This art icle was downloaded by: [ Ahsan Khandoker] On: 30 January 2012, At : 20: 09 Publisher: Taylor & Francis I nform a Lt d Regist ered in England and Wales Regist ered Num ber: 1072954 Regist ered office: Mort im er House, 37- 41 Mort im er St reet , London W1T 3JH, UK Computer Methods in Biomechanics and Biomedical Engineering Publicat ion det ails, including inst ruct ions f or aut hors and subscript ion inf ormat ion: ht t p: / / www. t andf online. com/ loi/ gcmb20 Understanding ageing effects using complexity analysis of foot–ground clearance during walking Chandan Karmakar a , Ahsan Khandoker a b , Rezaul Begg c & Marimut hu Palaniswami a a Depart ment of Elect rical and Elect ronic Engineering, The Universit y of Melbourne, Parkville, VIC, 3010, Aust ralia b Depart ment of Biomedical Engineering, Khalif a Universit y of Science, Technology and Research (KUSTAR), Abu Dhabi, UAE c Biomechanics Unit , SES/ ISEAL, Vict oria Universit y, Melbourne, VIC, 8001, Aust ralia Available online: 30 Jan 2012 To cite this article: Chandan Karmakar, Ahsan Khandoker, Rezaul Begg & Marimut hu Palaniswami (2012): Underst anding ageing ef f ect s using complexit y analysis of f oot –ground clearance during walking, Comput er Met hods in Biomechanics and Biomedical Engineering, DOI: 10. 1080/ 10255842. 2011. 628943 To link to this article: ht t p: / / dx. doi. org/ 10. 1080/ 10255842. 2011. 628943 PLEASE SCROLL DOWN FOR ARTI CLE Full t erm s and condit ions of use: ht t p: / / www.t andfonline.com / page/ t erm s- and- condit ions This art icle m ay be used for research, t eaching, and privat e st udy purposes. 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The publisher shall not be liable for any loss, act ions, claim s, proceedings, dem and, or cost s or dam ages what soever or howsoever caused arising direct ly or indirect ly in connect ion wit h or arising out of t he use of t his m at erial. Computer Methods in Biomechanics and Biomedical Engineering iFirst article, 2012, 1–11 Understanding ageing effects using complexity analysis of foot– ground clearance during walking Chandan Karmakara, Ahsan Khandokera,b*, Rezaul Beggc and Marimuthu Palaniswamia a Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC 3010, Australia; bDepartment of Biomedical Engineering, Khalifa University of Science, Technology and Research (KUSTAR), Abu Dhabi, UAE; cBiomechanics Unit, SES/ISEAL, Victoria University, Melbourne, VIC 8001, Australia Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 (Received 22 September 2010; final version received 29 September 2011) Ageing influences gait patterns which in turn can affect the balance control of human locomotion. Entropy-based regularity and complexity measures have been highly effective in analysing a broad range of physiological signals. Minimum toe clearance (MTC) is an event during the swing phase of the gait cycle and is highly sensitive to the spatial balance control properties of the locomotor system. The aim of this research was to investigate the regularity and complexity of the MTC time series due to healthy ageing and locomotors’ disorders. MTC data from 30 healthy young (HY), 27 healthy elderly (HE) and 10 falls risk (FR) elderly subjects with balance problems were analysed. Continuous MTC data were collected and using the first 500 data points, MTC mean, standard deviation (SD) and entropy-based complexity analysis were performed using sample entropy (SampEn) for different window lengths (m) and filtering levels (r). The MTC SampEn values were lower in the FR group compared to the HY and HE groups for all m and r. The HY group had a greater mean SampEn value than both HE and FR reflecting higher complexity in their MTC series. The mean SampEn values of HY and FR groups were found significantly different for m ¼ 2, 4, 5 and r ¼ (0.1– 0.9) £ SD, (0.3– 0.9) £ SD and (0.3 – 0.9) £ SD, respectively. They were also significant difference between HE and FR groups for m ¼ 4 – 5 and r ¼ (0.3 –0.7) £ SD, but no significant differences were seen between HY and HE groups for any m and r. A significant correlation of SampEn with SD of MTC was revealed for the HY and HE groups only, suggesting that locomotor disorders could significantly change the regularity or the complexity of the MTC series while healthy ageing does not. These results can be usefully applied to the early diagnosis of common gait pathologies. Keywords: sample entropy; gait; gait variability; minimum toe clearance 1. Introduction Fluctuation of gait variables from stride to stride, i.e. gait variability, is a quantifiable property of walking that is influenced significantly in magnitude and dynamics by ageing and neurodegenerative diseases. The magnitudes of variability in stride length and time are unchanged in healthy elderly (HE) people, whereas the dynamics of gait change with ageing (Hausdorff 2005). An important aspect of gait variability is its relationship to falls risk (FR). Falls increase mortality and morbidity by approximately 70% in those aged over 75 years (Close and Glucksman 2000; Cripps and Carman 2001). Previous studies have shown that ageing and pathology are associated with changes to fluctuations in many physiological time series signals, representative of biological control systems (Goldberger et al. 2002; Arking 2006), including gait parameters (Gabell and Nayak 1984; Hausdorff et al. 1997; Herman et al. 2005). Research into ageing and pathological gait has shown that the variabilities in time – distance parameters, such as walking speed, stance/swing times, step length and step width (Hausdorff et al. 1997, 2001; Maki 1997; Brach et al. 2008), are useful indicators of gait instability and FR. These findings suggest that conventional statistical *Corresponding author. Email: [email protected] ISSN 1025-5842 print/ISSN 1476-8259 online q 2012 Taylor & Francis http://dx.doi.org/10.1080/10255842.2011.628943 http://www.tandfonline.com descriptors of gait parameters cannot completely characterise gait changes due to ageing and FR. In a research effort to reveal highly sensitive markers for investigating FR in older populations, we have reported features of the minimum toe clearance (MTC) time series (Begg et al. 2007). MTC is the minimum vertical distance between the front part of the foot (shoe) and the ground, when the forward velocity of the foot is highest and the body is inherently unstable, an event that is critical to an older adult’s capacity to maintain stability. If the lower limb control parameters fall beyond safe boundaries, the consequences can be a tripping and an increased probability of falling. Thus, MTC has been the focus of many studies as an important parameter for ageing and FR assessment (Begg et al. 2005, 2007; Khandoker, Palaniswami, et al. 2008, Khandoker, Taylor, et al.2008). In previous work (Begg et al. 2007), we investigated the MTC variability [inter-quartile range (IQR)] and central tendency (median) statistics of young and elderly females and demonstrated that modulation of MTC central tendency and variability is one of a number of strategies adopted by elderly individuals to minimise tripping risk. In a study of older adults displaying characteristics of higher Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 2 C. Karmakar et al. level gait disorder (HLGD), the collective term suggested by Nutt et al. (1993) and Herman et al. has reported that the linear variability measures can only discriminate the HLGD group and the age-matched control group, whereas nonlinear techniques and fractal correlations not only differentiate the HLGD group from the age-matched controls but also discriminate between fallers and nonfallers within the HLGD group (Herman et al. 2005). Therefore, analysis of linear statistics does not directly address the complexity of the signal and thus may potentially overlook useful inherent information such as irregularity, dynamics and so on. Since the underlying mechanisms of human locomotor control are complex and nonlinear (Hausdorff et al. 1995, 1996; Costa et al. 2003; Jordan et al. 2007), application of nonlinear techniques might be more effective for discriminating age-affected and FR gait patterns from healthy young (HY) gait patterns. Therefore, we investigated scale-invariant nonlinear indices [Poincaré indices (SD1, SD2 and SD1/SD2), detrended fractal analysis slope (a), wavelet coefficient variance (Wv) and wavelet multiscale exponents (b)] of the MTC time series signal to reveal change in gait dynamics with advanced age and pathology (Khandoker, Palaniswami, et al. 2008). In that study, the scale-invariant indices did not show any significant change in the neuroautonomic control that would point to loss of gait dynamics with healthy ageing. Therefore, we hypothesised that the analyses of complexity of the stride-to-stride MTC time series structure might provide a more sensitive marker to discriminate ageing and FR gait pattern. In the present study, we investigated ageing and FR effects on gait dynamics by analysing nonlinear and complex characteristics of MTC fluctuations during treadmill walking, recorded from healthy subjects (young and elderly) and elderly subjects with a history of trip-related falls. The aim was to discover a suitable marker for gait dynamics that is sensitive to ageing and balance impairments. 2. Methods 2.1 Data MTC data of 30 HY [age (years) ¼ 28.4 ^ 6.4, height (cm) ¼ 171 ^ 12, mass (kg) ¼ 71.2 ^ 15.0]; 27 HE [age (years) ¼ 69.1 ^ 5.12, height (cm) ¼ 165 ^ 7.8, mass (kg) ¼ 66.8 ^ 8.4] and 10 FR [a history of falls was defined as an occurrence of one or more than one triprelated falls during the past 12 months, age (years) ¼ 72.2 ^ 3.1, height (cm) ¼ 166 ^ 12, mass (kg) ¼ 66.9 ^ 8.6] were taken from the gait database of the Biomechanics Unit at Victoria University. All participants were female and undertook informed-consent procedures as approved by the Victoria University Human Research Ethics Committee. Foot clearance data were collected using a 2D motion analysis system (Vicon Motus, Oxford, UK) during their steady-state walking on the treadmill. All participants were free from disease that might directly affect gait (mobility and balance), including any neurological, musculoskeletal, cardiovascular or respiratory disorders, and rheumatoid arthritis. Participants were of 65 þ age to be included in both HE and FR groups. In addition to be included in the FR group, the elderly had at least one tripping fall in the previous 12 months, whereas the HE did not have any falling history. Subjects were administered a 10-min warm-up period to familiarise with the treadmill, allowing their treadmill walking patterns to represent their natural overground walking pattern. During the warm-up period, the subjects were encouraged to explore different speeds by selfadjusting the range of treadmill speeds between 1.5 and 6.0 km/h. Subjects were also encouraged to walk at different step frequencies and lengths. This ‘warm-up’ process ensured the exploration of a range of available gait patterns. Following this warm-up period, the preferred walking speed (PWS) was determined from upper and lower limits of their comfortable