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Dear Biomch-L readers,
The (somewhat lengthy) note attached to this message contains some
comments on the ISB standardization proposal, from our "local"
standardization committee. A printed version has been sent to the
ISB committee, but I also post it on Biomch-L. Perhaps it helps
to stimulate further thoughts and discussions. I certainly do not
envy the ISB committee members, who have to make sense out of all these
(possibly conflicting) opinions. All the more reason to appreciate
their work on this very important matter.
In our comments below, those on PART 2 (segmental reference frames) are
the most essential. I would welcome to hear other opinions on this
problem, either on Biomch-L or privately.
-- Ton van den Bogert
Human Performance Laboatory
University of Calgary, Canada
---------------------------------------------------------------------------
COMMENTS ON "RECOMMENDATIONS FOR STANDARDIZATION IN THE
REPORTING OF KINEMATIC DATA" (Draft version 4.0)
by the ISB Committee for Standardization and Terminology
Ton van den Bogert
Gerald Cole
Janet Ronsky
Gordon Hamilton
Human Performance Laboratory, University of Calgary
2500 University Drive N.W.
Calgary, Alberta T2N 1N4
CANADA
First of all, we compliment the committee-members on their work. As demon-
strated by the length of this comment, we think this is a very important
step in the development of applied biomechanical analysis.
PART 1: DEFINITION OF A GLOBAL REFERENCE FRAME
In our opinion, the labeling of the coordinates (XYZ) is of minor impor-
tance. When reporting results of measurements, it is a good custom to
label a graph or a table not just as "X", but always add information such
as "medial", "lateral", etc., to help interpretation. Conversion between
different standards is never more complicated than a re-labeling of the
variables, and possibly changing a sign.
"Direction of travel" is not always a useful definition. For
instance, when analysing a side-step movement, it is possible that you may
want the X-axis pointing forward, and not in the direction of travel (which
is sideward). As mentioned above, the problem is easily solved by adding
information about the variables, and not just using the symbols.
PART 2: DEFINITION OF SEGMENTAL REFERENCE FRAMES
We consider this part to be the most important. When this part is done
carefully, many problems in parts 4, 5, and 6 can be avoided. It is here
that standardization is very important for reporting results of measure-
ments, because the reader does not have the information to make the conver-
sion from one standard to another.
The orientation of segment coordinate axes can be defined in two ways (Cole
et al., 1992):
(1) Use anatomical landmarks (as proposed by the ISB committee).
(2) Define the segment coordinate system to be aligned with the global
coordinate system, when the subject is standing in a well-defined
"anatomical" position.
One problem with method (1) is, that the committee (or sub-committees) must
make separate definitions for all segments. Preferably, the landmarks
should be chosen so that they are also useful to define the Joint Coordi-
nate Systems (part 5), so they must be close to the "functional joint
axes". When this is done, we may end up with non-orthogonal coordinate
axes. For instance, an axis through the epicondyles of the knee would be
used in the JCS for the knee joint, and the long axis of the femur would be
used in the JCS for the hip joint. These are most likely not perpendicu-
lar, so they cannot be used as coordinate axes for the femur reference
frame. This leaves us with two possibilities: either use two orthogonal
coordinate systems in each segment (one for each joint), or use one non-
orthogonal coordinate system.
Another consideration is, that the landmarks should remain visible
during gait analysis. For instance, landmarks on the medial and lateral
epicondyle of the femur might be good to define the Z-axis of the femur,
and the flexion-extension axis of the knee, but not practical for 3-D gait
analysis because the medial marker is obscured most of the time. The prob-
lem can be solved by using additional markers, and 3-D coordinate transfor-
mations, but this becomes cumbersome.
Method (2) is our preference because it is more practical. Markers
can be placed anywhere on the segment -- preferably on sites with minimal
skin movement -- and only 3 markers per segment are required. Also, the
orientation of a segment in the "standard" position may be more reproduci-
ble than the direction of axes based on palpable anatomical landmarks.
