Suppression of the spiral wave in cardiac tissue by using forcing currents with diversity

Wang Chun-Ni; Ma Jun

doi:10.7498/aps.62.084501

Abstract

Forcing currents are generated by using two types of constant currents to stimulate different areas of a medium. The external current is mapped into transmembrane current and stable gradient force is induced to drive the stable rotating spiral wave. The medium becomes homogeneous when the spiral wave is removed and the time series of sampled membrane potentials becomes stable value without considering noise. The scheme is confirmed to be effective in the presence of Gaussian white noise.

Keywords:

Authors and contacts

1.
Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11265008).

References

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[59]	Chen J X, Zhang H, Li Y Q 2009 J. Chem. Phys. 130 124510
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[68]	Ma J, Wu Y, Ying H P, Jia Y 2011 Chin. Sci. Bull. 56 151
[69]	Ma J, Tang J, Zhang A H, Jia Y 2010 Sci. China Phys. Mech. Astro. 53 172
[70]	Ma J, Tang J, Zhang A H, Jia Y 2010 J. Biol. Syst. 18 243
[71]	Huang L, Ma J, Tang J, Li F 2013 J. Biol. Syst. 21 1350002
[72]	Ma J, Huang L, Ying H P, Pu Z S 2012 Chin. Sci. Bull. 57 2094
[73]	Ma J, Tang J, Wang C N, Jia Y 2011 Int. J. Bifur. Chaos 21 587
[74]	Aliev R R, Panfilov A V 1996 Chaos, Soliton. Fract. 293 965
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Cited By

