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The time-varying elastic properties of the left ventricular muscle

The bulletin of mathematical biophysics volume 31, pages 75–92 (1969)Cite this article

Abstract

We combine two techniques in order to discuss the time-varying elastic properties of the left ventricular muscle. An analytic model for the shape and forces in the left ventricle is combined with the Fourier series representations of certain of the ventricular dimensions and pressure to derive expressions for the stress and strain in the left ventricle. The strain is thus a function of the elastic material properties, which are then expressed as functions of time by using Fourier series. The only data needed for a numerical study using these techniques are closed-chest determinations of the ventricular dimensions and the ventricular pressure.

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Abbreviations

p(t) :

time-varying left ventricle (LV) chamber pressure

w(t) :

time-varying LV width (or diameter)

l(t) :

time-varying LV length

h(t) :

time-varying LV thickness

a(t) :

time-varying LV model size parameter

A(t), B(t) :

time-varying parameters of the constituent stress systems of the model

σ(t):

time-varying stress tensor

ε(t):

time-varying strain tensor

E(t) :

time-varying Young's modulus of the cardiac muscle

ν(t):

time-varying Poisson's ratio of the cardiac muscle

K(t) :

time-varying bulk modulus of the cardiac muscle

μ(t):

time-varying shear modulus of the cardiac muscle

Literature

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  • Vayo, H. W. 1966. “The Motion of the Left Ventricle: I.”Bull. Math. Biophysics,28, 355–362.

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  • — 1967a. “The Motion of the Left Ventricle: II.” —Ibid.,,29, 499–512.

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  • — 1967b. “Fourier Series Analysis of Ventricular Dimensions.” InFactors Influencing Myocardial Contractility. R. D. Tanz, F. Kavalar and J. Roberts, eds. New York: Academic Press, 141–148.

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Author information

Affiliations

  1. N.A.S.A. Ames Research Center, Moffett Field, California

    Dhanjoo N. Ghista

  2. Mathematics Department, University of Toledo, Toledo, Ohio

    H. Westcott Vayo

Authors
  1. Dhanjoo N. Ghista
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  2. H. Westcott Vayo
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Ghista, D.N., Vayo, H.W. The time-varying elastic properties of the left ventricular muscle. Bulletin of Mathematical Biophysics 31, 75–92 (1969). https://doi.org/10.1007/BF02478210

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  • DOI: https://doi.org/10.1007/BF02478210

Keywords

  • Elastic Property
  • Fourier Series
  • Cardiac Cycle
  • Stress System
  • Ventricular Dimension