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Using detrended fluctuation analysis (DFA) to analyze whether vibratory insoles enhance balance stability for elderly fallers
Archives of Gerontology and Geriatrics 55 (2012) 673–676
Contents lists available at SciVerse ScienceDirect
Archives of Gerontology and Geriatrics journal homepage: www.elsevier.com/locate/archger
Using detrended fluctuation analysis (DFA) to analyze whether vibratory insoles enhance balance stability for elderly fallers Chien-Chih Wang *, Wen-Hung Yang Department of Industrial Engineering and Management, Ming Chi University of Technology, New Taipei City 243, Taiwan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 6 July 2011 Received in revised form 16 November 2011 Accepted 20 November 2011 Available online 12 December 2011
Falls are a common and devastating problem among elderly people. In a previous study, vibratory insoles were developed to improve postural stability for elderly fallers. To verify the effects of vibratory insoles, a two-stage experiment was conducted to collect center of pressure (COP) signals from 26 elderly fallers and 16 healthy young subjects while standing still. The DFA is used to analyze the behavior of different time-series data obtained from the trajectory of COP. Postural stability was compared by the DFA scaling exponent between a control condition (before using vibratory insoles) and a vibration condition (after using vibratory insoles). For elderly fallers, DFA scaling exponents 95% confidence interval were [1.434, 1.547] and [1.329, 1.451] under control and vibration conditions in the anteroposterior (AP) direction, respectively. The experimental results revealed that temporary stimuli of appropriate amplitude produced by vibration insoles enhanced postural stability in elderly fallers and was more obvious in the AP direction. ß 2011 Elsevier Ireland Ltd. All rights reserved.
Keywords: COP Time series Scaling exponent Temporary stimuli
1. Introduction A fall is a common accident that happens more often to elderly people, and it is associated with chronic deterioration in the neuromuscular and sensory systems. Sensory feedback is necessary for postural adjustments and facilitates to control of compensatory stepping reactions evoked by postural perturbation. Recent studies have explored the effects of mechanical stimulations on static balance to enhance postural feedback (Park et al., 2004). The stimulations are complex and depend on the frequency, amplitude and location of the stimulation (Kavounoudias et al., 2001). Foot pressure activates plantar mechanoreceptors that mediate postural adjustment during the stance phases of the step (Laughton et al., 2003; Novak and Novak, 2006). Application of subsensory noise to the feet has been demonstrated to improve postural stability in elderly fallers (Costa et al., 2007). The above studies have indicated that stimulations near the feet are able to improve postural control and stability in elderly fallers while they are standing still. This issue is being explored through various experimental and analytical techniques. The human postural-control system integrates various mechanisms that prevent the human body from falling in both static and dynamic conditions. The main tool used to investigate this complex balance system is the stabilogram, which measures
* Corresponding author. Tel.: +886 2 29089899x3106; fax: +886 2 2908 5900. E-mail address: [email protected] (C.-C. Wang). 0167-4943/$ – see front matter ß 2011 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.archger.2011.11.008
the time behavior of the COP of a person standing on top of a force platform. The COP signal, which can be used as a measure of postural stability, is measured in the horizontal plane in both the anteroposterior (AP) and mediolateral (ML) directions. Fig. 1(a) illustrates the displacement of the COP signal, and (b) and (c) show displacement in the AP and ML directions over time, respectively. The dynamic characteristics of COP are of fundamental importance even in the case of quiet standing, and a large number of recent studies, mostly in the last decade, have focused on the analysis of the non-stationary time properties of COP. In recent years, the DFA method (Peng et al., 1994) has become a widely used technique for the determination of (mono-) fractal scaling properties and detection of long-range correlations in noisy, non-stationary time series (Hu et al., 2001). One reason to employ the DFA method is to avoid spurious detection of correlations that are artifacts of non-stationarities in the time series. It has been successfully applied to the diverse field such as DNA sequences (Buldyrev et al., 1995), heart rate dynamics (Ashkenazy et al., 2001), and human gait (Liu et al., 1999), posture (Duarte and Sternad, 2008; Lin et al., 2008) and Parkinson’s disease (Minamisawa et al., 2009). Duarte assessed aging changes in postural sway using fractal and complexity and complexity measures of the COP during prolonged standing. The analysis results were showed that complexity in the human physiological system decreases with aging (Duarte and Sternad, 2008). Lin et al. (2008) assessed within and between day reliability of both COP measures of postural sway. Reliability of each COP measure was quantified using intraclass
C.-C. Wang, W.-H. Yang / Archives of Gerontology and Geriatrics 55 (2012) 673–676
Anteroposterior (mm)
a
20
b
10
AP(mm)
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0
-20 0
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c
20
40
60
40
60
20
-20 -20
ML(mm)
-10
-10
0
10
0
20
Mediolateral (mm)
-20 0
20
time(s) Fig. 1. COP signal and time series in AP and ML directions. (a) COP signal. (b) AP direction time-series data. (c) ML direction time-series data.
