Fig 1.
In the model, the common synaptic input to the motor neurons is the sum of 30 sine waves (frequencies: 1–30 Hz), each with an amplitude determined by a gain (G1F1-F30) that is determined by the values of a random variable with uniform distribution between 0 and 1.
The gain G2 determined the average power of the common input (low, medium, or high) and an offset was added that determined the average contraction level. For each motor unit, independent synaptic noise was added before the motor unit model determined the motor unit spike trains (timing of motor neuron action potentials). For each motor unit, the spike train was convolved with pre-defined templates for the motor unit twitch forces, and the raw and rectified motor unit action potentials. By summation of the force and the EMG signals for each motor unit, the force, EMG, and EMGnc for the full muscle were obtained. The cumulative spike train (CST) was calculated as the algebraic sum of all motor unit spike trains (neural drive to the muscle).
Fig 2.
Three representative examples of simulated forces with low (A), medium (B), and high (C) amplitudes of the variability of the common synaptic input to a population of 400 motor neurons.
Panel D illustrates the force standard deviation (mean±std) for all simulated conditions. Here, the symbols along each line represent different offsets of the common synaptic input and the different lines represent different amplitudes of common input variability and/or different number of motor units.
Fig 3.
Temporal and spectral representation of the cumulative spike train (CST; A, B), the rectified EMG and EMGnc (C, D), and force (E, F).
In panel D, the normalized power spectrum of the raw (unrectified) EMG signal in the 0–250 Hz range is included in the dashed box. In this example, the muscle consisted of 100 motor units, the amplitude of the variability of the common synaptic input was high (force standard deviation: 1.8%MVC), and the average contraction level was 14.9%MVC. The power spectra (B, D, F) indicate power only for integer frequencies that were the frequency components used to simulate the common input.
Fig 4.
Linear relations between the power at three frequencies (2 Hz: A, B. 15 Hz: C, D. 28 Hz: E, F) in the CST and the rectified EMG (A, C, F) as well as the CST and EMGnc (B, D, F).
The data in these examples represent simulations in which the muscle consisted of 100 motor units, the amplitude of the variability of the common synaptic input was high (force standard deviation: 1.8%MVC), and the average contraction level was 14.9%MVC. In each panel, each circle represents the power of the two signals in one of the 15 simulations conducted with these parameter values.
Fig 5.
Values of r2 for the linear relations between CST and rectified EMG and EMGnc respectively, as functions of the contraction levels across all simulations.
In each panel, black lines represent the relation between CST and rectified EMG (symbols represent average values for the 1–5 Hz, 6–15 Hz, and 16–30 Hz frequency bands, respectively; see inset in panel C), while grey lines represent the relation between CST and EMGnc (each line represents the same frequency bands as for CST-EMG). Panels A, B, C show results for simulations with 100 motor units, while panels D, E, F represent 400 motor units. Panels A, D represent low variability of the common synaptic input to the motor neurons, panels B, E medium variability, and panels C, F high variability.
Fig 6.
The relation between the average r2 (across all frequencies) for CST-EMG and the degree of amplitude cancellation in the EMG (black circles) across all simulation conditions.
In addition, the average r2 for CST-EMGnc (grey x’s) is included. Here, the value on the axis represents the level of amplitude cancellation from the EMG in the same simulation.