Thomas Mergner & Branislav Bolha (1997) A Modified Version of the Center-of-mass Balancing Hypothesis. Psycoloquy: 8(02) Posture Locomotion (4)

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Psycoloquy 8(02): A Modified Version of the Center-of-mass Balancing Hypothesis

Book review of Roberts on Posture-Locomotion

Thomas Mergner & Branislav Bolha
Neurologische Universitatsklinik
Breisacher Str. 64
D-79106 Freiburg, Germany

Wolfgang Becker
Sektion Neurophysiologie
Universitat Ulm
Oberer Eselsberg
D-89069 Ulm, Germany


We specifically comment on Roberts' account (1995) of the interaction of vestibular and neck reflexes by contrasting it with an alternative view. While concurring with most of his formal description of the reactions resulting from a variety of experimental manipulations, we try to put the interpretation of these reactions according to our view into a broader systems perspective. According to this view, body stabilization requires two distinct sequences of coordinate transformations: one chains the sensory signals arising in the head "down" to the central representations of the trunk, the legs and, ultimately, to the feet and their support, while the second chain of transformations relays information from the feet back to the legs and trunk representations. Vestibular-neck interaction would reflect but one transformation step of these chains. Our concept of coordinate transformation owes much to recent progress in vestibular psychophysics. We suggest that vestibular psychophysics may indeed fill the gap between the physiological basis (e.g., vestibulo- spinal and cervico-spinal reflexes in the decerebrate cat) on the one hand, and, on the other hand, the complex task of decoding the centrally evoked discharge pattern by naturally occurring stimuli, which may call for a Gestalt recognition mechanism as suggested by Roberts.


Balance, connectionism, gestalt, learning, locomotion, motor control, proprioception, recognition.
1. It is generally held that a human subject who is balancing upright on a movable platform, continuously tries to bring his body vertical (the line running through the body's center of mass, COM, and body support, i.e. feet) in alignment with the gravito-inertial vector experienced by the body in its own coordinates (we apologize for this "conventional" view, which violates some of Roberts' basic assumptions). Given that the subject indeed continuously attempts to null the angle between perceived body vertical and perceived gravito-inertial vertical, he first has to measure this angle. The vestibular organ seems to be suitable for this task; the vestibular semicircular canals measure head angular acceleration in three orthogonal planes, and the vestibular otolith system records the head angle relative to the gravito-inertial vertical. However, there is an obvious complication: the vestibular signals refer to the head, not the body. How can these signals then be used to balance the body?

2. We hold that, using proprioceptive input, the brain should be able to perform a 6D-coordinate transformation (3 rotational and 3 translational planes) of the craniocentric vestibular signals into trunk coordinates. The resulting information on trunk angular motion in space and trunk angle with respect to the gravito-inertial vertical could be fed into a motor system which would generate the postural reactions required to compensate for COM perturbation, taking into account the current state of legs and feet. Conceivably, the underlying motor command would use a coordinate system adapted to the particular situation of the effectors (mostly the leg muscles).

3. Our comment mainly concerns Roberts' discussion of this concept in his section "A model to clarify the effect of interaction" (i.e. vestibular-neck interaction). Roberts simplifies matters by focusing on independent, coplanar rotations of head and trunk. In this special case the transformation reduces to an algebraic summation of angles. Although Roberts' discussion of the involved vestibular-proprioceptive interaction in his various cases A-E tends to obscure the underlying general principle of coordinate transformation, we concur with his conclusions as to the animal's motor reactions. However, we would like to concentrate on one problem which is not solved in Roberts discussion, that is the non-ideal character of vestibular measurements.

