A numerical model for blood oxygenation in the pulmonary capillaries--effect of pulmonary membrane resistance

A study of the blood oxygenation in pulmonary capillaries is made by considering the transport mechanisms of molecular diffusion, convection and the facilitated diffusion due to the presence of haemoglobin. The resistance offered by the pulmonary membrane on the transport of gases has been incorporated. The resulting system of coupled, non-linear partial differential equations is solved numerically. It is found that, in the immediate neighbourhood of the entry, the amount of dissolved O2 decreases. This decreases further as the resistance offered by the pulmonary membrane increases. The rate of oxygenation of blood increases as the permeability coefficient for O2 (PO) increases. It is shown that the ideally permeable case for both O2 and CO2 can be approximated by taking PO approximately 10 cm/s. Further, it is shown that the oxygen takes longest and CO2 is the fastest to attain equilibration. The equilibration length increases as the resistance offered by the membrane increases. Finally, some of the pulmonary diseases such as pulmonary oedema and fibrosis have been analyzed.