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The α-motoneuron pool as transmitter of rhythmicities in cortical motor drive
Clinical Neurophysiology 121 (2010) 1633–1642
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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 Netherlands b Centre for Cognitive Neuroimaging, Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen Medical Centre, Department of Neurology/Clinical Neurophysiology, Nijmegen, The Netherlands c Faculty of Human Movement Sciences, Research Institute MOVE, VU University Amsterdam, The Netherlands
a r t i c l e
i n f o
Article history: Accepted 4 March 2010
Keywords: Motoneuron pool Corticomuscular coherence a-Motoneuron model Corticomuscular transmission Motor drive Motor unit firing
a b s t r a c t Objective: Investigate the effectiveness and frequency dependence of central drive transmission via the a-motoneuron pool to the muscle. Methods: We describe a model for the simulation of a-motoneuron firing and the EMG signal as response to central drive input. The transfer in the frequency domain is investigated. Coherence between stochastical central input and EMG is also evaluated. Results: The transmission of central rhythmicities to the EMG signal relates to the spectral content of the latter. Coherence between central input to the a-motoneuron pool and the EMG signal is significant whereby the coupling strength hardly depends on the frequency in a range from 1 to 100 Hz. Common central input to pairs of a-motoneurons strongly increases the coherence levels. The often-used rectification of the EMG signal introduces a clear frequency dependence. Conclusions: Oscillatory phenomena are strongly transmitted via the a-motoneuron pool. The motoneuron 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 a strong frequency dependency. We think that it should be avoided. Significance: Our findings show that rhythmicities are translated into a-motoneuron activity without strong non-linearities. Ó 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 patterns. Wollaston reported this already in 1810 (Brown, 2000). In pathological circumstances rhythmic drive to muscles can lead to disabling symptoms as in Parkinson’s disease and essential tremor (Schnitzler et al., 2009). Recently, long range interaction of oscillatory phenomena has also been given a meaning in selective communication between neuronal groups. The conceptual mechanism behind it, called communication through coherence (CTC, Fries, 2005), gets increasing support from experimental evidence (Womelsdorf et al., 2007). The concept comprises the assumption that selective communication between neuronal groups is enhanced by oscillatory activity in specific frequency bands that are roughly in the range 10 and 80 Hz. Corticospinal coherence is regarded as strong evidence for CTC since the distance
* Corresponding author at: Radboud University Nijmegen Medical Centre, 920 Department of Neurology/Clinical Neurophysiology, P.O. Box 9101, 6500HB Nijmegen, The Netherlands. Tel.: +31 24 3615284; fax: +31 24 3615097. E-mail address: [email protected] (D.F. Stegeman).
between the signal sources excludes irrelevant volume conduction mediated effects (Schoffelen et al., 2005; Van Elswijk et al., 2010). An interesting question for the corticospinal system is how cortical oscillations, after having descended the corticospinal tract, are translated by the a-motoneuron pool into motoneuron activity and ultimately into the EMG signal. Thereby, the properties of amotoneurons, especially their long afterhyperpolarization (AHP), are expected to be a non-linear obstacle in the transfer of oscillatory activity. Ways to analyze rhythmic coupling between cortex and muscle in the frequency domain have been proposed (e.g. Grosse et al., 2002), and a number of authors have already looked into the spinal transmission 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 corticospinal interaction apparently occurs. Second, since the a- and bfrequency bands are more or less in the order of the firing frequencies of a-motoneurons, attempts are made to relate the transmission efficiency directly to those firing frequencies (Myers et al., 2003; Farina et al., 2004). Third, the frequency content of the in-
1388-2457/$36.00 Ó 2010 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.clinph.2010.03.052
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volved electrophysiological signals (EEG, MEG, and EMG) plays a role. It leads for instance to the regular question whether the EMG signal should be rectified before a coherence analysis is done (Myers et al., 2003; Yao et al., 2007). In this context also the effect of the frequency content of the ‘synaptic noise’ at the input of the a-motoneurons can be added. It is caused by the motoneuron membrane dynamics reacting to excitatory and inhibitory input (Calvin and Stevens, 1968; Matthews, 1996). This modulating element may also play a part in transmitting central oscillatory phenomena to a muscle. The reported level of corticospinal coherence in the b- and the c-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 to the latter. It is to be expected that part of the potential frequency coupling between EEG or MEG over the motor areas and the information in corticospinal neuronal firings, will be lost across the amotoneuron pool (Fig. 1). Furthermore, quantitative insight in that loss and the non-linearity that is introduced, would ’inversely’ give an 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 different motor units (MUs) show a peak close to delay time zero (Farmer et al., 1997). This means that the probability of a MU firing rises around the time that another one fires. This coupling between firings of MU pairs is called ‘short-term synchrony’ (Sears and Stagg, 1976; Kirkwood et al., 1982). Synchronization is thought to be dominated by a common input (CI) due to branching of axons so that an axon can contribute as input to several a-motoneurons (Kirkwood and Sears, 1991). The cortical origin of motoneuron synchronization is supported by experimental evidence reported by Datta and Stephens (1990), Datta et al. (1991), and Schmied et al. (1999). The amount of CI which should be present can in principle be determined from the level of short-term synchrony (Kleine et al., 2001). We present a model study to obtain insight in the corticomuscular signal transmission considering the various frequency domains. Following the reasoning by Matthews (1999), we adopted a deliberately simple and elegant computational model of the a-motoneuron (Matthews, 1996) in which we believe that the essential elements
Σ
EPSP Filter
E+N
for the present purpose are available. The model only accounts for the steady state during a sustained isometric contraction. It has no elements which could mimic dynamic task behaviour. For instance, it cannot describe the recruitment of plateau potentials (Svirskis and Hounsgaard, 2003; Taylor and Enoka, 2004; Williams and Baker, 2009) in the motor unit firing dynamics. We purposeful restricted the model to the simplest, but still physiologically relevant forward transmission over the motoneuron pool without feedback elements to reveal the pure properties of this element in motor control. Our version of the model includes a pool of motoneurons. We also added the generation of motor unit action potentials, recorded at the skin surface, in response to the firings of each a-motoneuron. Furthermore, we adopted the phenomenon of short-term synchrony by assuming a common input to each pair of a-motoneurons (Moritz et al., 2005). To simulate cortical rhythmicity we modulated the cortical input to the motoneurons in different frequency ranges. Our goal was to investigate the effectiveness and the properties of oscillatory central drive transmission to the muscle, its relation with the firing patterns of the a-motoneurons, and the consequences for the surface EMG signal. We will distinguish the frequency aspects mentioned above and look at the transfer across the a-motoneuron pool basically by comparing it to a linear transfer function. Apart from being a usual first approach in system’s analysis, a linear transfer also is the implicit assumption behind the use of coherence as a measure of coupling between neuronal populations. We will therefore present the EMG signal in response to oscillatory corticospinal activity as a measure of transmission quality. Also, the coherence between stochastic cortical drive activity and the surface EMG signal is computed. Moreover, we compared the data with and without rectification 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 following main steps: (1) generating the firing pattern of an a-motoneuron; (2) introducing a certain level of common input to pairs of motor units to introduce short-term synchrony. The model was implemented in the Matlab environment (The MathWorks, Inc., Natick,
C
MUAP
EMG 50 MUs
AHP
Cortical drive
5 ms
5 ms
Motoneuron pool
Muscle
Fig. 1. Functional model scheme of the a-motoneuron in three stages (cortical drive, motoneuron pool, and muscle). Random firing events from the cortex, expressed as a mean value plus white noise, are summed and then filtered with EPSP characteristics. At box C the signal is compared to the threshold value. If higher, the a-motoneuron fires resulting in a firing event. The afterhyperpolarization phase is taken into consideration at C as well. The resulting firing pattern is convoluted with a MUAP wave shape giving the contribution of this a-motoneuron to the EMG signal.
