Abstract
The heart is the prime mover of blood. By periodic stimulation of its muscles it contracts periodically and pumps blood throughout the body. How the pump works is the subject of this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arts, T., and Reneman, R.S. (1980). Measurements of deformation of canine epicardium in vivo during cardiac cycle. Am. J. Physiol. 239: H432–H437.
Arts, T., Reneman, R.S., and Veenstra, P.C. (1982). Epicardial deformation and left ventricular wall mechanics during ejection in the dog. Am. J. Physiol. 243: H379–H390.
Bellhouse, B.J., and Bellhouse, F.H. (1969). Fluid mechanics of model normal and stenosed aortic valves. Circ. Res. 25: 693–704.
Bellhouse, B.J., and Bellhouse, F.H. (1972). Fluid mechanics of a model mitral valve and left ventricle. Cardiovasc. Res. 6:199–210.
Berne, R.M., and Sperelakis, N. (eds.) (1979). Handbook of Physiology. Sec. 2. The Cardiovascular System, Vol. 1. The Heart. American Physiological Society, Bethesda, MD.
Blum, W.F., McCulloch, A.D., and Lew, W.Y.W. (1995). Active force in rabbit ventricular myocytes. J. Biomech. 28: 1119–1122.
Brady, A.J. (1984). Passive stiffness of rat cardiac myocytes. J. Biomech. Eng. 106: 25–30.
Braunwald, E. (ed.) (1988). Heart Disease. 3rd Edition, Saunders Co., Philadelphia, PA.
Costa, K.D., Hunter, P.J., Rogers, J.M., Guccione, J.M., Waldman, L.K., and McCulloch, A.D. (1996). A three-dimensional finite element method for large elastic deformations of ventricular myocardium: Part 1 cylindrical and spherical polar coordinates. J. Biomech. Eng. Submitted.
Daniels, M., Noble, M.I.M., ter Keurs, H.E.D.J., and Wohlfart, B. (1984). Velocity of sarcomere shortening in rat cardiac muscle: relationship to force, sarcomere length, calcium and time. J. Physiol. 355: 367–381.
Debes, J.C., and Fung, Y.C. (1995). Biaxial mechanics of excised canine pulmonary arteries, Am. J. Physiol. 269: H433–H442.
Deng, S.X., Tomioka, J., Debes, J.C., and Fung, Y.C. (1994). New experiments on shear modulus of elasticity of arteries. Am. J. Physiol. 266: H1–H10.
Dieudonné, J.M. (1969). La determination experimentale des contraintes myocardiques. J. Physiol. (Paris) 61: 199–218.
Edman, K.A.P., and Nilsson, E. (1972). Relationship between force and velocity of shortening in rabbit papillary muscle. Acta Physiol. Scand. 85: 488–500.
Frank, O. (1899). Die grundform des arteriellen pulses. Erste Abhandlung, Mathematische Analyse. Z. Biol. 37: 483–526.
Fung, Y.C. (1965). Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, NJ.
Fung, Y.C. (1970). Mathematical representation of the mechanical properties of the heart muscle. J. Biomech. 3: 381–404.
Fung, Y.C. (1971). Stress-strain-history relation of soft tissues in simple elongation, In Biomechanics: Its Foundation and Objectives. (Fung, Y.C, Perrone, N, and Anliker, M., eds.), Prentice-Hall, Englewood Cliffs, NJ, pp. 181–208.
Fung, Y.C. (1973). Biorheology of soft tissues, Biorheology, 19: 139–155.
Fung, Y.C. (1979). Inversion of a class of nonlinear stress-strain relationships of biological soft tissues. J. Biomech. Eng, 101: 23–27.
Fung, Y.C. (1983). What principle governs the stress distribution in living organisms, In Biomechanics in China, Japan, and USA. (Fung, Y.C, Fukada, E., and Wang, J.J., eds.), Science Press, Beijing, pp. 1–13.
Fung, Y.C (1988). Cellular growth in soft tissues affected by the stress level in service, In Tissue Engineering. (Skalak, R., and Fox, C.F., eds.), Alan Liss, Inc., New York, pp. 45–50.
Fung, Y.C. (1990). Biomechanics: Motion, Flow, Stress and Growth, Springer-Verlag, New York.
Fung, Y.C. (1993a). A First Course in Continuum Mechanics, 3rd Edition, Prentice-Hall, Englewood Cliffs, NJ, pp. 165–180.
Fung, Y.C. (1993b). Biomechanics: Mechanical Properties of Living Tissues, 2nd Edition, Springer-Verlag, New York.
