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Citation

Winter DA, Patla AE, Prince F, Ishac M, Gielo-Perczak K. Stiffness control of balance in quiet standing. J Neurophysiol. 1998 Sep;80(3):1211-21. PUBMED - FULL TEXT

10 Word Summary

Quiet standing balance is controlled by passive means.

Abstract

Our goal was to provide some insights into how the CNS controls and maintains an upright standing posture, which is an integral part of activities of daily living. Although researchers have used simple performance measures of maintenance of this posture quite effectively in clinical decision making, the mechanisms and control principles involved have not been clear. We propose a relatively simple control scheme for regulation of upright posture that provides almost instantaneous corrective response and reduces the operating demands on the CNS. The analytic model is derived and experimentally validated. A stiffness model was developed for quiet standing. The model assumes that muscles act as springs to cause the center-of-pressure (COP) to move in phase with the center-of-mass (COM) as the body sways about some desired position. In the sagittal plane this stiffness control exists at the ankle plantarflexors, in the frontal plane by the hip abductors/adductors. On the basis of observations that the COP-COM error signal continuously oscillates, it is evident that the inverted pendulum model is severely underdamped, approaching the undamped condition. The spectrum of this error signal is seen to match that of a tuned mass, spring, damper system, and a curve fit of this "tuned circuit" yields omega n the undamped natural frequency of the system. The effective stiffness of the system, Ke, is then estimated from Ke = I omega n2, and the damping B is estimated from B = BW X I, where BW is the bandwidth of the tuned response (in rad/s), and I is the moment of inertia of the body about the ankle joint. Ten adult subjects were assessed while standing quietly at three stance widths: 50% hip-to-hip distance, 100 and 150%. Subjects stood for 2 min in each position with eyes open; the 100% stance width was repeated with eyes closed. In all trials and in both planes, the COP oscillated virtually in phase (within 6 ms) with COM, which was predicted by a simple 0th order spring model. Sway amplitude decreased as stance width increased, and Ke increased with stance width. A stiffness model would predict sway to vary as Ke-0.5. The experimental results were close to this prediction: sway was proportional to Ke(-0.55). Reactive control of balance was not evident for several reasons. The visual system does not appear to contribute because no significant difference between eyes open and eyes closed results was found at 100% stance width. Vestibular (otolith) and joint proprioceptive reactive control were discounted because the necessary head accelerations, joint displacements, and velocities were well below reported thresholds. Besides, any reactive control would predict that COP would considerably lag (150-250 ms) behind the COM. Because the average COP was only 4 ms delayed behind the COM, reactive control was not evident; this small delay was accounted for by the damping in the tuned mechanical system.

Notes

• CoM is related to CoP by fitting a tuned mass-spring-damper inverted pendulum to the recorded data
• Effective stiffness is defined as: $K_e = I:\omega^2$
• Damping is defined as: $b_e = BW\:I$
• Sway amplitude decreased as stance width increased, and Ke increased with stance width.
• CoP was only out of phase with CoM by 4 ms, thus no active control (time scale of ~100 ms) was assumed to occur.
• The relationship between CoM (x) and CoP (px) in the anterior-posterior direction (where W is the weight of the body minus the feet and h is the height of the CoM) can be given as:
• $\left( p_x - x \right) = -\frac{I}{Wh}\ddot{x}$
• The pendulum model says that the acceleration of the CoM is proportional to the difference in CoP and CoM position.
• In modeling the system CoM is the measured value and CoP is the control input.
• If now modeling the system is a rotational spring giving mechanical feedback to the pendulum's CoM, we get the following linear relations:
• $K\theta-Wh\theta=-I\ddot{\theta}$
• $\theta \approx \frac{x}{h}$
• $\frac{Kx}{Wh}-x=-\frac{I}{Wh}\ddot{x}$
• From here we now have a relation for px in terms of (Kx/Wh), an effective stiffness is defined as Ke=K-Wh
• Stiffness was fit for different stance widths, as stiffness was observed to change with a change in configuration.
• Stiffness increased in the M/L direction for increasing stance widths.
• 50% stance = 627 N*m/rad
• 150% stance = 3163 N*m/rad
• Maximum CoM excursion is predicted by the stiffness value in the relation K-0.55