Once again it has been shown, by Collins and Deluca, that the stabilometric signal contains two kinds of information that could be distinguished by an artifice of calculation: information about the movements of the center of pressure and information about the movements of the center of gravity.
The analysis used by Collins and Deluca (analysis of diffusion of the stabilogram) puts forwards new stabilometric parameters to characterize these two types of informations: the diffusion coefficients. But an experimental study of these parameters shows that they are either too poorly sensitive, or too strongly correlated to conventional stabilometric parameters to be useful.
This study underlines that the parameter of length of the statokinesigram remains the best measure of the «dance» of the center of pressure.
Introduction
When we try
to maintain an inverted broom on the fingertip of our index, we
have to move this finger rapidly and widely in different directions
to avoid equilibrium breakage of this kind of inverted pendulum,
while the centre of mass of the broom oscillates slowly and shortly,
and in a slower and shorter way as the control of its equilibrium
is better anticipated.
A similar phenomenon is observed
on stabilometric recordings of quiet standing human being, apparently
immobile: the centre of gravity sways a little and slowly while
the centre of pressure is animated with faster and ampler movements:
the «dance» of the centre of gravity and the «dance»
of the centre of pressure do not participate to the same rhythm.
Of course, the stabilometric signal
in itself doesn't distinguish these two phenomena but it contains
both, and Gurfinkel (1973) showed that it was theoretically possible
to split them because of their different frequency:
The amplitude of the «low»
frequency oscillations, inferior to 0,6 Hz, corresponds to the
amplitude of the oscillations of the centre of gravity, with a
relative error inferior to 10% at around 0,2 Hz but of 100% at
around 0,6 Hz (Gagey & Weber, 1995).
The amplitude of the «high»
frequency oscillations, in the 1 Hz frequency band, corresponds
to the amplitude of the oscillations of the centre of pressure,
with a relative error becoming weaker as the frequency rises.
These two phenomena oppose each
other not only by their frequency, but also by their role in the
control of orthostatic posture (quiet standing). The «dance»
of the centre of pressure controls actively the posture while
the «dance» of the centre of gravity is passively
controlled. This distinction appears clearly (fig.1) in the experiences
made by Gagey et al. (1985): the amplitude of the «low»
frequency oscillations (<0,6 Hz) varies in a systematic way
in response to a manipulation of one or another input of the fine
postural control system, while the amplitude of the «high»
frequency oscillations (in the 1 Hz band) stays aleatory in all
situations. Only the «low» frequency oscillations
are controlled by the inputs of the fine postural control system.