walking speed. This was achieved by having each subject to imagine ‘walking alone to a destination’ while the treadmill accelerated at 0.1 km/h for every six strides from a relatively slow initial speed until the subject reported a speed that was uncomfortable. The subject was unaware of the speed magnitudes. The speed of the treadmill was then increased marginally before undergoing the same rate of speed change, but in decreasing increments until the subject reported the speed to be uncomfortably slow. Once the subject reported an uncomfortable speed, the belt velocity continued to decrease before the rate of treadmill speed changed back to increasing increments. The procedure was repeated until PWS was determined from the average of three reported ‘uncomfortably fast’ speeds and three reported ‘uncomfortably slow’ speeds. This approach has been applied elsewhere by Dingwell and Marin (2006) and England and Granata (2007). The total number of gait cycles collected per subject (i.e. the number of MTC data) varied among the subjects due to their PWS (Table 1), but for analysis, the first 500 continuous gait cycles (and hence MTC data points) were used. The detailed procedure for gait data collection has been described previously by Begg et al. (2007). Briefly, two reflective markers were attached to each subject’s left shoe laterally at the fifth metatarsal head and the great toe. The foot markers were automatically digitised for the entire walking task and raw data were digitally filtered (Begg et al. 2007). Using a 2D geometric model of the foot (Begg et al. 2007), the marker positions and shoe dimensions were used to predict the position of the shoe/foot end point, i.e. the position on the shoe closest to the ground at MTC. The MTC of each stride was calculated by subtracting ground reference from the minimum vertical coordinate of the swing phase. 3 Computer Methods in Biomechanics and Biomedical Engineering Table 1. Major descriptive statistics of treadmill walking speed (km/h) and MTC (cm) of each subject groups (HY, HE and FR). MTC (mean ^ STD) Feature HY (n ¼ 30) HE (n ¼ 27) FR (n ¼ 10) ANOVA p-Value Treadmill speed Mean MTC SD MTC 4.68 ^ 0.56a 1.46 ^ 0.52a 0.25 ^ 0.05a 4.65 ^ 0.58 1.25 ^ 0.47 0.32 ^ 0.09c 3.27 ^ 0.67b 2.02 ^ 0.51b 0.47 ^ 0.16b 0.000 4.18E – 04 1.95E – 04 Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 Notes: ANOVA: p-value analysis among three groups. a Significantly different between HY and FR at p , 0:05. b Significantly different between HE and FR at p , 0:05. c Significantly different between HY and HE for that variable at p , 0:05. 2.2 Sample entropy Approximate entropy (ApEn) analysis is a nonlinear technique for quantifying the regularity of time series data. Signal with small ApEn value represents more regularity than signal with large ApEn value (Pincus and Goldberger 1994). ApEn provides an efficient and significant way to analyse the nonlinear behaviour of a system with finite number of data points. ApEn measures the negative average logarithmic conditional probability of a pattern to remain close on the next incremental comparison (Pincus 1991). ApEn of a time series is calculated using Equation 1: ApEn ðN; m; rÞ ¼ 2ln PN2m mþ1 ðrÞ i¼1 ln C i ; P N2mþ1 21 ln C m ðN 2 m þ 1Þ i ðrÞ i¼1 ð1Þ ðN 2 mÞ21 where N represents the number of data element in the time series signal, m represents the pattern length or run length and r is the tolerance or filter level which is normally taken as some percentage of standard deviation (SD) of the time series data. In Equation (1), C m calculates the total number of likelihood of all patterns of length m with tolerance r in the data-set. Although ApEn is easily applied to clinical cardiovascular and other time series, it leads to inconsistent result over a range of m and r values (Richman and Moorman 2000). Sample entropy (SampEn) is a related complexity measure, which avoids the self-matches and provides consistent result compared to ApEn. SampEn (m, r, N) is exactly equal to the negative logarithm of conditional probability of the two sequences that are similar for m data points with tolerance r will remain similar for m þ 1 over the set of N data points. The specific choices of m and r values depend on the length of data and the noise present in the data as described by Pincus and Goldberger (1994). Generally, m is as large as possible and r is as small as possible. For smaller r values, one usually achieves poor conditional probability estimates, whereas too much detailed system information is lost for larger r values (Pincus and Huang 1992). Based on the theoretical analysis of deterministic and stochastic processes (Pincus 1991; Pincus and Keefe 1992) and clinical applications (Kaplan et al. 1991; Pincus et al. 1991), m ¼ 2 – 3 and r ¼ 0:1 £ SD 2 0:25 £ SD were recommended for N ¼ 1000 to produce statistically valid ApEn. Since the bias is not present in the calculation of SampEn, it overcomes the problems of ApEn analysis. Therefore, SampEn, being less sensitive to the parameters (m and r), provides more reliable measurement than ApEn and gives consistent output for different combinations of parameters (Richman and Moorman 2000). For example, if the SampEn of a time series signal X is higher than time series Y for any m and r, then it remains higher for all values of m and r. As a result, the choice of m and r is not restricted in calculating SampEn. In this study, we have varied m from 2 to 4 and r from 0:1 £ SD to 0:9 £ SD for calculating SampEn values of MTC series. The algorithm for calculating SampEn from a time series signal is described in Appendix 6. 