Diffusion limitation of O2 supply to tissue in homogeneous and heterogeneous models.

The role of diffusion limitation in O2 supply was studied in cross-sectional elements of the Krogh cylinder model (with O2 supply from a central capillary) and of the solid cylinder model (with O2 supply from the outer surface). The effect of diffusion limitation was quantified in terms of the ratio O2 uptake/O2 requirement (= fraction of cross-sectional area supplied with O2), assuming local O2 requirement per unit volume to be constant and independent of PO2 at PO2 greater than 0. Calculations were performed for single cylinders of varied radius and O2 requirement (homogeneous models). Unequal distribution of diffusion conditions was represented by a model composed of three sorts of Krogh or solid cylinders, with radii in relation 3: square root of 3:1, but of equal cross-sectional area, i.e. number of cylinders of each sort in relation 1:3:9 (heterogeneous models). The results revealed the following main features. (1) At the same outer radius, diffusion limitation sets in at a smaller O2 requirement, and increases more steeply with increasing O2 requirement, in the homogeneous Krogh cylinder model compared with the homogeneous solid cylinder model. A similar behavior is observed when the radius of the cylinder section is increased at constant O2 requirement. (2) Diffusion limitation in the heterogeneous model sets in at a lower O2 requirement value, and increases more gradually with increasing O2 requirement, than in the corresponding homogeneous models with the same average cylinder diameter. This behavior is due to sequential onset, in the heterogeneous model, of anoxia in the cylinder sections of different radii. We conclude that diffusion heterogeneity has to be taken into account when the role of diffusion limitation in tissue O2 supply is investigated.