Sharan M, Singh M P, Singh B
Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi, Hauz Khas.
IMA J Math Appl Med Biol. 1991;8(2):125-40. doi: 10.1093/imammb/8.2.125.
A mathematical model is described for the process of gas exchange in pulmonary capillaries by taking into account the transport mechanisms of molecular diffusion, convection, and the facilitated diffusion due to haemoglobin. The nth-order one-step kinetics of oxygen uptake by haemoglobin has been incorporated. The rate k at which blood becomes oxygenated is determined by setting up an appropriate eigenvalue problem. This method eventually leads to a transcendental equation in k. A multiprecision technique due to Verma and Sharan (1980) is employed to obtain a physically acceptable solution. It is shown that, at equilibrium, the saturation of haemoglobin with oxygen computed from the analysis is fairly close to the data of Severinghaus (1966). It was found that 97.15% of the total haemoglobin combined with oxygen. The blood is oxygenated well before it leaves the pulmonary capillary. The dissolved oxygen takes longer to achieve equilibration whereas the carbon dioxide traverses a comparatively smaller distance in the capillary.
通过考虑分子扩散、对流以及血红蛋白介导的易化扩散等传输机制，描述了一个用于肺毛细血管气体交换过程的数学模型。该模型纳入了血红蛋白摄取氧气的n阶一步动力学。通过建立适当的特征值问题来确定血液被氧合的速率k。此方法最终导致一个关于k的超越方程。采用了Verma和Sharan（1980）提出的多精度技术来获得一个符合物理实际的解。结果表明，在平衡状态下，通过分析计算得到的血红蛋白氧饱和度与Severinghaus（1966）的数据相当接近。发现总血红蛋白的97.15%与氧气结合。血液在离开肺毛细血管之前就已充分氧合。溶解氧达到平衡所需时间更长，而二氧化碳在毛细血管中穿过的距离相对较短。
