Skip to main content
SpringerLink
Log in

A Structural Model of the Left Venricle Including Muscle Fibres and Coronary Vessels: Mechanical Behaviour in Normal Conditions

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

A structural model of the left ventricle is presented. It is a cylindricalthick-walled model composed of muscle fibre models and coronaryvessel models. The ventricular wall is divided in ten layers to accountfor the transmural variation of myofibre and coronary vessel orientation.These structures give the global performance of the ventricular modeldepending on their own behaviour and on the way they are interfaced.

The results refer both to the global ventricular performance and thebehaviour of the different components. In particular they suggest anappreciable contribute of the coronary capillary during the early fillingphase in enlarging the ventricle; during this phase the capillary vesselsexert an extensive force in the radial direction, due to inner coronarypressure, equal to 20--30 percent -- depending on the layer -- of the forceexerted by the fibres. This occurrence explains, in our opinion, theobserved cardiac function improvement when the arterial coronarypressure is increased, known as ’gardenhose‘ effect.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arts, T., Reneman, R.S. and Veenestra, P.C., ‘A model of the mechanics of the left ventricle’, Ann. Biomed. Eng., 7(1979) 299–318.

    Google Scholar 

  2. Arts, T. and Reneman, R.S., ‘Interaction between intramyocardial pressure and myocardial circulation’, J. Biomech. Eng., 107(1985) 51–56.

    Google Scholar 

  3. Nevo, E. and Lanir, Y., ‘Structural finite deformation of the left ventricle during diastole and systole’, J. Biomech. Eng., 111(1989) 342–349.

    Google Scholar 

  4. Guccione, J.M., Waldman, L.K. and McCulloch, A.D., ‘Mechanics of active contraction in cardiac muscle: part II–Cylindrical models of the systolic left ventricle’, J. Biomech. Eng., 115(1993) 82–90.

    Google Scholar 

  5. Guccione, J.M., McCulloch, A.D. and Waldman, L.K., ‘Passive material properties of intact ventricular myocardium determined from a cylindrical model’, J. Biomech. Eng., 113(1991) 42–55.

    Google Scholar 

  6. Beyar, R. and Sideman, S., ‘A computer study of the left ventricular performance based on fiber structure, sarcomere dynamics, and transmural electrical propagation velocity’, Circ. Res., 55(1984) 358–375.

    Google Scholar 

  7. Beyar, R., Ben-Ari, R., Gibbson-Kroeker, C.A., Tyberg, J.V. and Sideman, S., ‘Effect of interconnecting collagen fibres on left ventricular function and intramyocardial compression’, Cardiovasc. Res., 27(1993) 2254–2263.

    Google Scholar 

  8. Huyghe, J.M., Arts, T., Van Campen, D.H. and Reneman, R.S., ‘Porous medium finite element model of the beating ventricle’, Am. J. Physiol., 262(1992) H1256–H1267.

    Google Scholar 

  9. Bovendeerd, P.H.M., Arts, T., Huyghe, J.M., Van Campen, D.H. and Reneman, R.S., ‘Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study’, J. Biomech., 25(1992) 1129–1140.

    Google Scholar 

  10. Horowitz, A., Lanir, Y., Yin, F.C.P., Perl, M., Sheinman, I. and Strumpf, R.K., ‘Structural three-dimensional constitutive law for the passive myocardium’, J. Biomech. Eng., 110(1988) 200–207.

    Google Scholar 

  11. Horowitz, A., ‘Structural considerations in formulating material laws for the myocardium’, In: Glass, L., Hunter, P. and McCulloch, A. (eds.), Theory of Heart, Springer-Verlag, New York, 1991, pp. 32–38.

    Google Scholar 

  12. Hunter, P.J., Nielsen, P.M., Smaill, B.H., LeGrice, I.J. and Hunter, I.W., ‘An anatomical heart model with applications to myocardial activation and ventricularmechanics’, Crit. Rev. Biomed. Eng., 20(1992) 403–426.

    Google Scholar 

  13. McCulloch, A., Waldman, L., Rogers, J. and Guccione, J., ‘Large-scale finite element analysis of the beating heart’, Crit. Rev. Biomed. Eng., 20(1992) 427–449.

