Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Universiteitssingel 40, Room C5.568, 6229 ER, Maastricht, The Netherlands.
GROW School for Oncology and Reproduction, Maastricht University, Maastricht, The Netherlands.
Biomech Model Mechanobiol. 2023 Oct;22(5):1607-1623. doi: 10.1007/s10237-023-01711-8. Epub 2023 May 2.
Arteries exhibit fully nonlinear viscoelastic behaviours (i.e. both elastically and viscously nonlinear). While elastically nonlinear arterial models are well established, effective mathematical descriptions of nonlinear viscoelasticity are lacking. Quasi-linear viscoelasticity (QLV) offers a convenient way to mathematically describe viscoelasticity, but its viscous linearity assumption is unsuitable for whole-wall vascular applications. Conversely, application of fully nonlinear viscoelastic models, involving deformation-dependent viscous parameters, to experimental data is impractical and often reduces to identifying specific solutions for each tested loading condition. The present study aims to address this limitation: By applying QLV theory at the wall constituent rather than at the whole-wall level, the deformation-dependent relative contribution of the constituents allows to capture nonlinear viscoelasticity with a unique set of deformation-independent model parameters. Five murine common carotid arteries were subjected to a protocol of quasi-static and harmonic, pseudo-physiological biaxial loading conditions to characterise their viscoelastic behaviour. The arterial wall was modelled as a constrained mixture of an isotropic elastin matrix and four families of collagen fibres. Constituent-based QLV was implemented by assigning different relaxation functions to collagen- and elastin-borne parts of the wall stress. Nonlinearity in viscoelasticity was assessed via the pressure dependency of the dynamic-to-quasi-static stiffness ratio. The experimentally measured ratio increased with pressure, from 1.03 [Formula: see text] 0.03 (mean [Formula: see text] standard deviation) at 80-40 mmHg to 1.58 [Formula: see text] 0.22 at 160-120 mmHg. Constituent-based QLV captured well this trend by attributing the wall viscosity predominantly to collagen fibres, whose recruitment starts at physiological pressures. In conclusion, constituent-based QLV offers a practical and effective solution to model arterial viscoelasticity.
动脉表现出完全非线性粘弹性行为（即弹性和粘性非线性）。虽然弹性非线性动脉模型已经建立，但缺乏对非线性粘弹性的有效数学描述。准线性粘弹性（QLV）提供了一种方便的数学描述粘弹性的方法，但它的粘性线性假设不适合整个血管壁的应用。相反，涉及变形相关粘性参数的完全非线性粘弹性模型应用于实验数据是不切实际的，并且通常简化为为每个测试加载条件识别特定的解决方案。本研究旨在解决这一限制：通过在壁组成部分而不是整个壁水平上应用 QLV 理论，组成部分的变形相关相对贡献允许用一组独特的变形无关的模型参数来捕捉非线性粘弹性。对五只小鼠颈总动脉进行准静态和谐波、拟生理双轴加载条件的实验，以表征其粘弹性行为。动脉壁被建模为各向同性弹性蛋白基质和四组胶原纤维的约束混合物。通过为壁应力的胶原和弹性蛋白承载部分分配不同的松弛函数来实现基于组成部分的 QLV。通过评估粘弹性的压力依赖性来评估非线性。实验测量的比率随压力增加而增加，从 80-40mmHg 时的 1.03 [Formula: see text] 0.03（平均值 [Formula: see text] 标准差）增加到 160-120mmHg 时的 1.58 [Formula: see text] 0.22。基于组成部分的 QLV 通过将壁粘度主要归因于胶原纤维来很好地捕捉到这种趋势，胶原纤维在生理压力下开始募集。总之，基于组成部分的 QLV 为模拟动脉粘弹性提供了一种实用且有效的解决方案。
