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 well-known 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:

• Are these diffusion parameters helpful to clinicians? Which means are they sensible? Non redundant?
• Are they a good means to characterise the dance of the centre of pressure?

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 sub-groups separated by a rolling point from 0,4 to 2 s; each of the sub-groups 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 (X-mean, Y-mean, Area, Length, LFS, VFY and Romberg quotient) were studied with a correlation coefficient.

Results

Slope of the regression lines

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.

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).

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:

TAB. 4 ­ Variations of the slope of the first regression line between subjects standing with eyes open or closed.
Student's t-test 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.

TAB. 5 ­ Variations of the slope of the first regression line between subjects standing on a soft or hard surface.
Student's t-test 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.

TAB. 6 ­ Variations of the slope of the first regression line between subjects with or without drug.
Student's t-test 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:

TAB. 7 ­Variations of the slope of the second regression line between subjects standing with eyes open or closed.
Student's t-test 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.

TAB. 8 - Variations of the slope of the second regression line between subjects standing on a soft or hard surface.
Student's t-test 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.

TAB. 9 - Variations of the slope of the second regression line between subjects with or without drug.
Student's t-test 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).

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 t-test 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:

• 
  The two parts of the stabilometric signal, the dance of the centre of pressure and the dance of the centre of mass, are clearly separable by a calculation artifice,
• 
  Only the movements of the centre of mass possess the characteristics of movements controlled in a closed loop.

    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) Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Exp. Brain Res., 95, 308-18.

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, 89-92.

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 : 9-14.

(This work was partly paid by Rhône-Poulenc, Inc. that must be thanked)