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MA, version 7.6.0). Instead of the 1 ms time resolution used in the Matthews (1996) study, we used a time resolution of 0.5 ms. 2.1.1. Firing patterns The output from pyramidal neurons in the cortex is regarded as the input to each neuron in the a-motoneuron pool. These signals are assumed to be Poisson distributed spike trains which, as being central drive dependent, may have a time varying density (Fig. 1). The input to an a-motoneuron is the sum of such Poisson distributed spike trains which, when many events are summed, can well be approximated by a mean value plus Gaussian distributed white noise. The membrane dynamics resulting in the characteristics of excitatory postsynaptic potentials (EPSPs) will have an influence on how the input at the a-motoneuron’s membrane is transferred to that neuron. This is added in the model as a filter mimicking the frequency content of the EPSPs (Fig. 1). So then the input to the spike generator of the a-motoneuron (C in Fig. 1) is modelled as a mean value plus noise, which now is not white any longer, but has a frequency content dictated by the EPSP wave shape. This EPSP filter has the properties as used by Matthews (1996). Thereby, the membrane dynamics are taken from the autocorrelation function of synaptic noise expressed in a time constant of 4 ms as presented in Calvin and Stevens (1968). As suggested by Matthews (1996) for our 0.5 ms time resolution, we adapted that value to 5 ms. A crucial element in the model is to normalize the standard deviation of the membrane noise N to unity, further used as the amplitude unit in the drive to the neuron model (noise unit, NU). The membrane potential of the a-motoneuron in the spinal cord is assumed to increase, in physiological terms, due to the summation of EPSPs, approached by a steady drive E plus the synaptic noise N (Fig. 1). When threshold is reached, an action potential is thought to arise that elicits a motor unit firing event. Immediately following that instant, the membrane potential of the a-motoneuron jumps down with an amplitude shift A and then shows a long-lasting AHP phase. This phase consists of the lowered membrane potential to rise again exponentially with time constant s from the minimum level A, on which the central drive E + N is superimposed, to the resting state f(t) = 0. This AHP phase can be described by: t
f ðtÞ ¼ Aes þ E þ 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; Kleine et al., 2001). The next action potential is generated as soon as the threshold is reached again (f(t) = 0). The firing rate is tuned by choosing 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 a previous firing the next firing occurs when for the first time N exceeds 1.5 times its own standard deviation (NU). This combination of parameters generates physiologically realistic firing patterns for a moderate level of contraction with firing rates between 10 and 15 firings per second (Matthews, 1996; Kleine et al., 2001). The presented results are based on a population of 50 a-motoneurons. 2.1.2. Motor unit synchronization Short-term synchrony between MU pairs (described by e.g. Schmied et al., 2000 and Terry and Griffin, 2010) can be introduced by assuming a certain level of common input. This level can be determined by looking inversely to the nervous system. Firing patterns of pairs of MUs with a level of short-term synchrony in a physiological range (Farmer et al., 1997) can be generated with around 30% of CI to MU pairs (see results). When considering this level for more than two MUs, there are two basic possibilities: (1) 30% of the input is equal for all MUs;
(2) every pair of MUs shares 30% of their input, which is different from the shared input between all other pairs. In the first case, the 70% of not shared input to any of the single MUs is independent of the input to all others. In the second case, every MU has a 30% common input with any other MU. This common input is different for any pair. Assuming that the common input is caused by a shared wiring structure, the second model appears more realistic and 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 independent equally large white noise sources xj(t). To realize the second possibility, the normalized covariance matrix K of z (for 30% CI noise) should look like:
3 1 0:3 0:3 :: 6 0:3 1 :: 0:3 7 7 6 K ¼ Cov ðzÞ ¼ 6 7 4 0:3 :: 1 0:3 5 2
::
0:3 0:3
ð2Þ
1
In order to obtain noise input signals to the a-motoneurons being 30% common to each pair of MUs from independent noise signals, some algebraic operations must be performed. That is, we have to find a solution for the following equation:
z ¼Ax
ð3Þ
Where A is an R R matrix that should match with the covariance matrix K, which can be written as: 1
1
K ¼ A AT ¼ P K P T þ P K2 K2 P T
ð4Þ
Where K is the matrix with eigenvalues of K and P contains the corresponding eigenvectors. It follows that: 1
A ¼ P K2
ð5Þ
This can be used in combination with Eq. (3) to generate the R input signals z, obeying Eq. (2), to the MUs from the same number of independent 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 events must then be replaced with MUAP wave shapes by means of convolution. The main goal in defining the MUAPs was to come up with two EMG signals having the spectral distribution of a small muscle (FDI, Penn et al., 1999) and a larger upper extremity muscle (ECR, Huysmans et al., 2008), respectively, using wave shapes with a duration d of 15 ms and 25 ms (Fig. 2A and C, with frequency spectra in Fig. 2B and D). A half pulse shape was defined by:
hðtÞ ¼ 5 sin
1 t :exp 1 for 0 < t d=2 d=2 s d=2
pt
ð6Þ
For d=2 < t d a time and amplitude mirrored version of Eq. (6) following the zero value at t = d/2 was used. The value for the damping factor s is set at 0.18 ms. All 50 MUs were represented by the same long or short duration MUAP. To this end, the 50 single firing sequences are summed together and the surface EMG signal is created by convolution of the resulting sum of 50 firing patterns with one of the two MUAP wave shapes. To obtain a sufficient signal to noise ratio, the model was run for 100 or 150 s for, respectively, the frequency spectra and the coherence calculation (see below). 2.3. Motoneuron pool transfer estimation Signal transfer through the motoneuron pool will be expressed in amplitude modulation and coherence. The analyses were done
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Fig. 2. Short (A) and long MUAP (C) and their respective amplitude spectra (B and D).
in MATLAB (MathWorks, Natick, MA), with the help of FieldTrip, an open source toolbox for the analysis of neurophysiological data (Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, the Netherlands; see http://www.ru.nl/ neuroimaging/fieldtrip). The often-used rectification of the EMG signal as pre-processing option for computing corticomuscular coherence is discussed for instance by Myers et al. (2003), Farina et al. (2004), and Yao et al. (2007). To contribute to that discussion, the simulated surface EMG signals are also used after rectification. To study the influence of a central oscillatory modulation, sine waves with frequencies ranging from 1 to 100 Hz were superimposed on the summed 50 white noise inputs to the 50 a-motoneurons (signal x in Eq. (3)). The modulation amplitude was set arbitrarily to 5% of the white noise root mean square (RMS) amplitude for each of the 50 elements of x in Eq. (3). The effect of that modulation on the EMG spectrum will be presented. The signals were simulated for 100 s. Spectral content was taken as the average from 100 non-overlapping segments of 1 s, resulting in a 1 Hz frequency resolution. The most popular way of looking at the transfer of oscillatory phenomena is coherence analysis (e.g. Grosse et al., 2002):
jPxy ðf Þj C xy ðf Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pxx ðf ÞPyy ðf Þ
ð7Þ
Pxx and Pyy are the power spectral densities of two signals between which the coherence Cxy is computed, Pxy is the cross power spectral density. Coherence is computed between the summed white corticospinal neural input and the (non-rectified and rectified) interference EMG signals. In this case, the simulations were run, now for 150 s. The data is divided into non-overlapping epochs of 1 s each. A Hanning taper function is applied to each epoch before coherence is calculated. To test for the statistical significance a nonparametric permutation test was performed. The null-hypothesis states that there is no difference between conditions and so that the data are exchangeable. The data epochs were randomly shuffled 100 times after which a 95% confidence interval is created
by determining average and standard deviation over these random shuffles. Coherence values outside the confidence interval were considered as significant. For a more detailed description of this method 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 signals Fig. 3 shows frequency spectra of the firing patterns summed over 50 a-motoneurons for 0% and 30% CI. The MU firing frequency distribution, 10 and 15 Hz, determined by the choice for the distribution of mean drives E, is clearly recognized in the spectra of both patterns. The spectrum for 0% CI has the typical appearance of a socalled stochastic renewal process with augmentation around the mean firing frequency and its harmonics and a white spectral content for higher frequencies (Ten Hoopen, 1974; Pan et al., 1989). As can be seen, CI to MU pairs increases the amplitude of the spectral distribution of the summed a-motoneuron firing patterns. It does also result in a different spectral shape. The higher frequencies are less augmented by the CI than lower frequencies and also tend to a plateau value for the highest frequencies (>>100 Hz, see inset Fig. 3). To illustrate that 30% CI, having this substantial influence on these spectra, is a realistic choice, Fig. 4 shows a cross correlation histogram of the short-term synchrony that is realized by assuming this level of CI in the model (e.g. Farmer et al., 1997). Fig. 5A shows the frequency contents of the non-rectified EMG signals on the basis of 30% CI for the long MUAP wave shape. Here too, the peak around 13 Hz is caused by the mean MU firing frequency. Furthermore, Fig. 5B shows that rectification emphasizes the lower frequency contents, as expected. 3.1.2. Amplitude response to added oscillations of 1–100 Hz Fig. 6 presents the spectral content (along the axis indicated with output frequency) of the summed a-motoneuron spike patterns (Fig. 6A) and of the EMG signal without (Fig. 6B) and with (Fig. 6C) rectification using the long duration MUAP wave shape
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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 the spectrum 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 the firings of two different motor units when assuming a 30% common input to pairs of a-motoneurons.
