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在Greenberg-Hasting元胞自动机模型中引入了正常元胞和老化元胞，并规定只有老化元胞存在早期后除极化现象且早期后除极化可以激发其他元胞.在正常元胞和老化元胞均匀分布的情况下，研究了早期后除极化对螺旋波演化行为的影响，重点探讨了早期后除极化导致的螺旋波破碎方式.数值模拟结果表明：早期后除极化在比率约为26.4%的少数情况下不对螺旋波产生影响，在其他情况下则会对螺旋波产生各种影响，包括使螺旋波漫游、漂移、波臂发生形变以及导致螺旋波破碎和消失等.观察到早期后除极化通过传导障碍消失和通过转变为反靶波消失，早期后除极化导致螺旋波破碎有8种方式，包括非对称破缺导致的破碎、对称破缺导致的破碎、同时激发双波导致的破碎、非对称激发导致的破碎、整体传导障碍导致的破碎、整体快速破碎等.分析发现这些螺旋波破碎现象都与早期后除极化产生回火波有关，得到螺旋波破碎的总比率通常约为13.8%，但是在适当选取老化元胞密度和早期后除极化的激发下，螺旋波破碎比率可达到32.4%，这些结果与心律失常致死的统计结果基本一致，本文对产生这些现象的物理机理做了简要分析.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
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[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
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[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
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[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 物理学报 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 物理学报 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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