Muscle moment-arms: a key element in muscle-force estimation

Abstract

A clear and rigorous definition of muscle moment-arms in the context of musculoskeletal systems modelling is presented, using classical mechanics and screw theory. The definition provides an alternative to the tendon excursion method, which can lead to incorrect moment-arms if used inappropriately due to its dependency on the choice of joint coordinates. The definition of moment-arms, and the presented construction method, apply to musculoskeletal models in which the bones are modelled as rigid bodies, the joints are modelled as ideal mechanical joints and the muscles are modelled as massless, frictionless cables wrapping over the bony protrusions, approximated using geometric surfaces. In this context, the definition is independent of any coordinate choice. It is then used to solve a muscle-force estimation problem for a simple 2D conceptual model and compared with an incorrect application of the tendon excursion method. The relative errors between the two solutions vary between 0% and 100%.

Effects of glenoid inclination and acromion index on humeral head translation and glenoid articular cartilage strain

“…The undetermined problem of muscle force coordination was solved using an inverse dynamics approach followed by a nullspace optimization. 11,[18][19][20]36 A glenohumeral joint stability criterion based on a cost function was included to maintain the joint force away from the subluxation limit. The arm weight was estimated at 37.5 N (5% of volunteer's weight), applied at 320 mm from the joint center along the humeral axis.…”

Improving anterior deltoid activity in a musculoskeletal shoulder model – an analysis of the torque-feasible space at the sternoclavicular joint

“…The vectort a is the torques around the inertial frame axes centred at each of the three joints. The matrix W 0 ðkÞ is the generalised moment-arm matrix resulting from the projection of the moment-arms WðkÞ into the generalised coordinate space (Aeberhard et al 2009;Ingram et al 2013aIngram et al , 2013b. The projection matrix P 0 ðkÞ is defined as the partial derivative of the rotational velocity vectors with respect to the coordinate velocities (Aeberhard et al 2009).…”

“…The scapulo -thoracic contact is modelled by defining holonomic constraints between the two end-points on the scapula's medial border (TS and AI) and two ellipsoids approximating the contact surface (Ingram et al 2013a(Ingram et al , 2013b. The model has seven degrees of freedom (DOF ¼ 7).…”

“…The muscle forces are presented for quasi-static (T ¼ 20 s) abduction in the scapular plane. The kinematics of this motion were constructed using the methods from Ingram et al (2013a, 2013b), El Habachi et al (2014. The computation was done for 100 points evenly distributed between 0 8 and 140 8 abduction.…”

“…The projection matrix P 0 ðkÞ is defined as the partial derivative of the rotational velocity vectors with respect to the coordinate velocities (Aeberhard et al 2009). The tendon excursion method computes the generalised moment-arms directly (Ingram et al 2013a(Ingram et al , 2013b. Muscles can only pull and have a maximum isometric strengthf max .…”