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Department of Integrative Physiology, University of Colorado, Boulder, Colorado 80309-0354
Submitted 21 January 2003; accepted in final form 6 April 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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;
Thomas et al. 1991). When the
discharge rate is less than that required for a fused tetanus, the force
exerted by the motor unit will fluctuate about an average value. Because
discharge rates during voluntary contractions rarely achieve tetanic rates
(Enoka and Fuglevand 2001), the
force exerted by a muscle will include fluctuations in force due to the
submaximal activation of many motor units. Furthermore, the amplitude of the
force fluctuations increases as more motor units are recruited
(Christou et al. 2002;
Slifkin and Newell 1999;
Yao et al. 2000).
The contribution of a motor unit to the fluctuations in force changes as a
function of the contraction intensity. First, as the level of voluntary
activation of the motor-neuron pool increases, so does the discharge rate of
the activated motor neurons (Person and
Kudina 1972), which reduces the fluctuations in motor-unit force.
Second, the relative increment in whole muscle force attributed to the
recruitment of a motor unit declines with an increase in contraction intensity
(Fuglevand et al. 1993), which
causes high-threshold motor units to contribute less to the force
fluctuations. In contrast, the activation pattern of the motor-unit population
can enhance the force contributed by a single motor unit. For example,
increased levels of short-term synchronization, which appear to be caused by
greater amounts of branched common input
(Sears and Stagg 1976;
Semmler 2002), increase
motor-unit force and the fluctuations in whole muscle force
(Taylor et al. 2002;
Yao et al. 2000).
The purpose of this study was to identify those features of motor-unit
activity that are responsible for the variation in force fluctuations across
the operating range of the first dorsal interosseus muscle. This was
accomplished by comparing experimental observations with computer simulations
involving several models of motor-unit recruitment and rate coding
(Fuglevand et al. 1993;
Taylor et al. 2002). Each
model involved manipulation of a single variable so that it was possible to
examine the influence of recruitment range, the distribution of discharge
rates, short-term synchronization, and oscillation in excitatory drive on the
pattern of force fluctuations. The results indicate that variation in the
force fluctuations during voluntary contractions that spanned the operating
range of the muscle cannot be explained by a single mechanism that influences
motor-unit activity. This finding contrasts with some experimental
observations that the force fluctuations, particularly at low forces, are
largely attributable to discharge-rate variability
(Kornatz et al. 2002;
Laidlaw et al. 2000;
Patten and Kamen 2000).
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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Force measurement
Subjects sat facing a 17-in. computer monitor with the left arm abducted by 0.79 rad and the left hand resting prone on a platform. The monitor was 1.6 m in front of the subject at eye level. The height of the platform was adjusted so that the shoulders were horizontal. A vacuum foam pad was used to immobilize the elbow and forearm (Versaform pillow, Tumble Forms, Trenton, Ontario, Canada). The left hand and forearm were constrained by clamps to maintain an angle of 0.8 rad between the thumb and index finger (Fig. 1). The index finger was inserted into a splint that kept the interphalangeal joints extended.
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The abduction force exerted by the index finger was measured with a force
transducer (Model 13, Sensotec) that was aligned with the proximal
interphalangeal joint. A high sensitivity (0.051 V/N) transducer was used for
contractions that were <20% maximum voluntary contraction (MVC) force, and
a low-sensitivity (0.0059 V/N) transducer was used to measure force during
contractions that were 
20% MVC force. The signal-to-noise ratio for the
force transducer at the lowest force (0.8 N) for the steadiest subject was
3.82, and averaged 11.5 ± 7.28 (range: 3.82–24.6) for all
subjects at the minimum target force (2% MVC). Force was sampled at 500 Hz
using Spike2 software (CED, Cambridge, UK) and stored on a computer.
A horizontal line was placed on the computer monitor to indicate the target force for each trial. The gain of the force display was adjusted so that the target-force line was always at the same location on the monitor. The task involved matching the target force within 1 s of trial initiation and then sustaining the abduction force for 6 s. Each subject received visual feedback of the target force and the force exerted by the index finger during the first 3 s of a contraction, after which the monitor was blocked from the subject's view for the remainder of the trial. Before the start of data collection, the subject was instructed not to flex, extend, or rotate the index finger during the contractions. Furthermore, the subject was informed that a trial would be terminated if one of the experimenters observed any index finger motion besides abduction. Positions of the index finger and arm were constantly monitored by one of the investigators during each trial. At the conclusion of each trial, the force exerted during the entire contraction was displayed on the monitor for the subject to view.
