unknown user

05-19-1992, 05:51 AM

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.