Motor-Unit Synchronization Increases EMG Amplitude and Decreases Force Steadiness of Simulated Contractions

Wanxiang Yao,1 Rew J. Fuglevand,2 and Roger M. Enoka1

 1Department of Kinesiology and Applied Physiology, University of Colorado, Boulder, Colorado 80309-0354; and  2Department of Physiology, University of Arizona, Tucson, Arizona 85721


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Yao, Wanxiang, Rew J. Fuglevand, and Roger M. Enoka. Motor-Unit Synchronization Increases EMG Amplitude and Decreases Force Steadiness of Simulated Contractions. J. Neurophysiol. 83: 441-452, 2000. The purpose of the study was to determine the effect of motor-unit synchronization on the surface electromyogram (EMG) and isometric force using a computer model of muscle contraction. The EMG and force were simulated by generating muscle fiber action potentials, defining motor-unit mechanical characteristics and territories, estimating motor-unit action potentials, specifying motor-unit discharge times, and imposing various levels of motor-unit synchronization. The output (EMG and force) was simulated at 11 levels of excitation, ranging from 5 to 100% of maximum. To synchronize motor-unit activity, selected motor-unit discharge times were adjusted; however, the number of motor units recruited and the average discharge rate of each unit was constant across synchronization conditions for a given level of excitation. Two levels of synchronization were imposed on the discharge times: a moderate and a high level, which approximated the experimentally observed range of motor-unit synchronization. The moderate level of synchrony caused the average EMG to increase by ~65%, whereas the high level caused a 130% increase in the EMG with respect to the no-synchrony condition. Neither synchrony condition influenced the magnitude of the average force. However, motor-unit synchronization did increase the amplitude of the fluctuations in the simulated force, especially at intermediate levels of excitation. In conclusion, motor-unit synchronization increased the amplitude of the average rectified EMG and decreased the steadiness of the force exerted by the muscle in simulated contractions.


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Descending, spinal, and peripheral excitatory inputs to spinal motor neurons diverge extensively to make synaptic connections across a large segment of a motor neuron population (Buys et al. 1986; Fetz and Cheney 1980; Kirkwood and Sears 1978; Mendell and Henneman 1971). Such branching of presynaptic fibers will provoke near simultaneous excitatory potentials in motor neurons and thereby slightly increase the probability that some motor neurons will be brought to action-potential threshold at nearly the same time (Sears and Stagg 1976). Consequently, when the timing of action potentials discharged by motor neurons is compared, there is often a significant coincidence in the relative timing of these events between many pairs of motor units (Datta and Stephens 1990; Nordstrom et al. 1992; Sears and Stagg 1976). The magnitude of this synchronized discharge among motor units is variable and is influenced by such factors as the task that is examined, the motor units and muscles involved in the task, and the type of habitual physical activity performed by the individual (Bremner et al. 1991; Huesler et al. 1998; Schmied et al. 1994, 1998; Semmler and Nordstrom 1995, 1998; Sturm et al. 1997).

Attempts to identify the functional significance of motor-unit synchronization have focused on comparing levels in different groups of subjects and on examining its effects on the output of the motor-unit pool. The level of synchronization appears to be reduced between motor units in the hand muscles of individuals who require greater independent control of the fingers. This includes musicians (Semmler and Nordstrom 1998) and the dominant hand of control subjects (Semmler and Nordstrom 1995), but not muscles in the dominant arm of control subjects (Schmied et al. 1994; Semmler and Nordstrom 1998). In contrast, population and pair-wise assessments of motor-unit synchronization suggest that it is greater among motor units in the hand muscles of individuals who consistently perform such gross motor activities as strength training (Milner-Brown et al. 1975; Semmler and Nordstrom 1998). One commonly cited interpretation of these findings is that an enhancement of motor-unit synchronization contributes to training-induced increases in muscle strength.

Several observations also suggest that synchronization increases the variance in the electromyogram (EMG) and force signals during steady-state contractions. These findings range from a comparison of the force evoked by distributed and synchronous activation of ventral root filaments in experimental animals (Rack and Westbury 1969) to an increase in the amplitude of the power density spectrum derived from simulated EMG signals (Weytjens and van Steenberghe 1984). Furthermore, motor-unit synchronization may contribute to the fluctuations observed in the EMG, acoustic myogram, and acceleration signals (tremor) recorded from the hand during sustained submaximal contractions (Halliday et al. 1999; McAuley et al. 1997). Others, however, have found no significant associations between tremor amplitude and the level of motor-unit synchronization (Semmler and Nordstrom 1998).

On the basis of these reports, it is apparent that some uncertainty remains concerning the functional significance of motor-unit synchronization. The purpose of the study was to determine the effect of motor-unit synchronization on the simulated EMG and force for a human hand muscle, such as the first dorsal interosseus, during isometric contractions. We found that moderate to high levels of synchronization increased the amplitude of the average EMG, but not the average force, and increased the fluctuations in the force signal at submaximal intensities. Preliminary results have been presented in abstract form (Yao et al. 1997, 1998).


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The study involved computer simulations that were based on models previously described in detail by Fuglevand and colleagues (Fuglevand et al. 1992, 1993), with the addition of a model that manipulated the relative timing of action potentials (synchrony) across the pool of motor neurons. In general, these models represent the activation of a motor neuron pool that produces motor-unit action potentials and forces consistent with the known physiological properties of a human hand muscle. The simulations involved three main steps: 1) determination of the recruitment and discharge times of a population of 120 motor neurons in response to different levels of excitatory drive, 2) prediction of the isometric muscle force based on the nonlinear relationship between discharge rate and force for single motor units; and 3) simulation of the surface EMG derived from estimates of the number and location of muscle fibers for each motor unit and the conduction velocity of the muscle fiber action potentials. The output of the simulation was a surface-detected EMG and the associated net force exerted during steady-state isometric contractions that ranged from minimal to maximal levels of muscle activation. The magnitudes of the EMG and force were compared across different synchrony conditions.

