Movement variability near goal equivalent manifolds: fluctuations, control, and model-based analysis

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 Healthy Older Adults Enact Lateral Maneuvers While Walking

BACKGROUND

Walking requires frequent maneuvers to navigate changing environments with shifting goals. Humans accomplish maneuvers and simultaneously maintain balance primarily by modulating their foot placement, but a direct trade-off between these two objectives has been proposed. As older adults may rely more on foot placement to maintain lateral balance, they may be less able to adequately adapt stepping to perform lateral maneuvers.

RESEARCH QUESTION

How do older adults adapt stepping to enact lateral lane-change maneuvers, and how do physical and perceived ability influence their task performance?

METHODS

Twenty young (21.7 ± 2.6 yrs) and 18 older (71.6 ± 6.0 yrs) adults walked on a motorized treadmill in a virtual environment. Following an audible and visual cue, participants switched between two parallel paths, centered 0.6 m apart, to continue walking on their new path. We quantified when participants initiated the maneuver following the cue, as well as their step width, lateral position, and stepping variability ellipses at each maneuver step.

RESULTS

Young and older adults did not differ in when they initiated the maneuver, but participants with lower perceived ability took longer to do so. Young and older adults also did not exhibit differences in step width or lateral positions at any maneuver step, but participants with greater physical ability reached their new path faster. While only older adults exhibited stepping adaptations prior to initiating the maneuver, both groups traded off stability for maneuverability to enact the lateral maneuver.

SIGNIFICANCE

Physical and perceived balance ability, rather than age per se, differentially influenced maneuver task performance. Humans must make decisions related to the task of walking itself and do so based on both physical and perceived factors. Understanding and targeting these interactions may help improve walking performance among older adults.

From neural noise to co-adaptability: Rethinking the multifaceted architecture of motor variability

In the last decade, the source and the functional meaning of motor variability have attracted considerable attention in behavioral and brain sciences. This construct classically combined different levels of description, variable internal robustness or coherence, and multifaceted operational meanings. We provide here a comprehensive review of the literature with the primary aim of building a precise lexicon that goes beyond the generic and monolithic use of motor variability. In the pars destruens of the work, we model three domains of motor variability related to peculiar computational elements that influence fluctuations in motor outputs. Each domain is in turn characterized by multiple sub-domains. We begin with the domains of noise and differentiation. However, the main contribution of our model concerns the domain of adaptability, which refers to variation within the same exact motor representation. In particular, we use the terms learning and (social)fitting to specify the portions of motor variability that depend on our propensity to learn and on our largely constitutive propensity to be influenced by external factors. A particular focus is on motor variability in the context of the sub-domain named co-adaptability. Further groundbreaking challenges arise in the modeling of motor variability. Therefore, in a separate pars construens, we attempt to characterize these challenges, addressing both theoretical and experimental aspects as well as potential clinical implications for neurorehabilitation. All in all, our work suggests that motor variability is neither simply detrimental nor beneficial, and that studying its fluctuations can provide meaningful insights for future research.

Generalizing stepping concepts to non-straight walking

People rarely walk in straight lines. Instead, we make frequent turns or other maneuvers. Spatiotemporal parameters fundamentally characterize gait. For straight walking, these parameters are well-defined for the task of walking on a straight path. Generalizing these concepts to non-straight walking, however, is not straightforward. People follow non-straight paths imposed by their environment (sidewalk, windy hiking trail, etc.) or choose readily-predictable, stereotypical paths of their own. People actively maintain lateral position to stay on their path and readily adapt their stepping when their path changes. We therefore propose a conceptually coherent convention that defines step lengths and widths relative to predefined walking paths. Our convention simply re-aligns lab-based coordinates to be tangent to a walker's path at the mid-point between the two footsteps that define each step. We hypothesized this would yield results both more correct and more consistent with notions from straight walking. We defined several common non-straight walking tasks: single turns, lateral lane changes, walking on circular paths, and walking on arbitrary curvilinear paths. For each, we simulated idealized step sequences denoting "perfect" performance with known constant step lengths and widths. We compared results to path-independent alternatives. For each, we directly quantified accuracy relative to known true values. Results strongly confirmed our hypothesis. Our convention returned vastly smaller errors and introduced no artificial stepping asymmetries across all tasks. All results for our convention rationally generalized concepts from straight walking. Taking walking paths explicitly into account as important task goals themselves thus resolves conceptual ambiguities of prior approaches.

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.

Generalizing Stepping Concepts To Non-Straight Walking

People rarely walk in straight lines. Instead, we make frequent turns or other maneuvers. Spatiotemporal parameters fundamentally characterize gait. For straight walking, these parameters are well-defined for that task of walking on a straight path. Generalizing these concepts to non-straight walking, however, is not straightforward. People also follow non-straight paths imposed by their environment (store aisle, sidewalk, etc.) or choose readily-predictable, stereotypical paths of their own. People actively maintain lateral position to stay on their path and readily adapt their stepping when their path changes. We therefore propose a conceptually coherent convention that defines step lengths and widths relative to known walking paths. Our convention simply re-aligns lab-based coordinates to be tangent to a walker's path at the mid-point between the two footsteps that define each step. We hypothesized this would yield results both more correct and more consistent with notions from straight walking. We defined several common non-straight walking tasks: single turns, lateral lane changes, walking on circular paths, and walking on arbitrary curvilinear paths. For each, we simulated idealized step sequences denoting "perfect" performance with known constant step lengths and widths. We compared results to path- independent alternatives. For each, we directly quantified accuracy relative to known true values. Results strongly confirmed our hypothesis. Our convention returned vastly smaller errors and introduced no artificial stepping asymmetries across all tasks. All results for our convention rationally generalized concepts from straight walking. Taking walking paths explicitly into account as important task goals themselves thus resolves conceptual ambiguities of prior approaches.