Tests in our laboratory have shown that the standard deviation in the
orientation of the least reliable coordinate axis (determined from 10 cali-
bration trials) was 5 degrees, using method (2). We think that method (1)
will be less reproducible. If a joint coordinate system (JCS) is based on
the axes of the segmental reference frame, the axes obtained using method
(2) may not represent the functional axes. For instance, our flexion-
extension axis of the knee JCS, embedded in the femur, would be defined
perpendicular to the sagittal plane during standing. However, we doubt
that, for all joints, axes based on palpable landmarks can be found that
are significantly better at representing the "functional axes".
For kinematic analysis of a specific joint, the use of a JCS with
functional joint axes may be desirable. We are currently developing such
an analysis for the ankle joint, where the talocrural joint axis and the
subtalar joint axis are used as the first and third axis of the JCS (Bogert
and Nigg, 1992). We do not define these axes by anatomical landmarks, but
determine the position and orientation of the axes with respect to the seg-
mental reference frame (defined using method 2) using a mathematical pro-
cedure and a calibration measurement.
These comments probably reflect our experience with optical techniques
for gait analysis, rather than goniometric techniques. If possible, stan-
dards should be defined that can be used with both techniques. We believe
however, that optical techniques are much more common, especially in clini-
cal applications.
PART 3: GLOBAL DISPLACEMENTS
When quantifying global displacements of a segment, it becomes important
where the centre of the segmental reference frame was chosen. If, as pro-
posed, it is chosen in the centre of mass of the segment, it is necessary
to define where the centre of mass is with respect to anatomical landmarks.
Otherwise, results from different groups (with different assumptions for
mass distributions) will not be comparable. Why not just define one,
easily palpated, anatomical landmark to be the centre of the reference
frame? For quantifying segment translations, this point is just as good
(or bad) as any other point. But for reproducibility, a well-defined land-
mark offers a decided advantage.
Sometimes, one may want to calculate the position of the total body
centre of mass, which is a weighted average of the segment centres of mass.
It is only for this application that assumptions about mass distribution
are needed in kinematic analysis.
PART 4: GLOBAL ATTITUDES
Once the global and segment coordinate axes are defined, the only matter
left to standardize is: how to get three (meaningful) variables that define
the rotation matrix. We question why Cardanic angles with ZYX sequence are
proposed. A criterion to consider is: how easy is interpretation of these
three angles, compared to another sequence. We could not decide how to
judge this.
PART 5: RELATIVE ATTITUDES
We agree with the committee, that JCS angles are probably the best way to
quantify joint rotations. Helical angles may be mathematically better, but
are possibly too abstracted for clinicians. JCS angles can at least be
visualized with a physical (rather than mathematical) model: the 3-D
goniometer.
If at some time in the future the "helical angles" should be adopted,
it is possible to convert between the different standards, *if* the JCS
axes and segmental reference frames are properly standardized.
We protest against the statement that "this system allows sequence
independent rotations...". JCS angles are just as sequence dependent as
Euler/Cardanic angles, because a choice has to be made which axis is in the
proximal segment, and which axis is in the distal segment. This is a
geometric, rather than temporal, sequence dependency. For instance: a JCS
with the flexion axis in the distal segment and an internal rotation axis
in the proximal segment will give different results from the standard
Grood-Suntay convention. In fact, JCS angles are exactly the same as
Euler/Cardanic angles with a certain sequence, once the neutral position is
defined to be the position where the JCS axes are orthogonal. The differ-
ence is only a constant.
Note (a)
We propose to use the segmental coordinate systems, defined in part 2, as
the basis for the Joint Coordinate Systems (JCS). One JCS axis should be a
coordinate axis of the proximal segment, another should be a coordinate
axis of the second segment, and the third should be perpendicular to the
two. We think that this leads to interpretable attitude variables, if the
segmental reference frame is defined according to method (2), as described
under part 2, above.
