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  • Comments on Reponses to BIONET TOPICS 1, 2, and 3

    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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