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Summary of Curve Analysis Methods

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  • Summary of Curve Analysis Methods

    I appologize for the delay in getting this summary back to the list. The
    Holliday festivities took their toll on many of my best laid plans. Below
    is my original inquiry followed by the many responses. I would like to
    thank everyone who took the time to send me a reply. I appreciate your
    effort to educate me. Thanks!
    Mark W. Cornwall, PhD, PT, CPed
    Northern Arizona University

    Original message:

    I have need of some way to compare and assess the relationship between two
    or more motion vs time curves during walking. I am working in the foot and
    have 3D data on the tibia, hindfoot, midfoot and first ray during walking.
    I would like to know how much, if any motion at one segment contributes to
    another. I have used pearson correlation coefficients, but it seems to be
    fairly non-specific. Correlation of specific points on the curve also has
    proven disappointing. Does anyone out there have any suggestions? I would
    appreciate any help you could give me. Thanks in advance.



    Have you considered using a pattern recognition technique similar to that
    originally proposed by Freeman (1961) and expanded upon by Whiting, &
    Zernicke (1982). It is basically a chain- encoding technique to quantify
    the similarity between angle-angle plots. Don't see why it can't be
    adapted for open ended curves though. It involves overlaying a grid on the
    plot and transforming the curve into digital elements that follow changes
    in direction of the plot. Cross-correlation of pairs of integer chains
    results in a recognition coefficient.

    I'd be interested in what other people suggest.

    Ben Sidaway, Ph.D.
    Dept. of Physical Therapy
    Husson College, Bangor, ME


    Freeman, H. (1961). A technique for the classification and recognition of
    geometric patterns. Proceedings of the 3rd International Congress on
    Cybernetics. Namur, Belgium.

    Whiting, W. C., & Zernicke, R. F. (1982). Correlation of movement patterns
    via pattern recognition. Journal of Motor Behavior, 14, 135-142.

    ************************************************** *****


    Cross correlation? can detect phase lag at which correlation is greatest

    Trish Bate
    School of Physiotherapy
    Faculty of Health Sciences
    Latrobe University
    Phone :61(0)39 2855 2S9 or: 61(0)3 9481 1718
    Fax 61 (0)3 9285 S22S EMAIL

    ************************************************** ****

    Check with following references. If you have difficulty to get them, I can
    sent you the copies.

    Kadaba MP, et al.:Repeatability of kinematic, kinetic, and
    electromyographic data in normal adult gait. Journal of Orthopaedic
    Research, 7:849-860, 1989.
    Liu W, Siegler S, Hillstrom H, Whitney K:Three dimensional,
    six-degree-of-freedom kinematics of the human hindfoot during the stance
    phase of level walking. Human Movement Science (in press), 1996.

    Take care.

    Wen Liu
    Institute of Biomedical Engineering
    Drexel University
    Philadelphia, PA

    ************************************************** *****

    You might try a coherence analysis (using motion of the distal segment as
    input and motion of the proximal segment as output). I've often thought of
    trying this myself for the head and trunk, but have not had the time to
    pursue. Check out Bendat and Peirsol, Pandom Data: Analysis and
    Measurement Procedures. New York, Wiley, 1971. They give some
    illustrative examples which should make implementation a breeze - I'd
    love to know how this turns out! Ronny

    Chris A. McGibbon, PhD (Ronny)
    Technical Director
    MGH Biomotion Lab,
    Boston MA


    Hello Mark,

    If I understood your question well, then you probably you want to look in
    the method of
    across correlation" with or without phase lags. If you are interested only
    in the shape agreement of the curves then anycorrelation coeficient will be
    helpful although some limitations exist for the intraclass and the pearson
    (mainly due to assumptions of the mehods). Furthermore, the method of
    "agreement" presented by Bland and Altman, might help.

    Useful references might be:

    1) Bland and Altman: (1990) Comput. Biolo. Med. (20), pp.337-340
    2) SPSS manual, for cross correlation

    Good Luck!!! Let me know how you are doing at the moment I am also
    working in this.



    Hi Mark--I feel most qualified to discuss the relationship between the
    subtalar joint and the two adjacent joints, the talocrural and the
    transverse tarsal. My research looks at anatomical variation of the
    subtalar joint and its functional sigthat people with rigid subtalar joint
    (STJ) configurations had hypermobility at the transverse tarsal joi. In
    static standing, many of these people had normal ROM at tacrural jt but
    wentl into hyperpronation of the midfoot during gait. Another variation
    was people with rigid STJ configurations and normal transverse tarsal ROM
    went into genu recurvatum on static standing. The problem is complicated
    by age, weight, and activity level.

