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通过让心肌细胞钠离子通道的触发门变量延迟打开, 使介质具有激发延迟能力, 介质延迟激发时间随控制电压和刺激频率增加而增加, 当控制电压超过一个阈值时, 延迟激发介质具有低通滤波作用:低频波可以连续通过, 而高频波不能连续通过. 本文用Luo-Rudy相I模型研究了介质延迟激发对螺旋波和时空混沌的影响, 数值模拟结果表明: 当控制电压超过阈值时, 介质的延迟激发可有效消除螺旋波和时空混沌; 从小逐渐增大控制电压, 在钙最大电导率较小情况下, 延迟激发会导致介质激发性降低, 使螺旋波漫游幅度增大, 直至传导障碍导致螺旋波消失; 当钙最大电导率较大时, 延迟激发会导致螺旋波失稳变弱, 这样当控制电压增加到一定值时, 时空混沌可以演化成漫游螺旋波, 当控制参数被适当选取时, 观察到漫游幅度大的螺旋波漫游出系统边界消失现象, 继续增大控制电压将导致时空混沌直接消失.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 物理学报 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 物理学报 19 198201]
[18] 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]
[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 物理学报 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 物理学报 19 198201]
[18] 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]
[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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