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局部狭窄血管中血液振荡流的速度和切应力
引用本文:孙辉,柳兆荣.局部狭窄血管中血液振荡流的速度和切应力[J].上海力学,2002,23(2):148-156.
作者姓名:孙辉  柳兆荣
作者单位:复旦大学生物力学实验室,复旦大学生物力学实验室 上海 200433,上海 200433
基金项目:国家自然科学基金(10132020),复旦大学学生科技创新行动支持计划(B2404)
摘    要:本文建立一种分析局部缓慢狭窄血管中血液振荡流的数学模型,给出了血液的轴向流速,径向流速和切应力的包含压力梯度项的解析表达式,并讨论了血管内由局部狭窄引起的压力梯度沿轴向变化的规律。文章以局部余弦狭窄为例进行数值计算,详细讨论上游均匀管段压力梯度的定常部分和不同次谐波对狭窄管段内流速和切应力的影响。数值结果表明,与均匀管情况相比,在狭窄段内,血液振荡流轴向流速无论平均值还是脉动幅值均明显增大,且径向流速不再为零。但径向流速仍远小于轴向流速。同时,切应力也不再仅由轴向流速梯度提供,径向流速梯度也将产生切应力,但是在计算管壁切向上的切应力时,径向流速梯度的贡献仍相当大。与均匀管管壁切应力沿流运方向保持恒定不同。狭窄管管壁切应力(平均值和脉动值)将随着狭窄高度的增大而增大,在狭窄最大高度处达到最大,因而沿流动方向产生了较大的切应力梯度。

关 键 词:局部狭窄血管  血液振荡流  速度  切应力  压力梯度  粘性流体
修稿时间:2001年1月17日

Velocity and Shear Stress of Periodic Oscillatory Blood Flow in Vessel with Stenosis
SUN Hui,LIU Zhao-rong.Velocity and Shear Stress of Periodic Oscillatory Blood Flow in Vessel with Stenosis[J].Chinese Quarterly Mechanics,2002,23(2):148-156.
Authors:SUN Hui  LIU Zhao-rong
Abstract:In this paper, a mathematical model of periodic oscillatory blood flow in arteries with local stenosis was developed, and the analytic expressions of axial velocity, radial velocity and shear stress of periodic oscilatory blood flow corresponding to the pressure gradient were obtained, and the variation of pressure gradient along the axis which is caused by local stenosis in arteries was discussed. As an example, assuming the geometry of the local stenosis as a cosine form, a detailed discussion is performed through numerical calculation, which helps estimating how the steady pressure gradient and different harmonic components of pressure gradient at the upstream uniform segment influence the velocity and shear stress in the constricted region. Numerical results indicate that in the stenotic region of the artery not only the average but also the pulsatile amplitude of the axial velocity of the oscillatory blood flow will increase apparently comparing with the uniform segment. And the radial velocity will no longer be zero, although its value is still rather small when compared with the axial one. Meantime, the shear stress is now caused by the radial velocity gradient as well as the axial velocity gradient, although the contribution to the wall shear stress along the flow directoin of the radial one is relatively small. Unlike the uniform segment where the wall 'shear stress remains constant along the axis, in the constricted region, the wall shear stress enhances corresponding to the increase of the height of the stenosis and attains the peak value at the maximum height of the stenosis ,and thus a considerable value of shear stress gradient is noticed along the flow direction.
Keywords:stenosis  pressure gradient  oscillatory flow  wall shear stress  vascular remodeling
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