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Xiaogang Hu and Karl M. Newell

The purpose of this study was to investigate the mechanisms contributing to the different scaling functions between force and force variability in continuous and discrete isometric forces. Muscle forces were simulated with the Fuglevand et al. (1993) model of motor unit recruitment and rate coding, and a range of recruitment and firing properties were manipulated. The influence of time-to-peak force on the discrete force variability was also examined. The results revealed that the peak firing rate, the synchrony between motoneurons, and the recruitment range contributed to the different variability functions in continuous and discrete forces. The shorter time-to-peak force led to higher variability in the peak force. The findings show that the model can produce the distinct properties of the force variability scaling functions in continuous and discrete forces. The simulation results provide preliminary insight into the neuromuscular mechanisms of the different force variability functions in continuous and discrete isometric forces.

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Nobuyuki Inui

An experiment was conducted to examine the coupling of force variability in bimanual finger tapping sequences with asymmetrical forces. Right-handed participants were trained to produce bimanual finger tapping sequences consisted of an intertap interval of 500 ms and eight force conditions: two alternating force left high, two alternating force right high, two simultaneous force left high, and two simultaneous force right high conditions. During practice, visual force feedback was provided for both hands performing the bimanual tapping sequences. After practice, the participants produced the learned tapping sequences in the absence of feedback. Most importantly, whereas the peak force variability of the nondominant left hand was larger than that of the dominant right hand under the right high conditions, there was no left–right difference under the simultaneous left high conditions. This suggests that under the simultaneous left high conditions, both hemispheres were activated, resulting in overflow in the right hand, and bringing the two force variabilities closer together.

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Wan X. Yao

The purpose of this study was to examine the effect of motor-unit recruitment on force variability by using computer simulated isometric contractions of a hand muscle (i.e., first dorsal interosseus). The force was simulated at 10 levels of excitation, ranging from 10 to 100% of maximum. Two recruitment conditions were simulated to compare the relative effect of motor-unit recruitment (MUR) on the relationship of force variability and level of force. One condition (40%MUR) recruited all motor units at 40% of the maximum excitation level, and the other (50%MUR) recruited all motor units at 50% of the maximum. The 40%MUR condition had a greater number of motor units than the 50%MUR group before the excitation level reached 50% of the maximum. The results showed that force variability increased at a faster rate before the completion of motor-unit recruitment and, thereafter, increased at a slower rate. In addition, the 40%MUR group showed greater force variability than the 50%MUR group. These data suggest that motor-unit recruitment is an important factor in causing force variability.

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S. L. Hong, M-H. Lee and K.M. Newell

This experiment examined the magnitude and structure of force variability in isometric index finger force production tasks at 5, 15, 25, 35, 45, 55, 65, 75, 85, and 95% of maximal force in two different finger orientations. In the finger flexion task, the participants generated a downward isometric force through index finger flexion. In the finger abduction task, isometric force was generated by adducting the index finger (mediolateral motion of the middle finger and forearm were restricted). The task-related, normal force (Fz) and tangential forces (Fx and Fy) were collected with a three-dimensional force transducer. The standard deviation (SD) of the task-related force output (Fz) increased exponentially with force level. With increasing force level, approximate entropy (ApEn, a measure of irregularity) of Fz followed an inverted-U function for finger flexion, but decreased linearly in finger abduction. However, changes in the ApEn of the tangential forces were generally opposite to that of Fz, revealing compensations in the irregularity of force output between force dimensions. The findings provide evidence that force variability is related to muscle force-length characteristics (Feldman, 1966; Gottlieb & Agarwal, 1988).

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David E. Vaillancourt, Andrew B. Slifkin and Karl M. Newell

We examine the force fluctuations in the control of grip force to determine if force variability increases or decreases in relation to the degree of inter-digit individuation. This relation was examined in young (n = 7) and elderly (n = 7) participants, and in participants diagnosed with Parkinson's disease (n = 7). Force was produced under different force levels (5%, 25%, 50% MVC) with and without visual feedback. Force variability was assessed using the standard deviation and root mean square error, and inter-digit individuation was examined using cross-approximate entropy. Force variability increased with the force level, the removal of visual feedback, and also in the Parkinson's disease compared to the young and elderly matched control participants. There was a reduction in the degree of inter-digit individuation, with increases in force level, the removal of visual feedback, and in Parkinson's disease participants compared to the matched controls. Overall, there was a negative correlation between the degree of inter-digit individuation and force variability. The force fluctuations in precision grip revealed a continuum for the degree of inter-digit individuation in which task constraints, aging, and Parkinson's disease alter the coupling between the digits in controlling grip force.

