Force and torque production in static multifinger prehension: biomechanics and control. II. Control

 The coordination of digits during combined force/torque production tasks was further studied using the data presented in the companion paper [Zatsiorsky et al. Biol Cybern this issue, Part I]. Optimization was performed using as criteria the cubic norms of (a) finger forces, (b) finger forces normalized with respect to the maximal forces measured in single-finger tasks, (c) finger forces normalized with respect to the maximal forces measured in a four-finger task, and (d) finger forces normalized with respect to the maximal moments that can be generated by the fingers. All four criteria failed to predict antagonist finger moments when these moments were not imposed by the task mechanics. Reconstruction of neural commands: The vector of neural commands c was reconstructed from the equation c=W ⁻¹ F, where W is the finger interconnection weight matrix and F is the vector of finger forces. The neural commands ranged from zero (no voluntary force production) to one (maximal voluntary contraction). For fingers producing moments counteracting the external torque (`agonist' fingers), the intensity of the neural commands was well correlated with the relative finger forces normalized to the maximal forces in a four-finger task. When fingers produced moments in the direction of the external torque (`antagonist' fingers), the relative finger forces were always larger than those expected from the intensity of the corresponding neural commands. The individual finger forces were decomposed into forces due to `direct' commands and forces induced by enslaving effects. Optimization of the neural commands resulted in the best correspondence between actual and predicted finger forces. The antagonist moments are, at least in part, due to enslaving effects: strong commands to agonist fingers also activated antagonist fingers. Received: 8 August 2001 / Accepted in revised form: 7 February 2002     

Force and torque production in static multifinger prehension: biomechanics and control. I. Biomechanics

 We studied the coordinated action of fingers during static tasks involving exertion of force and torque on a handheld object. Subjects were asked to keep a handle with an attachment that allowed for independent change of the suspended load (0.5–2.0 kg) and external torque (0.375–1.5 N m) in a vertical position while applying minimal effort. Normal and shear forces were measured from the thumb; normal forces only were measured from the four fingers. Experimental results: (1) the thumb shear force increased during supination efforts and decreased during pronation efforts; (2) the total moment of the normal finger forces only counterbalanced approximately 50% of the external torque, hence shear forces accounted for approximately one-half of the total torque exerted on the object; (3) the total normal force increased with external torque, and the total force magnitude did not depend on the torque direction; (4) the forces of the `peripheral' (index and little) fingers depended mainly on the torque while the forces exerted by the `central' (middle and ring) fingers depended both on the load and torque; (5) there was a monotonic relationship between the mechanical advantage of a finger (i.e., its moment arm during torque production) and the force produced by that finger; and (6) antagonist finger moments acting opposite to the intended direction of the total moment were always observed – at low torques the antagonist moments were as high as 40–60% of the agonist moments. Modeling: A three-zone model of coordinated finger action is suggested. In the first zone of load/torque combinations, activation of antagonist fingers (i.e., fingers that generate antagonist moments) is necessary to prevent slipping. In the second zone, the activity of agonist fingers is sufficient for preventing slips. In the third zone, the performer has freedom to choose between either activating the antagonist fingers or redistributing activities amongst the agonist fingers. The findings of this study provide the foundation for neural network and optimization modeling described in the companion paper [Zatsiorsky et al. (2002) Biol Cybern DOI 10.1007/s00422-002-0320-7]. Received: 8 August 2001 / Accepted in revised form: 7 February 2002     

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

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. Received: 17 October 1997 / Accepted in revised form: 12 May 1998     

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

 Finger forces are known to change involuntarily during multi-finger force-production tasks, even when a finger's 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. Received: 7 December 2001 / Accepted in revised form: 17 April 2002 Correspondence to: F. Danion (e-mail: danion@laps.univ-mrs.fr, Tel.: +33-491-172265, Fax: +33-491-172252)     

Indices of nonlinearity in finger force interaction

Experiments with force production by subsets of fingers within the human hand have shown that finger interaction may be significantly nonlinear. In particular, this nonlinearity is reflected in the phenomenon of force deficit, a drop of the peak force of a finger when several fingers act simultaneously. We describe nonlinear effects in force relations within finger pairs, triplets, etc. Finger forces are represented as the sums of components resulting from force interactions within all subsets of the explicitly involved (master) fingers. The values of these components computed at extreme values of control signals, zero and unity, are taken as indices of such elementary force interactions. Indices of the first order reflect purposeful force production by a single master finger and its effects on forces produced by other fingers (enslaving). Indices of the second order reflect additional influences from pairs of simultaneously recruited master fingers, etc. Force interaction indices were computed based on finger forces measured in earlier experiments. Signs of indices alternated with their order, being positive for the indices of the first order (enslaving), negative for the indices of the second order (force deficit), positive for the indices of the third order, and mostly negative for the indices of the fourth order. Indices of the third and fourth orders reflect phenomena of force interaction not reported earlier. The study emphasizes the importance of nonlinear interactions among finger forces and introduces a set of independent indices that can be used to quantify such interactions in different subpopulations and their possible changes with practice and/or rehabilitation of the hand function.     