This avoids the proposed "subcommittees" that will have to define the
JCS axes. How would one define functional JCS axes in the hip joint?
Presumably, since there is no preferred direction in a ball-and-socket
joint, one would use axes of the segmental coordinate systems: the medio-
lateral axis of the pelvis and the long axis of the femur. Why not do the
same for the knee joint, and all other joints?
The enclosed manuscript (Cole et al., 1992) describes one possibility
to standardize JCS axes. The segment axes are defined to be aligned with
the global axes during standing. The proximal JCS axis is chosen to be the
medio-lateral axis of the proximal segment, the distal JCS axis is chosen
to be anterior-posterior, or inferior-superior axis of the distal segment
(choose the one that is closest to the long axis of the segment; the foot
is in this respect different from the other segments).
Note (b)
Quantification of translation in a joint, when defined as translation
between the origin of two coordinate systems, depends strongly on the
choice of the origin (a fixed "joint center"). We doubt that this is prac-
tical, because the amount of translation may be small compared to the
reproducibility. When an assumed "joint center" is too far from the actual
joint center, most of the calculated translation is not true translation,
but induced by rotation. Calculation of an "instantaneous helical axis"
(much more complex, and sensitive to skin movement errors and noise) seems
to be the only way to obtain insight in translational movements in a joint.
Note (c)
If a JCS convention is chosen, it can also be used to quantify global atti-
tudes (part 4). Just pretend that the global coordinate system is the
proximal segment, and the moving segment is the distal segment. This will
be more consistent than the proposed ZYX sequence.
PART 6: JOINT MOMENTS
This is the only part of the proposal that deals with kinetics, rather than
kinematics. If the proposal is limited to kinematics only, this part could
be taken out. If not, then we suggest to change the title of the proposal.
A joint moment M is a vector, and vectors should be decomposed into
orthogonal components when doing calculations. We may choose the global
coordinate system, or one of the segmental coordinate systems, to represent
the components of M. However, when the calculations are finished, is might
be good for presentation purposes to decompose M into non-orthogonal com-
ponents, corresponding to the orientation of the JCS axes at that instant.
This allows interpretation in terms of "flexion moment", "adduction
moment", etc. However, care must be taken that no further calculations are
done with these components, such as calculating joint power (moment, multi-
plied by angular velocity). These calculations require orthogonal com-
ponents, so that a proper dot-product can be calculated. A distinction
must be made between representations for calculation and for presentation
purposes.
One problem not mentioned in the proposal, is that the magnitude of
joint moments depends strongly on the assumed location of a joint center.
A standardized, fixed joint center, based on anatomical landmarks, would be
desirable. The alternative (using an instantaneous center of rotation) is
hardly practical for in vivo studies, because this is sensitive to measure-
ment errors (skin movement and noise).
When inertial forces are to be incorporated in the estimated joint
moments, the inertial properties of the segments (mass, center of mass,
moments of inertia) become important. Again, standardization is required.
This could be one more reason to remove inverse dynamics (joint moments)
from a proposal on standardization of kinematics.
PART 7: MINORITY REPORT
Using RST instead of XYZ would be no improvement. As we said about part 1,
it is just a matter of labelling.
The use of left-handed coordinate systems might lead to problems when doing
calculations (for instance calculating moments using a vector-product).
Similar to the moment representation discussed under part 6, we think that
a left-handed coordinate system for the opposite side of the body will be
good in the presentation stage. But do not do any calculations afterwards!
References
Bogert, A.J. van den, and B.M. Nigg (1992) An optimization method to deter-
mine anatomical axes of the ankle joint in vivo. Abstract, 8th
Congress of the European Society of Biomechanics, Rome, Italy.
Cole, G.K., B.M. Nigg, and J.L. Ronsky (1992) Application of the joint
coordinate system to 3D joint attitude and movement representation: a
standardization approach. Submitted.
