A great
wader taken at the very moment of its landing, such is the symbol
chosen by the first posturologists to express the meaning of their
research. This bird shows the dynamics of stabilisation in a very
strong way as its entire body stretches forward to its rest posture.
On the contrary, a human body at rest secretly and almost imperceptibly
continues its struggle with the forces of gravity.
Indeed our body never finds its balance, it keeps trying to reach this ideal and ever escaping state. Yet the dynamics of this search exist in a subtle way in man and only become apparent to those who attempt to decipher them. Now, directly concerning this constant effort of posturologists towards demonstrating the dynamics of stabilisation of the human body, appears the need for a new model of platform of Stabilometry. Some experiences have shown, indeed, that the nonlinear dynamic analysis of the stabilometric signal could be more efficient than its conventional analysis (Gagey et al., 1998). Unluckily, if the micro computers are now able to execute in a few seconds  instead of several hours  the new algorithms of this analysis (Le Van Quyen et al., 1999), the signal must still have an important number of points. 

But the actual normalised platform, with its 5 Hz sampling cadence, only has 256... One cannot simply increase the recording time in order to obtain more points, for that would tire the patients too much. Nor could one increase the sampling cadence of the actual normalised platform, for the distances between the successive sampling positions of the centre of pressure would then become too small for evaluation by that measurement chain (Gagey et al., 1999). Thus, a new model of platform of Stabilometry must be studied, that would be adapted to the requirements of a faster sampling while remaining as close as possible to the building standards defined by the Association Française de Posturologie in 1985 (Bizzo et al., 1985).
For the
building of this new platform the following changes in the specifications
of the normalised
platform can be proposed:
This model of platform will
be referred to as «platform AFP40/16», considering
its characteristics:
A prototype of this new platform
was built in order to try and answer experimentally two questions:
To allow platform AFP40/16 to be assimilated to an
AFP normalised platform, the one and only requirement is that
the distributions of the conventionnal stabilometric parameters
delivered by this platform are similar to the theoric distributions
of the normalised platform.
Such similarity is impossible
for the Length parameter and for all the parameters that derive
from it  LFA, speed Variance, acceleration Variance, VFY 
because the values of length and of its derivatives change according
to the sampling cadence (Gagey et al., 1999). Yet it is
possible to reconstitute a signal sampled at 5 Hz from a signal
sampled at 40 Hz, just by taking one point out of each 8. The
calculation of length, and of its derivatives, from this reconstituted
signal can give values similar to those of normalised platforms,
if the other changes brought to the building of platform AFP40/16
do not interfere.
As for the values of parameters
Xmean, Ymean, Area, Romberg Quotient, ANØ2X, ANØ2Y,
they stay the same whatever the sampling cadence of the signal
(Gagey et al., 1999). Only the other changes brought to
the building of platform AFP40/16 could modify the value of these
parameters by their intervention.
The experimental study of
the «normality» of platform AFP40/16 was run in two
different ways:
Comparison of recordings
Ten «normal» subjects
 i.e. free from sensations of vertigo, instability, actual
or recent back pain  have been recorded in open and closed
eyes situations, successively and at short intervals, on a normalised
platform (AFP5/12) and on platform AFP40/16. The parameters have
been calculated out of the total number of points of each signal.
The distributions of these two series of parameters have been
submitted to a mean comparison under the Student's t test (table
I).
There is no significant difference
between the distributions of parameters Xmean, Ymean, Area,
obtained for those 10 subjects on one platform and the other.
However there is a statistically very significant difference between
the distributions of length parameters, as could be expected.
The latter difference is due to the different sampling cadences
on one plaform and the other.
Platform 







40/16  Mean 






Standard Deviation 







5/12  Mean 






Standard Deviation 







Comparison  p < 






TABLE I  Comparison of the distributions
of parameters obtained from recordings on platforms AFP40/16 and
AFP5/12.
Means, standard deviations
and significance of the mean comparison of parameters Xmean,
Ymean, Area, Length, Length in X (L in X), Length in Y (L in
Y) obtained from the recordings of ten subjects on an AFP40/16
platform and on a normalised AFP5/12 platform.
Comparison to Normes85
From the recordings on platform
AFP40/16 of the ten «normal» subjects, the parameters
have been recalculated, no longer out of the total number of points,
but out of the 256 points obtained by reduction to a sampling
cadence of 5 Hz. The distribution of those parameters has
been compared to the distribution of the Normes85 parameters,
thanks to a mean comparison under the Student's t test (table
II).









