Dear all,

I posted an announcement regarding the work-energy relationship during human gait last Dec. After that, I received many useful and instructive responses. Here I summarized all responses and would like to share with everybody.

Best regards.

Feng Yang

************************************************** ***********************************************

(A). the original post

Dear all,

Recently, we have been studying the relationship between the joint work and body mechanical energy during human gait. It is assumed that the changes in body mechanical energy should equal the work conducted by the body joints during the same period of time, such as from right heel strike to right toe off.

We only concern our model on the sagittal plane. The body mechanical energy includes the body potential energy, the body kinetic energy (horizontal, vertical, and rotary parts). As for the joint work, only the lower extremity is considered. The joint work is calculated as the integration of the net joint moment along the joint angle time history. The net joint moment was computed using inverse dynamics.

So far, the time histories of the net joint moment, joint angle, and the body energy are very similar with the results published by other researchers. However, the match between the joint work and the changes in body mechanical energy seems very terrible. The difference between these two sides is very huge. Even we checked our program and experimental data for a pretty long time, we cannot solve this problem.

Does anybody have the similar experience to handle this issue? Is the assumption mentioned above is correct? Or the total joint work and the changes in body energy are not equal to each other at all during gait due to some energy losses (e.g. collision, thermal energy dissipation¡)?

Any suggestion and reference will be deeply appreciated.

Wish you all the best in New Year.

Feng

(B) the responses

1. "Ivan E. Rouse" irouse@lasierra.edu

Greetings Feng:

I am a physicist, that has taught many engineering mechanics classes over the years, and I am just getting up to speed in biomechanics so am not an expert by any means. However, I do have some thoughts about your comments below. See below for my reflections.

Recently, we have been studying the relationship between the joint work and body mechanical energy during human gait. It is assumed that the changes in body mechanical energy should equal the work conducted by the body joints during the same period of time, such as from right heel strike to right toe off.

Remember that this process just described is an inelastic collision and as such mechanical energy (kinetic plus potential) is NOT conserved. A significant amount of energy goes into heat etc when inelastic collisions take place!

We only concern our model on the sagittal plane. The body mechanical energy includes the body potential energy, the body kinetic energy (horizontal, vertical, and rotary parts). As for the joint work, only the lower extremity is considered.

This may be somewhat short signted but obviously pragmatic. We know that it is much harder to walk, run and jump for example without corresponding movement of our arms, torso etc. My hunch is that the work being done by the muscles on the arms, head and torso may account for some of your discrepancy. How well do you know the moments of inertia of the various body parts? Don't forget to account for the kinetic energy of the arms etc. if appropriate.

The joint work is calculated as the integration of the net joint moment along the joint angle time history. The net joint moment was computed using inverse dynamics.

This is technically the correct definition but how well does the inverse dynamics predict the forces and how well do you know the moment arms? Have you double-checked the inverse dynamics by using a force plate to actually measure the forces and compare to those obtained from the inverse dynamics?

So far, the time histories of the net joint moment, joint angle, and the body energy are very similar with the results published by other researchers. However, the match between the joint work and the changes in body mechanical energy seems very terrible. The difference between these two sides is very huge. Even we checked our program and experimental data for a pretty long time, we cannot solve this problem.

Remember that you are evidently obtaining acceleration form position vs time data. This involves a numerical second derivative which is ALWAYS very noisy!! Are you using any kind of smoothing to solve some of the noise problem? Also don't forget the comments above about the other likely issues that are involved.

I hope my comments have been helpful.

Ivan E. Rouse, PhD

Professor of Physics

La Sierra University

909-785-2137

2. "Don Hoover"

Feng,

This is an interesting question. Thanks for posting it on the listserv.

There is considerable rotary motion in the horizontal and frontal planes during normal gait, so it seems to me that you may want to rethink the assumption of your model only addressing the sagittal plane. There are many good textbooks and articles that suggest that the rotary motion in the frontal and horizontal planes contributes to lesser deviation in the body's center of mass, in lesser metabolic energy costs of gait (or oxygen utilization), etc. Moreover, we see increased metabolic energy costs when individuals have joints surgically fused which limits rotary motion in the sagittal, frontal, or horizontal planes during the gait cycle. So, in sum, it seems that by only considering the energy costs in the sagittal plane, you are missing the mechanical energy in the frontal and horizontal planes that is being absorbed and then released in the gluteus medius, for example, during the stance phase of the gait cycle.

