- Email: [email protected]
Effects of window size on ankle joint stiffness calculation during quiet standing: How the rule changes the result
Journal of Biomechanics 45 (2012) 2301–2305
Contents lists available at SciVerse ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Effects of window size on ankle joint stiffness calculation during quiet standing: How the rule changes the result Andrew W. Smith a,n, Del P. Wong b a b
Department of Health and Physical Education, The Hong Kong Institute of Education, Tai Po, New Territories, Hong Kong Special Administrative Region Technological and Higher Education Institute of Hong Kong (THEi), Hong Kong Special Administrative Region
a r t i c l e i n f o
abstract
Article history: Accepted 12 June 2012
Measuring ankle joint stiffness (AJS) during quiet standing QS using an inverted pendulum model typically involves a single calculation covering the entire period of QS. This study compared AJS using the same 20.0 s set of QS postural sway data but employing seven different calculation windows (0.25 s, 0.5 s, 1.0 s, 2.0 s, 5.0 s, 10.0 s and 20.0 s). AJS was calculated for both anterio-posterior AP and mediolateral ML directions of sway. Postural sway data from 19 subjects were used to calculate mean 7SD and time-normalized AJS over the same 20 s period of QS. Statistical power of this study was 0.99. The AJS had ICCs ranging from 0.47 to 0.85 with coefficient of variations ranging from 11.1% to 31.8%. There were significant differences in AJS between window sizes (P o0.0001) for both directions of sway. Specifically, AJS calculated by 1.0 s windows was significantly larger (P o 0.01) than others, except 0.5 s, while the AJS of the largest two windows 10.0 s and 20.0 s were significantly smaller (P o 0.01) than all others in both directions of sway. In conclusion, it is recommended that 1.0 s windows be used to calculate AJS and that stiffness analyzed as a continuous signal offers a more complete picture of how AJS behaves during QS. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Ankle joint stiffness Calculation Methodology Postural sway
Introduction Many studies of quiet standing (QS) utilize an inverted pendulum model (Winter et al., 1998) that describes how the center of pressure (COP) maintains balance by containing the center of mass (COM) within the base of support (BOS), the motion of which is referred to as postural sway. Ankle joint stiffness (AJS) plays a role in controlling postural sway. Some have proposed that AJS alone may be capable of maintaining upright posture (Winter et al., 1998, 2001, 2003). Others contend that passive AJS alone is insufficient and that QS requires active control (Morasso et al., 1999; Morasso and Schieppati, 1999; Morasso and Sanguineti, 2002; Casadio et al., 2005; Lakie et al., 2003; Edwards, 2007). The large range of reported AJS (90 Nm rad 1 to 800 Nm rad 1; Winter et al., 1998; Loram and Lakie, 2002; Peterka, 2002; Kiemel et al., 2008), leads us to question whether the calculation of AJS is affected by the time period over which the calculation is made. There is no previous study investigating how AJS is calculated and interpreted. Given that QS is not static, it is reasonable to query the appropriateness of calculating AJS as a single, static measure during QS. Consequently, we manipulated systematically
n
Corresponding author. Tel.: þ852 95040168; fax: þ 852 29487848. E-mail address: [email protected] (A.W. Smith).
0021-9290/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2012.06.001
how AJS was calculated using the same set of QS data from normal, healthy subjects. We hypothesized that calculating AJS using shorter sliding calculation windows, would result in values significantly different from a single calculation of AJS using the entire data set. Further, we hypothesized that we would be able to identify a window size that would be most sensitive to the fluctuations in AJS throughout QS.
