Goal Equivalent Manifold Research Articles

A model of task-level human stepping regulation yields semistable walking.

A simple lateral dynamic walker, with swing leg dynamics and three adjustable input parameters, is used to study how motor regulation affects frontal-plane stepping. Motivated by experimental observations and phenomenological models, we imposed task-level multi-objective regulation targeting the walker's optimal lateral foot placement at each step. The regulator prioritizes achieving step width and lateral body position goals to varying degrees by choosing a mixture parameter. Our model thus integrates a lateral mechanical template, which captures the fundamental mechanics of frontal-plane walking, with a lateral motor regulation template, an empirically verified model of how humans manipulate lateral foot placements in a goal-directed manner. The model captures experimentally observed stepping fluctuation statistics and demonstrates how linear empirical models of stepping dynamics can emerge from first-principles nonlinear mechanics. We find that task-level regulation gives rise to a goal-equivalent manifold in the system's extended state space of mechanical states and inputs, a subset of which contains a continuum of period-1 gaits forming a semistable set: perturbations off of any of its gaits result in transients that return to the set, though typically to different gaits.

A model of task-level human stepping regulation yields semistable walking.

A simple lateral dynamic walker, with swing leg dynamics and three adjustable input parameters, is used to study how motor regulation affects frontal plane stepping. Motivated by experimental observations and phenomenological models, we imposed task-level multiobjective regulation targeting the walker's optimal lateral foot placement at each step. The regulator prioritizes achieving step width and lateral body position goals to varying degrees by choosing a mixture parameter. Our model thus integrates a lateral mechanical template, which captures fundamental mechanics of frontal-plane walking, with a lateral motor regulation template, an empirically verified model of how humans manipulate lateral foot placements in a goal-directed manner. The model captures experimentally observed stepping fluctuation statistics and demonstrates how linear empirical models of stepping dynamics can emerge from first-principles nonlinear mechanics. We find that task-level regulation gives rise to a goal equivalent manifold in the system's extended state space of mechanical states and inputs, a subset of which contains a continuum of period-1 gaits forming a semistable set: perturbations off of any of its gaits result in transients that return to the set, though typically to different gaits.

How older adults regulate lateral stepping on narrowing walking paths

Walking humans often navigate complex, varying walking paths. To reduce falls, we must first determine how older adults purposefully vary their steps in contexts that challenge balance. Here, 20 young (21.7±2.6 yrs) and 18 older (71.6±6.0 yrs) healthy adults walked on virtual paths that slowly narrowed (from 45 cm to as narrow as 5 cm). Participants could switch onto an “easier” path whenever they chose. We applied our Goal Equivalent Manifold framework to quantify how participants adjusted their lateral stepping variability and step-to-step corrections of step width and lateral position as these paths narrowed. We also extracted these characteristics at the locations where participants switched paths. As paths narrowed, all participants reduced their lateral stepping variability, but older adults less so. To stay on the narrowing paths, young adults increasingly corrected step-to-step deviations in lateral position more, by correcting step-to-step deviations in step width less. Conversely, as older adults also increasingly corrected lateral position deviations, they did so without sacrificing correcting step-to-step deviations in step width, presumably to preserve balance. While older adults left the narrowing paths sooner, several of their lateral stepping characteristics remained similar to those of younger adults. Older adults largely maintained overall walking performance per se, but they did so by changing how they balanced the competing stepping regulation requirements intrinsic to the task: maintaining position vs. step width. Thus, balancing how to achieve multiple concurrent stepping goals while walking provides older adults the flexibility they need to appropriately adapt their stepping on continuously narrowing walking paths.

Recruit-aged adults may preferentially weight task goals over deleterious cost functions during short duration loaded and imposed gait tasks

Optimal motor control that is stable and adaptable to perturbation is reflected in the temporal arrangement and regulation of gait variability. Load carriage and forced-marching are common military relevant perturbations to gait that have been implicated in the high incidence of musculoskeletal injuries in military populations. We investigated the interactive effects of load magnitude and locomotion pattern on motor variability, stride regulation and spatiotemporal complexity during gait in recruit-aged adults. We further investigated the influences of sex and task duration. Healthy adults executed trials of running and forced-marching with and without loads at 10% above their gait transition velocity. Spatiotemporal parameters were analyzed using a goal equivalent manifold approach. With load and forced-marching, individuals used a greater array of motor solutions to execute the task goal (maintain velocity). Stride-to-stride regulation became stricter as the task progressed. Participants exhibited optimal spatiotemporal complexity with significant but not meaningful differences between sexes. With the introduction of load carriage and forced-marching, individuals relied on a strategy that maximizes and regulates motor solutions that achieve the task goal of velocity specifically but compete with other task functions. The appended cost penalties may have deleterious effects during prolonged execution, potentially increasing the risk of musculoskeletal injuries.

