A theoretical model for gas transport and acid/base regulation by blood flowing in microvessels

Abstract

An investigation was made of the coupling between O2 and CO2 transport by blood flowing in microvessels. The blood was treated as two continuous coexisting phases: a red blood cell (RBC) phase and a plasma phase. The microvessel was divided into two regions: the central, RBC-rich and the outer, cell-free region. The radial distribution of RBCs and transport of various species due to bulk convection and radial diffusion were taken into account. Chemical and transport processes which were included in the model are (1) interactions of hemoglobin with O2 and CO2, (2) the Bohr and Haldane effects (the inter-dependence of O2/CO2 transport), (3) CO2 hydration-dehydration reactions, (4) buffering actions of hemoglobin and plasma proteins, and (5) anion exchange across the red cell membrane. The governing equations of the model subjected to the imposed inlet and boundary conditions were solved numerically to provide the concentration distributions of various species in blood that are important in the simultaneous gas exchange and pH regulation process. Predictions of the new model of simultaneous O2/CO2 transport by flowing blood were shown to be in excellent agreement with prior workers' experimental results from large artificial membrane tubes. A previous mathematical model which treats blood as a homogeneous continuum and uses a local chemical equilibrium approximation to describe the gas transport was shown to satisfactorily predict the amount of O2 transport for blood oxygenation accompanied by CO2 elimination. However, the previous model significantly underpredicts O2 transfer for blood deoxygenation accompanied by CO2 uptake. Furthermore, the previous model disagrees substantially with the CO2 transport results under both oxygenation and deoxygenation conditions.