Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Numerical study of the death and breakup of spiral wave in the networks of thermosensitive neurons

Ma Jun Xie Zhen-Bo Chen Jiang-Xing

Numerical study of the death and breakup of spiral wave in the networks of thermosensitive neurons

Ma Jun, Xie Zhen-Bo, Chen Jiang-Xing
PDF
Get Citation
  • The experimential evidences confirm that spiral waves are observed in the disinhibited mammalian neocortex. The scheme of ceullar networks is used to simulate the formation and the evolution of spiral wave in the neocortical slices. The regular networks of neurons are constructed in the two-dimensional space, the dynamical properties of thermosensitive neurons is described by temperature factor, and the effect of membrane temperature on the evolution of spiral wave is investigated in detail. A statistical factor of synchronization is defined to measure the critical condition inducing phase transition of spiral wave (death or breakup) by the factor of temperature of membrane. It is confirmed that spiral wave is removed and the whole networks become homogeneous and synchronous completely when the membrane temperature exceeds a certain threshold; the breakup of spiral wave is induced in the presence of weak channel noise being considered. Furthermore, it is suggested that the mechanism of temporary heat stupor could be the blocking of spiral wave propagation in some functional domain.
    • Funds: Project supported by the National Natural Science Fundation of China (Grant No. 11005026) and the Educational Tutors Fund of Gansu Province, China (Grant No. 1010ZTC088).
    [1]

    Gray R A, Pertsov A M, Jalife J 1998 Nature 392 75

    [2]

    Biktashev V N, Holden A V 1998 Chaos 8 48

    [3]

    Cherry E M, Fenton F H 2008 New J. Phys. 10 125016

    [4]

    Fenton F H, Luther S, Otani N F 2009 Circulation 120 467

    [5]

    Garzon A, Roman O G, Fenton F H 2009 Phys. Rev. E 80 021932

    [6]

    Ma J, Ying H, Li Y L 2007 Chin. Phys. 16 955

    [7]

    Ma J, Jin W Y, Li Y L, Chen Y 2007 Acta Phys. Sin. 56 2456 (in Chinese) [马军, 靳伍银, 李延龙, 陈勇 2007 物理学报 56 2456]

    [8]

    Deng M Y, Shi J, Li H B, Kong L J, Liu M R 2007 Acta Phys. Sin.56 2012 (in Chinese) [邓敏艺, 施娟, 李华兵, 孔令江, 刘慕仁 2007 物理学报 56 2012]

    [9]

    Liu F C, Wang X F, Li X C, Dong L F 2007 Chin. Phys. 16 2640

    [10]

    Yin X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese) [尹小舟, 刘勇 2008物理学报 57 6844]

    [11]

    Tang J, Ma J, Yi M, Jia Y 2008 Chin. Phys. B 17 4100

    [12]

    Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 172844

    [13]

    Ma J, Yi M, Li B W, Li Y L 2008 Chin. Phys. B 17 2438

    [14]

    Gan Z N, Ma J, Zhang G Y, Chen Y 2008 Chin. Phys. B 17 4047

    [15]

    Zhang G Y, Ma J, Yu L C, Chen Y 2008 Chin. Phys. B 17 4107

    [16]

    Dai Y, Tang G N 2009 Acta Phys. Sin. 58 1491 (in Chinese) [戴瑜, 唐国宁 2009 物理学报 58 1491]

    [17]

    Zhang L S, Deng M Y, Kong L J, Liu M R, Tang G N 2009 ActaPhys. Sin. 58 4493 (in Chinese) [张立升, 邓敏艺, 孔令江, 刘慕仁, 唐国宁2009 物理学报 58 4493]

    [18]

    Qiu K, Tang J, Ma J, Luo J M 2010 Chin. Phys. B 19 030508

    [19]

    Gan Z N, Chen X M 2010 Chin. Phys. B 19 050514

    [20]

    Qian Y, Huang X D, Liao X H, Hu G 2010 Chin. Phys. B 19050513

    [21]

    Xie L L, Gao J H 2010 Chin. Phys. B 19 060516

    [22]

    Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 唐国宁 2010 物理学报 59 2319]

    [23]

    Tang D N, Zhang X, Ren W, Tang G N 2010 Acta Phys. Sin. 595313 (in Chinese) [唐冬妮, 张旭, 任卫, 唐国宁 2010 物理学报 59 5313]

    [24]

    Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟敏, 唐国宁 2010 物理学报 59 1593]

    [25]

