Sharan M, Singh M P, Aminataei A
Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi.
J Biomech Eng. 1990 Nov;112(4):457-63. doi: 10.1115/1.2891211.
A two layer model for the blood oxygenation in pulmonary capillaries is proposed. The model consists of a core of erythrocytes surrounded by a symmetrically placed plasma layer. The governing equations in the core describe the free molecular diffusion, convection, and facilitated diffusion due to the presence of haemoglobin. The corresponding equations in the plasma layer are based on the free molecular diffusion and the convective effect of the blood. According to the axial train model for the blood flow proposed by Whitmore (1967), the core will move with a uniform velocity whereas flow in the plasma layer will be fully developed. The resulting system of nonlinear partial differential equations is solved numerically. A fixed point iterative technique is used to deal with the nonlinearities. The distance traversed by the blood before getting fully oxygenated is computed. It is shown that the concentration of O2 increases continuously along the length of the capillary for a given ratio of core radius to capillary radius. It is found that the rate of oxygenation increases as the core to capillary ratio decreases. The equilibration length increases with a heterogeneous model in comparison to that in a homogeneous model. The effect of capillary diameters and core radii on the rate of oxygenation has also been examined.
提出了一种用于肺毛细血管血液氧合的两层模型。该模型由红细胞核心和对称放置的血浆层组成。核心中的控制方程描述了由于血红蛋白的存在而产生的自由分子扩散、对流和易化扩散。血浆层中的相应方程基于自由分子扩散和血液的对流效应。根据惠特莫尔（1967年）提出的血流轴向列车模型，核心将以均匀速度移动，而血浆层中的流动将充分发展。对由此产生的非线性偏微分方程组进行了数值求解。采用定点迭代技术处理非线性问题。计算了血液在完全氧合之前所经过的距离。结果表明，对于给定的核心半径与毛细血管半径之比，O2浓度沿毛细血管长度不断增加。发现氧合速率随着核心与毛细血管比率的降低而增加。与均匀模型相比，非均匀模型的平衡长度增加。还研究了毛细血管直径和核心半径对氧合速率的影响。
