Whiteley J P, Gavaghan D J, Hahn C E
Nuffield Department of Anaesthetics, University of Oxford, Radcliffe Infirmary, Woodstock Road, OX2 6HE, Oxford, UK.
Math Biosci. 2001 Feb;169(2):153-72. doi: 10.1016/s0025-5564(00)00060-2.
In this study we investigate the equations governing the transport of oxygen in pulmonary capillaries. We use a mathematical model consisting of a red blood cell completely surrounded by plasma within a cylindrical pulmonary capillary. This model takes account of convection and diffusion of oxygen through plasma, diffusion of oxygen through the red blood cell, and the reaction between oxygen and haemoglobin molecules. The velocity field within the plasma is calculated by solving the slow flow equations. We investigate the effect on the solution of the governing equations of: (i) mixed-venous blood oxygen partial pressure (the initial conditions); (ii) alveolar gas oxygen partial pressure (the boundary conditions); (iii) neglecting the convection term; and (iv) assuming an instantaneous reaction between the oxygen and haemoglobin molecules. It is found that: (a) equilibrium is reached much more rapidly for high values of mixed-venous blood and alveolar gas oxygen partial pressure; (b) the convection term has a negligible effect on the time taken to reach a prescribed degree of equilibrium; and (c) an instantaneous reaction may be assumed. Explanations are given for each of these results.
在本研究中，我们研究了肺毛细血管中氧气传输的控制方程。我们使用一个数学模型，该模型由一个完全被圆柱形肺毛细血管内的血浆包围的红细胞组成。该模型考虑了氧气在血浆中的对流和扩散、氧气在红细胞中的扩散以及氧气与血红蛋白分子之间的反应。通过求解缓慢流动方程来计算血浆内的速度场。我们研究了以下因素对控制方程解的影响：（i）混合静脉血氧分压（初始条件）；（ii）肺泡气氧分压（边界条件）；（iii）忽略对流项；以及（iv）假设氧气与血红蛋白分子之间存在瞬时反应。结果发现：（a）对于高混合静脉血和肺泡气氧分压值，平衡达到得要快得多；（b）对流项对达到规定平衡程度所需的时间影响可忽略不计；（c）可以假设存在瞬时反应。针对每个结果都给出了解释。
