Annals of Biomedical Engineering

, Volume 31, Issue 5, pp 536–547 | Cite as

Homogeneity of Cardiac Contraction Despite Physiological Asynchrony of Depolarization: A Model Study

  • R. C. P. Kerckhoffs
  • P. H. M. Bovendeerd
  • J. C. S. Kotte
  • F. W. Prinzen
  • K. Smits
  • T. Arts


The use of mathematical models combining wave propagation and wall mechanics may provide new insights in the interpretation of cardiac deformation toward various forms of cardiac pathology. In the present study we investigated whether combining accepted mechanisms on propagation of the depolarization wave, time variant mechanical properties of cardiac tissue after depolarization, and hemodynamic load of the left ventricle (LV) by the aortic impedance in a three-dimensional finite element model results in a physiological pattern of cardiac contraction. We assumed that the delay between depolarization for all myocytes and the onset of crossbridge formation was constant. Two simulations were performed, one in which contraction was initiated according to the regular depolarization pattern (NORM simulation), and another in which contraction was initiated after synchronous depolarization (SYNC simulation). In the NORM simulation propagation of depolarization was physiological, but wall strain was unphysiologically inhomogeneous. When simulating LV mechanics with unphysiological synchronous depolarization (SYNC) myofiber strain was more homogeneous and more physiologic. Apparently, the assumption of a constant delay between depolarization and onset of crossbridge formation results in an unrealistic contraction pattern. The present finding may indicate that electromechanical delay times are heterogeneously distributed, such that a contraction in a normal heart is more synchronous than depolarization. © 2003 Biomedical Engineering Society.

