Feedback control of heart rate during robotics-assisted tilt table exercise in patients after stroke: a clinical feasibility study

Abstract

Background: Patients with neurological disorders including stroke use rehabilitation to improve cognitive abilities, to regain motor function and to reduce the risk of further complications. Robotics-assisted tilt table technology has been developed to provide early mobilisation and to automate therapy involving the lower limbs. The aim of this study was to evaluate the feasibility of employing a feedback control system for heart rate (HR) during robotics-assisted tilt table exercise in patients after a stroke.

Methods: This feasibility study was designed as a case series with 12 patients ( $n=12$ ) with no restriction on the time post-stroke or on the degree of post-stroke impairment severity. A robotics-assisted tilt table was augmented with force sensors, a work rate estimation algorithm, and a biofeedback screen that facilitated volitional control of a target work rate. Dynamic models of HR response to changes in target work rate were estimated in system identification tests; nominal models were used to calculate the parameters of feedback controllers designed to give a specified closed-loop bandwidth; and the accuracy of HR control was assessed quantitatively in feedback control tests.

Results: Feedback control tests were successfully conducted in all 12 patients. Dynamic models of heart rate response to imposed work rate were estimated with a mean root-mean-square (RMS) model error of 2.16 beats per minute (bpm), while highly accurate feedback control of heart rate was achieved with a mean RMS tracking error (RMSE) of 2.00 bpm. Control accuracy, i.e. RMSE, was found to be strongly correlated with the magnitude of heart rate variability (HRV): patients with a low magnitude of HRV had low RMSE, i.e. more accurate HR control performance, and vice versa.

Conclusions: Feedback control of heart rate during robotics-assisted tilt table exercise was found to be feasible. Future work should investigate robustness aspects of the feedback control system. Modifications to the exercise modality, or alternative modalities, should be explored that allow higher levels of work rate and heart rate intensity to be achieved.

Keywords: Feedback control; Heart rate control; Heart rate dynamics; Neurorehabilitation; Rehabilitation robotics; Stroke.

Fig. 1

Erigo robotics-assisted tilt table

Fig. 2

Experimental setup—schematic. The control application continuously displays a target work rate, ${\text{WR}}^{\ast }$, on the biofeedback screen along with the actual work rate, WR. The latter is estimated from measured forces and angles. The locations of the force and position sensors are indicated with a red bar just below the thigh cuff and a red dot close to the hip joint, respectively. Heart rate is also recorded in real time

Fig. 3

Experimental setup—in situ

Fig. 4

Target work rate profile for system identification

Fig. 5

Target heart rate profile for feedback control

Fig. 6

Structure of feedback control loop. The generic variables r, y and u represent, respectively, target heart rate ${\text{HR}}^{\ast }$, measured heart rate HR, and target work rate ${\text{WR}}^{\ast }$, as indicated

Fig. 7

Dispersion of individually-estimated model parameters. The star denotes the average of all models and the dashed box bounds the 95 % confidence intervals for the mean $k=1.44$ bpm/W (95 % CI 0.94 bpm/W to 1.93 bpm/W) and $\tau =45.3$ s (95 % CI 34.5 s to 56.1 s). The legend on the right-hand side indicates individual patient identification numbers

Fig. 8

Raw data from system identification test for patient 8. The lower plot shows the target (${\text{WR}}^{\ast }$, black) and actual (WR, red) work rates. The upper plot shows the measured HR. The orange bar signifies the time period used for parameter estimation and model validation

Fig. 9

Validation of estimated model for patient 8. The measured HR data are plotted alongside the model-simulated HR

Fig. 10

Feedback control tests for patients 10 and 8. The upper plots show the measured HR (blue), the simulated HR (black, continuous) and the target HR (black, dashed). The lower plots show the target (${\text{WR}}^{\ast }$, black) and actual (WR, red) work rates. The orange bars signify the time periods used for outcome evaluation

Fig. 11

Correlations between HRV total power magnitude HRV-TP and RMS tracking error ${\text{RMSE}}_{\text{C}}$

Fig. 12

Correlations between HRV total power magnitude HRV-TP and average control signal power $P_{\mathrm{\nabla }u}$