EO  Student's t 








p < 








EC  Student's t 








p < 








TABLE II  Comparison to Normes85 of recording
results on platform AFP40/16.
Student's ttest of means
comparisons between the distributions of parameters published
in Normes85 and the distributions observed with the new platform,
after a reduction of the cadence to 5 Hz. (N=10).
The distributions of parameters
LFA, VFY, ANØ2Y and Romberg Quotient observed with the
new platform are statistically different from the distributions
published in Normes85. However these differences do not allow
us to draw the conclusion that the new platform cannot be assimilated
to a normalised platform. The number of subjects studied is limited,
and above all, the abnormal values of the individual parameters
have no systematic appearance (table III). On the contrary the
presence of aberrant subjects is more likely to come from specificity
in the subjects' recruitment than from a systematic difference
due to the platform. Complementary studies are clearly indispensable
in order to draw proper conclusions.




Variance  ANØ2X  ANØ2Y  RombergQ  
E.O. 
1.37 5.86 5.60 7.39 16.37 1.93 6.69 1.33 0.59 
113.8 99.4 287.3 109.9 123.9 111.2 56.7 102.1 71.7 
0.76 0.86 0.69 0.47 0.88 1.16 0.82 0.87 0.71 
0.50 0.73 0.87 1.12 3.99 14.99 4.11 0.43 0.56 
4.33 5.40 5.66 2.46 11.23 25.78 10.46 4.46 3.37 
23.05 12.54 3.88 1.65 1.87 12.81 9.59 5.45 27.36 
7.51 4.86 7.01 1.63 2.20 8.34 6.60 17.50 12.02 

E.C. 
0.50 8.83 6.98 1.58 15.69 4.08 6.30 5.16 2.54 
187.5 206.5 430.6 77.0 107.3 162.0 155.4 187.4 149.9 
0.88 1.37 0.87 0.71 0.77 1.33 0.87 1.14 0.78 
0.69 2.78 0.42 2.53 3.41 15.18 1.04 0.07 0.94 
5.67 11.94 7.23 4.21 12.48 27.21 9.19 7.64 5.49 
12.63 24.63 18.84 30.04 3.26 8.44 15.46 1.50 4.74 
13.30 23.69 44.91 23.34 47.06 27.30 16.75 10.01 31.77 
164.8 207.8 149.9 70.1 86.5 145.6 274.0 183.4 209.0 
TABLE III  Individual values of the stabilometric
parameters, calculated at 5 Hz, of the ten normal subjects.
The presence of aberrant
individual values (v) can be noticed, yet not a systematic
variation of the value of all the parameters.
The subjects' order is the same in the two parts of the table
(open eyes and closed eyes).
No measurement chain is perfect. There is always a
differential between the value delivered by the measurement chain
and the true value. The undimensional equation between that differential,
Di,
and the true value of a given measurement i:
is used in metrology to define a measurement
chain. That equation is called «the uncertainty» of
the measuring apparatus.
The determination of the
minimum necessary level of uncertainty of a measuring apparatus
obviously depends on what is expected from it. But that level
of uncertainty cannot be set exactly by any data. One can just
compare on the one hand the range of measurement expected from
the apparatus, and on the other hand its concrete performances,
in order to give the soundest foundations possible to a judgement
that will have to stay cautious anyway, in answer to the question:
is the uncertainty of the new platform «coherent»
with the measurements expected from it?
The range of measurements at 40 Hz
The mean length between two
successive elementary positions of the centre of pressure sampled
at 5 Hz by platform AFP5/12, is of 1.6 mm and 19% only of such
lengths are inferior or equal to 0.2 mm (Gagey et al.,
1999). But platform AFP40/16 samples eight times faster, so it
has to measure much smaller distances that have to be evaluated
theoretically and experimentally.
Theoretically, the mean length
of the statokinesigram for recordings of 51.2 s at 40 Hz is of
740 mm (Gagey et al., 1999), which represents a mean speed
of the centre of pressure of about 14 mm/s. We could expect the
elementary position change of the centre of pressure between two
successive samplings, i.e. with a 0.025 s interval, to be of an
average 0.36 mm.
In reality the analysis of
the distribution of the lengths of 10,655 elementary position
changes of the centre of pressure of normal subjects recorded
in open and closed eyes situations (fig. 1), shows that the median
of these lengths, measured by platform AFP40/16, is of 0.2 mm
and 15% of them are equal or inferior to a tenth of millimetre.
FIG. 1  Histogram of the lengths of elementary position changes measured with platform AFP40/16.
N = 10,655. 
The concrete performances of the platform
It is now possible to compare
the concrete performances of the platform with the expected range
of measurements and level of accuracy.
The resolution of the 16 bits
digitizer
When sampling at 40 Hz,
approximately half the measurements cannot be read correctly by
a 12 bits digitizer(1),
because of its resolution (Gagey et al., 1999). Therefore
it is important to check what happens at this cadence with a 16
bits digitizer.
If the whole scale is set
at 981 N, the last bit of the digitizer will number 0.03 N (only
half the voltage range, between 0 and 10 Volts, being used), which
corresponds, for an adult subject, to a position change of about
two hundredth of millimetres (Cf. in appendix 1, conversion
of Newtons to millimetres). Therefore the resolution of the 16
bits digitizer is much higher than required.
Note 1: In reality the resolution of a digitizer depends on the full scale of measurement. A 12 bits digitizer could read correctly the measurements if only it did a double reading, by programmatically adapting the full scale between the two measurements.
The differential with the
true value of the measurement
As a reminder, the platform
measures forces and not distances.
If the force produced by
a given and constant mass set on the platform is measured several
consecutive times, it appears that the measurement chain delivers
the true value of that force plus or minus a certain differential
with the true value. As this differential does not exclusively
depend on the measurement chain but on all the measuring conditions,
the equation between that differential, Di, and the true value of
the measurement, i:
will not define exactly the uncertainty of the platform, but it gives a good experimental approach to it.
Statistics describing the differential with the true value
Three aspects of the distribution
of this differential with the true value have been studied: Is
it normal? Is it constant? Does it depend on the force measured?
The 95% limit of certainty
of this distribution has been evaluated from these studies.
A known mass being set near
the centre of the platform, recordings are made of a series of
measurements of the value of the force applied on the platform
by that still mass. After checking that the mean value of these
numerous measurements (N > 1,000) corresponds to the true value
of the force, the differential with that true value is calculated
for each measurement:
where Dji stands for the differential
with the true value, i, of the jth measurement mj.
The distribution of the differential
with the true value is studied from such data.
The histogram of the distribution
of the differential with the true value (fig. 2) has been drawn
up out of 2,048 measurements of a force of 87.31 N produced by
a mass of 8.900 Kg set on the platform.
FIG. 2  Histogram of the distribution of differential with the true value of a force of 87.31 Newtons. (N = 2,048) 
Then the same measurements, of the same 87.31 N force, have been repeated five times in the same conditions at time intervals varying from 3 minutes to 48 hours. The parameters describing the distributions studied are laid out in table IV.








