Time-variant modelling of heart rate responses to exercise intensity during road cycling

The aim of this study was to determine if heart rate responses to training intensity during road cycling could be modelled with compact time-variant mathematical model structures. The model performance was evaluated in terms of model order (complexity), number of inputs and parameter estimation methods used (time-invariant vs. time-variant). Thirteen male cyclists performed two identical cycling tests of 27 km on the road. Uphill sections were introduced to induce dynamic variations in heart rate. The heart rate and training intensity, represented by power output and road inclination, were measured in real-time. Taking only power as system input allowed to explain the variations in heart rate in an accurate way R2 T = 0.86 ± 0.08, since adding the road inclination as an additional input did not significantly improve the modelling performance R2 T = 0.87 ± 0.08, P = 0.32. Furthermore, we demonstrated that models with first-order dynamics accurately describes the heart rate responses to power variations R2 T = 0.86 ± 0.08, but that more complex second-order model structures R2 T = 0.88 ± 0.08 were significantly better than the first-order model structures (P = 0.028). Finally, the heart rate dynamics appeared to be time-variant, since the time-variant model structures R2 T = 0.89 ± 0.07 were significantly better than the time-invariant model structures R2 T = 0.84 ± 0.08, P = 0.0002. So, compact time-variant second-order model structures could be used to model the heart rate response to training intensity as a basis for training optimisation.