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Novel strategies in feedforward adaptation to a position-dependent perturbation

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Abstract

To investigate the control mechanisms used in adapting to position-dependent forces, subjects performed 150 horizontal reaching movements over 25 cm in the presence of a position-dependent parabolic force field (PF). The PF acted only over the first 10 cm of the movement. On every fifth trial, a virtual mechanical guide (double wall) constrained subjects to move along a straight-line path between the start and target positions. Its purpose was to register lateral force to track formation of an internal model of the force field, and to look for evidence of possible alternative adaptive strategies. The force field produced a force to the right, which initially caused subjects to deviate in that direction. They reacted by producing deviations to the left, “into” the force field, as early as the second trial. Further adaptation resulted in rapid exponential reduction of kinematic error in the latter portion of the movement, where the greatest perturbation to the handpath was initially observed, whereas there was little modification of the handpath in the region where the PF was active. Significant force directed to counteract the PF was measured on the first guided trial, and was modified during the first half of the learning set. The total force impulse in the region of the PF increased throughout the learning trials, but it always remained less than that produced by the PF. The force profile did not resemble a mirror image of the PF in that it tended to be more trapezoidal than parabolic in shape. As in previous studies of force-field adaptation, we found that changes in muscle activation involved a general increase in the activity of all muscles, which increased arm stiffness, and selectively-greater increases in the activation of muscles which counteracted the PF. With training, activation was exponentially reduced, albeit more slowly than kinematic error. Progressive changes in kinematics and EMG occurred predominantly in the region of the workspace beyond the force field. We suggest that constraints on muscle mechanics limit the ability of the central nervous system to employ an inverse dynamics model to nullify impulse-like forces by generating mirror-image forces. Consequently, subjects adopted a strategy of slightly overcompensating for the first half of the force field, then allowing the force field to push them in the opposite direction. Muscle activity patterns in the region beyond the boundary of the force field were subsequently adjusted because of the relatively-slow response of the second-order mechanics of muscle impedance to the force impulse.

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Acknowledgements

This work was conducted while M.R. Hinder worked as a student intern in the Computational Neuroscience Laboratories at Advanced Telecommunications Research Institute International, Kyoto, Japan. We thank Dr. M. Kawato for this opportunity. We also thank D. Franklin and T. Yoshioka for assistance in conducting experiments at ATR, and D. Franklin for providing an earlier version of Figure 1. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada and the Gordon Diewert Memorial Scholarship.

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Correspondence to Theodore E. Milner.

Appendix

Appendix

Simulations to determine how the impedance of the arm transformed the force impulse of the PF into lateral displacement were carried out using a second-order model of the limb mechanics driven by joint torques, τr, derived from null-field movements such that

$$I(\theta)\ddot\theta + C(\theta,\dot\theta)\dot\theta+ B_{j} \dot\theta+ K_{j} (\theta- \theta_{\rm r}) = \tau_{\rm r} + \tau_{\text {PF}} $$

where I represents the inertia of the arm determined from anthropometric estimates, C represents Coriolis and centrifugal terms, Bj is the joint damping matrix, Kj is the joint stiffness matrix, θr(t) is the null field trajectory and τPF represents the joint torques imposed by the PF. Joint stiffness terms were scaled as a function of joint torque, corresponding to measurements made by Osu and Gomi (1999) and Perreault et al. (2004). Joint damping was proportional to joint stiffness and inversely proportional to joint velocity (Tee et al. 2004), with a proportionality constant chosen such that the damping ratio was approximately equal to that measured by Perreault et al. (2004). Joint torques, τr, were computed from inverse dynamics, using the trajectories and the hand forces recorded during null-field movements as in Franklin et al. (2003a). The above differential equation was solved using the Matlab function ode45.

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Hinder, M.R., Milner, T.E. Novel strategies in feedforward adaptation to a position-dependent perturbation. Exp Brain Res 165, 239–249 (2005). https://doi.org/10.1007/s00221-005-2294-x

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