Elsevier

Gait & Posture

Volume 60, February 2018, Pages 241-250
Gait & Posture

Review
The largest Lyapunov exponent of gait in young and elderly individuals: A systematic review

https://doi.org/10.1016/j.gaitpost.2017.12.016Get rights and content

Highlights

  • A systematic review of LyE of gait in young and old adults is conducted.

  • Different methodological approaches of quantifying the LyE is summarized.

  • LyE values of different body segments and joints in normal walking are categorized.

Abstract

The largest Lyapunov exponent (LyE) is an accepted method to quantify gait stability in young and old adults. However, a range of LyE values has been reported in the literature for healthy young and elderly adults in normal walking. Therefore, it has been impractical to use the LyE as a clinical measure of gait stability. The aims of this systematic review were to summarize different methodological approaches of quantifying LyE, as well as to classify LyE values of different body segments and joints in young and elderly individuals during normal walking. The Pubmed, Ovid Medline, Scopus and ISI Web of Knowledge databases were searched using keywords related to gait, stability, variability, and LyE. Only English language articles using the Lyapunov exponent to quantify the stability of healthy normal young and old subjects walking on a level surface were considered. 102 papers were included for full-text review and data extraction. Data associated with the walking surface, data recording method, sampling rate, walking speed, body segments and joints, number of strides/steps, variable type, filtering, time-normalizing, state space dimension, time delay, LyE algorithm, and the LyE values were extracted. The disparity in implementation and calculation of the LyE was from, (i) experiment design, (ii) data pre-processing, and (iii) LyE calculation method. For practical implementation of LyE as a measure of gait stability in clinical settings, a standard and universally accepted approach of calculating LyE is required. Therefore, future studies should look for a standard and generalized procedure to apply and calculate LyE.

Introduction

Falls are events whereby a standing person accidentally comes to a rest on the ground or other lower levels [1]. Falls are a significant health problem within the elderly population, and are the dominant cause of injury and death for individuals over 65 years old. One-third of the elderly community-dwelling population falls each year, with reports of 24% having serious injuries and 6% having fractures. Falls could have detrimental physical (decreased functional ability, deformity or disability), medical (hospitalization, surgical intervention, admission to a nursing home), psychological (fear of recurring falls), social (reduction or diminishing of social activities), and economic (loss of income, direct and indirect costs of medical care and rehabilitative programs) consequences [2,3]. It is therefore essential for clinicians to identify those at risk of falling, and to provide effective preventive and rehabilitative services. Analyzing the main risk factors of falls is therefore of fundamental importance, with many studies previously attempted to determine and classify fall risk factors in the elderly [[1],2,4,5]. Among the multifactorial risk factors of falls in the elderly, gait instability has persistently been reported as one of the main contributors [5,6]. Therefore, it is important to quantify gait stability in elderly people and to have a clear understanding of the differences in stability between the young and the elderly population, and also those at a risk of falling.

Stability is defined as the ability of the system (e.g., movement system) to maintain its original state under the influence of perturbations [7]. Gait stability could thus be considered as the ability of a walking individual’s motor system to maintain its walking state in the ubiquity of omnipresent disturbances and to avoid falling. Several methods have been developed to quantify gait stability (for a review see [6]), with the largest Lyapunov exponent (LyE; also known as the maximal Lyapunov exponent and local divergence exponent) gaining increasing interest during recent years. In the context of gait stability, the LyE quantifies the ability of the motor system to attenuate small perturbations, which are revealed as the divergence of the trajectories in state space. The LyE thus measures the exponential rate of divergence of trajectories of the state space constructed from kinematic data acquired from gait [8]. An inability of the motor system to diminish the perturbations results in a higher divergence of the trajectories of the state space and thus greater LyE values. Hence, the higher value of the LyE, the lower stability of the individual’s walking.

It is well established that LyE is a valid measure to quantify gait stability and thus to estimate fall risk [[9], [10], [11], [12], [13], [14], [15]]. However, there is some incongruity in the literature using LyE, which has resulted in diversified values of LyE being reported for young and old populations. For example, using Rosenstein’s method [16], the range of short-term LyE values for upper trunk in young adults calculated with velocity time series is 0.15–3.30, 0.10–2.85, and 0.27–2.40 for anterior-posterior (AP), mediolateral (ML) and vertical (VT) directions, respectively. Similarly, using Wolf’s method [17], the range of LyE values found in the literature for the lower trunk of elderly individuals calculated with acceleration time series is 0.75–1.62, 1.31–2.01, and 0.83–1.42 for AP, ML and VT directions, respectively. These broad ranges reported in the literature is most likely a result of using different methods to calculate LyE.

