Local dynamic stability versus kinematic variability of continuous overground and treadmill walking

This study quantified the relationships between local dynamic stabiliht and variabilitr during continuous overground and treadmill walking. Stride-to-stride standard deviations were computed from temporal and kinematic data. Marimum finite-time Lyapunov exponents were estimated to quantify local dynamic stability. Local stability of gait kinematics was shown to be achieved over multiple consecutive strides. Traditional measures of variability poorly predicted local stability. Treadmill walking was associated with significant changes in both variability and local stability. Thus, motorized treadmills may produce misleading or erroneous results in situations where changes in neuromuscular control are likely to affect the variability and/or stability of locomotion.

Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking

Patients with diabetic peripheral neuropathy are significantly more likely to fall while walking than subjects with intact sensation. While it has been suggested that these patients walk slower to improve locomotor stability, slower speeds are also associated with increased locomotor variability, and increased variability has traditionally been equated with loss of stability. If the latter were true, this would suggest that slowing down, as a locomotor control strategy, should be completely antithetical to the goal of maintaining stability. The present study resolves these seemingly paradoxical findings by using methods from nonlinear time series analysis to directly quantify the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Fourteen patients with severe peripheral neuropathy and 12 gender-, age-, height-, and weight-matched non-diabetic controls participated. Sagittal plane angles of the right hip, knee, and ankle joints and tri-axial accelerations of the trunk were measured during 10 min of continuous overground walking at self-selected speeds. Maximum finite-time Lyapunov exponents were computed for each time series to quantify the local dynamic stability of these movements. Neuropathic patients exhibited slower walking speeds and better local dynamic stability of upper body movements in the horizontal plane than did control subjects. The differences in local dynamic stability were significantly predicted by differences in walking speed, but not by differences in sensory status. These results support the hypothesis that reductions in walking speed are a compensatory strategy used by neuropathic patients to maintain dynamic stability of the upper body during level walking.

Variability in motor learning: relocating, channeling and reducing noise

Variability in motor performance decreases with practice but is never entirely eliminated, due in part to inherent motor noise. The present study develops a method that quantifies how performers can shape their performance to minimize the effects of motor noise on the result of the movement. Adopting a statistical approach on sets of data, the method quantifies three components of variability (tolerance, noise, and covariation) as costs with respect to optimal performance. T-Cost quantifies how much the result could be improved if the location of the data were optimal, N-Cost compares actual results to results with optimal dispersion at the same location, and C-Cost represents how much improvement stands to be gained if the data covaried optimally. The TNC-Cost analysis is applied to examine the learning of a throwing task that participants practiced for 6 or 15 days. Using a virtual set-up, 15 participants threw a pendular projectile in a simulated concentric force field to hit a target. Two variables, angle and velocity at release, fully determined the projectile's trajectory and thereby the accuracy of the throw. The task is redundant and the successful solutions define a nonlinear manifold. Analysis of experimental results indicated that all three components were present and that all three decreased across practice. Changes in T-Cost were considerable at the beginning of practice; C-Cost and N-Cost diminished more slowly, with N-Cost remaining the highest. These results showed that performance variability can be reduced by three routes: by tuning tolerance, covariation and noise in execution. We speculate that by exploiting T-Cost and C-Cost, participants minimize the effects of inevitable intrinsic noise.

Origins and violations of the 2/3 power law in rhythmic three-dimensional arm movements

The 2/3 power law, the nonlinear relationship between tangential velocity and radius of curvature of the end-effector trajectory, is thought to be a fundamental constraint of the central nervous system in the formation of rhythmic endpoint trajectories. However, studies on the 2/3 power law have been confined largely to planar drawing patterns of relatively small size. With the hypothesis that this strategy overlooks nonlinear effects that are constitutive in movement generation, the present experiments tested the validity of the power law in elliptical patterns that were not confined to a planar surface and which were performed by the unconstrained 7-degrees of freedom (DOF) arm, with significant variations in pattern size and workspace orientation. Data were recorded from five human subjects where the seven joint angles and the endpoint trajectories were analyzed. Additionally, an anthropomorphic 7-DOF robot arm served as a "control subject" whose endpoint trajectories were generated on the basis of the human joint angle data, modeled as simple harmonic oscillations. Analyses of the endpoint trajectories demonstrate that the power law is systematically violated with increasing pattern size, in both exponent and the goodness of fit. The origins of these violations can be explained analytically based on smooth, rhythmic trajectory formation and the kinematic structure of the human arm. We conclude that, in unconstrained rhythmic movements, the power law seems to be a by-product of a movement system that favors smooth trajectories, and that it is unlikely to serve as a primary movement-generating principle. Our data rather suggest that subjects employed smooth oscillatory pattern generators in joint space to realize the required movement patterns.

