The study, published in Frontiers in Control Engineering, reports a case study in which a 33-year-old woman with cerebral palsy walked on a treadmill governed by a self-paced heart rate control system. The system, first developed and validated with healthy participants, consists of two interacting feedback loops: one that keeps the walker’s heart rate on a prescribed target curve, and another that keeps her in a stable position on the treadmill belt. The researchers found that after customising the heart rate controller to the participant’s own cardiovascular response, the system achieved heart rate tracking errors as low as 2.38 beats per minute—accuracy comparable to what has been reported in healthy walkers—and that it could interact cleanly with a motor-driven body weight support system without degrading either function.

The motivation for the work lies in a growing body of evidence that interval-intensity training, in which exercise intensity is deliberately varied, offers rehabilitation benefits for people with a wide range of neurological impairments. Heart rate is the standard clinical proxy for exercise intensity, which has inspired decades of research into heart rate control systems. But conventional treadmill-based heart rate controllers have a fundamental drawback for neurologically impaired users: the machine determines the speed entirely on its own, and the human must follow. If the controller commands a pace the walker cannot sustain, the session may be interrupted or, worse, the walker may be placed at risk. The self-paced approach inverts this relationship. The treadmill adjusts its speed to maintain the walker’s relative position on the belt, and the walker is free to modulate her own speed within that constraint. The heart rate controller then calculates a reference treadmill speed, displayed in real time on a control unit at the front of the machine, which the walker follows to the best of her ability. The result is a system in which the human retains agency over her own movement while the machine steers the overall intensity.

Applying this system to people with gait impairments, however, raised two serious technical questions. The first concerned the heart rate response model at the core of the controller. In previous studies, this model—a first-order transfer function relating walking speed to heart rate, characterised by a gain and a time constant—was identified from healthy participants exercising at moderate to vigorous intensities, such as running. Neurologically impaired individuals typically exercise at much lower intensities, often at a comfortable walking speed. Moreover, maintaining balance and compensating for inefficient gait patterns imposes additional cardiovascular and muscular demands that healthy walkers do not face. The researchers hypothesised that the heart rate response model for a person with gait impairment could differ substantially from the healthy-participant model, potentially degrading control performance. The second question concerned interaction with body weight support systems, which are essential tools for evaluating and enhancing walking ability in people with gait impairments. Studies suggest that applying 20 to 40 percent body weight support at low exercise speeds can provide greater rehabilitation benefits. But such systems—an overhead harness connected to motors or springs, an antigravity treadmill, or a wearable exoskeleton—can alter the walker’s movement, limiting hip motion, affecting lateral and horizontal movements on the treadmill, or even worsening walking performance. The team needed to verify that their self-paced heart rate control system could coexist with a motor-driven body weight support system without either function interfering with the other.

To answer these questions, the researchers conducted a case study with a single participant with cerebral palsy—a female, 33 years old, weighing 49 kilograms and 164 centimetres tall, who could walk independently on the treadmill with the assistance of handrails. The experimental protocol was carefully staged. Three preliminary tests were completed before the formal evaluation. The first, an intensity evaluation test, aimed to establish an appropriate target heart rate for all subsequent tests. Using the nominal heart rate controller developed for healthy participants, the target heart rate was initially set to 130 beats per minute and then manually adjusted during the test until the participant could maintain the corresponding intensity relatively easily. The test revealed a unique advantage of the self-paced approach: when the set target intensity exceeded the participant’s tolerance level, she could continue the test at her desired intensity without interrupting the procedure—a feature that greatly enhanced the efficiency and safety of the test.

The second preliminary test was a plant model identification test, designed to estimate the participant’s own heart rate response model and thereby mitigate the impact of modelling errors. The test consisted of a one-minute warm-up, a one-minute rest, and a fifteen-minute formal measurement phase, during which the treadmill speed applied a square-wave signal with a six-minute period and an amplitude of 0.05 metres per second. Heart rate was recorded at 0.2 hertz, and measurements from 160 to 900 seconds were used as the estimation dataset. The data were detrended and fitted to a first-order model using a least-squares optimisation tool from the Matlab System Identification Toolbox. The resulting customised model achieved a normalised fit of 31.05 percent and a root-mean-square identification error of 3.25 beats per minute. Critically, the customised parameters differed dramatically from the healthy-participant nominal model: the gain was 79.74 beats per minute per metre per second, compared with 28.57 for the nominal model—a 179.1 percent increase—while the time constant was 35.10 seconds, compared with 70.56 seconds, a 50.3 percent reduction. These findings aligned with the researchers’ hypothesis that neurologically impaired individuals require additional and more dynamic cardiovascular and muscular activity than healthy participants to maintain balance and compensate for inefficient gait patterns.

