Simple Arm Model Cont.

Archive AnyScript Yahoo archive
1

I have continued looking into my simple arm model and I have a couple
more questions.

1.) First off, from my analysis, it looks like there is no
optimization going on within AnyBody. For example, when there are 5
muscles in the problem (brachialis, brachioradialis, biceps long and
short, and deltoid), after the inverse dynamics analysis, 3 of the
muscles have equal force values, and the other two have equal force
values. So five muscles is essentially represented as two; is this so
that equal muscle forces reduce the number of unknowns in the system
of equations?

For example in my model, the brachialis, brachioradialis, and biceps
short all have the same muscle force values (120 N), and the deltoid
and biceps long have the same muscle force (305 N). So instead of 5
unknowns for each the upper and lower limbs, there are 2 unknowns.
This reduces the number of unknowns to solve the equilibrium equations
quite easily. Mathematically, how is optimization utilized in this
case?

2.) Also, in my model looking at the brachialis and brachioradialis,
for example, how can they both be exerting the same force in an
optimal setting? Just looking at the moment free body diagram, the
brachioradialis has a longer moment arm so one would think that the
force in it would be greater than in the brachialis which has a
smaller moment arm.

3.) Lastly, if I am getting maximum muscle forces greater than my F0
input of 300 (deltoid and biceps long = 305), I can change the epsilon
values to result in more physiologically realizable results, right?

Thanks again for your help.
Sarah

2

Hi Sarah

> I have continued looking into my simple arm model and I have a
couple
> more questions.
>
> 1.) First off, from my analysis, it looks like there is no
> optimization going on within AnyBody. For example, when there are
5
> muscles in the problem (brachialis, brachioradialis, biceps long
and
> short, and deltoid), after the inverse dynamics analysis, 3 of the
> muscles have equal force values, and the other two have equal force
> values. So five muscles is essentially represented as two; is
this so
> that equal muscle forces reduce the number of unknowns in the
system
> of equations?

It would be typical for the solution of such a problem that some of
the muscles would end up with the same muscle activation. This is
due to the fact that the optimization algorithm at any time step
tries to minimized the muscles activity of the highest activated
muscle. This means that typically many muscles will be on the
activity envelope. If the muscles also ends up having the same force
value it could be beacuse they have the same moment arm and
strength ?

> For example in my model, the brachialis, brachioradialis, and
biceps
> short all have the same muscle force values (120 N), and the
deltoid
> and biceps long have the same muscle force (305 N). So instead of
5
> unknowns for each the upper and lower limbs, there are 2 unknowns.

The system do not couple the muscles together and reduce the numbers
of unknowns in this way. It will solve the problem with five
independent muscles. I think it is due to the mechanics of this
problem that you end up with this solution, but i will need to have
a closer look at the model in order to verify this.

> This reduces the number of unknowns to solve the equilibrium
equations
> quite easily. Mathematically, how is optimization utilized in this
> case?
>

> 2.) Also, in my model looking at the brachialis and
brachioradialis,
> for example, how can they both be exerting the same force in an
> optimal setting? Just looking at the moment free body diagram, the
> brachioradialis has a longer moment arm so one would think that the
> force in it would be greater than in the brachialis which has a
> smaller moment arm.

The optimization algorithm tries to minimize the muscle activity so
it will also depend on the strength relation between these two
muscles. If the brachioradialis muscle has a much lower strength
than brachialis you could end up with the solution you describe,
since it will try to use the brachialis muscle for unloading the
brachioradialis muscle.

> 3.) Lastly, if I am getting maximum muscle forces greater than my
F0
> input of 300 (deltoid and biceps long = 305), I can change the
epsilon
> values to result in more physiologically realizable results, right?
>
There is nothing in the algorithm that prevents the muscles from
being overloaded. In your case i am sure that the muscle activity is
larger than one meaning that muscle holds a larger load than its
strength. I am not sure what you mean by epsilon values, i think
that it could be moment arm values, strength values or mass
properties of the segments which could be wrong.

I hope this answered your questions otherwise please write again.