Hopes this helps,

Don

3. "Andy Ruina" -2 ruina@cornell.edu

If your joint torques and joint angular velocities are those which make for motion which is consistent with some motions of ANY collection of linked rigid objects then (theorem of mechanics, has nothing to do with biomechanics) the net joint work is the increase in kinetic plus potential of THAT same collection. Thus what you write reads like you have a calculation error.

This holds for collisions as well assuming you account for impulses appropriately.

This doesn't give you a clue, but it does say you are making a mistake. I would start with a simpler mechanical model, one where you can crack your calculation, in more detail, then you can learn perhaps the nature of your error.

-Andy

4. "Andy Ruina" -1 ruina@cornell.edu

I responded to your query. Then Manoj Srinivasan did and copied me. His response superficially may seem to slightly contradict mine. But I don't disagree with what he wrote. (Except perhaps his overconfidence about the relation between joint work and muscle work, which can be way off for tasks that are dominated by use of two-joint muscles. This two-joint muscle issue has no bearing on your accounting discrepancy.)

But reading his short essay makes me realize I was a bit unclear (misleading perhaps) in one regard. I should have added, say, a paragraph like this:

%%%%%%%%%

If your motion includes heel-strike you have to imagine that there is a joint between the foot and the ground. This might best be modeled as a sliding rather than rotational joint. Thus the work might be force times relative distance at that "joint". And still, as for all impulses, rotary or translational, you need to do the work accounting correctly at the impulses. Best probably, if you get things to work first in a regime with no impulses before you worry about how to do impulse accounting for heel-strike (which isn't hard, it¡¯s just another complication).

%%%%%%%%

-Andy

5. "Chris Kirtley" ckirtley@gmail.com

Dear Feng,

Here's an extract from my book, Clinical Gait Analysis: theory & practice...

The amount of work done (mechanical cost) by the body can be estimated by integrating the potential (mgh) and kinetic 1 ?/font>2 (mv2 + Iw2) energies of each body segment over the gait cycle (Cavagna et al 1963). The head, arms and trunk (HAT segment) are usually grouped together as one segment.

When the resting (minimum) potential energy is subtracted, the total is about 50 J over each gait cycle.

Alternatively, the power generated (ignoring eccentric contractions) at each joint can be summed over the gait cycle to calculate the total body work (TBW) or total lower-limb work (TLW), if the upper-limbs are ignored. This requires inverse dynamics (with a force platform). Whereas mechanical cost can be computed from kinematic data alone (Winter 1979).

TBW is larger, and the difference between the TBW and mechanical cost provides a measure of the 'power competition' which occurs when muscles work against each other? A common cause of inefficiency in pathological gait (Caldwell & Forrester 1992).

Chris

6. "Kim McKelvey" kim.mckelvey@gmail.com

Hi

Just a thought, but could you also have stored elastic potential energy in the body?

Kim

7. "Vladimir Zatsiorsky" vxz1@psu.edu

Dear Feng:

The discrepancy is explained in Chaper 6 of book by Zatsiorsky (2002) entitled Kinetics of Human Motion.

Best wishes,

VZ

8. "Manoj Srinivasan" ms285@cornell.edu

Feng,

Change in total energy of the body = Net work done by musculo-tendons minus |passive dissipation|

Assuming that replacing musculo-tendon work by joint-work is valid (it typically is), one possible source of discrepancy between joint-work calculations and total energy fluctuations is:

1. Passive dissipation: When the heel strikes the ground, a substantial amount of mechanical energy can be lost without active muscle negative work to heat. Many papers argue this to be the dominant energy loss in legged locomotion. See, for example:

Kuo, A. D., Donelan, J. M., and Ruina, A. (2005) Energetic consequences of walking like an inverted pendulum: Step-to-step transitions. Exercise and Sport Sciences Reviews, 33: 88-97.

Andy Ruina, John E. A. Bertram & Manoj Srinivasan. (2005) A collisional model of the energetic cost of support work qualitatively explains leg-sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition. Journal of theoretical biology. Volume 14, Issue 2, pages 170-192.

