Antagonistic activity of one-joint muscles in three-dimensions using non-linear optimisation

A. Jinha, Rachid Ait Haddou, P. Binding, W. Herzog*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Non-linear optimisation, such as the type presented by R.D. Crowninshield and R.A. Brand [The prediction of forces in joint structures: Distribution of intersegmental resultants, Exercise Sports Sci. Rev. 9 (1981) 159], has been frequently used to obtain a unique set of muscle forces during human or animal movements. In the past, analytical solutions of this optimisation problem have been presented for single degree-of-freedom models, and planar models with a specific number of muscles and a defined musculoskeletal geometry. Results of these studies have been generalised to three-dimensional problems and for general formulations of the musculoskeletal geometry without corresponding proofs. Here, we extend the general solution of the above non-linear, constrained, planar optimisation problem to three-dimensional systems of arbitrary geometry. We show that there always exists a set of intersegmental moments for which the given static optimisation formulation will predict co-contraction of a pair of antagonistic muscles unless they are exact antagonists. Furthermore, we provide, for a given three-dimensional system consisting of single joint muscles, a method that describes all the possible joint moments that give co-contraction for a given pair of antagonistic muscles.

Original languageEnglish (US)
Pages (from-to)57-70
Number of pages14
JournalMathematical Biosciences
Issue number1
StatePublished - Jul 1 2006

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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