Bilateral arm movements are coordinated via task-dependent negotiations between independent and codependent control, but not by a "coupling" control policy

Prior research has shown that coordination of bilateral arm movements might be attributed to either control policies that minimize performance and control costs regardless of bilateral symmetry or by control coupling, which activates bilaterally homologous muscles as a single unit to achieve symmetric performance. We hypothesize that independent bimanual control (movements of one arm are performed without influence on the other) and codependent bimanual control (two arms are constrained to move together with high spatiotemporal symmetry) are two extremes on a coordination spectrum that can be negotiated to meet infinite variations in task demands. To better understand and distinguish between these views, we designed a task where minimization of either control costs or asymmetry would yield different patterns of coordination. Participants made bilateral reaches with a shared visual cursor to a midline target. We then covertly varied the gain contribution of either hand to the shared cursor's horizontal position. Across two experiments, we show that bilateral coordination retains high task-dependent sensitivity to subtle visual feedback gain asymmetries applied to the shared cursor. Specifically, we found a change from strong spatial covariation between hands during equal gains to more independent control during asymmetric gains, which occurred rapidly and with high specificity to the dimension of gain manipulation. Furthermore, the extent of spatial covariation was graded to the magnitude of perpendicular gain asymmetry between hands. These findings suggest coordination of bilateral arm movements flexibly maneuvers along a continuous coordination spectrum in a task-dependent manner that cannot be explained by bilateral control coupling.NEW & NOTEWORTHY Minimization of performance and control costs and efferent coupling between bilaterally homologous muscle groups have been separately hypothesized to describe patterns of bimanual coordination. Here, we address whether the mechanisms mediating independent and codependent control between limbs can be weighted for successful task performance. Using bilaterally asymmetric visuomotor gain perturbations, we show bimanual coordination can be characterized as a negotiation along a spectrum between extremes of independent and codependent control, but not efferent control coupling.

Beyond simple laboratory studies: Developing sophisticated models to study rich behavior

Psychology and neuroscience are concerned with the study of behavior, of internal cognitive processes, and their neural foundations. However, most laboratory studies use constrained experimental settings that greatly limit the range of behaviors that can be expressed. While focusing on restricted settings ensures methodological control, it risks impoverishing the object of study: by restricting behavior, we might miss key aspects of cognitive and neural functions. In this article, we argue that psychology and neuroscience should increasingly adopt innovative experimental designs, measurement methods, analysis techniques and sophisticated computational models to probe rich, ecologically valid forms of behavior, including social behavior. We discuss the challenges of studying rich forms of behavior as well as the novel opportunities offered by state-of-the-art methodologies and new sensing technologies, and we highlight the importance of developing sophisticated formal models. We exemplify our arguments by reviewing some recent streams of research in psychology, neuroscience and other fields (e.g., sports analytics, ethology and robotics) that have addressed rich forms of behavior in a model-based manner. We hope that these "success cases" will encourage psychologists and neuroscientists to extend their toolbox of techniques with sophisticated behavioral models - and to use them to study rich forms of behavior as well as the cognitive and neural processes that they engage.

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.

How Healthy Older Adults Enact Lateral Maneuvers While Walking

Background

Walking requires frequent maneuvers to navigate changing environments with shifting goals. Humans accomplish maneuvers and simultaneously maintain balance primarily by modulating their foot placement, but a direct trade-off between these two objectives has been proposed. As older adults rely more on foot placement to maintain lateral balance, they may be less able to adequately adapt stepping to perform lateral maneuvers.

Research Question

How do older adults adapt stepping to enact lateral lane-change maneuvers, and how do physical and perceived ability influence their task performance?

Methods

Twenty young (21.7 ± 2.6 yrs) and 18 older (71.6 ± 6.0 yrs) adults walked on a motorized treadmill in a virtual environment. Following an audible and visual cue, participants switched between two parallel paths, centered 0.6m apart, to continue walking on their new path. We quantified when participants initiated the maneuver following the cue, as well as their step width, lateral position, and stepping variability ellipses at each maneuver step.

Results

Young and older adults did not differ in when they initiated the maneuver, but participants with lower perceived ability took longer to do so. Young and older adults also did not exhibit differences in step width or lateral positions at any maneuver step, but participants with greater physical ability reached their new path faster. While only older adults exhibited stepping adaptations prior to initiating the maneuver, both groups traded-off stability for maneuverability to enact the lateral maneuver.

Significance

Physical and perceived balance ability, rather than age per se, differentially influenced maneuver task performance. Humans must make decisions related to the task of walking itself and do so based on both physical and perceived factors. Understanding and targeting these interactions may help improve walking performance among older adults.

Between a Walk and a Hard Place: How Stepping Patterns Change While Navigating Environmental Obstacles

Maintaining a consistent relationship between each footfall and the body's motion is a key mechanism to maintain balance while walking. However, environmental features, for example, puddles/obstacles, impose additional constraints on foot placement. This study investigated how healthy young individuals alter foot placements to simultaneously manage body-centric and environmental constraints during an obstacle-crossing task. Consistent step length promotes balance for all steps, whereas accurate foot placement around the obstacle is essential to avoid a trip. While crossing an obstacle, any error in positioning one foot relative to the obstacle can be compensated by selecting the placement of the subsequent step. However, compensation will necessarily alter step length from its average value. The interstep covariance index computed from two consecutive foot placements was used to quantify this tradeoff between body-centric and environmental constraints for six consecutive steps while approaching, crossing, and resuming unobstructed gait after crossing the obstacle. The index declined only when either one or both feet were adjacent to the obstacle. The decline was driven in part by a tendency toward higher step length variability. Thus, changes in the stepping patterns to address the environmental constraint occurred at the cost of the body-centric constraint. However, the step length never ceased to be controlled; the interstep covariance index was positive for all steps. Overall, participants adapted foot placement control to account for the larger threat to balance. The environmental constraint was prioritized only when a potential trip posed greater threat to balance compared with the threat posed by variable step length.

