Clinical Neurophysiology xxx (2010) xxx–xxx

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Clinical Neurophysiology

journal homepage: www.elsevier .com/locate /c l inph

The a-motoneuron pool as transmitter of rhythmicities in cortical motor drive

Dick F. Stegeman a,c,*, Wendy J.M. van de Ven a, Gijs A. van Elswijk a, Robert Oostenveld b, Bert U. Kleine a

a Centre for Neuroscience, Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen Medical Centre,Department of Neurology/Clinical Neurophysiology, Nijmegen, The Netherlandsb Centre for Cognitive Neuroimaging, Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen Medical Centre,Department of Neurology/Clinical Neurophysiology, Nijmegen, The Netherlandsc Faculty of Human Movement Sciences, Research Institute MOVE, VU University Amsterdam, The Netherlands

a r t i c l e i n f o a b s t r a c t

Article history:Accepted 4 March 2010Available online xxxx

Keywords:Motoneuron poolCorticomuscular coherencea-Motoneuron modelCorticomuscular transmissionMotor driveMotor unit firing

1388-2457/$36.00 � 2010 International Federation odoi:10.1016/j.clinph.2010.03.052

* Corresponding author at: Radboud University NiDepartment of Neurology/Clinical Neurophysiology, Pgen, The Netherlands. Tel.: +31 24 3615284; fax: +31

E-mail address: d.stegeman@neuro.umcn.nl (D.F. S

Please cite this article in press as: Stegeman DF(2010), doi:10.1016/j.clinph.2010.03.052

Objective: Investigate the effectiveness and frequency dependence of central drive transmission via thea-motoneuron pool to the muscle.Methods: We describe a model for the simulation of a-motoneuron firing and the EMG signal as responseto central drive input. The transfer in the frequency domain is investigated. Coherence between stochas-tical central input and EMG is also evaluated.Results: The transmission of central rhythmicities to the EMG signal relates to the spectral content of thelatter. Coherence between central input to the a-motoneuron pool and the EMG signal is significantwhereby the coupling strength hardly depends on the frequency in a range from 1 to 100 Hz. Commoncentral input to pairs of a-motoneurons strongly increases the coherence levels. The often-used rectifica-tion of the EMG signal introduces a clear frequency dependence.Conclusions: Oscillatory phenomena are strongly transmitted via the a-motoneuron pool. The motoneu-ron firing frequencies do play a role in the transmission gain, but do not influence the coherence levels.Rectification of the EMG signal enhances the transmission gain, but lowers coherence and introduces astrong frequency dependency. We think that it should be avoided.Significance: Our findings show that rhythmicities are translated into a-motoneuron activity withoutstrong non-linearities.� 2010 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights

reserved.

1. Introduction

The physiological drive to a muscle tends to have rhythmic pat-terns. Wollaston reported this already in 1810 (Brown, 2000). Inpathological circumstances rhythmic drive to muscles can lead todisabling symptoms as in Parkinson’s disease and essential tremor(Schnitzler et al., 2009). Recently, long range interaction of oscilla-tory phenomena has also been given a meaning in selective com-munication between neuronal groups. The conceptualmechanism behind it, called communication through coherence(CTC, Fries, 2005), gets increasing support from experimental evi-dence (Womelsdorf et al., 2007). The concept comprises theassumption that selective communication between neuronalgroups is enhanced by oscillatory activity in specific frequencybands that are roughly in the range 10 and 80 Hz. Corticospinalcoherence is regarded as strong evidence for CTC since the distance

f Clinical Neurophysiology. Publish

jmegen Medical Centre, 920.O. Box 9101, 6500HB Nijme-24 3615097.tegeman).

et al. The a-motoneuron pool

between the signal sources excludes irrelevant volume conductionmediated effects (Schoffelen et al., 2005; Van Elswijk et al., 2010).An interesting question for the corticospinal system is how corticaloscillations, after having descended the corticospinal tract, aretranslated by the a-motoneuron pool into motoneuron activityand ultimately into the EMG signal. Thereby, the properties of a-motoneurons, especially their long afterhyperpolarization (AHP),are expected to be a non-linear obstacle in the transfer of oscilla-tory activity.

Ways to analyze rhythmic coupling between cortex and musclein the frequency domain have been proposed (e.g. Grosse et al.,2002), and a number of authors have already looked into the spinaltransmission and motoneuron firing patterns (e.g. Matthews,1999; Myers et al., 2003; Farina et al., 2004; Williams and Baker,2009). Different frequency bands play a role in the discussion. First,there is a specific a-, b-, or c-frequency band in which the cortico-spinal interaction apparently occurs. Second, since the a- and b-frequency bands are more or less in the order of the firing frequen-cies of a-motoneurons, attempts are made to relate the transmis-sion efficiency directly to those firing frequencies (Myers et al.,2003; Farina et al., 2004). Third, the frequency content of the in-

ed by Elsevier Ireland Ltd. All rights reserved.

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol

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volved electrophysiological signals (EEG, MEG, and EMG) plays arole. It leads for instance to the regular question whether theEMG signal should be rectified before a coherence analysis is done(Myers et al., 2003; Yao et al., 2007). In this context also the effectof the frequency content of the ‘synaptic noise’ at the input of thea-motoneurons can be added. It is caused by the motoneuronmembrane dynamics reacting to excitatory and inhibitory input(Calvin and Stevens, 1968; Matthews, 1996). This modulating ele-ment may also play a part in transmitting central oscillatory phe-nomena to a muscle.

