Variability in kinematic coupling assessed by vector coding and continuous relative phase

Abstract

Variability in the spatio-temporal coordination of human movement kinematics is often assessed by vector coding and continuous relative phase (CRP). To facilitate appropriate comparisons between the findings of studies that have used different techniques to assess variability, the purposes of this study were: (1) to determine if both vector coding and CRP behave according to dynamical systems theories on variability and state space transitions; and (2) to determine if trends in coordination variability during movement are consistent when using either vector coding or CRP. We present both a theoretical case (the Lorenz Attractor) and two experimental cases (rearfoot–forefoot coupling during overground walking for 22 subjects; the effect of treadmill speed on thigh-leg coupling for five subjects). In the theoretical case, variability quantified by CRP agreed with dynamical systems theory on state space transitions more so than variability quantified by vector coding. In experimental cases, this distinction was less clear, although CRP appeared to be a more conservative metric for variability. The magnitudes (all p<0.001) and timings (all p<0.04) of peaks in variability during the stance phase of overground walking depended on whether vector coding or CRP was used for two couplings. Similar distinctions were observed for peaks during the stride cycle of treadmill locomotion (all effect sizes >2.8). However, changes in the average variability during the stride cycle as speed increased were consistent for both methods (all effect sizes <0.2). The results suggest that comparisons between the findings of studies that have quantified variability using CRP and those that have used vector coding should be made with caution.