J Neurophysiol 99: 473– 483, 2008.
First published December 5, 2007; doi:10.1152/jn.00341.2007.
Coherent Motor Unit Rhythms in the 6 –10 Hz Range During
Time-Varying Voluntary Muscle Contractions: Neural Mechanism
and Relation to Rhythmical Motor Control
Sophia Erimaki1,2 and Constantinos N. Christakos1,2
1
Laboratory of Systems Physiology, Division of Basic Sciences, Medical School, University of Crete; and 2Computational Neuroscience
Group, Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, Heraklion, Crete, Greece
Submitted 27 March 2007; accepted in final form 3 December 2007
In a previous study (Erimaki and Christakos 1999), we
observed a tremor-like oscillation riding on top of the voluntary variations (ⱕ2 Hz) of the force produced by a human
finger muscle. This oscillation had its frequency in the range
6 –10 Hz and was accompanied by corresponding motor unit
(MU) firing synchrony. In parallel to the 6- to 10-Hz rhythmical synchrony, a slower synchrony of MU firing modulations
acted as the basis for the voluntary force variations.
Slow finger and wrist movements are also known to exhibit
a rhythmical component within the 6- to 10-Hz range (Kakuda
et al. 1999; Vallbo and Wessberg 1993). This component is
accompanied by corresponding coherent rhythms in the dis-
charges of the MUs (Kakuda et al. 1999) and the spindles
(Wessberg and Vallbo 1995) of the participating muscles. The
6- to 10-Hz movement component is believed to have a
supraspinal origin and to be a peripheral manifestation of
rhythmical motor control in humans (Farmer 1999; Vallbo and
Wessberg 1993).
More generally, 6- to 10-Hz coherent rhythms attributed to
network coupling at different supraspinal levels are thought to
be involved in rhythmical motor control (Evans and Baker
2003; Gross et al. 2002; McAuley and Marsden 2000;
McAuley et al. 1999; Pollok et al. 2005; Raethjen et al. 2004;
Welsh and Llinás 1997). The basis for such hypotheses has
often been the observation of weak 6- to 10-Hz coherence of
electromyograms (EMGs) to electroencephalograms (EEGs) or
magnetoencephalograms (MEGs)—i.e., coherence of synchronous MU firing rhythms to activities in cortical neuron populations. Notably, in other studies where such coherences were
uncommon, subcortical generators were assumed (Conway
et al. 1995; Marsden et al. 2001). Overall, however, there are
no specific demonstrations of the mechanism that generates the
basic rhythm in the postulated rhythmical control or of the way
such control is actually performed.
In the various hypotheses involving central generators, the
synchronous 6- to 10-Hz MU rhythms were clearly assumed to
manifest peripherally the postulated rhythmical control. However, there exist no systematic studies of this synchrony and its
dependencies, e.g., on movement parameters or, equivalently,
on the parameters of the muscle forces causing movements.
Yet, the question of the neural substrate of this synchrony is of
particular interest because it is directly related to the issue of
the generator and the functional relevance of the 6- to 10-Hz
rhythm.
Importantly, in steady muscle contractions, the 6- to 10-Hz
MU synchrony and tremor component seem to critically depend on the feedback from muscle spindles and to likely result
to some extent from rhythmical action in the spinal stretch
reflex loop (Christakos et al. 2006a). Analogously, the 6- to
10-Hz synchrony and force oscillation in time-varying contractions could also depend on spindle feedback.
In the present study, we systematically examined the above
questions for quasi-sinusoidal voluntary contractions of the
first dorsal interosseus (FDI) muscle of the hand, having wide
ranges of frequency and amplitude. We performed extensive
Address for reprint requests and other correspondence: C. N. Christakos,
Division of Basic Sciences, Medical School, University of Crete, 71003
Heraklion, Crete, Greece (E-mail: [email protected]).
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.
INTRODUCTION
www.jn.org
0022-3077/08 $8.00 Copyright © 2008 The American Physiological Society
473
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
Erimaki S, Christakos CN. Coherent motor unit rhythms in the
6 –10 Hz range during time-varying voluntary muscle contractions:
neural mechanism and relation to rhythmical motor control. J Neurophysiol 99: 473– 483, 2008. First published December 5, 2007;
doi:10.1152/jn.00341.2007. In quasi-sinusoidal (0.5–3.0 Hz) voluntary muscle contractions, we studied the 6- to 10-Hz motor unit (MU)
firing synchrony and muscle force oscillation with emphasis on their
neural substrate and relation to rhythmical motor control. Our analyses were performed on data from 121 contractions of a finger muscle
in 24 human subjects. They demonstrate that coherent 6- to 10-Hz
components of MU discharges coexist with carrier components and
coherent modulation components underlying the voluntary force variations. The 6- to 10-Hz synchrony has the frequency of the tremor
synchrony in steady contractions and is also widespread and in-phase.
Its strength ranges from very small to very large (MU/MU coherence
⬎0.50) among contractions; moreover, it is not related to the contraction parameters, in accord with the notion of a distinct 6- to 10-Hz
synaptic input to the MUs. Unlike the coherent MU modulations and
the voluntary force variations, the in-phase 6- to 10-Hz MU components are suppressed or even eliminated during ischemia, while the
respective force component is drastically reduced. These findings
agree with the widely assumed supraspinal origin of the MU modulations, but they also strongly suggest a key role for muscle spindle
feedback in the generation of the 6- to 10-Hz synaptic input. They
therefore provide important information for the study of generators of
the 6- to 10-Hz rhythm which subserves the postulated rhythmical
control and is manifested as force and movement components. Moreover, they argue for a participation of oscillating spinal stretch reflex
loops in the rhythm generation, possibly in interaction with supraspinal oscillators.
474
S. ERIMAKI AND C. N. CHRISTAKOS
analyses of the 6- to 10-Hz MU synchrony using a sensitive
and efficient technique (Christakos 1994, 1997), to study its
characteristics (extent, strength, and MU phases) and their
relation to the parameters of the voluntary contractions. We
also used ischemia tests to examine the involvement of muscle
spindle feedback in the generation of the particular rhythmical
synchrony and force oscillation. On the basis of our results, we
therefore considered possible underlying neural mechanisms,
also in relation to rhythmical motor control.
Preliminary reports have been presented in abstract form
(Christakos and Erimaki 2000; Christakos et al. 2006b; Papadimitriou et al. 2003).
METHODS
The experiments were conducted on 24 neurologically normal
volunteers (age 21– 48) who gave informed consent. Approval for this
study was obtained from the Ethics Committee of the University of
Crete Medical School.
In the recording sessions, the subjects assumed a comfortable
sitting position; their dominant hand and arm were secured on the
laboratory bench in front of a force transducer (WPI-Fort1000).
The subjects exerted nearly isometric abduction force on a
vertical plane with the lateral side of the horizontally extended
index finger by contracting the FDI muscle against the transducer.
The thumb and fingers 3–5 were constrained in flexion. Therefore
the force on the transducer in the direction of index abduction was
caused only by the FDI muscle because this is the sole agonist
(Stephens and Taylor 1972).
The subjects were instructed to have the FDI contraction force
follow a target curve displayed on the oscilloscope. This curve was a
sine wave (frequency between 0.5 and 3 Hz) around a horizontal line
representing a constant force level. Clearly, the subjects had continuous visual feedback of their actual force curve and, indirectly, their
mean force level. Wide ranges of values were used for the mean force
level [3–30% of maximal voluntary contraction (MVC); mean 15.4%,
SD 7.1%] and the relative amplitude of the voluntary force variations
(3– 42% of mean contraction level; mean 20.4%, SD 8.7%).
Simultaneous 2-min records were obtained of the muscle force and
the filtered (0.25–2.5 kHz) surface EMG (using Ag/AgCl disk electrodes) and intramuscular EMG (using bifilar nichrome wire electrodes, 40 ␮m) of the FDI muscle. The data were digitized at 5 kHz
and stored using the program LabView.
Discrimination of single-MU spike trains in the intramuscular
electrical activity, performed by a combination of a threshold operation and manual sorting, provided usually one and sometimes two
MUs per recording. Spike trains were represented as sequences of
zeroes and ones. All recorded signals, including the discrete sequences, were low-pass filtered at 250 Hz and resampled at 500 Hz for
analysis (Christakos et al. 1984). The filtering was digital and introduced no time shifts.
Ischemia
Ischemia of the arm was used to examine the possible involvement
of the feedback from muscle spindles in the generation of the 6- to
10-Hz MU synchrony and muscle force oscillation. During ischemia,
a decline, or even practical interruption, of such feedback is known to
occur and is related to one or both of the following.
1) A suppression of the force oscillation, in association with an
increase in interstitial potassium concentration (Lakie et al. 2004), or,
equivalently, a suppression of the impact of the internal-length input
on muscle spindle discharges (see Fig. 4 of Matthews and Stein 1969).