and 30% CI. For each repetition the 5% superimposed modulation to the white noise input of the model was added with increasing frequency from 1 to 100 Hz in 1 Hz steps (along the axis indicated with input frequency), resulting in a diagonal ridge in these three dimensional presentations. To illustrate the transfer of the modulating frequencies in more detail, Fig. 7 presents the diagonal ridges in Fig. 6 in the same order, but now also for the short duration MUAP wave shape. It is noted that the result in part A below 30 Hz can directly be compared and appears similar to the model result shown for the 13 Hz motoneuron in Fig. 5 from Matthews (1999). The choice for an EPSP filter (see Section 1 and Section 2.1.1) with a time constant of 5 ms was based on experi-
mental data (Calvin and Stevens, 1968; Matthews, 1996). The added modulation input is ’injected’ to the system before that EPSP filter (Fig. 1). As indicated already in the introduction, the properties of that filter may also influence the frequency transfer. As the membrane dynamics may vary between motoneurons of different muscles, we doubled the time constant to 10 ms (not shown). This has no noticeable influence on the results as presented in Fig. 7. When comparing Fig. 5A and B with Fig. 7B and C it already appears that the shape of the spectral contents is similar. That means that the transfer of rhythmic activity is about proportional to the spectral content of the EMG signal. That this is more or less the case is illustrated in Fig. 8B, where the ratio between the modulated amplitude (Fig. 7B) and the EMG spectral content (Fig. 5A) is presented. Fig. 8A shows this ratio for the MU firing pattern and Fig. 8C for the rectified EMG signal. Apart from a somewhat increased noise level because of the division operation, there is for Fig. 8A and B no clear sign of a preference for this modulation in a relevant specific frequency band, especially not in the region of the firing frequencies of the motoneurons. The ratio for the EMG signal tends to a value of 1 for the lowest frequencies (<20 Hz, Fig. 8B), meaning that the extra modulation is less or not transferred for those frequencies. For the rectified EMG, this ratio also approaches unity for the higher frequencies (>60 Hz, Fig. 8C). 3.2. Coherence analysis 3.2.1. Between white motoneuron input and EMG The coherence between the summed input to all motoneurons and the (rectified) EMG signal is computed for 0% and 30% CI for the long MUAP (Fig. 9). The CI level leading to short-term synchrony appears to be an utmost important factor that enhances coherence (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 should be realized that for a linear system, without independent noise
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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 and 100 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.
at the system’s input or output, the coherence would be 1 for all frequencies, independent of the frequency characteristics of the system’s transfer function. This is because in Eq. (7) the denominator corrects for the spectral content of both input and output. Even the highest values presented in Fig. 9B do not reach that unity value. Furthermore, the coherence also slightly decreases with increasing frequency. The a-motoneuron pool system obviously does not behave as a ‘noise free’ linear system. Another
essential point is that the firing frequencies of the motor units do not seem to play a substantial role in Fig. 9A and B, that is to say that they are not interfering with the transmission of cortical oscillations over the a-motoneuron pool in terms of the coherence between input and output. For the rectified EMG signal, however, the firing rates determine the upslope of the coherence from the lowest frequency up to the mean firing rate as shown in Fig. 9D.
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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.
A
Ratio
3 2 1
0
20
Ratio
80
100
80
100
80
100
B
3 2 1
0
20
40 60 Frequency (Hz)
C
3 Ratio
40 60 Frequency (Hz)
2 1 0
20
40 60 Frequency (Hz)
Fig. 8. (A) Ratio between the modulated amplitude as shown in Fig. 7A (bold) and the firing pattern spectral content as presented in Fig. 3 (bold). (B) Ratio between the modulated amplitude as shown in Fig. 7B (bold) and the EMG spectral content as 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.
3.2.2. With independent noise added When performing experiments of any kind, there will be measurement noise present. It can be that the input as defined is not
completely transferred to the system studied and that noise is added to the output signal. Any approach towards reality should therefore add some independent noise to the input or output of the system. Added input noise (part of the cortical output signal that is not transferred to the a-motoneuron pool) will decrease the level of coherence with a constant factor for all frequencies as long as that noise has the same spectral content as the input. The signal to noise ratio (SNR) of the input then decreases with a constant factor. When, however, independent white measurement noise is added to the output (the EMG signal) the coherence profile between input and EMG is affected (Fig. 10) because the white noise has been given the RMS amplitude of the EMG signal. The effect is largest in the low frequency regions (<20 Hz) where the EMG signal (Fig. 5A) and the amplitude transfer (Fig. 8B) are steeply decreasing. It follows more or less the frequency dependence of the amplitude response to added oscillations (Fig. 7). When using the short duration MUAP for the EMG signal (not shown), the frequency dependence is different, but also then following the amplitude response. Remarkably, the coherence with the rectified EMG signal (Fig. 10C and D) seems less affected. The level and frequency dependence especially in Fig. 10D are already seen without the addition of noise (Fig. 9D). 4. Discussion We argued that it is useful to compare the transfer across the amotoneuron pool to a linear transfer function because this is also the implicit assumption behind the use of coherence as a measure of coupling between neuronal populations. The results we show use a previously proposed a-motoneuron model that is relatively simple and has a clear physiological basis (Matthews, 1996). By adjusting the drive level E in Eq. (1), firing frequencies can be distributed and adjusted. Matthews (1999) showed the effect of such different levels of excitatory drive as being closely related to phys-
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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 signal for 0% CI. (D) Rectified EMG signal for 30% CI. The bold line indicates the 95% confidence interval of the bias.
iological MU behaviour, which confirms the realistic properties of this model approach. Our model extends this approach with a way to generate surface EMG patterns by extending the pool of firing motoneurons to repeated occurrences of motor unit action potentials. We refrained from diversification of motor unit properties and only took the eventual frequency content of the EMG signal as crucial element. We believed and confirmed in a pilot study that this provides a pure and sufficient view on the mechanism we were interested in, namely the essential determinants of corticomuscular transmission across the motoneuron pool.
An important property of motoneurons we did not include was the presence of plateau potentials caused by persistent inward currents (Hounsgaard et al., 1986; Heckmann et al., 2005). Within the context of the present level of model complexity, the inclusion of this property would introduce extra blocking of the input from the cortex to the a-motoneurons since the latter will fire more independent of the central drive. This appears in contrast to the result of a study dealing with a similar subject (Taylor and Enoka, 2004; Williams and Baker, 2009). These authors report on a decreased coherence after having removed persistent inward cur-
Fig. 10. Coherence between the input of all MUs and the (rectified) EMG signal for the long MUAP with added noise to the EMG signal. (A) EMG signal for 0% CI. (B) EMG signal for 30% CI. (C) Rectified EMG signal for 0% CI. (D) Rectified EMG signal for 30% CI. The bold line indicates the 95% confidence interval of the bias.
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rents in their motoneuron model. The reason for that apparently is the addition of independent input to maintain the mean firing rates of the a-motoneurons. The findings in the study of Williams and Baker (2009) on coherence differ also in another way. The levels of corticomuscular coherence they report are always far below what we found (<0.06) and they are shown to be much more related to the firing frequencies of the motoneurons. An explanation here could also be that in their model the motoneuron adds ’internal’ independent noise other than the EPSP input noise we simulated. The very low coherence levels are somewhat peculiar, though. Considered as a forward system with series elements, it would mean that corticomuscular coherence could never be larger than what the motoneuron pool transmits. Reported coherence levels, however, usually exceed these low values (e.g. Brown et al., 1998; Salenius and Hari, 2003; Riddle and Baker, 2005). Our approach is based on estimating the behaviour of the amotoneuron pool in a way that would clarify its deviation from a linear transfer system. The spectral content of the EMG signal is very much dominated by the spectral content of the MUAP (Fig. 5A). This is confirmed by using two different MUAPs, eliciting a different frequency dependence due to their own spectral contents. A convolution of the MUAP with a purely random Poisson type of firing patterns would have resulted in an EMG spectrum with the frequency distribution as shown in Fig. 2B and D. Another property of a linear transfer system is that the coherence between input and output is not frequency dependent, irrespective the frequency characteristics of the transfer function. This is certainly true as long as the transfer is noise free, in which case the coherence is 1 for all frequencies. When the spectral content of added independent noise has the same spectral properties as the input and output signals to which they are added, coherence is lower than 1, but still frequency independent. The fact that the coherence is lower than 1 and slightly frequency dependent (going down with higher frequencies), for EMG as shown in Fig. 9B, indicates non-linearity of the a-motoneuron pool model, but to a limited extent. Equal spectral properties of signal and measurement noise cannot be expected to be a realistic case. We therefore added independent white noise to the EMG signal. This induces an increased frequency dependence of the coherence (Fig. 9A and B against Fig. 10A and B). This is to be expected because the signal to noise ratio in the EMG signal is now frequency dependent, especially showing up in the lowest frequencies when the EMG signal loses power. It should be realized that by changing recording parameters for the EMG like interelectrode distance, electrode montages, or various forms of filtering (Staudenmann et al., 2009), its spectral content can be manipulated. This may improve the SNR at specific frequencies of interest. The coherence with the rectified EMG signal shows a strong frequency dependence already without the addition of independent recording noise (Fig. 9C and D), which is also hardly affected by adding noise. This stresses the strong non-linearity that is introduced by rectification, which also raises worries about the use of a rectified EMG signal before the coherence is computed. Rectification is often applied and also theoretically discussed (e.g. Myers et al., 2003; Farina et al., 2004; Yao et al., 2007). These papers relate coherence to the firing frequencies of the motoneurons. They state that rectification gives a better representation of the EMG at the firing rate frequencies since rectification enhances the spectral amplitude in that frequency range, which is confirmed in Fig. 5B. Although it is shown in the paper of Yao et al. (2007) that the coherence after rectification is slightly lower in the 10–20 Hz frequency band, this finding appears not to be significant. In our case, the coherence of the rectified EMG signal is lower than that of the EMG signal over the whole 1–100 Hz frequency band studied (lower half of Fig. 9 and Fig. 10). Thereby, the difference becomes larger at frequencies lower and higher than the motoneuron firing range.
