Yan Z Y, Acrivos A, Weinbaum S
Department of Mechanical Engineering, City College, City University of New York 10031.
Microvasc Res. 1991 Jul;42(1):17-38. doi: 10.1016/0026-2862(91)90072-j.
This paper analyzes an important underlying mechanism for the discharge hematocrit reduction observed in microvessels, which refers to the plasma skimming from the cell-free layer near the parent tube wall in the presence of a side branch. The three-dimensional theory recently developed by the authors (Yan et al., 1991, J. Fluid Mech., in press) for treating the simple shear flow past a side branch tube in a plane wall with suction is first summarized and then extended to treat T bifurcations from parent vessels with an upstream Poiseuille flow. For unequal vessel bifurcations, a fundamental new dimensionless group, Q = 1/8(qb/qp)(Rp/Rb)3, is derived whose value determines the shape of the upstream capture tube of the plasma phase, when the partitioning qb/qp of the flow into the side branch and the ratio Rp/Rb of the radii of the parent and side branch vessels are varied. Closed form expressions are then presented for the three-dimensional fluid capture tube shape upstream of the bifurcation which are valid when Q greater than 1 or Q less than 0.2. Based on this theory and its modification for an upstream Poiseuille velocity profile, the separating surface shape, the critical minimum fractional flux for incipient cell capture, and the discharge hematocrit defect and its dependence on the flow rate are predicted. It is shown, furthermore, that for flows typical of the microcirculation, a single dimensionless number, P = 3 pi Q(Rb/gamma 2), with gamma being the cell-free layer thickness, can be defined whose value determines the discharge hematocrit defect that arises from plasma skimming. The minimum critical flow rate for any red cells to enter the side branch is then given by the criterion P = 1. Although this theory does not account for the cell screening effect arising from the hydrodynamic interaction between the cells and the tube walls, it leads to predictions which exhibit the same trends as the experimental observations and is able to explain the results of several seemingly contradictory microvascular experiments that have puzzled investigators in recent years.
本文分析了微血管中观察到的排出血细胞比容降低的一个重要潜在机制，该机制指的是在存在侧支的情况下，血浆从靠近母管壁的无细胞层中被撇除。作者最近（Yan等人，1991年，《流体力学杂志》，即将发表）针对处理平面壁上带有抽吸的侧支管道的简单剪切流所发展的三维理论，首先进行了总结，然后扩展到处理具有上游泊肃叶流的母血管的T型分支。对于不等的血管分支，推导出一个基本的新无量纲组，Q = 1/8(qb/qp)(Rp/Rb)3，当流入侧支的流量分配qb/qp以及母血管和侧支血管半径之比Rp/Rb变化时，其值决定了血浆相上游捕获管的形状。然后给出了分支上游三维流体捕获管形状的封闭形式表达式，当Q大于1或Q小于0.2时有效。基于该理论及其对上游泊肃叶速度分布的修正，预测了分离表面形状、初始细胞捕获的临界最小分数通量、排出血细胞比容缺陷及其对流速的依赖性。此外，结果表明，对于微循环典型的流动，可以定义一个单一的无量纲数，P = 3πQ(Rb/γ2)，其中γ为无细胞层厚度，其值决定了由血浆撇除引起的排出血细胞比容缺陷。任何红细胞进入侧支的最小临界流速然后由准则P = 1给出。虽然该理论没有考虑细胞与管壁之间流体动力相互作用产生的细胞筛选效应，但它得出的预测结果与实验观察结果具有相同的趋势，并且能够解释近年来使研究人员感到困惑的几个看似相互矛盾的微血管实验的结果。
