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