    Google Scholar 

  14. Montevecchi, F.M. and Pietrabissa, R., ‘A model of multicomponent cardiac fibre’, J. Biomechanics, 20 (1987) 365–370.

    Google Scholar 

  15. Pietrabissa, R., Montevecchi, F.M. and Fumero, R., ‘Mechanical characterization of the model of the multi-component cardiac fibre’, J. Biomed. Eng., 13(1991) 407–414.

    Google Scholar 

  16. Brecher, G.A., ‘Critical review on recent work on ventricular diastolic suction’, Circ. Res., 6(1958) 554–566.

    Google Scholar 

  17. Roberts, W.C., Brownlee, W.J., Jones, A.A. and Luke, J.L., ‘Sucking action of the left ventricle. Demonstration of a physiologic principle by a gunshot wound penetrating only the right side of the heart’, Am. J. Cardiol., 43(1979) 1234–1237.

    Google Scholar 

  18. Sabbah, H.N., Anbe, D.T. and Stein, P.D., ‘Negative intraventricular pressure in patients with mitral stenosis: evidence of left-ventricular diastolic suction’, Am. J. Cardiol., 45(1980) 562–566.

    Google Scholar 

  19. Sabbah, H.N. and Stein, P.D., ‘Pressure diameter relations during early diastole in dogs. Incompatibility with the concept of passive left ventricle filling’, Circ. Res., 45(1981) 357–365.

    Google Scholar 

  20. Schipke, J.D., Stocks, I., Sunderdiek, U. and Arnold, G., ‘Effects of changes in aortic pressure and in coronary arterial pressure on left-ventricular geometry and function Anrep vs. gardenhose effect’, Basic. Res. Cardiol., 88(1993) 621–637.

    Google Scholar 

  21. Berne, R.M. and Rubio, R., ‘Coronary circulation’, In: Berne R.M. (ed.), Handbook of Physiology, American Physiological Society, Bethesda, MD, 1979, pp. 846–873.

    Google Scholar 

  22. Streeter Jr., D.D., ‘Gross morphology and fiber geometry of the heart’, In: Berne, R.M. (ed.) Handbook of Physiology, American Physiological Society, Bethesda, MD, 1979, pp. 339–350.

    Google Scholar 

  23. Wong, A.Y.K., ‘Application of Huxley's sliding filament theory to the mechanics of normal and hypertrophical cardiac muscle’, In: Mirsky I. (ed.), Cardiac Mechanics, John Wiley, New York, 1974, pp. 411–437.

    Google Scholar 

  24. Sonnenblick, E.H., ‘Force-velocity relations in mammalian heart muscle’, Am. J. Physiol., 202(1962) 931–939.

    Google Scholar 

  25. Julian, E.F., ‘Activation in skeletal muscle contraction model with a modification for insect fibrillar muscle’, Biophys. J., 9(1969) 547–570.

    Google Scholar 

  26. Adler, D. and Mahler, Y., ‘The contractile element behaviour as force generator and shortening generator: a well-defined representation of the contractile element in Hill's model’, J. Biomech., 12(1979) 239–243.

    Google Scholar 

  27. Beyar, R. and Sideman, R.S., ‘Time dependent coronary blood flow distribution in left-ventricular wall’, Am. J. Physiol., 252(1987) H417–H433.

    Google Scholar 

  28. Mantero, S., Pietrabissa, R. and Fumero, R., ‘The coronary bed and its role in the cardiovascular system: a review and an introductory single-branch model’, J. Biomed. Eng., 14(1992) 109–115.

    Google Scholar 

  29. Fung, Y.C., Biodynamics Circulation, Springer-Verlag, New York, 1984.

    Google Scholar 

  30. Fung, Y.C., Biomechanics, Springer-Verlag, New York, 1990.

    Google Scholar 

  31. Sponitz, H.M., Sonnenblick, E.H. and Spiro, D., ‘Relation of ultrastructure to function in intact heart. Sarcomere structure relative to pressure-volume curves of intact left ventricle of dog and cat’, Circ. Res., 18 (1966) 49–66.

    Google Scholar 

  32. Yoran, C., Covell, J.W. and Ross, J., ‘Structural basis for the ascending limb of left-ventricular function’, Circ. Res., 32(1973) 297–303.

