Left Ventricular Model Using Second Order Electromechanical Coupling: Effects of Viscoelastic Damping

It is known that the heart interacts with and adapts to its venous and arterial loading conditions. Various experimental studies and modeling approaches have been developed to investigate the underlying mechanisms. This paper presents a model of the left ventricle derived based on nonlinear stress-length myocardial characteristics integrated over truncated ellipsoidal geometry, and second-order dynamic mechanism for the excitation-contraction coupling system. The results of the model presented here describe the effects of the viscoelastic damping element of the electromechanical coupling system on the hemodynamic response. Different heart rates are considered to study the pacing effects on the performance of the left-ventricle against constant preload and afterload conditions under various damping conditions. The results indicate that the pacing process of the left ventricle has to take into account, among other things, the viscoelastic damping conditions of the myofilament excitation-contraction process.

Authors:

• Elie H. Karam
• Antoine B. Abche

Keywords:

• Myocardial sarcomere
• cardiac pump
• excitationcontraction coupling
• viscoelasicity

References:

[1] H. Suga, "Theoretical analysis of a left-ventricular pumping model
based on the systolic time-varying pressure/volume ratio." IEEE
Trans. Biomed. Eng., 18(1): 47-55, 1971.
[2] R. Dong, Y. Sun, F. J. Fetter, and S. A. Chiaramida, "Time-varying
left-ventricular elastance determined by finite element model."
Proceedings of the IEEE 30th Annual Northeast Bioengineering
Conference, 188-189, 2004.
[3] G. M. Drzewiecki, E. Karam, and W. Welkowitz, "Physiological Basis
for Mechanical Time-Variance in the Heart: Special Consideration of
Non-Linear Function." J. Theor. Biol., 465-486, 1989.
[4] E. Karam, "Modeling of Cardiac Growth and Hypertrophy-Regulating
Factors." Ph.D. Thesis. Rutgers, The State University of New Jersey,
1992.
[5] E. Karam, A. Abche, and G. M. Drzewiecki, "Left Ventricular
Hypertrophy Model Revisited." BIOMEDSIM, University of
Balamand, Lebanon, 2003.
[6] G. A. Langer, "Ion fluxes in cardiac excitation and contraction and their
relation to myocardial contractility." Phys. Rev., 48: 708-757, 1968.
[7] E. Sonnenblick, D. Spiro, and H. M. Spotnitz, "The ultrastructural basis
of Starling's law of the heart. The role of the sarcomere in determining
ventricular size and stroke volume." Am. Heart J., 68: 336, 1964.
[8] K. Sunagawa, A. Yamada, Y. Senda, Y. Kikuchi, T. Nakamura, T.
Shibahara, and Y. Nose, "Estimation of the hydromotive source
pressure from ejecting beats of the left ventricle." IEEE Trans.Biomed.
Eng., 27: 299-305, 1980.
[9] H.E.D.J. Ter Keurs, W. H. Rijnsburger, van Heuningen, M. J.
Najelsmit, "Tension development and sarcomere length in rat cardiac
taberculae: Evidence of length-dependent activation." In : Cardiac
Dynamics. Baan, J., A. C. Arntzenius, and E. L. Yellin (eds.),
Martinus Nijhoff Publishers, Boston, 1980.
[10] I. Mirsky, and W. M. Parmley, "Assessment of passive elastic stiffness
for isolated heart muscle and intact heart." Circ. Res., 33: 233-243,
1973.
[11] W. M. Parmley, D. L. Brutsaert, and E. H. Sonnenblick, "Effects of
altered loading on contractile events in isolated cat papillary muscle."
Circ. Res., 24: 521-532, 1969.
[12] J. Ross, Jr., E. H. Sonnenblick, J. W. Covell, G. A. Kaiser, and D.
Spiro, "Architecture of the heart in systole and diastole: Technique of
rapid fixation and analysis of left ventricular geometry." Circ. Res., 21:
409-421, 1967.
[13] T. Ihara, Y. Yamada, and K. Komamura, "Hemodynamic determinants
of left ventricular diastolic function: A model study." 18th Annual Conf.
of IEEE EMBS, Amsteram, 1996.