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QUANTIFICATION OF SPATIOTEMPORAL PARAMETER BEHAVIOR DURING WALKING SPEED TRANSITIONS

Claire H. Rodman and Anne E. Martin
Department of Mechanical Engineering at Pennsylvania State University, University Park, PA

INTRODUCTION

Constant speed walking has been rigorously investigated [1-6]. However, humans often start, stop, and change speeds [7]. These speed transitions have not been studied thoroughly, introducing the question: 
What biomechanical behaviors do healthy humans exhibit when transitioning between speeds?
The fundamental understanding gained by answering this could be applied to develop rehabilitation techniques (Kuo and Donelan, 2010) and assistive gait technologies [8,9] that restore both steady locomotion and the critical transitions between them. This work quantified spatiotemporal behavior (step time, length, and speed) during speed transitions on a treadmill, addressing the following hypotheses:
H1) The mean spatiotemporal parameters of the post-transition steady state would be different than those of the corresponding constant speed walking baseline;
H2) The step time and step length parameters both diverge more frequently in large transitions than small transitions; and​
H3) Transition magnitude affects both number of steps in the transition and mode of convergence.

METHODS

Top left: Execution of one speed transition with visual feedback notifying the subject of the step number, initial speed, and final speed. Top right: A sample plot of the speed parameter for one transition with regions and steps of interest denoted. Bottom right: A sample table of all possible combinations of transitions. The representative sample transition element is highlighted in red.
  • Subjects walked at five constant normalized speeds to establish a baseline and then performed speed transition trials between those same speeds
  • Transitions were quantified using metrics for each hypothesis such as converged difference, divergence, and convergence
  • Mixed effects models were used to test the hypotheses using the metrics  as dependent variables, transition magnitude and direction as fixed effects, and including per-subject random effects
  • Transitions were also grouped by small, medium, and large magnitude for additional categorical statistical analysis​

RESULTS AND DISCUSSION

Difference From Baseline

  • Subjects exhibited small, non-zero converged differences in step time and length (on the order of 0.01 s and 0.01 m) with signed transition magnitude as a significant fixed effect (t = -4.89 and t = -5.69, respectively; p < 0.001) 
  • The general trend of decreasing converged difference with increasing signed transition magnitude was not significant in speed (t = -1.52, p = 0.146)
  • For all parameters, the step-to-step variability during constant speed walking exceeded the converged differences; The magnitudes were likely on the order of measurement error ​
It is unlikely that subjects converged to meaningfully different post-transition states on average, refuting H1. 

Divergence

  • Because speed was prescribed, essentially all transitions of every magnitude exhibited divergence in speed, as expected
  • For small transitions, subjects either (1) diverged in step time but not length; (2) diverged in step length but not time; or (3) diverged in both step time and length
  • ​For medium and large transitions, essentially all transitions exhibited divergence in both step time and length
Picture
Percentage of small, medium, and large transitions that diverged in step time and/or length
The frequency of divergence in both step time and length is related to transition magnitude, supporting H2.

Convergence

  • The transition magnitude fixed effect slope was significant (t > 9.27, p < 0.001), with increasing transition magnitude corresponding to increasing number of steps to converge for all parameters​
  •  At all magnitudes, average speed required a greater number of steps to converge compared to step time and length (z > 8.43, p < 0.001)
  • Transition direction did not significantly influence steps to converge in any of the parameters (t < 1.57, p > 0.116)
  • As transition magnitude increased, indirect convergence increased for all three parameters (z > 4.32, p < 0.001)
  • The indirect convergence percentage for speed was higher than for step time and length (z > 5.91, p < 0.001)​
  • With increasing transition magnitude, the overshoot percentage increased significantly for step time (z > 4.01, p < 0.001)
Picture
Percentage of each convergence mode by transition magnitude
Increases in both number of steps to converge and rates of indirect convergence with increasing transition magnitude supported H3. 

ACKNOWLEDGEMENTS

The authors thank Penn State Clinical and Translational Science Institute for Study Finder, used to recruit subjects. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE1255832. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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