This post concerns a debate at the Midwest Graduate Students

Biomechanics Symposium on March 16. I apologize if I do not represent

the other party's arguments very well and invite his participation.

I also apologize for a longish post. However, I felt that the

debate was ended prematurely at the symposium and that further

discussion would be in order. It was suggested at the symposium that

debates such as these take place on the internet, which I agree to.

I welcome any feedback, particularily if I have made an error in my

thinking, which has been known to happen but which I do not believe

has occurred in this instance.

A statement was made that muscle forces are greater during the

concentric phase than during the eccentric phase. To prove this

vertical ground reaction forces were measured while the subject

completed an elbow curl holding a 25 pound weight. The ground reaction

forces showed greater deviations, both positive and negative, from

the weight of the individual plus twenty-five pounds during the

concentric phase than during the eccentric phase. This was given e

as proof that the muscle forces were larger during the concentric

phase. It is my assertion that this is not necessarily, or even

generally, true.

My Comments:

1) This test is not a good one for answering the question. What

the vertical ground reaction forces will show is the amount of

acceleration of the center of gravity of the body plus the weight.

The greater deviation in forces during the concentric phase

indicates that greater accleration occurred during the concentric

phase in this instance. However, by moving the arm slowly during

the concentric phase and dropping rapidly during the eccentric

phase I was able to produce greater deviations in force during

the eccentric phase. The point here is that this will not be

consistent and does not provide a good test for when muscle forces

will be greatest. To actually test to see when the muscle forces,

or more accurately, the muscle moments are greatest would require

collecting film or video data and would not be dependent on

force plate data.

2. (I apologize for not being able to write formulas very well with

the mail system I am using)

The moments at the elbow at any given point in time will follow

M(muscle)-M(weight)=I*alpha

where M(muscle) is the moment caused by the muscles and other

assorted forces (ligaments, bone-on-bone contact, etc.) and M(weight)

is the moment caused by the weight of the arm plus the external

weight (and is given as a negative).

By taking the integral of both sides of the equation, we get

Integral(M(muscle)-M(weight))=Integral(I*alpha).

Since the starting and ending conditions are at omega=0,

Integral(I*alpha)=0 so the equation ends up as

Integral(M(muscle))=Integral(M(weight)).

The value of M(weight) is not dependent on whether the movement

is concentric or eccentric so it is clear that the sum of the

muscle moments over time will be the same regardless of whether

the movement is concentric or eccentric. While at some points

during the movement the moments may be greater during one phase

rather than the other, the total moments must come out the same.

In fact there are two situations where the muscle forces

throughout the movement would obviously be the same. If the

motion occurs at a constant angular velocity, then alpha=0. If

this is true, than at any time and at any angle

M(muscle)=M(weight).

Since M(weight) is determined by the angular position than

M(muscle) will be the same at a given angular position whether

the forearm is moving up or down.

It may be argued that, in order to start and stop at either

end of the movement, the assumption that alpha=0 would not be

correct. If, however, the movement is a "mirror image", that is

accelerations are the same going up and down at any angle

(alpha=f(angle)) once again we have

M(muscle)=M(weight)+I*alpha,

which becomes

M(muscle)=g(angle)

where

g(angle)=M(weight)(angle)+I*alpha(angle).

Once again, the moment at any given angle is a function of that

angle and not of the direction of movement.

Given that I have provided two examples of situations where

the muscle force during the concentric phase is not greater than

the muscle force during the eccentric phase I think that it is

clear that it is not always true that concentric muscle forces

are larger than eccentric muscle forces.

The only counterargument I can think of is that it may be

that the antagonist muscle activity (for example the triceps)

is greater during the eccentric phase. I am fairly certain,

though, that this was not the point that was being made in the

debate.

Thank you for your help,

Phil Fink

Ph.D. Student

Purdue University

Biomechanics Symposium on March 16. I apologize if I do not represent

the other party's arguments very well and invite his participation.

I also apologize for a longish post. However, I felt that the

debate was ended prematurely at the symposium and that further

discussion would be in order. It was suggested at the symposium that

debates such as these take place on the internet, which I agree to.

I welcome any feedback, particularily if I have made an error in my

thinking, which has been known to happen but which I do not believe

has occurred in this instance.

A statement was made that muscle forces are greater during the

concentric phase than during the eccentric phase. To prove this

vertical ground reaction forces were measured while the subject

completed an elbow curl holding a 25 pound weight. The ground reaction

forces showed greater deviations, both positive and negative, from

the weight of the individual plus twenty-five pounds during the

concentric phase than during the eccentric phase. This was given e

as proof that the muscle forces were larger during the concentric

phase. It is my assertion that this is not necessarily, or even

generally, true.

My Comments:

1) This test is not a good one for answering the question. What

the vertical ground reaction forces will show is the amount of

acceleration of the center of gravity of the body plus the weight.

The greater deviation in forces during the concentric phase

indicates that greater accleration occurred during the concentric

phase in this instance. However, by moving the arm slowly during

the concentric phase and dropping rapidly during the eccentric

phase I was able to produce greater deviations in force during

the eccentric phase. The point here is that this will not be

consistent and does not provide a good test for when muscle forces

will be greatest. To actually test to see when the muscle forces,

or more accurately, the muscle moments are greatest would require

collecting film or video data and would not be dependent on

force plate data.

2. (I apologize for not being able to write formulas very well with

the mail system I am using)

The moments at the elbow at any given point in time will follow

M(muscle)-M(weight)=I*alpha

where M(muscle) is the moment caused by the muscles and other

assorted forces (ligaments, bone-on-bone contact, etc.) and M(weight)

is the moment caused by the weight of the arm plus the external

weight (and is given as a negative).

By taking the integral of both sides of the equation, we get

Integral(M(muscle)-M(weight))=Integral(I*alpha).

Since the starting and ending conditions are at omega=0,

Integral(I*alpha)=0 so the equation ends up as

Integral(M(muscle))=Integral(M(weight)).

The value of M(weight) is not dependent on whether the movement

is concentric or eccentric so it is clear that the sum of the

muscle moments over time will be the same regardless of whether

the movement is concentric or eccentric. While at some points

during the movement the moments may be greater during one phase

rather than the other, the total moments must come out the same.

In fact there are two situations where the muscle forces

throughout the movement would obviously be the same. If the

motion occurs at a constant angular velocity, then alpha=0. If

this is true, than at any time and at any angle

M(muscle)=M(weight).

Since M(weight) is determined by the angular position than

M(muscle) will be the same at a given angular position whether

the forearm is moving up or down.

It may be argued that, in order to start and stop at either

end of the movement, the assumption that alpha=0 would not be

correct. If, however, the movement is a "mirror image", that is

accelerations are the same going up and down at any angle

(alpha=f(angle)) once again we have

M(muscle)=M(weight)+I*alpha,

which becomes

M(muscle)=g(angle)

where

g(angle)=M(weight)(angle)+I*alpha(angle).

Once again, the moment at any given angle is a function of that

angle and not of the direction of movement.

Given that I have provided two examples of situations where

the muscle force during the concentric phase is not greater than

the muscle force during the eccentric phase I think that it is

clear that it is not always true that concentric muscle forces

are larger than eccentric muscle forces.

The only counterargument I can think of is that it may be

that the antagonist muscle activity (for example the triceps)

is greater during the eccentric phase. I am fairly certain,

though, that this was not the point that was being made in the

debate.

Thank you for your help,

Phil Fink

Ph.D. Student

Purdue University