Sasaki's rhythm
By Osamu Sasaki **, Jacques Martinerie ***, Michel Le Van Quyen ***,
Pierre-Marie Gagey *
* Institut de Posturologie, Paris
** Shinshu University, Matsumoto
*** LENA Salpêtrière, Paris

      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:

Eyes open /Eyes open
Eyes open /Eyes closed
Eyes open / Eyes open ± optokinetic stimulation

     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:

EO and EO,
EO and EC,

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. 1 - Projection on a three dimensions space of the clouds, the similitude coefficient of which are studied in a phase space of 8 dimensions.

FIG. 2 - Construction of the elementary vectors.
Every elementary vector defining the 8 coordinates of every point of a cloud is constituted by the duration of the 8 time intervals (n, n+1. n+7) which separate 9 identical events of the stabilogram, here the passage by a maximum.


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*

TAB. 1 - Averages and standard-deviations of the similitude coefficient according to the compared situations
     The similitude coefficient does not present significant difference, in X and in Y, between two successive recordings in EO/EO situations, and between two successive recordings in EO/EC situations.
     On the other hand, the similitude coefficient presents a significant difference, in Y, between two successive recordings realised in EO±OKN situations (t=2,59; p < 0,05), and the distribution of the similitude coefficient in X, in the comparison of the EO±OKN situations, presents a variance statistically very different (F=5,83; p < 0.01) from that of its distribution in the comparison of the EO/EO situations.

FIG. 3 - Distribution of the similitude coefficient in X, in comparisons of EO/EO and EO±OKN situations .
The variances of these two distributions are statistically very different (F=5,83)

     In the comparison EO±OKN, 5 subjects are outside the limits of normality defined by the comparison EO/EO.

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.

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.

Sasaki's rhythm
Area (mm2)
Not modified
< 0,05

N Area (mm2) p
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.

     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.


A.F.P. (1985) Normes 85. Editées par l'Association Posture et Équilibre, 66, rue de Lisbonne 75008 Paris.

Bernstein N. (1947) On the construction of movements. Medgiz (Moscow)

Bizzo G., Guillet N., Patat A., Gagey P.M. (1985) Specifications for building a vertical force platform designed for clinical stabilometry. Med. Biol. Eng. Comput., 23: 474-476.

Gagey PM., Ouaknine M., Sasaki O. (2001) Pour manifester la dynamique de la stabilisation: la plate-forme AFP40/16. In M. Lacour (Ed.) Posture et équilibre. Nouveautés 2001, conceptuelles, instrumentales et cliniques. Solal, Marseille, 95-106.

Le Van Quyen M., Martinerie J., Baulac M., Varela F. (1999) Anticipating epileptic seizure in real time by nonlinear analysis of similarity between EEG recording. Neuroreport 10:2149–2155

Martinerie J., Gagey P.M. (1992) Chaotic analysis of the stabilometric signal. In M.Woollacott & F. Horak (Eds) Posture and gait: control mechanisms. University of Oregon Books (Portland), Tome I: 404,407.

Micheau P., Kron A., Bourassa P. (2001) Analysis of human postural stability based on the inverted pendulum model with time-delay in feedback. Proceedings of the 2001 american control conference, 1-6, 2297-2298.

Murata A., Iwase H. (1998) Chaotic analysis of body sway. Proceedings of the 20th annual international conference of the ieee engineering in medicine and biology society, 20, PTS 1-6 20 (Pt 1-6) ; p.1557-1560.

Myklebust J.B., Prieto T., Myklebust B. (1995) Evaluation of nonlinear dynamics in postural steadiness time series. An. Biomed. Engn., 23: 711-9.

Peng C.K., Mietus J.E., Liu Y.H., Lee C., Hausdorff J.M., Stanley H.E., Goldberger A.L., Lipsitz L.A. (2002) Quantifying fractal dynamics of human respiration: Age and gender effects. Annals of biomedical engineering, 30, 5, 683-692.

Sasaki O., Usami S-I, Gagey P.M., Martinerie J., Le Van Quyen M., Arranz P. (2002) Role of visual input in nonlinear postural control system. Ex. Brain Res., 147:1–7

Shimizu Y., Thurner S., Ehrenberger K. (2002) Multifractal spectra as a measure of complexity in human posture. Fractals-complex geometry patterns and scaling in nature and society, 10, 1, 103-116.

Takagi A., Fujimura E., Suehiro S. (1985) A new method of statokinesigram area measurement. Application of a statistically calculated ellipse. In Igarashi M., Black F.O. (Eds) Vestibular and visual control of posture and locomotor equilibrium. Karger (Basel): 74-79.

Thomasson N. (1995) Traitement du signal stabilométrique par les techniques d’analyses non linéaires. Rapport LENA, Salpêtrière, Paris.

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