FIG.1 Mean values and standard deviation
of paired differences in the amplitude spectrum between two identical
situations (unbroken line) and two different situations (dotted
line) following the manipulation of a fine postural control system
input.
Between 0,04 Hz and 0,6 Hz the amplitude spectrum is repeatable
if the recording situations are identical (unbroken line). But
between 0,6 Hz and 1,2 Hz the amplitude spectrum is no longer
repeatable, and it is not systematically modified by a manipulation
of a fine postural control system input, it behaves like a stationary
aleatory phenomenon. N = 100 (from Gagey et al., 1985).
So the dance of the centre of pressure is a wellknown
phenomenon that obeys to a trivial mechanical logic.
Collins and Deluca have recently
demonstrated (1993) that this specific phase of «high»
frequency phenomena (in the 1 Hz band) was very clearly isolated
by a diffusion analysis of the stabilometric signal, which is
possible to parameter by some diffusion coefficients. This brings
the following questions:
Material and methods
Subjects
21 young men, between 19 and
27 years of age (mean age 23±4 years), in good health,
were selected by a series of stabilometric recordings in eyes
open and eyes closed situations that stayed within the normality
limits (A.F.P., 1985). They were paid, ignored the objectives
of the experiment, but they knew they were participating in a
pharmacodynamic study, as imposes actual legislation.
Stabilometric recordings
All recordings were performed
on a stabilometric platform, standardised by l'Association Française
de posturologie (French Posturology Association) (Bizzo et
al., 1985), computerised, validated by studies of the same
association (A.F.P., 1985), commercially available in southern
Europe (In France: Dynatronic, QFP, Satel, MidiCapteurs, Dune;
in Italy: CIA.Sistemi). The sampling is made at 5 Hz. The recording
time is 51,2 s. The analogic signal coming from each of the three
gauges was filtered by an antiwithdrawal filter, passing band
0/2 Hz, fourth order structure.
The visual environment is strictly normalised: target at 90 cm
(35 inches) in front of the subject, enlightened to 2000 lux,
with side panels at 50 cm (19 5/8 inches) from the subject.
Foot position on the platform is normalised: 30° between feet
with heels 2 cm (3/4 inch) apart; the barycenter of the support
surface always placed at the same point, no matter the shoe size
of the subject, on hard and foam rubber surfaces.
The recordings were realised before
and three hours after administration of Lorazepam (2,5 mg) and,
eight days later, the same day of the week, the same hours of
the day, before and three hours after administration of a placebo;
presentation of the placebo and Lorazepam was randomised. All
recordings were realised in eyes open and eyes closed situations,
with barefoot directly positioned on the platform, and then in
eyes open and eyes closed situations with barefoot resting on
a 1,5 cm (9/16 inch) thick expanded polystyrene surface, not standardised
but identical for all subjects of the experiment and renewed regularly.
Diffusion analysis
The mean quadratic distance
between all positions of the centre of pressure with equal time
lapses was calculated from a lissajou representation and for all
time intervals comprised between 0,2 s and 25 s. Thus, each quadratic
distance represents the real distance, brought to its square,
expressed in millimetres, between two positions of the centre
of pressure separated by a definite time interval. The grouping
of all the points that are representative of the mean quadratic
distance in function of the time interval constitute a cloud of
points, which is named «diffusion cloud».
The characterisation of the first part of the diffusion cloud,
corresponding to the «high» frequencies of the stabilogram,
has not been made in a theoretical manner taking all the points
of the diffusion cloud corresponding to time intervals <1 s,
but was studied by a regression algorithm proposed by Ouaknine
which permits to stay closer to the experimental data.
Algorithm of the two regression lines
The diffusion cloud's dots grouping,
of abscise 0,2 to 25 s, has been divided into two subgroups separated
by a rolling point from 0,4 to 2 s; each of the subgroups has
been submitted to a linear regression algorithm, repeated for
all the successive positions of the rolling point. Within all
the regression lines defined this way, the only couple that was
kept was the one formed by the two regression lines limiting the
smallest angle between them. We can see on figure 2 that the determination
of the first part of the diffusion cloud by this algorithm corresponds
closely the one that would have been made visually. The slope
of these two regression lines (P1 and P2), expressed in square
millimetres per second (so these parameters can have a dimension
equation), were kept as an expression close to the diffusion factors,
Ds and D1, proposed by Collins and Deluca (P1 = 2Ds; P2 = 2D1).
FIG. 2 Algorithm
of the two regression lines. Only the two regression lines forming between them the minimum angle (Ouakine) are shown. The slopes of these two lines, expressed in square millimetres per second, were used as close expressions of the diffusion factors. 
Statistical analysis
The distributions
of the slope of the first two lines of regression (P1 and P2)
were analysed in diverse experimental situations. The differences
between these distributions were studied by a comparison to zero
of their mean matched differences.
The comparisons between the slopes of regression and the conventional
stabilometric parameters (Xmean, Ymean, Area, Length, LFS, VFY
and Romberg quotient) were studied with a correlation coefficient.
Results
Slope of the regression lines
Situation  First Line: P1  Second Line: P2 
EO  18±9  1,9±2 
EC  40±20  1,9±3 
EO + Foam  25±14  1,7±1,7 
EC + Foam  71±33  2,8±3,9 
EO +Lora.  116±77  5,8±6,9 
EC +Lora.  211±129  7,8±9 
EO + Foam +Lora.  497±1060  6,4±11 
EC + Foam +Lora.  562±656  11,6±14 
TAB. 1 Means and standard deviations of the slopes, P1
and P2, of the regression lines according to experimental situations.
EO = Eyes open; EC = Eyes closed; Foam = feet resting on a soft
foam rubber surface; Lora: recordings taken three hours after
administration of Lorazepam (2,5 mg). The slopes values are expressed
in square millimetres per second.
Correlation coefficients between the slopes of the regression
lines and the conventional stabilometric parameters.
Situation  P. 2  Xmean  Ymean  Length  VFY  Area  LFS 
EO  0,42  0,1  0,03  0,87  0,53  0,74  0,7 
EC  0,04  0,02  0,29  0,93  0,52  0,49  0,84 
EO + Foam  0,38  0,02  0,3  0,94  0,3  0,73  0,84 
EC + Foam  0,1  0,24  0,22  0,88  0,79  0,39  0,73 
EO + Lora.  0,02  0,39  0,06  0,94  0,61  0,55  0,16 
EC + Lora.  0,31  0,2  0,74  0,23  0,22  0,38  0,22 
EO + Foam +Lora.  0,47  0,04  0,03  0,4  0,38  0,77  0,69 
EC + Foam + Lora.  0,15  0,05  0,3  0,06  0,11  0,05  0,22 
TAB. 2 Correlation coefficients between the slopes of
the first regression line, P1, and the other parameters
EO = Eyes open; EC = Eyes closed; Foam = Foam rubber: feet resting
on a soft surface; Lora: recordings taken three hours after administration
of Lorazepam (2,5 mg).
Situation 






