Quantifying time-varying dynamics of heart rate and oxygen uptake during incremental exercise tests

Abstract Biological systems have the ever-intriguing capacity to deal with disturbances and challenges from their environment. Exercise and sports are no different when it comes to studying systems (i.e. the human body) under stress. The goal of this study is to model the dynamic responses of heart rate (HR) and oxygen uptake (⩒O 2 ) during incremental exercise tests, and identify changes in the characteristic response time and amplitude gain. Therefore, we study data of 992 maximal effort running tests from an open access dataset. First order autoregressive-exogenous (ARX) models with time-varying parameters accurately fit the data (R² > 0.98) and indicate overall faster dynamics for ⩒O 2 in comparison to HR. Furthermore, the models demonstrate significant slowing down of these dynamics at exhaustion and during the first moments of recovery for both physiological variables. In addition, the (steady state) gain values for HR and ⩒O 2 decrease from start to end of the test. Finally, small but significant linear correlations are found between the model characteristics and ⩒O 2 max of the test subjects. The results illustrate that using low-complexity linear model structures with time-varying parameter estimates allows for capturing important non-linear behaviour of cardiorespiratory responses during exercise from rest to exhaustion and recovery afterwards.