Fast Oscillatory Commands from the Motor Cortex Can Be Decoded by the Spinal Cord for Force Control

Abstract

Oscillations in the beta and gamma bands (13-30 Hz; 35-70 Hz) have often been observed in motor cortical outputs that reach the spinal cord, acting on motoneurons and interneurons. However, the frequencies of these oscillations are above the muscle force frequency range. A current view is that the transformation of the motoneuron pool inputs into force is linear. For this reason possible roles for these oscillations are unclear, since if this transformation is linear, the high frequencies in the motoneuron inputs (e.g., 20 Hz from pyramidal tract neurons) would be filtered out by the muscle and have no effect on force control. A biologically inspired mathematical model of the neuromuscular system was used to investigate the impact of high-frequency cortical oscillatory activity on force control. The model simulation results evidenced that a typical motoneuron pool has a nonlinear behavior that enables the decoding of a high-frequency oscillatory input. An input at a single frequency (e.g., beta band) leads to an increase in the steady-state force generated by the muscle. When the input oscillation was amplitude modulated at a given low frequency, the force oscillated at this frequency. In both cases, the mechanism relies on the recruitment and derecruitment of motor units in response to the oscillatory descending drive. Therefore, the results from this study suggest a potential role in force control for cortical oscillations at frequencies at or above the beta band, despite the low-pass behavior of the muscles.

Significance statement: The role of cortical oscillations in motor control has been a long-standing question, one view being that they are an epiphenomenon. Fast oscillations are known to reach the spinal cord, and hence they have been thought to affect muscle behavior. However, experimental limitations have hampered further advances to explain how they could influence muscle force. An approach for such a challenge was adopted in the present research: to study the problem through computer simulations of an advanced biologically compatible mathematical model. Using such a model, we found that the well-known mechanism of recruitment and derecruitment of the spinal cord motoneurons can allow the muscle to respond to cortical oscillations, suggesting that these oscillations are not epiphenomena in motor control.

Keywords: conductance-based model; cortical oscillation; force control; motoneuron; motor control; simulation.

Figure 1.

Structure of the neuromuscular model used in this study. A, Schematic view of the overall model. The motor unit pool encompasses MNs and the respective MU. B, Schematic representation of muscle-specific motor units (MNs and MUs). Each of the 400 independent renewal point processes representing the descending axons activate synaptically ∼30% of the MNs. Besides the descending axons, each MN receives an IN input in the form of a Poisson point process. Each MU receives a train of action potentials from the respective MN and generates twitches that pass through a saturation nonlinearity and are summed with the contributions from the other MUs to produce the muscle force, F(t). C, Train of renewal point processes representing a train of spikes from a descending axon. D, Equivalent circuit used to represent each MN model. g_syn1 to g_synM, synaptic conductances of a dendrite activated by synapses 1 to M, respectively; g_c, coupling conductance; g_Ld and g_Ls, dendritic and somatic leakage conductances, respectively; g_Na, g_Kf, and g_Ks, conductances of Na+, fast K+, and slow K+, respectively; E_L, leakage potential; E_Na and E_K, Na+ and K+ equilibrium potentials, respectively; E_syn1 to E_synM, reversal potentials for synapses 1 to M, respectively; C_s and C_D, somatic and dendritic capacitances, respectively; V_S and V_D, somatic and dendritic membrane potentials, respectively. E, Spike trains of the MNs of the pool. F, force produced by a single MU.

Figure 2.

Mean firing rate of each descending axon as used in the simulation protocols. The mean basal firing rate for both cases was 65 spikes/s. A, The firing rate modulation began after 60 s with a 20 Hz sinusoidal signal of amplitude 20 spikes/s. After 120 s, the mean firing rate decresased to 58 spikes/s. B, The firing rate modulation began after 60 s with a 20 Hz sinusoidal signal, which was amplitude modulated by a sinusoidal signal of 1 Hz.

Figure 3.

Results from the simulation using the firing rate of the descending command shown in Figure 2A. A–C, Net dendritic synaptic conductance power spectrum with the mean basal firing rate of 65 spikes/s and no oscillation in the input (A), with the mean basal firing rate 65 spikes/s and 20 Hz oscillation in the input (B), and with 20 Hz oscillation and the mean firing rate decreased to 58 spikes/s (C). D–F, Coherence between the synaptic conductance and the CST of five randomly chosen MNs with the same MN pool inputs as in A–C, respectively. Individual data from the 100 randomly chosen CSTs are in light color, and the overall mean is in dark color. The 95% confidence level is shown as a dashed line. G, Force signal during the simulation. H, Corresponding raster plot of the MN spike trains during the simulation. The MNs are ordered according to the size principle (Henneman, 1957). The insets show 100 ms windows of the raster plot.