Adaptive multi-objective control explains how humans make lateral maneuvers while walking

To successfully traverse their environment, humans often perform maneuvers to achieve desired task goals while simultaneously maintaining balance. Humans accomplish these tasks primarily by modulating their foot placements. As humans are more unstable laterally, we must better understand how humans modulate lateral foot placement. We previously developed a theoretical framework and corresponding computational models to describe how humans regulate lateral stepping during straight-ahead continuous walking. We identified goal functions for step width and lateral body position that define the walking task and determine the set of all possible task solutions as Goal Equivalent Manifolds (GEMs). Here, we used this framework to determine if humans can regulate lateral stepping during non-steady-state lateral maneuvers by minimizing errors consistent with these goal functions. Twenty young healthy adults each performed four lateral lane-change maneuvers in a virtual reality environment. Extending our general lateral stepping regulation framework, we first re-examined the requirements of such transient walking tasks. Doing so yielded new theoretical predictions regarding how steps during any such maneuver should be regulated to minimize error costs, consistent with the goals required at each step and with how these costs are adapted at each step during the maneuver. Humans performed the experimental lateral maneuvers in a manner consistent with our theoretical predictions. Furthermore, their stepping behavior was well modeled by allowing the parameters of our previous lateral stepping models to adapt from step to step. To our knowledge, our results are the first to demonstrate humans might use evolving cost landscapes in real time to perform such an adaptive motor task and, furthermore, that such adaptation can occur quickly-over only one step. Thus, the predictive capabilities of our general stepping regulation framework extend to a much greater range of walking tasks beyond just normal, straight-ahead walking.

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.

Coupled and Synchronization Models of Rhythmic Arm Movement in Planar Plane

Nonlinear dynamics have become a new perspective on model human movement variability; however, it is still a debate whether chaotic behavior is indeed possible to present during a rhythmic movement. This paper reports on the nonlinear dynamical behavior of coupled and synchronization models of a planar rhythmic arm movement. Two coupling schemes between a planar arm and an extended Duffing-Van der Pol (DVP) oscillator are investigated. Chaos tools, namely phase space, Poincare section, Lyapunov Exponent (LE), and heuristic approach are applied to observe the dynamical behavior of orbit solutions. For the synchronization, an orientation angle is modeled as a single well DVP oscillator implementing a Proportional Derivative (PD)-scheme. The extended DVP oscillator is used as a drive system, while the orientation angle of the planar arm is a response system. The results show that the coupled system exhibits very rich dynamical behavior where a variety of solutions from periodic, quasi-periodic, to chaotic orbits exist. An advanced coupling scheme is necessary to yield the route to chaos. By modeling the orientation angle as the single well DVP oscillator, which can synchronize with other dynamical systems, the synchronization can be achieved through the PD-scheme approach.

Insight into the hierarchical control governing leg stiffness during the stance phase of running

Leg stiffness plays a key role in the storage and release of elastic energy during stance. However, the extent to which a runner is able to reuse stored energy remains a limiting factor in determining their running effectiveness. In this study, ten habitual rearfoot strikers and ten habitual forefoot strikers were asked to run on a treadmill in three footwear conditions: traditional, neutral, and minimal running shoes. We examined the effect of habitual foot strike pattern and footwear on leg stiffness control within three task-relevant phases of stance (i.e. touch-down, loading, unloading). Control was quantified using stride-to-stride leg stiffness time-series and the coefficient of variability and detrended fluctuation analysis (DFA). The results are interpreted within a theoretical framework that blends dynamic systems theory and optimal feedback control. Results indicate that leg stiffness control is tightly regulated by an active control process during the loading period of stance. In contrast, the touch-down and unloading phases are driven mostly by passive allometric control mechanisms. The effect of footwear on leg stiffness control was inconclusive due to inconsistent trends across three shoe types. However, stiffness control was affected by landing technique. Habitual rearfoot strike runners have reduced DFA values during the touch-down and unloading phases. These sub-phases are associated with an allometric control process and suggests that rearfoot strike runners express a reduction in system complexity for leg stiffness control and hence, a less adaptable system.

Viability, task switching, and fall avoidance of the simplest dynamic walker

Walking humans display great versatility when achieving task goals, like avoiding obstacles or walking alongside others, but the relevance of this to fall avoidance remains unknown. We recently demonstrated a functional connection between the motor regulation needed to achieve task goals (e.g., maintaining walking speed) and a simple walker's ability to reject large disturbances. Here, for the same model, we identify the viability kernel-the largest state-space region where the walker can step forever via at least one sequence of push-off inputs per state. We further find that only a few basins of attraction of the speed-regulated walker's steady-state gaits can fully cover the viability kernel. This highlights a potentially important role of task-level motor regulation in fall avoidance. Therefore, we posit an adaptive hierarchical control/regulation strategy that switches between different task-level regulators to avoid falls. Our task switching controller only requires a target value of the regulated observable-a "task switch"-at every walking step, each chosen from a small, predetermined collection. Because humans have typically already learned to perform such goal-directed tasks during nominal walking conditions, this suggests that the "information cost" of biologically implementing such controllers for the nervous system, including cognitive demands in humans, could be quite low.

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

BACKGROUND

Energy 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.

METHODS

Nine 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.

RESULTS

Our 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.

CONCLUSION

Individuals 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.

Running Injury Paradigms and Their Influence on Footwear Design Features and Runner Assessment Methods: A Focused Review to Advance Evidence-Based Practice for Running Medicine Clinicians

Many runners seek health professional advice regarding footwear recommendations to reduce injury risk. Unfortunately, many clinicians, as well as runners, have ideas about how to select running footwear that are not scientifically supported. This is likely because much of the research on running footwear has not been highly accessible outside of the technical footwear research circle. Therefore, the purpose of this narrative review is to update clinical readers on the state of the science for assessing runners and recommending running footwear that facilitate the goals of the runner. We begin with a review of basic footwear construction and the features thought to influence biomechanics relevant to the running medicine practitioner. Subsequently, we review the four main paradigms that have driven footwear design and recommendation with respect to injury risk reduction: Pronation Control, Impact Force Modification, Habitual Joint (Motion) Path, and Comfort Filter. We find that evidence in support of any paradigm is generally limited. In the absence of a clearly supported paradigm, we propose that in general clinicians should recommend footwear that is lightweight, comfortable, and has minimal pronation control technology. We further encourage clinicians to arm themselves with the basic understanding of the known effects of specific footwear features on biomechanics in order to better recommend footwear on a patient-by-patient basis.