Methods Nineteen healthy subjects (11 females, 8 males) participated in this study, making a single visit to our laboratory. Our study was conducted according to the Declaration of Helsinki and the protocol was fully approved by the Human Research Ethics Committee. Subjects’ height (1736.37101.0 mm), mass (70.8717.3 kg), and BMI (23.37 4.4 kg m 2) along with five QS trials (30 s) were recorded, the latter using eight video cameras (VICON MX, Oxford, UK) and three force platforms (AMTI, Massachusetts, USA; Kistler, Winterthur, Switzerland) sampled at 100 and 1000 Hz, respectively. We used the VICON Plug-In Gait& lower-body 15-marker model (sacrum and right and left mid-thigh, knee, mid-tibia, lateral malleolus, heel and second metatarsal head markers) plus six markers from the upper body model (right and left shoulder, elbow and wrist markers), defining a 12-segment body model. We calculated kinetics and kinematics including the COM. Motion data were filtered using quintic spline functions (Veldpaus et al., 1988). A VICON BodyBuilder& program calculated sway angles and sway moments of force related to both medio-lateral (ML) and anterio-posterior (AP) sway directions in each trial. Sway angle is the angular displacement from vertical of a vector connecting the mid-point of the right and left ankle joint centers (AJC) and the
2302
A.W. Smith, D.P. Wong / Journal of Biomechanics 45 (2012) 2301–2305
COM. Sway moment of force is the product of the vertical ground reaction force and the horizontal distance from the COP to the AJC. AJS is the slope of the regression of sway moment of force (Nm) on sway angle (rad) and expressed as Nm rad 1. To compare between subjects, AJS data were normalized using each subject’s mass–gravity–height (mgh) product gravitational spring (GS) that is required for viable balance (Winter et al., 1998). Normalized AJS greater than 1.0 indicates that AJS exceeds GS. To explore the effect of calculation window size on AJS, seven different regression window sizes were used. To establish a baseline for comparison to published data, AJS was calculated a single time using all data, i.e., 20.0 s. The same data were used to calculate AJS using window sizes of 0.25 s, 0.50 s, 1.0 s, 2.0 s, 5.0 s, and 10.0 s, resulting in 1976, 1951, 1901, 1801, 1501, and 1001 calculations, respectively. Each calculation window was shifted by 0.01 s between subsequent calculations covering the entire record. The AJS mean and SD as well as the time-normalized AJS signal were determined for each window size. Trials were 30 s in length and all calculations were made during the 5th–25th s of each trial to ensure that subjects were standing as motionless as possible while AJS was calculated. Subject’s mean AJS was calculated as the average of the 5 trials. One-way repeated measures ANOVA was used to examine the differences between window sizes in the ML and AP sway directions, respectively. Pairwise comparisons with Bonferroni adjustment were used when a significant difference was observed. Statistical power was also calculated. Significance level was defined as P r 0.05. The test–retest reliability of each parameter was assessed by intraclass correlation coefficient (ICC), whereas variance was assessed by coefficient of variation (CV). In addition, AJS coefficient of determination R2 was calculated, which gives an estimate of the goodness of fit of AJS to that of a linear spring (R2 ¼ 1.00;Winter et al., 1998). Furthermore, limits of agreement (Altman and Bland, 1983; Bland and Altman, 1986, 1995, 1999, 2007) were used to assess the agreement between the AJS calculation windows.
1. Results Subject data related to the calculation of sway angle and GS were as follows COM height: 1002.7 760.0 mm; AJC height 65.479.3 mm; GS, 655.6 7183.0 kg m2 s 2. The normalized AJS had ICCs ranging from 0.47 to 0.85 with CVs ranging from 6.5% to 22.8% (Table 1). Correlations between all seven calculation methods are shown in Table 2. The comparisons of AJS between the seven window sizes are found in Fig. 1 for the ML and AP directions of sway. Statistical power is 0.99. All means exceeded GS. ANOVA results showed significant differences between all window sizes in both AP (F¼22.4, Po0.0001) and ML (F¼29.4, Po0.0001) sway direction. Pairwise comparisons showed that the AJS value calculated by 1.0 s window size was significantly larger (Po0.01) than all others except 0.5 s in both sway directions, whereas that using 20.0 s window size was significantly smaller (Po0.01) than all other windows in both sway directions. All AJS data are presented in Fig. 2 for both the ML and AP directions of sway. Data are normalized to 100% of the QS trial, with the single AJS value from the 20.0 s window shown for comparison. The limits of agreement are shown in Fig. 3 top: ML direction; bottom: AP direction. The bias line and random error lines representing the 95% limits of agreement are also presented in this figure. Virtually all comparisons fall within 795% limits of agreement.
Table 1 Measurement reliability and variance (N ¼19).