Activation of the motor neuron pool

The distributions of properties across the motor-unit pool were based on associations that have been established in testing the Size Principle (Binder and Mendell 1990; Henneman 1979). These included the distributions of net synaptic input, recruitment thresholds, the time course and magnitude of twitch forces, innervation ratios, and the sizes of motor-unit territories (the cross-sectional area of muscle containing the fibers of a unit), and conduction velocities of muscle fiber action potentials. In general, the motor neuron with the lowest recruitment threshold was associated with the longest duration and weakest twitch force, the lowest innervation ratio, the smallest motor-unit territory, and the slowest conduction velocity of muscle fiber action potentials.

RECRUITMENT. Input to the model was an excitatory drive function [E(t)] that represented the net synaptic input to motor neurons during a voluntary muscle contraction (Heckman and Binder 1991). For simplicity, it was assumed that the input was uniformly distributed across the pool such that all neurons received the same level of excitatory drive. The recruitment thresholds (RT) of the 120 motor neurons in the pool were determined from an exponential function that assigned many neurons to have relatively low thresholds and progressively fewer neurons to have higher thresholds (Fuglevand et al. 1993). The range of recruitment thresholds across the pool was set at 12-fold (Gustafsson and Pinter 1984; Powers and Binder 1985). The units of measurement for recruitment threshold and excitatory drive were arbitrary excitation units. A motor neuron was recruited when the excitatory drive >=  RT for the motor neuron.

MOTOR-UNIT DISCHARGE TIMES. Once a motor neuron was recruited, the discharge behavior of the neuron was defined by four parameters: its minimum and maximum discharge rates, the relationship between excitatory drive and discharge rate, and the variability of discharge rate.

The minimum rate at which motor neurons discharged action potentials repetitively was assumed to be 8 impulses/s (imp/s) for all motor neurons (Monster and Chan 1977). The maximum discharge rate, however, varied across the pool such that the low-threshold units achieved higher rates at maximum activation (De Luca et al. 1982; Monster and Chan 1977; Tanji and Kato 1973); the maximum rate of motor neuron 1 was 35 imp/s and for motor neuron 120 it was 25 imp/s. Various permutations of the maximum rates had a minor effect on the output (EMG and force) of the model (Fuglevand et al. 1993).

The rate at which each active motor neuron discharged action potentials was defined by a linear relationship (gain = g) between discharge rate and excitation level (Kernell 1965; Schwindt and Crill 1984). For our simulations, the discharge rate of active motor neurons increased by g = 1.0 imp · s-1/excitation unit. The discharge rate of a motor neuron (DRi) was determined for all excitatory drive values E(t>=  recruitment threshold (RTi) of the neuron as
<IT>DR</IT><SUB><IT>i</IT></SUB>(<IT>t</IT>)<IT>=</IT><IT>g</IT><IT>·</IT>[<IT>E</IT>(<IT>t</IT>)<IT>−</IT><IT>RT</IT><SUB><IT>i</IT></SUB>]<IT>+</IT><IT>DR</IT><SUB><IT>min</IT></SUB> (1)
where DRmin represents the minimum discharge rate.

If the excitatory drive exceeded that needed to raise the discharge of the neuron to its assigned maximum rate, the discharge rate remained at the assigned maximum level. Maximum excitation represented the amount of excitation driving motor neurons during a maximum voluntary isometric contraction. In the simulation, this denoted the level of excitatory drive required to bring the highest threshold motor neuron to its assigned maximum discharge rate. In these simulations, the highest threshold motor neuron was recruited at 41% maximum excitation.

The intervals between successive action potentials discharged by a motor neuron were characterized as a random process distributed with a Gaussian probability function (Andreassen and Rosenfalck 1978). These intervals were normally distributed about the predicted mean discharge interval with a coefficient of variation equal to 0.2 (Nordstrom et al. 1992). This variability was introduced into the timing of all action potentials discharged by each active motor neuron at the various levels of excitatory drive (Fuglevand et al. 1993). The minimum acceptable interval between successive action potentials was 20 ms. The random adjustments to the timing of action potentials were initially made independently for each motor neuron.

Motor-unit force

TWITCH. The time course of the twitch response of a motor unit was modeled as the impulse response of a critically damped second-order system (Milner-Brown et al. 1973a). The distribution of twitch force magnitudes across the pool of motor units was modeled as an increasing exponential function with the lowest threshold motor unit assigned to have the smallest force and the highest threshold unit to have the greatest force. The range of twitch forces was set at 100 (Milner-Brown et al. 1973c; Monster and Chan 1977; Stephens and Usherwood 1977).

The distribution of contraction times was based on experimental observations that show low-force units to have contraction times spanning most of the range of observed values, whereas the strongest units tend to have briefer contraction times (Burke 1981; Stephens and Usherwood 1977; Young and Mayer 1981; cf. Bigland-Ritchie et al. 1998). The relationship between twitch force and contraction time therefore was approximated as an inverse power function (Fuglevand et al. 1993). The contraction time for the lowest threshold, weakest motor unit was 90 ms, and for the highest threshold, strongest unit it was 29 ms.