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To confirm that the firing rates indeed play a role here, we increased mean drive E and thus increased firing rates for all MUs. It may be clear from our point of view that despite this dependence, intermingling or even equating the firing rate frequency band with coherent corticospinal activity is not justified. With respect to rectification, we conclude that it introduces puzzling aspects in the already non-linear corticospinal coupling which should better be avoided. One might even suspect that coherences as found in some frequency bands and not in others is partly because of the properties of this neurophysiologically meaningless operation. Our model as a representation of the transmission over the motoneuron pool does not provide a potential physiological mechanism for increased coherences in frequency bands between 15 and 35 Hz or above. Another straightforward way in which we investigated motoneuron pool transfer estimation is by studying the influence of a central oscillatory modulation. For the level of input modulation we arbitrarily have chosen an amplitude of 5% of the white noise RMS amplitude. We were not interested in the actual height of the modulation amplitude, only in its relative effect. We introduced a modulation that about doubles the response to the modulated frequency (Fig. 8A). We further showed that the modulated signal transmitted by the motoneuron pool is about proportional to 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 decrease also for the higher frequencies, again indicating the strong divergence from linearity due to the process of rectification. The membrane dynamics determining the synaptic noise at the input of the a-motoneuron caused by the excitatory (and inhibitory) dynamics of the motoneuron throughput will principally influence the transmission of oscillatory phenomena to the muscle. However, adapting the EPSP filter settings within physiological limits did not change the results noticeably. Therefore, we conclude that this frequency element introduced does not play a significant role in the transmission through the a-motoneuron pool. The level of CI does appear to be an important factor in our results (Figs. 3, 9 and 10). Common input leads to short-term synchrony, meaning that different MUs tend to fire around the same time. We simulated the MU firing patterns for different levels and corresponding cross correlation histograms. By comparing this with experimental data (e.g. Farmer et al., 1997), the level can be between 20% and 30% (example in Fig. 4). We compared two levels of CI: 0% and 30%. The distribution of the amplitude spectrum of the MU firing pattern increases for the higher CI level (Fig. 3), due to summed simultaneous firings and MUAPs. The higher frequencies are less augmented than the lower ones and decline to the same level as the white spectral content of the higher frequencies for 0% CI. Especially, the coherence increases substantially with the level of CI. This effect is so strong that one could state that CI to pairs of motoneurons is needed to make corticomuscular coupling visible. Part of the regularly measured relatively low corticomuscular coherence values at or below 0.2 could vanish in statistical insignificance without the presence of a significant CI level (compare Fig. 9B with Fig. 9A). The consequences of our results for the CTC hypothesis in corticomuscular communication are certainly relevant and straightforward. The efferent part of movement control as modelled here does not largely influence oscillatory transmission, nor does it prefer or need specific frequency bands for that transmission. Corticospinal coupling that would use CTC, when present, could be searched in the closed loop behaviour in the motor control system, in specific interactions at the neuronal events between the corticomuscularversus the a-motoneuron level (not modelled here, see Zeitler et al. (submitted for publication)), or higher in the central nervous system.
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In conclusion, we investigated how the a-motoneuron affects signal transmission from the cortical motor drive. Therefore, we looked at the frequency contents of both firing pattern and EMG signal. Modulation of the input signal is transferred by the a-motoneuron to the output with an only limited level of non-linearity. The ratio of the modulation is approximately constant, meaning among others that there is no non-linear frequency preference caused by the firing frequencies. Coherence analysis between input and EMG signal also showed a slight decrease for the higher frequency components indicating non-linearity. When adding white measurement noise to the EMG, a frequency dependence shows up. The rectified EMG signal shows a frequency dependence without addition of noise, possibly caused by the operation of rectification that emphasizes the lower frequencies. This might be the reason rectification is used commonly for the computation of coherence. Nevertheless, on the basis of the presented results we would advise against rectification of the EMG signal. Acknowledgements This research was supported by grants of the Netherlands Organisation for Scientific Research (NWO; #051.02.050 to G.v.E. and D.F.S.). We would like to thank Ad Moerland, M.Sc., for his contribution to the implementation of the a-motoneuron model. References Brown P, Salenius S, Rothwell JC, Hari R. Cortical correlate of the Piper rhythm in humans. J Neurophysiol 1998;80:2911–7. Brown P. Cortical drives to human muscle: the Piper and related rhythms. Prog Neurobiol 2000;60:97–108. Calvin WH, Stevens CF. Synaptic noise and other sources of randomness in motoneuron interspike intervals. J Neurophysiol 1968;31:574–87. Datta AK, Stephens JA. Synchronization of motor unit activity during voluntary contraction in man. J Physiol 1990;422:397–419. Datta AK, Farmer SF, Stephens JA. Central nervous pathways underlying synchronization of human motor unit firing studied during voluntary contractions. J Physiol 1991;432:401–25. Farina D, Merletti R, Enoka RM. The extraction of neural strategies from the surface EMG. J Appl Physiol 2004;96:1486–95. Farmer S, Halliday DM, Conway BA, Stephens JA, Rosenberg JR. A review of recent applications 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 through neuronal coherence. Trends Cogn Sci 2005;9:474–80. Grosse P, Cassidy MJ, Brown P. EEG–EMG, MEG–EMG and EMG–EMG frequency analysis: physiological principles and clinical applications. Clin Neurophysiol 2002;113:1523–31. Heckmann CJ, Gorassini MA, Bennett DJ. Persistent inward currents in motoneuron dendrites: implications for motor output. Muscle Nerve 2005;31:135–56. Hounsgaard J, Hultborn H, Kiehn O. Transmitter-controlled properties of alphamotoneurons 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. Fatigue effects on tracking performance and muscle activity. J Electromyogr Kinesiol 2008;18:410–9.
