Coupling of posture and gait: mode locking and parametric excitation

 We investigate the temporal coordination of human gait and posture and infer the nature of their coupling. Participants viewed a sinusoidally oscillating visual display which induced medial-lateral postural sway during treadmill walking, while display frequency was varied (0.075–1.025 Hz). First, postural responses exhibited the usual low-pass characteristic but with an additional resonance peak near the preferred stride frequency, although shifted downward by 0.12 Hz; this provides evidence of a coupling from gait to posture. Second, the step cycle adapted to mode lock with the visual driver and postural sway, as well as displaying instances of intermittency (slipping in and out of phase) and quasiperiodicity (phase wandering); this provides evidence of a coupling from posture to gait. We observed a spectrum of integer mode locks, including a large 1:1 trapping region about the stride frequency and superharmonic entrainment (stride frequency > driver frequency) at lower driver frequencies. A coupled-oscillator model that incorporates a novel parametric coupling from posture to the gait “stiffness” term reproduces these features of the data, including the resonance peak shift. Biological coordination patterns may thus emerge naturally as properties of a system of appropriately coupled oscillators. Received: 23 June 1999 / Accepted in revised form: 10 January 2001     

Identification of the nonlinear state-space dynamics of the action-perception cycle for visually induced postural sway

Human subjects standing in a sinusoidally moving visual environment display postural sway with characteristic dynamical properties. We analyzed the spatiotemporal properties of this sway in an experiment in which the frequency of the visual motion was varied. We found a constant gain near 1, which implies that the sway motion matches the spatial parameters of the visual motion for a large range of frequencies. A linear dynamical model with constant parameters was compared quantitatively with the data. Its failure to describe correctly the spatiotemporal properties of the system led us to consider adaptive and nonlinear models. To differentiate between possible alternative structures we directly fitted nonlinear differential equations to the sway and visual motion trajectories on a trial-by-trial basis. We found that the eigenfrequency of the fitted model adapts strongly to the visual motion frequency. The damping coefficient decreases with increasing frequency. This indicates that the system destabilizes its postural state in the inertial frame. This leads to a faster internal dynamics which is capable of synchronizing posture with fast-moving visual environments. Using an algorithm which allows the identification of essentially nonlinear terms of the dynamics we found small nonlinear contributions. These nonlinearities are not consistent with a limit-cycle dynamics, accounting for the robustness of the amplitude of postural sway against frequency variations. We interpret our results in terms of active generation of postural sway specified by sensory information. We derive also a number of conclusions for a behavior-oriented analysis of the postural system.     

Relationship between Spectral Characteristics of Spontaneous Postural Sway and Motion Sickness Susceptibility

Motion sickness (MS) usually occurs for a narrow band of frequencies of the imposed oscillation. It happens that this frequency band is close to that which are spontaneously produced by postural sway during natural stance. This study examined the relationship between reported susceptibility to motion sickness and postural control. The hypothesis is that the level of MS can be inferred from the shape of the Power Spectral Density (PSD) profile of spontaneous sway, as measured by the displacement of the center of mass during stationary, upright stance. In Experiment 1, postural fluctuations while standing quietly were related to MS history for inertial motion. In Experiment 2, postural stability measures registered before the onset of a visual roll movement were related to MS symptoms following the visual stimulation. Study of spectral characteristics in postural control showed differences in the distribution of energy along the power spectrum of the antero-posterior sway signal. Participants with MS history provoked by exposure to inertial motion showed a stronger contribution of the high frequency components of the sway signal. When MS was visually triggered, sick participants showed more postural sway in the low frequency range. The results suggest that subject-specific PSD details may be a predictor of the MS level. Furthermore, the analysis of the sway frequency spectrum provided insight into the intersubject differences in the use of postural control subsystems. The relationship observed between MS susceptibility and spontaneous posture is discussed in terms of postural sensory weighting and in relation to the nature of the provocative stimulus.     

A dynamical model for reflex activated head movements in the horizontal plane

 We present a controls systems model of horizontal-plane head movements during perturbations of the trunk, which for the first time interfaces a model of the human head with neural feedback controllers representing the vestibulocollic (VCR) and the cervicocollic (CCR) reflexes. This model is homeomorphic such that model structure and parameters are drawn directly from anthropomorphic, biomechanical and physiological studies. Using control theory we analyzed the system model in the time and frequency domains, simulating neck movement responses to input perturbations of the trunk. Without reflex control, the head and neck system produced a second-order underdamped response with a 5.2 dB resonant peak at 2.1 Hz. Adding the CCR component to the system dampened the response by approximately 7%. Adding the VCR component dampened head oscillations by 75%. The VCR also improved low-frequency compensation by increasing the gain and phase lag, creating a phase minimum at 0.1 Hz and a phase peak at 1.1 Hz. Combining all three components (mechanics, VCR and CCR) linearly in the head and neck system reduced the amplitude of the resonant peak to 1.1 dB and increased the resonant frequency to 2.9 Hz. The closed loop results closely fit human data, and explain quantitatively the characteristic phase peak often observed. Received: 15 April 1996 / Accepted in revised form: 1 July 1996     