    Google Scholar 

  33. Spaan, J.A.E., Coronary Blood Flow, Kluwer Academic Publishers, Dordrecht, 1991.

  34. Downey, J.M. and Kirk, E.S., ‘Inhibition of coronary blood flow by a vascular waterfall mechanism’, Circ. Res., 36(1975) 753–760.

    Google Scholar 

  35. Rankin, J.S., McHale, P.A., Arentzen, C.E., Ling, D., Greenfield, J.C. Jr. and Anderson, R.W., ‘The three dimensional dynamic geometry of the left ventricle in the conscious dog’, Circ. Res., 39(1974) 304–313.

    Google Scholar 

  36. Olsen, C.G., Rankin, J.S., Arentzen, C.E., Ring, W.S., McHale, P.A. and Anderson, R.W., ‘The deformational characteristics of the left ventricle in the conscious dog’, Circ. Res., 49(1981) 843–855.

    Google Scholar 

  37. Ingels, N.B., Hansen, D.E., Daughters II, G.T., Stinson, E.B., Alderman, E.L. and Miller, D.C., ‘Relation between longitudinal, circumferential, and oblique shortening and torsional deformation in the left ventricle of the transplanted human heart’, Circ. Res., 64(1989) 915–927.

    Google Scholar 

  38. Grimm, A.F., Lin, H.L. and Grimm, B.R., ‘Left-ventricular free wall and intraventricular pressure-sarcomere length distribution’, Am. J. Physiol., 23(1980) H101–H107.

    Google Scholar 

  39. Van der Broek, J.H.J.M. and Van der Broek, M.H.L.M., ‘Application of an ellipsoidal heart model in studying left-ventricular contractions’, J. Biomech., 13(1980) 493–503.

    Google Scholar 

  40. Chilian, W.M. and Marcus, M.L., ‘Phasic coronary flow velocity in intramural and epicardial coronary arteries’, Circ. Res., 50(1982) 775–781.

    Google Scholar 

  41. Lee, J., Chambers, D.E., Akizuki, S. and Downey, J., ‘The role of vascular capacitance in the coronary arteries’, Circ. Res., 55(1984) 751–762.

    Google Scholar 

  42. Pietrabissa, R., Montevecchi, F.M. and Fumero, R., ‘Ventricle mechanics based on sarcomere and fibre models’, In: Spilker, R.L. and Simon, B.R., (eds), Computational Methods in Bioengineering, ASME, New York, 1988, pp. 399–410.

    Google Scholar 

  43. Humphrey, J.D., Strumpf, R.K. and Yin, F.C.P., ‘Determination of a constitutive relation for the passive myocardium: I. A new functional form’, J. Biomech. Eng., 112(1990) 333–339.

    Google Scholar 

  44. Guccione, J.M., McCulloch, A.D. and Waldman, L.K., ‘Passive material properties of intact ventricular myocardium determined from a cylindrical model’, J. Biomech. Eng., 113(1991) 42–55.

    Google Scholar 

  45. Fibich, G., Lanir, Y. and Liron, N., ‘Mathematical model of blood flow in a coronary capillary’, Am. J. Physiol., 265(1993) H1829–H1840.

    Google Scholar 

  46. Pollack, G.H. and Krueger, J.W., ‘Myocardial sarcomere mechanics: some parallel with skeletal muscle’, In: Baan, Y., Noordergraff, A. and Raines, J., (eds), Cardiovascular System Dynamics, MIT Press, Cambridge, 1978, pp. 3–10.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Bioingegneria, Politecnico di Milano, P.le Leonardo da Vinci, 32, 20133, Milano, Italy

    ALBERTO REDAELLI

  2. CeBITeC, Politecnico di Milano and Ospedale S. Raffaele, Milano, Italy

    RICCARDO PIETRABISSA

Authors
  1. ALBERTO REDAELLI
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. RICCARDO PIETRABISSA
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

REDAELLI, A., PIETRABISSA, R. A Structural Model of the Left Venricle Including Muscle Fibres and Coronary Vessels: Mechanical Behaviour in Normal Conditions. Meccanica 32, 53–70 (1997). https://doi.org/10.1023/A:1004229015882

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004229015882

Search

Navigation