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Prof. Hatze
01-24-2002, 11:24 PM
Dear List Members,

I would like to react to the responses of DRS. VAN DEN BOGERT, POLGAR,
GILL, AND O'CONNOR.

Let me begin with the excellent posting of DRS. POLGAR, GILL, AND
O'CONNOR. Being not a specialist in bone stress analysis, I can only
comment on their modeling approach. In this respect, I was particularly
impressed by their recognizing the necessity of possessing FIRST a more
complex FE model in order to justify simplifications of that model. They
suggest that simplification can be validated by showing that, for a
specific range of applications, the simplified model yields results not
significantly different from those of the more complicated model, or by
the fact that the simplified model produces results which agree well
with experiment. (In which case the more complex model was unnecessarily
complicated anyway). They exemplify their statement by demonstrating the
inappropriateness of modeling distributed muscle insertion forces along
a bone in the form of a point force applied to only one node,
representing the attachment area center. The authors also stress the
important fact that simplifications which may be appropriate for a
specific application may be totally inappropriate for another. In
addition, they emphasize the importance of biological realism of model
predictions. Congratulations to these authors for an excellent
contribution.

Dr. van den Bogert's opinions are actually much more "progressive" than
he himself modestly admits. Although at the beginning of his exposition
he expresses his reservations about adding more realism and complexity
to models, he is suggesting, and correctly so, the use of more realistic
and complex human body models in his comments on point 2 of the BIONET
TOPIC-2-posting. He quite aptly remarks that the bulk of body mass is
not bone but soft tissue wich may "wobble" relative to the skeleton, and
that special sensors or markers should be used to dedect these
submotions while others should record skeleton motion. However, any
subsequent analysis of such sensor outputs or marker trajectories
clearly presupposes the existence of hybrid rigido-viscoelastic body
models which would be more realistic and complex than existing ones, as
I have suggested in my TOPIC-2-posting.

A large part of Dr. van den Bogert's comments actually deals with the
MODELING ISSUE which ties in with the recently posted TOPIC 3. He firmly
believes that there exists an appropriate degree of model complexity for
each question, and refers to Occam's razor. In my opinion, this is not
necessarly true in general. I shall also show that Occam's razor concept
is not applicable to the present discussion.

Consider the FOLLOWING EXAMPLE based on recently conducted research. The
question (problem) is to find a model that permits an assessment of
various characteristics and properties of the muscle groups involved in
sportive jumping activities. The currently populary answer to this
question (solution of this problem) is well known: evaluation of
bi-legged maximum effort vertical jumps by means of a human body POINT
MASS MODEL using force plates. By computing the vertical impulse
resulting from the ground reaction forces exerted during the propulsive
motion phase, and by knowing the subject's mass, it is easy to calculate
the flight height of the body center of mass. The hypothesis is that
this flight height is a representative indicator of the muscular
capabilities mentioned above.

The situation changes dramatically if, instead of a point mass body
model, the more realistic but also more complex SEGMENT-STRUCTURED BODY
MODEL is used. It is easily shown that the performance criterion of
maximizing the absolute vertical height of the body mass centroid in
bi-legged vertical jumping is equivalent to maximizing the difference
between the vertical potential + kinetic energy of the c.m. at the end
and that at the begin of the motion. This energy difference is part of
the corresponding difference in the TOTAL mechanical energy content of
the segment-structured model which energy difference, in turn, is
generated by the muscle groups active during the vertical jump. Thus,
muscular energy production relates directly to the increase in the TOTAL
mechanical energy content of the segmented body model, of which the
vertical energy content of the mass centroid is only a part. (Other
segmental energy forms are comparatively large rotational and non-
vertical translational kinetic energies). It follows that, in principle,
the evaluation of the c.m. flight height in vertical jumping is not a
valid indicator of muscular capabilities.

The point I want to make is that one MAY THINK that the degree of model
complexity selected for solving a certain problem, or answer a certain
question, is adequate when, in fact, it is not. The example presented
above shows that the deficiency and inappropriateness of the simple
(point mass) model only became apparent AFTER the complex
(segment-structured) model was used for the analysis.