Postural Sway and Gaze Can Track the Complex Motion of a Visual Target

Variability is an inherent and important feature of human movement. This variability has form exhibiting a chaotic structure. Visual feedback training using regular predictive visual target motions does not take into account this essential characteristic of the human movement, and may result in task specific learning and loss of visuo-motor adaptability. In this study, we asked how well healthy young adults can track visual target cues of varying degree of complexity during whole-body swaying in the Anterior-Posterior (AP) and Medio-Lateral (ML) direction. Participants were asked to track three visual target motions: a complex (Lorenz attractor), a noise (brown) and a periodic (sine) moving target while receiving online visual feedback about their performance. Postural sway, gaze and target motion were synchronously recorded and the degree of force-target and gaze-target coupling was quantified using spectral coherence and Cross-Approximate entropy. Analysis revealed that both force-target and gaze-target coupling was sensitive to the complexity of the visual stimuli motions. Postural sway showed a higher degree of coherence with the Lorenz attractor than the brown noise or sinusoidal stimulus motion. Similarly, gaze was more synchronous with the Lorenz attractor than the brown noise and sinusoidal stimulus motion. These results were similar regardless of whether tracking was performed in the AP or ML direction. Based on the theoretical model of optimal movement variability tracking of a complex signal may provide a better stimulus to improve visuo-motor adaptation and learning in postural control.     

Self-organization of trajectory formation

 Most studies examining the stability and change of patterns in biological coordination have focused on identifying generic bifurcation mechanisms in an already active set of components (see Kelso 1994). A less well understood phenomenon is the process by which previously quiescent degrees of freedom (df ) are spontaneously recruited and active df suppressed. To examine such behavior, in part I we study a single limb system composed of three joints (wrist, elbow, and shoulder) performing the kinematically redundant task of tracing a sequence of two-dimensional arcs of monotonically varying curvature, κ. Arcs were displayed on a computer screen in a decreasing and increasing κ sequence, and subjects rhythmically traced the arcs with the right hand in the sagittal plane at a fixed frequency (1.0 Hz), with motion restricted to flexion-extension of the wrist, elbow, and shoulder. Only a few coordinative patterns among the three joints were stably produced, e.g., in-phase (flexion-extension of one joint coordinated with flexion-extension of another joint) and antiphase (flexion-extension coordinated with extension-flexion). As κ was systematically increased and decreased, switching between relative phase patterns was observed around critical curvature values, κ_c. A serendipitous finding was a strong 2:1 frequency ratio between the shoulder and elbow that occurred across all curvature values for some subjects, regardless of the wrist-elbow relative phase pattern. Transitions from 1:1 to 2:1 frequency entrainment and vice versa were also observed. The results indicate that both amplitude modulation and relative phase change are utilized to stabilize the end-effector trajectory. In part II, a theoretical model is derived from three coupled nonlinear oscillators, in which the relative phases (φ) between the components and the relative joint amplitudes (ρ) are treated as collective variables with arc curvature as a control parameter. Received: 2 February 1996/Accepted in revised form: 13 December 1996     

Lateral dynamic balance reactions to circular translation of the visual field

Lateral sway of subjects in spontaneous dynamic balance conditions on a seesaw platform was measured during a visual stimulation monocularly produced by a rotating glass covered with a prism membrane. Prism rotation induced the perception of a circular translation of the whole visual field and an ocular pursuit movement. Therefore, the retinal slip that occurs in normal pursuit was cancelled. Strong stereo-typed postural reactions were observed in a direction that depended upon both the vertical visual field deviation and the eye stimulated: upper position of the right visual field induced a leftward sway resulting from an extension of the right hemibody; symmetrical reactions occurred for the left stimulation. The results suggest that the postural reactions recorded depend on the isolated oculomotor activity and, in addition, on retinal afferences corresponding to the temporal crescent of the stimulated side, which orientates the postural reaction on the homolateral lower limb muscles.     

