DETECTION OF THE CRITICAL POINT INTERVAL OF

POSTURAL CONTROL STRATEGY USING WAVELET

TRANSFORM ANALYSIS

Neeraj Kumar Singh, Hichem Snoussi, David J. Hewson and Jacques Duchêne

Institut Charles Delaunay, FRE CNRS 2848, Université de Technologie de Troyes

12 rue Marie Curie, BP2060, 10010 Troyes, France

Keywords: Stabilogram, Centre of Pressure, Postural Control, Wavelet Transform Analysis.

Abstract: Postural balance is often studied in order to understand the effect of sensory degradation with age. The aim

of this study was to develop a new method of detecting the critical point interval (CPI) at which sensory

feedback is used as part of a closed-loop postural control strategy. Postural balance was evaluated using

centre of pressure (COP) displacements measured using a force plate for 17 control subjects and 10 elderly

subjects under control (eyes open) and experimental (eyes closed, vibration) conditions. A modified local-

maximum-modulus wavelet transform analysis using the power spectrum of COP signals was used to

calculate the critical point when closed-loop control occurs. Lower values of CPI are associated with

increased closed-loop postural control, indicating a quicker response to sensory input. This strategy of

postural control will require greater energy expenditure due to the repeated muscular interventions in order

to remain stable. The CPI for elderly subjects occurred significantly quicker than for control subjects,

indicating that posture was more closely controlled. Similar results were observed for eyes closed and

vibration conditions. The CPI parameter offers a new method of detecting differences in postural control

between different experimental conditions or changes due to ageing.

1 INTRODUCTION

Balance is regularly studied in order to better

understand postural control mechanisms. One reason

for the interest in balance is its relationship with

falls, which are a major problem in the elderly.

Indeed, a problem with balance is one of the most

commonly-cited risk factors for falls (Rubenstein

and Josephson, 2002). Balance is maintained using

the visual, vestibular, and proprioceptive systems.

Postural degradations occur with age, and can

also be artificially created by impairing one of the

sensory systems, for instance by closing a subject’s

eyes. The proprioceptive system can also be

impaired by applying vibration to the tibialis anterior

tendon when subjects are in a static upright position,

which creates an illusion of body inclination, thus

decreasing postural stability and increasing postural

sway (Roll and Vedel, 1982).

Balance can be measured either clinically, or

biomechanically, for which force-plate analysis is

often used. A range of different parameters can be

extracted from the centre of pressure (COP) obtained

from the force plate, including temporal and spectral

parameters, as well as those related to the

organisation of the trajectory of the COP. Pioneering

work in this area was performed by Collins and De

Luca (Collins and De Luca, 1994), who

hypothesised that upright stance was controlled by

open-loop and closed-loop strategies, which

correspond to posture control strategies without and

with sensory input, respectively. In the case of an

open-loop control, sensory feedback is not used,

whereas closed-loop control uses feedback from the

proprioceptive, vestibular, or visual systems to

maintain an upright stance. Collins and De Luca

identified the critical point at which open-loop and

closed-loop control strategies diverged, and

proposed a method by which this time could be

calculated (Collins and De Luca, 1994). Although

the proposed method is based on posture control

strategies, the method used to calculate the critical

time interval makes assumptions that the two points

used to fit the regression lines to the data occur

101

Singh N., Snoussi H., Hewson D. and Duchêne J. (2009).

DETECTION OF THE CRITICAL POINT INTERVAL OF POSTURAL CONTROL STRATEGY USING WAVELET TRANSFORM ANALYSIS.

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 101-106

DOI: 10.5220/0001541701010106

 SciTePress

between one second and 2.5 seconds (Collins and De

Luca, 1994).

The present paper describes a new method that

can be used to calculate the time at which a change

is made between open and closed loop control

strategies. The proposed method, based on wavelet

analysis will be used to calculate the critical point

interval of the COP signal for elderly and control

subjects, as well as for eyes closed and vibration

conditions.

2 METHODS

2.1 Subjects

Seventeen healthy control subjects and ten healthy

elderly subjects (4 males and 6 females) participated

in the study. Control subjects’ mean age, height and

weight were 33.3 ± 7.4y, 168.0 ± 6.5cm, and 65.7 ±

17.6kg, respectively. Elderly subjects’ mean age,

height and weight were 80.5 ± 4.7y, 165.6 ± 7.0cm,

and 71.9 ± 9.9kg, respectively. All subjects who

participated gave their written informed consent. No

subjects reported any previous musculoskeletal

dysfunction.

