Modelling heart rate dynamics in relation to speed and power output in sprint kayaking as a basis for training evaluation and optimisation

With the development of power output sensors in the field of paddle sports and the ongoing advancements in dynamical analysis of exercise data, this study aims to model the measurements of external training intensity in relation to heart rate (HR) time-series during flat-water kayak sprint. Nine elite athletes performed a total of 47 interval training sessions with incremental intensity (light to (sub-) maximal effort levels). The data of HR, speed and power output were measured continuously and rating of perceived exertion and blood lactate concentration ([BLa]) were sampled at the end of each interval stage. Different autoregressive-exogenous (ARX) modelling configurations are tested, and we report on which combination of input (speed or power), model order (1st or 2nd), parameter estimation method (time-(in)variant) and training conditions (ergometer or on-water) is best suited for linking external to internal measures. Average model R² values varied between 0.60 and 0.97, with corresponding average root mean square error values of 15.6 and 3.2 bpm. 1st order models with time-varying (TV) parameter estimates yield the best model performance (average R² = 0.94). At the level of the individual athlete, the TV modelling features (i.e., the model parameters and derivatives such as time constant values) show significant repeated measure correlations in relation to measures of exercise intensity. In conclusion, the study provides a comprehensive description of how the dynamic relationship between external load and HR for sprint kayaking training data can be modelled. Such models can be used as a basis for improving training evaluation and optimisation.