Advertisement

Bulletin of Mathematical Biology

, Volume 47, Issue 3, pp 409–424 | Cite as

The extension of two-dimensional cable theory to arteries and arterioles

  • Michael A. B. Deakin
  • T. O. Neild
  • R. G. Turner
Article

Abstract

Electrical polarization of an artery or an arteriole may be modeled by the use of equations developed for two-dimensional cable theory. Two special cases have previously been solved: those corresponding to the case in which the radius is either zero (one-dimensional cable theory) or infinite. This paper presents the general solution.

Keywords

Incomplete Gamma Function Double Series Circular Symmetry Outward Unit Vector Cable Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Abramowitz, M. and I. Stegun (Eds). 1965.Handbook of Mathematical Functions. New York: Dover.Google Scholar
  2. Erdélyi, A. (Ed.). 1954.Tables of Integral Transforms, Vol. 2. New York: McGraw-Hill.Google Scholar
  3. Jack, J. J. B., D. Noble and R. W. Tsien. 1975.Electric Current Flow in Excitable Cells. Oxford: Clarendon.Google Scholar
  4. Morse, P. M. and H. Feshbach. 1953.Methods of Theoretical Physics, Vol. 1. New York: McGraw-Hill.MATHGoogle Scholar
  5. Neild, T. O. 1983. “The Relation Between the Structure and Innervation of Small Arteries and Arterioles and the Smooth Muscle Membrane Potential Changes Expected at Different Levels of Sympathetic Nerve Activity.”Proc. R. Soc. B220, 237–249.CrossRefGoogle Scholar
  6. Roberts, G. E. and H. Kaufman. 1966.Table of Laplace Transforms. Philadelphia: Saunders.MATHGoogle Scholar
  7. Shiba, H. and Y. Kanno. 1971. “Further Study of the Two-dimensional Cable Theory: an Electric Model for a Flat Thin Association of Cells with a Directional Intercellular Communication.”Biophysik 7, 295–301.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1985

Authors and Affiliations

  • Michael A. B. Deakin
    • 1
  • T. O. Neild
    • 2
  • R. G. Turner
    • 3
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia
  2. 2.Department of PhysiologyMonash UniversityClaytonAustralia
  3. 3.Department of PhysicsMonash UniversityClaytonAustralia

Personalised recommendations