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1、中文摘要醫(yī)學(xué)研究發(fā)現(xiàn)，許多疾病與細(xì)胞膜離子通道的異變現(xiàn)象密切相關(guān)。如先天性肌強直癥的病變細(xì)胞中氯離子電導(dǎo)低于常值；在某些肌肉癱瘓的病變部位發(fā)現(xiàn)細(xì)胞膜對鈉離子通透性的異變。本文基于DuvaI、Adrian和Pappone等人對老鼠肌肉細(xì)胞進(jìn)行電壓鉗位實驗獲得的生理數(shù)據(jù)，以肌肉中的Hodgkin—Huxley模型(HHM模型)為研究對象，選取醫(yī)療上具有指導(dǎo)意義的漏電導(dǎo)和鈉離子通道反電動勢作為分岔參數(shù)，采用高維方程的代數(shù)判據(jù)進(jìn)行單參數(shù)和雙參數(shù)Hopf分岔分析，簡化了分析過程。本文在對電場作用下細(xì)胞膜電壓時空特性研究的基礎(chǔ)上，分析了外加極低頻電場下細(xì)胞膜電壓的變化規(guī)律，建立了外電場作用下改進(jìn)的
2、HHM模型，并沿用前述的高維方程的代數(shù)判據(jù)方法，選取漏電導(dǎo)、鈉離子通道反電動勢與外電場參數(shù)對改進(jìn)的HHM模型進(jìn)行了多參數(shù)Hopf分岔分析。研究結(jié)果發(fā)現(xiàn)，當(dāng)漏電導(dǎo)和鈉離子通道反電動勢變化時，HHM模型將產(chǎn)生動態(tài)Hopf分岔。仿真結(jié)果顯示此時細(xì)胞膜受刺激后產(chǎn)生連續(xù)的動作電位異變波形，符合醫(yī)學(xué)實驗中觀察到的病變現(xiàn)象，說明生理參數(shù)變化引發(fā)生物系統(tǒng)分岔可能是肌肉疾病的誘因。對外電場下改進(jìn)HHM模型的多參數(shù)分岔分析也表明，外電場參數(shù)與其它生理參數(shù)的變化將引發(fā)模型的分岔過程，這可能是電磁輻射致病的原因。關(guān)鍵詞：HHM模型，Hopf分岔，雙參數(shù)，多參數(shù)，代數(shù)判據(jù)ABSTRACTItISreported
3、thatmanydiseasesarerelatedwiththeaberranceofeelltrans—membraneionchannels．Forinstances．thechlorideconductancedecreasesinmyotoniacongenital，whiIethesodiumionspermeabilityisaberratedincertainparalysis．Thispaperemployedthephysiologicaldataobtmnedinratsmusclesvoltage—clampedexperimentscarriedbyDuval
4、、AdrianandPappone，andtooktheHodgkin—Huxleymodelformuscles(HHMmodel)asstudyobject．Firstly,withtheaidofalgebracriterioninhighdimensionequations，thedynamicHopf-bifureationanalysisaboutsingleparameterofleakageconductanceaswellassodiumionsanti—electromotiveforcewasperformedOnthemodel．Secondly,inthisp
5、aper,theHodgkin—Huxleymodelisstudiedwiththeleakageconductanceandthestrumreversalpotentialselectedasparametersforatwo—parameterHopf-bifurcationanalysis．Thirdly,thispaperalsodiscussedthemulti—paramemrHopf-bifurcationofmodifiedHHMmodelexposedtoexternalelectricalfields．Basedonresultsofspace—timechar
6、acteristicsoftrans—membranevoltage，thevariationofcelltrans—membranevoltageexposedtoextremelylowfrequencyelectricalfieldwasanalyzed．ThetraditionalHHMmodelwasmodifiedbyimportingnewparametersdenotingexternalelectricalfields．Accordingtoanalysis，whentheparameterofleakageconductanceandsodiumionsanti—e
7、lectromotiveforcevaries，thedynamicHopfbifurcationwouldemerge．Simulationsshowedthateellmembranewouldproducecontinuouswaveforrnsofactionpotentialunderbifurcationcondition．whichiScoincidentwiththeaberrancephenomenonofactionpote