The road towards understanding embodied decisions

Most current decision-making research focuses on classical economic scenarios, where choice offers are prespecified and where action dynamics play no role in the decision. However, our brains evolved to deal with different choice situations: "embodied decisions". As examples of embodied decisions, consider a lion that has to decide which gazelle to chase in the savannah or a person who has to select the next stone to jump on when crossing a river. Embodied decision settings raise novel questions, such as how people select from time-varying choice options and how they track the most relevant choice attributes; but they have long remained challenging to study empirically. Here, we summarize recent progress in the study of embodied decisions in sports analytics and experimental psychology. Furthermore, we introduce a formal methodology to identify the relevant dimensions of embodied choices (present and future affordances) and to map them into the attributes of classical economic decisions (probabilities and utilities), hence aligning them. Studying embodied decisions will greatly expand our understanding of what decision-making is.

Loaded forced-marching shifts mechanical contributions proximally and disrupts stride-to-stride joint work modulation in recruit aged women

BACKGROUND

Military personnel in combat roles often perform gait tasks with additional load, which can affect the contributions of joint mechanical work (positive and negative). Furthermore, different locomotion patterns can also affect joint specific work contributions. While mean behavior of joint work is important to understanding gait, changes in joint kinetic modulation, or the regulation/control of stride-to-stride joint work variability is necessary to elucidate locomotor system function. Suboptimal modulation exhibited as a stochastic time-series (large fluctuation followed by an opposite smaller fluctuation) could potentially affect locomotion efficiency and portend injury risk. It remains unclear how the locomotor system responds to a combination of load perturbations and varying locomotion patterns.

RESEARCH QUESTION

What are the interactive effects of load magnitude and locomotion pattern on joint positive/negative work and joint work modulation in healthy, active, recruit-aged women?

METHODS

Eleven healthy, active, recruit-aged (18-33 years) women ran and forced-marched (walking at a velocity an individual would typically jog) in bodyweight (BW), an additional 25 % of BW (+25 %BW) and an additional 45 % of BW (+45 %BW) conditions at a velocity above their gait transition velocity. Joint work was calculated as the time integral of joint power. Joint work modulation was assessed with detrended fluctuation analysis (DFA) on consecutive joint work time-series.

RESULTS

Joint work contributions shifted proximally for forced-marching demonstrated by lesser (p < .001) positive/negative ankle work but greater (p = .001) positive hip work contributions compared to running. Running exhibited optimal positive ankle work modulation compared to forced-marching (p = .040). Knee and ankle negative joint work modulation was adversely impacted compared to the hip during forced-marching (p < .001).

SIGNIFICANCE

Employing forced-marching gait while under loads of 25 and 45 % of BW reduces the ability of the plantar-flexors and knee extensors to optimally contribute to energy absorption and propulsion in recruit-aged women, potentially reducing metabolic efficiency and increasing injury risk.

A Hessian-based decomposition characterizes how performance in complex motor skills depends on individual strategy and variability

In complex real-life motor skills such as unconstrained throwing, performance depends on how accurate is on average the outcome of noisy, high-dimensional, and redundant actions. What characteristics of the action distribution relate to performance and how different individuals select specific action distributions are key questions in motor control. Previous computational approaches have highlighted that variability along the directions of first order derivatives of the action-to-outcome mapping affects performance the most, that different mean actions may be associated to regions of the actions space with different sensitivity to noise, and that action covariation in addition to noise magnitude matters. However, a method to relate individual high-dimensional action distribution and performance is still missing. Here we introduce a decomposition of performance into a small set of indicators that compactly and directly characterize the key performance-related features of the distribution of high-dimensional redundant actions. Central to the method is the observation that, if performance is quantified as a mean score, the Hessian (second order derivatives) of the action-to-score function determines how the noise of the action distribution affects performance. We can then approximate the mean score as the sum of the score of the mean action and a tolerance-variability index which depends on both Hessian and action covariance. Such index can be expressed as the product of three terms capturing noise magnitude, noise sensitivity, and alignment of the most variable and most noise sensitive directions. We apply this method to the analysis of unconstrained throwing actions by non-expert participants and show that, consistently across four different throwing targets, each participant shows a specific selection of mean action score and tolerance-variability index as well as specific selection of noise magnitude and alignment indicators. Thus, participants with different strategies may display the same performance because they can trade off suboptimal mean action for better tolerance-variability and higher action variability for better alignment with more tolerant directions in action space.

Walking humans trade off different task goals to regulate lateral stepping

People walk in complex environments where they must adapt their steps to maintain balance and satisfy changing task goals. How people do this is not well understood. We recently developed computational models of lateral stepping, based on Goal Equivalent Manifolds that serve as motor regulation templates, to identify how people regulate walking movements from step-to-step. In normal walking, healthy adults strongly maintain step width, but also lateral position on their path. Here, we used this framework to pose empirically-testable hypotheses about how humans might adapt their lateral stepping dynamics when asked to prioritize different stepping goals. Participants walked on a treadmill in a virtual-reality environment under 4 conditions: normal walking and, while given direct feedback at each step, walking while trying to maintain constant step width, constant absolute lateral position, or constant heading (direction). Time series of lateral stepping variables were extracted, and variability and statistical persistence (reflecting step-to-step regulation) quantified. Participants exhibited less variability of the prescribed stepping variable compared to normal walking during each feedback condition. Stepping regulation results supported our models' predictions: to maintain constant step width or position, people either maintained or increased regulation of the prescribed variable, but also decreased regulation of its complement. Thus, people regulated lateral foot placements in predictable and systematic ways determined by specific task goals. Humans regulate stepping movements to not only "just walk" (step without falling), but also to achieve specific goal-directed tasks within a specific environment. The framework and motor regulation templates presented here capture these important interactions.