FORCE-FREQUENCY RELATION. As outlined in Fuglevand et al. (1993), the nonlinear relationship between discharge rate and force was simulated by varying the impulse response magnitude as a function of the instantaneous discharge rate and contraction time of the motor unit. The general form of the relation between steady-state force and activation frequency was sigmoidal, but the specific shape varied depending on the contraction time of the unit. Motor units with longer duration contraction times required lower activation rates to attain half-maximal or maximal force compared with motor units with briefer contraction times. Muscle force was calculated as the sum of the forces exerted by the active motor units.

EMG simulation

A dipole representation of the transmembrane current was used to simulate individual muscle fiber action potentials in a three-dimensional muscle volume based on previously derived formulations (Andreassen and Rosenfalck 1981; Fuglevand et al. 1992). The model included the effects of anisotropic muscle conductance, innervation zone location, fiber length, electrode size, and electrode configuration. In these simulations, we used square electrodes (4 mm2) located over the surface of the muscle a few millimeters distal to the innervation zone.

MOTOR-UNIT TERRITORIES. The simulated muscle had a circular cross-section with a diameter of 15 mm. All muscle fibers were assumed to have the same diameter (56 µm), and the total number of fibers in the muscle was set at 71,747, compared with values of 40,500 for first dorsal interosseus and 10,200 for the first lumbrical (Feinstein et al. 1955). The number of fibers comprising a single motor unit was assumed to be directly proportional to the twitch force of the unit. The smallest motor unit innervated 28 fibers and the largest unit (motor unit 120) innervated 2,728 fibers. The fibers of a motor unit were assumed to be scattered over a broad region of the muscle cross-section and to intermingle with fibers belonging to many other units. The density of unit fibers within the territory of the motor unit was assumed to be 20 fibers/mm2. For simplicity, motor-unit territories were assumed to be circular and to be distributed randomly within the muscle (Fuglevand et al. 1992, 1993; Milner-Brown and Stein 1975).

MOTOR-UNIT ACTION POTENTIALS. The surface-recorded action potential for a motor unit was determined as the sum of the action potentials generated by the muscle fibers innervated by the motor neuron. The amplitude and duration of the muscle fiber action potentials varied as a function of the distance from the recording electrode (Fuglevand et al. 1992; Roeleveld et al. 1997). Additionally, the conduction velocity of muscle fiber action potentials was assumed to be inversely correlated with contraction time (Andreassen and Arendt-Nielsen 1987), with values ranging from 2.5 m/s for the unit with the longest contraction time (motor unit 1) to 5.5 m/s for the unit with the briefest contraction time (motor unit 120).

The computations to determine the motor-unit potentials were optimized by defining the cross-section of the muscle as a set of isopotential layers (Fuglevand et al. 1992). Each layer was 0.5 mm thick, and the muscle fibers of a motor unit in each layer presented a similar action potential (amplitude and duration) to the recording electrode. Consequently, only a single fiber potential was computed for each layer. The territory of each motor unit included parts of several isopotential layers. The number of motor-unit fibers within each isopotential layer was calculated from the product of the unit fiber density value and the area of the isopotential layer within the boundaries of the motor-unit territory. The muscle fiber potential corresponding to a particular layer was then scaled in amplitude by the number of motor-unit fibers within the layer. The motor-unit potential was subsequently computed as the sum of the isopotential-layer potentials.

The train of discharge times predicted from the motor neuron model determined the occurrence of each motor-unit action potential. The surface-recorded EMG for the whole muscle was simulated by summing the trains of action potentials generated by active motor units. The sum was then multiplied by a factor of 0.1 to estimate the attenuating effect of a 1.5-mm layer of relatively high-impedance tissue between the electrodes and muscle. This signal was then high-pass filtered (5 Hz) with a first-order digital filter to simulate the A-C coupling of bioamplifiers.

Motor-unit synchronization

To determine the effect of motor-unit synchronization on the simulated EMG-force relationship, the timing of the independently generated motor neuron action potentials was adjusted to impose a temporal association between some of the action potentials discharged by different motor neurons. The magnitude of the imposed synchronization was based on values reported in the literature; however, these values were derived from experiments that involved low-force contractions (<20% of maximum) and were assumed to remain valid for high-force contractions. The magnitude of motor-unit synchronization was assumed not to change as a function of excitation (Nordstrom et al. 1992) and to be distributed randomly over time contrary to the apparent clustering of synchrony that can occur between pairs of motor units (Dengler et al. 1984).

At each level of excitation, the action potentials chosen for a timing adjustment were selected randomly. For this purpose, each action potential was represented as an impulse with a duration of 1 ms (Fig. 1). The adjustments were performed such that every motor unit served as a reference unit to which other motor units had selected action potentials synchronized. A schematic diagram illustrating the process for motor unit 1 is shown in Fig. 1. The selection of the action potentials to be synchronized involved two steps: 1) the random selection of a proportion (e.g., 10%) of the action potentials discharged by the reference unit during the 10-s simulation, and 2) for each selected action potential of the reference motor unit, a proportion of the other active motor units (e.g., 10%) were randomly selected to have the timing of the nearest action potential adjusted so that it was coincident with the reference action potential. Figure 1 shows two action potentials (bolded impulses) discharged by motor unit 1 that were selected to be synchronized. For the first reference impulse, motor units 3, 4, 7, and 9 were then selected to have the timing of their closest impulse adjusted so that it was coincident with the bolded impulse; the arrows indicate the adjustments. For the second reference impulse, motor units 5, 6, 8, and 9 were selected for this adjustment.



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Fig. 1. Schematic diagram showing the scheme for adding synchrony to motor-unit activity. The action potentials (impulses) discharged by 10 of the motor units are shown. To establish some synchrony among the impulses, the timing of some impulses in randomly selected units was adjusted to coincide with randomly selected impulses of the reference unit. This process was repeated 120 times so that each unit in the pool served as the reference unit.

