A compartmental model for oxygen-carbon dioxide coupled transport in the microcirculation

We present a multicompartmental model for an oxygen-carbon dioxide transport system. The compartmental equations and their lumped parameters are derived through space averaging of the corresponding distributed model. The model can predict compartmental distributions of oxygen and carbon dioxide partial pressures, oxygen-hemoglobin saturation, and pH. Other unique features include the effects of the radial distribution of partial pressures and the difference in metabolic rates between vessel wall and tissue. A model for the cat brain, based on this formulation, is compared with results of experiments and with two types of earlier models: one without space averaging and one without carbon dioxide transport. The results suggest that space averaging the convective terms significantly affects the behavior of the model. This is consistent with conclusions from our earlier oxygen-only model. Our observations also demonstrate, however, significant differences between the results from the oxygen-carbon dioxide model and the oxygen-only model. For instance, at low blood flow rates or at low level of oxygen input, predicted oxygen partial pressures can differ by as much as 30% between the two models. Results obtained from the present model are supported by available experimental findings.