PAC2003: 8719Hh, 8719Nn, 8718Bb, 8710+e, 8719Xx

Electromechanics Eikonal-diffusion equation Hill 


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  1. 1.
    Aelen, F. W. L., T. Arts, D. G. M. Sanders, G. R. P. Thelissen, A. M. M. Muijtjens, F. W. Prinzen, and R. S. Reneman. Relation between torsion and cross-sectional area change in the human left ventricle. J. Biomech.30:207–212, 1997.Google Scholar
  2. 2.
    Aelen, F. W. L., T. Arts, D. G. M. Sanders, G. R. P. Thelissen, F. W. Prinzen, and R. S. Reneman. Kinematic analysis of left ventricular deformation in myocardial infarction using magnetic resonance cardiac tagging. Int. J. Card. Imaging15:241–251, 1999.Google Scholar
  3. 3.
    Allgower, E. L., and K. Georg. Numerical Continuation Methods: An Introduction. Berlin: Springer, 1990.Google Scholar
  4. 4.
    Arts, T., P. C. Veenstra, and R. S. Reneman. A model of the mechanics of the left ventricle. Ann. Biomed. Eng.7:299–318, 1979.Google Scholar
  5. 5.
    Arts, T., P. C. Veenstra, and R. S. Reneman. Epicardial deformation and left ventricular wall mechanics during ejection in the dog. Am. J. Physiol.243:H379–H390, 1982.Google Scholar
  6. 6.
    Bovendeerd, P. H. M., T. Arts, D. H. van Campen, and R. S. Reneman. Dependence of local left ventricular wall mechanics on myocardial fiber orientation: A model study. J. Biomech.25:1129–1140, 1992.Google Scholar
  7. 7.
    Bovendeerd, P. H. M., 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.27:941–951, 1994.Google Scholar
  8. 8.
    Brooks, A. N., and T. J. R. Hughes. Stream-line upwind/Petrov–Galerkin formulation for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput. Methods Appl. Mech. Eng.32:199–259, 1982.Google Scholar
  9. 9.
    Colli-Franzone, P., and L. Guerri. Spreading of excitation in 3D models of the anisotropic cardiac tissue. I. Validation of the eikonal model. Math. Biosci.113:145–209, 1993.Google Scholar
  10. 10.
    Colli-Franzone, P., L. Guerri, M. Pennacchio, and B. Taccardi. Spreading of excitation in 3D models of the anisotropic cardiac tissue. II. Effects of fiber architecture and ventricular geometry. Math. Biosci.113:145–209, 1998.Google Scholar
  11. 11.
    Colli-Franzone, P., L. Guerri, and S. Tentoni. Mathematical modeling of the excitation process in myocardial tissue: Influence of fiber rotation on wave-front propagation and potential field. Math. Biosci.101:155–235, 1990.Google Scholar
  12. 12.
    Delhaas, T., T. Arts, P. H. M. Bovendeerd, F. W. Prinzen, and R. S. Reneman. Subepicardial fiber strain and stress as related to left ventricular pressure and volume. Am. J. Physiol.264:H1548–H1559, 1993.Google Scholar
  13. 13.
    Durrer, D., R. T. van Dam, G. E. Freud, M. J. Janse, F. L. Meijler, and R. C. Arzbaecher. Total excitation of the isolated human heart. Circulation41:899–912, 1970.Google Scholar
  14. 14.
    Durrer, D., J. P. Roos, and J. Büller. The spread of excitation in the canine and human heart. In: International Symposium on Electrophysiology of the Heart, edited by G. Marchetti and B. Taccardi. Oxford, U.K.: Pergamon, 1964.Google Scholar
  15. 15.
    Gallagher, K. P., G. Osakada, O. M. Hess, A. Koziol, W. S. Kemper, and J. Ross, Jr. Subepicardial segmental function during coronary stenosis and the role of myocardial fiber orientation. Circ. Res.50:352–359, 1982.Google Scholar
  16. 16.
    Geerts, L., P. Bovendeerd, K. Nicolay, and T. Arts. Characterization of the normal cardiac myofiber field in goat measured with MR-diffusion tensor imaging. Am. J. Physiol.283:H139–H145, 2002.Google Scholar
  17. 17.
    Greenstein, J. L., R. Wu, S. Po, G. F. Tomaselli, and R. L. Winslow. Role of the calcium-independent transient outward current Ito1 in shaping action potential morphology and duration. Circ. Res.87:1026–1033, 2000.Google Scholar
  18. 18.
    Guccione, J. M., W. G. O'Dell, A. D. McCulloch, and W. C. Hunter. Anterior and posterior left ventricular sarcomere lengths behave similarly during ejection. Am. J. Physiol.272:H469–H477, 1997.Google Scholar
  19. 19.
