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Friedman, J., SKM, V., Zatsiorsky, V. M., & Latash, M. L. (2009). The sources of two components of variance: an example of multifinger cyclic force production tasks at different frequencies. Exp Brain Res, 196(2), 263–277.
Abstract: In a multifinger cyclic force production task, the finger force variance measured across trials can be decomposed into two components, one that affects the combined force output (“bad variance”) and one that does not (“good variance”). Previous studies have found similar time patterns of “bad variance” and force rate leading to an approximately linear relationship between them. Based on this finding and a recently developed model of multifinger force production, we expected the “bad variance” during cyclic force production to increase monotonically with the rate of force change, both within a cycle and across trials at different frequencies. Alternatively, “bad variance” could show a dependence on task frequency, not on actual force derivative values. Healthy subjects were required to produce cyclic force patterns to prescribed targets by pressing on unidimensional force sensors, at a frequency set by a metronome. The task was performed with only the index finger, and with all four fingers. In the task with all four fingers, the “good variance” increased approximately linearly with an increase in the force magnitude. The “bad variance” showed withinacycle modulation similar to that of the force rate. However, an increase in the frequency did not lead to an increase in the “bad variance” that could be expected based on the natural relationships between action frequency and the rate of force change modulation. The results have been interpreted in the framework of an earlier model of multifinger force production where “bad variance” is a result of variance of the timing parameter. The unexpected lack of modulation of the “bad variance” with frequency suggests a drop in variance of the timing parameter with increased frequency. This mechanism may serve to maintain a constant acceptable level of variance under different conditions.

Friedman, J., Latash, M. L., & Zatsiorsky, V. M. (2009). Prehension synergies: a study of digit force adjustments to the continuously varied load force exerted on a partially constrained handheld object. Exp Brain Res, 197(1), 1–13.
Abstract: We examined how the digit forces adjust when a load force acting on a handheld object continuously varies. The subjects were required to hold the handle still while a linearly increasing and then decreasing force was applied to the handle. The handle was constrained, such that it could only move up and down, and rotate about a horizontal axis. In addition, the moment arm of the thumb tangential force was 1.5 times the moment arm of the virtual finger (VF, an imagined finger with the mechanical action equal to that of the four fingers) force. Unlike the situation when there are equal moment arms, the experimental setup forced the subjects to choose between (a) sharing equally the increase in load force between the thumb and VF but generating a moment of tangential force, which had to be compensated by negatively covarying the moment due to normal forces, or (b) sharing unequally the load force increase between the thumb and VF but preventing generation of a moment of tangential forces. We found that different subjects tended to use one of these two strategies. These findings suggest that the selection by the CNS of prehension synergies at the VFthumb level with respect to the moment of force is nonobligatory and reflects individual subject preferences. This unequal sharing of the load by the tangential forces, in contrast to the previously observed equal sharing, suggests that the invariant feature of prehension may be a correlated increase in tangential forces rather than an equal increase.

Friedman, J., & Flash, T. (2009). Trajectory of the index finger during grasping. Exp Brain Res, 196(4), 497–509.
Abstract: The trajectory of the index finger during grasping movements was compared to the trajectories predicted by three optimizationbased models. The three models consisted of minimizing the integral of the weighted squared joint derivatives along the path (inertialike cost), minimizing torque change, and minimizing angular jerk. Of the three models, it was observed that the path of the fingertip and the joint trajectories, were best described by the minimum angular jerk model. This model, which does not take into account the dynamics of the finger, performed equally well when the inertia of the finger was altered by adding a 20 g weight to the medial phalange. Thus, for the finger, it appears that trajectories are planned based primarily on kinematic considerations at a joint level.

Shaklai, S., MimouniBloch, A., Levin, M., & Friedman, J. (2017). Development of finger force coordination in children. Experimental Brain Research, 235(12), 3709–3720.
Abstract: Coordination is often observed as body parts moving together. However, when producing force with multiple fingers, the optimal coordination is not to produce similar forces with each finger, but rather for each finger to correct mistakes of other fingers. In this study, we aim to determine whether and how this skill develops in children aged 412 years. We measured this sort of coordination using the uncontrolled manifold hypothesis (UCM). We recorded finger forces produced by 60 typically developing children aged between 4 and 12 years in a fingerpressing task. The children controlled the height of an object on a screen by the total amount of force they produced on force sensors. We found that the synergy index, a measure of the relationship between “good” and “bad” variance, increased linearly as a function of age. This improvement was achieved by a selective reduction in “bad” variance rather than an increase in “good” variance. We did not observe differences between males and females, and the synergy index was not able to predict outcomes of upper limb behavioral tests after controlling for age. As children develop between the ages of 4 and 12 years, their ability to produce negative covariation between their finger forces improves, likely related to their improved ability to perform dexterous tasks.

Liebermann, D. G., Biess, A., Friedman, J., Gielen, C. C. A. M., & Flash, T. (2006). Intrinsic joint kinematic planning. I: reassessing the Listing's law constraint in the control of threedimensional arm movements. Exp Brain Res, 171(2), 139–154.
Abstract: This study tested the validity of the assumption that intrinsic kinematic constraints, such as Listing's law, can account for the geometric features of threedimensional arm movements. In principle, if the arm joints follow a Listing's constraint, the hand paths may be predicted. Four individuals performed 'extended arm', 'radial', 'frontal plane', and 'random mixed' movements to visual targets to test Listing's law assumption. Threedimensional rotation vectors of the upper arm and forearm were calculated from threedimensional marker data. Data fitting techniques were used to test Donders' and Listing's laws. The coefficient values obtained from fitting rotation vectors to the surfaces described by a secondorder equation were analyzed. The results showed that the coefficients that represent curvature and twist of the surfaces were often not significantly different from zero, particularly not during randomly mixed and extended arm movements. These coefficients for forearm rotations were larger compared to those for the upper arm segment rotations. The mean thickness of the rotation surfaces ranged between approximately 1.7 degrees and 4.7 degrees for the rotation vectors of the upper arm segment and approximately 2.6 degrees and 7.5 degrees for those of the forearm. During frontal plane movements, forearm rotations showed large twist scores while upper arm segment rotations showed large curvatures, although the thickness of the surfaces remained low. The curvatures, but not the thicknesses of the surfaces, were larger for large versus small amplitude radial movements. In conclusion, when examining the surfaces obtained for the different movement types, the rotation vectors may lie within manifolds that are anywhere between curved or twisted manifolds. However, a twodimensional thick surface may roughly represent a global arm constraint. Our findings suggest that Listing's law is implemented for some types of arm movement, such as pointing to targets with the extended arm and during radial reaching movements.
