Elie H. Karam (1) , and Antoine B. Abche (2) 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, excitation- contraction coupling, viscoelasicity I. INTRODUCTION IFFERENT approaches have been followed in the modeling of the left-ventricular pump. Some of these approaches are: lumped time-varying elastance [1], finite element [2], and geometric integration of muscle characteristics [3], [4], [5]. The original model of our work [3], [4] has been built from serial and parallel arrangement of sarcomere units. Each sarcomere unit consists of parallel active and passive elements that were described by nonlinear stress-length functions. The myocardial functions were integrated over a cylindrical geometry of the structure to obtain the global left ventricular function. Time-variation was introduced via a lumped periodic excitation-contraction coupling mechanism of the myocardial fibers. The cardiovascular lumped system consisting of the left ventricular model with its venous preload and arterial load was used to study left ventricular hemodynamics, energetics, and physiological hypertrophy for varying chronic load conditions. II. DERIVATION OF THE MODIFIED MODEL In this work, a new relationship between ventricular pressure and volume is derived from myocardial properties integrated over a truncated ellipsoidal geometry. The Myocardial Unit The myocardial sarcomere is the essential force producing element in the heart. It consists of a parallel arrangement of actin and myosin fibrils (Fig.1). The Ca ++ concentration ([Ca ++ ]) controls the longitudinal force produced by these fibers in the process known as the excitation-contraction coupling mechanism [6]. Fig. 1 Model of the cardiac sarcomere unit. Upper drawing: functional structure consisting of the actin-myosin sliding filaments and an elastic element due to elastin and collagen connective mesh. Lower drawing represents a rectangular volume unit which embodies the sarcomere structure and prescribes the dimensions of the element. Experiments have been performed to obtain the function of the sarcomere. For example, the time development of muscle force (Fig.2a) originates from the periodic increase (release) and decrease (uptake) in [Ca ++ ]. The peak muscle force is found to increase with increasing muscle length (Fig.2b) i.e., the Starling law for muscle [7]. A maximum force occurs at an optimal length, thought to be the position of optimal fiber overlap. The model of the sarcomere unit consists of two basic elements: active contractile and passive elastic elements, arranged in parallel (Fig.1). The active element provides the force-generating mechanism, while the passive component imparts the stiffness to the sarcomere. The level of force Left Ventricular Model to Study the Combined Viscoelastic, Heart Rate, and Size Effects D Manuscript received June 5, 2006. (1) E. H. Karam is with the University of Balamand. P.O.Box 100, Tripoli, LEBANON (phone: 961-6930250; fax: 961-6930238; email: elie.karam@balamand.edu.lb) (2) A. B. Abche is with the University of Balamand. P.O.Box 100, Tripoli, LEBANON (email: antoine.abche@balamand.edu.lb) l h h [Ca ++ (t)] ∝EC(t) σ K{ l } σ H{ l } l World Academy of Science, Engineering and Technology International Journal of Bioengineering and Life Sciences Vol:1, No:3, 2007 159 International Scholarly and Scientific Research & Innovation 1(3) 2007 scholar.waset.org/1307-6892/4460 International Science Index, Bioengineering and Life Sciences Vol:1, No:3, 2007 waset.org/Publication/4460