A theoretical model is developed to investigate the influence of hemoglobin-based oxygen carriers (HBOCs) on oxygen transport in capillary-size vessels. A discrete cell model is presented with red blood cells (RBCs) represented in their realistic parachute shape flowing in a single file through a capillary. The model includes the free and Hb-facilitated transport of O2 and Hb-O2 kinetics in the RBC and plasma, diffusion of free O2 in the suspending phase, capillary wall, interstitium and tissue. A constant tissue consumption rate is specified that drives the simultaneous release of O2 from RBC and plasma as the cells traverse the capillary. The model mainly focuses on low capillary hematocrits and studies the effect of free hemoglobin affinity, cooperativity and concentration. The results are expressed in the form of cell and capillary mass transfer coefficients, or inverse transport resistances, that relate the spatially averaged flux of O2 coming out of the RBC and capillary to a driving force for O2 diffusion. The results show that HBOCs at a concentration of 7 g/dl reduce the intracapillary transport resistance by as much as 60% when capillary hematocrit is 0.2. HBOCs with high O2 affinity unload most O2 at the venular end, while those with low affinity supply O2 at the arteriolar end. A higher cooperativity did not favor O2 delivery due to the large variation in the mass transfer coefficient values during O2 unloading. The mass transfer coefficients obtained will be used in simulations of O2 transport in complex capillary networks.

The problem of diffusion of O(2) across the endothelial surface in precapillary vessels and its utilization in the vascular wall remains unresolved. To establish a relationship between precapillary release of O(2) and vascular wall consumption, we estimated the intravascular flux of O(2) on the basis of published in vivo measurements. To interpret the data, we utilized a diffusion model of the vascular wall and computed possible physiological ranges for O(2) consumption. We found that many flux values were not consistent with the diffusion model. We estimated the mitochondrial-based maximum O(2) consumption of the vascular wall (M(mt)) and a possible contribution to O(2) consumption of nitric oxide production by endothelial cells (M(NO)). Many values of O(2) consumption predicted from the diffusion model exceeded M(mt) + M(NO). In contrast, reported values of O(2) consumption for endothelial and smooth muscle cell suspensions and vascular strips in vitro do not exceed M(mt). We conjecture that most of the reported values of intravascular O(2) flux are overestimated, and the likely source is in the experimental estimates of convective O(2) transport at upstream and downstream points of unbranched vascular segments.

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