EMG measurement
Electromyographic (EMG) activity of the first dorsal interosseus muscle was
measured with silver–silver chloride electrodes (4-mm diameter) that
were attached to the skin. One electrode was placed over the belly of the
muscle (proximal one-third) and a second electrode was placed over the
metacarpophalangeal joint (Zijdewind et
al. 1999). The reference electrode was attached to the skin over
the styloid process of the ulna. The EMG signals were amplified (x1,000)
with an isolated bioamplifier (S-series, Coulbourn, Instruments, Allentown,
PA), passed through a band-pass filter (20 to 800 Hz; S-series, Coulbourn
Instruments), and sampled at 4 kHz (1401 plus, Cambridge Electronic Design,
UK).
Experimental protocol
The protocol consisted of two 6-s contractions at each of 9 target forces.
To determine the target forces, each subject first performed two or more MVCs
until the peak forces for at least two of the MVCs were within 5% of each
other. Performance during the MVCs was monitored for unwanted motion of the
index finger. The peak force exerted during an acceptable MVC trial was taken
as the MVC force (Allen et al.
1995). The 9 target forces corresponded to 2, 5, 15, 30, 50, 70,
85, 95, and 98% of MVC force. The order of the target forces was randomized
for each subject. Adequate rest was given between trials to minimize
fatigue—a minimum of 30 s or until the subject felt fully recovered from
the previous trial. At the conclusion of the protocol, the subject performed
another MVC for comparison with the value obtained at the beginning of the
protocol.
Motor-unit model
A model of recruitment and rate coding
(Fuglevand et al. 1993;
Taylor et al. 2002;
Yao et al. 2000) was used to
simulate the isometric force produced by a pool of 120 motor units
(Fig. 2). The model was
implemented in Matlab version 6.1 (The Mathworks, Natick, MA). The basic
parameters of the model were the same as those reported previously
(Taylor et al. 2002) and were
chosen to approximate the characteristics of the motor-unit population in the
first dorsal interosseus (Enoka and
Fuglevand 2001).
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In brief, the peak twitch forces of motor units [range: 1–100
arbitrary units (au)] were proportional to the recruitment threshold (range:
1–12 au) and were distributed exponentially across the population of 120
units. Because previous simulations (Enoka
et al. 2003) suggested that a reduction in the number of motor
units in the population by 25% and an increase in the range of twitch forces
across the population by 40% had little effect on force fluctuations, these
values were kept constant in the current simulations. The twitch contraction
time of each motor unit in the model was inversely proportional to peak twitch
force (range: 30–90 ms), and the force–frequency relation for each
motor unit depended on its peak twitch force and contraction time.
Excitation of the motor-unit pool was modeled as a ramp-and-hold function, with a 1-s ramp increase in excitation to the mean level that was held constant for the remaining 4 s of simulated force (Fig. 2, B–E). In some trials, a sinusoidal excitation function was superimposed on the constant excitation from 1 to 4 s to simulate the rhythmic drive of the motor-unit pool. The amplitude of the oscillating drive was a fixed percentage of the mean excitation for that trial.
Variability in discharge rate was manipulated by multiplying the instantaneous discharge frequency produced in response to the excitation function by a random value with a Gaussian distribution and a coefficient of variation (CV) of 10%. Although this value is lower than that used in previous versions of the model (20%), the results obtained with a CV of 10% more closely approximated the experimentally measured force variability. All motor units had a minimum discharge rate of 8 Hz, but peak discharge rate declined linearly with recruitment threshold. Discharge rates increased linearly with increased excitation. Once each model motor unit reached its assigned maximal rate, the rate was fixed despite any further increases in excitation. The first recruited unit (motor unit 1) had a maximal discharge rate of 35 Hz, whereas the peak value for motor unit 120 was 25 Hz.
Whole muscle force was simulated as the linear sum of the single motor-unit
forces. The force contributed by each motor unit was derived as the impulse
response each time an action potential was discharged by the motor neuron
(Fuglevand et al. 1993).
