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. 2009 Jan;101(1):31-41.
doi: 10.1152/jn.90362.2008. Epub 2008 Nov 19.

Circuits generating corticomuscular coherence investigated using a biophysically based computational model. I. Descending systems

Elizabeth R Williams  1 , Stuart N Baker
Affiliations

Circuits generating corticomuscular coherence investigated using a biophysically based computational model. I. Descending systems

Elizabeth R Williams et al. J Neurophysiol. 2009 Jan.

Abstract

Recordings of motor cortical activity typically show oscillations around 10 and 20 Hz; only those at 20 Hz are coherent with electromyograms (EMGs) of contralateral muscles. Experimental measurements of the phase difference between approximately 20-Hz oscillations in cortex and muscle are often difficult to reconcile with the known corticomuscular conduction delays. We investigated the generation of corticomuscular coherence further using a biophysically based computational model, which included a pool of motoneurons connected to motor units that generated EMGs. Delays estimated from the coherence phase-frequency relationship were sensitive to the width of the motor unit action potentials. In addition, the nonlinear properties of the motoneurons could produce complex, oscillatory phase-frequency relationships. This was due to the interaction of cortical inputs to the motoneuron pool with the intrinsic rhythmicity of the motoneurons; the response appeared more linear if the firing rate of motoneurons varied widely across the pool, such as during a strong contraction. The model was able to reproduce the smaller than expected delays between cortex and muscles seen in experiments. However, the model could not reproduce the constant phase over a frequency band sometimes seen in experiments, nor the lack of around 10-Hz coherence. Simple propagation of oscillations from cortex to muscle thus cannot completely explain the observed corticomuscular coherence.

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Figures

FIG. 1.
FIG. 1.
A: schematic of the model. B: waveform of motoneuron excitatory postsynaptic potential (EPSP). C: dependence of motoneuron firing rate on rate of excitatory synaptic input for motoneurons (MNs) 1 (top curve), 60, 100, and 177 (bottom curve). D: example raw data output from the model.
FIG. 2.
FIG. 2.
Results from simulations (4,017 s) using white-noise cortical inputs (A–G) and a cortical input modulated to produce spectral peaks at 10 and 20 Hz (H–N). A and H: power spectrum of cortical input. B and I: power spectrum of rectified electromyogram (EMG). C and J: coherence between cortical input and rectified EMG. D and K: motoneuron spike autocorrelation, averaged over all cells in the motoneuron pool. E and L: cross-correlation between motoneuron spikes, averaged over all possible pairs of motoneurons in the pool (E was smoothed using a Gaussian kernel, width 0.5 ms). F and M: power spectrum of the population spike activity of the motoneurons. Bin width of 1 ms in time domain plots. G and N: average coherence between motoneuron spike trains (averaged over 100 pairs of motoneurons, chosen at random).
FIG. 3.
FIG. 3.
Phase–frequency relationships calculated from the coherence between different outputs of the simulation. Signal pairs are denoted “output signal–reference signal”; a positive slope indicates that the output signal lags the reference. Error bars indicate 95% confidence limits on phase. A: cortical input–EMG coherence phase. B: schematic of the model showing the signals analyzed in each panel of the figure. C: coherence phase for total synaptic input–common input. D: population motoneuron spikes–total synaptic input to motoneurons. E: EMG, population MN spikes. Simulation was 4,017 s long.
FIG. 4.
FIG. 4.
A: cross-correlation histogram of MN spikes triggered by synaptic inputs, averaged over the entire motoneuron pool. B: coherence computed between a white-noise input signal and an output signal formed by convolution with the impulse response function in A. C: coherence phase estimated from this procedure (black), overlaid on the MN phase response determined from the model (blue, equivalent to Fig. 3D). D: like A, but on a longer timescale, showing small later-period components of the cross-correlation (smoothed with a Gaussian kernel, 0.5-ms width). E: coherence spectrum calculated for this impulse response, showing peaks due to band-pass filtering action. F: phase response calculated from this response (black), overlaid on model phase as in C. Simulation length was 4,000 s (black) and 4,017 s (blue).
FIG. 5.
FIG. 5.
A: spike-triggered average (STA) of the rectified EMG compiled using spikes from all motoneurons in the pool. Horizontal lines show the pretrigger baseline ±2SDs. The center of gravity (CoG) was calculated for the primary STA peak (shaded).
FIG. 6.
FIG. 6.
A: firing rate vs. motoneuron number at a contraction strength of 5% maximal voluntary contraction (MVC), for the standard model (black) and one where the parameter P has been rescaled to produce greater variation across the motoneuron pool (red). Corticomuscular coherence (B) and corticomuscular coherence phase (C), for the 2 simulations. D–F: plots similar to those of A–C, but for the comparison of contraction strengths of 5% MVC (black) and 20% MVC (blue). Simulation length was 8,034 s for all plots.
FIG. 7.
FIG. 7.
A: firing rates of individual motoneurons for the standard model (black) and a model in which persistent inward currents (PICs) were removed from the MNs (red). B: corticomuscular coherence. C: interspike interval (ISI) histograms from one MN. D: corticomuscular coherence phase for these 2 stimulations. Simulation length was 4,017 s.
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