Papathanasiou T K, Movchan A B, Bigoni D
Department of Mechanical, Aerospace and Civil Engineering, Brunel University London, Uxbridge UB8 3PH, UK.
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK.
Proc Math Phys Eng Sci. 2017 Jun;473(2202):20170015. doi: 10.1098/rspa.2017.0015. Epub 2017 Jun 7.
Closed circulatory systems display an exquisite balance between vascular elasticity and viscous fluid effects, to induce pulse-smoothing and avoid resonance during the cardiac cycle. Stents in the arterial tree alter this balance through stiffening and because a periodic structure is introduced, capable of interacting with the fluid in a complex way. While the former feature has been investigated, the latter received no attention so far. But periodic structures are the building blocks of metamaterials, known for their 'non-natural' behaviour. Thus, the investigation of a stent's periodic microstructure dynamical interactions is crucial to assess possible pathological responses. A one-dimensional fluid-structure interaction model, simple enough to allow an analytical solution for situations of interest involving one or two interacting stents, is introduced. It is determined: (i) whether or not frequency bands exist in which reflected blood pulses are highly increased and (ii) if these bands are close to the characteristic frequencies of arteries and finally, (iii) if the internal structure of the stent can sensibly affect arterial blood dynamics. It is shown that, while the periodic structure of an isolated stent can induce anomalous reflection only in pathological conditions, the presence of two interacting stents is more critical, and high reflection can occur at frequencies not far from the physiological values.
封闭循环系统在血管弹性和粘性流体效应之间展现出精妙的平衡，以在心动周期中实现脉搏平滑并避免共振。动脉树中的支架会通过硬化改变这种平衡，并且由于引入了周期性结构，该结构能够以复杂的方式与流体相互作用。虽然前者的特征已得到研究，但后者至今尚未受到关注。然而，周期性结构是超材料的基本组成部分，以其“非自然”行为而闻名。因此，研究支架的周期性微观结构动力学相互作用对于评估可能的病理反应至关重要。本文引入了一个一维流固相互作用模型，该模型足够简单，能够为涉及一个或两个相互作用支架的感兴趣情况提供解析解。确定了：（i）是否存在反射血脉冲大幅增加的频带；（ii）这些频带是否接近动脉的特征频率；最后，（iii）支架的内部结构是否会显著影响动脉血液动力学。结果表明，虽然孤立支架的周期性结构仅在病理条件下会引起异常反射，但两个相互作用支架的存在更为关键，并且在离生理值不远的频率处可能会出现高反射。
