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1Department of Integrative Physiology and 2Department of Electrical and Computer Engineering, University of Colorado, Boulder, Colorado
Submitted 18 April 2005; accepted in final form 27 June 2005
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ABSTRACT |
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INTRODUCTION |
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The different rates of increase in the fluctuations of motor output during the two tasks have been associated with the normalized variability (coefficient of variation, CV) in motor unit discharge rate (Mottram et al. 2005
). Nonetheless, the CV for motor unit discharge is not always a strong predictor of the motor output variability (Semmler et al. 1998
, 2000
) for at least three reasons: first, the amplitude of the CV for motor unit discharge provides only an average measure of the variability in discharge, which is modulated both by inputs to the motor neuron pool (De Luca et al. 1982
; Farmer et al. 1993
; McAuley and Marsden 2000
) and by synaptic noise (Calvin and Stevens 1968
; Jones et al. 2002
; Matthews 1996
). Second, the fluctuations in motor output are associated with the oscillatory activity of multiple active motor units (De Luca et al. 1985
), whereas the CV for discharge rate reflects the characteristics of a single motor unit. Third, the strength of the association between the variability in motor unit discharge and motor output depends on the difference between the target force and the recruitment threshold of the recorded motor unit (Moritz et al. 2005; Person and Kudina 1972
).
An alternative approach to identify the origin of the fluctuations in motor output is to compare the frequency content of the rate at which motor units discharge action potentials with the frequency content of the motor output. Accordingly, studies have demonstrated that slow (03 Hz) and fast (1632 Hz) oscillations in discharge rate during submaximal contractions (De Luca et al. 1982
, 1985
; Farmer et al. 1993
) can cause fluctuations in motor output at similar frequencies (Erimaki and Christakos 1999
; Halliday et al. 1999
; Kakuda et al. 1999
; Vaillancourt et al. 2002
).
One limitation of these coherence analyses, however, is that they only identify common frequencies in both signals. Such an analysis does not detect the influence of frequency modulation in dissimilar bands; for example, the contribution of motor unit discharge at 1322 Hz to the 8- to 12-Hz oscillations in force observed during isometric contractions (Elble and Randall 1976
). Furthermore, changes in the resonant frequency of the limb arising from variation in its inertia will affect the load-dependent component of the fluctuations in motor output (Halliday et al. 1999
; Mayston et al. 2001
; Stiles and Randall 1967
) and cause the frequency modulation of motor unit discharge to influence the motor output differently during the force and position tasks.
The purpose of the study was to examine the contribution of frequency modulation of motor unit discharge to the fluctuations in the motor output during sustained contractions with the force and position tasks. A multiple-regression analysis was used to compare the modulation of discharge rate and motor output during the two tasks. The hypothesis was that different frequencies in the motor unit discharge would contribute to the fluctuations in the motor output for the force and position tasks. Preliminary data have been presented previously in abstract form (Christou et al. 2004a
).
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METHODS |
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Fifteen healthy adult men (25.5 ± 5.9 yr; range, 2039 yr) participated in the study. All subjects were moderately active and were right-handed (average laterality quotient score was 0.73 ± 0.22; range: 0.181.0), as identified by the Edinburgh Handedness Inventory (Oldfield 1971
). None of the subjects had any known neurological disorder or cardiovascular disease and all subjects were naive to the purpose of the experiment. The Human Research Committee at the University of Colorado approved the procedures and the experiments were performed in accordance with the Declaration of Helsinki. Before participation in the study, all subjects gave written informed consent.
Each subject participated in one to three experimental sessions that were at least 1 wk apart. Each experiment involved recording the discharge of a single motor unit (n = 28) in the biceps brachii of the left arm. Single motor unit recordings were obtained from the same motor unit during two isometric contractions (force and position tasks) performed with the elbow flexor muscles by each subject.
Experimental arrangement
Details of the experimental setup, the preparation of the subjects, and the equipment used have been described previously (Mottram et al. 2005
). Briefly, subjects were seated upright in an adjustable chair with the nondominant arm abducted approximately 0.26 rad and the elbow resting on a padded support. The elbow joint was flexed to 1.57 rad and positioned midway between pronation and supination with the forearm parallel to the ground. The hand and forearm were secured in a modified wristhandthumb orthosis (Orthomerica, Newport Beach, CA).
