Mathematical modelling of the oxygen uptake kinetics during whole-body endurance exercise and recovery

In this study, we elucidate four different mathematical models of the kinetics of oxygen uptake during whole-body endurance exercise at different intensities and throughout the subsequent recovery periods. We employ the hypothetical inductive–deductive method and forecast four different models for the oxygen kinetic. The VO₂ development using these models compared with experimental results where an elite cross-country skier performed laboratory tests while running with poles on a treadmill, in which the rate of oxygen uptake and blood lactate concentration as a function of time were measured. The most developed model accounted for the delayed superimposed slow component of oxygen uptake and the influence of lactic power production on the oxygen kinetics. The rate of change in oxygen with this model is consistent with the accumulated oxygen deficit model and matched the data well, even for intensities above the lactate threshold and during recovery.