Effects of age and gender on finger coordination in MVC and submaximal force-matching tasks.

The objective of the study is to examine the effects of age and gender on finger coordination. Twelve young (24 +/- 8 yr; 6 men and 6 women) and 12 elderly (75 +/- 5 yr; 6 men and 6 women) subjects performed single-finger maximal contraction [maximal voluntary contraction (MVC)], four-finger MVC, and four-finger ramp force production tasks by pressing on individual force transducers. A drop in the force of individual fingers during four-finger MVC tasks compared with single-finger MVC tasks (force deficit) was larger, whereas unintended force production by other fingers during single-finger MVC tasks (enslaving) was smaller, in elderly than in young subjects and in women than in men. Force deficit was smaller and enslaving was larger in subjects with higher peak force. During the ramp task, the difference between the variance of total force and the sum of variances of individual forces showed a logarithmic relation to the level of total force, across all subject groups. These findings suggest that indexes of finger coordination scale with force-generating capabilities across gender and age groups.     

Age effects on force produced by intrinsic and extrinsic hand muscles and finger interaction during MVC tasks.

Finger-pressing forces are produced by activation of the intrinsic hand muscles, which are finger specific, and the extrinsic muscles that connect to multiple fingers. We tested a hypothesis of greater weakening of intrinsic hand muscles with age and quantified associated indexes of finger interaction such as enslaving (force production by unintended fingers) and force deficit (loss of finger force in multifinger tasks compared with single-finger tasks). Twelve young (23-35 yr old) and 12 elderly (70-95 yr old) men and women performed single-finger and four-finger maximal pressing tasks, in which force was applied at the proximal phalanges (PP, the intrinsic muscles are major focal force generators) and at the distal phalanges (DP, the extrinsic muscles are focal force generators). The decline in the peak force with age was greater at PP (30%) than at DP (19%). Larger indexes of finger interaction were observed at PP (enslaving = 17.2 +/- 9.4%, force deficit = 36.1 +/- 11.1%) than at DP (enslaving = 14.9 +/- 8.8%, force deficit = 27.7 +/- 10.8%) across ages and genders. We conclude that intrinsic hand muscles show disproportionate weakening with age. The greater indexes of finger interaction in PP tests with greater involvement of intrinsic hand muscles suggest that the finger interactions are predominantly of a central origin across ages and genders.     

Information transmission in non-visual fingertip matching along a horizontal track in the median plane

Non-visually triggered arm movements over a horizontal table at shoulder height were analysed by an Information Theory approach according to a method suggested by Sakitt et al. (1983) and Sakitt (1980). The movement track was along the subject's median line and was indicated by a vertical metal ridge fixed to the table. The observer passively moved the subject's left index finger along the left side of the ridge to the target position. The blindfolded subject then had to move his right index finger along the right side of the ridge to match the left finger position. Direct contact between the two fingers was prevented by the ridge. We compared our results, which involve the transmission of information through the arm and shoulder joints of both arms, whith those of Sakitt et al. which involved just one elbow joint. We supplemented our experimental results with simulations and show that the value for the transmitted information, obtained using the method of analysis suggested by Sakitt et al., is very dependent upon the number of trials, and number and spacing of the targets. Sakitt et al. suggest that the Information Theory approach permits easy comparison between different tasks and different observers. Our results suggest that comparisons should be made with caution.     

Coordination of contact forces during multifinger static prehension

This study investigated the effects of modifying contact finger forces in one direction-normal or tangential-on the entire set of the contact forces, while statically holding an object. Subjects grasped a handle instrumented with finger force-moment sensors, maintained it at rest in the air, and then slowly: (1) increased the grasping force, (2) tried to spread fingers apart, and (3) tried to squeeze fingers together. Analysis was mostly performed at the virtual finger (VF) level (the VF is an imaginable finger that generates the same force and moment as the four fingers combined). For all three tasks there were statistically significant changes in the VF normal and tangential forces. For finger spreading/squeezing the tangential force neutral point was located between the index and middle fingers. We conclude that the internal forces are regulated as a whole, including adjustments in both normal and tangential force, instead of only a subset of forces (normal or tangential). The effects of such factors as EFFORT and TORQUE were additive; their interaction was not statistically significant, thus supporting the principle of superposition in human prehension.     

Age-related changes in finger coordination in static prehension tasks.