The force applied at the wrist in the vertical direction was measured with a force transducer that was mounted on a custom-designed, adjustable support. The orthosis was rigidly attached to the force transducer. The MVC force of the elbow flexor muscles was measured at the wrist with the JR-3 Force-Moment Sensor (900-N range, 90.0 N/V JR-3, Woodland, CA) before performance of the force task, and with a Baldwin SR-4 load cell (2700-N range, 177 N/V; BaldwinLimaHamilton, Philadelphia, PA) before performance of the position task. The force exerted in the vertical direction was displayed on a 17-in. monitor that was located at eye level approximately 1.2 m in front of the subject.
Elbow angle during the position task was measured with an electrogoniometer (SG110 and K100, Biometrics, Cwmfelinfach, Gwent, UK) that was secured to the lateral side of the left elbow joint. A uniaxial piezoresistive accelerometer (model 7265A-HS, Endevco; linear range of acceleration response ± 100 m/s2, San Juan Capistrano, CA) was mounted on the orthosis near the thumb to record acceleration in the vertical direction. Output from the electrogoniometer and accelerometer was recorded on digital tape. Elbow angle was displayed on the same 17-in. monitor as the force trace.
The compressive force under the elbow joint was recorded with an Entran transducer (ELW-D1-100L, 273.37 mV range, Fairfield, NJ) that was placed under the padded elbow support. The compression force under the elbow was displayed on an oscilloscope and stored on digital tape.
Muscle fiber action potentials from single motor units in the biceps brachii were recorded with branched bipolar electrodes (stainless steel, 50-µm diameter; California Fine Wire, Grover Beach, CA). A disposable 25-gauge hypodermic needle was used to insert the branched bipolar electrode under the skin (not penetrating the fascia) and over the belly of the biceps brachii muscle for a distance of 38 cm, and was removed before recording motor unit activity. The electrode was inserted perpendicular to the direction of the muscle fibers and moved to optimize the detection of action potentials from a single motor unit. Once a motor unit was isolated, the electrode was not moved again until the experiment was completed. Single motor unit recordings were amplified (1,0002,000x), bandpass filtered (208,000 Hz), displayed on an oscilloscope, and stored on digital tape.
Experimental procedures
Subjects performed two submaximal isometric contractions (force and position tasks) with the elbow flexor muscles of the left arm. These two tasks were performed for identical durations on the same day in random order. Before the experimental session, each subject visited the laboratory for an introductory session to become familiar with the equipment and the procedures, and to perform several trials of the MVC task. The experimental session consisted of 1) an assessment of the MVC force for the elbow flexor muscles, 2) isolation and determination of the recruitment threshold of a single motor unit in the biceps brachii, 3) performance of the force task and a subsequent MVC, 4) performance of the position task and a subsequent MVC, and 5) repeat assessment of the recruitment threshold of the isolated motor unit. Steps 3 and 4 were performed in random order. Before initiating the second task (force or position), subjects rested until the MVC force was within 5% of the value recorded at the beginning of the protocol.
MVC FORCE.
The protocol began with the subject performing three isometric MVC trials with the elbow flexor muscles. The MVC task consisted of a gradual increase in force from zero to maximum in
3 s, with the maximal force held for 3 s. The greatest force achieved by the subject was defined as the MVC force and was used as the reference for determining the recruitment threshold of the isolated motor unit and the contraction intensity for the force and position tasks.
MOTOR UNIT RECRUITMENT THRESHOLD.
With the left wrist attached to the force transducer, the subject gradually increased the force exerted by the elbow flexor muscles to a level that was sufficient to sustain a minimal, repetitive discharge of an isolated motor unit. Subjects were given audio feedback of action potential discharge and visual feedback of elbow flexor force to assist in achieving and maintaining a minimal repetitive discharge rate. The force at which the discharge rate of the isolated motor unit was minimal and repetitive was defined as the recruitment threshold (Spiegel et al. 1996
). In two of 28 experiments, the isolated motor unit was lost between tasks.
FORCE AND POSITION TASKS. The position and force tasks were performed at a similar target force above the recruitment threshold of the isolated motor unit. For the force task, the subject was required to exert a force in the upward direction by contracting the elbow flexor muscles and matching the target force displayed on a monitor. For the position task, the subject was required to maintain the elbow joint angle at 1.57 rad while supporting an inertial load that was equivalent to the target force achieved during the force task. This was accomplished by hanging a weight from the wrist at the same point on the orthosis as the point of application for the force that was exerted during the force task. Thus the load torque about the elbow joint was identical within subjects for the two tasks. Subjects were provided with visual feedback of the force (0.3% MVC/cm) exerted at the wrist during the force task, and of the elbow angle (2.0°/cm) during the position task.
