Predictions of co-contraction depend critically on degrees-of-freedom in the musculoskeletal model.
In biomechanics, the calculation of individual muscle forces during movements is based on a model of the musculoskeletal system and a method for extracting a unique set of muscle forces. To obtain a unique set of muscle forces, non-linear, static optimisation is commonly used. However, the optimal solution is dependent on the musculoskeletal geometry, and single joints may be represented using one, two or three degrees-of-freedom. Frequently, a system with multiple degrees-of-freedom is replaced with a system that contains a subset of all the possible degrees-of-freedom. For example, the cat ankle joint is typically modelled as a planar joint with its primary degree-of-freedom (plantar-dorsiflexion), whereas, the actual joint has three rotational degrees-of-freedom. Typically, such simplifications are justified by the idea that the reduced case is contained as a specific solution of the more general case. However, here we demonstrate that the force-sharing solution space of a general, three degrees-of-freedom musculoskeletal system does not necessarily contain the solutions from the corresponding one or two degrees-of-freedom systems. Therefore, solutions of a reduced system, in general, are not sub-set solutions of the actual three degrees-of-freedom system, but are independent solutions that are often incompatible with solutions of the actual system. This result shows that representing a three degrees-of-freedom system as a one or two degrees-of-freedom system gives force-sharing solutions that cannot be extrapolated to the actual system, and vice-versa. These results imply that general solutions cannot be extracted from models with fewer degrees-of-freedom than the actual system. They further emphasise the need for precise geometric representation of the musculoskeletal system, if general force-sharing rules are to be derived.
Jinha
Azim
A
Human Performance Laboratory, The University of Calgary, 2500 University Drive NW, Calgary, AB, Canada T2N 1N4.
Ait-Haddou
Rachid
R
Herzog
Walter
W
D000465:Algorithms; D000818:Animals; D000843:Ankle Joint / Q000502:physiology*; D001696:Biomechanical Phenomena / Q000379:methods*; D002415:Cats; D006801:Humans; D008954:Models, Biological; D009068:Movement / Q000502:physiology; D009119:Muscle Contraction / Q000502:physiology*; D018482:Muscle, Skeletal / Q000502:physiology*; D016059:Range of Motion, Articular / Q000502:physiology*