COMz AJCz h GS %COMht
ICC
CV (%)
0.98 1.00 0.97 1.00 1.00
6.1 2.9 6.0 2.6 22.4
Anterio-posterior direction of sway AJS 0.25 s 0.83 0.5 s 0.82 1.0 s 0.79 2.0 s 0.67 5.0 s 0.47 10.0 s 0.51 20.0 s 0.56
SD
19.6 18.2 14.2 9.2 7.4 7.3 6.5
0.26 0.27 0.21 0.12 0.09 0.08 0.07
22.4 21.9 18.9 13.8 10.3 9.7 10.7
0.33 0.36 0.32 0.21 0.13 0.11 0.12
Medio-lateral direction of sway AJS 0.25 s 0.5 s 1.0 s 2.0 s 5.0 s 10.0 s 20.0 s
0.83 0.85 0.83 0.74 0.65 0.62 0.56
CV¼ coefficient of variance;, ICC¼intraclass correlation coefficient;, SD¼standard deviation;, COMz ¼vertical coordinate of COM; AJCz¼ vertical coordinate of the mid-ankle marker; h ¼ vertical distance between COM and AJC; mgh ¼gravitational spring (product of mass, gravity and h); %COMht¼ COM height as a percentage of subject’s height.
Table 2 Normalized AJS Window size correlation matrix (N ¼ 19). Anterio-posterior direction of sway
0.25s 0.5 s 1.0 s 2.0 s 5.0 s 10.0 s 20.0 s
0.25 s
0.5 s
1.0 s
2.0 s
5.0 s
10.0 s
20.0 s
1.00
0.98* 1.00
0.93* 0.97* 1.00
0.80* 0.84* 0.92* 1.00
0.37 0.43 0.51* 0.73* 1.00
0.03 0.03 0.12 0.35 0.83* 1.00
0.19 0.15 0.04 0.23 0.78* 0.92* 1.00
0.82* 0.87* 0.93* 1.00
0.53* 0.56* 0.67* 0.86* 1.00
0.33 0.34 0.44 0.68* 0.92* 1.00
0.24 0.24 0.34 0.53* 0.75* 0.86* 1.00
Medio-lateral direction of sway 0.25 s 1.00 0.98* 0.92* 0.5 s 1.00 0.97* 1.0 s 1.00 2.0 s 5.0 s 10.0 s 20.0 s n
Po 0.05.
Discussion This study aimed to assess the most appropriate way of calculating AJS throughout QS. Our hypotheses are supported in that there were significant differences in AJS between different window sizes with the 1.0 s window being significantly higher than all other windows, except 0.5 s. Using any window size less than 0.5 s or greater than 1.0 s resulted in smaller mean AJS values (Fig. 1). In addition, the 0.5 s and 1.0 s windows resulted in good reliability ICC: AP—0.82 and 0.79, ML—0.85 and 0.83, respectively, which strongly suggests that the optimum window
size is between 0.5 s and 1.0 s for calculating AJS. Since in this experiment, subjects were not consciously focusing on their sway, it would be interesting to see if the optimum AJS would shift in further experiments where subjects are asked to voluntarily manipulate their sway, either by exaggerating it or by consciously trying to suppress it. Paradoxically, there appeared to be an inverse relationship between the reliability of the AJS data and its variability. As shown in Fig. 1, the smaller window sizes were clearly more variable than the larger window sizes. However, the better
A.W. Smith, D.P. Wong / Journal of Biomechanics 45 (2012) 2301–2305
2303
2.5
b
c
a
d
b
c
a d
e
1.5
f
e
f
f
f
0.0
0.25s 0.50s 1.00s 2.00s 5.00s 10.00s 20.00s
R2 = 0.86
R2 = 0.84
R2 = 0.79
R2 = 0.69
R2 = 0.58
R2 = 0.48
R2 = 0.39
R2 = 0.68
R2 = 0.63
R2 = 0.59
R2 = 0.52
R2 = 0.44
0.5
R2 = 0.35
1.0
R2 = 0.26
Ankle Joint Stiffness (normalized)
2.0
0.25s 0.50s 1.00s 2.00s 5.00s 10.00s 20.00s
Anterior-Posterior
Medical-Lateral Swat Direction
Stiffness (normalized)
Stiffness (normalized)
Fig. 1. Comparison of ankle joint stiffness values calculated with different window sizes. R2 values are shown in white. ML¼ normalized stiffness in medio-lateral sway direction. AP ¼ normalized stiffness in anterio-posterior sway direction (GS ¼ 1.0;N ¼ 19: (a) significantly different from 0.5 s, 1.0 s, 10.0 s and 20.0 s, (b) significantly different from 0.25 s, 5.0 s, 10.0 s and 20.0 s, (c) significantly higher than others except for 0.5 s, (d) significantly different from 1.0 s, 5.0 s, 10.0 s and 20.0 s, (e) significantly different from others except 0.25 s, and (f) significantly different from all others).