Kirkwood PA, Sears TA, Tuck DL, Westgaard RH. Variations in the time course of the synchronization of intercostals motoneurons in the cat. J Physiol 1982;327:105–35. Kirkwood PA, Sears TA. Cross-correlation analyses of motoneuron inputs in a coordinated motor act. In: Kruger J, editor. Neuronal cooperativity. Berlin: Springer-Verlag; 1991. p. 225–48. Kleine BU, Stegeman DS, Mund D, Anders C. Influence of motoneuron firing synchronizations on SEMG characteristics in dependence of electrode position. J Appl Physiol 2001;91:1588–99. Matthews PB. Relationship of firing intervals of human motor units to the trajectory of post-spike after-hyperpolarization and synaptic noise. J Physiol 1996;492:597–628. Matthews PB. Properties of human motoneurons and their synaptic noise deduced from motor unit recordings with the aid of computer modelling. J Physiol Paris 1999;93:135–45. Moritz CT, Christou EA, Meyer FG, Enoka RM. Coherence at 16–32 Hz can be caused by 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-muscular analysis. J Neurosci Methods 2003;124:157–65. Pan ZS, Zhang Y, Parker PA. Motor unit power spectrum and firing rate. Med Biol Eng Comput 1989;27:14–8. Penn IW, Chuang TY, Chan RC, Hsu TC. EMG power spectrum analysis of first dorsal interosseous muscle in pianists. Med Sci Sports Exerc 1999;31:1834–8. Riddle CN, Baker SN. Manipulation of peripheral neural feedback loops alters human 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 of single wrist extensor motor units in sporadic amyotrophic lateral sclerosis. Clin Neurophysiol 1999;110:960–74. Schmied A, Pagni S, Sturm H, Vedel JP. Selective enhancement of motoneuron shortterm synchrony during an attention-demanding task. Exp Brain Res 2000;133:377–90. Schnitzler A, Münks C, Butz M, Timmermann L, Gross J. Synchronized brain network associated with essential tremor as revealed by magnetoencephalography. Mov Disord 2009;24:1629–35. Schoffelen JM, Oostenveld R, Fries P. Neuronal coherence as a mechanism of effective corticospinal interaction. Science 2005;308:111–3. Sears TA, Stagg D. Short-term synchronization of intercostal motoneurone activity. J Physiol 1976;263:357–81. Staudenmann D, Roeleveld K, Stegeman DF, van Dieën JH. Methodological aspects of SEMG recordings for force estimation – a tutorial and review. J Electromyogr Kinesiol 2009 [Epub ahead of print]. Svirskis G, Hounsgaard J. Influence of membrane properties on spike synchronization in neurons: theory and experiments. Network 2003;14:747–63. Taylor AM, Enoka RM. Quantification of the factors that influence discharge correlation in model motor neurons. J Neurophysiol 2004;91:796–814. Ten Hoopen M. Examples of power spectra of univariate point processes. Kybernetik 1974;16:145–53. Terry K, Griffin L. Coherence and short-term synchronization are insensitive to motor unit spike train nonstationarity. J Neurosci Methods 2010;185:185–98. Van Elswijk G, Maij F, Schoffelen JM, Overeem S, Stegeman DF, Fries P. Corticospinal b-band synchronization entails rhythmic gain modulation. J. Neurosci 2010;30:4481–8. Williams ER, Baker SN. Circuits generating corticomuscular coherence investigated using a biophysically based computational model. I. Descending systems. J Neurophysiol 2009;101:31–41. Womelsdorf T, Schoffelen JM, Oostenveld R, Singer W, Desimone R, Engel AK, Fries P. 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 on power and coherence analyses: an EEG and MEG study. J Neurosci Methods 2007;159:215–23.
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Clinical Neurophysiology journal homepage: www.elsevier.com/locate/clinph
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 Netherlands b Centre for Cognitive Neuroimaging, Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen Medical Centre, Department of Neurology/Clinical Neurophysiology, Nijmegen, The Netherlands c Faculty of Human Movement Sciences, Research Institute MOVE, VU University Amsterdam, The Netherlands
a r t i c l e
i n f o
Article history: Accepted 4 March 2010
Keywords: Motoneuron pool Corticomuscular coherence a-Motoneuron model Corticomuscular transmission Motor drive Motor unit firing
a b s t r a c t Objective: Investigate the effectiveness and frequency dependence of central drive transmission via the a-motoneuron pool to the muscle. Methods: We describe a model for the simulation of a-motoneuron firing and the EMG signal as response to central drive input. The transfer in the frequency domain is investigated. Coherence between stochastical central input and EMG is also evaluated. Results: The transmission of central rhythmicities to the EMG signal relates to the spectral content of the latter. Coherence between central input to the a-motoneuron pool and the EMG signal is significant whereby the coupling strength hardly depends on the frequency in a range from 1 to 100 Hz. Common central input to pairs of a-motoneurons strongly increases the coherence levels. The often-used rectification of the EMG signal introduces a clear frequency dependence. Conclusions: Oscillatory phenomena are strongly transmitted via the a-motoneuron pool. The motoneuron 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 a strong frequency dependency. We think that it should be avoided. Significance: Our findings show that rhythmicities are translated into a-motoneuron activity without strong non-linearities. Ó 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 patterns. Wollaston reported this already in 1810 (Brown, 2000). In pathological circumstances rhythmic drive to muscles can lead to disabling symptoms as in Parkinson’s disease and essential tremor (Schnitzler et al., 2009). Recently, long range interaction of oscillatory phenomena has also been given a meaning in selective communication between neuronal groups. The conceptual mechanism behind it, called communication through coherence (CTC, Fries, 2005), gets increasing support from experimental evidence (Womelsdorf et al., 2007). The concept comprises the assumption that selective communication between neuronal groups is enhanced by oscillatory activity in specific frequency bands that are roughly in the range 10 and 80 Hz. Corticospinal coherence is regarded as strong evidence for CTC since the distance
* Corresponding author at: Radboud University Nijmegen Medical Centre, 920 Department of Neurology/Clinical Neurophysiology, P.O. Box 9101, 6500HB Nijmegen, The Netherlands. Tel.: +31 24 3615284; fax: +31 24 3615097. E-mail address: [email protected] (D.F. Stegeman).
between the signal sources excludes irrelevant volume conduction mediated effects (Schoffelen et al., 2005; Van Elswijk et al., 2010). An interesting question for the corticospinal system is how cortical oscillations, after having descended the corticospinal tract, are translated by the a-motoneuron pool into motoneuron activity and ultimately into the EMG signal. Thereby, the properties of amotoneurons, especially their long afterhyperpolarization (AHP), are expected to be a non-linear obstacle in the transfer of oscillatory activity. Ways to analyze rhythmic coupling between cortex and muscle in the frequency domain have been proposed (e.g. Grosse et al., 2002), and a number of authors have already looked into the spinal transmission 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 corticospinal interaction apparently occurs. Second, since the a- and bfrequency bands are more or less in the order of the firing frequencies of a-motoneurons, attempts are made to relate the transmission efficiency directly to those firing frequencies (Myers et al., 2003; Farina et al., 2004). Third, the frequency content of the in-
1388-2457/$36.00 Ó 2010 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.clinph.2010.03.052
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volved electrophysiological signals (EEG, MEG, and EMG) plays a role. It leads for instance to the regular question whether the EMG signal should be rectified before a coherence analysis is done (Myers et al., 2003; Yao et al., 2007). In this context also the effect of the frequency content of the ‘synaptic noise’ at the input of the a-motoneurons can be added. It is caused by the motoneuron membrane dynamics reacting to excitatory and inhibitory input (Calvin and Stevens, 1968; Matthews, 1996). This modulating element may also play a part in transmitting central oscillatory phenomena to a muscle. The reported level of corticospinal coherence in the b- and the c-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 to the latter. It is to be expected that part of the potential frequency coupling between EEG or MEG over the motor areas and the information in corticospinal neuronal firings, will be lost across the amotoneuron pool (Fig. 1). Furthermore, quantitative insight in that loss and the non-linearity that is introduced, would ’inversely’ give an 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 different motor units (MUs) show a peak close to delay time zero (Farmer et al., 1997). This means that the probability of a MU firing rises around the time that another one fires. This coupling between firings of MU pairs is called ‘short-term synchrony’ (Sears and Stagg, 1976; Kirkwood et al., 1982). Synchronization is thought to be dominated by a common input (CI) due to branching of axons so that an axon can contribute as input to several a-motoneurons (Kirkwood and Sears, 1991). The cortical origin of motoneuron synchronization is supported by experimental evidence reported by Datta and Stephens (1990), Datta et al. (1991), and Schmied et al. (1999). The amount of CI which should be present can in principle be determined from the level of short-term synchrony (Kleine et al., 2001). We present a model study to obtain insight in the corticomuscular signal transmission considering the various frequency domains. Following the reasoning by Matthews (1999), we adopted a deliberately simple and elegant computational model of the a-motoneuron (Matthews, 1996) in which we believe that the essential elements
Σ
EPSP Filter
E+N
for the present purpose are available. The model only accounts for the steady state during a sustained isometric contraction. It has no elements which could mimic dynamic task behaviour. For instance, it cannot describe the recruitment of plateau potentials (Svirskis and Hounsgaard, 2003; Taylor and Enoka, 2004; Williams and Baker, 2009) in the motor unit firing dynamics. We purposeful restricted the model to the simplest, but still physiologically relevant forward transmission over the motoneuron pool without feedback elements to reveal the pure properties of this element in motor control. Our version of the model includes a pool of motoneurons. We also added the generation of motor unit action potentials, recorded at the skin surface, in response to the firings of each a-motoneuron. Furthermore, we adopted the phenomenon of short-term synchrony by assuming a common input to each pair of a-motoneurons (Moritz et al., 2005). To simulate cortical rhythmicity we modulated the cortical input to the motoneurons in different frequency ranges. Our goal was to investigate the effectiveness and the properties of oscillatory central drive transmission to the muscle, its relation with the firing patterns of the a-motoneurons, and the consequences for the surface EMG signal. We will distinguish the frequency aspects mentioned above and look at the transfer across the a-motoneuron pool basically by comparing it to a linear transfer function. Apart from being a usual first approach in system’s analysis, a linear transfer also is the implicit assumption behind the use of coherence as a measure of coupling between neuronal populations. We will therefore present the EMG signal in response to oscillatory corticospinal activity as a measure of transmission quality. Also, the coherence between stochastic cortical drive activity and the surface EMG signal is computed. Moreover, we compared the data with and without rectification 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 following main steps: (1) generating the firing pattern of an a-motoneuron; (2) introducing a certain level of common input to pairs of motor units to introduce short-term synchrony. The model was implemented in the Matlab environment (The MathWorks, Inc., Natick,
C
MUAP
EMG 50 MUs
AHP
Cortical drive
5 ms
5 ms
Motoneuron pool
Muscle
Fig. 1. Functional model scheme of the a-motoneuron in three stages (cortical drive, motoneuron pool, and muscle). Random firing events from the cortex, expressed as a mean value plus white noise, are summed and then filtered with EPSP characteristics. At box C the signal is compared to the threshold value. If higher, the a-motoneuron fires resulting in a firing event. The afterhyperpolarization phase is taken into consideration at C as well. The resulting firing pattern is convoluted with a MUAP wave shape giving the contribution of this a-motoneuron to the EMG signal.
