Algebraic analysis of the determinants of VO2,max

Considerable evidence exists to support the idea that maximum oxygen consumption in exercising mammals is determined by the quantitative interaction between diffusive and convective factors involved in the transport of oxygen between the environment and the muscle mitochondria. To complement experimental tests of this hypothesis as well as numerical modeling of the interaction between diffusion and convection, both in the lungs and tissues, this paper reports an analytical (algebraic) model of diffusive/convective interaction made possible by replacing oxygen by a hypothetical gas of similar effective solubility, obeying Henry's law. The model describes a homogeneous but potentially diffusion-limited lung arranged in series via the circulation with a homogeneous but potentially diffusion-limited muscle. Steady-state transport of gas through this system and its subsequent tissue utilization are described by three equations: (1) mass balance across the lungs, (2) diffusive transport across the lungs, and (3) diffusive transport in the tissues. The latter two equations involve interaction between diffusive and perfusive (convective) elements of gas transport. Independent variables in this analysis are inspired partial pressure, alveolar ventilation, cardiac output, effective solubility of the gas, and diffusing capacities of the lungs and of the tissues. Dependent variables are alveolar, arterial, and venous partial pressures and hence maximum O2 uptake by the tissues (VO2,max). Evaluation of this model in both normoxia and severe hypoxia is described. In normoxia, VO2,max is shown to be affected by all independent variables, but mostly by blood flow. However, in severe hypoxia, VO2,max, based on data from Operation Everest II, becomes more sensitive to muscle diffusing capacity and less so to blood flow. In normoxia, normal sea level values of the independent variables set VO2,max at a point where little further gain in VO2 would be seen without large increases in diffusive or convective properties. On the other hand, there is relatively little reserve, such that decreases in transport parameters would result in significant reductions in VO2,max.