The reported level of corticospinal coherence in the b- and thec-band between the MEG/EEG and surface EMG signals is variable,depending on task circumstances and muscle groups used (e.g.Brown et al., 1998; Salenius and Hari, 2003; Riddle and Baker,2005). It roughly ranges between 0.02 and 0.2, mostly closer tothe latter. It is to be expected that part of the potential frequencycoupling between EEG or MEG over the motor areas and the infor-mation in corticospinal neuronal firings, will be lost across the a-motoneuron pool (Fig. 1). Furthermore, quantitative insight in thatloss and the non-linearity that is introduced, would ’inversely’ givean estimate of the coupling between signals from cortical areas(EEG/MEG, especially from M1) and corticospinal motoneurons.

Cross correlation histograms between the firing patterns of dif-ferent motor units (MUs) show a peak close to delay time zero(Farmer et al., 1997). This means that the probability of a MU firingrises around the time that another one fires. This coupling betweenfirings of MU pairs is called ‘short-term synchrony’ (Sears andStagg, 1976; Kirkwood et al., 1982). Synchronization is thoughtto be dominated by a common input (CI) due to branching of axonsso that an axon can contribute as input to several a-motoneurons(Kirkwood and Sears, 1991). The cortical origin of motoneuron syn-chronization is supported by experimental evidence reported byDatta and Stephens (1990), Datta et al. (1991), and Schmied et al.(1999). The amount of CI which should be present can in principlebe determined from the level of short-term synchrony (Kleineet al., 2001).

We present a model study to obtain insight in the corticomuscu-lar signal transmission considering the various frequency domains.Following the reasoning by Matthews (1999), we adopted a deliber-ately simple and elegant computational model of the a-motoneuron(Matthews, 1996) in which we believe that the essential elements

ΣEPSPFilter

E+N

5 ms

Cortical drive Motoneuron po

Fig. 1. Functional model scheme of the a-motoneuron in three stages (cortical drive, mmean value plus white noise, are summed and then filtered with EPSP characteristics. At bresulting in a firing event. The afterhyperpolarization phase is taken into consideration atthe contribution of this a-motoneuron to the EMG signal.

Please cite this article in press as: Stegeman DF et al. The a-motoneuron pool(2010), doi:10.1016/j.clinph.2010.03.052

for the present purpose are available. The model only accounts forthe steady state during a sustained isometric contraction. It has noelements which could mimic dynamic task behaviour. For instance,it cannot describe the recruitment of plateau potentials (Svirskis andHounsgaard, 2003; Taylor and Enoka, 2004; Williams and Baker,2009) in the motor unit firing dynamics. We purposeful restrictedthe model to the simplest, but still physiologically relevant forwardtransmission over the motoneuron pool without feedback elementsto reveal the pure properties of this element in motor control. Ourversion of the model includes a pool of motoneurons. We also addedthe generation of motor unit action potentials, recorded at the skinsurface, in response to the firings of each a-motoneuron. Further-more, we adopted the phenomenon of short-term synchrony byassuming a common input to each pair of a-motoneurons (Moritzet al., 2005). To simulate cortical rhythmicity we modulated the cor-tical input to the motoneurons in different frequency ranges. Ourgoal was to investigate the effectiveness and the properties of oscil-latory central drive transmission to the muscle, its relation with thefiring patterns of the a-motoneurons, and the consequences for thesurface EMG signal. We will distinguish the frequency aspects men-tioned above and look at the transfer across the a-motoneuron poolbasically by comparing it to a linear transfer function. Apart frombeing a usual first approach in system’s analysis, a linear transfer alsois the implicit assumption behind the use of coherence as a measureof coupling between neuronal populations. We will therefore pres-ent the EMG signal in response to oscillatory corticospinal activityas a measure of transmission quality. Also, the coherence betweenstochastic cortical drive activity and the surface EMG signal is com-puted. Moreover, we compared the data with and without rectifica-tion of the simulated EMG signal.

2. Methods

2.1. Motoneuron model

The simulations make use of a model of the a-motoneuron,which is adapted from Matthews (1996), and contain the followingmain steps: (1) generating the firing pattern of an a-motoneuron;(2) introducing a certain level of common input to pairs of motorunits to introduce short-term synchrony. The model was imple-mented in the Matlab environment (The MathWorks, Inc., Natick,

C MUAP EMG

AHP50 MUs

5 ms

ol Muscle

otoneuron pool, and muscle). Random firing events from the cortex, expressed as aox C the signal is compared to the threshold value. If higher, the a-motoneuron firesC as well. The resulting firing pattern is convoluted with a MUAP wave shape giving

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol

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MA, version 7.6.0). Instead of the 1 ms time resolution used in theMatthews (1996) study, we used a time resolution of 0.5 ms.

2.1.1. Firing patternsThe output from pyramidal neurons in the cortex is regarded as

the input to each neuron in the a-motoneuron pool. These signalsare assumed to be Poisson distributed spike trains which, as beingcentral drive dependent, may have a time varying density (Fig. 1).The input to an a-motoneuron is the sum of such Poisson distrib-uted spike trains which, when many events are summed, can wellbe approximated by a mean value plus Gaussian distributed whitenoise. The membrane dynamics resulting in the characteristics ofexcitatory postsynaptic potentials (EPSPs) will have an influenceon how the input at the a-motoneuron’s membrane is transferredto that neuron. This is added in the model as a filter mimicking thefrequency content of the EPSPs (Fig. 1). So then the input to thespike generator of the a-motoneuron (C in Fig. 1) is modelled asa mean value plus noise, which now is not white any longer, buthas a frequency content dictated by the EPSP wave shape. ThisEPSP filter has the properties as used by Matthews (1996). Thereby,the membrane dynamics are taken from the autocorrelation func-tion of synaptic noise expressed in a time constant of 4 ms as pre-sented in Calvin and Stevens (1968). As suggested by Matthews(1996) for our 0.5 ms time resolution, we adapted that value to5 ms. A crucial element in the model is to normalize the standarddeviation of the membrane noise N to unity, further used as theamplitude unit in the drive to the neuron model (noise unit, NU).

