Previous reports show that the forces produced by the fingers of one hand drop exponentially over time in the absence of visual feedback on the forces. We study the force production by the index fingers of both hands with no visual feedback. Subjects produced a specified total force with a specific contribution from each finger by pressing on force sensors. We observed that in the absence of visual feedback: (1) The finger forces dropped with time by an amount proportional to the magnitude of the initial force. For low initial force values (<7 % of MVC of individual finger force), the finger forces showed an increase; (2) the total force (sum of finger forces) evolution showed similar features; (3) finger forces changed in a way that facilitated more equitable force production by the two fingers; (4) all the force-time changes resemble exponential functions with similar time constants (~15 s). We propose that two processes interact to produce these patterns. (1) RC back-coupling: The central nervous system defines referent coordinates (RCs) for the digit tips, and the difference between the referent and actual coordinates leads to force production. If actual coordinates are not allowed to move to referent ones, referent coordinates show a slow drift toward the actual ones, leading to a force drop. (2) Sensory adaptation: This process, possibly related to sensory receptor characteristics, leads to an increase in finger force. RC back-coupling provides a common account of this and other reported phenomena of hand force or position changes across transient, external perturbations.

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.

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The extrinsic digit muscles naturally couple wrist action and grip force in prehensile tasks. We explored the effects of wrist position on the steady-state grip force and grip-force change during imposed changes in the grip aperture (apparent stiffness). Subjects held an instrumented handle steady using a prismatic five-digit grip. The grip aperture was changed slowly, while the subjects were instructed not to react voluntarily to these changes. An increase in the aperture resulted in an increase in grip force and its contraction resulted in a proportional drop in grip force. The apparent stiffness values (between 4 and 6 N/cm) were consistent across a wide range of wrist positions. These values were larger when the subjects performed the task with eyes open as compared to eyes-closed trials. They were also larger for trials that started from a larger initial aperture. After a sequence of aperture increase and decrease to the initial width, grip force dropped by about 25% without the subjects being aware of this. We interpret the findings within the referent configuration hypothesis of grip force production. The results support the idea of back-coupling between the referent and actual digit coordinates. According to this idea, the central nervous system defines referent coordinates for the digit tips, and the difference between the referent and actual coordinates leads to force production. If actual coordinates are not allowed to move to referent ones, referent coordinates show a relatively slow drift towards the actual ones.

We applied the theory of synergies to analyze the processes that lead to unintentional decline in isometric fingertip force when visual feedback of the produced force is removed. We tracked the changes in hypothetical control variables involved in single fingertip force production based on the equilibrium-point hypothesis, namely, the fingertip referent coordinate (RFT) and its apparent stiffness (CFT). The system's state is defined by a point in the {RFT; CFT} space. We tested the hypothesis that, after visual feedback removal, this point (1) moves along directions leading to drop in the output fingertip force, and (2) has even greater motion along directions that leaves the force unchanged. Subjects produced a prescribed fingertip force using visual feedback, and attempted to maintain this force for 15 s after the feedback was removed. We used the “inverse piano” apparatus to apply small and smooth positional perturbations to fingers at various times after visual feedback removal. The time courses of RFT and CFT showed that force drop was mostly due to a drift in RFT towards the actual fingertip position. Three analysis techniques, namely, hyperbolic regression, surrogate data analysis, and computation of motor-equivalent and non-motor-equivalent motions, suggested strong co-variation in RFT and CFT stabilizing the force magnitude. Finally, the changes in the two hypothetical control variables {RFT; CFT} relative to their average trends also displayed covariation. On the whole the findings suggest that unintentional force drop is associated with (a) a slow drift of the referent coordinate that pulls the system towards a low-energy state, and (b) a faster synergic motion of RFT and CFT that tends to stabilize the output fingertip force about the slowly-drifting equilibrium point.

We explored unintentional changes in forces during performance of constant and cyclic force-production tasks (F-tasks) after visual feedback removal. Based on earlier studies, we expected all force parameters to drop exponentially with time. We also explored possible role of working memory in the force drop phenomena. Healthy subjects performed constant or cyclic isometric F-tasks with the index finger under visual feedback. The cyclic task was paced by a metronome. Removing visual feedback resulted in a consistent force drop in constant F-tasks and a qualitatively similar drift in the mean force in the cyclic F-task. Both were slow with characteristic times of about 10-20 s. In contrast, force amplitude in the cyclic F-task increased quickly (within 1-2 s). When the subjects were asked to stop producing force for 5 s after the visual feedback disappeared and then resume force production, no downward force drift was seen in constant F-tasks, while in cyclic F-tasks, the drift of the mean force was present and an exaggerated increase in force amplitude was also observed. We conclude that while working memory limitations may influence cyclic F-tasks, their role in determining the force drift in constant F-tasks is limited. The results of both experiments are interpreted within the referent configuration hypothesis supplemented with an idea of unintentional drift of referent coordinates (RC-back-coupling) induced by differences between the referent and actual body configurations.

Objectives We investigated the unintentional drift in total force and in sharing of the force between fingers in two-finger accurate force production tasks performed without visual feedback by patients with Parkinson’s disease (PD) and healthy controls. In particular, we were testing a hypothesis that adaptation to the documented loss of action stability could lead to faster force drop in PD. Methods PD patients and healthy controls performed accurate constant force production tasks without visual feedback by different finger pairs, starting with different force levels and different sharing patterns of force between the two fingers. Results Both groups showed an exponential force drop with time and a drift of the sharing pattern towards 50:50. The PD group showed a significantly faster force drop without a change in speed of the sharing drift. These results were consistent across initial force levels, sharing patterns, and finger pairs. A pilot test of four subjects, two PD and two controls, showed no consistent effects of memory on the force drop. Conclusions We interpret the force drop as a consequence of back-coupling between the actual and referent finger coordinates that draws the referent coordinate towards the actual one. The faster force drop in the PD group is interpreted as adaptive to the loss of action stability in PD. The lack of group differences in the sharing drift suggests two potentially independent physiological mechanisms contributing to the force and sharing drifts. Significance The hypothesis on adaptive changes in PD with the purpose to ensure stability of steady states may have important implications for treatment of PD. The speed of force drop may turn into a useful tool to quantify such adaptive changes.

Extrinsic digit muscles contribute to both fingertip forces and wrist movements (FDP and FPL – flexion, EDC - extension). Hence it is expected that finger forces depend on the wrist movement and position. We investigated the relation between grip force and wrist kinematics to examine whether and how the force: (1) scales with wrist flexion-extension (FE) angle; (2) can be predicted from accelerations induced during FE movement. In one experiment subjects naturally held an instrumented handle using a prismatic grasp and performed very slow FE movements. In another experiment, the same movement was performed cyclically at three prescribed frequencies. In quasistatic conditions, the grip force remained constant over the majority of the wrist range of motion. During the cyclic movements, the grip force changed. The changes were described with a linear regression model that represents the thumb and virtual finger (VF = four fingers combined) normal forces as the sum of the effects of the object’s tangential and radial accelerations and an object-weight-dependent constant term. The model explained 99% of the variability in the data. The independence of the grip force from wrist position agrees with the theory that that the thumb and VF forces are controlled with two neural variables that encode referent coordinates for each digit while accounting for changes in the position dependence of muscle forces, rather than a single neural variable like referent aperture. The results of the cyclical movement study extend the principle of superposition (some complex actions can be decomposed into independently controlled elemental actions) for a motor task involving simultaneous grip force exertion and wrist motion with significant length changes of the grip-force producing muscles.