A compartmental model for oxygen transport in brain microcirculation in the presence of blood substitutes

A compartmental model is developed for oxygen (O₂) transport in brain microcirculation in the presence of blood substitutes (hemoglobin-based oxygen carriers). The cerebrovascular bed is represented as a series of vascular compartments, on the basis of diameters, surrounded by a tissue compartment. A mixture of red blood cells (RBC) and plasma/extracellular hemoglobin solution flows through the vascular bed from the arterioles through the capillaries to the venules. Oxygen is transported by convection in the vascular compartments and by diffusion in the surrounding tissue where it is utilized. Intravascular resistance and the diffusive loss of oxygen from the arterioles to the tissue are incorporated in the model. The model predicts that most of the O₂ transport occurs at the level of capillaries. Results computed from the present model in the presence of hemoglobin-based oxygen carriers are consistent with those obtained from the earlier validated model (Sharan et al., 1989, 1998a) on oxygen transport in brain circulation in the absence of extracellular hemoglobin. We have found that: (a) precapillary PO₂ gradients increase as PO₂ in the arterial blood increases, P_50p (oxygen tension at 50% saturation of hemoglobin with O₂ in plasma) decreases, i.e. O₂ affinity of the extracellular hemoglobin is increased, the flow rate of the mixture decreases, hematocrit decreases at constant flow, metabolic rate increases, and intravascular transport resistance in the arterioles is neglected; (b) precapillary PO₂ gradients are not sensitive to (i) intracapillary transport resistance, (ii) cooperativity (n_p) of hemoglobin with oxygen in plasma, (iii) hemoglobin concentration in the plasma and (iv) hematocrit when accounting for viscosity variation in the flow; (c) tissue PO₂ is not sensitive to the variation of intravascular transport resistance in the arterioles. We also found that tissue PO₂ is a non-monotonic function of the Hill coefficient n_p for the extracellular hemoglobin with a maximum occurring when n_p equals the blood Hill coefficient. The results of the computations give estimates of the magnitudes of the increases in tissue PO₂ as arterial PO₂ increases, P_50p increases, flow rate increases, hematocrit increases, hemoglobin concentration in the plasma increases, metabolic rate decreases, the capillary mass transfer coefficient increases or the intracapillary transport resistance decreases.