# Lever arm calculation

Hi there,

I would like to know which of the following techniques is most accurate to find the lever arm of a muscle in AnyBody :

1. Divide the muscle moment by its force, by using the AnyForceMomentMeasure function

2. Use trigonometric functions to compute the perpendicular distance between the joint center and the muscle’s line of action defined by two points (i.e. origin_2_via-point or origin_2_insertion)

When I use those two techniques, they give me different results. How to explain it ?

Thanks

Pierre

Hi Pierre,
we usually follow the definiton of An et al.
K. N. An, K. Takahashi, T. P. Harrigan, and E. Y. Chao, “Determination of muscle orientations and moment arms.” J Biomech Eng, vol. 106, no. 3, pp. 280–282, Aug 1984.

Hi,

Ok but there is multiple methods exposed in this article. Does AnyBody uses the tendon excursion method or a geometric method with the center of rotation ?

The fact is that with the shoulder model of AnyBody, the lever arm are higher than the literature at the beginning of the movement. For example, we found 1.5 to 2 cm for the lever arm of the middle deltoid at 0° of elevation from in-vitro studies dealing with tendon excursion method, while AnyBody gives a lever arm of 3.5 cm with the following calculation for the division 4 of the deltoid (AnyForceMomentMeasure) :

Lever arm = (Muscle moment at the COR / muscle force)

Is this normal to get a value as high as 3.5 cm ?

Thank you.

Pierre

The moment arms of the muscle are conmputed by dividing the derivative of the
lengthening of the muscle-tendon unit (LmtDot) by the joint velocity.
It is not completely unusual to get such a large value, but I don’t really know the literature for shoulder.
Sebastian

Hi Sebastian,

From what I know, this is the definition of the tendon excursion method.

Which joint rotation do I have to consider for the deltoid lever arm ? I tried different angles, but I’m not so sure about the results. When I try with a simple 2D model, it works well with a direct muscle (origin to insertion). Then, if I add a via-point muscle and make it move, I don’t know how to compute it.

Thank you.

Pierre

Hi,
well it just depends on the degree of freedom you are interested in. If its the lever arm with respect to glenohumeral flexion its GHRot.
Best regards,
Sebastian

Hi,is the paper “An et al.
K. N. An, K. Takahashi, T. P. Harrigan, and E. Y. Chao, “Determination of muscle orientations and moment arms.” J Biomech Eng, vol. 106, no. 3, pp. 280–282, Aug 1984”. online free available?

Best regards

Hi, not to my knowledge.
Best regards,
Sebastian

Hi, you wrote that the lever arm is calculated by the derivation of the muscle-length devided by the joint velocity. What’s about a muscle which is spanning over two joints, shall I add both velocities?

Best regards

Hi,
the lever arm is with respect to one degree of freedom, so only one joint at the time should be used.
Best regards,
Sebastian