The third preliminary test, an amplitude evaluation test, determined the optimal amplitude for the square-wave target heart rate curve used in the formal tests. Using the customised heart rate controller, the target heart rate was set as a square wave with a mean of 120 beats per minute and an initial amplitude of 10 beats per minute. The four resulting speed changes led to noticeable differences between the reference and set treadmill speeds, attributed to the limited adaptability of the participant to follow speed changes. The amplitude was therefore manually reduced to 5 beats per minute, resulting in reduced speed differences and confirming that a 5-beat-per-minute amplitude was more suitable for this participant.

The formal tests were then divided into two series. The first series investigated the influence of modelling errors on control performance, using a constant heart rate reference and comparing the nominal controller with the customised controller. The results were striking. The customised controller achieved a root-mean-square heart rate tracking error of 2.38 beats per minute, compared with 3.91 beats per minute for the nominal controller—a 39.1 percent reduction. Even more dramatically, the customised controller reduced the average power of changes in the treadmill target speed from 8.4 × 10⁻⁴ to 0.4 × 10⁻⁴ square metres per second squared, a 95.2 percent reduction in oscillation. Notably, this improvement was achieved at a similar mean reference speed—0.24 metres per second for the customised controller versus 0.25 metres per second for the nominal controller—confirming that the gains in accuracy and smoothness were not obtained by simply slowing the participant down.

The second series of formal tests evaluated the control accuracy of the self-paced heart rate control system and its interaction with the motor-driven body weight support system. Both tests employed the customised heart rate controller and a square-wave target heart rate with a six-minute period and a 5-beat-per-minute amplitude. The first test incorporated 13.01 kilograms of body weight support, equivalent to 26.6 percent of the participant’s total body mass, while the second test was conducted without the support system. The results showed that the body weight support system actually improved heart rate tracking accuracy: the root-mean-square tracking error was 3.02 beats per minute with support, compared with 3.50 beats per minute without—a 14.5 percent improvement. The test with body weight support also achieved a higher mean reference treadmill speed with reduced oscillation, which the researchers attributed to a reduction in the cardiovascular and muscular effort required to support body weight and generate supporting forces on the handrails, thus necessitating a higher treadmill speed to reach the target heart rate. Crucially, the body weight support system had no meaningful influence on the automatic position control accuracy: the root-mean-square distance tracking error was 0.0159 metres with support versus 0.0164 metres without, a difference of only 3.0 percent. These results uncovered another advantage of the self-paced system: the distance feedback loop keeps the walker in a stable position on the treadmill, effectively suppressing any influence of the body weight support system on her horizontal movement.

The researchers emphasise that no measurements previously existed on the heart rate response of gait-impaired participants, so their study had to start from a well-analysed heart rate response model based on healthy participants, using the same model and controller structure but with the assumption that the parameters might differ. The vastly improved and highly accurate results achieved by only adapting the model and controller parameters show—empirically—that it is sufficient to change the parameters, not the structure, in this case. The heart rate tracking results are consistent with the team’s previous self-paced heart rate control study in healthy participants, which reported tracking errors between 2.04 and 4.29 beats per minute, and with other conventional, machine-determined heart rate control studies involving healthy individuals. The work was supported by the Swiss National Science Foundation. While the findings derive from a single case study and cannot be generalised, they represent a proof of concept that self-paced heart rate control—technology that hands agency back to the walker while steering exercise intensity with clinical precision—can be extended to the very populations who stand to benefit most from carefully dosed, interval-based rehabilitation training.

Subject of Research: Self-paced heart rate control during treadmill exercise for persons with gait impairment: a case study

Article Title: Self-paced heart rate control during treadmill exercise for persons with gait impairment: a case study

Article References: Self-paced heart rate control during treadmill exercise for persons with gait impairment: a case study. (n.d.). https://doi.org/10.3389/fcteg.2024.1343851

Image Credits: AI Generated

DOI: 10.3389/fcteg.2024.1343851

Keywords: rehabilitation engineering, heart rate control, treadmill exercise, cerebral palsy, gait impairment, body weight support, feedback control, self-paced walking, Self-paced, heart, rate, control