2.2 Centre of Pressure Data

Centre of pressure data were recorded using a Bertec

4060-08 force plate (Bertec Corporation, Columbus,

OH, USA), which amplifies, filters, and digitises the

raw signals from the strain gauge amplifiers inside

the force plate. The resulting output is a six-channel

16-bit digital signal containing the forces and

moments in the x, y, and z axes. The digital signals

were subsequently converted via an external

analogue amplifier (AM6501, Bertec Corporation).

The coordinates of the COP signals can be

calculated as follows:

APX ==

;

MLY ==

(1)

The initial COP signals were calculated with

respect to the centre of the force-plate before

normalisation by subtraction of the mean.

2.3 Data Acquisition and Processing

Data were recorded using the ProTags™ software

package (Jean-Yves Hogrel, Institut de Myologie,

Paris, France) developed in Labview® (National

Instruments Corporation, Austin TX, USA). Data

were sampled at 100 Hz, with an 8th-order low-pass

Butterworth filter with a cut-off frequency of 10 Hz.

All calculations of COP data were performed with

Matlab® (Mathworks Inc, Natick, MA, USA).

2.4 Experimental Protocol

Subjects were tested using two experimental

protocols with a Bertec 4060-80 force plate (Bertec

Corporation, Colombus, OH, USA). Elderly subjects

were tested with their eyes open, while control

subjects were tested with their eyes open, their eyes

closed, as well as with vibration (eyes closed).

For the vibration condition, vibration was

applied bilaterally using the VB115 vibrator

(Techno Concept, Cereste, France) to the tibialis

anterior tendon for 10 s at 50, 70, and 90 Hz.

Immediately after vibration, subjects were instructed

to step onto the force plate, in order to ensure

subjects were subjected to the post-vibratory

response.

After 12 s standing on the force plate, a second

verbal command was given for subjects to step down

backwards. Subjects remained as still as possible

with their arms placed at their sides throughout the

protocol, while no constraint was given over foot

position, with subjects tested barefoot.

Measurements were repeated five times for each

experimental condition, with 30 s between each test.

2.5 Identifying the Critical Point using

Wavelet Transform Analysis

2.5.1 Locating the Critical Point

The critical point is defined as the point at which

sway is controlled by the closed-loop (feedback)

system. When postural control changes from open-

loop to closed-loop, a local maximum should be

observable in the COP. When upright stance is under

open-loop control, sway moves toward a certain

direction reaching a local maximum, at which point

commands from the closed-loop system pull sway

away from the local maximum back to the

equilibrium position (Figure 1).

It has been shown that local maximum modulus

wavelet transform analysis is well-suited to the

detection of local maxima (Mallat and Hwang,

1992). The method used in the present study differs

only in that the power spectrum is used rather than

the modulus, as the power spectrum represents the

energy in sway.

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Figure 1: Feedback control and the local maxima of the

centre of pressure signal over time. Data are in arbitrary

units.

2.5.2 Wavelet Function and Frequency

Bands

The wavelet transform method is particularly

suitable for analyzing non-stationary signals in a

multi-scale manner by varying the scale coefficient

that represents frequency.

The wavelet transform formula is:

tfabaWT

∫

⎟

⎠

⎞

⎜

⎝

⎛

−

)(),(

2/1

(2)

where b is the translation parameter and a is the

scale (frequency), and WT(a,b) is the wavelet

coefficient.

The power spectrum PS(a,b) is defined as

),(),( baWTbaPS =

(3)

The wavelet function

(x) should satisfy a

number of constraints, including zero mean and

orthogonality (Muzzy et al., 1991). Some wavelet

functions are known to distort low frequency

components. In order to avoid this problem, Coiflets

wavelet functions were used.

The sway energy of COP signals has been shown

to be concentrated below 2 Hz (Ferdjallah et al.,

1999), with the principal COP energy being

distributed in the range of 0.1-0.5 Hz (Schmuckler,

1997, Loughlin et al., 1996). Preliminary findings

from the present study showed that most of sway

energy was less than 0.5 Hz, as shown in Figure 2.

For the wavelet function

(x), scale a determines

the frequency and b determines the translation. In

the present study, a was chosen to force the

frequency of wavelet transformation to the range of

0.1-2.0 Hz.

Figure 2: Sample power spectrum of COP data (AP

direction).

