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

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

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

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

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

Feedback control of heart rate during outdoor running: a smartphone implementation

AbstractThe aim was to develop and to investigate the technical feasibility of a novel smartphone-based mobile system for feedback control of heart rate during outdoor running. Accurate control is important because heart rate can be used for prescription of exercise intensity for development and maintenance of cardiorespiratory fitness.An Android smartphone was employed together with wearable, wireless sensors for heart rate and running speed. A simple feedback design algorithm appropriate for embedded mobile applications was developed. Controller synthesis uses a low-order, physiologically-validated plant model and requires a single bandwidth-related tuning parameter.Twenty real time controller tests demonstrated highly accurate tracking of target heart rate with a mean root-mean-square tracking error (RMSE) of less than 2 beats per minute (bpm); a sufficient level of robustness was demonstrated within the range of conditions tested. Adjustment of the tuning parameter towards lower closed-loop bandwidth gave markedly lower control signal power (0.0008 vs. 0.0030m2/s2, p<0.0001, low vs. high bandwidth), but at the cost of a significantly lower heart rate tracking accuracy (RMSE 1.99 vs. 1.67bpm, p<0.01).The precision achieved suggests that the system might be applicable for accurate achievement of prescribed exercise intensity for development and maintenance of cardiorespiratory fitness. High-accuracy feedback control of heart rate during outdoor running using smartphone technology is deemed feasible