rferdinands49

08-10-2003, 11:20 AM

Dear Biomch-L Readers,

I thank everyone for spending the time to give quality response. Special thanks

to Ton van den Bogert for his very detailed response that answered almost all my

queries on the subject. I also agree that this topic is an extremely important

one for biomechanics, and can be the subject of confusion. So I do think that

subsequent questions should be addressed directly to Biomch-L and not myself so

that these matters are brought out into open discussion.

Thanks also to Karen Siegel and the others for their informative responses.

Note that in Zajac's article he referred to inverse solution as the Netwon-Euler

iterative method only. Other methods such as Lagrange's equations,

Newton-Lagrange multiplier method, etc are referred to as coupled dynamic

equations of motion. As I understand it, this is not a terminology that I

favour, but the principle behind differentiating the two approaches is

necessary.

I look forward to further discussion on this topic.

Thank you.

Rene Ferdinands

Department of Physics &

Electronic Engineering

University of Waikato

Private Bag 3105

Hamilton

New Zealand

----------------------------------

Rene Ferdinands formulated some interesting questions on power analysis

using inverse dynamics.

As moderator, I would like to suggest that this topic is of general

interest and quite suitable for a public discussion. So, please post your

responses directly to Biomch-L@nic.surfnet.nl.

Below follows my own response.

> (a) From the inverse dynamics solution of two or more coupled rigid bodies,

what

> would the value of just the net joint torque multiplied the corresponding

> segment angular velocity compute (i.e. just P = Tw)? Anything meaningful?

This quantity would represent the mechanical power delivered by a hypothetical

motor that drives the joint. If the joint is driven by muscles that span only

one joint, the quantity P = Tw therefore directly represents the total

mechanical power delivered by those muscles. If some of the driving muscles

are biarticular, muscle mechanical power is much harder to estimate. It will

require estimates of individual muscle forces and lengh changes.

The fact that any muscle, even a single-joint muscle, causes motion in

all other joints, is not relevant here. P = Tw is part of an inverse

analysis, and still accurately represents the power required at that one

joint. When doing an inverse analysis, the accelerations induced elsewhere will

also be measured and thus automatically be accounted for in the power

calculations for those other joints.

> (b) If the net joint torque (from inverse dynamics) multiplied by the

difference

> in angular velocities of the adjacent segments was calculated would this

> satifactorily give the values of THE TOTAL SUM OF active muscle power flows in

> or out of the segment (i.e. P=T(w2-w1)). Is this always necessary or could

> sometimes P=Tw used?

If I understand your definition of these variables, the joint angular

velocity w is simply the relative rotation between the two segments (i.e. w =

w2-w1). So both equations would give the same value for joint power. I

do not have Winter's book here to confirm this definition.

Power flow (in and out of the segment) is a tricky concept. There is also

power flow due to the resultant joint force (P = F.v). Results will depend

on which reference frame is used to measure v. This was discussed on

Biomch-L some time ago in relation to analysis of treadmill locomotion. I

prefer to stay away from the concept of power flow. It can be useful but

only if interpreted carefully.

> (c) Can joint muscle power or absorption be calculated accurately using

Winter's

> approach using the joint torques found from an inverse dynamics solution? Is

> this what Winter meant or did he mean as in (ii) above?

Apart from the issue of bi-articular muscles, yes, I think that net muscle

power generation and absorption is equal to the joint power measured from

inverse dynamics. Note that I use "net muscle power". If there is

co-contraction

of antagonistic muscles, there is simultaneous positive and negative muscle

power. Only the total net value is "seen" by the inverse dynamic analysis.

> Is the methodology for

> calculating power flows correct in Winter?

Again, without looking at Winter's book, I do not think that Winter proposed

calculating power flow. I think his analysis was limited to calculation of

joint power.

> (d) Can the power flow equations easily applied to the 3D case since power is

a

> scalar quantity?

If you mean joint power, yes. One way to do this is to model the joint as a

mechanism with three successive hinge joints. This is the classic Grood-Suntay

joint coordinate system (JCS) which gives cardanic angles from the kinematic

analysis. The time derivatives of these angles are the joint angular

velocities.

If you use the same JCS to represent the joint moments, you will have a scalar

moment in in each of the three hinge joints and the power calculation

works exactly as in 2-D. You will get three joint powers, which can be added up

if you want the total for the entire cardanic joint complex. The three

individual joint powers can be interpreted as the power required for,

respectively, flexion, abduction, and rotation.