The 0.1-2.0 Hz frequency band can be divided

into sub sections for which different control systems

are thought to be involved. For instance, Diener and

Gagey suggested that the visual system dominates

frequency bands below 0.5 Hz (Diener et al., 1984,

Gagey et al., 1985). In contrast, Thurner and

colleagues reported that the visual system operates

in the range of 0-0.1 Hz, the vestibular system from

0.1-0.5 Hz, somatosensory activity from 0.5-1.0 Hz,

while sway over 1.0 Hz is directly controlled by the

central nervous system (Thurner et al., 2000). Based

on these findings, the frequencies of 0.5-1.0 Hz were

chosen for the present study as the zone in which

proprioceptive input predominates.

The relation between scale and frequency can be

shown as:

(4)

Where F

is the centre frequency, F

the

frequency for scale a, and P is the sampling period

(0.01 s).

It is evident that the scale a should be in the

range 0.5-1.0 Hz for the present study, given the use

of proprioceptive perturbations. To this end, a is

transformed using a base-2 logarithm, and thereafter

denoted as the new scale s. The lower and upper

bounds of scale s were chosen as 6.5 and 8,

respectively. This scale range corresponds to the

frequency bands in the range of [0.44, 0.88] Hz.

After determining scale s, translation b, and the

wavelet function, the power spectrum can be

calculated, an example of which is shown in Figure

DETECTION OF THE CRITICAL POINT INTERVAL OF POSTURAL CONTROL STRATEGY USING WAVELET

TRANSFORM ANALYSIS

103

Figure 3: Sample wavelet power spectrum of COP data

(ML direction). Darker and lighter areas represent larger

positive and negative power spectrum values, respectively.

2.5.3 Identifying the Critical Point Time

Interval

Postural control strategies can be changed from

open-loop control to closed-loop in which visual,

vestibular and somatosensory feedbacks can be used.

When feedback control is used, sway moves away

from the local maximum and back to the equilibrium

position. The critical point occurs at scale s and time

t, where the power spectrum is at the local

maximum. It is simply the local maximum of the

power spectrum wavelet transform method (LMPS),

which can be mathematically defined as:

),(),(

xsPSxsPS <

(5)

Where x is either the left or right neighbourhood

of x

, x

∈

R, and s is scale.

There are numerous local maxima within specific

frequency bands, which indicates that feedback

control has been started at time t and scale s.

Postural control corresponds to the frequency bands

rather than a single frequency, meaning that the

identification of maxima across the frequency range

was required. A local maximum line L

can be

defined as the line consisting of the local maxima at

time t across frequency bands from a to b:

}...),,({ bastsPSL

(6)

In the present study, local maxima lines were

identified in the frequency bands [a=0.44, b=0.88]

Hz. It is necessary to search for the local maximum

around time t within a 2Δt interval denoted by [t-Δt,

t+Δt]. If the local maximum line L

can be identified

within the time interval [t-Δt, t+Δt], it is concluded

that feedback control has been used at time t. The

time interval Δt used to search for the local

maximum line depends on the specific data. If Δt is

too small then too many local maxima will be

identified. In the present study Δt was chosen as

0.62 s. There are numerous such local maximum

lines for each scale. The mean of the length of these

local maxima lines was calculated and taken to be

the critical point interval (CPI). The average CPI for

all five trials for each subject for each experimental

condition was used for subsequent statistical

analysis.

2.6 Statistical Analysis

All statistical analyses were performed with the

Statistical Package for Social Sciences (SPSS Inc.,

Chicago, IL, USA). Analysis of variance was used to

compare results between conditions, with CPI as the

dependent variable and the experimental condition

as the independent variable. Data were expressed as

means and 95% confidence intervals. Alpha level

was set at p<0.05.

3 RESULTS

The CPI for elderly and control subjects under the

eyes open condition are presented in Figure 4.

Significantly higher values for CPI can be seen for

control subjects than for elderly subjects (p<0.05).

The CPI for AP displacement was significantly

lower than the corresponding value for ML

displacement for both control and elderly subjects

alike (Figure 4; p<0.05).

Figure 4: Critical point interval for elderly subjects and

control subjects in the eyes open condition. Data are

means and 95% confidence intervals. *Significantly

different from control subjects (p<0.05);

Significantly

different from ML displacement (p<0.05).

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The results for the eyes open and eyes closed

conditions are presented in Figure 5. Significantly

higher values for CPI were observed for the eyes

open condition than for eyes closed (p<0.05).

