Medical Engineering and Physics 37 (2015) 1152–1155
Contents lists available at ScienceDirect
Medical Engineering and Physics journal homepage: www.elsevier.com/locate/medengphy
Towards the assessment of local dynamic stability of level-grounded walking in an older population Dennis Hamacher a,∗, Daniel Hamacher a, Navrag B. Singh b, William R. Taylor b, Lutz Schega a a b
Department of Sport Science, Otto von Guericke University Magdeburg, Zschokkestr. 32, 39104 Magdeburg, Germany Institute for Biomechanics, ETH Zürich, Vladimir-Prelog-Weg 3-4, 8093 Zurich, Switzerland
a r t i c l e
i n f o
Article history: Received 5 December 2014 Revised 3 September 2015 Accepted 19 September 2015
Keywords: Local dynamic stability Gait Inertial sensor
a b s t r a c t Local dynamic stability is a critical aspect of stable gait but its assessment for use in clinical settings has not yet been sufficiently evaluated, particularly with respect to inertial sensors applied on the feet and/or trunk. Furthermore, key questions remain as to which state-space reconstruction is most reliable and valid. In this study, we evaluated the reliability as well as the ability of different sensor placement and state-spaces to distinguish between local dynamic stability in young and older adults. Gait data of 19 older and 20 young subjects were captured with inertial sensors twice within the first day as well as after seven days. 21 different signals (and combinations of signals) were used to span the system’s state-space to calculate different measures of local dynamic stability. Our data revealed moderate or high effect sizes in 12 of the 21 old vs. young comparisons. We also observed considerable differences in the reliability of these 12 results, with intra-class correlation coefficients ranging from 0.09 to 0.81. Our results demonstrate that in order to obtain reliable and valid estimates of gait stability λ of walking time series is best evaluated using trunk data or 1-dimensional data from foot sensors. © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
Introduction Measures of local dynamic stability (LDS) during walking are able to provide an understanding of an individual’s gait stability [1–3]. Such measures are capable of distinguishing between older and younger cohorts [4] with lower levels of LDS associated with a higher risk of falling [2,4]. However, measures of LDS, which can be quantified using the largest Lyapunov Exponents (λ [5]), have mostly been evaluated in young subjects walking on a treadmill [6,7] due to the requirement of collecting multiple strides for its assessment [8]. However, treadmill walking does not represent a physiological activity of daily living and is known to add external constraints, such as acting as a temporal pacemaker, and modifying LDS [9]. The type of walking (i.e. treadmill or overground) should therefore be considered in the protocol design. To ensure clinical relevance, a renewed validation of λ that addresses reliability and validity should be conducted in older people as demanded (but not yet undertaken) in the literature [10,11]. The calculation of λ is based on state-space representations [1], where the representation of a valid state-space could be any vector space containing a sufficient number of independent ∗
Corresponding author. Tel.: +49 391 6754936; fax: +49 391 6716754. E-mail addresses: [email protected], [email protected] (D. Hamacher), [email protected] (D. Hamacher), [email protected] (N.B. Singh), [email protected] (W.R. Taylor), [email protected] (L. Schega). http://dx.doi.org/10.1016/j.medengphy.2015.09.007 1350-4533/© 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
coordinates defining the state of the system at any instant in time [12]. For example, to calculate λ from a walking time series, statespaces could be built from anterior–posterior, medial–lateral, and superior–inferior accelerometer signals taken from the hip, knee and ankle joints [1,13], or from trunk position movements in all three directions [14]. Adequate state-spaces could be reconstructed from a single time series using the original dataset and its time delayed copies [15] or e.g. from time series of all angles and angular velocities at that joint [16]. In this case, λ is quantified as exponential rates of divergence of initially neighbouring trajectories in the state-space as they evolve in real time. Inertial sensors offer feasible options for flexible, mobile, and inexpensive usage in clinical settings. However, a recent test-retest reliability study of young subjects showed that robust inter-day assessment of gait stability is difficult using data from such accelerometer sensors [11]. In their study, gait data captured during outdoor walking was analysed, which had the benefit of allowing accurate capture of magnetometer data for assessing orientation. However, assessment within the constraints of indoor walking where magnetometer data is not necessarily accurate or reliable (which is comparable to clinical settings), might be more appropriate for the analysis of patients suffering from musculoskeletal deficits [17,18]. In order to establish the assessment of λ for overground walking using inertial sensors for clinical use, this study aimed to evaluate multiple state-space definitions (using different signal types) in both
D. Hamacher et al. / Medical Engineering and Physics 37 (2015) 1152–1155
young and elderly adults. Here, the following state-space reconstructions for evaluating λ were considered in terms of both reliability as well as validity [11,16,19]: (1) differences in the signal dimension (1D vs. 3D) might affect inter-day reliability as different sensor positions affect sensor orientation relative to the segment, (2) signal characteristics are different regarding linear acceleration and angular velocity, and it might be possible to improve reliability through combining these variables for estimation of λ [11], even when the signals stem from the same system, and (3) the reliability and validity of different measures of λ might be sensitive to different segment trajectories (e.g. trunk, foot), but test-retest data are only currently available derived from trunk movements [7,10,11]. The following two research questions were addressed: 1) What is the inter-session and inter-day test-retest reliability of LDS in an older cohort a function of differently reconstructed state-spaces? 2) Are measures of LDS able to distinguish between young and older adults as a function of differently reconstructed state-spaces? Methods Subjects Gait data of 19 healthy older (5 male, 14 female, age: 71 ± 4 years) and 20 healthy young subjects (8 Male, 12 female, age: 26 ± 4 years) were captured twice within the first day and also once after seven days. All participants provided their written informed consent after they were briefed about the research protocol, which complied with the principles of the Declaration of Helsinki and was approved by the board of the ethical committee of Otto von Guericke University, Magdeburg. Testing procedure A wireless inertial motion tracker (MTw, Xsens Technologies B.V., Enschede, The Netherlands; range of measurement of angular velocity: ± 1200 deg/s, range of measurement of acceleration: ± 160 m/s2 ) was fixed onto each of the subjects’ forefeet and trunk. Among other things, these sensors measure angular velocities and linear accelerations with a sampling rate of 75 Hz. Kinematic data were captured while the subjects twice walked a distance of 130 m (including one turn) in a straight line on a level hallway at their preferred walking speed. This procedure was repeated 1) after 5 min of rest without removing the sensors and 2), after 7 days at the same time of day.
