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jrhouck34
02-27-2000, 11:28 PM
To All,

Here is the summary of the replies to my questions on normalizing joint
moments and how to map the local moments. The original posting and the
responses are included.

In summary:

First question - normalization of joint moments

1. Some people suggested the reason for normalizing to both mass and
height is to render the variable demensionless

2. Other people agreed that the variability is not significantly
reduced by combining both mass and height (in adults)

3. Some people are suggesting the moments be normalized to another
variable (for example - mass times length to the 3/2 power 14.9 (0.6))

Joint Moments (not as much commentary as the normalization question)
1. Depends on the situation

2. One person wrote that the vector sum of the moments mapped into the
JCS do not vectorily sum. However, this is not necessarily the case.
Moments that sum appropriately can be calculated around the axis of the
JCS for example(non-orthogonal), however, since the axes themselves do
not intersect at a common point the calculated moments do not represent
a balance of the joint moments (See Andrews, JG, J Biomech,
17(2):155-158, 1984 he does a nice job explaining this issue).

I appreciate all the time people spent in answering the questions and
hope this posting is helpful to others.

Jeff Houck, PhD, PT

ORIGINAL POSTING
************************************************** *************
To All,

First Question - Recent papers reporting the net joint moments have
taken two approaches to decreasing variability across subjects. Some
studies (Eng and Winter, J
Biomech, 1995) divide the net joint moment by body mass. Other papers
(Berchuck, JBJS 1990, Holden and Stanhope, Gait & Posture, 7:1-6, 1998)
divide the net joint moment by % body weight * height. The reasoning
behind
the second approach is that both the ground reaction force (which is
correlated with body weight)and segment length (which is correlated with
height) are used to
estimate net joint moments.

However, a recent abstract by Sum et al(Sum et al, Gait & Posture, 7,
1998) suggests that using % body weight * height generally doesn't
decrease variability, except for the ankle dorsiflexion peak during
walking. In
addition, height explained little of the variability in the frontal
plane moments
(< 11%) and explained no additional variability once the moments had
been normalized
to body mass. This appears to suggest that normalizing to % body weight
* height
does not significantly reduce variability, and therefore, dividing net
joint
moments by body mass such as in the Eng and Winter(Eng and Winter, J
Biomech, 1995)
paper is adequate. Yet current studies appear to be dividing the net
joint
moments by % Body weight * height (Holden and Stanhope, Gait & Posture,
7:1-6, 1998). Are there other compelling arguments to make % body weight
* height the
standard over body mass?

Second question -- When moving to reporting three dimensional joint
moments there are three options when mapping the moments into the local
coordinate system. The moments can be reported in the proximal segments
coordinate system, distal segments coordinate system or mapped into the
non -
orthogonal axes of the joint coordinates used to estimate kinematics
(JCS).

Siegler and Liu (In Allard et al, Three Dimensional Analysis of Human
Locomotion, Wiley and Sons, Ltd, 1997 page 203) suggest that the moments
be mapped into the JCS. However, Andrews (Andrews, JG, J Biomech,
17(2):155-158, 1984) raised the issue that the joint center is not
common to all 3 axes when using the JCS. And therefore, "...the vector
sum [of the three joint torques] does not represent the combined turning
effect of all joint structures about a single point because the the
three axes do intersect at a common point."

Comparisons of mapping the net moments into the femoral coordinate
system and tibial coordinate system during walking suggest very close
approximations in the sagittal and frontal planes, however, the
differences are > 100 % in
the transverse plane(Pilot data). In terms of the transverse plane it
appears to make sense for interpreting muscle function to map the
moments into the local coordinate system of the distal segment. For
example the hamstrings are considered internal/external rotators because
of their relationship to the tibial long axis not the femoral long
axis.

What should the standard be for reporting local joint moments?

I will post all replies.


Thanks!

Jeff Houck, PhD, PT
Ithaca College - Rochester Campus
300 East River Road Suite 1-102
Rochester, NY 14623

jhouck@ithaca.edu



RESPONSES
************************************************** ***************
Hello Jeff,

I have a few comments and opinions about the joint moment issues you
raised. First of all, there is no RIGHT answer to any of your questions.
This is an important point that I believe is often lost. The important
thing to consider is what is most practical and logical for a given
application.

