Elsevier

Human Movement Science

Volume 30, Issue 5, October 2011, Pages 869-888
Human Movement Science

Human movement variability, nonlinear dynamics, and pathology: Is there a connection?

https://doi.org/10.1016/j.humov.2011.06.002Get rights and content

Abstract

Fields studying movement generation, including robotics, psychology, cognitive science, and neuroscience utilize concepts and tools related to the pervasiveness of variability in biological systems. The concept of variability and the measures for nonlinear dynamics used to evaluate this concept open new vistas for research in movement dysfunction of many types. This review describes innovations in the exploration of variability and their potential importance in understanding human movement. Far from being a source of error, evidence supports the presence of an optimal state of variability for healthy and functional movement. This variability has a particular organization and is characterized by a chaotic structure. Deviations from this state can lead to biological systems that are either overly rigid and robotic or noisy and unstable. Both situations result in systems that are less adaptable to perturbations, such as those associated with unhealthy pathological states or absence of skillfulness.

Highlights

► Exploration of variability using measures for nonlinear dynamics opens new vistas for research and treatment for movement dysfunction. ► Chaos could be a powerful component of the locomotive system and its structure can be controlled by the nervous system. ► An optimal state of variability that exhibits chaos is important for health and functional movement. ► Loss of this optimal state of variability renders the system more predictable and rigid. ► Increases beyond optimal variability render the system more noisy and unpredictable.

Introduction

One of the most common features of human movement is its variability. Human movement variability can be described as the normal variations that occur in motor performance across multiple repetitions of a task (Stergiou, Harbourne, & Cavanaugh, 2006). This variability is intrinsic in all biological systems and it can be observed quite easily. If a person tries to repeat the same movement twice, the two actions will never be identical. Bernstein (1967) used an expression “repetition without repetition” whereby each repetition of an act involved unique, non-repetitive neural and motor patterns. Recently, the role of movement variability in motor control has become an object of study in its own right (Bates, 1996, Newell and Corcos, 1993). Therefore, a number of questions have been raised (Stergiou et al., 2006). Examples of such questions are “How is variability controlled while learning a new skill?”, “Is variability associated with disease/health?”, and “What are the sources of variability, and how do they interact in the production of the observed variation in movement?”

In the past, variability in motor performance has been considered from a variety of theoretical perspectives (e.g., Newell & Corcos, 1993). A prominent theory is the Generalized Motor Program Theory (GMPT; Summers & Anson, 2009). This theory considers variation in a given movement pattern to be the result of error. This error in the ability to predict the necessary parameters for employing the underlying motor program results in variation in motor performance (Schmidt, 2003, Schmidt and Lee, 2005). With task-specific practice, prediction error is gradually eliminated or minimized, thereby optimizing the accuracy and efficiency of the movement pattern.

Another prominent theory is the uncontrolled manifold (UCM) hypothesis. Practically, motor variability has been associated with motor redundancy. Motor redundancy refers to having more elements than necessary to solve a task, resulting in the existence of multiple solutions to a given motor problem. Latash, Scholz, and Schöner (2002) described the UCM hypothesis to address this problem of motor redundancy. According to this hypothesis, when a multi-element system changes its state within a UCM computed for a particular performance variable (e.g., total force produced by a set of fingers), this variable is kept at a constant value. As long as the system does not leave the UCM, the hierarchically higher controller (e.g., central nervous system) does not need to interfere and, in that sense, the system of elemental variables does not need to be controlled within that manifold. If the system leaves the UCM and shows an acceptable error in the performance variable, the controller may have to interfere and introduce a correction (Latash, 2008). The UCM approach has been applied to several motor tasks such as maintaining quiet stance, finger force production, bimanual pointing, sit-to-stand, and pistol shooting (Domkin et al., 2002, Latash et al., 2001, Scholz et al., 2003) to discover coordination strategies of apparently redundant motor systems and uncover the functional purposes that variability plays in those motor tasks.