    Dai Y, Wei H M, Tang G N 2010 Acta Phys. Sin. 59 5979 (in Chinese) [戴瑜, 韦海明, 唐国宁 2010 物理学报 59 5979]

    [26]

    Wei H M, Tang G N 2011 Acta Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 物理学报 60 88 ]

    [27]

    Deng M Y, Tang G N, Kong L J, Liu M R 2010 Acta Phys. Sin.59 2339 (in Chinese) [邓敏艺, 唐国宁, 孔令江, 刘慕仁 2010 物理学报 59 2339]

    [28]

    Wei H M, Tang G N 2011 Acta Phys. Sin. 60 040504 (in Chinese) [韦海明, 唐国宁 2011 物理学报 60 66]

    [29]

    Deng M Y, Tang G N, Kong L J, Liu M R 2011 Chin. Phys. B 20020510

    [30]

    Yuan G Y 2011 Chin. Phys. B 20 040503

    [31]

    Fu Y Q, Zhang H, Cao Z J 2005 Phys. Rev. E 72 046206

    [32]

    Zhang H, Chen J X, Li Y Q 2006 J. Chem. Phys. 125 204503

    [33]

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

    [34]

    Yuan G Y, Yang S P, Wang G R, Chen S G 2008 Chin. Phys. B 171925

    [35]

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

    [36]

    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]

    [37]

    Chen J X, Zhang H, Li Y Q 2006 J. Chem. Phys. 124 014505

    [38]

    Chen J X, Hu B B 2008 Euro Phys. Lett. 84 34002

    [39]

    Chen J X, Xu J R, Yuan X P 2009 J. Phys. Chem. B 11 849

    [40]

    Tang J, Jia Y, Ma J 2009 Commun. Theor. Phys. 51 941

    [41]

    Ouyang Q, Felesselles J M 1996 Nature 379 143

    [42]

    Ouyang Q , Swinney H L, Li G 2000 Phys. Rev. Lett. 84 1047

    [43]

    Zhou L Q, Ouyang Q 2000 Phys. Rev. Lett. 85 1650

    [44]

    Fenton F H, Cherry E M, Hastings H M 2002 Chaos 12 852

    [45]

    Yang J Z, Xie F G, Qu Z L 2003 Phys. Rev. Lett. 91 148302

    [46]

    Bär M, Brusch L, Or-Guil M 2004 Phys. Rev. Lett. 92 119801

    [47]

    Huang X Y, Troy W C, Yang Q 2004 J. Neurosci. 24 9897

    [48]

    Schiff S J, Huang X Y, Wu J Y 2007 Phys. Rev. Lett. 98 178102

    [49]

    He D H, Shi P L, Stone L W 2003 Phys. Rev. E 67 27201

    [50]

    Woo S J, Lee J, Lee J K 2003 Phys. Rev. E 68 016208

    [51]

    Perc M 2007 Chaos, Solitons and Fractals 31 280

    [52]

    Ma J, Wu Y, Ying H P 2011 Chin. Sci. Bull. 56 151

    [53]

    Ma J, Yang L J, Wu Y 2010 Commun. Theor. Phys. 54 583

    [54]

    Ma J, Wang C N, Jin W Y 2010 Appl. Math. Comput. 217 3844

    [55]

    Hodgkin A L, Huxley A F 1952 J. Phys. London 117 500

    [56]

    Braun H A, Wissing H, Schäfer 1994 Nature 367 270

    [57]

    Braun H A, Schafer K, Voigt K 1997 J. Comp. Neurol. 4 335

    [58]

    Gong Y B, Xu B, Xu Q 2006 Phys. Rev. E 73 046137

    [59]

    Sun X J, Perc M, Lu Q S 2008 Chaos 18 023102

    [60]

    Sun X J, Lu Q S, Kurth J 2009 Int. J. Bifur. Chaos 19 737

    [61]

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

    [62]

    Yu G, Ma J, Tang J 2010 Int. J. Mod. Phys. B 24 4555

    [63]

    Fox R F, Lu Y N 1994 Phys. Rev. E 49 3421

  • [1]

    Gray R A, Pertsov A M, Jalife J 1998 Nature 392 75

    [2]

    Biktashev V N, Holden A V 1998 Chaos 8 48

    [3]

    Cherry E M, Fenton F H 2008 New J. Phys. 10 125016

    [4]

    Fenton F H, Luther S, Otani N F 2009 Circulation 120 467

    [5]