4. The vestibular semicircular canals mechanically integrate the head angular accelerations acting upon them, with the result that cupula deflection is proportional to head velocity. However, owing to the involved mechanism, this acceleration-to-velocity integration is "leaky". Its time constant is about 5 s in a monkey. For various vestibular functions it has been shown that this rather short time constant is centrally improved to about 20 s in both humans and monkeys; this holds for the vestibulo- ocular reflex (VOR) as well as for the conscious perception of self-rotation by humans. Furthermore psychophysical investigations of self-rotation perception in this laboratory (Mergner et al., 1991) led to the conclusion that the underlying vestibular signal is centrally distorted by a rather high detection threshold (unlike the VOR), which causes considerable underestimation of whole-body rotation (pure vestibular stimulation) of low velocity (e.g., small amplitude rotations at low frequency). Although the exact transfer characteristics of the vestibular signal used for postural control are, to our knowledge, not known at present, we deem it unlikely that it is better, in terms of its low frequency characteristics and threshold, than the signals involved in gaze stabilization and self-motion perception. This view is supported by a recent finding indicating that the vestibular threshold for posture control appears to be similar to the one described for self-motion perception (Peterka & Benolken, 1995). At first sight, the above limitation of the vestibular signal might be considered a special problem of the horizontal plane, since for vertical rotations the semicircular canals are functionally complemented by the otolith system. However, recent results suggest that signals derived from the otolith system may be in a similar way as inadequate as those obtained from the semicircular canals; the vestibular threshold for translatory self-motion perception was found to be of a similar order of magnitude as that for rotatory movements (Hlavacka et al., 1996). In the following paragraphs we therefore will proceed from the, admittedly still hypothetical, notion that whole-body motion in all planes, rotatory as well as translatory, is inadequately sensed when its frequency, and hence velocity, is low.

5. The situation is quite different with head rotation on the stationary trunk, or with trunk and head en-block rotation on the stationary feet. In the latter conditions the vestibular "error" appears to be reduced by the involvement of neck/leg proprioceptors. Our psychophysical investigations into the role of vestibular-neck/leg proprioceptive interaction for human self-motion perception suggest that it can be described by a linear, yet not straight forward, summation of vestibular and proprioceptive effects (Mergner et al., 1991; 1993). We provide a description of this interaction in some detail, along with the attempt of a functional interpretation.

6. We pose that axial proprioceptive input plays a dual role:

  (i) It helps to arrive at an internal notion of how the body's
  support moves in space; the proprioceptive input from the neck is
  used to first transform the vestibular signal into trunk coordinates;
  this transformation then is continued in downward direction, using
  proprioceptive input from lower body segments, until the vestibular
  signal is represented in foot coordinates (a zero signal then will
  mean that the feet are stationary in space, although the head may be
  moving). This view is supported by introspective descriptions of
  blindfolded subjects standing on a moving platform. They
  spontaneously report that the platform is moving, and they consider
  the movement of their own body in space only a consequence of
  platform motion, in accordance with the physics of the situation. In
  contrast, a patient with bilateral vestibular loss does not detect
  the motion, unless velocities or accelerations are high enough to
  stimulate somatosensory mechano-receptors. The important point in
  this scenario is that the proprioceptive inputs involved in these
  transformations apparently are distorted in a similar way as the
  vestibular signals. Referring to Figure 1B, (Figures 1A, 1B, and 1C
  appear at the end of this article) let lamda represent the vestibular
  transfer characteristics; head-in-space velocity, HS, then internally
  it is represented by lambda*HS (hs). Furthermore, let ht be a
  faithful proprioceptive representation of head-to- trunk velocity HT;
  by passing ht through an internal model of the vestibular transfer
  characteristics, ht is given "vestibular  color" (signal lambda*ht).
  The transformation ts = hs - lambda*ht = lambda* (HS-HT) then yields
  a representation of trunk (= head support) which is veridical if HS =
  HT, that is if the trunk is stationary.  Continuing in a similar way
  with axial proprioceptive signals from lower body segments, fs
  (foot-in- space velocity) is finally obtained, which again is
  veridical if the feet are stationary. Thus, in the physiologically
  prevalent condition of firm ground, the support is perceived as
  stationary, in spite of the inadequacy of the vestibular signal.
  However, when the support is moving, this inadequacy clearly affects
  the perception of this movement.

7. The scheme outlined above explains a set of surprising experimental observations. For example, if a subject's trunk is slowly rotating while his head is fixed in space, he will experience no trunk rotation in space, because lambda is approximately zero and, hence, ts is close to zero. Yet, he experiences a clear head-to-trunk displacement indicating that the proprioceptive representation ht, prior to passing through the vestibular model, veridically reports HT (cf. following paragraph).

  (ii) The second role of axial proprioception is to register head
  rotation relative to the trunk or body rotation to the body support.
  Psychophysical measurements indicate that the proprioceptive signals
  used for this task are almost ideal in terms of frequency
  characteristics and detection threshold, unlike those considered
  above. Indeed, subjects have no problem correctly estimating the
  rotation of their heads relative to their bodies, or their bodies'
  motion with respect to the body support, also at low
  frequencies/velocities, and even if support and body are rotating
  independently of each other.