Consistent Hand Dynamics Are Achieved by Controlling Variabilities Among Joint Movements During Fastball Pitching

This study aimed to determine whether covariations among joint movements are utilized to stabilize hand orientation and movement and to determine which of the upper or lower extremities make effective use of the covariation. Joint angles during pitching were measured in 12 skilled baseball pitchers, using a motion capture system. The joint angles in 10 successful trials were used for the reconstructed motions. The reconstructed motion in the first condition was the same as for the measured motion. In the second condition, the reconstructed motion was generated with joint angles that were pseudo-randomly selected to artificially break off covariation in the measured joint-angle combination. In the third and fourth conditions, the reconstructed motions were generated with the same joint-angle combinations as the measured angles in the throwing arm and the stride leg, respectively, but pseudo-randomly selected in the other joint angles. Ten reconstructed motions were generated for each condition. Standard deviations (SDs) of hand orientation and movement direction were calculated and compared among the conditions. All SDs for the first condition were the smallest among the conditions, indicating that the movements in the measured condition used the covariation in joint angles to make the hand movement stable. The results also illustrated that some SDs in the fourth condition were smaller than those in the third condition, suggesting that the lower extremity made effective use of the covariation. These results imply that it is necessary not only to reduce variability in each joint but also to regulate joint movements to stabilize hand orientation and movement.

Mechanisms of gait phase entrainment in healthy subjects during rhythmic electrical stimulation of the medial gastrocnemius

Studies have shown that human gait entrains to rhythmic bursts of ankle torque for perturbation intervals both slightly shorter and slightly longer than the natural stride period while walking on a treadmill and during overground walking, with phase alignment such that the torque adds to ankle push-off. This study investigated whether human gait also entrains to align the phase of rhythmic electrical stimulation of the gastrocnemius muscle with the timing of ankle push-off. In addition, this study investigated the muscle response to electrical stimulation at different phases of the gait cycle. We found that for both treadmill and overground walking entrainment was observed with phasing that aligned the stimuli with ankle push-off or just before foot contact. Achilles tendon wave speed measurements showed a significant difference (increase) in tendon load when electrical stimulation was applied just after foot contact and during swing phase, with a greater increase for higher amplitudes of electrical stimulation. However, stimulation did not increase tendon load when the timing coincided with push-off. Stride period measurements also suggest the effect of electrical stimulation is sensitive to the gait phase it is applied. These results confirmed that timing aligned with push-off is an attractor for electrical stimulation-induced perturbations of the medial gastrocnemius, and that the muscle response to stimulation is sensitive to timing and amplitude. Future research should investigate other muscles and timings and separate sensory vs. motor contributions to these phenomena.

The direction of postural threat alters balance control when standing at virtual elevation

Anxiogenic settings lead to reduced postural sway while standing, but anxiety-related balance may be influenced by the location of postural threat in the environment. We predicted that the direction of threat would elicit a parallel controlled manifold relative to the standing surface, and an orthogonal uncontrolled manifold during standing. Altogether, 14 healthy participants (8 women, mean age = 27.5 years, SD = 8.2) wore a virtual reality (VR) headset and stood on a matched real-world walkway (2 m × 40 cm × 2 cm) for 30 s at ground level and simulated heights (elevated 15 m) in two positions: (1) parallel to walkway, lateral threat; and (2) perpendicular to walkway, anteroposterior threat. Inertial sensors measured postural sway acceleration (e.g., 95% ellipse, root mean square (RMS) of acceleration), and a wrist-worn monitor measured heart rate coefficient of variation (HR CV). Fully factorial linear-mixed effect regressions (LMER) determined the effects of height and position. HR CV moderately increased from low to high height (p = 0.050, g = 0.397). The Height × Position interaction approached significance for sway area (95% ellipse; β = - 0.018, p = 0.062) and was significant for RMS (β = - 0.022, p = 0.007). Post-hoc analyses revealed that sagittal plane sway accelerations and RMS increased from low to high elevation in parallel standing, but were limited when facing the threat during perpendicular standing. Postural response to threat varies depending on the direction of threat, suggesting that the control strategies used during standing are sensitive to the direction of threat.

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

Introduction

During 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.

Methods

Eleven 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.

Results

There 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.

Discussion

This 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

BACKGROUND

Head-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 QUESTION

Were the participants' complaints a result of adverse effects of the smart glasses on the dynamics of lateral stepping and gait stability?

METHODS

Twenty 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.

RESULTS

The 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.

SIGNIFICANCE

Promising 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.

A real-time feedback method to reduce loading rate during running: Effect of combining direct and indirect feedback

Impact loading plays a key role in the pathophysiology of running-related injuries. Providing real-time feedback may be an effective strategy to reduce impact loading; however, it is currently unclear what an effective training method to help runners achieve a habitual low loading rate is. We subjected 20 healthy non-runners to a structured sequence of direct and indirect biofeedback designed to facilitate broader exploration of neuro-mechanical workspace for potential movement solutions (indirect feedback on cadence and foot-strike angle) and to refine and converge upon an optimal sub-set of that space to match the task goal (direct feedback on loading rate). While indirect biofeedback on foot-strike angle yielded a lower impact load than providing direct biofeedback on loading rate, compared to indirect biofeedback on foot-strike angle, providing direct feedback on loading rate statistically increased (+58%, p = 0.007) the range of goal-relevant solutions participants used to lower their impact loading. Results showed that structured feedback was effective in increasing the range of input parameters that match the task goal, hence expanding the size of goal-relevant solutions, which may benefit running performance under changing environmental constraints.

Variability of running coordination in experts and novices: A 3D uncontrolled manifold analysis

The uncontrolled manifold (UCM) approach has been widely used in recent studies to examine variability in daily tasks; however, it has not yet been used to study running or the effects of expertise. Therefore, the aim of this study was to analyse the synergy structure stabilizing the centre of mass (CoM) trajectory in experts compared to novices during running at two different speeds using a subject-specific 3D model. A total of 25 healthy young adults (13 experts, 12 novices) participated in the study. All subjects ran at 10 and 15 km h^-1 on a treadmill. In each case, kinematics of 20 consecutive gait cycles were recorded and the effects of expertise and gait cycle phase on the synergy structure were investigated at both speeds. Specifically, the variance affecting the CoM ( U C M ⊥ ) , the variance not affecting the CoM ( U C M ∥ ) , and their ratio ( U C M R a t i o ) were analysed. Descriptively, in both groups there was a synergy stabilizing the CoM trajectory in running. However, the ANOVA showed no differences in U C M R a t i o between the two groups. In novices, U C M ⊥ and U C M ∥ were significantly higher compared to experts at the 15 km h^-1 condition. In both groups, there was more variability in the stance phase compared to the flight phase in the majority of cases. The results indicate that experts adopted a more consistent running style. The stride-to-stride variability was diminished but not abolished. This difference was only visible at the 15 km h^-1 condition. Furthermore, variability was less constrained in the stance phase compared to the flight phase.