2. If you want to check your actual numerical method without having to worry about collisions, you might want to perform the same calculations for

A. a passive double pendulum with sufficiently low-friction bearings.

B. a person performing very-smooth motions in the sagittal plane.

If you have similar problems then, you'll have to rethink the details of your method.

Manoj

Manoj Srinivasan

Biorobotics and Locomotion Laboratory

Cornell University

9. "Rabinder Sahni" ezaleg2@yahoo.com

I too am quite interested with the info that you seek, I also need to know the amount of max.power that could be extracted from a prosthetic ankle in action of high active unilateral below knee amputee weighing around 60kgs height 6 feet.

Thanks

Mr.Rabinder Sahni

Prosthetics R&D,Designer lower limbs,Self user

INDIA

10. Ted Andresen, Tjacmc@aol.com

Dear Feng,

Recently, we have been studying the relationship between the joint work and body mechanical energy during human gait. It is assumed that the changes in body mechanical energy should equal the work conducted by the body joints during the same period of time, such as from right heel strike to right toe off.

I too thought that this was true, but when I carefully examined the few detailed results that I could find in the Internet I was surprised at the discrepancies. As I understand the issues it may be related to energy transfer between segments. Harris, et al, gives a good discussion of this in the section on ¡°Energy Calculations¡±. The Harris paper is at:

http://fig.cox.miami.edu/~cmallery/113/run.speed.energy.pdf

(For some reason, I have a Word copy of this paper. The link shown above is a pdf copy. I could not find a link to the Word version. It is very useful because it allows you to click on the graphs in the paper and see the supporting data. If you think that would be useful to you, I¡¯ll send you the Word version of the Harris paper as an attachment.)

We only concern our model on the sagittal plane. The body mechanical energy includes the body potential energy, the body kinetic energy (horizontal, vertical, and rotary parts). As for the joint work, only the lower extremity is considered. The joint work is calculated as the integration of the net joint moment along the joint angle time history. The net joint moment was computed using inverse dynamics.

There is a good discussion of the error sources involved in inverse dynamics at the bottom of this website in the section titled Limitations of Inverse Dynamics:

http://guardian.curtin.edu.au/cga/teach-in/inverse-dynamics.html

So far, the time histories of the net joint moment, joint angle, and the body energy are very similar with the results published by other researchers. However, the match between the joint work and the changes in body mechanical energy seems very terrible. The difference between these two sides is very huge. Even we checked our program and experimental data for a pretty long time, we cannot solve this problem.

This is just a thought. I assume that you are measuring the vertical ground Reactive Force (vGRF). I had seen some work where a researcher had measured the horizontal GRF. The made a comment at the end of the abstract that indicated that up to 30% of the energy in running was due to the hGRF. I found that a bit hard to believe, but maybe that is true. The paper can be found at:

http://jap.physiology.org/cgi/content/full/86/5/1657

In any event, you could eliminate the hGRF by ¡ making the subject run in place. That would give you the opportunity to get closer to a ¡°truth¡± model so you could see if you are make a simple calculational error somewhere in your analysis.

Don¡¯t pull your hair out over this. There¡¯s much, much more to come!

Ted Andresen

11. "F Borg"

Pax!

I think DA Winter has a quite detailed account of these sorts of energy calculations in his Biomechanics book. Some error could come from counting some contributions more than once or with the wrong sign. One way check the procedures by analyzing some very simple motion like standing up from a squatting position involving only work of the knee extensors.

What about dissipation? It does not have a direct role in the above calculations since it is already included in the effective forces (which may be produced with the aid of dissipation -- such as friction). If you jump from a chair onto a force plate your kinetical energy will indeed dissipate when you land on the force plate but the equation of motion (of the center of mass) is still given by

m a = F - mg // along the vertical z-direction, F is the ground reaction force and the integral \int F dz = Kin.E + Pot.E (from the Eq) is the work done (by knee extensors say) in order to stop the motion. While this is a form of a dissipative work ("muscular brake" in action) it is accounted for by the equations of motion. (If muscle could work in reserves it could store the breaking energy for use later without dissipation but the mechanical analysis would still the same.)

Best regards

Frank Borg

U of Jyväskylä, Chydenius Institute

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

Relax. Yahoo! Mail virus scanning helps detect nasty viruses!