Regarding normalization, I believe that the "best" reason to use a
[bodyweight * height] scheme is to render the resulting variable
dimensionless. In many other fields, this is the common interpretation
of
"normalized". Other than that, I agree that the data suggests little
improvement in terms of reducing variability. The "best" reason to use a
[bodyweight only] scheme seems to be it's existing wide-spread use. Both
seem to work reasonably well.

Regarding joint moment reference coordinate systems: proximal, distal or
global all have certain minor advantages and disadvantages over one
another.

I would note that their is a significant problem/difficulty/source of
confusion encountered when using a JCS description of the moments.
Namely,
due to the non-orthogonal nature of the JCS, the components of the
moment
are non-unique, and the magnitude of the moment is no longer the
Euclidean
norm (sum of the squares of the components). These disadvantages
outweigh,
in my opinion, any seeming advantage of having moments expressed in a
joint
coordinate system.

One additional comment: I believe that the "moment arms" reported by
some
graphics-based software systems used to develop and analyze models of
musculoskeletal structures, are consistent with the JCS moment
description.
Thus care must be taken in using/interpreting these values. I should
note
that I am not certain of this last statement, and would greatly
appreciate
clarification from anyone who knows better than I do.

And again, there is nothing "wrong" with this description, as long as
it's
implications and assumptions are understood by the end user of the data.

Well, those are my opinions for what they're worth (and we all know what
they say about opinions). Thanks for the interesting question.

-Mike-

--
Michael Schwartz, Ph.D.

Director of Bioengineering Research
Gillette Children's Specialty Healthcare

Assistant Professor
Orthopaedic Surgery, Biomedical Engineering
University of Minnesota

Phone:(651)229-3929 Fax:(651)229-3867




Jeff,

You asked very good questions.

To your first question, mechanically it makes sense to normalize joint
moments
to weight and height. Based on my observation, normalize joint moments
to
weight and height did reduce the inter-subject variations. However, the
purpose to normalize joint moments to anthropometry measures is not only
to
reduce the inter-subject variation, but also to eliminate the effect of
anthropometry measures on joint mements to fully reveal the difference
in
movements between subjects. From this point of view, it is not a bad
thing if
normalizing joint moments weight and height does not reduce
inter-subject
variation as much as normalizing them to weight only. It certainly
should not
be a reason to say it is not a good way of normalization. Recently, we
evaluated a patient's gait in stair climbing. His problem became clear
only
after we normalized his joint moments.

To your second question, I don't think there is or should be a stardard.
In
which coordinate system the joint moment should be expressed largely
depends
on research questions.

Hope this will help.

Bing

Bing Yu, Ph.D.
Assistant Professor
Division of Physical Therapy
The University of North Carolina at Chapel Hill


Dear Jeff,
I used the data we had collected in 847 children aged 6-18 years to show
you
the results of different types of normalization applied to maximum
isometric
knee extension torque data.( I attach a histograms from Statistica as a
knee_ext_torques.doc). The variability of body mass*body height
normalization is equel to the normalization by 4 power of body height
(30
%). The variability of body mass normalization is 35 %. The
distributions
of data obtained with all types of normalization data are normal (K-S
data).
So both Steve Stanhope and David Winter are right, however Steve's
normalization is slightly better. I prefer the body height normalization
in
children [2] when the body stature is the major growth factor. In adults
the
body mass*body height normalization may work better, because the growth
is
already completed and other factors may be more important.
You can also check the following papers:
[1] Lebiedowska M, Syczewska M, Graff K, Kalinowska M. (1996)
Application
of Biomechanical Growth Models in the Quantitative Evaluation of The
Child Motor System. Disability and Rehabilitation. Vol.18, No.3 137-142.
[2] Lebiedowska M. and Polisiakiewicz A. (1997) Changes in the lower leg
moment of inertia due to child's growth J. Biomechanics. Vol .30, No.7,
723:728.
Sincerely
Maria Lebiedowska Ph.D.
Director Motion Analysis Laboratory
Southern Illinois University, School of Medicine
751 North Rutledge LL 0300
P.O. Box 19652
Springfield, Il 62794-9652
Ph. (217) 782-6556
e-mail: mlebiedowska@siumed.edu



We systematically looked at various methods to normalize/scale gait data
using
data from 10 subjects who spanned a wide range of heights and weights.
With
regards to normalizing joint moments we found the following 3 factors
statistically equivalent
mass 15.0 (0.5)
mass times length 14.5 (0.6)
mass times length to the 3/2 power 14.9 (0.6)

compared to

no scaling 29.7 (1.2)

[Each value represents the corrected pooled inter-subject variation, for
the
hip, knee and ankle moments, 3 axes, at each 2% of the gait cycle, in N
m, and
its 95% confidence value]

As you can see each of these three methods reduced the inter-subject
variation
to about 50% of its not normalized values.

