Thank you very much to all those who replied to the request I posted (twice
somehow) for help with estimating anthropometric parameters for paraplegics.
While I am grateful for the assistance, I don't think we've got to the heart of
the question yet. I wish to be able to calculate parameters for a subjects who
clearly do not fit normative tables. Surely the same problem has been
approached by every researcher who has performed kinetic analyses. How do
people studying the kinetics of weightlifting derive these parameters? The
standard tables must be nearly bad for these people as they would be for
paraplegics. We need a method to CALCULATE values for any given population. The
geometric methods described below will assist, but they cannot provide the
whole solution. I would welcome a reply from people from people doing all kinds
of kinetic research to know how they get parameters for any nonstandard
populations.
Thank you once again to all those who replied before. I have included all your
responses below.
Regards
Peter Sinclair
The University of Sydney
bi_sinclair@coco.cchs.su.oz.au
From: SMTP%"IVMEMOL@HDETUD2.TUDELFT.NL" 27JAN1993 18:56:05.01
Maybe I can help tomorrow; together with Douglas Hobson I analyzed
anthropometric data from 122 people with cerebral palsy. He brought
the dataset with him from Memphis Tennessee when he vistited our
lab for his sabattical.
We used regression equations of Clauser, CE, JT McConville and JW Young
Weight, volume and center of mass of segments of human body
WrightPatterson Air Force Base Ohio(1969) AMRLTR6970
for example Center of Mass of Tibia:
0.309 * tibial height  0.558 * knee breadth +5,786 cm

The data about the CPsample is published as:
Hobson, DA and JFM Molenbroek
Anthropometry and Design for the disabled: Experiences with seating
design for cerebral palsy population
Applied Ergonomics 21(1990)1,4354
With regards
Johan FM Molenbroek
Delft University of Technology
The Netherlands
From: SMTP%"GA4020@SIUCVMB.SIU.EDU" 28JAN1993 02:20:32.14
although not directly designed for paraplegics, you might use part of
the Hanavan body model to predict the location of segmental mass
centers. The input data are radii of the distal and proximal ends of
the segment and the segment weight (which of course you have to derive
from some other means). The output will also include the moment of
inertia around the mass center.
The reference is: Hanavan, E.P. (1964) A mathematical model of the
human body. AMRL Technical Documentary Report 64102, WrightPatterson
Air Force Base.
The hanavan body model is a set of equations that predict the moment of
inertia and location of the center of mass of the frustum of a right
circular cone (the base of the cone with the tip cut off). The basic
assumption of the model is that the segment has a constant density
throughout the length of the segment. The application of this model to
a human body segment also assumes the segment to be shaped like the
frustum of a cone. Namely, for any of the extremity segments, the wider
proximal end is the base of the cone and the narrower distal end is the
top of the cone.
The input parameters to the model are: segment length, segment weight,
segment mass, radius of proximal end, and radius of distal end.
We obtain these values from:
segment length  position data of segment in space
segment mass  we use the values from Dempster predicting each segment
mass from total body mass
segment weight  mass * accel of gravity
radii  we measure the proximal and distal circumferences of each
segment
on each subject and calculate radii.
The equations are as follows. The variable names come directly from
hanavan. R is the proximal radius, RR the distal radius (R > RR).
SL, SM, SW are segment length, mass, and weight.
Eta is location of mass center expressed as a ratio of the length from
proximal end to mass center and the segment length (eg Eta = .5 is mass
center at mid point, Eta < .5 is mass center closer to proximal end).
Seg In is the moment of inertia in SI units.
