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

Williams ER, Baker SN - J. Neurophysiol. (2008)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Institute of Neuroscience, Newcastle University, Henry Wellcome Building, Newcastle upon Tyne, NE2 4HH, UK.

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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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).
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f4: 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).

Mentions: Second, the coherence phase appeared to oscillate with frequency, rather than showing a simple linear dependence. To understand this better, we computed a peristimulus time histogram of spikes from the motoneuron pool, triggered by the total synaptic inputs to the motoneuron pool, illustrated in Fig. 4A. The motoneuron pool impulse response consists of a facilitation (duration 8.8 ms) and a subsequent period of reduced firing probability. Kirkwood and Sears (1982) showed that the response of a cell to a synaptic input could be well represented by a mixture of the EPSP waveform and its derivative. The long duration of the peak in this instance indicates a dominant contribution from the EPSP time course; this is expected where the level of membrane noise in the responding cell is large compared with the EPSP, as in this case (Kirkwood and Sears 1982). The suppression following the peak reflects the refractory period of the motoneurons; cells that fire in the peak will not fire again shortly afterward (Perkel et al. 1967).


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

Williams ER, Baker SN - J. Neurophysiol. (2008)

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).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2637020&req=5

f4: 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).
Mentions: Second, the coherence phase appeared to oscillate with frequency, rather than showing a simple linear dependence. To understand this better, we computed a peristimulus time histogram of spikes from the motoneuron pool, triggered by the total synaptic inputs to the motoneuron pool, illustrated in Fig. 4A. The motoneuron pool impulse response consists of a facilitation (duration 8.8 ms) and a subsequent period of reduced firing probability. Kirkwood and Sears (1982) showed that the response of a cell to a synaptic input could be well represented by a mixture of the EPSP waveform and its derivative. The long duration of the peak in this instance indicates a dominant contribution from the EPSP time course; this is expected where the level of membrane noise in the responding cell is large compared with the EPSP, as in this case (Kirkwood and Sears 1982). The suppression following the peak reflects the refractory period of the motoneurons; cells that fire in the peak will not fire again shortly afterward (Perkel et al. 1967).

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Institute of Neuroscience, Newcastle University, Henry Wellcome Building, Newcastle upon Tyne, NE2 4HH, UK.

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.

Show MeSH
Related in: MedlinePlus