However, inverse dynamics software usually does not give joint moments

decomposed along the JCS axes. Instead, you may get Mx,My,Mz expressed

in an orthogonal segment-fixed XYZ reference frame, or in a global reference

frame. To use this for calculation of joint power, you need an angular

velocity vector expressed in the same reference frame. 3-D kinematic

analysis gives, at each time, a rotation matrix R that describes the relative

orientation between the two segments. The angular velocity vector w =

(wx,wy,wz) can be estimated from R and its time-derivative Rdot:

( 0 -wz wy )

( wz 0 -wx ) = inv(R)*Rdot

( -wy wx 0 )

Now joint power will be the dot product of M and w: P = Mx.wx + My.wy + Mz.wz.

You can interpret these three terms of the dot product as flexion, abduction,

and rotation power, as long as you are aware that these components do *not*

correspond to standard JCS definitions.

I worry a bit that some people may be mixing these two approaches and

multiply JCS angular velocities by the "corresponding" segment-fixed XYZ

components of the joint moment vector. This is only correct when the

JCS axes are aligned with the XYZ axes, i.e. when two of the three

joint rotations are zero.

The ISB has proposed standards for the reporting of joint motion (Wu

et al., J Biomech 35:543-548, 2002; http://www.isbweb.org/standards ) but has

not directly made recommendations on the reporting of joint moments. This

issue needs to be resolved. My suggestion would be to report joint moments

in the same JCS as joint motion, so that power calculations can be done as in my

first suggestion above. I would welcome some comments on this, especially from

the ISB standardization committee. Please change the "Subject" line when

responding to this standardization issue rather than to Rene Ferdinands'

questions.

> (e) How should power flows into or out of a segment be described taking into

> account statement (iv) by Zajac et al. Does this mean that P=T(w2-w1) give the

> net joint power which represents the SUMMED power by the net joint moment

> to/from ALL the segments?

I agree with Zajac's statement and I think this is one more reason why the

concept of "power flow into a segment" is not useful. Joint power itself is

still perfectly valid, I think, as long as it is interpreted with an awareness

of biarticular muscles and antagonistic co-contraction.

--

Ton van den Bogert

--

A.J. (Ton) van den Bogert, PhD

Department of Biomedical Engineering

Cleveland Clinic Foundation

9500 Euclid Avenue (ND-20)

Cleveland, OH 44195, USA

Phone/Fax: (216) 444-5566/9198

--------------------------------------------------------------------------------

----------------------------

Rene,

I think it might be easier to answer all your questions in a general way

rather than on a point-by-point basis because of the overlap across your

questions.

I agree with Zajac et al that coupled dynamics is the only way to estimate

the power delivered by a muscle to a segment. The P=Tw term reflects only a

portion of the energy transferred in or out of a segment by a given joint

moment. Coupled equations of motion must be used to calculate the

intersegmental forces and power associated with that joint moment, and this

term must be included when determining a joint moment's contribution to

segmental power. So if you wish to use Winter's segmental power equations,

the forces in the F*v terms must be obtained using coupled equations of

motion, not inverse dynamics.

If you want to study power but are only using inverse dynamics, you can

still calculate joint power P=T(w2-21). But as you noted, joint power

represents the net effect of the joint moment on the mechanical energy of

the whole body, not any one particular body segment. You can't use either

P=T(w2-21) or P=Tw to make any inferences about the effect of the joint

moment on the power of an individual segment. Our study using coupled

dynamics showed that a given joint moment can be associated with segmental

power that is several times larger or even opposite in sign than the joint

power (Gait & Posture, in press).

You are welcome to contact me if you would like to discuss this in more

detail.

Karen Lohmann Siegel, PT, MA

CDR, US Public Health Service

National Institutes of Health

Bldg 10, Rm 6s235

10 Center Drive, MSC 1604

Bethesda, MD 20892-1604

phone: 301-496-9890

fax: 301-480-9896

e-mail: karen_siegel@nih.gov

--------------------------------------------------------------------------------

----------------------------

Dear Rene:

Determining mechanical power and work in human movement is discussed in

detail in a book entitled Kinetics of Human Motion by V. Zatsiorsky (Human

Kinetics, 2002). I hope that at least some of the questions that you have

raised are answered there.

Sincerely,

Vladimir Zatsiorsky

--------------------------------------------------------------------------------

----------------------------

Rene,

First, I am an orthopedic surgeon, not a physicist, so you will not believe a

word I write.

You are obviously at point where you are questioning the accepted paradigms, as

there are conflicts.

Take a look at:

Zajac is right. It is impossible to contract only one muscle. (See some recent

work by Peter Huijling who shows that all muscles are connected). Biologic

structures are trusses (Thompson 1917, Gordon 1988). As in all trusses, there

are only tension and compression elements and zero joint moments. See my

website for a paper or two on the subject . Even

if you don't believe me, I would appreciate some constructive arguments.

