【作者】 耿建明；

【导师】 王江；

【作者基本信息】 天津大学 ， 控制理论与控制工程， 2005， 硕士

【摘要】 医学研究发现,许多疾病与细胞膜离子通道的异变现象密切相关。如先天性肌强直症的病变细胞中氯离子电导低于常值;在某些肌肉瘫痪的病变部位发现细胞膜对钠离子通透性的异变。本文基于Duval、Adrian和Pappone等人对老鼠肌肉细胞进行电压钳位实验获得的生理数据,以肌肉中的Hodgkin-Huxley模型(HHM模型)为研究对象,选取医疗上具有指导意义的漏电导和钠离子通道反电动势作为分岔参数,采用高维方程的代数判据进行单参数和双参数Hopf分岔分析,简化了分析过程。本文在对电场作用下细胞膜电压时空特性研究的基础上,分析了外加极低频电场下细胞膜电压的变化规律,建立了外电场作用下改进的HHM模型,并沿用前述的高维方程的代数判据方法,选取漏电导、钠离子通道反电动势与外电场参数对改进的HHM模型进行了多参数Hopf分岔分析。研究结果发现,当漏电导和钠离子通道反电动势变化时,HHM模型将产生动态Hopf分岔。仿真结果显示此时细胞膜受刺激后产生连续的动作电位异变波形,符合医学实验中观察到的病变现象,说明生理参数变化引发生物系统分岔可能是肌肉疾病的诱因。对外电场下改进HHM模型的多参数分岔分析也表明,外电场参数与其它生理参数的变化将引发模型的分岔过程,这可能是电磁辐射致病的原因。更多还原

【Abstract】 It is reported that many diseases are related with the aberrance of celltrans-membrane ion channels. For instances, the chloride conductance decreases inmyotonia congenital, while the sodium ions permeability is aberrated in certainparalysis. This paper employed the physiological data obtained in rats musclesvoltage-clamped experiments carried by Duval、Adrian and Pappone, and took theHodgkin-Huxley model for muscles(HHM model) as study object.Firstly, with the aid of algebra criterion in high dimension equations, the dynamicHopf-bifurcation analysis about single parameter of leakage conductance as well assodium ions anti-electromotive force was performed on the model.Secondly, in this paper, the Hodgkin-Huxley model is studied with the leakageconductance and the sodium reversal potential selected as parameters for a two-parameterHopf-bifurcation analysis.Thirdly, this paper also discussed the multi-parameter Hopf-bifurcation ofmodified HHM model exposed to external electrical fields. Based on results ofspace-time characteristics of trans-membrane voltage, the variation of celltrans-membrane voltage exposed to extremely low frequency electrical field wasanalyzed. The traditional HHM model was modified by importing new parametersdenoting external electrical fields. According to analysis, when the parameter of leakage conductance and sodiumions anti-electromotive force varies, the dynamic Hopf bifurcation would emerge.Simulations showed that cell membrane would produce continuous waveforms ofaction potential under bifurcation condition, which is coincident with the aberrancephenomenon of action potential observed in medical experiments. The analysis ofmodified HHM model exposed to external electrical fields also suggested bifurcationwould appear with the variation of parameters about external electrical fields, whichmay be accounted for diseases caused by electro-magnetic exposure.更多还原