Quadriceps moment arms on the 2392 model

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Ryan Bakker
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Quadriceps moment arms on the 2392 model

Post by Ryan Bakker » Mon Oct 28, 2013 1:17 pm

Hello
I am using the Gait 2392 model to calculate muscle forces required to perform various gait activities. I apply calculated CMC muscle forces to cadaveric knee specimens and record the ACL strain. In order to apply these muscle forces to my specimen I must first correct for the moment arm difference between the Opensim model and my cadaveric specimen.
I have plotted the knee_angle_r moment arm as a function on the knee angle for the rect_fem, vas_int, vas_lat, vas_med (the four quadriceps muscles), and is shown below
2392.png
2392
I have noticed that this does not closely follow the trends in the literature. Below, I have included a figure from Yamaguchi 1989 that shows the effective moment arm of the quad about the knee joint. (The flexion angle sign conventions are flipped)
Yamaguchi1989.png
Yamaguchi 1989
The trend from 2392 also does not match that of the BothLegs model. This model includes the patella and is similar to the the findings of Yamaguchi 1989
BothLegs.png
BothLegs
Why are the moment arms about the knee angle significantly different between these models? Should they have the same values? I understand that the patella was removed from the 2392 model to help with the kinematic constraints and may need to be readjusted to provide the same moment arm. Have they have been readjusted/is this what is meant by “the insertions of the quadriceps on the tibia are modeled as moving points in the tibial frame”? Is this a limitation of the model to remove these kinematic constraints?

Ajay, if you have the chance could you weigh in? I know you helped remove the patella from the 2392 so you may have the most insight.

Thank you

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Ajay Seth
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Re: Quadriceps moment arms on the 2392 model

Post by Ajay Seth » Sun Nov 03, 2013 10:48 pm

These are important concerns.

The gait23 models without patellae reflect muscle path kinematics that are identical to those with the patellae present. If you evaluate the moment-arm using muscle length to joint angle relationship (dL/dtheta) then the moment-arms should appear to be identical. Unfortunately, the effective torque experienced by the knee joint are very different (OpenSim switched to the effective torque method as of 2.4). Why? In the models with patellae, a patella is constrained to a tibia via coordinate couple constraints. Mechanically, they represent massless gearing between the rotation of the tibia (w.r.t. femur, specifically the knee_angle) and the rotation and translation of the patella (w.r.t tibia). When muscles pull on the patella they create constraint reaction forces that cause the knee to rotate. That is, the effective torque on the knee_angle coordinate is due to the coupling mechanism of the patella to the tibia. In the model without a patella, the points of attachment where also carefully prescribed with respect to the tibia as functions of the knee_angle and act as extensions of the tibia. The problem here, is that there isn't a representative mechanism for dragging the via point around and in the the case the via point motion is under tension it is doing additional (unaccounted) mechanical work on the system. In the patella model, part of the definition of a coupler constraint is that it does no work, and the work to move the point (fixed on the patella) has to come from the applied tension.

That makes a strong case for not using moving path points altogether and we are considering that. However, for the purpose of performing muscle-driven forward simulations, moving path points do enable modelers to eliminate light/massless bodies whose only purpose for existing is to manipulate the muscle path to produce desired moment-arms. The use of fake bodies are equally non-physical in my book but also have a very detrimental effect on computational performance. If one thinks of the moving path point as only specifying the instantaneous location of a via point (which neglects the work required to move the point around under tension) then you can see how an applied tension leads to the effective torque. This might be a trade-off a modeler may be willing to make for significant gains in performance. In fact, modeling the patella as fully constrained w.r.t the tibia is also incorrect, in my opinion. The patella articulates w.r.t. the femur (not the tibia) and constraint (or contact) forces should reflect the interaction between these bodies in order to correctly capture the transmission of muscle tension to bones. The next full-body model that we release will reflect these concerns and will not use moving path points or massless bodies.

For physically plausible mechanisms the dL/dtheta and effective torque (r = Tau/tension) must be (and are) the same. When OpenSim users' scalar multiply muscle tension with the the muscle moment-arm, they are clearly trying to compute the effective torque produced by that muscle. Here, the moment-arm is the transmission of tension to torque (more accurately generalized force), so we have adopted the effective-torque definition for moment-arm to provide consistency at the level of system dynamics. It is also fast and robust to compute across a range of constrained and unconstrained multibody mechanisms (see http://simtk-confluence.stanford.edu:80 ... 9103515834 for more details).

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Ryan Bakker
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Re: Quadriceps moment arms on the 2392 model

Post by Ryan Bakker » Fri Nov 08, 2013 9:18 am

Ajay

Thank you for taking the time to write a detailed response, it was very helpful and informative. I want to confirm that I understand the end consequence correctly.

“Unfortunately, the effective torque experienced by the knee joint are very different”. Ultimately, because the 2392 model has a larger moment arm then both the 2legs model and what is reported in Yamaguchi 1989, I expect the quadriceps muscles force will be smaller for a given simulation.

Thank you,
-Ryan

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Ajay Seth
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Re: Quadriceps moment arms on the 2392 model

Post by Ajay Seth » Mon Feb 03, 2014 11:36 am

Thanks to user inquiries, responses and a dynamics reminder from Ton van den Bogert, we were able to account for the work of the moving (musle) path point in the calculation of the effective torque. Therefore, moment-arms of muscles using moving path points will be consistent with identical paths implemented with points on constrained bodies (e.g. quadriceps via a patella).

Please note that even-though the moment-arm correctly accounts for the work to move the point (which was missing previously) and produces the correct joint moment, correct moment-arms do not equate to correct/accurate joint reaction forces. For example, moving path points for the quadriceps moving w.r.t. to the tibia can produce correct moment-arms but the knee joint reactions will be incorrect. This is because their is a large reaction force between the patella on the femur that guides the patella on the femur (which is real) that is unaccounted for and instead there is a constraint (yet fictitious) force that moves the path point in the tibia. A patella body moving (constrained or via custom joint) w.r.t. the femur is the only way to obtain correct inter-segmental forces and thus joint reactions even-though the muscle path point kinematics may be identical. Moving path points provide convenience and performance benefits by avoiding additional bodies and constraints and can provide accurate estimates of muscles forces and moments from static optimization and CMC. However, you must use caution when interpreting joint reaction forces from models with simplified knee (or other) mechanisms.

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Ajay Seth
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Re: Quadriceps moment arms on the 2392 model

Post by Ajay Seth » Mon Feb 03, 2014 11:38 am

The updates to the moment-arm calculation for moving path points will be included in the forthcoming release of OpenSim 3.2.

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