K.W.: Stabilometry, Frequency analysis, Ventilation, Postural control, Functional anatomy, vestibular function.
Until now the clinicians lacked norms to read the frequential analyses of the stabilometric signal of their patients. That work gives a first estimation of the theoretic normal values of the distribution parameters of the normalised amplitude of postural sway in the 0.2 Hz frequency band [NAØ2], a frequency band corresponding to the ventilation rhythm and on which ten years of clinical experience focus our attention.
Since the
middle of the XIXth century (Vierordt, 1864), many physiologists
have tried and observed how man stands upright. At first these
researches did not have any medical impact because the signals
of the initial material were hardly readable. Now it is acknowledged
that the force platforms in use for nearly 50 years (Ranquet,1953)
allow us, thanks to the developments of signal analysis techniques,
to explore the control of the orthostatic posture in an easy and
totally neutral way (AAN, 1992; Cambier, 1993). It is therefore
normal that clinicians should try and use these platforms in order
to examine the patients who have difficulties in standing upright
because of a clearly defined illness or of disorders still misunderstood.
But
the clinical use of those force platforms requires the existence
of norms to which the performances of the patient can be compared
(AFP, 1984). In the absence of any decision of the normalisation
committee of the International Society for Postural and Gait Research,
the Association Française de Posturologie has published,
first, building standards for a force platform (Bizzo et al.,
1985), then standards of recording conditions and of various spatial
parameters (AFP, 1985; 1986). But no norms of frequential analysis
of the stabilometric signal have been published so far. The present
work will try and fill that gap.
This
ten years delay may seem strange. Actually, it was hard to direct
such normalisation works prior to a long clinical experience,
as shown by the first attempts at using frequential analyses clinically
(Taguchi, 1978).
During those ten years it has been noticed (Gagey, 1986) and confirmed
(Guillemot & Duplan, 1995) that anomalies in the 0.2 Hz frequency
band appeared in patients who all showed, for various reasons,
functional disorders of the body axis. That distinctive feature
of postural sway in the 0.2 Hz frequency band in pathology already
gave a first reason for focusing our attention on that frequency.
Simultaneously,
several fundamental works confirmed that not only did the sway
in that frequency band share the same rhythm as ventilation, but
that it was also synchronous with ventilatory rhythm (Gurfinkel
& Elner, 1968; Le Roux et al., 1976; Hunter & Kearny,
1981; Bouisset & Duchêne, 1994).
The
0.2 Hz frequency band of postural sway therefore shows distinctive
features that justify special attention.
Stabilometric recordings
All recordings
have been performed on a prototype of stabilometry platform normalised
by the Association Française de Posturologie (Bizzo et
al., 1985), computerized, validated by the works of the same
Association (AFP, 1985), and commercially available in southern
Europe (CIA.Sistemi, Modena; Dynatronic, Céreste; QFP.systems,
SophiaAntipolis; Satel, Toulouse; Midicapteurs, Toulouse; Dune,
Mulhouse).
The
sampling is at 5 Hertz. The recording time is of 51.2 s. The analogic
signal issued by each of the three strain gauges was filtered
by an antiwithdrawal filter, 0/2 Hz running band, structure of
the fourth order.
The
visual environment is strictly normalised: target at 90 cm
in front of the subject, with a 2,000 lux light, lateral walls
at 50 cm. The position of the feet on the platform is normalised:
feet at 30°, with a 2 cm space between the heels; barycenter
of the polygon of support always situated at the same point, whatever
the subject's shoe size.
The
recordings have been realised in an open eyes situation, eyesight
corrected if necessary and according to the subject's habit, then
closed eyes in halflight.
Only
one series of recordings has been realised to study the distribution
of the ranges of postural sway.
Four series of recordings have been realised, at 8 days interval,
same hour and same day of the week, to study the repeatability
of the ranges of postural sway.
Groups
The groups
of normal subjects have not been rigorously formed by drawing
lots among the French population.
For the study of the distribution of the ranges of postural sway,
the first volunteers to have come have been questioned and, among
them, 36 men and 46 women, between 19 and 60 years of age (mean
age 35 years old), have been selected only on interrogation criteria:
absence of any acknowledged pathological symptom and especially
absence of any pain in the body axis in the three previous months.
For
the more constraining study of the repeatability of the amplitudes
of postural sway, 41 young men, between 18 and 26 years of age
(mean age 22 years old), paid, have been selected on more rigorous
criteria including a postural clinical examination (Gagey &
Weber, 1995) and a series of stabilometric recordings, the spatial
parameters of which had to be within the normality limits.
Frequential analysis
After its normalisation according to its mean value and the application of the Hamming window, the signal has been submitted to CooleyTurkey's algorithm of the FFT, that has given a value of the amplitude spectrum for each of the 125 elementary frequency bands at 0.02 Hz between 0 and 2.5 Hz.
Normalised amplitude of postural sway in the 0.2 Hz frequency band
The aim of the work is not the study of the absolute amplitude of postural sway in the given frequency band, but the study of their relative amplitude compared with those of the other frequency bands. We have used the normalised amplitude of postural sway in the 0.2 Hz frequency band (NAØ2) defined by the following formula:
where A represents the amplitude of each elementary
frequency band, f, given by the algorithm of the FFT.
The
limiting values used for the calculation will be discussed later.
Statistical analysis
The distribution
of that NAØ2 parameter (ANØ2 in French) has been
studied from the recordings, open eyes and closed eyes, of the
group of 82 normal subjects, for the leftright sway and the anteriorposterior
sway. In order to define, from the observed distribution, the
normal mean value and its standard deviation, a first class statistical
risk has consisted in eliminating the subjects situated more than
two standard deviations away from the mean of that basic distribution.
The
distribution of the paired difference of that NAØ2 parameter
between two recordings performed in similar conditions has been
studied from the four series of recordings, open eyes and closed
eyes, of the group of 41 normal subjects, for the leftright sway
and the anteriorposterior sway. In order to define, from the
observed distribution, the normal mean value of the paired difference
and its standard deviation, a first class statistical risk has
consisted in eliminating the subjects for which at least one recording
showed an NAØ2 parameter situated more than two standard
deviations away from the mean of theoretic normal distribution
previously defined.
Those
statistical risks will be discussed later.
Distribution of the normalised amplitude of postural sway in the 0.2 Hz frequency band, (NAØ2), in normal subjects
Leftright postural sway, open eyes situation
Among the 79 subjects remaining after application of the first class risk, the mean of the NAØ2 parameter for the leftright postural sway in an open eyes situation, is of 11.39 ± 6.95; confidence limit superior to 95%: 25; sum of the X2 = 14010 (fig. 1).
FIG. 1  Distribution
of the NAØ2 parameter in a normal population. Open eyes
situation, leftright postural sway. Histogram of the observed distribution, Gaussian curve of the theoretic distribution. 
Leftright postural sway, closed eyes situation
Among the 79 subjects remaining after application of the first class risk, the mean of the NAØ2 parameter for the leftright postural sway in a closed eyes situation is of 16.57 ± 10.41; confidence limit at 95%: 36.97; sum of the X2 = 32810 (fig. 2).
FIG. 2  Distribution
of the NAØ2 parameter in a normal population. Closed eyes
situation, leftright postural sway. Histogram of the observed distribution, Gaussian curve of the theoretic distribution. 

