感性神经元模型及其动力学特性研究  

Research on inductive neuron model and its dynamic characteristics

作　　者：吴静[1] 潘春宇 Wu Jing;Pan Chun-Yu(School of Automation Science and Electrical Engineering,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《物理学报》2022年第4期316-323,共8页Acta Physica Sinica

摘　　要：神经元的大小属于介观尺度范围,本文考虑神经元的电感特性,建立了由细胞膜电感、膜电容、钾离子忆阻器和氯离子电阻构成的神经元经典电路模型和介观电路模型.利用经典电路理论和介观电路的量子理论,推导了在外部冲击激励下神经元细胞膜电压响应的表达式.将枪乌贼神经元的电生理参数代入膜电压表达式并计算可知,两种模型下的膜电压均先增大后减小,最后达到零值的静息状态,且其能量主要集中在0—30 Hz的脑电频率范围内.进一步比较发现,介观电路模型下膜电压的峰值及达到峰值所需的时间(达峰时间)均低于经典电路模型下的值,并与枪乌贼轴突受到刺激后的实验结果更接近,说明介观电路模型更能反应神经元受到刺激后的生理特征.基于介观电路模型,随着外部激励强度的增加,膜电压的峰值增加且达峰时间变短.膜电压峰值及达峰时间等参数更易受神经元膜电容的影响.神经元的介观电路模型对于理解神经元受到刺激后的兴奋性,推动受大脑功能启发的量子神经网络的发展等具有重要意义.The size of neuron is on a mesoscopic scale.In this paper,considering the inductance characteristics of the neuron,the classical circuit model and mesoscopic circuit model of neuron including neuron membrane inductance,membrane capacitance,potassium ion memristor and chloride ion resistance are established.Based on the classical circuit theory and the quantum theory of mesoscopic circuit,the expression of neuron membrane voltage response under external impulse excitation is derived.Substituting the electrophysiological parameters of the squid neuron into the expression of membrane voltage,we find that the membrane voltages in both models first increase and then decrease,and finally reach their corresponding resting states of zero value,and their energy values are concentrated mainly in a range of 0–30 Hz in which the brainwave frequency is.Further comparisons show that the peak value of membrane voltage and the time required to reach the peak value(peak time)in the mesoscopic circuit model are lower than those in the classical circuit model,and are closer to the experimental results after the squid axon has been stimulated,indicating that the mesoscopic circuit model can better reflect the physiological characteristics of the stimulated neurons.Based on the mesoscopic circuit model,the peak value of membrane voltage increases and the peak time decreases with the increase of external excitation intensity.Parameters such as membrane voltage peak and peak time are more sensitive to the neuron membrane capacitance.The mesoscopic circuit model of the neuron is of great significance in understanding the excitability of the stimulated neuron and also in promoting the development of quantum neural networks inspired by brain function.

关 键 词：Hodgkin-Huxley神经元 电感 介观电路 量子理论 

分 类 号：Q424[生物学—神经生物学]