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Moments about ICR, continued

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  • Moments about ICR, continued

    Dear Biomch-L readers,

    Now that Herman Woltring has shown us the mathematical
    relationships between various definitions of joint
    moments/forces, as well as the 3-dimensional generalization, I
    want to point out a difference between two views on dynamic
    analysis. In my view this is important to clarify the discussion.

    Herman is deliberately limiting the discussion to *net* joint
    kinetics, i.e. the model consists of rigid links with one force
    and one moment transmitted by each joint. These variables are
    calculated, plus sometimes the joint powers (moment x angular velocity).
    The analysis essentially stops there, and individual muscles are
    not part of the model. This is probably a good method for clinical
    gait analysis, because no detailed information on muscle lines of
    action is needed, and no assumptions on load sharing of muscles have to
    be made. However, these joint forces and moments are not physical
    quantities but mathematical abstractions: they do not exist at all
    anywhere in the system. When I say 'not exist', I mean that there
    is no anatomical structure loaded by (= deformed as a function of)
    either the force or the moment. Is that not a good definition of
    'physical existence' of a force: that it produces a deformation
    somewhere that has a one-to-one relationship to the force? Hmm,
    you could even say that force is then also a mathematical
    abstraction, and that only stresses 'exist'. But let's accept the
    concept of force (muscle force, ligament force, contact force...)
    for now.

    Another way to look at 'net kinetics' analysis is as a
    transformation of the original kinematic, kinetic and
    anthropomorphic measurements, intended to facilitate the
    (clinical) quantification of 'gait quality' or the recognition of
    certain abnormalities. A mechanical interpretation of the
    resulting 'net kinetics' variables is not the real purpose of the
    analysis (apart from the fact that, strictly speaking, it is not
    even allowed - see above). Looking at it this way, I must agree
    with Ian Stokes that it does not really matter which reference
    point is used to calculate the joint moment. Just as long as you
    use the same reference point when comparing results, and the
    variables obtained still contain useful information. In fact,
    using a fixed point is to preferred above the elusive ICR. The
    ICR can only be estimated when the kinematic data are of
    sufficient quality, and even then requires sophisticated filtering
    and analysis methods. For such a 'net kinetic' analysis it might
    be more reliable to use the lateral epicondyle as reference at the
    knee, rather than the ICR, because it can be marked directly and
    measured by the measuring system. The choice of reference point
    does require standardization however, to avoid problems when
    comparing published results.

    Many biomechanicians however, *are* interested in real muscle
    forces and real joint forces, and try to estimate them as well as
    possible. These forces are not mathematical but physical
    quantities. There are of course the well-known indeterminacy
    problems because the equilibrium equations for moment and force
    often have too many unknowns. For some situations however, such an
    analysis is the right tool for the job. In that case, the reasoning
    of my previous posting applies: the ICR is the only point about which the
    moment arms of muscle forces (dL/dA) and joint forces (zero) are easy to
    obtain. (For simplicity I limit the discussion to 2D). Note that the
    'net joint force' resulting from this type of analysis is not the same
    as in the 'net kinetics' analysis, but is much larger (and more
    realistic). This force may also be only a resultant of several physical
    (contact & ligaments) forces, but the muscle forces that have been
    obtained are real physical quantities.

    So my revised opinion is: use the ICR as reference point when
    estimating muscle and joint forces. For a 'net kinetic' analysis,
    only standardization is required; there is no preferred reference
    point. Clinical usefulness seems to be more important than mechanical
    interpretation in that case.

    Finally, this is probably a very academic discussion without
    practical implications; the various definitions reviewed by Ian
    Stokes produce very similar results. But sometimes it is
    enlightening to think about why you do things one way, and not the
    other way.

    -- Ton van den Bogert
    University of Utrecht, Netherlands