Temporal and spatial goal-directed reaching in upper limb prosthesis users.

Understanding the fundamental characteristics of prosthetic movement control is imperative in improving prosthesis design and training. This study quantified how using an upper limb prosthesis affected performance during goal-directed reaching tasks. Nine prosthesis users with unilateral transradial limb absence and nine healthy controls completed a series of goal-directed reaching movements with different goals: one spatial and three temporal with different goal frequencies. We quantified end-point accuracy, smoothness, and peak speed for the spatial task and temporal accuracy, horizontal distance, and speed for the temporal task. For the temporal task, we also used a goal-equivalent manifold (GEM) approach to decompose variability in movement distance and speed into those perpendicular and tangential to the GEM. Detrended fluctuation analysis (DFA) quantified the temporal persistence of each time series. For the spatial task, movements made with prostheses were less smooth, had larger end-point errors, and had slower peak speed compared to those with control limbs (p < 0.041). For the temporal task, movements made with prostheses and intact limbs of prosthesis users and control limbs were similar in distance and speed and had similar timing errors (p > 0.138). Timing errors, distance, speed, and GEM deviations were corrected similarly between prosthetic limbs and control limbs (p > 0.091). The mean and variability of distance, speed, and perpendicular deviations decreased with increased goal frequency (p < 0.001). Our results suggest that prosthesis users have a sufficient internal model to successfully complete ballistic movements but are unable to accurately complete movements requiring substantial feedback.

Rethinking margin of stability: Incorporating step-to-step regulation to resolve the paradox

Derived from inverted pendulum dynamics, mediolateral Margin of Stability (MoSML) is a mechanically-grounded measure of instantaneous frontal-plane stability. However, average MoSML measures yield paradoxical results. Gait pathologies or perturbations often induce larger (supposedly “more stable”) average MoSML, despite clearly destabilizing factors. However, people do not walk “on average” – they walk (and sometimes lose balance) one step at a time. We assert the paradox arises because averaging MoSML discards crucial step-to-step dynamics. We present a framework unifying the inverted pendulum with Goal-Equivalent Manifold (GEM) analyses. We identify in the pendulum’s center-of-mass dynamics constant-MoSML manifolds, including one candidate “stability GEM” signifying the goal to maintain some constant MoSML∗. We used this framework to assess step-to-step MoSML dynamics of humans walking in destabilizing environments. While goal-relevant deviations were readily corrected, people did not exploit equifinality by allowing deviations to persist along this GEM. Thus, maintaining a constant MoSML∗ is inconsistent with observed step-to-step fluctuations in center-of-mass states. Conversely, the extent to which participants regulated fluctuations in mediolateral foot placements strongly predicted their regulation of center-of-mass fluctuations. Thus, center-of-mass dynamics may arise indirectly as a consequence of regulating mediolateral foot placements. To help resolve the paradox caused by averaging MoSML, we present a new statistic, Probability of Instability (PoIL), used here to predict lateral instability likelihood. Participants exhibited increased PoIL when destabilized (p = 9.45 × 10−34), despite exhibiting larger (“more stable”) average MoSML (p = 1.70 × 10−15). Thus, PoIL correctly captured people’s increased risk of losing lateral balance, whereas average MoSML did not. PoIL also helps explain why people’s average MoSML increased in destabilizing contexts.

Is there a trade-off between economy and task goal variability in transfemoral amputee gait?

