用p-V指数关系确定血管壁的周向应力  

ON DETERMINATION OF CIRCUMFERENTIAL STRESS IN ARTEAIAL WALL USING p-V EXPONENTIAL RELATIONSHIP

作　　者：柳兆荣[1] 滕忠照[1] 覃开蓉[1] 

机构地区：[1]复旦大学生物力学试验室,上海200433

出　　处：《力学学报》2002年第1期87-95,共9页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学重点基金(19732003);杰出青年基金(19702002)资助项目~~

摘　　要：通过检测，得到在体轴向伸长比条件下血管段的压力－容积（ｐ－Ｖ）数据，利用指数函数关系，求得在一定内压作用下血管壁周向应力沿壁厚的分布．并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，残余应力对血管壁周向应力的分布有很大影响，不考虑残余应力将使血管内壁处出现明显的周向应力集中，当考虑存在于血管壁内的残余应力后，周向应力沿壁厚的分布将变得较均匀，例如当内压ｐ＝１０ ｋＰａ时，血管内、外壁周向应力值之比，对前者将达１０以上，而对后者差不多只有２左右．所得结果与用Ｆｕｎｇ提出的应变能密度函数的计算结果作比较，发现二者符合得相当好．In this paper, the circumferential stress distribution along the arterial wall thickness was determined using p-V exponential relationship. This relationship provides a description of the wall properties through pressure-volume experimental data at in vivo axial extension ratio. Depending on assumptions of residual stress, the results obtained in rat abdominal aorta are different. If we assume zero residual stress, the results indicate that a strong circumferential stress concentration should appear in the inner arterial wall, even under normal physiological loading conditions (such as p =10kPa ), the inner wall to outer wall stress ratio will be above 10. 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 results obtained and the physiological behavior of the arterial wall, and the calculation results were consistent with that using strain energy function proposed by Fung. With the proposed method of this paper, it is believed that experimental procedures and data analysis are more streamlined and straightforward.

关 键 词：动脉管壁 残余应力 周向应力 应变能密度函数 压力-窄积指数关系 鼠腹主动脉 生物流体力学 

分 类 号：Q66[生物学—生物物理学] R318.01[医药卫生—生物医学工程]