Best regards
AnyBody Support

> Thanks again for your help.
> Sarah

3

Hi Sarah,

This is John with a couple of additional comments to the answer you
received yesterday from AnyBody Support:

> It would be typical for the solution of such a problem that some of
> the muscles would end up with the same muscle activation. This is
> due to the fact that the optimization algorithm at any time step
> tries to minimized the muscles activity of the highest activated
> muscle. This means that typically many muscles will be on the
> activity envelope. If the muscles also ends up having the same
force
> value it could be beacuse they have the same moment arm and
> strength ?

Actually, for single-joint muscles it is enough that they span the
same joint on the same side of the joint. They need not have the same
moment arm. If they play the same mechanical role in the system, then
they will typicaly have the same activation, and if they have the
same strength, then they will also have the same force. The situation
is more complicated for multi-joint muscles.

If two muscles span the same joint, and they do not have the same
activation, then logically you can decrease the activation of the
more activated muscle by increasing the activation of the less
activated muscle. Hence they end up with the same activation, which
is maximization of the endurance.

There are a couple of references you may want to look into:

  1. Tutorial “A study of studies” lesson 3:
    http://www.anybodytech.com/76.0.html

  2. Rasmussen, J., Damsgaard, M. & Voigt, M. (2001): Muscle
    recruitment by the min/max criterion - a comparative numerical study.
    Journal of Biomechanics, vol. 34, no. 3, pp. 409-415.

> > 2.) Also, in my model looking at the brachialis and
> brachioradialis,
> > for example, how can they both be exerting the same force in an
> > optimal setting?

This is precisely the situation described above. They are two single
joint muscles crossing the same joint. If they have the same
strength, they will also exert the same force because this is what
leads to minium maximum activity. If you give the two muscles
different strengths, then they will also end up with the different
forces you expect.

Just looking at the moment free body diagram, the
> > brachioradialis has a longer moment arm so one would think that
the
> > force in it would be greater than in the brachialis which has a
> > smaller moment arm.

It is a much debated issue what the right recruitment criterion is. A
recruitment that gives muscles with large moment arms more force can
be argued to advantageous in terms of metabolism and in terms of
reduction of joint forces. But it will be disadvantageous in terms of
endurance and the capacity for fast movement and maximum joint moment.

In the paper cited above you can see how different criteria lead to
different solutions. The quantitative difference in the solution
between those criteria which are physiologcally reasonable is not
very large.

> > 3.) Lastly, if I am getting maximum muscle forces greater than
my
> F0
> > input of 300 (deltoid and biceps long = 305), I can change the
> epsilon
> > values to result in more physiologically realizable results,
right?

That is actually wrong. The min/max criterion has the advantage that
it utilizes the available muscle strenth to the limit. This means
that if you get acitivities larger than 1 (= overloaded muscles) then
it is mathematically guaranteed that there is no other muscle
activation pattern that can give you a lower activity, i.e. the
organism is physically incapable of carrying the load. The only thing
you can do is to reduce the load or increase the muscle strength.

Best regards,
John

4

Hi John,

Thanks for getting back to me and clarifying some of the questions I have
been having. I am asking so many software behind-the-scenes questions
because as a PhD student, it is just not good enough for me to answer
superficial questions. I need to know the inner-workings of the software
so that I can have confidence in my model’s results. It is just not good
enough for me to say that the model solves for muscle recruitment using an
optimization technique. I need to know the mathematics written into the
code for my own ability to defend my results. Is there anyway I can get
this information?