BackgroundEnergy cost minimization has been widely accepted to regulate gait. Optimization principles have been frequently used to explain how individuals adapt their gait pattern. However, there have been rare attempts to account for the role of variability in this optimization process. Motor redundancy can enable individuals to perform tasks reliably while achieving energy optimization. However, we do not know how the non-goal-equivalent and goal-equivalent variability is regulated. In this study, we investigated how unilateral transfemoral amputees regulate step and stride variability based on the task to achieve energy economy.MethodsNine individuals with unilateral transfemoral amputation walked on a treadmill at speeds of 0.6, 0.8, 1.0, 1.2 and 1.4 m/s using their prescribed passive prostheses. We calculated the step-to-step and stride-to-stride variability and applied goal equivalent manifold (GEM) based control to decompose goal-equivalent and non-goal-equivalent manifold. To quantify the energy economy, the energy recovery rate (R) was calculated based on potential energy and kinetic energy. Comparisons were made between GEM variabilities and commonly used standard deviation measurements. A linear regression model was used to investigate the trade-off between R and GEM variabilities.ResultsOur analysis shows greater variability along the goal-equivalent manifold compared to the non-goal-equivalent manifold (p < 0.001). Moreover, our analysis shows lower energy recovery rate for amputee gait compared to nonamputee gait (at least 20% less at faster walking speed). We found a negative relationship between energy recovery rate and non-goal-equivalent variability. Compared to the standard deviation measurements, the variability decomposed using GEM reflected the preferred walking speed and the limitation of the passive prosthetic device.ConclusionIndividuals with amputation cleverly leverage task redundancy, regulating step and stride variability to the GEM. This result suggests that task redundancy enables unilateral amputees to benefit from motor variability in terms of energy economy. The differences observed between prosthetic step and intact step support the development of prosthetic limbs capable of enhancing positive work during the double support phase and of powered prosthesis controllers that allow for variability along the task space while minimizing variability that interferes with the task goal. This study provides a different perspective on amputee gait analysis and challenges the field to think differently about the role of variability.

Significance of trends in gait dynamics.

Trends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The averages of scaling exponents of ST and SL MARS residuals are slightly smaller than 0.5. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. 10.1371/journal.pcbi.1000856.

Load Magnitude and Locomotion Pattern Alter Locomotor System Function in Healthy Young Adult Women.

IntroductionDuring cyclical steady state ambulation, such as walking, variability in stride intervals can indicate the state of the system. In order to define locomotor system function, observed variability in motor patterns, stride regulation and gait complexity must be assessed in the presence of a perturbation. Common perturbations, especially for military populations, are load carriage and an imposed locomotion pattern known as forced marching (FM). We examined the interactive effects of load magnitude and locomotion pattern on motor variability, stride regulation and gait complexity during bipedal ambulation in recruit-aged females.MethodsEleven healthy physically active females (18–30 years) completed 1-min trials of running and FM at three load conditions: no additional weight/bodyweight (BW), an additional 25% of BW (BW + 25%), and an additional 45% of BW (BW + 45%). A goal equivalent manifold (GEM) approach was used to assess motor variability yielding relative variability (RV; ratio of “good” to “bad” variability) and detrended fluctuation analysis (DFA) to determine gait complexity on stride length (SL) and stride time (ST) parameters. DFA was also used on GEM outcomes to calculate stride regulation.ResultsThere was a main effect of load (p = 0.01) on RV; as load increased, RV decreased. There was a main effect of locomotion (p = 0.01), with FM exhibiting greater RV than running. Strides were regulated more tightly and corrected quicker at BW + 45% compared (p < 0.05) to BW. Stride regulation was greater for FM compared to running. There was a main effect of load for gait complexity (p = 0.002); as load increased gait complexity decreased, likewise FM had less (p = 0.02) gait complexity than running.DiscussionThis study is the first to employ a GEM approach and a complexity analysis to gait tasks under load carriage. Reduction in “good” variability as load increases potentially exposes anatomical structures to repetitive site-specific loading. Furthermore, load carriage magnitudes of BW + 45% potentially destabilize the system making individuals less adaptable to additional perturbations. This is further evidenced by the decrease in gait complexity, which all participants demonstrated values similarly observed in neurologically impaired populations during the BW + 45% load condition.

