No announcement yet.

Re: Kinematic Fitting vs. Functional Method

This topic is closed.
  • Filter
  • Time
  • Show
Clear All
new posts

  • Re: Kinematic Fitting vs. Functional Method

    Mike Schwartz wrote:

    > Kinematic fitting modifies some/all joint parameters and
    > joint angles, often in a nested manner, to minimize a cost
    > function (e.g. cost = sum of squared distances between
    > measured and predicted marker trajectories). Further
    > explanation can be found in Lu T-W and O'Connor JJ, J
    > Biomech, 32:129-134, Charleton et al, Gait Posture,
    > 20:213-221, or Rienbolt et al, J Biomech, 38:621-626.
    > As a personal note -- I have had **no end of grief** trying
    > to use optimization approaches. I believe that this is due to

    This is my personal experience also. It is easy to get carried away
    with this concept because mathematically it is perfectly valid, but in
    my experience you need to be very careful not have too many unknown
    model parameters.

    Let's say you have N unknown joint parameters p1...pN. And you have a
    model with M degrees of freedom q1...qM, and you capture Nf frames of
    motion data. Then the number of unknowns is N + M*Nf, since the model
    parameters do not change during movement. The number of forward
    kinematic equations is Nf times the number of markers times 3 (for 3D).
    For large enough number of frames, and when using more than M/3 markers,
    this will always exceed the number of unknowns. Then we can solve this
    with a least squares method and a cost function which is the sum of
    squared residuals as defined by Mike above.

    The nested optimization (guess p1...pN in the outer loop, and guess
    q1...qM in each frame in an inner loop) is just a way to partition the
    problem but it still should find the same solution.

    If you test this with simulated motion data, it always works. But in
    the real world there are errors in model and data which can easily
    produce false minima in the cost function. We got this optimization to
    work in our two-axis ankle model (Smith et al, J Biomech 1994) but
    discovered the following limitations:

    (1) Motion data must span sufficient range of motion in all joints.
    (2) Optimization must start from many initial guesses to ensure finding
    the global optimum.
    (3) Orientation of the subtalar joint in the horizontal plane was
    sensitive to measuring error.
    (4) With data collected during weightbearing, the method failed,
    probably because there was too much foot deformation which violated the
    ideal two-axis model.

    I expect that these problems get worse when trying to do this for
    multiple joints simultaneously. It may be possible if you carefully
    select a low number of joint parameters to estimate, leaving others
    fixed. For instance, the axial rotation axis of the knee would not be
    estimated from kinematics, but be anatomically defined along the line
    from knee center to ankle center. I would be interested in hearing
    Richard Baker's observations and opinions on this.

    Some other related comments.

    The kinematic fitting method is a "global optimization" approach (using
    the term coined by Lu & O'Connor), which assumes certain kinematic
    connections between body segments (hinge, ball, or even coupled
    rotation/translation as in the SIMM knee model). This contrasts with
    the 6-DOF method mentioned by Frank Buczek, which makes no such
    assumptions. The 6-DOF method does not suffer from potential modeling
    errors (since there are no joint models) but the global optimization
    approach has some nice advantages:

    (1) Fewer than 3 markers per segment are needed, so you can sometimes
    avoid using markers on "wobbly" sites.
    (2) Less sensitive to skin motion artifacts.
    (3) Degrees of freedom can be made compatible with whole body dynamics
    (4) Degrees of freedom can be made compatible with graphics (animation)

    Depending on the scientific question, subject population, and the
    movement being studied, we must carefully balance the effects of model
    error (in global optimization methods) against the effects of data error
    (greater in 6-DOF methods). In our lab we use global optimization
    methods, but in one of our projects we model each joint as three slider
    joints and three hinge joints, i.e. six degrees of freedom. This made
    the results compatible with historical data which used 6-DOF analysis.
    It also allowed the joints to "absorb" marker wobble at impact which
    would otherwise lead to (brief) overestimation of knee valgus and
    flexion. This was a problem because the movement was jump landing, and
    the subject population included some with the potential for substantial
    marker wobble.

    Incidentically, this example shows that the software tools for global
    optimization can be used for 6-DOF analysis. You can even model some
    joints with 6 DOF and other joints with 1 DOF in the same model. The
    6-DOF software tools probably do not have this versatility.

    The philosophical problem with 6-DOF analysis is that we have large skin
    marker errors, causing errors in translational motion in the joints
    which are usually larger than the translational motion itself.
    Therefore assuming zero translation is a logical approach, leading to
    global optimization with many practical advantages. But as the above
    example illustrates, modeling the translational motion can sometimes
    make the rotational motions more accurate. Even if the translational
    motion itself is poorly measured and of no interest.

    I agree with Dan Benoit that we must be very careful when presenting
    data on non-sagittal knee rotations. Apart from the skin movement
    problem, it is well known that these results are sensitive to the
    orientation of the joint coordinate system (Ramakrishnan & Kadaba,
    1991). This is the main motivation for using coordinate systems with
    functional axes, which are hopefully more reproducible than axes based
    on anatomy.

    I would like to propose that for joints or degrees of freedom that are
    very "stiff" with limited range of motion, the joint moment is
    potentially much more reliable than the joint motion. The joint moment
    can be quite large even when there is almost zero motion in the joint.
    Obviously the joint angle results would be totally overwhelmed by errors
    in that case.

    Generally I think there is no single correct model or marker set. It
    always depends on purpose of the study, movements, subjects, etc. It's
    best not to be dogmatic about these things. That is easy enough to say
    in basic research, but the clinical labs need standardized methods. I
    think it was Mike Schwarts who mentioned that he routinely uses standard
    and non-standard models and markersets simultaneously. To me this to be
    a very sensible way to gain insight into how much the results are
    affected by these choices. If not much, we gain some confidence in the
    results of our analysis.

    This was much more than I intended to write. This is a useful
    discussion and it is great to have these contributions in the Biomch-L


    Ton van den Bogert
    Biomch-L co-moderator


    Cleveland Clinic is ranked one of the top 3 hospitals in
    America by U.S.News & World Report. Visit us online at for a complete listing of
    our services, staff and locations.

    Confidentiality Note: This message is intended for use
    only by the individual or entity to which it is addressed
    and may contain information that is privileged,
    confidential, and exempt from disclosure under applicable
    law. If the reader of this message is not the intended
    recipient or the employee or agent responsible for
    delivering the message to the intended recipient, you are
    hereby notified that any dissemination, distribution or
    copying of this communication is strictly prohibited. If
    you have received this communication in error, please
    contact the sender immediately and destroy the material in
    its entirety, whether electronic or hard copy. Thank you.