Mean 





Standard Deviation 





Confidence Limits 95% 





N 





TABLE IV Mean, Standard deviation, confidence limit at 95% of the distributions of the differential with the true value studied during five series of measurements of the same force at different time intervals.
Unit: Newton.
Three series of measurements
have been made in the same conditions, but with different forces
applied on the platform. The parameters describing the distributions
of the differential with the true value studied in these conditions
are laid out in table V.






Mean 



Standard Deviation 



Confidence Limits 95% 



N 



TABLE V  Mean, Standarddeviation, confidence limit at 95% of the distributions of the differential with the true value studied during three series of measurements of different forces.
Unity: Newton.
According to the measurement
results laid out in tables IV and V, one has less than five chances
out of a hundred to be wrong in assuming that a force measure
delivered by this platform is true to the closest ± 0.2
N.
Now, this measurement of the forces at the closest ± 0.2
N corresponds to a measurement of the position of the centre of
pressure at the closest ± 0.1 mm, for an adult subject
approximately weighing 70 Kg (cf. Appendix 1).
The present
study aimed at answering two questions:
The first results are encouraging: it seems that this
platform can be assimilated to a normalised platform, yet complementary
studies are indispensable to be absolutely sure.
However, the uncertainty
of the measurements executed by the new platform appear to us
to be very compatible with the actual analysis of the signal,
as well as with its treatment by nonlinear dynamic analyses.
The platform measures forces and not distances. It is therefore necessary to convert millimetres into Newtons and vice and versa, thanks to equations of the platform:




FIG. 2  Plan of the platform. 
Where:
The referential Oxy has its origin in the centre of the equilateral
triangle at the vertexes of which the gauges are set, the Ox axis
parallel to the line connecting the right and left gauges (fig.
3)
L: Distance between the gauges; 400 millimetres according to the
AFP standards,
F: Sum of the forces measured by the gauges,
Fv, Fd, Fg: Forces measured respectively by the front, the right
and the left gauges.
(The developments of these formulas appear in the second lesson
of posturology [Gagey et al., 1993]).
Measurement of the elementary position changes of the centre
of pressure.
From those equations of the
platform it is possible to show, according to the measured variations
of the forces, dF, the variations of position of the Cartesian
projections, dX and dY, of the centre of pressure between two
successive samplings at times t and t+1:
Calculation of dX
If X[t]=0, the expression
of dX is simplified:

If we assume that the centre of pressure moves parallel to the Ox axis, then the variations of force, dF, measured by the right and left gauges are equal and of opposite signs and if we assume that the centre of pressure has moved to the left, it appears that:
If we assume that F[t+1]=F[t] we then have:


Calculation
of dY
When
the centre of pressure moves forward, the sum of the force variations
measured by the back gauges is equal to the force variation, dF,
measured by the front gauge, therefore:
We then have:
In the normal conditions of Stabilometry, we do not make an important error by assuming that F[t+1]=F[t]. If we replace L by its value, 400 mm, it then appears:

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Aknowledgments to Mr Guy BIZZO for his precious help.