Theoretical investigation on the effects of red blood cell aggregation on rheological properties of blood flowing through narrow tubes

用一些简单的模型从理论上估计了红细胞聚集和沉降对血液在狭窄管道中流动特性的影响。(1)聚集对窄水平管中血液表观粘度的影响：根据红细胞聚集倾向的程度，我们提出了两种流动模型，称为刚性核模型和双流体模型。在每个模型中，视粘度作为沉降程度的函数来计算。表观粘度随沉降程度的增加而迅速增加。这一预测与实验结果相吻合。这些模型还表明，在一定条件下，聚集性红细胞悬浮液的表观粘度低于非聚集性红细胞悬浮液。(2)聚集对窄水平管中血液的管内红细胞比容的影响：利用两种模型计算相对管内红细胞比容，并利用实验得到的无细胞层宽度与伪剪切率的关系表示为伪剪切率的函数。提示双流体模型可以定性地解释人血液相对管压比的剪切依赖性，在低剪切速率范围内，相对管压比大于1。(3)聚集对血液流动特性的时间依赖效应：利用我们之前提出的三层模型和岩心形成的动力学方程，分析了血液在低速率下流过狭窄垂直管的瞬态流动特性。聚集的红细胞核心的大小被预测为时间的函数。然后计算平均红细胞速度作为时间的函数。除了岩心形成初期的流动特性外，理论预测与实验结果吻合较好。

The effects of red cell aggregation and sedimentation on the flow properties of blood flowing through narrow tubes are theoretically estimated using some simple models.(1) Effects of aggregation on the apparent viscosity of blood in narrow horizontal tubes : Depending on a degree of aggregation tendency of red cells we proposed two flow models that are termed the rigid-core model and the two-fluid model. The apparent viscosity is calculated as a function of a degree of sedimentation in each model. The apparent viscosity increases rapidly with increasing a degree of sedimentation. This prediction is consistent with experimental results. These models also suggest the presence of a certain condition under which the apparent viscosity of aggregating red cell suspensions becomes lower than that of non-aggregating suspensions.(2) Effects of aggregation on the tube hematocrit of blood in narrow horizontal tubes : The relative tube hematocrits are calculated by using the two models and expressed as a function of pseudo-shear rate using a relationship between the width of cell-free layr and pseudo-shear rate obtained by experiments. It is suggested that the shear dependence of the relative tube hematocrit of human blood can be qualitatively explained by the two-fluid model and that the relative tube hematocrit becomes larger than unity in the range of low shear rates.(3) Time-dependent effects of aggregation on flow properties of blood : The transient flow properties of blood flowing through narrow vertical tubes at low rates are analyzed using the three-layr model and a kinetic equation for core formation, which are proposed in our previous paper. A size of the core of aggregating red cells is predicted as a function of time. Then mean red cell velocity is calculated as a function of time. Theoretical predictions are in good agreement with experimental results except flow behavior at the beginning of the core formation.