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To cause the sodium ion activation gate of cardiomyocyte delay to open, the ability of excitation delay should be given to the medium. The time of excitation delay of the medium increases as the control voltage and frequency of stimulation increase. When the control voltage exceeds a threshold value, the medium with excitation delay has the property of low-pass filtering: low-frequency waves can continuously pass through the medium, whereas the high-frequency wave does not pass consecutively. In this paper, the effect of excitation delay of the medium on spiral waves and spatiotemporal chaos is investigated by using Luo-Rudy phase I model. Numerical simulation results show that when the control voltage exceeds the threshold value, the excitation delay of the medium can effectively eliminate the spiral wave and spatiotemporal chaos. When the control voltage gradually increases from a small value, at a small maximal conductance of calcium channel, the excitation delay could reduce the excitability of the medium, making the amplitude of the spiral wave meander increase until conduction failure results in the disappearance of the spiral wave. Under a large maximal conductance of calcium channel, the excitation delay can reduce the unstability of the spiral wave so that spatiotemporal chaos evolve into meandering spiral waves when the control voltage is large enough. The phenomenon that the spiral wave with a large meandering motion of its tip moves out of the system is observed when the control voltage is properly chosen. Further increase of the control voltage leads to the disappearance of spatiotemporal chaos.
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Keywords:
- excitable medium /
- spiral wave /
- control voltage /
- excitation delay
[1] Davidenko J M, Pertsov A V, Salomonsz, Baxter W, Jalife J 1992 Nature 355 349
[2] Ouyang Q 2001 Physics30 30 (in Chinese) [欧阳颀 2001 物理 30 30]
[3] Plapp B B, Egolf D A, Bodenschatz E 1998 Phys. Rev. Lett. 81 5334
[4] Huang X, Xu W, Liang J, Takagaki K, Gao X, Wu J 2010 Neuron 68 978
[5] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[6] Liu G Q, Ying H P 2014 Chin. Phys. B 23 050502
[7] Deng M Y, Chen X Q, Tang G N 2014 Chin. Phys. B 23 120503
[8] Zhang H, Hu B, Hu G 2003 Phys. Rev. E 68 026134
[9] Yamazaki M, Honjo H, Ashihara T, Harada M, Sakuma I, Nakazawa K, Trayanova N, Horie M, Kalifa J, Jalife J, Kamiya K, Kodama I 2012 Heart Rhythm. 9 107
[10] Luengviriya J, Sutthiopad M, Phantu M, Porjai P, Kanchanawarin J, Mller S C, Luengviriya C 2014 Phys. Rev. E 90 052919
[11] Quail T, Shrier A, Glass L 2014 Phys. Rev. Lett. 113 158101
[12] Sutthiopad M, Luengviriya J, Porjai P, Tomapatanaget B, Mller S C, Luengviriya C 2014 Phys. Rev. E 89 052902
[13] Dai Y, Tang G N 2009 Acta Phys. Sin. 58 3 (in Chinese) [戴瑜, 唐国宁 2009 58 3]
[14] Yuan G Y, Zhang H, Xu A, Wang G 2013 Phys. Rev. E 88 022920
[15] Weise L D, Panfilov A V 2012 Phys. Rev. Lett. 108 228104
[16] Nie H, Gao J, Zhan M 2011 Phys. Rev. E 84 056204
[17] Qiao C Q, Wang L L, Li W H, Tang G N 2013 Acta Phys. Sin.19 198201 (in Chinese) [乔成功, 王利利, 李伟恒, 唐国宁 2013 19 198201]
[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] Tandri H, Weinberg S H, Chang K C, Zhu R, Trayanova N A, Tung L, Berger R D 2011 Sci. Transl. Med. 3 102ra96
[20] Morgan S W, Biktasheva I V, Biktashev V N 2008 Phys. Rev. E 78 046207
[21] Storm J F 1988 Nature 336 379
[22] Delmar M, Glass L, Michaels D C, Jalife J 1989 Circ. Res. 65 775
[23] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[24] Xie F, Qu Z L, Garfinkel A, Weiss J N 2001 Am. J. Physiol. Heart Circ. Physiol. 280 H1667
[25] Magome N, Kanaporis G, Moisan N, Tanaka K, Agladze K 2011 TissueEngineering: Part A 17 21
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[1] Davidenko J M, Pertsov A V, Salomonsz, Baxter W, Jalife J 1992 Nature 355 349
[2] Ouyang Q 2001 Physics30 30 (in Chinese) [欧阳颀 2001 物理 30 30]
[3] Plapp B B, Egolf D A, Bodenschatz E 1998 Phys. Rev. Lett. 81 5334
[4] Huang X, Xu W, Liang J, Takagaki K, Gao X, Wu J 2010 Neuron 68 978
[5] Zaikin A N, Zhabotinsky A M 1970 Nature 225 535
[6] Liu G Q, Ying H P 2014 Chin. Phys. B 23 050502
[7] Deng M Y, Chen X Q, Tang G N 2014 Chin. Phys. B 23 120503
[8] Zhang H, Hu B, Hu G 2003 Phys. Rev. E 68 026134
[9] Yamazaki M, Honjo H, Ashihara T, Harada M, Sakuma I, Nakazawa K, Trayanova N, Horie M, Kalifa J, Jalife J, Kamiya K, Kodama I 2012 Heart Rhythm. 9 107
[10] Luengviriya J, Sutthiopad M, Phantu M, Porjai P, Kanchanawarin J, Mller S C, Luengviriya C 2014 Phys. Rev. E 90 052919
[11] Quail T, Shrier A, Glass L 2014 Phys. Rev. Lett. 113 158101
[12] Sutthiopad M, Luengviriya J, Porjai P, Tomapatanaget B, Mller S C, Luengviriya C 2014 Phys. Rev. E 89 052902
[13] Dai Y, Tang G N 2009 Acta Phys. Sin. 58 3 (in Chinese) [戴瑜, 唐国宁 2009 58 3]
[14] Yuan G Y, Zhang H, Xu A, Wang G 2013 Phys. Rev. E 88 022920
[15] Weise L D, Panfilov A V 2012 Phys. Rev. Lett. 108 228104
[16] Nie H, Gao J, Zhan M 2011 Phys. Rev. E 84 056204
[17] Qiao C Q, Wang L L, Li W H, Tang G N 2013 Acta Phys. Sin.19 198201 (in Chinese) [乔成功, 王利利, 李伟恒, 唐国宁 2013 19 198201]
[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] Tandri H, Weinberg S H, Chang K C, Zhu R, Trayanova N A, Tung L, Berger R D 2011 Sci. Transl. Med. 3 102ra96
[20] Morgan S W, Biktasheva I V, Biktashev V N 2008 Phys. Rev. E 78 046207
[21] Storm J F 1988 Nature 336 379
[22] Delmar M, Glass L, Michaels D C, Jalife J 1989 Circ. Res. 65 775
[23] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[24] Xie F, Qu Z L, Garfinkel A, Weiss J N 2001 Am. J. Physiol. Heart Circ. Physiol. 280 H1667
[25] Magome N, Kanaporis G, Moisan N, Tanaka K, Agladze K 2011 TissueEngineering: Part A 17 21
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