Segmentation of endpoint trajectories does not imply segmented control

While it is generally assumed that complex movements consist of a sequence of simpler units, the quest to define these units of action, or movement primitives, remains an open question. In this context, two hypotheses of movement segmentation of endpoint trajectories in three-dimensional human drawing movements are reexamined: (1) the stroke-based segmentation hypothesis based on the results that the proportionality coefficient of the two-thirds power law changes discontinuously with each new "stroke," and (2) the segmentation hypothesis inferred from the observation of piecewise planar endpoint trajectories of three-dimensional drawing movements. In two experiments human subjects performed a set of elliptical and figure eight patterns of different sizes and orientations using their whole arm in three dimensions. The kinematic characteristics of the endpoint trajectories and the seven joint angles of the arm were analyzed. While the endpoint trajectories produced similar segmentation features to those reported in the literature, analyses of the joint angles show no obvious segmentation but rather continuous oscillatory patterns. By approximating the joint angle data of human subjects with sinusoidal trajectories, and by implementing this model on a 7-degree-of-freedom (DOF) anthropomorphic robot arm, it is shown that such a continuous movement strategy can produce exactly the same features as observed by the above segmentation hypotheses. The origin of this apparent segmentation of endpoint trajectories is traced back to the nonlinear transformations of the forward kinematics of human arms. The presented results demonstrate that principles of discrete movement generation may not be reconciled with those of rhythmic movement as easily as has been previously suggested, while the generalization of nonlinear pattern generators to arm movements can offer an interesting alternative to approach the question of units of action.

One-Handed Juggling: A Dynamical Approach to a Rhythmic Movement Task

The skill of rhythmically juggling a ball on a racket was investigated from the viewpoint of nonlinear dynamics. The difference equations that model the dynamical system were analyzed by means of local and nonlocal stability analyses. These analyses showed that the task dynamics offer an economical juggling pattern that is stable even for open-loop actuator motion. For this pattern, two types of predictions were extracted: (a) Stable periodic bouncing is sufficiently characterized by a negative acceleration of the racket at the moment of impact with the ball, and (b) a nonlinear scaling relation maps different juggling trajectories onto one topologically equivalent dynamical system. The relevance of these results for the human control of action was evaluated in an experiment in which subjects (N = 6) performed a comparable task of juggling a ball on a paddle. Task manipulations involved different juggling heights and gravity conditions of the ball. The following predictions were confirmed: (a) For stable rhythmic performance, the paddle's acceleration at impact is negative and fluctuations of the impact acceleration follow predictions from global stability analysis; and (b) for each subject, the realizations of juggling for the different experimental conditions are related by the scaling relation. These results permit one to conclude that humans reliably exploit the stable solutions inherent to the dynamics of the given task and do not overrule these dynamics by other control mechanisms. The dynamical scaling serves as an efficient principle for generating different movement realizations from only a few parameter changes and is discussed as a dynamical formalization of the principle of motor equivalence.

Validity and reliability of Kinect skeleton for measuring shoulder joint angles: a feasibility study

OBJECTIVE

To test the reliability and validity of shoulder joint angle measurements from the Microsoft Kinect™ for virtual rehabilitation.

DESIGN

Test-retest reliability and concurrent validity, feasibility study.

SETTING

Motion analysis laboratory.

PARTICIPANTS

A convenience sample of 10 healthy adults.

METHODS

Shoulder joint angle was assessed in four static poses, two trials for each pose, using: (1) the Kinect; (2) a three-dimensional motion analysis system; and (3) a clinical goniometer. All poses were captured with the Kinect from the frontal view. The two poses of shoulder flexion were also captured with the Kinect from the sagittal view.

MAIN OUTCOME MEASURES

Absolute and relative test-retest reliability of the Kinect for the measurement of shoulder angle was determined in each pose with intraclass correlation coefficients (ICCs), standard error of the measure and minimal detectable change. The 95% limits of agreement (LOA) between the Kinect and the standard methods for measuring shoulder angle were computed to determine concurrent validity.

