应用数学进展  >> Vol. 9 No. 2 (February 2020)

房室化神经元Chay模型的放电节律研究
Firing Rhythm of Compartmentalized Neuron Chay Model

DOI: 10.12677/AAM.2020.92024, PDF, HTML, XML, 下载: 148  浏览: 232 

作者: 程 璇, 刘深泉:华南理工大学数学学院,广东 广州

关键词: Chay模型房室模型发放模式ISI分岔Chay Model Compartment Model Firing Pattern ISI Bifurcation

摘要: 本文将螺旋神经节神经元的几何形态结构作为房室划分标准,构建了两房室神经元Chay模型、多房室神经元Chay模型,对房室化神经元Chay模型进行了非线性动力学分析和神经计算:1) 两房室神经元Chay模型。理论分析了在电生理参数的改变下得到的周期性发放,以及加周期分岔等分岔序列结构,并且运用快慢动力学研究了两类簇放电模式及其转迁机制。2) 15房室神经元Chay模型。数值模拟了生物信息的稳定传递、对于外界刺激位点的指向性和脱髓鞘的后果。3) 131房室神经元Chay模型。分别考察了内源和外源可变参数、中枢突的几何形态结构对第一动作电位潜伏期、发放率、最大电位、同步差等节律编码方式的影响。在对房室模型进行分岔、混沌等非线性动力学分析以及信息编码等神经计算的同时,验证并解释了神经元模型的信息传递特点以及退化机制。
Abstract: In this paper, taking the geometric morphology and structure of spiral ganglion neurons as the criteria of compartment division, two-compartment neuron Chay model and multi-compartment neuron Chay model were constructed. Then, the nonlinear dynamics analysis and neural computing of compartmentalized neuron Chay model were carried out: 1) Two-compartment neuron Chay model. We theoretically analyzed the periodic firing, as well as bifurcation sequence structures such as period adding bifurcation under the change of electrophysiological parameters, meanwhile two kinds of bursting patterns and their transition mechanisms were studied by using the fast-slow dynamics. 2) Fifteen-compartment neuron Chay model. The stable transmission of biological information, the directivity of external stimulation sites as well as the consequences of demyelination were numerically simulated. 3) One hundred and thirty-one-compartment neuron Chay model. They were investigated respectively that consisted of the effects of endogenic and extrinsic variable parameters as well as the geometric structure of the central axon on the rhythmic encoding methods such as the first spike latency, firing rate, maximum potential, and synchronization error. When the compartment models were used for nonlinear dynamic analysis including bifurcation, chaos and neural computing including information coding, the information transmission characteristics and degeneration mechanism of neuron models were verified and explained. 

文章引用: 程璇, 刘深泉. 房室化神经元Chay模型的放电节律研究[J]. 应用数学进展, 2020, 9(2): 204-219. https://doi.org/10.12677/AAM.2020.92024

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