基于麦克斯韦电磁场理论的神经元动力学响应与隐藏放电控制

Dynamic response and control of neuros based on electromagnetic field theory

钙、钾、钠等离子在细胞内连续泵送和传输时产生的时变电场不仅会影响神经元的放电活动,而且会诱导时变磁场去进一步调节细胞内离子的传播.根据麦克斯韦电磁场理论,时变的电场和磁场在细胞内外的电生理环境中会相互激发而产生电磁场.为了探究电磁场影响下的神经元放电节律转迁,本文在三维Hindmarsh-Rose(HR)神经元模型的基础上,引入磁通变量和电场变量,建立了一个五维HR神经元模型(简称EMFN模型).首先,结合Matcont软件分析了EMFN模型的平衡点分布与全局分岔性质,发现并分析了该模型存在的亚临界Hopf分岔、隐藏放电及其周期放电与静息态共存等现象.其次,利用双参数及单参数分岔、ISI分岔和最大Lyapunov指数等工具进行数值仿真,详细分析了EMFN模型存在的伴有混沌及无混沌的加周期分岔结构、混合模式放电和共存模式放电等现象,同时揭示了电场和磁场强度影响其放电节律的转迁规律.最后,利用Washout控制器将EMFN模型的亚临界Hopf分岔转化为超临界Hopf分岔,使其在分岔点附近的拓扑结构发生改变,由此达到消除其隐藏放电的目的.本文的研究结果证实了新建神经元模型具有丰富的放电节律,将影响神经元的信息传递和编码,为完善神经元模型,揭示电磁场对生物神经系统的影响,以及探求一些神经性疾病的致病机理提供了思路.

The time-varying electric fields generated by continuously pumping and transmitting calcium,potassium and sodium ions in cells not only affect the discharge activity of neurons,but also induce time-varying magnetic fields to further regulate the fluctuation of ions.According to the Maxwell's electromagnetic field theory,timevarying electric field and magnetic field can stimulate each other in the electrophysiological environment inside and outside the cells to produce electromagnetic field.In order to explore the discharge rhythm transition of neurons under the influence of electromagnetic fields,a five-dimensional(5D)HR neuron model(EMFN model for short)is established by introducing magnetic flux variable and electric field variable into a three-dimensional(3D)Hindmarsh-Rose(HR)neuron model.Firstly,the equilibrium distribution and global bifurcation properties of EMFN model are analyzed by Matcont software,then the existence of subcritical Hopf bifurcation,hidden discharge,coexistence of periodic discharge and resting state are found and analyzed.Secondly,by using the tools of two-parameter and one-parameter bifurcation,ISI bifurcation and the maximum Lyapunov exponent for numerical simulation,the period-adding bifurcation with and without chaos,mixed mode discharge and coexistence mode discharge in the EMFN model are analyzed in detail.At the same time,the transition law of discharge rhythm with the influence of electric field and magnetic field intensity is revealed.Finally,the Washout controller is used to convert the subcritical Hopf bifurcation into supercritical Hopf bifurcation,so the topological structure of EMFN model near the bifurcation point is changed for eliminating the hidden discharge.The research results of this paper confirm that the novel neuron model has rich discharge rhythm,which will affect the information transmission and coding,and provide some ideas for improving the neuron models,revealing the influence of electromagnetic field on biological nervous system,and exploring the pathogenic mechanism of some neurological diseases.