Simple tai chi exercise for improving elderly postural stability via complexity
index analysis
Cheng-Wei Huang1, Wei-Hsin Chen2, Heng-Hui Chu1, Bernard C. Jiang3 , Maysam Abbod4, and JiannShing Shieh1,5,6,
1
Department of Mechanical Engineering, Yuan Ze University, Taiwan
Department of Industrial Engineering and Management, Yuan Ze University, Taiwan
3
Department of Industrial Management, National Taiwan University of Science and Technology, Taipei, Taiwan
4
School of Engineering and Design, Brunel University, London UB8 3PH, UK
5
Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Taiwan
6
Center for Dynamical Biomarkers and Translational Medicine, National Central University, Taiwan.
2
jsshieh@saturn.yzu.edu.tw
Abstract: The main purpose of this study is to investigate twice a day simple 9 steps tai chi effects of the center of pressure
(COP) and physiological signals of eldery people. Data is collected from the COP signals, electromyography (EMG), and pulse
oximetry for one minute every two weeks for the period of 12 weeks. The COP signals are analyzed using multivariate
empirical mode decomposition and multivariate multiscale entropy in order to work out and compare the complexity index
(CI). Subjects in this experiment are over 65 years old who are divided into 11 men and 7 women, the average age is 74±8.18
years old. In conclusion, it is found that tai chi exercise can improve human body balance by just walking some simple steps in
our experiment. However, we cannot find any effect or improvement in the pulse oximetry and EMG signals analysis.
Keywords: Center of pressure (COP); Electromyography (EMG); multivariate empirical mode decomposition (MEMD; Multi
variate Multi-scale entropy (MMSE); complexity index (CI); Six-minute walk test; Timed up and go; tai chi.
1 INTRODUCTION
Falls are caused by many factors, including external
factors such as environment and multiple drugs. The
inherent risk factors such as age, a history of fall or
recurring nearly fall without fall events, diseases, cognitive
impairment, depression, sensory dysfunction, lower
extremity muscle strength, balance and gait problems, the
use of exercise walking aids, and daily living dysfunction.
There are many studies concerned with prevention of
falling which are based on the multifactorial assessment
tool to assess falling [1]. Elderly falling prevention
intervention strategies includes fall risk assessment,
multifactorial intervention, sport training, adjustment of
medication,
improved
environment
and
vision,
supplemental Vitamin D and calcium, pacemaker and
education.
Balance exercise such as tai chi not can only reduce
falling occurrences but also can get other physical and
mental health benefits at the same time. Reducing elderly
mental disorder treatment medication can significantly
reduce falls, but not easy to change the drug effects on the
elderly. Environmental improvement intervention is
suitable for the elderly who has fallen in the past. Cataract
surgery can reduce most of the elderly’s bad fall caused by
vision problems. However, exercising Tai chi can increase
leg muscle strength and effectively improves lower
extremity muscle strength. Tai chi exercise can also
increase balance and reduce the risk of falling for the
elderly [2].
Tai chi is one of Chinese traditional martial arts and a
treasure of Chinese culture, it emphasizes on physical,
mental and spiritual cultivation and practice. Tai chi is
categorized as a recreational sport of low-middle intensity
and aerobic, rhythmic, uncompetitive and whole-body
performing mode is suitable for various ages and can be
practiced anytime, and anywhere.
Center of pressure is an indirect measurement to
measure Medial-Lateral (M-L) and Anterior-Posterior (A-P)
[3] plane rocking postures. An effective nonlinear analysis
method can effectively describe the posture stability and
characteristics. The centre of pressure (COP) signals are
collected for body rocking posture using a force platform,
then the displacement of center of pressure displacement is
calculated for the Medial-Lateral and Anterior-Posterior
directions [4]. Furthermore, the M-L and A-P displacements
are analyzed for individual analysis. Therefore, the main
purpose of this study is to investigate twice a day simple 9
steps tai chi exercise effects on improving the center of
pressure (COP) and physiological signals.
2 METHOD
There are a few analysis algorithms, such as
multivariate empirical mode decomposition (MEMD) and
multivariate multiscale entropy (MMSE) that are used to
analyze the center of pressure (COP), electromyography
(EMG) data and other vital signs.
2.1 Analysis algorithms
In this study, MEMD and MMSE are used to analyze
the COP, EMG and other data.