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The time delay (used for the time delayed copies) corresponded with the first minimum mutual information for each participant [21], and the number of time delayed copies was calculated using the global false nearest neighbours method [22] where the appropriate number of copies was defined as the number where a manifest plateau began to appear. Both the embedded dimensions and mutual information were calculated for each subject, and the resulting median of all subjects was applied to calculate λ for the whole group for a particular signal combination. In order to ensure comparability of data from older and younger subjects, the same embedded dimensions and mutual information for each signal (signal combination) of the older subjects was also used for the younger subjects. The second step was to calculate λ by estimating the exponential rates of divergence of initially nearest neighbours as they evolved in real time, which provided a direct measure of the system’s sensitivity to extremely small perturbations. Here, we used Rosenstein and co-workers’ algorithm for the calculation of λ [5], which was implemented in MATLAB (version 2013a, The MathWorks BV, Natrick, USA). Approaches to calculate LDS using multiple repetitions of short walking distances have been published previously [23,24]. In the current study, we merged the data of 100 strides of two repetitions of 130 m which included one single turn (turn data removed). The time series were normalized to 10000 samples [18]. The distance of each point in state-space and the correlating nearest neighbour (Euclidean distance) were tracked for data of the same walk. After taking the logarithm of the mean divergence curve, LDS was computed as the slope of the linear fit through 0–0.5 strides for each signal (or combination) and for each subject. LDS was then interpreted such that positive exponents indicated local instability, while larger positive exponents indicated greater sensitivity to perturbations that occurred while walking [5,19]. Statistics For estimating the inter-session test-retest reliability, we used both trials of the first day. The inter-day test-retest reliability was calculated using data from the first trial of the first day and the trial captured on the second day. Intra-class correlation coefficients (ICC, 2.1; [25]) were calculated (using the IBM SPSS Statistics 20 software suite) where values between 0.0–0.40 were considered poor, from 0.40– 0.59 fair, from 0.60–0.74 good, and from 0.75–1.00 excellent [26]. Furthermore, the Bias and Limits of Agreement [27] were assessed to quantify the agreement between test and retest. Hedges’ g was calculated to estimate the effect size comparing old vs. young. We use the conventional values as benchmarks considering 0.2, 0.5 and 0.8 to be ‘small’, ‘medium’, and ‘large’ effects, respectively [28]. The precision on the effect sizes and Intra-class correlation coefficients were estimated with 95% confidence intervals.
Data analysis Results Heel strikes from 100 strides per subject were estimated as described in Hamacher et al. [20] after removing data captured in 2.5 m prior to and after turning. The first step in the calculation of λ was to reconstruct appropriate state-spaces with the aid of time-fixed delayed copies and/or with different signals representing the same movement. In order to explore the influence of different signals (and combinations of signals) used to span the system’s state-space on the reliability and validity of λ, we reconstructed 21 state-spaces which were different with respect to 1) data included from the different sensor axes, with the sensor fixed to the body parts in a way to coincide with the anatomical planes in normal standing (anterior–posterior, medial-lateral, and superior-inferior), 2) the trajectories of different segments (trunk vs. foot), and 3) the nature of the data (linear acceleration vs. angular velocity). Subsequently, we created time delayed copies to build an adequate high-dimensional state-space for LDS calculation.
Our data revealed effect sizes of 0.51 (medium effect) or higher (up to 1.33, large effect) in 12 of the 21 old vs. young state-space comparisons (Table 1). As a result, only λs calculated with these 12 different state-spaces are reported. Substantial differences were observed regarding the test-retest reliability, with ICC-values ranging from 0.09 to 0.81 (Table 1). Old vs. young comparison Anterior–posterior vs. medial–lateral vs. and superior–inferior λ calculated using linear acceleration signals or angular velocity signals in the superior-inferior direction did not reach medium or high effect sizes. Furthermore, we did not find any systematic differences with respect to λ calculated from data stemming from signals regarding anterior–posterior vs. medial–lateral direction.
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D. Hamacher et al. / Medical Engineering and Physics 37 (2015) 1152–1155
Table 1 Maximum Finite Lyapunov Exponents and the associated effect sizes (Hedges’ g (old vs. young comparison)), ICCs (test-retest comparison) of LDS for different combinations of signals to span the state-space. Only 12 state-spaces are considered whose corresponding Maximum Finite Lyapunov Exponents yielded Hedges’ g value of at least 0.5. The following acronyms are used: Acceleration = ACC, angle velocity = Ѳ, local coordination system = LCS, anterior–posterior = a–p, medio–lateral = m–l. Values presented in bold font indicate excellent reliability (ICC) or large effects (g), time delay = td, and number of time delayed copies = nTDC.
