Heart rate control during treadmill exercise using input-sensitivity shaping for disturbance rejection of very-low-frequency heart rate variability

AbstractBackgroundAutomatic and accurate control of heart rate (HR) during treadmill exercise is important for prescription and implementation of training protocols. The principal design issue for feedback control of HR is to achieve disturbance rejection of very-low-frequency heart rate variability (VLF-HRV) with a level of control signal activity (treadmill speed) which is sufficiently smooth and acceptable to the runner. This work aimed to develop a new method for feedback control of heart rate during treadmill exercise based on shaping of the input sensitivity function, and to empirically evaluate quantitative performance outcomes in an experimental study.MethodsThirty healthy male subjects participated. 20 subjects were included in a preceding study to determine an approximate, average nominal model of heart rate dynamics, and 10 were not. The design method guarantees that the input sensitivity function gain monotonically decreases with frequency, is therefore devoid of peaking, and has a pre-specified value at a chosen critical frequency, thus avoiding unwanted amplification of HRV disturbances in the very-low-frequency band. Controllers were designed using the existing approximate nominal plant model which was not specific to any of the subjects tested.ResultsAccurate, stable and robust overall performance was observed for all 30 subjects, with a mean RMS tracking error of 2.96beats/min and a smooth, low-power control signal. There were no significant differences in tracking accuracy or control signal power between the 10 subjects who were not in the preceding identification study and a matched subgroup of subjects who were (respectively: mean RMSE 2.69 vs. 3.28beats/min, p=0.24; mean control signal power 15.62 vs. 16.31×10−4m2/s2, p=0.37). Substantial and significant reductions over time in RMS tracking error and average control signal power were observed.ConclusionsThe input-sensitivity-shaping method provides a direct way to address the principal design challenge for HR control, namely disturbance rejection in relation to VLF-HRV, and delivered robust and accurate tracking with a smooth, low-power control signal. Issues of parametric and structural plant uncertainty are secondary because a simple approximate plant model, not specific to any of the subjects tested, was sufficient to achieve accurate, stable and robust heart rate control performance

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

Identification and comparison of heart-rate dynamics during cycle ergometer and treadmill exercise

Aim and methods: The aim of this study was to compare the dynamics of heart rate (HR) response to exercise using a cycle ergometer (CE) and a treadmill (TM). Using a sample of 25 healthy male participants, the time constant of HR dynamics was estimated for both modalities in response to square-wave excitation. Results: The principal finding was that the time constant of heart-rate dynamics around somewhat hard exercise intensity (Borg rating of perceived exertion = 13) does not differ significantly between the CE and TM (68.7 s ± 21.5 s vs. 62.5 s ± 18.5 s [mean ± standard deviation]; CE vs. TM; p = 0.20). An observed moderate level of evidence that root-mean-square model error was higher for the CE than for the TM (2.5 bpm ± 0.5 bpm vs. 2.2 bpm ± 0.5 bpm, p = 0.059) may reflect a decrease in heart rate variability with increasing HR intensity because, in order to achieve similar levels of perceived intensity, mean heart rate for the CE was approximately 25 bpm lower than for the TM. Conclusion and significance: These results have important implications for model-based design of automatic HR controllers, because, in principle, the same dynamic controller, merely scaled according to the differing steady-state gains, should be able to be applied to the CE and TM exercise modalities

Heart rate variability changes with respect to time and exercise intensity during heart-rate-controlled steady-state treadmill running

The aim of this work was to investigate the time and exercise intensity dependence of heart rate variability (HRV). Time-dependent, cardiovascular-drift-related increases in heart rate (HR) were inhibited by enforcing a constant heart rate throughout the exercise with a feedback control system. Thirty-two healthy adults performed HR-stabilised treadmill running exercise at two distinct exercise intensity levels. Standard time and frequency domain HRV metrics were computed and served as outcomes. Significant decreases were detected in 8 of the 14 outcomes for the time dependence analysis and in 6 of the 7 outcomes for the exercise intensity dependence analysis (excluding the experimental speed-signal frequency analysis). Furthermore, metrics that have been reported to reach an intensity-dependent near-zero minimum rapidly (usually at moderate intensity) were found to be near constant over time and only barely decreased with intensity. Taken together, these results highlight that HRV generally decreases with time and with exercise intensity. The intensity-related reductions were found to be greater in value and significance compared to the time-related reductions. Additionally, the results indicate that decreases in HRV metrics with time or exercise intensity are only detectable as long as their metric-specific near-zero minimum has not yet been reached

