An easy-to-use model for O2 supply to red muscle. Validity of assumptions, sensitivity to errors in data

An easy-to-use capillary cylinder model of O2 supply to muscle is presented that considers all those factors that are known to be most important for realistic results: (1) red blood cell (RBC) O2 unloading along the capillary, (2) effects of the particulate nature of blood, (3) free and hemoglobin-facilitated O2 diffusion and reaction kinetics inside RBCs, (4) free and myoglobin-facilitated O2 diffusion inside the muscle cell, and (5) carrier-free region separating RBC and tissue. In a first approach, a highly simplified yet reasonably accurate treatment of the complex three-dimensional oxygen diffusion field in and next to capillaries is employed. As an alternative, a more realistic description using RBC/capillary diffusing capacity has been included. Model development proceeds step by step and is designed to be easily comprehensible for a broad readership. In spite of the number of features accounted for, the model is simple to apply, even for scientists not specialized in the field of modeling. PO2 distributions calculated by the model are in good qualitative agreement with experimental data and with former modelling results. By means of suitable extensions to the model that are also developed it is shown for a wide range of muscle performances that quite generally the following complication may be neglected safely: (1) complexity of O2 diffusion field near capillaries, (2) deviations of capillary domain cross sections from the circular shape, (3) O2 diffusion parallel to the capillary direction, and (4) PO2 dependence of O2 consumption rate. Finally, a sensitivity analysis is performed in which propagation of errors in the input data into the results is investigated. The interpretation of the calculated sensitivities gives insights in the specific dependencies of muscular O2 supply on the various input parameters. Moreover, basic interrelations governing carrier-facilitated diffusional O2 transport to muscle become apparent and are discussed.