Left Ventricular Model to Study the Combined Viscoelastic, Heart Rate, and Size Effects

Authors: Elie H. Karam, Antoine B. Abche

Abstract:

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. The effects of left ventricular dimensions on the hemdynamic response have been examined. These effects are found to be different at different viscoelastic and pacing conditions.

Keywords: Myocardial sarcomere, cardiac pump, excitationcontractioncoupling, viscoelasicity

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332306

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.
[14] G. Drzewiecki, J-J Wang, J. K-J Li, J. Kedem, and H. Weiss, "Modeling of Mechanical Dysfunction in Regional Stunned Myocardium of the Left Ventricle." IEEE Trans. Biomed. Eng., Vol. 43, No. 12, December 1996.
[15] R. Beyar, and S. Sideman, "Relating Left Ventricular Dimension to Maximum Elastance." Am. J. Physiol., 251 (Regulatory Integrative Comp. Physiol. 20): R627-R635, 1986.
[16] R. W. Gulch, and R. Jacob, "Geometric and Muscle Physiological Determinants of cardiac Stroke Volume as Evaluated on the basis of Model Calculation." Basic Res. Cardiol., 83: 476-485, 1988.
[17] G. M. Drzewiecki, E. Karam, J. K-J Li, and A. Noordergraaf, "Cardiac Adaptation of Sarcomere Dynamics to Arterial Load: A Model of Hypertrophy." Am. J. Physiol., 263 (Heart Circ. Physiol. 32): H1054- H1063, 1992.