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In some cases, the extracellular concentration of potassium ions cannot be regarded as being constant. The potassium lateral diffusion leads to extracellular accumulation of potassium ions and the generation of potassium diffusive coupling. The effect of potassium diffusive coupling on spiral wave is investigated by using the Luo-Rudy phase I cardiac model with potassium diffusive coupling. The numerical results show that when the strength of potassium diffusive coupling is relatively strong, the potassium diffusive coupling makes extracellular potassium ion concentration rise first and then regularly oscillate, leading to the irregular meandering of spiral wave. It is observed that the width of spiral arm and the frequency of spiral wave decrease as the strength of potassium diffusive coupling increases. Thus, when the strength of the potassium diffusive coupling is strong enough, the potassium diffusive coupling can eliminate spiral wave and spatiotemporal chaos.
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Keywords:
- potassium diffusive coupling /
- spiral wave /
- spatiotemporal chaos
[1] Meron E, Pelc E P 1988 Phys. Rev. Lett. 60 1880
[2] Krinsky V I 1966 Biophysics 11 776
[3] Ma J, Pu Z S, Feng W J, Li W X 2005 Acta Phys. Sin. 54 4602 (in Chinese) [马军, 蒲忠胜, 冯旺军, 李维学 2005 物理学报 54 4602]
[4] Xiao X H, Tang G N 2011 Complexity Systems and Complexity Science 8 58 (in Chinese) [肖向华, 唐国宁 2011 复杂系统和复杂性科学 8 58]
[5] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 3070 (in Chinese) [钟敏, 唐国宁 2010 物理学报 59 3070]
[6] Bai Y Q, Zhu X 2010 Chin. Phys. Lett. 27 048201
[7] Wang P Y, Xie P, Yin H W 2003 Chin. Phys. 12 674
[8] Isomura A, Hörning M, Agladze K, Yoshikawa K 2008 Phys. Rev. E 78 066216
[9] Zhao L, Yang J P, Zheng J H 2013 Acta Phys. Sin. 62 028701 (in Chinese) [赵龙, 杨继平, 郑艳红 2013 物理学报 62 028701]
[10] Qian Y 2012 Chin. Phys. B 21 088201
[11] Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 190501 (in Chinese) [邝玉兰, 唐国宁 2012 物理学报 61 190501]
[12] Ouyang Q 2001 Physics 30 30 (in Chinese) [欧阳颀 2001 物理 30 30]
[13] He Y F, Liu F C, Fan W L, Dong L F 2012 Chin. Phys. B 21 034701
[14] Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 100504 (in Chinese) [邝玉兰, 唐国宁 2012 物理学报 61 100504]
[15] Pumir A, Nikolski M, Hörning M, Isomura A, Agladze K,Yoshikawa K, Gilmour R, Bodenschatz E, Krinsky V 2007 Phys. Rev. Lett. 99 208101
[16] Höning M, Takagi S, Yoshikawa K 2012 Phys. Rev. E 85 061906
[17] Tung L 1996 Proc. IEEE 84 366
[18] Kunze D L 1977 Circ Res. 41 122
[19] Kléber A G 1983 Circ. Res. 52 442
[20] Shaw R M, Rudy Y 1997 Cardiovasc. Res. 35 256
[21] Harris A S, Bisteni A, Russell R A, Brigham J C, Firestone J E 1954 Science 19 200
[22] Wu X X, Shuai J W 2012 Phys. Rev. E 85 061911
[23] Durand D M, Park E H, Jensen A L 2010 Phil. Trans. R. Soc. B 365 2347
[24] Postonv D E, Ryazanova L S, Sosnovtseva O V, Mosekilde E 2006 Int. J. Neur. Syst. 16 99
[25] Park E H, Durand D M 2006 J. Theor. Biol. 238 666
[26] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[27] Postnov D E, Mller F, Schuppner R B, Schimansky-Geier L 2009 Phys. Rev. E 80 031921
[28] 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)]
[29] Qu Z L, Xie F G, Garfinkel A,Weiss J N 2000 Ann. Biomed. Eng. 28 755
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[1] Meron E, Pelc E P 1988 Phys. Rev. Lett. 60 1880
[2] Krinsky V I 1966 Biophysics 11 776
[3] Ma J, Pu Z S, Feng W J, Li W X 2005 Acta Phys. Sin. 54 4602 (in Chinese) [马军, 蒲忠胜, 冯旺军, 李维学 2005 物理学报 54 4602]
[4] Xiao X H, Tang G N 2011 Complexity Systems and Complexity Science 8 58 (in Chinese) [肖向华, 唐国宁 2011 复杂系统和复杂性科学 8 58]
[5] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 3070 (in Chinese) [钟敏, 唐国宁 2010 物理学报 59 3070]
[6] Bai Y Q, Zhu X 2010 Chin. Phys. Lett. 27 048201
[7] Wang P Y, Xie P, Yin H W 2003 Chin. Phys. 12 674
[8] Isomura A, Hörning M, Agladze K, Yoshikawa K 2008 Phys. Rev. E 78 066216
[9] Zhao L, Yang J P, Zheng J H 2013 Acta Phys. Sin. 62 028701 (in Chinese) [赵龙, 杨继平, 郑艳红 2013 物理学报 62 028701]
[10] Qian Y 2012 Chin. Phys. B 21 088201
[11] Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 190501 (in Chinese) [邝玉兰, 唐国宁 2012 物理学报 61 190501]
[12] Ouyang Q 2001 Physics 30 30 (in Chinese) [欧阳颀 2001 物理 30 30]
[13] He Y F, Liu F C, Fan W L, Dong L F 2012 Chin. Phys. B 21 034701
[14] Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 100504 (in Chinese) [邝玉兰, 唐国宁 2012 物理学报 61 100504]
[15] Pumir A, Nikolski M, Hörning M, Isomura A, Agladze K,Yoshikawa K, Gilmour R, Bodenschatz E, Krinsky V 2007 Phys. Rev. Lett. 99 208101
[16] Höning M, Takagi S, Yoshikawa K 2012 Phys. Rev. E 85 061906
[17] Tung L 1996 Proc. IEEE 84 366
[18] Kunze D L 1977 Circ Res. 41 122
[19] Kléber A G 1983 Circ. Res. 52 442
[20] Shaw R M, Rudy Y 1997 Cardiovasc. Res. 35 256
[21] Harris A S, Bisteni A, Russell R A, Brigham J C, Firestone J E 1954 Science 19 200
[22] Wu X X, Shuai J W 2012 Phys. Rev. E 85 061911
[23] Durand D M, Park E H, Jensen A L 2010 Phil. Trans. R. Soc. B 365 2347
[24] Postonv D E, Ryazanova L S, Sosnovtseva O V, Mosekilde E 2006 Int. J. Neur. Syst. 16 99
[25] Park E H, Durand D M 2006 J. Theor. Biol. 238 666
[26] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[27] Postnov D E, Mller F, Schuppner R B, Schimansky-Geier L 2009 Phys. Rev. E 80 031921
[28] 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)]
[29] Qu Z L, Xie F G, Garfinkel A,Weiss J N 2000 Ann. Biomed. Eng. 28 755
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