Skip to main content
Log in

Mathematical Modeling of Mechanically Modulated Rhythm Disturbances in Homogeneous and Heterogeneous Myocardium with Attenuated Activity of Na+–K+ Pump

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

A mathematical model of the cardiomyocyte electromechanical function is used to study contribution of mechanical factors to rhythm disturbances in the case of the cardiomyocyte calcium overload. Particular attention is paid to the overload caused by diminished activity of the sodium-potassium pump. It is shown in the framework of the model, where mechano-calcium feedback is accounted for that myocardium mechanics may significantly enhance arrhythmogenicity of the calcium overload. Specifically, a role of cross-bridge attachment/detachment processes, a role of mechanical conditions of myocardium contractions (length, load), and a role of myocardium viscosity in the case of simulated calcium overload have been revealed. Underlying mechanisms are analyzed. Several approaches are designed in the model and compared to each other for recovery of the valid myocardium electrical and mechanical performance in the case of the partially suppressed sodium-potassium pump.

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

  • Antzelevitch, C., Fish, J., 2001. Electrical heterogeneity within the ventricular wall. Basic Res. Cardiol. 96(6), 517–527.

    Article  Google Scholar 

  • Bers, D.M., 2002. Cardiac excitation-contraction coupling. Nature 415(6868), 198–205.

    Article  Google Scholar 

  • Charlemagne, D., et al., 1994. Alteration of Na,K-ATPase subunit mRNA and protein levels in hypertrophied rat heart. J. Biol. Chem. 269(2), 1541–1547.

    Google Scholar 

  • DiFrancesco, D., Noble, D., 1985. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos. Trans. Roy. Soc. Lond. B Biol. Sci. 307(1133), 353–398.

    Article  Google Scholar 

  • Earm, Y.E., Noble, D., 1990. A model of the single atrial cell: relation between calcium current and calcium release. Proc. Roy. Soc. Lond. B Biol. Sci. 240(1297), 83–96.

    Article  Google Scholar 

  • Fuchs, F., Martyn, D., 2005. Length-dependent Ca(2+) activation in cardiac muscle: some remaining questions. J. Muscle Res. Cell Motil. 26(4–5), 199–212.

    Article  Google Scholar 

  • Gallagher, K.P., et al., 1986. The distribution of functional impairment across the lateral border of acutely ischemic myocardium. Circ. Res. 58(4), 570–583.

    Google Scholar 

  • Gordon, A.M., et al., 2001. Skeletal and cardiac muscle contractile activation: tropomyosin “rocks and rolls”. News Physiol. Sci. 16, 49–55.

    Google Scholar 

  • Hilgemann, D.W., Noble, D., 1987. Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms. Proc. Roy. Soc. Lond. B Biol. Sci. 230(1259), 163–205.

    Google Scholar 

  • Izakov, V., et al., 1991. Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading. Circ. Res. 69(5), 1171–1184.

    Google Scholar 

  • Katsnelson, L.B., Markhasin, V.S., 1996. Mathematical modeling of relations between the kinetics of free intracellular calcium and mechanical function of myocardium. J. Mol. Cell. Cardiol. 28(3), 475–486.

    Article  Google Scholar 

  • Katsnelson, L.B., et al., 2004. Influence of viscosity on myocardium mechanical activity: a mathematical model. J. Theor. Biol. 230(3), 385–405.

    Article  MathSciNet  Google Scholar 

  • Katz, A.M., 2000. Physiology of the Heart, 3rd edn. Lippincott Williams & Wilkins, Philadelphia.

    Google Scholar 

  • Kihara, Y., Morgan, J.P., 1991. Intracellular calcium and ventricular fibrillation. Studies in the aequorin-loaded isovolumic ferret heart. Circ. Res. 68(5), 1378–1389.

    Google Scholar 

  • Lakatta, E.G., Guarnieri, T., 1993. Spontaneous myocardial calcium oscillations: are they linked to ventricular fibrillation? J. Cardiovasc. Electrophysiol. 4(4), 473–489.

    Article  Google Scholar 

  • Lew, W.Y., 1987. Influence of ischemic zone size on nonischemic area function in the canine left ventricle Am. J. Physiol. 252(5 Pt 2), H990–997.

    Google Scholar 

  • Luo, C.H., Rudy, Y., 1994. A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation. Circ. Res. 74(6), 1097–1113.

    Google Scholar 

  • Markhasin, V.S., et al., 2003. Mechano-electric interactions in heterogeneous myocardium: development of fundamental experimental and theoretical models. Prog. Biophys. Mol. Biol. 82(1–3), 207–220.

    Article  Google Scholar 

  • Moss, R.L., et al., 2004. Myosin crossbridge activation of cardiac thin filaments: implications for myocardial function in health and disease. Circ. Res. 94(10), 1290–1300.

    Article  Google Scholar 

  • Mulieri, L.A., Alpert, N.R., 1984. Differential effects of BDM on activation and contraction. Biophys. J. 45, 47.

    Google Scholar 

  • Murray, J.M., Weber, A., 1981. Cooperativity of the calcium switch of regulated rabbit actomyosin system. Mol. Cell. Biochem. 35(1), 11–15.

    Article  Google Scholar 

  • Noble, D., 2002a. Modeling the heart–from genes to cells to the whole organ. Science 295(5560), 1678–1682.

    Article  Google Scholar 

  • Noble, D., 2002b. Modelling the heart: insights, failures and progress. Bioessays 24(12), 1155–1163.

    Article  MathSciNet  Google Scholar 

  • Noble, D., Varghese, A., 1998. Modelling of sodium-overload arrhythmias and their suppression. Can. J. Cardiol. 14(1), 97–100.

    Google Scholar 

  • Noble, D., et al., 1998. Improved guinea-pig ventricular cell model incorporating a diadic space, IKr and IKs, and length- and tension-dependent processes. Can. J. Cardiol. 14(1), 123–134.

    Google Scholar 

  • Solovyova, O., et al., 2002. Mechanical inhomogeneity of myocardium studied in parallel and serial cardiac muscle duplexes: experiments and models. Chaos Solitons Fractals 13(8), 1685–1711.

    Article  Google Scholar 

  • Solovyova, O., et al., 2003. Mechanical interaction of heterogeneous cardiac muscle segments in silico: effects on Ca2+ handling and action potential. Int. J. Bifurcat. Chaos 13(12), 3757–3782.

    Article  MATH  Google Scholar 

  • Solovyova, O., et al., 2006. Activation sequence as a key factor in spatio-temporal optimization of myocardial function. Phil. Trans. Roy. Soc. Lond. A 364, 1367–1383.

    Article  Google Scholar 

  • Tennant, L.R., Wiggers, C.J., 1935. The effect of coronary occlusion on myocardial contraction. Am. J. Physiol. 112, H351–361.

    Google Scholar 

  • Thandroyen, F.T., et al., 1991. Intracellular calcium transients and arrhythmia in isolated heart cells. Circ. Res. 69(3), 810–819.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Leonid B. Katsnelson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sulman, T., Katsnelson, L.B., Solovyova, O. et al. Mathematical Modeling of Mechanically Modulated Rhythm Disturbances in Homogeneous and Heterogeneous Myocardium with Attenuated Activity of Na+–K+ Pump. Bull. Math. Biol. 70, 910–949 (2008). https://doi.org/10.1007/s11538-007-9285-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-007-9285-y

Keywords

Navigation