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Large deformation analysis of some basic problems in biophysics

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Abstract

This study is concerned with the application of a possible form of a strain-energy function suitable for soft biological tissues. Two problems considered here are related to simultaneous extension and inflation of cylindrical arteries, and inflation of the left ventricle under a given internal pressure. The values of the material constants are obtained via comparison of theoretical results with experimental findings. Some details concerning the wall stresses and the elastic stiffness are also given in the paper. For each case, it is seen that experiment and theory are in good agreement.

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Literature

  • Blatz, P. J., B. M. Chu and H. Wayland. 1969. “On the mechanical behavior of elastic animal tissues.”Trans. Soc. Rheology,13, 83–102.

    Article  Google Scholar 

  • Demiray, H. 1972. “A note on the elasticity of soft biological tissues.”J. Biomech.,5, 309–311.

    Article  Google Scholar 

  • Demiray, H. 1975. “On the constitutive equations of biological materials.”J. Appl. Mech., ASME, 241 Series E, 242–243.

    Google Scholar 

  • Eringen, A. C. 1962.Nonlinear Theory of Continuous Media. New York: McGraw-Hill.

    Google Scholar 

  • Fung, Y. C. 1967. “Elasticity of soft tissues in simple elongation.”Am. J. Physiol.,213, 1532–1544.

    Google Scholar 

  • Gou, P. F. 1970. “Strain-energy functions for biological tissues.”J. Biomech.,3, 547–550.

    Article  Google Scholar 

  • Mirsky, I. and W. W. Parmley. 1972. “Assessment of passive elastic stiffness for isolated heart muscle and the intact heart.”Circ. Res.,33, 233–243.

    Google Scholar 

  • Mirsky, I. 1973. “Ventricular and arterial wall stresses based on large deformation analysis.”Biophys. J.,13, 1141–1159.

    MathSciNet  Google Scholar 

  • Monreo, R. G., W. J. Gamble, C. G. Lafarge, A. E. Kumar, J. Stark, G. L. Sanders, C. Phonphutmul, and M. Davis. 1972. “The Anrep effect reconsidered.”J. Clin. Invest. 51, 2573–2583.

    Article  Google Scholar 

  • Mooney, M. 1940. “A theory of large elastic deformation.”J. Appl. Phys.,11, 582–592.

    Article  MATH  Google Scholar 

  • Patel, D. C., J. S. Janicki and T. E. Carew. 1969. “Anisotropic elastic properties of the aorta in living dogs.”Circ. Res.,25, 765–779.

    Google Scholar 

  • Rivlin, R. S. 1960. “Large elastic deformation of isotropic materials.”Phil. Trans.,A.240 459–508.

    MathSciNet  Google Scholar 

  • Simon, B. R., A. S. Kobayashi, D. E. Strandness and C. A. Wiederhielm. 1972. “Reevaluation of arterial constitutive laws.”Circ. Res.,30, 491–500.

    Google Scholar 

  • Snyder, R. W. 1972. “Large deformation of isotropic biological tissue.”J. Biomech.,5, 601–606.

    Article  Google Scholar 

  • Spotnitz, H. M., E. H. Sonnenblick and D. Spiro. 1966. “Relation of ultrastructure of function in the intact heart: Sarcomere structure relative to pressure volume curves of intact left ventricle of dog and cat.”Circ. Res.,18, 49–66.

    Google Scholar 

  • Vaishnav, R. M., J. T. Youn, J. S. Janicki and J. D. Patel. 1972. “Nonlinear anisotropic properties of the canine aorta.”Biophys. J.,12, 1008–1027.

    Article  Google Scholar 

  • Vito, R. 1973. “A note on arterial elasticity.”J. Biomech.,6, 561–564.

    Article  Google Scholar 

  • Streeter, Jr. D. D., R. N. Vaishnav, D. J. Patel, H. M. Spotnitz, J. Ross, Jr. and E. H. Sonnenblick. 1970. “Stress distribution in the canine left ventricle during diastole and systole.”Biophys. J.,10, 345–363.

    Google Scholar 

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Demiray, H. Large deformation analysis of some basic problems in biophysics. Bltn Mathcal Biology 38, 701–712 (1976). https://doi.org/10.1007/BF02458644

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  • DOI: https://doi.org/10.1007/BF02458644

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