This study presents and evaluates a new mathematical model of V̇O2 on-kinetics, with the following properties: (i) a progressively slower primary phase following the size-principle of motor unit recruitment, explaining the delayed V̇O2 steady state seen in the heavy exercise intensity domain, and (ii) a severe-domain slow component modelled as a time-dependent decrease in efficiency. Breath-by-breath V̇O2 measurements from eight subjects performing step cycling transitions, in the moderate, heavy and severe exercise domains, were fitted to the conventional 3-phase model and the new model. Model performance was evaluated with a residual analysis and by comparing Bayesian (BIC) and corrected Akaike (AICc) information criteria. The residual analysis showed no systematic deviations, except perhaps for the initial part of the primary phase. BIC favored the new model, being 9.3 (SD 7.1) lower than the conventional model while AICc was similar between models. Compared to the conventional 3-phase model, the proposed model distinguishes between the kinetic adaptations in the heavy and severe domains by predicting a delayed steady state V̇O2 in the heavy and no steady state V̇O2 in the severe domain. This allows to determine when stable oxygen costs of exercise are attainable and it also represents a first step in defining time-dependent oxygen costs when stable energy conversion efficiency is not attainable.
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