Proceedings of the 29th Annual International Conference of the IEEE EMBS Cité Internationale, Lyon, France August 23-26, 2007.
FrP1A2.10
Understanding Ageing Effects by Approximate Entropy Analysis of gait variability Chandan K. Karmakar, Ahsan H. Khandoker, Rezaul K. Begg, Marimuthu Palaniswami, Simon Taylor
Abstract— Ageing influences gait patterns which in turn affects the control mechanism of human locomotor balance. The aim of this study is to investigate the relationship between approximate entropy (ApEn) and standard deviation (SD) of a gait variable (minimum toe clearance, MTC) for young and elderly gait patterns. MTC data of 30 healthy young (HY), 27 healthy elderly (HE) and 10 falls risk (FR) elderly subjects with balance problems were analyzed. The ApEn values of MTC were significantly correlated with SD of MTC in the three groups; however, such correlations were abolished in the randomly shuffled MTC data of HE and HY group. These findings have implications of understanding ageing effect on gait variability and the likely risks of tripping falls during gait. Results are also potentially useful for the early diagnosis of common gait pathologies.
I. INTRODUCTION
F
LUCTUATION of gait variables in stride to stride intervals, i.e. gait variability is a quantifiable measure of walking that has been shown to alter (both in terms of magnitude and dynamics) in ageing [1] and neurodegenerative disease [2]. The magnitudes of variability in stride length and time intervals are unaltered in healthy elderly, whereas the dynamics of gait change with ageing [3, 4]. An important aspect of gait variability measure is its relationship to falls risk. Falls increase the mortality and morbidity among elderly around 70% among the people aged above 75 [5, 6]. A number of studies have demonstrated that the degree of gait variability may be more related to falls risk than average values of gait parameters using basic time-distance parameters e.g. speed, stride length, stride time intervals [3, 4]. These findings suggest that conventional statistical measures of gait parameters are not sufficient to provide a more complete characterization of gait changes due to ageing and falls risk. Furthermore, it is not known the variability characteristics of a more sensitive gait parameter such as the minimum toe clearance (MTC) during walking which has close linkage with tripping falls [1]. Related to dynamical analysis of time series, approximate entropy (ApEn) provides a measure of the degree of irregularity or randomness within a series of data. ApEn was
Chandan K. Karmakar, Ahsan K. Khandoker and Marimuthu Palaniswami are with Department of Electrical & Electronic Engineering, The University of Melbourne, Melbourne, VIC 3010, Australia. E-mail: {c.karmakar, a.khandoker, swami}@ee.unimelb.edu.au. Rezaul K. Begg and Simon Taylor are with Biomechanics Unit, Center for Ageing, Rehabilitation, Exercise and Sport, Victoria University, Melbourne, VIC 8001, Australia. Email:
[email protected].
1-4244-0788-5/07/$20.00 ©2007 IEEE
pioneered by Pincus [7] as a measure of system complexity; smaller values indicate greater regularity whereas greater values suggest increased disorder, randomness and system complexity. A previous study [8] on the entropy of human gait (stride to stride intervals) in multiple scales discussed the scaling effect of entropy on various walking patterns, indicating the changes of multiscale entropy values with slow, normal and fast walking. In the present study, we investigate the effects of ageing and falls risk on ApEn of a gait variable [minimum toe clearance (MTC)] healthy young, healthy elderly and falls risk subjects during walking. Minimum toe clearance is the minimum vertical distance between the front part of the foot (shoe) and the ground, when the forward velocity of the foot is the highest and the position of the body is inherently unstable. Thus MTC has been the focus of many studies as an important parameter for ageing and falls-risk gait analysis [9]. With an aim to find a suitable marker of gait dynamics due to ageing and balance impairments, we apply ApEn analysis method to the MTC gait data obtained from healthy young, elderly subjects with and without balance problem, and explore ageing effect and balance impairments on ApEn of MTC results II. METHOD A. Gait Data MTC data of 30 healthy young (HY) (age (yr)=28.4 ± 6.4; height (cm)=171 ± 12; weight (kg)=71.2 ± 15.0), 27 healthy elderly (HE) (age (yr)=69.1 ± 5.12; height (cm)=165 ± 7.8; weight (kg)=66.8 ± 8.4) and 10 falls risk (FR) ((a history of falls was defined as an occurrence of one or more falls in the past 12 months; age (yr)=72.2 ± 3.1; height (cm)=166 ± 12; weight (kg)=66.9 ± 8.6) are taken from the gait database of the Biomechanics Unit of Victoria University. Foot clearance data of these subjects were collected using a 2D Motion Analysis system (Vicon Motus, Oxford, UK) during their continuous steady state walking on the treadmill at selfselected preferred walking speed. The total number of gait cycles analysed per subject (i.e., the number of MTC data) varied across the subjects due to their individual walking speeds. However, for ApEn analysis purposes, the first 500 continuous gait cycles (and hence MTC data points) were used. The detailed procedure for experimental set up and gait data collection protocol has been described in our previous study [1].