On the basis of the criteria derived from experimental measures of synchrony (described below), we used two levels of adjustments in the timing of the action potentials to represent moderate and high levels of synchrony. To effect a moderate level of synchrony, 10% of the impulses of each unit served as the reference impulse to which 10% of the other active units had impulses aligned. To produce a high level of synchrony, we used 15% of the impulses for the reference unit and 15% of the impulses discharged by other active units.

Two conditions were used in the alignment of the selected impulses: perfect synchrony and variable synchrony. The perfect-synchrony condition was achieved by aligning the selected impulses so that they were exactly coincident. The variable-synchrony condition was more physiological and involved the introduction of some variability into the adjustments so that the time separation between the synchronized impulses had a Gaussian distribution with a mean of 0 ms and a standard deviation (sigma ) of 1 or 2 ms.

Once the adjustments had been made for motor unit 1, the same process was repeated for motor unit 2, then motor unit 3, and so on, until all the active motor units were processed. When the adjustments were made for a specific motor unit, all other active motor units were candidates for the randomly selected adjustments; those previously adjusted were not excluded from subsequent reselection. Because of this recursive process, some impulses that were originally synchronized to one unit could subsequently be synchronized to a different unit.

Statistics

The outcome variables of the study were the mean and variability of the simulated EMG and force as a function of excitation. Because there was little variation for repeated simulations at each steady-state level in the calculated statistics for the relatively long-duration simulation, we report the results for one simulation trial only for each of the conditions. Average values for the rectified EMG were determined over the interval from 0.01 to 9.9 s at each level of excitation. The average values and the variability (standard deviation and coefficient of variation) of the force were determined over the interval from 1.0 to 9.9 s at each level of excitation. Power density spectra (Hamming window) were determined for the simulated EMG and force signals with a program written in MATLAB (Mathworks, Natick, MA). The block size for the fast Fourier transformation (FFT) was 2,048 points for the EMG and 1,024 points for the force, which yielded resolutions of 2.44 and 0.49 Hz, respectively. The blocks overlapped by one-half of block size, and the spectra were averaged across blocks for each trial. The mean values were subtracted from the simulated force records before performing the FFT so that the spectra would not be dominated by low-frequency signals.

The conventional procedure used to evaluate the degree of synchrony involves construction of cross-correlation histograms from the discharge times of pairs of motor units (Sears and Stagg 1976). The number of synchronized impulses in excess of that expected due to chance is computed from the peak in the cross-correlation histogram. This value is then normalized to some measure of baseline discharge rate, total number of impulses, or trial duration. For example, the common input strength (CIS) index of Nordstrom et al. (1992) normalizes the number of synchronous impulses to the trial duration. The CIS value therefore indicates the frequency of excess synchronous impulses for a pair of motor units. It is calculated as the number of counts in the peak (P) of the cross-correlation histogram above that expected due to chance divided by the duration (D) of the trial in seconds (Nordstrom et al. 1992); CIS = P/D. The expected number of synchronous impulses due to chance is estimated from the mean level of the histogram in the off-peak region.

Because synchrony was imposed randomly on selected motor units in the simulation, the CIS values for a few pairs of motor units may not be an accurate index of the overall synchrony within the population. However, it would not be practical to construct cross-correlation histograms and to calculate the CIS index for all combinations of motor units. Consequently, we devised a more economical method to appraise the level of synchrony across the population of active motor units. This involved dividing the entire simulation period into 1-ms bins and enumerating the number of impulses discharged by the active motor units in each bin. This distribution was used to generate a histogram that indicated the number of times one impulse, two impulses, three impulses, and so on, occurred within a 1-ms bin. The total number of coincident impulses (NCI) was then calculated from the histogram as
<IT>NCI</IT><IT>=</IT><LIM><OP>∑</OP><LL><IT>x</IT><IT>=2</IT></LL><UL><IT>N<SUB>u</SUB></IT></UL></LIM> <IT>n<SUB>x</SUB></IT><IT>·</IT><IT>c<SUB>x</SUB></IT>
where Nu was the number of active motor units, nx was the number of occurrences of x impulses, and cx was a weighting factor that represented the number of combinations of x impulses. The factor cx was computed from the binomial formula as
<IT>c<SUB>x</SUB></IT><IT>=</IT><FR><NU><IT>x</IT><IT>·</IT>(<IT>x</IT><IT>−1</IT>)</NU><DE><IT>2</IT></DE></FR>
The number of coincident impulses for a trial (NCI) was then compared with the number of coincident impulses computed from a histogram of independently active units (NCIindep), which was estimated from the Poisson distribution
<IT>n</IT>(<IT>x</IT>)<IT>=</IT><IT>N<SUB>B</SUB></IT><IT>·</IT><FENCE><FR><NU><IT>m<SUP>x</SUP></IT></NU><DE><IT>x</IT><IT>!</IT></DE></FR></FENCE><IT>·</IT><IT>e<SUP>−m</SUP></IT>
where n(x) is the expected number of occurrences of x impulses, NB is the total number of bins (trial duration/bin duration), and m is the mean number of impulses per bin (total number of impulses/NB). An index representing the degree of synchrony across the population of active motor units (i.e., the population synchrony index [PSI]) was calculated as
<IT>PSI</IT><IT>=</IT><FR><NU><IT>NCI</IT><IT>−</IT><IT>NCI</IT><SUB><IT>indep</IT></SUB></NU><DE><IT>NCI</IT><SUB><IT>indep</IT></SUB></DE></FR>
The population synchrony index (PSI) therefore provided a normalized value of the total number of coincident impulses for all active motor units in excess of that expected due to chance for independent activation of the units.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The output of the simulations comprised the surface-detected EMG and the whole-muscle force of the motor-unit pool in response to 11 steady-state levels of excitation: at 5% of maximum and then at 10-100% of maximum in 10% increments. The EMG was simulated at an effective rate of 5,000 samples/s and the force at 500 samples/s. The predictor variable was motor-unit synchronization. At each level of excitatory drive, the number of motor units recruited and the average discharge rate of each motor unit remained the same across the various synchronization conditions; these conditions ranged from zero synchronization to a high physiological level. Simply manipulating the timing of the action potentials discharged by the active motor units had a substantial influence on the output of the motor-unit pool. The principal effects are evident in Fig. 2, which shows the interference EMG, and the force during activation of the motor-unit pool for the zero and high-synchrony conditions (sigma  = 2 ms) at the 50% level of excitation. The slight asymmetry of the EMG signal about the isopotential level was a consequence of the proximity to the innervation zone (Fuglevand et al. 1992). Comparable EMG signals are often observed experimentally (Fig. 1 in Enoka et al. 1989; Fuglevand et al. 1993; Inbar et al. 1986). Motor-unit synchronization had a substantial effect on the amplitude of the EMG, but not the average force, although it did increase the amplitude of the force fluctuations.