The parameters of the basic model were adjusted to examine the influence of the pattern of excitation, recruitment range, and rate coding on the fluctuations in the simulated force. Only one parameter was adjusted in each simulation. The following parameters were varied and the results were compared with the basic model: 1) gain— the increase in instantaneous discharge rate with an increase in excitation was varied from one (basic model) to two; 2) nonuniform gain—a variation in gain between values of 2.0 and 0.75 across the motor-unit pool, which changed either proportionally or inversely with recruitment threshold; 3) minimum discharge rate— 4 and 10 Hz compared with 8 Hz in the basic model; 4) peak discharge rate—a 10-Hz increase in the peak discharge rate for all motor units; 5) range of peak discharge rates—a 20-Hz decline in peak discharge rate between motor unit 1 (35 Hz) and motor unit 120 (15 Hz), compared with a 10-Hz decrease in the basic model; 6) distribution of peak discharge rates—a higher discharge rate for motor unit 120 compared with motor unit 1, which was tested for each of the ranges and values of peak rates; 7) coefficient of variation for discharge rate—10 and 20%; 8) recruitment range—a recruitment threshold range of 54 and 69% compared with 41% of maximal excitation for the basic model; 9) oscillating activation—at frequencies of 1, 8, 10, 12, and 20 Hz with amplitudes of 2, 5, 10, and 20% of mean excitatory drive; and 10) motor-unit synchronization—a linear increase with excitation compared with no synchrony in the basic model.
A number of the changes to these 10 parameters either had no effect on the force fluctuations or greatly altered the magnitude and pattern of the force produced by the model. To simplify the comparisons in the present study, only the parameters that had a direct effect on the force fluctuations were analyzed further. Only 5 variations of the parameters listed above met this criterion and were compared with the basic model: 1) recruitment range of 69%; 2) motor-unit synchronization; 3) oscillating activation of 1 Hz at 2% of mean excitation, 12 Hz at 10%, and 20 Hz at 10%; 4) peak discharge rate increase by 10 Hz for all motor units; 5) range of peak discharge rates with motor unit 120 discharging at a 20-Hz lower peak rate than that of motor unit 1. Similar to the experimental trials, 10 simulations were run at each of 10 force levels (2, 5, 15, 30, 50, 70, 85, 95, 98, and 100% of maximal force) and force was sampled at 500 Hz.
As with the experimental trials, the simulated forces were quantified as a percentage of maximal force. Because the force–excitation relation depended on the parameters used in the model, the level of excitation required to simulate the target force was determined from polynomial functions that were fitted to the forces obtained with 10 simulations at each of 10 levels of excitation for the different models (Fig. 3).
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Because the distribution of discharge times has a significant effect on
force variability (Enoka et al.
2003; Taylor et al.
2002), the mean discharge rate and CV for discharge rate were kept
the same, except for the condition that involved an explicit comparison of the
effect of discharge-rate variability. The only condition in which this was not
possible was the synchronization condition. In this case, the mean rate was
the same as the other models across the different levels of excitation, but
the variability increased from 16.4 to 32% as the level of excitation
increased from a minimum to maximum; for comparison, the CV for discharge rate
increased from 10 to 15.6% in the basic model. The consequences of this
difference in variability are addressed in the DISCUSSION.
Synchronization was applied by adjusting some of the discharge times of
each motor unit to be approximately coincidental with the discharges of other
motor units. These methods were previously presented in detail
(Taylor et al. 2002). In the
present simulations, synchronization progressed linearly from low to high with
increased excitation. The number of discharge adjustments was defined by
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Data analysis
All data analysis was performed with custom-written programs in Matlab version 6.1 (The Mathworks). Analyses were performed separately for the visual (first 3 s) and nonvisual (last 3 s) parts of each target-matching trial. For the nonvisual portion of each trial, 2 s of data were used beginning 500 ms after visual feedback was removed. After the force data were detrended, the SD of force and CV for force (CV = SD/mean) were calculated. The same analysis was completed between 1 to 3 s for the visual portions of each trial and for the simulation data. The EMG data were analyzed over these same intervals of time.
A frequency analysis was performed on the force (experimental and simulated) and EMG using a modified Welch's periodogram method with a Hanning window (no overlap) that had the same length as the FFT block size (512 points). The mean force was subtracted from each signal during the analysis. The resolution of the power spectra was 0.976 Hz for force and 8.04 Hz for the interference EMG. The analyses determined the percentage of total power in each frequency bin, the maximal power, the frequency at maximal power, and the median frequency.
Statistical analysis
All statistics were performed on the single trial that most closely matched the target force. One subject had no reasonable data for the 70% target force. A 2-factor, repeated-measures analysis of variance (ANOVA) (2 levels of vision x 9 target forces) was used to compare the force variability during the visual and nonvisual conditions at the various target forces. Because the model did not include visual feedback, the statistical comparisons between the experimental and simulated data were made with the forces measured when the subjects did not have visual feedback.
A 2-factor, repeated-measures ANOVA was used to compare the experimental
and simulated coefficients of variation for force (2 between-subject factors)
across the 9 target forces (repeated-measure factor). Because there were 8
different model conditions (including 3 levels of oscillating drive), the
number of comparisons was limited by selecting those models that matched the
experimental data at 4 or more force levels. The alpha level for all
statistical tests was P 
0.05. Significant interactions were
followed by post hoc analyses (independent or dependent t-test with
Bonferroni corrections).
