## Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1145-1152 |

Number of pages | 8 |

Journal | Journal of Biomechanics |

Volume | 39 |

Issue number | 6 |

DOIs | |

State | Published - 2006 |

Externally published | Yes |

## Keywords

- Agonist
- Antagonist
- Force-sharing
- Movement control
- Muscle
- Optimisation

## ASJC Scopus subject areas

- Biophysics
- Orthopedics and Sports Medicine
- Biomedical Engineering
- Rehabilitation