Modeling of Cardiac Muscle Contraction Based on the Cross-Bridge Mechanism

  • Hidenobu Mashima
  • Kazuyuki Kabasawa
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 37)


A mathematical model was developed for the cardiac muscle contraction, assuming that the attachment and detachment cycle of the cross-bridge is activated by the internal calcium concentration and the rate constant of the cycle depends on the sliding velocity of myofilaments. The inputs of the model are the rates of calcium release and uptake, while the output is the tension curve of the muscle. The variables are factored into a series of realizable functions and most constants were determined from the dynamic constants for the tetanic contraction of frog ventricular muscle at 20° C. Using this model, the calcium transient curve as well as the change in the number of cross-bridges in each state of the cycle during a given experimental twitch tension curve was calculated with a PDP 11/60 computer, by selecting the input parameters so that the output curve fit the experimental curve. When the twitch tension was increased by increasing initial muscle length, the rate of calcium release increased and that of uptake decreased. At higher external calcium concentrations, the similar changes in the input parameters were observed. In the presence of 5×10−8 g/ml adrenalin the duration of activation was markedly prolonged, while the rates of calcium release and uptake show little change.


Calcium Release Thin Filament Tension Curve Tetanic Contraction Contractile Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allen, D.G. and Blinks, J.R. (1978). Calcium transients in aequorin-injected frog cardiac muscle. Nature 273: 509 - 513.PubMedCrossRefGoogle Scholar
  2. Akazawa, K., Yamamoto, M., Fujii, K. and Mashima, H. (1976). A mechanochemical model for the steady and transient contractions of the skeletal muscle. Jpn. J. Physiol. 26: 9-28.PubMedCrossRefGoogle Scholar
  3. Chaplain, R.A. and Frommelt, B. (1971). A mechanochemical model for muscular contraction. I: The rate of energy liberation at steady state velocities of shortening and lengthening. J. Mechanochem. Cell Motility 1: 41-56.Google Scholar
  4. Deshcherevskii, V.I. (1968). Two models of muscular contraction. Biofisika 13: 1093 - 1101.Google Scholar
  5. Fabiato, A. and Fabiato, F. (1975). Contractions induced by a calcium-triggered release of calcium from the sarcoplasmic reticulum of single skinned cardiac cells. J. Physiol. 249: 489 - 495.Google Scholar
  6. Gibbs, C. and Loiselle, D. (1978). The energy output of tetanized cardiac muscle: species differences. Pflügers Arch. 373: 31 - 38.PubMedCrossRefGoogle Scholar
  7. Hill, A.V. and Woledge, R.C. (1962). An examination of absolute values in myothermic measurements. J. Physiol. 162: 311 - 333.PubMedGoogle Scholar
  8. Huxley, A.F. (1957). Muscle structure and theories of contraction. Prog. Biophys. Biophys. Chem. 7: 255-318.Google Scholar
  9. Huxley, A.F. and Simmons, R.M. (1971). Proposed mechanism of force generation in striated muscle. Nature 233: 533 - 538.PubMedCrossRefGoogle Scholar
  10. Huxley, H.E. (1957). The double array of filaments in cross-striated muscle. J. Biophys. Biochem. Cytol. 3: 631-848.Google Scholar
  11. Huxley, H.E. (1972). The molecular basis of contraction in cross-striated muscle. In: Structure and Function of Muscle, 2nd ed., ed. by Boume, G.H., Academic Press, London, Vol. 1, 301 - 387.Google Scholar
  12. Julian, F.J., Sollins, K.R. and Sollins, M.R. (1974). A model for the transient and steady state mechanical behavior of contracting muscle. Biophs. J. 14: 546-562.CrossRefGoogle Scholar
  13. Mashima, H., Akazawa, K., Kushima, H. and Fujii, K. (1972). The force-load-velocity relation and the viscous-like force in the frog skeletal muscle. Jpn. J. Physiol. 22: 103-120.PubMedCrossRefGoogle Scholar
  14. Mashima, H. (1977a). Tetanic contraction and tension-length relation of frog ventricular muscle. Jpn. J. Physiol. 27: 321-335.CrossRefGoogle Scholar
  15. Mashima, H. (1977b). The force-load-velocity relation and the internal load of tetanized frog cardiac muscle. Jpn. J. Physiol. 27: 485-501.Google Scholar
  16. Mashima, H. (1978). Dynamics of contraction with special reference to calcium. Recent Advances in Studies on Cardiac Structure and Metabolism, 11, Heart Function and Metabolism, 149 - 157.Google Scholar
  17. Niedergerke, R. (1963). Movements of Ca in beating ventricles of the frog heart. J. Physiol. 167: 551 - 580.PubMedGoogle Scholar
  18. Volkenstein, M.V. (1989). Muscular contraction. Biochim. Biophys. Acta 180: 562-572.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Hidenobu Mashima
    • 1
  • Kazuyuki Kabasawa
    • 1
  1. 1.Department of Physiology, School of MedicineJuntendo UniversityTokyoJapan

Personalised recommendations