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

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.