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Effects of anisotropy and nonhomogeneity on left ventricular stresses in the intact heart

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Abstract

The qualitative effects of anisotropy and nonhomogeneity are considered in the evaluation of left ventricular stresses in the intact heart. Maximum stresses and their location are significantly dependent on the nonhomogeneity factors and to a lesser degree on anisotropy of the ventricular wall material. If the circumferential elastic modulus is assumed to vary in a parabolic manner through the wall thickness, maximum stresses occur within the endocardial layers, a result in qualitative agreement with experimental studies.

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Literature

  • Bieniek, M., W. R. Spillers and A. M. Freudenthal. 1962. “Nonhomogeneous Thick-walled Cylinder under Internal Pressure.”A.R.S.,32, 8, 1249–1255.

    MATH  Google Scholar 

  • Ghista, Dhanjoo N. and Harold Sandler. 1969. “An Analytic Elastic-viscoelastic Model for the Shape and the Forces of the Left Ventricle.”J. Biomechanics,2, (1), 35–47.

    Article  Google Scholar 

  • Grant, R. P. 1965. “Notes on the Muscular Architecture of the Left Ventricle.”Circulation,32, 301–308.

    Google Scholar 

  • Johnson, J. R. and J. R. DiPalma. 1939. “Intramyocardial Pressure and Its Relation to Aortic Blood Pressure.”Am. J. Physiol.,125, 234–243.

    Google Scholar 

  • Laszt, I. and A. Müller. 1958. “Der myokardial Druck.”Helv. Physiol. Pharmacol. Acta,16, 88–106.

    Google Scholar 

  • Lekhnitskii, S. G. 1963.Theory of Elasticity of an Anisotropic Elastic Body. San Francisco: Holder-Day, p. 19.

    MATH  Google Scholar 

  • Love, A. E. H. 1944. “A Treatise on the Mathematical Theory of Elasticity.” Fourth Edition. New York: Dover Publications, p. 283.

    MATH  Google Scholar 

  • Mirsky, I. 1967. “Pulse Velocities in an Orthotropic Elastic Tube.”Bull. Math. Biophysics,29, 311–318.

    Google Scholar 

  • —. 1969. “Left Ventricular Stresses in the Intact Human Heart.”Biophysical J.,9, 189–208.

    Article  Google Scholar 

  • Streeter, D. D. and D. Bassett. 1966. “An Engineering Analysis of Myocardial Fibre Orientation in Pig’s Left Ventricle in Systole.”Anat. Rec.,145, 503–511.

    Article  Google Scholar 

  • —, H. M. Spotnitz, D. J. Patel, J. Ross, Jr and E. H. Sonnenblick. 1969.Circ. Research,24, 339–347.

    Google Scholar 

  • Timoshenko, S. 1940.Theory of Plates and Shells. New York: McGraw-Hill Book Co. p. 365.

    MATH  Google Scholar 

  • Wong, A. Y. K. and P. M. Rautaharju. 1968. “Stress Distribution within the Left Ventricular Wall Approximated as a Thick Ellipsoidal Shell.”Am. Heart J.,75, 649–662.

    Article  Google Scholar 

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  1. Department of Medicine, Division of Mathematical Biology, Harvard Medical School and, Peter Bent Brigham Hospital, Boston, Massachusetts

    I. Mirsky

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  1. I. Mirsky
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Mirsky, I. Effects of anisotropy and nonhomogeneity on left ventricular stresses in the intact heart. Bulletin of Mathematical Biophysics 32, 197–213 (1970). https://doi.org/10.1007/BF02476885

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  • DOI: https://doi.org/10.1007/BF02476885

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