2.3 Surrogate analysis To prove any intrinsic relationship of the locomotor control system with SampEn, we followed a method of surrogate data analysis introduced by Theiler et al. (1992). This analysis preserves the rank distribution of the data but changes the temporal relationship among the data points. Since the SampEn measurement represents the temporal relationship among the data point, we changed the temporal relationship by shuffling data points and then measuring the changed SampEn. For each MTC series of all subjects, 10 surrogate MTC series were obtained by randomly shuffling the original series. Each of these surrogate data-sets comprised the same MTC distribution (i.e. same mean, SD and higher moments) as that of original data-sets and differed only in the sequential ordering of MTC series. After each surrogation, we calculated the SampEn, and the surrogated SampEn was taken as the average of those 10 SampEn values. It was assumed that destroying nonlinear structure by surrogation of the original data series would result in a statistically significant difference between the calculated nonlinear index of the original series and the randomly selected surrogate data series (Theiler et al. 4 C. Karmakar et al. 1992). In this study, we performed the surrogate test to determine the presence of nonlinear deterministic mechanisms in the MTC signals and verified whether the significant relationship of SampEn with SD of MTC holds. Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 2.4 Receiver-operating curve analysis and statistics To provide the relative importance of features, receiveroperating curve (ROC) analysis was used (Hanley and McNeil 1982), with the areas under the curves for each feature represented by the ROC area. An ROC area of 0.5 means that the distributions of the features are similar in two groups with no discriminatory power. Conversely, an ROC area of 1.0 would mean that the distributions of the features of the two groups do not overlap at all. This was done by automatic selection of different thresholds or cutoff points and calculating the sensitivity/specificity pair for each of them using a computer program developed in MATLAB. Sensitivity is the true positive rate (value higher than the cut-off point), whereas specificity is the true negative rate (value lower than the cut-off point). The optimum threshold was selected as the cut-off point at which the highest accuracy (minimal false-negative and false-positive results) was obtained. ROC plots are used to gauge the predictive ability of a classifier over a wide range of threshold values. ROC curves were plotted using results to examine qualitatively the effect of threshold variation on the classification performance. The area under ROC curve was approximated numerically using the trapezoidal rules (Hanley and McNeil 1982) where the larger the ROC area the better the discriminatory performance. In this study, ROC analysis is used to define the discriminatory ability of SampEn between (1) HY and FR; (2) HY and HE; (3) HE and FR for varying parameter (m and r) values. MATLAB statistics toolbox was used to perform a multivariate repeated measures ANOVA (within three groups HY, HE and FR) to test the influence of ageing and FR on treadmill walking speed, mean MTC and SD of MTC and reported significant results if p , 0:05. Multivariate ANOVA was also performed on SampEn values within those groups and reported significant results if p , 0:01. To test the differences between group means of SampEn values when ANOVA was significant, we used Bonferroni post hoc tests and reported significant results if p , 0:01. 3. Results The descriptive statistics of MTC signals for all subject groups are presented in Table 1. There was a considerable variation of MTC statistics across HY, HE and FR groups. The walking speed of HY and HE groups were not significantly different (p $ 0:05); however, the FR group walked significantly slower than both the HY and HE groups (p , 0:05). MTC central tendency statistics measured using mean was found to decrease in the HE group but increase in the FR group when compared to the HY group. SD of MTC increased significantly with ageing (HE group) and pathology (FR group). The change of SampEn values of MTC signal with m ¼ 2– 5 and r ¼ 0.1 £ SD – 0.9 £ SD for HY, HE and FR groups is demonstrated in Figure 1. For all values of m and r, the mean SampEn values of FR group were found to be lower than both HY and HE groups. Moreover, the mean SampEn values of HY group were found to be higher than HE group, i.e. for any m and r, based on the mean SampEn values, the three groups can be sorted as HY . HE . FR. Mean SampEn values of all three groups were not presented for m ¼ 4 –5 and r ¼ 0.1 £ SD as no match was found in the MTC signal of all subjects for such a small tolerance with large pattern length. The mean and standard deviation of SampEn (STD) values of three groups for m ¼ 2–5 and r ¼ 0.1 £ SD– 0.9 £ SD are summarised in Table 2. For m ¼ 2, SampEn values among three groups were significantly (p , 0:01) different only for r ¼ 0.1 £ SD, 0.2 £ SD and 0.7 £ SD, whereas no significant difference was found among SampEn values of three groups for m ¼ 3. On the other hand, SampEn values for m ¼ 4 and 5 were found to be significantly (p , 0:01) different for all r except 0.2 £ SD. From the post hoc test, the SampEn values were significantly (p , 0:01) different between the HY and FR groups for m ¼ 2, 4, 5 and r ¼ (0.1–0.9) £ SD, (0.3–0.9) £ SD, (0.3–0.9) £ SD, respectively. Between HE and