λ Old Segment
Signal
Foot
ACC
Trunk Foot Trunk Foot Foot + Trunk Trunk Foot + Trunk
Gyr ACC ACC Gyr ACC ACC + Gyr ACC Gyr ACC + Gyr ACC + Gyr
a–p m–l a–p m–l
λ Young
Old vs. Young
Test-Retest Reliability
mean
SD
mean
SD
Hedges’ g
ICC Inter-session
ICC Inter-day
0.532 0.636 0.821 1.079 0.794 1.458 1.145 0.789 0.946 1.483 1.104 1.193
0.039 0.059 0.08 0.136 0.05 0.101 0.162 0.049 0.074 0.104 0.156 0.093
0.5 0.573 0.762 1.005 0.741 1.319 1.064 0.715 0.855 1.358 1.036 1.083
0.043 0.086 0.093 0.114 0.074 0.104 0.097 0.071 0.085 0.099 0.101 0.105
0.76 [0.75; 0.78] 0.83 [0.81; 0.86] 0.67 [0.64; 0.69] 0.58 [0.54; 0.62] 0.82 [0.80; 0.84] 1.33 [1.30; 1.36] 0.60 [0.56; 0.64] 1.18 [1.16; 1.20] 1.12 [1.09; 1.14] 1.21 [1.18; 1.24] 0.51 [0.47; 0.55] 1.09 [1.05; 1.12]
0.78 [0.47, 0.92] 0.49 [0.01; 0.79] 0.59 [0.16; 0.84] 0.81 [0.45; 0.95] 0.09 [–0.51; 0.63] 0.37 [–0.26; 0.78] 0.67 [0.15; 0.90] 0.17 [–0.45; 0.68] 0.38 [–0.24; 0.79] 0.59 [0.01; 0.87] 0.63 [0.20; 0.88] 0.46 [–0.15; 0.82]
0.80 [0.54, 0.92] 0.64 [0.27; 0.84] 0.65 [0.23; 0.85] 0.68 [0.26; 0.89] 0.44 [–0.09; 0.78] 0.28 [–0.27; 0.70] 0.52 [0.01; 0.82] 0.41 [–0.13; 0.76] 0.34 [–0.21; 0.73] 0.41 [–0.14; 0.76] 0.51 [–0.01; 0.88] 0.38 [–0.16; 0.75]
1D. vs. 3D Regarding the dimension of the signals used to reconstruct the state-space, we found a slight trend indicating that larger effect sizes appear in λs calculated using 3D signals than when using 1D signals, with the highest effect size occurring in 3D foot angular velocity data (Hedges’ g = 1.33). Linear acceleration vs. angular velocity vs. combination of linear acceleration and angular velocity signals λ calculated using either linear acceleration signals or angular velocity signals only exhibited low effect sizes. Trunk signals vs. foot signals vs. combination of trunk and foot signals λs calculated based on foot trajectories always yielded higher effects than λ calculated using time series from trunk signals when comparing old vs young. When foot and trunk trajectories are both incorporated in the reconstruction of the state-space, the effect sizes were improved (Hedges’ g: 1.09 – 1.21). Test-retest reliability While the inter-session ICC-values ranged from 0.09 (foot, linear acceleration + angular velocity) – 0.81 (trunk, linear acceleration, medial–lateral), inter-day values ranged from 0.28 (foot, 3D angular velocity) to 0.80 (foot, linear acceleration, anterior–posterior). The highest reliability values were observed when λ was calculated based on 1D-signals (inter-session ICC: 0.49 – 0.81). Discussion Kinematic parameters derived from treadmill-walking are known not to represent those obtained from walking on level ground [9,29,30]. While LDS has been assessed and evaluated in both research [1] and clinical [31] settings using inertial sensors in treadmill walking, this study provides the first evaluation of these measures in older individuals using data derived from level overground walking using inertial sensor devices. The approach is feasible for use in medical centres and would therefore be a first step towards translating the potential for assessing gait stability into clinical settings. Also, the current work provides the first data that addresses LDS during indoor walking in an older cohort, and which has been evaluated with respect to 1) its inter-session and inter-day test-retest reliability and 2) its ability to distinguish from LDS of younger cohorts. In addition, we have compared 21 different state-space definitions (as a preprocessing step in order to calculate LDS) that affect reliability and validity of gait stability quantified with the largest finite Lyapunov
td
nTDC
18 11 10 10 18 9 9 18 17 8 9 15
9 8 7 4 4 4 2 4 3 2 2 2
Exponents. Our data indicate that, in order to receive sufficiently reliable and valid results, λ of walking time series should be evaluated including medial-lateral linear acceleration signals, 3D linear acceleration signals or 3D linear acceleration + angular velocity signals of the trunk. When using time series of foot trajectories, 1D linear acceleration or angular velocity data (but not in the superior-inferior direction) should be used to best reconstruct the state space. The possible benefits of further data collected from other joints remains to be assessed. It should be noted that the cohorts in our study were not matched with respect to body mass and height meaning that differences in LDS could also stem from anthropometric differences. Nevertheless, the current study aims to elucidate walking behaviour of ordinary healthy older and ordinary healthy young individuals which includes groups with naturally different anthropometric properties. Our data depict a trend showing that the reconstruction method either increases the validity or the reliability. This means that gait stability calculated using a reconstruction method that yields high validity (Hedges’ g > 1.0) is likely to result in low reliability and vice versa. However, moderate reliability values were also accompanied by moderate validity values for space states that included trunk measures or 1D measures of the foot. The relatively narrow confidence intervals of these measures (Table 1) indicate good generalizability of our data. The considerable differences in ability to distinguish between old and young were not expected since the use of different signals (which represent observations from the same dynamic process) should theoretically lead to the same outcome [6]. In practice, however, the results of Gates and Dingwell [16], who evaluated the effect of different state-space descriptions on LDS of shoulder movements of a sawing task, demonstrate that values of stability are virtually invariant. The authors therefore advised against the use of state-spaces composed of positions and their derivations (velocity) in order to reduce redundant information that could negatively influence the outcome. In contrast, our results suggest that reconstructing the state space with combinations of signals (e.g. angular velocity + linear acceleration or foot + trunk data) leads to good or excellent validity. However, we do not consider these signal combinations to be redundant as the acceleration signal and the velocity signal from our work stem from different sources (accelerometer and gyroscope). In the study of Gates and Dingwell [16], the velocity was a mathematical derivation of the positions and, therefore, redundant. Most ICC values determined in our study are roughly comparable with those of the literature. However, wide confidence intervals (Table 1) indicate low generalizability. The reliability of LDS in our old cohort was slightly higher than the reliability of a group of young subjects reported by van Schooten and co-workers (ICC based on 200 strides of 1D trunk acceleration signals: 0.38–0.92 [11]). This
D. Hamacher et al. / Medical Engineering and Physics 37 (2015) 1152–1155
phenomenon might be due to the high inter-subject variability of our older cohort. Furthermore, our ICC values are similar to the values of healthy individuals between the age of 20 and 69 years (ICC based on 70 strides of 1D trunk acceleration signals: 0.50–0.88 [32]) who walked on a treadmill. The repeatability might have been so high because the use of a treadmill is known to reduce both inter- and intrasubject variability through governing walking speed. Comparing our outcomes with those of older individuals or patients with paresis of the lower extremities (ICC based on 1D trunk acceleration signals: 0.75–0.89; [31]), we revealed slightly lower reliability which might be due to high inter-subject variability caused by the disease and/or by barefoot walking. Our data additionally indicate that the stability of foot trajectories is more valid than the stability of trunk trajectories. These results are not consistent with those of Kang and Dingwell [33], who reported that LDS of trunk data is better able to distinguish old from young cohorts than LDS based on foot trajectories. In their study, however, subjects walked on a treadmill where the trajectories of the feet were mainly governed by an external pacemaker. This might have eliminated some differences/variations in foot trajectory data (especially in the stance phase) between the older and young cohort that might have naturally occurred during normal overground walking. We speculate that treadmill walking would have prevented the discriminative capability of LDS derived from foot trajectories, but less so in those of the relatively free moving trunk. Furthermore, when data was added by means of combining different signals, validity of the results generally improved. It is conceivable that the proposed method is suitable for long-term monitoring of mobility (see also e.g. [34] for an overview) in order to assess gait stability. The results of this study indicate that the estimation of local dynamic stability in elderly subjects might be optimally obtained choosing a compromise with regards to the validity and the reproducibility of the used data to span the state space. Furthermore, our data show that LDS is sensitive to age-related degeneration and might be suitable for early monitoring of geriatric or neurological pathologies. In addition, LDS calculated from kinematic gait data derived from inertial sensors is a promising methodology in clinical settings to quantify therapy efficacy. Conflict of interest There are no conflicts of interest. Funding None. Ethical approval Ethical approval was given by the ethics committee of the University of Magdeburg, Germany. Reference number: 157/12. References [1] Dingwell JB, Cusumano JP. Nonlinear time series analysis of normal and pathological human walking. Chaos 2000;10:848–63. [2] Toebes MJP, Hoozemans MJM, Furrer R, Dekker J, Van Dieën JH. Local dynamic stability and variability of gait are associated with fall history in elderly subjects. Gait Posture 2012;36:527–31. [3] Bruijn SM, Meijer OG, Beek PJ, Van Dieen JH. Assessing the stability of human locomotion: a review of current measures. J R Soc Interface 2013;10. [4] Hamacher D, Singh NB, Van Dieën JH, Heller MO, Taylor WR. Kinematic measures for assessing gait stability in elderly individuals: A systematic review. J R Soc Interface 2011;8:1682–98.