Anteriorposterior postural sway, open eyes situation
Among the 79 subjects remaining after application of the first class risk, the mean of the NAØ2 parameter for the anteriorposterior postural sway in an open eyes situation is of 8.37 ± 4.86; limit of confidence superior to 95%: 17.9; sum of the X2 = 7377 (fig. 3).
FIG. 3  Distribution
of the NAØ2 parameter in a normal population. Open eyes
situation, anteriorposterior postural sway. Histogram of the observed distribution, Gaussian curve of the theoretic distribution. 

Anteriorposterior postural sway, closed eyes situation
Among the 79 subjects remaining after application of the first class risk, the mean of the NAØ2 parameter for the anteriorposterior postural sway in a closed eyes situation is of 14.65 ± 7.98; limit of confidence superior to 95%: 30.3; sum of the X2 = 23878 (fig. 4).
FIG. 4  Distribution
of the NAØ2 parameter in a normal population. Closed eyes
situation, anteriorposterior postural sway. Histogram of the observed distribution, Gaussian curve of the theoretic distribution. 

Distribution of the paired difference of the normalised amplitude of postural sway in the 0.2 Hz frequency band (NAØ2) between two similar recordings of normal subjects.
Leftright postural sway, open eyes situation
Among the 170 repetitions remaining after application of the first class risk, the mean of the paired difference of the NAØ2 parameter for the leftright postural sway in an open eyes situation is of  0.17 * 9.04; limits of confidence at 95%: 17.89 / + 17.55 (fig. 5).
FIG. 5  Distribution
of the paired difference of the NAØ2 parameter between
two similar recordings in a normal population. Open eyes situation,
leftright postural sway. Histogram of the observed distribution, Gaussian curve of the theoretic distribution 

Leftright postural sway, closed eyes situation
Among the 222 repetitions remaining after application of the first class risk, the mean of the paired difference of the NAØ2 parameter for the leftright postural sway in a closed eyes situation is of  0.23 ±11.28; limits of confidence at 95%:  22.34 / + 21.88 (fig. 6).
FIG. 6  Distribution of the
paired difference of the NAØ2 parameter between two similar
recordings in a normal population. Closed eyes situation, leftright
postural sway. Histogram of the observed distribution, Gaussian curve of the theoretic distribution. 

Anteriorposterior postural sway, open eyes situation
Among the 168 repetitions remaining after application of the first class risk, the mean of the paired difference of the NAØ2 parameter for the anteriorposterior postural sway in an open eyes situation is of 0.35 ± 5.56; limits of confidence at 95%:  10.55 / + 11.25 (fig. 7).
FIG. 7  Distribution
of the paired difference of the NAØ2 parameter between
two similar recordings in a normal population. Open eyes situation,
anteriorposterior postural sway. Histogram of the observed distribution, Gaussian curve of the theoretic distribution. 

