Skip to main content
Log in

Spatial energy balance within a structural model of the left ventricle

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

A model describing the local instantaneous energetic needs within the left ventricle (LV) myocardium is presented. The model, which combines the myocardial oxygen consumption (MVO2) with the mechanical activity of the cardiac muscle, is based on the theory of cross bridge kinetics between the actin and myosin fibers within the sarcomere. The microscale relationship between the stress, stress development, strain rate and basal metabolism demand is incorporated into the LV model which describes the mechanical activities of different layers within the myocardium. The model shows a significant increase in the oxygen consumption in the endocardial layers as compared with the epicardial layers. Integrating the spatial and temporal oxygen consumption distribution within the myocardium yields the total myocardial oxygen consumption. The quantitative relationships between the heat rate, stress, contractility and external work and the MVO2 are in agreement with known data. The model thus offers a tool to assess the local instantaneous as well as the time averaged overall energy consumption, over a wide range of loading conditions of the LV.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Altman, R.L. and D.S. Dittmer. Respiration and Circulation. Bethesda, Maryland: Federation of American Societies for Experimental Biology, 1971, p. 310.

    Google Scholar 

  2. Angrep, G.V. On the part played by the suprarenals in the normal vascular reactions of the body.J. Physiol., London 45:307–317, 1912.

    Google Scholar 

  3. Arnoll, G. and W. Lochner. Die temperaturabhangigkeet der Sauerstoffwendbrauches still gestellter, Kunstlich perfudierter warmbluterherzen 34° und 4°C.Pfluegers Arch. Eur. J. Physiol. 284:169–175, 1965.

    Google Scholar 

  4. Baller, D., H.J. Bretschneider and G. Hellige. Validity of myocardial oxygen consumption parameters.Clin. Cardiol. 2:217–327, 1979.

    Google Scholar 

  5. Beyar, R. and S. Sideman. A model for left ventricular contraction combining the force length velocity relationship with the time varying elastance theory.Biophys. J. 45:1167–1177, 1984.

    CAS  PubMed  Google Scholar 

  6. Beyar, R. and S. Sideman. A computer study of the left ventricular performance based on the fiber structure, sarcomere dynamics and transmural electrical propagation velocity.Circ. Res. 55:358–374, 1984.

    CAS  PubMed  Google Scholar 

  7. Beyar, R. and S. Sideman. Time dependent coronary blood flow distribution in the left ventricular wall.Am. J. Physiol. (Heart Circ. Physiol.) in press, 1986.

  8. Binak, K.N., N. Harmanci, N. Sirmaci, N. Ataman and H. Ogan. Oxygen extraction rate of the myocardium at rest and on exercise in various conditions.Br. Heart J. 29:422–427, 1967.

    CAS  PubMed  Google Scholar 

  9. Bing, R.J., M.M. Hammond, J.C. Handelsman, S.M. Powers, F.C. Spencer, J.E. Eckenhoff, W.T. Goodale, J.H. Hafkenshell and S.S. Dety. Measurement of coronary blood flow, oxygen consumption and efficiency of the left ventricle in man.Heart J. 38:1–24, 1949.

    CAS  Google Scholar 

  10. Braunwald, E. Control of myocardial oxygen consumption: Physiologic and chemical consideration.Am. J. Cardiol. 27:426–432, 1971.

    Article  Google Scholar 

  11. Bretschneider, H.J. Die haemodynamischen determianten des myocardialen sauerstaffverbrauchs. In:Die Therapeutisch Anwendung β-Sympathikoly ischer Stoffe, edited by H.J. Dengler. Stuttgart: Schattauer, 1972, p. 45.

    Google Scholar 

  12. Burns, J.W. and J.W. Covell. Myocardial oxygen consumption during isotonic and isovolumic contractions in the intact heart.Am. J. Physiol. 223:6:1491–1497, 1972.

    CAS  PubMed  Google Scholar 

  13. Gamble, W.J., C.G. Lafarge, D.C. Fyler, J. Weisal and R.G. Monroe. Regional coronary venous oxygen saturation and myocardial oxygen tension following abrupt changes in ventricular pressure in the isolated dog heart.Circ. Res. 34:672–681, 1974.

    CAS  PubMed  Google Scholar 

  14. Gibbs, C.L. and J.B. Chapman. Cardiac energetics. In:Handbook of Physiology, Vol. 1, The Heart, edited by R.M. Berne, N. Sperelakis and S.R. Geiger. Bethesda, Maryland: Am. Physiol. Soc., 1979, pp. 755–804.

    Google Scholar 

  15. Graham, T.P., J.W. Covel, E.H. Sonnenblick, J. Ross and E. Braunwald. Control of myocardial oxygen consumption: Relative influence of contractile state and tension development.J. Clin. Invest. 47:376–385, 1968.

