Simulating Cardiac Mechanoenergetics in the Left Ventricle

  • M. Vendelin
  • P. H. M. Bovendeerd
  • V. Saks
  • J. Engelbrecht
  • T. Arts
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2674)


Distribution of myocardial perfusion and oxygen consumption within the cardiac wall is spatially heterogeneous. The cause of this heterogeneity is still unclear, but it is expected to be in close relation with the heterogeneity in mechanical function in the heart. In order to study the mechanical contraction and energy consumption by the cardiac wall, we developed a finite element model of the left ventricle with active properties described by the Huxley-type cross-bridge model. Here we present an overview of the developed model and the following simulation results obtained by the model. First, an important property of energy transformation from biochemical form to mechanical work in the cardiac muscle, the linear relationship between the oxygen consumption and the stress-strain area, is replicated by a cross-bridge model. Second, by using the developed cross-bridge model, the correlation between ejection fraction of the left ventricle and heterogeneity of sarcomere strain, developed stress and ATP consumption in the left ventricular wall is established. Third, an experimentally observed linear relationship between oxygen consumption and the pressure-volume area can be predicted theoretically from a linear relationship between the oxygen consumption and the stress-strain area.


Oxygen Consumption Cardiac Muscle Left Ventricular Wall Sarcomere Length Myosin Head 
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. [1]
    T. Arts, P.C. Veenstra, and R.S. Reneman. Epicardial deformation and left ventricular wall mechanisms during ejection in the dog. Am J Physiol, 243(3):H379–H390, 1982.Google Scholar
  2. [2]
    J.B. Bassingthwaighte, D.A. Beard, and Z. Li. The mechanical and metabolic basis of myocardial blood flow heterogeneity. Basic Res Cardiol, 96(6):582–594, 2001.CrossRefGoogle Scholar
  3. [3]
    P.H.M. Bovendeerd, J.M. Huyghe, T. Arts, D.H. van Campen, and R.S. Reneman. Influence of endocardial-epicardial crossover of muscle fibers on left ventricular wall mechanics. J Biomech, 27(7): 941–951, 1994.CrossRefGoogle Scholar
  4. [4]
    D.L. Brutsaert, N.M. de Clerck, M.A. Goethals, and P.R. Housmans. Relaxation of ventricular cardiac muscle. J Physiol (Lond), 283:469–480, 1978.Google Scholar
  5. [5]
    R. Cooke and E. Pate. The effects of adp and phosphate on the contraction of muscle fibers. Biophys J, 48(5):789–798, 1985.CrossRefGoogle Scholar
  6. [6]
    R. Cooke, H. White, and E. Pate. A model of the release of myosin heads from actin in rapidly contracting muscle fibers. Biophys J, 66(3 Pt 1): 778–788, 1994.Google Scholar
  7. [7]
    A. Deussen, C.W. Flesche, T. Lauer, M. Sonntag, and J. Schrader. Spatial heterogeneity of blood flow in the dog heart. II. Temporal stability in response to adrenergic stimulation. Pflugers Arch, 432(3):451–461, 1996.CrossRefGoogle Scholar
  8. [8]
    E. Eisenberg and T.L. Hill. Muscle contraction and free energy transduction in biological systems. Science, 227(4690):999–1006, 1985.CrossRefGoogle Scholar
  9. [9]
    G. Gong, K. Ugurbil, and J. Zhang. Transmural metabolic heterogeneity at high cardiac work states. Am J Physiol, 277(1 Pt 2):H236–H242, 1999.Google Scholar
  10. [10]
    A.B. Groeneveld, J.H. van Beek, and D.J. Alders. Assessing heterogeneous distribution of blood flow and metabolism in the heart. Basic Res Cardiol, 96(6):575–581, 2001.CrossRefGoogle Scholar
  11. [11]
    T.L. Hill. Theoretical formalism for the sliding filament model of contraction of striated muscle. Part I. Prog Biophys Mol Biol, 28:267–340, 1974.CrossRefGoogle Scholar
  12. [12]
    R. Hisano and G. Cooper. Correlation of force-length area with oxygen consumption in ferret papillary muscle. Circ Res, 61(3):318–328, 1987.Google Scholar
  13. [13]
    P.J. Hunter, A.D. McCulloch, and H.E. ter Keurs. Modelling the mechanical properties of cardiac muscle. Prog Biophys Mol Biol, 69(2–3):289–331, 1998.CrossRefGoogle Scholar