Significantly lower values of CPI were observed for

AP displacement when compared to ML

displacement for both eyes open and eyes closed

conditions (Figure 5; p<0.05).

Figure 5: Critical point interval for control subjects in the

eyes open and eyes closed conditions. Data are means and

95% confidence intervals. *Significantly different from

eyes open (p<0.05);

Significantly different from ML

displacement (p<0.05).

In respect to vibration, there was no significant

difference between conditions for ML displacement

(Figure 6). In contrast, both 70 Hz and 90 Hz

vibrations significantly decreased CPI values in

comparison to the 0 Hz and 50 Hz vibration

condition (Figure 6; p<0.05).

Figure 6: Critical point interval for control subjects in the

eyes open, eye close and vibration condition. Data are

means and 95% confidence intervals. *Significantly

different from eyes closed (p<0.05);

Significantly

different from ML displacement (p<0.05).

4 DISCUSSION

Lower values of CPI are associated with increased

closed-loop postural control. In essence, the lower

the CPI value, the quicker the response to sensory

input, and thus the greater reliance on closed-loop

control. Lower values of CPI can therefore be

interpreted as a less efficient open-loop control, thus

requiring an earlier intervention of the closed-loop

system. This strategy of postural control will require

greater energy expenditure due to the repeated

muscular interventions in order to remain stable.

The CPI parameter proposed in the present paper

was able to distinguish between all of the different

experimental conditions tested. In respect to

differences between AP and ML displacements, CPI

values were lower for AP than for ML displacement

for all experimental conditions indicating less

postural stability. This result was expected given

that ML displacement is more stable than AP

displacement due to the anatomy of the ankle and

knee joints, which limit movement in the ML

direction. In addition, subjects’ feet are placed in a

series position for the ML direction, as opposed to

the parallel positioning for AP.

In respect to differences with ageing, elderly

subjects had lower CPI values than control subjects

for both AP and ML displacement. Such results are

indicative of an earlier feedback control for elderly

subject, which is due to a tightly controlled posture

in elderly subjects, as reported previously for other

parameters such as Detrended Fluctuation Analysis

(DFA). In studies of DFA, elderly subjects had less

complex patterns of AP displacement, which is

indicative of a tight postural control used to reduce

displacement as much as possible in order to

maintain a stable posture (Amoud et al., 2007a,

Norris et al., 2005).

The differences observed between eyes open

(EO) and eyes closed (EC) conditions were in

agreement with those between elderly and control

subjects. The CPI values were greater for EO than

for EC for both AP and ML displacements. The lack

of visual information required subjects to tightly

control displacement in both AP and ML directions

using the closed-loop system in order to maintain

equilibrium.

The effect of the vibration applied to the tibialis

anterior tendon is to decrease the stability of the

postural control system by invoking an illusion of

tilt. The vibration required to invoke this effect must

be at least 70 Hz. This effect is only seen in the AP

direction in which the tendinous vibration was

applied.

The results for all experimental comparisons

demonstrate that a decreased ability to maintain

postural stability can be identified by an increased

use of the closed-loop postural control system. Such

DETECTION OF THE CRITICAL POINT INTERVAL OF POSTURAL CONTROL STRATEGY USING WAVELET

TRANSFORM ANALYSIS

105

results might seem contradictory at first, in that both

elderly subjects and subjects with no visual feedback

can tightly control their postural equilibrium.

However, similar results have been reported for

COP signals for a range of parameters such as

entropy and DFA (Amoud et al., 2007b, Norris et

al., 2005, Amoud et al., 2007a), as well as for other

physiological signals such as force production

(Challis, 2006). It has also been suggested that

physiological control processes become less

complex with age as well as when disease is present

(Goldberger et al., 2002).

5 CONCLUSIONS

In conclusion, the CPI parameter offers a new

method of detecting differences in postural control

between different experimental conditions or

changes due to ageing. Lower values of CPI reflect

greater reliance on closed-loop postural control,

which requires greater energy expenditure due to the

repeated muscular interventions in order to remain

stable.

ACKNOWLEDGEMENTS

This study was undertaken as part of the

PARAChute research programme (ANR-05-RNTS-

01801; RNTS-03-B-254; ESF 3/1/3/4/07/3/3/011;

ERDF 2003-2-50-0014 and 2006-2-20-0011; CACR

E200308251).

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