The membrane potential of the a-motoneuron in the spinal cordis assumed to increase, in physiological terms, due to the summa-tion of EPSPs, approached by a steady drive E plus the synapticnoise N (Fig. 1). When threshold is reached, an action potential isthought to arise that elicits a motor unit firing event. Immediatelyfollowing that instant, the membrane potential of the a-motoneu-ron jumps down with an amplitude shift �A and then shows along-lasting AHP phase. This phase consists of the lowered mem-brane potential to rise again exponentially with time constant sfrom the minimum level �A, on which the central drive E + N issuperimposed, to the resting state f(t) = 0. This AHP phase can bedescribed by:

f ðtÞ ¼ �Ae�ts þ Eþ N ð1Þ

We used a value for A = 20 NU, and a time constant s = 30 ms,approaching the behaviour of biceps MUs (Matthews, 1996; Kleineet al., 2001). The next action potential is generated as soon as thethreshold is reached again (f(t) = 0). The firing rate is tuned bychoosing the drive E differently for each motoneuron of the pool.We used equally spaced values of E in NU between �1.5 and +1.For instance, E = �1.5 NUs means that for large t (>>30 ms) after aprevious firing the next firing occurs when for the first time N ex-ceeds 1.5 times its own standard deviation (NU). This combinationof parameters generates physiologically realistic firing patterns fora moderate level of contraction with firing rates between 10 and15 firings per second (Matthews, 1996; Kleine et al., 2001). The pre-sented results are based on a population of 50 a-motoneurons.

2.1.2. Motor unit synchronizationShort-term synchrony between MU pairs (described by e.g. Sch-

mied et al., 2000 and Terry and Griffin, 2010) can be introduced byassuming a certain level of common input. This level can be deter-mined by looking inversely to the nervous system. Firing patternsof pairs of MUs with a level of short-term synchrony in a physio-logical range (Farmer et al., 1997) can be generated with around30% of CI to MU pairs (see results).

When considering this level for more than two MUs, there aretwo basic possibilities: (1) 30% of the input is equal for all MUs;

Please cite this article in press as: Stegeman DF et al. The a-motoneuron pool(2010), doi:10.1016/j.clinph.2010.03.052

(2) every pair of MUs shares 30% of their input, which is differentfrom the shared input between all other pairs. In the first case,the 70% of not shared input to any of the single MUs is independentof the input to all others. In the second case, every MU has a 30%common input with any other MU. This common input is differentfor any pair. Assuming that the common input is caused by ashared wiring structure, the second model appears more realisticand was used.

For this aspect in the model we have i = 1. . .R a-motoneurons (R= 50) with equally large input noise signals zi(t) and j = 1. . .R inde-pendent equally large white noise sources xj(t). To realize the sec-ond possibility, the normalized covariance matrix K of z (for 30% CInoise) should look like:

K ¼ CovðzÞ ¼

1 0:3 0:3 ::

0:3 1 :: 0:30:3 :: 1 0:3:: 0:3 0:3 1

26664

37775 ð2Þ

In order to obtain noise input signals to the a-motoneurons being30% common to each pair of MUs from independent noise signals,some algebraic operations must be performed. That is, we have tofind a solution for the following equation:

z ¼ A � x ð3Þ

Where A is an R � R matrix that should match with the covariancematrix K, which can be written as:

K ¼ A � AT ¼ P � K � PT þ P �K12 �K1

2 � PT ð4Þ

Where K is the matrix with eigenvalues of K and P contains the cor-responding eigenvectors. It follows that:

A ¼ P �K12 ð5Þ

This can be used in combination with Eq. (3) to generate the R inputsignals z, obeying Eq. (2), to the MUs from the same number of inde-pendent drive inputs x from the cortex.

2.2. Simulating the EMG signal

To simulate (surface) EMG signals, motor unit action potentials(MUAPs) should be included in the model. The firing pattern eventsmust then be replaced with MUAP wave shapes by means of con-volution. The main goal in defining the MUAPs was to come upwith two EMG signals having the spectral distribution of a smallmuscle (FDI, Penn et al., 1999) and a larger upper extremity muscle(ECR, Huysmans et al., 2008), respectively, using wave shapes witha duration d of 15 ms and 25 ms (Fig. 2A and C, with frequencyspectra in Fig. 2B and D). A half pulse shape was defined by:

hðtÞ ¼ 5 � sinpt

d=2

� �:exp

1s

td=2� 1

� �for 0 < t � d=2 ð6Þ

For d=2 < t � d a time and amplitude mirrored version of Eq. (6) fol-lowing the zero value at t = d/2 was used. The value for the dampingfactor s is set at 0.18 ms.

All 50 MUs were represented by the same long or short durationMUAP. To this end, the 50 single firing sequences are summed to-gether and the surface EMG signal is created by convolution of theresulting sum of 50 firing patterns with one of the two MUAP waveshapes. To obtain a sufficient signal to noise ratio, the model wasrun for 100 or 150 s for, respectively, the frequency spectra andthe coherence calculation (see below).

2.3. Motoneuron pool transfer estimation

Signal transfer through the motoneuron pool will be expressedin amplitude modulation and coherence. The analyses were done

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol

Fig. 2. Short (A) and long MUAP (C) and their respective amplitude spectra (B and D).