correlation coefficient and standard error of measurement. From the analysis result, DFA exponents were relatively more reliable than Hurst rescaled range analysis. Minamisawa et al. (2009) applied DFA to COP data from Parkinson’s disease and healthy elderly persons. They showed a significant difference in the crossover point dividing the short and long term fluctuation. The important assumption of this study is that elderly fallers can effectively improve postural stability through plantar vibratory stimulations. For this reason, vibratory insoles based on stochastic resonance were designed to produce physical stimulation to the soles of the feet (Yang, 2010). When a faint background of random pulses could amplify weak signals sent from the feat to the brain. The stochastic resonance is the effect of boost weak signals by noise. Therefore, if the original postural orientation signal is too weak for the poorly performing sensory system (mechanoreceptors) of the elderly subject, the addition of a noise component (vibrating insole) can increase the strength of the total signal above a detection threshold and thus enable a postural adjustment reaction. In this paper, the objectives are to understand the effects of vibratory insoles on improving postural stability and compare the variability of the DFA scaling exponents before and after using vibratory insoles in both elderly fallers and healthy young subjects. Through a standing still experiment and the DFA scaling exponent calculation, the effects of vibratory insoles are discussed for elderly fallers and healthy young subjects. 2. Materials and methods To verify the effects of vibratory insoles, a two-stage experiment (before and after using vibratory insoles) was conducted to measure COP signals for elderly fallers and healthy young subjects while standing still. A DFA technique used to analyze COP signals and the scaling exponent was adopted to evaluate the effect. 2.1. Design of vibratory insoles Vibratory insoles based on stochastic resonance were designed to enhance the postural stability for elderly fallers (Yang, 2010). For the design of vibratory insoles, assumption the ability of an individual to detect a sub-threshold tactile stimulus can be significantly enhanced by the presence of a particular, nonzero level of noise. Sub-sensory mechanical noise was applied to the soles of the feet via vibrating insoles. The vibration as a kind of noise and controlled the degree of vibration intensity via the variable resistor and calculate the electric power of vibratory shoes as a noise according to the different degree of noise. The vibratory
shoes the variable resistor, in according to the feelings of each subject to adjust the degree of vibration intensity, so that the vibratory shoes can be the effect of the physical sense of the balance system. There are six vibratory degree 0 V, 10 V, 20 V, 30 V, 40 V, and 50 V can be adjusted on these shoes. 0 V is represented the maximal vibratory strength and 50 V is indicated the minimal one. Fig. 2(a) shows that three eccentric vibratory motors were embedded in the insoles. The vibratory insoles were installed inside the shoes, and the shoes are shown in Fig. 2(b). 2.2. Experiment and COP signal collection The subjects were 26 elderly fallers with mobility in a longterm care center with an average age of 83.3 4.8 years and 16 healthy young people with an average age of 25.2 3.8 years. The local ethics committee approved this experiment and written informed consent was obtained from all subjects. COP signals were obtained from a force plate (CATSYS 20001) with a signal sampling frequency of 40 Hz. The experimental process was divided into two stages. Stage 1: Due to the short duration of available recordings, this study focused on COP fluctuations that can be accounted for by regulatory mechanisms operating over a short time. Subjects were asked to take off their shoes and stand on a force plate with their eyes open for 65 s to complete a COP signal measurement before using the vibratory shoes. This stage was defined as the control condition. The subjects rested for 1 min before moving on to stage 2. Stage 2: The subjects wore the vibratory shoes, and the assistant activated the vibratory device. The eccentric vibratory motors delivered slight vibratory stimuli to the soles of the feet. The assistant determined the acceptable vibratory strength by adjusting it randomly while asking the subjects if they felt any discomfort or pain. After adjusting the vibratory strength, a nurse accompanied the subjects on a 10-min walk. The 10-min walking test was believed to reflect activities of daily living (Olsson et al., 2005; Yang, 2010). However, if subjects felt uncomfortable, the vibratory strength was adjusted. After walking for 10 min, the assistant turned off the vibratory motors. After resting for 1 min, the subjects took off the shoes and stood still on the force plate for 65 s to complete the COP signal measurement after using the vibratory shoes. In this study, stage 2 was defined as the vibration condition in comparison to the control condition of stage 1.
C.-C. Wang, W.-H. Yang / Archives of Gerontology and Geriatrics 55 (2012) 673–676
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Fig. 2. Components of (a) vibratory insoles (Yang, 2010) and (b) vibratory shoes (Yang, 2010).
