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神经动力学研究进展和若干思考

韩芳 王青云

韩芳, 王青云. 神经动力学研究进展和若干思考. 力学学报, 2022, 54(12): 1-9 doi: 10.6052/0459-1879-22-404
引用本文: 韩芳, 王青云. 神经动力学研究进展和若干思考. 力学学报, 2022, 54(12): 1-9 doi: 10.6052/0459-1879-22-404
Han Fang, Wang Qingyun. Research advances and some thoughts on neurodynamics. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 1-9 doi: 10.6052/0459-1879-22-404
Citation: Han Fang, Wang Qingyun. Research advances and some thoughts on neurodynamics. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 1-9 doi: 10.6052/0459-1879-22-404

神经动力学研究进展和若干思考

doi: 10.6052/0459-1879-22-404
基金项目: 国家自然科学基金资助项目(11932003, 11972115, 12272092)
详细信息
    作者简介:

    王青云, 教授, 主要研究方向: 神经与智能系统动力学. E-mail: nmqingyun@163.com

  • 中图分类号: O313

RESEARCH ADVANCES AND SOME THOUGHTS ON NEURODYNAMICS

  • 摘要: 神经动力学是动力学与控制学科的基础性分支, 属于力学与脑科学、智能科学的国际前沿交叉学科领域, 主要是通过动力学与控制的基本理论和方法, 建立合理的模型来探究神经系统电生理动力学行为和脑认知功能的机理. 近年来, 国内外学者在神经动力学的基础研究方面取得了显著成果, 包括神经元和神经元网络动力学行为的深入研究、大脑不同功能结构的建模分析以及神经疾病关联脑区的网络动力学建模与控制等. 本文首先对国内外神经动力学研究领域取得的进展做了较全面的概括分析, 特别是给出了建模方面的发展历程. 进而, 基于解析生物神经网络及其动力学的研究成果, 对神经动力学未来的研究方向提出了一些思考展望, 期望神经动力学的研究将助力具备较强可解释性和泛化能力的类脑智能原理和方法的突破及在重大工程中的应用.

     

  • 图  1  皮质−丘脑环路网络框架图: (a)原始的皮质−丘脑网络, 由皮质子网络和丘脑子网络两部分组成. PY: 兴奋性锥体神经元集群, IN1: 抑制性中间神经元集群, TC: 丘脑中继神经元集群, RE: 丘脑网状核神经元集群. (b)王青云教授团队[41-44]所建立的皮质−丘脑网络, 其中在皮质子网络中引入了第二抑制性中间神经元集群IN2

    Figure  1.  Framework diagram of the cortico-thalamic circuit network.(a) The original cortico-thalamic network consists two parts: cortical sub-network and thalamic brain network. PY: excitatory pyramidal neuronal population, IN1: inhibitory interneuronal population, TC: thalamic relay neuronal population, RE: thalamic reticular nucleus neuronal population. (b) The cortico-thalamic network established by Qingyun Wang et al.[41-44], in which a second inhibitory interneuron population IN2 was introduced in the cortical subnetwork

