Bulletin of Mathematical Biology

, Volume 40, Issue 2, pp 247–255 | Cite as

On the nerve impulse equation: The dynamic responses of nerve impulse

  • Chun Chiang


With the assumption of dipole interaction with the membrane matrix, the dipole barrier under an applied field shows a minimum in its time transient. Kinetic equations governing the migration of ions are presented. Na+ activation, Na+ inactivation and K+ delay are all part of the same mechanism in this model with no other separate assumptions needed. Voltage Clamp equation and action potential equation are presented.


Nerve Impulse Membrane Matrix Giant Axon Nerve Axon Current Voltage Relation 
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  1. Cole, K. S. 1968.Membranes, Ions and Impulses. p. 569. Berkeley: University of California Press.Google Scholar
  2. Frankenhaeuser, B. and A. F. Huxley. 1964. “The Action Potential in the Myelinated Nerve Fibre ofXenopus Laevis as Computed on the Basis of Voltage Clamp Data.”J. Physiol., Lond.,171, 302–315.Google Scholar
  3. Hodgkin, A. L. and A. F. Huxley. 1952a. “A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve.”J. Physiol., Lond.,117, 500–544.Google Scholar
  4. ——. 1952b. “Currents Carried by Sodium and Potassium Ions Through the Membrane of the Giant Axon of Loligo.”J. Physiol., Lond.,116, 449–472.Google Scholar
  5. ——. 1952c. “The Components of Membrane Conductance in the Giant Axon of Loligo.”J. Physiol., Lond.,116, 473–496.Google Scholar
  6. —— and B. Katz. 1952. “Measurement of Current-Voltage Relations in the Membrane of the Giant Axon of Loligo.”J. Physiol., Lond.,116, 424–448.Google Scholar
  7. — and B. Katz. 1949. “The Effect of Sodium Ions on the Electrical Activity of the Giant Axon of the Squid.”J. Physiol., Lond.,108, 37–77.Google Scholar
  8. — 1958. “Ionic Movements and Electrical Activity in Giant Nerve Fibres.”Proc. R. Soc., B148, 1–37.CrossRefGoogle Scholar
  9. Huxley, A. F. 1959. “Ion Movements During Nerve Activity.”Ann. N.Y. Acad. Sci.,81, 221–246.Google Scholar
  10. Lee, C. Y. and C. Chiang. 1976. “Nerve Excitations by the Coupling of the Dipoles and the Membrane Matrix.”Bull. Math. Biol.,38, 59–70.MATHCrossRefGoogle Scholar
  11. Noble, D. 1966. “Applications of Hodgkin-Huxley Equations to Excitable Tissues.”Physiol. Rev.,46, 1–50.Google Scholar
  12. Wei, L. Y. 1969a. “Role of Surface Dipoles on Axon Membrane.”Science, N.Y.,163, 280–282.Google Scholar
  13. — 1969b. “Molecular Mechanisms of Nerve Excitation and Conduction.”Bull. Math. Biophys.,31, 39–58.Google Scholar
  14. — 1971a. “Possible Origin of Action Potential and Birefringence Change in Nerve Axon.”,33, 521–537.Google Scholar
  15. — 1971b. “Quantum Theory of Nerve Excitation.”,33, 187–194.Google Scholar
  16. — 1972. “Dipole Theory of Heat Production and Absorption in Nerve Axon.”Biophys. J.,12, 1159–1170.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1978

Authors and Affiliations

  • Chun Chiang
    • 1
  1. 1.Institute of PhysicsAcademia SinicaTaipeiTaiwan, The Republic of China

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