Modelling the rate-dependency of the mechanical behaviour of the aortic heart valve: An experimentally guided theoretical framework

Abstract

A theoretical framework, based on extant experimental findings, is presented to devise a novel viscous dissipation function Wv in order to model the rate-dependent mechanical behaviour of the aortic heart valve. The experimental data encompasses Cauchy stress-stretch (σ−λ) curves obtained across a 10,000-fold range of stretch rates (λ˙), from quasi-static (λ˙= 0.001 s−1) to upper-range of physiological (λ˙= 12.4 s−1) deformation rates. The analysis of the data elicits two important trends: (i) the mechanical behaviour of the aortic valve across the tested rates is rate-dependent, with specimens becoming stiffer by increasing rate; and (ii) there appears to be a plateau in the rate-effects on the σ−λ curves; i.e. the rate-effects approach an asymptote with increase in the stretch rate λ˙. Guided by these empirical observations, we devise our new Wv function and demonstrate that the well-known form of the dissipation function commonly used in the literature is a special case of our proposed Wv. The ensuing model is then compared against the experimental σ−λ curves and is shown to provide favourable predictions. An important advantage of the employed modelling framework is that it allows the incorporation of the rate of deformation, which is a direct experimental control parameter, as an explicit modelling variable. The application of the proposed model is thereby recommended for heart valves and other soft tissues that exhibit similar rate-dependent features.