A New Dissipation Function to Model the Rate-Dependent Mechanical Behavior of Semilunar Valve Leaflets

Abstract

A new dissipation function Wv is devised and presented to capture the rate-dependent mechanical behavior of the semilunar heart valves. Following the experimentally-guided framework introduced in our previous work (Anssari-Benam et al., 2022 "Modelling the Rate-Dependency of the Mechanical Behaviour of the Aortic Heart Valve: An Experimentally Guided Theoretical Framework," J. Mech. Behav. Biomed. Mater., 134, p. 105341), we derive our proposed Wv function from the experimental data pertaining to the biaxial deformation of the aortic and pulmonary valve specimens across a 10,000-fold range of deformation rate, exhibiting two distinct rate-dependent features: (i) the stiffening effect in σ-λ curves with increase in rate; and (ii) the asymptotic effect of rate on stress levels at higher rates. The devised Wv function is then used in conjunction with a hyperelastic strain energy function We to model the rate-dependent behavior of the valves, incorporating the rate of deformation as an explicit variable. It is shown that the devised function favorably captures the observed rate-dependent features, and the model provides excellent fits to the experimentally obtained σ-λ curves. The proposed function is thereby recommended for application to the rate-dependent mechanical behavior of heart valves, as well as other soft tissues that exhibit a similar rate-dependent behavior.

Keywords: dissipation function; modeling; rate-dependency; semilunar heart valves.