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MA, version 7.6.0). Instead of the 1 ms time resolution used in the Matthews (1996) study, we used a time resolution of 0.5 ms. 2.1.1. Firing patterns The output from pyramidal neurons in the cortex is regarded as the input to each neuron in the a-motoneuron pool. These signals are assumed to be Poisson distributed spike trains which, as being central drive dependent, may have a time varying density (Fig. 1). The input to an a-motoneuron is the sum of such Poisson distributed spike trains which, when many events are summed, can well be approximated by a mean value plus Gaussian distributed white noise. The membrane dynamics resulting in the characteristics of excitatory postsynaptic potentials (EPSPs) will have an influence on how the input at the a-motoneuron’s membrane is transferred to that neuron. This is added in the model as a filter mimicking the frequency content of the EPSPs (Fig. 1). So then the input to the spike generator of the a-motoneuron (C in Fig. 1) is modelled as a mean value plus noise, which now is not white any longer, but has a frequency content dictated by the EPSP wave shape. This EPSP filter has the properties as used by Matthews (1996). Thereby, the membrane dynamics are taken from the autocorrelation function of synaptic noise expressed in a time constant of 4 ms as presented in Calvin and Stevens (1968). As suggested by Matthews (1996) for our 0.5 ms time resolution, we adapted that value to 5 ms. A crucial element in the model is to normalize the standard deviation of the membrane noise N to unity, further used as the amplitude unit in the drive to the neuron model (noise unit, NU). The membrane potential of the a-motoneuron in the spinal cord is assumed to increase, in physiological terms, due to the summation of EPSPs, approached by a steady drive E plus the synaptic noise N (Fig. 1). When threshold is reached, an action potential is thought to arise that elicits a motor unit firing event. Immediately following that instant, the membrane potential of the a-motoneuron jumps down with an amplitude shift A and then shows a long-lasting AHP phase. This phase consists of the lowered membrane potential to rise again exponentially with time constant s from the minimum level A, on which the central drive E + N is superimposed, to the resting state f(t) = 0. This AHP phase can be described by: t
f ðtÞ ¼ Aes þ E þ 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; Kleine et al., 2001). The next action potential is generated as soon as the threshold is reached again (f(t) = 0). The firing rate is tuned by choosing 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 a previous firing the next firing occurs when for the first time N exceeds 1.5 times its own standard deviation (NU). This combination of parameters generates physiologically realistic firing patterns for a moderate level of contraction with firing rates between 10 and 15 firings per second (Matthews, 1996; Kleine et al., 2001). The presented results are based on a population of 50 a-motoneurons. 2.1.2. Motor unit synchronization Short-term synchrony between MU pairs (described by e.g. Schmied et al., 2000 and Terry and Griffin, 2010) can be introduced by assuming a certain level of common input. This level can be determined by looking inversely to the nervous system. Firing patterns of pairs of MUs with a level of short-term synchrony in a physiological range (Farmer et al., 1997) can be generated with around 30% of CI to MU pairs (see results). When considering this level for more than two MUs, there are two basic possibilities: (1) 30% of the input is equal for all MUs;
(2) every pair of MUs shares 30% of their input, which is different from the shared input between all other pairs. In the first case, the 70% of not shared input to any of the single MUs is independent of the input to all others. In the second case, every MU has a 30% common input with any other MU. This common input is different for any pair. Assuming that the common input is caused by a shared wiring structure, the second model appears more realistic and 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 independent equally large white noise sources xj(t). To realize the second possibility, the normalized covariance matrix K of z (for 30% CI noise) should look like:
3 1 0:3 0:3 :: 6 0:3 1 :: 0:3 7 7 6 K ¼ Cov ðzÞ ¼ 6 7 4 0:3 :: 1 0:3 5 2
::
0:3 0:3
ð2Þ
1
In order to obtain noise input signals to the a-motoneurons being 30% common to each pair of MUs from independent noise signals, some algebraic operations must be performed. That is, we have to find a solution for the following equation:
z ¼Ax
ð3Þ
Where A is an R R matrix that should match with the covariance matrix K, which can be written as: 1
1
K ¼ A AT ¼ P K P T þ P K2 K2 P T
ð4Þ
Where K is the matrix with eigenvalues of K and P contains the corresponding eigenvectors. It follows that: 1
A ¼ P K2
ð5Þ
This can be used in combination with Eq. (3) to generate the R input signals z, obeying Eq. (2), to the MUs from the same number of independent 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 events must then be replaced with MUAP wave shapes by means of convolution. The main goal in defining the MUAPs was to come up with two EMG signals having the spectral distribution of a small muscle (FDI, Penn et al., 1999) and a larger upper extremity muscle (ECR, Huysmans et al., 2008), respectively, using wave shapes with a duration d of 15 ms and 25 ms (Fig. 2A and C, with frequency spectra in Fig. 2B and D). A half pulse shape was defined by:
hðtÞ ¼ 5 sin
1 t :exp 1 for 0 < t d=2 d=2 s d=2
pt
ð6Þ
For d=2 < t d a time and amplitude mirrored version of Eq. (6) following the zero value at t = d/2 was used. The value for the damping factor s is set at 0.18 ms. All 50 MUs were represented by the same long or short duration MUAP. To this end, the 50 single firing sequences are summed together and the surface EMG signal is created by convolution of the resulting sum of 50 firing patterns with one of the two MUAP wave shapes. To obtain a sufficient signal to noise ratio, the model was run for 100 or 150 s for, respectively, the frequency spectra and the coherence calculation (see below). 2.3. Motoneuron pool transfer estimation Signal transfer through the motoneuron pool will be expressed in amplitude modulation and coherence. The analyses were done
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Fig. 2. Short (A) and long MUAP (C) and their respective amplitude spectra (B and D).
in MATLAB (MathWorks, Natick, MA), with the help of FieldTrip, an open source toolbox for the analysis of neurophysiological data (Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, the Netherlands; see http://www.ru.nl/ neuroimaging/fieldtrip). The often-used rectification of the EMG signal as pre-processing option for computing corticomuscular coherence is discussed for instance by Myers et al. (2003), Farina et al. (2004), and Yao et al. (2007). To contribute to that discussion, the simulated surface EMG signals are also used after rectification. To study the influence of a central oscillatory modulation, sine waves with frequencies ranging from 1 to 100 Hz were superimposed on the summed 50 white noise inputs to the 50 a-motoneurons (signal x in Eq. (3)). The modulation amplitude was set arbitrarily to 5% of the white noise root mean square (RMS) amplitude for each of the 50 elements of x in Eq. (3). The effect of that modulation on the EMG spectrum will be presented. The signals were simulated for 100 s. Spectral content was taken as the average from 100 non-overlapping segments of 1 s, resulting in a 1 Hz frequency resolution. The most popular way of looking at the transfer of oscillatory phenomena is coherence analysis (e.g. Grosse et al., 2002):
jPxy ðf Þj C xy ðf Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pxx ðf ÞPyy ðf Þ
ð7Þ
Pxx and Pyy are the power spectral densities of two signals between which the coherence Cxy is computed, Pxy is the cross power spectral density. Coherence is computed between the summed white corticospinal neural input and the (non-rectified and rectified) interference EMG signals. In this case, the simulations were run, now for 150 s. The data is divided into non-overlapping epochs of 1 s each. A Hanning taper function is applied to each epoch before coherence is calculated. To test for the statistical significance a nonparametric permutation test was performed. The null-hypothesis states that there is no difference between conditions and so that the data are exchangeable. The data epochs were randomly shuffled 100 times after which a 95% confidence interval is created
by determining average and standard deviation over these random shuffles. Coherence values outside the confidence interval were considered as significant. For a more detailed description of this method 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 signals Fig. 3 shows frequency spectra of the firing patterns summed over 50 a-motoneurons for 0% and 30% CI. The MU firing frequency distribution, 10 and 15 Hz, determined by the choice for the distribution of mean drives E, is clearly recognized in the spectra of both patterns. The spectrum for 0% CI has the typical appearance of a socalled stochastic renewal process with augmentation around the mean firing frequency and its harmonics and a white spectral content for higher frequencies (Ten Hoopen, 1974; Pan et al., 1989). As can be seen, CI to MU pairs increases the amplitude of the spectral distribution of the summed a-motoneuron firing patterns. It does also result in a different spectral shape. The higher frequencies are less augmented by the CI than lower frequencies and also tend to a plateau value for the highest frequencies (>>100 Hz, see inset Fig. 3). To illustrate that 30% CI, having this substantial influence on these spectra, is a realistic choice, Fig. 4 shows a cross correlation histogram of the short-term synchrony that is realized by assuming this level of CI in the model (e.g. Farmer et al., 1997). Fig. 5A shows the frequency contents of the non-rectified EMG signals on the basis of 30% CI for the long MUAP wave shape. Here too, the peak around 13 Hz is caused by the mean MU firing frequency. Furthermore, Fig. 5B shows that rectification emphasizes the lower frequency contents, as expected. 3.1.2. Amplitude response to added oscillations of 1–100 Hz Fig. 6 presents the spectral content (along the axis indicated with output frequency) of the summed a-motoneuron spike patterns (Fig. 6A) and of the EMG signal without (Fig. 6B) and with (Fig. 6C) rectification using the long duration MUAP wave shape
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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 the spectrum 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 the firings of two different motor units when assuming a 30% common input to pairs of a-motoneurons.
