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In this paper, the effects of the aging and systole of heart on the dynamics of spiral wave are studied by using the Greenberg-Hasting cellular automaton model. In this model the neighbor radius and the excitation threshold are increased in order to simulate the aging of heart, and the neighbor radius is changed alternately to simulate heart systole and diastole. The results show that the aging of heart can induce some influences on spiral wave, such as make spiral wave meandering, and even cause spiral wave to disappear; in addition, it can shorten the wavelength and keep period fixed, and also elongate the wavelength and increase the period of spiral wave. If the aging and the regular systole of heart take place at the same time, we observe some phenomena, such as different spiral wave patterns, the spiral wave breakup and disappearance. We also obtain the probabilities of heart failure, ventricular fibrillation and death. These results are essentially consistent with the results of relevant epidemiological survey.
[1] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[2] Bär M, Gottschalk N, Eiswirth M, Ertl G 1994 J. Chem. Phys. 100 1202
[3] Witkowski F X, Leon L J, Penkoske P A, Giles W R, Spanoll M L, Ditto W L, Winfree A T 1998 Nature 392 78
[4] Fenton F H, Cherry E M, Hasting H M, Evans S J 2002 Chaos 12 852
[5] Qian Y, Song X Y, Shi W, Chen G Z, Xue Y, 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱郁, 宋宣玉, 时伟, 陈光旨, 薛郁 2006 55 4420]
[6] Liu F C, Wang X F, Li X C, Dong L F 2007 Chin. Phys. 16 2640
[7] Yin X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese) [尹小舟, 刘勇 2008 57 6844]
[8] Ma J, Jin W Y, Yi M, Li Y L 2008 Acta Phys. Sin. 57 2832 (in Chinese) [马 军, 靳伍银, 易 鸣, 李延龙 2008 57 2832]
[9] Liu Y, Li S R, Ma J, Ying H P 2009 Chin. Phys. B 18 98
[10] Deng M Y, Tang G N, Kong L J, Liu M R 2010 Acta Phys. Sin. 59 2339 (in Chinese) [邓敏艺, 唐国宁, 孔令江, 刘慕仁 2010 59 2339]
[11] Bär M, Eiswirth M 1993 Phys. Rev. E 48 1635
[12] Dai Y, Tang G N 2009 Acta Phys. Sin. 58 1491 (in Chinese) [戴瑜, 唐国宁 2009 58 1491]
[13] Wang S H, Choe W G, Lee K J 2000 Phys. Rev. E 62 4799
[14] Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 唐国宁 2010 59 2319]
[15] Gan Z N, Ma J, Zhang G Y, Chen Y 2008 Acta Phys. Sin. 57 5400 (in Chinese) [甘正宁, 马军, 张国勇, 陈勇2008 57 5400]
[16] Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[17] Yang J Z, Zhang M 2005 Chin. Phys. Lett. 22 3195
[18] Wei H M, Tang G N 2011 Acta Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 60 030501]
[19] Zhang H, Ruan X S, Hu B, Ouyang Q 2004 Phys. Rev. E 70 016212
[20] Zhang H, Li B W, Sheng Z M, Cao Z J, Hu G 2006 Europhys. Lett. 76 1109
[21] Olivetti G, Melissari M, Capasso J M, Anversa P 1991 Circ. Res. 68 1560
[22] Greenberg J M, Hastings S P 1978 SIAM J. Appl. Math. 34 515
[23] Kohl P, Camelliti P, Burton F L, Smith G L 2005 J. Electrocardiology 38 45