A head-worn display (“smart glasses”) has adverse impacts on the dynamics of lateral position control during gait

BackgroundHead-worn displays (e.g., “smart glasses”) are an emerging technology to provide information, and in many situations they might be used while walking. However, little evidence exists regarding the effects of head-worn displays on walking performance. We found earlier that “smart glasses” had smaller adverse effects on measures of gait variability in the anterior-posterior direction vs. other types of information displays. Participants, however, complained about motion sickness and perceived instability while using smart glasses. Research questionWere the participants’ complaints a result of adverse effects of the smart glasses on the dynamics of lateral stepping and gait stability? MethodsTwenty individuals walked on a treadmill in four different conditions; single-task walking, and three dual-task walking conditions, the latter using smart glasses, smartphone, and a paper-based system to provide secondary cognitive tasks. We assessed the dynamics of lateral stepping and gait stability using the goal equivalent manifold and maximum Lyapunov exponent, respectively. ResultsThe dynamics of the lateral stepping were more adversely affected using smart glasses compared to the other types of information displays. However, stability measures revealed that the participants were more unstable when they used the smartphone and paper-based system. SignificancePromising results in terms of stability and adaptability suggest that head-worn display technology is a potentially useful alternative to smartphones and other types of information displays for reducing the risk of a fall. Results regarding perceptions of instability and a loss of control over lateral stepping, however, imply that this technology requires further development prior to real-work implementations.

Exploration of different classes of metrics to characterize motor variability during repetitive symmetric and asymmetric lifting tasks

The substantial kinematic degrees-of-freedom available in human movement lead to inherent variations in a repetitive movement, or motor variability (MV). Growing evidence suggests that characterizing MV permits a better understanding of potential injury mechanisms. Several diverse methods, though, have been used to quantify MV, but limited evidence exists regarding the merits of these methods in the occupational context. In this work, we explored different classes of methods for characterizing MV during symmetric and asymmetric box lifting tasks. Kinematic MV of both the whole-body center-of-mass (COM) and the box were quantified, using metrics derived from a linear method (Standard Deviation), a non-linear method (Sample Entropy; an index of movement regularity), and a novel application of an equifinality method (Goal Equivalent Manifold; an index related to the set of effective motor solutions). Our results suggest that individuals manipulate regularity and the set of effective motor solutions to overcome unwanted motor noises related to the COM. These results, together with earlier evidence, imply that individuals may prioritize stability over variability with increasing task difficulty. Task performance also appeared to deteriorate with decreasing variability and regularity of the COM. We conclude that diverse metrics of MV may be complimentary to reveal differences in MV.

Humans use multi-objective control to regulate lateral foot placement when walking.

A fundamental question in human motor neuroscience is to determine how the nervous system generates goal-directed movements despite inherent physiological noise and redundancy. Walking exhibits considerable variability and equifinality of task solutions. Existing models of bipedal walking do not yet achieve both continuous dynamic balance control and the equifinality of foot placement humans exhibit. Appropriate computational models are critical to disambiguate the numerous possibilities of how to regulate stepping movements to achieve different walking goals. Here, we extend a theoretical and computational Goal Equivalent Manifold (GEM) framework to generate predictive models, each posing a different experimentally testable hypothesis. These models regulate stepping movements to achieve any of three hypothesized goals, either alone or in combination: maintain lateral position, maintain lateral speed or “heading”, and/or maintain step width. We compared model predictions against human experimental data. Uni-objective control models demonstrated clear redundancy between stepping variables, but could not replicate human stepping dynamics. Most multi-objective control models that balanced maintaining two of the three hypothesized goals also failed to replicate human stepping dynamics. However, multi-objective models that strongly prioritized regulating step width over lateral position did successfully replicate all of the relevant step-to-step dynamics observed in humans. Independent analyses confirmed this control was consistent with linear error correction and replicated step-to-step dynamics of individual foot placements. Thus, the regulation of lateral stepping movements is inherently multi-objective and balances task-specific trade-offs between competing task goals. To determine how people walk in their environment requires understanding both walking biomechanics and how the nervous system regulates movements from step-to-step. Analogous to mechanical “templates” of locomotor biomechanics, our models serve as “control templates” for how humans regulate stepping movements from each step to the next. These control templates are symbiotic with well-established mechanical templates, providing complimentary insights into walking regulation.