2.3. DFA DFA (Peng et al., 1994) is a scaling analysis technique used to provide a simple quantitative parameter (scaling exponent) to represent the correlation properties of a signal. DFA is advantageous because it can systematically eliminate trends of various orders caused by external effects and reduce noise caused by imperfect measurement. To illustrate a DFA algorithm, an elderly faller COP series in the AP direction is shown in Fig. 3(a) as an example. The DFA procedure is described as follows: Step 1: Briefly, the COP series (of total length N) is first integrated as follows: yðkÞ ¼
k X ¯ ½XðtÞ X
(1)
t¼1
where X(t) is the sequence at time t, and X¯ is the average of the entire time series. Step 2: Next, the integrated time series y(k) is divided into subsequences of equal length n. In each box of length n, a leastsquares line is fit to the data (representing the trend in that box) (see Fig. 3(b)). The y-coordinate of the straight line segment is denoted by yn(k).
Step 3: We detrend the integrated time series y(k) by subtracting the local trend yn(k) in each box. The root-mean square fluctuation of this integrated and detrended time series is calculated as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X 2 (2) ½yðkÞ yn ðkÞ FðnÞ ¼ t N k¼1 The computation is repeated over all time scales (box sizes) to provide a relationship between F(n), the average fluctuation as a function of box size, and box size n (such as the number of positions in a box that is the window of observation). Typically, F(n) will increase with box size n. According to the recommendations made by Peng et al. (1994), the range nmin ffi 5 and nmax ffi N/4 may be selected. Step 4: A linear relationship on a log–log graph indicates the presence of scaling. Under such conditions, the fluctuations can be characterized by the scaling exponent (a), which is the slope of the line relating log10F(n) to log10 n (Fig. 3(c)). If the signal behaves as the fraction Gaussian noise, a range from 0 to 2; if the signal behaves as the fraction Brownian, a range from 0 to 1. a = 0.5 indicates that the changes in the values of a time series are random. When a < 0.5 the signal is anti-persistent, while a > 0.5 indicate positive persistency in the signal (Lin et al., 2008).
Fig. 3. DFA algorithm and scaling exponent (a). (a) Original signal. COP series of the AP direction X(t) of 2400 data points. (b) Integrated signal. Integrated time series y(k). The vertical block dashed lines indicate a box of size n = 200, and the red solid straight lines represent the ‘trend’ estimated in each box by a least-squares fit. (c) DFA scaling exponent (a) for the signal shown in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
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C.-C. Wang, W.-H. Yang / Archives of Gerontology and Geriatrics 55 (2012) 673–676
Table 1 Comparisons of the DFA scaling exponent (a) between the control and vibration conditions for elderly fallers and healthy young subjects for 65 s after starting the experiment. DFA scaling exponent (a)
Control Vibration p-Value control vs. vibration
Elderly fallers 95% confidence interval
Healthy young 95% confidence interval
ML
AP
ML
AP
[1.322,1.419] [1.255,1.385] 0.18
[1.292,1.389] [1.199,1321] 0.08
[0.924,1.116] [1.019,1.201] 0.164
[0.853,0.927] [0.830,0.969] 0.68
Table 2 Comparisons of the DFA scaling exponent (a) between the control and vibration conditions for elderly fallers and healthy young subjects for 30 s after starting the experiment. DFA scaling exponent (a)
Control Vibration p-Value control vs. vibration
Elderly fallers 95% confidence interval
Healthy young 95% confidence interval
ML
AP
ML
AP
[1.522,1.619] [1.465,1.595] 0.16
[1.434,1.547] [1.329,1.451] 0.009
[1.285,1.455] [1.349,1.531] 0.26
[1.201,1.319] [1.127,1.233] 0.07
Some difference exists regarding how these exponents are to be practically interpreted. However, Collins et al. (1995) have suggested that greater persistence of the COP series is correlated with increased muscle activity and a decline in postural stability. Greater anti-persistence has been suggested to reflect a more tightly controlled postural system (Amoud et al., 2007). Therefore, the DFA scaling exponent (a) was adopted to compare the effect of using vibratory insoles. 3. Results To understand the effects of vibratory insoles on improving postural stability, the variability of the DFA scaling exponents (a) is compared before and after using the vibratory insoles in both elderly fallers and healthy young subjects. Due to the short experimental time to use the vibratory insoles (only 10 min), the stability improving effects may not continue. Hence, two types of signal length are discussed between the entire signals (for 65 s) and the signals of 30 s after starting the experiment. Tables 1 and 2 present comparisons of the DFA scaling exponent (a) between the control and vibration conditions for elderly fallers and healthy young subjects for 65 s and 30 s after starting the experiment, respectively. The two-sample t-test was used to