In two previous studies, Bruijn et al. [6] and Hamacher et al. [18] reviewed different measures of gait stability. However, these studies provide a general overview of the LyE method and have not discussed the methodological factors that affect LyE value in detail. It could also be argued that although these studies suggest that LyE method is able to discriminate young and old individuals, they reviewed a low number of studies on LyE. Therefore, a comprehensive systematic review of LyE method in which the LyE values of young and old individuals, as well as the factors that influence its value is detailed, seems essential.

The aims of this systematic review were therefore to: (i) summarize different methodological approaches used in the literature to quantify the LyE of young and elderly individuals during normal walking, and (ii) classify the LyE values of different body segments and joints in young and elderly individuals during normal walking. Normal walking is considered as walking with the preferred speed on a level surface (either treadmill or over-ground) without any interference. The current study is intended to help future researchers/practitioners use appropriate experimental designs, data processing and calculation methods, as well establish a database of LyE values for different body segments and joints to compare their results. The inclusion of the results of young individuals in this review provides reference values for comparison with elderly individuals, as well as with the results of studies on other populations.

Section snippets

Literature search strategy

A comprehensive electronic database search was performed in September 2016 to find all papers that used LyE to quantify dynamic stability of human locomotion. The searched databases were Pubmed, Ovid Medline, Scopus and ISI Web of Knowledge. No date restriction was used for the search. Keywords included in the literature search were (similar for all databases):

  • (i)

    Gait OR Walk* OR Locomotion OR Ambulat*

  • (ii)

    Variability OR Stability OR Balance OR Lyapunov exponent OR Divergence exponent

  • (iii)

    1 AND 2

Only

Included studies

The initial electronic database search yielded a total of 3553 papers. After removing duplicates, 3104 remained for title and abstract screening. Title and abstract screening resulted in 201 articles remaining. No additional articles were found through the manual search of the reference lists of the papers. Finally, considering the inclusion/exclusion criteria, full text review of the remaining papers led to 102 papers to be included in this systematic review (Fig. 1).

Data extracted

The results of the data

Discussion

The demand for a valid method to evaluate gait stability is growing in order to advance the efficacy of fall prevention strategies in clinical settings [18]. Although LyE has been proven as a valid measure to quantify gait stability and fall risk, its effectiveness as a routine procedure to measure gait stability of young and old adults in clinical settings is still ambiguous. A part of this ambiguity is due to the varied methods implemented in the studies to calculate LyE, which has resulted

Conclusions

In conclusion, the diversity in implementation of the LyE method in investigating gait dynamic stability arises from three main sources: (i) experiment design, (ii) data pre-processing, and (iii) LyE calculation method. These differences prevented to have a relatively reliable LyE value for young and elderly individuals in normal walking. For practical implementation of LyE as a measure of gait dynamic stability in clinical settings, it is necessary to know the exact or range of LyE values- for

Conflicts of interest statement

There is not any type of conflict of interest associated with this manuscript.

References (36)

  • D.H. Gates et al.

    Comparison of different state space definitions for local dynamic stability analyses

    J. Biomech.

    (2009)
  • K.S. van Schooten et al.

    Assessing gait stability: the influence of state space reconstruction on inter- and intra-day reliability of local dynamic stability during over-ground walking

    J. Biomech.

    (2013)
  • S.M. Bruijn et al.

    Statistical precision and sensitivity of measures of dynamic gait stability

    ‎J. Neurosci. Methods

    (2009)
  • H.G. Kang et al.

    Intra-session reliability of local dynamic stability of walking

    Gait Posture

    (2006)
  • S.A. England et al.

    The influence of gait speed on local dynamic stability of walking

    Gait Posture

    (2007)
  • E.R. Vieira et al.

    Prevention of falls in older people living in the community

    BMJ

    (2016)
  • A. Lee et al.

    Preventing falls in the geriatric population

    Perm. J.

    (2013)
  • K. James et al.

    Falls and Falls Prevention in the Elderly: Insights from Jamaica, WHO Background Paper to the Global Report on Falls Among Older Persons

    (2007)
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