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[5] Rosenstein MT, Collins JJ, Deluca CJ. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets. Physica D 1993;65:117–34. [6] Bruijn SM, Ten Kate WR, Faber GS, Meijer OG, Beek PJ, van Dieen JH. Estimating Dynamic Gait Stability Using Data from Non-aligned Inertial Sensors. Ann Biomed Eng 2010;38:2588–93. [7] Reynard F, Terrier P. Local dynamic stability of treadmill walking: intrasession and week-to-week repeatability. J Biomech. [8] Bruijn SM, van Dieën JH, Meijer OG, Beek PJ. Statistical precision and sensitivity of measures of dynamic gait stability. J Neurosci Methods 2009;178:327–33. [9] Terrier P, Dériaz O. Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking. J NeuroEng Rehabil 2011;8:1–13. [10] Kang HG, Dingwell JB. Intra-session reliability of local dynamic stability of walking. Gait Posture 2006;24:386–90. [11] Van Schooten KS, Rispens SM, Pijnappels M, Daffertshofer A, van Dieen JH. Assessing gait stability: the influence of state space reconstruction on inter- and intraday reliability of local dynamic stability during over-ground walking. J Biomech 2013;46:137–41. [12] Dingwell JB, Cusumano JP, Cavanagh PR, Sternad D. Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. J Biomech Eng 2001;123:27–32. [13] Lockhart TE, Liu J. Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics 2008;51:1860–72. [14] Dingwell JB, Marin LC. Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. J Biomech 2006;39:444–52. [15] Takens F. Detecting strange attractors in turbulence. In: Rand D, Young L-S, editors. Dynamical systems and turbulence, Warwick 1980. Berlin Heidelberg: Springer; 1981. p. 366–81. [16] Gates DH, Dingwell JB. Comparison of different state space definitions for local dynamic stability analyses. J Biomech 2009;42:1345–9. [17] Hilfiker R, Vaney C, Gattlen B, Meichtry A, Deriaz O, Lugon-Moulin V, et al. Local dynamic stability as a responsive index for the evaluation of rehabilitation effect on fall risk in patients with multiple sclerosis: a longitudinal study. BMC Res Notes 2013;6:1–9. [18] Terrier P, Dériaz O. Non-linear dynamics of human locomotion: Effects of rhythmic auditory cueing on local dynamic stability. Front Physiol 2013;4 SEP:1–13. [19] Kantz H, Schreiber T. Nonlinear time series analysis. Cambridge University Press; 2004. [20] Hamacher D, Hamacher D, Taylor WR, Singh NB, Schega L. Towards clinical application: repetitive sensor position re-calibration for improved reliability of gait parameters. Gait Posture 2014;39:1146–8. [21] Fraser AM, Swinney HL. Independent coordinates for strange attractors from mutual information. Phys Rev A 1986;33:1134–40. [22] Kennel MB, Brown R, Abarbanel HDI. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 1992;45:3403–11. [23] Van Schooten KS, Rispens SM, Elders PJM, van Dieën JH, Pijnappels M. Toward ambulatory balance assessment: Estimating variability and stability from short bouts of gait. Gait Posture 2014;39:695–9. [24] Terrier P, Reynard F. To what extent does not wearing shoes affect the local dynamic stability of walking? Effect size and intrasession repeatability. J Appl Biomech 2014;30:305–9. [25] Shrout PE, Fleiss JL. Intraclass correlations: Uses in assessing rater reliability. Psychol Bull 1979;86:420–8. [26] Cicchetti DV. Guidelines, criteria, and rules of thumb for evaluating normed and standardized assessment instruments in psychology. Psychol Assess 1994;6:284– 90. [27] Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;1:307–10. [28] Nakagawa S, Cuthill IC. Effect size, confidence interval and statistical significance: A practical guide for biologists. Biol Rev 2007;82:591–605. [29] Wearing SC, Reed LF, Urry SR. Agreement between temporal and spatial gait parameters from an instrumented walkway and treadmill system at matched walking speed. Gait Posture 2013. [30] Paterson KL, Lythgo ND, Hill KD. Gait variability in younger and older adult women is altered by overground walking protocol. Age Ageing 2009;38:745–8. [31] Reynard F, Vuadens P, Deriaz O, Terrier P. Could local dynamic stability serve as an early predictor of falls in patients with moderate neurological gait disorders? A reliability and comparison study in healthy individuals and in patients with paresis of the lower extremities. PLoS ONE 2014;9. [32] Reynard F, Terrier P. Local dynamic stability of treadmill walking: Intrasession and week-to-week repeatability. J Biomech 2014;47:74–80. [33] Kang HG, Dingwell JB. Dynamic stability of superior vs. inferior segments during walking in young and older adults. Gait Posture 2009;30:260–3. [34] Culhane KM, O’Connor M, Lyons D, Lyons GM. Accelerometers in rehabilitation medicine for older adults. Age Ageing 2005;34:556–60.
