A new dissipation function to model the rate-dependent mechanical behaviour of semilunar valve leaflets

A new dissipation function Wv is devised and presented to capture the rate-dependent mechanical behaviour of the semilunar heart valves. Following the experimentally-guided framework introduced in our previous work (J. Mech. Behav. Biomed. Mater. (2022), https://doi.org/10.1016/j.jmbbm.2022.105341), 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 s-? 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 behaviour of the valves, incorporating the rate of deformation as an explicit variable. It is shown that the devised function favourably 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 behaviour of heart valves, as well as other soft tissues that exhibit a similar rate-dependent behaviour.