在体轴向伸长比条件下血管壁的周向应力分布

On Circumferential Stress in Arterial Wall at in Vivo Axial Extension Ratio

本文通过检测在体轴向伸长比条件下血管段的压力一容积数据,利用应变能密度函数,求得血管壁周向应力沿壁厚的分布。文章以正常大鼠腹主动脉为例进行计算,结果发现,在生理压力作用下(例如p=13.3kPa),不考虑残余应力确实出现在血管内壁处的周向应力集中,血管内、外壁处的应力值之比可达15左右;而存在于实际动脉管中的残余应力会使血管壁中的周向应力沿壁厚的分布明显趋于均匀,血管内、外壁处的周向应力之比差不多只有2左右。结果与血管的生理事实一致,同时也与Fung等对其他动物所得的血管力学特性相符合。实践表明,本文方法具有实验数据拟合较简便,结果对初值的依赖不敏感,以及检测数据精度易于控制,对实验条件要求较低的特点。

In this paper, the circumferential stress distribution along the arterial wall thickness was determined using a strain energy density function. This function provides a description of the wall properties through intraluminal pressure - volume experimental data in vivo axial extension ratio. Depending on assumptions of residual stress, the results obtained in rat abdominal aorta are different. If zero residual stress is assumed, the results indicate that a strong circumferential stress concentration should appear in the inner arterial wall, even under normal physiological loading condi-tions(such as p = 13. 3kPa), the inner wall to outer wall stress ratio will be about 15. However, if residual stress were considered in calculation, the circumferential stress distribution over the cross - section of the wall will be rather uniform and the inner wall to outer wall stress ratio will only be almost 2. Corroboration was observed between the calculation results and the physiological behavior of the arterial wall. The calculation results were consistent with the mechanical properties of the vessel wall proposed by Fung et al. With the proposed method of this paper, it is believed that experimental procedures and data analysis are more streamlined and straightforward.