热敏神经元网络中螺旋波死亡和破裂的数值模拟

马军; 谢振博; 陈江星

doi:10.7498/aps.61.038701

摘要

实验发现大脑皮层内出现螺旋波且螺旋波对神经元电信号传递有积极作用.利用细胞网络方法从对大脑皮层观察到的螺旋波进行数值模拟.以包含温度因子的热敏神经元模型在二维空间构造规则网络,研究了神经元膜片温度参数对神经元网络中螺旋波演化影响;定义了一类统计同步因子来刻画温度因子引起螺旋波相变(破裂和死亡)的临界条件.发现在规则网络下,当温度超过一定值后螺旋波会死亡和消失而导致整个网络达到均匀同步;在考虑了弱通道噪声情况下,螺旋波温度超越一定临界值则引起螺旋波的破裂.进一步分析了暂时性发烧昏迷的可能机制在于神经系统某些功能区螺旋波传播电信号的中断.

关键词:

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:

作者及机构信息

1.
兰州理工大学物理系, 兰州 730050;

2.
甘肃省工业过程先进控制重点实验室, 兰州 730050;

3.
杭州电子科技大学物理系, 杭州 310018

基金项目: 国家自然科学基金(批准号: 11005026)和甘肃省教育厅研究生导师基金(批准号: 1010ZTC088)资助的课题.

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).

参考文献

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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
[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
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[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

施引文献

[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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