Feedback control of heart rate during treadmill exercise based on a two-phase response model

This work investigated automatic control of heart rate during treadmill exercise. The aim was to theoretically derive a generic feedback design strategy that achieves a constant input sensitivity function for linear, time-invariant plant models, and to empirically test whether a compensator C2 based on a second-order model is more dynamic and has better tracking accuracy than a compensator C1 based on a first-order model. Twenty-three healthy participants were tested using first and second order compensators, C1 and C2, respectively, during 35-minute bouts of constant heart rate treadmill running. It was found that compensator C2 was significantly more accurate, i.e. it had 7 % lower mean root-mean-square tracking error (1.98 vs. 2.13 beats per minute, p = 0.026), and significantly more dynamic, i.e. it had 17 % higher mean average control signal power (23.4 × 10−4 m2/s2 vs. 20.0 × 10−4 m2/s2, p = 0.011), than C1. This improvement likely stems from the substantially and significantly better fidelity of second-order models, compared to first order models, in line with classical descriptions of the different phases of the cardiac response to exercise. These outcomes, achieved using a treadmill, are consistent with previous observations for the cycle ergometer exercise modality. In summary, whenever heart rate tracking accuracy is of primary importance and a more dynamic control signal is acceptable, the use of a compensator based on a second-order nominal model is recommended

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

Self-paced heart rate control for treadmill exercise

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

Time dependence of heart rate variability during treadmill running

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

Heart rate control using first- and second-order models during treadmill exercise

Heart rate control using first- and second-order models was compared using a novel control design strategy which shapes the input sensitivity function. Ten participants performed two feedback control test series on a treadmill with square wave and constant references. Using a repeated measures, counterbalanced study design, each series compared controllers C1 and C2 based on first- and second-order models, respectively. In the first series, tracking accuracy root-mean-square tracking error (RMSE) was not significantly lower for C2: 2.59 bpm vs. 2.69 bpm (mean, C1 vs. C2), p = 0.79. But average control signal power was significantly higher for C2: 11.29 × 10^{−4} m2/s2 vs. 27.91 × 10^{−4} m2/s2, p = 3.1 × 10^{−10}. In the second series, RMSE was also not significantly lower for C2: 1.99 bpm vs. 1.94 bpm, p = 0.39; but average control signal power was again significantly higher for C2: 2.20 × 10^{−4} m2/s2 vs. 2.78 × 10^{−4} m2/s2, p = 0.045. The results provide no evidence that controllers based on second-order models lead to better tracking accuracy, despite the finding that they are significantly more dynamic. Further investigation using a substantially larger sample size is warranted

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

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

Technical feasibility of constant-load and high-intensity interval training for cardiopulmonary conditioning using a re-engineered dynamic leg press

Background: Leg-press devices are one of the most widely used training tools for musculoskeletal strengthening of the lower-limbs, and have demonstrated important cardiopulmonary benefits for healthy and patient populations. Further engineering development was done on a dynamic leg-press for work-rate estimation by integrating force and motion sensors, power calculation and a visual feedback system for volitional work-rate control. This study aimed to assess the feasibility of the enhanced dynamic leg press for cardiopulmonary exercise training in constant-load training and high-intensity interval training. Five healthy participants aged 31.0 ± 3.9 years (mean ± standard deviation) performed two cardiopulmonary training sessions: constant-load training and high-intensity interval training. Participants carried out the training sessions at a work rate that corresponds to their first ventilatory threshold for constant-load training, and their second ventilatory threshold for high-intensity interval training. Results: All participants tolerated both training protocols, and could complete the training sessions with no complications. Substantial cardiopulmonary responses were observed. The difference between mean oxygen uptake and target oxygen uptake was 0.07 ± 0.34 L/min (103 ±17%) during constant-load training, and 0.35 ± 0.66 L/min (113 ±27%) during high-intensity interval training. The difference between mean heart rate and target heart rate was −7 ± 19 bpm (94 ±15%) during constant-load training, and 4.2 ± 16 bpm (103 ±12%) during high-intensity interval training. Conclusions: The enhanced dynamic leg press was found to be feasible for cardiopulmonary exercise training, and for exercise prescription for different training programmes based on the ventilatory thresholds

Control systems for function restoration, exercise, fitness and health in spinal cord injury

