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  • Summary of Responses

    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

    Phone651)229-3929 Fax651)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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