Nonlinear dynamics and dynamical systems approaches and methodologies are increasingly being implemented in biomechanics and human movement research. Based on the early insights of Nicolai Bernstein (1967), a significantly different outlook on the movement control “problem” over the last few decades has emerged. From a focus on relatively simple movements has arisen a research focus with the primary goal to study movement in context, allowing the complexity of patterns to emerge. The approach taken is that the control of multiple degrees-of-freedom systems is not necessarily more difficult or complex than that of systems only comprising a few degrees of freedom. Complex patterns and dynamics might not require complex control structures. In this paper we present a tutorial overview of the mathematical underpinnings of nonlinear dynamics and some of its basic analysis tools. This should provide the reader with a basic level of understanding about the mathematical principles and concepts underlying pattern stability and change. This will be followed by an overview of dynamical systems approaches in the study of human movement. Finally, we discuss recent progress in the application of nonlinear dynamical techniques to the study of human locomotion, with particular focus on relative phase techniques for the assessment of coordination.
Richard E.A. Van Emmerik, Michael T. Rosenstein, William J. McDermott and Joseph Hamill
Ugo H. Buzzi and Beverly D. Ulrich
The purpose of this study was to examine the dynamic stability of two groups of children with different dynamic resources in changing contexts. The stability of the lower extremity segments of preadolescent children (8–10 years old) with and without Down syndrome (DS) was evaluated as children walked on a motorized treadmill at varying speeds. Tools from nonlinear dynamics, maximum Lyapunov exponent, and approximate entropy were used to assess the behavioral stability of segmental angular displacements of the thigh, shank, and foot. Our results suggest that children with DS show decreased dynamic stability during walking in all segments and that this might be a consequence of inherently different subsystem constraints between these groups. Differences between groups also varied, though not uniformly, with speed, suggesting that inherent differences could further constrain the behavioral response to changing task demands.
Stephen M. Glass, Brian L. Cone, Christopher K. Rhea, Donna M. Duffy and Scott E. Ross
. 18 Because the theory and application of nonlinear dynamics with respect to health care is relatively new, the study of postural control comprises more in the domain of linear analysis of balance behaviors. Further complicating the question of whether postural behavior varies by sex is the matter of
Fatemeh Azadinia, Ismail Ebrahimi-Takamjani, Mojtaba Kamyab, Morteza Asgari and Mohamad Parnianpour
– 620 . PubMed ID: 23065907 doi: 10.1002/j.1532-2149.2012.00226.x Stergiou , N. ( 2004 ). Innovative analyses of human movement . Champaign, IL : Human Kinetics Publishers . Stergiou , N. , & Decker , L.M. ( 2011 ). Human movement variability, nonlinear dynamics, and pathology: Is there a
Michael Buchecker, Stefan Wegenkittl, Thomas Stöggl and Erich Müller
.1080/00222895.2013.866932 Newell , K.M. ( 1998 ). Degrees of freedom and the development of postural center of pressure profiles . In K.M. Newell & P.C.M. Molenaar (Eds.), Applications of nonlinear dynamics to developmental process modeling (pp. 63 – 84 ). Mahwah, NJ : Lawrence Erlbaum Associates . Nigg , B
Philippe Terrier and Fabienne Reynard
Local dynamic stability (stability) quantifies how a system responds to small perturbations. Several experimental and clinical findings have highlighted the association between gait stability and fall risk. Walking without shoes is known to slightly modify gait parameters. Barefoot walking may cause unusual sensory feedback to individuals accustomed to shod walking, and this may affect stability. The objective was therefore to compare the stability of shod and barefoot walking in healthy individuals and to analyze the intrasession repeatability. Forty participants traversed a 70 m indoor corridor wearing normal shoes in one trial and walking barefoot in a second trial. Trunk accelerations were recorded with a 3D-accelerometer attached to the lower back. The stability was computed using the finite-time maximal Lyapunov exponent method. Absolute agreement between the forward and backward paths was estimated with the intraclass correlation coefficient (ICC). Barefoot walking did not significantly modify the stability as compared with shod walking (average standardized effect size: +0.11). The intrasession repeatability was high (ICC: 0.73–0.81) and slightly higher in barefoot walking condition (ICC: 0.81–0.87). Therefore, it seems that barefoot walking can be used to evaluate stability without introducing a bias as compared with shod walking, and with a sufficient reliability.