RESULTS

While the Kinect provided to be highly reliable (ICC 0.76-0.98) for measuring shoulder angle from the frontal view, the 95% LOA between the Kinect and the two measurement standards were greater than ±5° in all poses for both views.

CONCLUSIONS

Before the Kinect is used to measure movements for virtual rehabilitation applications, it is imperative to understand its limitations in precision and accuracy for the measurement of specific joint motions.

Diffusive, Synaptic, and Synergetic Coupling: An Evaluation Through In-Phase and Antiphase Rhythmic Movements

The in-phase and antiphase patterns of interlimb l:1 frequency locking were contrasted with respect to models of coordination dynamics in biological movement systems that are based on diffusive coupling, synaptic coupling, and synergetic principles. Predictions were made from each model concerning the stable relative phase phi between the rhythmic units, its standard deviation SDphi and the self-chosen coupled frequency omegasubc;. The experimental task involved human subjects oscillating two handheld pendulums either in-phase or antiphase. The eigenfrequencies of the two hand-pendulum systems were manipulated by varying the length and mass of each pendulum individually. Relative to an eigenfrequency difference of Delta equal to zero, |Deltaomega| > 0 displaced phi from phi = 0 and phi = pi, and amplified SDphi. omegasubc; decreased with |Deltaomega|. Both the displacement of phi and SDphi were greater in the antiphase mode. Additionally, the displacement of phi increased more sharply with |Delta| for antiphase than for in-phase coordination. In contrast, omegasubc; was identical for the two coordination modes. Of the models of interlimb coordination dynamics, the synergetic model was the most successful in addressing the pattern of dependencies of phi and SDphi. The specific forms of the functions relating omegasubc; and phi to Deltaomega pose challenges for all three models, however

Bouncing a ball: tuning into dynamic stability

Rhythmically bouncing a ball with a racket was investigated and modeled with a nonlinear map. Model analyses provided a variable defining a dynamically stable solution that obviates computationally expensive corrections. Three experiments evaluated whether dynamic stability is optimized and what perceptual support is necessary for stable behavior. Two hypotheses were tested: (a) Performance is stable if racket acceleration is negative at impact, and (b) variability is lowest at an impact acceleration between -4 and -1 m/s2. In Experiment 1 participants performed the task, eyes open or closed, bouncing a ball confined to a 1-dimensional trajectory. Experiment 2 eliminated constraints on racket and ball trajectory. Experiment 3 excluded visual or haptic information. Movements were performed with negative racket accelerations in the range of highest stability. Performance with eyes closed was more variable, leaving acceleration unaffected. With haptic information, performance was more stable than with visual information alone.

Force and timing variability in rhythmic unimanual tapping

In 3 experiments the interdependencies between timing and force production in unimanual paced and self-paced rhythmic tapping tasks were examined as participants (N = 6 in each experiment) tapped (a) to 1 of 3 target periods (333 ms, 500 ms, and 1,000 ms), while they simultaneously produced a constant peak force (PF) over a 50-s trial; (b) to produce 1 of 3 target forces (5, 10, and 15 N) at their preferred frequency, while keeping their rhythm as invariant as possible; and (c) to all combinations of target force and period. The results showed that (a) magnitudes of force and period were largely independent; (b) variability in timing increased proportionally with tapping period, and the variability in force increased with peak force; (c) force variability decreased at faster tapping rates; and (d) timing variability decreased with increasing force levels. (e) Analysis of tap-to-tap variability revealed adjustments over sequences of taps and an acceleration in the tapping rate in unpaced conditions. The interdependencies of force and time are discussed with respect to the challenges they provide for an oscillator-based account.

Dynamics of a bouncing ball in human performance

On the basis of a modified bouncing-ball model, we investigated whether human movements utilize principles of dynamic stability in their performance of a similar movement task. Stability analyses of the model provided predictions about conditions indicative of a dynamically stable period-one regime. In a series of experiments, human subjects bounced a ball rhythmically on a racket and displayed these conditions supporting that they attuned to and exploited the dynamic stability properties of the task.

