Muscle behaviors when changing the dimensions

[M.Ali Akhras]

Hi everybody,

I have a basic question, I have to success in explaining the problem. When trying to run two similar simulations with different muscle sizes, each is made by one segment that rotate about z axis and two muscles (agonist and antagonist muscles), in both the tendon slack to optimal fiber length ratio =3. In the first simulation, the muscle-tendon length is 3cm (Lm_opt=3*1/4cm and Lt_slack=3*3/4cm). In the second simulation, the muscle-tendon length is 35 cm (Lm_opt=35*1/4cm and Lt_slack=35*3/4cm). In both simulations, the initial muscle length = optimal fiber length and muscle-tendon length Lmt=Lm_opt+Lt_slack. After 0.5 sec, I apply an external force to angularly shift the segment.

What I obtain is similar muscle behaviors in terms of force development before applying the external force, and completely two different muscle behaviors at and after applying the external force. In the first case, the muscle generating force opposite to the external force tries to compensate it by slowing increasing the force and therefore the moment applied on the segment, instead the other muscle decreases everything. This is very fine....in the second case, the muscle forces rapidly vary and the outcome is that the segment rotates.

I don't see why the muscle behaviors are different in the two case just because I increases the muscle tendon length from 3 to 35 cm keeping the tendon slack to fiber length ratio the same as well as the other muscle parameters (i.g. isometric force, pennation angle, max contraction velocity)

What is the reason?

Thanks
Ali

[jimmy d]

Hi Ali,

It was difficult from the description and figures given but what it may be is that the force you are applying may cause similar angular displacement of the segment, but that displacement would result in the muscles being on different normalized proportions of their respective force length curves.

Hope that helps,
-james

[M.Ali Akhras]

Hi james,
Thank you very much for your help.
Ok, to let you better understand how the two different models look like, please see the attached picture. However I agree that the angular displacement of the segment would be similar in both cases (short and long muscles), but I don't understand why the muscle dynamics is different as the two muscle in both cases (short and long) have the same dynamic properties (pennation angle=0, vMax=10, Fiso=61, Lslak/Lopt=3.3).
If we apply an external torque on the segment-tip (clockwise direction), the joint net torque in both models should be the same as well because the muscle arms are the same in both models (long and short muscles) and the forces generated by muscles should be the same as well in both cases. What I obtained is that the short muscles were able to resist an external torque (angular displacement is small <90°), instead long muscle can not maintain the posture of the segment when applying the same external torque (angular displacement is big <90°, it's around 180°). Please note the excitation level is always constant for all the muscles and the initial fiber lengths are equal to the optimal fiber length.
If you look at the previous plots (from 0.5 sec to a bit later, let's say 0.6 sec) of long muscle model, you notice that the force muscle "1" increases but its moment decreases suddenly after a very short time increase which is not the case in short muscles. Do you have any explanation or suggestion for that?

Thanks again,
Ali