Introduction

     Man standing at rest is never in a state of balance, he stabilizes himself - i.e. he keeps coming back to his position of balance, but is unable to remain in that position. Indeed, the equal and opposite resultants of the forces acting on his body mass - due to gravity and to ground resistance - respectively apply to his center of gravity (CoG) and to his center of pressure (CoP), and equilbrium is reached only if those two points are (very briefly) alined on the same vertical.
     Two basic mechanical models are therefore available to describe the dynamics of postural stabilization, depending on whether the CoG or the CoP is being mobilized in order to reach the vertical line drawn from the other center. Each model corresponds to very different tactics that we could usefully refer to as "tactics of the CoP" and "tactics of the CoG".

FIG. 1 - The two stabilization tactics To maintain the CoG and the CoP close to the same vertical, either the CoG (left) or the CoP (right) can be mobilized.

The requirements of the tactics of the CoG

     Let us assume, by hypothesis, that the "tactics of the CoG" only are active and the "tactics of the CoP" are at rest, that is to say that the CoP is fixed and considered merely as a point. The only way to shift the body's CoG then consists in changing the geometry of the body itself, by moving the knees, hips and arms - so that the composition of all the mass centers of the body parts leads to a new position of the CoG close to the vertical of the CoP (fig. 2).

FIG. 2 - Tactics of the CoG The CoP is fixed, reduced to a point (red Cone). The CoG alone can be moved by changing the body's geometry, by playing with kinetic energy. Under such conditions, the subject manages to stabilize himself for a moment, but at the cost of an important expenditure of energy. (You can load the real film, but mind you! It could take a long time)

     In order to work well, such stabilization tactics have to meet a temporal requirement: the new CoG has to be set by the "tactics of the CoG" before the old CoG goes beyond the limits that the "instruction" of the fine postural control system imposes on its clearance - that is to say well before the vertical of gravity goes beyond the limits of the support basis.
     By comparing the movements of the CoG around the fixed CoP, to the sway of a pendulum, described by the equation:

where:

a: maximum distance of clearance of the pendulum imposed by the "instruction" (in a normal subject in an open eyes situation as defined by Normes85, we can estimate that a is approximately equal to the radius of a circle of 100 mm2 of area, that is to say about 4 millimeters).
T: natural period of the pendulum, about 3.3 seconds for a normal subject (Bizzo, 1974).

     We can say that, in the absence of any reaction of the "tactics of the CoG", the CoG would reach the limits imposed on its clearance when:

     That is to say:

     The period of the "tactics of the CoG" should therefore be, at least, inferior to the quarter of the period of the inverted human pendulum.
    That temporal requirement of the "tactics of the CoG", that necessity to feel the imbalance and to react rapidly, in less than 8 tenth of a second, implies the intervention of important accelerations, that would be about sixteen times more important than the acceleration of the CoG.
    In order to meet that requirement while at the same time saving energy, the "tactics of the CoG" use body parts whose moments of inertia are smaller than that of the whole body. Stabilizing thanks to the "tactics of the CoG" therefore requires two systems that have different moments of inertia.
     Men have not waited all this reasoning to understand that they had to wave their arms and wiggle their hips when their CoP is set on the ground!

The requirements of the tactics of the CoP

     Let us assume, by hypothesis, that the "tactics of the CoP" only are active and the "tactics of the CoG" are at rest, that is to say that we consider the geometry of the body cannot be deformed. When the CoG shifts away from the vertical of the CoP, the only way to bring the CoG back to its mean position consists in shifting the CoP beyond the vertical of the CoG so as to create a return torque (figure 3).

FIG. 3 - The work of the torques A: situation of balance B: when the CoG shifts away from the vertical of the CoP, a torque is created and tends to increase that gap C: the CoP is shifted beyond the vertical of the CoG, the direction of the torque is reversed and it therefore tends to bring the CoG back to its mean position.

     The body does not need to change its geometry in any way in order to stabilize, the mere movements of the CoP suffice. The obvious illustration for those tactics is that of the inverted broom held in equilibrium on a finger (Roberts T.D.M., 1995; Gagey et al., 1997). That example underlines the fact that the tactics of the CoP necessarily use two systems - a passive inertial system that is the broom itself, and an active system whose role is here played by the subject's hand shifting the CoP. Those two systems are connected, via the project of stabilization and via physical contact, but they are independent.