The detuning factor in the dynamics of interlimb rhythmic coordination

Dynamical models of two coupled biological oscillators interpret the detuning term as an arithmetic difference between the uncoupled frequencies, delta omega = (omega 1-omega 2). This delta omega interpretation of detuning was addressed in four experiments in which human subjects oscillated pendulums in their right and left hands in 1:1 frequency locking in antiphase (Experiments 1-3) or inphase (Experiment 4). Differences between the uncoupled frequencies were manipulated through differences in the equivalent simple pendulum lengths, and the effects of this manipulation on the detuning of relative phase from pi or O and the standard deviation of relative phase SD phi were measured. In Experiment 1, the same values of omega i were satisfied by several different physical configurations. The experiment confirmed that the detuning term is related strictly to the uncoupled frequencies rather than to other physical characteristics of the oscillators. Experiments 2, 3 and 4 showed, however, that the particular dependency of fixed point drift and SD phi on delta omega depends on the particulars of omega 1 and omega 2. With variations in delta omega brought about by different omega 1 and omega 2 that always formed a constant ratio, fixed point drift related inversely to delta omega, and SD phi varied with delta omega in ways that depended on the magnitude of the constant ratio. These outcomes do not conform to expectations from models of coordination dynamics that interpret detuning as (omega 1-omega 2).

Sinusoidal visuomotor tracking: intermittent servo-control or coupled oscillations?

In visuomotor tasks that involve accuracy demands, small directional changes in the trajectories have been taken as evidence of feedback-based error corrections. In the present study variability, or intermittency, in visuomanual tracking of sinusoidal targets was investigated. Two lines of analyses were pursued: First, the hypothesis that humans fundamentally act as intermittent servo-controllers was re-examined, probing the question of whether discontinuities in the movement trajectory directly imply intermittent control. Second, an alternative hypothesis was evaluated: that rhythmic tracking movements are generated by entrainment between the oscillations of the target and the actor, such that intermittency expresses the degree of stability. In 2 experiments, participants (N = 6 in each experiment) swung 1 of 2 different hand-held pendulums, tracking a rhythmic target that oscillated at different frequencies with a constant amplitude. In 1 line of analyses, the authors tested the intermittency hypothesis by using the typical kinematic error measures and spectral analysis. In a 2nd line, they examined relative phase and its variability, following analyses of rhythmic interlimb coordination. The results showed that visually guided corrective processes play a role, especially for slow movements. Intermittency, assessed as frequency and power components of the movement trajectory, was found to change as a function of both target frequency and the manipulandum's inertia. Support for entrainment was found in conditions in which task frequency was identical to or higher than the effector's eigenfrequency. The results suggest that it is the symmetry between task and effector that determines which behavioral regime is dominant.

An Experimental Note on Defining Frequency Competition in Intersegmental Coordination Dynamics

Synchronous coordination between two body segments departs from phase locking at 0 or pi radians when the segments are asymmetrical. In models of coordination dynamics, this detuning is typically quantified by Deltaomega = (omega1 - omega2), where omega1 and omega2 are the uncoupled frequencies of the two segments. An experiment is reported in which the magnitude of Deltaomega not equal 0 was satisfied by different ratios Omega of omega1 and omega2. The degree of detuning was found to vary systematically with Omega and Deltaomega. This result corroborates previous research using the complementary manipulation of varying Deltaomega for a fixed Omega. A challenge for future dynamical modeling is identifying precisely how the detuning quantity incorporates both the absolute and relative differences in the. uncoupled segmental frequencies.

Bouncing a ball: tuning into dynamic stability

Rhythmically bouncing a ball with a racket was investigated and modeled with a nonlinear map. Model analyses provided a variable defining a dynamically stable solution that obviates computationally expensive corrections. Three experiments evaluated whether dynamic stability is optimized and what perceptual support is necessary for stable behavior. Two hypotheses were tested: (a) Performance is stable if racket acceleration is negative at impact, and (b) variability is lowest at an impact acceleration between -4 and -1 m/s2. In Experiment 1 participants performed the task, eyes open or closed, bouncing a ball confined to a 1-dimensional trajectory. Experiment 2 eliminated constraints on racket and ball trajectory. Experiment 3 excluded visual or haptic information. Movements were performed with negative racket accelerations in the range of highest stability. Performance with eyes closed was more variable, leaving acceleration unaffected. With haptic information, performance was more stable than with visual information alone.