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A framework for incorporating 3D hyperelastic vascular wall models in 1D blood flow simulations
Biomechanics and Modeling in Mechanobiology ( IF 3.5 ) Pub Date : 2021-03-08 , DOI: 10.1007/s10237-021-01437-5
Alberto Coccarelli 1 , Jason M Carson 1, 2, 3 , Ankush Aggarwal 4 , Sanjay Pant 1
Affiliation  

We present a novel framework for investigating the role of vascular structure on arterial haemodynamics in large vessels, with a special focus on the human common carotid artery (CCA). The analysis is carried out by adopting a three-dimensional (3D) derived, fibre-reinforced, hyperelastic structural model, which is coupled with an axisymmetric, reduced order model describing blood flow. The vessel transmural pressure and lumen area are related via a Holzapfel–Ogden type of law, and the residual stresses along the thickness and length of the vessel are also accounted for. After a structural characterization of the adopted hyperelastic model, we investigate the link underlying the vascular wall response and blood-flow dynamics by comparing the proposed framework results against a popular tube law. The comparison shows that the behaviour of the model can be captured by the simpler linear surrogate only if a representative value of compliance is applied. Sobol’s multi-variable sensitivity analysis is then carried out in order to identify the extent to which the structural parameters have an impact on the CCA haemodynamics. In this case, the local pulse wave velocity (PWV) is used as index for representing the arterial transmission capacity of blood pressure waveforms. The sensitivity analysis suggests that some geometrical factors, such as the stress-free inner radius and opening angle, play a major role on the system’s haemodynamics. Subsequently, we quantified the differences in haemodynamic variables obtained from different virtual CCAs, tube laws and flow conditions. Although each artery presents a distinct vascular response, the differences obtained across different flow regimes are not significant. As expected, the linear tube law is unable to accurately capture all the haemodynamic features characterizing the current model. The findings from the sensitivity analysis are further confirmed by investigating the axial stretching effect on the CCA fluid dynamics. This factor does not seem to alter the pressure and flow waveforms. On the contrary, it is shown that, for an axially stretched vessel, the vascular wall exhibits an attenuation in absolute distension and an increase in circumferential stress, corroborating the findings of previous studies. This analysis shows that the new model offers a good balance between computational complexity and physics captured, making it an ideal framework for studies aiming to investigate the profound link between vascular mechanobiology and blood flow.



中文翻译:

将 3D 超弹性血管壁模型纳入 1D 血流模拟的框架

我们提出了一个新的框架来研究血管结构对大血管动脉血流动力学的作用,特别关注人类颈总动脉 (CCA)。通过采用三维 (3D) 衍生的、纤维增强的超弹性结构模型进行分析,该模型与描述血流的轴对称降阶模型相结合。血管跨壁压力和管腔面积通过 Holzapfel-Ogden 类型的定律相关,并且还考虑了沿血管厚度和长度的残余应力。在对所采用的超弹性模型进行结构表征后,我们通过将提出的框架结果与流行的管法进行比较来研究血管壁反应和血流动力学的联系。比较表明,模型的行为可以通过更简单的线性代理来捕获,前提是应用了具有代表性的合规值。然后进行 Sobol 的多变量敏感性分析,以确定结构参数对 CCA 血流动力学的影响程度。在这种情况下,局部脉搏波速度(PWV)被用作表示血压波形的动脉传输能力的指标。敏感性分析表明,一些几何因素,如 以局部脉搏波速度(PWV)作为衡量血压波形动脉传输能力的指标。敏感性分析表明,一些几何因素,如 以局部脉搏波速度(PWV)作为衡量血压波形动脉传输能力的指标。敏感性分析表明,一些几何因素,如无压力内半径和张角,对系统的血流动力学起主要作用。随后,我们量化了从不同虚拟 CCA、管律和流动条件获得的血流动力学变量的差异。尽管每条动脉都呈现出不同的血管反应,但在不同流动状态下获得的差异并不显着。正如预期的那样,线性管法无法准确捕获表征当前模型的所有血流动力学特征。通过研究轴向拉伸对 CCA 流体动力学的影响,进一步证实了敏感性分析的结果。这个因素似乎不会改变压力和流量波形。相反,它表明,对于轴向拉伸的容器,血管壁表现出绝对膨胀的衰减和周向应力的增加,证实了先前研究的结果。该分析表明,新模型在计算复杂性和物理捕获之间提供了良好的平衡,使其成为旨在研究血管力学生物学和血流之间深刻联系的研究的理想框架。

更新日期:2021-03-08
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