Vladimir M. Zatsiorsky

Enslaving effects in multi-finger force production

Abstract. When a person produces isometric force with one, two, or three fingers, the other fingers of the hand also produce a certain force. Enslaving is the involuntary force production by fingers not explicitly involved in a force-production task. This study explored the enslaving effects (EE) in multi-finger tasks in which the contributions of the flexor digitorum profundus (FDP), flexor digitorum superficialis (FDS), and intrinsic muscles (INT) were manipulated. A new experimental technique was developed that allows the redistribution of the muscle activity between the FDP, FDS, and INT muscles. In the experiment, ten subjects were instructed to perform maximal voluntary contractions with all possible one-, two-, three-, and four-finger combinations. The point of force application was changed in parallel for the index, middle, ring, and little fingers from the middle of the distal phalanx, to the distal interphalangeal joint, and then to the proximal interphalangeal joint. It was found that: (1) the EE of similar amplitude were present in various experimental conditions that involved different muscle groups for force production; (2) the EE were large on average – the slave fingers could produce forces reaching 67.5% of the maximal forces produced by themselves in a single-finger task; (3) the EE were larger for neighboring fingers; and (4) the EE were non-additive – in most cases, the EE from two or three fingers were smaller than the EE from at least one finger. EE among different muscles suggest a widespread neural interaction among the structures controlling flexor muscles in the hand as the main mechanism of finger enslaving.

Force sharing among fingers as a model of the redundancy problem.

Abstract The aim of this study was to test Bernstein’s idea that motor synergies provide solutions to the motor redundancy problem. Forces produced by individual fingers of one hand were recorded in one-, two-, three-, and four-finger tasks. The subjects (n=10) were asked to produce maximal total force (maximal voluntary contraction, MVC) and to match a ramp total force profile using different combinations of fingers. We found that individual finger forces were smaller in multifinger MVC tasks than in single-finger tasks. The deficit increased with the number of fingers involved. A saturation effect was observed: when several effectors were involved, adding a new effector did not significantly change the total force output. The data confirmed the idea that the central neural drive arriving at the level of synergies has a certain limit, a ceiling, that cannot be exceeded. The central nervous system cannot maximally activate the muscles serving all the fingers at the same time. Secondly, during the course of ramp trials, forces produced by individual fingers were linearly related to each other. Hence, a force sharing pattern was established at the beginning of the trial and did not change during the ramp period. A hypothesis is suggested that force distribution among fingers may be organized so as to minimize unnecessary rotational moment with respect to the functional longitudinal axis of the hand. Finally, in the four-finger trials, variance of the total maximal force output in ten consecutive attempts was smaller than the sum of variances of the maximal individual finger forces. The finding suggests that the control system of the motor tasks studied involves at least two levels, a central neural drive level and a synergy level. At the synergy level, an intercompensation in individual finger force production is observed.

Coordinated force production in multi-finger tasks: finger interaction and neural network modeling

Abstract During maximal voluntary contraction (MVC) with several fingers, the following three phenomena are observed: (1) the total force produced by all the involved fingers is shared among the fingers in a specific manner (sharing); (2) the force produced by a given finger in a multi-finger task is smaller than the force generated by this finger in a single-finger task (force deficit); (3) the fingers that are not required to produce any force by instruction are involuntary activated (enslaving). We studied involuntary force production by individual fingers (enslaving effects, EE) during tasks when (an)other finger(s) of the hand generated maximal voluntary pressing force in isometric conditions. The subjects (n = 10) were instructed to press as hard as possible on the force sensors with one, two, three and four fingers acting in parallel in all possible combinations. The EE were (A) large, the slave fingers always producing a force ranging from 10.9% to 54.7% of the maximal force produced by the finger in the single-finger task; (B) nearly symmetrical; (C) larger for the neighboring fingers; and (D) non-additive. In most cases, the EE from two or three fingers were smaller than the EE from at least one finger (this phenomenon was coined occlusion). The occlusion cannot be explained only by anatomical musculo-tendinous connections. Therefore, neural factors contribute substantially to the EE. A neural network model that accounts for all the three effects has been developed. The model consists of three layers: the input layer that models a central neural drive; the hidden layer modeling transformation of the central drive into an input signal to the muscles serving several fingers simultaneously (multi-digit muscles); and the output layer representing finger force output. The output of the hidden layer is set inversely proportional to the number of fingers involved. In addition, direct connections between the input and output layers represent signals to the hand muscles serving individual fingers (uni-digit muscles). The network was validated using three different training sets. Single digit muscles contributed from 25% to 50% of the total finger force. The master matrix and the enslaving matrix were computed; they characterize the ability of a given finger to enslave other fingers and its ability to be enslaved. Overall, the neural network modeling suggests that no direct correspondence exists between neural command to an individual finger and finger force. To produce a desired finger force, a command sent to an intended finger should be scaled in accordance with the commands sent to the other fingers.