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in MATLAB (MathWorks, Natick, MA), with the help of FieldTrip, anopen source toolbox for the analysis of neurophysiological data(Donders Institute for Brain, Cognition and Behaviour, RadboudUniversity Nijmegen, the Netherlands; see http://www.ru.nl/neuroimaging/fieldtrip).

The often-used rectification of the EMG signal as pre-processingoption for computing corticomuscular coherence is discussed forinstance by Myers et al. (2003), Farina et al. (2004), and Yaoet al. (2007). To contribute to that discussion, the simulated surfaceEMG signals are also used after rectification.

To study the influence of a central oscillatory modulation, sinewaves with frequencies ranging from 1 to 100 Hz were superim-posed on the summed 50 white noise inputs to the 50 a-motoneu-rons (signal x in Eq. (3)). The modulation amplitude was setarbitrarily to 5% of the white noise root mean square (RMS) ampli-tude for each of the 50 elements of x in Eq. (3). The effect of thatmodulation on the EMG spectrum will be presented. The signalswere simulated for 100 s. Spectral content was taken as the aver-age from 100 non-overlapping segments of 1 s, resulting in a1 Hz frequency resolution.

The most popular way of looking at the transfer of oscillatoryphenomena is coherence analysis (e.g. Grosse et al., 2002):

Cxyðf Þ ¼jPxyðf Þjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Pxxðf ÞPyyðf Þp ð7Þ

Pxx and Pyy are the power spectral densities of two signals betweenwhich the coherence Cxy is computed, Pxy is the cross power spectraldensity.

Coherence is computed between the summed white corticospi-nal neural input and the (non-rectified and rectified) interferenceEMG signals. In this case, the simulations were run, now for150 s. The data is divided into non-overlapping epochs of 1 s each.A Hanning taper function is applied to each epoch before coher-ence is calculated. To test for the statistical significance a non-parametric permutation test was performed. The null-hypothesisstates that there is no difference between conditions and so thatthe data are exchangeable. The data epochs were randomly shuf-fled 100 times after which a 95% confidence interval is created

Please cite this article in press as: Stegeman DF et al. The a-motoneuron pool(2010), doi:10.1016/j.clinph.2010.03.052

by determining average and standard deviation over these randomshuffles. Coherence values outside the confidence interval wereconsidered as significant. For a more detailed description of thismethod see Schoffelen et al. (2005) and Womelsdorf et al. (2007).

3. Results

3.1. Amplitude response

3.1.1. Spectral analysis of summed firing patterns and EMG signalsFig. 3 shows frequency spectra of the firing patterns summed

over 50 a-motoneurons for 0% and 30% CI. The MU firing frequencydistribution, 10 and 15 Hz, determined by the choice for the distri-bution of mean drives E, is clearly recognized in the spectra of bothpatterns. The spectrum for 0% CI has the typical appearance of a so-called stochastic renewal process with augmentation around themean firing frequency and its harmonics and a white spectral con-tent for higher frequencies (Ten Hoopen, 1974; Pan et al., 1989). Ascan be seen, CI to MU pairs increases the amplitude of the spectraldistribution of the summed a-motoneuron firing patterns. It doesalso result in a different spectral shape. The higher frequenciesare less augmented by the CI than lower frequencies and also tendto a plateau value for the highest frequencies (>>100 Hz, see insetFig. 3). To illustrate that 30% CI, having this substantial influence onthese spectra, is a realistic choice, Fig. 4 shows a cross correlationhistogram of the short-term synchrony that is realized by assum-ing this level of CI in the model (e.g. Farmer et al., 1997).

Fig. 5A shows the frequency contents of the non-rectified EMGsignals on the basis of 30% CI for the long MUAP wave shape. Heretoo, the peak around 13 Hz is caused by the mean MU firing fre-quency. Furthermore, Fig. 5B shows that rectification emphasizesthe lower frequency contents, as expected.

3.1.2. Amplitude response to added oscillations of 1–100 HzFig. 6 presents the spectral content (along the axis indicated

with output frequency) of the summed a-motoneuron spike pat-terns (Fig. 6A) and of the EMG signal without (Fig. 6B) and with(Fig. 6C) rectification using the long duration MUAP wave shape

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol

Fig. 3. Averaged amplitude spectrum of summed MU firing patterns for 0% and 30% common input shown for a frequency range between 0 and 100 Hz. Inset shows thespectrum for frequencies up to 1000 Hz, which is the Nyquist frequency in the simulation.

Fig. 4. Cross correlation histogram showing the short-term synchrony between thefirings of two different motor units when assuming a 30% common input to pairs ofa-motoneurons.

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and 30% CI. For each repetition the 5% superimposed modulation tothe white noise input of the model was added with increasing fre-quency from 1 to 100 Hz in 1 Hz steps (along the axis indicatedwith input frequency), resulting in a diagonal ridge in these threedimensional presentations.

To illustrate the transfer of the modulating frequencies inmore detail, Fig. 7 presents the diagonal ridges in Fig. 6 in thesame order, but now also for the short duration MUAP waveshape. It is noted that the result in part A below 30 Hz can di-rectly be compared and appears similar to the model resultshown for the 13 Hz motoneuron in Fig. 5 from Matthews(1999). The choice for an EPSP filter (see Section 1 and Sec-tion 2.1.1) with a time constant of 5 ms was based on experi-