Vestibular postural control model

Current models for physiological components and a posture control experiment conducted with three normal subjects form the basis for a model which seeks to describe quantitatively the control of body sway when only vestibular motion cues are used. Emphasis is placed on delineating the relative functional roles of the linear and the angular acceleration sensors and on modeling the functional interface between these sensors and the initiation of compensatory responses at the ankle joint.The model predicts the form of the postural response to a small sway disturbance; including initial detection of sway, characteristics of the transient correction, and maintenance of stability. The model suggests that postural stability requires a short time constant integration of semicircular canal output. Separation of semicircular canal and utricular otolith function into sway motion detector and static reference sensors respectively is demonstrated.This work was supported by NASA under Grant NGR-22-009-156.     

Effects of excessive body weight on postural control

Research that evaluated both static and dynamic stability was performed, to clarify the impact of excessive body weight on postural control. The spontaneous center of foot pressure (CP) motion during quiet stance and a range of forward voluntary CP displacements were studied in 100 obese, and 33 lean women. Characteristics of postural sway were acquired while the subjects were standing quiet on a force plate with eyes open (EO) and with eyes closed (EC). Their anterior range of CP voluntary displacements was assessed upon a range of maximal whole body leanings which were directed forward. A substantial reduction of postural sway was observed in all patients which had increased body weight. Main postural sway parameters i.e., the total path length as well as its directional components were negatively correlated with the body mass and body mass index (BMI). The range of a whole body voluntary forward leaning, did not exhibit any significant change in patients with an obesity grade of I and II. Such a deficit was, however, found in subjects with a body mass index above 40. In conclusion, the increased body weight imposed new biomechanical constraints, that resulted in functional adaptation of the control of the erect posture. This functional adaptation was characterized by a reduced postural sway associated with a substantial reduction of the dynamic stability range in subjects with BMI>40.     

Unintentional Interpersonal Synchronization Represented as a Reciprocal Visuo-Postural Feedback System: A Multivariate Autoregressive Modeling Approach

People’s behaviors synchronize. It is difficult, however, to determine whether synchronized behaviors occur in a mutual direction—two individuals influencing one another—or in one direction—one individual leading the other, and what the underlying mechanism for synchronization is. To answer these questions, we hypothesized a non-leader-follower postural sway synchronization, caused by a reciprocal visuo-postural feedback system operating on pairs of individuals, and tested that hypothesis both experimentally and via simulation. In the behavioral experiment, 22 participant pairs stood face to face either 20 or 70 cm away from each other wearing glasses with or without vision blocking lenses. The existence and direction of visual information exchanged between pairs of participants were systematically manipulated. The time series data for the postural sway of these pairs were recorded and analyzed with cross correlation and causality. Results of cross correlation showed that postural sway of paired participants was synchronized, with a shorter time lag when participant pairs could see one another’s head motion than when one of the participants was blindfolded. In addition, there was less of a time lag in the observed synchronization when the distance between participant pairs was smaller. As for the causality analysis, noise contribution ratio (NCR), the measure of influence using a multivariate autoregressive model, was also computed to identify the degree to which one’s postural sway is explained by that of the other’s and how visual information (sighted vs. blindfolded) interacts with paired participants’ postural sway. It was found that for synchronization to take place, it is crucial that paired participants be sighted and exert equal influence on one another by simultaneously exchanging visual information. Furthermore, a simulation for the proposed system with a wider range of visual input showed a pattern of results similar to the behavioral results.     

Enhancing human balance control with galvanic vestibular stimulation

 With galvanic vestibular stimulation (GVS), electrical current is delivered transcutaneously to the vestibular afferents through electrodes placed over the mastoid bones. This serves to modulate the continuous firing levels of the vestibular afferents, and causes a standing subject to lean in different directions depending on the polarity of the current. Our objective in this study was to test the hypothesis that the sway response elicited by GVS can be used to reduce the postural sway resulting from a mechanical perturbation. Nine subjects were tested for their postural responses to both galvanic stimuli and support-surface translations. Transfer-function models were fit to these responses and used to calculate a galvanic stimulus that would act to counteract sway induced by a support-surface translation. The subjects' responses to support-surface translations, without and with the stabilizing galvanic stimulus, were then measured. With the stabilizing galvanic stimulus, all subjects showed significant reductions in both sway amplitude and sway latency. Thus, with GVS, subjects maintained a more erect stance and followed the support-surface displacement more closely. These findings suggest that GVS could possibly form the basis for a vestibular prosthesis by providing a means through which an individual's posture can be systematically controlled. Received: 11 May 2000 / Accepted in revised form: 20 November 2000     

Modulation of Visually Evoked Postural Responses by Contextual Visual,Haptic and Auditory Information: A ‘Virtual Reality Check’

