Identification of heart rate dynamics during treadmill exercise: comparison of first- and second-order models

Background: Characterisation of heart rate (HR) dynamics and their dependence on exercise intensity provides a basis for feedback design of automatic HR control systems. This work aimed to investigate whether the second-order models with separate Phase I and Phase II components of HR response can achieve better fitting performance compared to the first-order models that do not delineate the two phases. Methods: Eleven participants each performed two open-loop identification tests while running at moderate-to-vigorous intensity on a treadmill. Treadmill speed was changed as a pseudo-random binary sequence (PRBS) to excite both the Phase I and Phase II components. A counterbalanced cross-validation approach was implemented for model parameter estimation and validation. Results: Comparison of validation outcomes for 22 pairs of first- and second-order models showed that root-mean-square error (RMSE) was significantly lower and fit (normalised RMSE) significantly higher for the second-order models: RMSE was 2.07 bpm ± 0.36 bpm vs. 2.27 bpm ± 0.36 bpm (bpm = beats per min), second order vs. first order, with p = 2.8 × 10^{−10} ; fit was 54.5% ± 5.2 % vs. 50.2% ± 4.8 %, p = 6.8 × 10^{−10}. Conclusion: Second-order models give significantly better goodness-of-fit than firstorder models, likely due to the inclusion of both Phase I and Phase II components of heart rate response. Future work should investigate alternative parameterisations of the PRBS excitation, and whether feedback controllers calculated using second-order models give better performance than those based on first-order models

Heart rate regulation during cycle-ergometer exercise using damped parameter estimation method

© 2016 IEEE. This paper is devoted to the problem of heart rate regulation using a model-based control strategy and a realtime damped parameter estimation scheme. The controller is a time-varying integral sliding mode controller. A recursive damped parameter estimation method is also developed, by incorporation of a weighting upon the one-step parameter variation, which in contrast to the conventional parameter estimation schemes (e.g. recursive least squares (RLS) method) can avoid the occurrence of the so-called blowup phenomena. The calculated control signals are transmitted to the subjects employing a synchronized biofeedback mechanism. The proposed control and estimation scheme were experimentally verified using twelve healthy male subjects and the results demonstrated that the designed scheme is able to regulate the HR of the exercising subjects to a predetermined HR profile preventing overshooting in the HR responses