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mental data (Calvin and Stevens, 1968; Matthews, 1996). Theadded modulation input is ’injected’ to the system before thatEPSP filter (Fig. 1). As indicated already in the introduction, theproperties of that filter may also influence the frequency trans-fer. As the membrane dynamics may vary between motoneuronsof different muscles, we doubled the time constant to 10 ms (notshown). This has no noticeable influence on the results as pre-sented in Fig. 7. When comparing Fig. 5A and B with Fig. 7Band C it already appears that the shape of the spectral contentsis similar. That means that the transfer of rhythmic activity isabout proportional to the spectral content of the EMG signal.That this is more or less the case is illustrated in Fig. 8B, wherethe ratio between the modulated amplitude (Fig. 7B) and theEMG spectral content (Fig. 5A) is presented. Fig. 8A shows thisratio for the MU firing pattern and Fig. 8C for the rectifiedEMG signal. Apart from a somewhat increased noise levelbecause of the division operation, there is for Fig. 8A and B noclear sign of a preference for this modulation in a relevant spe-cific frequency band, especially not in the region of the firingfrequencies of the motoneurons. The ratio for the EMG signaltends to a value of 1 for the lowest frequencies (<20 Hz,Fig. 8B), meaning that the extra modulation is less or nottransferred for those frequencies. For the rectified EMG, this ratioalso approaches unity for the higher frequencies (>60 Hz,Fig. 8C).

3.2. Coherence analysis

3.2.1. Between white motoneuron input and EMGThe coherence between the summed input to all motoneurons

and the (rectified) EMG signal is computed for 0% and 30% CI forthe long MUAP (Fig. 9). The CI level leading to short-term syn-chrony appears to be an utmost important factor that enhancescoherence (Fig. 9B against Fig. 9A and Fig. 9D against Fig. 9C).Furthermore, the coherence becomes lower after rectification(Fig. 9C against Fig. 9A and Fig. 9D against Fig. 9B). It shouldbe realized that for a linear system, without independent noise

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol

Fig. 5. Frequency content of EMG signals on the basis of 30% CI for the long MUAP wave shape before (A) and after (B) rectification.

Fig. 6. Amplitude spectra of the spike pattern, the EMG signal, and the rectified EMG signal (A, B, and C, respectively) containing a superimposed modulation between 1 and100 Hz on the input. Common input of 30% between pairs of MU was assumed. The long duration MUAP is used for computation of the EMG signals.

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at the system’s input or output, the coherence would be 1 for allfrequencies, independent of the frequency characteristics of thesystem’s transfer function. This is because in Eq. (7) the denom-inator corrects for the spectral content of both input and output.Even the highest values presented in Fig. 9B do not reach thatunity value. Furthermore, the coherence also slightly decreaseswith increasing frequency. The a-motoneuron pool system obvi-ously does not behave as a ‘noise free’ linear system. Another

Please cite this article in press as: Stegeman DF et al. The a-motoneuron pool(2010), doi:10.1016/j.clinph.2010.03.052

essential point is that the firing frequencies of the motor unitsdo not seem to play a substantial role in Fig. 9A and B, that isto say that they are not interfering with the transmission of cor-tical oscillations over the a-motoneuron pool in terms of thecoherence between input and output. For the rectified EMG sig-nal, however, the firing rates determine the upslope of the coher-ence from the lowest frequency up to the mean firing rate asshown in Fig. 9D.

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol

Fig. 7. Amplitude spectra with superimposed modulation presenting the diagonal ridges in Fig. 6. Here, the difference between long duration (bold) and short duration(dotted) MUAPs is shown. Common input of 30% between pairs of MU was assumed.

0 20 40 60 80 1001

2

3A

Frequency (Hz)

Rat

io

0 20 40 60 80 1001

2

3B

Frequency (Hz)

Rat

io

0 20 40 60 80 1001

2

3C

Frequency (Hz)

Rat

io

Fig. 8. (A) Ratio between the modulated amplitude as shown in Fig. 7A (bold) andthe firing pattern spectral content as presented in Fig. 3 (bold). (B) Ratio betweenthe modulated amplitude as shown in Fig. 7B (bold) and the EMG spectral contentas presented in Fig. 5A. (C) Ratio between modulated amplitude as shown in Fig. 7C(bold) and the rectified EMG spectral content as in Fig. 5B.

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3.2.2. With independent noise addedWhen performing experiments of any kind, there will be mea-

surement noise present. It can be that the input as defined is not

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completely transferred to the system studied and that noise isadded to the output signal. Any approach towards reality shouldtherefore add some independent noise to the input or output ofthe system. Added input noise (part of the cortical output signalthat is not transferred to the a-motoneuron pool) will decreasethe level of coherence with a constant factor for all frequenciesas long as that noise has the same spectral content as the input.The signal to noise ratio (SNR) of the input then decreases with aconstant factor. When, however, independent white measurementnoise is added to the output (the EMG signal) the coherence profilebetween input and EMG is affected (Fig. 10) because the whitenoise has been given the RMS amplitude of the EMG signal. The ef-fect is largest in the low frequency regions (<20 Hz) where theEMG signal (Fig. 5A) and the amplitude transfer (Fig. 8B) are stee-ply decreasing. It follows more or less the frequency dependence ofthe amplitude response to added oscillations (Fig. 7). When usingthe short duration MUAP for the EMG signal (not shown), the fre-quency dependence is different, but also then following the ampli-tude response. Remarkably, the coherence with the rectified EMGsignal (Fig. 10C and D) seems less affected. The level and frequencydependence especially in Fig. 10D are already seen without theaddition of noise (Fig. 9D).

4. Discussion

We argued that it is useful to compare the transfer across the a-motoneuron pool to a linear transfer function because this is alsothe implicit assumption behind the use of coherence as a measureof coupling between neuronal populations. The results we showuse a previously proposed a-motoneuron model that is relativelysimple and has a clear physiological basis (Matthews, 1996). Byadjusting the drive level E in Eq. (1), firing frequencies can be dis-tributed and adjusted. Matthews (1999) showed the effect of suchdifferent levels of excitatory drive as being closely related to phys-

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol

Fig. 9. Coherence between the input of all MUs and the (rectified) EMG signal for the long MUAP. (A) EMG signal for 0% CI. (B) EMG signal for 30% CI. (C) Rectified EMG signalfor 0% CI. (D) Rectified EMG signal for 30% CI. The bold line indicates the 95% confidence interval of the bias.