test whether the population mean was significantly different. For 65 s, elderly fallers and healthy young subjects showed no statistically significant differences in the DFA scaling exponent values between the control and vibration conditions (Table 1). However, for 30 s after starting the experiment, elderly fallers showed statistically significant differences (p-value = 0.009) in the DFA scaling exponent values between the control and vibration conditions in the AP direction (Table 2). This result indicated that the foot stimulation caused by the vibratory insoles improved postural stability for elderly fallers while standing still. The healthy young subjects showed no significant differences in the DFA scaling exponent values between the control and vibration conditions for 30 s after starting the experiment (Table 2). 4. Conclusions This study emphasized the COP data analysis instead of the vibratory insole’s design. Based on the DFA concept, the experimental results revealed that the scaling exponent values for elderly fallers after using the vibratory insoles were significantly larger than those before using the vibratory insoles. This finding indicates that temporary stimuli of appropriate amplitude produced by the vibratory insoles are essential for enhancing balance in elderly fallers, especially in the AP direction, for a short time duration (30 s). However, postural stability was not significantly increased in
healthy young subjects by using vibratory insoles. For 65 s, the postural stability for elderly fallers and healthy young subjects showed no statistically significant increase by using the vibratory insoles. We will focus on finding hidden and important information about the complex fluctuation of the COP series and enhance the vibratory insole’s design in future studies. Conflict of interest statement None. References Amoud, H., Abadi, M., Hewson, D.J., Michel-Pellegrino, V., Doussot, M., Duchene, J., 2007. Fractal time series analysis of postural stability in elderly and control subjects. J. NeuroEng. Rehabil. 4, 1–12. Ashkenazy, Y., Ivanov, P.C., Havlin, S., Peng, C.K., Goldberger, A.L., Stanley, H.E., 2001. Magnitude and sign correlations in heartbeat fluctuations. Phys. Rev. Lett. 86, 1900–1903. Buldyrev, S.V., Goldberger, A.L., Havlin, S., Mantegna, R.N., Matsa, M.E., Peng, C.K., Simons, M., Stanley, H.E., 1995. Long-range correlation properties of coding and noncoding DNA sequence. Phys. Rev. E 51, 5084–5091. Collins, J.J., De Luca, C.J., Burrows, A., Lipsitz, L.A., 1995. Age-related changes in open-loop and closed-loop postural control mechanisms. Exp. Brain Res. 104, 480–492. Costa, M., Priplata, A.A., Lipsitz, L., Wu, A.Z., Huang, N.E., Goldberger, A.L., Peng, C.K., 2007. Noise and poise: enhancement of postural complexity in the elderly with a stochastic-resonance-based therapy. Europhys. Lett. 77, 68008. Duarte, M., Sternad, D., 2008. Complexity of human postural control in young and older adults during prolonged standing. Exp. Brain Res. 191, 265–276. Hu, K., Ivanov, P.C., Chen, Z., Carpena, P., Stanley, H.E., 2001. Effect of trends on detrended fluctuation analysis. Phys. Rev. E 64, 011114. Kavounoudias, A., Roll, R., Roll, J.P., 2001. Foot sole and ankle muscle inputs contribute jointly to human erect posture regulation. J. Physiol. 532, 869–878. Laughton, C.A., Slavin, M., Katdare, K., Nolan, L., Bean, J.F., Kerrigan, D.C., Phillips, E., Lipsitz, L.A., Collins, K.J., 2003. Aging, muscle activity, and balance control: physiological changes associated with balance impairment. Gait Posture 18, 101–108. Lin, D., Soel, H., Nussbaum, M.A., Madigan, M.L., 2008. Reliability of COP-based postural sway measures and age-related differences. Gait Posture 28, 337–342. Liu, Y., Gopikrishnan, P., Cizeau, P., Meyer, M., Peng, C.K., Stanley, H.E., 1999. Statistical properties of the volatility of price fluctuations. Phys. Rev. E 60, 1390–1400. Minamisawa, T., Takakura, K., Yamaguchi, T., 2009. Detrended fluctuation analysis of temporal variation of the center of pressure (COP) during quiet standing in Parkinsonian patients. J. Phys. Ther. Sci. 21, 287–292. Novak, P., Novak, V., 2006. Effect of step-synchronized vibration stimulation of soles on gait in Parkinson’s disease: a pilot study. J. NeuroEng. Rehabil. 3, 1–7. Olsson, L.G., Swedberg, K., Clark, A.L., Witte, K.K., Cleland, J.G.F., 2005. Six minute corridor walk test as an outcome measure for the assessment of treatment in randomized, blinded intervention trials of chronic heart failure: a systematic review. Eur. Heart J. 26, 778–793. Park, S., Horak, F.B., Kuo, A.D., 2004. Postural feedback responses scale with biomechanical constraints in human standing. Exp. Brain Res. 154, 417–427. Peng, C.K., Buldyrev, S.V., Havlin, Simons, S.M., Stanley, H.E., Goldberger, A.L., 1994. Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 1685–1689. Yang, W.H., 2010. Data mining on physiological signal—integrate dissimilarity approach and signal reconstruction for complexity analysis. Dissertation. Yuan Ze University.
