Elsevier

Gait & Posture

Volume 46, May 2016, Pages 194-200
Gait & Posture

The gait standard deviation, a single measure of kinematic variability

https://doi.org/10.1016/j.gaitpost.2016.03.015Get rights and content

Highlights

  • Proposes a single measure of gait kinematic variability: GaitSD.

  • Provides reference data for various measures of gait variability: GaitSD, CMC, W-CV.

  • Establishes the precision with respect to the number of strides processed.

  • Discusses the effect of kinetics normalisation scheme on variability.

  • Showed that gait variability continue to decrease until skeletal maturity.

Abstract

Measurement of gait kinematic variability provides relevant clinical information in certain conditions affecting the neuromotor control of movement. In this article, we present a measure of overall gait kinematic variability, GaitSD, based on combination of waveforms’ standard deviation. The waveform standard deviation is the common numerator in established indices of variability such as Kadaba's coefficient of multiple correlation or Winter's waveform coefficient of variation.

Gait data were collected on typically developing children aged 6–17 years. Large number of strides was captured for each child, average 45 (SD: 11) for kinematics and 19 (SD: 5) for kinetics. We used a bootstrap procedure to determine the precision of GaitSD as a function of the number of strides processed. We compared the within-subject, stride-to-stride, variability with the, between-subject, variability of the normative pattern. Finally, we investigated the correlation between age and gait kinematic, kinetic and spatio-temporal variability.

In typically developing children, the relative precision of GaitSD was 10% as soon as 6 strides were captured. As a comparison, spatio-temporal parameters required 30 strides to reach the same relative precision. The ratio stride-to-stride divided by normative pattern variability was smaller in kinematic variables (the smallest for pelvic tilt, 28%) than in kinetic and spatio-temporal variables (the largest for normalised stride length, 95%). GaitSD had a strong, negative correlation with age. We show that gait consistency may stabilise only at, or after, skeletal maturity.

Introduction

Clinical gait analysis tends to focus on the shape of the kinematic and kinetic waveforms during a walking stride (e.g. [1]). However, variability of the gait pattern may provide additional, relevant, information about a condition or pre-post an intervention [2]. Mathematical tools to report the variability in kinematic, kinetic or electromyographic (EMG) data exist but there is no tool to summarise overall gait kinematic variability. The aim of this study was to propose and validate such a tool.

Research regarding variability in gait analysis data began with the reliability of electromyographic waveforms [3]. Hershler and Milner introduced the variance ratio (VR) to estimate the repeatability of EMG waveforms over several gait cycles. In [4], Kadaba et al. used the variance ratio for EMG data but later [5] introduced the Coefficient of Multiple Correlation (CMC) to estimate the repeatability of kinematic and kinetic waveforms. In [5], Kadaba et al. did not use VR or CMC to measure variability of EMG data but the waveform coefficient of variation (W-CV) described by Winter [6]. Subsequent research regarding variability in gait waveforms utilised these indices.

Dynamic stability is another field of human motion analysis interested in kinematic variability of gait. Researchers developed additional tools such as detrended fluctuation analysis, fractal dynamics or the Lyapounov exponent (e.g. [7], [8]). Although related to variability, these tools do not measure variability per se but how well, or how fast, one adapts for the variability during movement. These tools require large number of strides and may not be easily used in the context of clinical gait analysis, where small number of strides, typically 10 or less, is captured during overground walking.

The VR, CMC or W-CV indices are all dimensionless ratios. This allows the comparison of variability in data expressed in different units or waveforms that vary over markedly different amplitudes. For example, Tirosh et al. used the VR to compare confidence in the mean waveforms from different treatment of EMG data and with respect to kinematic and kinetic data [9]. However, ratios cannot be combined to obtain a summary index across multiple variables. VR and CMC are two ways to express the same relationship in the data, and VR and W-CV ratios share the same numerator, the variance around the mean waveform. This variance can be combined across several variables to create a summary index of gait variability, which we will call GaitSD.