EO 






EC 






EO+Foam 






EC+Foam 






EO+Lora. 






EC+Lora. 






EO+Foam+Lora. 






EC+Foam+Lora. 






TAB. 3 Correlation coefficients between the slopes of
the second regression line, P2, and conventional stabilometric
parameters.
EO = Eyes open; EC = Eyes closed; Foam = Foam rubber: feet resting
on a soft surface; Lora: recordings taken three hours after administration
of Lorazepam (2,5 mg).
Distribution of the slope of the first regression line according
to the experimental situations
The mean matched
differences between the values of the slope of the first regression
line in different experimental situations were compared to zero
by the Student tests and the results are presented in the following
tables:
Drug 




Surface 




± Vision 








TAB. 4 Variations of the slope of
the first regression line between subjects standing with eyes
open or closed.
Student's ttest of the comparison to zero of the mean matched
differences of the slope of the first line in eyes open or closed
situations, in the four recording conditions: with or without
drug administration, hard or soft surface.
Drug 




Eyes 




Soft or hard s. 








TAB. 5 Variations of the slope of the first regression
line between subjects standing on a soft or hard surface.
Student's ttest of the comparison to zero of the mean matched
differences of the slope of the first line in soft or hard surface
situations, in the four recording conditions: with or without
drug administration, open or closed eyes.
Surface 




Eyes 




± drug 








TAB. 6 Variations of the slope of the first regression
line between subjects with or without drug.
Student's ttest of the comparison to zero of the mean matched
differences of the slope of the first line in 'with or without
drug' situations, in the four recording conditions: hard or soft
surface, open or closed eyes.
Distribution of the slope of the second regression line according
to the experimental situations
The mean matched differences between the values of
the slope of the second regression line in different experimental
situations were compared to zero by the Student tests and the
results are presented in the following table:
Drug 




Surface 




± Vision 








TAB. 7 Variations of the slope of the second regression
line between subjects standing with eyes open or closed.
Student's ttest of the comparison to zero of the mean matched
differences of the slope of the second line in eyes open or closed
situations, in the four recording conditions: with or without
drug administration, hard or soft surface.
Drug 




Eyes 




Hard or Soft S. 