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B. Approximate Entropy Analysis Approximate Entropy (ApEn) analysis is a nonlinear technique for quantifying the regularity of time series data. A smaller value of ApEn represents more regularity in the data series whereas a larger value means that the data are more irregular [7]. ApEn provides an efficient and significant way to analyze the nonlinear behavior of a system with finite number of data points. ApEn measures the negative average logarithmic conditional probability of a pattern to remain close on next incremental comparison [10]. ApEn of MTC was calculated using the following equation:
( N − m)
−1
ApEn( N , m, r ) = − ln ( N − m + 1)
N −m
∑ ln c
i =1 N − m +1 −1
∑
m +1 i
(r )
relationship was shown to exist between HY and HE subjects. TABLE I MEAN AND STANDARD DEVIATION OF APE N OF MTC OF HEALTHY YOUNG (HY), HEALTHY ELDERLY (HE) AND FALLS RISK (FR) GROUPS WITH DIFFERENT TOLERANCE (r). APE N = APPROXIMATE ENTROPY, MEAN = AVERAGE APPROXIMATE ENTROPY, STD = STANDARD DEVIATION OF APPROXIMATE E NTROPY AND SD = STANDARD DEVIATION OF MTC DATA POINTS. ANOVA ANALYSIS SHOWS ONLY P VALUES. r 0.1*SD 0.2*SD 0.3*SD 0.4*SD 0.5*SD 0.6*SD 0.7*SD 0.8*SD 0.9*SD
(1)
m i
ln c (r )
i =1
Where N represents the number of data element, m represents the pattern length and r is the tolerance which is normally taken as some percentage of standard deviation of the data. In our work with MTC data we have calculated all ApEn for N=500, m=3 and r varies from 0-90% of SD calculated from the MTC data points. In equation (1), C calculates the total number likelihood of all patterns of length m with tolerance r in the data set. So the ApEn measures the logarithmic likelihood of all patterns that are closer for a length m will remain closer for the pattern with length m+1. According to the mathematical context of ApEn, smaller r value represents more detailed information of the system. The specific choice of r depends on the system noise and the system itself described by Pincus [7]. C. Surrogate Analysis and statistics To prove any intrinsic relationship of locomotor control system with ApEn, we followed a method of surrogate data analysis introduced by Theiler et al. [11]. This analysis preserves the rank distribution of the data but change the temporal relationship of the data points. Since the ApEn measurement represents the temporal relationship among the data points, we have changed the temporal relationship by shuffling data points and then measured the changed ApEn. Here we have surrogated each data 10 times and calculated the ApEn. The surrogated ApEn is taken as the average of those 10 ApEn values. We have used MATLAB statistics toolbox to perform a multivariate ANOVA (within three groups namely, HY, HE & FR) to examine the influence of ageing and falls risk on ApEn. III. RESULT Fig. 1 demonstrated the change of ApEn with m=3 and r=0.1*SD to 0.9*SD of MTCdata for HY, HE and FR subjects. For r
