Analysis of oxygen delivery and uptake relationships in the Krogh tissue model

Normally, tissue O₂ uptake (V̇O₂) is set by metabolic activity rather than O₂ delivery (Q̇O₂ = blood flow x arterial O₂ content). However, when Q̇O₂ is reduced below a critical level, V̇O₂ becomes limited by O₂ supply. Experiments have shown that a similar critical Q̇O₂ exists, regardless of whether O₂ supply is reduced by progressive anemia, hypoxemia, or reduction in blood flow. This appears inconsistent with the hypothesis that O₂ supply limitation must occur by diffusion limitation, since very different mixed venous PO₂ values have been seen at the critical point with hypoxic vs. anemic hypoxia. The present study sought to begin clarifying this paradox by studying the theoretical relationship between tissue O₂ supply and uptake in the Krogh tissue cylinder model. Steady-state O₂ uptake was computed as O₂ delivery to tissue representative of whole body was gradually lowered by anemic, hypoxic, or stagnant hypoxia. As diffusion began to limit uptake, the fall in V̇O₂ was computed numerically, yielding a relationship between Q̇O₂ and V̇O₂ in both supply-independent and O₂ supply-dependent regions. This analysis predicted a similar biphasic relationship between Q̇O₂ and V̇O₂ and a linear fall in V̇O₂ at O₂ deliveries below a critical point for all three forms of hypoxia, as long as intercapillary distances were ≤80 μm. However, the analysis also predicted that O₂ extraction at the critical point should exceed 90%, whereas real tissues typically extract only 65-75% at that point. When intercapillary distances were larger than ~80 μm, critical, O₂ extraction ratios in the range of 65-75% could be predicted, but the critical point became highly sensitive to the type of hypoxia imposed, contrary to experimental findings. Predicted gas exchange in accord with real data could only be simulated when a postulated 30% functional peripheral O₂ shunt (arterial admixture) was combined with a tissue composed of Krogh cylinders with intercapillary distances of ≤80 μm. The unrealistic efficacy of tissue O₂ extraction predicted by the Krogh model (in the absence of postulated shunt) may be a consequence of the assumed homogeneity of tissues, because real tissues exhibit many forms of heterogeneity among capillary units. Alternatively, the failure of the original Krogh model to fully predict tissue O₂ supply dependency may arise from basic limitations in the assumptions of that model.