The durations of the two tasks, which were not performed to failure, were identical within subjects and were based on target force. The duration of each task decreased linearly with target force: contraction duration was 300 s for target forces that were 05% MVC force and declined to 60 s for target forces that were 3550% MVC force.
Data analysis
Force, acceleration, and elbow angle were recorded on digital tape and subsequently digitized (A/D converter, 12-bit resolution) and analyzed off-line using the Spike2 (version 5.02) data-analysis system (Cambridge Electronic Design, Cambridge, UK). The single motor unit recordings were digitized at 18.5k samples/s, and the force, position, and acceleration signals were digitized at 200 samples/s.
The MVC force was quantified as the peak force obtained during the MVC task. Fluctuations in the vertical direction were quantified during the position and force tasks by calculating the SD of acceleration and detrended force, respectively, at the start, middle, and end (20-s intervals) of each contraction.
Action potentials discharged by single motor units in biceps brachii were discriminated using a computerized, spike-sorting algorithm (Spike2, version 5.02; Cambridge Electronic Design), which identified the potentials belonging to a single motor unit based on waveform amplitude, duration, and shape. The recruitment threshold of the isolated motor units ranged from 3 to 44% of MVC. The CV for discharge rate was determined for the first, middle, and last 20 s of contraction time (Fig. 1); for one subject the first, middle, and last 15 s were analyzed because the contraction lasted only 45 s. To ensure discrimination accuracy, the interspike intervals (ISIs) of identified motor units were manually examined for every trial. Trials that contained abnormally long or short ISIs (force task: 29% of trials, position task: 47% of trials) were visually discriminated on a spike-by-spike basis. Mean discharge rate was determined from the ISIs using custom-designed software written in Matlab (The MathWorks, Natick, MA). The ISIs were detrended before determining the SD and CV for the discharge rate, and then converted to instantaneous frequencies. For each subject, discharge times that were <4 pps or >50 pps (1.6 ± 4.4% of discharges) were considered outliers as a result of discrimination error and were not included in subsequent analyses. The incidence of double discharges that were removed for this purpose was similar between the force and position tasks.
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) and might not reveal the presence of the slow modulation of the discharge rate around the frequency
. Rather, the analysis estimated the instantaneous discharge rate of the motor unit as the intensity of the point process (Brown et al. 2002
(t|Ht) measures the probability that a discharge occurs over the interval (t, t + dt) given the prior history Ht of the point process. The discharge rate of the motor unit was estimated with a kernel approach (Gerstner and Kistler 2002
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(t|Ht) was then quantified using spectral analysis based on the Welch method (Brillinger 2001Statistical analysis
The dependent variables for the motor output were the SDs of acceleration (position task) and detrended force (force task) in the vertical direction. The dependent variables for the motor unit discharge were the CV for motor unit discharge (CV = (SD/mean motor unit discharge) x 100). The statistical comparisons of the power spectra for motor unit discharge during the force and position tasks (absolute and % change), and for the SD of the force or acceleration (% total power) were performed with a 1-Hz resolution from 0.5 to 25.5 Hz (26 frequency bins). The dependent variables for the frequency modulation of motor unit discharge were the absolute power (s2), and total power (% change) for the motor unit discharge during the force and position tasks (spectrum from 0 to 26 Hz). The dependent variable for the frequency modulation of the SD for force or acceleration was the power from 0 to 26 Hz, expressed as a percentage of the total power from 0 to 100 Hz.