8. The two roles of axial proprioception (i and ii) for motion perception are centrally linked so as to provide a consistent picture of the subjects' dynamical situation at perceptual level. Indeed, subjects' estimates of body motion in space, obtained in one set of experiments, could be predicted from their estimates of support motion in space and of body motion relative to the support, in another set of experiments. For example, isolated neck proprioceptive stimulation during low-frequency body rotation under the stationary head evokes an illusion of head rotation in space. The magnitude and frequency characteristics of this illusion can be predicted by adding the perception of head-on-trunk rotation with the perception of trunk-in-space rotation (which, as discussed above, tends towards zero as the frequency of the sinusoidal rotation declines). Thus, the occurrence of one illusion (body stationary) engenders a second one (head rotating in space); the two illusions unravel the existence of two different proprioceptive signals at each axial joint. One of them mimics the characteristics of the vestibular channel and is involved in the down- transformation (support motion in space; left pathway in Figure 1B), whereas the second one retains the full bandwidth and sensitivity of the proprioceptors and helps in reconstructing body or head motion in space by superimposing signals of relative motion between body segments and support on the signal of support motion in space obtained from the down-transformation. We shall refer to this reconstruction as up-transformation (right pathway in Figure 1B).

9. In previous papers we have pointed out that the present concept applies also to object motion perception (Mergner et al., 1992) and retrospective object localization (Maurer et al., 1997) in space in conditions in which external (e.g., visual or auditory) space references are missing. Consider a subject trying to estimate the location of a visual object in space during head, trunk, or platform motion. Although it would appear straight forward to obtain this estimate by summing an object-on-retina signal (visual) and an eye-in-orbit signal (efference copy) directly with the vestibular signal of head-in-space motion, this is apparently not what happens. Rather, the visuo-oculomotor signal is summed with the perceptual signal of head in space (hs' in Figure 1B), which is the ultimate result of the successive down- and up-transformations.

10. It is worth stressing once more the advantage of the down- and up-transformation of the vestibular signal for the perception of trunk or head motion in space. The perception resulting from the described vestibular- proprioceptive interaction is veridical if the body support is stationary (in most conditions of everyday life we are standing or walking on firm ground), while a perception based exclusively on vestibular signals would be erroneous. We suggest that similar arguments hold for the vestibular signal involved in the aforementioned balancing task. According to our concept the subject would not transform the vestibular signal directly to COM coordinates. Instead, he would first perform a down- transformation to support coordinates. From this transformation he would obtain a representation of the kinematic state of the support (veridical in the naturally prevailing case of support stationarity). Only then would he derive a description of COM behavior by the ensuing up- transformation.

11. We here suggest that psychophysical findings may serve as a blueprint for developing a concept of posture control. One may object to such a suggestion that it is not clear at present to what extent perception and posture control are interrelated or resemble each other. It is certainly true that we perform most of our postural reactions automatically, and that we do not consciously detect, for example, a spontaneous slight forward body excursion which then is balanced by a compensatory lean backwards. However, this lack of conscious perception probably does not reflect a fundamental difference between the signals subserving postural reactions and those involved in perception, but may depend on where the focus of attention is directed. There is considerable experimental evidence that postural reactions depend on how stimuli, and their context, are perceived, rather than on their actual physical properties, as repeatedly stressed in Roberts' book.

12. A distinct advantage of psychophysical experiments over measurements of posture control is that perception lacks the negative feed back character of posture control. Psychophysical experiments can be performed in an open loop manner, so to speak, and can be used to examine the (perceptual) state of various body parts (head, trunk) under different aspects (movement in space, movement relative to each other) and for a variety of stimulus conditions (whole body rotation, isolated head rotation, etc.). In contrast, postural reactions act to modify and reduce the involved sensory signals. This has led researchers in the past to evaluate mainly the very early part of the postural reactions (as reflected in the EMG), which is hardly a solution to the problem. Furthermore, because of the complicated biomechanical situation of an upright subject, it is difficult to derive from the observed motor reactions the organization of the underlying signals.