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Fig. 2. Comparison of the output from simulations of the no- and high-synchrony conditions (sigma  = 2 ms). For each case, the level of excitation was the same (50% of maximum). The average rectified electromyogram (EMG) was 0.14 mV for the no-synchrony condition and 0.33 mV for the high-synchrony condition. The average force was 7,851 arbitrary units (au) for the no-synchrony condition and 7,892 for the high-synchrony condition. Adjusting the timing of the action potentials had a marked effect of the amplitude of the simulated EMG and little effect on the magnitude of the average simulated force.

Comparison of synchronization indices

Figure 3 compares the population synchrony index (PSI) with the common input strength (CIS) (Nordstrom et al. 1992) estimate of synchrony for two randomly selected pairs of motor units across three levels of synchronization (none, moderate, and high). These indexes were derived from a simulation in which 84 motor units were activated for a duration of 30 s. The trial was divided into 30,000 bins, each with a duration of 1 ms, and the number of impulses within each bin was counted. In the no-synchrony condition (Fig. 3A, left column), the total number of bins contained one, two, three, etc., impulses (bars) essentially identical to that predicted to occur due to chance from the Poisson distribution (open circle ). Approximately 11,000 of the 30,000 bins contained a single impulse, ~5,000 bins had 2 coincident impulses, and rarely were there cases in which >5 motor units discharged impulses synchronously. In the moderate-synchrony condition (Fig. 3A, middle column), the number of cases in which there was one or two impulses in each bin decreased with respect to that expected due to chance. Furthermore, there was an increase in the number of cases in which four or more motor units discharged synchronously. This shift in the distribution is reflected in a greater PSI, from near zero for the no-synchrony condition to 0.94 for the moderate-synchrony condition. In the high-synchrony condition (Fig. 3A, right column), there was a marked reduction in the number of cases with one or two impulses in each bin and a substantial increase in the number of cases in which five or more motor units discharged at the same time (see inset). There was about a twofold increase in the PSI from the moderate- to the high-synchrony condition.



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Fig. 3. Comparison of population and pair-wise estimates of synchrony for 3 levels of motor-unit synchronization. Each column represents a different level of synchrony applied to a simulation trial in which 84 motor units were active (20% of maximum excitation) for 30 s. Left column: data for the no-synchrony condition. Middle columns: data for a moderate-synchrony condition in which 10% of the action potentials discharged by each motor unit served as the reference event to which 10% of the other active motor units had their nearest action potential aligned with sigma  = 2 ms. Right column: data from a high-synchrony condition in which 15% of the action potentials were synchronized (sigma  = 2 ms) with 15% of the active other motor units. Top row of histograms shows the distribution of action potentials for the 3 synchrony conditions. Bars indicate the number of occurrences over the 30-s simulation in which there were different numbers of impulses in each 1-ms bin. Circles denote the predicted number of occurrences of action potentials due to chance, as calculated from a Poisson distribution. The population synchrony index (PSI) is shown for each condition. Inset for the high-synchrony condition shows on an expanded scale the number of occurrences in which 5 or more units discharged synchronously. Rows B and C represent cross-correlation histograms and associated cumulative sums (cusum) for 2 randomly selected pairs of motor units; motor units 12 and 18 for B, and 15 and 22 for C. Dashed vertical lines denote the limits of the synchronous peak as estimated from the cusum.

There was a good correspondence between the PSI values and common input strength (CIS) values calculated from the cross-correlation histograms for selected pairs of motor units. For example, the cross-correlation histograms for two pairs of units are shown in Fig. 3, B and C, for each of the synchrony conditions. Plotted above each histogram is the corresponding cumulative sum (cusum) (Ellaway 1978), which was used to identify the location of the peak in the cross-correlation histogram. For the moderate-synchrony condition, the CIS values were 1.02 and 0.94 extra synchronous impulses/second for the two pairs of units. The CIS values for these two pairs doubled (2.01 and 1.83 extra synchronous impulses/second, respectively) under the condition that imposed high synchrony. These CIS values were within the range of experimental values reported for motor units in the first dorsal interosseus muscle of humans (0-3.0 extra synchronous impulses/second) (Semmler et al. 1997). The widths of the synchronous peaks shown in Fig. 3 with sigma  = 2 ms ranged from 8 to 14 ms, which is similar to that reported by others (Schmied et al. 1994; Semmler et al. 1997). Therefore the amount of synchrony imposed in the current simulations was similar to that found experimentally.

