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RE: Wobbling mass model

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  • RE: Wobbling mass model

    Dear BIOMCH-L readers,

    Last weekend this list has seen a few excellent contributions from
    Herman Woltring that will certainly stimulate some discussion. Let's
    hope Herman will not leave the list for too long a period.

    The 'wobbling mass model' is an excellent example showing how (forward
    dynamics) simulation models can be used to test the influence of
    modelling assumptions. Although few details of the results were given, I
    suspect that the overestimation of joint contact forces occurred
    primarily during the impact phase of the landing when high accelerations
    occur. These accelerations are overestimated in the rigid-body
    simulation. In normal athletes the effect of the wobbling will damp out
    quickly after impact. Not so for some heavier joggers, who give the
    impression that 'wobbling mass' is an important aspect of their

    In an 'inverse dynamics' analysis, using the same rigid body model does
    not give such errors, because the accelerations responsible for the
    impact forces are not simulated with the model. Either accelerations
    measured on a living (non-rigid) subject are used, or a force plate is
    used for a 'bottom-up' analysis. But other errors can be made. If
    acceleration of the trunk is measured, any existing high-frequency
    acceleration peaks would be underestimated because of the low-pass
    filtering associated with skin movement and numerical differentiation of
    noisy kinematical data. The 'bottum-up' analysis is less sensitive to
    this, and does give you impact peaks. But you would tend to
    overestimate impact forces in the more proximal joints if the model does
    not take the damping properties of joint cartilage into account.

    This raises another question that has been bothering me for some time.
    What is the physiological significance of impact forces? Is the peak
    force really a good parameter to quantify joint loading, or do we have
    to take the duration of the force into account? Even if forces can be
    accurately calculated the damage would probably be related to the
    deformation caused by the force. Because of visco-elastic
    properties, an impulse that lasts only one millisecond simply has no
    time to cause deformation. So, it may not be worthwhile to make models
    that calculate such short impulses accurately.

    An illustrative example is a horse, wearing iron shoes and walking on
    hard roads. The mass of the hoof plus iron undergoes enormous
    decelerations during impact, which leads to very large (but very short)
    peak forces. These forces are real, and not the result of incorrect
    modeling. However, there is no indication that this causes damage in
    the joint between the hoof and the rest of the limb.

    Any opinions?

    -- Ton van den Bogert
    Faculty of Veterinary Medicine
    University of Utrecht