Theoretical analysis of oxygen supply to contracted skeletal muscle.

Honig and collaborators reported striking contradictions in current understanding of O2 supply to working skeletal muscle. Therefore we re-examined the problem by means of a new composite computer simulation. As inclusion of erythrocytic O2 desaturation and oxygen transport and consumption inside the muscle cell into a single model would entail immense numerical difficulties, we broke up the whole process into its several components: O2 desaturation of erythrocytes O2 transport and consumption in muscle fiber capillary transit time characterizing the period of contact between red cell and muscle fiber. "Erythrocyte model" as well as "muscle fiber model" both consist of a central core cylinder surrounded by a concentric diffusion layer representing the extracellular resistance to O2 diffusion (Fig. 1). Resistance layers in both models are to be conceived of as one and the same anatomical structure--even though in each model their shape is adapted to the respective geometry. By means of this overlap region a spatial connexion between both is given, whereas temporal coherence governing O2 fluxes and red cell spacing is derived from capillary transit time. Analysis of individual components is outlined as follows: Assuming axial symmetry of the problem a numerical algorithm was employed to solve the parabolic system of partial differential equations describing red cell O2 desaturation. Hb-O2 reaction kinetics, free and facilitated O2 diffusion in axial and radial directions, and red cell movement in capillary were considered. Resulting time courses of desaturation, which are considerably faster than the ones computed by Honig et al., are given in the following table (see also Fig. 3). (Formula: see text) Furthermore, we studied the respective importance of the several processes included in our model: Omission of longitudinal diffusion increased desaturation time by 15% to 23%, whereas effects of reaction kinetics and axial movement were 5% and 2% respectively. For time courses see Fig. 2. Nature and magnitude of extra-erythrocytic resistance to O2 diffusion playing a prominent part in O2 desaturation are scarcely explored. Calculated desaturation times based upon our new estimates (line 3 of above table) correspond well, however, with findings by Sinha, who observed 1.75 to 4-fold prolongation in omental and mesenteric capillaries compared to desaturation through equivalent plasma layers. The 3-dimensional elliptic system of partial differential equations describing stationary O2 transport through resistance layer and subsequent free and facilitated O2 diffusion and O2 consumption in muscle fiber was solved analytically.(ABSTRACT TRUNCATED AT 400 WORDS)