Effects of body lean and visual information on the equilibrium maintenance during stance

Maintenance of equilibrium was tested in conditions when humans assume different leaning postures during upright standing. Subjects (n=11) stood in 13 different body postures specified by visual center of pressure (COP) targets within their base of support (BOS). Different types of visual information were tested: continuous presentation of visual target, no vision after target presentation, and with simultaneous visual feedback of the COP. The following variables were used to describe the equilibrium maintenance: the mean of the COP position, the area of the ellipse covering the COP sway, and the resultant median frequency of the power spectral density of the COP displacement. The variability of the COP displacement, quantified by the COP area variable, increased when subjects occupied leaning postures, irrespective of the kind of visual information provided. This variability also increased when vision was removed in relation to when vision was present. Without vision, drifts in the COP data were observed which were larger for COP targets farther away from the neutral position. When COP feedback was given in addition to the visual target, the postural control system did not control stance better than in the condition with only visual information. These results indicate that the visual information is used by the postural control system at both short and long time scales.

Tendon action of two-joint muscles: Transfer of mechanical energy between joints during jumping, landing, and running

The amount of mechanical energy transferred by two-joint muscles between leg joints during squat vertical jumps, during landings after jumping down from a height of 0.5 m, and during jogging were evaluated experimentally. The experiments were conducted on five healthy subjects (body height, 1.68-1.86 m; and mass, 64-82 kg). The coordinates of the markers on the body and the ground reactions were recorded by optical methods and a force platform, respectively. By solving the inverse problem of dynamics for the two-dimensional, four-link model of a leg with eight muscles, the power developed by the joint (net muscular) moments and the power developed by each muscle were determined. The energy transferred by two-joint muscles from and to each joint was determined as a result of the time integration of the difference between the power developed at the joint by the joint moment, and the total power of the muscles serving a given joint. It was shown that during a squat vertical jump and in the push-off phase during running, the two-joint muscles (rectus femoris and gastrocnemius) transfer mechanical energy from the proximal joints of the leg to the distal ones. At landing and in the shock-absorbing phase during running, the two-joint muscles transfer energy from the distal to proximal joints. The maximum amount of energy transferred from the proximal joints to distal ones was equal to 178.6 +/- 45.7 J (97.1 +/- 27.2% of the work done by the joint moment at the hip joint) at the squat vertical jump. The maximum amount of energy transferred from the distal to proximal joints was equal to 18.6 +/- 4.2 J (38.5 +/- 36.4% of work done by the joint moment at the ankle joint) at landing. The conclusion was made that the one-joint muscles of the proximal links compensate for the deficiency in work production of the distal one-joint muscles by the distribution of mechanical energy between joints through the two-joint muscles. During the push-off phase, the muscles of the proximal links help to extend the distal joints by transferring to them a part of the generated mechanical energy. During the shock-absorbing phase, the muscles of the proximal links help the distal muscles to dissipate the mechanical energy of the body.

On the fractal properties of natural human standing.

We analyzed the temporal evolution of the displacement of the center of pressure (COP) during prolonged unconstrained standing (30 min) in non-impaired human subjects. The COP represents the collective outcome of the postural control system and the force of gravity and is the main parameter used in studies on postural control. Our analysis showed that the COP displacement during human standing displays fractal properties that were quantified by the Hurst exponent obtained from the classical rescaled adjusted range analysis. The average fractal or Hurst exponent (H) was 0.35+/-0.06. The presence of long-range correlations from a few seconds to several minutes due to the fractal characteristics of the postural control system has several important implications for the analysis of human balance.