Fung, Y.C, and Liu., S.Q. (1995). Determination of the mechanical properties of the different layers of blood vessels in vivo. Proc. U.S. Natl. Acad. Sci. 92: 2169–2173.
Fung, Y.C., Fronek, K., and Patitucci, P. (1979). Pseudoelasticity of arteries and the choice of its mathematical expression, Am. J. Physiol. 237, H620–H631.
Fung, Y.C, Liu, S.Q., and Zhou, J. (1993). Remodeling of the constitutive equation while a blood vessel remodels itself under stress, J. Biomech. Eng. 115: 453–459.
Gorlin, R., and Gorlin, S.G. (1951). Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. Am. Heart J. 41: 1–29.
Green, A.E., and Adkins, J.E. (1960). Large Elastic Deformations and Non-linear Continuum Mechanics. Oxford Univ. Press, London.
Guccione, J.M., and McCulloch, A.D. (1991). Finite element modeling of ventricular mechanics. In Theory of Heart, pp. 124-144, see Glass et al. (1991).
Guccione, J.M., and McCulloch, A.D. (1993). Mechanics of active contraction in cardiac muscle: Part 1—constitutive relations for fiber stress that describe deactivation. J. Biomech Eng. 115: 72–81.
Guccione, J.M., Costa, K.D., and McCulloch, A.D. (1995). Finite element stress analysis of left ventricular mechanics in the beating heart. J. Biomech. 28: 1167–1177.
Guccione, J.M., McCulloch, A.D., and Waldman, L.K. (1991). Passive material properties of intact ventricular myocardium determined for a cylindrical model. J. Biomech Eng. 113: 42–55.
Hales, S. (1733). Statical Essays: II. Haemostaticks. Innays and Manby, London. Reprinted by Hafner, New York.
Hashima, A.R., Young, A.A., McCulloch, A.D., and Waldman, L.K. (1993). Nonhomogeneous analysis of epicardial strain distributions during acute myocardial ischemia in the dog. J. Biomech. 26: 19–35.
Henderson, Y, and Johnson, F.E. (1912). Two modes of closure of the heart valves. Heart 4: 69–82.
Hill, A.V. (1939). The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. London (Biol.) B 126: 136–195.
Holmes, J.W., Yamashita, H., Waldman, L.K., and Covell, J.W. (1994). Scar remodeling and transmural deformation after infarction in the pig. Circulation 90: 411–420.
Horowitz, A. (1991). Structural considerations in formulating material laws for the myocardium. In Theory of Heart, pp. 31-58, see Glass et al. (1991).
Hort, W. (1960). Makroskopische und mikrometrische Untersuchungen am Myokard verschieden stark gefullter linker kammern. Virchows Arch. Path. Anat. 333: 523–564.
Humphrey, J.D., and Yin, F.C.P. (1989a). Biomechanical experiments on excised myocardium: theoretical considerations. Am. J. Physiol. 22: 377–383.
Humphrey, J.D., and Yin, F.C.P. (1989b). Constitutive relations and finite deformations of passive cardiac tissue II: stress analysis in the left ventricle. Circ. Res. 65: 805–817.
Humphrey, J.D., Strumpf, R.K., and Yin, F.C.P. (1990). Biaxial mechanical behavior of excised ventricular epicardium. Am. J. Physiol. 259: H101–H108.
Humphrey, J.D., Strumpf, R.K., Halperine, H., and Yin, E (1991). Toward a stress analysis in the heart. In Theory of Heart, pp. 59-75, see Glass et al. (1991).
Hunter, W.C., Janicki, J.S., Weber, K.T., and Noordergraaf, A. (1983). Systolic mechanical properties of the left ventricle: effects of volume and contractile state. Circ. Res. 52: 319–327.
Huntsman, L.L., Rondinone, J.F., and Martyn, D.A. (1983). Force-length relations in cardiac muscle segments. Am. J. Physiol. 244: H701–H707.
Janz, R.F., and Grimm, A.F. (1973). Deformation of the diastolic left ventricle. I. Nonlinear elastic effects. Biophys. J. 13: 689–704.
Janz, R.F., and Waldron, R.J. (1976). Some implications of a constant fiber stress hypothesis in the diastolic left ventricle. Bull. Math. Biol 38: 401–413.
Janz, R.F., Grimm, A.F, Kubert, B.R., and Moriarty, T.F. (1974). Deformation of the diastolic left ventricle. II. Nonlinear geometric effects. J. Biomech. 7: 509–516.
