Sasaki'rhythm

Introduction
      The body of standing man is built as an inverted pendulum possessing a great number of degrees of freedom. We observe that it can lock, or not, a more or less big number of these degrees of freedom to control its upright position at rest, what represents a possibility of very numerous postural tactics, in theory.
     Now, the investigation of these various tactics by stabilometry is never made practically, as far as we knew, although we had two types of analysis to study them: analysis of shear forces and analysis of the rhythm of centre of pressure movements.
     Indeed, the period of a pendulum being a function of its length, if the length of human pendulum is divided by unlocking some of its degrees of freedom, then the period of each of the parts is inevitably lower than that of the whole, the pendum with a single degree of freedom.
     We put forward that these modifications of periodicity can be read on the recordings of the centre of pressure by studying the rhythm of the 'dance' movements of this application point of the reaction forces. We suggest naming this rhythm: " Sasaki's rhythm ". [By rhythm of a phenomenon, we mean the series of intervals of time, which separate similar events of this phenomenon.]
As locking/unlocking degree of freedom is not considered as an aleatory phenomenon of motor control (Bernstein, on 1947), this hypothesis includes:
1) That the rhythm of the dance of the centre of pressure is stationary,
2) That it can be modified in certain situations,
3) That these modifications can be considered as a change of postural tactics as far as one notices that they allow to react effectively to disturbances.
     We show that these three conditions were verified by the experience of Sasaki and coll. (2002).

Material and Method
Recordings :
23 subjects (3 Women and 20 Men) were recorded on a standardised stabilometry platform of the French Association of Posturologie (Bizzo et al., 1985; AFP, 1985; Gagey et al., 2001) in three series, randomised, of two successive recordings in the following situations:

     The optokinetic stimulation (OKN) was always the same: 60 °/s, rightwards, during 60 seconds, not trying to follow a target. Ten minutes rest between every series.
Signal Analysis
     Global parameters: Five global parameters were calculated: The area of the 90 % confidence ellipse (Takagi and al ., 1985), the length of the stabilogram in X, in Y, in XY, the Romberg's quotient .
     Structural parameters: The similitude coefficient of Le Van Quyen and coll. (1999) was calculated in each of the three series of recordings, by comparing the stabilograms in each serie:

In X and in Y.
The similitude coefficient expresses, by means of an intercorrelation, the degree of resemblance between two clouds of points, built in a phase space of 8 dimensions (Fig. 1), from the data of every recording, every point of a cloud being defined by a vector of eight parameters, every successive parameter of which represents the duration of the interval of time, which separate two identical events of the stabilogram (Fig. 2), in X and in Y.

FIG. 4 - Distribution of the similitude coefficient in Y, in the comparisons of EO/EO and EO±OKN situations.
In the comparison EO±OKN, 7 subjects are outside the limits of normality defined by the comparison EO/EO.
On the whole, 11 subjects out of 23 modified their Sasaki's rhythm under optokinetic stimulation, either in X, or in Y, or in X and in Y.
All the subjects reported a sensation of vection during the optokinetic stimulation.

Discussion
Stationnarity: Given that there is no statistically significant difference of the similitude coefficient, not only in the comparisons of EO/EO situations, in X and in Y, but also in the comparisons of EO/EC situations, in X and in Y, one can admit that Sasaki's rhythm, according to this experience, would be stationary.
Variability: Given that there is a statistically significant difference of the similitude coefficient in Y between the comparisons of EO/EO and EO±OKN situations, one notices, at least in this experience, that Sasaki's rhythm is modifiable according to compulsory situations for postural control.
Tactics: When one studies the global parameters of the 11 subjects, which modify their Sasaki's rhythm under optokinetic stimulation, one observes identical postural performances, while the 12 subjects, which do not modify their Sasaki's rhythm under optokinetic stimulation present significantly degraded postural performances (Tab.2).
So, the change of Sasaki's rhythm appears as a tactics used to guarantee postural performances in situations that compromise the stability of the subject.

N Area (mm2) p
+OKN -OKN
Not modified 12 150±110 300±200 < 0,05
Modified 11 180±90 220±90 ns
TAB 2 - Averages and standard-deviations of statokinesigram area in EO±OKN situations as the subjects modify or not their Sasaki's rhythm.
One can notice additionally that the 11 subjects which modify their Sasaki's rhythm under optokinetic stimulation behave as blind persons in the EO/EC series. The postural "blindness" in the EO/EC series and the change of Sasaki's rhythm in the EO±OKN series indicate, in two different manners, that these subjects integrate the visual information differently.

Conclusion
The rhythm of the dance of the centre of pressure, or "Sasaki's rhythm" as we suggest calling it, can be studied by a technique of nonlinear dynamic analysis, coherent with the notlinear dynamic nature of the postural control (Martinerie and al ., on 1992; Myklebust and al ., on 1995; Thomasson, on 1995; Cao and al ., on 1998; Murata and al ., on 1998; Micheau and al ., on 2001; Sasaki and al ., on 2001; Peng and al ., on 2002; Shimizu and al ., on 2002).
This study shows that Sasaki's rhythm is stationary, modifiable when the postural control is perturbed by particular situations, and that this modification of Sasaki's rhythm guarantees the preservation of good postural performances.
We put forward that modifications of this rhythm reflect the locking/unlocking of degrees of freedom of the human being inverted pendulum.

References

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Situations	Similitude in X	Similitude in Y
EO/EO	0.859±0.121	0.926±0.123
EO/EC	0.929±0.100	0.892±0.101
EO±OKN	0.755±0.272	0.804±0.197*

Sasaki's rhythm	N	Area (mm²)		p
		+OKN	-OKN
Not modified	12	150±110	300±200	< 0,05
Modified	11	180±90	220±90	ns