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

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Computational Mechanics ’86

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Summary

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.

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References

  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.

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  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.

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  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.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Tohoku University, Sendai, 980, Japan

    H. Abé

Authors
  1. H. Abé
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Editor information

Editors and Affiliations

  1. Department of Nuclear Engineering, The University of Tokyo, 3-1, Hongo 7-chome, Bunkyo-ku, Tokyo 113, Japan

    Genki Yagawa

  2. Center for the Advancement of Computational Mechanics, School of Civil Engineering, Georgia Institute of Technology, 225, North Avenue, Atlanta, GA, 30332, USA

    Satya N. Atluri

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© 1986 Springer Japan

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Abé, H. (1986). Constitutive Equations of Arterial and Ventricular Wall Tissues Based on Pressure-Volume Relations. In: Yagawa, G., Atluri, S.N. (eds) Computational Mechanics ’86. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68042-0_115

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  • DOI: https://doi.org/10.1007/978-4-431-68042-0_115

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68044-4

  • Online ISBN: 978-4-431-68042-0

  • eBook Packages: Springer Book Archive

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