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Van Den Bogert, Ton
07-17-2007, 12:41 PM
In last Friday's posting, Steve Piazza said that in our 1994 paper we
"found group average axis orientations that were within 5 to 10 degrees
of the group average orientations reported in a previous cadaver study".
I actually think we were even able to determine *individual* subjects'
axes within 5-10 degrees.

(In response to Thomas Greiner's comment about terminology: when I
mention degrees, this always refers to a single orientation parameter at
a time, i.e. the inclination from the horizontal plane or the deviation
from the sagittal plane. Yes, strictly speaking the differences in
these parameters should not be interpreted as orientation differences,
but it is not bad unless you are near a pole of the spherical coordinate
system.)

Unlike in Steve's recent study, we had no gold standard of the true axes
in our subjects, but if our errors were much larger than 5-10 degrees
(as Steve suggests), and random, we would have seen a larger standard
deviation. If the errors were much larger, and systematic, we would
have seen a larger difference between my average and the average of
Inman's cadaver results. So I conclude that our errors in axis
estimates were less than 10 degrees. This was also supported by the
sensitivity analyses.

Our results for inclination of the subtalar joint axis: 37.4 +- 2.7
degrees (mean and SD of 14 subjects). Inman's cadaver study: 42 +- 9
degrees.

Still, I did not feel comfortable using this method in subject-specific
modeling because I could not determine that these axes also existed
during weightbearing. Steve's results suggest that there is a similar
problem during passive motion. In these conditions, a 2-axis
subject-specific model may still be appropriate but the method for
identifying the parameters is too sensitive to error. So, right now, I
no longer try to estimate subject-specific axes, I just use Inman's axes
in each subject. It is still better than modeling the ankle as a ball
joint, I suppose. In case anyone is wondering, this is important when
using joint moments to estimate muscle forces.

Steve made a very nice animation to illustrate of the ill-posedness of
the problem
(http://www.biomechanics.psu.edu/research/spiazza/universal_joints.avi).
This shows that you only need to perturb the marker data by a few mm to
obtain a drastically different estimate of the axes of rotation.

However, you need certain correlations in those perturbations (between
markers, between markers and joint angle) to get that result. Measuring
errors are not correlated like that. Don't understimate the power of
combining a large number of noisy measurements into an accurate estimate
of a single model parameter. This is well known in statistics, of
course. If you average N values, each having a random error E, the
error in the average is only E/sqrt(N). Now, in foot motion data the
errors are not all random, some of it is correlated to joint motion (as
we discussed before in relation to skin movement error). But there is
probably sufficient lack of correlation (between markers, and between
markers and joint angles) that the error can be reduced significantly by
the parameter estimation procedure.

Steve attributed his errors of 20-40 degrees to "non-revolute behavior".
That makes sense to me. Non-revolute behavior causes errors that are
perfectly correlated between markers attached to the same bone, and
during passive movement induced by external force the error may also be
nearly perfectly correlated to joint angle. Not a good situation for
the 2-axis estimation problem.

I know that there are others who use subject-specific functional ankle
axes (Michael Pierrynowski at McMaster University, B.J. Fregly at
University of Florida, maybe more). I am hoping they would be willing
to share their experiences here also.

Ton van den Bogert

--

A.J. (Ton) van den Bogert, PhD
Department of Biomedical Engineering
Cleveland Clinic Foundation
http://www.lerner.ccf.org/bme/bogert/

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