Thanks for helping answer some of my questions.
Sarah

> Hi Sarah,
>
> This is John with a couple of additional comments to the answer you
> received yesterday from AnyBody Support:
>
> > It would be typical for the solution of such a problem that some of
> > the muscles would end up with the same muscle activation. This is
> > due to the fact that the optimization algorithm at any time step
> > tries to minimized the muscles activity of the highest activated
> > muscle. This means that typically many muscles will be on the
> > activity envelope. If the muscles also ends up having the same
> force
> > value it could be beacuse they have the same moment arm and
> > strength ?
>
> Actually, for single-joint muscles it is enough that they span the
> same joint on the same side of the joint. They need not have the same
> moment arm. If they play the same mechanical role in the system, then
> they will typicaly have the same activation, and if they have the
> same strength, then they will also have the same force. The situation
> is more complicated for multi-joint muscles.
>
> If two muscles span the same joint, and they do not have the same
> activation, then logically you can decrease the activation of the
> more activated muscle by increasing the activation of the less
> activated muscle. Hence they end up with the same activation, which
> is maximization of the endurance.
>
> There are a couple of references you may want to look into:
>
> 1. Tutorial “A study of studies” lesson 3:
> http://www.anybodytech.com/76.0.html
>
> 2. Rasmussen, J., Damsgaard, M. & Voigt, M. (2001): Muscle
> recruitment by the min/max criterion - a comparative numerical study.
> Journal of Biomechanics, vol. 34, no. 3, pp. 409-415.
>
> > > 2.) Also, in my model looking at the brachialis and
> > brachioradialis,
> > > for example, how can they both be exerting the same force in an
> > > optimal setting?
>
> This is precisely the situation described above. They are two single
> joint muscles crossing the same joint. If they have the same
> strength, they will also exert the same force because this is what
> leads to minium maximum activity. If you give the two muscles
> different strengths, then they will also end up with the different
> forces you expect.
>
> Just looking at the moment free body diagram, the
> > > brachioradialis has a longer moment arm so one would think that
> the
> > > force in it would be greater than in the brachialis which has a
> > > smaller moment arm.
>
> It is a much debated issue what the right recruitment criterion is. A
> recruitment that gives muscles with large moment arms more force can
> be argued to advantageous in terms of metabolism and in terms of
> reduction of joint forces. But it will be disadvantageous in terms of
> endurance and the capacity for fast movement and maximum joint moment.
>
> In the paper cited above you can see how different criteria lead to
> different solutions. The quantitative difference in the solution
> between those criteria which are physiologcally reasonable is not
> very large.
>
> > > 3.) Lastly, if I am getting maximum muscle forces greater than
> my
> > F0
> > > input of 300 (deltoid and biceps long = 305), I can change the
> > epsilon
> > > values to result in more physiologically realizable results,
> right?
>
> That is actually wrong. The min/max criterion has the advantage that
> it utilizes the available muscle strenth to the limit. This means
> that if you get acitivities larger than 1 (= overloaded muscles) then
> it is mathematically guaranteed that there is no other muscle
> activation pattern that can give you a lower activity, i.e. the
> organism is physically incapable of carrying the load. The only thing
> you can do is to reduce the load or increase the muscle strength.
>
> Best regards,
> John
>
>
>
>
>
> AnyBody Technology provides free support on the use of the AnyBody
> Modeling System and the Scripting language AnyScript. Other users are
> welcome to join the discussions.
>
>
> YAHOO! GROUPS LINKS
> Visit your group “anyscript” on the web.
> To unsubscribe from this group, send an email to:
> anyscript-unsubscribe@yahoogroups.com
> Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
>

–
Sarah R. Sullivan
PhD Candidate, Biomedical Engineering
Rutgers, The State University of New Jersey
Piscataway, NJ 08854
sarsulli@eden.rutgers.edu
908-420-3371

5

Hi Sarah,

It is only natural and very welcome that you make an effort to dig
deeply into the mathematics of the problem.

There is a rather thorough mathematical explanation in the Journal of
Biomechanics paper cited below. I did not fully understand from your
question whether you have studied that paper and whether it fails to
answer your questions about the recruitment?

