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

Ma Jun; Xie Zhen-Bo; Chen Jiang-Xing

doi:10.7498/aps.61.038701

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.

Keywords:

Authors and contacts

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
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).

References

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[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
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[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

Cited By

[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 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 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 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 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 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 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 59 5313]
[24]	Zhong M, Tang G N 2010 Acta Phys. Sin. 59 1593 (in Chinese) [钟敏, 唐国宁 2010 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 59 5979]
[26]	Wei H M, Tang G N 2011 Acta Phys. Sin. 60 030501 (in Chinese) [韦海明, 唐国宁 2011 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 59 2339]
[28]	Wei H M, Tang G N 2011 Acta Phys. Sin. 60 040504 (in Chinese) [韦海明, 唐国宁 2011 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 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

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Vol. 61, Issue 3 - 2012-02-05

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