Externally generated visual motion signals can cause the illusion of self-motion in space (vection) and corresponding visually evoked postural responses (VEPR). These VEPRs are not simple responses to optokinetic stimulation, but are modulated by the configuration of the environment. The aim of this paper is to explore what factors modulate VEPRs in a high quality virtual reality (VR) environment where real and virtual foreground objects served as static visual, auditory and haptic reference points. Data from four experiments on visually evoked postural responses show that: 1) visually evoked postural sway in the lateral direction is modulated by the presence of static anchor points that can be haptic, visual and auditory reference signals; 2) real objects and their matching virtual reality representations as visual anchors have different effects on postural sway; 3) visual motion in the anterior-posterior plane induces robust postural responses that are not modulated by the presence of reference signals or the reality of objects that can serve as visual anchors in the scene. We conclude that automatic postural responses for laterally moving visual stimuli are strongly influenced by the configuration and interpretation of the environment and draw on multisensory representations. Different postural responses were observed for real and virtual visual reference objects. On the basis that automatic visually evoked postural responses in high fidelity virtual environments should mimic those seen in real situations we propose to use the observed effect as a robust objective test for presence and fidelity in VR.     

Modeling human postural sway using an intermittent control and hemodynamic perturbations

Ground reaction force during human quiet stance is modulated synchronously with the cardiac cycle through hemodynamics [1]. This almost periodic hemodynamic force induces a small disturbance torque to the ankle joint, which is considered as a source of endogenous perturbation that induces postural sway. Here we consider postural sway dynamics of an inverted pendulum model with an intermittent control strategy, in comparison with the traditional continuous-time feedback controller. We examine whether each control model can exhibit human-like postural sway, characterized by its power law behavior at the low frequency band 0.1–0.7 Hz, when it is weakly perturbed by periodic and/or random forcing mimicking the hemodynamic perturbation. We show that the continuous control model with typical feedback gain parameters hardly exhibits the human-like sway pattern, in contrast with the intermittent control model. Further analyses suggest that deterministic, including chaotic, slow oscillations that characterize the intermittent control strategy, together with the small hemodynamic perturbation, could be a possible mechanism for generating the postural sway.     

Postural Stability in Young Adults with Down Syndrome in Challenging Conditions

To evaluate postural control and performance in subjects with Down syndrome (SwDS), we measured postural sway (COP) in quiet stance in four 20-second tests: with eyes open or closed and on hard or foam surface. Ten SwDS and eleven healthy subjects participated, aged 29.8 (4.8) and 28.4 (3.9), respectively. The time-series recorded with the sampling rate of 100 Hz were used to evaluate postural performance (COP amplitude and mean velocity) and strategies (COP frequency, fractal dimension and entropy). There were no intergroup differences in the amplitude except the stance on foam pad with eyes open when SwDS had larger sway. The COP velocity and frequency were larger in SwDS than controls in all trials on foam pad. During stances on the foam pad SwDS increased fractal dimension showing higher complexity of their equilibrium system, while controls decreased sample entropy exhibiting more conscious control of posture in comparison to the stances on hard support surface. This indicated that each group used entirely different adjustments of postural strategies to the somatosensory challenge. It is proposed that the inferior postural control of SwDS results mainly from insufficient experience in dealing with unpredictable postural stimuli and deficit in motor learning.     

Comparing internal models of the dynamics of the visual environment

It is well known that the human postural control system responds to motion of the visual scene, but the implicit assumptions it makes about the visual environment and what quantities, if any, it estimates about the visual environment are unknown. This study compares the behavior of four models of the human postural control system to experimental data. Three include internal models that estimate the state of the visual environment, implicitly assuming its dynamics to be that of a linear stochastic process (respectively, a random walk, a general first-order process, and a general second-order process). In each case, all of the coefficients that describe the process are estimated by an adaptive scheme based on maximum likelihood. The fourth model does not estimate the state of the visual environment. It adjusts sensory weights to minimize the mean square of the control signal without making any specific assumptions about the dynamic properties of the environmental motion.We find that both having an internal model of the visual environment and its type make a significant difference in how the postural system responds to motion of the visual scene. Notably, the second-order process model outperforms the human postural system in its response to sinusoidal stimulation. Specifically, the second-order process model can correctly identify the frequency of the stimulus and completely compensate so that the motion of the visual scene has no effect on sway. In this case the postural control system extracts the same information from the visual modality as it does when the visual scene is stationary. The fourth model that does not simulate the motion of the visual environment is the only one that reproduces the experimentally observed result that, across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases but the phase remains roughly constant. Our results suggest that the human postural control system does not estimate the state of the visual environment to respond to sinusoidal stimuli.     