Jones, R.T. (1969). Blood flow. In Annual Review of Fluid Mechanics. (Sears, W.R., and van Dyke, M., eds.), Annual Reviews, Palo Alto, CA.
Jones, R.T. (1972). Fluid dynamics of heart assist devices. In Biomechanics: Its Foundations and Objectives. (Fung, Y.C., Perrone, N, and Anliker, M, eds.), Prentice-Hall, Englewood Cliffs, NJ, Chapter 1, pp. 549–565.
Krueger, J.W., Tsujioka, K., Okada, T., Peskin, C.S., and Lacker, H.M. (1988). A “give” in tension and sarcomere dynamics in cardiac muscle relaxation. Adv. Exp. Med. Biol. 226: 567–580.
Lacker, H.M., and Peskin, C.S. (1986). A mathematical method for unique determination of crossbridge properties from steady-state mechanical and energetic experiments on macroscopic muscle. In Some Mathematical Questions in Biology—Muscle Physiology. (Miura, R.M., ed.), American Mathematics Society, Providence, RI, pp. 121–153.
Lamé, E. (1852). Leçons sur la Théorie de l’Elasticité. Paris.
Lanir, Y. (1983). Constitutive equation for fibrous connective tissue. J. Biomech. 16: 1–12.
Lee, C.S.F., and Talbot, L. (1979). A fluid mechanical study on the closure of heart valves. J. Fluid Mech. 91: 41–63.
LeGrice, I.J., Smail, B.H., Chai, L.Z., Edgar, S.G., Gavin, J. B., and Hunter, P.J. (1995). Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. 269: H571–H582.
MacKenna, D.A., Omens, J.H., McCulloch, A.D., and Covell, J.W. (1994). Contribution of collagen matrix to passive left ventricular mechanics in isolated rat hearts. Am. J. Physiol. 266: H1007–H1018.
McCulloch, A.D. (1995). Cardiac mechanics. In Biomedical Engineering Handbook. (Bronzino, J.D., ed.), Chapter 31, pp. 418–439. CRC Press, Inc. Boca Raton, FL.
McCulloch, A.D., and Omens, J.H. (1991). Factors affecting the regional mechanics of the diastolic heart. In Theory of Heart, pp. 87-119, see Glass et al. (1991).
McCulloch, A.D., and Omens, J.H. (1991). Non-homogeneous analysis of three-dimensional transmural finite deformation in canine ventricular myocardium. J. Biomech. 24: 539–548.
McCulloch, A.D., Smail, B.H., and Hunter, P.J. (1987). Left ventricular epicardial deformation in isolated arrested dog heart. Am. J. Physiol. 252: H233–H241.
McDonald, D.A. (1974). Blood Flow in Arteries. Williams & Wilkins, Baltimore, MD.
Meier, G.D., Bove, A.A., Santamore, W.P., and Lynch, P.R. (1980). Contractile function in canine right ventricle. Am. J. Physiol. 239: H794–H804.
Mirsky, I. (1973). Ventricular and arterial wall stresses based on large deformation analysis. Biophys. J. 13: 1141–1159.
Mirsky, I. (1979). Elastic properties of the myocardium: A quantitative approach with physiological and clinical applications. In Handbook of Physiology, Sec. 2, Vol. 1. The Heart. (Berne, R.M., and Sperelakis, N., eds.), American Physiological Society, Bethesda, MD., pp. 497–531.
Netter, F. (1969). The Ciba Collection of Medical Illustrations, Vol. 5, Heart, CIBA Publications Dept., Summit, NJ.
Omens, J.H., and Covell, J.W. (1991). Transmural distribution of myocardial tissue growth induced by volume-overload hypertrophy in the dog. Circulation 84: 1235–1245.
Omens, J.H., and Fung, Y.C. (1989). Residual strain in the rat left ventricle. Circ. Res. 66: 37–45.
Omens, J.H., Mac Kenna, D.A., and McCulloch, A.D. (1993). Measurement of strain and analysis of stress in resting rat left ventricular myocardium. J. Biomech. 26: 665–676.
Omens, J.H., May, K.D., and McCulloch, A.D. (1991). Transmural distribution of three-dimensional strain in the isolated arrested canine left ventricle. Am. J. Physiol. 261: H918–H928.
Omens, J.H., Rockman, H.A., and Covell, J.W. (1994). Passive ventricular mechanics in tight-skin mice. Am. J. Physiol. 266: H1169–H1176.