Two-factor ANOVAs [two tasks x three time points (start, middle, end)] with repeated measures on task and time were used to compare the CV for discharge rate, elbow force, absolute power for motor unit discharge rate, and the change in the SDs of acceleration and detrended force (SPSS version 11.5). A three-factor ANOVA (two tasks x two time points (start and end) x 26 frequency bins) with repeated measures on task, time, and frequency bin was used to compare the absolute power for the motor unit discharge rate and the % total power for the SD for force and acceleration. Two-factor ANOVAs (two tasks x 26 frequency bins) with repeated measures on task and frequency bin were performed at each time point (start, middle, and end) to compare the absolute power and power (% change) between tasks at the respective time points. Bivariate linear regression analyses examined the association between the CV for discharge and fluctuations in motor output (SDs of force or acceleration) and stepwise, multiple-regression analyses evaluated the contribution of each frequency bin from the motor unit discharge (26 frequency bins) to the CV for discharge and fluctuations in motor output for the two tasks. For these analyses, the 84 rows consisted of the 28 motor units at each of the three time points, whereas the columns consisted of the independent variables (26 columns for the power of the signal in 0 to 1-Hz frequency bins at each of the three time points) and the dependent variables (four columns for the SD of force or acceleration, and the CV for discharge rate for the force or position task at each of the three time points). Dependent t-tests were used to compare the MVC force before and after task performance.
When ANOVAs yielded significant interactions, post hoc comparisons (dependent t-tests or Bonferroni adjustment for multiple comparisons) were performed to locate differences between and within tasks at the appropriate time points. The alpha level for all statistical tests was 0.05, except for paired comparisons when the alpha level was adjusted with a Bonferroni correction, and for post hoc analyses, when values of P
0.11 were considered significant. Our criteria for post hoc comparisons were less strict for two reasons: First, the statistical power was much lower for paired t-tests compared with interactions among multiple levels. Second, even within a subject, there is a large amount of variability in the frequency that the peaks occur in the power spectrum. The 1-Hz-bin resolution used in this study for statistical comparisons may thus have significantly influenced the statistical power for post hoc comparisons across individual bins. Data are reported as means ± SD within the text and displayed as means ± SE in the figures.
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RESULTS |
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Despite the similarity in the forces exerted during the two tasks, there were differences in the rates of change in the fluctuations in motor output (force and acceleration). The SD for force and acceleration increased progressively during the two tasks (main effect for time P < 0.001; Fig. 3). The relative increase in the fluctuations in acceleration during the position task (90 ± 72% at task termination) was greater than that for the fluctuations in force during the force task (19 ± 41% at task termination, task x time interaction, P < 0.001).
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The CV for discharge rate was similar at the start (23.3 ± 7.9 and 21.8 ± 10.2%) and end (23.1 ± 8.1 and 26.5 ± 9.8%) of the force and position tasks, respectively (task x time interaction, P = 0.10), and did not change during either task (main effect time, P = 0.13). Nonetheless, there was a modest association between the CV for discharge rate and the absolute fluctuations (SD) in motor output (force or acceleration) across the three time points for both the force task (P = 0.001, r2 = 0.18) and the position task (P < 0.001, r2 = 0.31; Fig 4).
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The spectra for motor unit discharge rate were similar across time (start and end) for the force and position tasks [time main effect (P = 0.13), time x frequency (P = 0.74), task x time (P = 0.51), task x time x frequency (P = 0.08); Fig. 5; A and B], and were also similar when the ANOVA was performed at all three time points. However, a significant task x frequency interaction (P < 0.001) indicated that the frequency modulation differed between the force and position tasks when collapsed across all time points. Post hoc analyses indicated that 0 to 1- and 18 to 26-Hz frequencies had a trend toward being significantly different (P < 0.08). Because of a borderline task x time x frequency interaction (P = 0.08), the task x frequency interaction was examined independently at each point of time (start and end). There was a significant task x frequency interaction at the start (P = 0.005), but not at the end (P > 0.98) of the tasks. The differences at the start of the task were attributed to a significant difference at the 0 to 1-Hz frequency bin (P = 0.05; Fig. 5A).
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Power spectra of SD for force or acceleration
The spectra for motor output (SD for force or acceleration), expressed as a percentage of the total power from 0 to 100 Hz, were similar across time (start and end) for the force and position tasks [time main effect (P = 0.29), time x frequency (P = 0.24), task x time (P = 0.26), task x time x frequency (P = 0.34)], and were also similar when the ANOVA was performed at all three time points. However, a significant task x frequency interaction (P < 0.001) indicated that the frequency modulation differed between the force and position tasks when collapsed across all time points. Post hoc analyses indicated that the power was different at all 26 frequencies (P
0.01). Most of the power in the force spectra occurred at 03 Hz, whereas the majority of the power in the acceleration spectra occurred at 37 Hz.
