Models of passive and active dendrite motoneuron pools and their differences in muscle force control

Abstract

Motoneuron (MN) dendrites may be changed from a passive to an active state by increasing the levels of spinal cord neuromodulators, which activate persistent inward currents (PICs). These exert a powerful influence on MN behavior and modify the motor control both in normal and pathological conditions. Motoneuronal PICs are believed to induce nonlinear phenomena such as the genesis of extra torque and torque hysteresis in response to percutaneous electrical stimulation or tendon vibration in humans. An existing large-scale neuromuscular simulator was expanded to include MN models that have a capability to change their dynamic behaviors depending on the neuromodulation level. The simulation results indicated that the variability (standard deviation) of a maintained force depended on the level of neuromodulatory activity. A force with lower variability was obtained when the motoneuronal network was under a strong influence of PICs, suggesting a functional role in postural and precision tasks. In an additional set of simulations when PICs were active in the dendrites of the MN models, the results successfully reproduced experimental results reported from humans. Extra torque was evoked by the self-sustained discharge of spinal MNs, whereas differences in recruitment and de-recruitment levels of the MNs were the main reason behind torque and electromyogram (EMG) hysteresis. Finally, simulations were also used to study the influence of inhibitory inputs on a MN pool that was under the effect of PICs. The results showed that inhibition was of great importance in the production of a phasic force, requiring a reduced co-contraction of agonist and antagonist muscles. These results show the richness of functionally relevant behaviors that can arise from a MN pool under the action of PICs.

Appendix: Geometric and electrotonic properties of the motoneuron pool

The passive characteristics of each single MN model (see section 2.1.1) depended on the geometric and electrotonic properties of the cell (Equations A1 to A5), which were based on data from type-specified (i.e., S-, FR-, and FF-type) cat MNs (Fleshman et al. 1988; Zengel et al. 1985). In this study, the parameters varied linearly within each type of MNs (see Table 3), resulting in a piece-wise linear approximation of how these parameters vary along the whole pool. Figure 10 shows an example for the range of rheobase currents adopted in the SOL MN pool. All the parameters were made equal for the different motor nuclei (i.e., SOL, MG, LG, and TA) and the differences between them were only in the numbers of each MU type (Table 4).

$$ {g_c} = \frac{2}{{\frac{{{R_i}.{l_D}}}{{\pi .r_D^2}} + \frac{{{R_i}.{l_S}}}{{\pi .r_S^2}}}} $$

(A1)

$$ {g_{{lD}}} = \frac{{2.\pi .{r_D}.{l_D}}}{{{R_{{m,D}}}}} $$

(A2)

$$ {g_{{lS}}} = \frac{{2.\pi .{r_S}.{l_S}}}{{{R_{{m,S}}}}} $$

(A3)

$$ {C_D} = 2.\pi .{r_D}.{l_D}.{C_m} $$

(A4)

$$ {C_S} = 2.\pi .{r_S}.{l_S}.{C_m} $$

(A5)

Fig. 10

Range of rheobase currents for the SOL MN pool. Within each MN type (the range is bounded by dots) the values varied linearly, resulting in a piece-wise linear variation along the pool

Table 3 Range of values adopted for the geometric and electrotonic parameters of MN models

Table 4 MU number adopted in each motor nucleus of the neuromuscular system