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  • ISB Standards for the Reporting of Kinematic Data

    __________________________________________________ __

    ISB Standardization and Terminology Committee

    RECOMMENDATIONS FOR STANDARDIZATION IN THE
    REPORTING OF KINEMATIC DATA

    DRAFT Version 4.1
    April 3, 1992

    __________________________________________________ __

    The Standardization and Terminology Committee of the
    International Society of Biomechanics has been charged
    by the Society with the development of standards for use
    in the field of kinematic and kinetic analyses of human
    and animal movement.

    Many other efforts of this nature are in progress and
    the committee has received input in its deliberations
    from a number of groups and individuals. At the First
    International Symposium on Three Dimensional Motion
    Analysis in Montreal Canada in July 1991, a round table
    was held to discuss the topic of standardization. An
    apparent consensus of panel members and meeting
    participants was that each investigator should be free
    to collect and process their data according to the
    conventions and methods of their choice, but that a
    standard set of conventions for the presentation of data
    in the refereed literature would be welcomed by most
    workers. A major effort towards standardization of
    protocols for gait analysis is also underway by a
    European Community group (CAMARC). Clearly
    standardization is a topic for the 1990's and the ISB
    intends to take a leadership position in this area.

    The committee has decided to make its first task the
    definition of a series of reference frames and
    conventions for the description of the absolute and
    relative orientations of body segments. In the future,
    we intend to address the issue of terminology extending
    the work of Winter (1987) and Vaughan, Davis and
    O'Connor (1992).

    This first step, described below, leans heavily on the
    work of biomechanists such as Chao, Grood, Suntay,
    Sommer and Buczek and employs the 4 x 4 matrix notation
    for the description of segment position and orientation.
    An ad hoc committee of ISB members has already provided
    input on early drafts of this document and suggestions
    have been incorporated from a number of other
    individuals. We would stress that this is still a
    consultative document and represents a first foundation
    on which an eventual standard can be built.

    Each section is organized in the form of the need for
    the standard, a recommendation, a suggested notation,
    and notes concerning implementation.

    __________________________________________________ __

    PART 1. DEFINITION OF A GLOBAL REFERENCE FRAME

    Need: A global inertial reference frame with the
    direction of the global axes being consistent, no matter
    which activities or subjects are being studied, or which
    investigator is conducting the experiment.

    Notation: Xg, Yg, Zg

    Recommendation: A right handed orthogonal triad
    fixed in the ground (assuming performer is on level
    ground) with the +Xg axis forward and horizontal, +Yg
    axis upward, the +Zg axis to the right and horizontal
    (see figure 1). All directions are given for the
    subject facing in the direction of work or travel
    that is of most interest to the particular activity. If
    forces are being measured, it is recommended that the
    origin of the XgYgZg reference frame be located at the
    center of the top surface of one of the force platforms
    being used. A ground reaction force convention (i.e. forces
    applied to the body not forces applied to the platform)
    should be used such that ground reaction force components
    acting along the respective axes should be designated with
    the same conventions i.e. positive Fx is acting in the
    forward horizontal direction, positive Fy in the upward
    vertical, and positive Fz in the right lateral
    direction.

    Notes: a. The directions have been chosen so that
    for those conducting two dimensional studies, Xg,Yg will
    lie in a sagittal plane. This will be consistent with the
    three dimensional convention.

    b. In tasks such as exercise in zero gravity, the
    Xg axis should be defined according to some arbitrary
    but visible surface in the environment and in a
    direction that is meaningful to the task.

    c. Where there is no clear direction of travel or
    work for the definition of positive Xg (as is the
    case for insect flight) one should be defined by the
    investigator.

    In cases of locomotion on inclined planes, the Yg
    axis will remain vertical and the Xg and Zg axes will be
    in the same horizontal plane.


    d. We acknowledge that there may be situations
    where non-Cartesian axes are more appropriate to the
    task being studied (for example cylindrical coordinates
    are useful for the study of asymmetric manual exertion).
    Since the majority of studies use a Cartesian approach,
    it will be left to individual investigators to devise
    systems for the reporting of more unique situations.

    __________________________________________________ __

    PART 2: DEFINITION OF SEGMENTAL LOCAL CENTER OF MASS
    REFERENCE FRAMES

    Need: A coherent system to describe segment pose
    (position and attitude) with respect to global.

    Recommendation: A series of right handed orthogonal
    triads fixed at the segmental centers of mass with two of the
    axes defined relative to anatomically identifiable reference
    points. The third is automatically defined as being mutually
    perpendicular to the other two (as defined by a right hand
    rule.) The positive Yi should be in a proximal direction, and
    the positive Zi should be to the right of the subject (see figure 1).

    Notation: Xi, Yi, Zi

    Notes: Sub groups of specialists in each region of
    the body will be recruited by the ISB Standardization
    Committee to formulate the appropriate anatomical
    landmarks to be used in the orientation of the axes for
    each segment of the body.