Equations:
Delta = (3 * SW) / (SL * (R^2 + R * RR + RR^2) * 3.14159)
Mu = RR / R
Sigma = 1 + Mu + Mu^2
Eta = (1 + 2 * Mu + 3 * Mu^2) / (4 * Sigma)
Aa = (9 / (20 * 3.14159)) * ((1 + Mu^2 + Mu^3 + Mu^4) / Sigma^2)
Bb = (3 / 80) * ((1 +4 * Mu + 10 * Mu^2 + 4 * Mu ^3 + Mu^4) /
Sigma^2)
Seg In = (Aa * SM^2) / (Delta * SL) + (Bb * SM * SL^2)

Here is some test data for you to check the equations:
Total body mass = 83.4
SL = 0.353
SM = 8.34 ( this was a sub's thigh = 0.10 * body mass)
SW = 81.8154
R = 0.1003
RR = 0.0653
Delta = 10614.2246
Mu = 0.6508
Sigma = 2.0743
Eta = 0.4305 (notice how similar to other predictions of CM location)
Aa = 0.0625
Bb = 0.0795
Seg In = 0.0837 (a very reasonable number)
Good luck with this, Peter. If you have trouble let me know.
Paul DeVita
email: ga4020@siucvmb.siu.edu
From: SMTP%"GA4020@SIUCVMB.SIU.EDU" 30JAN1993 03:17:16.44
From: SMTP%"blacknl@tuns.ca" 28JAN1993 05:51:50.48
I am doing some research work in structural and functional anthropometry
of wheelchair mobile paraplegics. I attempted to perform some
work using the methods decribed by Jensen (1979), J. of Biomechanics.
However, I found it difficult to get subjects to volunteer for the
slides necessary for his method. Please keep me posted of your
progress.
Sincerely,
John Kozey
ps I am using the account of Nancy Black for this letter. Please respond
to her account.
From: SMTP%"MICHEL@physocc.lan.mcgill.ca" 28JAN1993 09:10:21.51
Our laboratory is also currently facing the problem of getting
good anthropometrical estimates of paraplegics and paraparetics.
We are working presently on using Hatze's equations even
though the density of the segments will have errors.
We would appreciate it very much if you could send us the replies
you will get with your query so that we could improve our kinetic
measurement.
Thank you for your time.
Michel Ladouceur, M.Sc.
Human Gait Laboratory
School of P. & O. T.
McGill University
Montreal, Canada
email: michel@physocc.lan.mcgill.can
From: SMTP%"steiner@clio.rz.uniduesseldorf.de" 28JAN1993 21:11:09.93
I had intended to post a similar call for help, but know I am lazy enough
to ask you to summarize the answers you get and either post them on BIOMCHL
or send them to me.
We are working on FES for paraplegics and need the data to feed our dynamical
simulation program.
Thank you for your kind help
Yours
Rene Steiner
Neurologisches Therapiecentrum
Hohensandweg 37
D4000 Duesseldorf 13
Germany
steiner@clio.rz.uniduesseldorf.de
From: SMTP%"E_DOW@uvmvax.uvm.edu" 2FEB1993 04:05:21.83
I wonder why you want to do this? There is some school of thought that
anthropometrics is not everything it has been cracked up to be! It
certainly helps in defining the range of values for design purposes
but is dangerous if you expect to design for the "average" person. I
find it interesting to think in terms of an "average para's" legs.
Of what use would it be considering that the legs are nonfunctional?
I think you might be hard pressed to find the data you are looking for
considering how different every para is....even more so than ablebodied
people.
Good luck!..
Jerry Weisman
Vermont Rehab Engineering Center
University of Vermont
Weisman@uvmgen.uvm.edu
From: SMTP%"marko@robo.fer.unilj.si" 4FEB1993 01:59:59.57
All anthropometric variables you want: mass, location of mass
centre can be foud in Winter DA, Biomechanics of human movement,
John Willey&Sons, New York 1979.
I modelled shank and thigh as truncated cone with bigger
and smaller radius. This is not published yet, but:
from body mass and hight and according to Winter body density,
segment densities and segment masses are determined. From mass and
density segment volume can be found. You can also express mass
location in terms of r1 and r2 of cone. And you can express volume
in terms of r1 and r2. Both nonlinear equations include two radius
r1 and r2 and can be solved with appropriate numeric method
(NewtonRaphson). Works.
I don't have experience with CT scans, but for body density
non CT scan measurements would only count.
With best regards,
Marko Munih
Marko Munih, M. Sc. Faculty of El. & Comp. Eng.
Teaching Assistant Trzaska 25, 61000 Ljubljana, Slovenia
marko@robo.fer.unilj.si tel.: +386 1 265 161
fax.: +386 1 264 990
somehow) for help with estimating anthropometric parameters for paraplegics.