Two-factor, repeated-measures ANOVAs were also used to compare the median frequency of the force and EMG power spectra. Stepwise regression analysis was used to detect significant linear associations between force fluctuations (SD and CV for force) and power at each frequency bin of the force signal (1–12 Hz of the experimental data and 1–35 Hz of the model data). Similar regression analyses were used to examine the associations between the force fluctuations and the EMG power spectrum, and the power spectra for EMG and force.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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Experimental measurements
Because of the progressive enhancement of motor-unit activity during the voluntary contractions, the amplitude of the interference EMG (y) increased linearly with target force (x) for all subjects (y = 0.0147x +0.1309; r2 = 0.77). The mean force, SD of force, and CV for force were similar for the visual and nonvisual parts of each voluntary contraction (P > 0.05). Although the force fluctuations during visual feedback tended to be of greater magnitude, the pattern across target forces was similar to that observed during the absence of the visual feedback. The fluctuations during visual feedback had a mean CV of 4.2 ± 2.2% at 2% MVC, which decreased to 1.7 ± 0.78% at 30% MVC and then increased again to 2.3 ± 1.0% at 98% MVC. The remainder of this report, however, focuses on the fluctuations during the absence of visual feedback for comparison with the simulated forces. The SD of force increased (P < 0.05) nonlinearly with target force (Fig. 4A; Table 1). Furthermore, the CV for force declined from a maximum at 2% MVC to a minimum at 30% MVC (P < 0.05), after which it increased to a plateau that began at 50% MVC (Fig. 4B; Table 1). These results did not appear to be influenced by fatigue, given that the MVC forces were similar (P > 0.1) at the beginning (25.7 ± 7.3 N; range: 18.3–36.0 N) and end of the protocol (26.6 ± 5.8 N; range 19.4–34.0 N).
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Maximal power in the force spectra during the experimental measurements (Fig. 5) occurred at low frequencies (1.37 ± 1.07 Hz; range: 0.98–6.08 Hz). On average, 42.8 ± 5.8% of the total power in the force signal was contained in the frequency bin corresponding to the maximal power. The median frequency in the force spectra tended to decrease as excitation increased, declining from 1.47 ± 1.8 Hz at the target force of 2% MVC to 0.22 ± 0.43 Hz at the target force of 70% MVC.
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Maximal power in the interference EMG spectra (not shown) occurred at higher frequencies (68.4 ± 23.2 Hz; range: 32.2–145 Hz). On average only 8.71 ± 2.79% of the total power in the EMG signal was contained in the frequency bin where maximal power was located, which indicates that the power was distributed more broadly in the EMG spectrum than in the force spectrum. The median frequency of the EMG tended to decrease (range: 93.8–69.7 Hz) with target force; however, this decrease did not reach statistical significance (P = 0.06 for 5% compared with 98% MVC).
There was a significant positive association between the percentage of total power at 0.98 Hz in the force spectrum and the SD of force (r2 = 0.12, P < 0.01). Similarly, the 0.98 and 9.8 Hz frequencies of the force power spectra were significantly related to the CV for force (r2 = 0.21 and 0.01; P < 0.01, respectively). There was also a significant positive relation between the SD of force and the total power in the interference EMG signal from 50 to 75 Hz (r2 = 0.16, P < 0.01); however, there was no significant association between the CV for force and the EMG power spectrum (P > 0.05). There were also some significant associations between the force and interference EMG spectra. For example, the power at 0.98 Hz in the force signal was negatively associated with the percentage total power in the EMG signal from 200 to 225 Hz (r2 = 0.09, P < 0.01), whereas the power in the force spectrum between 4.8 and 6.8 Hz was positively correlated with the EMG power between 125 and 150 Hz (r2 = 0.09, P < 0.01). Furthermore, the power at 8.8 Hz of the force signal was positively associated with the EMG power spectra in the range 225–250 Hz (r2 = 0.06, P < 0.05).
Simulated forces
The various models used in the study had obvious effects on the discharge times of the motor units. These effects are characterized in raster plots for three of the models: basic, 1-Hz oscillation, and synchronization models (Fig. 6). The raster plots show the discharge times of selected motor units during a 3-s interval when the model was being excited to exert a force of 30% MVC. Compared with the basic model, there are marked changes in the discharge times for the other two models. For example, the oscillations are apparent in the discharge times for the 1-Hz oscillation model and the discharge times are much more variable for the synchronization model.