2.5 2.0 1.5 1.0 0.5 0.0 0
20
AP-0.25s
1.5 1.0 0.5 0.0
ML-0.25s
40 60 Quiet Standing (%) ML-20.0s
80
AP-0.25s
0
1.0 0.5 0.0
ML-0.25s
ML-20.0s
AP-0.25s
80
100 AP-20.0s
20 ML-0.25s
40 60 Quiet Standing (%) ML-20.0s
80
AP-0.25s
100 AP-20.0s
2.5 2.0 1.5 1.0 0.5 0.0 0
20 ML-0.25s
Stiffness (normalized)
1.5
40 60 Quiet Standing (%)
0.5 0.0
AP-20.0s
2.0
20
1.0
100
2.5
0
1.5
AP-20.0s
2.0
20
2.0
100
2.5
0
Stiffness (normalized)
ML-20.0s
80
Stiffness (normalized)
Stiffness (normalized)
ML-0.25s
40 60 Quiet Standing (%)
2.5
40 60 Quiet Standing (%) ML-20.0s
80
AP-0.25s
100 AP-20.0s
2.5 2.0 1.5 1.0 0.5 0.0
0
20 ML-0.25s
40 60 Quiet Standing (%) ML-20.0s
80
AP-0.25s
100 AP-20.0s
Fig. 2. Ankle joint stiffness data (N¼ 19) normalized to 100% of QS calculated using 6 different window sizes compared to the single 20.0 s calculation in both the ML (solid lines) and AP (dashed lines) directions of sway.
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Fig. 3. Limits of agreement of 6 ankle joint stiffness calculation windows showing the pairwise difference between each window size and the 20 s calculation versus the mean ankle joint stiffness (normalized) (N ¼19). 7 95% limits of agreement and bias shown in dotted and dashed lines, respectively.
reliability seen with the smaller window sizes may be, in large part, due to there being more data points available for analysis. For example, AJS calculated using 0.25 s windows had almost twice as much data as the AJS calculation using 10.0 s windows. Our results suggest that previously reported AJS from normal subjects (Winter et al., 1998; Loram and Lakie, 2002; Kiemel et al., 2008; Peterka, 2002) might be affected by the time period over which AJS was calculated. Studies using quite long periods 120 s or more tended to report smaller AJS values (Peterka, 2002) than did studies with shorter periods 30–40 s (Winter et al., 1998; Loram and Lakie, 2002). Until now, AJS has not been considered on a time-series basis. However, as shown in Fig. 2, there may be valuable information garnered from such analysis as it demonstrates the variability of AJS during QS. AJS variability had been noted previously (Winter et al., 1998) but not specifically analyzed as we have done. Analyzing AJS as a continuous signal offers a more complete picture of how AJS behaves during QS.
Conflict of interest statement We hereby stipulate that there were no financial or personal relationships with other people or organizations that inappropriately influenced or biased this work.
Acknowledgments We would like to thank Franciska Ulmer, M.Sc., for her assistance in the collection of these data. References Altman, D.G., Bland, J.M., 1983. Measurement in medicine: the analysis of method comparison studies. The Statistician 32, 307–317. Bland, J.M., Altman, D.G., 1986. Statistical methods for assessing agreement between two methods of clinical measurement. The Lancet 327, 307–310. Bland, J.M., Altman, D.G., 1995. Comparing methods of measurement: why plotting difference against standard method is misleading. The Lancet 346, 1085–1087.
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Bland, J.M., Altman, D.G., 1999. Measuring agreement in method comparison studies. Statistical Methods in Medical Research 8, 135–160. Bland, J.M., Altman, D.G., 2007. Agreement between methods of measurement with multiple observations per individual. Journal of Biopharmaceutical Statistics 17, 571–582. Casadio, M., Morasso, P.G., Sanguineti, V., 2005. Direct measurement of ankle stiffness during quiet standing: implications for control modelling and clinical application. Gait and Posture 21 (4), 410–424. Edwards, W.T., 2007. Effect of joint stiffness on standing stability. Gait and Posture 253, 432–439. Kiemel, T., Elahi, A.J., Jeka, J.J., 2008. Identification of the plant for upright stance in humans: multiple movement patterns from a single neural strategy. Journal of Neurophysiology 1006, 3394–3406. Lakie, M., Caplan, N., Loram, I.D., 2003. Human balancing of an inverted pendulum with a compliant linkage: neural control by anticipatory intermittent bias. Journal of Physiology 551 (Pt 1), 357–370. Loram, I.D., Lakie, M., 2002. Direct measurement of human ankle stiffness during quiet standing: the intrinsic mechanical stiffness is insufficient for stability. Journal of Physiology 5453, 1041–1053.
