Homogeneity of Cardiac Contraction Despite Physiological Asynchrony of Depolarization: A Model Study
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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
- 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.
- 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.
- Allgower, E. L., and K. Georg. Numerical Continuation Methods: An Introduction. Berlin: Springer, 1990.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Kreyszig, E. Advanced Engineering Mathematics, 8th ed. New York: Wiley, 1999.
- 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.
- 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.
- Malvern, L. E. Introduction to the Mechanics of a Continuous Medium. Englewood Cliffs, NJ: Prentice Hall, 1969.
- 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.
- Massing, G. K., and T. N. James. Anatomical configuration of the HIS bundle and bundle branches in the human heart. Circulation53:609–621, 1976.
- 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.
- Myerburg, R. J., K. Nilsson, and H. Gelband. Physiology of canine intraventricular conduction and endocardial excitation. Circ. Res.30:217–243, 1972.
- Nash, M. P., and P. J. Hunter. Computational mechanics of the heart. From tissue structure to ventricular function. J. Elast.61:113–141, 2000.
- 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.
- Novak, V. P., F. C. P. Yin, and J. D. Humphrey. Regional mechanical properties of passive myocardium. J. Biomech.27:403–412, 1994.
- Omens, J. H., and Y. C. Fung. Residual strain in rat left ventricle. Circ. Res.66:37–45, 1990.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Scher, A. M., A. C. Young, A. L. Malmgren, and R. V. Erickson. Activation of the interventricular septum. Circ. Res.3:56–64, 1955.
- 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.
- 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.
- Taber, L. A., M. Yang, and W. W. Podszus. Mechanics of ventricular torsion. J. Biomech.29:745–752, 1996.
- 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.
- 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).
- Usyk, T. P., I. J. LeGrice, and A. D. McCulloch. Computational model of three-dimensional cardiac electromechanics. Comput. Visual Sci.4:249–257, 2002.
- 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.
- Vassal-Adams, P. R.Ultrastructure of the human atrioventricular conduction tissues. Eur. Heart J.4:449–460, 1983.
- 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.
- 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.
- 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.
- Waldman, L. K., J. W. Covell. Effects of ventricular pacing on finite deformation in canine left ventricles. Am. J. Physiol.252:H1023–H1030, 1987.
- Wells, P. N. T. Physical Principles of Ultrasonic Diagnosis. New York: Academic, 1969.
- 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.
- 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.
- Yin, F. C. P., C. C. H. Chan, and R. M. Judd. Compressibility of perfused passive myocardium. Am. J. Physiol.271:H1864–H1870, 1996.
- Homogeneity of Cardiac Contraction Despite Physiological Asynchrony of Depolarization: A Model Study
Annals of Biomedical Engineering
Volume 31, Issue 5 , pp 536-547
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Eikonal-diffusion equation
- Industry Sectors