Ono, S., Waldman, L.K., Yamashita, H., Covell, J.W, and Ross, Jr., J. (1995). Effect of coronary artery reperfusion on transmural mycoardial remodeling in dogs. Circulation 91: 1143–1153.
Parmley, W.W., and Sonnenblick, E.H. (1967). Series elasticity of heart muscle: Its relation to contractile element velocity and proposed muscle models. Circ. Res. 20: 112–123.
Parmley, W, and Talbot, L. (1979). Heart as a pump. In Handbook of Physiology. Sec. 2. The Cardiovascular System, Vol. 1, The Heart. (Berne, R.M., and Sperelakis, N., eds.), American Physiological Society, Bethesda, MD, pp. 429–460.
Parmley, W.W., Brutsaert, D.L., and Sonnenblick, E.H. (1969). The effects of altered loading on contractile events in isolated cat papillary muscle. Circ. Res. 24: 521–532.
Panerai, R.B. (1980). A model of cardiac muscle mechanics and energetics. J. Biomech. 13: 929–940.
Peskin, C.S. (1977). Numerical analysis of blood flow in the heart. J. Comput. Phys. 25: 220–252.
Peskin, C.S., and Wolfe, A.W. (1978). The aortic sinus vortex. Fed. Proc. 37: 2784–2792.
Pinto, J.G., and Fung, Y.C. (1973a). Mechanical properties of the heart muscle in the passive state. J. Biomech. 6: 597–616.
Pinto, J.G., and Fung, Y.C. (1973b). Mechanical properties of stimulated papillary muscle in quick-release experiments. J. Biomech. 6: 617–630.
Prinzen, F.W, Arts, T., Van der Vusse, G.J., Comans, W.A., and Reneman, R.S. (1986). Gradients in fiber shortening and metabolism across the left ventricler wall. Am. J. Physiol. 250: H255–H264.
Rodriquez, E.K., Hoger, A., and McCulloch, A.D. (1994). Stress-dependent finite growth in soft elastic tissues. J. Biomech. 27: 455–467.
Rodriquez, E.K., Omens, J.H., Waldman, L.K., and McCulloch, A.D. (1993). Effect of residual stress on transmural sarcome length distributions in rat left ventricle. Am. J. Physiol. 264: H1048–H1056.
Rogers, J.M., and McCulloch, A.D. (1994). A collocation-Galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng. 41: 743–757.
Scher, A.M. and Spach, M.S. (1979). Cardiac depolarization and repolarization and the electrocardiogram. In Handbook of Physiology, Sec. 2, Vol. 1, The Heart. (Berne, R.M., and Sperelakis, N., eds.), American Physiological Society, Bethesda, MD, pp. 357–392.
Smail, B.H., and Hunter, P.J. (1991). Structure and function of the diastolic heart. In Theory of Heart, pp. 1-30, see Glass et al. (1991).
Sonnenblick, E.H. (1964). Series elastic and contractile elements in heart muscle: Changes in muscle length. Am. J. Physiol. 207: 1330–1338.
Sonnenblick, E.H., Ross, Jr., Covell, J.W., Spontnitz, H.M., and Spiro, D. (1967). Ultrastructure of the heart in systole and diastole: Changes in sarcomere length. Circ. Res. 21: 423–431.
Streeter, Jr., D. (1979). Gross morphology and fiber geometry of the heart. In Handbook of Physiology, Sec. 2, Cardiovascular System. Vol. 1. The Heart. (Berne, R.M., and Sperelakis, N., eds.), American Physiology Society, Bethesda, MD, pp. 61–112.
Streeter, Jr., D., and Hanna, W.T. (1973). Engineering mechanics for successive states in canine left ventricular myocardium. I. Cavity and wall geometry. II. Fiber angle and sarcomere length. Circ. Res. 33: 639–655(I), 656-664(II).
Streeter, D., Jr., Spotnitz, H.M., Patel, D.J., Ross, Jr., J., and Sonnenblick, E.H. (1969). Fiber orientation in the canine left ventricle during diastole and systole. Circ. Res. 24: 339–347.
Suga, H., Sagawa, K., and Shoukas, A.A. (1973). Load independence of the instantaneous pressure-volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio. Circ. Res. 32: 314–322.
Takamizawa, K., and Hayshi, K. (1987). Strain energy density function and uniform strain hypothesis for arterial mechanics. J. Biomech. 20: 7–17.