    The convention that the positive Zi direction is to
    the right implies that positive movements and moments
    about the Xi and Yi axes of a segment on the left side
    of the body will have the opposite effects of movements
    and moments of similar sign on the right side of the
    body (figure 2). This difference will be accounted for
    by describing the movements and moments in their
    anatomical terms in any presentation of the data (see
    below). This convention has been chosen to avoid the
    use of both left and right handed coordinate systems.

    __________________________________________________ __

    Part 3: Global displacements

    Need: Specification of displacements relative to the
    Global Reference Frame

    Recommendation: Report the coordinates of local
    center of mass reference frame origins with respect to
    the global origin in meters. The position of the local
    origin will represent the first column of the 4 x 4
    matrix in the local to global transformation matrix
    (see below).

    Notation: xi,yi,zi

    __________________________________________________ __

    Part 4: Global Attitudes.

    Need: To express the orientation of a segment with
    respect to the global reference frame.

    Recommendation: A standard ZYX decomposition of the
    lower right 3x3 rotation submatrix of the 4 x 4 matrix
    defining the local to global transformation.

    {X}g = [Tlg] {x}l

    where {X}g = [1 Xi Yi Zi] T

    {x}l = [1 xl yl zl] T

    where [Tlg] is the local to global coordinate
    transformation describing the pose of the local
    coordinate frame with respect to the global frame.

    and [Tlg] = 1 0 0 0
    Xi c11i c12i c13i
    Yi c21i c22i c23i
    Zi c31i c32i c33i

    Xi,Yi,Zi is the location of the origin of the ith
    local center of mass reference frame with respect to the
    global frame, xl,yl,zl are the coordinates of a point
    with respect to the local origin and cij are the
    direction cosines expressing the orientation of the
    local axes with respect to global. c11i, c21i, c31i are
    the direction cosines of the local xi axes with respect
    to Xg,Yg, and Zg respectively.

    Notation: If A, B, G are ordered series of rotations
    about z, y and x axes respectively then:


    1 0 0 0
    X cAcB cAsBsG-sAcG cAsBcG+sAsG
    Y sAcB sAsBsG+cAcG sAsBcG-cAsG
    Z -sB cBsG cBcG


    Where sA = sine A and cA = cosine A etc.
    The individual Euler angles can be found as follows:

    Bi = arcsin (-c31i)

    Ai = arcsin(c21i/cosBi)
    Ai = arccos(c11i/cosBi)

    Gi = arcsin(c32i/cosBi)
    Gi = arccos(c33i/cosBi)

    __________________________________________________ __

    Part 5: Relative attitudes.

    Need: A system to express the relative orientation
    of the body segments with respect to each other.

    Recommendation: Joint coordinate systems (which
    might better be called Joint Rotation Conventions)
    defined for each joint individually. This system allows
    sequence independent rotations about axes which can be
    anatomically meaningful at the sacrifice of establishing
    a reference frame with non-orthogonal axes. As long as
    force and moments are not resolved along these non-
    orthogonal axes, this does not present a problem. This
    approach allows the preservation of an important linkage
    with clinical medicine where the use of independent
    paired rotations (ad/ab, internal/external etc.) is
    common usage.

    We further propose that no particular system of
    symbolic nomenclature be adopted for the description of
    joint motion but that accepted anatomical nomenclature
    be used in presentations.

    The most well known example of such systems are
    those developed for the knee by Grood and Suntay (1983)
    and Chao (1986) (figure 3). Two body fixed axes are
    established relative to anatomical landmarks, one in
    each body on opposing sides of the joint. The third
    axes, called the floating axis, is defined as being
    perpendicular to each of the two body fixed axes.

    Notation:
    A=rotation about the proximal body fixed axis
    G=rotation about the distal body fixed axis
    B=rotation about floating axis

    Notes:

    We propose that sub-groups of specialists in each
    region of the body will be recruited by the ISB
    Standardization Committee to formulate the appropriate
    joint rotation conventions for each joint of the body.
    These groups might also address the issue of accuracy
    (which no doubt varies between joints) and the question
    of the relationship between the (usually) surface
    markers and the actual anatomical arrangement.

    In order to determine these angles from
    conventional segment pose data, the following points
    are important:

    a. The orientation of the proximal and distal axes
    must be carefully specified.

    b. The choice of the location of the origins
    drastically affects the distraction displacement terms.

    c. The Euler angle set in part 4 (Global attitudes)
    should match the angle decomposition for joints as
    closely as possible.

    Woltring (1990, 1991) and others have supported the use
    of helical axes for the description of joint motion since it
    avoids some problems - such as gimbal lock - inherent in Euler
    angle representations. More recently, Woltring suggests the
    use of :"an attitude vector standard". At present, we are not
    proposing a standard for this approach as debate continues on
    its clinical application. Should there be widespread support
    for such a representation we would certainly consider a recom-
    mendation for standardization of helical axis representation.