    表  1  典型的神经元模型汇总

    Table  1.   Typical neuronal models

    序号模型名称提出背景及时间模型描述模型特点
    1 HH模型[2] 基于对乌贼的神经刺激电位数据推导得出(1952) 动作电位的变化受到神经轴突膜中的K+, Na+通道电流和漏电流的影响; 包含与Na+相关的两个门控变量(m, h)和与K+相关的一个门控变量(n)对应的微分方程 该模型能够准确地解释实验结果, 量化描述了神经元膜电位上电压与电流的变化过程; 时间复杂度较高, 不适合在大型网络中使用
    2 FHN模型[3] 简化的HH模型, 定性模拟神经元的振荡行为(1955) 包含一个代表神经元膜电位变化的快子系统和一个代表通道失活的慢子系统的模型 包含双稳定性的、描述振荡峰放电动力学的简化模型
    3 HR模型[4] 根据电压钳实验所获得的大量关于蜗牛神经细胞的数据而提出的模型(1984) 包含一个产生动作电位的快子系统和一个调节尖峰模式的慢子系统 它不仅是神经元簇行为的一个数学模型, 也是一类可兴奋的神经元模型, 能模拟软体动物神经元的重复峰和不规则行为. 由于形式简单, 便于计算, 被认为是分析现实神经元网络的理想模型
    4 ML模型[5] 再现巨大藤壶纤维中与钙离子和钾离子电导相关的各种振荡行为(1981) 动作电位变化受到瞬时激活Ca2+电流、较慢激活K+电流和漏电流的影响; 包含与K+相关的门控变量(w)对应的微分方程 阶数较低, 参数简单且具有生理意义, 可以较全面反应神经元的各种特性
    5 Chay模型[6] 重现胰腺β细胞的放电行为(1985) 动作电位受到混合Na+-Ca2+, K+通道电流和漏电流的影响; 包含与K+相关的门控变量(n)和与Ca2+相关的门控变量(C)对应的微分方程 能较好地模拟实际可激发细胞的周期性放电、混沌放电和峰放电模式
    6 Izhikevich
    模型[7]
    通过对HH模型进行分岔分析, 并结合IF模型的计算效率提出(2003) 包含两个微分方程, 分别描述动作电位和恢复变量的变化 能模拟丰富的脉冲放电形式, 同时具有很高的计算性能, 适合于大型网络的仿真
    7 IF模型[8] 简单描述神经元对外部输入的响应(1907) 动作电位仅受到漏电流的影响; 当膜电位达到设定阈值, 一个尖峰出现, 之后被重置为静息状态 该模型是对生物神经元的一种形式化描述, 对神经元的信息处理过程进行抽象, 通常被用于电路模拟
    下载: 导出CSV

