Gait & Posture 38 (2013) 345–348
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Assessment of differenced center of pressure time series improves detection of age-related changes in postural coordination Adam J. Strang a,*, Angela DiDomenico b, William P. Berg c, Raymond W. McGorry b a
Consortium Research Fellows Program, 4214 King St., Alexandria, VA 22302, United States Liberty Mutual Research Institute for Safety, 71 Frankland Road, Hopkinton, MA 01748, United States c Department of Kinesiology and Health, 106 Phillips Hall, 420 S. Oak Street, Oxford, OH 45056, United States b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 27 August 2012 Received in revised form 18 October 2012 Accepted 6 November 2012
Center of Pressure (CoP) time series exhibit non-stationarity. Most CoP analyses assume a stationary signal, which could lead to measurement inaccuracy. Despite this, few researchers have reported the incidence of CoP non-stationarity or employed procedures to mitigate non-stationarity prior to timeseries analysis. Differencing is a pre-processing technique that reduces non-stationarity, though it has only recently been used with CoP data. This study sought to report the incidence of CoP non-stationarity in a sample data set and determine whether differencing mitigated any CoP non-stationarity that was detected. In addition, researchers examined whether analysis of differenced CoP improved the ability to detect age-related changes in postural coordination. ß 2012 Elsevier B.V. All rights reserved.
Keywords: Center of Pressure Postural coordination Non-stationarity Differencing Time series
1. Introduction Center of Pressure (CoP) time-series analysis is the prevailing method for examining human postural coordination in stance [1,2]. It is known that CoP time series exhibit non-stationarity (i.e., unstable mean and variance over time), which can negatively affect the sensitivity and accuracy of time-series measures, since most assume a stationary signal [3,4]. Few studies have investigated the incidence of non-stationarity in CoP data [3–5]. Newell et al.  performed the most rigorous assessment in a study that recorded CoP in stance from participants aged 3–92 years. Using an Analysis of Variance approach, researchers determined that all of the CoP time-series examined in that study contained signiﬁcant time-domain non-stationarity. A few studies have employed a pre-processing technique known as differencing to mitigate CoP non-stationarity [2,5,6]. Differencing refers to deriving a new time series from the sampled data according to xi+1 xi, where xi is the ith sampled data point. Advantages of differencing over other detrending techniques (e.g., high-pass ﬁlter, empirical mode decomposition, polynomial line ﬁt) include computational simplicity, effectiveness , and the rendering of transformed data that retains face and content
* Corresponding author. Tel.: +1 513 505 6855. E-mail addresses: [email protected]
(A.J. Strang), [email protected]
(A. DiDomenico), [email protected]
(W.P. Berg), [email protected]
(R.W. McGorry). 0966-6362/$ – see front matter ß 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.gaitpost.2012.11.006
validity. Face validity is attributed to the sampling rate of CoP being ﬁxed, which makes differencing equivalent to obtaining the ﬁrst-order derivative of CoP position (CoPpos), i.e., CoP instantaneous velocity (CoPvel). Content validity comes from research indicating that postural sway velocity, as opposed to position and acceleration, is the most accurate and relied-upon kinesthetic information used in maintaining human balance . A known disadvantage of differencing is noise ampliﬁcation , which can result in increased time-domain variance and a shift in spectral power toward higher frequencies. In support of differencing, Ramdani et al.  showed that this technique was necessary for detecting differences in CoP between eyes-open and eyes-closed stance using Sample Entropy (SEn), a nonlinear measure that assumes stationarity. In another study, Rhea et al.  examined the inﬂuence of noise and sampling frequency on the accuracy and reliability of three entropy measures, i.e., Approximate Entropy, SEn, and Recurrence Quantiﬁcation Analysis Entropy, and determined that estimates for all three measures were more robust to noise and increasing sampling rates when derived from differenced CoP. The purpose of the current experiment was to report the incidence of CoP non-stationarity in a sample data set and determine whether differencing mitigated CoP non-stationarity that was detected using an objective inferential method. This study also sought to examine whether analysis of differenced CoP improved the ability to detect age-related changes in postural coordination.
A.J. Strang et al. / Gait & Posture 38 (2013) 345–348
346 2. Methods 2.1. Participants
Forty-ﬁve men between the ages of 18 and 65 years, who were free of musculoskeletal and cardiovascular pathology, participated. Mean (SD) age, height and body mass of participants were 40.5 (14.8) years, 1.77 (0.07) m and 83.6 (14.1) kg. 2.2. Apparatus
CoPRD and CoPRV were subjected to similar measures: Rectiﬁed Mean Amplitude (MA), Mean Spectral Frequency (MF), SEn , and Detrended Fluctuation Analysis (DFA) . Prior to applications of SEn, CoPRD and CoPRV were converted to Z-scores. CoPRD (M = 4, r = .04) and CoPRV (M = 4, r = .12) SEn parameters were established separately, mimicking the methodological use  of an optimization procedure . DFA scaling exponents (a) were estimated using window ranges of 5–20 for CoPRD and CoPRV, respectively, following visual inspection indicating that long-range correlations across that range ﬁt a linear trend for both data types.
