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Study on the control of spiral waves in coupled excitable media

Zhou Zhen-Wei Chen Xing-Ji Tian Tao-Tao Tang Guo-Ning

Study on the control of spiral waves in coupled excitable media

Zhou Zhen-Wei, Chen Xing-Ji, Tian Tao-Tao, Tang Guo-Ning
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  • The control of spiral waves in three-layer coupled excitable media is studied by using the Bär model. The bidirectional coupling between adjacent layers is adopted. We use planar waves generated by a local periodic signal added to the second layer to eliminate spiral waves in the media. The numerical results show that when the couplings among three layer media meet some conditions the spiral waves in the media can be controlled. The control of spiral waves may be achieved by using the complementary coupling strategy. The interaction between planar wave and low-frequency spiral wave can produce high-frequency spiral wave, leading to failure to eliminate spiral waves. There exists an optimal drive width. Both larger and smaller drive width may need larger coupling strength between the first and third layers. The control results depending on the control opportunity are observed. We hope that this study will contribute to the design of the implantable cardioverter defibrillator.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11165004).
    [1]

    Witkowski F X, Joshua L L, Penkoske P A, Giles W R, Spano M L, Ditto W L, Winfree A T 1998 Nature 392 78

    [2]

    Gray R A, Jalife J, Panfilov A V, Baxter W T, Cabo C, Davidenko J M, Pertsov A M 1995 Science 270 1222

    [3]

    Yuan G Y, Xu L, Xu A G, Wang G R, Yang S P 2011 Chaos, Solitons and Fractals 44 728

    [4]

    Hendrey M, Ott E, Antonsen Jr T M 2000 Phys. Rev. E 61 4943

    [5]

    Wang C N, Yang L J, Yuan L H, Ma J 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3913

    [6]

    Ma J, Tang J, Wang C N, Jia Y 2011 Int. J. Bifurc. Chaos 21 587

    [7]

    Wang Q Y, Perc M, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681

    [8]

    Yuan G Y, Wang G R, Chen S G 2005 Commun. Theor. Phys. 44 858

    [9]

    Cao Z J, Li P F, Zhang H, Xie F G, Hu G 2007 Chaos 17 015107

    [10]

    de la Casa M A, de la Rubia F J, Ivanov P C 2007 Chaos 17 015109

    [11]

    Cao Z J, Zhang H, Xie F G, Hu G 2006 Europhys. Lett. 75 875

    [12]

    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]

    [13]

    Ma J, Jia Y, Yi M, Tang J, Xia Y F 2009 Chaos, Solitons and Fractals 41 1331

    [14]

    Sakaguchi H, Fujimoto T 2003 Phys. Rev. E 67 067202

    [15]

    Zykov V S, Mikhailov A S, Müller S C 1997 Phys. Rev. Lett. 78 3398

    [16]

    Qian Y, Song X Y, Shi W, Chen G Z, Xue Y 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱郁, 宋宣玉, 时伟, 陈光旨, 薛郁 2006 物理学报 55 4420]

    [17]

    Gray R A , Chattipakorn N 2005 Proc. Natl. Acad. Sci. U.S.A. 102 4672

    [18]

    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]

    [19]

    Piller L W 1970 Electronic Instrumentation Theory of Cardiac Technology (London: Staples Press)

    [20]

    Walker R G, Koster R W, Sun C, Moffat G, Barger J, Dodson P P, Chapman F W 2009 Resuscitation 80 773

    [21]

    Stamp A T, Osipov G V, Collins J J 2002 Chaos 12 931

    [22]

    Allessie M, Kirchhof C, Scheffer G J, Chorro F, Brugada J 1991 Circulation 84 1689

    [23]

    Yu C G, Bai R, Chen D L, Huang Y 2008 Cardiac Electrophysiology Basic and Clinical (WuHan: Huazhong University of Science and Technology Press) p4 (in Chinese) [余承高, 白融, 陈栋梁, 黄勇 2008 心脏电生理学基础与临床 (武汉: 华中科技大学出版社) 第4页]

    [24]

    Antzelevitch C 2001 Cardiovascular Research 50 426

    [25]

    Wang J M, Xue Y 2011 International Conference on Network Computing and Information Security Guilin, China, May 14-15, 2011 pp49-53

    [26]

    Yuan G Y, Yang S P, Wang G R, Chen S G 2005 Acta Phys. Sin. 54 1510 (in Chinese) [袁国勇, 杨世平, 王光瑞, 陈式刚 2005 物理学报 54 1510]