J Neurophysiol • VOL
Data analysis
Analyses were performed in both the frequency and the time
domains using MATLAB (The MathWorks, Natick, MA). The analysis methods, including those regarding measurement of the MU
synchrony, are briefly presented here, but were previously described
in more detail (Christakos 1997; Christakos et al. 2006a).
Frequency-domain analysis, performed via the Fast Fourier transform on pairs of recorded activities, included (Wang et al. 2004):
1) segmentation of the 2-min time series into 60, 2-s-long segments;
2) mean removal and windowing (Hanning) for each data segment;
3) computation of the auto-spectra and the cross-spectrum from each
segment; and 4) final estimation of the auto-spectra and the crossspectrum of the activity pair by averaging the estimates from the
individual segments. The coherence spectrum was subsequently estimated as the squared modulus of the cross-spectrum divided by the
product of the individual auto-spectra.
Amplitudes of the voluntary variations and the 6- to 10-Hz oscillations of the force in the different contractions were estimated as the
square root of the total power (integral) within the frequency bands of
the corresponding auto-spectral deflections. For each contraction,
these values were subsequently presented as a percentage of mean
contraction level.
Time-domain analysis consisted of cross-correlation computations
for pairs of activities over the 2-min time records.
In the study of the synchrony of both the MU modulations and the
6- to 10-Hz MU rhythms, we used a combination of unit-to-aggregate
(UTA) coherence and cross-correlation analyses (Christakos 1994,
1997; Christakos and Giatroudaki 1998; Christakos et al. 2006a; see
also Christakos et al. 1994; Iyer et al. 1994, where certain principles
of this technique were used). The unitary signal was MU activity and
the aggregate signal was the muscle force waveform (or the rectified
surface EMG).
Specifically, UTA coherence computations on a sample of pairs of
simultaneously recorded MU/force activities were used for: 1) identification of correlated MUs, given that a significant such coherence
indicates the presence of a correlated subset to which the given unit
belongs; 2) estimation of the extent of the MU synchrony (proportion
of the correlated units within the active population) as the fraction of
nonzero coherences in the sample; 3) obtaining information on the
strength of the synchrony and its distribution within the population;
moreover, 4), MU/force cross-correlation computations for the coherent MUs in the sample were used for estimation of phases of the MUs
in terms of delays of the MUs relative to the force signal (common
reference signal). It is noteworthy that such cross-correlograms represent spike-triggered averages with the spikes at zero delay. They
thus provide straightforward information on the time relation between
MU spikes and muscle force signals, even when the MU/force
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
Experiments
2) A reduction in spindle sensitivity (Matthews 1933; see also
Burne et al. 1984; Lippold 1970) and/or a partial blockade of the
conduction of spindle output via group Ia afferents (Cody et al. 1987;
Cresswell and Loescher 2000; Fellows et al. 1993; Haque and Burne
2003).
Such effects limiting spindle feedback are present after an interval
ranging from a few to about 10 min after ischemia onset.
Our ischemia experiments were therefore conducted as follows: A
sphygmomanometer cuff applied to the upper arm was inflated to 200
mmHg. The subjects had paresthesias immediately after inflation of
the cuff. Within the next 5 min they reported increasing numbness,
which was verified using the two-point discrimination test. After
about 8 min, they showed complete loss of touch and deep sensation
for the hand and forearm. Thus the recordings usually started after 10
min from initiation of the ischemia procedure and lasted 2 min.
However, in certain cases, the start of the recordings was 5– 8 min
after ischemia onset because the subjects reported some discomfort. In
all recording periods, no pain was reported by the subjects.
6- TO 10-Hz SYNCHRONY IN TIME-VARYING MUSCLE CONTRACTIONS
Statistical tests
All data were analyzed using the SPSS v12.0 statistical package.
Estimates of the Spearman rank-order correlation coefficient were
used to examine possible relationships between such variables as
mean level of contraction, frequency and amplitude of voluntary force
variations, and 6- to 10-Hz MU/force coherence. The independentsamples t-test was used to compare the frequencies of the 6- to 10-Hz
force oscillation in time-varying contractions and the tremor of steady
contractions. Finally, to compare the conditions in the ischemia tests
and to assess the effects of ischemia on the 6- to 10-Hz MU synchrony
and force oscillation, Friedman ANOVA by ranks was used for
multiple within-subjects comparisons (preischemia, ischemia, and
postischemia). All tests were performed at the P ⬍ 0.05 level.
RESULTS
In agreement with previous observations (Erimaki and
Christakos 1999; Iyer et al. 1994), under conditions of quasisinusoidally varying voluntary muscle force (0.5- to 3.0-Hz
range), the force auto-spectrum displayed a dominant component at the frequency of the voluntary force variations. In all
121 contractions studied, the auto-spectra of MU activities
J Neurophysiol • VOL
exhibited a corresponding component, indicative of the presence of MU firing modulations. These modulations were correlated to the force variations and among themselves, as was
indicated by corresponding components in the MU/force coherence spectra (METHODS).
In the example of Fig. 1, for a quasi-sinusoidal muscle
contraction at 2 Hz (middle column), a large and sharp peak is
seen at this frequency in the force auto-spectrum (left vertical
dotted line). The corresponding peak in the MU1 auto-spectrum represents the modulation component of the MU’s discharge. This component is coherent to the 2-Hz force variations (MU1/force coherence ⫽ 0.61) and thus to the modulation components of other MUs (METHODS). The component at 6
Hz (arrow) represents the carrier of the modulated discharge of
MU1, where the carrier rate equals the intrinsic firing rate of a
unit for a steady contraction at the same force level (Iyer et al.
1994).
In the example of Fig. 2, for a second, simultaneously
recorded unit (MU2), a modulation component is again seen at
2 Hz, showing coherence to the respective force (0.75) and
MU1 component (0.44; left vertical dotted line). In this case
the carrier rate of the unit is 11 Hz (arrow), i.e., MU2 is smaller
than MU1 (Milner-Brown et al. 1973).
These MU firing patterns consisting of carrier and coherent
modulation components were typical of our sample of 133
randomly selected MUs during the time-varying contractions
of the 24 subjects of this study. The estimated MU/force
coherence at the modulation frequency varied from contraction
to contraction. This is seen in Fig. 3, where data of mean and
SD of this coherence in the different contractions, grouped
according to the frequency of the voluntary force variations,
are presented. Notably, statistical analysis did not reveal a
relationship between the particular frequency and the corresponding MU/force coherence (Spearman rank-correlation
coefficient ⫽ 0.05, P ⬎ 0.50).
Over the entire sample, such coherences were generally high
(range 0.13– 0.97; mean 0.70, SD 0.18). Accordingly, a widespread and strong synchrony of modulated MU discharges
underlies the generation of time-varying muscle force. Detailed
examination of other characteristics of the MU modulation
synchrony in sinusoidal contractions has been performed in our
previous studies (Erimaki and Christakos 1999; Iyer et al.
1994). Here the analysis is restricted to MU firing patterns in
time-varying contractions because they provide a necessary
basis for studying the 6- to 10-Hz MU rhythms and synchrony
that constitute the main focus of the present investigation.
6- to 10-Hz oscillation and synchrony in quasi-sinusoidal
muscle contractions
One characteristic feature of the 0.5- to 3.0-Hz quasi-sinusoidal contractions was the presence of a more or less clear
superimposed oscillation on the voluntary variations of the
muscle force. This force oscillation had its frequency in the 6to 10-Hz range and was accompanied by corresponding
rhythms in MU activities, which were coherent to it and thus to
one another (METHODS). This 6- to 10-Hz synchrony was identified as significant MU/force coherence(s) per contraction or
was at least detected as significant EMG/force coherence
(METHODS).
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
coherence is too low for reliable phase estimation from the
cross-spectrum.
Compared with traditional MU/MU analysis, this technique requires a much smaller sample of easily recorded activity pairs, it
shows higher sensitivity in detecting synchrony, and it provides
information in a compact form (Christakos 1994). Moreover, the use
of a reference signal (muscle force) enables one to estimate the
individual MU phases, compared with the MU phase differences that
are provided by MU/MU analyses. Overall, this technique of analysis
of population synchrony is thus both sensitive and efficient.
For the 60 segments used in the spectral analyses, and for the
smooth data tapering used for leakage suppression, the threshold for
a significant coherence at the 99% confidence level is about 0.08
(Rosenberg et al. 1989; Wang et al. 2004).
In the contractions where the 6- to 10-Hz MU/force coherence(s)
was(were) not statistically significant by this criterion, we performed
additional computations of coherence between the rectified EMG and
the muscle force signal. This is an aggregate-to-aggregate (ATA)
coherence and is widely used in the analysis of neural population
synchrony (e.g., Grosse et al. 2002), including sometimes assessment
of the strength of such synchrony. In our study, we used the EMG/
force coherence only for detection of synchrony and determination of
its frequency, by taking advantage of properties that make it much
higher than the MU/MU and the MU/force coherence.
