Kinetic analysis of oxygen dynamics under a variable work rate

Measurements of oxygen uptake are central to methods for the assessment of physical fitness and endurance capabilities in athletes. Two important parameters extracted from such data of incremental exercise tests are the maximal oxygen uptake and the critical power. A commonly accepted model of the dynamics of oxygen uptake during exercise at a constant work rate comprises a constant baseline oxygen uptake, an exponential fast component, and another exponential slow component for heavy and severe work rates. We have generalized this model to variable load protocols with differential equations that naturally correspond to the standard model for a constant work rate. This provides the means for predicting the oxygen uptake response to variable load profiles including phases of recovery. The model parameters have been fitted for individual subjects from a cycle ergometer test, including the maximal oxygen uptake and critical power. The model predictions have been validated by data collected in separate tests. Our findings indicate that the oxygen kinetics for a variable exercise load can be predicted using the generalized mathematical standard model. Such models can be applied in the field where the constant work rate assumption generally is not valid.