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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.
Replies:
Mark,
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.
Cheers,
Ben Sidaway, Ph.D.
Dept. of Physical Therapy
Husson College, Bangor, ME
bsidaway@husson.husson.edu
References.
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.
************************************************** *****
Mark:
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 P.Bate@Latrobe.edu.au
************************************************** ****
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
sg94k483@dunx1.ocs.drexel.edu
************************************************** *****
Mark,
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
ronny@gait52.mgh.harvard.edu
***********************************************
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.
Dimitrios
D.Tsirakos@mmu.ac.uk
***********************************************
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!
Jan
BRUCKNER@neu.edu
**************************************************
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
l.abraham@mail.utexas.edu
http://www.edb.utexas.edu/coe/depts/kin/
*************************************************
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
disappointing.
There are no simple anatomical correlations and it is NOT the mathematics
that is at fault.
Regards
Craig Nevin
CNEVIN@anat.uct.ac.za
*************************************************
***********************************************
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
atyler@saunix.sau.edu
************************************************
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
VXZ1@PSUVM.PSU.EDU>
*************************************************
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
krebs@gait52.mgh.harvard.edu
*************************************************
Mark,
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
Bing.Yu@css.unc.edu
*************************************************
Mark,
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
Bing.Yu@css.unc.edu
***********************************************
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
assistance.
DR. GREGORY S. RASH
Director, Gait & Biomechanics Lab
Phone: (502) 582-7657
GSRASHO1@ULKYVM.LOUISVILLE.EDU
************************************************** **************
Mark,
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: Richard.Smith@cchs.usyd.edu.au +
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
AUSTRALIA
************************************************
Check at the libarary at: http://www.arielnet.com
Gideon Ariel
ariell@ix.netcom.com
************************************************
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: R.Smith@cchs.usyd.edu.au
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.)
FAAPSM
Senior Lecturer, Division of Podiatry,
e-mail: a.keenan@uws.edu.au
ph: (046) 20.3335
fax: (046) 25.4252
UNIVERSITY OF WESTERN SYDNEY MACARTHUR
P.O. Box 555
Campbelltown NSW 2560
Australia
********************************************
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
TSRHGAIT@ix.netcom.com
*****************************************
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
email: mark.cornwall.nau.edu
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.
Replies:
Mark,
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.
Cheers,
Ben Sidaway, Ph.D.
Dept. of Physical Therapy
Husson College, Bangor, ME
bsidaway@husson.husson.edu
References.
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.
************************************************** *****
Mark:
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 P.Bate@Latrobe.edu.au
************************************************** ****
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
sg94k483@dunx1.ocs.drexel.edu
************************************************** *****
Mark,
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'dlove to know how this turns out! Ronny
Chris A. McGibbon, PhD (Ronny)
Technical Director
MGH Biomotion Lab,
Boston MA
ronny@gait52.mgh.harvard.edu
***********************************************
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.
Dimitrios
D.Tsirakos@mmu.ac.uk
***********************************************
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!
Jan
BRUCKNER@neu.edu
**************************************************
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
l.abraham@mail.utexas.edu
http://www.edb.utexas.edu/coe/depts/kin/
*************************************************
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
disappointing.
There are no simple anatomical correlations and it is NOT the mathematics
that is at fault.
Regards
Craig Nevin
CNEVIN@anat.uct.ac.za
*************************************************
***********************************************
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
atyler@saunix.sau.edu
************************************************
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
VXZ1@PSUVM.PSU.EDU>
*************************************************
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
krebs@gait52.mgh.harvard.edu
*************************************************
Mark,
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
Bing.Yu@css.unc.edu
*************************************************
Mark,
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
Bing.Yu@css.unc.edu
***********************************************
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
assistance.
DR. GREGORY S. RASH
Director, Gait & Biomechanics Lab
Phone: (502) 582-7657
GSRASHO1@ULKYVM.LOUISVILLE.EDU
************************************************** **************
Mark,
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: Richard.Smith@cchs.usyd.edu.au +
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
AUSTRALIA
************************************************
Check at the libarary at: http://www.arielnet.com
Gideon Ariel
ariell@ix.netcom.com
************************************************
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: R.Smith@cchs.usyd.edu.au
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.)
FAAPSM
Senior Lecturer, Division of Podiatry,
e-mail: a.keenan@uws.edu.au
ph: (046) 20.3335
fax: (046) 25.4252
UNIVERSITY OF WESTERN SYDNEY MACARTHUR
P.O. Box 555
Campbelltown NSW 2560
Australia
********************************************
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
TSRHGAIT@ix.netcom.com
*****************************************
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
email: mark.cornwall.nau.edu