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     

Prehension synergy: use of mechanical advantage during multifinger torque production on mechanically fixed and free objects

The aim of this study was to test the mechanical advantage (MA) hypothesis in multifinger torque production tasks in humans: fingers with longer moment arms produce greater force magnitudes during torque production tasks. There were eight experimental conditions: two prehension types determined by different mechanical constraints (i.e., fixed- and free-object prehension) with two torque directions (supination and pronation) and two torque magnitudes (0.24 and 0.48 N·m). The subjects were asked to produce prescribed torques during the fixed-object prehension or to maintain constant position of the free hand-held object against external torques. The index of MA was calculated for agonist and antagonist fingers, which produce torques in the same and opposite directions to the target torques, respectively. Within agonist fingers, the fingers with longer moment arms produced greater grasping forces while within antagonist fingers, the fingers with shorter moment arms produced greater forces. The MA index was greater in the fixed-object condition as compared with the free-object condition. The MA index was greater in the pronation condition than in the supination condition. This study supports the idea that the CNS utilizes the MA of agonist fingers, but not of antagonist fingers, during torque production in both fixed- and free-object conditions.     

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.     

Acute effects of static stretching on maximal eccentric torque production in women

The purpose of this study was to examine the acute effects of static stretching on peak torque (PT) and the joint angle at PT during maximal, voluntary, eccentric isokinetic muscle actions of the leg extensors at 60 and 180 degrees x s(-1) for the stretched and unstretched limbs in women. Thirteen women (mean age +/- SD = 20.8 +/- 0.8 yr; weight +/- SD = 63.3 +/- 9.5 kg; height +/- SD = 165.9 +/- 7.9 cm) volunteered to perform separate maximal, voluntary, eccentric isokinetic muscle actions of the leg extensors with the dominant and nondominant limbs on a Cybex 6000 dynamometer at 60 and 180 degrees x s(-1). PT (Nm) and the joint angle at PT (degrees) were recorded by the dynamometer software. Following the initial isokinetic assessments, the dominant leg extensors were stretched (mean stretching time +/- SD = 21.2 +/- 2.0 minutes) using 1 unassisted and 3 assisted static stretching exercises. After the stretching (4.3 +/- 1.4 minutes), the isokinetic assessments were repeated. The statistical analyses indicated no changes (p > 0.05) from pre- to poststretching for PT or the joint angle at PT. These results indicated that static stretching did not affect PT or the joint angle at PT of the leg extensors during maximal, voluntary, eccentric isokinetic muscle actions at 60 and 180 degrees x s(-1) in the stretched or unstretched limbs in women. In conjunction with previous studies, these findings suggested that static stretching may affect torque production during concentric, but not eccentric, muscle actions.     

Age-related changes in multifinger synergies in accurate moment of force production tasks.

The purpose of this investigation was to document and quantify age-related differences in the coordination of fingers during a task that required production of an accurate time profile of the total moment of force by the four fingers of a hand. We hypothesized that elderly subjects would show a decreased ability to stabilize a time profile of the total moment of force, leading to larger indexes of moment variability compared with young subjects. The subjects followed a trapezoidal template on a computer screen by producing a time profile of the total moment of force while pressing down on force sensors with the four fingers of the right (dominant) hand. To quantify synergies, we used the framework of the uncontrolled manifold hypothesis. The elderly subjects produced larger total force, larger variance of both total force and total moment of force, and larger involvement of fingers that produced moment of force against the required moment direction (antagonist moment). This was particularly prominent during supination efforts. Young subjects showed covariation of commands to fingers across trials that stabilized the moment of total force (moment-stabilizing synergy), while elderly subjects failed to do so. Both subject groups showed similar indexes of covariation of commands to the fingers that stabilized the time profile of the total force. The lack of moment-stabilizing synergies may be causally related to the documented impairment of hand function with age.     

Balancing on a narrow ridge: biomechanics and control.

The balance of standing humans is usually explained by the inverted pendulum model. The subject invokes a horizontal ground-reaction force in this model and controls it by changing the location of the centre of pressure under the foot or feet. In experiments I showed that humans are able to stand on a ridge of only a few millimetres wide on one foot for a few minutes. In the present paper I investigate whether the inverted pendulum model is able to explain this achievement. I found that the centre of mass of the subjects sways beyond the surface of support, rendering the inverted pendulum model inadequate. Using inverse simulations of the dynamics of the human body, I found that hip-joint moments of the stance leg are used to vary the horizontal component of the ground-reaction force. This force brings the centre of mass back over the surface of support. The subjects generate moments of force at the hip-joint of the swing leg, at the shoulder-joints and at the neck. These moments work in conjunction with a hip strategy of the stance leg to limit the angular acceleration of the head-arms-trunk complex. The synchrony of the variation in moments suggests that subjects use a motor programme rather than long latency reflexes.     

