title: Vector field statistics for objective center-of-pressure trajectory analysis during gait, with evidence of scalar sensitivity to small coordinate system rotations.
abstract: Center of pressure (COP) trajectories summarize the complex mechanical interaction between the foot and a contacted surface. Each trajectory itself is also complex, comprising hundreds of instantaneous vectors over the duration of stance phase. To simplify statistical analysis often a small number of scalars are extracted from each COP trajectory. The purpose of this paper was to demonstrate how a more objective approach to COP analysis can avoid particular sensitivities of scalar extraction analysis. A previously published dataset describing the effects of walking speed on plantar pressure (PP) distributions was re-analyzed. After spatially and temporally normalizing the data, speed effects were assessed using a vector-field paired Hotelling's T2 test. Results showed that, as walking speed increased, the COP moved increasingly posterior at heel contact, and increasingly laterally and anteriorly between ∼60 and 85% stance, in agreement with previous independent studies. Nevertheless, two extracted scalars disagreed with these results. Furthermore, sensitivity analysis found that a relatively small coordinate system rotation of 5.5° reversed the mediolateral null hypothesis rejection decision. Considering that the foot may adopt arbitrary postures in the horizontal plane, these sensitivity results suggest that non-negligible uncertainty may exist in mediolateral COP effects. As compared with COP scalar extraction, two key advantages of the vector-field approach are: (i) coordinate system independence, (ii) continuous statistical data reflecting the temporal extents of COP trajectory changes.
authors.affiliation: Department of Bioengineering, Shinshu University, Japan. Electronic address: tpataky@shinshu-u.ac.jp.
authors.forename: Todd C
authors.initials: TC
authors.lastname: Pataky
authors.affiliation: Research Institute for Sport and Exercise Science, Liverpool John Moores University, UK.
authors.forename: Mark A
authors.initials: MA
authors.lastname: Robinson
authors.affiliation: Research Institute for Sport and Exercise Science, Liverpool John Moores University, UK.
authors.forename: Jos
authors.initials: J
authors.lastname: Vanrenterghem
authors.affiliation: Institute of Ageing and Chronic Disease, University of Liverpool, UK.
authors.forename: Russell
authors.initials: R
authors.lastname: Savage
authors.affiliation: Institute of Ageing and Chronic Disease, University of Liverpool, UK.
authors.forename: Karl T
authors.initials: KT
authors.lastname: Bates
authors.affiliation: Institute of Ageing and Chronic Disease, University of Liverpool, UK.
authors.forename: Robin H
authors.initials: RH
authors.lastname: Crompton
mesh_terms: D000328:Adult; D001696:Biomechanical Phenomena; D005528:Foot / Q000502:physiology*; D005684:Gait / Q000502:physiology*; D006365:Heel / Q000502:physiology; D006801:Humans; D008297:Male; D008954:Models, Biological; D015233:Models, Statistical; D004856:Postural Balance / Q000502:physiology*; D011312:Pressure; D012399:Rotation; D062211:Spatio-Temporal Analysis; D016138:Walking / Q000145:classification* / Q000502:physiology
keywords: Continuum statistics; Gait analysis; Kinematics; Random field theory; Statistical parametric mapping