Best regards,
John

— In anyscript@yahoogroups.com, “Sarah R. Sullivan” <sarsulli@e…>
wrote:
> Hi John,
>
> Thanks for getting back to me and clarifying some of the questions
I have
> been having. I am asking so many software behind-the-scenes
questions
> because as a PhD student, it is just not good enough for me to
answer
> superficial questions. I need to know the inner-workings of the
software
> so that I can have confidence in my model’s results. It is just
not good
> enough for me to say that the model solves for muscle recruitment
using an
> optimization technique. I need to know the mathematics written
into the
> code for my own ability to defend my results. Is there anyway I
can get
> this information?
>
> Thanks for helping answer some of my questions.
> Sarah
>
>
> > Hi Sarah,
> >
> > This is John with a couple of additional comments to the answer
you
> > received yesterday from AnyBody Support:
> >
> > > It would be typical for the solution of such a problem that
some of
> > > the muscles would end up with the same muscle activation. This
is
> > > due to the fact that the optimization algorithm at any time
step
> > > tries to minimized the muscles activity of the highest
activated
> > > muscle. This means that typically many muscles will be on the
> > > activity envelope. If the muscles also ends up having the same
> > force
> > > value it could be beacuse they have the same moment arm and
> > > strength ?
> >
> > Actually, for single-joint muscles it is enough that they span
the
> > same joint on the same side of the joint. They need not have the
same
> > moment arm. If they play the same mechanical role in the system,
then
> > they will typicaly have the same activation, and if they have the
> > same strength, then they will also have the same force. The
situation
> > is more complicated for multi-joint muscles.
> >
> > If two muscles span the same joint, and they do not have the same
> > activation, then logically you can decrease the activation of the
> > more activated muscle by increasing the activation of the less
> > activated muscle. Hence they end up with the same activation,
which
> > is maximization of the endurance.
> >
> > There are a couple of references you may want to look into:
> >
> > 1. Tutorial “A study of studies” lesson 3:
> > http://www.anybodytech.com/76.0.html
> >
> > 2. Rasmussen, J., Damsgaard, M. & Voigt, M. (2001): Muscle
> > recruitment by the min/max criterion - a comparative numerical
study.
> > Journal of Biomechanics, vol. 34, no. 3, pp. 409-415.
> >
> > > > 2.) Also, in my model looking at the brachialis and
> > > brachioradialis,
> > > > for example, how can they both be exerting the same force in
an
> > > > optimal setting?
> >
> > This is precisely the situation described above. They are two
single
> > joint muscles crossing the same joint. If they have the same
> > strength, they will also exert the same force because this is
what
> > leads to minium maximum activity. If you give the two muscles
> > different strengths, then they will also end up with the
different
> > forces you expect.
> >
> > Just looking at the moment free body diagram, the
> > > > brachioradialis has a longer moment arm so one would think
that
> > the
> > > > force in it would be greater than in the brachialis which
has a
> > > > smaller moment arm.
> >
> > It is a much debated issue what the right recruitment criterion
is. A
> > recruitment that gives muscles with large moment arms more force
can
> > be argued to advantageous in terms of metabolism and in terms of
> > reduction of joint forces. But it will be disadvantageous in
terms of
> > endurance and the capacity for fast movement and maximum joint
moment.
> >
> > In the paper cited above you can see how different criteria lead
to
> > different solutions. The quantitative difference in the solution
> > between those criteria which are physiologcally reasonable is not
> > very large.
> >
> > > > 3.) Lastly, if I am getting maximum muscle forces greater
than
> > my
> > > F0
> > > > input of 300 (deltoid and biceps long = 305), I can change
the
> > > epsilon
> > > > values to result in more physiologically realizable results,
> > right?
> >
> > That is actually wrong. The min/max criterion has the advantage
that
> > it utilizes the available muscle strenth to the limit. This means
> > that if you get acitivities larger than 1 (= overloaded muscles)
then
> > it is mathematically guaranteed that there is no other muscle
> > activation pattern that can give you a lower activity, i.e. the
> > organism is physically incapable of carrying the load. The only
thing
> > you can do is to reduce the load or increase the muscle strength.
> >
> > Best regards,
> > John
> >
> >
> >
> >
> >
> > AnyBody Technology provides free support on the use of the
AnyBody
> > Modeling System and the Scripting language AnyScript. Other users
are
> > welcome to join the discussions.
> >
> >
> > YAHOO! GROUPS LINKS
> > Visit your group “anyscript” on the web.
> > To unsubscribe from this group, send an email to:
> > anyscript-unsubscribe@yahoogroups.com
> > Your use of Yahoo! Groups is subject to the Yahoo! Terms of
Service.
> >
>
>
> –
> Sarah R. Sullivan
> PhD Candidate, Biomedical Engineering
> Rutgers, The State University of New Jersey
> Piscataway, NJ 08854
> sarsulli@e…
> 908-420-3371