Abstract
The potential and current distribution in a nerve bundle is studied mathematically under various situations. Relations are derived expressing the effect of many fibers on the external potential, the value of the potential for a given nerve excitation pattern with and without the nerve sheath, the potential of a single fiber for a given outside potential pattern, and the effect of varying the frequency of alternating current stimulation. Results of the latter study are used to account for experimental deviations of the two-factor theory, and good agreement with the experimental results is found.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Boole, G. 1946.A Treatise on the Calculus of Finite Differences. New York: G. E. Stechert and Co.
Campbell, G. A. and R. M. Foster. 1942. “Fourier Integrals for Practical Applications.” American Telephone and Telegram Co.
Churchill, R. V. 1944.Modern Operational Mathematics in Engineering. New York: McGraw-Hill Book Co., Inc.
Curtis, H. J. and K. S. Cole. 1938. “Transverse Electric Impedance of the Squid Giant Axon.”Jour. Gen. Physiol.,21, 757–65.
Erlanger, J. and H. S. Gasser. 1937.Electrical Signs of Nervous Activity. Philadelphia: University of Pennsylvania Press.
Gasser, H. S. and H. Grundfest. 1939. “Axon Diameters in Relation to the Spike Dimensions and the Conduction Velocity in Mammalian A Fibers.”Am. Jour. Physiol.,127, 393–414.
Grundfest, H. 1952. “Mechanism and Properties of Bioelectric Potentials.”Modern Trends in Physiology and Biochemistry, pp. 193–228. New York: Academic Press, Inc.
Hill, A. V. 1936. “Excitation and Accommodation in Nerve.”Proc. Roy. Soc. Lond. B,119, 305–55.
—, B. Katz, and D. Y. Solandt. 1936. “Nerve Excitation by Alternating Current.”Ibid.,121, 74–133.
Hodgkin, A. L. 1937. “A Local Electric Response in Crustacean Nerve.”Jour. Physiol.,91, 5p-7p.
— 1954. “A Note on Conduction Velocity.”Ibid.,125, 221–24.
— and A. F. Huxley. 1939. “Action Potentials Recorded from Inside a Nerve Fibre.”Nature,144, 710–11.
— and —. 1952. “A Quantitative Description of Membrane Current and Its Applicatio to Conduction and Excitation in Nerve.”Jour. Physiol.,117, 500–44.
Hodgkin, A. L. and W. A. H. Rushton. 1946. “The Electrical Constants of a Crustacean Nerve Fibre.”Proc. Roy. Soc. Lon. B.,133, 444–79.
Kato, 1934.The Microphysiology of Nerve. Tokyo: Maruzen Co.
Katz, B. 1939a.Electrical Excitation of Nerve. London: Oxford University Press.
— 1939b. “Nerve Excitation by High-Frequency Alternating Current.”Jour. Physiol.,96, 202–24.
Lorente de Nó, R. 1947. “A Study of Nerve Physiology. I.”Studies from the Rockefeller Institute for Medical Research,131, New York: Rockefeller Institute.
— 1950. “The Ineffectiveness of the Connective Tissue Sheath of Nerve as a Diffusion Barrier.”Jour. Cell. Comp. Physiol.,35, 195–240.
— 1952. “Observations on the Properties of the Epineurium of Frog Nerve.”Cold Spr. Harbor Symp.,17, 299–315.
Lussier, J. J. and W. A. H. Rushton. 1952. “The Excitability of a Single Fibre in a Nerve Trunk.”Jour. Physiol.,117, 87–108.
Page, L. and N. I. Adams. 1931.Principles of Electricity. New York: D. Van Nostrand Co., Inc.
Patlak, C. S. and H. D. Landhal. 1949. “A Note on the Two-Factor Theory with Rectification as Applied to Alternating Current Stimulation.”Bull. Math. Biophysics,11, 149–55.
Rashbass, C. and W. A. H. Rushton. 1949. “The Relation of Structure to the Spread of Excitation in the Frog's Sciatic Trunk.”Jour. Physiol.,110, 110–35.
Rashevsky, N. 1948.Mathematical Biophysics, Rev. Ed. Chicago: University of Chicago Press.
Rosenblueth, A., N. Wiener, W. Pitts, and J. Garcia Ramos, (with the assistance of F. Webster). 1948. “An Account of the Spike Potential of Axons.”Jour. Cell. Comp. Physiol.,32, 275–317.
Rushton, W. A. H. 1927. “The Effect upon the Threshold for Nervous Excitation of the Length of Nerve Exposed, and the Angle between Current and Nerve.”Jour. Physiol.,63, 357–77.
— 1951. “A Theory of the Effects of Fibre Size in Medullated Nerve.”Ibid.,115, 101–22.
Shanes, A. M. 1954. “Effect of Sheath Removal on the Sciatic of the Toad, Bufo marinus.”Jour. Cell. Comp. Physiol.,43, 87–98.
Sneddon, I. N. 1951.Fourier Transforms. New York: McGraw-Hill Book Co., Inc.
Stämpfli, R. 1954. “Saltatory Conduction in Nerve.”Physiol. Rev.,34, 101–12.
Tasaki, I. 1953.Nervous Transmission. Springfield, Ill.: Charles C. Thomas.
Taylor, R. E. 1950. “Studies of the Effect of Externally Applied Currents on Frog Nerve.” Doctoral Dissertation, University of Rochester, Rochester, New York.
— 1952. “The Distribution of Membrane Current in Nerve with Longitudinal Linearly Increasing Applied Current.”Bull. Math. Biophysics,14, 265–92.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Patlak, C.S. Potential and current distribution in nerve: The effect of the nerve sheath, the number of fibers, and the frequency of alternating current stimulation. Bulletin of Mathematical Biophysics 17, 287–307 (1955). https://doi.org/10.1007/BF02477755
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02477755