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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To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

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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

************************************************** ******

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------