13. Accordingly, posturographic studies in man and animals so far have provided only limited evidence for the original concept of an additive vestibular-proprioceptive interaction. The original hints for such an interaction were based on qualitative observations and inferences (von Holst & Mittelstaedt, 1950; Roberts, 1978). The fact that they received considerable attention until today is mainly because of their plausibility. A few studies reported interactions of vestibulo-spinal and cervico-spinal reflexes, compatible with the concept, but they were restricted to very particular experimental conditions in the decerebrate cat (Lindsay et al., 1976; Manzoni et al., 1983). Postural adjustments of spontaneously behaving cats and horses were said to be reminiscent of vestibular-neck interaction as predicted by the linear addition concept (Roberts, 1978), but these observations certainly do not prove it. Neuron recordings from vestibular structures in the brain do not provide clear arguments either; although many of these neurons exhibit a linear vestibular-neck interaction, only in a small proportion of these neurons do the two inputs match in such way as to completely cancel each other during head rotation on the stationary trunk (as expected from the concept; Boyle & Pompeiano, 1981; Anastasopoulos & Mergner, 1982; Mergner et al., 1985).

14. Semiquantitative evidence for some aspects of the more complex concept outlined here comes from studies on galvanic vestibular stimulation. Consider a blindfolded subject swaying in the left-to-right direction. Depending on head position, different vestibular receptor units will be activated. Yet, the postural response remains the same. According to our concept, this would be due to a coordinate transformation from the vestibular signal into foot coordinates. As part of this transformation, during a static horizontal head turn, the neck input would rotate the vector signaled by the vestibular afferents in such a way as to exactly compensate for the directional change these afferents underwent because of the head turn. However, if the head turn does not change the direction of the vestibular vector, as it is the case if the labyrinth is stimulated galvanically, the rotation performed by the neck input should become visible: the direction of the vestibularly evoked lean would follow the change in head orientation. There are a number of studies which showed that this does indeed happen (Nashner & Wolfson, 1974; Lund & Broberg, 1983; Tokita et al., 1989; Hlavacka et al., 1996).

15. The notion of down- and up-transformation appears to explain some puzzling findings from earlier postural studies. For example, electromyographic responses evoked by galvanic vestibular stimulation have shorter latencies in the soleus muscles, when subjects maintain their balance by their feet muscles as compared to responses in the triceps brachii muscles, when they maintain their balance by holding a support with their arms (Britton et al., 1993). Such a time difference would indeed result, if the sequence of down- and up-transformation of the vestibular signal would proceed as a series of temporally distinct steps propagated along the spinal representations of the body segments. There is, in fact, direct electrophysiological evidence from experiments in cats that vestibular signals do not only travel in caudal direction in the spinal cord, but also back in cranial direction, while they receive muscle afferent input from limbs and neck (Coulter et al., 1976).

16. Furthermore, activation of muscle proprioceptive input by vibration at the backside of the body (signaling muscle stretch as if the body were bending forward) leads to a (compensatory) body lean backward. There is one noticeable exception; vibration of dorsal neck muscles leads to a body lean forward. Referring to Figures 1A-C, (Figures 1A, 1B, and 1C appear at the end of this article) soleus vibration creates an error signal that is fed into the vestibular loop (box I in Figure 1C; 'down- transformation') in order to compensate for the 'kinematic' transformation of the vestibular signal (if present) by variations of the body-to-foot angle (box 'coordinate transformation'). The down-transformation depicted in Figure 1C (box I) creates a signal representing the behavior of foot-in-space. The subsequent up- transformation (box II) then occurs at the set point of a proprioceptive stabilization loop where the proprioceptive signal is added with the foot-in-space signal, creating a representation of body in space. Given that the down- transformation has a slightly lower gain than the up- transformation (because the former mimics the vestibular transfer function), the body-in-space signal during soleus vibration indicates a slight (non-existing) forward inclination, which then leads to a compensatory backward lean. The situation is different with vibration of the neck; the proprioceptive signal it induces undergoes only a down-transformation corresponding to the head-neck joint before reaching the level of COM representation (the following down- and up-transformations can be disregarded here, because the leg proprioceptive signals are assumed to be zero). Hence, the COM representation indicates a backward body inclination caused by a corresponding (non- existing) platform tilt backward and thus provokes a compensatory lean forward. Note that in the context of psychophysics, when a head-in-space movement is to be recorded, also the up-transformation at the head-to-trunk joint would be involved.