Synchronization increased EMG amplitude

The effect of imposing synchronization on the trains of motor-unit action potentials was quantified from the average rectified EMG and the average force during the steady-state period of each simulation for the different levels of synchrony. The effects of two levels of synchronization are compared with the no-synchrony condition in Fig. 4. Synchronization had a negligible effect on the magnitude of the steady-state force, but it had a substantial effect on the amplitude of the average EMG. The average force achieved during all levels of excitation was not influenced by the presence of motor-unit synchronization or the variability (sigma ) in the imposed synchronization (Table 1). In contrast, the average EMG detected during maximum excitation was profoundly influenced by variation in the timing of the action potentials (Table 1). The presence of variability (sigma  = 1 and 2 ms) in the alignment of the synchronized impulses reduced the EMG amplitude compared with the no-variability condition (sigma  = 0 ms). For the most physiological simulation (sigma  = 2 ms), moderate synchrony increased EMG amplitude by ~65%, whereas the high-synchrony condition caused an increase of ~130% relative to the no-synchrony condition (Table 1).



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Fig. 4. Simulated relationship between the EMG and excitation (A) and between force and excitation (B) for the no-synchrony (), moderate-synchrony (black-down-triangle ), and high-synchrony () conditions. Variability was sigma  = 2 ms for the synchrony conditions. The presence of synchronization in the trains of action potentials discharged by motor units had a marked effect on the amplitude of the average, rectified EMG (A). In contrast, synchronization did not alter the average force as a function of excitation level (B).


                              
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Table 1. Average EMG and force for the maximum level of excitation of the three synchrony conditions without (sigma  = 0 ms) and with (sigma  = 1 and 2 ms) variability in the alignment of the impulses

Differences in the timing of the impulses had a marked influence on both the total power and the distribution of power in the EMG power spectra (Fig. 5). The total power in the spectra increased with the level of excitation and the amount of synchronization (Table 2). For example, the increase in total power at 100% excitation compared with 50% excitation for the two synchrony conditions averaged ~80%. Similarly, the total power at 100% excitation for the high-synchrony condition was 94% greater than that for the moderate-synchrony condition. The shift in the distribution of power was evident by a decrease in the median frequency and the location of the peak frequency for the two synchrony conditions (Table 2). This shift in power distribution to lower frequencies for the synchrony conditions presumably was caused by a decrease in the number of independent impulses and an increase in the superposition of constituent action potentials.



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Fig. 5. Power spectra derived from the simulated EMG (A-C) and force (D-F) with various degrees of imposed motor-unit synchronization. Top row (A and D) corresponds to spectra for the no-synchrony condition at 50% excitation, the middle row (B and E) indicates spectra for the high level of synchrony (sigma  = 2 ms) at 50% excitation, and the bottom row (C and F) was derived from the high level of synchrony (sigma  = 2 ms) at 100% excitation.


                              
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Table 2. Power spectra characteristics of the simulated EMG and force for the no-, moderate-, and high-synchrony conditions at 50 and 100% excitation

Synchronization decreased force steadiness

Although the presence of motor-unit synchronization did not influence the magnitude of the average force (Fig. 4), it did decrease the steadiness of the force signal (Fig. 2). This effect was quantified as the absolute (standard deviation) and normalized (coefficient of variation) fluctuations in the simulated force during steady-state excitation. As found experimentally with submaximal forces (Enoka et al. 2000; Galganski et al. 1993; Keen et al. 1994), the standard deviation increased and the coefficient of variation decreased as a function of excitation level for all conditions (Fig. 6). Furthermore, the magnitude of the force fluctuations, both the standard deviation and the coefficient of variation, increased with the level of synchrony. The effect of motor-unit synchronization on the coefficient of variation of the force fluctuations was greatest at the lower levels of excitation (Fig. 6B).



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Fig. 6. Fluctuations in the simulated force as a function of excitation level for the no-synchrony (), moderate-synchrony (black-down-triangle ), and high-synchrony () conditions. Variability was sigma  = 2 ms for the synchrony conditions. Fluctuations were quantified as the standard deviation (A) and the coefficient of variation (B) during the period of steady-state excitation.

The total power in the power density spectrum of the force signals increased with both the level of excitation and the level of synchronization (Figs. 2 and 5 and Table 2). For the high-synchrony condition, for example, the total power (0-250 Hz, with the average removed) increased from 633 to 979 au2 · Hz (a 55% increase) when excitation increased from 50 to 100% excitation (Fig. 5, F vs. E). The total power at 100% excitation for the high-synchrony condition was 424% greater than that for the no-synchrony condition (Fig. 5, F vs. D). Similarly, the magnitude of the peak power increased with both synchronization and excitation (Table 2), which indicates that the simulated force became more tremulous when the timing of the action potentials was adjusted and when there was an increase in the number of action potentials. For the moderate level of synchronization, peak power was greatest at intermediate levels of excitation (e.g., 50% excitation in Table 2). Despite these effects, the median frequency for the power spectra derived from the simulated forces was similar across all conditions (range: 4.9-9.8 Hz).


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The purpose of the study was to determine the effect of motor-unit synchronization on the surface EMG and the isometric force. Because of the difficulty associated with experimentally manipulating the timing of action potentials discharged by concurrently active motor neurons (however, cf. Guimaraes et al. 1994), we used a computer-simulation approach as a tractable means to evaluate the influence of synchronization on motor-unit output. With this approach, it was possible to assess the influence of specified amounts of synchrony on EMG and force without changing either the average discharge rate or the number of active motor units. An increase in the amount of motor-unit synchronization had three main effects: 1) an increase in the average rectified EMG; 2) a pronounced increase in the force fluctuations, but not the average force; and 3) an increase in the power in the low-frequency domains of the EMG power spectra.