We studied age-related changes in the performance of maximal and accurate submaximal force and moment production tasks. Elderly and young subjects pressed on six dimensional force sensors affixed to a handle with a T-shaped attachment. The weight of the whole system was counterbalanced with another load. During tasks that required the production of maximal force or maximal moment by all of the digits, young subjects were stronger than elderly. A greater age-related deficit was seen in the maximal moment production tests. During maximal force production tests, elderly subjects showed larger relative involvement of the index and middle fingers; they moved the point of thumb force application upward (toward the index and middle fingers), whereas the young subjects rolled the thumb downward. During accurate force/moment production trials, elderly persons were less accurate in the production of both total moment and total force. They produced higher antagonistic moments, i.e., moment by fingers that acted against the required direction of the total moment. Both young and elderly subjects showed negative covariation of finger forces across repetitions of a ramp force production task. In accurate moment production tasks, both groups showed negative covariation of two components of the total moment: those produced by the normal forces and those produced by the tangential forces. However, elderly persons showed lower values of the indexes of both finger force covariation and moment covariation. We conclude that age is associated with an impaired ability to produce both high moments and accurate time profiles of moments. This impairment goes beyond the well-documented deficits in finger and hand force production by elderly persons. It involves worse coordination of individual digit forces and of components of the total moment. Some atypical characteristics of finger forces may be viewed as adaptive to the increased variability in the force production with age.     

Tactile feedback plays a critical role in maximum finger force production

This study investigates the role of cutaneous feedback on maximum voluntary force (MVF), finger force deficit (FD) and finger independence (FI). FD was calculated as the difference between the sum of maximal individual finger forces during single-finger pressing tasks and the maximal force produced by those fingers during an all-finger pressing task. FI was calculated as the average non-task finger forces normalized by the task-finger forces and subtracted from 100 percent. Twenty young healthy right-handed males participated in the study. Cutaneous feedback was removed by administering ring block digital anesthesia on the 2nd, 3rd, 4th and 5th digits of the right hands. Subjects were asked to press force sensors with maximal effort using individual digits as well as all four digits together, with and without cutaneous feedback. Results from the study showed a 25% decrease in MVF for the individual fingers as well as all the four fingers pressing together after the removal of cutaneous feedback. Additionally, more than 100% increase in FD after the removal of cutaneous feedback was observed in the middle and ring fingers. No changes in FI values were observed between the two conditions. Results of this study suggest that the central nervous system utilizes cutaneous feedback and the feedback mechanism plays a critical role in maximal voluntary force production by the hand digits.     

Finger force vectors in multi-finger prehension

In a majority of studies on grasp, only normal forces were measured and only when a zero torque was exerted on a hand-held object. This study concerns finger force vectors during the torque production tasks. Subjects (n=8) stabilized a handle with an attachment that allowed for change of external torque from -1.5 to 1.5 Nm. Forces and moments exerted by the digit tips on the object were recorded. At the large (>-0.375 Nm) supination torques the index/middle and ring/little pairs of fingers generated oppositely directed tangential forces. The index and middle finger produced forces in a downward direction and therefore did not support the load. At a zero torque and pronation torques, the middle, ring and little fingers produced forces along nearly the same direction. The vector of the index finger force was always directed differently from the vectors of other finger forces, the angles ranged from 19 degrees 30' to 47 degrees 40'. The points of force application were systematically displaced with the torque, with the exception of the little finger. Tangential finger forces contributed substantially to the total torque exerted on the hand-held object.     

One Digit Interruption: The Altered Force Patterns during Functionally Cylindrical Grasping Tasks in Patients with Trigger Digits

Most trigger digit (TD) patients complain that they have problems using their hand in daily or occupational tasks due to single or multiple digits being affected. Unfortunately, clinicians do not know much about how this disease affects the subtle force coordination among digits during manipulation. Thus, this study examined the differences in force patterns during cylindrical grasp between TD and healthy subjects. Forty-two TD patients with single digit involvement were included and sorted into four groups based on the involved digits, including thumb, index, middle and ring fingers. Twelve healthy subjects volunteered as healthy controls. Two testing tasks, holding and drinking, were performed by natural grasping with minimal forces. The relations between the force of the thumb and each finger were examined by Pearson correlation coefficients. The force amount and contribution of each digit were compared between healthy controls and each TD group by the independent t test. The results showed all TD groups demonstrated altered correlation patterns of the thumb relative to each finger. Larger forces and higher contributions of the index finger were found during holding by patients with index finger involved, and also during drinking by patients with affected thumb and with affected middle finger. Although no triggering symptom occurred during grasping, the patients showed altered force patterns which may be related to the role of the affected digit in natural grasping function. In conclusion, even if only one digit was affected, the subtle force coordination of all the digits was altered during simple tasks among the TD patients. This study provides the information for the future studies to further comprehend the possible injuries secondary to the altered finger coordination and also to adopt suitable treatment strategies.     

