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

A theoretical framework, based on extant experimental findings, is presented to devise a novel viscous dissipation function in order to model the rate-dependent mechanical behaviour of the aortic heart valve. The experimental data encompasses Cauchy stress-stretch () curves obtained across a 10,000-fold range of stretch rates (), from quasi-static ( 0.001 s−1) to upper-range of physiological ( 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 curves; i.e. the rate-effects approach an asymptote with increase in the stretch rate . Guided by these empirical observations, we devise our new function and demonstrate that the well-known form of the dissipation function commonly used in the literature is a special case of our proposed . The ensuing model is then compared against the experimental 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.