Joel T. Fuller, Clint R. Bellenger, Dominic Thewlis, John Arnold, Rebecca L. Thomson, Margarita D. Tsiros, Eileen Y. Robertson and Jonathan D. Buckley
Stride-to-stride fluctuations in running-stride interval display long-range correlations that break down in the presence of fatigue accumulated during an exhaustive run. The purpose of the study was to investigate whether long-range correlations in running-stride interval were reduced by fatigue accumulated during prolonged exposure to a high training load (functional overreaching) and were associated with decrements in performance caused by functional overreaching.
Ten trained male runners completed 7 d of light training (LT7), 14 d of heavy training (HT14) designed to induce a state of functional overreaching, and 10 d of light training (LT10) in a fixed order. Running-stride intervals and 5-km time-trial (5TT) performance were assessed after each training phase. The strength of long-range correlations in running-stride interval was assessed at 3 speeds (8, 10.5, and 13 km/h) using detrended fluctuation analysis.
Relative to performance post-LT7, time to complete the 5TT was increased after HT14 (+18 s; P < .05) and decreased after LT10 (–20 s; P = .03), but stride-interval long-range correlations remained unchanged at HT14 and LT10 (P > .50). Changes in stride-interval long-range correlations measured at a 10.5-km/h running speed were negatively associated with changes in 5TT performance (r –.46; P = .03).
Runners who were most affected by the prolonged exposure to high training load (as evidenced by greater reductions in 5TT performance) experienced the greatest reductions in stride-interval long-range correlations. Measurement of stride-interval long-range correlations may be useful for monitoring the effect of high training loads on athlete performance.
Jeffrey P. Kaipust, Jessie M. Huisinga, Mary Filipi and Nicholas Stergiou
The purpose of this study was to determine the differences in gait variability between patients with multiple sclerosis (MS) and healthy controls during walking at a self-selected pace. Methods: Kinematics were collected during three minutes of treadmill walking for 10 patients with MS and 10 healthy controls. The Coefficient of Variation (CoV), the Approximate Entropy (ApEn) and the Detrended Fluctuation Analysis (DFA) were used to investigate the fluctuations present in stride length and step width from continuous strides. Results: ApEn revealed that patients with MS had significantly lower values than healthy controls for stride length (p < .001) and step width (p < .001). Conclusions: ApEn results revealed that the natural fluctuations present during gait in the stride length and step width time series are more regular and repeatable in patients with MS. These changes implied that patients with MS may exhibit reduced capacity to adapt and respond to perturbations during gait.
Jia Yi Chow, Keith Davids, Chris Button and Robert Rein
From a nonlinear dynamics perspective, presence of movement variability before a change in preferred movement patterns is hypothesized to afford the necessary adaptability and flexibility for seeking novel functional behaviors. In this study, four novice participants practiced a discrete multiarticular movement for 12 sessions over 4 weeks. Cluster analysis procedures revealed how changes between preferred movement patterns were affected with and without the presence of variability in movement clusters before a defined change. Performance improved in all participants as a function of practice. Participants typically showed evidence of change between preferred movement clusters and higher variability in the use of movement clusters within a session. However, increasing variability in movement clusters was not always accompanied by transition from one preferred movement cluster to another. In summary, it was observed that intentional and informational constraints play an important role in influencing the specific pathway of change for individual learners as they search for new preferred movement patterns.
Christopher K. Rhea, Jed A. Diekfuss, Jeffrey T. Fairbrother and Louisa D. Raisbeck
.4085/1062-6050-46.1.85 10.4085/1062-6050-46.1.85 Stergiou , N. , & Decker , L.M. ( 2011 ). Human movement variability, nonlinear dynamics, and pathology: Is there a connection? Human Movement Science, 30 ( 5 ), 869 – 888 . PubMed ID: 21802756 doi:10.1016/j.humov.2011.06.002 10.1016/j.humov.2011.06.002 Stergiou