Modeling and static optimization of the ethanol production in a cascade reactor. II. Static optimization

In Part I(1) of this research a complex model was obtained for describing the ethanol fermentation in a cascade reactor. This complexity is due to both the nonlinearity and the large scale representation. Based on techniques of partitioning and relaxation, a decentralized successive approximation method is developed for static optimization. The influence of the way of fermentation during continuous culture in multistage fermentors is studied in the case of a double inhibition of cell growth and product formation by both substrate and final product. The optimal number of reactors is discussed with respect to the strength of the ethanol inhibition, while the interest of head feeding or distributed feeding is evaluated in relation to the strength of substrate inhibition.     

A comparison of prehension force control in young and elderly individuals

Age-related changes were investigated in the control of precision grip force during the lifting and holding of objects with slippery (silk) and nonslippery (sandpaper) surface textures. Two groups of active elderly adults comprising individuals aged 69–79 years (n = 10), and 80–93 years (n = 10) together with a group of young adults aged 18–32 years (n = 10) participated in the study. Each subject lifted a free weight (3N) during which time gripping and lifting forces were monitored. The elderly subjects, especially the individuals in the 81–93 year group, had a larger number of fluctuations in the grip force rate curve and longer force application time than the younger subjects during lifting. The effect of prior experience with one surface on the following different surface was more pronounced in the younger subjects than the elderly subjects. These results suggest a decline in programmed force production capacity with increased age. The fingers of the elderly subjects were more slippery and they exhibited a greater safety margin of the grip force while holding the object than the younger adults. The overall results demonstrated that precision grip force control capacity declines with advancing age. It is suggested that this decline is due mainly to age-related changes in skin properties, and cutaneous sensibility functions, and in part to central nervous system function.     

Force production by depolymerizing microtubules: load-velocity curves and run-pause statistics.

Experiments indicate that depolymerization of microtubules generates sufficient force to produce the minus-end-directed transport of chromosomes during mitosis (Koshland et al., 1988). In vitro, analogous transport of kinesin-coated microspheres exhibits a paradoxical effect. Minus-end-directed transport of the microspheres driven by depolymerization is enhanced by the presence of ATP, which fuels the motor action of kinesin driving the microspheres in the opposite direction, toward the plus end of the microtubule. Here we present a mathematical model to explain this behavior. We postulate that a microsphere at the plus end of the microtubule facilitates depolymerization and hence enhances minus-end-directed transport. The force-velocity curve of the model is derived; it has the peculiar feature that velocity is maximal at some positive load (opposing the motion) rather than at zero load. The model is used to simulate the stochastic process of microsphere-facilitated depolymerization-driven transport. Simulated trajectories at low load show distinctive runs and pauses, the statistics of which are calculated from the model. The statistics of the process provide sufficient information to determine all of the model's parameters.     

Control of locomotion in vitro: II. Chemical stimulation.

Previous studies have described the presence of alternating activity induced in left and right ventral roots of the neonate rat in vitro brainstem-spinal cord preparation, following application of certain neuroactive substances to the bathing solution. The present findings show the presence of chemically induced, adult-like coordinated airstepping demonstrated by electromyographic recordings in the hindlimb-attached in vitro brainstem-spinal cord preparation. Analysis of muscular activity demonstrated alternation between antagonists of one limb and between agonists of different limbs, as well as a proximodistal delay in agonists active at different joints of the same limb. Neuroactive agents were applied independently to either the brainstem or spinal cord bath. The substances surveyed in the present studies included some of those used previously, as well as additional compounds: bicuculline and picrotoxin (gamma-aminobutyric acid-ergic antagonists), N-methyl-D-aspartic acid (excitatory amino acid agonist), substance P, acetylcholine, carbachol (cholinergic agonist), and serotonin. Application of these substances to the brainstem bath produced rhythmic airstepping. Application of dopamine, aspartate, glutamate, and N-methyl-D-aspartic acid to the spinal cord bath also produced rhythmic airstepping, while application of acetylcholine produced tonic, long-lasting co-contractions. These findings reveal the presence of several neurochemical systems in the central nervous system that can be activated at birth to induce coordinated airstepping in the neonate rat in vitro brainstem-spinal cord preparation.     