    __________________________________________________ __

    Part 6 Joint Moments

    Need: A system to report net joint moments that will
    avoid confusion concerning the anatomical actions being
    represented. Such a system needs to be consistent
    across joints and across sides of the body.

    Recommendation: Net joint moments should be reported
    according to the conventions described by Winter (1987)
    such that net moments tending to cause extension,
    internal rotation, and abduction are positive.

    Notation: Mfe, Mie, Mbd for moments tending to cause
    flexion/extension, internal/external rotation, and
    abduction/adduction respectively.

    Notes: Any definition of joint moments assumes a
    definition of joint axis system. See Part 5 relative
    Attitudes above for the recommended approach.

    __________________________________________________ __


    Part 7 Minority report

    Professor John Paul, a member of the ISB Standardization
    and Terminology Committee made two recommendations that
    have not been incorporated into the present version due
    to divided opinion from those who have reviewed these
    initial standards. They are reproduced here so that
    members will have a chance to comment on these views.

    With reference to Part 1:

    "Many equipment manufacturers already format data
    according to their own XYZ system. I feel that we
    should avoid the awkward transposition exemplified by
    Yisb = Z kister etc. I suggest that ISB could avoid
    these problems by using hitherto not generally used
    symbols which do not suggest an anatomical part (e.g.
    avoid A H K). What about RST?"

    With reference to Part 2:

    "All humans and animals have left and right sides. Why
    standardize on a right handed system of axes? The only
    difference between the two is a minor matter of signs
    before some terms in mathematics which can easily be
    incorporated into the software! International Standards
    Organization Technical Committee 168 Working Group 3 -
    Prosthetics and Orthotics Testing specifies the
    "Forward, Outward, Upwards" system which is right handed
    or left handed as appropriate. It has the advantage
    exemplified by having the same sign for the moment
    produced at the left hip by the left gluteus medius as
    the moment produced by the right hip by right gluteus
    medius."
    __________________________________________________ __

    REFERENCES

    Beggs, J. S. (1966) Advanced Mechanism, New York,
    Macmillan

    Buczek, F. L. (1990) Three-Dimensional Kinematics and
    Kinetics of the Ankle and Knee Joints During Uphill,
    Level, and Downhill Walking, Ph.D.. thesis, The
    Pennsylvania State University.

    Chao E.Y.S. Biomechanics of Human Gait. In Frontiers in
    Biomechanics, Schmid-Schonbein G.W., Woo S.L-Y., and
    Zweifach, B.W. (Eds). New York, Springer Verlag.

    Grood, E. S. and W. J. Suntay (1983) A Joint Co-ordinate
    System for the Clinical Description of Three-Dimensional
    Motions: Application to the Knee, J. Biomechanical
    Engr. 105:136-144

    Kinzel, G. L., A. S. Hall, and B. M. Hillberry (1972)
    Measurement of the Total Motion between Two Body
    Segments-1.Analytical Development, J. Biomechanics,
    5:93-105.

    Sommer, H. J., and F. L. Buczek (1990) Least Squares
    Estimation of the Instant Screw Axis and Angular
    Acceleration Axis 1990 Advances in Bioengineering, ASME.

    Vaughan C. L., Davis, B.L. and O'Connor J. (1992) The
    Gait Lab. Champaign, IL Human Kinetics Publishers

    Winter D.A. (1987) The Biomechanics and Motor Control of
    Gait. Waterloo, ONT. University of Waterloo Press.

    Woltring, H.J. (1990) 3-D attitude representation: a new
    standardization proposal. In Hogfors, C. (Ed).
    Proceedings of the Fourth Biomechanics Seminar. Centre
    for Biomechanics, Chalmers University of Technology and
    Gothenburg University, Sweden. Biomechanics Seminar 4. p
    58-61. (ISBN 1100-2247).

    Woltring, H.J. (1991) Representation and calculation of
    3D joint movement. Human Movement Science, 10: 603-616.

    __________________________________________________ __

    Figure 1. Conventions for global reference frame
    Figure 2. The same rotations about segmental local center of mass
    reference frames produce anatomically different motions on the left and
    right sides of the body.
    Figure 3. A joint coordinate system for the knee joint.

    __________________________________________________ __

    A Project of the ISB Standardization and Terminology
    Committee


    Prof D.W. Grieve
    Prof J.P. Paul
    Prof D.A.Winter
    Prof P.R. Cavanagh, Chair

    Input on these draft recommendations should to sent to:


    Peter.R. Cavanagh,
    The Center for Locomotion Studies
    Penn State University
    University Park
    PA 16802
    USA

    Tel: +814-865-1972
    FAX: +814-863-4755
    EMail PRC@ECL.PSU.EDU (Internet)

    Note: Formatted copies of this document with embedded figures
    are available on the BIOMCH-L list on the listserver @ HEARN.

    Microsoft WORD 4.0/5.0 files for the Macintosh
    and WordPerfect 5.1 for MS-DOS compatible platforms are
    available. The BIOMCH-L moderators will post details of
    the relevant file names in the near future.

    PRC
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