A numerical model for the simultaneous transport of oxygen and carbon dioxide in the systemic capillaries and surrounding tissue

A mathematical model is formulated for the simultaneous transport of oxygen (O2) and carbon dioxide (CO2) in the systemic capillaries and surrounding tissue. The model takes into account the molecular diffusion, convection and the consumption of O2 and the production of CO2 in the tissue due to metabolism. The interaction of O2 and CO2 in the blood is incorporated using non-linear functions to represent O2 and CO2 dissociation curves depending on both O2 and CO2 in the blood. The formulation leads to a coupled system of nonlinear partial differential equations. A finite difference technique of O((Δ r1)2, (Δ r2)2, Δ z) along with a line iterative approach is described to solve the governing equations of the model together with the physiologically relevant boundary conditions. It is shown that the interaction of O2 and CO2 in the blood plays an important role in the removal of CO2 from the tissue whereas its effect is not significant on the delivery of O2 to tissue. It is found that by considering the interaction of O2 and CO2 in the blood, the accumulation of the total CO2 is reduced by about 44% of the total CO2 exchanged in the tissue. The sensitivity analysis shows that the PO2 (PCO2) in the tissue decreases (increases) with the decrease of blood velocity and increase of metabolic rate. © 2006 IOS Press and the authors.