A third theoretical perspective briefly presented here is the Dynamical Systems Theory (DST) which proposes that biological systems self-organize according to environmental, biomechanical, and morphological constraints to find the most stable solution for producing a given movement (Clark and Phillips, 1993, Hamill et al., 1999, Kamm et al., 1990, Kelso, 1995, Thelen, 1995, Thelen and Ulrich, 1991). Increased variability in a movement pattern generally indicates loss of stability, while decreased variability generally indicates a highly stable behavior. The GMPT, UCM, and DST perspectives are similar in that they all recognize that decreased variability results from the efficient execution of a given movement pattern. DST focuses more on behavioral transitions and provides tools to describe such phenomena. Specifically, DST suggests that, in certain dynamical systems and under certain conditions, when variability increases and reaches a specific critical point, the system becomes highly unstable and switches to a new, more stable movement pattern (with less variability). This proposition is a significant step forward because it explains transitions between behavioral states and implies that a persistent lack of movement variability may indicate rigid, inflexible motor behaviors with limited adaptability to changing task or environmental demands. However, a significant limitation of DST is that it does not account for the observation that some behaviors, which appear to be highly stable, paradoxically are performed in variable ways. This is especially evident when we observe elite sports players or musicians performing (e.g., Michael Jordan taking a jump shot or Yo-Yo Ma playing the cello). Not only is their performance more consistent than that of less capable individuals, but they also seem to have developed an infinite number of ways of performing. If we actually consider fundamental motor skills (i.e., gait) as activities when applied in “real life” contexts, we can actually say that every single one of us is a Michael Jordan in our abilities to walk through crowds or on diverse and challenging terrains. Therefore, it seems that in this sense, variability is closely related with a rich behavioral state.

The idea that variability decreases with skill acquisition in one context (motor learning paradigm) and increases with skill acquisition in another context (the development of a behavioral repertoire) is readily explained by the way in which variability is measured. Typical motor learning curves are constructed using traditional variability measures of skill performance to capture error in performance. Such linear statistical measures quantify the magnitude of variation in a set of values independently of their order in the distribution. The magnitude of variability continuously decreases and eventually plateaus as motor learning occurs. In contrast, variation in how a motor behavior emerges in time is best captured by measures where the temporal organization in distribution of values is the facet of interest. Temporal organization (or structure) of variability is quantified by the degree to which values emerge in an orderly manner, often across a range of time scales. Therefore, recent theoretical approaches have suggested that variability contains important information about movement (Amato, 1992, Cavanaugh et al., 2005, Harbourne and Stergiou, 2009, Newell and Corcos, 1993). These approaches have now propagated in the human movement literature and lead the development of alternative theoretical frameworks and methodologies to study human movement related injuries and treatments.

Much of the controversy that exists in the literature with respect to human movement variability stems from the methodology used. Traditional linear measures, such as the standard deviation or the range, are measures of centrality and thus provide a description of the amount or magnitude of the variability around a central point (Fig. 1). From a human movement perspective, this approach in evaluating variability has led several practitioners and scientists to believe that the mean is the standard of performance and everything away from the mean is error. From a statistical standpoint, the valid usage of traditional linear measures to study variability assumes that variations between repetitions of a task are random and independent (of past and future repetitions) (Lomax, 2007). However, previous studies have shown that such variations are distinguishable from noise (Delignières and Torre, 2009, Dingwell and Cusumano, 2000, Dingwell and Kang, 2007, Stergiou et al., 2004a). In addition, several studies have indicated that these variations have a deterministic origin (Dingwell and Cusumano, 2000, Dingwell and Kang, 2007, Harbourne and Stergiou, 2009, Miller et al., 2006). Thus, they are neither random nor independent. For instance, although variations between strides during walking appear to vary randomly, with no correlation between the present and future strides, the healthy adult locomotor system actually possesses “motor memory”, such that the fluctuations from one stride to the next display a subtle, “hidden” temporal structure. Mathematical tools, such as entropic or fractal measures or tools developed for the study of deterministic chaos have enabled the evaluation of this temporal structure of variability. From this approach, how human movement evolves over time becomes of importance. Therefore, the focus is not on the standard of performance represented by the average but rather on the exploratory nature of movement, which enhances practice and quality of performance.

