MECHANICS OF RED-CELL MOTION THROUGH VERY NARROW CAPILLARIES
MECHANICS OF RED-CELL MOTION THROUGH VERY NARROW CAPILLARIES
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DOI：
10.1098/rspb.1969.0088
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发表时间：
1969-01-01
期刊：
影响因子：
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通讯作者：
FITZGERALD, JM
中科院分区：
文献类型：
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作者：
FITZGERALD, JM
在最近的一篇论文中，Lighthill(1968)建立了可压缩颗粒在狭窄、充满流体的弹性管中的运动模型；该模型涉及颗粒和壁面之间的薄层润滑层，所获得的结果以各种速度、阻力、间隙和润滑膜厚度参数之间的关系的形式表示。这项工作的一个重要生物学动机是红血球在狭窄的毛细血管中移动的问题。本文详细考察了莱特希尔模型的近似和假设，并从几个方面对其进行了扩展。首先，讨论了颗粒的弹性行为，特别与红细胞有关，红细胞被认为是由充满流体的柔性膜组成的。结果表明，当这种红细胞在毛细管中的运动速度增加时，其边缘的粘性阻力的增加往往会使毛细红细胞“弯曲”，从而使其更容易进入给定直径的毛细管中。此外，对轮缘周围不均匀的润滑压力的弹性响应模数还表明取决于膜的“抗变形能力”和单元的几何形状。其次，建立了圆管中轴对称颗粒流动的数学模型。对于毛细管流的各种速度和膜厚，结果以颗粒所经历的间隙和阻力的形式表示。得到了比莱特希尔估计的阻力大得多的阻力；对于直径为5到7μm的毛细血管中的正常流动，这些阻力范围是相应的具有全血粘度的泊松流体预期阻力的4.5到7倍。并不是说这些结果适用于所有的毛细血管或毛细血管网络，而是仅适用于所考虑的直径范围内的那些非常窄的毛细血管。同样重要的是阻力与速度的非线性关系。随着压力梯度的减小，红细胞的速度迅速下降；这一点将参照自动调节现象进行详细讨论。最后，考虑了不对称性和管孔率的影响。结果表明，与轴对称的偏差往往随流体中压力的增加而减小；这是由于颗粒的可压缩性质，这意味着即使对于红细胞可能不是轴对称的构型，毛细管流的结果也是合理有效的。等离子体通过毛细管壁的泄漏不会在很大程度上影响毛细管的流动特性，也不会显著增加由于在小膜厚时润滑失效而导致流动“卡住”的可能性。
In a recent paper, Lighthill (1968) has formulated a model of compressible pellet movement through narrow, fluid-filled, elastic tubes; the model involves a thin lubricating layer of fluid between the pellet and the wall, and the results obtained are expressed in the form of relationships between various velocity, resistance, clearance, and lubrication-film thickness parameters. An important biological motivation for this work was the problem of the movement of red blood cells through narrow capillaries. The present paper examines in detail the approximations and assumptions of Lighthill’s model, and extends the investigation in several directions. First, the elastic behaviour of the pellet is discussed with particular relevance to the red cell, which is considered to consist of a fluid-filled flexible membrane. It is shown, in particular, that as the velocity of such a red cell in a capillary increases, the consequent increase in viscous drag on the rim tends to ‘bow’ the cell, and allow it to fit more easily into a capillary of given diameter. Further, the modulus of elastic response to the non-uniform lubrication pressures around the rim is shown to depend on the membrane’s ‘resistance to deformation’ and the geometry of the cell. Next, a model of axisymmetric pellet flow through a tube is set up. Results are expressed in terms of clearance and resistance experienced by the pellet, for various velocities and film thicknesses typical of capillary flows. Much greater resistances than those estimated by Lighthill are obtained; for normal flow in capillaries of 5 to 7μm diameter, these range from 4.5 to 7 times that expected for a corresponding Poiseuille fluid flow with whole-blood viscosity. It is not suggested that these results are true of all capillaries, or of a capillary network, but only of those very narrow capillaries in the diameter range being considered. Of equal importance is the nonlinear dependence of resistance on velocity. The red cell velocity falls off very rapidly as the pressure gradient is reduced; this is discussed in detail with reference to the phenomenon of auto-regulation. Finally, the effects of asymmetry and tube porosity are considered. It is shown that deviations from axisymmetry tend to be reduced by pressures developed in the fluid; this is due to the compressible nature of the pellets, and means that the results obtained for capillary flow are reasonably valid even for configurations in which the red cells may not be axisymmetric. Leakage of plasma through the walls of the capillary is shown not to affect the flow characteristics of a capillary to any great extent, or to significantly increase the possibility of ‘seizing-up’ of the flow due to failure of lubrication at small film thicknesses.