Specifically, for a large extent of population synchrony and high
concentration of units’ phases, the ATA coherence has large values
and represents a great overestimation of the true UTU and UTA
coherences (Christakos 1997). Examples of such overestimation have
been presented in various experimental studies (e.g., Christakos et al.
1994, 2006a; Hamm et al. 1999). One example can also be seen in our
Fig. 4, as the 6- to 10-Hz MU synchrony was found to be both
widespread and in phase (RESULTS). In addition, the ATA coherence
may exhibit saturation effects, particularly in cases where the UTU
coherence is not very low.
Consequently, ATA coherence analysis can provide an easy and
sensitive means of detection of population synchrony, but needs to be
used with great caution in assessing the strength of such synchrony.
Therefore in all cases where the 6- to 10-Hz MU/force coherence was
not statistically significant with 99% confidence, whereas the EMG/
force coherence was significant, the synchrony was considered present
but minimal, with a very limited influence on the corresponding force
oscillation (Christakos et al. 2006a).
475
476
S. ERIMAKI AND C. N. CHRISTAKOS
Rel. Power
MU1
MU1/Force record
MU1/Force correlogram
1s
Raw force
0.05
40
Force
Abs. Power
Auto-spectrum
0.006
3%
MVC
5%MVC
0
-0.05
High-pass
filtered force
0.1
Coherence
MU1/Force
1%
MVC
5%MVC
-0.1
-500
0
20
0
500
40
Frequency (Hz)
FIG. 1. Involuntary force oscillation and synchrony in a time-varying voluntary muscle contraction (subject 4). Left column: auto-spectra and coherence
spectrum of simultaneously recorded motor unit (MU1) spike activity and muscle force signal, during a quasi-sinusoidal contraction at 2 Hz and around 5%
maximal voluntary contraction (MVC). Note in the force auto-spectrum the dominant component at 2 Hz (left vertical dotted line) and the local peak at 6 Hz
(right vertical dotted line and figure insert), which represents a superimposed involuntary oscillation. Also note in the MU1 auto-spectrum corresponding
components at 2 Hz (modulation component) and 6 Hz (which is also the unit’s carrier rate, arrow). Finally, note in the MU1/force coherence spectrum the
components at 2 and 6 Hz, which indicate the presence of synchrony within the population of active MUs at both frequencies (the horizontal dotted line represents
the coherence significance threshold). Middle column: time records of the raw and high-pass-filtered (4-Hz cutoff) force signal shown together with the MU1
spikes. The records show parallel 2-Hz variations in the force signal and the MU1 firing rate, and also a tendency for the MU1 spikes to occur rhythmically at
the minima of the 6-Hz force oscillation. Right column: corresponding normalized MU1/force cross-correlograms. Both cross-correlograms show a 6-Hz
oscillation, whereas the one for the high-pass-filtered force signal also verifies the locking of the MU1 spikes to the minima of the 6-Hz force oscillation.
In the example of Fig. 1, the time records of the raw and
high-pass-filtered (4-Hz cutoff) force signal in the middle
column show a superimposed oscillation at 6 Hz. In the left
column, this oscillation is represented by a local peak in the
force auto-spectrum (right vertical dotted line and figure insert). According to the time records, most of the spikes of the
simultaneously recorded MU1 tend to occur rhythmically at, or
near, the local minima of the 6-Hz force oscillation, in a
one-to-one relation on average. This is represented by the 6-Hz
component in the MU1 auto-spectrum (left column) obtained
from the entire 2-min time series. A corresponding large
component is also evident in the MU1/force coherence spectrum (0.60), indicating the presence of a correlated subset of
MUs at 6 Hz, to which MU1 belongs (METHODS). Finally, the
apparent locking of the spikes of MU1 to the minima of the
6-Hz force oscillation is verified by the central trough at zero
lag in the oscillatory MU1/force cross-correlogram (right column, bottom) obtained from the 2-min time series. It should be
noted that in this case the coherent rhythm in the firing of MU1
coincides with the carrier of the MU’s modulated discharge.
In the example of Fig. 2, the auto-spectrum of the concurrently active MU2 also reveals the presence of a 6-Hz component (right dotted line), which coexists with the 11-Hz carrier
component of the unit (arrow). As the high MU2/force coherence (0.61) indicates, this 6-Hz component is correlated to the
6-Hz force oscillation and thus to the corresponding compoJ Neurophysiol • VOL
nents of other MUs (METHODS). This is verified by the 0.37
MU1/MU2 coherence at 6 Hz. It is worth noting that even
though the carrier rate of MU2 (11 Hz) is higher than the
frequency of the fast force oscillation (6 Hz), the time
record of the high-pass-filtered force and the corresponding
MU/force cross-correlogram (not shown) again revealed
that some MU2 spikes tended to occur rhythmically near the
local minima of the 6-Hz oscillation, whereas the remaining
spikes were interspersed. This explains the observed MU2/
force coherence at 6 Hz.
Overall, a 6- to 10-Hz MU component showing coherence to
the muscle force, such as in Figs. 1 and 2, characterized MU
firing in the 121 time-varying contractions studied in the 24
subjects. The observed frequency (Hz) of synchrony had a
mean value of 7.8 and SD 1.1.
The MU/force coherence was reliably identified with 99%
confidence (value ⱖ0.08) in 106 of the 121 contractions. In
these contractions, a locking of spikes to the local minima of
the 6- to 10-Hz oscillation was indicated by MU/force crosscorrelation analysis.
Interestingly, for all 117 MUs recorded in the 106 contractions, the MU carrier rates were higher than, or equal to, the
frequency of synchrony (observed range 6.0 –19.5 Hz; mean
11.7, SD 2.5). In other words, among the randomly selected
MUs in this sample, there existed last-recruited, relatively large
ones that fired at (11%), or just above, the frequency of
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
0
1
6- TO 10-Hz SYNCHRONY IN TIME-VARYING MUSCLE CONTRACTIONS
1
MU/Force
Coherence
1
1s
18%
MVC
1
EMG/Force
0
20
40
Raw force
12%
MVC
High-pass
filtered force
18%
MVC
0.5%
MVC
Frequency (Hz)
1
MU1/MU2
0
20
40
Frequency (Hz)
FIG. 2. Analyses for a second, simultaneously recorded unit (MU2) in the
contraction of Fig. 1. Top to bottom: MU2 auto-spectrum, MU2/force coherence spectrum, and MU1/MU2 coherence spectrum. Note in the auto-spectrum
the modulation component at 2 Hz (left vertical dotted line), the component at
the frequency of the involuntary oscillation (6 Hz, right vertical dotted line),
and the MU2 carrier component at 11 Hz (arrow). Also note in the MU2/force
coherence spectrum the components at 2 and 6 Hz, indicating the presence of
MU synchrony at both frequencies. This is verified by the components at 2 and
6 Hz in the MU1/MU2 coherence spectrum.
synchrony (e.g., Fig. 1), whereas smaller MUs fired at higher
rates (e.g., Fig. 2).
In the remaining 15 contractions, EMG/force coherence
analysis (METHODS) revealed the presence of 6- to 10-Hz synchrony (mean frequency 8.0 Hz, SD 0.79 Hz) that was too
weak to be reliably identified as significant MU/force coherence. In the example of Fig. 4, the MU/force coherence shows
both a large peak (0.81) at the modulation frequency, 0.5 Hz,
and a very small (0.07) but distinct peak at 6.5 Hz (right dotted
MU/Force Coherence
1
0
1
1.5
2
2.5
3
Modulation frequency (Hz)
FIG. 3. Distribution of MU/force coherence values in the 0.5- to 3.0-Hz
range, for the total of 133 recorded MUs. These values are grouped according
to the frequency of the voluntary force variations. Bars represent mean ⫾ SD.
Note the great variability of the MU synchrony at the modulation frequency
from contraction to contraction.
J Neurophysiol • VOL
FIG. 4. Minimal 6- to 10-Hz synchrony in a time-varying voluntary muscle
contraction (subject 3). Left column: MU/force and EMG/force coherence
estimates for simultaneously recorded motor unit (MU) spike activity, EMG,
and muscle force signal, during a quasi-sinusoidal contraction at 0.5 Hz and
around 18% MVC. Note in the MU/force coherence spectrum (top) the large
component at 0.5 Hz (left vertical dotted line). Also note the small peak at 6.5
Hz (right vertical dotted line), which is below the significance threshold. In
contrast, the EMG/force coherence spectrum (bottom) shows a large peak at
6.5 Hz, which gives an overestimated picture of the true MU synchrony at that
frequency. Right column: time records of the raw and high-pass-filtered (4-Hz
cutoff) force signal shown together with the MU spikes. Note the parallel
0.5-Hz variations in the force signal and the MU firing rate. Also note the small
6.5-Hz oscillation and the apparently random occurrence of the MU spikes
relative to it.
line). The latter was the frequency of the 6- to 10-Hz synchrony in the particular contraction, as is indicated by the
corresponding clear peak (0.54) at 6.5 Hz in the EMG/force
coherence spectrum. Such contractions were observed in 6 of
the 24 subjects who, however, showed significant MU/force
coherence in other contractions irrespective of conditions.