    [27]

    Li G Z, Chen Y Q, Tang G N 2012 Acta Phys. Sin. 61 020502 (in Chinese) [黎广钊, 陈咏琪, 唐国宁 2012 物理学报 61 020502]

    [28]

    Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635

    [29]

    Li X C, Wu X Y, Zhang S, Zhou Z H, Li L, Liang Z G, Li W M 2008 Chinese Journal of Cardiac Pacing and Electrophysiology 22 347 (in Chinese) [李秀春, 吴晓羽, 张姝, 周中华, 李磊, 梁兆光, 李为民 2008 中国心脏起搏与心电生理杂志 22 347]

  • [1]

    Witkowski F X, Joshua L L, Penkoske P A, Giles W R, Spano M L, Ditto W L, Winfree A T 1998 Nature 392 78

    [2]

    Gray R A, Jalife J, Panfilov A V, Baxter W T, Cabo C, Davidenko J M, Pertsov A M 1995 Science 270 1222

    [3]

    Yuan G Y, Xu L, Xu A G, Wang G R, Yang S P 2011 Chaos, Solitons and Fractals 44 728

    [4]

    Hendrey M, Ott E, Antonsen Jr T M 2000 Phys. Rev. E 61 4943

    [5]

    Wang C N, Yang L J, Yuan L H, Ma J 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 3913

    [6]

    Ma J, Tang J, Wang C N, Jia Y 2011 Int. J. Bifurc. Chaos 21 587

    [7]

    Wang Q Y, Perc M, Duan Z S, Chen G R 2008 Phys. Lett. A 372 5681

    [8]

    Yuan G Y, Wang G R, Chen S G 2005 Commun. Theor. Phys. 44 858

    [9]

    Cao Z J, Li P F, Zhang H, Xie F G, Hu G 2007 Chaos 17 015107

    [10]

    de la Casa M A, de la Rubia F J, Ivanov P C 2007 Chaos 17 015109

    [11]

    Cao Z J, Zhang H, Xie F G, Hu G 2006 Europhys. Lett. 75 875

    [12]

    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]

    [13]

    Ma J, Jia Y, Yi M, Tang J, Xia Y F 2009 Chaos, Solitons and Fractals 41 1331

    [14]

    Sakaguchi H, Fujimoto T 2003 Phys. Rev. E 67 067202

    [15]

    Zykov V S, Mikhailov A S, Müller S C 1997 Phys. Rev. Lett. 78 3398

    [16]

    Qian Y, Song X Y, Shi W, Chen G Z, Xue Y 2006 Acta Phys. Sin. 55 4420 (in Chinese) [钱郁, 宋宣玉, 时伟, 陈光旨, 薛郁 2006 物理学报 55 4420]

    [17]

    Gray R A , Chattipakorn N 2005 Proc. Natl. Acad. Sci. U.S.A. 102 4672

    [18]

    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]

    [19]

    Piller L W 1970 Electronic Instrumentation Theory of Cardiac Technology (London: Staples Press)

    [20]

    Walker R G, Koster R W, Sun C, Moffat G, Barger J, Dodson P P, Chapman F W 2009 Resuscitation 80 773

    [21]

    Stamp A T, Osipov G V, Collins J J 2002 Chaos 12 931

    [22]

    Allessie M, Kirchhof C, Scheffer G J, Chorro F, Brugada J 1991 Circulation 84 1689

    [23]

    Yu C G, Bai R, Chen D L, Huang Y 2008 Cardiac Electrophysiology Basic and Clinical (WuHan: Huazhong University of Science and Technology Press) p4 (in Chinese) [余承高, 白融, 陈栋梁, 黄勇 2008 心脏电生理学基础与临床 (武汉: 华中科技大学出版社) 第4页]

    [24]

    Antzelevitch C 2001 Cardiovascular Research 50 426

    [25]

    Wang J M, Xue Y 2011 International Conference on Network Computing and Information Security Guilin, China, May 14-15, 2011 pp49-53

    [26]

    Yuan G Y, Yang S P, Wang G R, Chen S G 2005 Acta Phys. Sin. 54 1510 (in Chinese) [袁国勇, 杨世平, 王光瑞, 陈式刚 2005 物理学报 54 1510]

    [27]

    Li G Z, Chen Y Q, Tang G N 2012 Acta Phys. Sin. 61 020502 (in Chinese) [黎广钊, 陈咏琪, 唐国宁 2012 物理学报 61 020502]