    表  2  癫痫和帕金森疾病的动力学模型汇总

    Table  2.   Dynamical models of epilepsy and Parkinson's disease

    疾病模型尺度模型提出背景模型特点
    癫痫 神经场模型 Zetterberg等[53]首次报道了在神经场模型中研究阵发性尖峰的尝试(1978) 该模型旨在代表一个局部神经元群体, 包含三个亚组神经元(两个兴奋和一个抑制), 并与正反馈和负反馈环连接
    神经元网络 Traub等[54]建立CA2-CA3神经元网络模型探究癫痫样活动的传播(1987) 通过计算机模拟(1000个神经元模型细胞阵列), 研究了从CA2到CA3的癫痫样场电位传播的机制
    神经元 Lytton等[55]在单细胞水平上提出了一个丘脑皮层神经元的计算机模型(1992) 该神经元模型包括9个电压依赖的离子通道, 并考虑了树突形态
    神经元网络 Destexhe[56]提出丘脑皮质神经元网络(1999) 该模型由不同的一维层的皮质和丘脑细胞组成, 提示丘脑皮层回路可产生两种类型的棘慢波振荡
    神经场模型 Wendling等[39]表明神经场模型可以产生与颞叶癫痫记录的癫痫样信号惊人相似的信号(2002) 该模型考虑局部神经元群之间的相互作用, 常用于解释波形的数据
    平均场模型 Robinson等[57]提出了一个结构相似的皮质丘脑模型, 并进行了分岔和参数敏感性分析(2003) 该模型显示出许多与相关波(慢波、θ波、α波、纺锤波)有关的“正常”行为, 以及引发失神发作的“病理”行为
    神经场模型 Taylor等[40]提出了皮质环路网络动力学模型(2011) 该模型由皮质兴奋性锥体神经元集群和两个具有不同时间尺度的抑制性中间神经元集群组成, 可模拟出失神癫痫发作的2~4赫兹左右的棘慢波振荡
    神经场模型 Fan等[45]提出了改进的皮质-丘脑网络, 对癫痫失神发作的棘慢波振荡动力学进行探究(2016) 改进的模型网络由皮质子网络和丘脑子网络两部分组成, 其中皮质子网络由一个兴奋性锥体神经元集群和两个具有快慢时间尺度的抑制性中间神经元集群组成
    神经元网络 Zhang等[58]提出了DG-CA3神经元网络模型探究神经元颞叶癫痫样放电的产生(2017) 该模型考虑了齿状回和CA3内部的多种类型神经元, 通过突触连接形成神经元网络, 可实现发作间期、发作前期和发作期的转迁
    帕金森疾病 神经元网络 最常见也是最具有代表性的为Terman等[47]提出的丘脑底核−苍白球神经元网络模型(2002) 该模型包含一定数量的丘脑底核神经元和苍白球外侧神经元, 后续被用于模拟帕金森中的异常同步振荡和簇放电等行为
    平均场模型 van Albada等[59]提出皮层−基底节−丘脑结构的平均场模型探究核团的放电率变化(2009) 该模型考虑帕金森疾病状态下神经元集群的放电率和放电模式的转迁
    神经元网络 So等[60]基于Terman等[47]的工作重构了基底节丘脑神经元网络的拓扑构型(2011) 该模型包含基底节和丘脑两部分, 能够更有效地模拟与帕金森症有关的各种病态特征
    神经元模型与平均场模型的耦合 Kerr等[61]构造了一个由神经元网络和平均场两种尺度合成的用于研究大脑信息流的帕金森症模型(2013) 该模型证实大脑的大尺度振荡环境(即场模型)对神经元子网络中的信息处理具有较强的影响
    神经元网络 Yu等[62]提出了带纹状体微环路的基底节−丘脑模型, 进一步完善了So等[60]的模型(2019) 该模型更详细地模拟了基底节内部的神经元网络, 包含了纹状体内部的三种类型神经元, 可用于探究帕金森中的异常贝塔振荡起源
    神经元网络 Yu等[63]提出了初级运动皮层−基底节−丘脑网络的详细动力学模型(2022) 该模型中初级运动皮层采用分层结构, 模拟帕金森疾病中各种病态特征, 并复现临床中观察到的异常相位幅值耦合现象
    下载: 导出CSV
  • [1] Freeman WJ. Mesoscopic neurodynamics: From neuron to brain. Journal of Physiology-Paris, 2000, 94(5-6): 303-322 doi: 10.1016/S0928-4257(00)01090-1
    [2] Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 1952, 117(4): 500-544 doi: 10.1113/jphysiol.1952.sp004764
    [3] Fitzhugh R. Mathematical models of threshold phenomena in the nerve membrane. Bulletin of Mathematical Biology, 1955, 17(4): 257-278
    [4] Hindmarsh JL, Rose RM. A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society B: Biological Sciences, 1984, 221(1222): 87-102
    [5] Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 1981, 35(1): 193-213 doi: 10.1016/S0006-3495(81)84782-0
    [6] Chay TR. Chaos in a three-variable model of an excitable cell. Physica D: Nonlinear Phenomena, 1985, 16(2): 233-242 doi: 10.1016/0167-2789(85)90060-0
    [7] Izhikevich EM. Simple model of spiking neurons. IEEE Transactions on Neural Networks, 2015, 14: 1569-1572
    [8] Lapicque, L. Recherches quantitatives sur l’excitation ´electrique des nerfs trait´ee comme une polarisation. J. Physiol. Pathol. Gen., 1907, 9: 620-635
    [9] Rinzel J. Bursting oscillations in an excitable membrane model. Springer Berlin Heidelberg, 1985, 47(3): 357-366
    [10] Izhikevich EM. Neural excitability, spiking and bursting. International Journal of Bifurcation and Chaos, 2012, 10(6): 1171-1266
    [11] 王青云, 陆启韶. 兴奋性化学突触耦合的神经元的同步. 动力学与控制学报, 2020, 18(1): 1-5 (Wang Rubin. Research advances in neurodynamics. Journal of Dynamics and Control, 2020, 18(1): 1-5 (in Chinese) doi: 10.6052/1672-6553-2020-013
