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Anatomical kinematic constraints: consequences on musculo-tendon forces and joint reactions

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Abstract

This paper presents a new method to estimate both musculo-tendon forces and detailed joint reactions during gait, using an original 3D lower limb musculo-skeletal model with 5 degrees of freedom: spherical joint at the hip and parallel mechanisms at both knee and ankle. This can be realized by employing a typical set of natural coordinates into a three-steps process. First, the kinematic constraints associated with the kinematic models are applied through a global optimization method on the marker-based kinematics. Consistent time derivatives of the positions are computed by projecting the velocities and accelerations in the null space of the Jacobian matrix. Then, a Lagrangian formulation of the equations of motion is proposed, introducing Lagrange multipliers and allowing a straight access to the musculo-tendon forces. Thanks to a parameter reduction procedure, the Lagrange multipliers are cancelled and the musculo-tendon forces can be computed directly, using a static optimization algorithm with a typical cost function. Finally, the equations of motion are rewritten with the Lagrange multipliers to compute detailed joint reactions (since they represent directly joint contact and ligament forces). Results show that the estimated musculo-tendon forces are consistent with measured EMG signals. Moreover, the use of “anatomically” consistent kinematic models allows computing total joint reaction at hip joint and detailed joint reactions at both knee and ankle joints that are temporally consistent with the forces measured on the subject (i.e., knee joint contact forces) and the forces published in the literature (i.e., hip joint contact forces). Next step will be to optimize simultaneously musculo-tendon forces and joint reactions to investigate and understand the interactions acting into the musculo-skeletal system during gait.

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Authors and Affiliations

  1. Laboratoire de Biomécanique et Mécanique des Chocs, Université de Lyon, UMR T9406, Université Lyon 1, IFSTTAR, 69622, Lyon, France

    Florent Moissenet, Laurence Chèze & Raphaël Dumas

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  1. Florent Moissenet
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  2. Laurence Chèze
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  3. Raphaël Dumas
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Correspondence to Florent Moissenet.

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Moissenet, F., Chèze, L. & Dumas, R. Anatomical kinematic constraints: consequences on musculo-tendon forces and joint reactions. Multibody Syst Dyn 28, 125–141 (2012). https://doi.org/10.1007/s11044-011-9286-3

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