Constitutive Equations of Arterial and Ventricular Wall Tissues Based on Pressure-Volume Relations

Conference paper


The present method of derivation of the constitutive equation is based on pressure-volume (p-V) relation of the blood vessel or the heart, differing from the works reported so far with the use of the mechanical behavior of the dissected small specimens.

The existance of the (pseudo) strain energy density function is assumed for the deformation of arterial tissues and also for the deformation of left ventricular wall tissues in the passive state and during isovolumic contractions.

A simple mathematical model is used in which the effect of physical and geometrical nonlinearities are taken into account. The strain energy density function is determined analytically from the p-V relation obtained experimentally. The biaxial stress- strain relation is also derived in a simple manner and it is used as the constitutive equation of the arterial or the left ventricular wall tissues.


Left Ventricle Constitutive Equation Left Ventricular Wall Geometrical Nonlinearity Muscular Tissue 
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  1. 1.
    Abé, H.; Ishikawa, N.; Mechanical behavior of vascular wall—Analysis based on finite deformation theory and strain energy density function. Japanese J. Medical Electronics and Biological Eng. 23–6 (1985) 29–34.Google Scholar
  2. 2.
    Abé, H. et al.; Stresses in left ventricular wall and biaxial stress-strain relation of the cardiac muscle fiber for the potassium-arrested heart. Trans. ASME, J. Biomechanical Eng. 100 (1978) 116–121.CrossRefGoogle Scholar
  3. 3.
    Abé, H. et al.; Stress-strain relation of cardiac muscle determined from ventricular pressure-time relationships during isovolumic contractions. J. Biomech. 14 (1981) 357–360.CrossRefGoogle Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • H. Abé
    • 1
  1. 1.Department of Mechanical EngineeringTohoku UniversitySendai, 980Japan

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