and 30% CI. For each repetition the 5% superimposed modulation to the white noise input of the model was added with increasing frequency from 1 to 100 Hz in 1 Hz steps (along the axis indicated with input frequency), resulting in a diagonal ridge in these three dimensional presentations. To illustrate the transfer of the modulating frequencies in more detail, Fig. 7 presents the diagonal ridges in Fig. 6 in the same order, but now also for the short duration MUAP wave shape. It is noted that the result in part A below 30 Hz can directly be compared and appears similar to the model result shown for the 13 Hz motoneuron in Fig. 5 from Matthews (1999). The choice for an EPSP filter (see Section 1 and Section 2.1.1) with a time constant of 5 ms was based on experi-
mental data (Calvin and Stevens, 1968; Matthews, 1996). The added modulation input is ’injected’ to the system before that EPSP filter (Fig. 1). As indicated already in the introduction, the properties of that filter may also influence the frequency transfer. As the membrane dynamics may vary between motoneurons of different muscles, we doubled the time constant to 10 ms (not shown). This has no noticeable influence on the results as presented in Fig. 7. When comparing Fig. 5A and B with Fig. 7B and C it already appears that the shape of the spectral contents is similar. That means that the transfer of rhythmic activity is about proportional to the spectral content of the EMG signal. That this is more or less the case is illustrated in Fig. 8B, where the ratio between the modulated amplitude (Fig. 7B) and the EMG spectral content (Fig. 5A) is presented. Fig. 8A shows this ratio for the MU firing pattern and Fig. 8C for the rectified EMG signal. Apart from a somewhat increased noise level because of the division operation, there is for Fig. 8A and B no clear sign of a preference for this modulation in a relevant specific frequency band, especially not in the region of the firing frequencies of the motoneurons. The ratio for the EMG signal tends to a value of 1 for the lowest frequencies (<20 Hz, Fig. 8B), meaning that the extra modulation is less or not transferred for those frequencies. For the rectified EMG, this ratio also approaches unity for the higher frequencies (>60 Hz, Fig. 8C). 3.2. Coherence analysis 3.2.1. Between white motoneuron input and EMG The coherence between the summed input to all motoneurons and the (rectified) EMG signal is computed for 0% and 30% CI for the long MUAP (Fig. 9). The CI level leading to short-term synchrony appears to be an utmost important factor that enhances coherence (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 should be realized that for a linear system, without independent noise
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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 and 100 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.
at the system’s input or output, the coherence would be 1 for all frequencies, independent of the frequency characteristics of the system’s transfer function. This is because in Eq. (7) the denominator corrects for the spectral content of both input and output. Even the highest values presented in Fig. 9B do not reach that unity value. Furthermore, the coherence also slightly decreases with increasing frequency. The a-motoneuron pool system obviously does not behave as a ‘noise free’ linear system. Another
essential point is that the firing frequencies of the motor units do not seem to play a substantial role in Fig. 9A and B, that is to say that they are not interfering with the transmission of cortical oscillations over the a-motoneuron pool in terms of the coherence between input and output. For the rectified EMG signal, however, the firing rates determine the upslope of the coherence from the lowest frequency up to the mean firing rate as shown in Fig. 9D.
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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.
A
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Fig. 8. (A) Ratio between the modulated amplitude as shown in Fig. 7A (bold) and the firing pattern spectral content as presented in Fig. 3 (bold). (B) Ratio between the modulated amplitude as shown in Fig. 7B (bold) and the EMG spectral content as 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.
3.2.2. With independent noise added When performing experiments of any kind, there will be measurement noise present. It can be that the input as defined is not
completely transferred to the system studied and that noise is added to the output signal. Any approach towards reality should therefore add some independent noise to the input or output of the system. Added input noise (part of the cortical output signal that is not transferred to the a-motoneuron pool) will decrease the level of coherence with a constant factor for all frequencies as long as that noise has the same spectral content as the input. The signal to noise ratio (SNR) of the input then decreases with a constant factor. When, however, independent white measurement noise is added to the output (the EMG signal) the coherence profile between input and EMG is affected (Fig. 10) because the white noise has been given the RMS amplitude of the EMG signal. The effect is largest in the low frequency regions (<20 Hz) where the EMG signal (Fig. 5A) and the amplitude transfer (Fig. 8B) are steeply decreasing. It follows more or less the frequency dependence of the amplitude response to added oscillations (Fig. 7). When using the short duration MUAP for the EMG signal (not shown), the frequency dependence is different, but also then following the amplitude response. Remarkably, the coherence with the rectified EMG signal (Fig. 10C and D) seems less affected. The level and frequency dependence especially in Fig. 10D are already seen without the addition of noise (Fig. 9D). 4. Discussion We argued that it is useful to compare the transfer across the amotoneuron pool to a linear transfer function because this is also the implicit assumption behind the use of coherence as a measure of coupling between neuronal populations. The results we show use a previously proposed a-motoneuron model that is relatively simple and has a clear physiological basis (Matthews, 1996). By adjusting the drive level E in Eq. (1), firing frequencies can be distributed and adjusted. Matthews (1999) showed the effect of such different levels of excitatory drive as being closely related to phys-
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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 signal for 0% CI. (D) Rectified EMG signal for 30% CI. The bold line indicates the 95% confidence interval of the bias.
iological MU behaviour, which confirms the realistic properties of this model approach. Our model extends this approach with a way to generate surface EMG patterns by extending the pool of firing motoneurons to repeated occurrences of motor unit action potentials. We refrained from diversification of motor unit properties and only took the eventual frequency content of the EMG signal as crucial element. We believed and confirmed in a pilot study that this provides a pure and sufficient view on the mechanism we were interested in, namely the essential determinants of corticomuscular transmission across the motoneuron pool.
An important property of motoneurons we did not include was the presence of plateau potentials caused by persistent inward currents (Hounsgaard et al., 1986; Heckmann et al., 2005). Within the context of the present level of model complexity, the inclusion of this property would introduce extra blocking of the input from the cortex to the a-motoneurons since the latter will fire more independent of the central drive. This appears in contrast to the result of a study dealing with a similar subject (Taylor and Enoka, 2004; Williams and Baker, 2009). These authors report on a decreased coherence after having removed persistent inward cur-
Fig. 10. Coherence between the input of all MUs and the (rectified) EMG signal for the long MUAP with added noise to the EMG signal. (A) EMG signal for 0% CI. (B) EMG signal for 30% CI. (C) Rectified EMG signal for 0% CI. (D) Rectified EMG signal for 30% CI. The bold line indicates the 95% confidence interval of the bias.