The amount of synchronization used in the simulations was comparable to that observed experimentally. This was accomplished by randomly selecting 10 or 15% of the action potentials discharged by each motor unit and adjusting the timing of these action potentials to coincide with those discharged by 10 or 15% of the other active motor units. The timing adjustments were made so that the action potentials were either exactly coincident or had some degree of variability (sigma  = 1 or 2 ms). In initial simulations, we also used another alignment scheme in which motor units with similar recruitment thresholds were induced to have greater synchrony than motor units with disparate thresholds (Datta and Stephens 1990; Schmied et al. 1993, 1994). However, this scheme had similar effects on the simulated EMG and force to the random scheme described in this report (Yao et al. 1997, 1998).

The appropriateness of these imposed levels of synchronization was verified by computing measures of synchronization for the population and pairs of motor units. From calculations of the CIS index, it was apparent that the high level of synchronization was comparable to that observed experimentally, which meant that the simulated range included the physiologically relevant limits. The amount of synchronization typically measured experimentally between pairs of motor units falls around the moderate level of synchronization imposed in the simulation. Furthermore, the simulations indicated that a standard deviation (sigma ) of 2 ms when aligning synchronous impulses produced cross-correlation histograms that were similar to those observed experimentally (Nordstrom et al. 1992).

Increase in average EMG

The primary findings of the study were that motor-unit synchronization increased the magnitude of the average rectified EMG and the fluctuations (variability) in the simulated force, but not the average force. Although the number of action potentials discharged by the active motor units was similar across synchronization conditions at each level of excitation, the average EMG was substantially greater for the moderate- and high-synchrony conditions compared with the no-synchrony condition. At the maximum level of excitation, for example, the average EMG was 229% greater (sigma  = 0 ms) and 133% greater (sigma  = 2 ms) for the high-synchrony conditions. This effect can be explained by a reduction in the cancellation of the EMG signal that occurs when positive and negative phases of action potentials overlap (shaded regions in Fig. 7). With perfect synchrony (bottom panel in Fig. 7), there is little cancellation, and both the interference pattern and the average rectified EMG are larger. There were many more coincident impulses for the high-synchrony conditions (Fig. 3), which meant that for a given number of action-potential trains (a function of excitation level) there was less cancellation of the EMG signal.



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Fig. 7. Schematic diagram showing how synchrony can minimize cancellation in the surface EMG. Top panel: action potentials for 3 motor units in which the discharge times were determined randomly and independent of one another. A surface electrode detects the temporal sum (4th trace) of these action potential trains. Shaded areas indicated periods when the positive phase of one action potential overlaps in time with the negative phase of another leading to signal cancellation. Bottom panel: same motor units as in top panel with the timing of the action potentials synchronized. With complete synchronization, there is little cancellation.

This rationale suggests that some of the increase in EMG was due to a reduction in the cancellation due to overlapping positive and negative phases of action potentials. One outcome of this interpretation is that the intensity of multiunit neurophysiological signals (e.g., electromyogram, electroencephalogram, electroneurogram) depends not only on the number of units that are active and their discharge rates but also on the relative timing of the activity across the population. Consequently, some of the experimentally observed increases in EMG, such as those that occur during fatiguing contractions or as a consequence of physical activity interventions, may be partially explained by variation in the amount of cancellation associated with changes in the level of motor-unit synchronization.

As has been observed experimentally for isometric contractions (Matthews and Muir 1980), there was no peak around the tremor frequency (~10 Hz) in the power spectra derived from the simulated EMG. Rather, the peak power in the EMG spectra across the 11 levels of synchronization for the moderate- and high-synchrony conditions occurred in the range of 12-41 Hz. For the no-synchrony condition, the peak power in the EMG spectrum occurred in the range of 19-63 Hz. The median frequency across the 11 levels of excitation for the moderate- and high-synchrony conditions averaged 48 Hz (range: 44-51 Hz) compared with 76 Hz (61-85 Hz) for the no-synchrony condition. One prominent feature of the EMG spectra was the emergence of a peak at ~30 Hz for high levels of excitation (80-100%). For example, compare the distinct peak in the spectrum of Fig. 5C with that in Fig. 5B. The distinct peak was evident in the spectra for the two synchrony conditions at excitation levels >= 80%. A broader peak was present in the spectra for the no-synchrony condition at the two highest levels of excitation. This means that at high levels of excitation, the superimposition of the motor-unit action potentials produced a net shape that was dominated by a ~30-Hz modulation in the interference EMG.

Decrease in force steadiness

When a previously untrained individual performs a strength-training program, the short-term increase in strength appears to be mediated by neural mechanisms rather than by muscle hypertrophy (Semmler and Enoka 2000). One mechanism commonly identified as responsible for this adaptation is a training-induced increase in motor-unit synchronization. The basis for this suggestion can be traced to studies performed by Milner-Brown et al. (1973b, 1975) in which they found that the levels of synchronization among populations of motor units in a hand muscle increased after participation in a strength-training program. Similarly, Semmler and Nordstrom (1998) reported that the level of synchronization between pairs of motor units in the first dorsal interosseus muscle was greatest among weightlifters, less in untrained subjects, and least in musicians. Although these studies suggest that motor-unit synchronization may change with strength training, neither study provides evidence that an increase in synchronization by itself causes an increase in muscle force.