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iological MU behaviour, which confirms the realistic properties ofthis model approach. Our model extends this approach with away to generate surface EMG patterns by extending the pool of fir-ing motoneurons to repeated occurrences of motor unit actionpotentials. We refrained from diversification of motor unit proper-ties and only took the eventual frequency content of the EMG sig-nal as crucial element. We believed and confirmed in a pilot studythat this provides a pure and sufficient view on the mechanism wewere interested in, namely the essential determinants of cortico-muscular transmission across the motoneuron pool.

Fig. 10. Coherence between the input of all MUs and the (rectified) EMG signal for the lonfor 30% CI. (C) Rectified EMG signal for 0% CI. (D) Rectified EMG signal for 30% CI. The b

Please cite this article in press as: Stegeman DF et al. The a-motoneuron pool(2010), doi:10.1016/j.clinph.2010.03.052

An important property of motoneurons we did not include wasthe presence of plateau potentials caused by persistent inward cur-rents (Hounsgaard et al., 1986; Heckmann et al., 2005). Within thecontext of the present level of model complexity, the inclusion ofthis property would introduce extra blocking of the input fromthe cortex to the a-motoneurons since the latter will fire moreindependent of the central drive. This appears in contrast to the re-sult of a study dealing with a similar subject (Taylor and Enoka,2004; Williams and Baker, 2009). These authors report on a de-creased coherence after having removed persistent inward cur-

g MUAP with added noise to the EMG signal. (A) EMG signal for 0% CI. (B) EMG signalold line indicates the 95% confidence interval of the bias.

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol

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rents in their motoneuron model. The reason for that apparently isthe addition of independent input to maintain the mean firingrates of the a-motoneurons. The findings in the study of Williamsand Baker (2009) on coherence differ also in another way. The lev-els of corticomuscular coherence they report are always far belowwhat we found (<0.06) and they are shown to be much more re-lated to the firing frequencies of the motoneurons. An explanationhere could also be that in their model the motoneuron adds ’inter-nal’ independent noise other than the EPSP input noise we simu-lated. The very low coherence levels are somewhat peculiar,though. Considered as a forward system with series elements, itwould mean that corticomuscular coherence could never be largerthan what the motoneuron pool transmits. Reported coherencelevels, however, usually exceed these low values (e.g. Brownet al., 1998; Salenius and Hari, 2003; Riddle and Baker, 2005).

Our approach is based on estimating the behaviour of the a-motoneuron pool in a way that would clarify its deviation from alinear transfer system. The spectral content of the EMG signal isvery much dominated by the spectral content of the MUAP(Fig. 5A). This is confirmed by using two different MUAPs, elicitinga different frequency dependence due to their own spectral con-tents. A convolution of the MUAP with a purely random Poissontype of firing patterns would have resulted in an EMG spectrumwith the frequency distribution as shown in Fig. 2B and D.

Another property of a linear transfer system is that the coher-ence between input and output is not frequency dependent, irre-spective the frequency characteristics of the transfer function.This is certainly true as long as the transfer is noise free, in whichcase the coherence is 1 for all frequencies. When the spectral con-tent of added independent noise has the same spectral propertiesas the input and output signals to which they are added, coherenceis lower than 1, but still frequency independent. The fact that thecoherence is lower than 1 and slightly frequency dependent (goingdown with higher frequencies), for EMG as shown in Fig. 9B, indi-cates non-linearity of the a-motoneuron pool model, but to a lim-ited extent. Equal spectral properties of signal and measurementnoise cannot be expected to be a realistic case. We therefore addedindependent white noise to the EMG signal. This induces an in-creased frequency dependence of the coherence (Fig. 9A and Bagainst Fig. 10A and B). This is to be expected because the signalto noise ratio in the EMG signal is now frequency dependent, espe-cially showing up in the lowest frequencies when the EMG signalloses power. It should be realized that by changing recordingparameters for the EMG like interelectrode distance, electrodemontages, or various forms of filtering (Staudenmann et al.,2009), its spectral content can be manipulated. This may improvethe SNR at specific frequencies of interest.

The coherence with the rectified EMG signal shows a strong fre-quency dependence already without the addition of independentrecording noise (Fig. 9C and D), which is also hardly affected byadding noise. This stresses the strong non-linearity that is intro-duced by rectification, which also raises worries about the use ofa rectified EMG signal before the coherence is computed. Rectifica-tion is often applied and also theoretically discussed (e.g. Myerset al., 2003; Farina et al., 2004; Yao et al., 2007). These papers relatecoherence to the firing frequencies of the motoneurons. They statethat rectification gives a better representation of the EMG at thefiring rate frequencies since rectification enhances the spectralamplitude in that frequency range, which is confirmed in Fig. 5B.Although it is shown in the paper of Yao et al. (2007) that thecoherence after rectification is slightly lower in the 10–20 Hz fre-quency band, this finding appears not to be significant. In our case,the coherence of the rectified EMG signal is lower than that of theEMG signal over the whole 1–100 Hz frequency band studied (low-er half of Fig. 9 and Fig. 10). Thereby, the difference becomes largerat frequencies lower and higher than the motoneuron firing range.