2.1.1 Multivariate empirical mode decomposition
The MEMD algorithm basically comes from empirical
mode decomposition (EMD), which was proposed by
Huang et al [5], and has been widely used in nonlinear and
non-stationary data analysis based on the inherent
characteristics of the time series. EMD has groups of
intrinsic mode functions (IMF) corresponding to the modal
function within the system in different mechanism of
reaction. The first step to calculate the EMD is to find the
upper and lower envelope, which is based on the signal in
the local maximum and local minimum value to define. The
upper envelope is the cubic spline to link with the local
maximum value of the continuous curve, and the lower
envelope is the cubic spline to connect to the local
minimum value of the continuous curve. Average upper and
lower envelope is seen as a signal of a trend. The average
envelope can be regarded as a possible intrinsic mode
functions.
The possible intrinsic mode functions separation from
the signal process is called sifting process. The intrinsic
mode functions obtained from the sifting process must
satisfy the following two conditions, otherwise it must run
the sifting process again [6]. (1) In the whole time series,
the number of all local extrema and zero-crossing
difference cannot be more than one. (2) In any one time
point, the average envelope must tend to zero.
If these two conditions are satisfied, the separated
signals called intrinsic mode functions (IMF) will be
recorded as c1. Original signal and c1 subtraction can get
residual signal. The residual signal is used as input to the
decomposition of next intrinsic mode functions. Repeating
this process can gradually decomposed for different
intrinsic mode functions until the residual signal is a
monotonic function.
Original signal after the n times decomposition can get
different n groups IMFs signals. The relationship between
decomposed by the empirical mode decomposition method
signals and the original signal can be expressed by equation
(1)
𝑋(𝑋) = ∑𝑋
(1)
𝑋=1 𝑋𝑋 + 𝑋𝑋
where X(t) is the original signal, ci represent the number i
IMF, rn is number n times residual signal.
In order to diversely extend the application of EMD,
MEMD method is being developed to decompose diversely
nonlinear and non-stationary signals [7]. MEMD method
not only overcomes the limit of a single EMD input, but
also addresses the computing burden in calculating the
noise signal residues in different channels after adding
white noise. In addition, it is similar to EMD as a dyadic
filter is used for multivariable input of each channel. Also it
has the advantage of correction to align the corresponding
IMFs from different channels to the same frequency range
[8]. In the MEMD method, the average value of m (t) is
calculated by multivariate enveloped K direction vectors as
illustrated in equation (2)
𝑋𝑋
𝑋(𝑋) = 𝑋−1 ∑𝑋
(𝑋)
(2)
𝑋=1 𝑋
𝑋𝑋
𝑋
were the {𝑋 (𝑋)}𝑋=1 is a multivariable envelope in the
vectors, along the K direction that predict multi-channel
input s (t) and multivariate IMF calculations via the s (t)-m
(t) and stopping criteria. This process is repeated until all
predicted standard signal is satisfied to the standard EMD
stops.
Recently a study [6] has reported that the human body
center of pressure signal is lower than 2 Hz. Accordingly,
taking the Fourier transform for each IMF can indicate the
frequency range of the original signal, therefore a 2 Hz
reference was chosen for analysing the IMFs.
2.1.2 Multivariate multiscale entropy
Entropy-based algorithms for measuring the complexity
of physiologic time series have been widely used. These
have proved to be useful in discriminating between healthy
and disease patients [9]. Normally, healthy systems
generate much more complex outputs than disease ones.
Traditional algorithms are single-scale based and fail to
account for the multiple time scales inherent in physiologic
systems.
Similar to EMD and MEMD, multivariate multiscale
entropy (MMSE) is the evolution of multiscale entropy
(MSE). MSE is developed by Costa et al [10] and used to
evaluate the complexity of signals over different time
scales. Based on the approximate entropy, this method uses
sample entropy to quantify the regularity of the finite length
time series, which has been applied effectively in analysis
of physiology, biology, and geosciences data [11][12][13].