Humans control stride-to-stride stepping movements differently for walking and running, independent of speed

As humans walk or run, external (environmental) and internal (physiological) disturbances induce variability. How humans regulate this variability from stride-to-stride can be critical to maintaining balance. One cannot infer what is “controlled” based on analyses of variability alone. Assessing control requires quantifying how deviations are corrected across consecutive movements. Here, we assessed walking and running, each at two speeds. We hypothesized differences in speed would drive changes in variability, while adopting different gaits would drive changes in how people regulated stepping. Ten healthy adults walked/ran on a treadmill under four conditions: walk or run at comfortable speed, and walk or run at their predicted walk-to-run transition speed. Time series of relevant stride parameters were analyzed to quantify variability and stride-to-stride error-correction dynamics within a Goal-Equivalent Manifold (GEM) framework. In all conditions, participants’ stride-to-stride control respected a constant-speed GEM strategy. At each consecutively faster speed, variability tangent to the GEM increased (p ≤ 0.031), while variability perpendicular to the GEM decreased (p ≤ 0.044). There were no differences (p ≥ 0.999) between gaits at the transition speed. Differences in speed determined how stepping variability was structured, independent of gait, confirming our first hypothesis. For running versus walking, measures of GEM-relevant statistical persistence were significantly less (p ≤ 0.004), but showed minimal-to-no speed differences (0.069 ≤ p ≤ 0.718). When running, people corrected deviations both more quickly and more directly, each indicating tighter control. Thus, differences in gait determined how stride-to-stride fluctuations were regulated, independent of speed, confirming our second hypothesis.

Information presentation through a head-worn display ("smart glasses") has a smaller influence on the temporal structure of gait variability during dual-task gait compared to handheld displays (paper-based system and smartphone).

The need to complete multiple tasks concurrently is a common occurrence both daily life and in occupational activities, which can often include simultaneous cognitive and physical demands. As one example, there is increasing availability of head-worn display technologies that can be employed when a user is mobile (e.g., while walking). This new method of information presentation may, however, introduce risks of adverse outcomes such as a decrement to gait performance. The goal of this study was thus to quantify the effects of a head-worn display (i.e., smart glasses) on motor variability during gait and to compare these effects with those of other common information displays (i.e., smartphone and paper-based system). Twenty participants completed four walking conditions, as a single task and in three dual-task conditions (three information displays). In the dual-task conditions, the information display was used to present several cognitive tasks. Three different measures were used to quantify variability in gait parameters for each walking condition (using the cycle-to-cycle standard deviation, sample entropy, and the “goal-equivalent manifold” approach). Our results indicated that participants used less adaptable gait strategies in dual-task walking using the paper-based system and smartphone conditions compared with single-task walking. Gait performance, however, was less affected during dual-task walking with the smart glasses. We conclude that the risk of an adverse gait event (e.g., a fall) in head-down walking conditions (i.e., the paper-based system and smartphone conditions) were higher than in single-task walking, and that head-worn displays might help reduce the risk of such events during dual-task gait conditions.

Temporal changes in motor variability during prolonged lifting/lowering and the influence of work experience

Existing research indicates that repetitive motions are strongly correlated with the development of work-related musculoskeletal disorders (WMSDs). Resulting from the redundant degrees-of-freedom in the human body, there are variations in motions that occur while performing a repetitive task. These variations are termed motor variability (MV), and may be beneficial for reducing WMSD risks. To better understand the potential role of MV in preventing injury risk, we evaluated the effects of fatigue on MV using data collected during a lab-based prolonged, repetitive lifting/lowering task. We also investigated whether experienced workers used different motor control strategies than novices to adapt to fatigue. MV of the whole-body center-of-mass (COM) and box trajectory were quantified using cycle-to-cycle standard deviation, sample entropy, and goal equivalent manifold (GEM) methods. In both groups, there were significantly increased variations of the COM with fatigue, and with a more substantial increase in a direction that did not affect task performance. Fatigue deteriorated the task goal and made it more difficult for participants to maintain their performance. Experienced workers also had higher MV than novices. Based on these results, we conclude that flexible motor control strategies are employed to reduce fatigue effects during a prolonged repetitive task.

