神经纤维动作电位传递速度的模型与分析
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摘要
神经传导速度的测定是较为敏感和重要的神经功能评价指标之一，已广泛用
于神经性疾病的临床诊断和愈后功能检查，同时在电生理基础研究和运动医学研
究中也具有十分重要的意义。到目前为止，神经纤维动作电位传递速度的实验测
量技术已发展的较为成熟，其中比较典型的方法是两点测试法，这种测量方法虽
然简单，但误差较大，且单纯的实验方法缺乏理论依据。20 世纪中期，大批学
者曾对兴奋在有髓及无髓神经纤维上的传递速度与纤维直径及温度的关系做了
仿真，仿真结果与实验结果相吻合。但是，到目前为止对于动作电位在无髓鞘及
有髓鞘神经纤维上的传递速度的定量分析却很少。
本文首先分析了动作电位在无髓神经纤维上的传递机制，得出了可用跨膜电
流的移动速度来等效动作电位传递速度的结论，结合电缆模型与 H-H 模型，建
立了动作电位传递期间神经纤维的等效电路模型，并在此基础上推导出计算传递
速度的公式，对其进行了验证。接下来，应用与无髓鞘神经纤维相类似的方法，
分析了动作电位在有髓鞘神经纤维上的传递机制，同样得出了可用跨膜电流的移
动速度来等效动作电位传递速度的结论，利用 McNeal 模型和 CRRSS 模型，建
立了有髓神经纤维在兴奋传递期间等效电路模型，并推导出了速度的计算模型。
最后，分别仿真了有髓及无髓神经纤维细胞膜各参数的变化对兴奋传递速度的影
响，增强了两个计算模型的可应用性。
The nerve conduction velocity is one of the important and sensitive deliberated
index of the nerve function, which is applied widely into the clinic diagnosis and
function examination after healed of some neural disease. And it is also very
important for the basic research on nerve electrophysiology and the research on
movement medicine. Up to now, the experimental measure technology of the velocity
of action potential propagated along nerve fibers, in which the typical method is the
two spots measurement. Although this method is very simple, the error is great, and
the experimental method lacks of the theoretic basis. In the middle of 20 century, a
great lot of scholars simulated the relation between the velocity of action potential
propagated along a myelinated fiber or an unmyelinated fiber and the fiber diameter
or the temperature. The results were according to the experimental results. But by far,
there are lacking in the quantitative analysis of the velocity of action potential
propagated along a myelinated fiber and an unmyelinated fiber.
In this paper, we first analyze the mechanism of action potential propagated along
an unmyelinated fiber, and present a hypothesis that the velocity of transmembrane
current is the equivalent of the propagation velocity of action potential. Then using
the H-H model and the cable equation we obtain the formula of the velocity. In
succession, we apply a similar method to analyze the mechanism of action potential
propagated along a myelinated fiber. Using the McNeal model and the CRRSS model,
we obtain the formula of the velocity. In the end, we simulate the influence of each
membrane parameter to the propagation velocity for myelinated fibers and
unmyelinated fibers, respectively, which can enhance the usability of the two
computational models.
于神经性疾病的临床诊断和愈后功能检查，同时在电生理基础研究和运动医学研
究中也具有十分重要的意义。到目前为止，神经纤维动作电位传递速度的实验测
量技术已发展的较为成熟，其中比较典型的方法是两点测试法，这种测量方法虽
然简单，但误差较大，且单纯的实验方法缺乏理论依据。20 世纪中期，大批学
者曾对兴奋在有髓及无髓神经纤维上的传递速度与纤维直径及温度的关系做了
仿真，仿真结果与实验结果相吻合。但是，到目前为止对于动作电位在无髓鞘及
有髓鞘神经纤维上的传递速度的定量分析却很少。
本文首先分析了动作电位在无髓神经纤维上的传递机制，得出了可用跨膜电
流的移动速度来等效动作电位传递速度的结论，结合电缆模型与 H-H 模型，建
立了动作电位传递期间神经纤维的等效电路模型，并在此基础上推导出计算传递
速度的公式，对其进行了验证。接下来，应用与无髓鞘神经纤维相类似的方法，
分析了动作电位在有髓鞘神经纤维上的传递机制，同样得出了可用跨膜电流的移
动速度来等效动作电位传递速度的结论，利用 McNeal 模型和 CRRSS 模型，建
立了有髓神经纤维在兴奋传递期间等效电路模型，并推导出了速度的计算模型。
最后，分别仿真了有髓及无髓神经纤维细胞膜各参数的变化对兴奋传递速度的影
响，增强了两个计算模型的可应用性。
The nerve conduction velocity is one of the important and sensitive deliberated
index of the nerve function, which is applied widely into the clinic diagnosis and
function examination after healed of some neural disease. And it is also very
important for the basic research on nerve electrophysiology and the research on
movement medicine. Up to now, the experimental measure technology of the velocity
of action potential propagated along nerve fibers, in which the typical method is the
two spots measurement. Although this method is very simple, the error is great, and
the experimental method lacks of the theoretic basis. In the middle of 20 century, a
great lot of scholars simulated the relation between the velocity of action potential
propagated along a myelinated fiber or an unmyelinated fiber and the fiber diameter
or the temperature. The results were according to the experimental results. But by far,
there are lacking in the quantitative analysis of the velocity of action potential
propagated along a myelinated fiber and an unmyelinated fiber.