Contents lists available at SciVerse ScienceDirect
Archives of Gerontology and Geriatrics journal homepage: www.elsevier.com/locate/archger
Using detrended fluctuation analysis (DFA) to analyze whether vibratory insoles enhance balance stability for elderly fallers Chien-Chih Wang *, Wen-Hung Yang Department of Industrial Engineering and Management, Ming Chi University of Technology, New Taipei City 243, Taiwan
A R T I C L E I N F O
A B S T R A C T
Article history: Received 6 July 2011 Received in revised form 16 November 2011 Accepted 20 November 2011 Available online 12 December 2011
Falls are a common and devastating problem among elderly people. In a previous study, vibratory insoles were developed to improve postural stability for elderly fallers. To verify the effects of vibratory insoles, a two-stage experiment was conducted to collect center of pressure (COP) signals from 26 elderly fallers and 16 healthy young subjects while standing still. The DFA is used to analyze the behavior of different time-series data obtained from the trajectory of COP. Postural stability was compared by the DFA scaling exponent between a control condition (before using vibratory insoles) and a vibration condition (after using vibratory insoles). For elderly fallers, DFA scaling exponents 95% confidence interval were [1.434, 1.547] and [1.329, 1.451] under control and vibration conditions in the anteroposterior (AP) direction, respectively. The experimental results revealed that temporary stimuli of appropriate amplitude produced by vibration insoles enhanced postural stability in elderly fallers and was more obvious in the AP direction. ß 2011 Elsevier Ireland Ltd. All rights reserved.
Keywords: COP Time series Scaling exponent Temporary stimuli
1. Introduction A fall is a common accident that happens more often to elderly people, and it is associated with chronic deterioration in the neuromuscular and sensory systems. Sensory feedback is necessary for postural adjustments and facilitates to control of compensatory stepping reactions evoked by postural perturbation. Recent studies have explored the effects of mechanical stimulations on static balance to enhance postural feedback (Park et al., 2004). The stimulations are complex and depend on the frequency, amplitude and location of the stimulation (Kavounoudias et al., 2001). Foot pressure activates plantar mechanoreceptors that mediate postural adjustment during the stance phases of the step (Laughton et al., 2003; Novak and Novak, 2006). Application of subsensory noise to the feet has been demonstrated to improve postural stability in elderly fallers (Costa et al., 2007). The above studies have indicated that stimulations near the feet are able to improve postural control and stability in elderly fallers while they are standing still. This issue is being explored through various experimental and analytical techniques. The human postural-control system integrates various mechanisms that prevent the human body from falling in both static and dynamic conditions. The main tool used to investigate this complex balance system is the stabilogram, which measures
* Corresponding author. Tel.: +886 2 29089899x3106; fax: +886 2 2908 5900. E-mail address: [email protected] (C.-C. Wang). 0167-4943/$ – see front matter ß 2011 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.archger.2011.11.008
the time behavior of the COP of a person standing on top of a force platform. The COP signal, which can be used as a measure of postural stability, is measured in the horizontal plane in both the anteroposterior (AP) and mediolateral (ML) directions. Fig. 1(a) illustrates the displacement of the COP signal, and (b) and (c) show displacement in the AP and ML directions over time, respectively. The dynamic characteristics of COP are of fundamental importance even in the case of quiet standing, and a large number of recent studies, mostly in the last decade, have focused on the analysis of the non-stationary time properties of COP. In recent years, the DFA method (Peng et al., 1994) has become a widely used technique for the determination of (mono-) fractal scaling properties and detection of long-range correlations in noisy, non-stationary time series (Hu et al., 2001). One reason to employ the DFA method is to avoid spurious detection of correlations that are artifacts of non-stationarities in the time series. It has been successfully applied to the diverse field such as DNA sequences (Buldyrev et al., 1995), heart rate dynamics (Ashkenazy et al., 2001), and human gait (Liu et al., 1999), posture (Duarte and Sternad, 2008; Lin et al., 2008) and Parkinson’s disease (Minamisawa et al., 2009). Duarte assessed aging changes in postural sway using fractal and complexity and complexity measures of the COP during prolonged standing. The analysis results were showed that complexity in the human physiological system decreases with aging (Duarte and Sternad, 2008). Lin et al. (2008) assessed within and between day reliability of both COP measures of postural sway. Reliability of each COP measure was quantified using intraclass
C.-C. Wang, W.-H. Yang / Archives of Gerontology and Geriatrics 55 (2012) 673–676
Anteroposterior (mm)
a
20
b
10
AP(mm)
674
20
0
-20 0
0
c
20
40
60
40
60
20
-20 -20
ML(mm)
-10
-10
0
10
0
20
Mediolateral (mm)
-20 0
20
time(s) Fig. 1. COP signal and time series in AP and ML directions. (a) COP signal. (b) AP direction time-series data. (c) ML direction time-series data.