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None of the motor-unit models was able to simulate the observed patterns of fluctuations in force (SD and CV for force) across the operating range of the muscle. Four models, however, approximated the experimentally measured coefficients of variation for force at 4 or more levels of force (Fig. 7B). The two most accurate models were the basic model and the model with an excitatory drive that fluctuated at 20 Hz (20-Hz oscillation), which had simulated CVs for force that were similar to the experimental measures at 2, 5, 50, 70, 85, 95, and 98% MVC. The synchronization model approximated the experimental CVs for force at 2, 5, 95, and 98% MVC. The fourth successful model, which included an excitatory drive that oscillated at 1 Hz (1-Hz oscillation), matched the experimental coefficients of variation for force at 2, 5, 70, 95, and 98% MVC.
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The models that could not approximate the experimental CVs for force at a minimum of 4 force levels had greater CVs for force than the experimental data (Fig. 7C). Thus they could match only the experimental force variability at high forces. The model with a 20-fold range in recruitment values could approximate the experimental force only at 70, 95, and 98% of MVC and the model that involved the 12-Hz oscillation could achieve a match only at 95 and 98% of MVC. Neither an increase in the peak discharge rate of motor unit 1 nor an increase in the difference between the peak discharge rates of motor units 1 and 120 could approximate the experimental force variation at any force level.
The frequency content of the simulated forces varied for the 4 models that matched the experimental measurements (Fig. 5). For example, although the median frequency generally increased with target force, the increase was from 3.4 to 7.9 Hz in the basic model, from 3.02 to 6.64 Hz in the 20-Hz oscillation model, and from 1.66 to 4.59 Hz in the synchronization model. In contrast to the other models and similar to the experimental findings, the median frequency in the force spectra for the 1-Hz oscillation model decreased with force (0.98–0.10 Hz). Furthermore, only the 1-Hz oscillation model reproduced the average frequency at which the maximal power occurred (0.99 ± 0.53 Hz) and percentage of total power at that frequency (37.5 ± 2.25%) as observed experimentally (1.37 ± 1.07 Hz and 42.8 ± 5.8%, respectively). The other three models exhibited higher frequencies of maximal power (basic: 5.11 ± 5.54 Hz; 20-Hz oscillation: 5.16 ± 5.32 Hz; and synchronization: 3.6 ± 1.71 Hz) and lower percentage of total power at that frequency (basic: 23 ± 4.24%; 20-Hz oscillation: 23.3 ± 2.7%; and synchronization: 24.2 ± 4.4%) compared with the experimental data.
Furthermore, three of the successful models (basic, 20-Hz oscillation, and 1-Hz oscillation) exhibited a distinct secondary peak in the force spectrum (Fig. 5). The frequency at which the secondary peak occurred increased with excitation, in parallel with the change in the mean discharge rate. For example, the basic model exhibited a second peak in the power spectrum that progressed from approximately 9 to 24 Hz as the target force increased from 2 to 85% MVC. In contrast, the power in the force spectra for the experimental data and the synchronization model was largely contained within a single range of low frequencies.
For these 4 models, the power in various frequencies of the force spectrum was significantly associated with the SD (Table 2) and CV for force (Table 3). With the exception of the synchronization model, the SD of force increased when there was more power at higher frequencies (>15 Hz) and less power at lower frequencies (<10 Hz) (Table 2). In contrast, the CV for force increased when there was greater power at lower frequencies (<10 Hz) and less power at higher frequencies (>20 Hz) (Table 3). These associations between the simulated force spectra and the SD and CV for force are contrary to those observed for the experimental data.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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The findings of this study extended previous investigations of force
variability exhibited by the first dorsal interosseus by quantifying the time-
and frequency-domain characteristics of force and EMG across a large range of
isometric forces (2–98% of MVC). The results indicate that the relation
between the CV for force and mean force can be characterized by a cubic
polynomial, which differs from the hyperbolic relation observed at low forces
(Enoka et al. 2003;
Jones et al. 2002). The
simulations confirm that discharge characteristics of the motor-unit
population, such as synchronization and low-frequency common oscillation, are
likely contributors to the observed time- and frequency-domain features of the
force signal. Disparities between the simulations and the experimental
observations, however, suggest that multiple mechanisms contribute to force
variability across the operating range of the muscle.
Experimental data
Previous studies that quantified the variability in the abduction force
exerted by the index finger during isometric contractions with the first
dorsal interosseus muscle included no more than 5 force levels up to maximal
contraction strengths of 75% MVC force. In studies that included forces
30% MVC, the CV for force generally decreased as the mean force increased
(Laidlaw et al. 1999,
2000). In one study that
included forces 75% MVC, however, the CV for force declined to 20% MVC and
increased at 50 and 75% MVC (Burnett et al.
