Left Ventricular Model to Study the Combined Viscoelastic, Heart Rate, and Size Effects
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.
[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.
[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.
@article{"International Journal of Medical, Medicine and Health Sciences:53570", author = "Elie H. Karam and Antoine B. Abche", title = "Left Ventricular Model to Study the Combined Viscoelastic, Heart Rate, and Size Effects ", 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", volume = "1", number = "3", pages = "159-10", }