17. Conceivably, the set point of the proprioceptive stabilization also receives signals other than those of the upward transformation reflecting more global aspects of the behavioral situation. For example, if the subject is sitting rather than standing (such that his equilibrium is safe), there is less need for balancing. Possibly then, the vestibular signal and its down-transformation might be 'disabled', and the remaining up-transformation during soleus vibration would perceptually be reinterpreted as a toes-up tilt with the stabilized trunk as a reference.

18. In summary we feel that the psychophysical approach may help to formulate a more comprehensive concept on postural control mechanisms than hitherto was possible with posturographic or electrophysiological means alone (for a more detailed description, see Mergner et al., 1997). Furthermore, we belief that important impulses for the understanding of these problems will come from computer simulations, and that a concept as the one presented here will help to set up the framework for these simulations. We think that this approach is more promising in the long range than that of Roberts, who makes a big leap from a reflex-minded view of postural stabilization, on the one hand, to a Gestalt approach of the problems, on the other hand. Finally we hope, as probably most readers do, that a future version of his interesting and challenging book will contain at least the most relevant scientific literature.


Anastasopoulos, D. & Mergner, T. (1982) Canal-neck interaction in vestibular nuclear neurons of the cat. Exp. Brain Res., 46: 269-280.

Boyle, R. & Pompeiano, O. (1981) Convergence and interaction of neck and macular vestibular inputs. J. Neurophysiol., 45.

Britton T.C., Day B.L., Brown P., Rothwell J.C., Thompson P.D. & Marsden, C.D. (1993) Postural electromyographic responses in the arm and leg following galvanic vestibular stimulation in man. Exp. Brain Res., 94:143-151.

Coulter, J.D., Mergner, T. & Pompeiano, O. (1976) Effects of static tilt on cervical spinoreticular tract neurons. J. Neurophysiol., 39:45-62.

Hlavacka, F., Krizkova, M., Bodor, O. & Mergner, T. (1996) Adjustment of equilibrium point in human stance following galvanic vestibular stimulation: Influence of trunk and head position. In: Motor Control

VII. Gantchev, G., Gurfinkel, V., Stuart, D. & M. Wiesendanger (eds).

Motor Control Press, Tuscon, Arizona, p 289-293.

Hlavacka, F., Mergner, T., Bolha, B. (1996) Human self-motion perception during translatory vestibular and proprioceptive stimulation. Neurosci. Lett, 210: 83-86.

Lindsay, K.W., Roberts, T.D. & Rosenberg, J.R. (1976) Asymmetric tonic labyrinth reflexes and their interaction with neck reflexes in the decerebrate cat. J. Physiol. (Lond.) 261:583-601.

Lund, S. & Broberg, C. (1983) Effects of different head positions on postural sway in man induced by a reproducible vestibular error signal. Acta Physiol. Scand., 117:307-9.

Manzoni, D., Pompeiano, O., Srivastava, U.C. & Stampacchia, G. (1983) Responses of forelimb extensors to sinusoidal stimulation of macular labyrinth and neck receptors. Arch. Ital. Biol., 121:205-14.

Maurer, C., Kimmig, H., Trefzer, A.& Mergner, T. (1997) Visual object localization through vestibular and neck inputs. I. Localization with respect to space and relative to the head and trunk mid-saggital planes. J Vestib Res (in press).

Mergner, T., Becker, W. & Deecke, L. (1985) Canal-neck interaction in vestibular neurons of the cat's cerebral cortex. Exp. Brain Res., 61:94-108.

Mergner, T., Hlavacka, F. & Schweigart, G. (1993) Interaction of vestibular and proprioceptive inputs. J. Vest. Res., 3:41-57.

Mergner, T., Huber, W. & Becker, W. (1997) Vestibular-neck interaction and transformations of sensory coordinates. J. Vestib. Res., 7 (in press).

Mergner, T., Rottler, G., Kimmig, H. & Becker, W. (1992) Role of vestibular and neck inputs for the perception of object motion in space. Exp. Brain Res., 89:655-668.

Mergner, T., Siebold, C., Schweigart, G. & Becker, W. (1991) Human perception of horizontal head and trunk rotation in space during vestibular and neck stimulation. Exp. Brain Res., 85:389-404.

Nashner, L.M. & Wolfson, P. (1974) Influence of head position and proprioceptive cues on short latency postural reflexes evoked by galvanic stimulation of the human labyrinth. Brain Res., 67:86-8.

