Prediction of Microcirculatory Oxygen Transport by Erythrocyte/Hemoglobin Solution Mixtures

A mathematical model has been developed to predict oxygen transport by erythrocyte/acellular hemoglobin solution mixtures flowing in arteriolar-sized vessels (20 to 100 μm diameter). The model includes erythrocyte and extracellular hemoglobin solution phases, radial hematocrit and velocity gradients, axial convection, and radial diffusion of both oxygen and oxyhemoglobin. Model simulations were compared with experimental data from anin vitrocapillary model where all of the geometric, physical, and transport parameters are known accurately. A new approach to shear augmentation of transport in 25-μm-diameter conduits was developed. Comparison of theory with experiment suggests that shear augmentation in this flow regime is primarily an extracellular phenomenon produced by cell–cell interactions. Negligible shear augmentation was seen in erythrocyte suspensions in plasma due to the relatively low solubility of oxygen in the plasma phase. Good agreement was found between the theoretical simulations and experimental data for release experiments even neglecting shear augmentation. However, treatment of shear augmentation significantly improved agreement between theoretical simulations and experimental data for oxygen uptake. The model was used to determine the effects on oxygen transport of varying extracellular hemoglobin concentration and extracellular hemoglobin oxygen binding characteristics. It is known that hemoglobin solutions transport oxygen more efficiently than erythrocyte suspensions of the same overall hemoglobin content. Model simulations show that erythrocyte/hemoglobin solution mixtures with 30% extracellular hemoglobin transport oxygen with virtually the same efficiency as pure hemoglobin solutions of the same overall hemoglobin content. Additional simulations predict that erythrocyte/hemoglobin solution mixtures transport oxygen more efficiently than Rbc suspensions, even if the extracellular hemoglobin has a high oxygen affinity.