Finally and importantly, the 6- to 10-Hz synchrony for each
of the 24 subjects had the frequency (Hz) of the subject’s
tremor synchrony in steady contractions, as this frequency was
estimated in a preceding study (Christakos et al. 2006a) (mean
7.8 vs. 7.6, SD 1.1 vs. 1.1; t ⫽ ⫺1.211; P ⬎ 0.20).
Characteristics of the 6- to 10-Hz MU firing synchrony
As described earlier, in 106 of the 121 muscle contractions
of this study, significant 6- to 10-Hz coherence to the force was
exhibited by all 117 analyzed MUs, including 11 pairs of
simultaneously recorded units. This is a very high incidence
(88%), considering the strict criterion of 99% confidence, and
reveals a large extent of the particular synchrony within the
active MU population. It should be stressed that in the remaining 15 contractions that showed minimal such synchrony, all
16 analyzed MUs, including one pair, did exhibit small coherence peaks at the frequency of the synchrony (e.g., Fig. 4).
These coherences were in the range 0.05– 0.07 and were
therefore significant by the usually assumed 95% confidence
criterion (0.04 in the case of 60 segments).
Accordingly, since there was practically no exception in
the entire sample of 133 randomly selected MUs regarding
the presence of coherence to the force, it can be concluded
that the 6- to 10-Hz MU synchrony was widespread in the
time-varying contractions of this study.
In what follows the analyses are performed on the sample of
117 MUs for which the coherence to the force was ⱖ0.08
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
Coherence
MU2/Force
0.5
MU/Force record
MU2
Rel. Power
Auto-spectrum
0.006
477
478
S. ERIMAKI AND C. N. CHRISTAKOS
1
Frequency of synchrony
7-8 Hz
8-9 Hz
9-10 Hz
MU/Force Coherence
6-7 Hz
0
1
5
10
15
20
Subject #
FIG. 5. Distribution of significant MU/force coherence values in the 6- to
10-Hz range according to subject and frequency of the involuntary force
oscillation. The data were obtained from 117 MUs showing significant synchrony in the preceding frequency range. Bars represent mean ⫾ SD. Note the
great variability of the 6- to 10-Hz MU synchrony across subjects and
contractions.
J Neurophysiol • VOL
⫺0.137; P ⬎ 0.15); 2) the amplitude of the voluntary force
variations (Spearman rank-correlation coefficient ⫺0.05; P ⬎
0.60); 3) the frequency of the latter (Spearman rank-correlation
coefficient 0.025; P ⬎ 0.80); and 4) the product of amplitude
and frequency, representing the contraction speed (Spearman
rank-correlation coefficient 0.028; P ⬎ 0.50).
Finally, in all 117 cases, MU/force cross-correlation analysis
revealed a clear tendency for some MU spikes to occur rhythmically near the local minima of the 6- to 10-Hz oscillation
(mean delay 2.79 ms, 95% confidence interval 2.32–3.26 ms).
This was the case irrespective of the MUs’ carrier rates. Thus
the MUs had in-phase components at the frequency of the 6- to
10-Hz oscillation, which coexisted with the components at the
MU intrinsic carrier rates and those at the modulation frequency.
Therefore the strength of the widespread, in-phase, and
uniform 6- to 10-Hz synchrony can be estimated in terms of
MU/MU coherences by squaring the estimates of the respective
MU/force coherences (Christakos 1997). Thus the MU/MU
coherences are found to be in the range 0.0064 – 0.61, i.e., the
strength of the 6- to 10-Hz synchrony in the time-varying
contractions ranged from very small to very large, as it did in
the steady contractions of the same subjects in our preceding
study (Christakos et al. 2006a).
It is worth noting that the values of the MU1/force, MU2/
force, and MU1/MU2 coherences in Figs. 1 and 2 verify this
square relationship, and this was also the case for the other 10
pairs of simultaneous MUs. It is also noteworthy that, according to this relationship: 1) the MU/force coherence is much
higher than the MU/MU coherence, and thus facilitates the
identification of correlated MUs; and 2) in the 15 contractions
with MU/force coherences ⬍0.08, the MU/MU coherences
were ⬍0.0064, i.e., the synchrony detected by EMG/force
analysis was indeed minimal.
Effects of ischemia on the 6- to 10-Hz synchrony
and force oscillation
Ischemia of the arm was used as a means of blocking muscle
spindle feedback (METHODS) during 16 sinusoidal contractions
of the FDI muscle in eight of our subjects.
The general, clear effect of ischemia was the suppression,
even close to elimination, of the 6- to 10-Hz MU components
and synchrony. This effect was accompanied by a drastic
reduction of the amplitude of the corresponding force oscillation. Furthermore, removal of the occlusion reinstated the
coherent MU rhythms and the initial oscillation.
In the example of Fig. 6 (left column), for a 0.5-Hz muscle
contraction, the force and MU auto-spectra initially show a
distinct component at 8.5 Hz (right vertical dotted line),
whereas the MU has its carrier at 12 Hz (arrow). The 8.5-Hz
component is accompanied by a 0.41 MU/force coherence. As
seen in the middle column, 10 –12 min of ischemic occlusion
did not significantly change the firing rate of the MU. However, it largely suppressed the 8.5-Hz MU and force component
and it practically eliminated the respective MU/force coherence. Finally, removal of the occlusion led to a situation similar
to that before ischemia (right column). Notably, in Fig. 6, the
8.5-Hz coherence component after ischemia is larger than that
in the preischemia phase (0.65 vs. 0.41), but in other tests the
opposite was the case (Table 1).
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
because this allows direct comparisons to the data of our
preceding study concerning tremor synchrony in steady contractions. For these 117 MUs, the range of estimated MU/force
coherences was 0.08 – 0.78 (mean 0.32, SD 0.16). Notably, the
MU/EMG coherences had values similar to those of MU/force
coherences over the entire sample of 117 MUs (but also over
the sample of the 16 MUs from contractions showing minimal
synchrony).
Interestingly, in each of the 11 pairs of simultaneously
recorded MUs, the individual MU/force coherences had similar
values (usually within 10% of their mean), as in the examples
of Figs. 1 and 2. A scatter diagram constructed from the
differences between coherences in such MU pairs and the
corresponding differences of firing rates did not show any
obvious trend (Spearman r ⫽ 0.04, P ⬎ 0.90).
Because the sample of 11 MU pairs was too small to allow
for any conclusions, we examined the possible relation between MU coherence and MU firing rate over the entire sample
of 117 MUs since the rate characterizes an MU (size, type;
Milner-Brown et al. 1973). This statistical analysis did not
reveal a significant relationship either (Spearman rank-correlation coefficient ⫺0.12, P ⬎ 0.20). It thus seems that the 6- to
10-Hz MU synchrony had a fairly uniform strength in each
contraction, as it also did in the steady contractions of the same
subjects (Christakos et al. 2006a).
Figure 5 summarizes across subjects the 6- to 10-Hz MU/
force coherence data from the 106 contractions (117 MUs),
plotted versus the corresponding frequencies of synchrony.
Accordingly, the strength of the 6- to 10-Hz synchrony varied
widely among subjects and contractions.
Since the observations on this strength were obtained for
broad ranges of values for the parameters of the varying
contractions, its possible dependence on such parameters was
examined. Statistical analyses did not reveal a relationship in
the 106 contractions between the MU/force coherence and:
1) the mean force level (Spearman rank-correlation coefficient
6- TO 10-Hz SYNCHRONY IN TIME-VARYING MUSCLE CONTRACTIONS
479
Table 1 summarizes the conditions and effects in the ischemia tests. Accordingly, the mean force level and the amplitude
of the voluntary force variations did not change in the three
phases of the tests; the same applies to the firing rates of the
MUs. However, during ischemia the 6- to 10-Hz MU synchrony was much weaker and the amplitude of the corresponding force oscillation was much smaller. Finally, the return to
the initial values in the postischemia phase indicates that the
effects of ischemia were transient. It should be emphasized that
in 7 of the 16 tests, the 6- to 10-Hz synchrony was practically
eliminated (as in Fig. 6), irrespective of its initial strength
(initial MU/force coherence in the range 0.11– 0.50). Overall,
these observations thus strongly suggest an involvement of
muscle spindle feedback in the generation of the 6- to 10-Hz
synchrony.
