Johnson G A, Borovetz H S, Anderson J L
Department of Mechanical Engineering, University of Pittsburgh, PA 15261.
J Biomech. 1992 Jan;25(1):91-100. doi: 10.1016/0021-9290(92)90248-y.
Simulations of blood flow in natural and artificial conduits usually require large computers for numerical solution of the Navier-Stokes equations. Often, physical insight into the fluid dynamics is lost when the solution is purely numerical. An alternative to solving the most general form of the Navier-Stokes equations is described here, wherein a functional form of the solution is assumed in order to simplify the required computations. The assumed forms for the axial pressure gradient and velocity profile are chosen such that conservation of mass is satisfied for fully established pulsatile flow in a straight, deformable vessel. The resulting equations are cast in finite-difference form and solved explicitly. Results for the limiting cases of rigid wall and zero applied pressure are found to be in good agreement with analytical solutions. Comparison with the experimental results of Klanchar et al. [Circ. Res. 66, 1624-1635 (1990]) also shows good agreement. Application of the model to realistic physiological parameter values provides insight as to the influence of the pulsatile nature of the flow field on wall shear development in the presence of a moving wall boundary. Specifically, the model illustrates the dependence of flow rate and shear rate on the amplitude of the vessel wall motion and the phase difference between the applied pressure difference and the oscillations of the vessel radius. The present model can serve as a useful tool for experimentalists interested in quantifying the magnitude and character of velocity profiles and shearing forces in natural and artificial biologic conduits.
对天然和人造管道中的血流进行模拟通常需要大型计算机来对纳维-斯托克斯方程进行数值求解。通常，当解决方案完全是数值解时，就会失去对流体动力学的物理洞察。本文描述了一种求解纳维-斯托克斯方程最一般形式的替代方法，其中假设了解的函数形式以简化所需的计算。选择轴向压力梯度和速度剖面的假设形式，以便在直管、可变形血管中充分建立的脉动流中满足质量守恒。所得方程以有限差分形式表示并显式求解。发现刚性壁和零外加压力的极限情况的结果与解析解非常吻合。与克兰查尔等人的实验结果[《循环研究》66, 1624 - 1635 (1990)]的比较也显示出良好的一致性。将该模型应用于实际生理参数值，有助于了解在存在移动壁边界的情况下，流场的脉动性质对壁面剪切发展的影响。具体而言，该模型说明了流速和剪切率对血管壁运动幅度以及外加压力差与血管半径振荡之间相位差的依赖性。本模型可作为一个有用的工具，供有兴趣量化天然和人造生物管道中速度剖面和剪切力的大小及特征的实验人员使用。
