Identification of heart rate dynamics during moderate-to-vigorous treadmill exercise

Abstract

Background: Heart rate can be used to prescribe exercise intensity for development and maintenance of cardiorespiratory fitness. The aim of this study was to identify the dynamics of heart rate response during moderate-to-vigorous treadmill exercise and to explore parameter dependencies with respect to time, intensity level and step-change direction. The focus was on simple approximate models for subsequent design of heart rate control systems. Methods: 24 healthy, able-bodied male subjects each did two separate, 35-min tests on a treadmill, one at moderate and one at vigorous intensity. Each test had four individual upward and downward steps (1-4). Heart rate responses were modelled as first-order transfer functions with steady-state gain k and time constant $$\tau$$ τ. Models were estimated both for the overall testing periods and for individual step responses within each test. Results: There were no significant differences in the overall mean values of k [24.3 vs 24.1 bpm/(m/s), $$p = 0.88$$ p = 0.88 ] and $$\tau$$ τ (55.7 vs 59.5 s, $$p = 0.53$$ p = 0.53 ) between the two intensity levels. The overall nominal gain for both conditions was $$k = 24.2 \pm 8.3$$ k = 24.2 ± 8.3 , 21.9-26.6 bpm/(m/s) (mean $$\pm$$ ± standard deviation, 95 % confidence interval), and the overall nominal time constant was $$\tau = 57.6 \pm 23.6$$ τ = 57.6 ± 23.6 , 50.9-64.3 s. Analysis of models estimated from the individual steps revealed a significant difference in steady-state gain k for upward and downward steps [30.2 vs 23.6 bpm/(m/s), $$p < 0.001$$ p < 0.001 ], but no difference in time constant $$\tau$$ τ between these two directions (57.5 vs 54.4 s, $$p = 0.52$$ p = 0.52 ). For gain k, there was no significant main effect of intensity ( $$p = 0.35$$ p = 0.35 ) or intensity-time ( $$p = 0.86$$ p = 0.86 ) interactions, but there was a significant main effect of time ( $$p < 0.001$$ p < 0.001 ). Pairwise comparison with respect to time showed a significant difference between the upward steps at times 1 and 3 [33.0 vs 27.3 bpm/(m/s), $$p < 0.01$$ p < 0.01 ], but no significant difference between the downward steps at times 2 and 4 [24.4 vs 22.8 bpm/(m/s), $$p = 1.0$$ p = 1.0 ]. For time constant $$\tau$$ τ , there were no significant main effects of intensity ( $$p = 0.36$$ p = 0.36 ) or time ( $$p = 0.89$$ p = 0.89 ), or intensity-time interactions ( $$p = 0.23$$ p = 0.23 ). Conclusions: The tight CI-bounds obtained, and the observed parameter dependencies, suggest that the overall nominal model with$$k = 24.2$$k = 24.2 and$$\tau = 57.6$$τ = 57.6 might serve as the basis for design of a linear time-invariant (LTI) feedback system for real-time control of heart rate. Future work should focus on this hypothesis and on direct comparison of LTI and nonlinear/time-varying control approaches.