To investigate the time dependence of the heart rate variability (HRV) during treadmill running, a feedback control loop was implemented to eliminate the potentially confounding influence of cardiovascular drift. Without cardiovascular drift, observed changes in HRV can be directly attributed to time only and not to drift-related increases in heart rate. To quantify the time-dependence of HRV, standard HRV metrics for two consecutive windows of equal duration (12.5 min) were computed and compared. Eight participants were included. The outcome measures showed an overall tendency to decrease over time. Seven of the 10 HRV metrics were significantly lower (p<0.05); three HRV metrics showed moderate evidence of decrease over time, viz. average control power P∇u (p = 0.053), very-low frequency power (VLF) of the RR-signal (p = 0.072) and low frequency power (LF) of the RR-signal (p = 0.12). Taken together, these results provide evidence of a decrease in HRV over time during treadmill running; the employment of feedback control of heart rate is important as cardiovascular drift was eliminated. Further work is required to optimize the experimental design and to use a larger sample size to improve the statistical power of the results.
Introduction: With conventional heart rate (HR) control systems, the exercising person is bound to walk or run at a pace determined by the feedback. This may be challenging for people with impairments that make it difficult for them to achieve a smooth, continuous pace. The aim of this work was to assess the technical feasibility of a novel self-paced heart rate control strategy and to compare its accuracy with conventional heart rate control. Methods: We propose a self-paced heart rate control system that embeds an automatic positioning controller within the heart rate control loop. The treadmill speed command is decoupled from the heart rate compensator, whereas speed is determined by the exerciser’s own volition: target speed is displayed visually to the person and, when they try to follow this target, the position controller sets the treadmill speed while keeping the person at a safe reference position on the track. A further novel contribution of this work is a new input-sensitivity-shaping, frequency-domain design strategy for feedback control of position. Results: Experimental evaluation with four participants showed that self-paced heart rate control is technically feasible: all participants were able to accurately follow the target running speed calculated by the HR compensator and presented to them visually; for all four participants, self-paced HR tracking accuracy was not substantially different from conventional HR control performance; on average, the self-paced heart rate controller gave slightly better performance than conventional HR control, with RMS tracking error of 2.98 beats per minute (bpm) vs 3.11 bpm and higher average control signal power. Conclusion: The proposed self-paced heart rate control strategy with embedded automatic position control is deemed feasible. This approach may be helpful for people with gait impairments or other limitations that make it difficult for them to follow an imposed treadmill speed.
Abstract 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 $$p = 2.8 \times 10^{-10}$$ p=2.8×10-10 ; fit was $$54.5\% \pm 5.2$$ 54.5%±5.2 % vs. $$50.2\% \pm 4.8$$ 50.2%±4.8 %, $$p = 6.8 \times 10^{-10}$$ p=6.8×10-10 . Conclusion Second-order models give significantly better goodness-of-fit than first-order 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.
Background The response of heart rate to changes in exercise intensity is comprised of several dynamic modes with differing magnitudes and temporal characteristics. Investigations of empirical identification of dynamic models of heart rate showed that second-order models gave substantially and significantly better model fidelity compared to the first order case. In the present work, we aimed to reanalyse data from previous studies to more closely consider the effect of including a zero and a pure delay in the model. Methods This is a retrospective analysis of 22 treadmill (TM) and 54 cycle ergometer (CE) data sets from a total of 38 healthy participants. A linear, time-invariant plant model structure with up to two poles, a zero and a dead time is considered. Empirical estimation of the free parameters was performed using least-squares optimisation. The primary outcome measure is model fit, which is a normalised root-mean-square model error. Results A model comprising parallel connection of two first-order transfer functions, one with a dead time and one without, was found to give the highest fit (56.7 % for TM, 54.3 % for CE), whereby the non-delayed component appeared to merely capture initial transients in the data and the part with dead time likely represented the true dynamic response of heart rate to the excitation. In comparison, a simple first-order model without dead time gave substantially lower fit than the parallel model (50.2 % for TM, 47.9 % for CE). Conclusions This preliminary analysis points to a linear first-order system with dead time as being an appropriate model for heart rate response to exercise using treadmill and cycle ergometer modalities. In order to avoid biased estimates, it is vitally important that, prior to parameter estimation and validation, careful attention is paid to data preprocessing in order to eliminate transients and trends.
The response of heart rate to changes in exercise intensity is comprised of several dynamic modes with differing magnitudes and temporal characteristics. Investigations of empirical identification of dynamic models of heart rate showed that second-order models gave substantially and significantly better model fidelity compared to the first order case. In the present work, we aimed to reanalyse data from previous studies to more closely consider the effect of including a zero and a pure delay in the model.
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