In the recruitment criteria tutorial, there are a lot of choice between Min/MaxStrict, Quadratic and Auxiliary criteria.

In the tutorial you use these Auxiliary criteria :
[i]
Type = MR_QuadraticAux;
AuxLinearTerm.Weight = 0.1;

…

Type = MR_MinMaxAux;
AuxQuadraticTerm.Weight = 1;

[/i]And then you say :

“…Please notice, however, that the effect of the Weight property, i.e. the in the objective function, is somewhat problem dependent because the size of the sum that it multiplies depends on the number of muscles in the system while the size of the variable remains between 0 and 1 for normal problems. So models with many muscles would typically require a smaller value of …”

“…So the conclusion is that the MinMaxAux criterion, despite its attractive features, should be used with care in models where there is a chance that some model parts are independent of each other…”

Does the shoulder model is considered a model with many muscles and in which there are parts independant of each other ? Which auxiliary criterion and weight value should I use for my shoulder model that would account for the theory of Pragmann (2006) ?

Independent subsystems have to be mechanically separated, i.e. they should share no or at most a few muscles between them. The typical examples is the two arms lifting different weights. In this case, we would expect the recruitment in one arm to be independent of the recruitment in the other, but this is not the case when you use the auxiliary term.

As far at I remember Marit Praagman’s paper, she needs a constant coefficient on one of the terms in her objective function, and she has no way of determining it, so she picks one rather at random. I do not think that is a good approach. I would rather recommend that you begin with the value of and then look at the results you are getting and increase or decrease the value accordingly. If your result has no clear muscle activity envelope, then the auxiliary coefficient is too large. If you get recruitment patterns with abrupt changes of muscle activation, then it is too small.

I got it. I put a value of 1 to begin, but I will decrease it a little be and check the enveloppe. It is difficult to know which value would give a more realistic recruitment for shoulder movement.

Moreover, in the following paper :

Westerhoff P, Graichen F, Bender A, Halder A, Beier A, Rohlmann A, Bergmann G.: In vivo measurement of shoulder joint loads during activities of daily living. J Biomech. 42(12) 1840-9, 2009

it is said that for some movement involving semi-static positions, we must reconsider the energy-related optimization criteria used in musculoskeletal models, because they do not simulate the stabilization effect of such movements and the antagonist muscle activity. Do you agree with such statement ?? Can an axillary criterion resolve this issue ?

Nobody knows whether energy-related criteria have any merit or not. It is true that they tend to minimize antagonist muscle activity but we do not know whether this is wrong.

The muscle recruitment optimization problem has an objective function and one or more constraints. People tend to believe that the objective function should be responsible for the antagonism, but it may just as well be hidden in the constraints. For instance, if the glenoid contact is modeled correctly, then that influences the constraints of the problem and requires antagonism regardless of the objective function used.

The auxiliary term does not increase antagonism - it reduces it.

Thank you for this answer. It will help me to clarify the choice of the recruitment criterion in my study.

When you say that the auxilliary term decrease the antagonist action, is this because it also decrease the synergism ? Does synergism and antagonist actions are related ?

Yes, mathematically they are difficult to distinguish, and there is no clear definition of antagonism anyway. I usually characterize it as muscles doing negative work when the overall work is positive, but they may help relieve the load of other muscles, so it it really hard in practice to say what is antagonist and what is not.

If you run a simulation and plot Pm for all of the muscles, then anything below zero will be antagonist according to that definition.

Ok thank you. I’ll have a look at this parameter in the future.

I have another question about the quadratic criterion. In the tutorial, it says :

Quadratic muscle recruitment is often used in the biomechanical literature and many scientists support this method. Its muscle recruitment often agree well with experimental measurements of muscle activity and the resulting joint reaction forces have also been shown in several cases to agree well with experimental data. Physically, the method is related to well-known concepts such as the root mean square of a series of numbers and also to the field of elasticity. It is a fact that, had the muscles been purely linear passive-elastic elements capable of pushing as well as pulling, then the force distribution over the muscles would become quadratic, owing to the fact that the elastic energy stored in a muscle would be a quadratic function of the force it carries.

I just want to justify my choice of this criterion in my study and I though that it would be correct to use the content of this statement in my own words. So, this content refer to which published work exactly ? Is it from your own experience or it is specific papers ?

There are certainly papers advocating the quadratic criterion, but you have to look for them yourself - it is late Friday evening here and I have other things to do

The fact that the quadratic criterion is related to elastic energy was pointed out to me by an old professor many years ago. It requires that the muscles can push as well as pull, so it is not exactly the same, but it can probably be shown quite easily if you make a little one-dimensional example that stretches two elastics with different stifnesses.

Yes sure! I did not expect a fast answer like this one. You are really dedicated to the AnyScript Community ! It’s really appreciated.

I just wanted to verify that this exact statement was not coming from a paper whose reference may not have been included in the tutorials for more brevity.

Actually, I already use the answers that you gave me about the recruitment criteria. I refer to your papers and the Damsgaard paper in my work. Upon acceptation of my future papers, will it be possible to add them to your publication list ?