2000). Furthermore, the results obtained with previous simulations
(Enoka et al. 2003;
Jones et al. 2002), which
predicted the pattern of force variability at higher forces, also showed a
hyperbolic decline in CV for force as the mean level of force increased.
In contrast, the data included in the current report were obtained from a
greater range of excitation levels and demonstrate a different relation
between the CV for force and the mean force. The relation constituted an
initial decrease in the CV for force to a minimum around 30% MVC force
followed by an increase to a plateau that began at 50% MVC force. These
results are consistent with those observed in other muscles, such as
quadriceps femoris (Christou et al.
2002). The similarity of the relation for such different muscle
groups, combined with the absence of an effect of visual feedback on the
change in the amplitude of the force fluctuations, suggests that it may be a
consequence of the activation signal sent to muscles during isometric
contractions. Because of the nonlinear effects of summing motor-unit
potentials on the time- and frequency-domain characteristics of the EMG signal
(Day and Hulliger 2001;
Fuglevand et al. 1993),
however, there were only weak (r2 = 0.0083 ±
0.0015), although statistically significant, associations between the force
fluctuations and the EMG. Consequently, the potential contributions of various
activation strategies were examined with models of motor-unit recruitment and
rate coding.
Mechanisms responsible for force variability
Three categories of mechanisms could influence the motor output from a
population of motor units: 1) organization of the motor-unit pool;
2) recruitment and rate-coding properties of the motor units; and
3) the activation pattern of the motor-unit population. Organization
of the motor-unit pool includes the number of motor units in the muscle and
the twitch force properties of those motor units. Because the force
contributed by a single motor unit to the net muscle force declines as the
number of active motor units increases
(Fuglevand et al. 1993), a
muscle with fewer motor units might exhibit greater force fluctuations.
Similarly, briefer twitches are associated with less fusion in motor-unit
force at a given activation rate, which causes greater force variability, at
submaximal levels of excitation. Findings from training programs
(Keen et al. 1994;
Kornatz et al. 2002;
Laidlaw et al. 1999) suggest,
however, that reorganization of the motor-unit pool is not a significant
contributor to force variability. For example, the magnitude of fluctuations
in the abduction force exerted by the index finger decreased during the first
4 wk of strength training without altering either the amplitude or the time
course of the spike-triggered average twitch forces
(Keen et al. 1994).
Furthermore, simulation studies indicate that a 25% reduction in the number of
motor units and a 40% increase in the range of twitch forces for a population
of motor units does not significantly influence the CV for force
(Enoka et al. 2003;
Taylor et al. 2000). This
magnitude of reduction was used to approximate the loss that could be expected
during healthy aging in humans.
The recruitment and rate-coding properties of the motor-unit pool, which
constitute the second category of mechanisms, correspond to the discharge
characteristics of the motor units with variation in the level of excitation.
This includes such characteristics as the range of motor-unit recruitment, the
discharge rates of the motor units in the population, and the variability of
discharge rate at a given level of excitation. Motor-unit recruitment and
discharge-rate modulation influence force by altering the amount of twitch
fusion. Previous simulations have demonstrated that variation in the CV for
discharge rate can cause pronounced changes in the force fluctuations
(Enoka et al. 2003;
Taylor et al. 2000).
Consistent with this effect, experimental measurements have demonstrated
significant associations between the CVs for the discharge rate of motor units
in the first dorsal interosseus and the abduction force exerted by the index
finger (Kornatz et al. 2002;
Laidlaw et al. 2000). There
have been exceptions to this observation, however, given that Semmler et al.
(2000) found greater
variability in index finger force between young and old adults, but no
difference in the CV for discharge rate. Furthermore, Patten and Kamen
(2000) found that a 2-wk
intervention designed to improve the ability of young and old adults to match
a force–time template was associated with changes in the recruitment
threshold and the discharge rates of motor units in tibialis anterior.
The third category of mechanisms involves the activation pattern of the
population of motor units, which includes both short-term synchronization and
common rhythmic modulation of discharge rates. As with the CV for discharge
rate, computer simulations have demonstrated that motor-unit synchronization
can increase force fluctuations (Yao et
al. 2000). The experimental findings with the first dorsal
interosseus muscle, however, are mixed. There was a positive association
between the amount of motor-unit synchronization and the fluctuations in index
finger acceleration during slow anisometric contractions performed by young
adults (Semmler et al. 2001),
but not between motor-unit synchronization and the fluctuations in index
finger force during low-force isometric contractions performed by young and
old adults (Semmler et al.
