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Re: BioNet Controversial Topic #4: knee joint DoUF

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  • Re: BioNet Controversial Topic #4: knee joint DoUF

    Dear Colleagues:

    I very much enjoyed reading Alberto Leardini's introduction to this
    topic. It is a question that we have wrestled with recently. I believe
    some answers can be given from a practical point of view.

    The question is:

    > How many independent degrees of unresisted freedom has the human knee joint?

    As Alberto already stated from the start: the easy answer is: 6, because there
    is translation and rotation in all three directions. This is too easy. If
    your measurements are sufficiently accurate, you will get this same answer
    for any mechanism that you can test. In fact, you can get any answer,
    dependent on how closely you look at joint motion. So obviously this answer
    does not give any insight at all. Maybe the question can be rephrased to
    apply to a specific situation.

    Joint testing
    -------------
    One practical question could be: if you want to test a knee joint (or
    a computational model of one), which variables should be inputs (controlled)
    and which are outputs (measured)?

    In my view there is only one correct way to set up such mechanical tests,
    and this approach has been used by, among others, Leendert Blankevoort
    (for specimens and computational models) and by the Prof. Woo's group in
    Pittsburgh for robotic testing of cadaver joints.

    Input variables:
    3-D force across the joint
    flexion angle
    varus-valgus torque
    internal-external rotation torque

    Output variables:
    3-D translational motion
    varus-valgus angle
    internal-external rotation angle

    So there are six input variables and five output variables. But only one
    of the input variables is a kinematic variable. The stiffness in the other
    degrees of freedom is potentially very large, so it is better to use force
    control than position control for those. So, in this sense, we have
    assumed that there is only one kinematic degree of freedom. But note that
    we measure the other five as output variables, so we do recognize the fact
    that there is motion in the other five degrees of freedom.

    This approach requires a sophisticated loading device where flexion angle
    is controlled but all other motions are left free to move under the influence
    of a controlled force. A robot arm with mixed force/position feedback is
    the ideal device to do this.

    In the absence of forces and torques, you will get an unloaded path of flexion
    (I have heard Prof. Woo talk about this), where the other kinematic degrees of
    freedom are dependent on flexion angle only, i.e. the knee behaves as a pure 1-DOF
    mechanism. However, this path may be sensitive to perturbations, indicating
    that the (partially) unloaded joint is perhaps better described as having more
    than 1 DOF.

    As mentioned by Alberto, Blankevoort also observed this sensitivity and then
    decided to determine helical axes as a function of knee flexion while applying
    3 Nm of internal or external rotation torque. This made the results
    reproducible. I sometimes wonder if this sensitivity problem is worse in cadaver
    joints than in vivo. Do they become more lax after dissection, and during
    testing?

    Forward dynamics
    ----------------
    The extra DOFs that exist when close to the neutral position can be important. We
    are doing some work where we try to predict landing movements with forward
    dynamics. If the knee joint is modeled as a 1-DOF mechanism, there is no
    possibility for an independent internal tibial rotation at impact. This then
    means that there is a large effective inertia for internal tibial rotation,
    since the thigh has to rotate internally too. This will lead to overestimating
    the joint loading during impact. I have no numbers yet to illustrate this,
    we are just about to do a comparison between a 1-DOF and 2-DOF knee model.

    This would probably have relevance also to design of total knee replacements.
    A joint with 1 DOF may perform well for slow movements but maybe not during
    impacts.

    Other than impact response, I see no reason to have more than 1 DOF in the
    knee joint when the knee is only considered for its function within a larger system,
    rather than studied for its own sake. The component of the 3-D kinematics that is
    not coupled to flexion is so small that it can't possibly have an influence on
    muscle function or whole body movement. The lower extremity model of SIMM
    (http://www.musculographics.com) does it this way. Flexion is the only DOF and
    the other five have a fixed relationship to flexion angle. So it has a built-in
    unloaded path of flexion, with infinite stiffness for deviations from this path.
    It is not a simple hinge, but it has one degree of freedom.

    Ton van den Bogert

    --

    A.J. (Ton) van den Bogert, PhD
    Department of Biomedical Engineering
    Cleveland Clinic Foundation
    9500 Euclid Avenue (ND-20)
    Cleveland, OH 44195, USA
    Phone/Fax: (216) 444-5566/9198

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