The bulletin of mathematical biophysics

, Volume 15, Issue 4, pp 489–500 | Cite as

Determination of diffusion and permeability coefficients in nerve trunks

  • George W. Schmidt
Article

Abstract

A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.

Keywords

Permeability Coefficient Interstitial Space Legendre Polynomial Nerve Trunk Fiber Area 

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Literature

  1. Doetsch, G. 1950.Handbuch der Laplace Transformation. Basel: Verlag Birkhäuser Basel.Google Scholar
  2. Hobson, E. W. 1931.The Theory of Spherical and Ellipsoidal Harmonics. Cambridge: Cambridge University Press.MATHGoogle Scholar
  3. Opatowski, I. and G. W. Schmidt. 1952. “Determination of Diffusion and Permeability Coefficients in Muscle.”Bull. Math. Biophysics,14, 45–65.MathSciNetGoogle Scholar
  4. Truant, A. P. 1953. Personal Communication.Google Scholar

Copyright information

© University of Chicago 1953

Authors and Affiliations

  • George W. Schmidt
    • 1
  1. 1.Committee on Mathematical BiologyThe University of ChicagoChicagoUSA

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