Cardiovascular Engineering Research Lab (CERL), School of Mechanical and Design Engineering, University of Portsmouth, Anglesea Road, Portsmouth, PO1 3DJ, United Kingdom.
National Heart and Lung Institute, Heart Science Centre, Imperial College London, Middlesex, United Kingdom.
J Mech Behav Biomed Mater. 2022 Oct;134:105341. doi: 10.1016/j.jmbbm.2022.105341. Epub 2022 Jul 8.
A theoretical framework, based on extant experimental findings, is presented to devise a novel viscous dissipation function W in order to model the rate-dependent mechanical behaviour of the aortic heart valve. The experimental data encompasses Cauchy stress-stretch (σ-λ) curves obtained across a 10,000-fold range of stretch rates (λ˙), from quasi-static (λ˙= 0.001 s) to upper-range of physiological (λ˙= 12.4 s) 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 σ-λ curves; i.e. the rate-effects approach an asymptote with increase in the stretch rate λ˙. Guided by these empirical observations, we devise our new W function and demonstrate that the well-known form of the dissipation function commonly used in the literature is a special case of our proposed W. The ensuing model is then compared against the experimental σ-λ 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.
本文提出了一个理论框架，基于现有的实验结果，设计了一个新的粘性耗散函数 W，以模拟主动脉心脏瓣膜的率相关力学行为。实验数据包括跨越 10000 倍拉伸速率范围（λ˙）的柯西应力-拉伸（σ-λ）曲线，从准静态（λ˙= 0.001 s）到生理范围的上限（λ˙= 12.4 s）变形速率。数据分析揭示了两个重要趋势：（i）在所测试的速率范围内，主动脉瓣的力学行为是速率相关的，随着速率的增加，试件变得更加坚硬；（ii）在 σ-λ 曲线上，似乎存在一个速率效应的平台；即随着拉伸速率 λ˙的增加，速率效应趋近于渐近线。基于这些经验观察，我们设计了新的 W 函数，并证明了文献中常用的耗散函数的常见形式是我们提出的 W 的一个特例。随后，将所提出的模型与实验 σ-λ 曲线进行比较，并证明其提供了有利的预测。所采用的建模框架的一个重要优点是，它允许将变形速率作为一个直接的实验控制参数，作为显式的建模变量进行合并。因此，建议将所提出的模型应用于表现出类似速率相关特征的心脏瓣膜和其他软组织。