Anteriorposterior postural sway, closed eyes situation
Among the 222 repetitions remaining after application of the first class risk, the mean of the paired difference of the NAØ2 parameter for the anteriorposterior postural sway in a closed eyes situation is of 1.85 ± 9.85; limits of confidence at 95%:  17.46 / + 21.16 (fig. 8).
FIG. 8  Distribution
of the paired difference of the NAØ2 parameter between
two similar recordings in a normal population. Closed eyes situation,
anteriorposterior postural sway. Histogram of the observed distribution, Gaussian curve of the theoretic distribution. 

The choice of the limits of the frequency band
The limits
of the 0.2 Hz frequency band have been set at 0.16 and 0.24 Hz
to cover a standard range of ventilatory rhythms (Thayer et
al., 1996), but also to take into account the ten years of
clinical experience during which fundamentals of the amplitude
spectrum have been frequently observed in that scale.
The
inferior limit of the reference frequency band has been set at
0.04 Hz to eliminate the effects of possible deviation. Indeed,
it sometimes happens that the position of the pressure center
deviates in a regular and continuous way during the whole time
of the recording session.
The
superior limit of the reference frequency band has been set at
0.6 Hz to take into account the ambiguity of the stabilometric
signal. Because it measures forces, the stabilometry platform
records the effects of all the accelerations acting on the corporal
mass: acceleration of gravity and accelerations of postural sway.
But we know that for the lower frequencies we only make a small
relative mistake by assimilating the pressure center to the projection
of the gravity center on the plane of the polygon of support.
However that mistake quickly grows with frequency, and approaches
100% at 0.6 Hz (Gurfinkel, 1973; Gagey & Weber, 1995). When
we want to limit the studies to postural sway of the full corporal
mass  the only one to be controlled by the postural system (Gagey
et al., 1985)  it is useless to take into account the
frequency bands of the FFT superior to 0.6 Hz.
First class risks
A group
of «normal» subjects always comprises subjects who
are aberrant compared to the studied variable and those subjects
considerably modify the mean and most of all the variance of the
observed distribution of that variable. To decide whether or not
we will take such subjects into account in the estimation of the
parameters of the theoretic normal distribution of the variable,
always represents a risk that can be guided only by considerations
which are extrinsic to the statistical analysis.
In
order to estimate the mean and the variance of the theoretic normal
distribution of the NAØ2 parameter, the risk consisted
in eliminating all aberrant subjects situated more than two standard
deviations away from the mean of the observed distribution. That
risk is generous, and needs explaining.
The
exclusion criteria during the forming of the group of «normal»
subjects were only based on the results of an interrogation, which
is hardly restrictive (the complementary explorations of an aberrant
subject from that group of «normal» subjects, for
instance, led to the diagnosis and surgical treatment of an acoustical
neurinoma that the subject was unaware of). Moreover, clinical
experience teaches us to suspect a link between an abnormal amplitude
of postural sway around 0.2 Hz and the existence of functional
disorders of the body axis  and we know the prevalence of such
minor functional disorders to be high in the population. For those
various reasons, it seemed wise to take a very restrictive first
class risk.
In
order to estimate the mean and variance of the theoretic normal
distribution of the paired difference of the NAØ2 parameter
between two similar recordings, the risk consisted in eliminating
the comparisons made on an abnormal parameter, because the study
tries and defines the repeatability of the NAØ2 parameter
in a «normal» population.
Influence of the sway plane on the NAØ2 parameter
In an open eyes situation, there is a statistically very significant difference (p<0.01) between the distributions of the NAØ2 parameter for the leftright sway and for the anteriorposterior sway. That difference disappears in a closed eyes situation.
Influence of vision on the NAØ2 parameter
Whatever
the sway plane, there is a statistically very significant difference
(p<0.001) between the distributions of the NAØ2 parameter
in open eyes and closed eyes situations. That difference is surprising.
To our knowledge it has never been pointed out, and even less
explained.
We
can notice that an occlusion of the eyes leads to a redestribution
of the «weight» of the many afferences participating
in the control of the orthostatic posture. The increase, in a
closed eyes situation, of the relative importance of the proprioceptive
information given by the body axis, could explain that increase
of the percentage of the amplitudes of postural sway in the 0.2
Hz band. That hypothesis, not yet checked, is based on the priviledged
relations that seem to show between the 0.2 Hz sway and the functionning
of the body axis.
Conclusion
That study, in the normal subject, of the amplitude of postural sway in the 0.2 Hertz frequency band, is limited in many ways. Yet it is enough for a first clinical approach to the 0.2 Hz phenomenon, the results of which will show whether or not it is useful to return to that statistical analysis with more means.
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We thank RhônePoulenc society for their financial support.