  14. [14]
    P.M. Janssen and W.C. Hunter. Force, not sarcomere length, correlates with prolongation of isosarcometric contraction. Am J Physiol, 269(2 Pt 2):H676–H685, 1995.Google Scholar
  15. [15]
    R.B. King, J.B. Bassingthwaighte, J.R. Hales, and L.B. Rowell. Stability of heterogeneity of myocardial blood flow in normal awake baboons. Circ Res, 57(2):285–295, 1985.Google Scholar
  16. [16]
    P.M. Nielsen, I.J. Le Grice, B.H. Smaill, and P.J. Hunter. Mathematical model of geometry and fibrous structure of the heart. Am J Physiol, 260(4 Pt 2):H1365–H1378, 1991.Google Scholar
  17. [17]
    E. Pate and R. Cooke. A model of crossbridge action: the effects of ATP, ADP and Pi. J Muscle Res Cell Motil, 10(3):181–196, 1989.CrossRefGoogle Scholar
  18. [18]
    V.A. Saks, Z.A. Khuchua, E.V. Vasilyeva, O.Y. u. Belikova, and A.V. Kuznetsov. Metabolic compartmentation and substrate channelling in muscle cells. role of coupled creatine kinases in in vivo regulation of cellular respiration-a synthesis. Mol Cell Biochem, 133–134:155–192, 1994.Google Scholar
  19. [19]
    U. Schwanke, S. Cleveland, E. Gams, and J.D. Schipke. Correlation between heterogeneous myocardial flow and oxidative metabolism in normoxic and stunned myocardium. Basic Res Cardiol, 96(6):557–563, 2001.CrossRefGoogle Scholar
  20. [20]
    D.D. Streeter. Gross morphology and fiber geometry of the heart. In R.M. Berne, editor, Handbook of physiology — The cardiovascular system I, pages 61–122. Am. Physiol. Soc., Bethesda, MD, 1979.Google Scholar
  21. [21]
    H. Suga. Ventricular energetics. Physiol Rev, 70(2):247–277, 1990.Google Scholar
  22. [22]
    T.W. Taylor, Y. Goto, K. Hata, T. Takasago, A. Saeki, T. Nishioka, and H. Suga. Comparison of the cardiac force-time integral with energetics using a cardiac muscle model. J Biomech, 26(10):1217–1225, 1993.CrossRefGoogle Scholar
  23. [23]
    T.W. Taylor, Y. Goto, and H. Suga. Variable cross-bridge cycling-ATP coupling accounts for cardiac mechanoenergetics. Am J Physiol, 264(3 Pt 2):H994–1004, 1993.Google Scholar
  24. [24]
    R. van Heuningen, W.H. Rijnsburger, and H.E. ter Keurs. Sarcomere length control in striated muscle. Am J Physiol, 242(3):H411–H420, 1982.Google Scholar
  25. [25]
    M. Vendelin, P.H. Bovendeerd, J. Engelbrecht, and T. Arts. Optimizing ventricular fibers: uniform strain or stress, but not atp consumption, leads to high efficiency. Am J Physiol Heart Circ Physiol, 283(3): H1072–H1081, 2002.Google Scholar
  26. [26]
    M. Vendelin, P.H.M. Bovendeerd, T. Arts, J. Engelbrecht, and D.H. van Campen. Cardiac mechanoenergetics replicated by cross-bridge model. Ann Biomed Eng, 28(6):629–640, 2000.CrossRefGoogle Scholar
  27. [27]
    M. Vendelin, O. Kongas, and V. Saks. Regulation of mitochondrial respiration in heart cells analyzed by reaction-diffusion model of energy transfer. Am J Physiol Cell Physiol, 278(4):C747–C764, 2000.Google Scholar
  28. [28]
    J.R. Williamson, C. Ford, J. Illingworth, and B. Safer. Coordination of citric acid cycle activity with electron transport flux. Circ. Res., 38(5 Suppl 1):I39–I51, 1976.Google Scholar
  29. [29]
    A.Y. Wong. Mechanics of cardiac muscle, based on huxley’s model: mathematical stimulation of isometric contraction. J Biomech, 4(6):529–540, 1971.CrossRefGoogle Scholar
  30. [30]
    J. Zhang and K.M. McDonald. Bioenergetic consequences of left ventricular remodeling. Circulation, 92(4):1011–1019, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • M. Vendelin
    • 1
  • P. H. M. Bovendeerd
    • 2
  • V. Saks
    • 4
  • J. Engelbrecht
    • 1
  • T. Arts
    • 2
    • 3
  1. 1.Intitute of Cybernetics at Tallinn Technical UniversityTallinnEstonia
  2. 2.Department of Biomedical EngineeringEindhoven University of TechnologyThe Netherlands
  3. 3.Cardiovascular Research InstituteMaastricht UniversityThe Netherlands
  4. 4.Laboratory of Fundamental and Applied Bioenergetics, INSERM E0221Joseph Fourier UniversityGrenobleFrance

Personalised recommendations