    Google Scholar 

  16. Gregg, D.E., E.M. Khonri and C.R. Rayford. Systems and coronary energetics in the resting unanesthesized dog.Circ. Res. 16:102–113, 1965.

    CAS  PubMed  Google Scholar 

  17. Hasselbach, W. Relaxation and the sarcotubular calcium pump.Fed. Proc. 23:909–912, 1964.

    CAS  PubMed  Google Scholar 

  18. Huxley, A.F. Energetics of muscle.Chem. Br. 6:477–479, 1970.

    CAS  PubMed  Google Scholar 

  19. Huxley, A.F. Muscle structures and theories of contraction.Prog. Biophys. Chem. 7:255–256.

  20. Hoffman, J.I.E. Determinants and prediction of transmural myocardial perfusion.Circulation 58:381–391, 1978.

    CAS  PubMed  Google Scholar 

  21. Johnson, E.A. Force interval relationship of cardiac muscle. In:Handbook of Physiology, Sect. 2, edited by R.M. Berne, N. Sperelakis and S.R. Geiger. Bethesda, Maryland: Am. Physiol. Soc., 1979, pp. 475–496.

    Google Scholar 

  22. Katz, a.M. Biochemical basis of cardiac contraction. In:Cardiac Mechanics, edited by I. Mirsky, D.N. Ghista and S. Harold. New York: Wiley, 1974, pp. 67–86.

    Google Scholar 

  23. Klocke, F.J., E. Braunwald and J. Ross. Oxygen cost of electrical activation of the heart.Ave. Res. 18:357–365, 1966.

    CAS  Google Scholar 

  24. Klocke, F.E. and A.K. Ellis. Control of coronary blood flow.Ann. Rev. Med. 31:489–508, 1980.

    Article  CAS  PubMed  Google Scholar 

  25. McKeever, W.P., D.E. Gregg and P.C. Ranney. Oxygen uptake of the nonworking left ventricle,Circ. Res. 6:612–623, 1958.

    CAS  PubMed  Google Scholar 

  26. Messer, J.V., R.J. Wangman, H.L. Levie, W.A. Neill, N. Krasnow and R. Gorlin. Patterns of human myocardial oxygen extraction during rest and exercise,J. Clin. Invest. 41:725–742, 1962.

    CAS  PubMed  Google Scholar 

  27. Monroe, R.G., W.G. Gamble, A.E. Kumar, J. Stark, R. Plange, G.L. Sanders, G.L. Phornfutkul and M. Davis. The Anrep effect reconsidered.J. Clin. Invest. 51:2573–2583, 1972.

    CAS  PubMed  Google Scholar 

  28. Parmley, W.W. and J.V. Tyberg. Determination of myocardial oxygen demand,Prog. Cardiol. 5:19–36, 1976.

    Google Scholar 

  29. Rushmer, R.F.Cardiovascular dynamics, Philadelphia: Saunders, 1968, p. 31.

    Google Scholar 

  30. Skelton, C.L., H.N. Coleman, K. Wildenthal and E. Braunwald. Augmentation of myocardial oxygen consumption in hyperthyroid cats.Circ. Res. 27:301–309, 1970.

    CAS  PubMed  Google Scholar 

  31. Skelton, C.L. and E.H. Sonnenblick. Myocardial energetics. In:Cardiac Mechanics, edited by I. Mirsky, D.N. Ghista and H. Sandler. New York: Wiley 1974, pp. 112–140.

    Google Scholar 

  32. Strauser, D.E. Myocardial oxygen consumption in chronic heart disease: Rate of wall stress, hypertrophy and coronary reserve.Am. J. Cardiol. 44:730–740, 1979.

    Google Scholar 

  33. Weber, K.T. Seminars on myocardial oxygen utilization physiological and chemical correlates.Am. J. Cardiol. 44:719–721, 1979.

    CAS  PubMed  Google Scholar 

  34. Weber, K.T. and J.S. Janicki. The metabolic demand and oxygen supply of the heart: Physiological and chemical considerations.Am. J. Cardiol. 44:722–729, 1979.

    CAS  PubMed  Google Scholar 

  35. Weiss, H.R., J.A. Newbauer, J.A. Lipp and A.K. Sinha. Quantitative determination of regional oxygen consumption in the dog heart.Circ. Res. 42:394–401, 1978.

    CAS  PubMed  Google Scholar 

  36. Wong, A.Y.K. Some proposals in cardiac muscle mechanics and energetics.Bull. Math. Biol. 35:357–399, 1973.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Beyar, R., Sideman, S. Spatial energy balance within a structural model of the left ventricle. Ann Biomed Eng 14, 467–487 (1986). https://doi.org/10.1007/BF02367366

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02367366

Keywords

Navigation