基于描述函数方法的神经群自激振荡特性分析

王俊松; 徐瑶

doi:10.7498/aps.63.068701

摘要

在无外界刺激时神经群表现为节律性自激振荡，自激振荡是非线性系统特有的一种运动形式. 在非线性描述函数法理论框架下，对神经群模型自激振荡特性进行分析，并揭示其产生机理. 神经群模型的sigmoid非线性函数（简称为S函数）是其自激振荡的根源. 首先，求解S函数的描述函数；然后，基于S 函数的描述函数得到神经群模型正反馈回路S函数和负反馈回路S函数的等效增益，在此基础上将神经群模型转化为可用描述函数法分析的典型结构形式；最后，应用描述函数法理论对神经群模型自激振荡特性进行理论分析，得到自激振荡特性的定量描述，并通过仿真分析对理论分析结果进行了验证. 理论分析及仿真分析结果表明基于描述函数方法的神经群自激振荡特性分析方法是正确有效的. S 函数是神经系统的典型非线性环节，S函数的处理方法及神经群自激振荡特性分析方法对于其他神经模型的自激振荡特性分析具有参考价值.

关键词:

Abstract

Neural mass model (NMM) can generate spontaneous oscillation even in a resting state. However, it remains little known which mechanism is responsible for NMM’s spontaneous oscillation. From dynamical theory, spontaneous oscillation is an intrinsic property of nonlinear system, which means that the sigmoid nonlinear function (S function) of NMM plays a key role in the emergence of its spontaneous oscillation. In this study, describing function approach is employed to analyze the spontaneous oscillation characteristics of a kind of extended NMM. Firstly, the describing function of S function is derived, through which the two S functions in excitatory and inhibitory feedback loop, respectively, are approximated. Secondly, the NMM is transformed into a typical block diagram composed of a nonlinear unit and a linear unit. Thirdly, in the theoretical framework of describing function approach, theoretical analysis of the spontaneous oscillation characteristics of NMM is conducted, and the oscillation frequencies are determined. The simulation results demonstrate that the theoretical results are correct and the employed approach is effective. Since S function exists extensively in neural system, the proposed approach has a potential application in the spontaneous oscillation analysis of other neural model.

Keywords:

作者及机构信息

王俊松^1,2,
徐瑶¹

1.
天津医科大学生物医学工程学院, 天津 300070;

2.
约翰霍普金斯大学神经科学系, 巴尔的摩 21218

基金项目: 国家自然科学基金重大项目（批准号：91132722）资助的课题.

Authors and contacts

Wang Jun-Song^1,2,
Xu Yao¹

1.
School of Biomedical Engineering, Tianjin Medical University, Tianjin 300070, China;

2.
Department of Neuroscience, Johns Hopkins University, Baltimore 21218, USA

Funds: Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91132722).

参考文献

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施引文献

[1]	Uhlhaas P J, Singer W 2010 Nat. Rev. Neurosci. 11 100
[2]	Schnitzler A, Gross J 2005 Nat. Rev. Neurosci. 6 285
[3]	Liu S B, Wu Y, Hao Z W, Li Y J, Jia N 2012 Acta Phys. Sin. 61 020503 (in Chinese) [刘少宝, 吴莹, 郝忠文, 李银军, 贾宁 2012 61 020503]
[4]	Gu H G, Hui L, Jia B 2012 Acta Phys. Sin. 61 080504 (in Chinese) [古华光, 惠磊, 贾冰 2012 61 080504]
[5]	Jansen B H, Rit V G 1995 Biol. Cybern. 73 357
[6]	Deco G, Jirsa V K, Robinson P A, Breakspear M, Friston K 2008 PLOS. Comput. Biol. 4 e1000092
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[8]	Destexhe A, Sejnowski T J 2009 Biol. Cybern. 101 1
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[14]	Babajani A, Soltanian-Zadeh H 2006 IEEE Trans. Biomed. Eng. 53 1794
[15]	David O, Friston K J 2003 NeuroImage 20 1743
[16]	Buzsáki G, Draguhn A 2004 Science 304 1926
[17]	Cui D, Li X L, Ji X Q, Liu L X 2011 Sci. China: Inf. Sci. 54 1283 (in Chinese) [崔冬, 李小俚, 吉学青, 刘兰祥 2011 中国科学: 信息科学 54 1283]
[18]	van Rotterdam A, Lopes da Silva F H, van den Ende J, Viergever M A, Hermans A J 1982 Bull. Math. Biol. 44 283
[19]	Abbas B F, Hamid S Z 2010 NeuroImage 52 793
[20]	Hu S S 2007 Automatic Control Principle (5th Ed.) (Beijing: Science Press) pp408–422 (in Chinese) [胡寿松 2007 自动控制原理 (第五版) (北京: 科学出版社)第408–422 页]

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