Jerk (time derivative of acceleration) of the endpoint of a multi-joint kinematic chain can be represented as the sum of terms related to jerks, accelerations, and velocities in individual joints. We investigated the relative contribution of these terms during simulations of planar movement of a 3-segment kinematic chain and also during unconstrained movements at different velocities, over different amplitudes, and with different intentionally changed curvature. Our results demonstrate that the term related to individual joint jerks dominates in the total endpoint jerk. This domination was particularly strong during voluntary movements and was not as striking during the simulations based on 5th-order polynomial functions for individual joint trajectories. Thus, the minimum-jerk criterion for multi-joint movements can be well approximated by minimization of the jerk-related terms for individual joints. The decomposition of endpoint jerk into its terms shows potential limitations of the commonly used 5th-order polynomial modeling for describing voluntary multi-joint movements.
Jozsef Laczko, Slobodan Jaric, Jozsef Tihanyi, Vladimir M. Zatsiorsky and Mark L. Latash
Simon R. Goodman, Mark L. Latash, Sheng Li and Vladimir M. Zatsiorsky
This study involved an optimization, numerical analysis of a network for two-hand multi-finger force production, analogous in its structure to the double-representation mirror image (DoReMi) network suggested earlier based on neurophysiological data on cortical finger representations. The network accounts for phenomena of enslaving (unintended finger force production), force deficit (smaller force produced by a finger in multi-finger tasks as compared to its single-finger task), and bilateral deficit (smaller forces produced in two-hand tasks as compared to one-hand tasks). Matrices of connection weights were computed, and the results of optimization were compared to the experimental data on finger forces during one- and two-hand maximal force production (MVC) tasks. The network was able to reproduce the experimental data in two-hand experiments with high accuracy (average error was 1.2 N); it was also able to reproduce findings in one-hand multi-finger MVC tasks, which were not used during the optimization procedure, although with a somewhat higher error (2.8 N). Our analysis supports the feasibility of the DoReMi network. It suggests that within-a-hand force deficit and bilateral force deficit are phenomena of different origins whose effects add up. Is also supports a hypothesis that force deficit and enslaving have different neural origins.
Halla B. Olafsdottir, Sun Wook Kim, Vladimir M. Zatsiorsky and Mark L. Latash
We tested the ability of healthy elderly persons to use anticipatory synergy adjustments (ASAs) prior to a self-triggered perturbation of one of the fingers during a multifinger force production task. An index of a force-stabilizing synergy was computed reflecting covariation of commands to fingers. The subjects produced constant force by pressing with the four fingers of the dominant hand on force sensors against constant upwardly directed forces. The middle finger could be unloaded either by the subject pressing the trigger or unexpectedly by the experimenter. In the former condition, the synergy index showed a drop (interpreted as ASA) prior to the time of unloading. This drop started later and was smaller in magnitude as compared with ASAs reported in an earlier study of younger subjects. At the new steady state, a new sharing pattern of the force was reached. We conclude that aging is associated with a preserved ability to explore the flexibility of the mechanically redundant multifinger system but a decreased ability to use feed-forward adjustments to self-triggered perturbations. These changes may contribute to the documented drop in manual dexterity with age.
Wei Zhang, Halla B. Olafsdottir, Vladimir M. Zatsiorsky and Mark L. Latash
We studied the mechanical variables (the grip force and the total moment of force) and multidigit synergies at two levels (the virtual finger-thumb level, VF-TH, and the individual finger level, IMRL) of a hypothetical control hierarchy during accurate rotation of a hand-held instrumented handle. Synergies were defined as covaried changes in elemental variables (forces and moments of force) that stabilize the output at a particular level. Indices of multidigit synergies showed higher values at the hierarchically higher level (VF-TH) for both normal and tangential forces. The moment of force was stabilized at both hierarchical levels during the steady-state phases but not during the movement. The results support the principles of superposition and of mechanical advantage. They also support an earlier hypothesis on an inherent tradeoff between synergies at the two hierarchical levels, although the controller showed more subtle and versatile synergic control than the one hypothesized earlier.
Xun Niu, Alexander V. Terekhov, Mark L. Latash and Vladimir M. Zatsiorsky
The goal of the research is to reconstruct the unknown cost (objective) function(s) presumably used by the neural controller for sharing the total force among individual fingers in multifinger prehension. The cost function was determined from experimental data by applying the recently developed Analytical Inverse Optimization (ANIO) method (Terekhov et al. 2010). The core of the ANIO method is the Theorem of Uniqueness that specifies conditions for unique (with some restrictions) estimation of the objective functions. In the experiment, subjects (n = 8) grasped an instrumented handle and maintained it at rest in the air with various external torques, loads, and target grasping forces applied to the object. The experimental data recorded from 80 trials showed a tendency to lie on a 2-dimensional hyperplane in the 4-dimensional finger-force space. Because the constraints in each trial were different, such a propensity is a manifestation of a neural mechanism (not the task mechanics). In agreement with the Lagrange principle for the inverse optimization, the plane of experimental observations was close to the plane resulting from the direct optimization. The latter plane was determined using the ANIO method. The unknown cost function was reconstructed successfully for each performer, as well as for the group data. The cost functions were found to be quadratic with nonzero linear terms. The cost functions obtained with the ANIO method yielded more accurate results than other optimization methods. The ANIO method has an evident potential for addressing the problem of optimization in motor control.
Mark L. Latash, Jae Kun Shim, Fan Gao and Vladimir M. Zatsiorsky
We review a series of studies that show stabilization of the moment of a couple produced by a set of digits in many maximal and submaximal accurate force production tasks that have no requirements for the moment. In particular, an unusual and novel multi-digit force production task shows stabilization of the total moment while the total force requires extensive practice to be stabilized. Similar results were obtained in persons with Down syndrome during easier tasks. During prehension, changes in digit forces and coordinates of their points of application suggest the presence of two multi-digit synergies whose purpose is to assure a certain grip force and a certain total moment, respectively. Elderly persons show impaired production of both maximal and submaximal moments that goes beyond their documented loss of muscle force. We conclude that moment production (keeping rotational equilibrium) is a central constraint in a variety of multi-digit tasks that has received little attention. Analysis of digit interaction for moment production during handwriting could signify a major step towards understanding the control of this action.
Luis Mochizuki, Marcos Duarte, Alberto Carlos Amadio, Vladimir M. Zatsiorsky and Mark L. Latash
We investigated changes in postural sway and its fractions associated with manipulations of the dimensions of the support area. Nine healthy adults stood as quietly as possible, with their eyes open, on a force plate as well as on 5 boards with reduced support area. The center of pressure (COP) trajectory was computed and decomposed into rambling (Rm) and trembling (Tr) trajectories. Sway components were quantified using RMS (root mean square) value, average velocity, and sway area. During standing on the force plate, the RMS was larger for the anterior-posterior (AP) sway components than for the mediolateral (ML) components. During standing on boards with reduced support area, sway increased in both directions. The increase was more pronounced when standing on boards with a smaller support area. Changes in the larger dimension of the support area also affected sway, but not as much as changes in the smaller dimension. ML instability had larger effects on indices of sway compared to AP instability. The average velocity of Rm was larger while the average velocity of Tr was smaller in the AP direction vs. the ML direction. The findings can be interpreted within the hypothesis of an active search function of postural sway. During standing on boards with reduced support area, increased sway may by itself lead to loss of balance. The findings also corroborate the hypothesis of Duarte and Zatsiorsky that Rm and Tr reveal different postural control mechanisms.