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Hirokazu Sasaki, Junya Masumoto and Nobuyuki Inui

The present study examined whether the elderly produced a hastened or delayed tap with a negative or positive constant intertap interval error more frequently in self-paced tapping than in the stimulus-synchronized tapping for the 2 N target force at 2 or 4 Hz frequency. The analysis showed that, at both frequencies, the percentage of the delayed tap was larger in the self-paced tapping than in the stimulus-synchronized tapping, whereas the hastened tap showed the opposite result. At the 4 Hz frequency, all age groups had more variable intertap intervals during the self-paced tapping than during the stimulus-synchronized tapping, and the variability of the intertap intervals increased with age. Thus, although the increase in the frequency of delayed taps and variable intertap intervals in the self-paced tapping perhaps resulted from a dysfunction of movement timing in the basal ganglia with age, the decline in timing accuracy was somewhat improved by an auditory cue. The force variability of tapping at 4 Hz further increased with age, indicating an effect of aging on the control of force.

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Roger J. Paxton, Caitlin Feldman-Kothe, Megan K. Trabert, Leah N. Hitchcock, Raoul F. Reiser II and Brian L. Tracy


The purpose was to determine the effect of peripheral neuropathy (PN) on motor output variability for ankle muscles of older adults, and the relation between ankle motor variability and postural stability in PN patients.


Older adults with (O-PN) and without PN (O), and young adults (Y) underwent assessment of standing postural stability and ankle muscle force steadiness.


O-PN displayed impaired ankle muscle force control and postural stability compared with O and Y groups. For O-PN, the amplitude of plantarflexor force fluctuations was moderately correlated with postural stability under no-vision conditions (r = .54, p = .01).


The correlation of variations in ankle force with postural stability in PN suggests a contribution of ankle muscle dyscontrol to the postural instability that impacts physical function for older adults with PN.

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Nobuyuki Inui

An experiment was conducted to examine contextual effects of the magnitude of changes in force on force control in a finger-tapping sequence with an accentuated- (accentuated-force condition) or attenuated-force tap (attenuated-force condition). Participants were trained to produce a finger-tapping sequence with an intertap interval of 500 ms and four force patterns. During practice, visual force feedback pertaining to the two target forces in the tapping sequences was provided. After practice, the participants reproduced the learned tapping sequences in the absence of feedback. A main result was that the last accentuated-force tap affected the first three taps of the tapping sequence. For the accentuated-force conditions, the larger the difference between the first three target forces and the last target force, the larger the first three forces. This indicates the contextual effect of serial position for force control. This effect was not observed, however, under the attenuated-force conditions.

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Bouwien C.M. Smits-Engelsman, Gerard P. Van Galen and Jacques Duysens

Ninety-four participants (age 5–93 years) performed isometric force production tasks at five different levels of their maximum voluntary contraction (MVC) with either one or two index fingers. Research questions were whether variability measures in the bimanual task condition were different compared to the unimanual condition and whether this difference showed a developmental trend. Results showed that force regulation was more demanding during bimanual tasks (33% increase in error). During development signal-to-noise ratio (SNR) increased threefold from 5–12 years of age and again 60% from 12 years to adulthood. SNR for the elderly was comparable to values of 9 to 10-year-olds. SNR decreased in the bimanual task, particularly for the older persons. For adults and elderly, optimal SNR levels were observed around 36% of their MVC. In younger children, however, the inverted U-shape in the SNR over the full range of forces was not yet present.

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Joseph P. Stitt and Karl M. Newell

This paper presents the stochastic modeling of isometric force variability in the steady-state time series recorded from the index finger of young adults in the act of attempting to hold different levels of constant force. The isometric force time series were examined by assuming that the stochastic (random) models were linear. System identification techniques were employed to estimate the parameters of each linear model. Once the models were parameterized, the values of the estimated parameters were compared to determine if a single linear time-invariant model was applicable across the entire isometric force range. Although the overall random models were found to be nonlinear functions of the target force level, within a fixed target level, linear modeling provided adequate estimates of the underlying processes thus enabling the use of well-known linear system identification algorithms.