TAB. 8  Variations of the slope of the
second regression line between subjects standing on a soft or
hard surface.
Student's ttest of the comparison to zero of the mean matched
differences of the slope of the second line in 'soft or hard surface'
situations, in the four recording conditions: with or without
drug administration, open or closed eyes.
Sol 




Eyes 




± Drug 








TAB. 9  Variations of the slope of the second regression line
between subjects with or without drug.
Student's ttest of the comparison to zero of the mean matched
differences of the slope of the second line in 'with or without
drug' situations, in the four recording conditions: hard or soft
surface, open or closed eyes.
Discussion
Is the slope of the first regression line a useful parameter?
The slope
of the first regression line is a very sensible parameter. The
range of its experimental variations may be considerable, in a
1 to 30 ratio if we refer to this study's results (tab. 1). The
differences observed between the distributions of this parameter
under the influence of diverse manipulations are, in average,
statistically very significant (tab. 4, 5, 6).
But this parameter is redundant;
there is a very strong correlation between the length of the statokinesigram
and the slope of the first regression line (tab. 2). And when,
in three situations (eyes closed on hard or soft surface and eyes
open on soft surface three hours after drug administration; cf.
tab. 2), this correlation disappears, the length of the statokinesigram
is the most discriminative parameter between the diverse experimental
situations (tab. 10).
Surface 



Eyes 



P.1 



Length 



TAB. 10 Variations of the slope of the first regression
line, P1, and of the length of the statokinesigram, depending
on the subject being recorded before or three hours after administration
of the drug.
Student's ttest of the comparison to zero of the mean matched
differences of these two parameters, before and three hours after
drug administration, in the three recording conditions where the
correlation between the length of the statokinesigram and the
slope of the first regression line disappears.
Sensible, but less discriminative
than the length of the statokinesigram, the slope of the first
regression line and consequently the Diffusion coefficient, Ds,
seem not to be a useful parameter for the clinician.
Which parameter characterises best the dance of the centre
of pressure?
The correlation, very strong, that exists between the
slope of the first regression line and the length of the statokinesigram
isn't strange because these two parameters are calculated from
the same quadratic distance expression:

with k = 1 for the calculation of the length
of the statokinesigram and k close to 1 for the slope of the first
regression line.
Nevertheless, the length of the
statokinesigram is the parameter most strongly linked to the moving
of the centre of pressure, it expresses its real moving (k = 1),
it integrates its slightest variations. On the other hand, the
slope of the first regression line which expresses virtual moving
(k > 1) of the centre of pressure, reflects less precisely
the real moving.
Is the slope of the second regression line a useful parameter?
The slope of the second regression line appears, throughout
this study, to be of little sensibility, the extent of its experimental
variations is limited (tab. 1), and it is very little discriminative
(cf. tab. 7, 8 & 9). It then seems, from the results of this
study, that the slope of the second regression line, or the diffusion
coefficient D1, is not a useful parameter for the clinician.
Conclusion
The stabilogram
diffusion analysis proposed by Collins and Deluca is a very interesting
analysis. It confirms that:
We can question the pertinence
of the term «open loop control» to qualify the dance
of the centre pressure.
But, according to the present study,
it doesn't seem that the diffusion coefficients are useful parameters
because they are redundant at times, and have to little sensibility
at other times.
References
A.F.P. (1985) Normes 85. Éditées par l'Association
Française de Posturologie, 4, avenue de Corbéra,
75012 Paris.
Collins J.J., De Luca C.J. (1993) Openloop and closedloop control
of posture: a randomwalk analysis of centerofpressure trajectories.
Exp. Brain Res., 95, 30818.
Gagey P.M., Bizzo G., Debruille O., Lacroix D. (1985) The one
hertz phenomenon. In: Igarashi M., Black F.O. (Eds) Vestibular
and visual control on posture and locomotor equilibrium. Karger,
Basel, 8992.
Gagey P.M., Weber B. (1995) Posturologie; Régulation
et dérèglements de la station debout. Masson,
Paris.
Gurfinkel V.S. (1973) Physical foundations of stabilography. Agressologie,
14, C : 914.
(This work was partly paid by RhônePoulenc, Inc. that must be thanked)