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Morasso, P.G., Schieppati, M., 1999. Can muscle stiffness alone stabilize upright standing? Journal of Neurophysiology 823, 1622–1626. Morasso, P.G., Sanguineti, V., 2002. Ankle muscle stiffness alone cannot stabilize balance during quiet standing. Journal of Neurophysiology 884, 2157–2162. Morasso, P.G., Baratto, L., Capra, R., Spada, G., 1999. Internal models in the control of posture. Neural Networks 127-8, 1173–1180. Peterka, R.J., 2002. Sensorimotor integration in human postural control. Journal of Neurophysiology 883, 1097–1118. Veldpaus, F.E., Woltring, H.J., Dortmans, L.J., 1988. A least-squares algorithm for the equiform transformation from spatial marker co-ordinates. Journal of Biomechanics 21, 45–54. Winter, D.A., Patla, A.E., Prince, F., Ishac, M., Gielo-Perczak, K., 1998. Stiffness control of balance in quiet standing. Journal of Neurophysiology 803, 1211–1221. Winter, D.A., Patla, A.E., Rietdyk, S., Ishac, M., 2001. Ankle muscle stiffness in the control of balance during quiet standing. Journal of Neurophysiology 856, 2630–2633. Winter, D.A., Patla, A.E., Ishac, M., Gage, W.H., 2003. Motor mechanisms of balance during quiet standing. Journal Electromyography and Kinesiology 131, 49–56.
Contents lists available at SciVerse ScienceDirect
Journal of Biomechanics journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com
Short communication
Effects of window size on ankle joint stiffness calculation during quiet standing: How the rule changes the result Andrew W. Smith a,n, Del P. Wong b a b
Department of Health and Physical Education, The Hong Kong Institute of Education, Tai Po, New Territories, Hong Kong Special Administrative Region Technological and Higher Education Institute of Hong Kong (THEi), Hong Kong Special Administrative Region
a r t i c l e i n f o
abstract
Article history: Accepted 12 June 2012
Measuring ankle joint stiffness (AJS) during quiet standing QS using an inverted pendulum model typically involves a single calculation covering the entire period of QS. This study compared AJS using the same 20.0 s set of QS postural sway data but employing seven different calculation windows (0.25 s, 0.5 s, 1.0 s, 2.0 s, 5.0 s, 10.0 s and 20.0 s). AJS was calculated for both anterio-posterior AP and mediolateral ML directions of sway. Postural sway data from 19 subjects were used to calculate mean 7SD and time-normalized AJS over the same 20 s period of QS. Statistical power of this study was 0.99. The AJS had ICCs ranging from 0.47 to 0.85 with coefficient of variations ranging from 11.1% to 31.8%. There were significant differences in AJS between window sizes (P o0.0001) for both directions of sway. Specifically, AJS calculated by 1.0 s windows was significantly larger (P o 0.01) than others, except 0.5 s, while the AJS of the largest two windows 10.0 s and 20.0 s were significantly smaller (P o 0.01) than all others in both directions of sway. In conclusion, it is recommended that 1.0 s windows be used to calculate AJS and that stiffness analyzed as a continuous signal offers a more complete picture of how AJS behaves during QS. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Ankle joint stiffness Calculation Methodology Postural sway
Introduction Many studies of quiet standing (QS) utilize an inverted pendulum model (Winter et al., 1998) that describes how the center of pressure (COP) maintains balance by containing the center of mass (COM) within the base of support (BOS), the motion of which is referred to as postural sway. Ankle joint stiffness (AJS) plays a role in controlling postural sway. Some have proposed that AJS alone may be capable of maintaining upright posture (Winter et al., 1998, 2001, 2003). Others contend that passive AJS alone is insufficient and that QS requires active control (Morasso et al., 1999; Morasso and Schieppati, 1999; Morasso and Sanguineti, 2002; Casadio et al., 2005; Lakie et al., 2003; Edwards, 2007). The large range of reported AJS (90 Nm rad 1 to 800 Nm rad 1; Winter et al., 1998; Loram and Lakie, 2002; Peterka, 2002; Kiemel et al., 2008), leads us to question whether the calculation of AJS is affected by the time period over which the calculation is made. There is no previous study investigating how AJS is calculated and interpreted. Given that QS is not static, it is reasonable to query the appropriateness of calculating AJS as a single, static measure during QS. Consequently, we manipulated systematically
n
Corresponding author. Tel.: þ852 95040168; fax: þ 852 29487848. E-mail address: [email protected] (A.W. Smith).