Please cite this article in press as: Stegeman DF et al. The a-motoneuron pool(2010), doi:10.1016/j.clinph.2010.03.052

To confirm that the firing rates indeed play a role here, we in-creased mean drive E and thus increased firing rates for all MUs.It may be clear from our point of view that despite this depen-dence, intermingling or even equating the firing rate frequencyband with coherent corticospinal activity is not justified. With re-spect to rectification, we conclude that it introduces puzzling as-pects in the already non-linear corticospinal coupling whichshould better be avoided. One might even suspect that coherencesas found in some frequency bands and not in others is partly be-cause of the properties of this neurophysiologically meaninglessoperation. Our model as a representation of the transmission overthe motoneuron pool does not provide a potential physiologicalmechanism for increased coherences in frequency bands between15 and 35 Hz or above.

Another straightforward way in which we investigated moto-neuron pool transfer estimation is by studying the influence of acentral oscillatory modulation. For the level of input modulationwe arbitrarily have chosen an amplitude of 5% of the white noiseRMS amplitude. We were not interested in the actual height ofthe modulation amplitude, only in its relative effect. We intro-duced a modulation that about doubles the response to the modu-lated frequency (Fig. 8A). We further showed that the modulatedsignal transmitted by the motoneuron pool is about proportionalto the spectra of the firing pattern and the EMG frequency(Fig. 8A and B), apart from the lowest frequencies in the EMG signal(Fig. 8B). The rectified EMG signal (Fig. 8C) shows a strong decreasealso for the higher frequencies, again indicating the strong diver-gence from linearity due to the process of rectification.

The membrane dynamics determining the synaptic noise at theinput of the a-motoneuron caused by the excitatory (and inhibi-tory) dynamics of the motoneuron throughput will principallyinfluence the transmission of oscillatory phenomena to the muscle.However, adapting the EPSP filter settings within physiologicallimits did not change the results noticeably. Therefore, we con-clude that this frequency element introduced does not play a sig-nificant role in the transmission through the a-motoneuron pool.

The level of CI does appear to be an important factor in our re-sults (Figs. 3, 9 and 10). Common input leads to short-term syn-chrony, meaning that different MUs tend to fire around the sametime. We simulated the MU firing patterns for different levelsand corresponding cross correlation histograms. By comparing thiswith experimental data (e.g. Farmer et al., 1997), the level can bebetween 20% and 30% (example in Fig. 4). We compared two levelsof CI: 0% and 30%. The distribution of the amplitude spectrum ofthe MU firing pattern increases for the higher CI level (Fig. 3),due to summed simultaneous firings and MUAPs. The higher fre-quencies are less augmented than the lower ones and decline tothe same level as the white spectral content of the higher frequen-cies for 0% CI. Especially, the coherence increases substantiallywith the level of CI. This effect is so strong that one could state thatCI to pairs of motoneurons is needed to make corticomuscular cou-pling visible. Part of the regularly measured relatively low cortico-muscular coherence values at or below 0.2 could vanish instatistical insignificance without the presence of a significant CI le-vel (compare Fig. 9B with Fig. 9A).

The consequences of our results for the CTC hypothesis in corti-comuscular communication are certainly relevant and straightfor-ward. The efferent part of movement control as modelled here doesnot largely influence oscillatory transmission, nor does it prefer orneed specific frequency bands for that transmission. Corticospinalcoupling that would use CTC, when present, could be searched inthe closed loop behaviour in the motor control system, in specificinteractions at the neuronal events between the corticomuscular-versus the a-motoneuron level (not modelled here, see Zeitleret al. (submitted for publication)), or higher in the central nervoussystem.

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In conclusion, we investigated how the a-motoneuron affectssignal transmission from the cortical motor drive. Therefore, welooked at the frequency contents of both firing pattern and EMGsignal. Modulation of the input signal is transferred by the a-moto-neuron to the output with an only limited level of non-linearity.The ratio of the modulation is approximately constant, meaningamong others that there is no non-linear frequency preferencecaused by the firing frequencies. Coherence analysis between inputand EMG signal also showed a slight decrease for the higher fre-quency components indicating non-linearity. When adding whitemeasurement noise to the EMG, a frequency dependence showsup. The rectified EMG signal shows a frequency dependence with-out addition of noise, possibly caused by the operation of rectifica-tion that emphasizes the lower frequencies. This might be thereason rectification is used commonly for the computation ofcoherence. Nevertheless, on the basis of the presented results wewould advise against rectification of the EMG signal.

Acknowledgements

This research was supported by grants of the Netherlands Orga-nisation for Scientific Research (NWO; #051.02.050 to G.v.E. andD.F.S.). We would like to thank Ad Moerland, M.Sc., for his contri-bution to the implementation of the a-motoneuron model.

References

Brown P, Salenius S, Rothwell JC, Hari R. Cortical correlate of the Piper rhythm inhumans. J Neurophysiol 1998;80:2911–7.

Brown P. Cortical drives to human muscle: the Piper and related rhythms. ProgNeurobiol 2000;60:97–108.

Calvin WH, Stevens CF. Synaptic noise and other sources of randomness inmotoneuron interspike intervals. J Neurophysiol 1968;31:574–87.

Datta AK, Stephens JA. Synchronization of motor unit activity during voluntarycontraction in man. J Physiol 1990;422:397–419.

Datta AK, Farmer SF, Stephens JA. Central nervous pathways underlyingsynchronization of human motor unit firing studied during voluntarycontractions. J Physiol 1991;432:401–25.

Farina D, Merletti R, Enoka RM. The extraction of neural strategies from the surfaceEMG. J Appl Physiol 2004;96:1486–95.

Farmer S, Halliday DM, Conway BA, Stephens JA, Rosenberg JR. A review of recentapplications of cross-correlation methodologies to human motor unit recording.J Neurosci Methods 1997;74:175–87.