Contents lists available at ScienceDirect
Medical Engineering and Physics journal homepage: www.elsevier.com/locate/medengphy
Towards the assessment of local dynamic stability of level-grounded walking in an older population Dennis Hamacher a,∗, Daniel Hamacher a, Navrag B. Singh b, William R. Taylor b, Lutz Schega a a b
Department of Sport Science, Otto von Guericke University Magdeburg, Zschokkestr. 32, 39104 Magdeburg, Germany Institute for Biomechanics, ETH Zürich, Vladimir-Prelog-Weg 3-4, 8093 Zurich, Switzerland
a r t i c l e
i n f o
Article history: Received 5 December 2014 Revised 3 September 2015 Accepted 19 September 2015
Keywords: Local dynamic stability Gait Inertial sensor
a b s t r a c t Local dynamic stability is a critical aspect of stable gait but its assessment for use in clinical settings has not yet been sufficiently evaluated, particularly with respect to inertial sensors applied on the feet and/or trunk. Furthermore, key questions remain as to which state-space reconstruction is most reliable and valid. In this study, we evaluated the reliability as well as the ability of different sensor placement and state-spaces to distinguish between local dynamic stability in young and older adults. Gait data of 19 older and 20 young subjects were captured with inertial sensors twice within the first day as well as after seven days. 21 different signals (and combinations of signals) were used to span the system’s state-space to calculate different measures of local dynamic stability. Our data revealed moderate or high effect sizes in 12 of the 21 old vs. young comparisons. We also observed considerable differences in the reliability of these 12 results, with intra-class correlation coefficients ranging from 0.09 to 0.81. Our results demonstrate that in order to obtain reliable and valid estimates of gait stability λ of walking time series is best evaluated using trunk data or 1-dimensional data from foot sensors. © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
Introduction Measures of local dynamic stability (LDS) during walking are able to provide an understanding of an individual’s gait stability [1–3]. Such measures are capable of distinguishing between older and younger cohorts [4] with lower levels of LDS associated with a higher risk of falling [2,4]. However, measures of LDS, which can be quantified using the largest Lyapunov Exponents (λ [5]), have mostly been evaluated in young subjects walking on a treadmill [6,7] due to the requirement of collecting multiple strides for its assessment [8]. However, treadmill walking does not represent a physiological activity of daily living and is known to add external constraints, such as acting as a temporal pacemaker, and modifying LDS [9]. The type of walking (i.e. treadmill or overground) should therefore be considered in the protocol design. To ensure clinical relevance, a renewed validation of λ that addresses reliability and validity should be conducted in older people as demanded (but not yet undertaken) in the literature [10,11]. The calculation of λ is based on state-space representations [1], where the representation of a valid state-space could be any vector space containing a sufficient number of independent ∗
Corresponding author. Tel.: +49 391 6754936; fax: +49 391 6716754. E-mail addresses: [email protected], [email protected] (D. Hamacher), [email protected] (D. Hamacher), [email protected] (N.B. Singh), [email protected] (W.R. Taylor), [email protected] (L. Schega). http://dx.doi.org/10.1016/j.medengphy.2015.09.007 1350-4533/© 2015 IPEM. Published by Elsevier Ltd. All rights reserved.
coordinates defining the state of the system at any instant in time [12]. For example, to calculate λ from a walking time series, statespaces could be built from anterior–posterior, medial–lateral, and superior–inferior accelerometer signals taken from the hip, knee and ankle joints [1,13], or from trunk position movements in all three directions [14]. Adequate state-spaces could be reconstructed from a single time series using the original dataset and its time delayed copies [15] or e.g. from time series of all angles and angular velocities at that joint [16]. In this case, λ is quantified as exponential rates of divergence of initially neighbouring trajectories in the state-space as they evolve in real time. Inertial sensors offer feasible options for flexible, mobile, and inexpensive usage in clinical settings. However, a recent test-retest reliability study of young subjects showed that robust inter-day assessment of gait stability is difficult using data from such accelerometer sensors [11]. In their study, gait data captured during outdoor walking was analysed, which had the benefit of allowing accurate capture of magnetometer data for assessing orientation. However, assessment within the constraints of indoor walking where magnetometer data is not necessarily accurate or reliable (which is comparable to clinical settings), might be more appropriate for the analysis of patients suffering from musculoskeletal deficits [17,18]. In order to establish the assessment of λ for overground walking using inertial sensors for clinical use, this study aimed to evaluate multiple state-space definitions (using different signal types) in both
D. Hamacher et al. / Medical Engineering and Physics 37 (2015) 1152–1155
young and elderly adults. Here, the following state-space reconstructions for evaluating λ were considered in terms of both reliability as well as validity [11,16,19]: (1) differences in the signal dimension (1D vs. 3D) might affect inter-day reliability as different sensor positions affect sensor orientation relative to the segment, (2) signal characteristics are different regarding linear acceleration and angular velocity, and it might be possible to improve reliability through combining these variables for estimation of λ [11], even when the signals stem from the same system, and (3) the reliability and validity of different measures of λ might be sensitive to different segment trajectories (e.g. trunk, foot), but test-retest data are only currently available derived from trunk movements [7,10,11]. The following two research questions were addressed: 1) What is the inter-session and inter-day test-retest reliability of LDS in an older cohort a function of differently reconstructed state-spaces? 2) Are measures of LDS able to distinguish between young and older adults as a function of differently reconstructed state-spaces? Methods Subjects Gait data of 19 healthy older (5 male, 14 female, age: 71 ± 4 years) and 20 healthy young subjects (8 Male, 12 female, age: 26 ± 4 years) were captured twice within the first day and also once after seven days. All participants provided their written informed consent after they were briefed about the research protocol, which complied with the principles of the Declaration of Helsinki and was approved by the board of the ethical committee of Otto von Guericke University, Magdeburg. Testing procedure A wireless inertial motion tracker (MTw, Xsens Technologies B.V., Enschede, The Netherlands; range of measurement of angular velocity: ± 1200 deg/s, range of measurement of acceleration: ± 160 m/s2 ) was fixed onto each of the subjects’ forefeet and trunk. Among other things, these sensors measure angular velocities and linear accelerations with a sampling rate of 75 Hz. Kinematic data were captured while the subjects twice walked a distance of 130 m (including one turn) in a straight line on a level hallway at their preferred walking speed. This procedure was repeated 1) after 5 min of rest without removing the sensors and 2), after 7 days at the same time of day.