There is an abundance of other examples of inadequate biomechanical
models currently in use. A. V. Hill's mathematical force-velocity model,
for instance, does not account for the well known inflection point at
about 0.8 Fmax, and totally fails at positive (stretching) velocities;
current architectural models of the myostructures ignore the important
phenomenon of intra- and intermuscular parallel myofascial force
transfer; etc.

The CONCEPT OF OCCAM'S RAZOR (www.nwmangum.com/Occam.htm) is not
applicable to the current debate as it either relates to observed data
originating from a black-box object and used to construct by INDUCTIVE
REASONING one of infinitely many possible models, or it concerns the
creation of universal models with a subject domain that is of unlimited
complexity, such as in philosophy or metaphysics. In biomechanics we are
not interested in creating nebulous philosophical or metaphysical
models. We are also very seldom confronted with balck-box model
building. In this sense, Dr. van den Bogert's example of trying to fit a
10th order polynomial to five data points does not really reflect the
essence of the problem. Because if, by some method, it had been
established that a 10th order polynomial is the lowest degree polynomial
representing a certain validated model, then the situation would be
reversed in that not the use of this polynomial would be incorrect but
the data set of 5 points would be too small. In biomechanics, we are
interested in down-to-earth models that use deduction as much as
possible, as I have stressed under point 1 of the recent TOPIC
3-posting.

Also, I totally disagree with the statement that "... simpler models are
more likely to be correct than complex ones, in other words, THAT
"NATURE" PREFERS SIMPLICITY" (end of the webpage containing an
exposition on Occam's razor). Nature certainly DOES NOT "prefer
simplicity " as is more than obvious from current research on the human
and animal genetic code, on the structure of the universe, on the
molecular structure of myoproteins, etc. In fact, evolution shows us
that nature appears to tend to create more and more complex structures.
In reality, it is the human mind that tries to simplify things. Because
it cannot consciously grasp and analyse complex processes such as the
dynamics of multi-body systems, we use mechanomathematical models to
obtain by computer simulation information on system behavior that would
otherwise not be available.

In conclusion, I feel the CORRECT BIOMECHANICAL MODELING APPROACH is to

A) create a (descriptive) mechanical or mechanomathematical model of the
relevant attributes of a biological object, event, or process, by
employing as much as possible DEDUCTIVE METHODS and aiming for MAXIMUM
COMPLEXITY, subject to the constraints imposed by practicality. The
strive for maximum complexity simply means the incorporation into the
model structure of as many as possible known and relevant features of
the biosystem in question. This minimizes the chance of including
black-box subsystem features. Deduction implies the use of known
functional relationships such as, for instance, laws of energy
conservation, Newton's laws, etc. It is, however, of the UTMOST
IMPORTANCE to realize that, apart from economical constraints, a
deliberate a priori reduction of the model maximum complexity in the
designing stage is equivalent to stating that the functional
significance of the interactions of the model subsystems as well as the
model behavior itself IS KNOWN to the modeler beforehand. This is
generally NOT the case.

B) Validate the (functional) model by simulating responses of the real
biosystem for all modes of operation for which experimental responses of
the natural system are available. Compare the responses and check
whether or not they are within the prescribed range of accuracy.

C) If necessary (and possible) improve the model until acceptable
agreement between model and biosystem responses is achieved.

D) If required and permissible for certain applications, simplify the
model making sure that the responses of the simplified model do not
deviate substantially from those of the complex base model. (The
replicative validity must also be preserved. For a discussion see H.
Hatze, J. of Biomechanics 35/1, pp.109-115).

Finally, I would like to underscore the remarks made by Dr. van den
Bogert with respect to the other points of my original posting except,
perhaps, that in the present sense there is no connection between the
cut-off frequency in data filtering and model complexity. (The criteria
for designing optimal cut-off filters are a very complicated issue). His
views on muscle force estimation will be appropriately dealt with once
these discussion topics appear on BIOMCH-L. Thanks are due to Dr. van
den Bogert for submitting his valuable contribution.

Herbert Hatze





************************************************** ******
Prof. Dr. Herbert Hatze
Head, Department and Laboratory of Biomechanics, ISW,
University of Vienna

Auf der Schmelz 6 Tel: + 43 1 4277 48880
A-1150 WIEN Fax: + 43 1 4277 48889
AUSTRIA e-mail: herbert.hatze@univie.ac.at
************************************************** ******

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