Abstract
In this chapter, we briefly discuss the continuum mechanics approach to determining biomechanical constitutive relations and performing stress analyses, with particular emphasis on applications to the noncontracting heart. Examples taken from our own work illustrate possible avenues toward the eventual goal of estimating mechanical stresses in the heart and using this information to understand better certain aspects of cardiac mechanics.
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References
R.J. Atkin and N. Fox. An Introduction to the Theory of Elasticity. Longman Press, London, 1980.
R.M. Berne and M.N. Levy. Cardiovascular Physiology. The C.V. Mosby Co., St. Louis, MO, 1986.
T.K. Borg and J.B. Caulfield. Collagen in the heart. Tex. Rep. Biol Med., 39: 321–333, 1979.
P.H. Chew, F.C.P. Yin, and S.L. Zeger. Biaxial stress-strain properties of canine pericardium. J. Mol. Cell. Cardiol., 18: 567–578, 1986.
L.L. Demer and F.C.P. Yin. Passive biaxial mechanical properties of isolated canine myocardium. J. Physiol. (London), 339: 615–630, 1983.
A.E. Green and J.E. Adkins. Large Elastic Deformations. Oxford University Press, Oxford, 1970.
H.R. Halperin, P.H. Chew, M.L. Weisfeldt, K. Sagawa, J.D. Humphrey, and F.C.P. Yin. Transverse stiffness: A method for estimation of myocardial wall stress. Circ. Res., 61: 695–703, 1987.
R.M. Huisman, P. Sipkema, N. Westerhof, and G. Elzinga. Comparison of models used to calculate left ventricular wall force. Med. Biol. Eng. Comput., 18: 133–144, 1980.
J.D. Humphrey, H.R. Halperin, and F.C.P. Yin. Small indentation superimposed on a finite equibiaxial stretch: Implications to cardiac mechanics. ASME J. Appl. Mech., 1990. (submitted).
J.D. Humphrey, R.K. Strumpf, and F.C.P. Yin. Biaxial mechanical behavior of excised ventricular epicardium. Am. J. Physiol., 259: H101-H108, 1990.
J.D. Humphrey, R.K. Strumpf, and F.C.P. Yin. Determination of a constitutive relation for passive myocardium: II. Parameter identification. ASME J. Biomech. Eng., 112: 340–346, 1990.
J.D. Humphrey, R.K. Strumpf, and F.C.P. Yin. Determination of a constitutive relation for passive myocardium: I. A new functional form. ASME J. Biomech. Eng., 112: 333–339, 1990.
J.D. Humphrey and F.C.P. Yin. Biaxial mechanical behavior of excised epicardium. ASME J. Biomech. Eng., 110: 349–351, 1988.
J.D. Humphrey and F.C.P. Yin. Biaxial mechanical properties of passive myocardium. In A. Yettram, editor, Material Properties and Stress Analysis in Biomechanics. Manchester University Press, Manchester, England, 1989.
J.D. Humphrey and F.C.P. Yin. Constitutive relations and finite deformations of passive cardiac tissue: II. Stress analysis in the left ventricle. Circ. Res., 65: 805–817, 1989.
P.J. Hunter and B.H. Smaill. The analysis of cardiac function: A continuum approach. Prog. Biophys. Mol. Biol., 52: 101–164, 1988.
I. Mirsky. Assessment of passive elastic stiffness of cardiac muscle: Mathematical concepts, physiologic and clinical considerations, directions of future research. Prog. Cardiovasc. Dis., 18: 277–308, 1976.
T. Moriarty. The law of Laplace: Its limitations as a relation for diastolic pressure, volume or wall stress of the left ventricle. Circ. Res., 46: 321–331, 1980.
J.H. Omens and Y.C. Fung. Residual stress in the left ventricle. In A.H. Erdman, editor, 1987 ASME Advances in Bioengineering. New York, 1987.
T.F. Robinson. The physiological relationship between connective tissue and contractile elements in heart muscle. Einstein Q., 1: 121–127, 1983.
K. Sagawa, L. Maughan, H. Suga, and K. Sunagawa. Cardiac Contraction and the Pressure-Volume Relationship. Oxford University Press, New York, 1988.
D.D. Streeter. Handbook of Physiology, Volume 1. American Physiological Society, Bethesda, MD, 1979. Section 2.
C. Truesdell and W. Noll. The nonlinear field theories of mechanics. In S. Flugge, editor, Handbuch der Physik, Volume III, Springer-Verlag, Berlin, 1965.
L.K. Waldman, Y.C. Fung, and J.W. Covell. Transmural myocardial deformation in the canine left ventricle. Circ. Res., 57: 152–163, 1985.
R.H. Woods. A few applications of a physical theorem to membranes in the human body in the state of tension. J. Anai. Physiol., 26: 262–270, 1892.
F.C.P. Yin. Applications of the finite-element method to ventricular mechanics. CRC Crit. Rev. Biomed. Eng., 12: 311–342, 1985.
F.C.P. Yin. Ventricular wall stress. Circ. Res., 49: 829–842, 1981.
F.C.P. Yin, P.H. Chew, and S.L. Zeger. An approach to quantification of biaxial tissue stress-strain data. J. Biomech., 19: 27–37, 1986.
F.C.P. Yin, R.K. Strumpf, P.H. Chew, and S.L. Zeger. Quantification of the mechanical properties of noncontracting canine myocardium under simultaneous biaxial loading. J. Biomech., 20: 577–589, 1987.
O.C. Zienkiewicz. The Finite Element Method. McGraw Hill, New York, 1979.
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Humphrey, J., Strumpf, R., Halperin, H., Yin, F. (1991). Toward a Stress Analysis in the Heart. In: Glass, L., Hunter, P., McCulloch, A. (eds) Theory of Heart. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3118-9_3
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DOI: https://doi.org/10.1007/978-1-4612-3118-9_3
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