Department of Civil & Environmental Engineering, University of Cyprus, Nicosia, CY-1678, Cyprus.
Department of Civil Engineering, University of Thessaly, Volos, GR-38334, Greece.
Comput Biol Med. 2017 Oct 1;89:337-354. doi: 10.1016/j.compbiomed.2017.07.028. Epub 2017 Aug 2.
Arteries undergo large deformations under applied intraluminal pressure and may exhibit small hysteresis due to creep or relaxation process. The mechanical response of arteries depends, among others, on their topology along the arterial tree. Viscoelasticity of arterial tissues, which is the topic investigated in this study, is mainly a characteristic mechanical response of arteries that are located away from the heart and have increased smooth muscle cells content.
The arterial wall viscosity is simulated by adopting a generalized Maxwell model and the method of internal variables, as proposed by Bonet and Holzapfel et al. The total stresses consist of elastic long-term stresses and viscoelastic stresses, requiring an iterative procedure for their calculation. The cross-section of the artery is modeled as a circular ring, consisting of a single homogenized layer, under a time-varying blood pressure. Two different loading approximations for the aortic pressure vs time are considered. A novel numerical method is developed in order to solve the controlling integro-differential equation.
A large number of numerical investigations are performed and typical response time-profiles are presented in pictorial form. Results suggest that the viscoelastic arterial response is mainly affected by the ratio of the relaxation time to the characteristic time of the response and by the pressure-time approximation. Numerical examples, based on data available in the literature, are conducted.
The investigation presented in this study reveals the effect of each material parameter on the viscoelastic arterial response. Thus, a better understanding of the behavior of viscoelastic arteries is achieved.
动脉在受到腔内压力作用时会发生较大的变形，并且由于蠕变或松弛过程，可能会出现较小的滞后现象。动脉的力学响应取决于其在动脉树中的拓扑结构等因素。本研究中研究的动脉组织粘弹性主要是远离心脏且平滑肌细胞含量增加的动脉的主要力学响应特征。
采用广义 Maxwell 模型和 Bonet 和 Holzapfel 等人提出的内变量方法模拟动脉壁粘性。总应力由弹性长期应力和粘弹性应力组成，需要迭代计算。动脉的横截面建模为一个圆形环，由一个均质层组成，在时变血压下。考虑了两种不同的主动脉压力随时间变化的加载近似值。为了解决控制积分微分方程，开发了一种新的数值方法。
进行了大量的数值研究，并以图形形式呈现了典型的响应时间曲线。结果表明，粘弹性动脉响应主要受松弛时间与响应特征时间之比以及压力-时间近似值的影响。基于文献中可用的数据进行了数值示例。
本研究的调查揭示了每个材料参数对粘弹性动脉响应的影响。因此，对粘弹性动脉的行为有了更好的理解。
