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Frequency-dependent changes in the extracellular potassium ion concentration have been added to the Luo-Rudy phase I heart model. Effects of the delayed restoration of extracellular potassium ion concentration on spiral waves are studied. Numerical simulation results show that due to the state of spiral wave, the delayed restoration of extracellular potassium ion concentration can lead to periodic oscillations of concentration, and the period and amplitude of the oscillation increase with the delayed recovery time, resulting in the emergence of various phenomena, such as the breathing spiral wave, the coexistence of multiple spiral waves, the meandering of spiral waves in the manner of Lévy flight, and the disappearance of spiral wave through different ways. These results are compatible with the experimental results.
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Keywords:
- potassium ion concentration /
- time delay /
- spiral wave /
- spatiotemporal chaos
[1] Wolff J, Rotermund H H 2003 New J. Phys. 5 60
[2] Glass L 1996 Phys. Today 49 40
[3] Witkowski F X, Joshua Leon L, Penkoske P A, Giles W R, Spano M L, Ditto W L, Winfree A T 1998 Nature 392 78
[4] Winfree A T 1972 Science 175 634
[5] Field R J, Burger M 1985 Oscillations and Travelling Waves in Chemical Systems (New York: John Wiley and Sons) p441
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[7] Meron E, Pelc E P 1988 Phys. Rev. Lett. 60 1880
[8] Krinsky V 1966 Biophysics 11 776
[9] Liu G Q, Ying H P 2014 Chin. Phys. B 23 050502
[10] Zhang Q L, L L, Zhang Y 2011 Chin. Phys. B 20 090514
[11] Yuan X P, Chen J X, Zhao Y H, Lou Q, Wang L L, Shen Q 2011 Chin. Phys. Lett. 28 100505
[12] Wang C N, Ma J 2013 Acta Phys. Sin. 62 084501 (in Chinese) [王春妮, 马军 2013 物理学报 62 084501]
[13] Zhou Z W, Wang L L, Qiao C G, Chen X J, Tian T T, Tang G N 2013 Acta Phys. Sin. 62 150508 (in Chinese) [周振玮, 王利利, 乔成功, 陈醒基, 田涛涛, 唐国宁 2013 物理学报 62 150508]
[14] Gao J Z, Xie L L, Xie W M, Gao J H 2011 Acta Phys. Sin. 60 080503 (in Chinese) [高加振, 谢玲玲, 谢伟苗, 高继华 2011 物理学报 60 080503]
[15] Kléber A G 1983 Circ. Res. 52 442
[16] Kunze D L 1977 Circ. Res. 41 122
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[18] Yehia A R, Jeandupeux D, Alonso F, Guevara M R 1999 Chaos 9 916
[19] Wu R, Patwardhan A 2004 Circ. Res. 94 634
[20] Fenton F H, Cherry E M, Hastings H M, Evans S J 2002 Chaos 12 852
[21] Walker M L, Wan X, Kirsch G E, Rosenbaum D S 2003 Circulation 108 2704
[22] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[23] Zhang X M 2007 Ph. D. Dissertation (Beijing: Graduate School of Beijing Normal University) (in Chinese) [张晓明 2007 博士学位论文 (北京: 北京师范大学研究生院)]
[24] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[25] Qu Z L, Xie F G, Garfinkel A, Weiss J N 2000 Ann. Biomed. Eng. 28 755
[26] Barthelemy P, Bertolotti1 J, Wiersma D S 2008 Nature 453 495
[27] Zou X Q, Levine H 1993 Phys. Rev. E 47 R800
[28] Hwang S, Yea K, Lee K J 2004 Phys. Rev. Lett. 92 198103
-
[1] Wolff J, Rotermund H H 2003 New J. Phys. 5 60
[2] Glass L 1996 Phys. Today 49 40
[3] Witkowski F X, Joshua Leon L, Penkoske P A, Giles W R, Spano M L, Ditto W L, Winfree A T 1998 Nature 392 78
[4] Winfree A T 1972 Science 175 634
[5] Field R J, Burger M 1985 Oscillations and Travelling Waves in Chemical Systems (New York: John Wiley and Sons) p441
[6] Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science 252 123
[7] Meron E, Pelc E P 1988 Phys. Rev. Lett. 60 1880
[8] Krinsky V 1966 Biophysics 11 776
[9] Liu G Q, Ying H P 2014 Chin. Phys. B 23 050502
[10] Zhang Q L, L L, Zhang Y 2011 Chin. Phys. B 20 090514
[11] Yuan X P, Chen J X, Zhao Y H, Lou Q, Wang L L, Shen Q 2011 Chin. Phys. Lett. 28 100505
[12] Wang C N, Ma J 2013 Acta Phys. Sin. 62 084501 (in Chinese) [王春妮, 马军 2013 物理学报 62 084501]
[13] Zhou Z W, Wang L L, Qiao C G, Chen X J, Tian T T, Tang G N 2013 Acta Phys. Sin. 62 150508 (in Chinese) [周振玮, 王利利, 乔成功, 陈醒基, 田涛涛, 唐国宁 2013 物理学报 62 150508]
[14] Gao J Z, Xie L L, Xie W M, Gao J H 2011 Acta Phys. Sin. 60 080503 (in Chinese) [高加振, 谢玲玲, 谢伟苗, 高继华 2011 物理学报 60 080503]
[15] Kléber A G 1983 Circ. Res. 52 442
[16] Kunze D L 1977 Circ. Res. 41 122
[17] Cukierman S, Carvalho 1982 J. Gen. Physiol. 79 1017
[18] Yehia A R, Jeandupeux D, Alonso F, Guevara M R 1999 Chaos 9 916
[19] Wu R, Patwardhan A 2004 Circ. Res. 94 634
[20] Fenton F H, Cherry E M, Hastings H M, Evans S J 2002 Chaos 12 852
[21] Walker M L, Wan X, Kirsch G E, Rosenbaum D S 2003 Circulation 108 2704
[22] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[23] Zhang X M 2007 Ph. D. Dissertation (Beijing: Graduate School of Beijing Normal University) (in Chinese) [张晓明 2007 博士学位论文 (北京: 北京师范大学研究生院)]
[24] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[25] Qu Z L, Xie F G, Garfinkel A, Weiss J N 2000 Ann. Biomed. Eng. 28 755
[26] Barthelemy P, Bertolotti1 J, Wiersma D S 2008 Nature 453 495
[27] Zou X Q, Levine H 1993 Phys. Rev. E 47 R800
[28] Hwang S, Yea K, Lee K J 2004 Phys. Rev. Lett. 92 198103
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