局部扩张动脉管血液振荡流的切应力分布

本文求解局部缓慢扩张动脉管中血液振荡流的基本方程，得到血管内血液的流速与压力梯度的关系。通过导出压力梯度沿局部扩张管轴向的变化特性。建立利用扩张段上游血管均匀段中心流速波形确定局部扩张管中血液流的速度和切应力分布的方法，文章以人体颈动脉余弦扩张为例进行分析。详细讨论了局部扩张对血管壁切应力及其梯度分布的影响。数值结果表明，在与刚性均匀管中管壁切应力沿轴向保持不变不同，在局部扩张段，管壁切应力将随着血管半径的增大而减小，因而管壁切应力梯度一般不为零，甚至在某些位置达到相当大的数值。另外，随着血管扩张程度的增加，管壁切应力还将进一步减小，而且管壁切应力梯度也将进一步增大，血管扩张导致管壁切应力的这些变化将直接影响血管壁的结构和功能，使其产生适应性的变化。

Shear Stress Distribution of Oscillatory Blood Flow in Local Expansion Artery

Through solving the fundamental equations of periodic oscillatory blood flow in local slow expansion artery, the relation between velocity and pressure gradient in the tube was obtained. The variation of pressure gradient along the axis in local vessel expansion region, and then a method determining the distribution of blood flow velocity and shear stress by centerline velocity at the axis of the upstream uniform segment was determined. As an example, the human carotid with local cosine form expansion was analyzed and the effects of local expansion on the distribution of wall shear stress and its gradient were discussed in detail. Numerical results show that in contrast to the rigid uniform tube, in local region with slow expansion, the wall shear stress is no longer constant along the axis but decreases with the enhancement of the vessel radius, which leads to the gradient of wall shear stress unequal to zero, even amounting to a considerable value in some regions. Furthermore, the more the vessel expansion is, the less the wall shear stress will be and the more the gradient of wall shear stress will be. These changes of wall shear stress caused by vessel expansion will influence the structure and function of the vessel and make the vessel change adaptively.