Steve

Stephen M. Levin, MD

Potomac Back Center

--------------------------------------------------------------------------------

----------------------------

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------

I thank everyone for spending the time to give quality response. Special thanks

to Ton van den Bogert for his very detailed response that answered almost all my

queries on the subject. I also agree that this topic is an extremely important

one for biomechanics, and can be the subject of confusion. So I do think that

subsequent questions should be addressed directly to Biomch-L and not myself so

that these matters are brought out into open discussion.

Thanks also to Karen Siegel and the others for their informative responses.

Note that in Zajac's article he referred to inverse solution as the Netwon-Euler

iterative method only. Other methods such as Lagrange's equations,

Newton-Lagrange multiplier method, etc are referred to as coupled dynamic

equations of motion. As I understand it, this is not a terminology that I

favour, but the principle behind differentiating the two approaches is

necessary.

I look forward to further discussion on this topic.

Thank you.

Rene Ferdinands

Department of Physics &

Electronic Engineering

University of Waikato

Private Bag 3105

Hamilton

New Zealand

----------------------------------

Rene Ferdinands formulated some interesting questions on power analysis

using inverse dynamics.

As moderator, I would like to suggest that this topic is of general

interest and quite suitable for a public discussion. So, please post your

responses directly to Biomch-L@nic.surfnet.nl.

Below follows my own response.

> (a) From the inverse dynamics solution of two or more coupled rigid bodies,

what

> would the value of just the net joint torque multiplied the corresponding

> segment angular velocity compute (i.e. just P = Tw)? Anything meaningful?

This quantity would represent the mechanical power delivered by a hypothetical

motor that drives the joint. If the joint is driven by muscles that span only

one joint, the quantity P = Tw therefore directly represents the total

mechanical power delivered by those muscles. If some of the driving muscles

are biarticular, muscle mechanical power is much harder to estimate. It will

require estimates of individual muscle forces and lengh changes.

The fact that any muscle, even a single-joint muscle, causes motion in

all other joints, is not relevant here. P = Tw is part of an inverse

analysis, and still accurately represents the power required at that one

joint. When doing an inverse analysis, the accelerations induced elsewhere will

also be measured and thus automatically be accounted for in the power

calculations for those other joints.

> (b) If the net joint torque (from inverse dynamics) multiplied by the

difference

> in angular velocities of the adjacent segments was calculated would this

> satifactorily give the values of THE TOTAL SUM OF active muscle power flows in

> or out of the segment (i.e. P=T(w2-w1)). Is this always necessary or could

> sometimes P=Tw used?

If I understand your definition of these variables, the joint angular

velocity w is simply the relative rotation between the two segments (i.e. w =

w2-w1). So both equations would give the same value for joint power. I

do not have Winter's book here to confirm this definition.

Power flow (in and out of the segment) is a tricky concept. There is also

power flow due to the resultant joint force (P = F.v). Results will depend

on which reference frame is used to measure v. This was discussed on

Biomch-L some time ago in relation to analysis of treadmill locomotion. I

prefer to stay away from the concept of power flow. It can be useful but

only if interpreted carefully.

> (c) Can joint muscle power or absorption be calculated accurately using

Winter's

> approach using the joint torques found from an inverse dynamics solution? Is

> this what Winter meant or did he mean as in (ii) above?

Apart from the issue of bi-articular muscles, yes, I think that net muscle

power generation and absorption is equal to the joint power measured from

inverse dynamics. Note that I use "net muscle power". If there is

co-contraction

of antagonistic muscles, there is simultaneous positive and negative muscle

power. Only the total net value is "seen" by the inverse dynamic analysis.

> Is the methodology for

> calculating power flows correct in Winter?

Again, without looking at Winter's book, I do not think that Winter proposed

calculating power flow. I think his analysis was limited to calculation of

joint power.

> (d) Can the power flow equations easily applied to the 3D case since power is

a

> scalar quantity?

If you mean joint power, yes. One way to do this is to model the joint as a

mechanism with three successive hinge joints. This is the classic Grood-Suntay

joint coordinate system (JCS) which gives cardanic angles from the kinematic

analysis. The time derivatives of these angles are the joint angular

velocities.

If you use the same JCS to represent the joint moments, you will have a scalar

moment in in each of the three hinge joints and the power calculation

works exactly as in 2-D. You will get three joint powers, which can be added up

if you want the total for the entire cardanic joint complex. The three

individual joint powers can be interpreted as the power required for,

respectively, flexion, abduction, and rotation.