While I am grateful for the assistance, I don't think we've got to the heart of
the question yet. I wish to be able to calculate parameters for a subjects who
clearly do not fit normative tables. Surely the same problem has been
approached by every researcher who has performed kinetic analyses. How do
people studying the kinetics of weightlifting derive these parameters? The
standard tables must be nearly bad for these people as they would be for
paraplegics. We need a method to CALCULATE values for any given population. The
geometric methods described below will assist, but they cannot provide the
whole solution. I would welcome a reply from people from people doing all kinds
of kinetic research to know how they get parameters for any nonstandard
populations.
Thank you once again to all those who replied before. I have included all your
responses below.
Regards
Peter Sinclair
The University of Sydney
bi_sinclair@coco.cchs.su.oz.au
From: SMTP%"IVMEMOL@HDETUD2.TUDELFT.NL" 27JAN1993 18:56:05.01
Maybe I can help tomorrow; together with Douglas Hobson I analyzed
anthropometric data from 122 people with cerebral palsy. He brought
the dataset with him from Memphis Tennessee when he vistited our
lab for his sabattical.
We used regression equations of Clauser, CE, JT McConville and JW Young
Weight, volume and center of mass of segments of human body
WrightPatterson Air Force Base Ohio(1969) AMRLTR6970
for example Center of Mass of Tibia:
0.309 * tibial height  0.558 * knee breadth +5,786 cm

The data about the CPsample is published as:
Hobson, DA and JFM Molenbroek
Anthropometry and Design for the disabled: Experiences with seating
design for cerebral palsy population
Applied Ergonomics 21(1990)1,4354
With regards
Johan FM Molenbroek
Delft University of Technology
The Netherlands
From: SMTP%"GA4020@SIUCVMB.SIU.EDU" 28JAN1993 02:20:32.14
although not directly designed for paraplegics, you might use part of
the Hanavan body model to predict the location of segmental mass
centers. The input data are radii of the distal and proximal ends of
the segment and the segment weight (which of course you have to derive
from some other means). The output will also include the moment of
inertia around the mass center.
The reference is: Hanavan, E.P. (1964) A mathematical model of the
human body. AMRL Technical Documentary Report 64102, WrightPatterson
Air Force Base.
The hanavan body model is a set of equations that predict the moment of
inertia and location of the center of mass of the frustum of a right
circular cone (the base of the cone with the tip cut off). The basic
assumption of the model is that the segment has a constant density
throughout the length of the segment. The application of this model to
a human body segment also assumes the segment to be shaped like the
frustum of a cone. Namely, for any of the extremity segments, the wider
proximal end is the base of the cone and the narrower distal end is the
top of the cone.
The input parameters to the model are: segment length, segment weight,
segment mass, radius of proximal end, and radius of distal end.
We obtain these values from:
segment length  position data of segment in space
segment mass  we use the values from Dempster predicting each segment
mass from total body mass
segment weight  mass * accel of gravity
radii  we measure the proximal and distal circumferences of each
segment
on each subject and calculate radii.
The equations are as follows. The variable names come directly from
hanavan. R is the proximal radius, RR the distal radius (R > RR).
SL, SM, SW are segment length, mass, and weight.
Eta is location of mass center expressed as a ratio of the length from
proximal end to mass center and the segment length (eg Eta = .5 is mass
center at mid point, Eta < .5 is mass center closer to proximal end).
Seg In is the moment of inertia in SI units.
Equations:
Delta = (3 * SW) / (SL * (R^2 + R * RR + RR^2) * 3.14159)
Mu = RR / R
Sigma = 1 + Mu + Mu^2
Eta = (1 + 2 * Mu + 3 * Mu^2) / (4 * Sigma)
Aa = (9 / (20 * 3.14159)) * ((1 + Mu^2 + Mu^3 + Mu^4) / Sigma^2)
Bb = (3 / 80) * ((1 +4 * Mu + 10 * Mu^2 + 4 * Mu ^3 + Mu^4) /
Sigma^2)
Seg In = (Aa * SM^2) / (Delta * SL) + (Bb * SM * SL^2)

Here is some test data for you to check the equations:
Total body mass = 83.4
SL = 0.353
SM = 8.34 ( this was a sub's thigh = 0.10 * body mass)
SW = 81.8154
R = 0.1003
RR = 0.0653
Delta = 10614.2246
Mu = 0.6508
Sigma = 2.0743
Eta = 0.4305 (notice how similar to other predictions of CM location)
Aa = 0.0625
Bb = 0.0795
Seg In = 0.0837 (a very reasonable number)
Good luck with this, Peter. If you have trouble let me know.