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The time delay (used for the time delayed copies) corresponded with the first minimum mutual information for each participant [21], and the number of time delayed copies was calculated using the global false nearest neighbours method [22] where the appropriate number of copies was defined as the number where a manifest plateau began to appear. Both the embedded dimensions and mutual information were calculated for each subject, and the resulting median of all subjects was applied to calculate λ for the whole group for a particular signal combination. In order to ensure comparability of data from older and younger subjects, the same embedded dimensions and mutual information for each signal (signal combination) of the older subjects was also used for the younger subjects. The second step was to calculate λ by estimating the exponential rates of divergence of initially nearest neighbours as they evolved in real time, which provided a direct measure of the system’s sensitivity to extremely small perturbations. Here, we used Rosenstein and co-workers’ algorithm for the calculation of λ [5], which was implemented in MATLAB (version 2013a, The MathWorks BV, Natrick, USA). Approaches to calculate LDS using multiple repetitions of short walking distances have been published previously [23,24]. In the current study, we merged the data of 100 strides of two repetitions of 130 m which included one single turn (turn data removed). The time series were normalized to 10000 samples [18]. The distance of each point in state-space and the correlating nearest neighbour (Euclidean distance) were tracked for data of the same walk. After taking the logarithm of the mean divergence curve, LDS was computed as the slope of the linear fit through 0–0.5 strides for each signal (or combination) and for each subject. LDS was then interpreted such that positive exponents indicated local instability, while larger positive exponents indicated greater sensitivity to perturbations that occurred while walking [5,19]. Statistics For estimating the inter-session test-retest reliability, we used both trials of the first day. The inter-day test-retest reliability was calculated using data from the first trial of the first day and the trial captured on the second day. Intra-class correlation coefficients (ICC, 2.1; [25]) were calculated (using the IBM SPSS Statistics 20 software suite) where values between 0.0–0.40 were considered poor, from 0.40– 0.59 fair, from 0.60–0.74 good, and from 0.75–1.00 excellent [26]. Furthermore, the Bias and Limits of Agreement [27] were assessed to quantify the agreement between test and retest. Hedges’ g was calculated to estimate the effect size comparing old vs. young. We use the conventional values as benchmarks considering 0.2, 0.5 and 0.8 to be ‘small’, ‘medium’, and ‘large’ effects, respectively [28]. The precision on the effect sizes and Intra-class correlation coefficients were estimated with 95% confidence intervals.
Data analysis Results Heel strikes from 100 strides per subject were estimated as described in Hamacher et al. [20] after removing data captured in 2.5 m prior to and after turning. The first step in the calculation of λ was to reconstruct appropriate state-spaces with the aid of time-fixed delayed copies and/or with different signals representing the same movement. In order to explore the influence of different signals (and combinations of signals) used to span the system’s state-space on the reliability and validity of λ, we reconstructed 21 state-spaces which were different with respect to 1) data included from the different sensor axes, with the sensor fixed to the body parts in a way to coincide with the anatomical planes in normal standing (anterior–posterior, medial-lateral, and superior-inferior), 2) the trajectories of different segments (trunk vs. foot), and 3) the nature of the data (linear acceleration vs. angular velocity). Subsequently, we created time delayed copies to build an adequate high-dimensional state-space for LDS calculation.
Our data revealed effect sizes of 0.51 (medium effect) or higher (up to 1.33, large effect) in 12 of the 21 old vs. young state-space comparisons (Table 1). As a result, only λs calculated with these 12 different state-spaces are reported. Substantial differences were observed regarding the test-retest reliability, with ICC-values ranging from 0.09 to 0.81 (Table 1). Old vs. young comparison Anterior–posterior vs. medial–lateral vs. and superior–inferior λ calculated using linear acceleration signals or angular velocity signals in the superior-inferior direction did not reach medium or high effect sizes. Furthermore, we did not find any systematic differences with respect to λ calculated from data stemming from signals regarding anterior–posterior vs. medial–lateral direction.
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Table 1 Maximum Finite Lyapunov Exponents and the associated effect sizes (Hedges’ g (old vs. young comparison)), ICCs (test-retest comparison) of LDS for different combinations of signals to span the state-space. Only 12 state-spaces are considered whose corresponding Maximum Finite Lyapunov Exponents yielded Hedges’ g value of at least 0.5. The following acronyms are used: Acceleration = ACC, angle velocity = Ѳ, local coordination system = LCS, anterior–posterior = a–p, medio–lateral = m–l. Values presented in bold font indicate excellent reliability (ICC) or large effects (g), time delay = td, and number of time delayed copies = nTDC.
λ Old Segment
Signal
Foot
ACC
Trunk Foot Trunk Foot Foot + Trunk Trunk Foot + Trunk
Gyr ACC ACC Gyr ACC ACC + Gyr ACC Gyr ACC + Gyr ACC + Gyr
a–p m–l a–p m–l
λ Young
Old vs. Young
Test-Retest Reliability
mean
SD
mean
SD
Hedges’ g
ICC Inter-session
ICC Inter-day
0.532 0.636 0.821 1.079 0.794 1.458 1.145 0.789 0.946 1.483 1.104 1.193
0.039 0.059 0.08 0.136 0.05 0.101 0.162 0.049 0.074 0.104 0.156 0.093
0.5 0.573 0.762 1.005 0.741 1.319 1.064 0.715 0.855 1.358 1.036 1.083
0.043 0.086 0.093 0.114 0.074 0.104 0.097 0.071 0.085 0.099 0.101 0.105
0.76 [0.75; 0.78] 0.83 [0.81; 0.86] 0.67 [0.64; 0.69] 0.58 [0.54; 0.62] 0.82 [0.80; 0.84] 1.33 [1.30; 1.36] 0.60 [0.56; 0.64] 1.18 [1.16; 1.20] 1.12 [1.09; 1.14] 1.21 [1.18; 1.24] 0.51 [0.47; 0.55] 1.09 [1.05; 1.12]
0.78 [0.47, 0.92] 0.49 [0.01; 0.79] 0.59 [0.16; 0.84] 0.81 [0.45; 0.95] 0.09 [–0.51; 0.63] 0.37 [–0.26; 0.78] 0.67 [0.15; 0.90] 0.17 [–0.45; 0.68] 0.38 [–0.24; 0.79] 0.59 [0.01; 0.87] 0.63 [0.20; 0.88] 0.46 [–0.15; 0.82]
0.80 [0.54, 0.92] 0.64 [0.27; 0.84] 0.65 [0.23; 0.85] 0.68 [0.26; 0.89] 0.44 [–0.09; 0.78] 0.28 [–0.27; 0.70] 0.52 [0.01; 0.82] 0.41 [–0.13; 0.76] 0.34 [–0.21; 0.73] 0.41 [–0.14; 0.76] 0.51 [–0.01; 0.88] 0.38 [–0.16; 0.75]