Increased gait variability may not imply impaired stride-to-stride control of walking in healthy older adults: Winner: 2013 Gait and Clinical Movement Analysis Society Best Paper Award

Older adults exhibit increased gait variability that is associated with fall history and predicts future falls. It is not known to what extent this increased variability results from increased physiological noise versus a decreased ability to regulate walking movements. To “walk”, a person must move a finite distance in finite time, making stride length (Ln) and time (Tn) the fundamental stride variables to define forward walking. Multiple age-related physiological changes increase neuromotor noise, increasing gait variability. If older adults also alter how they regulate their stride variables, this could further exacerbate that variability. We previously developed a Goal Equivalent Manifold (GEM) computational framework specifically to separate these causes of variability. Here, we apply this framework to identify how both young and high-functioning healthy older adults regulate stepping from each stride to the next. Healthy older adults exhibited increased gait variability, independent of walking speed. However, despite this, these healthy older adults also concurrently exhibited no differences (all p>0.50) from young adults either in how their stride variability was distributed relative to the GEM or in how they regulated, from stride to stride, either their basic stepping variables or deviations relative to the GEM. Using a validated computational model, we found these experimental findings were consistent with increased gait variability arising solely from increased neuromotor noise, and not from changes in stride-to-stride control. Thus, age-related increased gait variability likely precedes impaired stepping control. This suggests these changes may in turn precede increased fall risk.

Goal equivalent manifold analysis of task performance in non-specific LBP and healthy subjects during repetitive trunk movement: Effect of load, velocity, symmetry

Motor abundance allows reliability of motor performance despite its variability. The nature of this variability provides important information on the flexibility of control strategies. This feature of control may be affected by low back pain (LPB) and trunk flexion/extension conditions.Goal equivalent manifold (GEM) analysis was used to quantify the ability to exploit motor abundance during repeated trunk flexion/extension in healthy individuals and people with chronic non-specific LBP (CNSLBP).Kinematic data were collected from 22 healthy volunteers and 22 CNSLBP patients during metronomically timed, repeated trunk flexion/extension in three conditions of symmetry, velocity, and loading; each at two levels. A goal function for the task was defined as maintaining a constant movement time at each cycle. Given the GEM, flexibility index and performance index were calculated respectively as amounts of goal-equivalent variability and the ratio of goal-equivalent to non-goal-equivalent variability.CNSLBP group was as similar as healthy individuals in both flexibility index (p=0.41) and performance index (p=0.24). Performance index was higher in asymmetric (p<0.001), high velocity (p<0.001), and loaded (p=0.006) conditions.Performance and flexibility in using motor abundance were influenced by repeated trunk flexion/extension conditions. However, these measures were not significantly affected by CNSLBP.

Error Correction and the Structure of Inter-Trial Fluctuations in a Redundant Movement Task.

We study inter-trial movement fluctuations exhibited by human participants during the repeated execution of a virtual shuffleboard task. Focusing on skilled performance, theoretical analysis of a previously-developed general model of inter-trial error correction is used to predict the temporal and geometric structure of variability near a goal equivalent manifold (GEM). The theory also predicts that the goal-level error scales linearly with intrinsic body-level noise via the total body-goal sensitivity, a new derived quantity that illustrates how task performance arises from the interaction of active error correction and passive sensitivity properties along the GEM. Linear models estimated from observed fluctuations, together with a novel application of bootstrapping to the estimation of dynamical and correlation properties of the inter-trial dynamics, are used to experimentally confirm all predictions, thus validating our model. In addition, we show that, unlike “static” variability analyses, our dynamical approach yields results that are independent of the coordinates used to measure task execution and, in so doing, provides a new set of task coordinates that are intrinsic to the error-regulation process itself.

Effects of local and widespread muscle fatigue on movement timing.