Revealing the optimal thresholds for movement performance: A systematic review and meta-analysis to benchmark pathological walking behaviour

In order to address whether increased levels of movement output variability indicate pathological performance, we systematically reviewed and synthesized meta-analysis data on healthy and pathological motor behavior. After screening up to 24'000 reports from four databases, 85 studies were included containing 2409 patients and 2523 healthy asymptomatic controls. The optimal thresholds of variability with uncertainty boundaries (in % Coefficient of Variation ± Standard Error) were estimated in 7 parameters: stride time (2.34 ± 0.21), stride length (2.99 ± 0.37), step length (3.34 ± 0.84), swing time (2.94 ± 0.60), step time (3.35 ± 0.23), step width (15.87 ± 1.86), and dual-limb support time (6.08 ± 2.83). All spatio-temporal parameters exhibited a positive effect size (pathology led to increased variability) except step width variability (Effect Size = -0.21). By objectively benchmarking thresholds for pathological motor variability also presented through a case-study, this review provides access to movement signatures to understand neurological changes in an individual that are apparent in movement variability. The comprehensive evidence presented now qualifies stride time variability as a movement biomarker, endorsing its applicability as a viable outcome measure in clinical trials.

Multi-objective control in human walking: insight gained through simultaneous degradation of energetic and motor regulation systems

Minimization of metabolic energy is considered a fundamental principle of human locomotion, as demonstrated by an alignment between the preferred walking speed (PWS) and the speed incurring the lowest metabolic cost of transport. We aimed to (i) simultaneously disrupt metabolic cost and an alternate acute task requirement, namely speed error regulation, and (ii) assess whether the PWS could be explained on the basis of either optimality criterion in this new performance and energetic landscape. Healthy adults (N = 21) walked on an instrumented treadmill under normal conditions and, while negotiating a continuous gait perturbation, imposed leg-length asymmetry. Oxygen consumption, motion capture data and ground reaction forces were continuously recorded for each condition at speeds ranging from 0.6 to 1.8 m s^-1, including the PWS. Both metabolic and speed regulation measures were disrupted by the perturbation (p < 0.05). Perturbed PWS selection did not exhibit energetic prioritization (although we find some indication of energy minimization after motor adaptation). Similarly, PWS selection did not support prioritization of speed error regulation, which was found to be independent of speed in both conditions. It appears that, during acute exposure to a mechanical gait perturbation of imposed leg-length asymmetry, humans minimize neither energetic cost nor speed regulation errors. Despite the abundance of evidence pointing to energy minimization during normal, steady-state gait, this may not extend acutely to perturbed gait. Understanding how the nervous system acutely controls gait perturbations requires further research that embraces multi-objective control paradigms.

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.

Years of running experience influences stride-to-stride fluctuations and adaptive response during step frequency perturbations in healthy distance runners

RESEARCH QUESTION

The current study investigated stride-to-stride fluctuations of step rate and contact time in response to enforced step frequency perturbations as well as adaptation and de-adaptation behavior.

METHODS

Forty distance runners ran at a self-selected speed and were asked to match five different enforced step frequencies (150, 160, 170, 180, and 190 beats per min). The influence of experience was explored, because running is a skill that presumably gets better with practice, and increased years of running experience is protective against injury. Detrended fluctuation analysis was used to determine the strength of long-range correlations in gait fluctuations at baseline, during the perturbation, and post-perturbation. Adaptive response was measured by the ability to match, rate of matching, and aftereffect of step frequency perturbations.

RESULTS

The structure of stride-to-stride fluctuations for step rate and contact time did not change during the perturbation or post-perturbation compared to baseline. However, fluctuations in step rate were affected by the level of perturbation. Runners with the most experience had a less persistent structural gait pattern for both step rate and contact time at baseline. Highly experienced runners also demonstrated the best adaptive response. They better matched the enforced step frequency, reached the enforced step frequency sooner, and returned to preferred step frequency more quickly following removal of the perturbation.

SIGNIFICANCE

These findings indicate baseline locomotor flexibility may be beneficial to achieve task demands and return to a stable state once the task is complete. Increased locomotor flexibility may also be a contributing factor for reduced injury risk in experienced runners.

Tightening Up the Control of Treadmill Walking: Effects of Maneuverability Range and Acoustic Pacing on Stride-to-Stride Fluctuations

The correlational structure of stride-to-stride fluctuations differs between healthy and pathological gait. Uncorrelated and anti-persistent stride-to-stride fluctuations are believed to indicate pathology whereas persistence represents healthy functioning. However, this reading can be questioned because the correlational structure changes with task constraints, like acoustic pacing, signifying the tightness of control over particular gait parameters. We tested this "tightness-of-control interpretation" by varying the maneuverability range during treadmill walking (small, intermediate, and large walking areas), with and without acoustic pacing. Stride-speed fluctuations exhibited anti-persistence, suggesting that stride speeds were tightly controlled, with a stronger degree of anti-persistence for smaller walking areas. Constant-speed goal-equivalent-manifold decompositions revealed simultaneous control of stride times and stride lengths, especially for smaller walking areas to limit stride-speed fluctuations. With acoustic pacing, participants followed both constant-speed and constant-stride-time task goals. This was reflected by a strong degree of anti-persistence around the stride-time by stride-length point that uniquely satisfied both goals. Our results strongly support the notion that anti-persistence in stride-to-stride fluctuations reflect the tightness of control over the associated gait parameter, while not tightly regulated gait parameters exhibit statistical persistence. We extend the existing body of knowledge by showing quantitative changes in anti-persistence of already tightly regulated stride-speed fluctuations.