[24] Gu D F, Huang G Y, He J, Wu X G, Duan X F, Stephen M M, Paul K W 2003 Chin. J. Cardiology 31 3 ( in Chinese) [顾东风, 黄广勇, 何江, 吴锡桂, 段秀芳, Stephen M M, Paul K W 2003 中华心血管病杂志 31 3]
[25] Wang L 2011 South China Journal of Cardiovascular Diseases 17 178 (in Chinese) [王林 2011 岭南心血管病杂志 17 178]
[26] Zhou Z Q, Hu D Y, Chen J, Zhang R H, Li K B, Zhao X L 2004 Chin. J. Intern. Med. 43 491 (in Chinese) [周自强, 胡大一, 陈捷, 张仁汉, 李奎宝, 赵秀丽 2004 中华内科杂志 43 491]
[27] Kannel W B, Ho K, Thom T 1994 Br. Heart J. 72 (Supplement) S 3
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[1] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[2] Bär M, Gottschalk N, Eiswirth M, Ertl G 1994 J. Chem. Phys. 100 1202
[3] Witkowski F X, Leon L J, Penkoske P A, Giles W R, Spanoll M L, Ditto W L, Winfree A T 1998 Nature 392 78
[4] Fenton F H, Cherry E M, Hasting H M, Evans S J 2002 Chaos 12 852
[5] Qian Y, Song X Y, Shi W, Chen G Z, Xue Y, 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱郁, 宋宣玉, 时伟, 陈光旨, 薛郁 2006 55 4420]
[6] Liu F C, Wang X F, Li X C, Dong L F 2007 Chin. Phys. 16 2640
[7] Yin X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese) [尹小舟, 刘勇 2008 57 6844]
[8] Ma J, Jin W Y, Yi M, Li Y L 2008 Acta Phys. Sin. 57 2832 (in Chinese) [马 军, 靳伍银, 易 鸣, 李延龙 2008 57 2832]
[9] Liu Y, Li S R, Ma J, Ying H P 2009 Chin. Phys. B 18 98
[10] Deng M Y, Tang G N, Kong L J, Liu M R 2010 Acta Phys. Sin. 59 2339 (in Chinese) [邓敏艺, 唐国宁, 孔令江, 刘慕仁 2010 59 2339]
[11] Bär M, Eiswirth M 1993 Phys. Rev. E 48 1635
[12] Dai Y, Tang G N 2009 Acta Phys. Sin. 58 1491 (in Chinese) [戴瑜, 唐国宁 2009 58 1491]
[13] Wang S H, Choe W G, Lee K J 2000 Phys. Rev. E 62 4799
[14] Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 唐国宁 2010 59 2319]
[15] Gan Z N, Ma J, Zhang G Y, Chen Y 2008 Acta Phys. Sin. 57 5400 (in Chinese) [甘正宁, 马军, 张国勇, 陈勇2008 57 5400]
[16] Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 17 2844
[17] Yang J Z, Zhang M 2005 Chin. Phys. Lett. 22 3195
[18] Wei H M, Tang G N 2011 Acta Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 60 030501]
[19] Zhang H, Ruan X S, Hu B, Ouyang Q 2004 Phys. Rev. E 70 016212
[20] Zhang H, Li B W, Sheng Z M, Cao Z J, Hu G 2006 Europhys. Lett. 76 1109
[21] Olivetti G, Melissari M, Capasso J M, Anversa P 1991 Circ. Res. 68 1560
[22] Greenberg J M, Hastings S P 1978 SIAM J. Appl. Math. 34 515
[23] Kohl P, Camelliti P, Burton F L, Smith G L 2005 J. Electrocardiology 38 45
[24] Gu D F, Huang G Y, He J, Wu X G, Duan X F, Stephen M M, Paul K W 2003 Chin. J. Cardiology 31 3 ( in Chinese) [顾东风, 黄广勇, 何江, 吴锡桂, 段秀芳, Stephen M M, Paul K W 2003 中华心血管病杂志 31 3]
[25] Wang L 2011 South China Journal of Cardiovascular Diseases 17 178 (in Chinese) [王林 2011 岭南心血管病杂志 17 178]
[26] Zhou Z Q, Hu D Y, Chen J, Zhang R H, Li K B, Zhao X L 2004 Chin. J. Intern. Med. 43 491 (in Chinese) [周自强, 胡大一, 陈捷, 张仁汉, 李奎宝, 赵秀丽 2004 中华内科杂志 43 491]
[27] Kannel W B, Ho K, Thom T 1994 Br. Heart J. 72 (Supplement) S 3
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