correlation coefficient and standard error of measurement. From the analysis result, DFA exponents were relatively more reliable than Hurst rescaled range analysis. Minamisawa et al. (2009) applied DFA to COP data from Parkinson’s disease and healthy elderly persons. They showed a significant difference in the crossover point dividing the short and long term fluctuation. The important assumption of this study is that elderly fallers can effectively improve postural stability through plantar vibratory stimulations. For this reason, vibratory insoles based on stochastic resonance were designed to produce physical stimulation to the soles of the feet (Yang, 2010). When a faint background of random pulses could amplify weak signals sent from the feat to the brain. The stochastic resonance is the effect of boost weak signals by noise. Therefore, if the original postural orientation signal is too weak for the poorly performing sensory system (mechanoreceptors) of the elderly subject, the addition of a noise component (vibrating insole) can increase the strength of the total signal above a detection threshold and thus enable a postural adjustment reaction. In this paper, the objectives are to understand the effects of vibratory insoles on improving postural stability and compare the variability of the DFA scaling exponents before and after using vibratory insoles in both elderly fallers and healthy young subjects. Through a standing still experiment and the DFA scaling exponent calculation, the effects of vibratory insoles are discussed for elderly fallers and healthy young subjects. 2. Materials and methods To verify the effects of vibratory insoles, a two-stage experiment (before and after using vibratory insoles) was conducted to measure COP signals for elderly fallers and healthy young subjects while standing still. A DFA technique used to analyze COP signals and the scaling exponent was adopted to evaluate the effect. 2.1. Design of vibratory insoles Vibratory insoles based on stochastic resonance were designed to enhance the postural stability for elderly fallers (Yang, 2010). For the design of vibratory insoles, assumption the ability of an individual to detect a sub-threshold tactile stimulus can be significantly enhanced by the presence of a particular, nonzero level of noise. Sub-sensory mechanical noise was applied to the soles of the feet via vibrating insoles. The vibration as a kind of noise and controlled the degree of vibration intensity via the variable resistor and calculate the electric power of vibratory shoes as a noise according to the different degree of noise. The vibratory
shoes the variable resistor, in according to the feelings of each subject to adjust the degree of vibration intensity, so that the vibratory shoes can be the effect of the physical sense of the balance system. There are six vibratory degree 0 V, 10 V, 20 V, 30 V, 40 V, and 50 V can be adjusted on these shoes. 0 V is represented the maximal vibratory strength and 50 V is indicated the minimal one. Fig. 2(a) shows that three eccentric vibratory motors were embedded in the insoles. The vibratory insoles were installed inside the shoes, and the shoes are shown in Fig. 2(b). 2.2. Experiment and COP signal collection The subjects were 26 elderly fallers with mobility in a longterm care center with an average age of 83.3 4.8 years and 16 healthy young people with an average age of 25.2 3.8 years. The local ethics committee approved this experiment and written informed consent was obtained from all subjects. COP signals were obtained from a force plate (CATSYS 20001) with a signal sampling frequency of 40 Hz. The experimental process was divided into two stages. Stage 1: Due to the short duration of available recordings, this study focused on COP fluctuations that can be accounted for by regulatory mechanisms operating over a short time. Subjects were asked to take off their shoes and stand on a force plate with their eyes open for 65 s to complete a COP signal measurement before using the vibratory shoes. This stage was defined as the control condition. The subjects rested for 1 min before moving on to stage 2. Stage 2: The subjects wore the vibratory shoes, and the assistant activated the vibratory device. The eccentric vibratory motors delivered slight vibratory stimuli to the soles of the feet. The assistant determined the acceptable vibratory strength by adjusting it randomly while asking the subjects if they felt any discomfort or pain. After adjusting the vibratory strength, a nurse accompanied the subjects on a 10-min walk. The 10-min walking test was believed to reflect activities of daily living (Olsson et al., 2005; Yang, 2010). However, if subjects felt uncomfortable, the vibratory strength was adjusted. After walking for 10 min, the assistant turned off the vibratory motors. After resting for 1 min, the subjects took off the shoes and stood still on the force plate for 65 s to complete the COP signal measurement after using the vibratory shoes. In this study, stage 2 was defined as the vibration condition in comparison to the control condition of stage 1.
C.-C. Wang, W.-H. Yang / Archives of Gerontology and Geriatrics 55 (2012) 673–676
675
Fig. 2. Components of (a) vibratory insoles (Yang, 2010) and (b) vibratory shoes (Yang, 2010).
