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以Luo-Rudy相I心脏模型为基础,研究心脏中螺旋波和时空混沌的控制,提出了两种控制方法: (Ⅰ)通过交替改变细胞外钾离子浓度来产生平面波,再利用弱外电场辅助平面波抑制螺旋波和时空混沌; (Ⅱ)先提高细胞外钾离子浓度,然后利用外电场激发波的方式产生平面波,再用平面波去抑制螺旋波和时空混沌. 研究结果表明,只要适当选择控制参数,这两种方法都能够有效抑制螺旋波和时空混沌. 当心肌出现局部缺血时,在心肌缺血处就会出现高的细胞外钾离子浓度,在这种情况下, 可以采用电场发射波的方法来抑制心脏中的螺旋波和时空混沌.对这些控制方法的优点和控制机制做了解释.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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