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.

When we walk, we walk in real-world contexts and with specific goal to achieve. Side-to-side movements are paramount because walking bipeds (humans, animals, robots, etc.) are inherently more unstable laterally. This is particularly important in older adults as sideways falls greatly increase hip fracture risk. Additionally, we normally walk on paths that limit (more or less) our lateral movements. Appropriately regulating lateral stepping movements is thus critical to achieving successful locomotion in any such context. Here, we use appropriate models to test competing hypotheses about how humans regulate lateral stepping movements from each step to the next to identify what task goals they try to achieve. Our work both bridges and unifies perspectives from dynamic walking and computational motor control to provide a coherent theoretical and computational framework from which to study motor regulation in the context of goal-directedness across a wide range of walking tasks and/or conditions.

Multifractality of Unperturbed and Asymmetric Locomotion

The purpose of this study was to explore the extent of multifractality in unperturbed and constrained locomotion, and to determine if multifractality predicted gait adaptability. Young, healthy participants (n = 15) walked at preferred and slow speeds, as well as asymmetrically (one leg at half speed) on a split-belt treadmill. Stride time multifractality was assessed via local detrended fluctuation analysis, which evaluates the evolution of fluctuations both spatially and temporally. Unperturbed walking exhibited monofractal behavior. Asymmetric walking displayed greater multifractality in the faster moving limb, indicating more intermittent periods of extreme high or low variance. Multifractality was not associated with adaptation to asymmetric walking. These findings further suggest that unperturbed locomotion is monofractal and establish that perturbed walking yields multifractal behavior.

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.

A Poincare map based analysis of stroke patients' walking after a rehabilitation by a robot

Since the past decade, rehabilitation robots have become common technologies for recovering gait ability after a stroke. Nevertheless, it is believed that these robots can be further enhanced. Hence, several researches are making progress in optimizing gait rehabilitation robots. However, most of these researches have only assessed the robots and their controllers in improving spatiotemporal and kinetic features of walking. There are not many researchers have focused on the robots' controllers' effects on the central nervous or neuromuscular systems. On the other hand, recently computational methods have been utilized to investigate the rehabilitations of neural disorders, through developing neuromechanical models. However, these methods have neither studied the robot-assisted gait rehabilitation, nor have they theoretically proved why rehabilitation exercises enhance patients' walking ability. Therefore, this paper merged a theoretical approach into a computational method to investigate the effects of gait rehabilitation robots on post-stroke neuromuscular system. To this end, a neuromechanical model of gait has been developed and thereby, the Poincare maps of intact and stroke people have been obtained. Comparison of these maps revealed why a stroke reduces the stability of walking. Then, the effect of an impedance controller, which is used in a rehabilitative robot, is scrutinized in stabilizing a walking motion. Obtaining the Poincare map of this close-loop system, proved that this controller improves motion stability. Finally, the effect of this controller is investigated by simulations and experiments. The experimental tests are performed by Arman rehabilitative robot. Clinical Reference Number: IR.TMU.REC.1394.254.

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 (L_n) and time (T_n) 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.

Classifying the variability in impact and active peak vertical ground reaction forces during running using DFA and ARFIMA models

The vertical ground reaction force (VGRF) during rear-foot striking running typically exhibits peaks referred to as the impact peak and the active peak; their timings and magnitudes have been implicated in injury. Identifying the structure of time-series can provide insight into associated control processes. The purpose here was to detect long-range correlations associated with the time from first contact to impact peak (TIP) and active peak (TAP); and the magnitudes of impact (IPM) and active peaks (APM) using a Detrended Fluctuation Analysis, and Auto-Regressive Fractionally Integrated Moving Average models. Twelve subjects performed an 8min trial at their preferred running speed on an instrumented treadmill. TIP, TAP; IPM, and APM were identified from the VGRF profile for each footfall. TIP and TAP time-series did not demonstrate long-range correlations, conversely IPM and APM time-series did. Short range correlations appeared as well as or instead of long range correlations for IPM. Conversely pure powerlaw behaviour was demonstrated in 11 of the 24 time series for APM, and long range dependencies along with short range correlations were present in a further 9 time series. It has been hypothesised that control mechanisms for IPM and APM are different, these results support this hypothesis.

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.

During the repeated execution of precision movement tasks, humans face two formidable challenges from the motor system itself: dimensionality and noise. Human motor performance involves biomechanical, neuromotor, and perceptual degrees of freedom far in excess of those theoretically needed to prescribe typical goal-directed tasks. At the same time, noise is present in the human body across multiple scales of observation. This high-dimensional and stochastic character of biological movement is the fundamental source of variability ubiquitously observed during task execution. However, it is becoming clear that these two challenges are not merely impediments to be overcome, but rather hold a key to understanding how humans maintain motor performance under changing circumstances, such as those caused by fatigue, injury, or aging. In this work, by studying skilled human participants as they play a virtual shuffleboard game, we demonstrate the fundamental importance of adopting a dynamical perspective when analyzing the motor variability observed over many trials. Using this dynamical approach, we can not only study the geometry of observed inter-trial variability, but can also theoretically describe and experimentally characterize how it is temporally generated and regulated. Furthermore, our theoretical framework and model-based data analysis approach helps to unify previous variability analysis approaches based on stability, correlation, control theory, or task manifolds alone. This conceptual unification supports the idea that such seemingly disparate features of motor variability arise from a single, relatively simple underlying neurophysiological process of motor regulation.

Comparing dynamical systems concepts and techniques for biomechanical analysis

Traditional biomechanical analyses of human movement are generally derived from linear mathematics. While these methods can be useful in many situations, they do not describe behaviors in human systems that are predominately nonlinear. For this reason, nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature. These analysis techniques have provided new insights into how systems (1) maintain pattern stability, (2) transition into new states, and (3) are governed by short- and long-term (fractal) correlational processes at different spatio-temporal scales. These different aspects of system dynamics are typically investigated using concepts related to variability, stability, complexity, and adaptability. The purpose of this paper is to compare and contrast these different concepts and demonstrate that, although related, these terms represent fundamentally different aspects of system dynamics. In particular, we argue that variability should not uniformly be equated with stability or complexity of movement. In addition, current dynamic stability measures based on nonlinear analysis methods (such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics, but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored. Finally, systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.