Takamizawa, K., and Matsuda, T. (1990). Kinematics for bodies undergoing residual stress and its applications to the left ventricle. J. Appl. Mech. 57: 321–329.
ter Keurs, H.E.D.J. (1983). Calcium in contractility. In Cardiac Metabolism, (Drake-Holland, A.J., and Noble, M.I.M., eds.), Wiley, New York, pp. 73–99.
ter Keurs, H.E.D.J., Rijnsburger, W.H., Van Heuningen, R., and Nagelsmit, M.J. (1980). Tension development and sarcomere length in rat cardiac trabeculate: evidence of length-dependent activation. Circ. Res. 46: 703–713.
Tong, P., and Fung, Y.C. (1976). The Stress-Strain Relationship for the Skin. J. Biomech. 9: 649–657.
Tözeren, A. (1985). Continuum rheology of muscle contraction and its application to cardiac contractillity. Biophys. J., 47: 303–309.
Vaishnav, R.N., and Vossoughi, J. (1983). Estimation of the residual strains in aortic segments. In Biomedical Engineering, II, Recent Developments. (Hall, C.W., ed.), Pergamon Press, New York, pp. 330–333.
Van Leuven, S.L., Waldman, L.K., McCulloch, A.D., and Covell, J.W. (1994). Gradients of epicardial strain across the perfusion boundary during acute myocardial ischemia. Am. J. Physiol. 267: H2348–H2362.
Villarreal, F.J., Waldman, L.K., and Lew, W.Y.W. (1988). A technique for measuring regional two-dimensional finite strains in canine left ventricle. Circ. Res. 62: 711–721.
Villarreal, F.J., Lew, W.Y.W., Waldman, L.K., and Covell, J.W. (1991). Transmural myocardial deformation in the ischemic canine left ventricle. Circ. Res. 68: 368–381.
Waldman, L.K. (1983). On the Mechanical Coupling of the Heart to the Circulation. Ph.D. thesis. University of California, San Diego, CA.
Waldman, L.K. (1991). Multidimensional measurements of regional strains in the intact heart. In Theory of Heart, pp. 145-174, see Glass et al. (1991).
Waldman, L.K., and Covell, J.W (1987). Effects of ventricular pacing on finite deformation in canine left ventricle. Am. J. Physiol. 252: H1023–H1030.
Waldman, L.K., and McCulloch, A.D. (1993). Nonhomogeneous ventricular wall strain: Analysis of errors and accuracy. J. Biomech. Eng. 115: 497–502.
Waldman, L.K., Fung, Y.C., Covell, J.W. (1985). Transmural myocardial deformation in the canine left ventricle: normal in vivo three-dimensional finite strains. Circ. Res. 57: 152–163.
Waldman, L.K., Nosan, D., Villarreal, F.J., and Covell, J.W. (1988). Relation between transmural deformation and local myofiber direction in canine left ventricle. Circ. Res. 63: 550–562.
Wetterer, E., and Kenner, T. (1968). Die Dynamik des Arterien-Pulses. Springer-Verlag, Berlin.
Whittaker, P., Kloner, R.A., Boughner, D.R., and Pickering, J.G. (1994). Quantitative assessment of myocardial collagen with picrosirius red staining and circularly polarized light. Basic Res. in Cardiol 89: 397–410.
Wong, A.Y.K., and Rautaharju, P.M. (1968). Stress distribution within the left ventricular wall approximated as a thick ellipsoidal shell. Am. Heart J. 75: 649–662.
Xie, J.P., Zhou, J., and Fung, Y.C. (1995). Bending of blood vessel wall: Stress-strain laws of the intima-media and adventitial layers. J. Biomech. Eng. 117: 136–145.
Yoran C, Covell, J.W, and Ross, Jr., J. (1973). Structural basis for the ascending limb of left ventricular function. Circ. Res. 32: 297–303.
Young, A. (1991). Epicardial deformation from coronary cinéangiogranis. In Theory of Heart, pp. 175-207, see Glass et al. (1991).
Yu, Q., Zhou, J.B., and Fung, Y.C. (1993). Neutral axis location in Bending and Young’s modulus of different layers of arterial wall. Am. J. Physiol. 265: H52–H60.
Zhou, J. (1992). Theoretical Analysis of Bending Experiments on Aorta and Determination of Constitutive Equations of materials in Different Layers of Arterial Walls. Doctoral Dissertation, University of California, San Diego, CA.
Zienkiewicz, O.C., and Morgan, K. (1982). Finite Elements and Approximation. Wiley, New York.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fung, Y.C. (1997). The Heart. In: Biomechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2696-1_2
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2696-1_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2842-9
Online ISBN: 978-1-4757-2696-1
eBook Packages: Springer Book Archive