1. Effects of ischemia on 6- to 10-Hz MU synchrony
and corresponding force oscillation
TABLE
Condition
Preischemia
Ischemia
Postischemia
P
ContrLev
MUcr
VolOscilAmpl
VolMU/F Coh
InvOscilAmpl
InvMU/F Coh
16.4 (9.3)
9.5 (2.5)
24.1 (9.1)
0.68 (0.22)
1.7 (0.6)
0.30 (0.10)
16.3 (9.5)
10.7 (3.0)
23.0 (7.9)
0.67 (0.23)
0.8 (0.4)
0.1 (0.09)
16.2 (9.5)
10.2 (3.3)
23.1 (9.3)
0.60 (0.24)
1.6 (0.6)
0.28 (0.10)
0.174
0.10
0.465
0.35
⬍0.001*
⬍0.001*
Values are means ⫾ SD; n ⫽ 16 contractions. Conditions and effects of
ischemia test with regard to mean contraction level (ContrLev, %MVC),
intrinsic MU carrier rate (MUcr, Hz), amplitude of voluntary force oscillation
(VolOscilAmpl, % of ContrLev) and respective MU/force coherence
(VolMU/F Coh), and amplitude of involuntary force oscillation (InvOscilAmpl, % of ContrLev) and respective MU/force coherence (InvMU/F Coh).
Friedman analysis of variance by ranks for multiple within-subjects comparison was used for statistical evaluation. *P values ⬍0.05 indicate statistically
significant results (bottom two rows).
J Neurophysiol • VOL
In contrast, according to Table 1, the modulation components of the force and MU signals, and the corresponding
synchrony, were preserved during ischemia. Therefore their
generation does not seem to depend on spindle feedback, i.e.,
their mechanism is likely different from that of the 6- to 10-Hz
synchrony and oscillation. It should be noted that because of
the difficulty of the task, the size of the slow force component
sometimes differed between the preischemia and the ischemia
conditions (e.g., in Fig. 6, the amplitude of the 0.5-Hz force
variation was about 75% of that in the preischemia contraction). However, it could be larger in either case.
DISCUSSION
The results of this study, obtained from a large sample of
subjects and muscle contractions under various conditions of
contraction level and speed: 1) demonstrate the presence
of 6- to 10-Hz firing synchrony of MUs, coexisting with the
synchrony of the MU firing modulations that underlie the
voluntary force variations; 2) provide a broad view of
the characteristics of the 6- to 10-Hz synchrony; 3) reveal
that, unlike the modulation synchrony, the synchrony in the
6- to 10-Hz range highly likely depends on the feedback
from muscle spindles; and 4) facilitate the study of underlying neural mechanisms, also in relation to the hypothesized rhythmical motor control.
Different types of MU firing synchrony in time-varying
muscle contractions
The existence of synchronous MU firing modulations during
sinusoidal voluntary variations of the muscle force has been
reported before (Erimaki and Christakos 1999; Iyer et al. 1994;
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
FIG. 6. Effects of ischemia on the 6- to
10-Hz force oscillation and synchrony during
a quasi-sinusoidal muscle contraction at 0.5
Hz and around 15% MVC (subject 19). All 3
columns as in left column of Fig. 1. Note in
all columns the 0.5-Hz component in the MU
and force auto-spectra and the MU/force coherence spectrum (left vertical dotted line)
and also the 12-Hz component representing
the MU carrier (arrow). Also note BEFORE
and AFTER ischemia the component at 8.5
Hz (right vertical dotted line) in the same
spectra, representing an involuntary oscillation and the corresponding synchrony. Finally, note during ISCHEMIA the great suppression to elimination of the 8.5-Hz component, which reveals a selective effect of
ischemia on the involuntary force oscillation
and synchrony.
480
S. ERIMAKI AND C. N. CHRISTAKOS
J Neurophysiol • VOL
These behaviors, which point to a common neural mechanism under static and dynamic conditions, seem to contradict
the conclusion of Kakuda et al. (1999) that 6- to 10-Hz
synchrony characterizes slow movement and is absent or weak
under steady conditions. The existence of significant such
synchrony during steady muscle contractions has been demonstrated in many previous studies (e.g., Elble and Randall 1976;
Erimaki and Christakos 1999; Farmer et al. 1993; Halliday
et al. 1999; Raethjen et al. 2000; Semmler et al. 2003).
Moreover, the strength of the 6- to 10-Hz synchrony (MU/
force coherence) in our present sample of varying contractions
and the preceding sample of steady contractions, from the same
subjects, had similar ranges (0.08 – 0.78 vs. 0.08 – 0.90) and
nearly identical means (0.32 vs. 0.34) as well as SDs (0.16
vs. 0.17).
It is noteworthy that Vallbo and Wessberg (1993) argued
that the 6- to 10-Hz movement “discontinuities” they observed
were not tremor because of their nonsymmetric appearance.
However, rhythms in movement velocity and acceleration,
which show coherence to MU activity, necessarily result
through complex transformations from coherent muscle force
oscillations. Therefore the 6- to 10-Hz synchrony during movement could not be of a nature and origin different from those
of the synchrony underlying the 6- to 10-Hz force oscillation in
time-varying contractions or, equivalently, the tremor in steady
contractions. Both the force and the movement rhythms could
thus be classified as action tremors.
Regarding the role of MU synchrony in the generation of the
6- to 10-Hz force oscillation, it should be stressed that such an
oscillation was present in a fraction of the present contractions,
where the synchrony was practically absent. This was also the
case for about one half of the contractions studied during
ischemia. In analogy to tremor (Allum et al. 1978; Christakos
1982a,b; Taylor 1962) and, contrary to the conclusion of
Kakuda et al. (1999), a distinct force component is expected at,
or just above, the MU recruitment rate, even in the absence of
synchrony. It reflects the intrinsic rhythmicity and the relatively large sizes of the last-recruited MUs. In the presence of
MU synchrony, the component caused by the in-phase rhythms
of all active MUs is additional (Christakos 1986) and prevails
or dominates, except when the synchrony is weak (Christakos
et al. 2006a).
Finally, our MU/force and EMG/force coherence analyses
also revealed the presence of a third type of MU synchrony, in
the range 15–30 Hz (Erimaki and Christakos 2006). Our results
on this type of synchrony will be reported elsewhere.
Origins of the modulation and the 6- to 10-Hz
MU synchrony
In view of our ischemia observations on the synchrony of
MU modulations, the underlying common drive to MNs seems
not to depend on spindle feedback (see also Kamen and
DeLuca 1992). Since, in addition, the FDI muscle lacks recurrent inhibition (Katz and Pierrot-Deseilligny 1999), this drive
is with high likelihood of supraspinal origin (see also DeLuca
and Erim 2002). This view is supported by observations
regarding cortical influences on MNs (Gibbs et al. 1999;
McKiernan et al. 2000) and also by the ability of our subjects
to determine by volition the frequency and amplitude of the
force variations in their contractions.
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
see also DeLuca and Mambrito 1987; Farmer et al. 1993;
Knight and Kamen 2007; Sosnoff et al. 2005; van Bolhuis et al.
1997). The here-demonstrated widespread and generally strong
modulation synchrony is in accord with the notion of a common drive to the ␣-motoneuron (MN) pool (DeLuca and Erim
1994; see also Farmer et al. 1993; Henneman and Mendell
1981; Semmler et al. 1997). In the present case, the activities
composing the drive presumably are coherent, quasi-sinusoidally modulated spike trains (see, e.g., the behavior of pyramidal tract neurons in the study of Baker et al. 2001, their
Fig. 5). They thus cause, through synaptic action, coherent
waves in the membrane potential of the MNs and hence
coherent MU firing modulations.
In parallel to the modulation synchrony, there exists a 6- to
10-Hz firing synchrony of MUs and a corresponding muscle
force oscillation. According to our results, the active MUs
exhibit 6- to 10-Hz rhythms that are in-phase (i.e., coherent at
zero lag), irrespective of the MUs’ intrinsic (carrier) discharge
rates.
Importantly, the MU firing rates in the contractions of our
subjects were usually higher than the frequency of the 6- to
10-Hz synchrony, but in 11% of the cases, contrary to the
observations of Wessberg and Kakuda (1999), they were equal
to it. This reveals that the recruitment rate of MUs coincides
with the frequency of the 6- to 10-Hz synchrony, as it does in
the case of the tremor of steady contractions (Christakos et al.
2006a). Last-recruited, relatively large MUs firing at minimal
rates thus tend to show rhythmical spikes near the minima of
the 6- to 10-Hz force oscillation in a one-to-one relation;
smaller MUs firing at higher rates tend to show spikes near
such minima as well as additional interspersed spikes.
The in-phase MU rhythms in the 6- to 10-Hz range presumably reflect in-phase oscillations in the membrane potential of
␣-MNs, caused by a common, rhythmical synaptic input.