Adaptability of stride-to-stride control of stepping movements in human walking

Humans continually adapt their movements as they walk on different surfaces, avoid obstacles, etc. External (environmental) and internal (physiological) noise-like disturbances, and the responses that correct for them, each contribute to locomotor variability. This variability may sometimes be detrimental (perhaps increasing fall risk), or sometimes beneficial (perhaps reflecting exploration of multiple task solutions). Here, we determined how humans regulated stride-to-stride fluctuations in walking when presented different task goals that allowed them to exploit inherent redundancies in different ways. Fourteen healthy adults walked on a treadmill under each of four conditions: constant speed only (SPD), constant speed and stride length (LEN), constant speed and stride time (TIM), or constant speed, stride length, and stride time (ALL). Multiple analyses tested competing hypotheses that participants might attempt to either equally satisfy all goals simultaneously, or instead adopt systematic intermediate strategies that only partly satisfied each individual goal. Participants exhibited similar average stepping behavior, but significant differences in variability and stride-to-stride serial correlations across conditions. Analyses of the structure of stride-to-stride fluctuation dynamics demonstrated humans resolved the competing goals presented not by minimizing errors equally with respect to all goals, but instead by trying to only partly satisfy each goal. Thus, humans exploit task redundancies even when they are explicitly removed from the task specifications. These findings may help identify when variability is predictive of, or protective against, fall risk. They may also help inform rehabilitation interventions to better exploit the positive contributions of variability, while minimizing the negative.

Influence of contextual task constraints on preferred stride parameters and their variabilities during human walking

Walking is not always a free and unencumbered task. Everyday activities such as walking in pairs, in groups, or on structured walkways can limit the acceptable gait patterns, leading to motor behavior that differs from that observed in more self-selected gait. Such different contexts may lead to gait performance different than observed in typical laboratory experiments, for example, during treadmill walking. We sought to systematically measure the impact of such task constraints by comparing gait parameters and their variability during walking in different conditions over-ground, and on a treadmill. We reconstructed foot motion from foot-mounted inertial sensors, and characterized forward, lateral and angular foot placement while subjects walked over-ground in a straight hallway and on a treadmill. Over-ground walking was performed in three variations: with no constraints (self-selected, SS); while deliberately varying walking speed (self-varied, SV); and while following a toy pace car programmed to vary speed (externally-varied, EV). We expected that these conditions would exhibit a statistically similar relationship between stride length and speed, and between stride length and stride period. We also expected treadmill walking (TM) would differ in two ways: first, that variability in stride length and stride period would conform to a constant-speed constraint opposite in slope from the normal relationship; and second, that stride length would decrease, leading to combinations of stride length and speed not observed in over-ground conditions. Results showed that all over-ground conditions used similar stride length-speed relationships, and that variability in treadmill walking conformed to a constant-speed constraint line, as expected. Decreased stride length was observed in both TM and EV conditions, suggesting adaptations due to heightened awareness or to prepare for unexpected changes or problems. We also evaluated stride variability in constrained and unconstrained tasks. We observed that in treadmill walking, lateral variability decreased while forward variability increased, and the normally-observed correlation between wider foot placement and external foot rotation was eliminated. Preferred stride parameters and their variability appear significantly influenced by the context and constraints of the walking task.

Quickly making the correct choice

In daily life, unconscious choices guide many of our on-going actions. Such choices need to be made quickly, because the options change as the action progresses. We confirmed that people make reasonable choices when they have to quickly decide between two alternatives, and studied the basis of such decisions. The task was to tap with their finger on as many targets as possible within 2 min. A new target appeared after every tap, sometimes accompanied by a second target that was easier to hit. When there was only one target, subjects had to find the right balance between speed and accuracy. When there were two targets, they also had to choose between them. We examined to what extent subjects switched to the target that was easier to hit when it appeared some time after the original one. Subjects generally switched to the easier target whenever doing so would help them hit more targets within the 2-min session. This was so, irrespective of whether the different delays were presented in separate sessions or were interleaved within one session. Whether or not they switched did not depend on how successful they were at hitting the targets on earlier attempts, but it did depend on the position of the finger at the moment that the easy target appeared. We conclude that people have continuous access to reasonable estimates of how long various movement options would take and of how precise the endpoints are likely to be, given the instantaneous circumstances.

Identifying stride-to-stride control strategies in human treadmill walking

Variability is ubiquitous in human movement, arising from internal and external noise, inherent biological redundancy, and from the neurophysiological control actions that help regulate movement fluctuations. Increased walking variability can lead to increased energetic cost and/or increased fall risk. Conversely, biological noise may be beneficial, even necessary, to enhance motor performance. Indeed, encouraging more variability actually facilitates greater improvements in some forms of locomotor rehabilitation. Thus, it is critical to identify the fundamental principles humans use to regulate stride-to-stride fluctuations in walking. This study sought to determine how humans regulate stride-to-stride fluctuations in stepping movements during treadmill walking. We developed computational models based on pre-defined goal functions to compare if subjects, from each stride to the next, tried to maintain the same speed as the treadmill, or instead stay in the same position on the treadmill. Both strategies predicted average behaviors empirically indistinguishable from each other and from that of humans. These strategies, however, predicted very different stride-to-stride fluctuation dynamics. Comparisons to experimental data showed that human stepping movements were generally well-predicted by the speed-control model, but not by the position-control model. Human subjects also exhibited no indications they corrected deviations in absolute position only intermittently: i.e., closer to the boundaries of the treadmill. Thus, humans clearly do not adopt a control strategy whose primary goal is to maintain some constant absolute position on the treadmill. Instead, humans appear to regulate their stepping movements in a way most consistent with a strategy whose primary goal is to try to maintain the same speed as the treadmill at each consecutive stride. These findings have important implications both for understanding how biological systems regulate walking in general and for being able to harness these mechanisms to develop more effective rehabilitation interventions to improve locomotor performance.