Sharp M K, Thurston G B, Moore J E
Department of Civil Engineering, University of Utah, Salt Lake City 84112, USA.
Biorheology. 1996 May-Jun;33(3):185-208. doi: 10.1016/0006-355X(96)00017-0.
An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient delta P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The delta P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published delta P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion. Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%. In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.
利用一种解析解来计算广义麦克斯韦流体在直刚性管中脉动流动（有或无轴向血管运动）时血液粘弹性对代表大动脉中血流的速度分布和剪切应力的影响。测量得到的总体流量Q波形被用作主动脉和股动脉计算的起点，由此导出轴向压力梯度ΔP波，该波将再现粘弹性流动的起始Q波。然后，利用ΔP波来计算粘弹性流动和纯粘性流动的速度分布。对于冠状动脉，采用已发表的ΔP和轴向血管加速度波形，通过类似的程序来确定粘弹性和血管运动的单独及综合影响。将粘性流动与粘弹性流动的局部速度差异在所有情况下均小于局部峰值速度的约2%。峰值壁面剪切应力差异小于约3%。在冠状动脉中，无论是否考虑轴向血管运动，粘性流动和粘弹性流动之间的壁面剪切应力差异都很小。然而，壁面剪切应力波形的形状及其差异在静止血管和运动血管情况下有显著变化。壁面剪切应力差异的峰值与流动的组合驱动力中的大时间梯度相对应。
