RESEARCH ADVANCES AND SOME THOUGHTS ON NEURODYNAMICS
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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.Abstract: Neurodynamics is a foundational branch of dynamics and control, which belongs to the international frontier of the interdisciplinary field of mechanics, brain science and intelligence science. Based on the basic theories and methods of dynamics and control, the study of neurodynamics mainly focuses on establishing reasonable models to explore the mechanisms of electrophysiological dynamic behaviors of nervous system and brain cognitive functions. In recent years, scholars at home and abroad have obtained remarkable achievements in the foundational research of neurodynamics, including the in-depth study of the dynamical behavior of neurons and neural networks, the modeling and analysis of different functional structures of the brain, and the network dynamics modeling and control of brain regions associated with nervous disease. In this paper, we firstly overviewed elaborately the recent advancements in the field of neurodynamics. Especially, development history for advancement of neural modeling is exhibited. Then, by analyzing the research outcomes of biological neural networks and their dynamics, some thoughts and prospects for future research are put forward. It is expected that neurodynamics will contribute to the breakthroughs of the theories and methods of brain-like intelligence and intelligent equipment with strong interpretability and generalization ability, and finally their applications in major engineering projects.
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Key words:
- neurodynamics /
- research advance /
- modeling analysis /
- neural network /
- brain-like intelligence
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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 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 
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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
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