Non-Euclidean Stress-Free Configuration of Arteries Accounting for Curl of Axial Strips Sectioned from Vessels.
Non-Euclidean Stress-Free Configuration of Arteries Accounting for Curl of Axial Strips Sectioned from Vessels.
复制标题
动脉的非欧几里得无应力配置考虑了从血管切下的轴向条带的卷曲。
DOI：
10.1115/1.4025328
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Nakayama Y
中科院分区：
文献类型：
--
作者：
Takamizawa K;Nakayama Y
众所周知，动脉会受到残余应力的影响。在早期的研究中，在应力分析中考虑了径向切割消除的动脉环中的残余应力。然而，研究发现，从动脉切开的轴向条带也卷曲成弧形，表明轴向残余应力从动脉壁上消除。为了准确地分析生理载荷条件下的应力和应变分布，必须考虑周向和轴向残余应力的联合消除。在本研究中，利用黎曼几何建立了动脉无应力构型的数学模型。用猪和人颈总动脉的指数应变能函数分析了在非加载和生理加载条件下动脉壁的应力。在猪动脉中，生理负荷下的周向应力分布与无残余应变的相比趋于均匀，而轴向应力分布的梯度随着管壁厚度的增加而增加。这一行为表现出与最近一项研究中观察到的几乎相同的模式，在该研究中，考虑了周向和轴向残余应变的近似分析，而在基于其他最近研究数据的两层模型中，在生理条件下，人颈总动脉的周向和轴向应力从内表面到外表面增加。在这两种分析中，Riemannian几何都适合定义具有周向和轴向残余应变的动脉壁的无应力构型。
It is well known that arteries are subject to residual stress. In earlier studies, the residual stress in the arterial ring relieved by a radial cut was considered in stress analysis. However, it has been found that axial strips sectioned from arteries also curled into arcs, showing that the axial residual stresses were relieved from the arterial walls. The combined relief of circumferential and axial residual stresses must be considered to accurately analyze stress and strain distributions under physiological loading conditions. In the present study, a mathematical model of a stress-free configuration of artery was proposed using Riemannian geometry. Stress analysis for arterial walls under unloaded and physiologically loaded conditions was performed using exponential strain energy functions for porcine and human common carotid arteries. In the porcine artery, the circumferential stress distribution under physiological loading became uniform compared with that without axial residual strain, whereas a gradient of axial stress distribution increased through the wall thickness. This behavior showed almost the same pattern that was observed in a recent study in which approximate analysis accounting for circumferential and axial residual strains was performed, whereas the circumferential and axial stresses increased from the inner surface to the outer surface under a physiological condition in the human common carotid artery of a two-layer model based on data of other recent studies. In both analyses, Riemannian geometry was appropriate to define the stress-free configurations of the arterial walls with both circumferential and axial residual strains.