Importantly, the strength of the 6- to 10-Hz synchrony was
here found to vary widely among contractions, but not to
depend on either the mean level and other parameters of the
contractions or the MU firing rates. The 6- to 10-Hz synaptic
input seems therefore to be a distinct one, additional to the
common drive that underlies the voluntary force variations
through the MU recruitment and rate-coding mechanisms (DeLuca and Erim 1994; Freund 1983).
Such 6- to 10-Hz membrane oscillations ride on top of the
coherent slower waves that underlie the MU modulations. Thus
within the frequency-modulation pattern of cell firing, grouped
MN spikes from different MUs tend to occur rhythmically near
the local maxima of the 6- to 10-Hz membrane oscillations.
[Analogous behaviors have been shown in intracellular studies
of respiratory high-frequency oscillations (Huang et al. 1996;
Parkis et al. 2003), where MNs fired at local peaks of the
membrane oscillations.] Each time, superposition of the corresponding grouped twitches forms a cycle of a 6- to 10-Hz force
oscillation.
Importantly, for each of our subjects, the 6- to 10-Hz
synchrony had the frequency of the tremor synchrony in steady
muscle contractions. It also shared other important characteristics with the tremor synchrony (Christakos et al. 2006a),
being widespread, in-phase and of fairly uniform strength, and
showing great variability in strength and lack of strength
dependence on the mean force level. Furthermore, this synchrony also seems to depend on spindle feedback.
6- TO 10-Hz SYNCHRONY IN TIME-VARYING MUSCLE CONTRACTIONS
J Neurophysiol • VOL
loop due to signal transmission delays, where the muscle delay
(primarily) and the conduction delay compose a loop delay
corresponding to a frequency in the 6- to 10-Hz range. In this
case, in-phase Ia activities reflecting the ongoing force oscillation or tremor (Hagbarth and Young 1979; Koehler et al.
1984; Windhorst 1978) constitute a common 6- to 10-Hz
synaptic input to the MNs.
In the case of antagonistic muscles acting around a joint, an
involvement of coupled such loops is expected. Mechanical
coupling is effected through the segment to which the two
antagonists are attached, and neural coupling is also present
through action in spinal circuits, such as those of reciprocal Ia
inhibition. Longer loops (e.g., transcortical; Stein and Oguztoreli 1976) could also be responsible for rhythmical synchrony
(at somewhat lower frequencies because the muscle delay is
much longer than the conduction delay).
Regarding the possible interaction with a supraspinal oscillator, Gross et al. (2002) observed a flow of the abovementioned 8-Hz signal from the level of MU activity (EMG) to
those of the cerebellum and the somatosensory cortex. Muscle
spindles with their tremor-related rhythmical activity thus seem
to be part of the 6- to 10-Hz rhythm generator. This fact is in
favor of the possibility of loop action, or interaction with a
central oscillator, underlying the 6- to 10-Hz synchrony.
Clearly, for such interactions, the degree of the involvement of
the spinal stretch reflex loop in any given contraction will
depend on the loop gain.
In general, a high sensitivity of primary spindle endings to
minute length changes is known to exist (Christakos and
Windhorst 1986; Kakuda 2000; Matthews and Stein 1969;
Wessberg and Valbo 1995). On the other hand, evidence and
arguments disputing 1) the adequacy of the loop gain in
causing MU synchrony and 2) the appropriateness of the
timing of the neural and mechanical events associated with
loop tremor have been presented (Durbaba et al. 2005; Valbo
and Wessberg 1996). However, in both our present study and
our preceding study (2006a), the strength of the 6- to 10-Hz
synchrony ranged from minimal to very large, sometimes
being low and difficult to measure. The apparent absence of
synchrony could therefore reflect differences in spindle sensitivity and Ia synaptic efficacy (i.e., in loop gain) among
different contractions. Moreover, the above-assumed sequence
of events during loop action (Christakos et al. 2006a) is based
on well-known facts.
More generally, the frequency of the tremor synchrony
within subjects is known to differ among different muscles,
further arguing for an important role for loop action, even if a
central generator is also involved. This view is in accord with
the more general belief that central rhythms result from interactions between central and peripheral systems, or even reflect
the action of peripheral generators (see review by McAuley
and Marsden 2000; see also Sowman et al. 2006).
Functional relevance of the coherent 6- to 10-Hz rhythms
In line with Bernstein’s (1967) view, oscillations such as
tremors have been considered in various studies advantageous
in regard to linearization of muscle properties, execution and
timing of movements, etc. (see review by Windhorst 2007).
However, there is uncertainty with respect not only to such
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
The situation is quite different with respect to the 6- to
10-Hz synchrony of MUs. Specifically, in about one half of our
ischemia tests, the suppression of this synchrony was practically complete (MU/force coherence ⬍0.08, or MU/MU coherence ⬍0.0064), whereas in the ones showing measurable
residual synchrony the ischemic block may have only been
inadequate. At the same time, during our recording intervals
(starting at 10 min, or sometimes 5– 8 min, after ischemia
onset), spindle feedback was limited because of reduced 1)
length input to spindles, 2) spindle sensitivity, and 3) conduction of spindle output by group Ia fibers (METHODS). Moreover,
a further limitation of the synaptic impact of Ias on MNs
probably occurred due to enhanced Ia presynaptic inhibition.
This rise is expected from action in group III–IV afferents
(Avela et al. 2001; Kalezic et al. 2004) because increases in
other metabolic substances accompany the increase in interstitial potassium concentration that was described by Lakie et al.
(2004).
Therefore the observed suppression, or even practical elimination, of the 6- to 10-Hz MU synchrony strongly suggests
that muscle spindle feedback is actually necessary for the
generation and/or maintenance of this synchrony.
With respect to point 3), it should be noted that in the
H-reflex studies by Hayashi et al. (1987) and Pierrot-Deseilligny et al. (1981), the conduction block of Ia afferent fibers
occurred after about 15 min of ischemia. However, in experiments performed by us on the FDI muscle, an H-reflex decline
was sometimes evident before 10 min of ischemia. The great
difficulty in obtaining a consistent H-reflex in the case of this
phasic muscle (Schieppati 1987) prevented us from reaching
definitive conclusions, but we nevertheless consider a relatively early Ia blockade to be a possible effect of ischemia (see
also Cresswell and Loscher 2000).
Given the likely critical role of spindle feedback in the
generation of the 6- to 10-Hz synchrony, there exist two
obvious possibilities related to mechanisms that were previously considered in isolation or in combination:
The first possibility is that group Ia afferent signals provide
a necessary bias or trigger input to a central oscillator that
independently causes the 6- to 10-Hz MU synchrony. This
possibility is worth examining in relation to hypotheses implicating supraspinal oscillators, such as the olivo-cerebellar system exhibiting intrinsic 5- to 12-Hz rhythms (Welsh and Llinás
1997), the cerebello-thalamo-cortical network generating 8-Hz
oscillatory drive on spinal MNs (Schnitzler et al. 2006), and the
cortico-cortical interactions in the 6- to 15-Hz range (Raethjen
et al. 2004). The consideration of Ia central projections could
facilitate such investigations.
The second possibility is that an oscillating spindle-feedback
loop generates the 6- to 10-Hz synchrony of MUs, possibly
alone or in interaction with a supraspinal oscillator. This
question is presently easier to approach because there are
well-known facts on the signal flow around, and the rhythmical
action within, the spinal stretch reflex loop (Durbaba et al.
2005; Hagbarth and Young 1979; Lippold 1970; Stein and
Oguztoreli 1976).
For this loop such a role seems to some extent inevitable
(Christakos et al. 2006a), considering: 1) the fairly fixed time
relation between the Ia bursts and the decaying phase of the
cycles of the 6- to 10-Hz force oscillation (velocity component); and 2) the self-oscillatory tendencies exhibited by this
481
482
S. ERIMAKI AND C. N. CHRISTAKOS
ACKNOWLEDGMENTS
We thank the subjects who participated in these studies. We also thank Dr.
Y. Dalezios for valuable advice on the statistical analyses.
GRANTS
This study was supported in part by BIOTECH Grant ERB BIO4 CT98-0546
and European Social Fund and National Resources Grant PYTHAGORAS-II
2090.
REFERENCES
Allum JH, Dietz V, Freund HJ. Neuronal mechanisms underlying physiological tremor. J Neurophysiol 41: 557–571, 1978.
Avela J, Kyrolainen H, Komi PV. Neuromuscular changes after long-lasting
mechanically and electrically elicited fatigue. Eur J Appl Physiol 85:
317–325, 2001.
Baker SN, Spinks R, Jackson A, Lemon RN. Synchronization in monkey
motor cortex during a precision grip task. I. Task-dependent modulation in
single-unit synchrony. J Neurophysiol 85: 869 – 885, 2001.
Bernstein N. The Co-ordination and Regulation of Movements (Papers
translated from Russian and German). New York: Pergamon Press, 1967,
chap. 4.
Burne JA, Lippold OCJ, Pryor M. Proprioceptors and normal tremor.
