Heart Rate Dynamics Identification and Control in Cycle Ergometer Exercise: Comparison of First- and Second-Order Performance

Background: Accurate and robust feedback control of human heart rate is important for exercise testing and prescription. Feedback controllers can be designed using first-order, linear, time-invariant models of heart rate dynamics, but it remains to investigate whether second-order models lead to better identification and control performance. The distinguishing contribution of this research is the direct employment of established physiological principles to determine model structure, and to focus the feedback-design goals: cardiac physiology proposes a two-phase second-order response, delineated into fast and slow components; the natural phenomenon of broad-spectrum heart-rate variability motivates a novel feedback design approach that appropriately shapes the input-sensitivity function. Aim: The aim of this work was to compare the fidelity of first- and second-order models of heart rate response during cycle-ergometer exercise, and to compare the accuracy and dynamics of feedback controllers that were designed using the two model structures. Methods: Twenty-seven participants each took part in two identification tests to generate separate estimation and validation data sets, where ergometer work rate was a pseudo-random binary sequence and in two feedback tests where controllers were designed using the first- or second-order models. Results: Second-order models gave substantially and significantly higher model fit (51.9% vs. 47.9%, p < 0.0001; second order vs. first order) and lower root-mean-square model error (2.93 bpm vs. 3.21 bpm, p < 0.0001). There was modest improvement in tracking accuracy with controllers based on second-order models, where mean root-mean-square tracking errors were 2.62 bpm (second order) and 2.77 bpm (first order), with p = 0.052. Controllers based on second-order models were found to be substantially and significantly more dynamic: mean values of average control signal power were 9.61 W2 and 7.56 W2, p < 0.0001. Conclusion: The results of this study confirm the hypotheses that second-order models of heart-rate dynamics give better fidelity than first-order models, and that feedback compensator designs that use the additional dynamic mode give more accurate and more dynamic closed-loop control performance.