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Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking?

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  • Jonathan B Dingwell
  • Joby John
  • Joseph P Cusumano

Abstract

It is widely accepted that humans and animals minimize energetic cost while walking. While such principles predict average behavior, they do not explain the variability observed in walking. For robust performance, walking movements must adapt at each step, not just on average. Here, we propose an analytical framework that reconciles issues of optimality, redundancy, and stochasticity. For human treadmill walking, we defined a goal function to formulate a precise mathematical definition of one possible control strategy: maintain constant speed at each stride. We recorded stride times and stride lengths from healthy subjects walking at five speeds. The specified goal function yielded a decomposition of stride-to-stride variations into new gait variables explicitly related to achieving the hypothesized strategy. Subjects exhibited greatly decreased variability for goal-relevant gait fluctuations directly related to achieving this strategy, but far greater variability for goal-irrelevant fluctuations. More importantly, humans immediately corrected goal-relevant deviations at each successive stride, while allowing goal-irrelevant deviations to persist across multiple strides. To demonstrate that this was not the only strategy people could have used to successfully accomplish the task, we created three surrogate data sets. Each tested a specific alternative hypothesis that subjects used a different strategy that made no reference to the hypothesized goal function. Humans did not adopt any of these viable alternative strategies. Finally, we developed a sequence of stochastic control models of stride-to-stride variability for walking, based on the Minimum Intervention Principle. We demonstrate that healthy humans are not precisely “optimal,” but instead consistently slightly over-correct small deviations in walking speed at each stride. Our results reveal a new governing principle for regulating stride-to-stride fluctuations in human walking that acts independently of, but in parallel with, minimizing energetic cost. Thus, humans exploit task redundancies to achieve robust control while minimizing effort and allowing potentially beneficial motor variability.Author Summary: Existing principles used to explain how locomotion is controlled predict average, long-term behavior. However, neuromuscular noise continuously disrupts these movements, presenting a significant challenge for the nervous system. One possibility is that the nervous system must overcome all neuromuscular variability as a constraint limiting performance. Conversely, we show that humans walking on a treadmill exploit redundancy to adjust stepping movements at each stride and maintain performance. This strategy is not required by the task itself, but is predicted by appropriate stochastic control models. Thus, the nervous system simplifies control by strongly regulating goal-relevant fluctuations, while largely ignoring non-essential variations. Properly determining how stochasticity affects control is critical to developing biological models, since neuro-motor fluctuations are intrinsic to these systems. Our work unifies the perspectives of time series analysis researchers, motor coordination researchers, and motor control theorists by providing a single dynamical framework for studying variability in the context of goal-directedness.

Suggested Citation

  • Jonathan B Dingwell & Joby John & Joseph P Cusumano, 2010. "Do Humans Optimally Exploit Redundancy to Control Step Variability in Walking?," PLOS Computational Biology, Public Library of Science, vol. 6(7), pages 1-15, July.
  • Handle: RePEc:plo:pcbi00:1000856
    DOI: 10.1371/journal.pcbi.1000856
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    References listed on IDEAS

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    1. Costa, M. & Peng, C.-K. & L. Goldberger, Ary & Hausdorff, Jeffrey M., 2003. "Multiscale entropy analysis of human gait dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 53-60.
    2. Gates, Deanna H. & Su, Jimmy L. & Dingwell, Jonathan B., 2007. "Possible biomechanical origins of the long-range correlations in stride intervals of walking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 259-270.
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    Cited by:

    1. Philippe Terrier, 2012. "Step-to-Step Variability in Treadmill Walking: Influence of Rhythmic Auditory Cueing," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-9, October.
    2. Jie Zhang & Kai Zhang & Jianfeng Feng & Michael Small, 2010. "Rhythmic Dynamics and Synchronization via Dimensionality Reduction: Application to Human Gait," PLOS Computational Biology, Public Library of Science, vol. 6(12), pages 1-11, December.
    3. Jonathan B Dingwell & Joseph P Cusumano, 2019. "Humans use multi-objective control to regulate lateral foot placement when walking," PLOS Computational Biology, Public Library of Science, vol. 15(3), pages 1-28, March.
    4. Marietta Kirchner & Patric Schubert & Magnus Liebherr & Christian T Haas, 2014. "Detrended Fluctuation Analysis and Adaptive Fractal Analysis of Stride Time Data in Parkinson's Disease: Stitching Together Short Gait Trials," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-6, January.
    5. Joby John & Jonathan B Dingwell & Joseph P Cusumano, 2016. "Error Correction and the Structure of Inter-Trial Fluctuations in a Redundant Movement Task," PLOS Computational Biology, Public Library of Science, vol. 12(9), pages 1-30, September.
    6. Julius Verrel & Didier Pradon & Nicolas Vuillerme, 2012. "Persistence of Motor-Equivalent Postural Fluctuations during Bipedal Quiet Standing," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-8, October.
    7. Christopher A Rábago & Jonathan B Dingwell & Jason M Wilken, 2015. "Reliability and Minimum Detectable Change of Temporal-Spatial, Kinematic, and Dynamic Stability Measures during Perturbed Gait," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-22, November.

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