FR groups, significant differences in SampEn were found for m ¼ 4–5 and r ¼ (0.3–0.7) £ SD. However, no significant difference was found between HY and HE for all values of m and r. ROC areas were calculated to quantify the discriminating power of SampEn between (1) HY and FR (HY/FR); (2) HY and HE (HY/HE); (3) HE and FR (HE/FR; Table 2). The maximum ROC area ( ¼ 0.98) between HY and FR groups was found for m ¼ 4, r ¼ 0.3 £ SD and m ¼ 5, r ¼ 0.5 £ SD. The maximum ROC area ( ¼ 0.88) between HE and FR was found for m ¼ 4, r ¼ 0.3 £ SD. The ROC area between HYand HE was found to be low for all m and r. The maximum ROC area ( ¼ 0.64) between HY and HE groups was found for m ¼ 5, r ¼ 0.2 £ SD. The relationship between SampEn (m ¼ 4, r ¼ 0.3 £ SD) and the standard deviation of MTC (SD MTC) for HY, HE and FR groups is shown in Figure 2. The SD MTC had a significant relationship with SampEn for HY (R ¼ 2 0.60; p ¼ 0.0004) and HE (R ¼ 2 0.61; p ¼ 0.0007) groups. However, these relationships were not significant for surrogated SampEn with the same m and r values (p ¼ 0:89 for HYand p ¼ 0:02 for HE – Figure 3). For the FR group the relationship of both SampEn and surrogated SampEn values with SD MTC was also not significant (R ¼ 2 0.13, p ¼ 0.7160 and R ¼ 0.30, p ¼ 0.39, respectively – Figures 2 and 3). 5 Computer Methods in Biomechanics and Biomedical Engineering 3 3 HE (n =27) HY (n =30) FR (n =10) 2.5 2 SampEn SampEn 2 1.5 1 0.5 m=2 0 1 2 3 4 5 k 6 7 8 0 9 10 3 HE (n =27) HY (n =30) FR (n =10) 0 1 2 3 4 5 k 6 7 8 9 10 HE (n =27) HY (n =30) FR (n =10) 2.5 2 SampEn 2 SampEn Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 m=3 3 2.5 1.5 1 1.5 1 0.5 0 1.5 1 0.5 0 HE (n =27) HY (n =30) FR (n =10) 2.5 0.5 m=4 0 1 2 3 4 5 6 7 8 9 10 k 0 m=5 0 1 2 3 4 5 6 7 8 9 10 k Figure 1. Error bar plot of SampEn for m ¼ 2 2 5 with r ¼ ðk=10Þ £ SD for HY, HE and FR group. k is scale for SD ranges 0 – 9. SD, standard deviation of MTC series. 4. Discussion In common with many time-dependent physiological parameters employed in medical diagnostics, human gait is a complex, chaotic activity, exhibiting the classical features of nonlinear dynamical systems. One of the fundamental limitations to traditional gait biomechanics is the lack of nonlinearity considerations. Furthermore, traditional Newtonian mechanics-based approaches, with linear or angular kinematics and elementary force– time measures the usual dependent variables, are unable to embrace these concepts in their experimental designs and analysis. Quantifying the dynamics of gait variables’ time series has been of considerable interest because it can be used in developing dynamical control system models for application to gait diagnostics (Hausdorff et al. 1998, 2001, 2003). Gait variability measures, for example, are more closely related to FR than the more traditional descriptors of gait speed, stride length and stride time (Maki 1997; Hausdorff et al. 2001). The observation that gait variability measures have been considerably more effective in predicting abnormalities gave substantial motivation to the present study of ageing and pathology effects on gait. The present results demonstrated the presence of nonlinear properties in MTC time series data from steadystate walking, supporting our previous findings (Khandoker, Taylor, et al. 2008). The data presented above indicated that the nonlinear property (SampEn) of MTC regulation did not breakdown with healthy ageing, rather they suggested more automatic and less constrained balance control in healthy (HY or HE group) adults’ gait. The FR group, however, displayed significantly lower SampEn values compared with HY and HE subjects, suggesting a more constrained mode of balance control in FR walking. Using SampEn of centre of pressure data during quiet standing (Borg and Laxåback 2010) examined the relationship between SampEn and sway/balance in elderly participants. They found higher SampEn in the anterior – posterior (A/P) direction (more efficient balance) compared to the mediolateral (M/L) direction. The breakdown of long-range correlations in time series signals of biological systems has been linked to the degeneration of the underlying levels of input (external or internal), which serve as a self-organizing operational network (Hausdorff et al. 1997, 2001; Goldberger et al. 2002). The increased deterministic structure in the FR group might influence the decreased SampEn value as shown in this study. 6 C. Karmakar et al. Table 2. Comparison of mean and SD of SampEn of HY, HE and FR groups with m ¼ 2 2 5 and different tolerance r. SampEn (mean ^ STD) Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 m HY (n ¼ 30) r HE (n ¼ 27) FR (n ¼ 10) a ROC area ANOVA p-Value HY/FR HY/HE HE/FR 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 £ £ £ £ £ £ £ £ £ SD SD SD SD SD SD SD SD SD 2.71 ^ 0.11 2.03 ^ 0.09 1.63 ^ 0.09 1.35 ^ 0.08 1.14 ^ 0.08 0.97 ^ 0.07 0.84 ^ 0.07 0.72 ^ 0.07 0.63 ^ 0.06 2.64 ^ 0.18 1.98 ^ 0.18 1.58 ^ 0.18 1.31 ^ 0.17 1.10 ^ 0.16 0.94 ^ 0.14 0.80 ^ 0.13 0.69 ^ 0.12 0.60 ^ 0.11 2.55 ^ 0.11 1.87 ^ 0.09a 1.48 ^ 0.10a 1.21 ^ 0.09a 1.01 ^ 0.09a 0.85 ^ 0.08a 0.72 ^ 0.08a 0.62 ^ 0.07a 0.53 ^ 0.06a 0.0067* 0.0066* 0.0101 0.0116 0.0106 0.0103 0.0099* 0.0105 0.0102 0.86 0.90 0.90 0.90 0.91 0.90 0.89 0.89 0.89 0.62 0.56 0.53 0.52 0.52 0.52 0.51 0.53 0.53 0.79 0.83 0.82 0.81 0.81 0.81 0.81 0.81 0.80 3 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 £ £ £ £ £ £ £ £ £ SD SD SD SD SD SD SD SD SD 2.65 ^ 0.20 1.98 ^ 0.11 1.60 ^ 0.10 1.32 ^ 0.09 1.11 ^ 0.09 0.94 ^ 0.08 0.81 ^ 0.08 0.69 ^ 0.07 0.60 ^ 0.07 2.58 ^ 0.23 