Neurophysiological validation of simultaneous intrinsic and reflexive joint impedance estimates

Abstract

Background: People with brain or neural injuries, such as cerebral palsy or spinal cord injury, commonly have joint hyper-resistance. Diagnosis and treatment of joint hyper-resistance is challenging due to a mix of tonic and phasic contributions. The parallel-cascade (PC) system identification technique offers a potential solution to disentangle the intrinsic (tonic) and reflexive (phasic) contributions to joint impedance, i.e. resistance. However, a simultaneous neurophysiological validation of both intrinsic and reflexive joint impedances is lacking. This simultaneous validation is important given the mix of tonic and phasic contributions to joint hyper-resistance. Therefore, the main goal of this paper is to perform a group-level neurophysiological validation of the PC system identification technique using electromyography (EMG) measurements.

Methods: Ten healthy people participated in the study. Perturbations were applied to the ankle joint to elicit reflexes and allow for system identification. Participants completed 20 hold periods of 60 seconds, assumed to have constant joint impedance, with varying magnitudes of intrinsic and reflexive joint impedances across periods. Each hold period provided a paired data point between the PC-based estimates and neurophysiological measures, i.e. between intrinsic stiffness and background EMG, and between reflexive gain and reflex EMG.

Results: The intrinsic paired data points, with all subjects combined, were strongly correlated, with a range of [Formula: see text] in both ankle plantarflexors and dorsiflexors. The reflexive paired data points were moderately correlated, with [Formula: see text] in the ankle plantarflexors only.

Conclusion: An agreement with the neurophysiological basis on which PC algorithms are built is necessary to support its clinical application in people with joint hyper-resistance. Our results show this agreement for the PC system identification technique on group-level. Consequently, these results show the validity of the use of the technique for the integrated assessment and training of people with joint hyper-resistance in clinical practice.

Keywords: Electromyography; Joint resistance; Parallel-cascade model; System identification; Validation.

Fig. 1

Experimental setup overview. Participants were seated on an adjustable chair with their right foot connected to an actuator, applying perturbations around the ankle joint. Feedback was given using a (blue) 2D trace on both torque (y-axis) and an impedance parameter (x-axis). On the y-axis, a (red) torque target was shown around either 0 or −5 Nm. On the x-axis, (black-dashed) reference lines were shown with the average magnitude of the impedance parameter from previously completed 60 s hold periods at each torque level. In the specific example situation depicted, a participant would have had the following two tasks: (1) (y-axis) keep voluntary torque stable within the target boundaries around −5 Nm; and (2) (x-axis) keep the impedance parameter stable and away from the black-dashed reference lines shown

Fig. 2

Parallel-cascade joint impedance model with intrinsic and reflexive pathway. The intrinsic pathway was modelled as a 2nd-order mass-spring-damper system with parameters: inertia I, damping B and stiffness K. The reflexive pathway was modelled based on the 40 ms delayed, half-wave rectified velocity using 2nd-order muscle activation dynamics and a parameter for reflexive gain G

Fig. 3

Data analysis methodology. a Background and reflexive EMG activity were calculated using the perturbation onset as reference. Background activity was based on the 40 ms period before perturbation onset, while reflexive activity was based on a 20 ms period about 40 ms after perturbation onset. b Absolute and c normalized correlation analysis. Both plots show a representative example using the intrinsic stiffness and SOL background EMG outcome measures collected at a 0 Nm torque target. A total least squares (TLS) fit shows the slope and intercept of the datasets of each individual participant

Fig. 4

Time series of measured and processed signals, typical example for a single representative participant. (Left) Four consecutive dorsiflexion perturbations with perturbation onset (grey-dashed vertical lines). The response to the position perturbations are shown for the high-pass filtered, rectified EMG of Triceps Surae (TS) and TA as well as measured ankle joint torque. (Right) Two consecutive 60s hold periods (grey background) with transition period. 2D feedback was provided on torque and intrinsic stiffness. The time series show the voluntary modulation of the low-pass filtered torque and active torque target (red), intrinsic stiffness K, background SOL EMG activity, reflexive gain G and reflexive SOL EMG activity. The PC algorithm parameters K and G were computed continuously, while the EMG activity computations were performed around every perturbation onset

Fig. 5

Ensemble averages (±SD) of hold periods with modulated impedance, typical examples for a single representative participant. Ensemble averages of the measured signals, created by aligning all step perturbations at perturbation onset (grey-dashed vertical lines). %VAF was computed using the measured and modeled torque ensemble of both step and pulse perturbations. The K (Nm/rad) and G (Nm/rad/s) parameter values provided represent the mean value across each hold period. All torque ensembles were normalized by subtracting the average background torque to enhance visualization of intrinsic and reflexive torque effects. All three hold periods were executed at a 0 Nm torque target

Fig. 6

Linear associations between Z-score normalized joint impedance parameters and EMG activity across all participants. All datasets are shown for all hold periods across both torque levels. The TLS fit is shown for both torque levels to help visualize and interpret the linear associations