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rents in their motoneuron model. The reason for that apparently is the addition of independent input to maintain the mean firing rates of the a-motoneurons. The findings in the study of Williams and Baker (2009) on coherence differ also in another way. The levels of corticomuscular coherence they report are always far below what we found (<0.06) and they are shown to be much more related to the firing frequencies of the motoneurons. An explanation here could also be that in their model the motoneuron adds ’internal’ independent noise other than the EPSP input noise we simulated. The very low coherence levels are somewhat peculiar, though. Considered as a forward system with series elements, it would mean that corticomuscular coherence could never be larger than what the motoneuron pool transmits. Reported coherence levels, however, usually exceed these low values (e.g. Brown et al., 1998; Salenius and Hari, 2003; Riddle and Baker, 2005). Our approach is based on estimating the behaviour of the amotoneuron pool in a way that would clarify its deviation from a linear transfer system. The spectral content of the EMG signal is very much dominated by the spectral content of the MUAP (Fig. 5A). This is confirmed by using two different MUAPs, eliciting a different frequency dependence due to their own spectral contents. A convolution of the MUAP with a purely random Poisson type of firing patterns would have resulted in an EMG spectrum with the frequency distribution as shown in Fig. 2B and D. Another property of a linear transfer system is that the coherence between input and output is not frequency dependent, irrespective the frequency characteristics of the transfer function. This is certainly true as long as the transfer is noise free, in which case the coherence is 1 for all frequencies. When the spectral content of added independent noise has the same spectral properties as the input and output signals to which they are added, coherence is lower than 1, but still frequency independent. The fact that the coherence is lower than 1 and slightly frequency dependent (going down with higher frequencies), for EMG as shown in Fig. 9B, indicates non-linearity of the a-motoneuron pool model, but to a limited extent. Equal spectral properties of signal and measurement noise cannot be expected to be a realistic case. We therefore added independent white noise to the EMG signal. This induces an increased frequency dependence of the coherence (Fig. 9A and B against Fig. 10A and B). This is to be expected because the signal to noise ratio in the EMG signal is now frequency dependent, especially showing up in the lowest frequencies when the EMG signal loses power. It should be realized that by changing recording parameters for the EMG like interelectrode distance, electrode montages, or various forms of filtering (Staudenmann et al., 2009), its spectral content can be manipulated. This may improve the SNR at specific frequencies of interest. The coherence with the rectified EMG signal shows a strong frequency dependence already without the addition of independent recording noise (Fig. 9C and D), which is also hardly affected by adding noise. This stresses the strong non-linearity that is introduced by rectification, which also raises worries about the use of a rectified EMG signal before the coherence is computed. Rectification is often applied and also theoretically discussed (e.g. Myers et al., 2003; Farina et al., 2004; Yao et al., 2007). These papers relate coherence to the firing frequencies of the motoneurons. They state that rectification gives a better representation of the EMG at the firing rate frequencies since rectification enhances the spectral amplitude in that frequency range, which is confirmed in Fig. 5B. Although it is shown in the paper of Yao et al. (2007) that the coherence after rectification is slightly lower in the 10–20 Hz frequency band, this finding appears not to be significant. In our case, the coherence of the rectified EMG signal is lower than that of the EMG signal over the whole 1–100 Hz frequency band studied (lower half of Fig. 9 and Fig. 10). Thereby, the difference becomes larger at frequencies lower and higher than the motoneuron firing range.
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To confirm that the firing rates indeed play a role here, we increased mean drive E and thus increased firing rates for all MUs. It may be clear from our point of view that despite this dependence, intermingling or even equating the firing rate frequency band with coherent corticospinal activity is not justified. With respect to rectification, we conclude that it introduces puzzling aspects in the already non-linear corticospinal coupling which should better be avoided. One might even suspect that coherences as found in some frequency bands and not in others is partly because of the properties of this neurophysiologically meaningless operation. Our model as a representation of the transmission over the motoneuron pool does not provide a potential physiological mechanism for increased coherences in frequency bands between 15 and 35 Hz or above. Another straightforward way in which we investigated motoneuron pool transfer estimation is by studying the influence of a central oscillatory modulation. For the level of input modulation we arbitrarily have chosen an amplitude of 5% of the white noise RMS amplitude. We were not interested in the actual height of the modulation amplitude, only in its relative effect. We introduced a modulation that about doubles the response to the modulated frequency (Fig. 8A). We further showed that the modulated signal transmitted by the motoneuron pool is about proportional to 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 decrease also for the higher frequencies, again indicating the strong divergence from linearity due to the process of rectification. The membrane dynamics determining the synaptic noise at the input of the a-motoneuron caused by the excitatory (and inhibitory) dynamics of the motoneuron throughput will principally influence the transmission of oscillatory phenomena to the muscle. However, adapting the EPSP filter settings within physiological limits did not change the results noticeably. Therefore, we conclude that this frequency element introduced does not play a significant role in the transmission through the a-motoneuron pool. The level of CI does appear to be an important factor in our results (Figs. 3, 9 and 10). Common input leads to short-term synchrony, meaning that different MUs tend to fire around the same time. We simulated the MU firing patterns for different levels and corresponding cross correlation histograms. By comparing this with experimental data (e.g. Farmer et al., 1997), the level can be between 20% and 30% (example in Fig. 4). We compared two levels of CI: 0% and 30%. The distribution of the amplitude spectrum of the MU firing pattern increases for the higher CI level (Fig. 3), due to summed simultaneous firings and MUAPs. The higher frequencies are less augmented than the lower ones and decline to the same level as the white spectral content of the higher frequencies for 0% CI. Especially, the coherence increases substantially with the level of CI. This effect is so strong that one could state that CI to pairs of motoneurons is needed to make corticomuscular coupling visible. Part of the regularly measured relatively low corticomuscular coherence values at or below 0.2 could vanish in statistical insignificance without the presence of a significant CI level (compare Fig. 9B with Fig. 9A). The consequences of our results for the CTC hypothesis in corticomuscular communication are certainly relevant and straightforward. The efferent part of movement control as modelled here does not largely influence oscillatory transmission, nor does it prefer or need specific frequency bands for that transmission. Corticospinal coupling that would use CTC, when present, could be searched in the closed loop behaviour in the motor control system, in specific interactions at the neuronal events between the corticomuscularversus the a-motoneuron level (not modelled here, see Zeitler et al. (submitted for publication)), or higher in the central nervous system.
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In conclusion, we investigated how the a-motoneuron affects signal transmission from the cortical motor drive. Therefore, we looked at the frequency contents of both firing pattern and EMG signal. Modulation of the input signal is transferred by the a-motoneuron to the output with an only limited level of non-linearity. The ratio of the modulation is approximately constant, meaning among others that there is no non-linear frequency preference caused by the firing frequencies. Coherence analysis between input and EMG signal also showed a slight decrease for the higher frequency components indicating non-linearity. When adding white measurement noise to the EMG, a frequency dependence shows up. The rectified EMG signal shows a frequency dependence without addition of noise, possibly caused by the operation of rectification that emphasizes the lower frequencies. This might be the reason rectification is used commonly for the computation of coherence. Nevertheless, on the basis of the presented results we would advise against rectification of the EMG signal. Acknowledgements This research was supported by grants of the Netherlands Organisation for Scientific Research (NWO; #051.02.050 to G.v.E. and D.F.S.). We would like to thank Ad Moerland, M.Sc., for his contribution to the implementation of the a-motoneuron model. References Brown P, Salenius S, Rothwell JC, Hari R. Cortical correlate of the Piper rhythm in humans. J Neurophysiol 1998;80:2911–7. Brown P. Cortical drives to human muscle: the Piper and related rhythms. Prog Neurobiol 2000;60:97–108. Calvin WH, Stevens CF. Synaptic noise and other sources of randomness in motoneuron interspike intervals. J Neurophysiol 1968;31:574–87. Datta AK, Stephens JA. Synchronization of motor unit activity during voluntary contraction in man. J Physiol 1990;422:397–419. Datta AK, Farmer SF, Stephens JA. Central nervous pathways underlying synchronization of human motor unit firing studied during voluntary contractions. J Physiol 1991;432:401–25. Farina D, Merletti R, Enoka RM. The extraction of neural strategies from the surface EMG. J Appl Physiol 2004;96:1486–95. Farmer S, Halliday DM, Conway BA, Stephens JA, Rosenberg JR. A review of recent applications 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 through neuronal coherence. Trends Cogn Sci 2005;9:474–80. Grosse P, Cassidy MJ, Brown P. EEG–EMG, MEG–EMG and EMG–EMG frequency analysis: physiological principles and clinical applications. Clin Neurophysiol 2002;113:1523–31. Heckmann CJ, Gorassini MA, Bennett DJ. Persistent inward currents in motoneuron dendrites: implications for motor output. Muscle Nerve 2005;31:135–56. Hounsgaard J, Hultborn H, Kiehn O. Transmitter-controlled properties of alphamotoneurons 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. Fatigue effects on tracking performance and muscle activity. J Electromyogr Kinesiol 2008;18:410–9.
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