Peterka, R.J. & Benolken, M.S. (1995) Role of somatosensory and vestibular cues in attenuating visually induced human postural sway. Exp. Brain Res. 105:101-10.

Roberts, T.D.M. (1978) Neurophysiology of Postural Mechanism (2nd ed.), London: Butterworths.

Roberts, T.D.M. (1995) Understanding Balance: The Mechanics of Posture and Locomotion. Chapman & Hall.

Roberts, T.D.M. (1996) Precis of: Understanding Balance: The Mechanics of Posture and Locomotion. PSYCOLOQUY 7(2) posture-locomotion.1.roberts.

Tokita, T., Ito, Y. & Takagi, K. (1989) Modulation by head and trunk positions of the vestibulo-spinal reflexes evoked by galvanic stimulation of the labyrinth. Observations by labyrinthine evoked EMG. Acta Otololaryngol. (Stockholm)

von Holst, E. & Mittelstaedt, H. (1950) Das Reafferenzprinzip (Wechselwirkungen zwischen Zetralnervensystem und Peripherie). Naturwissenschaften, 37:464-476.



                    |       |
                    |   @   |         @= VEST
                    |  |    |
                     - v   -        <--- (b)
                 ----- |    ----
                 \     v       /
                  \    |      /
                   \   v     /
                    \  |    /
                     \ v   /
                      \|  /
                      |v  |
                      || O|            O= COM
                     / v  \
                    /  | |  \
                   /   v    \
                   |   | |   |
                   |   v    |
                   |   | |   |
                    |  v   |
                    |  | |  |
                    |  v   |
                     | | | |
                     | v  |
                     | | | |
                      |v |
                      || ||
                      |v | -        <--- (a)
                     | | |   |


     .  space     .
     . reference  .
     .            .
         hs|(lambda HS)                           |
           |                                      |hs`
lambda ht v+ ht |+
       --->0                                  --->0
          -|                                      +
           |                                      |
           | ts                                   | ts`
lambda tl v+ tl |+
       --->0                                  --->0
          -|                                      +
           |                                      |
           | ls                                   | ls`
lambda lf v+ lf |+
       --->0                                  --->0
          -|                                      +
           |                                      |
           | fs                                   | fs`
           |                                      |
           |    ----------------------------      |
           |    |          .............    |     |
           |    |  foot    .  space     .   |     |
            --->|support re. reference  .   |-----
                |          .            .   |
                |          .............    |


           PHYSICS      .                SENSORY AND
                        .               CENTRAL PROCESSING
          --------------.,  Neural   ,<-----------------
          |             ., Controller,                  |
          |             .,,,,,,,,,,,,,                  |
          |             .                               |
          |  bio-      D I R E C T  L O O P             |
          |  mecha-     .                               |
ext. | nics . ,,|,,, torque v- .,,,,,,,,,,,,, ,+|II, BODY re-->O----.-- ----->, Leg ,--->O------.----->O , FOOT + | BrF ., Prop , | ,+ ,
               |        .,,,,,,,,,,,,,    |      |    ,,|,,,
               |        .                Vibrat. |      |
               |        .                        |      |
               |        .                        |      |
               |        .                        |      |
displacem. V(+) . ,,|,,,, | FOOT ,,,,,,,, BrS.,,,,,,,,,,,,, , v(-), | Supp. ----->,COORD ,---->, Vest ,--->O----->O------ re ,TRANSF, ., System , ,+ I , SPACE ,,,,,,,, .,,,,,,,,,,,,, | ,,,,,,,
                        .               Galv.


Figures 1A, 1B: Conceptual model of vestibular-proprioceptive interaction for postural stabilization. The down- and up-transformation hypothesis is depicted for a standing subject literally (1A) and in the form of a signal flow diagram (1B; VEST., vestibular system; COM, center of body mass; lambda, vestibular transfer characteristics; HS, head-in-space velocity; hs, ht, ts, tl, lf, ls, and fs, internal velocity signals of head-in- space, head-to-trunk, trunk-in-space, trunk-to-leg, leg- to-foot, leg-in-space, and foot-in-space, respectively).

Figure 1C: Depiction of the concept in terms of a wiring diagram for a condition in which the subject stabilizes body posture by applying muscle torque across the ankle joints. I, down-transformation. II, up-transformation. For details, see text.

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