1.94 ^ 0.21 1.56 ^ 0.20 1.28 ^ 0.18 1.07 ^ 0.17 0.91 ^ 0.16 0.77 ^ 0.15 0.67 ^ 0.13 0.58 ^ 0.12 2.54 ^ 0.17 1.84 ^ 0.08 1.46 ^ 0.10 1.19 ^ 0.09 0.99 ^ 0.09 0.83 ^ 0.08 0.70 ^ 0.07 0.60 ^ 0.07 0.52 ^ 0.06 0.2332 0.0467 0.0283 0.0367 0.0285 0.0313 0.0369 0.0482 0.0579 0.66 0.86 0.88 0.87 0.87 0.88 0.86 0.84 0.83 0.58 0.50 0.51 0.51 0.51 0.51 0.51 0.51 0.51 0.60 0.74 0.77 0.79 0.78 0.77 0.77 0.76 0.76 4 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 £ £ £ £ £ £ £ £ SD SD SD SD SD SD SD SD 1.97 ^ 0.21 1.58 ^ 0.11 1.31 ^ 0.10 1.09 ^ 0.09 0.93 ^ 0.09 0.80 ^ 0.08 0.68 ^ 0.08 0.59 ^ 0.07 1.91 ^ 0.24 1.55 ^ 0.22b 1.27 ^ 0.19b 1.07 ^ 0.18b 0.90 ^ 0.17b 0.76 ^ 0.15b 0.66 ^ 0.14 0.56 ^ 0.13 1.74 ^ 0.13 1.31 ^ 0.08a 1.08 ^ 0.08a 0.90 ^ 0.08a 0.75 ^ 0.07a 0.63 ^ 0.07a 0.54 ^ 0.06a 0.47 ^ 0.06a 0.86 0.98 0.97 0.97 0.95 0.94 0.93 0.90 0.51 0.52 0.53 0.53 0.53 0.51 0.51 0.51 0.79 0.88 0.87 0.87 0.86 0.85 0.84 0.83 5 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 £ £ £ £ £ £ £ £ SD SD SD SD SD SD SD SD 2.00 ^ 0.48 1.56 ^ 0.14 1.29 ^ 0.09 1.09 ^ 0.09 0.93 ^ 0.09 0.79 ^ 0.08 0.68 ^ 0.08 0.58 ^ 0.07 1.88 ^ 0.60 1.49 ^ 0.29b 1.22 ^ 0.19b 1.04 ^ 0.18b 0.89 ^ 0.17b 0.75 ^ 0.16b 0.65 ^ 0.14 0.56 ^ 0.13 1.77 ^ 0.21 1.26 ^ 0.13a 1.05 ^ 0.07a 0.87 ^ 0.07a 0.73 ^ 0.07a 0.62 ^ 0.07a 0.54 ^ 0.06a 0.46 ^ 0.06a 0.0162 8.35E – 05* 2.60E – 04* 5.96E – 04* 0.0010* 0.0015* 0.0032* 0.0054* 0.4070 9.47E – 04* 1.10E – 04* 1.44E – 04* 5.05E – 04* 0.0014* 0.0041* 0.0066* 0.62 0.94 0.97 0.98 0.97 0.94 0.93 0.91 0.64 0.62 0.58 0.54 0.50 0.50 0.50 0.51 0.55 0.81 0.85 0.87 0.87 0.86 0.83 0.81 Notes: SampEn, sample entropy; mean, average sample entropy; STD, standard deviation of sample entropy; SD, standard deviation of MTC data points. p-Value shows the difference between mean values of three groups using ANOVA analysis. ROC are calculated for HY/FR, HY/HE and HE/FR. *Mean values of three groups are significantly different. a Significantly different between HY and FR at p , 0:01. b Significantly different between HE and FR at p , 0:01. Use of nonlinear variability indices (ApEn and Poincaré plot indices) were previously reported by our group to distinguish walking patterns of elderly subjects with a history of balance impairments and falls from those of healthy peers (Khandoker, Palaniswami, et al. 2008). In that study, it has been shown that HE has lower ApEn values (greater regularity or reduced randomness and system complexity) than FR elderly for m ¼ 2 and r ¼ 0.15 £ SD. For better understanding the complexity measure of the MTC signal, we extended the data-set and calculated ApEn for m ¼ 3 and over the range of tolerance r ¼ (0 –0.9) £ SD (Karmakar et al. 2007). In that study, we found that for m ¼ 3 and r ¼ (0 – 0.26) £ SD the relationships among three groups based on mean ApEn value were FR . HE . HY, whereas reciprocal relationship FR , HE , HY was found for r ¼ (0.26 – 0.9) £ SD (Figure 4). This inconsistency in ApEn might be due to the impact of bias in ApEn calculation (Richman and Moorman 2000). To avoid the bias effect of ApEn, SampEn (Richman and Moorman 2000) is developed based on the approach of Grassberger and co-workers (Grassberger and Procaccia 1983; Grassberger 1988; Grassberger et al. 1991). SampEn is derived from the ApEn which removes the bias that influences ApEn calculations. A principal advantage in the application of ApEn to biological signals is that ApEn statistics may be calculated for relatively short data series which make it desirable for routine diagnosis of gait impairments. 7 Computer Methods in Biomechanics and Biomedical Engineering 1.9 1.8 1.7 1.6 Healthy Young y =–1.23x +1.88 R =–0.60, p =0.0004 1.5 SampEn HY HE FR Healthy Elderly y =–1.42x+1.99 R =–0.61, p =0.0007 1.4 1.3 1.1 1 0.9 0.1 Falls Risk y =–0.07x +1.22 R =– 0.13, p =0.7160 0.2 0.3 0.4 0.5 0.6 0.7 0.8 SD MTC Figure 2. Relationship of SampEn (m ¼ 4; r ¼ 0:3 £ SD) with SD of MTC series for HY, HE and FR subjects. R is correlation coefficient. 1.9 1.8 1.7 1.6 1.5 SampEn Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 1.2 1.4 Healthy Young y =0.03x+1.73 R =0.02, p =0.89 Falls Risk y =0.11x+1.69 R =0.30, p =0.39 1.3 Healthy Elderly y =– 0.42x +1.85 R =0.44, p =0.02 1.2 HY HE FR 1.1 1 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 SD MTC Figure 3. Relationship of SampEn (m ¼ 4; r ¼ 0:3 £ SD) with SD of surrogated MTC series for HY, HE and FR subjects. R is correlation coefficient. 8 C. Karmakar et al. 1.4 1.2 1 ApEn 0.8 0.6 0.4 HE (n =27) 0.2 HY (n =30) FR (n =10) 0 0 1 2 3 4 5 6 7 8 9 10 Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 k Figure 4. Error bar plot of ApEn for m ¼ 3 with r ¼ ðk=10Þ £ SD for HY, HE and FR group. k is scale for SD ranges 0 – 9. SD, standard deviation of MTC series. Referring to both theoretical analysis and clinical applications, Pincus and Goldberger (1994) concluded that m ¼ 2 – 3 and r ¼ (0.1 – 0. 