The (somewhat lengthy) note attached to this message contains some
comments on the ISB standardization proposal, from our "local"
standardization committee. A printed version has been sent to the
ISB committee, but I also post it on Biomch-L. Perhaps it helps
to stimulate further thoughts and discussions. I certainly do not
envy the ISB committee members, who have to make sense out of all these
(possibly conflicting) opinions. All the more reason to appreciate
their work on this very important matter.
In our comments below, those on PART 2 (segmental reference frames) are
the most essential. I would welcome to hear other opinions on this
problem, either on Biomch-L or privately.
-- Ton van den Bogert
Human Performance Laboatory
University of Calgary, Canada
---------------------------------------------------------------------------
COMMENTS ON "RECOMMENDATIONS FOR STANDARDIZATION IN THE
REPORTING OF KINEMATIC DATA" (Draft version 4.0)
by the ISB Committee for Standardization and Terminology
Ton van den Bogert
Gerald Cole
Janet Ronsky
Gordon Hamilton
Human Performance Laboratory, University of Calgary
2500 University Drive N.W.
Calgary, Alberta T2N 1N4
CANADA
First of all, we compliment the committee-members on their work. As demon-
strated by the length of this comment, we think this is a very important
step in the development of applied biomechanical analysis.
PART 1: DEFINITION OF A GLOBAL REFERENCE FRAME
In our opinion, the labeling of the coordinates (XYZ) is of minor impor-
tance. When reporting results of measurements, it is a good custom to
label a graph or a table not just as "X", but always add information such
as "medial", "lateral", etc., to help interpretation. Conversion between
different standards is never more complicated than a re-labeling of the
variables, and possibly changing a sign.
"Direction of travel" is not always a useful definition. For
instance, when analysing a side-step movement, it is possible that you may
want the X-axis pointing forward, and not in the direction of travel (which
is sideward). As mentioned above, the problem is easily solved by adding
information about the variables, and not just using the symbols.
PART 2: DEFINITION OF SEGMENTAL REFERENCE FRAMES
We consider this part to be the most important. When this part is done
carefully, many problems in parts 4, 5, and 6 can be avoided. It is here
that standardization is very important for reporting results of measure-
ments, because the reader does not have the information to make the conver-
sion from one standard to another.
The orientation of segment coordinate axes can be defined in two ways (Cole
et al., 1992):
(1) Use anatomical landmarks (as proposed by the ISB committee).
(2) Define the segment coordinate system to be aligned with the global
coordinate system, when the subject is standing in a well-defined
"anatomical" position.
One problem with method (1) is, that the committee (or sub-committees) must
make separate definitions for all segments. Preferably, the landmarks
should be chosen so that they are also useful to define the Joint Coordi-
nate Systems (part 5), so they must be close to the "functional joint
axes". When this is done, we may end up with non-orthogonal coordinate
axes. For instance, an axis through the epicondyles of the knee would be
used in the JCS for the knee joint, and the long axis of the femur would be
used in the JCS for the hip joint. These are most likely not perpendicu-
lar, so they cannot be used as coordinate axes for the femur reference
frame. This leaves us with two possibilities: either use two orthogonal
coordinate systems in each segment (one for each joint), or use one non-
orthogonal coordinate system.
Another consideration is, that the landmarks should remain visible
during gait analysis. For instance, landmarks on the medial and lateral
epicondyle of the femur might be good to define the Z-axis of the femur,
and the flexion-extension axis of the knee, but not practical for 3-D gait
analysis because the medial marker is obscured most of the time. The prob-
lem can be solved by using additional markers, and 3-D coordinate transfor-
mations, but this becomes cumbersome.
Method (2) is our preference because it is more practical. Markers
can be placed anywhere on the segment -- preferably on sites with minimal
skin movement -- and only 3 markers per segment are required. Also, the
orientation of a segment in the "standard" position may be more reproduci-
ble than the direction of axes based on palpable anatomical landmarks.
