神经元网络中分布式电流诱导靶波机理研究

胡柏林; 马军; 李凡; 蒲忠胜

doi:10.7498/aps.62.058701

摘要

以四变量的Hodgkin-Huxley神经元模型构建规则网络来研究分布式电流刺激诱导靶波问题. 在一个二维规则网络的局部方形区域输入恒定刺激电流I1, 其余区域结点上的神经元输入刺激电流I2 来刻画分布式电流. 分别研究了耦合强度、刺激电流I1作用区域(受控神经元个数)、分布式电流梯度(I=I1-I2)对靶波形成的影响. 研究发现: 刺激的区域越小, 需要的电流梯度(I)越大; 耦合强度越大, 诱导靶波所需要的电流梯度(I)也越大. 最后讨论了分布式电流作用和靶波的形成机理. 进一步研究发现, 诱导的靶波对通道噪声有较强的抗干扰性.

关键词:

Abstract

The formation of target wave in the network of Hodgkin-Huxley neuron with four variables is investigated by inputing a distribuled current. A stimulus current (I1) is input in to a local square area, and another stimulus current (I2) is input into the nodes of the network thus the distributed current is depicted. The development of target wave is measured by changing the coupling intensity, the size (number of the controlled neurons) of the local area into which current I1 is input, the gradient current (I =I1-I2). It is found that higher gradient current (I) is necessary to induce target wave when local area into which current I1 is input is smaller in size and the coupling intensity is higher in value. Finally, the potential mechanisms of the stimulus current and target wave formation are discussed in brief. Eextensive numerical results confirm that the developed target wave is robust to a certain channel noise.

Keywords:

作者及机构信息

1.
兰州理工大学物理系, 兰州 730050

基金项目: 国家自然科学基金(批准号: 11265008) 资助的课题.

Authors and contacts

1.
Department of Physics, Lanzhou University of Techology, Lanzhou 730050, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11265008).