Two coupled oscillators as a model for the coordinated finger tapping by both hands

Recently, it was found that rhythmic movements (e.g. locomotion, swimmeret beating) are controlled by mutually coupled endogeneous neural oscillators (Kennedy and Davis, 1977; Pearson and Iles, 1973; Stein, 1974; Shik and Orlovsky, 1976; Grillner and Zangger, 1979). Meanwhile, it has been found out that the phase resetting experiment is useful to investigate the interaction of neural oscillators (Perkel et al., 1963; Stein, 1974). In the preceding paper (Yamanishi et al., 1979), we studied the functional interaction between the neural oscillator which is assumed to control finger tapping and the neural networks which control some tasks. The tasks were imposed on the subject as the perturbation of the phase resetting experiment. In this paper, we investigate the control mechanism of the coordinated finger tapping by both hands. First, the subjects were instructed to coordinate the finger tapping by both hands so as to keep the phase difference between two hands constant. The performance was evaluated by a systematic error and a standard deviation of phase differences. Second, we propose two coupled neural oscillators as a model for the coordinated finger tapping. Dynamical behavior of the model system is analyzed by using phase transition curves which were measured on one hand finger tapping in the previous experiment (Yamanishi et al., 1979). Prediction by the model is in good agreement with the results of the experiments. Therefore, it is suggested that the neural mechanism which controls the coordinated finger tapping may be composed of a coupled system of two neural oscillators each of which controls the right and the left finger tapping respectively.     

Neural Coding of Finger and Wrist Movements

Previous work (Schieber and Hibbard, 1993) has shown that single motor cortical neurons do not discharge specifically for a particular flexion-extension finger movement but instead are active with movements of different fingers. In addition, neuronal populations active with movements of different fingers overlap extensively in their spatial locations in the motor cortex. These data suggested that control of any finger movement utilizes a distributed population of neurons. In this study we applied the neuronal population vector analysis (Georgopoulos et al., 1983) to these same data to determine (1) whether single cells are tuned in an abstract, three-dimensional (3D) instructed finger and wrist movement space with hand-like geometry and (2) whether the neuronal population encodes specific finger movements. We found that the activity of 132/176 (75%) motor cortical neurons related to finger movements was indeed tuned in this space. Moreover, the population vector computed in this space predicted well the instructed finger movement. Thus, although single neurons may be related to several disparate finger movements, and neurons related to different finger movements are intermingled throughout the hand area of the motor cortex, the neuronal population activity does specify particular finger movements.     

Removal of Heavy Metals from Sewage Sludge Used as Soil Fertilizer

This work has examined sewage sludge of the following heavy metal concentrations (mg/kg): Cd-3.43; Co-5.25; Cu-131; Fe-51300; Mn-177; Ni-37.5; Pb-104; Zn-3300. Metals speciation by sequential extraction according to Tessier et al. (1979), and Rudd et al. (1988), and a procedure recommended by European Community Bureau of Reference (BCR) (Ure et al., 1993; Quevauiller et al., 1996; Davidson et al., 1999), as well as analysis of chemical forms of metals, have been carried out. It has been found that only Zn concentration is higher than the value permissible for agricultural sewage sludge application (2500 mg/kg). The results obtained by Tessier et al. (1979) Tessier, A., Campbell, P. C. and Bisson, M. 1979. Sequential extraction procedure for the speciation of particulate trace metals.. Anal. Chem., 51: 844–851. [Crossref], [Web of Science ®] [Google Scholar], and BCR procedures (Ure et al., 1993; Quevauiller et al., 1996; Davidson et al., 1999) appeared to be consistent. A comparison of the sequential analysis and the analysis of chemical forms of metals indicates that the sum of metal concentrations for the exchangeable, carbonate and bound to Fe/Mn oxyhydroxides forms (found by Tessier et al., 1979, and BCR analyses (Ure et al., 1993; Quevauiller et al., 1996; Davidson, et al., 1999)) corresponds to the sum of sulfate, oxide, metallic and siliceous forms. The concentrations of the forms bound to organic matter or sulfides correspond to the sulfide form while the residue corresponds to the ferrate form. Preparative extraction of metals from the sewage sludge using sodium salt of ethylenediaminetetraacetic acid (EDTA-Na), sodium pyrophosphate (V) and ammonia water has also been investigated. As far as the examined leaching agents are concerned, EDTA-Na appeared to be the best. Single leaching with this agent results in the following metal concentrations remaining in the sludge (mg/kg): Cd-1.1; Co-2.1; Cu-105; Fe-17700; Mn-28.3; Ni-12.8; Pb-44; Zn-1200. They meet the requirements of Polish regulations concerning the use of sewage sludge as a soil fertilizer.