Repetitive movements can cause muscle fatigue, leading to motor reorganization, performance deficits, and/or possible injury. The effects of fatigue may depend on the type of fatigue task employed, however. The purpose of this study was to determine how local fatigue of a specific muscle group versus widespread fatigue of various muscle groups affected the control of movement timing. Twenty healthy subjects performed an upper extremity low-load work task similar to sawing for 5 continuous minutes both before and after completing a protocol that either fatigued all the muscles used in the task (widespread fatigue) or a protocol that selectively fatigued the primary muscles used to execute the pushing stroke of the sawing task (localized fatigue). Subjects were instructed to time their movements with a metronome. Timing error, movement distance, and speed were calculated for each movement. Data were then analyzed using a goal-equivalent manifold approach to quantify changes in goal-relevant and non-goal-relevant variability. We applied detrended fluctuation analysis to each time series to quantify changes in fluctuation dynamics that reflected changes in the control strategies used. After localized fatigue, subjects made shorter, slower movements and exerted greater control over non-goal-relevant variability. After widespread fatigue, subjects exerted less control over non-goal-relevant variability and did not change movement patterns. Thus, localized and widespread muscle fatigue affected movement differently. Local fatigue may reduce the available motor solutions and therefore cause greater movement reorganization than widespread muscle fatigue. Subjects altered their control strategies but continued to achieve the timing goal after both fatigue tasks.

An Alternative Perspective on Postural Stability and Variability

In this issue of Exercise and Sport Sciences Reviews, the article “Task-Dependent Postural Control Throughout the Lifespan” by Haddad et al. (2) promotes two major ideas: 1) Postural control is highly task dependent and 2) Postural variability is functional — it reflects the availability of multiple solutions (resulting from kinematic and neuromuscular redundancy) and may play an exploratory role by generating sensory information. These ideas are central to an ecological-dynamical perspective on postural control. Haddad et al. (2) make important contributions to that perspective by summarizing recent findings on postural control across the lifespan and by emphasizing the relevance of this approach for clinical and rehabilitation applications. Postural stability typically is described in terms of minimizing spontaneous postural sway and counteracting perturbations that displace the center of mass away from a single reference point centered within the base of support. The alternative proposed by Haddad et al. (2) is that successful postural control amounts to achieving body configurations that fall somewhere within a stable subspace of the postural configuration space (depicted graphically in Configuration Space Diagrams). Variability within the stable region of the configuration space is acceptable and will not lead to falls. The boundary of the stable region is the reference for upright stance; there is not just one body configuration that is most desirable or stable. The boundaries are dynamic; they change on a moment-to-moment basis as the actor moves, the environment changes, or task demands arise and dissolve. What is “stable” reflects suprapostural task goals and the behavioral (including social) and environmental contexts. Configuration space diagrams potentially are useful, but there is a need to develop the idea beyond its current qualitative descriptive form. The uncontrolled manifold (4), goal-equivalent manifold (1), and the Tolerance-Noise-Covariation (3) methods may be well suited for that purpose. These methods differ in important ways yet share in common the idea that motor performance can be understood by describing how relatively microscopic motor system degrees of freedom (DF) map onto relatively macroscopic task variables. In redundant systems, many combinations of the microscale DF preserve a value of the task variable. This is equivalent to saying that there is a stable subregion (or manifold) of the configuration space, whose dimensions are the microscale DF, within which the task variable remains constant. Variations within that manifold can remain unchecked without leading to task failure. For quiet stance, joint angles can serve as the microscale DF and center of mass position can serve as the task variable, but expanding this idea to incorporate the approach of Haddad et al. (2) requires defining the task variable in terms of the functional goals of the suprapostural task. Postural variability is informative for postural control; Postural sway generates information (visual, somatosensory, vestibular, etc.) that is specific to the changing position of the body and thus can be useful for controlling posture. A challenge that remains for researchers is to determine whether (and when) postural sway is explicitly exploratory (i.e., it is an intentional information-seeking act) rather than performatory (in the service of a behavioral goal) or unintended noise. At some level, this may not matter; regardless of intent, postural sway may provide information useful for postural control. But the term “exploratory” connotes an intention, and, if this is indeed the case, then efforts to model postural control will benefit from fleshing out this idea more definitely. Lastly, the authors raise important implications for rehabilitation. Models that account for properties of the actor, task, and environment may be more useful in clinical settings than models based on quiet stance. Quiet stance may lack the sensitivity and specificity desirable in a diagnostic tool for clinical applications because the absence of an explicit suprapostural task leaves postural control underconstrained. Potentially fruitful directions for clinical research may be to identify the limits to which an actor’s postural control system is appropriately adaptive so as to support a variety of suprapostural task goals and to track the evolution of the stable region during the course of rehabilitation.