Herbert Hatze

06-16-1997, 12:53 AM

BIOMECHANICAL DATA FILTERING IN RELATION TO THE GENERAL INVERSE

DYNAMICS PROBLEM

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

phenomenon".

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

LARGE (stochastic and deterministic) PERTURBATIONS OF NEURAL CONTROL INPUTS

(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

DYNAMICS PROBLEM

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

phenomenon".

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

LARGE (stochastic and deterministic) PERTURBATIONS OF NEURAL CONTROL INPUTS

(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