    [12] 王海侠, 陆启韶, 郑艳红. 神经元模型的复杂动力学: 分岔与编码. 动力学与控制学报, 2009, 7(4): 293-296 (Wang Haixia, Lu Qishao, Zheng Yanhong. Complex dynamics of the neuronal model: bifurcation and encoding. Journal of Dynamics and Control, 2009, 7(4): 293-296 (in Chinese)
    [13] Canavier CC. Reciprocal excitatory synapses convert pacemaker-like Firing into burst firing in a simple model of coupled neurons. Neurocomputing, 2000, 32: 331-338
    [14] Booth V, Bose A. Transitions between different synchronous firing modes using synaptic depression. Neurocomputing, 2002, 44: 61-67
    [15] Casado JM. Synchronization of two Hodgkin–Huxley neurons due to internal noise. Physics Letters A, 2003, 310(5-6): 400-406 doi: 10.1016/S0375-9601(03)00387-6
    [16] Wang Q, Perc M, Duan Z, et al. Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2009, 80(2): 026206
    [17] Wang Q, Duan Z, Perc M, et al. Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability. Europhysics Letters, 2008, 83(5): 50008 doi: 10.1209/0295-5075/83/50008
    [18] Wu J, Ma S. Coherence resonance of the spiking regularity in a neuron under electromagnetic radiation. Nonlinear Dynamics, 2019, 96: 1895-1908 doi: 10.1007/s11071-019-04892-z
    [19] Lü M, Ma J. Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing, 2016, 205: 375-381
    [20] Dayan P, Abbott LF. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. The MIT Press, 2001
    [21] Abbott LF. Theoretical neuroscience rising. Neuron, 2008, 60(3): 489-495 doi: 10.1016/j.neuron.2008.10.019
    [22] Olshausen BA, Field DJ. Sparse coding of sensory inputs. Current Opinion in Neurobiology, 2004, 14(4): 481-487 doi: 10.1016/j.conb.2004.07.007
    [23] Chaudhuri R, Fiete I. Computational principles of memory. Nature Neuroscience, 2016, 19(3): 394-403
    [24] Wang XJ. Decision making in recurrent neuronal circuits. Neuron, 2008, 60(2): 215-234 doi: 10.1016/j.neuron.2008.09.034
    [25] Diedrichsen J, Shadmehr R, Ivry RB. The coordination of movement:optimal feedback control and beyond. Trends in Cognitive Sciences, 2010, 14(1): 31-39
    [26] Beck C, Neumann H. Interactions of motion and form in visual cortex-A neural model. J. Physiol. Paris, 2010, 104(1-2): 61-70 doi: 10.1016/j.jphysparis.2009.11.005
    [27] Pinotsis DA, Schwarzkopf DS, Litvak V, et al. Dynamic causal modelling of lateral interactions in the visual cortex. NeuroImage, 2012, 66: 563-576
    [28] Guzman SJ. Synaptic mechanisms of pattern completion in the hippocampal CA3 network. Science, 2016, 353(6304): 1117-1123
    [29] 宋健, 刘深泉, 臧杰. 基于基底神经节机理的行为决策模型. 动力学与控制学报, 2020, 18(6): 1-31 (Song Jian, Liu Shenquan, Zang Jie. Behavior decision-making model based on basal ganglia mechanism. Journal of Dynamics and Control, 2020, 18(6): 1-31 (in Chinese) doi: 10.1126/science.aaf1836
    [30] Humphries MD, Stewart RD, Gurney KN. A physiologically plausible model of action selection and oscillatory activity in the basal ganglia. The Journal of Neuroscience, 2006, 26(50): 12921-12942 doi: 10.1523/JNEUROSCI.3486-06.2006
    [31] Gurney K, Prescott TJ, Redgrave P. A computational model of action selection in the basal ganglia. I: A new functional anatomy. Biological Cybernetics, 2001, 84(6): 401-410