Anterior–posterior (AP) and medial-lateral (ML) CoP were sampled at 100 Hz from two force plates (Model #9286AA, Kistler Instruments AG, Winterthur, Switzerland).
3. Results and discussion
3.1. Determining the incidence of CoPRD non-stationarity and whether differencing mitigated these effects
Participants performed three trials (each lasting 60 s) in a single laboratory session where they were asked to stand ‘‘as still as possible’’ with feet placed shoulder width apart near the center of adjacent force plates. Participants stood with arms at their sides and directed their gaze on an eye-level target located 7 m away. All participants wore athletic shoes (Nike Bandolier II) provided by experimenters. 2.4. Data analysis The ﬁrst 1000 CoP data points were cropped. A single corrupt trial was removed from analysis. The remaining CoP time-series were mean-centered and subjected to a 12.5 Hz 2nd order Butterworth low-pass ﬁlter. From the ﬁltered data, 95% Elliptical Area (EA)  and two-dimensional (2D) Path Length (PL)  were derived. EA and PL do not lend themselves to differencing, since assumptions of stationarity are irrelevant for 2D metrics, but were included due to their popularity. Centered AP and ML CoP were converted to Resultant Vector Distance (CoPRD) qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ time series according to AP2i þ ML2i to eliminate bias in uni-planar CoP, since planar axes are referenced to the force plate, not the participant [1,6]. CoPRD were differenced and divided by the common sampling period (0.01 s), returning a set of CoP resultant velocity (CoPRV) time series (Fig. 1).
10 8 6
4 2 0
Time (s) (b) 60
40 20 0 -20 -40 -60
Time (s) Fig. 1. Representative CoPRD (a) and CoPRV (b) time series from a 36-year-old participant in this experiment.
The Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test examines the null hypothesis that a time series is stationary along a deterministic (stationary) trend . This test was chosen over others (e.g., qualitative assessment of the auto-correlation function , Dickey–Fuller test) because of its popularity , easy interpretation, and quick calculation using free software . Independent KPSS tests (a = .01) were applied to all CoPRD and CoPRV. Results revealed that 69 of 134 (51%) CoPRD contained signiﬁcant non-stationarity. None of the CoPRV was shown to exhibit signiﬁcant non-stationarity. This indicates that differencing eliminated non-stationarity in all cases. 3.2. Examining whether assessments of differenced CoP improved detection and delineation of age-related changes in postural stability Pearson-product-moment correlations (r; a = .05) comprised of CoP measures and Age were used to address this issue. Fig. 2 reveals that increase in Age was associated with a decrease in SEn and increase in DFA for assessments of both CoPRD and CoPRV. In addition, increase in Age was associated with a decrease in MF for assessment of CoPRV. No relationships with Age were detected for EA, PL, or MA. These ﬁndings indicate that increase in Age was associated with decreases in the fractal complexity (DFA) and speed (MF) of CoP trajectories, accompanied by an increase in CoP temporal regularity (SEn). However, no changes in CoP area (EA), amount (PL), or dispersion (MA) were associated with an increase in Age. Findings from DFA and SEn are consistent with previous ﬁndings examining age-related changes in postural coordination that employed fractal  and entropy measures  and may indicate a more attention-demanding  and/or more rigid  postural coordination with increase in Age. To determine whether correlation strengths observed for SEn and DFA for assessments of CoPRV were statistically stronger than that detected for CoPRD, step-wise regressions (a = .05) were used. In these analyses, SEn and DFA from CoPRD assessments were set as ﬁrst-order predictors of Age, while estimates from CoPRV assessments served as second-order predictors. The impetus was to determine whether the amount of variability (r2) accounted for by the second-order models was greater than that of the ﬁrst-order models. If so, this would imply that assessments of differenced CoP improved the ability to account for age-related changes in postural coordination for these measures. For SEn, the second-order model exhibited improvement, F-change (1, 42) = 6.31, p = .02, r2 change = .113, while the second-order model for DFA did not, F-change (1, 42) = .49, p = .07, r2 change = .061. In considering these ﬁndings along with that indicating a signiﬁcant MF-Age relationship when CoPRV, but not CoPRD, was assessed, it appears that differencing slightly improved the ability to detect age-related changes in postural coordination.
A.J. Strang et al. / Gait & Posture 38 (2013) 345–348
Fig. 2. Scatterplots depicting relationships between CoP measures and Age. 2D measures plots (EA and PL) are presented using open triangles (a and b), CoPRD measures with open circles (c, e, g, and i), and CoPRV measures with crosses (d, f, h, and j). Pearson product-moment correlations (r) for each relationship are provided with asterisks (*) denoting signiﬁcant relationship at r-crit two-tailed, df = 43, a = .05 = .294.
A.J. Strang et al. / Gait & Posture 38 (2013) 345–348
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