Muscle synergies during shifts of the center of pressure by standing persons: identification of muscle modes

Abstract.When a standing person performs a movement such that the center of gravity shifts, the activity of postural muscles adjusts to keep the balance. We assume that such adjustments are controlled using a small set of central variables, while each variable induces changes in the activity of a subgroup of postural muscles. The purpose of this study has been to identify such muscle groups (muscle modes or M-modes) and compare them across tasks and subjects. Four tasks required the subjects to release a load from extended arms leading to a center of pressure (COP) shift prior to the load release. The fifth task required an explicit COP shift by voluntary sway. Electromyographic activity of 11 postural muscles on one side of the body was integrated over a 100-ms interval corresponding to the early stage of the COP shift, and this integrated EMG activity was subjected to a principal component (PC) analysis across multiple repetitions of each task. Three PCs were identified and associated with a “push-back M-mode,” a “push-forward M-mode,” and a “mixed M-mode.” Cluster analysis of the PC vectors across tasks and across subjects confirmed the existence of distinctive push-forward and push-back muscle groups. PC vectors were also compared across tasks and across subjects using cosines as a measure of colinearity between pairs of vectors. In general, M-modes were similar across both tasks and subjects. We conclude that shifts of the COP, whether implicit or explicit, are controlled using a small set of central variables associated with changes in the activity of robust subsets of postural muscles. These results can be used for future analysis of muscle synergies associated with postural tasks.

A mode hypothesis for finger interaction during multi-finger force-production tasks

Abstract. Finger forces are known to change involuntarily during multi-finger force-production tasks, even when a fingers involvement in a task is not consciously changed (the enslaving effect). Furthermore, during maximal force-production (MVC) tests, the force produced by a given finger in a multi-finger task is smaller than the force generated by this finger in its single-finger MVC test (the force-deficit effect). A set of hypothetical control variables – modes – is introduced. Modes can be estimated based on individual finger forces during single-finger MVC tests. We show that a simple formal model based on modes with only one free parameter accounts for finger forces during a variety of multi-finger MVC tests. The free parameter accounts for the force-deficit effect, and its value depends only on the number of explicitly involved fingers. This approach offers a simple framework for the analysis of finger interaction during multi-finger actions.

Contribution of the extrinsic and intrinsic hand muscles to the moments in finger joints

OBJECTIVE The purpose of this current work is to develop a method of estimating force produced by the extrinsic and intrinsic hand muscles, and to estimate the contribution of these muscles to the finger joint moments. DESIGN Experimental methods and a biomechanical model were developed for the estimation of (a) moments produced at finger joints, and (b) contribution of the intrinsic and extrinsic muscles to the moments, (c) forces of the extrinsic and intrinsic muscles within individual fingers. BACKGROUND Because of the differential insertions of the extrinsic flexors, it is possible to isolate their mechanical effect at finger joints. METHODS During the experiment, the location of force application was varied in parallel along individual fingers. The points of force application were on the distal phalanx, at the distal interphalangeal joint, or at the proximal interphalangeal joint. RESULTS When the point of force application was varied in the proximal direction from the distal phalanx to the proximal interphalangeal joint the moment at a given joint decreased. The intrinsic and extrinsic muscle forces were dependent on the experimental conditions. The extrinsic muscles were the major contributors in counterbalancing finger joint moments when the point of force application was distal beyond the proximal interphalangeal joint. CONCLUSION This current work provides both an experimental protocol and a biomechanical model that allows estimation of the contribution of the intrinsic and extrinsic muscles to finger joint moments. RELEVANCE This study suggests ways of identifying the source of functional deficiency in the hand.

A central back-coupling hypothesis on the organization of motor synergies: a physical metaphor and a neural model

Abstract.We offer a hypothesis on the organization of multi-effector motor synergies and illustrate it with the task of force production with a set of fingers. A physical metaphor, a leaking bucket, is analyzed to demonstrate that an inanimate structure can show apparent error compensation among its elements. A neural model is developed using tunable back-coupling loops as means of assuring error compensation in a task-specific way. The model demonstrates non-trivial features of multi-finger interaction such as delayed emergence of force stabilizing synergies and simultaneous stabilization of the total force and total moment produced by the fingers. The hypothesis suggests that neurophysiological structures involving short-latency feedback may play a central role in the formation of motor synergies.