From an evaluation perspective, these two approaches are complimentary since each explores different aspects of variability (Harbourne and Stergiou, 2009, Stergiou et al., 2004a). As mentioned above, conventional statistical tools quantify the magnitude of variation in a set of values independently of their order in the distribution; this works properly for linear systems. In contrast, variation in how a motor behavior emerges in time is best captured by tools developed for the study of nonlinear systems. These tools that have been used in the literature for this purpose include approximate entropy, sample entropy, correlation dimension, largest Lyapunov exponent, and detrended fluctuation analysis (Bruijn et al., 2009, Cavanaugh et al., 2010, Delignières et al., 2003, Donker et al., 2007, Gates and Dingwell, 2007, Gates and Dingwell, 2008, Hausdorff, 2009, Liao et al., 2008; Kurz & Hou, 2010; Kurz et al., 2010, Sosnoff et al., 2006, Sosnoff and Voudrie, 2009, Stins et al., 2009, Vaillancourt et al., 2004, Yang and Wu, 2010).

Section snippets

Further theoretical developments

There is a growing body of literature showing that the cycle-to-cycle variation seen in a wide variety of physiological systems is nontrivial and may offer insight into the control of these systems (Bassingthwaighte, Liebovitch, & West, 1994). This intrinsic movement variability is highly suggestive of a fundamental feature of the neural control of movement. Cai et al. (2006) provided some evidence with respect to this issue by studying the ability of spinal mice to learn to step. In their

Variability does not equate with stability

Before we will continue with the presentation of our experimental work, which is based on the above proposition, we would like to address an issue where we believe that there is confusion in the literature. As mentioned above, variability was interpreted traditionally as noise superimposed upon a signal, where the signal is the intended movement and the variability is random noise about this intended movement (Newell & Corcos, 1993). The focus of this approach was to quantify the amount of

Experimental work from our laboratory exploring the above theoretical frameworks

Armed with the above tools a great number of investigators have explored important questions on variability and sought to provide support for or against the above-mentioned theoretical frameworks. Here we will present some of our work including posture and gait from healthy and pathological populations at different stages of the lifespan.

Concluding comments

In conclusion, using analysis for nonlinear dynamical systems to human behavior provides a better understanding of variability and how it relates to pathology. In this context, the theoretical model of optimal movement variability developed by our research group provides the framework for interpreting both simulated and empirical results. Fields studying movement generation, including robotics, psychology, and neuroscience have utilized concepts and tools related to the pervasiveness of

Acknowledgments

This work is supported by the NIH (K25HD047194), the NIDRR (H133G040118 and H133G080023) and the Nebraska Research Initiative.

References (147)

  • K.P. Granata et al.

    Reply to the Letter to the Editor

    Gait and Posture

    (2007)
  • J. Hamill et al.

    A dynamical systems approach to lower extremity running injuries

    Clinical Biomechanics (Bristol, Avon)

    (1999)
  • H. Johansson et al.

    Activity in receptor afferents from the anterior cruciate ligament evokes reflex effects on fusimotor neurones

    Neuroscience Research

    (1990)
  • K. Jordan et al.

    Long range correlations in the stride interval of running

    Gait and Posture

    (2006)
  • H.G. Kang et al.

    Intra-session reliability of local dynamic stability of walking

    Gait and Posture

    (2006)
  • E. Kapreli et al.

    The anterior cruciate ligament deficiency as a model of brain plasticity

    Medical Hypotheses

    (2006)
  • H. Korn et al.

    Is there chaos in the brain? II. Experimental evidence and related models

    Comptes Rendus Biologies

    (2003)
  • M.J. Kurz et al.

    A template for the exploration of chaotic locomotive patterns

    Chaos, Solitons, and Fractals

    (2005)
  • A. Kyvelidou et al.

    Reliability of center of pressure measures for assessing the development of sitting postural control

    Archives of Physical Medicine and Rehabilitation

    (2009)
  • A. Kyvelidou et al.

    Reliability of center of pressure measures for assessing the development of sitting postural control in infants with or at risk of cerebral palsy

    Archives for Physical Medicine and Rehabilitation

    (2010)
  • G.A. Lanza et al.

    Prognostic role of heart rate variability in patients with a recent acute myocardial infarction

    American Journal of Cardiology

    (1998)
  • L. Li et al.

    Stability and variability may respond differently to changes in walking speed

    Human Movement Science

    (2005)
  • F. Liao et al.