0021-9290/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2012.06.001
how AJS was calculated using the same set of QS data from normal, healthy subjects. We hypothesized that calculating AJS using shorter sliding calculation windows, would result in values significantly different from a single calculation of AJS using the entire data set. Further, we hypothesized that we would be able to identify a window size that would be most sensitive to the fluctuations in AJS throughout QS.
Methods Nineteen healthy subjects (11 females, 8 males) participated in this study, making a single visit to our laboratory. Our study was conducted according to the Declaration of Helsinki and the protocol was fully approved by the Human Research Ethics Committee. Subjects’ height (1736.37101.0 mm), mass (70.8717.3 kg), and BMI (23.37 4.4 kg m 2) along with five QS trials (30 s) were recorded, the latter using eight video cameras (VICON MX, Oxford, UK) and three force platforms (AMTI, Massachusetts, USA; Kistler, Winterthur, Switzerland) sampled at 100 and 1000 Hz, respectively. We used the VICON Plug-In Gait& lower-body 15-marker model (sacrum and right and left mid-thigh, knee, mid-tibia, lateral malleolus, heel and second metatarsal head markers) plus six markers from the upper body model (right and left shoulder, elbow and wrist markers), defining a 12-segment body model. We calculated kinetics and kinematics including the COM. Motion data were filtered using quintic spline functions (Veldpaus et al., 1988). A VICON BodyBuilder& program calculated sway angles and sway moments of force related to both medio-lateral (ML) and anterio-posterior (AP) sway directions in each trial. Sway angle is the angular displacement from vertical of a vector connecting the mid-point of the right and left ankle joint centers (AJC) and the
2302
A.W. Smith, D.P. Wong / Journal of Biomechanics 45 (2012) 2301–2305
COM. Sway moment of force is the product of the vertical ground reaction force and the horizontal distance from the COP to the AJC. AJS is the slope of the regression of sway moment of force (Nm) on sway angle (rad) and expressed as Nm rad 1. To compare between subjects, AJS data were normalized using each subject’s mass–gravity–height (mgh) product gravitational spring (GS) that is required for viable balance (Winter et al., 1998). Normalized AJS greater than 1.0 indicates that AJS exceeds GS. To explore the effect of calculation window size on AJS, seven different regression window sizes were used. To establish a baseline for comparison to published data, AJS was calculated a single time using all data, i.e., 20.0 s. The same data were used to calculate AJS using window sizes of 0.25 s, 0.50 s, 1.0 s, 2.0 s, 5.0 s, and 10.0 s, resulting in 1976, 1951, 1901, 1801, 1501, and 1001 calculations, respectively. Each calculation window was shifted by 0.01 s between subsequent calculations covering the entire record. The AJS mean and SD as well as the time-normalized AJS signal were determined for each window size. Trials were 30 s in length and all calculations were made during the 5th–25th s of each trial to ensure that subjects were standing as motionless as possible while AJS was calculated. Subject’s mean AJS was calculated as the average of the 5 trials. One-way repeated measures ANOVA was used to examine the differences between window sizes in the ML and AP sway directions, respectively. Pairwise comparisons with Bonferroni adjustment were used when a significant difference was observed. Statistical power was also calculated. Significance level was defined as P r 0.05. The test–retest reliability of each parameter was assessed by intraclass correlation coefficient (ICC), whereas variance was assessed by coefficient of variation (CV). In addition, AJS coefficient of determination R2 was calculated, which gives an estimate of the goodness of fit of AJS to that of a linear spring (R2 ¼ 1.00;Winter et al., 1998). Furthermore, limits of agreement (Altman and Bland, 1983; Bland and Altman, 1986, 1995, 1999, 2007) were used to assess the agreement between the AJS calculation windows.