An information theoretic approach to macromolecular modeling: II. Force fields

In this article, we explore the information content of molecular force-field calculations. We make use of exhaustive lattice models of molecular conformations and reduced alphabet sequences to determine the relative resolving power of pairwise interaction-based force fields. We find that sequence-specific interactions that operate over longer distances offer greater amounts of information than nearest-neighbor or non-sequence-specific interactions. In a companion article in this issue, we explored the information content of sequence alignment procedures and the calculation of gap penalties. Both articles have implications for protein and nucleic-acid computations.     

Cardiovascular control during voluntary static exercise in humans with tetraplegia.

The purpose of the present study was 1) to investigate whether an increase in heart rate (HR) at the onset of voluntary static arm exercise in tetraplegic subjects was similar to that of normal subjects and 2) to identify how the cardiovascular adaptation during static exercise was disturbed by sympathetic decentralization. Mean arterial blood pressure (MAP) and HR were noninvasively recorded during static arm exercise at 35% of maximal voluntary contraction in six tetraplegic subjects who had complete cervical spinal cord injury (C(6)-C(7)). Stroke volume (SV), cardiac output (CO), and total peripheral resistance (TPR) were estimated by using a Modelflow method simulating aortic input impedance from arterial blood pressure waveform. In tetraplegic subjects, the increase in HR at the onset of static exercise was blunted compared with age-matched control subjects, whereas the peak increase in HR at the end of exercise was similar between the two groups. CO increased during exercise with no or slight decrease in SV. MAP increased approximately one-third above the control pressor response but TPR did not rise at all throughout static exercise, indicating that the slight pressor response is determined by the increase in CO. We conclude that the cardiovascular adaptation during voluntary static arm exercise in tetraplegic subjects is mainly accomplished by increasing cardiac pump output according to the tachycardia, which is controlled by cardiac vagal outflow, and that sympathetic decentralization causes both absent peripheral vasoconstriction and a decreased capacity to increase HR, especially at the onset of exercise.     

Modeling and static optimization of the ethanol production in a cascade reactor. I. Modeling

Let us consider the modeling of a cascade reactor for the production of ethanol. The rates of reaction in alcoholic fermentation are modeled so that it can assume both ethanol and substrate inhibition, in relation to the observed results.A nonstructured model, based on biomass, substrate, and ethanol concentrations, is developed and identified. It is a complex model, this being due to the nonlinearity between the specific rate of ethanol production and the growth rate and, on the other hand, the study of the static optimization of ethanol fermentation is performed.     

Force Control Is Related to Low-Frequency Oscillations in Force and Surface EMG

Force variability during constant force tasks is directly related to oscillations below 0.5 Hz in force. However, it is unknown whether such oscillations exist in muscle activity. The purpose of this paper, therefore, was to determine whether oscillations below 0.5 Hz in force are evident in the activation of muscle. Fourteen young adults (21.07±2.76 years, 7 women) performed constant isometric force tasks at 5% and 30% MVC by abducting the left index finger. We recorded the force output from the index finger and surface EMG from the first dorsal interosseous (FDI) muscle and quantified the following outcomes: 1) variability of force using the SD of force; 2) power spectrum of force below 2 Hz; 3) EMG bursts; 4) power spectrum of EMG bursts below 2 Hz; and 5) power spectrum of the interference EMG from 10–300 Hz. The SD of force increased significantly from 5 to 30% MVC and this increase was significantly related to the increase in force oscillations below 0.5 Hz (R ² = 0.82). For both force levels, the power spectrum for force and EMG burst was similar and contained most of the power from 0–0.5 Hz. Force and EMG burst oscillations below 0.5 Hz were highly coherent (coherence = 0.68). The increase in force oscillations below 0.5 Hz from 5 to 30% MVC was related to an increase in EMG burst oscillations below 0.5 Hz (R ² = 0.51). Finally, there was a strong association between the increase in EMG burst oscillations below 0.5 Hz and the interference EMG from 35–60 Hz (R ² = 0.95). In conclusion, this finding demonstrates that bursting of the EMG signal contains low-frequency oscillations below 0.5 Hz, which are associated with oscillations in force below 0.5 Hz.