Journal of Computational Neuroscience

, Volume 33, Issue 3, pp 515–531 | Cite as

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

  • Leonardo Abdala EliasEmail author
  • Vitor Martins Chaud
  • André Fabio Kohn


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.


Bistability Nonlinearities in force control Electromyogram L-type calcium channel Persistent inward current Plateau potential 



Active dendrite




Basal torque




Coefficient of variation




Excitatory post-synaptic potential


Extra torque


Inhibitory post-synaptic potential




Lateral Gastrocnemius


Medial Gastrocnemius




Maximum torque


Motor unit




Passive dendrite


Persistent inward current


Soleus muscle


Tibialis anterior


Triceps Surae



This work was funded by FAPESP (State of São Paulo Funding Agency) and CNPq (The National Council for Scientific and Technological Development). L.A. Elias and V.M. Chaud hold scholarships from FAPESP (#2009/15802-0) and CNPq (#132776/2011-1), respectively. The authors are grateful to Dr. F.H. Magalhães for his insights and valuable discussions.

Conflict of interest statement

The authors declare that there is no conflict of interest with any financial organization regarding the material discussed in this manuscript.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Leonardo Abdala Elias
    • 1
    Email author
  • Vitor Martins Chaud
    • 1
  • André Fabio Kohn
    • 1
  1. 1.Biomedical Engineering Laboratory, Escola Politécnica, PTC, Universidade de São Paulo, Av. Prof. Luciano GualbertoSão PauloBrazil

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