    If any of this sounds helpful to you, I'll be happy to tell you more!



    Your question suggests you wish to find a causal relationship between the
    motion of different segments. This can be done quantitatively using
    dynamical equations of motion for the multibody system under observation.
    For example, in recent years Felix Zajac and his students have published a
    number of papers showing how movement of one segment influences that of
    another. To do this for a particular patient or data set would require
    full anthropometrics as well as kinematics and kinetics.

    I suspect, however, that you might be just as interested in how kinematic
    aspects of segment motions co-vary. This would be addressed somewhat by
    the correlations you describe. Cross correlation and least-squares methods
    of comparing curves have been used for this purpose in the past. I believe
    all of this is very difficult and requires a keen insight as well as good
    quantitative skills.

    Good luck!

    Larry Abraham, EdD
    Kinesiology & Health Education
    The University of Texas at Austin Austin,
    TX 78712 USA
    (512)471-1273 FAX (512)471-8914


    Hi Mark

    The situation is extremely complex. So lets stick to the facts. There is
    a definite relation between tibia rotation and foot dorsiflexion. See:
    Olerud C, Rosendahl Y. Torsion transmitting properties of the hind foot.
    Clinical orthopeadics and related research, 214:285- 294, 1987

    This motion extends to supination of the first ray. See: Hicks JH. The
    mechanics of the foot. Part 2: The planter aponeurosis and the arch.
    Journal of anatomy, 88:25-30, 1954.

    Also see Morris 1977 (Journal title not in front of me - but it provides an
    excellent account of movements you may wish to study).

    As for inter-individual comparisons, these are counfounded by differences
    in ankle kinematics. See: Lundberg A, Sveensson ok, Nemeth G, Selvik G.
    The axis of rotation of the ankle joint. Journal of bone and joint
    surgery, 71B:94-99, 1989.

    This explains why Correlation of specific points on the curve are

    There are no simple anatomical correlations and it is NOT the mathematics
    that is at fault.

    Craig Nevin



    Hello Mark,

    Two thoughts. You might want to plot angle-angle diagrams to get a
    qualitative feel for the relationship between the motion of two segments
    (e.g., if you're interested in coordination issues or movement
    "strategies"). However, if you are really interested in the contribution
    of the motion of one segment to another, it seems to me that you would need
    to do an inverse dynamics analysis.

    I hope you will post a summary of responses; I'd be interested in ideas for
    other approaches.

    Amy E. Tyler, Ph.D.
    Assistant Professor
    Physical Therapy Department
    St. Ambrose University
    518 W. Locust St.
    Davenport, IA 52803
    (3 1 9) 3 3 3- 64 12


    Dear Mark:
    We developed a method of comparing time series curves, the LOCAL
    PROPORTIONAL SCALING (LPS). A detailed description of the method will
    appear in MOTOR CONTROL journal (1997, vol. 1, *1).

    Vladimir Zatsiorsky


    Why not use cross-correlation? As long the phase relationship is the same,
    time domain techniques like x-corr work well. If not, then frequency
    domain compar-isons are needed.
    Dave Krebs



    You may try Coefficient of Multiple Correlation (CMC) advocated by Kadaba
    et al. (1989). This CMC can be used as a measure for the similarity of the
    waveforms of a group of curves. Kadaba, M.P., Ramakrishnan, M.E., Gainey,
    W.J., Gorton, G., Cochran, G.V.B., Reproducibility of kinematic, kinetic,
    and electromyogradhic data in normal adult gait. Journal of Orthopedic
    Research, 1989, 7: 849-860.

    I used this CMC to evaluate intra-subject reproducibility of the kinematics
    and kinetics of the lower extremity in stair climbing. Let me know if you
    need more information about this parameter.

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



    I think I misunderstood what you really need in my last reply. I thought
    that you wanted to evaluate similarity of different curves. After reading
    your original message one more time, I realized that what you really need
    is a model for calculating segment contributions to a given segment's
    motion. I used a mathematic model to evaluate the contribution of arm
    motions to the whole body motion in my dissertaion. Pecently, I am
    modifying this model for some research projects in rehabilitation. With
    some modifications, you can use this model and the CMC I mentioned in my
    last reply to analyze segment contributions to a given segment's motion.
    Let me know if you are interested in. I will fax the model to you.

