Antagonistic muscle force

I’m using AnyBody modeling system v4.0.2 AMMR 1. Why default standing model predict Rectus Abdominis muscle force while it’s an antagonistic muscle in standing? We know that the optimization based model can’t predict Antagonistic muscle force.In addition it predicts some Externus and Internus muscle force too.

Thank you in advance,

Dear Mohammad,

This has been already addressed here as well as on our wiki page for this (here).

Best regards,
Mohammad S. Shourijeh, PhD
AnyBody Team

Hi Mohammad,

As Mohammad S. Shourijeh correctly states, optimization-based models will predict antagonistic muscle actions when multi-articular muscles are present in the system. However, it is less well known that these methods also predict antagonism for systems with only mono-articular muscles, if the problem is three-dimensional. This was first show theoretically by

Jinha, A. et al., 2006. Antagonistic activity of one-joint muscles in three-dimensions using non-linear optimisation. Mathematical Biosciences, 202(1), p.57-70.

It is also very easy to show it numerically in AnyBody with a very simple model.

Best regards,

Dear Mohammad and John,
Thank you for your responses. I have some points for each response.

  1. The Rectus Abdominis is not multi-articular and is entirely in front of the spine; but is active in the standing posture. However, you may flex the model by 5 degrees and find that its force vanishes.

  2. With thanks to John for the paper introduced to me, I found that multi-articular muscles gain forces in nonlinear optimization. Of course, they emphasize that linear optimization can not predict antagonistic muscle force. In the standingmodel, you may switch the solver to linear opt. and find that Rectus Abdominus is still active.

Regarding to these findings, one may conclude that in the standing posture there may be an extensor moment, at least in one level, that the solver has to make anterior muscles active to balance that moment.

The main question is to find the force that may produce this extensor moment in the standing posture. You may notice that the segments’ center of mass are located in front of the joints at all levels and cannot be the case.

Thanks in advance,

Hi again,

The attachments of the Rectus Abdominis muscle are pelvis and Thorax, meaning that it spans the joints between Thorax, L1 to L5, Sacrum, and Pelvis segments and therefore it is multi-articular. If your model looks different, which shouldn’t be the case, please attach it to your next message.
If you change the kinematics of a 3D model, the equilibrium requirements will change and will obviously lead to a different set of optimal muscle forces.

Re the linear and nonlinear optimization, again at a simple case of 1-dof system with uni-articular muscles, a linear optimizer will recruit an agonist muscle with the largest moment arm ONLY whereas a nonlinear optimizer will use ALL agonists simultaneously; that is the main difference between the two.

Nevertheless, as I noted before, this is not the case in your application, and the mathematical problem gets much more complicated in 3D models with multi-articular muscles.

A couple more publications that might be worth looking at are followed:

  • Raikova, R. T., and Prilutsky, B. I., 2001. “Sensitivity of predicted muscle forces to parameters of the optimization-based human leg model revealed by analytical and numerical analyses”. Journal of Biomechanics, 34(10), pp. 1243-1255

  • Kerwin, J., and Challis, D., 1993. “An analytical examination of muscle force estimations using optimization techniques”. Journal of Engineering in Medicine, 207, pp. 139-148.

Hope it helps,
Mohammad Sharif Shourijeh