    [32] Dura-Bernal S, Zhou X, Neymotin SA, et al. Cortical spiking network interfaced with virtual musculoskeletal arm and robotic arm. Frontiers in Neurorobotics, 2015, 9: 13
    [33] Taegyo K, Hamade KC, Dmitry T, et al. Reward based motor adaptation mediated by basal ganglia. Frontiers in Computational Neuroscience, 2017, 11: 19
    [34] Todorov DI, Capps RA, Barnett WH, et al. The interplay between cerebellum and basal ganglia in motor adaptation: A modeling study. PLoS ONE, 2019, 14(4): e0214926 doi: 10.1371/journal.pone.0214926
    [35] Rabinovich MI, Muezzinoglu MK. Nonlinear dynamics of the brain: emotion and cognition. Physics-Uspekhi, 2010, 53(4): 357-372 doi: 10.3367/UFNe.0180.201004b.0371
    [36] Kriegeskorte N. Deep neural networks: A new framework for modeling biological vision and brain information processing. Annual Review of Vision Science, 2015, 1(1): 417
    [37] 王如彬, 王毅泓, 徐旭颖等. 认知神经科学中蕴藏的力学思想与应用. 力学进展, 2020, 50(1): 450-505 (Wang Rubin, Wang Yihong, Xu Xuying, et al. Mechanical thoughtsand applications in cognitive neuroscience. Advances in Mechanics, 2020, 50(1): 450-505 (in Chinese) doi: 10.1146/annurev-vision-082114-035447
    [38] 彭俊, 王如彬, 王毅泓. 大脑血液动力学现象中的能量编码. 力学学报, 2019, 51(4): 1202-1209 (Peng Jun, Wang Rubin, Wang Yihong. Energy coding of hemodynamic phenomena in the brain. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(4): 1202-1209 (in Chinese)
    [39] Wendling F, Bartolomei F, Bellanger JJ, et al. Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. European Journal of Neuroscience, 2002, 15: 1499-1508 doi: 10.1046/j.1460-9568.2002.01985.x
    [40] Taylor PN, Baier G. A spatially extended model for macroscopic spike-wave-discharges. Journal of Computational Neuroscience, 2011, 31(3): 679-684
    [41] 韩芳, 樊登贵, 张丽媛等. 神经系统疾病与认知动力学(Ⅰ): 癫痫发作的动力学与控制. 力学进展, 2022, 52(2): 339-396 (Han Fang, Fan Denggui, Zhang Liyuan, et al. Neurological disease and cognitive dynamics (I): Dynamics and control of epileptic seizures. Advances in Mechanics, 2022, 52(2): 339-396 (in Chinese) doi: 10.1007/s10827-011-0332-1
    [42] Fan D, Wang Q, Matjaz P. Disinhibition-induced transitions between absence and tonic-clonic epileptic seizures. Scientific Reports, 2015, 5: 12618 doi: 10.1038/srep12618
    [43] Wang Z, Wang Q. Eliminating absence seizures through the deep brain stimulation to thalamus reticular nucleus. Frontiers in Computational Neuroscience, 2017, 11: 22
    [44] Zhang L, Wang Q, Baier G. Spontaneous transitions to focal-onset epileptic seizures: A dynamical study. Chaos, 2020, 30(10): 103114 doi: 10.1063/5.0021693
    [45] Fan D, Liu S, Wang Q. Stimulus-induced epileptic spike-wave discharges in thalamocortical model with disinhibition. Scientific Reports, 2016, 6: 37703 doi: 10.1038/srep37703
    [46] Yang C, Luan G, Liu Z, et al. Dynamical analysis of epileptic characteristics based on recurrence quantification of SEEG recordings. Physica A, 2019, 523: 507-515 doi: 10.1016/j.physa.2019.02.017
    [47] Terman D, Rubin JE, Yew AC, et al. Activity patterns in a model for the subthalamopallidal network of the basal ganglia. The Journal of Neuroscience: The Official Journal of the Society for Neuroscience, 2002, 22(7): 2963-2976 doi: 10.1523/JNEUROSCI.22-07-02963.2002
