Modeling V?O2 and V?CO2 with Hammerstein-Wiener Models

V̇ O2 and V̇CO2 measurements are central to methods for assessment of physical fitness and endurance capabilities in athletes. As measuring V̇ O2 and V̇CO2 is difficult outside a lab, models with good prediction properties are necessary for online analysis and modeling in the field. Easier to measure are heart rate and during cycling also power. Thus, the here described models are based on either one of them or both. It is commonly accepted that the relationship between power and V̇ O2, V̇CO2 and heart rate can be described by a linear and a nonlinear component. The latter describes a drift over time without increase in workload. Thus, block-structured systems such as Hammerstein-Wiener models with linear and nonlinear elements can be employed for modeling and prediction. Modeling and prediction power of these models is compared with a dynamic model based on physiological evidence. Our findings show that the simpler Hammerstein-Wiener model performs slightly better for both modeling and prediction with the advantage of being easier to estimate and evaluate. Overall, both models performed with errors smaller than the range of the natural variability of the modeled quantities. Thus, such models allow for applications in the field where V̇ O2 and V̇CO2 cannot be measured.