Effort minimization and synergistic muscle recruitment for three-dimensional force generation

Daniele Borzelli, Denise J. Berger, Dinesh K. Pai, Andrea d'Avella

Research output: Contribution to journalArticlepeer-review


To generate a force at the hand in a given spatial direction and with a given magnitude the central nervous system (CNS) has to coordinate the recruitment of many muscles. Because of the redundancy in the musculoskeletal system, the CNS can choose one of infinitely many possible muscle activation patterns which generate the same force. What strategies and constraints underlie such selection is an open issue. The CNS might optimize a performance criterion, such as accuracy or effort. Moreover, the CNS might simplify the solution by constraining it to be a combination of a few muscle synergies, coordinated recruitment of groups of muscles. We tested whether the CNS generates forces by minimum effort recruitment of either individual muscles or muscle synergies. We compared the activation of arm muscles observed during the generation of isometric forces at the hand across multiple three-dimensional force targets with the activation predicted by either minimizing the sum of squared muscle activations or the sum of squared synergy activations. Muscle synergies were identified from the recorded muscle pattern using non-negative matrix factorization. To perform both optimizations we assumed a linear relationship between rectified and filtered electromyographic (EMG) signal which we estimated using multiple linear regressions. We found that the minimum effort recruitment of synergies predicted the observed muscle patterns better than the minimum effort recruitment of individual muscles. However, both predictions had errors much larger than the reconstruction error obtained by the synergies, suggesting that the CNS generates three-dimensional forces by sub-optimal recruitment of muscle synergies.

Original languageEnglish
Article number186
JournalFrontiers in Computational Neuroscience
Issue numberDEC
Publication statusPublished - Dec 20 2013


  • Directional tuning
  • Effort minimization
  • Isometric force
  • Muscle synergies
  • Non-negative matrix factorization

ASJC Scopus subject areas

  • Neuroscience (miscellaneous)
  • Cellular and Molecular Neuroscience


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