However, inverse dynamics software usually does not give joint moments

decomposed along the JCS axes. Instead, you may get Mx,My,Mz expressed

in an orthogonal segment-fixed XYZ reference frame, or in a global reference

frame. To use this for calculation of joint power, you need an angular

velocity vector expressed in the same reference frame. 3-D kinematic

analysis gives, at each time, a rotation matrix R that describes the relative

orientation between the two segments. The angular velocity vector w =

(wx,wy,wz) can be estimated from R and its time-derivative Rdot:

( 0 -wz wy )

( wz 0 -wx ) = inv(R)*Rdot

( -wy wx 0 )

Now joint power will be the dot product of M and w: P = Mx.wx + My.wy + Mz.wz.

You can interpret these three terms of the dot product as flexion, abduction,

and rotation power, as long as you are aware that these components do *not*

correspond to standard JCS definitions.

I worry a bit that some people may be mixing these two approaches and

multiply JCS angular velocities by the "corresponding" segment-fixed XYZ

components of the joint moment vector. This is only correct when the

JCS axes are aligned with the XYZ axes, i.e. when two of the three

joint rotations are zero.

The ISB has proposed standards for the reporting of joint motion (Wu

et al., J Biomech 35:543-548, 2002; http://www.isbweb.org/standards ) but has

not directly made recommendations on the reporting of joint moments. This

issue needs to be resolved. My suggestion would be to report joint moments

in the same JCS as joint motion, so that power calculations can be done as in my

first suggestion above. I would welcome some comments on this, especially from

the ISB standardization committee. Please change the "Subject" line when

responding to this standardization issue rather than to Rene Ferdinands'

questions.

> (e) How should power flows into or out of a segment be described taking into

> account statement (iv) by Zajac et al. Does this mean that P=T(w2-w1) give the

> net joint power which represents the SUMMED power by the net joint moment

> to/from ALL the segments?

I agree with Zajac's statement and I think this is one more reason why the

concept of "power flow into a segment" is not useful. Joint power itself is

still perfectly valid, I think, as long as it is interpreted with an awareness

of biarticular muscles and antagonistic co-contraction.

--

Ton van den Bogert

--

A.J. (Ton) van den Bogert, PhD

Department of Biomedical Engineering

Cleveland Clinic Foundation

9500 Euclid Avenue (ND-20)

Cleveland, OH 44195, USA

Phone/Fax: (216) 444-5566/9198

--------------------------------------------------------------------------------

----------------------------

Rene,

I think it might be easier to answer all your questions in a general way

rather than on a point-by-point basis because of the overlap across your

questions.

I agree with Zajac et al that coupled dynamics is the only way to estimate

the power delivered by a muscle to a segment. The P=Tw term reflects only a

portion of the energy transferred in or out of a segment by a given joint

moment. Coupled equations of motion must be used to calculate the

intersegmental forces and power associated with that joint moment, and this

term must be included when determining a joint moment's contribution to

segmental power. So if you wish to use Winter's segmental power equations,

the forces in the F*v terms must be obtained using coupled equations of

motion, not inverse dynamics.

If you want to study power but are only using inverse dynamics, you can

still calculate joint power P=T(w2-21). But as you noted, joint power

represents the net effect of the joint moment on the mechanical energy of

the whole body, not any one particular body segment. You can't use either

P=T(w2-21) or P=Tw to make any inferences about the effect of the joint

moment on the power of an individual segment. Our study using coupled

dynamics showed that a given joint moment can be associated with segmental

power that is several times larger or even opposite in sign than the joint

power (Gait & Posture, in press).

You are welcome to contact me if you would like to discuss this in more

detail.

Karen Lohmann Siegel, PT, MA

CDR, US Public Health Service

National Institutes of Health

Bldg 10, Rm 6s235

10 Center Drive, MSC 1604

Bethesda, MD 20892-1604

phone: 301-496-9890

fax: 301-480-9896

e-mail: karen_siegel@nih.gov

--------------------------------------------------------------------------------

----------------------------

Dear Rene:

Determining mechanical power and work in human movement is discussed in

detail in a book entitled Kinetics of Human Motion by V. Zatsiorsky (Human

Kinetics, 2002). I hope that at least some of the questions that you have

raised are answered there.

Sincerely,

Vladimir Zatsiorsky

--------------------------------------------------------------------------------

----------------------------

Rene,

First, I am an orthopedic surgeon, not a physicist, so you will not believe a

word I write.

You are obviously at point where you are questioning the accepted paradigms, as

there are conflicts.

Take a look at:

Zajac is right. It is impossible to contract only one muscle. (See some recent

work by Peter Huijling who shows that all muscles are connected). Biologic

structures are trusses (Thompson 1917, Gordon 1988). As in all trusses, there

are only tension and compression elements and zero joint moments. See my

website for a paper or two on the subject . Even

if you don't believe me, I would appreciate some constructive arguments.

Steve

Stephen M. Levin, MD

Potomac Back Center

--------------------------------------------------------------------------------

----------------------------

---------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

---------------------------------------------------------------