In this paper, we first analyze the mechanism of action potential propagated along
an unmyelinated fiber, and present a hypothesis that the velocity of transmembrane
current is the equivalent of the propagation velocity of action potential. Then using
the H-H model and the cable equation we obtain the formula of the velocity. In
succession, we apply a similar method to analyze the mechanism of action potential
propagated along a myelinated fiber. Using the McNeal model and the CRRSS model,
we obtain the formula of the velocity. In the end, we simulate the influence of each
membrane parameter to the propagation velocity for myelinated fibers and
unmyelinated fibers, respectively, which can enhance the usability of the two
computational models.
引文
参考文献
[1] Bradley J. Roth，Peter J. Basser，A Model of the Stimulation of a Nerve Fiber by
Electromagenetic Induction，IEEE Transactions on Biomedical Engineering，
1990，Vol.37：588-596
[2] Fotini A. Papadopoulou， Stavros M. panas， Estimation of the nerve conduction
velocity distribution by peeling sampled compound action potentials， IEEE
Transaction on magnetics， 1999，Vol.3：1801-1804
[3] A.L.Hodgkin，The conduction of the nervous impulse，Liverpool University press,
1964
[4] Robert. Plonsey， Roger C.Barr， Bioelectricity:a quantitative approach，Plenum
press，New York and London，1988
[5] F.Rattay，Modeling of the excitation and the propagation of nerve impulses by
natural and artificial stimulations，Mathematics and Computers in Stimulation，
1995，Vol.39：589-595
[6] N.H.Sabah，Aspects of nerve conduction，IEEE Engineering in Medicine and
Biology.， 2000：111-118
[7] F.Rattay，M.Aberham，Modeling axon membranes for functional electrical
stimulation，IEEE Transactions on Biomedical Engineering， 1993，Vol.40：
1201-1209
[8] S.Y.Chiu，J.M.Richie，R.B.Rogart，D.Stagg，A quantitative description of
membrane currents in rabbit myelinated nerve，J.Physiol，1979 ，Vol.292：
149-166
[9] N.A.Hutchinson,，Z.J.Koles，R.S.Smith，Conduction velocity in myelinated nerve
fibers of Xenopus Laevis，J.Physiol， 1970，Vol.208：279-289
[10]J.W.Moore，R.W.Joyner，M.H.Brill，S.D.Waxman，M.N.Joa，Stimulations of
conduction in uniform myelinated fibers，J.Biophys， 1978，Vol.21：147-160
52
参考文献
[11]L.Goldman，J.S.Albus，Computation of impulse conduction in myelinated fibers:
theoretical basis of the velocity-diameter relation，J.Biophys， 1968，Vol.8：
596-607
[12]W.A.H.Rushton，A theory of the effects of fiber size in medullated nerve，
J.Physiol， 1951，Vol.115：101-122
[13]R.Fitzhugh，Computation of impulse initiation and saltatory conduction in a
myelinated nerve fiber，J.Biophys，1962， Vol.2：11-21
[14]蔡体导，有髓鞘神经纤维冲动传导的计算机模拟，生理学报，1978，Vol.30：
187-199
[15] W.F.Pickard，Estimating the velocity of propagation along myelinated and
unmyelinated fibers，Math.Biosci， 1969，Vol.5：305-319
[16]Frankenhaeuser B.，A.F. Huxley，The action potential in the myelinated nerve
fiber of Xenopus Laevis，J. Physiol，1964，Vol.171：302-315
[17]刘心东，蒋大宗，复合动作电位传播速度分布的复时谱估计方法的仿真研究，
生物医学工程学杂志，1995，12(2)：147-151
[18]W.F.Pickard，On the propagation of the nervous impulse down medullated and
