Are Complex Control Signals Required for Human Arm Movement?. Paul L. Gribble, David J. Ostry, Vittorio Sanguineti, and Rafael Laboissiere McGill. University, Montreal, Quebec, Department of Informatics, Systems and Telecommunications, University of Genova, Italy, Institute de la Communication Parlee, Grenoble, France.
APStracts 4:327N, 1997.
ABSTRACT
It has been proposed that the control signals underlying voluntary human arm movement have a ``complex'' non-monotonic time-varying form, and a number of empirical findings have been offered in support of this idea cite Gomi_and_Kawato_1996,Latash_and_Gottlieb_1991}. In this paper we address three such findings using a model of two-joint arm motion based on the lambda version of the equilibrium-point hypothesis. The model includes six one- and two-joint muscles, reflexes, modeled control signals, muscle properties and limb dynamics. First, we address the claim that ``complex'' equilibrium trajectories are required in order to account for non-monotonic joint impedance patterns observed during multi-joint movement {Gomi_and_Kawato_1996}. Using constant-rate shifts in the neurally specified equilibrium of the limb, and constant cocontraction commands, we obtain patterns of predicted joint stiffness during simulated multi-joint movements which match the non-monotonic patterns reported empirically. We then use the algorithm proposed by citeN Gomi_and_Kawato_1996 to compute a hypothetical equilibrium trajectory from simulated stiffness, viscosity and limb kinematics. Like that reported by {Gomi_and_Kawato_1996}, the resulting trajectory was non-monotonic, first leading then lagging the position of the limb. Second, we address the claim that high levels of stiffness are required to generate rapid single-joint movements when simple equilibrium shifts are used. We compare empirical measurements of stiffness during rapid single-joint movements {Bennett_1993} with the predicted 0stiffness of movements generated using constant-rate equilibrium shifts and constant cocontraction commands. Single-joint movements are simulated at a number of speeds, and the procedure used by {Bennett_1993} to estimate stiffness is followed. We show that when the magnitude of the cocontraction command is scaled in proportion to movement speed, simulated joint stiffness varies with movement speed in a manner comparable to that reported by \citeN{Bennett_1993}. Third, we address the related claim that non-monotonic equilibrium shifts are required to generate rapid single-joint movements. Using constant-rate equilibrium shifts and constant cocontraction commands, rapid single-joint movements are simulated in the presence of external torques. We use the procedure reported by {Latash_and_Gottlieb_1991} to compute hypothetical equilibrium trajectories from simulated torque and angle measurements during movement. As in {Latash_and_Gottlieb_1991}, a non-monotonic function is obtained, even though the control signals used in the simulations are constant-rate changes in the equilibrium position of the limb. Differences between the ``simple'' equilibrium trajectory proposed in the present paper and those which are derived from the procedures used by {Gomi_and_Kawato_1996} and {Latash_and_Gottlieb_1991} 

Received 24 April 1997; accepted in final form 14 November 1997.
APS Manuscript Number J323-7.
Article publication pending J. Neurophysiol.
ISSN 1080-4757 Copyright 1997 The American Physiological Society.
Published in APStracts on 12 December 1997