Given a one-dimensional discrete time series {Xi… Xn},
MSE firstly constructs multiple coarse-grained time series
using the scale factor 𝑋. Each element of the time series,
{y(1)}, is according to equation (3)
(𝑋)
𝑋𝑋 = 1⁄𝑋 ∑𝑋𝑋
(3)
𝑋=(𝑋−1)𝑋+1 𝑋𝑋 1 ≤ 𝑋 ≤ 𝑋/𝑋
For scale one, the time series{y(1)}is simply the original
time series. The length of each coarse-grained time series is
equal to the length of the original time series divided by the
scale factor τ. Then, the sample entropy is calculated for
each coarse-grained time series plotted as a function of the
scale factor τ [10]. Sample entropy reflects the conditional
probability that two sequences of m consecutive data points
which are similar to each other which remains similar when
one more consecutive point is included, and being “similar”
means that the value of a specific measure of distance is
less than r [8]. The complexity degree of different
combinations in each direction is measured in terms of the
complexity index (CI), which is defined as the area under
the MSE curve over all scales.
MMSE calculates the relative complexity of the
multichannel signals through the plot of the multivariate
sample entropy. This makes it possible to assess structural
complexity of multivariate physical or physiological
systems, together with more degrees of freedom and
enhanced rigor in the analysis. In the MMSE, if the
multivariable sample entropy value is higher than most of
the other scale, multivariable time-series is considered to be
more complex than the others. This is the same with the
original MSE [2].
2.2 Experiment
The purpose of this experiment is to improve elderly
balance by performing nine steps tai chi exercise, and test
whether it can improve the heart and lung function. This
work is done in corporation with Taiwan Taoyuan Senior
Citizens’ Home.
Subjects in this experiment are over 65 years old who
are 11 men and 7 women, and average age is 74±8.18 years
old. The physical condition of these subjects is able to walk
by themselves, do not need to be supported, and can stand
on their own.
2.2.1 Measuring instruments
In order to assess the improvement of body balance, the
force platform measurement instrument developed in the
previous research is being used. The system is named as
Center of Pressure and Complexity Monitor System
(CPCMS) (Fig. 1). The pressure measurement platform is
designed to receive raw data of the balance signal. When
the subject stands on the balance measurement device, the
pressure measurement platform can receive raw COP
signal.
Fig. 1. Center of Pressure and Complexity Monitor System
(CPCMS)
Pulse oximeter measures oxygen saturation is a
noninvasive method to monitor the oxygen saturation. This
device is small, light-weight, reusable and portable as
shown in Fig. 2(a). The sensor is shown in Fig. 2(b).This
product is developed by Tatung Company. The device is
connected to a computer to record SPO2 and heart rate.
(a)
(b)
Fig. 2 (a) The Tatung Pulse oximeter. (b) Tatung Pulse
oximeter sensor
In this study the NeXus-10 Bluetooth Biofeedback (Fig.
3.) is used to collect EMG signal. Fig. 4. shows the
experiment setup which shows the subject standing on the
CPCMS and wearing Tatung pulse oximeter and NeXus-10
Bluetooth Biofeedback to collect all the data.
Fig. 3. NeXus-10 Bluetooth Biofeedback
to take 60 seconds break, then do the time-up-and-go test
one time. The distance of walking is 3 meters. Take another
60 seconds break for next test, 6-minute walk test where the
distance is measured. Since all the subjects are elderlies,
there is a person who helps them in case of any danger.
(c)
Fig. 4. Experiment schematic diagram. (a) Pulse oximeter
sensor (b) CPCMS (c) EMG connect to NeXus-10.
2.2.2 Experimental procedure
The experiment period for the nine steps tai chi exercise
experiment is 12 weeks conducted in the Taiwan Taoyuan
Senior Citizens’ Home, data is collected every two weeks.
Subjects do the exercise in the morning and evening every
day. Rehabilitation division staff assists with the
experiments. The experiment flowchart is shown in Fig. 5.
Research group
Explain experiment
processes and sign
subjects consents form
Subjects
Sign the form
2.3 Data analysis
The analysis procedure consists of two parts. During the
experiment, COP, SPO2 and EMG signals are recorded.
SPO2 signal provides blood oxygen percentage, heart rate,
where the respiration rate and psychological stress index
(PSI) are inferred. From the result, the second part involves
analyzing the tai chi exercise affect on the subjects’ heart
and lung function. The COP and EMG analysis process is
shown in Fig. 6.
Human body center of pressure can be used to assess
personal balance mechanism. Since the human body center
of pressure signal frequency is very low, the force platform
sample rate is 500 Hz so wethe signal is resampled at 50
Hz. After the calculation, M-L and A-P signals are aquired.