unmedullated fibers，J.Theoret.Biol.， 1966，Vol.11：30-45
[19]G.Morita，Y.X.Tu etc.，Estimation of the conduction velocity distribution of
human sensory nerve fibers，Journal of Electromyography and Kinesiology，
2002，Vol.12：37-43
[20]T.Erneux，G.Nicolis，Propagation waves in discrete bistable reaction-diffusion
systems，Physica D， 1993，Vol.67：237-244
[21]A.C.Giese，Cell physiology 5th Ed.， W.B.Saunders Company，1979
[22]刘亚宁，电磁生物效应，北京邮电大学出版社，2002
[23]顾方舟，生物医学工程学丛书 1，天津科技翻译出版公司，1998
[24]黄诒焯，郑筱祥，生理功能的工程分析，高等教育出版社，1993
[25]丘冠英，彭银祥，生物物理学，武汉大学出版社，2000
53
参考文献
[26]J.M.Ferrero，J.F.Saiz etc.，Analitycal derivation of the internodal transfer function
in myelinated fibers，Proceedings of the 15th Annual International Conference of
the IEEE，1993：1484 -1485
[27]S.Binczak，J.C.Eilbeck，A.C.Scott，Ephaptic coupling of myelinated nerve fibers，
Physica D，2001，Vol.148：159-174
[28]W.A.Wesselink ， J.Holsheimer etc. ， A simulation model of the electrical
characteristics of human myelinated sensory nerve fibers，the 19th International
Conference of IEEE EMBS，1997
[29] W.M.Grill，A.G.Richardson，C.C.McIntyre，Influence of the myelinated sheath
on excitation properties of nerve fibers，the 22nd Annual EMBS International
Conference，2000
[30]H.Mino，W.M.Grill，Modeling of mammalian myelinated nerve with stochastic
sodium ionic channels，the 22nd Annual EMBS International Conference，2000
[31]J.A.Halter，B.Zupan，An electrodiffusion model of the mammalian myelinated
nerve fiber，IEEE EMBC and CMBEC，1995
[32]J.A.Halter，J.W.Clark，Study of conduction in a new model of the myelinated
nerve fiber，IEEE Engineering in Medicine﹠Biology Society 11th Annual
International Conference，1989
[33]D.Gu，R.E.Gander，Determination of nerve conduction velocity distribution from
sampled compound action potential signals，IEEE Transaction On Biomedical
Engineering，1996，Vol.43：829-838
[34]陈宜张，神经系统电生理学，北京人民卫生出版社，1983
[35]洪维恩，数学魔法师 Maple6，人民邮电出版社，2001
[36]陈小霞，Maple 指令参考手册，国防工业出版社，2002
[1] Bradley J. Roth，Peter J. Basser，A Model of the Stimulation of a Nerve Fiber by
Electromagenetic Induction，IEEE Transactions on Biomedical Engineering，
1990，Vol.37：588-596
[2] Fotini A. Papadopoulou， Stavros M. panas， Estimation of the nerve conduction
velocity distribution by peeling sampled compound action potentials， IEEE
Transaction on magnetics， 1999，Vol.3：1801-1804
[3] A.L.Hodgkin，The conduction of the nervous impulse，Liverpool University press,
1964
[4] Robert. Plonsey， Roger C.Barr， Bioelectricity:a quantitative approach，Plenum
press，New York and London，1988
[5] F.Rattay，Modeling of the excitation and the propagation of nerve impulses by
natural and artificial stimulations，Mathematics and Computers in Stimulation，
1995，Vol.39：589-595
[6] N.H.Sabah，Aspects of nerve conduction，IEEE Engineering in Medicine and
Biology.， 2000：111-118
[7] F.Rattay，M.Aberham，Modeling axon membranes for functional electrical
stimulation，IEEE Transactions on Biomedical Engineering， 1993，Vol.40：
1201-1209
[8] S.Y.Chiu，J.M.Richie，R.B.Rogart，D.Stagg，A quantitative description of
membrane currents in rabbit myelinated nerve，J.Physiol，1979 ，Vol.292：
149-166
