View Full Version : RE: Wobbling mass model

unknown user
02-23-1991, 12:03 PM
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