Association between modulation of motor unit discharge and motor output
Although the CV for discharge rate was similar and did not change with time for the two tasks, different frequencies from the power spectra of the motor unit discharge predicted the CV for discharge rate during the force and position tasks. The best predictor of the CV for discharge rate during the force task (R2 = 0.72, P < 0.001; Fig. 6) was modulation of the motor unit discharge at 12 Hz (r = 0.17, P = 0.005), 23 Hz (r = 0.12, P = 0.05), 1213 Hz (r = 0.13, P = 0.03), and 1415 Hz (r = 0.20, P = 0.001). In contrast, the best predictor of the CV for discharge rate during the position task (R2 = 0.68, P < 0.001) was modulation of the motor unit discharge at 01 Hz (r = 0.22, P = 0.001) and 12 Hz (r = 0.23, P < 0.001).
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DISCUSSION |
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Relation between discharge rate variability and fluctuations in motor output
In agreement with other studies (Enoka et al. 2003
; Knight and Kamen 2004
; Komatz et al. 2005
; Laidlaw et al. 2000
; Moritz et al. 2005; Taylor et al. 2003
), the current results demonstrated a modest, but significant, association between the CV for discharge rate and the absolute fluctuations in motor output for both tasks. The CV for discharge rate, however, could not explain the greater rate of increase in the fluctuations in the motor output during the position task. Although the CV for discharge rate was greater when the subjects performed the position task, especially at the end of the task, this difference was not statistically significant. Furthermore, although this result contrasts with the findings of the previous study (Mottram et al. 2005
), the data differed for the two studies in two ways: first, four motor units used in the previous study were excluded as a result of insufficient discharges at the end of the task for performing spectral analyses. Second, the current study analyzed 20-s periods, whereas the previous study examined 20- to 30-s periods. Because the CV for discharge rate is highly sensitive to the addition or subtraction of even a few discharges (Christou et al. 2004
; Moritz et al. 2005), the discrepant findings between studies on the CV for discharge rate is not unexpected. Finally, despite the greater number of discharges included in the previous study, the task x time interaction for the CV for discharge rate barely reached significance (P = 0.035), whereas in the current study it did not reach significance (P = 0.10). This discrepancy underscores the sensitivity of each motor unit to the CV for discharge rate, and the observation that the CV for discharge rate of single motor units is not always related to the fluctuations in motor output.
Frequency modulation between tasks
Neither the CV for discharge rate nor the power spectra for motor unit discharge could explain the different rates of increase in the fluctuations in motor output for the two tasks. Rather, modulation of specific frequencies in the motor unit discharge was associated with both the variability in motor unit discharge rate and the fluctuations in motor output (Fig. 5C; Figs. 6 and 7). For example, modulation of motor unit discharge rate at 13, 1213, and 1415 Hz during the force task and 02 Hz during the position task predicted approximately 70% of the variance in discharge rate variability. Similarly, modulation of motor unit discharge rate at 56, 910, 1213, and 1415 Hz during the force task and 67, 1415, 1719, 2021, and 2324 Hz during the position task predicted approximately 50% of the variance in the fluctuations in motor output. The modulation (1-Hz resolution) occurred in both the positive and negative directions during the two tasks. The different direction of the correlation coefficients may indicate that an increase or a decrease in the power in a given frequency bin was associated with the CV for discharge rate or the fluctuations in motor output. This result likely underscores the difference in synaptic inputs to the motor neuron pools between the two tasks.
Correlational methods are often used to identify the modulation of motor unit discharge at common frequencies and thereby provide information about strategies used by the nervous system to perform various tasks (Hamm et al. 2001
; Myers et al. 2004
). At least two different methods have been used. One approach has been to perform a finite Fourier transform on the discrete discharge times of motor units (Brillinger 1978
; Rosenberg et al. 1989
) and to identify common frequencies in the discharge rates with a coherence analysis (Farmer et al. 1993
; Halliday et al. 1999
; Kilner et al. 2002
; Semmler et al. 2002
, 2004
). Significant peaks in a coherence spectrum can be identified, for example, as values exceeding the 95% confidence interval above the zero or mean level of coherence (Moritz et al. 2005a
; Rosenberg et al. 1989
). Results from these studies indicate that motor unit pairs often exhibit common modulation of discharge rate in the 1 to 12- and 16 to 32-Hz frequency bands.