We describe original research contributions to the engineering development of systems which aim to restore function and enable effective exercise for people with spinal cord injury (SCI). Our work utilises functional electrical stimulation (FES) of paralysed muscle. Improving function and general health through participation in exercise is vital to the enhancement of quality of life, well-being and promotion of longevity. Crucial to the development of this research has been judicious use of advanced methods of feedback control engineering; this has been a key enabling factor in many of our original contributions. The consequences of a spinal cord injury can be severe. The primary effects may include; paralysis and loss of sensation in the legs, arms and trunk; disruption of bladder and bowel function; and disruption of the autonomic regulation of blood pressure, heart rate and lung function. If the abdominal and chest muscles are paralysed, breathing will be compromised, and patients with a high-level cervical injury may require mechanical ventilation. These primary effects of a spinal cord injury may, over time, lead to a range of debilitating secondary medical complications. These include reduced cardiovascular fitness, urinary tract infection and an associated risk of kidney disease, reduced bone mineral density, the possible development of pressure sores, and muscle spasticity. People with paralysed chest and abdominal muscles are at increased risk of respiratory infection. Consideration of these factors has led us to focus our research programme in this field on novel engineering solutions which have relevance to the secondary consequences of spinal cord injury, and which may help to alleviate some of their effects. In this thesis we describe our contributions in the following areas: 1. Control of Paraplegic Standing; This work concerns upright stance, and aims to provide; (i) automatic feedback control of balance during stance, with the arms free for functional tasks; (ii) methods and apparatus for dynamic standing therapy, which may help to enhance the individual's retained balance skills. This area of work has successfully demonstrated the automatic control of balance during quiet standing in paraplegic subjects. Further, we have established the feasibility of ankle stiffness control in paraplegic subjects using FES, and we have shown that this can be combined with volitional upper-body inputs to achieve stable, arm-free balance. 2. Lower-limb Cycling: Lower-limb cycling, achieved through electrical stimulation of paralysed leg-actuating muscles, is an effective exercise intervention. We have described refinements to the engineering design of an FES-cycling system, based upon the adaptation of commercially-available recumbent tricycles (of various designs), some of which are equipped with an auxiliary electric motor. We have contributed new methods of feedback control of key variables including cycle cadence and exercise workrate. These contributions have facilitated further detailed study of the effect of the exercise on cardiopulmonary fitness, bone integrity, spasticity, muscle condition, and factors relating to the likelihood of skin breakdown (i.e. the development of pressure sores). 3. Upper-limb Exercise in Tetraplegia; We have developed a new exercise modality for patients with a cervical-level injury and significant loss of arm function. The system allows effective arm ergometry by combining volitional motion with electrical stimulation of the paralysed upper-arm muscles. This work has developed new apparatus and exercise testing protocols, and has examined the effect of the exercise on cardiopulmonary fitness and muscle strength in experiments with tetraplegic subjects. 4. Modelling and Control of Stimulated Muscle; This fundamental area of research has investigated dynamic modelling and feedback control design approaches for electrically-stimulated muscle. This work has been applied in the three areas mentioned above. We identify promising areas for future research. These include extension of work on lower- limb cycling to patients with incomplete injuries, to those with cervical-level injuries, and to children with SCI. We wish to participate in a multi-centre clinical study of implanted nerve- root stimulation technology for restoration of bladder and bowel control, and for lower-limb exercise (including cycling). We have initiated a study of treadmill-based gait therapy for incomplete-lesion patients. The goals of this study are to develop test protocols for accurate characterisation of cardiopulmonary status, and to determine whether this form of cyclical lower-limb exercise has a positive impact on retained voluntary leg function. It is often the case that it is those people most severely affected by neurological impairment who stand to gain the most from these approaches (e.g. high-level tetraplegia, paediatric spinal cord injury, etc.). We must therefore continue to seek ways in which the work can be developed for the maximum benefit of these patients. In conclusion, this thesis has described original research contributions to the engineering development of systems which aim to restore important function and to enable effective exercise for people with spinal cord injury. An important facet of our work has been the application of feedback control methods; this has been an enabling factor in several areas of study. We have focused on areas which promise improved fitness and general health, and which may alleviate some of the secondary consequences of spinal cord injury. This work encompasses fundamental research, clinical studies, and the pursuit of technology transfer into clinical practice. Finally, we recognise the growing awareness of and interest in central nervous system plasticity, and in the broad field of central neural regeneration and repair. It is therefore timely to ask whether cyclical exercise interventions can lead to improvement of volitional function in patients with incomplete or discomplete lesions. Such improvements may, we speculate, result from the strengthening of muscles which retain at least partial volitional control, or from neural plasticity and re-organisation, or from regeneration effects (neurogenesis and functional connectivity). A key requirement in this line of investigation, and a major challenge, will be to develop or to utilise methods which can detect changes in a patient's volitional function and neurological status, and which can isolate the source of such changes. Should reliable methods become available, the way to the study of recovery of function through cyclical exercise would be opened. These considerations will remain, we propose, an indispensable complement to cell-based surgical interventions which may become available in the future

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 feedbackdesign goals: cardiac physiology proposes a two-phase second-order response, delineated into fast and slow components; the natural phenomenon of broadspectrum 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 pseudorandombinary 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 W^2 and 7.56 W^2, 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