    Multi-resolution entropy analysis of gait symmetry in neurological degenerative diseases and amyotrophic lateral sclerosis

    Medical Engineering and Physics

    (2008)
  • D.J. Miller et al.

    An improved surrogate method for detecting the presence of chaos in gait

    Journal of Biomechanics

    (2006)
  • H.D.I. Abarbanel

    Analysis of observed chaotic data

    (1996)
  • K.T. Alligood et al.

    Chaos: an introduction to dynamical systems

    (1997)
  • I. Amato

    Chaos breaks out at NIH, but order may come of it

    Science

    (1992)
  • S.P. Arnoczky et al.

    Anterior cruciate ligament replacement using patellar tendon. An evaluation of graft revascularization in the dog

    Journal of Bone and Joint Surgery

    (1982)
  • J.B. Bassingthwaighte et al.

    Fractal measures of heterogeneity and correlation

  • B.T. Bates

    Single-subject methodology: An alternative approach

    Medicine and Science in Sports and Exercise

    (1996)
  • N.A. Bernstein

    The coordination and regulation of movements

    (1967)
  • J.S. Brach et al.

    Too much or too little step width variability is associated with a fall history in older persons who walk at or near normal gait speed

    Journal of Neuroengineering and Rehabilitation

    (2005)
  • T.G. Buchman et al.

    Complex systems analysis: A tool for shock research

    Shock

    (2001)
  • L.L. Cai et al.

    Implications of assist-as-needed robotic step training after a complete spinal cord injury on intrinsic strategies of motor learning

    Journal of Neuroscience

    (2006)
  • J.T. Cavanaugh et al.

    Detecting altered postural control after cerebral concussion in athletes with normal postural stability

    British Journal of Sports Medicine

    (2005)
  • J.T. Cavanaugh et al.

    Recovery of postural control after cerebral concussion: New insights using approximate entropy

    Journal of Athletic Training

    (2006)
  • J.T. Cavanaugh et al.

    A nonlinear dynamic approach for evaluating postural control: New directions for the management of sport-related cerebral concussion

    Sports Medicine

    (2005)
  • J.T. Cavanaugh et al.

    Nonlinear analysis of ambulatory activity patterns in community-dwelling older adults

    The Journals of Gerontology. Series A, Biological Sciences and Medical Sciences

    (2010)
  • J.E. Clark et al.

    A longitudinal study of intralimb coordination in the first year of independent walking: A dynamical systems analysis

    Child Development

    (1993)
  • J.E. Deffeyes et al.

    Use of information entropy measures of sitting postural sway to quantify developmental delay in infants

    Journal of Neuroengineering and Rehabilitation

    (2009)
  • D. Delignières et al.

    A methodological note on nonlinear time series analysis: Is the open- and closed-loop model of Collins and De Luca (1993) a statistical artifact?

    Journal of Motor Behavior

    (2003)
  • D. Delignières et al.

    Fractal dynamics of human gait: A reassessment of the 1996 data of Hausdorff et al

    Journal of Applied Physiology

    (2009)
  • S. Demura et al.

    Body-sway characteristics during a static upright posture in the elderly

    Geriatrics and Gerontology International

    (2008)
  • R.P. Di Fabio et al.

    Effect of knee joint laxity on long-loop postural reflexes: Evidence for a human capsular-hamstring reflex

    Experimental Brain Research

    (1992)
  • J.B. Dingwell et al.

    Nonlinear time series analysis of normal and pathological human walking

    Chaos

    (2000)
  • J.B. Dingwell et al.

    Differences between local and orbital dynamic stability during human walking

    Journal of Biomechanical Engineering

    (2007)
  • D. Domkin et al.

    Structure of joint variability in bimanual pointing tasks

    Experimental Brain Research

    (2002)
  • S.F. Donker et al.

    Regularity of center-of-pressure trajectories depends on the amount of attention invested in postural control

    Experimental Brain Research

    (2007)
  • P. Dyhre-Poulsen et al.

    Muscular reflexes elicited by electrical stimulation of the anterior cruciate ligament in humans

    Journal of Applied Physiology

    (2000)
  • E. Fedrizzi et al.

    Predictors of independent walking in children with spastic diplegia

    Journal of Child Neurology

    (2000)
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