Another approach is to analyze the interspike intervals derived from the motor unit discharge, which can be smoothed to produce a continuous signal before being compared with another continuous signal in either the time or the frequency domain (De Luca et al. 1982
; Kamen and De Luca 1992
; Vaillancourt et al. 2002
). One application of this approach is to perform a correlational analysis of the smoothed ISIs with the force exerted by the muscle in which the motor units are located. This type of analysis has consistently found that most of the power in the motor output and motor unit discharge spectra occur at low frequencies (03 Hz). Furthermore, a cross-correlation analysis on the ISIs for pairs of motor units has indicated that they share a common low-frequency modulation of discharge rate (De Luca and Erim, 1994
).
The current study performed an analysis on the ISIs to examine frequency modulation of motor unit discharge, as done previously (De Luca et al. 1982
; Vaillancourt et al. 2002
). In contrast to prior studies, the present investigation examined modulation at multiple frequencies without the constraint of matching frequencies in the motor unit discharge and the motor output. The results indicated that most of the power in the force spectrum occurred at 03 Hz, yet the fluctuations in force during the force task were associated with frequency modulation of motor unit discharge at 56, 910, 1213, and 1415 Hz. Similarly, most of the power in the acceleration spectrum during the position task occurred at 37 Hz, yet the fluctuations in acceleration were associated with frequency modulation of motor unit discharge at 67, 1415, 1719, 2021, and 2324 Hz. The strongest contributor to the force fluctuations was the modulation of motor unit discharge at 56 Hz (r = 0.43), whereas the dominant effects for the fluctuations in acceleration occurred at frequencies of 67 Hz (r = 0.38) and 1415 Hz (r = 0.47). Furthermore, the results indicated that there was a difference in frequency modulation of motor unit discharge at 01 Hz at the onset of the two tasks (Fig. 5A), and that the percentage change in the power from the start to the end differed between tasks (Fig. 5C).
Potential mechanisms for the difference in modulation of motor unit discharge
Because the same motor unit was monitored during both tasks, the differential frequency modulation of motor unit discharge for the two tasks likely involved differences in synaptic input to the motor neuron pool. The differences in low-frequency modulation (01 Hz) at the beginning of the task may reflect differences in a feature of the central command known as "common drive" (Christou et al. 2004
; De Luca et al. 1982
; Vaillancourt et al. 2002
). Common drive is proposed to arise from neural centers including the brain stem, and is considered a source of the low-frequency (12 Hz) oscillations that are manifested in the discharge rates of the concurrently active motor units. In addition, the increase in the fluctuations in acceleration during the position task was associated with modulation at higher bandwidths (1424 Hz) compared with the force task (915 Hz). It has been suggested that the neural commands contributing to coherence in motor unit discharge at these higher bandwidths (1632 Hz) are also centrally mediated (Farmer et al. 1993
; Mayston et al. 2001
). Nonetheless, there is evidence to suggest that muscle spindle afferents discharge at frequencies around 25 Hz during low-force contractions (Al-Falahe et al. 1990
; Vallbo 1981
), and the 25-Hz peak in the power spectrum during a position task performed with the index finger has been attributed to the spinal reflex loop (Sakamoto et al. 1992
). Because the activation of the muscle spindle is likely greater during the position task than the force task (Akazawa et al. 1983
; De Serres et al. 2002
; Hulliger 1993
; Kakuda et al. 1996
), it is possible that the enhanced contribution of motor unit discharge from 14 to 24 Hz to the fluctuations in motor output for the position task arises from enhanced afferent input (Farmer et al. 1993
).
In summary, modulation of motor unit discharge at different frequencies was able to predict both the CV for discharge rate and the fluctuations in motor output during the force and position tasks. The two tasks exhibited differences in low-frequency modulation (01 Hz) at the onset of the contraction and the greater rate of increase in the fluctuations in motor output during the position task was predicted by modulation at higher frequencies in motor unit discharge (position task: 67, 1415, 1719, 2021, and 2324 Hz; force task: 56, 910, 1213, and 1415 Hz). These differences indicate that the frequency modulation of discharge rate for the same motor units varied with the type of load supported during the submaximal isometric contractions.
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GRANTS |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Address for reprint requests and other correspondence: R. M. Enoka, Department of Integrative Physiology, University of Colorado, Boulder, CO 80309-0354 (E-mail: enoka{at}colorado.edu)
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