View Full Version : Data Smoothing and Inverse Dynamics

Herbert Hatze
06-16-1997, 12:53 AM

Since my last posting on the subject on 2 June, I have received numerous private comments
which prompted me to mail one more posting on this topic.

First and foremost, I would like to express my thanks to all who have appreciated my efforts to
bring clarity into the current discussion. Further to this, I received many comments that were
rather critical of the various statements made by Mr. Giakas in his posting. Indeed, Mr. Giakas
himself confessed to having erred with his critique on the concept of determining the optimal
regularization parameter alpha for computing the optimal filtering windows in the derivative
domains. Of even greater concern, however, is the fact that apparently NONE of the reviewers
of the respective publication, which is to appear in erroneous form in the August-issue of the
Journal of Biomechanics, was able to detect this fundamental flaw.

One of the private communicators sent me the following comment which, I feel, is very much
to the point and which I can fully underscore: "The internet has many advantages as a means
for exchanging scientific knowledge, including rapid access to information and a mass
audience. I am, however, concerned that there may be too many people who rely upon this
type of communication and neglect what is still the most important source of knowledge on
any scientific subject: a comprehensive search and critical review of the relevant peer-
reviewed literature. The fact that your original posting was necessary is evidence of this

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. 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.

In general, however, the required output functions of a motion analysis are complex and, of
course, NOT known beforehand. Some years ago, I (and others) had the idea of REPLACING
the highly instable process of inverse dynamics by simulation, i.e. by seeking (by means of
some algorithm) those input functions (muscle torques or neural muscle control inputs) to a
sufficiently complex and realistic model of the human neuromusculoskeletal system, which
would generate the obseved motion given, of course, all external forces and all sets of
subject-specific parameters.

And this is the point at which the FUNDAMENTAL PROBLEM OF INVERSE DYNAMICS is
encountered: Recent simulation (and experimental) results have clearly demonstrated that
(or of muscle torques) have comparatively LITTLE INFLUENCE ON THE STABILITY OF THE
RESULTING MOTION TRAJECTORY. In other words, comparatively chaotic neural control
inputs may produce highly coordinated movements. The CONVERSE is, however, also true:
Already slight inaccuracies in the observed motion will produce large errors in the inverse
dynamics computation of quantities like muscle torques, joint loads, etc., with the error
amplitudes depending, of course, on the particular inertial and myodynamic properties of the
system in question. The BIOMECHANICAL INVERSE DYNAMICS PROBLEM is therefore
HIGHLY ILL-CONDITIONED and does, in fact, belong to the class of socalled
INCORRECTLY-POSED PROBLEMS which, by definition, are non-physical and do not
POSSESS UNIQUE SOLUTIONS (Morozov, 1984; Hatze, 1990). In essence this means that
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.

A final word regarding my concern about the many and frequent attempts of re-inventing the
wheel, not only in data smoothing and derivative computation, but also in a number of other
biomechanical subdisciplines. Recently, I observe an increasing number of publications (also
in MUSCLE MECHANICS) in which mainly young researchers present "novel" or
"revolutionary" ideas and findings, which at a closer look, turn out to be either trivial, or are
reproductions of already well-known results, or, in the worst case, are fundamentally incorrect.
(See the letter to the editor and discussions on muscle mechanics in the J. of Biomechanics a
few months ago). My feeling is that there must be something wrong with both, the education in
biomechanics and the peer review system if these trends, as they do, can continue unabated
for years.

H.Hatze, Ph.D.
Professor of Biomechanics
University of Vienna