Robert J. Peterka

Postural control model interpretation of stabilogram diffusion analysis

Abstract. Collins and De Luca [Collins JJ, De Luca CJ (1993) Exp Brain Res 95: 308–318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior.

Multisensory control of human upright stance

The interaction of different orientation senses contributing to posture control is not well understood. We therefore performed experiments in which we measured the postural responses of normal subjects and vestibular loss patients during perturbation of their stance. Subjects stood on a motion platform with their eyes closed and auditory cues masked. The perturbing stimuli consisted of either platform tilts or external torque produced by force-controlled pull of the subjects’ body on a stationary platform. Furthermore, we presented trials in which these two stimuli were applied when the platform was body-sway referenced (i.e., coupled 1:1 to body position, by which ankle joint proprioceptive feedback is essentially removed). We analyzed subjects’ postural responses, i.e., the excursions of their center of mass (COM) and center of pressure (COP), using a systems analysis approach. We found gain and phase of the responses to vary as a function of stimulus frequency and in relation to the absence versus presence of vestibular and proprioceptive cues. In addition, gain depended on stimulus amplitude, reflecting a non-linearity in the control. The experimental results were compared to simulation results obtained from an ‘inverted pendulum’ model of posture control. In the model, sensor fusion mechanisms yield internal estimates of the external stimuli, i.e., of the external torque (pull), the platform tilt and gravity. These estimates are derived from three sensor systems: ankle proprioceptors, vestibular sensors and plantar pressure sensors (somatosensory graviceptors). They are fed as global set point signals into a local control loop of the ankle joints, which is based on proprioceptive negative feedback. This local loop stabilizes the body-on-foot support, while the set point signals upgrade the loop into a body-in-space control. Amplitude non-linearity was implemented in the model in the form of central threshold mechanisms. In model simulations that combined sensor fusion and thresholds, an automatic context-specific sensory re-weighting across stimulus conditions occurred. Model parameters were identified using an optimization procedure. Results suggested that in the sway-referenced condition normal subjects altered their postural strategy by strongly weighting feedback from plantar somatosensory force sensors. Taking this strategy change into account, the model’s simulation results well paralleled all experimental results across all conditions tested.

Effect of altered sensory conditions on multivariate descriptors of human postural sway

Abstract Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P=3.2·10−10). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P=1.7·10−10), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.

Simplifying the complexities of maintaining balance

Insights are provided by simple closed-loop models of human postural control. In developing a quantitative model to help us understand the postural control system, one might be tempted to capture as much of the complexity as is known about each of the subsystems. However, this article will follow the approach of Occams Razor. That is, we begin with the simplest possible representation of each of the subsystems and only add complexity as necessary to be consistent with experimental data. For example, a control model with PD control and a positive force feedback loop provides a better explanation of the low-frequency dynamic behavior than the PID control model. Since both models have the same number of parameters, Occams Razor favors the positive force feedback model over the PID model or any variation on the PID model that includes additional parameters. While there is some experimental evidence that positive force feedback plays a role in some aspects of motor control its contribution to postural control is unknown. Our model that includes positive force feedback represents a quantitative hypothesis that motivates additional experiments to confirm, or refute the contribution of positive force feedback to human postural control and to investigate the dynamic properties of this feedback loop. An important feature clearly revealed by the model-based interpretation of experimental data is the ability of the human postural control system to alter its source of sensory orientation cues as environmental conditions change. Our relatively simple models allowed us to apply systems identification methods in order to estimate the relative contributions (sensory weights) of various sensory orientation cues in different environmental conditions However, our simple models do not predict how the sensory weights should change as a function of environmental conditions or provide insight into the neural mechanisms that cause these changes.

Diabetic neuropathy and surface sway-referencing disrupt somatosensory information for postural stability in stance

In order to determine the type of somatosensory information for postural control that is most affected by neuropathy, we compared the relative effects of three methods of sway-referencing the surface in a group of subjects with profound loss of somatosensory function associated with sensory polyneuropathy from diabetes with age-matched control subjects. Sway-referencing disrupted somatosensory feedback for postural control by servo-controlling the dorsi- and plantar-flexion rotation of the support surface in proportion to anterior-posterior excursion of (1) ankle angle, (2) center of body mass (CoM) angle or (3) filtered center of pressure (CoP). Postural sway in subjects with somatosensory loss was significantly larger than normal on a firm surface but not on the sway-referenced surfaces, suggesting that sway-referencing disrupts somatosensory information for postural control already disrupted by neuropathy. Control subjects standing on any sway-referenced surface swayed significantly more than neuropathy subjects who stood on a firm surface, suggesting that sway-referencing disrupts more somatosensory information than disrupted by severe neuropathy. CoP sway-referencing was less sensitive than ankle or CoM sway-referencing for distinguishing postural sway in subjects with somatosensory loss from age-matched control subjects. Given that filtered CoP sway-referencing disrupts the ability to utilize somatosensory information related to surface reactive force to a greater extent than the other two methods of sway-referencing, then these results support the hypothesis that subjects with diabetic peripheral neuropathy have lost more CoP information, than ankle or CoM angle information, for controlling postural sway in stance.