J Physiol 348: 559 –572, 1984.
J Neurophysiol • VOL
Christakos CN. A study of the electromyogram using a population stochastic
model of skeletal muscle. Biol Cybern 45: 5–12, 1982a.
Christakos CN. A study of the muscle force waveform using a population
stochastic model of skeletal muscle. Biol Cybern 44: 91–106, 1982b.
Christakos CN. The mathematical basis of population rhythms in nervous and
neuromuscular systems. Int J Neurosci 29: 103–107, 1986.
Christakos CN. Analysis of synchrony (correlations) in neural populations by
means of unit-to-aggregate coherence computations. Neuroscience 58: 43–
57, 1994.
Christakos CN. On the detection and measurement of synchrony in large
neural populations by coherence analysis. J Neurophysiol 78: 3453–3459,
1997.
Christakos CN, Cohen MI, Sica AL, Huang WX, See WR, Barnhardt R.
Analysis of recurrent laryngeal inspiratory discharges in relation to fast
rhythms. J Neurophysiol 72: 1304 –1316, 1994.
Christakos CN, Erimaki S. Components of physiological tremor in static and
dynamic muscle contractions. Eur J Neurosci 12, S11: 149, 2000.
Christakos CN, Giatroudaki M. Unit-to-aggregate coherence and correlation
analysis of synchrony in neural populations. Soc Neurosci Abstr 24: 674,
1998.
Christakos CN, Papadimitriou NA, Erimaki S. Parallel neuronal mechanisms underlying physiological force tremor in steady muscle contractions
of humans. J Neurophysiol 95: 53– 66, 2006a.
Christakos CN, Plumis NA, Erimaki S. Synchronized 6 –12 Hz motor unit
rhythms in steady and slowly varying muscle contractions: underlying
mechanism and implications for motor control. Soc Neurosci Abstr 652.2,
2006b.
Christakos CN, Rost I, Windhorst U. The use of frequency domain techniques in the study of signal transmission in skeletal muscle. Pfluegers Arch
400: 100 –105, 1984.
Christakos CN, Windhorst U. Spindle gain increase during muscle unit
fatigue. Brain Res 365: 388 –392, 1986.
Cody FW, Goodwin CN, Richardson HC. Effects of ischaemia upon reflex
electromyographic responses evoked by stretch and vibration in human wrist
flexor muscles. J Physiol 391: 589 – 609, 1987.
Conway BA, Halliday DM, Farmer SF, Shahani U, Maas P, Weir AI,
Rosenberg JR. Synchronization between motor cortex and spinal motoneuronal pool during the performance of a maintained motor task in man.
J Physiol 489: 917–924, 1995.
Cresswell AG, Loscher WN. Significance of peripheral afferent input to the
alpha-motoneurone pool for enhancement of tremor during an isometric
fatiguing contraction. Eur J Appl Physiol 82: 129 –136, 2000.
De Luca CJ, Erim Z. Common drive of motor units in regulation of muscle
force. Trends Neurosci 17: 299 –305, 1994.
De Luca CJ, Erim Z. Common drive in motor units of a synergistic muscle
pair. J Neurophysiol 87: 2200 –2204, 2002.
De Luca CJ, Mambrito B. Voluntary control of motor units in human
antagonist muscles: coactivation and reciprocal activation. J Neurophysiol
58: 525–542, 1987.
Durbaba R, Taylor A, Manu CA, Buonajuti M. Stretch reflex instability
compared in three different human muscles. Exp Brain Res 163: 295–305,
2005.
Elble RJ, Randall JE. Motor unit activity responsible for the 8- to 12-Hz
component of human physiological finger tremor. J Neurophysiol 39:
370 –383, 1976.
Erimaki S, Christakos CN. Occurrence of widespread motor-unit firing
correlations in muscle contractions: their role in the generation of tremor and
time-varying voluntary force. J Neurophysiol 82: 2839 –2846, 1999.
Erimaki S, Christakos CN. Study of 15–30 Hz motor unit firing synchrony in
steady and slowly varying muscle contractions. Soc Neurosci Abstr 652.1,
2006.
Evans CM, Baker SN. Task-dependent intermanual coupling of 8-Hz discontinuities during slow finger movements. Eur J Neurosci 18: 453– 456, 2003.
Farmer SF. Pulsatile central nervous control of human movement. J Physiol
517: 3–3(1), 1999.
Farmer SF, Bremner FD, Halliday DM, Rosenberg JR, Stephens JA. The
frequency content of common synaptic inputs to motoneurones studied
during voluntary isometric contraction in man. J Physiol 470: 127–155,
1993.
Fellows SJ, Domges F, Topper R, Thilmann AF, Noth J. Changes in the
short- and long-latency stretch reflex components of the triceps surae muscle
during ischaemia in man. J Physiol 472: 737–748, 1993.
Freund H-J. Motor unit and muscle activity in voluntary control. Physiol Rev
63: 387– 436, 1983.
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
issues, but also to the issue of rhythmical motor control, in
spite of the existence of attractive hypotheses.
Thus the relevance of the coherent 6- to 10-Hz rhythms is
unknown according to certain studies (e.g., Evans and Baker
2003), whereas McAuley et al. (1999) consider rhythmical
control as one of many alternatives. At the same time, the
hypothesis of Llinás and collaborators (1997, 2005) considers
that intrinsic 5- to 12-Hz rhythms in the inferior olive act as a
timing mechanism for complex movements and secure temporally coherent activities in motor circuits. Similarly, the hypothesis of Wessberg and Valbo (1993) assumes the 6- to
10-Hz movement rhythm to represent a series of bipolar pulses
in motor command, effecting intermittent control. In line with
this, Schnizler and Gross (2005) consider finger movements as
a series of micromovements controlled by the cerebellothalamo-cortical loop. Notably, in a modeling study by Kistemaker et al. (2006), an intermittent control signal did provide
faster movement and better agreement with experimental data.
According to our results, the 6- to 10-Hz neural rhythm that
is manifested as force and movement components may to some
extent reflect action in coupled spinal stretch reflex loops. This
rhythm is projected centrally via group Ia afferents, thus
resulting in corticomuscular coherence. Even in the absence of
an interacting central generator, the central projections of this
rhythm could provide a basis for spatially restricted control of
the contractions of muscles acting around a joint.
A more specific application of elementary rhythmical control at spinal levels is suggested by our observation of MUs
being recruited at the frequency of the 6- to 10-Hz synchrony.
Accordingly, the in-phase membrane oscillations of MNs,
whether caused by a central generator or loop action, or both,
determine the recruitment rate of MUs in each muscle (Henneman 1979). Indeed, in preliminary experiments (Christakos
et al. 2006b), we induced transient pauses in MU firing by
varying the level of the voluntary force of the FDI muscle
around the recruitment threshold of MUs. After a pause, each
MU resumed firing with spikes near the minima of the 6- to
10-Hz force oscillation in a one-to-one relation, thus joining
the group of active MUs showing in-phase components in the
6- to 10-Hz range.
6- TO 10-Hz SYNCHRONY IN TIME-VARYING MUSCLE CONTRACTIONS
J Neurophysiol • VOL
McKiernan BJ, Marcario JK, Karrer JH, Cheney PD. Correlations between corticomotoneuronal (CM) cell postspike effects and cell-target
muscle covariation. J Neurophysiol 83: 99 –115, 2000.
Milner-Brown HS, Stein RB, Yemm R. Changes in firing rate of human
motor units during linearly changing voluntary contractions. J Physiol 230:
371–390, 1973.
Papadimitriou NA, Erimaki S, Plumis N, Christakos CN. Motor unit firing
rhythmicity and spinal strech reflex oscillations as the two parallel mechanisms of physiological force tremor. Soc Neurosci Abstr 914.5, 2003.
Parkis MA, Feldman JL, Robinson DM, Funk GD. Oscillations in endogenous inputs to neurons affect excitability and signal processing. J Neurosci
23: 8152– 8158, 2003.
Pierrot-Deseilligny E, Morin C, Bergego C, Tankov N. Pattern of group I
fibre projections from ankle flexor and extensor muscles in man. Exp Brain
Res 42: 337–350, 1981.
Pollok B, Sudmeyer M, Gross J, Schnitzler A. The oscillatory network of
simple repetitive bimanual movements. Cogn Brain Res 25: 300 –311, 2005.
Raethjen J, Lindemann M, Morsnowski A, Dumpelmann M, Wenzelburger R, Stolze H, Fietzek U, Pfister G, Elger CE, Timmer J, Deuschl
G. Is the rhythm of physiological tremor involved in cortico-cortical
interactions? Mov Disord 19: 458 – 465, 2004.
Raethjen J, Pawlas F, Lindemann M, Wenzelburger R, Deuschl G.
Determinants of physiologic tremor in a large normal population. Clin
Neurophysiol 111: 1825–1837, 2000.