    Garzon A, Roman O G, Fenton F H 2009 Phys. Rev. E 80 021932

    [6]

    Ma J, Ying H, Li Y L 2007 Chin. Phys. 16 955

    [7]

    Ma J, Jin W Y, Li Y L, Chen Y 2007 Acta Phys. Sin. 56 2456 (in Chinese) [马军, 靳伍银, 李延龙, 陈勇 2007 物理学报 56 2456]

    [8]

    Deng M Y, Shi J, Li H B, Kong L J, Liu M R 2007 Acta Phys. Sin.56 2012 (in Chinese) [邓敏艺, 施娟, 李华兵, 孔令江, 刘慕仁 2007 物理学报 56 2012]

    [9]

    Liu F C, Wang X F, Li X C, Dong L F 2007 Chin. Phys. 16 2640

    [10]

    Yin X Z, Liu Y 2008 Acta Phys. Sin. 57 6844 (in Chinese) [尹小舟, 刘勇 2008物理学报 57 6844]

    [11]

    Tang J, Ma J, Yi M, Jia Y 2008 Chin. Phys. B 17 4100

    [12]

    Ma J, Wang C N, Jin W Y, Li Y L, Pu Z S 2008 Chin. Phys. B 172844

    [13]

    Ma J, Yi M, Li B W, Li Y L 2008 Chin. Phys. B 17 2438

    [14]

    Gan Z N, Ma J, Zhang G Y, Chen Y 2008 Chin. Phys. B 17 4047

    [15]

    Zhang G Y, Ma J, Yu L C, Chen Y 2008 Chin. Phys. B 17 4107

    [16]

    Dai Y, Tang G N 2009 Acta Phys. Sin. 58 1491 (in Chinese) [戴瑜, 唐国宁 2009 物理学报 58 1491]

    [17]

    Zhang L S, Deng M Y, Kong L J, Liu M R, Tang G N 2009 ActaPhys. Sin. 58 4493 (in Chinese) [张立升, 邓敏艺, 孔令江, 刘慕仁, 唐国宁2009 物理学报 58 4493]

    [18]

    Qiu K, Tang J, Ma J, Luo J M 2010 Chin. Phys. B 19 030508

    [19]

    Gan Z N, Chen X M 2010 Chin. Phys. B 19 050514

    [20]

    Qian Y, Huang X D, Liao X H, Hu G 2010 Chin. Phys. B 19050513

    [21]

    Xie L L, Gao J H 2010 Chin. Phys. B 19 060516

    [22]

    Tang D N, Tang G N 2010 Acta Phys. Sin. 59 2319 (in Chinese) [唐冬妮, 唐国宁 2010 物理学报 59 2319]

    [23]

    Tang D N, Zhang X, Ren W, Tang G N 2010 Acta Phys. Sin. 595313 (in Chinese) [唐冬妮, 张旭, 任卫, 唐国宁 2010 物理学报 59 5313]

    [24]

    Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟敏, 唐国宁 2010 物理学报 59 1593]

    [25]

    Dai Y, Wei H M, Tang G N 2010 Acta Phys. Sin. 59 5979 (in Chinese) [戴瑜, 韦海明, 唐国宁 2010 物理学报 59 5979]

    [26]

    Wei H M, Tang G N 2011 Acta Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 物理学报 60 88 ]

    [27]

    Deng M Y, Tang G N, Kong L J, Liu M R 2010 Acta Phys. Sin.59 2339 (in Chinese) [邓敏艺, 唐国宁, 孔令江, 刘慕仁 2010 物理学报 59 2339]

    [28]

    Wei H M, Tang G N 2011 Acta Phys. Sin. 60 040504 (in Chinese) [韦海明, 唐国宁 2011 物理学报 60 66]

    [29]

    Deng M Y, Tang G N, Kong L J, Liu M R 2011 Chin. Phys. B 20020510

    [30]

    Yuan G Y 2011 Chin. Phys. B 20 040503

    [31]

    Fu Y Q, Zhang H, Cao Z J 2005 Phys. Rev. E 72 046206

    [32]

    Zhang H, Chen J X, Li Y Q 2006 J. Chem. Phys. 125 204503

    [33]

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

    [34]

    Yuan G Y, Yang S P, Wang G R, Chen S G 2008 Chin. Phys. B 171925

    [35]

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

    [36]

    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]

    [37]

    Chen J X, Zhang H, Li Y Q 2006 J. Chem. Phys. 124 014505

    [38]