2000). In contrast to the absence of an effect attributed to
short-term synchronization during isometric contractions, Halliday et al.
(1999) found that the
amplitude of physiological tremor was associated with significant coherence in
the bandwidths of 1–12 and 15–32 Hz for motor-unit discharge. The
frequency–domain correlation in motor-unit discharge is interpreted to
represent rhythmic inputs to the motor neurons (Brown 2000; De Luca and Erim
2002; Farmer et al. 1993; Kakuda et al. 1999; Kilner et al. 2002). Thus it
does appear that common inputs to motor neurons can contribute to the force
fluctuations, at least during low-force contractions.
Comparison of the model and experimental force variability
To distinguish among potential mechanisms, the CVs for force that were obtained with the different models were compared with the experimental measurements across a wide range of contraction intensities. Two of the models (basic and 20-Hz oscillation) matched the experimental force variability at 6 of the 9 target forces, whereas another 2 models (synchronization and 1-Hz oscillation) were similar at 4 or 5 of the 9 forces. With the exception of the synchronization model, the other 7 models all exhibited a hyperbolic relation between target force and the CV for force, rather than the cubic function with a minimum at about 30% MVC force observed in the experimental measurements. The overall shape of the relation between mean force and CV for force was similar for the synchronization model and the experimental data. The synchronization model, however, showed an initial decline in the magnitude of the CV to a minimum at 15% MVC force compared with the experimental data, which declined to a minimum at 30% MVC force before increasing again. Although several of these models demonstrated relatively constant values for the CV at intermediate target forces (15–30% MVC force), they all failed to reach a plateau of greater values at target forces above 50% MVC.
The results obtained with the synchronization model provided new
information on the contribution of discharge rate variability to the
fluctuations in force. Previous simulations have demonstrated that
physiological differences in the CV for discharge rate (10 vs. 40%) can cause
marked differences in the force fluctuations
(Enoka et al. 2003;
Taylor et al. 2000). Although
the CV for discharge rate was approximately twice as large during the current
simulations with the synchronization model, the force fluctuations (SD and CV)
were similar to those observed with the other models. The lack of a parallel
effect of discharge variability in the synchronization and basic models
suggests that the presence of motor-unit synchronization may act in some
instances to dampen the effect of discharge-rate variability on force
fluctuations. Although synchronization augments motor-unit twitches
(Taylor et al. 2002), this
effect is substantial only for high-threshold motor units whose recruitment
contributes the least to the net force
(Fuglevand et al. 1993).
Nonetheless, the relation between the CV for force and the target force
approached a plateau at high target forces with the synchronization model
compared with the other models (Fig.
6B), which suggests that motor-unit synchronization
likely contributed to the relation observed in the experimental
measurements.
Complexity of the model
The study of physiological mechanisms usually requires the construction of a theoretical model of the system to determine the role of factors that influence its function. The theoretical construct can then be implemented in a computational model to identify causal relations between the factors included in the model. Because the model is necessarily more simplistic than the physiological system, it is easier to isolate the variables that are important to the phenomenon of interest. Furthermore, the failures of the model are often as instructive as successes because they indicate areas of the theoretical construct that need to be modified. Accordingly, the current simulations provided a key new insight on the origin of the force fluctuations: the temporal relations between the discharge times of all the motor units in a muscle are crucial to reproduce the patterns of force variability that were observed experimentally. However, there remain some differences between the experimental data and the model as it is currently implemented.
The simulated coefficients of variation for force had a consistent DC shift
relative to the experimental data, especially at low forces. Two features of
the model may have been responsible for this difference in the normalized
force fluctuations: the linear summation of motor-unit force and the uniform
excitation function. Studies conducted on the hindlimb muscles of cats
indicate that the force produced by multiple motor units is often not
equivalent to the algebraic sum of the forces from the individual motor units
(Clamann and Schelhorn 1988;
Perreault et al. 2003;
Powers and Binder 1991). The
degree of nonlinearity in these studies depended on the magnitude of the force
that was produced and the type of muscle contraction. It is hypothesized that
the nonlinear summation of force depends on the mechanical interactions
between the muscle fibers and connective tissue. Because the magnitude and
pattern of nonlinearity reported in the literature are variable, forces were
assumed to sum linearly in the model. However, if the force produced by a
group of motor units is greater than the linear sum of the individual forces,
the force produced by the model might underestimate the corresponding
experimental values and result in a larger CV for force, as was observed at
low forces. Provided this effect is uniform across the population, errors in
estimating force amplitude should not influence the variation in force
fluctuations with contraction intensity, which depend on the degree of twitch
fusion and the timing of motor-unit twitches.