FIG. 4 - The tactics ofthe CoP      The tactics of the CoP require two independent, but coupled, systems: a purely inertial system, represented on the figure by the black pendulum, and a dynamic system, represented by the subject's hand shifting the CoP. (You can load the real film, but mind you! It could take a long time)

     The tactics of the CoP have to meet the same temporal requirement as the tactics of the CoG. The same reasoning, the same calculations can apply, they lead to the same conclusion: those two coupled systems must have different moments of inertia. The moment of inertia of the dynamic system that shifts the CoP must be largely inferior to the moment of inertia of the passive inertial system. We can indeed easily check that it is not so difficult to stabilize on the tip of one's finger an inverted pendulum with a fairly important inertia like a broom, whereas one is totally unable to stabilize a pen, whose moment of inertia is much smaller.
     Maurice Ouaknine made a robot that stabilizes an inverted pendulum following those tactics.

FIG. 5 - The two coupled systems with different moments of inertia of the tactics of the CoP.      The fact there are two systems allows a different acceleration, faster for the active part than for the passive one, so that a stabilization of the mass of the pendulum by the movements of the CoP is made possible. (CGS Units; delay; ranges and frequencies: approximate means from experimental data)

Discussion

The real stabilization
     Needless to say that in real facts, man never uses only the tactics of the CoG or only the tactics of the CoP to stabilize, but a subtile mixture of both. We have already analyzed, in mono- as well as bi-podal situations, the mechanisms of the real position shifts of the CoP under the sole of the subject's feet, due to muscular tensing (Gagey, 1998). We observe that, in a monopodal situation, the "tactics of the CoP" are widely used, which could explain the bad results of the elderly during the test of stabilization on one foot - the results being all the lower than the subject is more used to stabilize himself thanks to tactics of the CoG.
     The possible role of the "keyboard of the metatarsals" in the quick and fine mobilization of the center of pressure has already been mentioned. It is obvious that the moments of inertia intervening in the mobilization of those anatomical parts do correspond to the requirements of the tactics of the CoP. On the contrary, the sharpness of the control of the stabilization of man standing at rest and even more the necessary economy of its intervention do not quite fit with certain conceptions according to which the leg muscles act as a motor on the whole body mass around the axis of the ankles. It is likely that the tactics of the CoP intervene proportionally more than the tactics of the CoG in the real stabilization of man standing at rest.

The traps of language

     Following electromyographic studies of the reactions of the normal subject to destabilizations, Nashner and coll. have indeed observed that two strategies of stabilization exist, distinguished by the temporal organization of the series of electric muscular events (Nashner L.M., Mc Collum G., 1985). When muscular tensing began at the level of the leg muscles and then reached the proximal muscles, those authors spoke of an "ankle strategy". When, on the contrary, the muscular tensing began at the level of the hip muscles and then reached the distal muscles, they spoke of a "hip strategy". Those denominations, absolutely normal in the context of Nashner's experiments, run the risk of becoming traps of language if we keep using them in a different context of reflection. By the way, it may be useful to remind that since his thesis (1970), Nashner focused his attention on the postural system taken as a control system of posture. He studied its input loops and output tactics, but not its mechanics. Indeed, it is normal to adopt a reducing point of view in the course of a fundamental study, but one must know how to free oneself of it and not only when one wants to build robots or cure patients.
     We believe that the expression "ankle strategy" should be banished from our vocabulary because, unavoidably, it focuses our attention on those joints, whereas the CoP is not at the level of the ankles and, indeed, nothing particularly important occurs at their level as far as stabilization is concerned (Guilleminot et al., 2001). What is worse, that expression diverts our attention from the muscles proper to the foot, whereas it is absolutely not proved that those muscles do not intervene in the mechanisms of mobilization of the CoP. On the contrary, the requirements of the tactics of the CoP lead us to think that they are perfectly indicated to intervene in the mechanisms of mobilization of the CoP, and even that they could be the main factors of the sharpness of the control of the orthostatic posture already observed by Magnus (1924).
     The expression "tactics of the hip", on the contrary, seems to be safe to use, as it focuses attention on an area quite close to the CoG.

Conclusion

     The reference to those biomechanical models would justify, if necessary, the therapists' interest in finding out which tactics of stabilization are used by their elderly patients - tactics of the CoG or tactics of the CoP (Villeneuve-Parpay et al., 2001; Villeneuve-Parpay et al., under publication).
     Those reflections also raise a few other questions for the therapists, for instance:

• Is it useful to strengthen the muscles proper to the foot in elderly patients that show a tendency to use the tactics of the hip (Woollacott, 1986)?
• Is it possible, in the same subjects, to stimulate again the use of the tactics of the CoP thanks to exercises on a platform of postural re-education (Gagey, 1993)?

Bibliography

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