Annals of Biomedical Engineering

, Volume 39, Issue 1, pp 147–160 | Cite as

An Optimization Approach to Inverse Dynamics Provides Insight as to the Function of the Biarticular Muscles During Vertical Jumping

  • Daniel J. CleatherEmail author
  • Jon E. Goodwin
  • Anthony M. J. Bull


Traditional inverse dynamics approaches to calculating the inter-segmental moments are limited in their ability to accurately reflect the function of the biarticular muscles. In particular they are based on the assumption that the net inter-segmental moment is zero and that total joint moments are independent of muscular activity. Traditional approaches to calculating muscular forces from the inter-segmental moments are based on a consideration of joint moments which do not encapsulate the potential moment asymmetry between segments. In addition, traditional approaches may artificially constrain the activity of the biarticular muscles. In this study, an optimization approach to the simultaneous inverse determination of inter-segmental moments and muscle forces (the 1-step method) based on a consideration of segmental rotations was employed to study vertical jumping and contrasted with the more traditional 2-step approach of determining inter-segmental moments from an inverse dynamics analysis then muscle forces using optimization techniques. The 1-step method resulted in significantly greater activation of both the monoarticular and biarticular musculature which was then translated into significantly greater joint contact forces, muscle powers, and inter-segmental moments. The results of this study suggest that traditional conceptions of inter-segmental moments do not completely encapsulate the function of the biarticular muscles and that joint function can be better understood by recognizing the asymmetry in inter-segmental moments.


Musculoskeletal modeling Muscle force Joint contact force Muscle power Inter-segmental moments 



Anterior tibial shear


Inverse optimization approach (biarticular muscles with standard upper bounds)


Inverse optimization approach (selected biarticular muscles have double the standard upper bound)


Global coordinate system


Local coordinate system


Inverse optimization approach (only monoarticular muscles)


Patellofemoral joint contact force


Posterior tibial shear


Tibiofemoral joint contact force


Traditional method of calculating joint moments


Traditional method of calculating muscle forces (biarticular muscles with standard upper bounds)


Traditional method of calculating muscle forces (only monoarticular muscles)



The authors would like to thank the anonymous reviewers for the clarity of their thoughts which greatly increased the transparency of this article.


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Copyright information

© Biomedical Engineering Society 2010

Authors and Affiliations

  • Daniel J. Cleather
    • 1
    • 2
    Email author
  • Jon E. Goodwin
    • 1
  • Anthony M. J. Bull
    • 2
  1. 1.St. Mary’s University CollegeTwickenhamUK
  2. 2.Department of BioengineeringImperial College LondonLondonUK

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