A theoretical model for studying the rate of oxygenation of blood in pulmonary capillaries

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Abstract
A mathematical analysis of the process of gas exchange in the lung is presented taking into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion of the species due to haemoglobin. Since the rate at which blood gets oxygenated in the pulmonary capillaries is very fast, it is difficult to set up an experimental study to determine the effects of various parameters on equilibration rate. The proposed study is aimed at determining the effects of various physiological parameters on equilibration rate in pathological conditions. Among the significant results are that 1. dissolved oxygen takes longer to achieve equilibration across the pulmonary membrane and carbon dioxide attains equilibration faster, 2. the equilibration length increases with increase in blood velocity, haemoglobin concentration, calibre of pulmonary capillaries and fall in alveolar PO2, 3. the alveolar PCO2 and forward and backward reaction rates of haemoglobin with CO2 do not materially affect the equilibration rate or length. 4. At complete equilibration, by the end of the pulmonary capillary 92% of the total haemoglobin has combined with oxygen and 8% free pigment is left which is present as carbamino haemoglobin, met haemoglobin, carboxy haemoglobin etc. These results are of some importance for anaemic conditions, muscular exercise, meditation, altitude physiology, hypo-ventilation, hyperventilation, etc.