Use of wavelet coherence to assess two-joint coordination during quiet upright stance

Joint coordination plays a critical role in maintaining postural stability, yet there is limited existing work describing joint coordination patterns in the time–frequency domain. Here, two-joint coordination was examined during quiet upright stance. A wavelet coherence method was applied to quantify the coherence between ankle–trunk and ankle–head angles in the sagittal and frontal planes. Wavelet coherence results indicated intermittent joint coordination particularly for frequencies of 2.5–4.0 Hz. Coherence results were further processed to estimate mean time intervals between coherence instances, coherence burst frequency, and the ratio of in-phase versus anti-phase behaviors. Time intervals between intermittent coherence were 1.3–1.5 sec, coherence burst frequency was ~0.4 Hz, and phase ratios were ~1.0. Intermittent “bursting” of postural muscles may account for the finding of intermittent coherence in the noted frequency band. Some age and/or gender differences in coherence were found, and may be related to comparable differences in postural control ability or strategies. Results from application of this new method support earlier evidence that kinematic coordination is achieved intermittently rather than continuously during quiet upright stance. This method may provide richer information regarding such coordination, and could be a useful approach in future studies.     

Getting Your Sea Legs

Sea travel mandates changes in the control of the body. The process by which we adapt bodily control to life at sea is known as getting one''s sea legs. We conducted the first experimental study of bodily control as maritime novices adapted to motion of a ship at sea. We evaluated postural activity (stance width, stance angle, and the kinematics of body sway) before and during a sea voyage. In addition, we evaluated the role of the visible horizon in the control of body sway. Finally, we related data on postural activity to two subjective experiences that are associated with sea travel; seasickness, and mal de debarquement. Our results revealed rapid changes in postural activity among novices at sea. Before the beginning of the voyage, the temporal dynamics of body sway differed among participants as a function of their (subsequent) severity of seasickness. Body sway measured at sea differed among participants as a function of their (subsequent) experience of mal de debarquement. We discuss implications of these results for general theories of the perception and control of bodily orientation, for the etiology of motion sickness, and for general phenomena of perceptual-motor adaptation and learning.     

Sinusoidal galvanic stimulation of the labyrinths and postural responses

We studied the effect of sinusoidal stimulation of the labyrinths on postural reflexes in man, using a 0.3 Hz current of alternating polarity and +/- 1 mA intensity for stimulation. The test subjects were tested binaurally by the bipolar method (BB), with two electrodes on the mastoid processes, and binaurally by the monopolar method (BM), with electrodes localized bilaterally on the mastoid process and the hand. Stabilographic postural parameters were measured in 22 subjects in five experimental situations. Each situation lasted 60 s. Body sway, detected by astabilometer, was recorded on a Philips FM tape-recorder and then analysed off-line on a PDP-11/34 computer. On BB stimulation of the labyrinths, the variance of body sway in the left-right (LR) direction increased more than in the anteroposterior (AP) direction. In BM stimulation, only the variance of LR sway increased. Other posturographic parameters displayed a similar effect. From the aspect of body sway frequency, BB stimulation produced a peak in the course of the power spectral density of the lateral stabilogram at 0.3 Hz. In this experimental situation, a habituation effect was manifested, depending on the subject. It can be stated that binaural bipolar (BB) stimulation of the labyrinths selectively influences lateral body sway, while the increase in AP body sway in this situation is merely a concomitant phenomenon.     

Shannon and Renyi entropies to classify effects of Mild Traumatic Brain Injury on postural sway

Background

Mild Traumatic Brain Injury (mTBI) has been identified as a major public and military health concern both in the United States and worldwide. Characterizing the effects of mTBI on postural sway could be an important tool for assessing recovery from the injury.

Methodology/Principal Findings

We assess postural sway by motion of the center of pressure (COP). Methods for data reduction include calculation of area of COP and fractal analysis of COP motion time courses. We found that fractal scaling appears applicable to sway power above about 0.5 Hz, thus fractal characterization is only quantifying the secondary effects (a small fraction of total power) in the sway time series, and is not effective in quantifying long-term effects of mTBI on postural sway. We also found that the area of COP sensitively depends on the length of data series over which the COP is obtained. These weaknesses motivated us to use instead Shannon and Renyi entropies to assess postural instability following mTBI. These entropy measures have a number of appealing properties, including capacity for determination of the optimal length of the time series for analysis and a new interpretation of the area of COP.

Conclusions

Entropy analysis can readily detect postural instability in athletes at least 10 days post-concussion so that it appears promising as a sensitive measure of effects of mTBI on postural sway.

Availability

The programs for analyses may be obtained from the authors.