Non-linear stimulus-response behavior of the human stance control system is predicted by optimization of a system with sensory and motor noise

We developed a theory of human stance control that predicted (1) how subjects re-weight their utilization of proprioceptive and graviceptive orientation information in experiments where eyes closed stance was perturbed by surface-tilt stimuli with different amplitudes, (2) the experimentally observed increase in body sway variability (i.e. the “remnant” body sway that could not be attributed to the stimulus) with increasing surface-tilt amplitude, (3) neural controller feedback gains that determine the amount of corrective torque generated in relation to sensory cues signaling body orientation, and (4) the magnitude and structure of spontaneous body sway. Responses to surface-tilt perturbations with different amplitudes were interpreted using a feedback control model to determine control parameters and changes in these parameters with stimulus amplitude. Different combinations of internal sensory and/or motor noise sources were added to the model to identify the properties of noise sources that were able to account for the experimental remnant sway characteristics. Various behavioral criteria were investigated to determine if optimization of these criteria could predict the identified model parameters and amplitude-dependent parameter changes. Robust findings were that remnant sway characteristics were best predicted by models that included both sensory and motor noise, the graviceptive noise magnitude was about ten times larger than the proprioceptive noise, and noise sources with signal-dependent properties provided better explanations of remnant sway. Overall results indicate that humans dynamically weight sensory system contributions to stance control and tune their corrective responses to minimize the energetic effects of sensory noise and external stimuli.

Contribution of Sensorimotor Integration to Spinal Stabilization in Humans

The control of upper body (UB) orientation relative to the pelvis in the frontal plane was characterized by analyzing responses to external perturbations consisting of continuous pelvis tilts (eyes open [EO] and eyes closed [EC]) and visual surround tilts (EO) at various amplitudes. Lateral sway of the lower body was prevented on all tests. UB sway was analyzed by calculating impulse-response functions (IRFs) and frequency-response functions (FRFs) from 0.023 to 10.3 Hz for pelvis tilt tests and FRFs from 0.041 to 1.5 Hz for visual tests. For pelvis tilt tests, differences between FRFs were limited to frequencies<3 Hz and were dependent on stimulus amplitude. IRFs were nearly identical across all pelvis tilt tests for the first 0.2 s, but showed amplitude-dependent changes in their time course at longer time lags. The availability of visual orientation cues (EO vs. EC) had only a small effect on the UB sway during pelvis tilt tests. This small effect of vision was consistent with the small UB sway evoked on visual tilt tests. Experimental results were interpreted using a feedback model of UB orientation control that included time-delayed sensory integration, short-latency reflexive mechanisms, and intrinsic biomechanical properties of the UB. Variation in model parameters indicated that subjects shifted toward reliance on vestibular information and away from proprioceptive information as pelvis tilt amplitudes increased. For visual tilt stimuli, model parameters indicated that subjects shifted toward reliance on vestibular and proprioceptive information and away from visual information as the stimulus amplitude increased.

Sensory reweighting dynamics in human postural control

Healthy humans control balance during stance by using an active feedback mechanism that generates corrective torque based on a combination of movement and orientation cues from visual, vestibular, and proprioceptive systems. Previous studies found that the contribution of each of these sensory systems changes depending on perturbations applied during stance and on environmental conditions. The process of adjusting the sensory contributions to balance control is referred to as sensory reweighting. To investigate the dynamics of reweighting for the sensory modalities of vision and proprioception, 14 healthy young subjects were exposed to six different combinations of continuous visual scene and platform tilt stimuli while sway responses were recorded. Stimuli consisted of two components: 1) a pseudorandom component whose amplitude periodically switched between low and high amplitudes and 2) a low-amplitude sinusoidal component whose amplitude remained constant throughout a trial. These two stimuli were mathematically independent of one another and, thus, permitted separate analyses of sway responses to the two components. For all six stimulus combinations, the sway responses to the constant-amplitude sine were influenced by the changing amplitude of the pseudorandom component in a manner consistent with sensory reweighting. Results show clear evidence of intra- and intermodality reweighting. Reweighting dynamics were asymmetric, with slower reweighting dynamics following a high-to-low transition in the pseudorandom stimulus amplitude compared with low-to-high amplitude shifts, and were also slower for inter- compared with intramodality reweighting.

Influence of Stance Width on Frontal Plane Postural Dynamics and Coordination in Human Balance Control

The influence of stance width on frontal plane postural dynamics and coordination in human bipedal stance was studied. We tested the hypothesis that when subjects adopt a narrow stance width, they will rely heavily on nonlinear control strategies and coordinated counter-phase upper and lower body motion to limit center-of-mass (CoM) deviations from upright; as stance increases, the use of these strategies will diminish. Freestanding frontal plane body sway was evoked through continuous pseudorandom rotations of the support surface on which subjects stood with various stimulus amplitudes. Subjects were either eyes open (EO) or closed (EC) and adopted various stance widths. Upper body, lower body, and CoM kinematics were summarized using root-mean-square and peak-to-peak measures, and dynamic behavior was characterized using frequency-response and impulse-response functions. In narrow stance, CoM frequency-response function gains were reduced with increasing stimulus amplitude and in EO compared with EC; in wide stance, gain reductions were much less pronounced. Results show that the narrow stance postural system is nonlinear across stimulus amplitude in both EO and EC conditions, whereas the wide stance postural system is more linear. The nonlinearity in narrow stance is likely caused by an amplitude-dependent sensory reweighting mechanism. Finally, lower body and upper body sway were approximately in-phase at low frequencies (<1 Hz) and out-of-phase at high frequencies (>1 Hz) across all stance widths, and results were therefore inconsistent with the hypothesis that subjects made greater use of coordinated counter-phase upper and lower body motion in narrow compared with wide stance conditions.

Vibrotactile Biofeedback Improves Tandem Gait in Patients with Unilateral Vestibular Loss

In a crossover design, subjects with unilateral vestibular loss (UVL) practiced tandem gait with eyes closed on two days, two weeks apart, with and without vibrotactile biofeedback (BF) applied to the lateral trunk. Results showed an immediate improvement in postural stability (reduction of lateral center‐of‐mass displacement, trunk tilt, and medial–lateral step width) that was significantly larger than effects of practice alone. However, BF did not increase the rate of improvement or retention of improved stability during gait.