Personally I prefer the third approach since it is based on some nice
physical
and mechanical assumptions. These are contained in a paper we have
written
which is currently under review.

I hope these data help.

Cheers ...


Michael Raymond Pierrynowski, Ph.D. 1 905 525-9140 x22910 (phone)
Human Movement Laboratory 1 905 522-6095 (fax)
School of Rehabilitation Science McMaster University, HSC 1J11
Hamilton, Ontario L8N 3Z5
CANADA



Jeff,

I've been looking at the development of walking patterns in children
between
the ages of 5 and 12. The height of these children varied from 100 to
160cm. It was necessary to ensure that variation in this group of
children
due to height (and weight) differences was eliminated from the analysis.
At
the ESMAC 1999 conference I was very politely but firmly informed that
analysis of gait data should be made using dimensionless quantities (Hof
AL.
Scaling gait data to body size. Gait and Posture. 1996;6:265.). Using
dimensionless quantities is the only mathematically correct way of doing
it.
Scaling moments by body weight may remove a great deal of the
variability
and the additional use of height may not reduce the variablitily
further,
but at least you then know that your variability is due to other sources
and
not height differences.
Body weight scaling of moments is 'arbitrary' scaling by body weight and
height at least has a mathematical foundation in that it leads to
dimensionless quantities.

Why are you trying to use normalisation to reduce the variability of
your
results? Differences in weight and height of subjects should be taken
into
account by using dimensionless quantities. The variability is then the
variability due to other factors such as marker placement differences,
different walking styles and so on. If you want to examine the reasons
for
differences between subjects data try examining the effects of
differences
in speed of walking. You would of course have to use a dimensionless
form
of speed.


Jeff,

I've been looking at the development of walking patterns in children
between
the ages of 5 and 12. The height of these children varied from 100 to
160cm. It was necessary to ensure that variation in this group of
children
due to height (and weight) differences was eliminated from the analysis.
At
the ESMAC 1999 conference I was very politely but firmly informed that
analysis of gait data should be made using dimensionless quantities (Hof
AL.
Scaling gait data to body size. Gait and Posture. 1996;6:265.). Using
dimensionless quantities is the only mathematically correct way of doing
it.
Scaling moments by body weight may remove a great deal of the
variability
and the additional use of height may not reduce the variablitily
further,
but at least you then know that your variability is due to other sources
and
not height differences.
Body weight scaling of moments is 'arbitrary' scaling by body weight and
height at least has a mathematical foundation in that it leads to
dimensionless quantities.

Why are you trying to use normalisation to reduce the variability of
your
results? Differences in weight and height of subjects should be taken
into
account by using dimensionless quantities. The variability is then the
variability due to other factors such as marker placement differences,
different walking styles and so on. If you want to examine the reasons
for
differences between subjects data try examining the effects of
differences
in speed of walking. You would of course have to use a dimensionless
form
of speed.



Jeff

Peak muscular force is known to be proportional to body mass (BM) raised
to
the 2/3 power. Moment arm lengths should be proportional to stature, or,
using
geometric scaling, proportional to BM raised to the 1/3 power. Moments
are
forces * Length, so the next step is to combine these (BM^2/3 * BM^1/3)
to
find BM^1. One would therefore predict then that moments resulting from
muscular force should be directly proportional to BM. At the least, this
should apply to peak moments.

Watch the units you end up with. Seems to me your resulting units, after
normalization would be something like m*m /s/s. Forgive the poor
notation
necessitated by the email medium.

Final Comment: I think we should avoid allowing statistics to overrule
physics, at least in the absence of a good physical rationale. If one
doesn't
get a significant reduction in variability using a particular
normalization
technique, I think we simply need to look deeper at the causes of
variability.

__________________________________________________

E C "Ned" Frederick, PhD Phone:+1 (603)772.4689
Exeter Research, Inc. Fax:+1 (603)658.0210
80 Haigh Road nederick@exeter-research.com
Brentwood, NH 03833, USA http://www.exeter-research.com

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