End Points of Planar Reaching Movements Are Disrupted by Small Force Pulses: An Evaluation of the Hypothesis of Equifinality

Abstract

A single force pulse was applied unexpectedly to the arms of five normal human subjects during nonvisually guided planar reaching movements of 10-cm amplitude. The pulse was applied by a powered manipulandum in a direction perpendicular to the motion of the hand, which gripped the manipulandum via a handle at the beginning, at the middle, or toward the end the movement. It was small and brief (10 N, 10 ms), so that it was barely perceptible. We found that the end points of the perturbed motions were systematically different from those of the unperturbed movements. This difference, dubbed "terminal error," averaged 14.4 +/- 9.8% (mean +/- SD) of the movement distance. The terminal error was not necessarily in the direction of the perturbation, although it was affected by it, and it did not decrease significantly with practice. For example, while perturbations involving elbow extension resulted in a statistically significant shift in mean end-point and target-acquisition frequency, the flexion perturbations were not clearly affected. We argue that this error distribution is inconsistent with the "equilibrium point hypothesis" (EPH), which predicts minimal terminal error is determined primarily by the variance in the command signal itself, a property referred to as "equifinality." This property reputedly derives from the "spring-like" properties of muscle and is enhanced by reflexes. To ensure that terminal errors were not due to mid-course voluntary corrections, we only accepted trials in which the final position was already established before such a voluntary response to the perturbation could have begun, that is, in a time interval shorter than the minimum reaction time (RT) for that subject. This RT was estimated for each subject in supplementary experiments in which the subject was instructed to move to a new target if perturbed and to the old target if no perturbation was detected. These RT movements were found to either stop or slow greatly at the original target, then re-accelerate to the new one. The average latency of this second motion was used to estimate the voluntary RT for each subject (316 ms mean). Additionally, we found that the hand neither exerted target-oriented force against the handle nor drifted toward the desired end point just before coming to rest, making it unlikely that the mechanical properties of the manipulandum prevented the hand from reaching its intended target.

Intrinsic Musculoskeletal Properties Stabilize Wiping Movements in the Spinalized Frog

“…In several recent studies, however, total viscoelasticity of arm movements in humans has been estimated to be quite low Kawato, 1996, 1997;Popescu and Rymer, 2000;Mah, 2001;Hinder and Milner, 2003;Popescu et al, 2003). These studies suggest that human arm movements do not possess stability properties similar to those demonstrated here.…”

“…This observation might suggest basic limitations in the degree of stability that intrinsic properties are capable of conferring in this experimental system. To obtain the more precise accuracy characteristic of many human behaviors, such as those studied by others (Popescu and Rymer, 2000;Hinder and Milner, 2003;Popescu et al, 2003), it might therefore be necessary to rely more on afferent feedback for the regulation of stability.…”

Handedness can be explained by a serial hybrid control scheme

“…We chose a hybrid model and not a model where movements of each arm were explained solely by its own controller, i.e impedance mechanisms for the nondominant arm, and predictive mechanisms for the dominant arm. A pure impedance mechanism has been shown to be inadequate for movement production, mainly because of the requirement for non-biological control inputs at initiation, and non-biological stiffnesses required to generate those movements (Popescu et al, 2000; 2003a, 2003b). Further, human arm movements exhibit task-dynamic-dependent stiffness suggesting they involve some type of predictive controller (Gomi and Osu, 1998).…”

Evidence for the Flexible Sensorimotor Strategies Predicted by Optimal Feedback Control

“…However, perturbations introduced late in the movement may be more informative because they are not fully corrected, in contradiction with alternative models and, somewhat paradoxically, in agreement with optimal feedback control. Such phenomena have been observed with both visual target perturbations (Komilis et al, 1993) and mechanical limb perturbations (Popescu and Rymer, 2000). In the case of limb perturbations, the correction reflects both neural feedback and musculoskeletal impedance, which are seamlessly integrated (Nicols and Houk, 1976) and difficult to disentangle.…”