I posted an announcement regarding the work-energy relationship during human gait last Dec. After that, I received many useful and instructive responses. Here I summarized all responses and would like to share with everybody.

Best regards.

Feng Yang

************************************************** ***********************************************

(A). the original post

Dear all,

Recently, we have been studying the relationship between the joint work and body mechanical energy during human gait. It is assumed that the changes in body mechanical energy should equal the work conducted by the body joints during the same period of time, such as from right heel strike to right toe off.

We only concern our model on the sagittal plane. The body mechanical energy includes the body potential energy, the body kinetic energy (horizontal, vertical, and rotary parts). As for the joint work, only the lower extremity is considered. The joint work is calculated as the integration of the net joint moment along the joint angle time history. The net joint moment was computed using inverse dynamics.

So far, the time histories of the net joint moment, joint angle, and the body energy are very similar with the results published by other researchers. However, the match between the joint work and the changes in body mechanical energy seems very terrible. The difference between these two sides is very huge. Even we checked our program and experimental data for a pretty long time, we cannot solve this problem.

Does anybody have the similar experience to handle this issue? Is the assumption mentioned above is correct? Or the total joint work and the changes in body energy are not equal to each other at all during gait due to some energy losses (e.g. collision, thermal energy dissipation¡)?

Any suggestion and reference will be deeply appreciated.

Wish you all the best in New Year.

Feng

(B) the responses

1. "Ivan E. Rouse" irouse@lasierra.edu

Greetings Feng:

I am a physicist, that has taught many engineering mechanics classes over the years, and I am just getting up to speed in biomechanics so am not an expert by any means. However, I do have some thoughts about your comments below. See below for my reflections.

Recently, we have been studying the relationship between the joint work and body mechanical energy during human gait. It is assumed that the changes in body mechanical energy should equal the work conducted by the body joints during the same period of time, such as from right heel strike to right toe off.

Remember that this process just described is an inelastic collision and as such mechanical energy (kinetic plus potential) is NOT conserved. A significant amount of energy goes into heat etc when inelastic collisions take place!

We only concern our model on the sagittal plane. The body mechanical energy includes the body potential energy, the body kinetic energy (horizontal, vertical, and rotary parts). As for the joint work, only the lower extremity is considered.

This may be somewhat short signted but obviously pragmatic. We know that it is much harder to walk, run and jump for example without corresponding movement of our arms, torso etc. My hunch is that the work being done by the muscles on the arms, head and torso may account for some of your discrepancy. How well do you know the moments of inertia of the various body parts? Don't forget to account for the kinetic energy of the arms etc. if appropriate.

The joint work is calculated as the integration of the net joint moment along the joint angle time history. The net joint moment was computed using inverse dynamics.

This is technically the correct definition but how well does the inverse dynamics predict the forces and how well do you know the moment arms? Have you double-checked the inverse dynamics by using a force plate to actually measure the forces and compare to those obtained from the inverse dynamics?

So far, the time histories of the net joint moment, joint angle, and the body energy are very similar with the results published by other researchers. However, the match between the joint work and the changes in body mechanical energy seems very terrible. The difference between these two sides is very huge. Even we checked our program and experimental data for a pretty long time, we cannot solve this problem.

Remember that you are evidently obtaining acceleration form position vs time data. This involves a numerical second derivative which is ALWAYS very noisy!! Are you using any kind of smoothing to solve some of the noise problem? Also don't forget the comments above about the other likely issues that are involved.

I hope my comments have been helpful.

Ivan E. Rouse, PhD

Professor of Physics

La Sierra University

909-785-2137

2. "Don Hoover"

Feng,

This is an interesting question. Thanks for posting it on the listserv.

There is considerable rotary motion in the horizontal and frontal planes during normal gait, so it seems to me that you may want to rethink the assumption of your model only addressing the sagittal plane. There are many good textbooks and articles that suggest that the rotary motion in the frontal and horizontal planes contributes to lesser deviation in the body's center of mass, in lesser metabolic energy costs of gait (or oxygen utilization), etc. Moreover, we see increased metabolic energy costs when individuals have joints surgically fused which limits rotary motion in the sagittal, frontal, or horizontal planes during the gait cycle. So, in sum, it seems that by only considering the energy costs in the sagittal plane, you are missing the mechanical energy in the frontal and horizontal planes that is being absorbed and then released in the gluteus medius, for example, during the stance phase of the gait cycle.

