Motor equivalence expresses the idea that movement components reorganize in the face of perturbations to preserve the value of important performance variables, such as the hand's position in reaching. A formal method is introduced to evaluate this concept quantitatively: changes in joint configuration due to unpredictable elbow perturbation lead to a smaller change in performance variables than expected given the magnitude of joint configuration change. This study investigated whether motor equivalence was present during the entire movement trajectory and how magnitude of motor equivalence was affected by constraints imposed by two different target types. Subjects pointed to spherical and cylindrical targets both with and without an elbow joint perturbation produced by a low- or high-stiffness elastic band. Subjects' view of their arm was blocked in the initial position, and the perturbation condition was randomized to avoid prediction of the perturbation or its magnitude. A modification of the uncontrolled manifold method variance analysis was used to investigate how changes in joint configuration on perturbed vs. nonperturbed trials (joint deviation vector) affected the hand's position or orientation. Evidence for motor equivalence induced by the perturbation was present from the reach onset and increased with the strength of the perturbation after 40% of the reach, becoming more prominent as the reach progressed. Hand orientation was stabilized more strongly by motor equivalent changes in joint configuration than was three-dimensional position regardless of the target condition. Results are consistent with a recent model of neural control that allows for flexible patterns of joint coordination while resisting joint configuration deviations in directions that affect salient performance variables. The observations also fit a general scheme of synergic control with referent configurations defined across different levels of the motor hierarchy.

We use an approach rooted in the recent theory of synergies to analyze possible co-variation between two hypothetical control variables involved in finger force production based in the equilibrium-point hypothesis. These control variables are the referent coordinate (R) and apparent stiffness (C) of the finger. We tested a hypothesis that inter-trial co-variation in the {R; C} space during repeated, accurate force production trials stabilizes the fingertip force. This was expected to correspond to a relatively low amount of inter-trial variability affecting force and a high amount of variability keeping the force unchanged. We used the “inverse piano” apparatus to apply small and smooth positional perturbations to fingers during force production tasks. Across trials, R and C showed strong co-variation with the data points lying close to a hyperbolic curve. Hyperbolic regressions accounted for over 99% of the variance in the {R; C} space. Another analysis was conducted by randomizing the original {R; C} data sets and creating surrogate data sets that were then used to compute predicted force values. The surrogate sets always showed much higher force variance compared to the actual data, thus reinforcing the conclusion that finger force control was organized in the {R; C} space, as predicted by the equilibrium-point hypothesis, and involved co-variation in that space stabilizing total force.

The concept of motor equivalent combinations of arm muscles, or M-modes, was investigated during reaching to insert a pointer into a cylindrical target with and without an elbow perturbation. Five M-modes across 15 arm/scapula muscles were identified by principal component analysis with factor extraction. The relationship between small changes in the M-modes and changes in the position/orientation of the pointer were investigated by linear regression analyses. The results revealed a motor equivalent organization of the M-modes for perturbed compared with non-perturbed reaches, both with respect to hand position and orientation, especially in the first 100-ms postperturbation. Similar findings were obtained for motor equivalence computed based on changes in the joint configuration, although the kinematically defined motor equivalence was stronger for pointer orientation. The results support the hypothesis that the nervous system organizes muscles into M-modes and flexibly scales M-mode activation to preserve stable values of variables directly related to performance success.

We explored stability of multi-finger cyclical accurate force production action by analysis of responses to small perturbations applied to one of the fingers and inter-cycle analysis of variance. Healthy subjects performed two versions of the cyclical task, with and without an explicit target. The “inverse piano” apparatus was used to lift/lower a finger by 1 cm over 0.5 s; the subjects were always instructed to perform the task as accurate as they could at all times. Deviations in the spaces of finger forces and modes (hypothetical commands to individual fingers) were quantified in directions that did not change total force (motor equivalent) and in directions that changed the total force (non-motor equivalent). Motor equivalent deviations started immediately with the perturbation and increased progressively with time. After a sequence of lifting-lowering perturbations leading to the initial conditions, motor equivalent deviations were dominating. These phenomena were less pronounced for analysis performed with respect to the total moment of force with respect to an axis parallel to the forearm/hand. Analysis of inter-cycle variance showed consistently higher variance in a subspace that did not change the total force as compared to the variance that affected total force. We interpret the results as reflections of task-specific stability of the redundant multi-finger system. Large motor equivalent deviations suggest that reactions of the neuromotor system to a perturbation involve large changes of neural commands that do not affect salient performance variables, even during actions with the purpose to correct those salient variables. Consistency of the analyses of motor equivalence and variance analysis provides additional support for the idea of task-specific stability ensured at a neural level.