    [28]

    Bär M, Eiswirth M 1993 Phys. Rev. E 48 R1635

    [29]

    Li X C, Wu X Y, Zhang S, Zhou Z H, Li L, Liang Z G, Li W M 2008 Chinese Journal of Cardiac Pacing and Electrophysiology 22 347 (in Chinese) [李秀春, 吴晓羽, 张姝, 周中华, 李磊, 梁兆光, 李为民 2008 中国心脏起搏与心电生理杂志 22 347]

  • [1] Li Qian-Yun,  Huang Zhi-Jing,  Tang Guo-Ning. Eliminating spiral wave and spatiotemporal chaos in cardiac tissues by suppressing the rotation of spiral wave tip. Acta Physica Sinica, 2018, 67(24): 248201. doi: 10.7498/aps.67.20181291
    [2] Zhou Zhen-Wei, Wang Li-Li, Qiao Cheng-Gong, Chen Xing-Ji, Tian Tao-Tao, Tang Guo-Ning. Terminating spiral waves and spatiotemporal chaos in heart by synchronous repolarization. Acta Physica Sinica, 2013, 62(15): 150508. doi: 10.7498/aps.62.150508
    [3] Wang Xiao-Yan, Wang Peng, Li Qian-Yun, Tang Guo-Ning. Terminating spiral wave and spatiotemporal chaos in cardiac tissues by using late sodium current. Acta Physica Sinica, 2017, 66(13): 138201. doi: 10.7498/aps.66.138201
    [4] Control of spiral waves in excitable media under polarized electric fields. Acta Physica Sinica, 2020, (): . doi: 10.7498/aps.69.20191934
    [5] Chen Xing-Ji, Tian Tao-Tao, Zhou Zhen-Wei, Hu Yi-Bo, Tang Guo-Ning. Synchronization of two spiral waves interacting through a passive medium. Acta Physica Sinica, 2012, 61(21): 210509. doi: 10.7498/aps.61.210509
    [6] Pan Fei, Wang Xiao-Yan, Wang Peng, Li Wei-Xin, Tang Guo-Ning. Controlling spiral wave and spatiotemporal chaos in cardiac tissues by slowing sodium channel activation and inactivation. Acta Physica Sinica, 2016, 65(19): 198201. doi: 10.7498/aps.65.198201
    [7] Qiao Cheng-Gong, Wang Li-Li, Li Wei-Heng, Tang Guo-Ning. Potassium diffusive coupling-induced the variation of spiral wave in cardiac tissues. Acta Physica Sinica, 2013, 62(19): 198201. doi: 10.7498/aps.62.198201
    [8] Pan Fei, Li Wei-Xin, Wang Xiao-Yan, Tang Guo-Ning. Terminating the spiral wave and spatiotemporal chaos in cardiac tissue using the low-pass filtering scheme. Acta Physica Sinica, 2015, 64(21): 218202. doi: 10.7498/aps.64.218202
    [9] Kuang Yu-Lan, Tang Guo-Ning. Suppressions of spiral waves and spatiotemporal chaos in cardiac tissue. Acta Physica Sinica, 2012, 61(10): 100504. doi: 10.7498/aps.61.100504
    [10] Kuang Yu-Lan, Tang Guo-Ning. Eliminate spiral wave and spatiotemporal chaos by using short-term cardiac memory. Acta Physica Sinica, 2012, 61(19): 190501. doi: 10.7498/aps.61.190501
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  • Received Date:  03 April 2012
  • Accepted Date:  23 May 2012
  • Published Online:  05 November 2012

Study on the control of spiral waves in coupled excitable media

  • 1. College of Physics and Technology, Guangxi Normal University, Guilin 541004, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11165004).

Abstract: The control of spiral waves in three-layer coupled excitable media is studied by using the Bär model. The bidirectional coupling between adjacent layers is adopted. We use planar waves generated by a local periodic signal added to the second layer to eliminate spiral waves in the media. The numerical results show that when the couplings among three layer media meet some conditions the spiral waves in the media can be controlled. The control of spiral waves may be achieved by using the complementary coupling strategy. The interaction between planar wave and low-frequency spiral wave can produce high-frequency spiral wave, leading to failure to eliminate spiral waves. There exists an optimal drive width. Both larger and smaller drive width may need larger coupling strength between the first and third layers. The control results depending on the control opportunity are observed. We hope that this study will contribute to the design of the implantable cardioverter defibrillator.

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