1D. vs. 3D Regarding the dimension of the signals used to reconstruct the state-space, we found a slight trend indicating that larger effect sizes appear in λs calculated using 3D signals than when using 1D signals, with the highest effect size occurring in 3D foot angular velocity data (Hedges’ g = 1.33). Linear acceleration vs. angular velocity vs. combination of linear acceleration and angular velocity signals λ calculated using either linear acceleration signals or angular velocity signals only exhibited low effect sizes. Trunk signals vs. foot signals vs. combination of trunk and foot signals λs calculated based on foot trajectories always yielded higher effects than λ calculated using time series from trunk signals when comparing old vs young. When foot and trunk trajectories are both incorporated in the reconstruction of the state-space, the effect sizes were improved (Hedges’ g: 1.09 – 1.21). Test-retest reliability While the inter-session ICC-values ranged from 0.09 (foot, linear acceleration + angular velocity) – 0.81 (trunk, linear acceleration, medial–lateral), inter-day values ranged from 0.28 (foot, 3D angular velocity) to 0.80 (foot, linear acceleration, anterior–posterior). The highest reliability values were observed when λ was calculated based on 1D-signals (inter-session ICC: 0.49 – 0.81). Discussion Kinematic parameters derived from treadmill-walking are known not to represent those obtained from walking on level ground [9,29,30]. While LDS has been assessed and evaluated in both research [1] and clinical [31] settings using inertial sensors in treadmill walking, this study provides the first evaluation of these measures in older individuals using data derived from level overground walking using inertial sensor devices. The approach is feasible for use in medical centres and would therefore be a first step towards translating the potential for assessing gait stability into clinical settings. Also, the current work provides the first data that addresses LDS during indoor walking in an older cohort, and which has been evaluated with respect to 1) its inter-session and inter-day test-retest reliability and 2) its ability to distinguish from LDS of younger cohorts. In addition, we have compared 21 different state-space definitions (as a preprocessing step in order to calculate LDS) that affect reliability and validity of gait stability quantified with the largest finite Lyapunov
td
nTDC
18 11 10 10 18 9 9 18 17 8 9 15
9 8 7 4 4 4 2 4 3 2 2 2
Exponents. Our data indicate that, in order to receive sufficiently reliable and valid results, λ of walking time series should be evaluated including medial-lateral linear acceleration signals, 3D linear acceleration signals or 3D linear acceleration + angular velocity signals of the trunk. When using time series of foot trajectories, 1D linear acceleration or angular velocity data (but not in the superior-inferior direction) should be used to best reconstruct the state space. The possible benefits of further data collected from other joints remains to be assessed. It should be noted that the cohorts in our study were not matched with respect to body mass and height meaning that differences in LDS could also stem from anthropometric differences. Nevertheless, the current study aims to elucidate walking behaviour of ordinary healthy older and ordinary healthy young individuals which includes groups with naturally different anthropometric properties. Our data depict a trend showing that the reconstruction method either increases the validity or the reliability. This means that gait stability calculated using a reconstruction method that yields high validity (Hedges’ g > 1.0) is likely to result in low reliability and vice versa. However, moderate reliability values were also accompanied by moderate validity values for space states that included trunk measures or 1D measures of the foot. The relatively narrow confidence intervals of these measures (Table 1) indicate good generalizability of our data. The considerable differences in ability to distinguish between old and young were not expected since the use of different signals (which represent observations from the same dynamic process) should theoretically lead to the same outcome [6]. In practice, however, the results of Gates and Dingwell [16], who evaluated the effect of different state-space descriptions on LDS of shoulder movements of a sawing task, demonstrate that values of stability are virtually invariant. The authors therefore advised against the use of state-spaces composed of positions and their derivations (velocity) in order to reduce redundant information that could negatively influence the outcome. In contrast, our results suggest that reconstructing the state space with combinations of signals (e.g. angular velocity + linear acceleration or foot + trunk data) leads to good or excellent validity. However, we do not consider these signal combinations to be redundant as the acceleration signal and the velocity signal from our work stem from different sources (accelerometer and gyroscope). In the study of Gates and Dingwell [16], the velocity was a mathematical derivation of the positions and, therefore, redundant. Most ICC values determined in our study are roughly comparable with those of the literature. However, wide confidence intervals (Table 1) indicate low generalizability. The reliability of LDS in our old cohort was slightly higher than the reliability of a group of young subjects reported by van Schooten and co-workers (ICC based on 200 strides of 1D trunk acceleration signals: 0.38–0.92 [11]). This
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phenomenon might be due to the high inter-subject variability of our older cohort. Furthermore, our ICC values are similar to the values of healthy individuals between the age of 20 and 69 years (ICC based on 70 strides of 1D trunk acceleration signals: 0.50–0.88 [32]) who walked on a treadmill. The repeatability might have been so high because the use of a treadmill is known to reduce both inter- and intrasubject variability through governing walking speed. Comparing our outcomes with those of older individuals or patients with paresis of the lower extremities (ICC based on 1D trunk acceleration signals: 0.75–0.89; [31]), we revealed slightly lower reliability which might be due to high inter-subject variability caused by the disease and/or by barefoot walking. Our data additionally indicate that the stability of foot trajectories is more valid than the stability of trunk trajectories. These results are not consistent with those of Kang and Dingwell [33], who reported that LDS of trunk data is better able to distinguish old from young cohorts than LDS based on foot trajectories. In their study, however, subjects walked on a treadmill where the trajectories of the feet were mainly governed by an external pacemaker. This might have eliminated some differences/variations in foot trajectory data (especially in the stance phase) between the older and young cohort that might have naturally occurred during normal overground walking. We speculate that treadmill walking would have prevented the discriminative capability of LDS derived from foot trajectories, but less so in those of the relatively free moving trunk. Furthermore, when data was added by means of combining different signals, validity of the results generally improved. It is conceivable that the proposed method is suitable for long-term monitoring of mobility (see also e.g. [34] for an overview) in order to assess gait stability. The results of this study indicate that the estimation of local dynamic stability in elderly subjects might be optimally obtained choosing a compromise with regards to the validity and the reproducibility of the used data to span the state space. Furthermore, our data show that LDS is sensitive to age-related degeneration and might be suitable for early monitoring of geriatric or neurological pathologies. In addition, LDS calculated from kinematic gait data derived from inertial sensors is a promising methodology in clinical settings to quantify therapy efficacy. Conflict of interest There are no conflicts of interest. Funding None. Ethical approval Ethical approval was given by the ethics committee of the University of Magdeburg, Germany. Reference number: 157/12. References [1] Dingwell JB, Cusumano JP. Nonlinear time series analysis of normal and pathological human walking. Chaos 2000;10:848–63. [2] Toebes MJP, Hoozemans MJM, Furrer R, Dekker J, Van Dieën JH. Local dynamic stability and variability of gait are associated with fall history in elderly subjects. Gait Posture 2012;36:527–31. [3] Bruijn SM, Meijer OG, Beek PJ, Van Dieen JH. Assessing the stability of human locomotion: a review of current measures. J R Soc Interface 2013;10. [4] Hamacher D, Singh NB, Van Dieën JH, Heller MO, Taylor WR. Kinematic measures for assessing gait stability in elderly individuals: A systematic review. J R Soc Interface 2011;8:1682–98.