MEMD is used to filter out noise and then use MMSE to
calculate entropy value. Finally, the complexity index (CI)
is calculated to assess the difference of human body balance
ability due to the tai chi exercise.
COP Signal
Measure the COP,
SPO2, EMG, time-up-andgo, and 6-minute walk bef
ore doing tai chi
Measure COP, SPO2 and
EMG together
EMG signal
Resampling
ML/AP
MEMD
Do time-up-and-go
and 6-minute walk
Repeat the measurement
procedure every two weeks
for six times
MSE/MMSE
End of one measurement
CI
Check if finish the whole
experiment
NO
Do tai chi exercise
everyday
YES
End of whole experiment
Result and discussion
Fig. 6. COP and EMG analysis process flow chart
3 ANALYSIS RESULT
Fig. 5. Experiment flowchart
The subjects are asked to stand on the CPCMS and
connect the SPO2 and EMG device at the same time to
measure COP, SPO2 and EMG. Each measurement lasts for
60 seconds, then 60 seconds break, then the measurement is
repeated. This procedure is repeated more than three times.
After finishing the procedure above, the subjects are asked
The COP displacements in two directions of anteriorposterior (AP) and the medial-lateral (ML) are often used to
characterize the COP stabilogram. Before performing the
MSE and MMSE analysis, the IMF selection has to be
made. MEMD is performed first, then the Fourier transform
for each IMF to get the frequency range. The frequencies
for each IMF are shown in Table 1. IMF 5+6 are selected
since these indicate less than 2 Hz signals.
X
Y
Table 1. IMF frequencies
CPCMS
IMF 2
IMF 3
IMF 5
9.17±1.71
4.22±0.84
1.24±0.26
9.53±1.59
4.54±1.04
1.22±0.24
IMF 6
0.73±0.18
0.73±0.15
Tables 2 and 3 show the results of MSE of AP and ML.
From the results it is obvious that CI of the 6th measurement
is higher than the 1st measurement in both AP and ML
directions. MMSE is also used to combine both ML and AP
directions into one result. Table 4 shows the CI value of the
MMSE. From the result, it can be seen that CI of 6th is
higher than 1st. For the time-up-and-go test, the subjects
need to stand up from a chair and walk to a 3-meter far
target then walk back to sit down. The shorter finish time
means the speed and stability of walking increase. Table 5
indicates that the time to finish the procedure is shorter
after 6th time measurement. The same trend can be seen for
the time-up-and-go test, the longer distance is the better. As
illustrated in Table 6. Tables 7 and 8 show the analysis
results for pulse oximetry. The heart rate, blood oxygen
concentration and respiration rate are extracted from the
pulse oximetry. The results indicate no regular changes or
improvements in these four parts. The p-value for before
and after doing the tai chi exercise are bigger than 0.05.
Table 2. CI of MSE in ML
MSE_ML
nth
CI
P-value
1
5.651±2.22
2
5.458±1.842
1 vs 2
0.704
3
5.629±2.572
1 vs 3
0.971
4
6.288±2.678
1 vs 4
0.265
5
5.823±2.171
1 vs 5
0.691
6
6.687±2.122
1 vs 6
0.079
Note: 1 vs 6 represents a comparison of 1st with 6th
Table 3. CI of MSE in AP
MSE_AP
nth
CI
P-value
1
7.386±2.406
2
8.38±2.822
1 vs 2
0.134
3
7.492±2.797
1 vs 3
0.885
4
8.973±3.679
1 vs 4
0.072
5
8.331±2.253
1 vs 5
0.108
6
9.318±2.397
1 vs 6
0.020
Note: 1 vs 6 represents a comparison of 1st with 6th
Table 4. CI of MMSE
MMSE
nth
CI
P-value
1
13.095±1.887
2
14.687±1.639
1 vs 2
0.003
3
14.042±1.559
1 vs 3
0.132
4
14.409±1.93
1 vs 4