25) £ SD values, and an N of 10m , or preferably 30m, will yield statistically reliable and reproducible results. SampEn inherits all those properties and more consistent over the range of values for both m and r, as shown in Figure 1. Hence, we conclude that for complexity analysis of MTC signals it is preferable to use SampEn rather than ApEn. From ROC area analysis (Table 2), it is evident that healthy gait and FR gait can be distinguished using SampEn as the maximum ROC area between HY/FR (0.98) and HE/FR (0.88) for m ¼ 4 and r ¼ 0.3 £ SD. In contrast, SampEn appears to be less suitable for determining ageing effects because no significant difference was found in the obtained values of SampEn for all ranges of m and r. The use of surrogate data was designed to destroy the underlying control mechanism (time series structure in stride-to-stride MTC) and increase randomness. Significant correlation of SD with SampEn (Figure 2) for HY and HE groups confirmed a locomotor control mechanism common to both healthy groups. In addition, these correlations became insignificant after surrogation of MTC signal, which indicates that MTC control in young and elderly walkers is not random from stride to stride and the MTC output in ageing is modulated by a mechanism that remains to be explored. On the other hand, for FR subjects, the correlation was found to be insignificant, which may indicate absence of locomotor control. The MTC nonlinear dynamics observed in this study do not support the hypothesis that healthy ageing is associated with the changes in neuroautonomic control that lead to loss of all aspects of physiological dynamics (Hausdorff et al. 1997; Goldberger et al. 2002; Costa et al. 2003). This conforms to the observation that the nonlinear indices – wavelet-based multiscale exponent (b), detrended fluctuation analysis exponent (a) and Poincaré plot index of MTC variability (SD1/SD2) – also do not show significant changes due to ageing, which was reported in our previous study (Khandoker, Palaniswami, et al. 2008). Moreover, the hypothesis of a breakdown of nonlinear cardiac dynamics with healthy ageing has also been challenged by Schmitt and Ivanov (2007), who reported that fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age. There is, however, also evidence that the loss of complexity or entropy is not a universal principle underlying change with age and disease (Vaillancourt and Newell 2002). Although we found that nonlinear properties (complexity or randomness) of MTC gait dynamics remained unchanged with healthy ageing, significant increase in MTC variability as measured by SD in HE subjects is in agreement with previous findings (Begg et al. 2007; Khandoker, Taylor, et al. 2008; Table 1). We also identified a further increase in MTC variability (e.g. SD of MTC; Table 1) of FR elderly subjects. Thus, healthy ageing appears to be accompanied only by an increase in MTC variability as measured by SD, whereas the nonlinear properties remain generally unchanged. This important dissociation between MTC variability and nonlinear organisation of MTC fluctuations may be specific to ageing and suggests that locomotor control with advanced age is conceptually different from pathological conditions (e.g. balance impairments). More specifically, the augmented MTC variability with advanced age may suggest a reduced responsiveness to external and internal stimuli, and thus, a reduced strength of feedback interactions. This may not be the case with pathological conditions such as balance impairments. 5. Conclusion This study showed that the nonlinear characteristics are present in MTC gait variables during unconstrained walking on a treadmill at PWS. The results highlight the useful application of SampEn to quantify nonlinearity in MTC series for discriminating the walking of adult populations (young and elderly; fallers and nonfallers). The advantages of SampEn over ApEn for measuring complexity of short-length biological time series signals are also emphasised here. These results will advance our understanding of the complex dynamics of human locomotor control and contribute to falls prevention by developing diagnostic markers to identify elderly individuals at risk of falling. Walking speed may influence MTC fluctuation patterns, and this manipulation should also be examined in future work to quantify dynamical properties of human Computer Methods in Biomechanics and Biomedical Engineering gait control under changing speed conditions. Further experiments should also be carried out to show whether falls prevention interventions such as exercise programs can improve the gait function of FR elderly by monitoring change in SampEn values. The significance of deriving potential markers for normal, age-affected and pathology-related gaits is considerable with many applications to exercise, rehabilitation and sport science (running analysis, cyclical sports activities such as cycling). Acknowledgements Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 MFC gait data for this study were taken from VU Biomechanics database. Several people have contributed to the creation of the gait database, especially Simon Taylor of the VU Biomechanics Unit. References Arking R. 2006. Biology of aging: observations and principles. New York: Oxford University Press. Begg RK, Best RJ, Dell’Oro L. 2007. Minimum foot clearance during walking: strategies for the minimization of triprelated falls. Gait Posture. 25(2):191 –198. Begg RK, Palaniswami M, Owen B. 2005. Support vector machines for automated gait classification. IEEE Trans Biomed Eng. 52(5):828– 838. Borg FG, Laxåback G. 2010. Entropy of balance – some recent results. J NeuroEng Rehab. 7:38. Brach JS, Studenski S, Perera S, Vanswearingen JM, Newman AB. 2008. Stance time and step width variability have unique contributing impairments in older persons. Gait Posture. 27(3):431– 439. Close J, Glucksman E. 2000. Falls in the elderly: what can be done? Med J Aust. 173:176 – 177. Costa M, Peng CK, Goldberger AL, Hausdroff JM. 2003. Multiscale entropy analysis of human gait dynamics. Physica A. 330(1):53– 60. Cripps R, Carman J. 2001. Falls by the elderly in Australia trends and data for 1998. Canberra: Australian Institute of Health and Welfare. Dingwell JB, Marin LC. 2006. Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. J Biomech. 39:444– 452. England SA, Granata KP. 2007. The influence of gait speed on local dynamic stability of walking. Gait Posture. 25:172 – 178. Gabell A, Nayak USI. 1984. The effect of age and variability in gait. J Gerontol. 39:662– 666. Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PC, Peng CK, Stanley HE. 2002. Fractal dynamics in physiology: alterations with disease and aging. Proc Nat Acad Sci. 19(1):2466– 2472. Grassberger P. 1988. Finite sample corrections to entropy and dimension estimates. Phys Lett A. 128(6 – 7):369– 373. Grassberger P, Procaccia I. 1983. Estimation of the Kolmogrov entropy from a chaotic signal. Phys Rev A. 28:2591 – 2593. Grassberger P, Schreiber T, Schaffrath C. 1991. Nonlinear time sequence analysis. Int J Bifur Chaos. 1(3):521 – 547. 9 Hanley JA, McNeil BJ. 1982. The meaning and use of the area under receiver operating characteristic (ROC) curve. Radiology. 143:29– 36. Hausdorff JM. 2005. Gait variability: methods, modeling and meaning. J NeuroEng Rehab. 2:19. Hausdorff JM, Cudkowicz ME, Firtion R, Wei JY, Goldberger AL. 1998. Gait variability and basal ganglia disorders: stride-to-stride variations of gait cycle timing in Parkinson’s disease and Huntington’s disease. Mov Disord. 13: 428– 437. Hausdorff JM, Edelberg HK, Mitchell SL, Goldberger AL, Wei JY. 1997. Increased gait unsteadiness in communitydwelling elderly fallers. Arch Phys Med Rehab. 78:278 – 283. Hausdorff JM, Peng CK, Ladin Z, Wei JY, Goldberger AL. 1995. Is walking a random walk? Evidence for long-range correlations in the stride interval of human gait. J Appl Physiol. 78:349 – 358. Hausdorff JM, Purdon PL, Peng CK, Ladin Z, Goldberger AL. 1996. Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. J Appl Physiol. 80:1448 – 1457. Hausdorff JM, Rios DA, Edelberg HK. 2001. Gait variability and fall risk in community-living older adults: a 1-year prospective study. Arch Phys Med Rehab. 82:1050 – 1056. Hausdorff JM, Schaafsma JD, Balash Y, Bartels AL, Gurevich T, Giladi N. 2003. Impaired regulation of stride variability in Parkinson’s disease subjects with freezing of gait. Exp Brain Res. 149:187 – 194. Herman T, Giladi N, Gurevich T, Hausdorff JM. 2005. Gait instability and fractal dynamics of older adults with a ‘cautious’ gait: why do certain older adults walk fearcully? Gait Posture. 21:178 – 185. Jordan K, Challis JH, Newell KM. 2007. Walking speed influences on gait cylcle variability. Gait Posture. 26:128 – 134. Kaplan DT, Furman MI, Pincus SM, Ryan SM, Lipsitz LA, Goldberger AL. 1991. Aging and the complexity of cardiovascular dynamics. Biophys J. 59:945 – 949. Karmakar CK, Khandoker AH, Begg RK, Palaniswami M, Taylor S. 2007. Understanding ageing effects by approximate entropy analysis of gait variability. IEEE Engineering in Medicine and Biology Conference IEEE Press Lyon, France. p. 1965– 1968. Khandoker AH, Palaniswami M, Begg RK. 2008. A comparative study on approximate entropy measure and poincaré plot indexes of minimum foot clearance variability in the elderly during walking. J NeuroEng Rehab. 5:4. Khandoker AH, Taylor SB, Karmakar CK, Begg RK, Palaniswami M. 2008. Investigating scale invariant dynamics in minimum toe clearance variability of the young and elderly during treadmill walking. IEEE Transact Neural Syst Rehab Eng. 16(4):380– 389. Maki BE. 1997. Gait changes in older adults: predictors of falls or indicators of fear. J Am Geriatr Soc. 45(3):278– 283. Nutt JG, Marsden CD, Thompson PD. 1993. Human walking and higher-level gait disorders, particularly in the elderly. Neurology. 43:268 –279. Pincus SM. 1991. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci. 88:2297 – 2301. Pincus SM, Goldberger AL. 1994. Physiological time-series analysis: what does regularity quantify. Am J Physiol. 266:1643 – 1656. 10 C. Karmakar et al. 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Testing for nonlinearity in time series: the method of surrogate data. Physica. 58:77– 94. Vaillancourt D, Newell K. 2002. Changing complexity in human behaviour and physiology through aging and disease. Neurobiol Aging. 23:1 – 11. 11 Computer Methods in Biomechanics and Biomedical Engineering Step 6: Similarly for the window with length m þ 1 define Appendix A. SampEn algorithm The steps for calculating SampEn are (Richman and Moorman 2000): Step 1: Form a time series uð1Þ; uð2Þ; . . . ; uðNÞ. These are N raw data values sampled from desired measurements. Step 2: Fix m and r, an integer and real number, respectively. The value of m represents the length of the comparing window and r specifies the filtering level. Step 3: Form a sequence of vectors xð1Þ; xð2Þ; . . . ; xðN 2 m þ 1Þ in R m , real m-dimensional space defined by xðiÞ ¼ ½uðiÞ; . . . ; uði þ m 2 1Þ
. 21 Step 4: Calculate Bm times the number i ðrÞ as ðN 2 m 2 1Þ of vectors xðjÞ within r of xðiÞ where 1 # j # N 2 m and j – i. Step 5: Now define, average number of matches for window of length m: B m ðrÞ ¼ ½N 2 m
21 N 2m X Downloaded by [Ahsan Khandoker] at 20:09 30 January 2012 i¼1 Bm i ðrÞ: A m ðrÞ ¼ ½N 2 m
21 N 2m X Am i ðrÞ; i¼1 m where Am i ðrÞ is defined in similar way of Bi ðrÞ for the window length of m þ 1. Step 7: Then the SampEn is defined as  m  A ðrÞ ; Samp EnðN; m; rÞ ¼ 2ln m B ðrÞ where ln represents the natural logarithm. For a fixed m and r, the total number of matches of length m and m þ 1 can be defined as B ¼ ½ðN 2 m 2 1ÞðN 2 mÞ=2
B m ðrÞ
and A ¼ ½ðN 2 m 2 1Þ ðN 2 mÞ=2
A m ðrÞ
. Hence the SampEn can be expressed as (Figures 1 – 4 and Tables 1 and 2) SampEnðN; m; rÞ ¼ 2ln ðA=BÞ: