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Suppressions of spiral waves and spatiotemporal chaos in cardiac tissue are investigated by using the Luo-Rudy phase I model. Two control methods are proposed. (Ⅰ) A planar wave is generated by alternately changing the extracellular potassium ion concentration, and then a weak external electric field is used to help plane wave to suppress spiral waves and spatiotemporal chaos. (Ⅱ) The extracellular potassium ion concentration is first enhanced. Planar waves are then generated by the wave emission induced by an external electric field. We use the planar waves to suppress the spiral waves and spatiotemporal chaos. The results show that the control methods can effectively suppress spiral waves and spatiotemporal chaos when relevant parameters are appropriately chosen. When regional myocardial ischemia occurs, high extracellular potassium ion concentration will appear where myocardial ischemia occurs. The methods of wave emission can be used to suppress spiral waves and spatiotemporal chaos in heart in this case. The advantages and mechanism of the control methods are explained.
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Keywords:
- cardiac tissue /
- spiral waves /
- spatiotemporal chaos /
- extracellular potassium ion concentration
[1] Meron E, Pelc E P 1988 Phys. Rev. Lett. 60 1880
[2] Ma J, Wu N J, Ying H P, Pu Z S 2006 Chin. J. Comput. Phys. 23 243
[3] Ma J, Pu Z S, Feng W J, Li W X 2005 Acta Phys. Sin. 54 4602 (in Chinese) [马军, 蒲忠盛, 冯旺军, 李维学 2005 54 4602]
[4] Yi X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese) [尹小舟, 刘勇 2008 57 6844]
[5] 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 60 080503]
[6] Gabbay M, Ott E, Guzdar P N 1999 Phys. Rev. E 59 2443
[7] Krinsky V I, Hamm E, Voignier V 1996 Phys. Rev. Lett. 76 3854
[8] Kheowan O U, Zykov V S, Rangsiman O, Muller S C 2001 Phys. Rev. Lett. 86 2170
[9] Osipov G V, Collins J J 1999 Phys. Rev. E 60 54
[10] Qu Z L, Weiss J N 2005 Am. J. Physiol. Heart Circ. Physiol. 289 1692
[11] Zhong M,Tang G N 2010 Acta Phys. Sin. 59 3070 (in Chinese) [钟敏, 唐国宁 2010 59 3070]
[12] Ouyang Q 2001 Physics 30 31 (in Chinese) [欧阳颀 2001 物理 30 31]
[13] Young J B, Abraham W T, Smith A L 2003 The Journal of the American Medical Association 289 2685
[14] Wathen M S, Degroot P J, Sweeney M O, Stark A J, Otterness M F, Adkisson W O, Canby R C, Khalighi K, Machado C, Rubenstein D S, Volosin K J 2004 Circulation 110 2591
[15] White J B, Walcott G P, Pollard A E, Ideker R E 1998 Circulation 97 1738
[16] Pumir A, Krinsky V 1999 J. Theor. Biol. 199 311
[17] Pumir A, Nikolski M, Hörning M, Isomura A, Agladze K, Yoshikawa K, Gilmour R, Bodenschatz E, Krinsky V 2007 Phys. Rev. Lett. 99 208101
[18] Hörning M, Takagi S, Yoshikawa K 2010 Phys. Rev. E 82 021926
[19] Kleber A G 1983 Circ. Res. 52 442
[20] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[21] Wu J H, Han Q S 1988 Computational Fluid Dynamics Theory, Mmethod and Application 05 (Beijing: Science press) p105 (in Chinese) [吴江航, 韩庆书 1988 计算流体力学的理论,方法及应用 05 (北京:科学出版社) 第105页]
[22] Cui H, Sun L, Wang Z R 2006 J. Pract. Electrocardiol. 15 116 (in Chinese) [崔红, 孙玲, 王志榕 2006 实用心电学杂志 15 116]
[23] Shaw R M, Rudy Y 1997 Cardiovasc. Res. 35 256
[24] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟敏, 唐国宁 2010 59 1593]
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[1] Meron E, Pelc E P 1988 Phys. Rev. Lett. 60 1880
[2] Ma J, Wu N J, Ying H P, Pu Z S 2006 Chin. J. Comput. Phys. 23 243
[3] Ma J, Pu Z S, Feng W J, Li W X 2005 Acta Phys. Sin. 54 4602 (in Chinese) [马军, 蒲忠盛, 冯旺军, 李维学 2005 54 4602]
[4] Yi X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese) [尹小舟, 刘勇 2008 57 6844]
[5] 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 60 080503]
[6] Gabbay M, Ott E, Guzdar P N 1999 Phys. Rev. E 59 2443
[7] Krinsky V I, Hamm E, Voignier V 1996 Phys. Rev. Lett. 76 3854
[8] Kheowan O U, Zykov V S, Rangsiman O, Muller S C 2001 Phys. Rev. Lett. 86 2170
[9] Osipov G V, Collins J J 1999 Phys. Rev. E 60 54
[10] Qu Z L, Weiss J N 2005 Am. J. Physiol. Heart Circ. Physiol. 289 1692
[11] Zhong M,Tang G N 2010 Acta Phys. Sin. 59 3070 (in Chinese) [钟敏, 唐国宁 2010 59 3070]
[12] Ouyang Q 2001 Physics 30 31 (in Chinese) [欧阳颀 2001 物理 30 31]
[13] Young J B, Abraham W T, Smith A L 2003 The Journal of the American Medical Association 289 2685
[14] Wathen M S, Degroot P J, Sweeney M O, Stark A J, Otterness M F, Adkisson W O, Canby R C, Khalighi K, Machado C, Rubenstein D S, Volosin K J 2004 Circulation 110 2591
[15] White J B, Walcott G P, Pollard A E, Ideker R E 1998 Circulation 97 1738
[16] Pumir A, Krinsky V 1999 J. Theor. Biol. 199 311
[17] Pumir A, Nikolski M, Hörning M, Isomura A, Agladze K, Yoshikawa K, Gilmour R, Bodenschatz E, Krinsky V 2007 Phys. Rev. Lett. 99 208101
[18] Hörning M, Takagi S, Yoshikawa K 2010 Phys. Rev. E 82 021926
[19] Kleber A G 1983 Circ. Res. 52 442
[20] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[21] Wu J H, Han Q S 1988 Computational Fluid Dynamics Theory, Mmethod and Application 05 (Beijing: Science press) p105 (in Chinese) [吴江航, 韩庆书 1988 计算流体力学的理论,方法及应用 05 (北京:科学出版社) 第105页]
[22] Cui H, Sun L, Wang Z R 2006 J. Pract. Electrocardiol. 15 116 (in Chinese) [崔红, 孙玲, 王志榕 2006 实用心电学杂志 15 116]
[23] Shaw R M, Rudy Y 1997 Cardiovasc. Res. 35 256
[24] Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟敏, 唐国宁 2010 59 1593]
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