Antagonistic activity of one-joint muscles in three-dimensions using non-linear optimisation.
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.
Jinha
A
A
Human Performance Laboratory, The University of Calgary, Calgary, AB, Canada T2N 1N4.
Ait-Haddou
R
R
Binding
P
P
Herzog
W
W
D000818:Animals; D001696:Biomechanical Phenomena; D002415:Cats; D006801:Humans; D007596:Joints / Q000502:physiology*; D008433:Mathematics; D008954:Models, Biological; D009119:Muscle Contraction / Q000502:physiology; D018482:Muscle, Skeletal / Q000502:physiology; D017711:Nonlinear Dynamics