I-A/B) Hypothèse raideur-masse & cohérence expérimentale
    I completely agree with the inverted pendulum model and the basic dynamics is not restricted to the rigid one d.o.f. model. The main point is that this is an unstable mechanical system that can be stabilized in two ways:
in a passive way, by means of a suitable joint stiffness, or
in an active way, by means of a suitable controller.
    People can stabilize inverted pendulums even with zero stiffness at the "pseudo-ankle" joint. An example is a person standing on stilts or a person balancing a stick on his hand or other part of the body. In the common standing posture there is probably a combination of the two mechanisms and the open problem is to devise a clinically valuable method for evaluating their relative role.
    From this point of view the biomechanical/neuromotor significance of the VFY parameter is somehow mysterious, although the underlying correlation between speed and position is certainly intriguing.

I-C) Cascade d'erreurs
    In addition to the objections above to the biological significance of the parameter, I must say that its formal definition is somehow unsatisfactory:
it is a "hybrid parameter" (the first term of the sum is not a real speed) for which the term weighted speed variance is inappropriate,
it is not normalized (it is dependent on the sampling frequency and on the observation time).
    By the way, I agree with those who think that the sampling frequency of 5 Hz is too low. This value is appropriate for studying the mechanics of the plant but not for the dynamics of the control mechanism that is certainly much higher.

II-A/B/C/D)
    First of all, let me say that I still did not find in the literature a clear and well principled definition of the ankle vs. hip strategy (or, more generally, a distal vs. proximal strategy).
    As regards the correlation among the COM-COP difference and the COM acceleration (eq. 2), as I tried to say in the JNP paper (Morasso & Shieppati, 1999), there is no point to prove it experimentally, it is just a consequence of Newton's law. The fact that the correlation is "only" 0.91 and not 1.00 is probably due to the measurement errors that are unavoidable and difficult to evaluate with stereophotogrammetric measurements and complex ergometric models.

III-A/B/C)
    I must confess that the contrast between the two diagrams on the left and the two diagrams of the right of fig. 12 for me is highly mysterious.
    As regards the proposed method for estimating stiffness and damping I think that it is correct only if you ignore the active intervention of the controller. Otherwise, as I think it is the case, the ankle stiffness is grossly over-estimated. Please note that, coming from the school of Emilio Bizzi of the MIT, I am very sensitive to the importance of muscle stiffness in motor control. Unfortunately I came to the conclusion that posture control is somehow a special case and stiffness, in this case, can only play a partial and possibly marginal role.
    I do not think that the "pinned polymer" metaphor has a biological significance. Rather, I agree with part of the Collins & De Luca algorithm, i.e. the analysis of the COP path with a moving window. In fact, in our lab we developed a variant of this mechanism which is meant to evaluate the discontinuous structure of the neuromuscular control action by means of what we call sway density curve. The paper is not ready yet and we are in the course of validating the data. Tentatively it seems that these new parameters are more stable and better discriminate normals and parkinson patients than either the Collins & De Luca parameters and the standard SP, SA parameters. At the same time we are building a computer controlled electro-mechanical device, to be overlaied on a force-platform, that is meant to estimate directly the ankle stiffness during standing. This work is carried out in the clinical bioengineering center of the rehabilitation hospital in Arenzano together with Dr. Luigi Baratto, neurologist and physiatrist.

DISCUSSION

Pierre-Marie GAGEY wrote:
    I would like to add something that puzzles me: the center of pressure is not at the ankle axis. You would say: very well known!... Of course, but you don't move the center of pressure and the ankle with the same muscles. You can get a rough stabilisation around the ankle by calf muscles stiffness, and a fine tuning by...? Why not feet own muscles? Professor BESSOU from Toulouse shears the same hypothesis, but we never read any paper on this matter. There is some coherence between this hypothesis and the clinical experience I told you.

P.D. Morasso replied:
    My understanding is that, at least ignoring second order effects, the same ankle muscles move the ankle joint (if the foot is not on the floor) or shift the COP (if the foot is on the floor). In the latter case, if
you schematize the foot as a rigid body it is sufficient to write the equilibrium equation and see that the COP position is proportional to the net ankle torque. I think that the foot own muscles may affect the distribution of contact forces but not so much the COP position, which is an integrated variable.

References
Morasso P.G., Shieppati M. (1999) Can Muscle Stiffness alone stabilize upright standing? J. Neurophysiol. 83: 1622-26.

Address: Pietro G. Morasso - University of Genova, DIST Via Opera Pia, 13, I-16145 Genova (Italy) V:+39 010 3532749; F:+39 010 3532154/3532948; E: morasso@dist.unige.it
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