Rosenberg JR, Amjad AM, Breeze P, Brillinger DR, Halliday DM. The
Fourier approach to the identification of functional coupling between neuronal spike trains. Prog Biophys Mol Biol 53: 1–31, 1989.
Schieppati M. The Hoffmann reflex: a means of assessing spinal reflex
excitability and its descending control in man. Prog Neurobiol 28: 345–376,
1987.
Schnitzler A, Gross J. Normal and pathological oscillatory communication in
the brain. Nat Rev Neurosci 6: 285–296, 2005.
Schnitzler A, Timmermann L, Gross J. Physiological and pathological
oscillatory networks in the human motor system. J Physiol (Paris) 99: 3–7,
2006.
Semmler JG, Kornatz KW, Enoka RM. Motor-unit coherence during isometric contractions is greater in a hand muscle of older adults. J Neurophysiol 90: 1346 –1349, 2003.
Semmler JG, Nordstrom MA, Wallace CJ. Relationship between motor unit
short-term synchronization and common drive in human first dorsal interosseus muscle. Brain Res 767: 314 –329, 1997.
Sosnoff JJ, Vaillancourt DE, Larsson L, Newell KM. Coherence of EMG
activity and single motor unit discharge patterns in human rhythmical force
production. Behav Brain Res 158: 301–310, 2005.
Sowman PF, Brinkworth RS, Turker KS. Periodontal anaesthesia reduces
common 8 Hz input to masseters during isometric biting. Exp Brain Res 169:
326 –337, 2006.
Stein RB, Oguztoreli MN. Tremor and other oscillations in neuromuscular
systems. Biol Cybern 22: 147–157, 1976.
Stephens JA, Taylor A. Fatigue of maintained voluntary muscle contraction
in man. J Physiol 220: 1–18, 1972.
Taylor A. The significance of grouping of motor unit activity. J Physiol 162:
259 –269, 1962.
Vallbo AB, Wessberg J. Organization of motor output in slow finger movements in man. J Physiol 469: 673– 691, 1993.
van Bolhuis BM, Medendorp WP, Gielen CC. Motor unit firing behavior in
human arm flexor muscles during sinusoidal isometric contractions and
movements. Exp Brain Res 117: 120 –130, 1997.
Wang SY, Lin X, Yianni J, Miall Cr, Aziz TZ, Stein JF. Optimizing
coherence estimation to assess the functional correlation of tremor-related
activity between the subthalamic nucleus and the forearm muscles. J Neurosci Methods 136: 197–205, 2004.
Welsh JP, Llinás R. Some organizing principles for the control of movement
based on olivocerebellar physiology. Prog Brain Res 114: 449 – 461, 1997.
Wessberg J, Kakuda N. Single motor unit activity in relation to pulsatile
motor output in human finger movements. J Physiol 517: 273–285, 1999.
Wessberg J, Vallbo AB. Coding of pulsatile motor output by human muscle
afferents during slow finger movements. J Physiol 485: 271–282, 1995.
Wessberg J, Vallbo AB. Pulsatile motor output in human finger movements
is not dependent on the stretch reflex. J Physiol 493: 895–908, 1996.
Windhorst U. Origin and nature of correlations in the Ia feedback pathway of
the muscle control system. Biol Cybern 31: 71–79, 1978.
Windhorst U. Muscle proprioceptive feedback and spinal networks. Brain Res
Bull 73: 155–202, 2007.
99 • FEBRUARY 2008 •
www.jn.org
Downloaded from http://jn.physiology.org/ by 10.220.33.4 on June 16, 2017
Gibbs J, Harrison LM, Stephens JA, Evans AL. Does abnormal branching
of inputs to motor neurones explain abnormal muscle cocontraction in
cerebral palsy? Dev Med Child Neurol 41: 465– 472, 1999.
Gross J, Timmermann L, Kujala J, Dirks M, Schmitz F, Salmelin R,
Schnitzler A. The neural basis of intermittent motor control in humans.
Proc Natl Acad Sci USA 99: 2299 –2302, 2002.
Grosse P, Cassidy MJ, Brown P. EEG-EMG, MEG-EMG and EMG-EMG
frequency analysis: physiological principles and clinical applications. Clin
Neurophysiol 113: 1523–1531, 2002.
Hagbarth KE, Young RR. Participation of the stretch reflex in human
physiological tremor. Brain 102: 509 –526, 1979.
Halliday DM, Conway BA, Farmer SF, Rosenberg JR. Load-independent
contributions from motor-unit synchronization to human physiological
tremor. J Neurophysiol 82: 664 – 675, 1999.
Hamm TM, Trank TV, Turkin VV. Correlations between neurograms and
locomotor drive potentials in motoneurons during fictive locomotion: implications for the organization of locomotor commands. Prog Brain Res 123:
331–339, 1999.
Haque AR, Burne JA. The effect of background contraction and prolonged
ischemia on the tendon reflex (Abstract). Proc Aust Physiol Pharmacol Soc
33: 40, 2003.
Hayashi R, Becker WJ, White DG, Lee RG. Effects of ischemic nerve block
on the early and late components of the stretch reflex in the human forearm.
Brain Res 403: 341–344, 1987.
Henneman E. Functional organization of motoneuron pools: the size-principle. In: Integration in the Nervous System, edited by Asanuma H, Wilson
VJ. Tokyo: Igaku-Shoin, 1979.
Henneman E, Mendell LM. Functional organization of motoneuron pool and
its inputs. In: Handbook of Physiology. The Nervous System. Motor Control.
Bethesda, MD: Am. Physiol. Soc., 1981, sect. 1, vol. II, pt. 1, p. 423–507.
Huang WX, Cohen MI, Yu Q, See WR, He Q. High-frequency oscillations
in membrane potentials of medullary inspiratory and expiratory neurons
(including laryngeal motoneurons). J Neurophysiol 76: 1405–1412, 1996.
Iyer MB, Christakos CN, Ghez C. Coherent modulations of human motor
unit discharges during quasi-sinusoidal isometric muscle contractions. Neurosci Lett 170: 94 –98, 1994.
Kakuda N. Response of human muscle spindle afferents to sinusoidal stretching with a wide range of amplitudes. J Physiol 527: 397– 404, 2000.
Kakuda N, Nagaoka M, Wessberg J. Common modulation of motor unit
pairs during slow wrist movement in man. J Physiol 520: 929 –940, 1999.
Kalezic I, Bugaychenko LA, Kostyukov AI, Pilyavskii AI, Ljubisavljevic
M, Windhorst U, Johansson H. Fatigue-related depression of the feline
monosynaptic gastrocnemius-soleus reflex. J Physiol 556: 283–296, 2004.
Kamen G, De Luca CJ. Firing rate interactions among human orbicularis oris
motor units. Int J Neurosci 64: 167–175, 1992.
Katz R, Pierrot-Deseilligny E. Recurrent inhibition in humans. Prog Neurobiol 57: 325–355, 1999.
Kistemaker DA, Van Soest AJ, Bobbert MF. Is equilibrium point control
feasible for fast goal-directed single-joint movements? J Neurophysiol 95:
2898 –2912, 2006.
Knight CA, Kamen G. Modulation of motor unit firing rates during a complex
sinusoidal force task in young and older adults. J Appl Physiol 102:
122–129, 2007.
Koehler W, Hamm TM, Enoka RM, Stuart DG, Windhorst U. Contractions of single motor units are reflected in membrane potential changes of
homonymous alpha-motoneurons. Brain Res 296: 379 –384, 1984.
Lakie MD, Hayes NR, Combes N, Langford N. Is postural tremor size
controlled by interstitial potassium concentration in muscle? J Neurol
Neurosurg Psychiatry 75: 1013–1018, 2004.
Lang EJ, Sugihara I, Llinás R. Olivocerebellar modulation of motor cortex
ability to generate vibrissal movements in rat. J Physiol 571: 101–120, 2006.
Lippold OCJ. Oscillation in the stretch reflex arc and the origin of the
rhythmical, 8 –12 C–S component of physiological tremor. J Physiol 206:
359 – 82, 1970.
Marsden JF, Brown P, Salenius S. Involvement of the sensorimotor cortex in
physiological force and action tremor. Neuroreport 12: 1937–1941, 2001.
Matthews BH. Nerve endings in mammalian muscle. J Physiol 78: 1–53, 1933.
Matthews PB, Stein RB. The sensitivity of muscle spindle afferents to small
sinusoidal changes of length. J Physiol 200: 723–743, 1969.
McAuley JH, Farmer SF, Rothwell JC, Marsden CD. Common 3 and 10 Hz
oscillations modulate human eye and finger movements while they simultaneously track a visual target. J Physiol 515: 905–917, 1999.
McAuley JH, Marsden CD. Physiological and pathological tremors and
rhythmic central motor control. Brain 123: 1545–1567, 2000.
483