1. Results Subject data related to the calculation of sway angle and GS were as follows COM height: 1002.7 760.0 mm; AJC height 65.479.3 mm; GS, 655.6 7183.0 kg m2 s 2. The normalized AJS had ICCs ranging from 0.47 to 0.85 with CVs ranging from 6.5% to 22.8% (Table 1). Correlations between all seven calculation methods are shown in Table 2. The comparisons of AJS between the seven window sizes are found in Fig. 1 for the ML and AP directions of sway. Statistical power is 0.99. All means exceeded GS. ANOVA results showed significant differences between all window sizes in both AP (F¼22.4, Po0.0001) and ML (F¼29.4, Po0.0001) sway direction. Pairwise comparisons showed that the AJS value calculated by 1.0 s window size was significantly larger (Po0.01) than all others except 0.5 s in both sway directions, whereas that using 20.0 s window size was significantly smaller (Po0.01) than all other windows in both sway directions. All AJS data are presented in Fig. 2 for both the ML and AP directions of sway. Data are normalized to 100% of the QS trial, with the single AJS value from the 20.0 s window shown for comparison. The limits of agreement are shown in Fig. 3 top: ML direction; bottom: AP direction. The bias line and random error lines representing the 95% limits of agreement are also presented in this figure. Virtually all comparisons fall within 795% limits of agreement.
Table 1 Measurement reliability and variance (N ¼19).
COMz AJCz h GS %COMht
ICC
CV (%)
0.98 1.00 0.97 1.00 1.00
6.1 2.9 6.0 2.6 22.4
Anterio-posterior direction of sway AJS 0.25 s 0.83 0.5 s 0.82 1.0 s 0.79 2.0 s 0.67 5.0 s 0.47 10.0 s 0.51 20.0 s 0.56
SD
19.6 18.2 14.2 9.2 7.4 7.3 6.5
0.26 0.27 0.21 0.12 0.09 0.08 0.07
22.4 21.9 18.9 13.8 10.3 9.7 10.7
0.33 0.36 0.32 0.21 0.13 0.11 0.12
Medio-lateral direction of sway AJS 0.25 s 0.5 s 1.0 s 2.0 s 5.0 s 10.0 s 20.0 s
0.83 0.85 0.83 0.74 0.65 0.62 0.56
CV¼ coefficient of variance;, ICC¼intraclass correlation coefficient;, SD¼standard deviation;, COMz ¼vertical coordinate of COM; AJCz¼ vertical coordinate of the mid-ankle marker; h ¼ vertical distance between COM and AJC; mgh ¼gravitational spring (product of mass, gravity and h); %COMht¼ COM height as a percentage of subject’s height.
Table 2 Normalized AJS Window size correlation matrix (N ¼ 19). Anterio-posterior direction of sway
0.25s 0.5 s 1.0 s 2.0 s 5.0 s 10.0 s 20.0 s
0.25 s
0.5 s
1.0 s
2.0 s
5.0 s
10.0 s
20.0 s
1.00
0.98* 1.00
0.93* 0.97* 1.00
0.80* 0.84* 0.92* 1.00
0.37 0.43 0.51* 0.73* 1.00
0.03 0.03 0.12 0.35 0.83* 1.00
0.19 0.15 0.04 0.23 0.78* 0.92* 1.00
0.82* 0.87* 0.93* 1.00
0.53* 0.56* 0.67* 0.86* 1.00
0.33 0.34 0.44 0.68* 0.92* 1.00
0.24 0.24 0.34 0.53* 0.75* 0.86* 1.00
Medio-lateral direction of sway 0.25 s 1.00 0.98* 0.92* 0.5 s 1.00 0.97* 1.0 s 1.00 2.0 s 5.0 s 10.0 s 20.0 s n
Po 0.05.
