Mechanics of Active Contraction in Cardiac Muscle: Part II—Cylindrical Models of the Systolic Left Ventricle

Abstract

Models of contracting ventricular myocardium were used to study the effects of different assumptions concerning active tension development on the distributions of stress and strain in the equatorial region of the intact left ventricle during systole. Three models of cardiac muscle contraction were incorporated in a cylindrical model for passive left ventricular mechanics developed previously [Guccione et al. ASME Journal of Biomechanical Engineering, Vol. 113, pp. 42-55 (1991)]. Systolic sarcomere length and fiber stresses predicted by a general "deactivation" model of cardiac contraction [Guccione and McCulloch, ASME Journal of Biomechanical Engineering, Vol. 115, pp. 72-81 (1993)] were compared with those computed using two less complex models of active fiber stress: In a time-varying "elastance" model, isometric tension development was computed from a function of peak intracellular calcium concentration, time after contraction onset and sarcomere length; a "Hill" model was formulated by scaling this isometric tension using the force-velocity relation derived from the deactivation model. For the same calcium ion concentration, the sarcomeres in the deactivation model shortened approximately 0.1 microns less throughout the wall at end-systole than those in the other models. Thus, muscle fibers in the intact ventricle are subjected to rapid length changes that cause deactivation during the ejection phase of a normal cardiac cycle. The deactivation model predicted rather uniform transmural profiles of fiber stress and cross-fiber stress distributions that were almost identical to those of the radial component. These three components were indistinguishable from the principal stresses. Transmural strain distributions predicted at end-systole by the deactivation model agreed closely with experimental measurements from the anterior free wall of the canine left ventricle.

A Novel Method for Quantifying Smooth Regional Variations in Myocardial Contractility Within an Infarcted Human Left Ventricle Based on Delay-Enhanced Magnetic Resonance Imaging

“…For the active stress, we use a time-varying function of the sarcomere length-dependent contractile force generated by the myocytes, originally proposed in Refs. [20,21] …”

Numerical Evaluation of Myofiber Orientation and Transmural Contractile Strength on Left Ventricular Function

“…The active tension T 0 is defined by a time-varying elastance model and is a function of time t, peak intracellular calcium concentration Ca 0 , sarcomere length l, and maximum isometric tension T max achieved at the longest sarcomere length and maximum peak intracellular calcium concentration [15]. At end-systole (i.e., t ¼ t 0 in Eqs.…”

“…Both the passive and active material laws were implemented through the use of a material subroutine in the FE solver LS-DYNA (Livermore Software Technology Corporation, Livermore, CA, U.S.A). The material constants for both passive and active myocardium were chosen based on previous studies [15,18,19] (Table 1). Some parameters (i.e., c and B) were adjusted to obtain the end-diastolic volume (EDV) and end-systolic volume (ESV) prescribed in previous work [3,20].…”

Reduction in Left Ventricular Wall Stress and Improvement in Function in Failing Hearts using Algisyl-LVR

“…Active contraction during systole is modeled by increasing the stiffness of the LV along the myofiber direction. This increase in stiffness is a function of time and depends on experimentally determined variables such as the intracellular calcium concentration and the sarcomere length 19 .…”