Fries P. A mechanism for cognitive dynamics: neuronal communication throughneuronal coherence. Trends Cogn Sci 2005;9:474–80.

Grosse P, Cassidy MJ, Brown P. EEG–EMG, MEG–EMG and EMG–EMG frequencyanalysis: physiological principles and clinical applications. Clin Neurophysiol2002;113:1523–31.

Heckmann CJ, Gorassini MA, Bennett DJ. Persistent inward currents in motoneurondendrites: implications for motor output. Muscle Nerve 2005;31:135–56.

Hounsgaard J, Hultborn H, Kiehn O. Transmitter-controlled properties of alpha-motoneurons causing long-lasting motor discharge to brief excitatory inputs.Prog Brain Res 1986;64:39–49.

Huysmans MA, Hoozemans MJ, van der Beek AJ, de Looze MP, van Dieën JH. Fatigueeffects on tracking performance and muscle activity. J Electromyogr Kinesiol2008;18:410–9.

Please cite this article in press as: Stegeman DF et al. The a-motoneuron pool(2010), doi:10.1016/j.clinph.2010.03.052

Kirkwood PA, Sears TA, Tuck DL, Westgaard RH. Variations in the time course of thesynchronization of intercostals motoneurons in the cat. J Physiol1982;327:105–35.

Kirkwood PA, Sears TA. Cross-correlation analyses of motoneuron inputs in acoordinated motor act. In: Kruger J, editor. Neuronalcooperativity. Berlin: Springer-Verlag; 1991. p. 225–48.

Kleine BU, Stegeman DS, Mund D, Anders C. Influence of motoneuron firingsynchronizations on SEMG characteristics in dependence of electrode position. JAppl Physiol 2001;91:1588–99.

Matthews PB. Relationship of firing intervals of human motor units to the trajectoryof post-spike after-hyperpolarization and synaptic noise. J Physiol1996;492:597–628.

Matthews PB. Properties of human motoneurons and their synaptic noise deducedfrom motor unit recordings with the aid of computer modelling. J Physiol Paris1999;93:135–45.

Moritz CT, Christou EA, Meyer FG, Enoka RM. Coherence at 16–32 Hz can be causedby short-term synchrony of motor units. J Neurophysiol 2005;94:105–18.

Myers LJ, Lowery M, O’Malley M, Vaughan CL, Heneghan C, St Clair GA, et al.Rectification and non-linear pre-processing of EMG signals for cortico-muscularanalysis. J Neurosci Methods 2003;124:157–65.

Pan ZS, Zhang Y, Parker PA. Motor unit power spectrum and firing rate. Med Biol EngComput 1989;27:14–8.

Penn IW, Chuang TY, Chan RC, Hsu TC. EMG power spectrum analysis of first dorsalinterosseous muscle in pianists. Med Sci Sports Exerc 1999;31:1834–8.

Riddle CN, Baker SN. Manipulation of peripheral neural feedback loops altershuman corticomuscular coherence. J Physiol 2005;566:625–39.

Salenius S, Hari R. Synchronous cortical oscillatory activity during motor action.Curr Opin Neurobiol 2003;13:678–84.

Schmied A, Pouget J, Vedel JP. Electrochemical coupling and synchronous firing ofsingle wrist extensor motor units in sporadic amyotrophic lateral sclerosis. ClinNeurophysiol 1999;110:960–74.

Schmied A, Pagni S, Sturm H, Vedel JP. Selective enhancement of motoneuron short-term synchrony during an attention-demanding task. Exp Brain Res2000;133:377–90.

Schnitzler A, Münks C, Butz M, Timmermann L, Gross J. Synchronized brain networkassociated with essential tremor as revealed by magnetoencephalography. MovDisord 2009;24:1629–35.

Schoffelen JM, Oostenveld R, Fries P. Neuronal coherence as a mechanism ofeffective corticospinal interaction. Science 2005;308:111–3.

Sears TA, Stagg D. Short-term synchronization of intercostal motoneurone activity. JPhysiol 1976;263:357–81.

Staudenmann D, Roeleveld K, Stegeman DF, van Dieën JH. Methodological aspects ofSEMG recordings for force estimation – a tutorial and review. J ElectromyogrKinesiol 2009 [Epub ahead of print].

Svirskis G, Hounsgaard J. Influence of membrane properties on spikesynchronization in neurons: theory and experiments. Network2003;14:747–63.

Taylor AM, Enoka RM. Quantification of the factors that influence dischargecorrelation in model motor neurons. J Neurophysiol 2004;91:796–814.

Ten Hoopen M. Examples of power spectra of univariate point processes. Kybernetik1974;16:145–53.

Terry K, Griffin L. Coherence and short-term synchronization are insensitive tomotor unit spike train nonstationarity. J Neurosci Methods 2010;185:185–98.

Van Elswijk G, Maij F, Schoffelen JM, Overeem S, Stegeman DF, Fries P. Corticospinalb-band synchronization entails rhythmic gain modulation. J. Neurosci2010;30:4481–8.

Williams ER, Baker SN. Circuits generating corticomuscular coherence investigatedusing a biophysically based computational model. I. Descending systems. JNeurophysiol 2009;101:31–41.

Womelsdorf T, Schoffelen JM, Oostenveld R, Singer W, Desimone R, Engel AK, FriesP. Modulation of neuronal interactions through neuronal synchronization.Science 2007;316:1609–12.

Yao B, Salenius S, Yue GH, Brown RW, Liu JZ. Effects of surface EMG rectification onpower and coherence analyses: an EEG and MEG study. J Neurosci Methods2007;159:215–23.

as transmitter of rhythmicities in cortical motor drive. Clin Neurophysiol