View Full Version : Data Smoothing and Inverse Dynamics

Jesus Dapena
06-17-1997, 09:13 AM
To the Biomch-L readership:

In a message of June 16, Prof. Hatze says:

> Next, I would like to respond to Dr. Dapena's posting of 2 June because
> it touches upon the important issue of the INVERSE DYNAMICS PROBLEM. Dr.
> Dapena proposes that the degree of data smoothing be determined by the
> degree of agreement between the results obtained and the laws of
> mechanics. This suggestion involves, at least partly, a circular argument
> because it presumes the availability of detailed A-PRIORI INFORMATION on
> quantities which are, in fact, the expected RESULT of an intended motion
> analysis procedure. If it is known from DEDUCTIVE REASONING (LAWS OF
> MECHANICS) that, for instance, the total angular momentum about the c.m.
> during a specific motion (e.g. airborne movements) must remain constant,
> then the whole exercise of performing a motion analysis to find that
> angular moment function is futile except, perhaps, for testing the
> performance of some data smoothing algorithm.

Prof. Hatze's objection would be valid if I were trying to prove
that angular momentum is constant in the air. In such case, I would indeed
have a circular argument. However, that would not be my purpose. My
purpose would be to obtain the NUMERICAL VALUE of that constant angular
momentum, not to verify whether it is constant or not! Therefore, the
argument is not circular.

> But even then, the test results would be VALID ONLY for this particular
> phase of the motion, this specific set of noise-contaminated input data,
> and this particular biomechanical inverse dynamics model.

OK, here are my answers to these points:

> VALID ONLY for this particular phase of the motion ...
The researcher would look for a smoothing factor that would work
well for various parts of the trial (say, the airborne phases of all the
run-up steps being analyzed, as well as the final airborne phase of the bar
clearance), so the smoothing would be reasonably valid for the entire trial.

> (VALID ONLY for) this specific set of noise-contaminated input data ...
Of course. Why would anyone need it to be valid for a different
set of data?? Perhaps Prof. Hatze is referring to the inconvenience of
having to decide on a smoothing factor separately for each individual trial.
Well, in my case, I just "bite the bullet" and do it for every trial
separately. I don't find it to be that much work. But a point to consider
is that, in my experience, for trials that come out of the same filming
session, with similar image scale and image quality, the optimum smoothing
factors (as decided through the method that I described in my Biomch-L
message of June 2) tend to be quite similar for all trials. Therefore
(except for anal-retentive types such as myself!) it should be OK to decide
upon a smoothing factor based on a few trials, and then keep using that same
value for the rest of the trials, without having to check every trial one
by one.

> (VALID ONLY for) this particular biomechanical inverse dynamics model ...
Of course, why would I need it to be valid for a different model??

My position is that it would indeed be very nice to have some
method for deciding the optimum smoothing factor in an automatic way. As
soon as I find one that works to my satisfaction, I will certainly adopt it.
Unfortunately, I still have not found it. Until then, I will use what I
think makes the best sense. For me, that is the approach that I described
in my June 2 message.

> ... the neuromusculosceletal inverse problem is basically a "forbidden"
> one, and that an observed motion is an unsuitable function set to be used
> for obtaining those kinetic quantities that generated the motion in
> question.

In this regard, I am very much in agreement with Prof. Hatze.
While I don't think that we should throw away all torque values obtained
through inverse dynamics, we certainly have to relegate them to the status
of mere rough "ballpark" figures, and therefore treat them with great
caution: With respect to second derivative data, smoothing is helpful, but
it cannot do miracles ---and it can also be dangerous.

Jesus Dapena
Jesus Dapena
Department of Kinesiology
Indiana University
Bloomington, IN 47405, USA