A sensitivity analysis of an inverted pendulum balance control model

Balance control models are used to describe balance behavior in health and disease. We identified the unique contribution and relative importance of each parameter of a commonly used balance control model, the Independent Channel (IC) model, to identify which parameters are crucial to describe balance behavior. The balance behavior was expressed by transfer functions (TFs), representing the relationship between sensory perturbations and body sway as a function of frequency, in terms of amplitude (i.e., magnitude) and timing (i.e., phase). The model included an inverted pendulum controlled by a neuromuscular system, described by several parameters. Local sensitivity of each parameter was determined for both the magnitude and phase using partial derivatives. Both the intrinsic stiffness and proportional gain shape the magnitude at low frequencies (0.1–1 Hz). The derivative gain shapes the peak and slope of the magnitude between 0.5 and 0.9 Hz. The sensory weight influences the overall magnitude, and does not have any effect on the phase. The effect of the time delay becomes apparent in the phase above 0.6 Hz. The force feedback parameters and intrinsic stiffness have a small effect compared with the other parameters. All parameters shape the TF magnitude and phase and therefore play a role in the balance behavior. The sensory weight, time delay, derivative gain, and the proportional gain have a unique effect on the TFs, while the force feedback parameters and intrinsic stiffness contribute less. More insight in the unique contribution and relative importance of all parameters shows which parameters are crucial and critical to identify underlying differences in balance behavior between different patient groups.Biomechatronics & Human-Machine Contro

The reliance on vestibular information during standing balance control decreases with severity of vestibular dysfunction

The vestibular system is involved in gaze stabilization and standing balance control. However, it is unclear whether vestibular dysfunction affects both processes to a similar extent. Therefore, the objective of this study was to determine how the reliance on vestibular information during standing balance control is related to gaze stabilization deficits in patients with vestibular dysfunction. Eleven patients with vestibular dysfunction and twelve healthy subjects were included. Gaze stabilization deficits were established by spontaneous nystagmus examination, caloric test, rotational chair test, and head impulse test. Standing balance control was assessed by measuring the body sway (BS) responses to continuous support surface rotations of 0.5° and 1.0° peak-to-peak while subjects had their eyes closed. A balance control model was fitted on the measured BS responses to estimate balance control parameters, including the vestibular weight, which represents the reliance on vestibular information. Using multivariate analysis of variance, balance parameters were compared between patients with vestibular dysfunction and healthy subjects. Robust regression was used to investigate correlations between gaze stabilization and the vestibular weight. Our results showed that the vestibular weight was smaller in patients with vestibular dysfunction than in healthy subjects (F = 7.67, p = 0.011). The vestibular weight during 0.5° peak-to-peak support surface rotations decreased with increasing spontaneous nystagmus eye velocity (ρ = -0.82, p < 0.001). In addition, the vestibular weight during 0.5° and 1.0° peak-to-peak support surface rotations decreased with increasing ocular response bias during rotational chair testing (ρ = -0.72, p = 0.02 and ρ = -0.67, p = 0.04, respectively). These findings suggest that the reliance on vestibular information during standing balance control decreases with the severity of vestibular dysfunction. We conclude that particular gaze stabilization tests may be used to predict the effect of vestibular dysfunction on standing balance control.Biomechatronics & Human-Machine Contro

Assessment of the underlying systems involved in standing balance: The additional value of electromyography in system identification and parameter estimation

Background: Closed loop system identification (CLSIT) is a method to disentangle the contribution of underlying systems in standing balance. We investigated whether taking into account lower leg muscle activation in CLSIT could improve the reliability and accuracy of estimated parameters identifying the underlying systems. Methods: Standing balance behaviour of 20 healthy young participants was measured using continuous rotations of the support surface (SS). The dynamic balance behaviour obtained with CLSIT was expressed by sensitivity functions of the ankle torque, body sway and muscle activation of the lower legs to the SS rotation. Balance control models, 1) without activation dynamics, 2) with activation dynamics and 3) with activation dynamics and acceleration feedback, were fitted on the data of all possible combinations of the 3 sensitivity functions. The reliability of the estimated model parameters was represented by the mean relative standard errors of the mean (mSEM) of the estimated parameters, expressed for the basic parameters, the activation dynamics parameters and the acceleration feedback parameter. To investigate the accuracy, a model validation study was performed using simulated data obtained with a comprehensive balance control model. The accuracy of the estimated model parameters was described by the mean relative difference (mDIFF) between the estimated parameters and original parameters. Results: The experimental data showed a low mSEM of the basic parameters, activation dynamics parameters and acceleration feedback parameter by adding muscle activation in combination with activation dynamics and acceleration feedback to the fitted model. From the simulated data, the mDIFF of the basic parameters varied from 22.2-22.4% when estimated using the torque and body sway sensitivity functions. Adding the activation dynamics, acceleration feedback and muscle activation improved mDIFF to 13.1-15.1%. Conclusions: Adding the muscle activation in combination with the activation dynamics and acceleration feedback to CLSIT improves the accuracy and reliability of the estimated parameters and gives the possibility to separate the neural time delay, electromechanical delay and the intrinsic and reflexive dynamics. To diagnose impaired balance more specifically, it is recommended to add electromyography (EMG) to body sway (with or without torque) measurements in the assessment of the underlying systems.Biomechatronics & Human-Machine Contro