    Hunter, P. J., A. D. McCulloch, and H. E. D. J. ter Keurs. Modeling the mechanical properties of cardiac muscle. Prog. Biophys. Mol. Biol.69:289–331, 1998.Google Scholar
  20. 20.
    ter Keurs, H. E. D. J., J. J. J. Bucx, P. P. de Tombe, P. Backx, and T. Iwazumi. The effects of sarcomere length and Ca++ on force and velocity of shortening in cardiac muscle. In: Molecular Mechanisms of Muscle Contraction, edited by H. Suga and G. H. Pollack. New York: Plenum, 1988, pp. 581–593.Google Scholar
  21. 21.
    Kreyszig, E. Advanced Engineering Mathematics, 8th ed. New York: Wiley, 1999.Google Scholar
  22. 22.
    LeGrice, I. J., B. H. Smaill, L. Z. Chai, S. G. Edgar, J. B. Gavin, and P. J. Hunter. Laminar structure of the heart: Ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol.269:H571–H582, 1995.Google Scholar
  23. 23.
    Lin, D. H. S., and F. C. P. Yin. A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus. J. Biomech. Eng.120:504–517, 1998.Google Scholar
  24. 24.
    Malvern, L. E. Introduction to the Mechanics of a Continuous Medium. Englewood Cliffs, NJ: Prentice Hall, 1969.Google Scholar
  25. 25.
    Marcus, J. T., M. J. W. Götte, A. C. van Rossum, J. P. A. Kuijer, R. M. Heethaar, L. Axel, and A. Visser. Myocardial function in infarcted and remote regions early after infarction in man: Assessment by magnetic resonance tagging and strain analysis. Magn. Reson. Med.38:803–810, 1997.Google Scholar
  26. 26.
    Massing, G. K., and T. N. James. Anatomical configuration of the HIS bundle and bundle branches in the human heart. Circulation53:609–621, 1976.Google Scholar
  27. 27.
    Muzikant, A. L., and C. S. Henriquez. Validation of three-dimensional conduction models using experimental mapping: Are we getting closer?Prog. Biophys. Mol. Biol.69:205–223, 1998.Google Scholar
  28. 28.
    Myerburg, R. J., K. Nilsson, and H. Gelband. Physiology of canine intraventricular conduction and endocardial excitation. Circ. Res.30:217–243, 1972.Google Scholar
  29. 29.
    Nash, M. P., and P. J. Hunter. Computational mechanics of the heart. From tissue structure to ventricular function. J. Elast.61:113–141, 2000.Google Scholar
  30. 30.
    Nikolić, S., E. L. Yellin, K. T. Tamura, H. Vetter, T. Tamura, J. S. Meisner, and R. W. M. Frater. Passive properties of canine left ventricle: Diastolic stiffness and restoring forces. Circ. Res.62:1210–1222, 1988.Google Scholar
  31. 31.
    Novak, V. P., F. C. P. Yin, and J. D. Humphrey. Regional mechanical properties of passive myocardium. J. Biomech.27:403–412, 1994.Google Scholar
  32. 32.
    Omens, J. H., and Y. C. Fung. Residual strain in rat left ventricle. Circ. Res.66:37–45, 1990.Google Scholar
  33. 33.
    Pandit, S. V., R. B. Clark, W. R. Giles, and S. S. Demir. A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys. J.81:3029–3051, 2001.Google Scholar
  34. 34.
    Prinzen, F. W., C. H. Augustijn, T. Arts, M. A. Allessie, and R. S. Reneman. Redistribution of myocardial fiber strain and blood flow by asynchronous activation. Am. J. Physiol.259:H300–H308, 1990.Google Scholar
  35. 35.
    Prinzen, F. W., W. C. Hunter, B. T. Wyman, and E. R. McVeigh. Mapping of regional myocardial strain and work during ventricular pacing: Experimental study using magnetic resonance imaging tagging. J. Am. Coll. Cardiol.33:1735–1742, 1999.Google Scholar
  36. 36.
    Prinzen, F. W., and M. Peschar. Relation between the pacing induced sequence of activation and left ventricular pump function in animals. PACE25:484–498, 2002.Google Scholar
  37. 37.
    Rijcken, J., P. H. M. Bovendeerd, A. J. G. Schoofs, D. H. van Campen, and T. Arts. Optimization of cardiac fiber orientation for homogeneous fiber strain at beginning of ejection. J. Biomech.30:1041–1049, 1997.Google Scholar
  38. 38.
    Rijcken, J., P. H. M. Bovendeerd, A. J. G. Schoofs, D. H. van Campen, and T. Arts. Optimization of cardiac fiber orientation for homogeneous fiber strain during ejection. Ann. Biomed. Eng.27:289–297, 1999.Google Scholar
  39. 39.