Tests in our laboratory have shown that the standard deviation in the
orientation of the least reliable coordinate axis (determined from 10 cali-
bration trials) was 5 degrees, using method (2). We think that method (1)
will be less reproducible. If a joint coordinate system (JCS) is based on
the axes of the segmental reference frame, the axes obtained using method
(2) may not represent the functional axes. For instance, our flexion-
extension axis of the knee JCS, embedded in the femur, would be defined
perpendicular to the sagittal plane during standing. However, we doubt
that, for all joints, axes based on palpable landmarks can be found that
are significantly better at representing the "functional axes".
For kinematic analysis of a specific joint, the use of a JCS with
functional joint axes may be desirable. We are currently developing such
an analysis for the ankle joint, where the talocrural joint axis and the
subtalar joint axis are used as the first and third axis of the JCS (Bogert
and Nigg, 1992). We do not define these axes by anatomical landmarks, but
determine the position and orientation of the axes with respect to the seg-
mental reference frame (defined using method 2) using a mathematical pro-
cedure and a calibration measurement.
These comments probably reflect our experience with optical techniques
for gait analysis, rather than goniometric techniques. If possible, stan-
dards should be defined that can be used with both techniques. We believe
however, that optical techniques are much more common, especially in clini-
cal applications.
PART 3: GLOBAL DISPLACEMENTS
When quantifying global displacements of a segment, it becomes important
where the centre of the segmental reference frame was chosen. If, as pro-
posed, it is chosen in the centre of mass of the segment, it is necessary
to define where the centre of mass is with respect to anatomical landmarks.
Otherwise, results from different groups (with different assumptions for
mass distributions) will not be comparable. Why not just define one,
easily palpated, anatomical landmark to be the centre of the reference
frame? For quantifying segment translations, this point is just as good
(or bad) as any other point. But for reproducibility, a well-defined land-
mark offers a decided advantage.
Sometimes, one may want to calculate the position of the total body
centre of mass, which is a weighted average of the segment centres of mass.
It is only for this application that assumptions about mass distribution
are needed in kinematic analysis.
PART 4: GLOBAL ATTITUDES
Once the global and segment coordinate axes are defined, the only matter
left to standardize is: how to get three (meaningful) variables that define
the rotation matrix. We question why Cardanic angles with ZYX sequence are
proposed. A criterion to consider is: how easy is interpretation of these
three angles, compared to another sequence. We could not decide how to
judge this.
PART 5: RELATIVE ATTITUDES
We agree with the committee, that JCS angles are probably the best way to
quantify joint rotations. Helical angles may be mathematically better, but
are possibly too abstracted for clinicians. JCS angles can at least be
visualized with a physical (rather than mathematical) model: the 3-D
goniometer.
If at some time in the future the "helical angles" should be adopted,
it is possible to convert between the different standards, *if* the JCS
axes and segmental reference frames are properly standardized.
We protest against the statement that "this system allows sequence
independent rotations...". JCS angles are just as sequence dependent as
Euler/Cardanic angles, because a choice has to be made which axis is in the
proximal segment, and which axis is in the distal segment. This is a
geometric, rather than temporal, sequence dependency. For instance: a JCS
with the flexion axis in the distal segment and an internal rotation axis
in the proximal segment will give different results from the standard
Grood-Suntay convention. In fact, JCS angles are exactly the same as
Euler/Cardanic angles with a certain sequence, once the neutral position is
defined to be the position where the JCS axes are orthogonal. The differ-
ence is only a constant.
Note (a)
We propose to use the segmental coordinate systems, defined in part 2, as
the basis for the Joint Coordinate Systems (JCS). One JCS axis should be a
coordinate axis of the proximal segment, another should be a coordinate
axis of the second segment, and the third should be perpendicular to the
two. We think that this leads to interpretable attitude variables, if the
segmental reference frame is defined according to method (2), as described
under part 2, above.