Most research efforts about gait variability have focused on the reliability of the gait experiment and researchers have mostly been interested in between-session variability (between days, between assessors or both) [10]. The within-session (and intra-subject) variability has been calculated in some studies, but mainly to compare with the variability between-sessions. Intra-subject gait variability per se has been studied in normal adults or children [5], [6], [11] as well as in populations with various motor control problems: ataxia [12], stroke [13], spastic diplegia [14] or spastic hemiplegia [15], or skeletal problems such as scoliosis [16]. Most of the above studies utilised Kadaba's CMC or Winter's W-CV to measure variability of the kinematic and kinetic waveforms. However, the precision of the measurement of variability may depend on the number of strides captured and processed. Researchers used varying number of strides to calculate variability, a minimum of 2 strides was reported in [13], 3 in [5], 4 in [15], 5 in [16], 9 in [6], and 10 in [11], [12], [14]. What is the precision of the waveforms variability calculated from two strides, and from ten strides? We will address this question and provide reference data for the precision of CMC, W-CV and the newly introduced GaitSD.

The definition of gait in the dictionary encompass two concepts. The first refers to the pattern of movement of the limbs that form the manner of walking. The second refers to different pace of forward progression adopted by horses and other animals (e.g. walk, trot, and gallop). In the scientific literature, search results about “gait variability” mostly refer to the second concept, and report the variability of spatio-temporal parameters such as walking speed, cadence and stride length. We will compare kinematic variability with the variability of spatio-temporal parameters.

Sutherland et al. have shown that gait pattern may mature as early as age 4 [17]. However, little is known about the consistency of the pattern once it has matured. Does gait consistency continue to improve after the pattern has matured? We will try to answer this question and provide reference data about the kinematic, kinetic and spatio-temporal variability in typically developing children.

Section snippets

Gait kinematic variability: GaitSD

In 1978, Hershler and Milner presented the analogy between the variance ratio and the analysis of variance [3]. If we consider N waveforms X defined over T time samples and a regression model of the data by the mean waveform:Xij=X¯j+ijwith Xij a waveform from the stride i defined over j time samples, X¯j the mean of the N waveforms defined for each time instant j: X¯j=1Ni=1NXij and ∈ij the residuals.

The variance of the residuals, which we will call GVSD2 for later use, is calculated from the

Results

Data was collected on 14 females and 21 males (Subject demographics, Table 1). There were no significant differences in age, height and mass between males and females. The average number of strides collected per subject was 45 (SD: 11) for kinematic and spatio-temporal data and 19 (SD: 5) for kinetic data.

Fig. 1A presents the effect of m, the number of strides, on GaitSD. The number of strides m had little effect on mean GaitSD. This was expected given the 2000 random samples and calculation.

Discussion

The aim of this study was to propose a tool to summarise gait kinematic variability. We explained the relationship between indices of variability found in the literature and identified the gait variable standard deviation (GVSD) as the common numerator between the indices and the true measure of variability. We introduced an overall measure of gait kinematic variability, GaitSD, as the pooled standard deviation of 15 kinematic variables commonly used in gait normalcy indices [18], [19].

We

Conclusion

GaitSD summarises a subject's kinematic variability during walking in a single number. The main clinical application of GaitSD may be to help understand different conditions affecting gait or the effect on kinematic variability pre-/post-intervention [2]. Our results showed that GaitSD reached a satisfying precision (SD(GaitSD)/GaitSD  10%) as soon as 6 strides were processed. Comparatively, single kinematic or kinetic variables required 10–15 strides and spatio-temporal parameters required more

Conflict of interest statement

Each author certifies that he or she has no commercial associations that might pose a conflict of interest in connection with the article.

Acknowledgement

This work has been funded through a Clinical Science theme grant from the Murdoch Childrens Research Institute. We would like to acknowledge Tandy Hasting-Ison, Jill Rodda and Pam Thomason senior physiotherapists at the Hugh Williamson Gait Analysis Laboratory, for their participation to data collection. Adrienne Fosang, senior physiotherapist at The Royal Children's Hospital, coordinated patient recruitment and participated to data collection. She is gratefully acknowledged.

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