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Knee Kinematics Estimation Using Multi-Body Optimisation Embedding a Knee Joint Stiffness Matrix: A Feasibility Study

Author

Listed:
  • Vincent Richard
  • Giuliano Lamberto
  • Tung-Wu Lu
  • Aurelio Cappozzo
  • Raphaël Dumas

Abstract

The use of multi-body optimisation (MBO) to estimate joint kinematics from stereophotogrammetric data while compensating for soft tissue artefact is still open to debate. Presently used joint models embedded in MBO, such as mechanical linkages, constitute a considerable simplification of joint function, preventing a detailed understanding of it. The present study proposes a knee joint model where femur and tibia are represented as rigid bodies connected through an elastic element the behaviour of which is described by a single stiffness matrix. The deformation energy, computed from the stiffness matrix and joint angles and displacements, is minimised within the MBO. Implemented as a “soft” constraint using a penalty-based method, this elastic joint description challenges the strictness of “hard” constraints. In this study, estimates of knee kinematics obtained using MBO embedding four different knee joint models (i.e., no constraints, spherical joint, parallel mechanism, and elastic joint) were compared against reference kinematics measured using bi-planar fluoroscopy on two healthy subjects ascending stairs. Bland-Altman analysis and sensitivity analysis investigating the influence of variations in the stiffness matrix terms on the estimated kinematics substantiate the conclusions. The difference between the reference knee joint angles and displacements and the corresponding estimates obtained using MBO embedding the stiffness matrix showed an average bias and standard deviation for kinematics of 0.9±3.2° and 1.6±2.3 mm. These values were lower than when no joint constraints (1.1±3.8°, 2.4±4.1 mm) or a parallel mechanism (7.7±3.6°, 1.6±1.7 mm) were used and were comparable to the values obtained with a spherical joint (1.0±3.2°, 1.3±1.9 mm). The study demonstrated the feasibility of substituting an elastic joint for more classic joint constraints in MBO.

Suggested Citation

  • Vincent Richard & Giuliano Lamberto & Tung-Wu Lu & Aurelio Cappozzo & Raphaël Dumas, 2016. "Knee Kinematics Estimation Using Multi-Body Optimisation Embedding a Knee Joint Stiffness Matrix: A Feasibility Study," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-18, June.
  • Handle: RePEc:plo:pone00:0157010
    DOI: 10.1371/journal.pone.0157010
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    References listed on IDEAS

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    1. P. Koell & L. Cheze & R. Dumas, 2010. "Prediction of internal spine configuration from external measurements using a multi-body model of the spine," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 13(S1), pages 79-80.
    2. M.S. Andersen & M. Damsgaard & B. MacWilliams & J. Rasmussen, 2010. "A computationally efficient optimisation-based method for parameter identification of kinematically determinate and over-determinate biomechanical systems," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 13(2), pages 171-183.
    3. M.S. Andersen & M. Damsgaard & J. Rasmussen, 2009. "Kinematic analysis of over-determinate biomechanical systems," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 12(4), pages 371-384.
    4. R. Dumas & T. Robert & V. Pomero & L. Cheze, 2012. "Joint and segment coordinate systems revisited," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 15(S1), pages 183-185.
    5. J. Clément & N. Hagemeister & R. Dumas & M. Kanhonou & J.A. de Guise, 2014. "Influence of biomechanical multi-joint models used in global optimisation to estimate healthy and osteoarthritis knee kinematics," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 17(S1), pages 76-77, August.
    6. Saulo Martelli & Giordano Valente & Marco Viceconti & Fulvia Taddei, 2015. "Sensitivity of a subject-specific musculoskeletal model to the uncertainties on the joint axes location," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 18(14), pages 1555-1563, October.
    7. N. Hagemeister & M. Senk & R. Dumas & L. Chèze, 2011. "Effect of axis alignment on shoulder kinematics," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 14(08), pages 755-761.
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