The divergence of the simulated coefficients of variation for force from
the experimental data around 15 to 30% MVC may also be influenced by the
simplified excitation function of the current motor-unit model. For example,
the CV for force for the 20-Hz oscillation model had one of the best fits to
the experimental CVs at different force levels and the 1-Hz oscillation model
provided a good approximation of the experimental forces in the frequency
domain. Thus the variation in force fluctuations may be attributable to
rhythmicities in the discharge rate of motor units. Because the individual
motor units operate on the steep portion of the force–frequency relation
at moderate forces, relatively small changes in instantaneous discharge rate
in this region would have a large influence on motor-unit force. Furthermore,
all motor units in the model received the same excitatory drive, including the
oscillatory drive that was imposed on the discharge frequency with zero phase
delay between motor units. However, recordings from the cortex of nonhuman
primates indicate that there is variability in the time delay between
oscillations (Murthy and Fetz
1996). With asynchronous modulation, fewer motor units would
discharge with similar timing, which might reduce the fluctuations in the
force signal. To address this possibility, we are currently developing a more
realistic model of synaptic activation of the pool of motor neurons
(Taylor and Enoka 2002).
Comparison of model and experimental power spectra
As reported previously, both the experimental and simulated forces
contained significant power in the frequency spectrum below 2 Hz in the
frequency domain (De Luca et al.
1982; Vaillancourt and Newell
2003; Vaillancourt et al.
2002). The low-frequency component observed in the models without
oscillating activation is likely a result of the mechanical characteristics of
force production; the one feature of the models that was consistent across
conditions was the process of summation of motor-unit twitches to produce
whole muscle force. However, the low-frequency component contained more power
for the 1-Hz oscillation model compared with that of the other models. Thus
the current simulation results indicate that the low-frequency component in
the force spectrum is attributable to both a low-frequency modulation of motor
neuron discharge and a mechanical component ascribed to the summation of motor
unit twitches.
In addition to the low-frequency peak in the power spectra, however, three
of the most explanatory models (basic, 1-Hz oscillation, and 20-Hz
oscillation) also exhibited secondary peaks at higher frequencies that were
not present in the experimental records. Because the secondary peaks
corresponded to the mean discharge rates at each target force, the average
frequencies increased with the level of excitation and were less distinct in
models with greater variability in discharge rate. For example, the secondary
peaks in the power spectra broadened but the average frequency remained
similar when the CV for discharge rate was doubled (10 to 20%). This effect
was less obvious with the synchronization model, presumably because of the
greater variability in discharge rate. Despite the relatively large amplitude
(10%) of the modulation in excitation for the 20-Hz oscillation model, the
most significant secondary peak paralleled the mean discharge rate and not the
imposed 20-Hz oscillation. These results suggest that the high-frequency
fluctuations often observed in acceleration records
(Halliday et al. 1999;
McAuley et al. 1997) are
probably not attributable to high-frequency modulation of synaptic input to
motor neurons.
Although the regression analyses identified statistically significant associations between the fluctuations in force (SD and CV) and spectral characteristics of the simulated and experimental forces, the coefficients of determination were low (average r2 = 0.18 ± 0.10). Furthermore, the sign of these correlations sometimes differed for the experimental and simulated forces. For example, the low frequencies of the simulated forces, with the exception of the synchronization model, were negatively related to the SD of force, whereas the low frequencies in the experimental force were positively associated with the SD of force. In contrast, the amplitude of the CV for force, in both the experimental and simulated records, increased with power in the low frequencies in the force spectra. These results underscore the inadequacy of any single mechanism for predicting the composite structure of the force signal.
In conclusion, force variability changes nonlinearly across the entire range of excitation levels that impinge on the motor-neuron population. The results of the modeling work suggest that manipulation of recruitment and rate coding alone could not adequately describe the patterns of force fluctuations. The pattern of force variability, however, does appear to rely on the composite activity of the motor-unit population. Alterations in the relative timing of action potentials attributed to different activation patterns reproduced some features of the experimental force signal and patterns of variability. Consequently, the pattern of force fluctuations most likely depends on the interaction of multiple features of motor-unit activity.
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONDISCLOSURESREFERENCES |
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FOOTNOTES |
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Address for reprint requests: R. M. Enoka, Department of Integrative Physiology, University of Colorado, Boulder, CO 80309-0354 (E-mail: roger.enoka{at}colorado.edu).
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