Discussion This study aimed to assess the most appropriate way of calculating AJS throughout QS. Our hypotheses are supported in that there were significant differences in AJS between different window sizes with the 1.0 s window being significantly higher than all other windows, except 0.5 s. Using any window size less than 0.5 s or greater than 1.0 s resulted in smaller mean AJS values (Fig. 1). In addition, the 0.5 s and 1.0 s windows resulted in good reliability ICC: AP—0.82 and 0.79, ML—0.85 and 0.83, respectively, which strongly suggests that the optimum window
size is between 0.5 s and 1.0 s for calculating AJS. Since in this experiment, subjects were not consciously focusing on their sway, it would be interesting to see if the optimum AJS would shift in further experiments where subjects are asked to voluntarily manipulate their sway, either by exaggerating it or by consciously trying to suppress it. Paradoxically, there appeared to be an inverse relationship between the reliability of the AJS data and its variability. As shown in Fig. 1, the smaller window sizes were clearly more variable than the larger window sizes. However, the better
A.W. Smith, D.P. Wong / Journal of Biomechanics 45 (2012) 2301–2305
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2.5
b
c
a
d
b
c
a d
e
1.5
f
e
f
f
f
0.0
0.25s 0.50s 1.00s 2.00s 5.00s 10.00s 20.00s
R2 = 0.86
R2 = 0.84
R2 = 0.79
R2 = 0.69
R2 = 0.58
R2 = 0.48
R2 = 0.39
R2 = 0.68
R2 = 0.63
R2 = 0.59
R2 = 0.52
R2 = 0.44
0.5
R2 = 0.35
1.0
R2 = 0.26
Ankle Joint Stiffness (normalized)
2.0
0.25s 0.50s 1.00s 2.00s 5.00s 10.00s 20.00s
Anterior-Posterior
Medical-Lateral Swat Direction
Stiffness (normalized)
Stiffness (normalized)
Fig. 1. Comparison of ankle joint stiffness values calculated with different window sizes. R2 values are shown in white. ML¼ normalized stiffness in medio-lateral sway direction. AP ¼ normalized stiffness in anterio-posterior sway direction (GS ¼ 1.0;N ¼ 19: (a) significantly different from 0.5 s, 1.0 s, 10.0 s and 20.0 s, (b) significantly different from 0.25 s, 5.0 s, 10.0 s and 20.0 s, (c) significantly higher than others except for 0.5 s, (d) significantly different from 1.0 s, 5.0 s, 10.0 s and 20.0 s, (e) significantly different from others except 0.25 s, and (f) significantly different from all others).
2.5 2.0 1.5 1.0 0.5 0.0 0
20
AP-0.25s
1.5 1.0 0.5 0.0
ML-0.25s
40 60 Quiet Standing (%) ML-20.0s
80
AP-0.25s
0
1.0 0.5 0.0
ML-0.25s
ML-20.0s
AP-0.25s
80
100 AP-20.0s
20 ML-0.25s
40 60 Quiet Standing (%) ML-20.0s
80
AP-0.25s
100 AP-20.0s
2.5 2.0 1.5 1.0 0.5 0.0 0
20 ML-0.25s
Stiffness (normalized)
1.5
40 60 Quiet Standing (%)
0.5 0.0
AP-20.0s
2.0
20
1.0
100
2.5
0
1.5
AP-20.0s
2.0
20
2.0
100
2.5
0
Stiffness (normalized)
ML-20.0s
80
Stiffness (normalized)
Stiffness (normalized)
ML-0.25s
40 60 Quiet Standing (%)
2.5
40 60 Quiet Standing (%) ML-20.0s
80
AP-0.25s
100 AP-20.0s
2.5 2.0 1.5 1.0 0.5 0.0
0
20 ML-0.25s
40 60 Quiet Standing (%) ML-20.0s
80
AP-0.25s
100 AP-20.0s
Fig. 2. Ankle joint stiffness data (N¼ 19) normalized to 100% of QS calculated using 6 different window sizes compared to the single 20.0 s calculation in both the ML (solid lines) and AP (dashed lines) directions of sway.
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Fig. 3. Limits of agreement of 6 ankle joint stiffness calculation windows showing the pairwise difference between each window size and the 20 s calculation versus the mean ankle joint stiffness (normalized) (N ¼19). 7 95% limits of agreement and bias shown in dotted and dashed lines, respectively.
reliability seen with the smaller window sizes may be, in large part, due to there being more data points available for analysis. For example, AJS calculated using 0.25 s windows had almost twice as much data as the AJS calculation using 10.0 s windows. Our results suggest that previously reported AJS from normal subjects (Winter et al., 1998; Loram and Lakie, 2002; Kiemel et al., 2008; Peterka, 2002) might be affected by the time period over which AJS was calculated. Studies using quite long periods 120 s or more tended to report smaller AJS values (Peterka, 2002) than did studies with shorter periods 30–40 s (Winter et al., 1998; Loram and Lakie, 2002). Until now, AJS has not been considered on a time-series basis. However, as shown in Fig. 2, there may be valuable information garnered from such analysis as it demonstrates the variability of AJS during QS. AJS variability had been noted previously (Winter et al., 1998) but not specifically analyzed as we have done. Analyzing AJS as a continuous signal offers a more complete picture of how AJS behaves during QS.
Conflict of interest statement We hereby stipulate that there were no financial or personal relationships with other people or organizations that inappropriately influenced or biased this work.
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