2.3. DFA DFA (Peng et al., 1994) is a scaling analysis technique used to provide a simple quantitative parameter (scaling exponent) to represent the correlation properties of a signal. DFA is advantageous because it can systematically eliminate trends of various orders caused by external effects and reduce noise caused by imperfect measurement. To illustrate a DFA algorithm, an elderly faller COP series in the AP direction is shown in Fig. 3(a) as an example. The DFA procedure is described as follows: Step 1: Briefly, the COP series (of total length N) is first integrated as follows: yðkÞ ¼
k X ¯ ½XðtÞ X
(1)
t¼1
where X(t) is the sequence at time t, and X¯ is the average of the entire time series. Step 2: Next, the integrated time series y(k) is divided into subsequences of equal length n. In each box of length n, a leastsquares line is fit to the data (representing the trend in that box) (see Fig. 3(b)). The y-coordinate of the straight line segment is denoted by yn(k).
Step 3: We detrend the integrated time series y(k) by subtracting the local trend yn(k) in each box. The root-mean square fluctuation of this integrated and detrended time series is calculated as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X 2 (2) ½yðkÞ yn ðkÞ FðnÞ ¼ t N k¼1 The computation is repeated over all time scales (box sizes) to provide a relationship between F(n), the average fluctuation as a function of box size, and box size n (such as the number of positions in a box that is the window of observation). Typically, F(n) will increase with box size n. According to the recommendations made by Peng et al. (1994), the range nmin ffi 5 and nmax ffi N/4 may be selected. Step 4: A linear relationship on a log–log graph indicates the presence of scaling. Under such conditions, the fluctuations can be characterized by the scaling exponent (a), which is the slope of the line relating log10F(n) to log10 n (Fig. 3(c)). If the signal behaves as the fraction Gaussian noise, a range from 0 to 2; if the signal behaves as the fraction Brownian, a range from 0 to 1. a = 0.5 indicates that the changes in the values of a time series are random. When a < 0.5 the signal is anti-persistent, while a > 0.5 indicate positive persistency in the signal (Lin et al., 2008).
Fig. 3. DFA algorithm and scaling exponent (a). (a) Original signal. COP series of the AP direction X(t) of 2400 data points. (b) Integrated signal. Integrated time series y(k). The vertical block dashed lines indicate a box of size n = 200, and the red solid straight lines represent the ‘trend’ estimated in each box by a least-squares fit. (c) DFA scaling exponent (a) for the signal shown in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
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Table 1 Comparisons of the DFA scaling exponent (a) between the control and vibration conditions for elderly fallers and healthy young subjects for 65 s after starting the experiment. DFA scaling exponent (a)
Control Vibration p-Value control vs. vibration
Elderly fallers 95% confidence interval
Healthy young 95% confidence interval
ML
AP
ML
AP
[1.322,1.419] [1.255,1.385] 0.18
[1.292,1.389] [1.199,1321] 0.08
[0.924,1.116] [1.019,1.201] 0.164
[0.853,0.927] [0.830,0.969] 0.68
Table 2 Comparisons of the DFA scaling exponent (a) between the control and vibration conditions for elderly fallers and healthy young subjects for 30 s after starting the experiment. DFA scaling exponent (a)
Control Vibration p-Value control vs. vibration
Elderly fallers 95% confidence interval
Healthy young 95% confidence interval
ML
AP
ML
AP
[1.522,1.619] [1.465,1.595] 0.16
[1.434,1.547] [1.329,1.451] 0.009
[1.285,1.455] [1.349,1.531] 0.26
[1.201,1.319] [1.127,1.233] 0.07
Some difference exists regarding how these exponents are to be practically interpreted. However, Collins et al. (1995) have suggested that greater persistence of the COP series is correlated with increased muscle activity and a decline in postural stability. Greater anti-persistence has been suggested to reflect a more tightly controlled postural system (Amoud et al., 2007). Therefore, the DFA scaling exponent (a) was adopted to compare the effect of using vibratory insoles. 3. Results To understand the effects of vibratory insoles on improving postural stability, the variability of the DFA scaling exponents (a) is compared before and after using the vibratory insoles in both elderly fallers and healthy young subjects. Due to the short experimental time to use the vibratory insoles (only 10 min), the stability improving effects may not continue. Hence, two types of signal length are discussed between the entire signals (for 65 s) and the signals of 30 s after starting the experiment. Tables 1 and 2 present comparisons of the DFA scaling exponent (a) between the control and vibration conditions for elderly fallers and healthy young subjects for 65 s and 30 s after starting the experiment, respectively. The two-sample t-test was used to test whether the population mean was