This avoids the proposed "subcommittees" that will have to define the
JCS axes. How would one define functional JCS axes in the hip joint?
Presumably, since there is no preferred direction in a ball-and-socket
joint, one would use axes of the segmental coordinate systems: the medio-
lateral axis of the pelvis and the long axis of the femur. Why not do the
same for the knee joint, and all other joints?
The enclosed manuscript (Cole et al., 1992) describes one possibility
to standardize JCS axes. The segment axes are defined to be aligned with
the global axes during standing. The proximal JCS axis is chosen to be the
medio-lateral axis of the proximal segment, the distal JCS axis is chosen
to be anterior-posterior, or inferior-superior axis of the distal segment
(choose the one that is closest to the long axis of the segment; the foot
is in this respect different from the other segments).
Note (b)
Quantification of translation in a joint, when defined as translation
between the origin of two coordinate systems, depends strongly on the
choice of the origin (a fixed "joint center"). We doubt that this is prac-
tical, because the amount of translation may be small compared to the
reproducibility. When an assumed "joint center" is too far from the actual
joint center, most of the calculated translation is not true translation,
but induced by rotation. Calculation of an "instantaneous helical axis"
(much more complex, and sensitive to skin movement errors and noise) seems
to be the only way to obtain insight in translational movements in a joint.
Note (c)
If a JCS convention is chosen, it can also be used to quantify global atti-
tudes (part 4). Just pretend that the global coordinate system is the
proximal segment, and the moving segment is the distal segment. This will
be more consistent than the proposed ZYX sequence.
PART 6: JOINT MOMENTS
This is the only part of the proposal that deals with kinetics, rather than
kinematics. If the proposal is limited to kinematics only, this part could
be taken out. If not, then we suggest to change the title of the proposal.
A joint moment M is a vector, and vectors should be decomposed into
orthogonal components when doing calculations. We may choose the global
coordinate system, or one of the segmental coordinate systems, to represent
the components of M. However, when the calculations are finished, is might
be good for presentation purposes to decompose M into non-orthogonal com-
ponents, corresponding to the orientation of the JCS axes at that instant.
This allows interpretation in terms of "flexion moment", "adduction
moment", etc. However, care must be taken that no further calculations are
done with these components, such as calculating joint power (moment, multi-
plied by angular velocity). These calculations require orthogonal com-
ponents, so that a proper dot-product can be calculated. A distinction
must be made between representations for calculation and for presentation
purposes.
One problem not mentioned in the proposal, is that the magnitude of
joint moments depends strongly on the assumed location of a joint center.
A standardized, fixed joint center, based on anatomical landmarks, would be
desirable. The alternative (using an instantaneous center of rotation) is
hardly practical for in vivo studies, because this is sensitive to measure-
ment errors (skin movement and noise).
When inertial forces are to be incorporated in the estimated joint
moments, the inertial properties of the segments (mass, center of mass,
moments of inertia) become important. Again, standardization is required.
This could be one more reason to remove inverse dynamics (joint moments)
from a proposal on standardization of kinematics.
PART 7: MINORITY REPORT
Using RST instead of XYZ would be no improvement. As we said about part 1,
it is just a matter of labelling.
The use of left-handed coordinate systems might lead to problems when doing
calculations (for instance calculating moments using a vector-product).
Similar to the moment representation discussed under part 6, we think that
a left-handed coordinate system for the opposite side of the body will be
good in the presentation stage. But do not do any calculations afterwards!
References
Bogert, A.J. van den, and B.M. Nigg (1992) An optimization method to deter-
mine anatomical axes of the ankle joint in vivo. Abstract, 8th
Congress of the European Society of Biomechanics, Rome, Italy.
Cole, G.K., B.M. Nigg, and J.L. Ronsky (1992) Application of the joint
coordinate system to 3D joint attitude and movement representation: a
standardization approach. Submitted.