[9] N.A.Hutchinson,，Z.J.Koles，R.S.Smith，Conduction velocity in myelinated nerve
fibers of Xenopus Laevis，J.Physiol， 1970，Vol.208：279-289
[10]J.W.Moore，R.W.Joyner，M.H.Brill，S.D.Waxman，M.N.Joa，Stimulations of
conduction in uniform myelinated fibers，J.Biophys， 1978，Vol.21：147-160
52
参考文献
[11]L.Goldman，J.S.Albus，Computation of impulse conduction in myelinated fibers:
theoretical basis of the velocity-diameter relation，J.Biophys， 1968，Vol.8：
596-607
[12]W.A.H.Rushton，A theory of the effects of fiber size in medullated nerve，
J.Physiol， 1951，Vol.115：101-122
[13]R.Fitzhugh，Computation of impulse initiation and saltatory conduction in a
myelinated nerve fiber，J.Biophys，1962， Vol.2：11-21
[14]蔡体导，有髓鞘神经纤维冲动传导的计算机模拟，生理学报，1978，Vol.30：
187-199
[15] W.F.Pickard，Estimating the velocity of propagation along myelinated and
unmyelinated fibers，Math.Biosci， 1969，Vol.5：305-319
[16]Frankenhaeuser B.，A.F. Huxley，The action potential in the myelinated nerve
fiber of Xenopus Laevis，J. Physiol，1964，Vol.171：302-315
[17]刘心东，蒋大宗，复合动作电位传播速度分布的复时谱估计方法的仿真研究，
生物医学工程学杂志，1995，12(2)：147-151
[18]W.F.Pickard，On the propagation of the nervous impulse down medullated and
unmedullated fibers，J.Theoret.Biol.， 1966，Vol.11：30-45
[19]G.Morita，Y.X.Tu etc.，Estimation of the conduction velocity distribution of
human sensory nerve fibers，Journal of Electromyography and Kinesiology，
2002，Vol.12：37-43
[20]T.Erneux，G.Nicolis，Propagation waves in discrete bistable reaction-diffusion
systems，Physica D， 1993，Vol.67：237-244
[21]A.C.Giese，Cell physiology 5th Ed.， W.B.Saunders Company，1979
[22]刘亚宁，电磁生物效应，北京邮电大学出版社，2002
[23]顾方舟，生物医学工程学丛书 1，天津科技翻译出版公司，1998
[24]黄诒焯，郑筱祥，生理功能的工程分析，高等教育出版社，1993
[25]丘冠英，彭银祥，生物物理学，武汉大学出版社，2000
53
参考文献
[26]J.M.Ferrero，J.F.Saiz etc.，Analitycal derivation of the internodal transfer function
in myelinated fibers，Proceedings of the 15th Annual International Conference of
the IEEE，1993：1484 -1485
[27]S.Binczak，J.C.Eilbeck，A.C.Scott，Ephaptic coupling of myelinated nerve fibers，
Physica D，2001，Vol.148：159-174
[28]W.A.Wesselink ， J.Holsheimer etc. ， A simulation model of the electrical
characteristics of human myelinated sensory nerve fibers，the 19th International
Conference of IEEE EMBS，1997
[29] W.M.Grill，A.G.Richardson，C.C.McIntyre，Influence of the myelinated sheath
on excitation properties of nerve fibers，the 22nd Annual EMBS International
Conference，2000
[30]H.Mino，W.M.Grill，Modeling of mammalian myelinated nerve with stochastic
sodium ionic channels，the 22nd Annual EMBS International Conference，2000
[31]J.A.Halter，B.Zupan，An electrodiffusion model of the mammalian myelinated
nerve fiber，IEEE EMBC and CMBEC，1995
[32]J.A.Halter，J.W.Clark，Study of conduction in a new model of the myelinated
nerve fiber，IEEE Engineering in Medicine﹠Biology Society 11th Annual
International Conference，1989
[33]D.Gu，R.E.Gander，Determination of nerve conduction velocity distribution from
sampled compound action potential signals，IEEE Transaction On Biomedical
Engineering，1996，Vol.43：829-838
[34]陈宜张，神经系统电生理学，北京人民卫生出版社，1983
[35]洪维恩，数学魔法师 Maple6，人民邮电出版社，2001
[36]陈小霞，Maple 指令参考手册，国防工业出版社，2002