A Model of Cardiac Muscle Dynamics

Abstract

A mathematical model is presented describing the time-and length-dependent behavior of cardiac muscle. The model describes a wider variety of experimental data than do previously published models. It incorporates a modification of the Hill equation describing the force-velocity relation. Based on the sliding filament theory, the revised equation includes the effects of finite cross-bridge compliance proposed by A. F. Huxley. The essential simplicity of the Hill equation is retained; however, the model successfully predicts force development during both isometric and isotonic contractions, observed deactivation of the contractile element during isotonic shortening, and the apparent dependence of series elastic stiffness on time after stimulation during quick-release and quick-stretch experiments. KEY WORDScomputer model isotonic contraction quick release cross-bridge compliance isometric contraction shortening lengthening contractile element length clamp active state• Detailed experimental studies on isolated cardiac muscle have improved our understanding of its dynamic behavior and made it feasible to relate the performance of the heart to muscle behavior. Such an analysis requires constitutive equations describing the properties of heart muscle in its passive (unstimulated) and active states. Muscle fibers are highly anisotropic, having a principal direction along which active force is generated, and most experimental studies have focused on this direction, giving little attention to properties in the plane perpendicular to force generation. The present paper presents an analytical description of the properties of heart muscle along its principal direction under uniaxial loading. The model incorporates descriptions of the forcevelocity relation during nonisotonic contractions and during lengthening, the dependence of activation on the contraction mode, and the dependence of the maximum velocity of shortening on muscle length.Previous muscle models fall into two major categories. The first category employs a kinetic model like the one proposed by A. F. Huxley (1);

I-Wire Heart-on-a-Chip II: Biomechanical analysis of contractile, three-dimensional cardiomyocyte tissue constructs

“…Subsequent trials revealed that at the reduced length, the construct has a much lower linear passive stiffness and retains some prestress even at low initial stretch. These results indicate that the stiffness which appeared linear at the original length is actually part of an exponential or partially nonlinear stiffness function common in biological tissues [11;26]. …”

I-Wire Heart-on-a-Chip I: Three-dimensional cardiac tissue constructs for physiology and pharmacology

“…The isolated papillary muscle, ventricular strips, and Purkinje fiber preparations have proven to be critical in understanding the passive and active electromechanical properties of cardiac tissue [27;28]. Full mechanical characterization of the passive and active elastomechanics of a single, end-supported cardiomyocyte can be accomplished using optical sensing and mechanical feedback control [29], albeit with rather expensive hardware (IonOptix, Westwood, MA, USA).…”

A Technical Model of the Left Heart — Development and Isovolumetric Experiments - Ein technisches Modell des linken Herzens - Entwicklung und Isovolumetrische Experimente

“…HilTs mathematical expression for the contraction velocity of the contractile element under dif f erent loads has been expanded to simulate heart-muscle by addition of a time-dependent »active state« and lengthdependent factors, reflecting the dependence of the actively developed force on muscle-length, in the studies of Grood et al [9] and Fung [7). Examination of heart-muscle dynamics showed that five properties are most relevant: the influence of diastolic pressure on the filling-volume, the dependence of ejection-volume on the presystolic The Hill-model contains a contractile element (CE), which represents the force-velocity relations, and a series elastic element (SE) which is used in explaining muscle reaction during rapid length-changes.…”

“…Grood [9], going on this assumption, f urther hypothesized that the parallel elastic element is only stressed at high muscle-lengths and arrived at a muscle model shown in Fig. Grood [9], going on this assumption, f urther hypothesized that the parallel elastic element is only stressed at high muscle-lengths and arrived at a muscle model shown in Fig.…”