Mathematical Modeling of Respiratory Gas Exchange in Capillary Tube Oxygenators with Steady Blood Flow
HARRY DIAMOND LABS ADELPHI MD ADELPHI United States
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A mathematical model for the transport of oxygen and carbon dioxide to blood flowing in semipermeable tubes under steady-flow conditions is presented. The model considers the membrane resistance to gas transport and allows for an additional interfacial resistance protein deposition, etc. The possibility of gas transport augmentation due to rotation of erythrocytes in the velocity field is included in the model however, no evidence of this augmentation was found in the flow range in which the model was compared with experimental data. The partial differential equation for the gas transport was solved numerically using a digital computer. Simultaneous solutions for oxygen and carbon dioxide were obtained, and the pH was computed for any point in the tube. Comparison of experimental data obtained by the author and other investigators with the curves predicted by the model shows excellent agreement. The numerical solution of the transport equation yields the bulk average values of pH, carbon dioxide partial pressure, and oxygen saturation, as well as the internal value of these parameters as a function of tube length and radius. A simple steady flow design equation, which is a reasonable approximation of the computer results for a wide range of venous blood conditions, is presented.