Identifying time-varying dynamics of heart rate and oxygen uptake from single ramp incremental running tests

Objective. The fact that ramp incremental exercise yields quasi-linear responses for pulmonary oxygen uptake ( V ˙ O 2 ) and heart rate (HR) seems contradictory to the well-known non-linear behavior of underlying physiological processes. Prior research highlights this issue and demonstrates how a balancing of system gain and response time parameters causes linear V ˙ O 2 responses during ramp tests. This study builds upon this knowledge and extracts the time-varying dynamics directly from HR and V ˙ O 2 data of single ramp incremental running tests. Approach. A large-scale open access dataset of 735 ramp incremental running tests is analyzed. The dynamics are obtained by means of 1st order autoregressive and exogenous models with time-variant parameters. This allows for the estimates of time constant (τ) and steady state gain (SSG) to vary with work rate. Main results. As the work rate increases, τ-values increase on average from 38 to 132 s for HR, and from 27 to 35 s for V ˙ O 2 . Both increases are statistically significant (p < 0.01). Further, SSG-values decrease on average from 14 to 9 bpm (km·h ⁻¹) ⁻¹ for HR, and from 218 to 144 ml·min ⁻¹ for V ˙ O 2 (p < 0.01 for decrease parameters of HR and V ˙ O 2 ). The results of this modeling approach are line with literature reporting on cardiorespiratory dynamics obtained using standard procedures. Significance. We show that time-variant modeling is able to determine the time-varying dynamics HR and V ˙ O 2 responses to ramp incremental running directly from individual tests. The proposed method allows for gaining insights into the cardiorespiratory response characteristics when no repeated measurements are available.