    Rodriguez, E. K., J. H. Omens, L. K. Waldman, and A. D. McCulloch. Effect of residual stress on transmural sarcomere length distribution in rat left ventricle. Am. J. Physiol.264:H1048–H1056, 1993.Google Scholar
  40. 40.
    Sah, R., R. J. Ramirez, and P. H. Backx. Modulation of Ca2+ release in cardiac myocytes by changes in repolarization rate—role of phase-1 action potential repolarization in excitation-contraction coupling. Circ. Res.90:165–173, 2002.Google Scholar
  41. 41.
    Scher, A. M., A. C. Young, A. L. Malmgren, and R. V. Erickson. Activation of the interventricular septum. Circ. Res.3:56–64, 1955.Google Scholar
  42. 42.
    Scher, A. M., A. C. Young, A. L. Malmgren, and R. R. Paton. Spread of electrical activity through the wall of the left ventricle. Circ. Res.1:539–547, 1953.Google Scholar
  43. 43.
    Streeter, D. D. Gross morphology and fiber geometry of the heart. In: Handbook of Physiology—The Cardiovascular System I, edited by R. M. Berne, Bethesada, MD: American Physiology Society, 1979, Chap. 4, pp. 61–112.Google Scholar
  44. 44.
    Taber, L. A., M. Yang, and W. W. Podszus. Mechanics of ventricular torsion. J. Biomech.29:745–752, 1996.Google Scholar
  45. 45.
    Tomlinson, K. A. Finite element solution of an eikonal equation for excitation wave-front propagation in ventricular myocardium. PhD thesis, The University of Auckland, 2000.Google Scholar
  46. 46.
    van der Toorn, A., P. Barenbrug, G. Snoep, F. H. van der Veen, T. Delhaas, F. W. Prinzen, and T. Arts. Transmural gradients of cardiac myofiber shortening in aortic valve stenosis patients using MRI-tagging. (in press).Google Scholar
  47. 47.
    Usyk, T. P., I. J. LeGrice, and A. D. McCulloch. Computational model of three-dimensional cardiac electromechanics. Comput. Visual Sci.4:249–257, 2002.Google Scholar
  48. 48.
    Usyk, T. P., R. Mazhari, and A. D. McCulloch. Effect of laminar orthotropic myofiber architecture on regional stress and strain in the canine left ventricle. J. Elast.61:143–164, 2000.Google Scholar
  49. 49.
    Vassal-Adams, P. R.Ultrastructure of the human atrioventricular conduction tissues. Eur. Heart J.4:449–460, 1983.Google Scholar
  50. 50.
    Verbeek, X. A. A. M., K. Vernooy, M. Peschar, T. van der Nagel, A. van Hunnik, and F. W. Prinzen. Quantification of interventricular asynchrony during LBBB and ventricular pacing. Am. J. Physiol.283:H1370–H1378, 2002.Google Scholar
  51. 51.
    Vergroesen, I., M. I. M. Noble, and J. A. E. Spaan. Intramyocardial blood volume change in first moments of cardiac arrest in anesthetized goats. Am. J. Physiol.253:H307–H316, 1987.Google Scholar
  52. 52.
    Villareal, F. J., W. Y. W. Lew, L. K. Waldman, and J. W. Covell. Transmural myocardial deformation in the ischemic canine left ventricle. Circ. Res.68:368–381, 1991.Google Scholar
  53. 53.
    Waldman, L. K., J. W. Covell. Effects of ventricular pacing on finite deformation in canine left ventricles. Am. J. Physiol.252:H1023–H1030, 1987.Google Scholar
  54. 54.
    Wells, P. N. T. Physical Principles of Ultrasonic Diagnosis. New York: Academic, 1969.Google Scholar
  55. 55.
    Westerhof, N., G. Elzinga, and G. C. van den Bos. Influence of central and peripherical changes on the hydraulic input impedance of the systemic arterial tree. Med. Biol. Eng.11:710–723, 1973.Google Scholar
  56. 56.
    Wyman, B. T., W. C. Hunter, F. W. Prinzen, and E. R. McVeigh. Mapping propagation of mechanical activation in the paced heart with MRI tagging. Am. J. Physiol.276:H881–H891, 1999.Google Scholar
  57. 57.
    Yin, F. C. P., C. C. H. Chan, and R. M. Judd. Compressibility of perfused passive myocardium. Am. J. Physiol.271:H1864–H1870, 1996.Google Scholar

Copyright information

© Biomedical Engineering Society 2003

Authors and Affiliations

  • R. C. P. Kerckhoffs
    • 1
  • P. H. M. Bovendeerd
    • 1
  • J. C. S. Kotte
    • 1
  • F. W. Prinzen
    • 1
  • K. Smits
    • 1
  • T. Arts
    • 1
  1. 1.Department of Biomedical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

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