Torus obstacle method as a wrapping approach of the deltoid muscle group for humeral abduction in musculoskeletal simulation

Musculoskeletal models of the shoulder complex are valuable research aids to investigate tears of the supraspinatus and the resulting mechanical impact during abduction of the humerus. One of the major contributors to this motion is the deltoid muscle group and for this, an accurate modeling of the lines of action is indispensable. The aim of this work was to utilize a torus obstacle wrapping approach for the deltoids of an existing shoulder model and assess the feasibility of the approach during humeral abduction. The shoulder model from the AnyBody™ modeling system was used as a platform. The size of the tori is based on a magnetic resonance imaging (MRI) approach and several kinematic couplings are implemented to determine the trajectories of the tori during abduction. To assess the model behavior, the moment arms of the virtual muscle elements and the resultant glenohumeral joint reaction force (GHJF) were compared with reference data from the literature during abduction of the humerus in the range 20°–120°. The root mean square error for the anterior, lateral and posterior part between the simulated muscle elements and reference data from the literature was 3.9, 1.7 and 5.8 mm, respectively. The largest deviation occurred on the outer elements of the muscle groups, with 12.6, 10.4 and 20.5 mm, respectively. During abduction, there is no overlapping of the muscle elements and these are in continuous contact with the torus obstacles, thus enabling a continuous force transmission. This results in a rising trend of the resultant GHJF. The torus obstacle approach as a wrapping method for the deltoid muscles provides a guided muscle pathing by simultaneously approximating the curvature of the deltoid muscle. The results from the comparison of the simulated moment arms and the resultant GHJF are in accordance with those in the literature in the range 20°–120° of abduction. Although this study shows the strength of the torus obstacle as a wrapping approach, the method of fitting the tori according to MRI data was not suitable. A cadaver study is recommended to better validate and mathematically describe the torus approach.