Hopes this helps,

Don

3. "Andy Ruina" -2 ruina@cornell.edu

If your joint torques and joint angular velocities are those which make for motion which is consistent with some motions of ANY collection of linked rigid objects then (theorem of mechanics, has nothing to do with biomechanics) the net joint work is the increase in kinetic plus potential of THAT same collection. Thus what you write reads like you have a calculation error.

This holds for collisions as well assuming you account for impulses appropriately.

This doesn't give you a clue, but it does say you are making a mistake. I would start with a simpler mechanical model, one where you can crack your calculation, in more detail, then you can learn perhaps the nature of your error.

-Andy

4. "Andy Ruina" -1 ruina@cornell.edu

I responded to your query. Then Manoj Srinivasan did and copied me. His response superficially may seem to slightly contradict mine. But I don't disagree with what he wrote. (Except perhaps his overconfidence about the relation between joint work and muscle work, which can be way off for tasks that are dominated by use of two-joint muscles. This two-joint muscle issue has no bearing on your accounting discrepancy.)

But reading his short essay makes me realize I was a bit unclear (misleading perhaps) in one regard. I should have added, say, a paragraph like this:

%%%%%%%%%

If your motion includes heel-strike you have to imagine that there is a joint between the foot and the ground. This might best be modeled as a sliding rather than rotational joint. Thus the work might be force times relative distance at that "joint". And still, as for all impulses, rotary or translational, you need to do the work accounting correctly at the impulses. Best probably, if you get things to work first in a regime with no impulses before you worry about how to do impulse accounting for heel-strike (which isn't hard, it¡¯s just another complication).

%%%%%%%%

-Andy

5. "Chris Kirtley" ckirtley@gmail.com

Dear Feng,

Here's an extract from my book, Clinical Gait Analysis: theory & practice...

The amount of work done (mechanical cost) by the body can be estimated by integrating the potential (mgh) and kinetic 1 ?/font>2 (mv2 + Iw2) energies of each body segment over the gait cycle (Cavagna et al 1963). The head, arms and trunk (HAT segment) are usually grouped together as one segment.

When the resting (minimum) potential energy is subtracted, the total is about 50 J over each gait cycle.

Alternatively, the power generated (ignoring eccentric contractions) at each joint can be summed over the gait cycle to calculate the total body work (TBW) or total lower-limb work (TLW), if the upper-limbs are ignored. This requires inverse dynamics (with a force platform). Whereas mechanical cost can be computed from kinematic data alone (Winter 1979).

TBW is larger, and the difference between the TBW and mechanical cost provides a measure of the 'power competition' which occurs when muscles work against each other? A common cause of inefficiency in pathological gait (Caldwell & Forrester 1992).

Chris

6. "Kim McKelvey" kim.mckelvey@gmail.com

Hi

Just a thought, but could you also have stored elastic potential energy in the body?

Kim

7. "Vladimir Zatsiorsky" vxz1@psu.edu

Dear Feng:

The discrepancy is explained in Chaper 6 of book by Zatsiorsky (2002) entitled Kinetics of Human Motion.

Best wishes,

VZ

8. "Manoj Srinivasan" ms285@cornell.edu

Feng,

Change in total energy of the body = Net work done by musculo-tendons minus |passive dissipation|

Assuming that replacing musculo-tendon work by joint-work is valid (it typically is), one possible source of discrepancy between joint-work calculations and total energy fluctuations is:

1. Passive dissipation: When the heel strikes the ground, a substantial amount of mechanical energy can be lost without active muscle negative work to heat. Many papers argue this to be the dominant energy loss in legged locomotion. See, for example:

Kuo, A. D., Donelan, J. M., and Ruina, A. (2005) Energetic consequences of walking like an inverted pendulum: Step-to-step transitions. Exercise and Sport Sciences Reviews, 33: 88-97.

Andy Ruina, John E. A. Bertram & Manoj Srinivasan. (2005) A collisional model of the energetic cost of support work qualitatively explains leg-sequencing in walking and galloping, pseudo-elastic leg behavior in running and the walk-to-run transition. Journal of theoretical biology. Volume 14, Issue 2, pages 170-192.

