An algorithm to allow humerus translation in the indeterminate problem of shoulder abduction

The shoulder is one of the most complex joints of the human body, mainly because of its large range of motion, but also because of its active muscular stabilisation. Actually, the numerous stabilizing muscles and degrees of freedom yield indeterminate biomechanical models. To solve this indeterminate, most models use reverse dynamics with a simplified ball-socket joint, preventing therefore the natural humerus translation. In this paper, an algorithm was specifically developed to solve the indeterminate problem by a feedback control of muscle activation, allowing the natural humerus translation. Abduction was considered in the scapular plane, accounting for the three deltoid parts and the rotator cuff muscles. The major aim of this study was to validate the numerical algorithm, which was here restricted to two-dimensions in order to compare the numerical solution to a known algebraic one. This comparison gave a relative error below 0.1%. The joint reaction force was comparable to other models and the humerus translation was in agreement with in vivo or in vitro studies.