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[5] Rosenstein MT, Collins JJ, Deluca CJ. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets. Physica D 1993;65:117–34. [6] Bruijn SM, Ten Kate WR, Faber GS, Meijer OG, Beek PJ, van Dieen JH. Estimating Dynamic Gait Stability Using Data from Non-aligned Inertial Sensors. Ann Biomed Eng 2010;38:2588–93. [7] Reynard F, Terrier P. Local dynamic stability of treadmill walking: intrasession and week-to-week repeatability. J Biomech. [8] Bruijn SM, van Dieën JH, Meijer OG, Beek PJ. Statistical precision and sensitivity of measures of dynamic gait stability. J Neurosci Methods 2009;178:327–33. [9] Terrier P, Dériaz O. Kinematic variability, fractal dynamics and local dynamic stability of treadmill walking. J NeuroEng Rehabil 2011;8:1–13. [10] Kang HG, Dingwell JB. Intra-session reliability of local dynamic stability of walking. Gait Posture 2006;24:386–90. [11] Van Schooten KS, Rispens SM, Pijnappels M, Daffertshofer A, van Dieen JH. Assessing gait stability: the influence of state space reconstruction on inter- and intraday reliability of local dynamic stability during over-ground walking. J Biomech 2013;46:137–41. [12] Dingwell JB, Cusumano JP, Cavanagh PR, Sternad D. Local dynamic stability versus kinematic variability of continuous overground and treadmill walking. J Biomech Eng 2001;123:27–32. [13] Lockhart TE, Liu J. Differentiating fall-prone and healthy adults using local dynamic stability. Ergonomics 2008;51:1860–72. [14] Dingwell JB, Marin LC. Kinematic variability and local dynamic stability of upper body motions when walking at different speeds. J Biomech 2006;39:444–52. [15] Takens F. Detecting strange attractors in turbulence. In: Rand D, Young L-S, editors. Dynamical systems and turbulence, Warwick 1980. Berlin Heidelberg: Springer; 1981. p. 366–81. [16] Gates DH, Dingwell JB. Comparison of different state space definitions for local dynamic stability analyses. J Biomech 2009;42:1345–9. [17] Hilfiker R, Vaney C, Gattlen B, Meichtry A, Deriaz O, Lugon-Moulin V, et al. Local dynamic stability as a responsive index for the evaluation of rehabilitation effect on fall risk in patients with multiple sclerosis: a longitudinal study. BMC Res Notes 2013;6:1–9. [18] Terrier P, Dériaz O. Non-linear dynamics of human locomotion: Effects of rhythmic auditory cueing on local dynamic stability. Front Physiol 2013;4 SEP:1–13. [19] Kantz H, Schreiber T. Nonlinear time series analysis. Cambridge University Press; 2004. [20] Hamacher D, Hamacher D, Taylor WR, Singh NB, Schega L. Towards clinical application: repetitive sensor position re-calibration for improved reliability of gait parameters. Gait Posture 2014;39:1146–8. [21] Fraser AM, Swinney HL. Independent coordinates for strange attractors from mutual information. Phys Rev A 1986;33:1134–40. [22] Kennel MB, Brown R, Abarbanel HDI. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys Rev A 1992;45:3403–11. [23] Van Schooten KS, Rispens SM, Elders PJM, van Dieën JH, Pijnappels M. Toward ambulatory balance assessment: Estimating variability and stability from short bouts of gait. Gait Posture 2014;39:695–9. [24] Terrier P, Reynard F. To what extent does not wearing shoes affect the local dynamic stability of walking? Effect size and intrasession repeatability. J Appl Biomech 2014;30:305–9. [25] Shrout PE, Fleiss JL. Intraclass correlations: Uses in assessing rater reliability. Psychol Bull 1979;86:420–8. [26] Cicchetti DV. Guidelines, criteria, and rules of thumb for evaluating normed and standardized assessment instruments in psychology. Psychol Assess 1994;6:284– 90. [27] Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. Lancet 1986;1:307–10. [28] Nakagawa S, Cuthill IC. Effect size, confidence interval and statistical significance: A practical guide for biologists. Biol Rev 2007;82:591–605. [29] Wearing SC, Reed LF, Urry SR. Agreement between temporal and spatial gait parameters from an instrumented walkway and treadmill system at matched walking speed. Gait Posture 2013. [30] Paterson KL, Lythgo ND, Hill KD. Gait variability in younger and older adult women is altered by overground walking protocol. Age Ageing 2009;38:745–8. [31] Reynard F, Vuadens P, Deriaz O, Terrier P. Could local dynamic stability serve as an early predictor of falls in patients with moderate neurological gait disorders? A reliability and comparison study in healthy individuals and in patients with paresis of the lower extremities. PLoS ONE 2014;9. [32] Reynard F, Terrier P. Local dynamic stability of treadmill walking: Intrasession and week-to-week repeatability. J Biomech 2014;47:74–80. [33] Kang HG, Dingwell JB. Dynamic stability of superior vs. inferior segments during walking in young and older adults. Gait Posture 2009;30:260–3. [34] Culhane KM, O’Connor M, Lyons D, Lyons GM. Accelerometers in rehabilitation medicine for older adults. Age Ageing 2005;34:556–60.