Cortical dynamics during preparation and execution of reactive balance responses with distinct postural demands

The contributions of the cerebral cortex to human balance control are clearly demonstrated by the profound impact of cortical lesions on the ability to maintain standing balance. The cerebral cortex is thought to regulate subcortical postural centers to maintain upright balance and posture under varying environmental conditions and task demands. However, the cortical mechanisms that support standing balance remain elusive. Here, we present an EEG-based analysis of cortical oscillatory dynamics during the preparation and execution of balance responses with distinct postural demands. In our experiment, participants responded to backward movements of the support surface either with one forward step or by keeping their feet in place. To challenge the postural control system, we applied participant-specific high accelerations of the support surface such that the postural demand was low for stepping responses and high for feet-in-place responses. We expected that postural demand modulated the power of intrinsic cortical oscillations. Independent component analysis and time-frequency domain statistics revealed stronger suppression of alpha (9–13 Hz) and low-gamma (31–34 Hz) rhythms in the supplementary motor area (SMA) when preparing for feet-in-place responses (i.e., high postural demand). Irrespective of the response condition, support-surface movements elicited broadband (3–17 Hz) power increase in the SMA and enhancement of the theta (3–7 Hz) rhythm in the anterior prefrontal cortex (PFC), anterior cingulate cortex (ACC), and bilateral sensorimotor cortices (M1/S1). Although the execution of reactive responses resulted in largely similar cortical dynamics, comparison between the bilateral M1/S1 showed that stepping responses corresponded with stronger suppression of the beta (13–17 Hz) rhythm in the M1/S1 contralateral to the support leg. Comparison between response conditions showed that feet-in-place responses corresponded with stronger enhancement of the theta (3–7 Hz) rhythm in the PFC. Our results provide novel insights into the cortical dynamics of SMA, PFC, and M1/S1 during the control of human balance.Biomechatronics & Human-Machine Contro

Evidence in support of the Independent Channel Model describing the sensorimotor control of human stance using a humanoid robot

The Independent Channel (IC) model is a commonly used linear balance control model in the frequency domain to analyze human balance control using system identification and parameter estimation. The IC model is a rudimentary and noise-free description of balance behavior in the frequency domain, where a stable model representation is not guaranteed. In this study, we conducted firstly time-domain simulations with added noise, and secondly robot experiments by implementing the IC model in a real-world robot (PostuRob II) to test the validity and stability of the model in the time domain and for real world situations. Balance behavior of seven healthy participants was measured during upright stance by applying pseudorandom continuous support surface rotations. System identification and parameter estimation were used to describe the balance behavior with the IC model in the frequency domain. The IC model with the estimated parameters from human experiments was implemented in Simulink for computer simulations including noise in the time domain and robot experiments using the humanoid robot PostuRob II. Again, system identification and parameter estimation were used to describe the simulated balance behavior. Time series, Frequency Response Functions, and estimated parameters from human experiments, computer simulations, and robot experiments were compared with each other. The computer simulations showed similar balance behavior and estimated control parameters compared to the human experiments, in the time and frequency domain. Also, the IC model was able to control the humanoid robot by keeping it upright, but showed small differences compared to the human experiments in the time and frequency domain, especially at high frequencies. We conclude that the IC model, a descriptive model in the frequency domain, can imitate human balance behavior also in the time domain, both in computer simulations with added noise and real world situations with a humanoid robot. This provides further evidence that the IC model is a valid description of human balance control.Biomechatronics & Human-Machine Contro