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


    I have used the coefficient of multiple determination numerous times for
    this type of application. The original reference is to: Winer, B.
    Statistical Principles in Experimental Design pp 261-288 McGraw Hill, 1971.
    I am at home now & don't have access to citations in our field. Kadaba
    was the lst to apply it to determining if angle graphs were similar. I lst
    saw it when it was presented at either ASB or the Gait meeting by a Mayo
    Clinic individual (Eric ???), I have presented data at the 1995 & 1996 ASB
    meetings using the CMD & at the 1996 Gait meeting. I would be happy to
    send you the Kadaba reference (J. Biomechanics ...1992? ... 1994?) on
    Monday. Also, I would be
    happy to send you some Quick Basic source code which computes the CMD on
    two wave forms. Good luck & let me know if I can be of any further

    Director, Gait & Biomechanics Lab
    Phone: (502) 582-7657

    ************************************************** **************


    Do you have a decoder for binhex? and Word6.0 for windows? If you do I
    could send you my lecture notes on statistics in biomechanics which include
    some material on this problem. I know Eudora will decode the file I send
    but do you have Eudora?

    Richard Smith e-mail: +
    Head, Biomechanics Division,
    Faculty of Health Sciences,
    The University of Sydney voice: +61 2 9351 9462
    East Street, Lidcombe, NSW 2141 fax: +61 2 9351 9520


    Check at the libarary at:

    Gideon Ariel

    Hi Mark,

    My apologies for the delay in responding to your posting, but I have been
    away partaking in the festive spirit. Ah, the wonders of the overindulgence
    associated with religious occassions!

    Yep, this is a tricky area of statistical analysis. There are a couple of
    avenues which may be of interest.

    David Winter's Co-effecient of Variation may be worth looking at (Winter,
    D.A, 1979 "Biomechanics of human movement", Wiley, New York and Winter,
    D.A., 1984 "Kinematic and kinetic patterns in human gait: variability and
    compensating effects", in Human Movement Sciences, 3, 51-76). Winter
    developed a method of anaylsing the difference in standard deviations of
    averaged curves (such as numerous gait cycles) at each percentile and then
    averaged these differences over the hundred percentiles. It is good in
    establishing variation of the peaks and troughs of curves, but
    unfortunately, it does not reflect "goodness of fit" for the curves. This
    sounds like a variation on the analysis you have already undertaken, but may
    be worth investigating.

    Richard Smith, the Head of the Biomechanics department of the University of
    Sydney has also developed a process of analysising the "fit" of curves onto
    one another, particularly to evaluate relationships between the different
    motions in segmental 3-D analysis of the lower limb. Basically, the premise
    is to establish and evaluate how averaged curves can be manipulated to fit
    on one another. This is undertaken using graphical translation of the
    curves which is then recalculated into statistical information. While
    providing an indication of the difference between curves, it also provides
    an estimation of how the curves are related.

    While this has not yet been published, I am sure he would be more than
    delighted to provide you with further information. He can be contacted at
    his e-mail address:

    I would be very interested to see what other ideas you have Mark, as this
    issue has plagued me for years!

    Every best wish

    Anne-Maree Keenan, B.App.Sc.(Pod), M.App.Sc
    M.A.Pod.A (N.S.W.)

    Senior Lecturer, Division of Podiatry,
    ph: (046) 20.3335
    fax: (046) 25.4252

    P.O. Box 555
    Campbelltown NSW 2560


    Hi Dr. Cornwall,

    I am sorry I can't be of any help to you ! We have tried the pearson
    correlation coefficients as well. I would love to know if you heard of a
    better measure of the similarity between two curves.

    Thanks very much,

    Suzanne Halliday
    Clinical Coordinator
    Texas Scottish Rite Hospital
    Movement Science Laboratory
    ph (214)559-7580


    Thanks again to all those who replied. The information was extremely helpful.

    Mark W. Cornwall, PhD, PT, CPed
    Gait Research Laboratory
    Department of Physical Therapy
    Northern Arizona University
    P.O. Box 15105
    Flagstaff, AZ 86011
    Voice: (520) 523-1606
    FAX: (520) 523-9289