Indeed, when a large proportion of motor units comprising a muscle are stimulated synchronously at subtetanic rates, not only is the force profile less smooth but the average force may be less than that exerted when the motor units are activated asynchronously (Clamann and Schelhorn 1988; Rack and Westbury 1969). Although the mechanisms underlying this nonlinear attenuation in force have not been fully identified, it appears that such factors as series compliance and frictional interactions among muscle fibers must play a role (Clamann and Schelhorn 1988; Powers and Binder 1991; Troiani et al. 1999). Because nonlinear summation of force across motor units was not a feature of the present model, diminished muscle force with more synchronized activity was not produced in the simulations (e.g., Fig. 2). Nonetheless, the deficit in average force that is observed experimentally only occurs when at least 25% of the entire muscle fiber population is activated synchronously (Clamann and Schelhorn 1988). Otherwise, in less-synchronized and more natural conditions, such as those simulated in the present study, synchronous activity has little influence on average force.

The results of the simulations demonstrate that when the amount of motor-unit activity remains constant, the average force is not enhanced, at any level of excitation, by the inclusion of motor-unit synchronization in the activation scheme. The absence of an effect on the average force begs the question of why motor-unit synchronization might increase in muscles subjected to a strength-training stimulus. One possibility is that increased levels of synchronization may promote higher initial discharge rates by motor neurons during rapid contractions, which appear to enhance the rate of increase in force (van Cutsem et al. 1998).

When motor units discharge action potentials within the range commonly observed during voluntary contractions, the net force is not completely steady but exhibits some degree of variability (McAuley et al. 1997). Experimental studies have found that the amplitude of these force fluctuations (standard deviation) increases as a function of force (Enoka et al. 2000; Galganski et al. 1993; Keen et al. 1994). The simulations produced a similar effect (Fig. 6). Furthermore, the standard deviation of the force fluctuations was greater at most excitation levels (20-100%) for the high-synchrony condition. When the fluctuations were normalized to the average force (coefficient of variation), the fluctuations were greatest at low levels of excitation, as has been found experimentally, and were greater for the high-synchrony condition. The coefficient of variation had values of ~8% at the lowest level of excitation (Fig. 6), which is similar to the values measured for young (7%) and old (11%) adults when they exerted a force that was 5% of the maximum voluntary contraction force with the first dorsal interosseus muscle (Galganski et al. 1993). Similarly, the coefficient of variation had values that ranged from 2 to 5% at the highest level of excitation (Fig. 6), which was comparable to the values measured for young (3%) and old (4%) adults when they exerted a force that was 75% of the maximum voluntary contraction force with the first dorsal interosseus muscle (Enoka et al. 2000). Despite these similarities, the decline in the coefficient of variation as a function of excitation level for the simulated forces was not as monotonic as that observed experimentally. Nonetheless, these results suggest that motor-unit synchronization could contribute to a decline in steadiness, such as occurs in older adults.

The total power in the spectra derived from the force signals was influenced by the quantity of motor-unit activity (% excitation) and by the timing of the action potentials (level of synchronization). Of these two effects, the level of synchronization had the greater influence on the total power in a spectrum (Table 2), which means that increases in motor-unit synchronization accounted for more of the variance of the force signal. A prominent low-frequency (~3 Hz) peak in the power density spectrum derived from the simulated force exemplified this effect. These spectra were similar to those observed experimentally (Homberg et al. 1986; Matthews and Muir 1980). The one exception was the emergence of a peak in the force spectra at ~30 Hz at high levels of excitation (Fig. 5F). The appearance of this peak coincided with a similar peak in the EMG spectra and was more pronounced for the two synchrony conditions. However, there were no other peaks in the spectra for any level of excitation or synchronization, which suggests that the peaks observed at 10, 20, and 40 Hz in the EMG, acoustic myogram, and acceleration records of sustained contractions (McAuley et al. 1997) cannot be explained by short-term motor-unit synchronization.

In contrast, Halliday et al. (1999) estimated that motor-unit synchronization accounts for ~20% of the fluctuations in finger acceleration in the frequency ranges of 1-12 and 15-30 Hz during a postural trial. This conclusion was derived from a coherence analysis that was based on comparing the timing of motor-unit action potentials with the frequency spectra of surface EMG and acceleration. They observed peaks in the EMG spectrum at ~12 and 25 Hz, which were attributed to motor-unit synchronization. These results have been interpreted to indicate that rhythmic modulation of motor-unit synchronization in the frequency range of 15-30 Hz is related to rhythmic cortical activity (Farmer et al. 1993; Halliday et al. 1999). In the current simulations, however, the randomly distributed synchronization had a substantial effect on the power in the EMG spectrum in the 15- to 30-Hz frequency band but did not produce a peak in the 1- to 12-Hz range. These simulations suggest that low-frequency modulation of action potential timing may be a more significant contributor to the distribution of power in the EMG spectrum than modulation in the higher band.

In summary, the presence of synchronized activity among motor units during simulated isometric contractions substantially increased the amplitude of the average EMG, but not the average force, and caused pronounced fluctuations in the force of submaximal contractions.


    ACKNOWLEDGMENTS

We thank Dr. Sophie J. De Serres for assistance with data analysis and Dr. John G. Semmler for commenting on a draft of the manuscript.

This study was supported by National Institutes of Health Grants NS-20544 to R. M. Enoka and AR-42893 to A. J. Fuglevand.

Present address of W. Yao: Dept. of Health, Physical Education, Recreation and Coaching, University of Wisconsin, Whitewater, WI 53190.


    FOOTNOTES

Address reprint requests to R. M. Enoka.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 21 January 1999; accepted in final form 8 September 1999.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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