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. 1973 Nov;13(11):1141–1159. doi: 10.1016/S0006-3495(73)86051-5

Ventricular and Arterial Wall Stresses Based on Large Deformation Analyses

I Mirsky
PMCID: PMC1484386  PMID: 4754195

Abstract

Assuming a spherical geometry for the left ventricle and a cylindrical geometry for arteries, wall stresses and elastic stiffnesses are evaluated on the basis of a large elastic deformation theory. On the basis of canine pressure-volume data, the numerical results indicate marked gradients of stress in the endocardial layers even for thin-walled vessels, a result not predicted by the classical theory of elasticity. These high gradients of stress are due to the fact that the elastic stiffness of the wall material increases with the stress which reaches maximum levels in the endocardial layers. The high stresses may be responsible for ischemia of the left ventricle and be a triggering mechanism for atherosclerosis.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. BURCH G. E., RAY C. T., CRONVICH J. A. Certain mechanical peculiarities of the human cardiac pump in normal and diseased states. Circulation. 1952 Apr;5(4):504–513. doi: 10.1161/01.cir.5.4.504. [DOI] [PubMed] [Google Scholar]
  2. BURTON A. C. The importance of the shape and size of the heart. Am Heart J. 1957 Dec;54(6):801–810. doi: 10.1016/0002-8703(57)90186-2. [DOI] [PubMed] [Google Scholar]
  3. Fung Y. C. Elasticity of soft tissues in simple elongation. Am J Physiol. 1967 Dec;213(6):1532–1544. doi: 10.1152/ajplegacy.1967.213.6.1532. [DOI] [PubMed] [Google Scholar]
  4. Ghista D. N., Sandler H. An analytic elastic-viscoelastic model for the shape and the forces in the left ventricle. J Biomech. 1969 Mar;2(1):35–47. doi: 10.1016/0021-9290(69)90040-2. [DOI] [PubMed] [Google Scholar]
  5. Gou P. F. Strain energy function for biological tissues. J Biomech. 1970 Nov;3(6):547–550. doi: 10.1016/0021-9290(70)90038-2. [DOI] [PubMed] [Google Scholar]
  6. Gould P., Ghista D., Brombolich L., Mirsky I. In vivo stresses in the human left ventricular wall: analysis accounting for the irregular 3-dimensional geometry and comparison with idealised geometry analyses. J Biomech. 1972 Sep;5(5):521–539. doi: 10.1016/0021-9290(72)90009-7. [DOI] [PubMed] [Google Scholar]
  7. Mirsky I. Effects of anisotropy and nonhomogeneity on left ventricular stresses in the intact heart. Bull Math Biophys. 1970 Jun;32(2):197–213. doi: 10.1007/BF02476885. [DOI] [PubMed] [Google Scholar]
  8. Mirsky I. Left ventricular stresses in the intact human heart. Biophys J. 1969 Feb;9(2):189–208. doi: 10.1016/S0006-3495(69)86379-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Mirsky I., Parmley W. W. Assessment of passive elastic stiffness for isolated heart muscle and the intact heart. Circ Res. 1973 Aug;33(2):233–243. doi: 10.1161/01.res.33.2.233. [DOI] [PubMed] [Google Scholar]
  10. Mirsky I. Pulse velocities in initially stressed cylindrical rubber tubes. Bull Math Biophys. 1968 Jun;30(2):299–308. doi: 10.1007/BF02476697. [DOI] [PubMed] [Google Scholar]
  11. Monroe R. G., Gamble W. J., LaFarge C. G., Kumar A. E., Stark J., Sanders G. L., Phornphutkul C., Davis M. The Anrep effect reconsidered. J Clin Invest. 1972 Oct;51(10):2573–2583. doi: 10.1172/JCI107074. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Patel D. J., Janicki J. S., Carew T. E. Static anisotropic elastic properties of the aorta in living dogs. Circ Res. 1969 Dec;25(6):765–779. doi: 10.1161/01.res.25.6.765. [DOI] [PubMed] [Google Scholar]
  13. Patel D. J., Janicki J. S. Static elastic properties of the left coronary circumflex artery and the common carotid artery in dogs. Circ Res. 1970 Aug;27(2):149–158. doi: 10.1161/01.res.27.2.149. [DOI] [PubMed] [Google Scholar]
  14. SANDLER H., DODGE H. T. LEFT VENTRICULAR TENSION AND STRESS IN MAN. Circ Res. 1963 Aug;13:91–104. doi: 10.1161/01.res.13.2.91. [DOI] [PubMed] [Google Scholar]
  15. Simon B. R., Kobayashi A. S., Strandness D. E., Wiederhielm C. A. Reevaluation of arterial constitutive relations. A finite-deformation approach. Circ Res. 1972 Apr;30(4):491–500. doi: 10.1161/01.res.30.4.491. [DOI] [PubMed] [Google Scholar]
  16. Spotnitz H. M., Sonnenblick E. H., Spiro D. Relation of ultrastructure to function in the intact heart: sarcomere structure relative to pressure volume curves of intact left ventricles of dog and cat. Circ Res. 1966 Jan;18(1):49–66. doi: 10.1161/01.res.18.1.49. [DOI] [PubMed] [Google Scholar]
  17. Streeter D. D., Jr, Vaishnav R. N., Patel D. J., Spotnitz H. M., Ross J., Jr, Sonnenblick E. H. Stress distribution in the canine left ventricle during diastole and systole. Biophys J. 1970 Apr;10(4):345–363. doi: 10.1016/S0006-3495(70)86306-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Vaishnav R. N., Young J. T., Janicki J. S., Patel D. J. Nonlinear anisotropic elastic properties of the canine aorta. Biophys J. 1972 Aug;12(8):1008–1027. doi: 10.1016/S0006-3495(72)86140-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Wong A. Y., Rautaharju P. M. Stress distribution within the left ventricular wall approximated as a thick ellipsoidal shell. Am Heart J. 1968 May;75(5):649–662. doi: 10.1016/0002-8703(68)90325-6. [DOI] [PubMed] [Google Scholar]

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