    Chen J X, Hu B B 2008 Euro Phys. Lett. 84 34002

    [39]

    Chen J X, Xu J R, Yuan X P 2009 J. Phys. Chem. B 11 849

    [40]

    Tang J, Jia Y, Ma J 2009 Commun. Theor. Phys. 51 941

    [41]

    Ouyang Q, Felesselles J M 1996 Nature 379 143

    [42]

    Ouyang Q , Swinney H L, Li G 2000 Phys. Rev. Lett. 84 1047

    [43]

    Zhou L Q, Ouyang Q 2000 Phys. Rev. Lett. 85 1650

    [44]

    Fenton F H, Cherry E M, Hastings H M 2002 Chaos 12 852

    [45]

    Yang J Z, Xie F G, Qu Z L 2003 Phys. Rev. Lett. 91 148302

    [46]

    Bär M, Brusch L, Or-Guil M 2004 Phys. Rev. Lett. 92 119801

    [47]

    Huang X Y, Troy W C, Yang Q 2004 J. Neurosci. 24 9897

    [48]

    Schiff S J, Huang X Y, Wu J Y 2007 Phys. Rev. Lett. 98 178102

    [49]

    He D H, Shi P L, Stone L W 2003 Phys. Rev. E 67 27201

    [50]

    Woo S J, Lee J, Lee J K 2003 Phys. Rev. E 68 016208

    [51]

    Perc M 2007 Chaos, Solitons and Fractals 31 280

    [52]

    Ma J, Wu Y, Ying H P 2011 Chin. Sci. Bull. 56 151

    [53]

    Ma J, Yang L J, Wu Y 2010 Commun. Theor. Phys. 54 583

    [54]

    Ma J, Wang C N, Jin W Y 2010 Appl. Math. Comput. 217 3844

    [55]

    Hodgkin A L, Huxley A F 1952 J. Phys. London 117 500

    [56]

    Braun H A, Wissing H, Schäfer 1994 Nature 367 270

    [57]

    Braun H A, Schafer K, Voigt K 1997 J. Comp. Neurol. 4 335

    [58]

    Gong Y B, Xu B, Xu Q 2006 Phys. Rev. E 73 046137

    [59]

    Sun X J, Perc M, Lu Q S 2008 Chaos 18 023102

    [60]

    Sun X J, Lu Q S, Kurth J 2009 Int. J. Bifur. Chaos 19 737

    [61]

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

    [62]

    Yu G, Ma J, Tang J 2010 Int. J. Mod. Phys. B 24 4555

    [63]