2. If you want to check your actual numerical method without having to worry about collisions, you might want to perform the same calculations for

A. a passive double pendulum with sufficiently low-friction bearings.

B. a person performing very-smooth motions in the sagittal plane.

If you have similar problems then, you'll have to rethink the details of your method.

Manoj

Manoj Srinivasan

Biorobotics and Locomotion Laboratory

Cornell University

9. "Rabinder Sahni" ezaleg2@yahoo.com

I too am quite interested with the info that you seek, I also need to know the amount of max.power that could be extracted from a prosthetic ankle in action of high active unilateral below knee amputee weighing around 60kgs height 6 feet.

Thanks

Mr.Rabinder Sahni

Prosthetics R&D,Designer lower limbs,Self user

INDIA

10. Ted Andresen, Tjacmc@aol.com

Dear Feng,

Recently, we have been studying the relationship between the joint work and body mechanical energy during human gait. It is assumed that the changes in body mechanical energy should equal the work conducted by the body joints during the same period of time, such as from right heel strike to right toe off.

I too thought that this was true, but when I carefully examined the few detailed results that I could find in the Internet I was surprised at the discrepancies. As I understand the issues it may be related to energy transfer between segments. Harris, et al, gives a good discussion of this in the section on ¡°Energy Calculations¡±. The Harris paper is at:

http://fig.cox.miami.edu/~cmallery/113/run.speed.energy.pdf

(For some reason, I have a Word copy of this paper. The link shown above is a pdf copy. I could not find a link to the Word version. It is very useful because it allows you to click on the graphs in the paper and see the supporting data. If you think that would be useful to you, I¡¯ll send you the Word version of the Harris paper as an attachment.)

We only concern our model on the sagittal plane. The body mechanical energy includes the body potential energy, the body kinetic energy (horizontal, vertical, and rotary parts). As for the joint work, only the lower extremity is considered. The joint work is calculated as the integration of the net joint moment along the joint angle time history. The net joint moment was computed using inverse dynamics.

There is a good discussion of the error sources involved in inverse dynamics at the bottom of this website in the section titled Limitations of Inverse Dynamics:

http://guardian.curtin.edu.au/cga/teach-in/inverse-dynamics.html

So far, the time histories of the net joint moment, joint angle, and the body energy are very similar with the results published by other researchers. However, the match between the joint work and the changes in body mechanical energy seems very terrible. The difference between these two sides is very huge. Even we checked our program and experimental data for a pretty long time, we cannot solve this problem.

This is just a thought. I assume that you are measuring the vertical ground Reactive Force (vGRF). I had seen some work where a researcher had measured the horizontal GRF. The made a comment at the end of the abstract that indicated that up to 30% of the energy in running was due to the hGRF. I found that a bit hard to believe, but maybe that is true. The paper can be found at:

http://jap.physiology.org/cgi/content/full/86/5/1657

In any event, you could eliminate the hGRF by ¡ making the subject run in place. That would give you the opportunity to get closer to a ¡°truth¡± model so you could see if you are make a simple calculational error somewhere in your analysis.

Don¡¯t pull your hair out over this. There¡¯s much, much more to come!

Ted Andresen

11. "F Borg"

Pax!

I think DA Winter has a quite detailed account of these sorts of energy calculations in his Biomechanics book. Some error could come from counting some contributions more than once or with the wrong sign. One way check the procedures by analyzing some very simple motion like standing up from a squatting position involving only work of the knee extensors.

What about dissipation? It does not have a direct role in the above calculations since it is already included in the effective forces (which may be produced with the aid of dissipation -- such as friction). If you jump from a chair onto a force plate your kinetical energy will indeed dissipate when you land on the force plate but the equation of motion (of the center of mass) is still given by

m a = F - mg // along the vertical z-direction, F is the ground reaction force and the integral \int F dz = Kin.E + Pot.E (from the Eq) is the work done (by knee extensors say) in order to stop the motion. While this is a form of a dissipative work ("muscular brake" in action) it is accounted for by the equations of motion. (If muscle could work in reserves it could store the breaking energy for use later without dissipation but the mechanical analysis would still the same.)

Best regards

Frank Borg

U of Jyväskylä, Chydenius Institute

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

Relax. Yahoo! Mail virus scanning helps detect nasty viruses!