Anssari-Benam Afshin, Tseng Yuan-Tsan, Pani Martino, Bucchi Andrea
Cardiovascular Engineering Research Lab (CERL), School of Mechanical and Design Engineering, University of Portsmouth, Anglesea Road, Portsmouth PO1 3DJ, UK.
National Heart and Lung Institute, Heart Science Centre, Imperial College London, Middlesex UB9 6JH, UK.
J Biomech Eng. 2023 Jul 1;145(7). doi: 10.1115/1.4056917.
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.
设计并提出了一种新的耗散函数(Wv)，以捕捉半月形心脏瓣膜的速率依赖性力学行为。遵循我们先前工作中引入的实验指导框架（安萨里 - 贝纳姆等人，2022年《模拟主动脉心脏瓣膜力学行为的速率依赖性：一个实验指导的理论框架》，《机械行为与生物医学材料杂志》，第134卷，第105341页），我们从与主动脉和肺动脉瓣膜标本在10000倍变形速率范围内的双轴变形相关的实验数据中推导我们提出的(Wv)函数，该函数呈现出两个不同的速率依赖性特征：（i）(\sigma - \lambda)曲线中随着速率增加的硬化效应；以及（ii）在较高速率下速率对应力水平的渐近效应。然后将设计的(Wv)函数与超弹性应变能函数(We)结合使用，以模拟瓣膜的速率依赖性行为，将变形速率作为一个显式变量纳入其中。结果表明，设计的函数能够很好地捕捉观察到的速率依赖性特征，并且该模型对实验获得的(\sigma - \lambda)曲线提供了极佳的拟合。因此，建议将所提出的函数应用于心脏瓣膜以及其他表现出类似速率依赖性行为的软组织的速率依赖性力学行为。