    Fox R F, Lu Y N 1994 Phys. Rev. E 49 3421

  • [1] Zhao Long, Yang Ji-Ping, Zheng Yan-Hong. Modulation of nonlinear coupling on the synchronization induced by linear coupling. Acta Physica Sinica, 2013, 62(2): 028701. doi: 10.7498/aps.62.028701
    [2] Xu Ying, Wang Chun-Ni, Jin Wu-Yin, Ma Jun. Investigation of emergence of target wave and spiral wave in neuronal network induced by gradient coupling. Acta Physica Sinica, 2015, 64(19): 198701. doi: 10.7498/aps.64.198701
    [3] 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
    [4] 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
    [5] Wang Peng, Li Qian-Yun, Tang Guo-Ning. Spontaneous generation of spiral wave in the array of Hindmarsh-Rose neurons. Acta Physica Sinica, 2018, 67(3): 030502. doi: 10.7498/aps.67.20172140
    [6] Wang Peng, Li Qian-Yun, Huang Zhi-Jing, Tang Guo-Ning. Spontaneous formation of ordered waves in chaotic neuronal network with excitory-inhibitory connections. Acta Physica Sinica, 2018, 67(17): 170501. doi: 10.7498/aps.67.20180506
    [7] Yu Wei, Deng Zi-Long, Wu Su-Chen, Yu Cheng, Wang Chao. Hydrodynamics of double emulsion passing through a microfuidic Y-junction. Acta Physica Sinica, 2019, 68(5): 054701. doi: 10.7498/aps.68.20181877
    [8] Tian Chang-Hai, Deng Min-Yi, Kong Ling-Jiang, Liu Mu-Ren. Cellular automaton simulation with directed small-world networks for the dynamical behaviors of spiral waves. Acta Physica Sinica, 2011, 60(8): 080505. doi: 10.7498/aps.60.080505
    [9] Huang Zhi-Jing, Li Qian-Yun, Bai Jing, Tang Guo-Ning. Entropy measurement of ordered patterns in neuronal network with repulsive coupling. Acta Physica Sinica, 2019, 68(11): 110503. doi: 10.7498/aps.68.20190231
    [10] Liu Shao-Bao, Wu Ying, Hao Zhong-Wen, Li Yin-Jun, Jia Ning. Effects of sodium and potassium ion channel fluctuation on the spatiotemporal patterns of neuronal network. Acta Physica Sinica, 2012, 61(2): 020503. doi: 10.7498/aps.61.020503
    [11] Chen Yong, Jin Wu-Yin, Ma Jun, Li Yan-Long. Suppression of meandering spiral waves in the excitable media due to a perturbation with stochastic phase. Acta Physica Sinica, 2007, 56(4): 2456-2465. doi: 10.7498/aps.56.2456
    [12] Zhang Guo-Yong, Chen Yong, Gan Zheng-Ning, Ma Jun. Instability of spiral wave in small-world networks. Acta Physica Sinica, 2008, 57(9): 5400-5406. doi: 10.7498/aps.57.5400
    [13] Wei Hai-Ming, Tang Guo-Ning. Numerical simulation study on effects of alternansbehavior on spiral waves. Acta Physica Sinica, 2011, 60(4): 040504. doi: 10.7498/aps.60.040504
    [14] 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
    [15] 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
    [16] Dong Li-Fang, Bai Zhan-Guo, He Ya-Feng. Sparse and dense spiral waves in heterogeneous excitable media. Acta Physica Sinica, 2012, 61(12): 120509. doi: 10.7498/aps.61.120509
    [17] Zhou Zhen-Wei, Chen Xing-Ji, Tian Tao-Tao, Tang Guo-Ning. Study on the control of spiral waves in coupled excitable media. Acta Physica Sinica, 2012, 61(21): 210506. doi: 10.7498/aps.61.210506
    [18] Chen Xing-Ji, Qiao Cheng-Gong, Wang Li-Li, Zhou Zhen-Wei, Tian Tao-Tao, Tang Guo-Ning. Evolution of spiral waves in indirectly coupled excitable medium with time-delayed coupling. Acta Physica Sinica, 2013, 62(12): 128201. doi: 10.7498/aps.62.128201
    [19] Cheng Yu-Guo, Cheng Mou-Sen, Wang Mo-Ge, Li Xiao-Kang. Numerical study on the effects of magnetic field on helicon plasma waves and energy absorption. Acta Physica Sinica, 2014, 63(3): 035203. doi: 10.7498/aps.63.035203
    [20] Li Wei-Heng, Li Wei-Xin, Pan Fei, Tang Guo-Ning. Transformation of spiral wave to plan wave in the two layers of coupled excitable media. Acta Physica Sinica, 2014, 63(20): 208201. doi: 10.7498/aps.63.208201
  • Citation:
Metrics
  • Abstract views:  1631
  • PDF Downloads:  571
  • Cited By: 0
Publishing process
  • Received Date:  23 April 2011
  • Accepted Date:  25 May 2011
  • Published Online:  15 March 2012

Numerical study of the death and breakup of spiral wave in the networks of thermosensitive neurons

  • 1. Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China;
  • 2. Key Laboratory of Gansu Advanced Control for Industria Processes, Lanzhou 730050, China;
  • 3. Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China
Fund Project:  Project supported by the National Natural Science Fundation of China (Grant No. 11005026) and the Educational Tutors Fund of Gansu Province, China (Grant No. 1010ZTC088).

Abstract: The experimential evidences confirm that spiral waves are observed in the disinhibited mammalian neocortex. The scheme of ceullar networks is used to simulate the formation and the evolution of spiral wave in the neocortical slices. The regular networks of neurons are constructed in the two-dimensional space, the dynamical properties of thermosensitive neurons is described by temperature factor, and the effect of membrane temperature on the evolution of spiral wave is investigated in detail. A statistical factor of synchronization is defined to measure the critical condition inducing phase transition of spiral wave (death or breakup) by the factor of temperature of membrane. It is confirmed that spiral wave is removed and the whole networks become homogeneous and synchronous completely when the membrane temperature exceeds a certain threshold; the breakup of spiral wave is induced in the presence of weak channel noise being considered. Furthermore, it is suggested that the mechanism of temporary heat stupor could be the blocking of spiral wave propagation in some functional domain.

Reference (63)

Catalog

    /

    返回文章
    返回