Paul DeVita
email: ga4020@siucvmb.siu.edu
From: SMTP%"GA4020@SIUCVMB.SIU.EDU" 30JAN1993 03:17:16.44
From: SMTP%"blacknl@tuns.ca" 28JAN1993 05:51:50.48
I am doing some research work in structural and functional anthropometry
of wheelchair mobile paraplegics. I attempted to perform some
work using the methods decribed by Jensen (1979), J. of Biomechanics.
However, I found it difficult to get subjects to volunteer for the
slides necessary for his method. Please keep me posted of your
progress.
Sincerely,
John Kozey
ps I am using the account of Nancy Black for this letter. Please respond
to her account.
From: SMTP%"MICHEL@physocc.lan.mcgill.ca" 28JAN1993 09:10:21.51
Our laboratory is also currently facing the problem of getting
good anthropometrical estimates of paraplegics and paraparetics.
We are working presently on using Hatze's equations even
though the density of the segments will have errors.
We would appreciate it very much if you could send us the replies
you will get with your query so that we could improve our kinetic
measurement.
Thank you for your time.
Michel Ladouceur, M.Sc.
Human Gait Laboratory
School of P. & O. T.
McGill University
Montreal, Canada
email: michel@physocc.lan.mcgill.can
From: SMTP%"steiner@clio.rz.uniduesseldorf.de" 28JAN1993 21:11:09.93
I had intended to post a similar call for help, but know I am lazy enough
to ask you to summarize the answers you get and either post them on BIOMCHL
or send them to me.
We are working on FES for paraplegics and need the data to feed our dynamical
simulation program.
Thank you for your kind help
Yours
Rene Steiner
Neurologisches Therapiecentrum
Hohensandweg 37
D4000 Duesseldorf 13
Germany
steiner@clio.rz.uniduesseldorf.de
From: SMTP%"E_DOW@uvmvax.uvm.edu" 2FEB1993 04:05:21.83
I wonder why you want to do this? There is some school of thought that
anthropometrics is not everything it has been cracked up to be! It
certainly helps in defining the range of values for design purposes
but is dangerous if you expect to design for the "average" person. I
find it interesting to think in terms of an "average para's" legs.
Of what use would it be considering that the legs are nonfunctional?
I think you might be hard pressed to find the data you are looking for
considering how different every para is....even more so than ablebodied
people.
Good luck!..
Jerry Weisman
Vermont Rehab Engineering Center
University of Vermont
Weisman@uvmgen.uvm.edu
From: SMTP%"marko@robo.fer.unilj.si" 4FEB1993 01:59:59.57
All anthropometric variables you want: mass, location of mass
centre can be foud in Winter DA, Biomechanics of human movement,
John Willey&Sons, New York 1979.
I modelled shank and thigh as truncated cone with bigger
and smaller radius. This is not published yet, but:
from body mass and hight and according to Winter body density,
segment densities and segment masses are determined. From mass and
density segment volume can be found. You can also express mass
location in terms of r1 and r2 of cone. And you can express volume
in terms of r1 and r2. Both nonlinear equations include two radius
r1 and r2 and can be solved with appropriate numeric method
(NewtonRaphson). Works.
I don't have experience with CT scans, but for body density
non CT scan measurements would only count.
With best regards,
Marko Munih
Marko Munih, M. Sc. Faculty of El. & Comp. Eng.
Teaching Assistant Trzaska 25, 61000 Ljubljana, Slovenia
marko@robo.fer.unilj.si tel.: +386 1 265 161
fax.: +386 1 264 990