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施引文献

[1]	Tang X W 2003 Principle of Brain function (Hangzhou: Zhejiang University Publishing House) (In Chinese) [唐孝威 2003 脑功能原理 (杭州: 浙江大学出版社)]
[2]	Liu Z R, Wen T Q, Yao X D 2006 Brain and Nonlinear Dynamics (Beijing: Science Press) (In Chinese) [刘曾荣, 文铁桥, 姚晓东 2006 脑与非线性动力学 (北京: 科学出版社)]
[3]	Rabinovich M I, Varona P, Selverston A I, Abarbanel H D 2006 Rev. Mod. Phys. 78 1213
[4]	Wang Q Y, Shi X, Lu Q S 2008 Dynamics of synchronization in the Coupled neuronal network Beijing: Science Press (in Chinese) [王青云, 石霞, 陆启韶 2008 神经元耦合系统的同步动力学 (北京: 科学出版社)]
[5]	Ermentrout G B, Terman D H 2010 Mathematical Foundations of Neuroscienc: Interdisciplinary Applied Mathematics (1st Edn.) (Springer)
[6]	Izhikevich E M 2007 Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (The MIT Press Cambridge, Massachusetts London)
[7]	Ma J, Tang J 2011 Optimal Control for Patterns in Space-time System (Wuhan: Huazhong University of Science and Technology Publishing House) (in Chinese)[马军, 唐军 2011 时空系统斑图优化控制 (武汉: 华中科技大学出版社)]
[8]	Izhikevich E M 2004 IEEE T Neural Networ 15 1063
[9]	Li Y Y, Jia B, Gu H G 2012 Acta Phys. Sin. 61 070504 (in Chinese) [李玉叶, 贾冰, 古华光 2012 物理学报 61 070504]
[10]	Li Y Y, Jia B, Gu H G 2012 Commun. Theory. Phys. 57 817
[11]	Zhou C S, Kurth J 2003 Chaos 13 401
[12]	Chen H S, Zhang J Q 2008 Phys. Rev. E 77 026207.
[13]	Liu F, Yu Y G, Wang W 2001 Phys. Rev. E 63 051912
[14]	Gu H G, Yang M H, Li L 2003 Phys. Lett. A 319 89
[15]	Tessone C J, Wio H S 2007 Physica A 374 46
[16]	Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[17]	Benzit R, Sutera A, Vulpiani A 1981 J. Phys. A Math. Gen. 14 L453
[18]	Gammaitoni L, Hänggi P, Marchesoni F 2009 Eur. Phys. J. B 69 1
[19]	Wei D Q, Zhang B, Qiu D Y, Luo X S 2010 Chin. Phys. B 19 100513
[20]	Wang Q Y, Perc M, Duan Z S 2010 Int. J. Mod. Phys. B 24 1201
[21]	Wang Q Y, Perc M, Duan Z S, Chen G R 2009 Chaos 19 023112
[22]	Ning W L, Zhang Z Z, Zeng S Y 2012 Chin. Phys. B 21 028702
[23]	Perc M 2005 Phys. Rev. E 72 016207
[24]	Zaikin A A, Kurths J, Schimansky-Geier L 2000 Phys. Rev. Lett. 85 227
[25]	Ozer M, Perc M, Uzuntarla M 2009 Phys. Lett. A 373 964
[26]	Luo J M, Zhan M 2008 Phys. Lett. A 372 2415
[27]	Qian Y, Huang X D, Hu G 2010 Phys. Rev. E 81 036101
[28]	Qian Y, Wang C J, Shi H S 2011 Chin. Phys. B 20 108201
[29]	Makkes van der Deijl G B, Panfilov A V 2008 Phys. Rev. E 78 012901
[30]	Keldermann R H, Nash M P, Panfilov A V 2007 J. Stat. Phys. 128 375
[31]	Tang D N, Zhang X, Ren W, Tang G N 2012 Acta. Phys. Sin. 59 5313 (in Chinese) [唐冬妮, 张旭, 任卫, 唐国宁 2012 物理学报 59 5313]
[32]	Ma J, Wu N J, Ying H P, Yuan L H 2006 Commun. Theor. Phys. 45 121
[33]	Clayton R H, Panfilov A V 2008 Prog. Biophys Mol. Biol. 96 19
[34]	Tusscher K H, Hren R, Panfilov A V 2007 Circ. Res. 100 e87
[35]	Tusscher K H, Panfilov A V 2008 Prog Biophys Mol. Biol. 96 152
[36]	Tusscher K H, Mourad A, Nash M P 2009 Exp. Physiol. 94 553
[37]	Chen J X, Mao J W, Hu B B 2009 Phys. Rev. E 79 066209
[38]	Chen J X, Xu J R, Yuan X P 2009 J. Phys. Chem. B 113 849
[39]	Ma J, Ying H P, Pan G W, Pu Z S 2005 Chin. Phys. Lett. 22 2176
[40]	Cao Z J, Li P F, Zhang H 2007 Chaos 17 015107
[41]	Wu N J, Zhang H, Ying H P 2006 Phys. Rev. E 73 060901
[42]	Zhan M, Zou W, Liu X 2010 Phys. Rev. E 81 036211
[43]	Luo J M, Zhang B S, Zhan M 2009 Chaos 19 033133
[44]	Luo J M, Zhan M 2008 Phys. Rev. E 78 016214
[45]	Davidsen J, Zhan M, Kapral R 2008 Phys. Rev. Lett. 101 208302
[46]	Cai M C, Pan J T, Zhang H 2012 Phys. Rev. E 86 016208
[47]	Gao X, Feng X, Cai M C 2012 Phys. Rev. E 85 016213
[48]	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 040504]
[49]	Dong L F, Yue H, Fan W L, Li Y Y, Yang Y J, Xiao H 2011 Acta Phys. Sin. 60 065206 (in Chinese) [董丽芳, 岳晗, 范伟丽, 李媛媛, 杨玉杰, 肖红 2011 物理学报 60 065206]
[50]	Weise L D, Panfilov A V 2011 PLoS One. 6 e27264
[51]	Sridhar S, Sinha S, Panfilov A V 2010 Phys. Rev. E 82 051908
[52]	Keldermann R H, Nash M P, Panfilov A V 2009 Physica D 238 1000
[53]	Keldermann R H, Tusscher K H, Nash M P 2008 Am. J. Physiol Heart Circ Physiol 294 H764
[54]	Barbieri R, Frank L M, Nguyen D P 2004 Neural Comput 16 277
[55]	Ma J, Huang L, Ying H P, Pu Z S 2012 Chin. Sci. Bull. 57 2094
[56]	Ma J, Xie Z B, Chen J X 2012 Acta Phys. Sin. 61 038701 (in Chinese) [马军, 谢振博, 陈江星 2012 物理学报 61 038701]
[57]	Ma J, Wang C N, Jin W Y, Wu Y 2010 Appl. Math. Comput. 217 3844
[58]	Hodgkin A L, Huxley A F 1952 J. Physiol (London) 117 500
[59]	Fox R F, Lu Y N 2004 Phys. Rev. E 49 3421
[60]	Hu B B, Zhang H 2003 Int. J. Mod. Phys. B 17 3988
[61]	Zhang H, Hu B B, Hu G 2003 Phys. Rev. E 68 026134

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