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J Neurophysiol (July 5, 2007). doi:10.1152/jn.00287.2007
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Submitted on March 14, 2007
Accepted on June 6, 2007

Equilibrium point control cannot be refuted by experimental reconstruction of equilibrium point trajectories

Dinant Arne Kistemaker1*, Arthur (Knoek) J Van Soest1, and Maarten Frank Bobbert1

1 Faculteit der Bewegingswetenschapen, Vrije Universiteit, Amsterdam, NH, Netherlands

* To whom correspondence should be addressed. E-mail: d.kistemaker{at}fbw.vu.nl.

In the literature it has been hotly debated whether the brain uses internal models or equilibrium point (EP) control to generate arm movements. EP-control involves specification of EP-trajectories, time series of arm configurations in which internal forces and external forces are in equilibrium; if the arm is not in a specified EP, it is driven towards this EP by muscle forces arising due to central drive, reflexes and muscle mechanics. EP-control has been refuted by researchers claiming that EP-trajectories underlying movements of subjects were complex. These researchers used an approach that involves applying force perturbations during movements of subjects and fitting a mass-spring-damper model to the kinematic responses, and then to reconstruct the EP-trajectory using the estimated stiffness, damping and measured kinematics. In this study we examined the validity of this approach using an EP-controlled musculoskeletal model of the arm. We used the latter model to simulate unperturbed and perturbed maximally fast movements and optimized the parameter values of a mass-spring-damper model to make it reproduce as best as possible the kinematic responses. It was shown that estimated stiffness not only depended on the 'true' stiffness of the musculoskeletal model but on all of its dynamical parameters. Furthermore it was shown that reconstructed EP-trajectories were in agreement with those presented in the literature, but did not resemble the simple EP-trajectories that had been used to generate the movement of the model. It was concluded that the refutation of EP-control on the basis of results obtained with mass-spring-damper models was unjust.




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J. Wong, E. T. Wilson, N. Malfait, and P. L. Gribble
The Influence of Visual Perturbations on the Neural Control of Limb Stiffness
J Neurophysiol, January 1, 2009; 101(1): 246 - 257.
[Abstract] [Full Text] [PDF]




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