    [48] Tass PA. Stochastic phase resetting of two coupled phase oscillators stimulated at different times. Physical Review E, 2003, 67(5): 05190
    [49] Popovych OV, Tass PA. Multisite delayed feedback for electrical brain stimulation. Frontiers in Physiology, 2018, 9: 46 doi: 10.3389/fphys.2018.00046
    [50] Yu Y, Hao Y, Wang Q. Model-based optimized phase-deviation deep brain stimulation for Parkinson's disease. Neural Networks, 2019, 122: 308-319
    [51] Fan D, Wang Z, Wang Q. Optimal control of directional deep brain stimulation in the parkinsonian neuronal network. Communications in Nonlinear Science and Numerical Simulation, 2016, 36: 219-237 doi: 10.1016/j.cnsns.2015.12.005
    [52] Fan D, Wang Q. Improving desynchronization of parkinsonian neuronal network via triplet-structure coordinated reset stimulation. Journal of Theoretical Biology, 2015, 370: 157-170 doi: 10.1016/j.jtbi.2015.01.040
    [53] Zetterberg LH, Kristiansson L, Mossberg K. Performance of a model for a local neuron population. Biol. Cybern., 1978, 31(1): 15-26
    [54] Traub RD, Knowles WD, Miles R, et al. Models of the cellular mechanism underlying propagation of epileptiform activity in the CA2-CA3 region of the hippocampal slice. Neuroscience, 1987, 21(2): 457-470 doi: 10.1016/0306-4522(87)90135-7
    [55] Lytton WW, Sejnowski TJ. Computer model of ethosuximide's effect on a thalamic neuron. Ann. Neurol., 1992, 32(2): 131-139
    [56] Destexhe A. Can GABAA conductances explain the fast oscillation frequency of absence seizures in rodents? European JournaL of Neuroscience, 1999, 11(6): 2175-2181
    [57] Robinson PA, Rennie CJ, Rowe DL, et al. Neurophysical modeling of brain dynamics. Neuropsychopharmacology. 2003, Suppl. 1: S74-9
    [58] Zhang L, Fan D, Wang Q. Transition dynamics of a dentate Gyrus-CA3 neuronal network during temporal lobe epilepsy. Frontiers in Computational Neuroscience, 2017, 11: 61 doi: 10.3389/fncom.2017.00061
    [59] Albada S, Robinson PA. Mean-field modeling of the basal ganglia-thalamocortical system. I: Firing rates in healthy and parkinsonian states. Journal of Theoretical Biology, 2009, 257(4): 642-66361
    [60] So RQ, Kent AR, Grill WM. Relative contributions of local cell and passing fiber activation and silencing to changes in thalamic fidelity during deep brain stimulation and lesioning: a computational modeling study. Journal of Computational Neuroscience, 2012, 32(3): 499-519
    [61] Kerr CC, van Albada SJ, Neymotin SA, et al. Cortical information flow in Parkinson’s disease: A composite network/field model. Frontiers in Computational Neuroscience, 2013, 7(39): 1-14
    [62] Yu Y, Wang Q. Oscillation dynamics in an extended model of thalamic-basal ganglia. Nonlinear Dynamics, 2019, 98: 1065-1080 doi: 10.1007/s11071-019-05249-2
    [63] Yu Y, Han F, Wang Q. Exploring phase-amplitude coupling from primary motor cortex-basal ganglia-thalamus network model. Neural Networks. 2022, 153: 130-141
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  • 收稿日期:  2022-08-31
  • 录用日期:  2022-10-09
  • 网络出版日期:  2022-10-10

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