Robust control of heart rate for cycle ergometer exercise

The objective was to assess the performance and robustness of a novel strategy for automatic control of heart rate (HR) during cycle ergometry. Control design used a linear plant model and direct shaping of the closed-loop input-sensitivity function to achieve an appropriate response to disturbances attributable to broad-spectrum heart rate variability (HRV). The controller was evaluated in 73 feedback control experiments involving 49 participants. Performance and stability robustness were analysed using a separately identified family of 73 plant models. The controller gave highly accurate and stable HR tracking performance with mean root-mean-square tracking error between 2.5 beats/min (bpm) and 3.1 bpm, and with low average control signal power. Although plant parameters varied over a very wide range, key closed-loop transfer functions remained invariant to plant uncertainty in important frequency bands, while infinite gain margins and large phase margins (>62◦) were preserved across the whole plant model family. Highly accurate, stable and robust HR control can be achieved using LTI controllers of remarkably simple structure. The results highlight that HR control design must focus on disturbances caused by HRV. The input-sensitivity approach evaluated in this work provides a transparent method of addressing this challenge

Exploring Cardiac Responses of Pain and Distress

Pain and distress stand at the intersection of multiple health crises and are leading contributors to disability. Current pain assessments rely on self-reports—which assume a capacity to understand and verbalize mental/emotional states—and behavioral observation which can be subject to limitations and misinterpretation. Methods to evaluate pain/distress can be substantially enhanced with biometrics that incorporate the physiological aspects of the full pain experience. This chapter explores how induced pressure pain influences cardiac activity elicited via the autonomic nervous system. We aim to uncover signatures in cardiac responses via personalized analysis of the frequencies and the timings of the heart’s inter-beat-interval. Autonomic responses such as cardiac activity serve as inevitable processes, which cannot be volitionally controlled—they exhibit a narrow range of dynamics, helping provide robust signatures of the body’s responses to pain/distress. We find that pain elicits shifts in the heart rate variability metrics of the cardiac signal, alluding to changes in sympathetic and parasympathetic nervous system activation. Unique relationships are also observed between metrics obtained from the physiological data and self-reported pain ratings. The implications of this work are discussed in the context of precision medicine with possible applications in clinical populations such as autism

A unified heart rate control approach for cycle ergometer and treadmill exercise

Objective: To develop a unified heart rate (HR) control approach for cycle ergometer (CE) and treadmill(TM) exercise, and to empirically compare the common controller’s performance between the CE andTM. Methods: The control method used frequency-domain shaping of the input-sensitivity function to addressrejection of disturbances arising from broad-spectrum heart rate variability (HRV). A single controllerwas calculated using an approximate, nominal linear plant model and an input-sensitivity bandwidthspecification. Fifty HR control tests were executed using the single controller: 25 healthy male participantseach did one test on the CE and one on the TM. Results: There was no significant difference in mean root-mean-square HR tracking error: 3.10 bpm ±0.68 bpm and 2.85 bpm ± 0.75 bpm (mean ± standard deviation, bpm = beats/min); CE vs. TM; p = 0.13.But mean normalised average control signal power was significantly different: 1.59 bpm2± 0.27 bpm2vs. 1.36 bpm2± 0.28 bpm2; CE vs. TM; p = 3.5 × 10−4. Conclusion and significance: The lower values for RMS tracking error and control signal power for the TMpoint to decreasing HRV intensity with increasing HR, because, in order to match perceived exertion forthe two modalities, mean HR for the TM was set 20 bpm higher than for the CE. These HR-intensity-dependent differences in HRV are consistent with previous observations in the literature. The unified HRcontrol approach for CE and TM exercise gave accurate, stable and robust performance in all tests, thuslending support to the concept that HRV disturbance rejection is the main issue in HR control design