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J Physiol (2003), 551.1, p. 4
© Copyright 2003 The Physiological Society
DOI: 10.1113/jphysiol.2003.044792
Email: r.fitzpatrick{at}unsw.edu.au
My own agility amazes me. How can this bulk move with a liveliness to rival, perhaps not Nureyev, but at least Fantasia's hippo doing Ponchielli's Dance of the Hours? The answer, in part, may lie in the observations of Lakie et al. (2003) reported in this issue of The Journal of Physiology. The upright human body could be balanced simply by making its joints stiff with tendons and muscles, and the stiffer the better. However, the authors show that the ankle is kept compliant and the pendulum unstable. A more complex control is then used to stabilise it. The aphorism of designing for mobility: 'make it as unstable as possible and control it like mad', seems to apply to human balance.
How does it work? Consider a mass-spring model of a balanced inverted pendulum (Fig. 1). Omitted are viscous elements, an articulated pendulum, antagonist muscles, non-linearities and other refinements to make the pendulum a real-life standing person. Gravity pulls it forward while the calf muscles pull it back. These must be balanced over a finite time period to hold the pendulum between the toe and heel limits.
Gravity acts on the pendulum to produce a torque that is a function of instantaneous position. This gives the load elastic stiffness. This load elastic element (LEE) has stiffness approximated by mgh for small angles of lean. Elastic stiffness is a part of dynamic stiffness or impedance, but these also include viscous, inertial and other components associated with time derivatives of position. The calf muscles pull the other way, coupled to the pendulum by the series elastic element (SEE) comprising Achilles' tendons and the feet.
Assume for now infinitely stiff calf muscles and ignore the inertia of the mass. Just two elastic elements oppose each other. If SEE is stretched to produce the same torque as LEE, the pendulum is held balanced. If SEE is stiffer than LEE, the pendulum is stable and will return to the start position when perturbed because SEE, being stiffer, produces more incremental torque than LEE. If SEE is not as stiff as LEE, the pendulum, although balanced, will be unstable. Any perturbation will cause it to continue falling because SEE cannot match the torque of LEE. This paper shows that this is the situation of human standing where SEE is estimated to be 80-90 % of LEE. It will in fact be worse than this because it is based on the LEE for static equilibrium, but in the dynamic system, natural resonance and the moment of inertia will bring it down to less than 50 %. Morasso & Schieppati (1999) give a concise theoretical account of this. Either way, passive elements make an unstable pendulum.
The muscle pulling on the other end of the series elastic element is also an elastic element (CEE) by virtue of its activity-dependent crossbridge linkage. Being in series with SEE, the combined stiffness of muscle and tendon will be lower than that of tendon alone for any constant contraction.
Co-contraction will stiffen a joint by engaging the series elastic element of the antagonist muscle so that it pulls the pendulum from the other side. Parallel SEEs then have the stiffness of their sum. A modest level of co-contraction would probably raise the total SEE stiffness by the 25 % or so required to be stiffer than LEE. However, we don't stand this way. Tibialis anterior activity is invariably silent unless we sway right back over the ankles. We choose to stand with the body unstable, leaning forward, and controlled by activity in one direction.
If passive stiffness and constant contraction cannot balance the pendulum, what can? It must be modulated activity of the muscle. This activity needs to give the contractile unit negative stiffness so that the in-series total can be stiffer than SEE alone. Muscles can do this by generating more force as they shorten.
Tonic stretch reflexes act continuously and generate force as a function of muscle length. They therefore can also be considered an elastic element (SREE) that augments, albeit with a delay, the stiffness of the contractile unit. Even so, increasing elastic stiffness of the muscle does not help balance the pendulum.
However, stretch reflexes are elusive. They are also driven by higher time derivatives of position so that phase-advanced viscous and inertial responses step in to create a greater dynamic stiffness. It is conceivable that these responses at appropriate gain can bring the dynamic stiffness of muscle and tendon up to a level that will control the pendulum.
Intermittent control. In their preceding papers the authors identify the components that create total ankle stiffness during standing (Loram et al. 2001; Loram & Lakie, 2002) and show that it relies substantially on intermittent control (IC) by ballistic movements rather than instantaneous elastic stiffness. The problem here is the long time (
) taken to detect a disturbance, transmit and process the signal, and then generate torque. Temporal prediction of position based on ongoing afferent input can be used to produce anticipatory responses that will offset the time delay problem. However, the problem may not be so great with the inertial properties of the mass added to the model. Inertial lag can buy the time needed for discrete intermittent responses. This we know from the ease of balancing an upright broom on the palm of the hand and the impossibility of doing it with a pencil.
An important question is whether we can distinguish stretch reflex from intermittent control during continuous behaviours. With transmission delays and dynamic responses, stretch reflexes could produce under-damped oscillatory responses that may look very similar to the behaviour seen here. Examining Fig. 4 does not reveal an abrupt change in behaviour that would indicate the transition from stretch reflex to intermittent control. It is all a matter of degree. The key is in response times and bandwidths, but it is going to be difficult to untangle them in a system that can adapt and weight co-contraction, stretch reflexes and intermittent control to achieve a performance that matches any task we throw at it. Looking at adaptations to changing tasks may be a fruitful approach.
Kangaroos are magnificent movers. They achieve this with extremely compliant Achilles' tendons that retrieve the kinetic energy lost with each landing and release it with the next launch. Can they stand on two feet as we do? No. The legs act as struts while the balance activity is in the tail. Can they balance on two feet? Those who have boxed with a kangaroo will know how they balance by bouncing up and down on their toes while they jab at you. This intermittent ballistic control, a consequence of their extremely compliant series elastic element, is as Lakie et al. (2003) show. I remember watching as a child that greatest exponent of the sweet science, Muhammad Ali, taking the title from Sonny Liston. My attention was drawn to those bouncing, floating feet. Like Sonny, I never saw the punch. Why then do we go to all this trouble to control an unstable body when such control could be achieved easily with more elastic stiffness? No doubt the answer is to maintain mobility.
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Figure 1. Mass-spring model of standing | ||
Lakie M, Caplan N & Loram ID (2003). J Physiol 551, 357-370. [Abstract/Full Text]
Loram ID, Kelly SM & Lakie M (2001). J Physiol 532, 879-891. [Abstract/Full Text]
Loram ID & Lakie M (2002). J Physiol 540, 1111-1124. [Abstract/Full Text]
Morasso PG & Schieppati M (1999). J Neurophysiol 83, 1622-1626.
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  I. D Loram, C. N Maganaris, and M. Lakie Human postural sway results from frequent, ballistic bias impulses by soleus and gastrocnemius J. Physiol., April 1, 2005; 564(1): 295 - 311. [Abstract] [Full Text] [PDF]
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I. D Loram, C. N Maganaris, and M. Lakie Active, non-spring-like muscle movements in human postural sway: how might paradoxical changes in muscle length be produced? J. Physiol., April 1, 2005; 564(1): 281 - 293. [Abstract] [Full Text] [PDF]
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I. D. Loram, C. N. Maganaris, and M. Lakie Paradoxical muscle movement in human standing J. Physiol., May 1, 2004; 556(3): 683 - 689. [Abstract] [Full Text] [PDF]
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