2017 Front Physiol. 8 404
[19] Dutta S, Mincholé A, Zacur E, Quinn T A, Taggart P, Rodriguez B 2016 Prog. Biophys. Mol. Biol. 120 236
[20] Greenberg J M, Hastings S P 1978 SIAM J. Appl. Math. 34 515
[21] Yan G X, Rials S J, Wu Y, Liu T X, Xu X P, Marinchak R A, Kowey P R 2001 Am. J. Physiol. Heart Circ. Physiol. 281 H1968
[22] Duff H J, Mitchell L B, Gillis A M, Sheldon R S, Chudleigh L, Cassidy P, Chiamvimonvat N, Wyse D C 1993 Circulation 88 1056
[23] Andreoli A, Di P G, Pinelli G, Grazi P, Tognetti F, Testa C 1987 Stroke 18 558
[24] Reinelt P, Karth G D, Geppert A, Heinz G 2001 Intensive Care Med. 27 1466
[25] Huikuri H V, Gastellanos A, Myerburg R J 2001 N. Engl. J. Med. 345 1473
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[1] Cross M C, Hohenberg P C 1993 Rev. Mod. Phys. 65 851
[2] Lee K J, Cox E C, Goldstein R E 1996 Phys. Rev. Lett. 76 1174
[3] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[4] Huang X, Xu W, Liang J, Takagaki K, Gao X, Wu J 2010 Neuron 68 978
[5] Plapp B B, Egolf D A, Bodenschatz E, Pesch W 1998 Phys. Rev. Lett. 81 5334
[6] Larionova Y, Egorov O, Cabrera-Granado E, Esteban-Martin A 2005 Phys. Rev. A 72 033825
[7] Mller S C, Plesser T, Hess B 1985 Science 230 661
[8] Liu G Q, Ying H P, Luo H L, Liu X X, Yang J H 2016 Int. J. Bifurcat. Chaos 26 1650236
[9] Chen J X, Guo M M, Ma J 2016 EPL 113 38004
[10] Chen J X, Zhang H, Qiao L Y, Liang H, Sun W G 2018 Commun. Nonlinear Sci. Numer. Simulat. 54 202
[11] Fenton F H, Cherry E M, Hastings H M, Evans S J 2002 Chaos 12 852
[12] Ashihara T, Yao T, Namba T, Kawase A, Ikeda T, Nakazawa K, Ito M 2002 Circ. J. 66 505
[13] Wei H M, Tang G N 2011 Acta Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 60 030501]
[14] Weiss J N, Garfinkel A, Karagueuzian H S, Chen P S, Qu Z L 2010 Heart Rhythm. 7 1891
[15] Zimik S, Vandersickel N, Nayak A R, Panfilov A V, Pandit R 2015 PLoS ONE 10 e0130632
[16] Vandersickel N, Kazbanov I V, Nuitermans A, Weise L D, Pandit R, Panfilov A V 2014 PLoS ONE 9 e84595
[17] Wang X Y, Wang P, Tang G N 2017 Acta Phys. Sin. 66 068201 (in Chinese) [王小艳, 汪芃, 唐国宁 2017 66 068201]
[18] Vandersickel N, Nieuwenhuyse E V, Seemann G, Panfilov A V 2017 Front Physiol. 8 404
[19] Dutta S, Mincholé A, Zacur E, Quinn T A, Taggart P, Rodriguez B 2016 Prog. Biophys. Mol. Biol. 120 236
[20] Greenberg J M, Hastings S P 1978 SIAM J. Appl. Math. 34 515
[21] Yan G X, Rials S J, Wu Y, Liu T X, Xu X P, Marinchak R A, Kowey P R 2001 Am. J. Physiol. Heart Circ. Physiol. 281 H1968
[22] Duff H J, Mitchell L B, Gillis A M, Sheldon R S, Chudleigh L, Cassidy P, Chiamvimonvat N, Wyse D C 1993 Circulation 88 1056
[23] Andreoli A, Di P G, Pinelli G, Grazi P, Tognetti F, Testa C 1987 Stroke 18 558
[24] Reinelt P, Karth G D, Geppert A, Heinz G 2001 Intensive Care Med. 27 1466
[25] Huikuri H V, Gastellanos A, Myerburg R J 2001 N. Engl. J. Med. 345 1473
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