[1]	Hagan P S 1982 SIAM J. Appl. Math. 42 762
[2]	Braune M, Engel H 1993 Chem. Phys. Lett. 204 257
[3]	Nettesheim S, von Oertzen A, Rotermund H H, Ertl G 1993 J. Chem. Phys. 98 9977
[4]	Koch A J, Meinhardt H 1994 Rev. Mod. Phys. 66 1481
[5]	Barkley D 1994 Phys. Rev. Lett. 72 164
[6]	Merzhanov A G, Rumanov E N 1999 Rev. Mod. Phys. 71 1173
[7]	Meron E, Pelcé P 1988 Phys. Rev. Lett. 60 1880
[8]	Barkley D 1992 Phys. Rev. Lett. 68 2090
[9]	Amemiya T, Kádár S, Kettunen P, Showalter K 1996 Phys. Rev. Lett. 77 3244
[10]	Scott S, Wang J Showalter K 1997 J. Chem. Soc. Faraday. Trans. 93 1733
[11]	Starobin J M, Starmer C F 1997 Phys. Rev. E 55 1193
[12]	Osipov G V, Shulgin B V, Collins J J 1998 Phys. Rev. E 58 6955
[13]	LeBlanc V, Wulff C 2000 J. Nonlinear Sci. 10 569
[14]	Zhou L Q, Ouyang Q 2000 Phys. Rev. Lett. 85 1650
[15]	Fenton F H, Cherry E M, Hastings H M 2002 Chaos 12 852
[16]	Ashwin P, Melbourne I, Nicol M 2001 Physica D 156 364
[17]	Sandstede B, Scheel A 2001 Phys. Rev. Lett. 86 171
[18]	Sandstede B, Scheel A 2000 Phys. Rev. E 62 7708
[19]	Mikhailov A S, Showalter K 2006 Phys. Rep. 425 79
[20]	Vanag V K, Epstein I R 2001 Science 294 835
[21]	Henry H 2004 Phys. Rev. E 70 026204
[22]	Steinbock O, Mller S C, Zykov V S 1993 Nature 366 322
[23]	Rohlf K, Glass L, Kapral R 2006 Chaos 16 037115
[24]	Biktashev V N, Holden A V 1996 Proc. R. Soc. Lond. B 263 1373
[25]	Biktashev V N, Holden A V 1998 Chaos 8 48
[26]	Qu Z L, Xie F G, Garfinkel A, Weiss N J 2000 Ann. Biomed. Eng. 28 755
[27]	Xie F, Qu Z, Garfinkel A, Weiss J N 2002 Am. J. Physiol. Heart Circ. Physiol. 283 H448
[28]	Nash M P, Panfilov A V 2004 Progr. Biophys. Mol. Biol. 85 501
[29]	Honjo H, Yamazaki M, Kamiya K, Kodama I 2007 Circ. J. 71 (Suppl. A) A26
[30]	Panfilov A V, Mller S C, Zykov V S 2000 Phys. Rev. E 61 4644
[31]	Stamp A T, Osipov G V, Collins J J 2002 Chaos 12 931
[32]	Ashihara T, Namba T, Ito M, Ikeda T, Nakazawa K, Trayanova N 2004 J. Cardiovasc. Electrophysiol. 15 226
[33]	Ma J, Ying H P, Li Y L 2007 Chin. Phys. 16 955
[34]	Weise L D, Panfilov A V 2011 PLoS ONE 6 e27264
[35]	Shajahan T K, Nayak A R, Pandit R 2009 PLoS ONE 4 e4738
[36]	Cysyk J, Tung L 2008 Biophys. J. 94 1533
[37]	Ouyang Q 2000 Pattern Formation in Reaction-Diffusion Systems (Shanghai:Shanghai Scientific & Technological Education Publishing House) pp73-77 (in Chinese) [欧阳颀 2000 反应扩散系统中的斑图动力学(上海:上海科技教育出版社)第73–77页]
[38]	Zhang H, Cao Z J, Wu N J, Ying H P, Hu G 2005 Phys. Rev. Lett. 94 188301
[39]	Cao Z J, Li P F, Zhang H, Xie F G, Hu G 2007 Chaos 17 015107
[40]	Gao X, Feng X, Cai M C, Li B W, Ying H P, Zhang H 2012 Phys. Rev. E 85 016213
[41]	Deng L Y, Zhang H, Li Y Q 2010 Phys. Rev. E 86 016204
[42]	Wu N J, Zhang H, Ying H P, Cao Z J, Hu G 2006 Phys. Rev. E 73 060901
[43]	Nie H C, Gao J H, Zhan M 2011 Phys. Rev. E 84 056204
[44]	Zhan M, Zou W, Liu X 2010 Phys. Rev. E 81 036211
[45]	Zhan M, Luo J M, Gao J H 2007 Phys. Rev. E 75 016214
[46]	Yang J Z, Xie F G, Qu Z L, Garfinkel A 2003 Phys. Rev. Lett. 91 148302
[47]	Yang J Z, Zhang M 2006 Phys. Lett. A 352 69
[48]	Yang J Z, Garfinkel A 2003 Phys. Rev. E 68 066312
[49]	Gu G F, L Y P, Tang G N 2010 Chin. Phys. B 19 050515
[50]	Chen X J, Tian T T, Zhou Z W, Hu Y B, Tang G N 2012 Acta Phys. Sin. 61 210509 (in Chinese) [陈醒基, 田涛涛, 周振玮, 胡一博, 唐国宁2012 61 210509]
[51]	Zhou Z W, Chen X J, Tian T T, Tang G N 2012 Acta Phys. Sin. 61 210506 (in Chinese) [周振玮, 陈醒基, 田涛涛, 唐国宁 2012 61 210506]
[52]	Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 190501 (in Chinese) [邝玉兰, 唐国宁2012 61 190501]
[53]	Li G Z, Chen Y Q, Tang G N, Liu J X 2011 Chin. Phys. Lett. 28 020504
[54]	Kuang Y L, Tang G N 2012 Acta Phys. Sin. 61 100504 (in Chinese) [邝玉兰, 唐国宁2012 61 100504]
[55]	Dong L F, Wang H F, Liu F C, He Y F 2007 New J. Phys. 9 330
[56]	He Y F, Liu F C, Fan W L, Dong L F 2012 Chin. Phys. B 21 034701
[57]	Dong L F, Bai Z G, He Y F 2012 Acta Phys. Sin. 61 120509 (in Chinese) [董丽芳, 白占国, 贺亚峰2012 61 120509]
[58]	Chen J X, Xu J R, Yuan X P, Ying H P 2009 J. Phys. Chem. B 113 849
[59]	Chen J X, Zhang H, Li Y Q 2009 J. Chem. Phys. 130 124510
[60]	Chen J X, Mao J W, Hu B, Xu J R, He Y F, Li Y, Yuan X P 2009 Phys. Rev. E 79 066209
[61]	Yuan G Y 2011 Chin. Phys. B 20 040503
[62]	Yuan G Y, Yang S P, Wang G R, Chen S G 2008 Chin. Phys. B 17 1925
[63]	Yuan G Y, Xu L, Xu A G, Wang G R, Yang S P 2011 Chaos, Soliton. Fract. 44 728
[64]	Qian Y 2012 Chin. Phys. B 21 088201
[65]	Qian Y, Wang C J, Shi H S 2010 Chin. Phys. B 20 108201
[66]	Qian Y, Huang X D, Liao X H 2010 Chin. Phys. B 19 050513
[67]	Ma J, Ying H P, Pan G W, Pu Z S 2005 Chin. Phys. Lett. 22 2176
[68]	Ma J, Wu Y, Ying H P, Jia Y 2011 Chin. Sci. Bull. 56 151
[69]	Ma J, Tang J, Zhang A H, Jia Y 2010 Sci. China Phys. Mech. Astro. 53 172
[70]	Ma J, Tang J, Zhang A H, Jia Y 2010 J. Biol. Syst. 18 243
[71]	Huang L, Ma J, Tang J, Li F 2013 J. Biol. Syst. 21 1350002
[72]	Ma J, Huang L, Ying H P, Pu Z S 2012 Chin. Sci. Bull. 57 2094
[73]	Ma J, Tang J, Wang C N, Jia Y 2011 Int. J. Bifur. Chaos 21 587
[74]	Aliev R R, Panfilov A V 1996 Chaos, Soliton. Fract. 293 965
[75]	Purmir A, Krinsky V I 1996 Physica D 91 205
[76]	Keener J P 1996 J. Theor. Biol. 178 313
[77]	Purmir A, Krinsky V I 1997 J. Theor. Biol. 185 189

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