Figure 4.

Spectra and coherences of inputs and outputs when the firing rate of the descending command is as shown in Figure 2B. A, B, Net synaptic conductance spectrum with no modulation in the input (A) and with the modulated input (B). C, D, Coherence between synaptic conductance and the CST of five randomly chosen MNs of the pool with no oscillation in the input (C) and with the modulated input (D). Individual data from 100 randomly chosen CSTs are in light color, and the mean is in dark color. The 95% confidence level is shown as a dashed line. E, F, Force spectrum with no modulation in the input (E) and with the modulated input (F).

Figure 5.

Results from the simulation using the firing rate of the descending command shown in Figure 2B. A, Muscle force signal during a 15 s window. When the synaptic inputs were modulated (starting at 60 s), the muscle force began to oscillate at 1 Hz. B, Raster plot of the MN spike trains during the 15 s window. The dot colors specify the values of the MN ARs, which are indicated by the color bars. C, D, Darker line, Mean spectrum of the CST of five randomly chosen MNs from the 5% of the MNs from the pool with the lowest AR; lighter line, mean spectrum of the CST of five randomly chosen MNs from the 5% of the MNs from the pool with the highest AR. The spectra were normalized by the maximal power of the each spectrum (C) and by the power at 20 Hz (D). Individual data from the 100 randomly chosen CSTs are in light color.

Figure 6.

The dashed vertical line indicates the beginning of the 20 Hz input oscillation. The amplitude of the 20 Hz oscillation is different for each case. A, Amplitude of 10 spikes/s; FR(t) = 65 + 10 sin(2π20t). B, Amplitude of 20 spikes/s; FR(t) = 65 + 20 sin(2π20t). C, Amplitude of 30 spikes/s; FR(t) = 65 + 30 sin(2π20t). With the increase in oscillation amplitude, there is an increase in the steady-state mean force value.

Figure 7.

The dashed vertical line indicates the beginning of the input amplitude-modulated oscillations. The carrier frequency is different in each case. A, Carrier frequency at 20 Hz; FR(t) = 65 + 20 sin(2π20t) · [1 + 0.5 sin(2πt)]. B, Carrier frequency at 40 Hz; FR(t) = 65 + 20 sin(2π40t) · [1 + 0.5 sin(2πt)]. C, Carrier frequency at 80 Hz; FR(t) = 65 + 20 sin(2π80t) · [1 + 0.5 sin(2πt)]. The 1 Hz oscillation in muscle force appears for all the carrier oscillation frequencies, although with a lower amplitude for higher frequencies.

Figure 8.

The dashed vertical line indicates the beginning of the input amplitude-modulated oscillations. A different component was added to the neuromuscular model in each case. The basal firing rate was adjusted for each case so the mean contraction level was 10% MVC. A, Descending commands with a gamma point process with shape factor 7 [basal firing rate, 65 spikes/s; FR(t) = 65 + 20 sin(2π20t); IN ISI, 8 ms]. B, Renshaw cells were added to the model [basal firing rate, 108 spikes/s; FR(t) = 108 + 40 sin(2π20t); IN ISI, 3 ms]. C, Active dendrites were added to the model [basal firing rate, 33 spikes/s; FR(t) = 33 + 20 sin(2π20t); IN ISI, 12 ms].

Figure 9.

Simulation using a CSI formed by a 1 Hz sinusoid added to a 20 Hz sinusoid. A, Force signal during a 15 s window. The force oscillated at 1 Hz. B, Coherence between synaptic conductance and the CST of five randomly chosen MNs of the. Individual data from 100 randomly chosen CSTs are in gray, and the mean is in black. The 95% confidence level is shown as a dashed line. C, Darker line, Mean spectrum of the CST of five randomly chosen MNs from the 5% of the MNs from the pool with the lowest AR; lighter line, mean spectrum of the CST of five randomly chosen MNs from the 5% of the MNs from the pool with the highest AR. Individual data from the 100 randomly chosen CSTs are lighter gray.