0.013
5
13.858±1.557
1 vs 5
0.105
6
14.577±1.433
1 vs 6
0.006
Note: 1 vs 6 represents a comparison of 1st with 6th
Table 5. Time-up-and-go result
Time-up-and-go
nth
Time(s)
P-value
1
16.195±6.124
2
15.54±4.42
1 vs 2
0.599
3
14.78±3.97
1 vs 3
0.216
4
14.1±3.27
1 vs 4
0.184
5
14.45±3.25
1 vs 5
0.241
6
13.72±3.14
1 vs 6
0.060
Note: 1 vs 6 represents a comparison of 1st with 6th
Table 6. 6-minute walk test
6-minute walk
nth
distance(m)
P-value
1
262.756±61.603
2
272.806±67.3
1 vs 2
0.234
3
289.243±70.513
1 vs 3
0.011
4
297.52±70.513
1 vs 4
0.000
5
295.698±75.078
1 vs 5
0.005
6
305.052±72.974
1 vs 6
0.000
Note: 1 vs 6 represents a comparison of 1st with 6th
Table 7. Pulse oximetry analysis result for heart rate
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
mean
SD
p-value
1
88.4
72.13
85.09
58.71
69.94
92.42
66.36
77.61
19.87
78.1
88.08
84.6
59.39
67.53
65.86
60.13
71.57
86.75
71.81
16.89
2
79.65
71.03
90.35
60.29
76.76
85.69
69.73
78.1
85.84
85.34
85.84
85.41
59.2
83.54
59.66
58.49
75.81
81.25
76.22
10.68
0.272
HR
3
79.66
71.03
86.51
107.31
78.87
73.77
62.84
84.6
86.65
84.6
86.65
81.66
72.07
87.29
53.45
55.11
76.04
87.02
78.62
12.85
0.425
4
87.69
72.39
99.24
42
65.5
75.1
70.52
83.08
88.55
83.08
88.55
77.08
79.51
98.8
58.94
64.09
69.13
81.56
76.93
14.21
0.685
5
74.84
74.99
83.78
81.74
64.38
73.92
65.93
97.19
89
77.34
81.18
90.01
74.86
80.75
55.64
67.24
73.99
39.86
74.81
13.24
0.588
6
90.2
73.99
94
50.33
66.67
75.45
72.03
76.94
92.98
73.1
70.48
90.14
69.37
72.46
59.46
55.06
73.61
90.36
74.81
12.78
1.000
Table 8. Pulse oximetry analysis result for blood oxygen
concentration
1
2
3
1
96.92
94.34
96.04
2
95.41
64.43
94.14
SPO2
3
95.41
64.45
96.39
4
96.73
97.04
95.13
5
99
95.85
94.55
6
97.37
96.56
92.45
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
mean
SD
p-value
90.68
96.24
97.69
99
91.43
99
99
98.34
99
98.07
98.93
98.96
98.32
95.94
94.36
96.79
2.61
99
96.18
97.15
99
99
99
99
99
91.13
97.16
95.87
93.05
95.08
92.68
94.43
94.48
7.92
0.232
90.94
95.25
95.13
93.89
99
99
99
99
91.45
94.15
93.86
93.91
98.28
92.74
97.74
93.87
7.8
0.355
97.56
81.99
95.36
93
96.78
95.42
96.78
95.42
94.24
94.65
96.79
96.56
95.65
97.43
97.07
95.2
3.51
0.533
99
90.94
96.21
98.44
98.24
94.9
98.06
83.55
94.73
95.53
93.64
95.65
97.3
98.25
98.64
95.69
3.73
0.611
99
94.7
99
99
98.24
96.37
98.97
83.55
93.76
96.59
92.61
96.3
96.57
99
96.84
95.94
3.75
0.506
4 CONCLUSSION AND DISCUSION
The MSE result of both COP directions and the
MMSE combination method show that the tai chi exercise
can improve human body balance even when just walking
few simple steps. However, in this experiment no,
improvement due to the pulse oximetry and EMG signals
analysis is found. Furhermore more rigorous study can be
conducted to investigate the relation between complexity of
the COP data, physical ability and tai chi. In the future, this
experiment can be extended to elderlies with diseases, and
then construct an evaluation index for home care with the
healthy or diseased elderlies.
ACKNOWLEDGEMENT
This research is supported by National Science
Council in Taiwan through Grant NSC102-2221-E-155028-MY3. This research is also supported by the Center for
Dynamical Biomarkers and Translational Medicine,
National Central University, Taiwan which is sponsored by
National Science Council (NSC102-2911-I-008-001).
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