significantly different. For 65 s, elderly fallers and healthy young subjects showed no statistically significant differences in the DFA scaling exponent values between the control and vibration conditions (Table 1). However, for 30 s after starting the experiment, elderly fallers showed statistically significant differences (p-value = 0.009) in the DFA scaling exponent values between the control and vibration conditions in the AP direction (Table 2). This result indicated that the foot stimulation caused by the vibratory insoles improved postural stability for elderly fallers while standing still. The healthy young subjects showed no significant differences in the DFA scaling exponent values between the control and vibration conditions for 30 s after starting the experiment (Table 2). 4. Conclusions This study emphasized the COP data analysis instead of the vibratory insole’s design. Based on the DFA concept, the experimental results revealed that the scaling exponent values for elderly fallers after using the vibratory insoles were significantly larger than those before using the vibratory insoles. This finding indicates that temporary stimuli of appropriate amplitude produced by the vibratory insoles are essential for enhancing balance in elderly fallers, especially in the AP direction, for a short time duration (30 s). However, postural stability was not significantly increased in
healthy young subjects by using vibratory insoles. For 65 s, the postural stability for elderly fallers and healthy young subjects showed no statistically significant increase by using the vibratory insoles. We will focus on finding hidden and important information about the complex fluctuation of the COP series and enhance the vibratory insole’s design in future studies. Conflict of interest statement None. References Amoud, H., Abadi, M., Hewson, D.J., Michel-Pellegrino, V., Doussot, M., Duchene, J., 2007. Fractal time series analysis of postural stability in elderly and control subjects. J. NeuroEng. Rehabil. 4, 1–12. Ashkenazy, Y., Ivanov, P.C., Havlin, S., Peng, C.K., Goldberger, A.L., Stanley, H.E., 2001. Magnitude and sign correlations in heartbeat fluctuations. Phys. Rev. Lett. 86, 1900–1903. Buldyrev, S.V., Goldberger, A.L., Havlin, S., Mantegna, R.N., Matsa, M.E., Peng, C.K., Simons, M., Stanley, H.E., 1995. Long-range correlation properties of coding and noncoding DNA sequence. Phys. Rev. E 51, 5084–5091. Collins, J.J., De Luca, C.J., Burrows, A., Lipsitz, L.A., 1995. Age-related changes in open-loop and closed-loop postural control mechanisms. Exp. Brain Res. 104, 480–492. Costa, M., Priplata, A.A., Lipsitz, L., Wu, A.Z., Huang, N.E., Goldberger, A.L., Peng, C.K., 2007. Noise and poise: enhancement of postural complexity in the elderly with a stochastic-resonance-based therapy. Europhys. Lett. 77, 68008. Duarte, M., Sternad, D., 2008. Complexity of human postural control in young and older adults during prolonged standing. Exp. Brain Res. 191, 265–276. Hu, K., Ivanov, P.C., Chen, Z., Carpena, P., Stanley, H.E., 2001. Effect of trends on detrended fluctuation analysis. Phys. Rev. E 64, 011114. Kavounoudias, A., Roll, R., Roll, J.P., 2001. Foot sole and ankle muscle inputs contribute jointly to human erect posture regulation. J. Physiol. 532, 869–878. Laughton, C.A., Slavin, M., Katdare, K., Nolan, L., Bean, J.F., Kerrigan, D.C., Phillips, E., Lipsitz, L.A., Collins, K.J., 2003. Aging, muscle activity, and balance control: physiological changes associated with balance impairment. Gait Posture 18, 101–108. Lin, D., Soel, H., Nussbaum, M.A., Madigan, M.L., 2008. Reliability of COP-based postural sway measures and age-related differences. Gait Posture 28, 337–342. Liu, Y., Gopikrishnan, P., Cizeau, P., Meyer, M., Peng, C.K., Stanley, H.E., 1999. Statistical properties of the volatility of price fluctuations. Phys. Rev. E 60, 1390–1400. Minamisawa, T., Takakura, K., Yamaguchi, T., 2009. Detrended fluctuation analysis of temporal variation of the center of pressure (COP) during quiet standing in Parkinsonian patients. J. Phys. Ther. Sci. 21, 287–292. Novak, P., Novak, V., 2006. Effect of step-synchronized vibration stimulation of soles on gait in Parkinson’s disease: a pilot study. J. NeuroEng. Rehabil. 3, 1–7. Olsson, L.G., Swedberg, K., Clark, A.L., Witte, K.K., Cleland, J.G.F., 2005. Six minute corridor walk test as an outcome measure for the assessment of treatment in randomized, blinded intervention trials of chronic heart failure: a systematic review. Eur. Heart J. 26, 778–793. Park, S., Horak, F.B., Kuo, A.D., 2004. Postural feedback responses scale with biomechanical constraints in human standing. Exp. Brain Res. 154, 417–427. Peng, C.K., Buldyrev, S.V., Havlin, Simons, S.M., Stanley, H.E., Goldberger, A.L., 1994. Mosaic organization of DNA nucleotides. Phys. Rev. E 49, 1685–1689. Yang, W.H., 2010. Data mining on physiological signal—integrate dissimilarity approach and signal reconstruction for complexity analysis. Dissertation. Yuan Ze University.