The shoulder is one of the most mobile and complex joints in the body. The shoulder bones provide few constraints on motion;​ therefore, stability must be maintained by muscles and ligaments. The mobility of the shoulder allows great versatility, but also makes it prone to injury. A better understanding of the role of the muscles in shoulder mechanics is needed to improve the treatment of shoulder injuries and pathologies. Computational models provide a valuable framework for investigating complicated mechanical systems and characterizing joint mechanics. Previous shoulder models have used simple representations of muscle architecture and geometry that may not capture the details of muscle mechanics needed to fully understand muscle function. The purpose of this dissertation was to create a detailed 3D finite element model of the deltoid and the four rotator cuff muscles. This model was then used to characterize the muscle contributions to joint motion and stability.

The model was constructed from magnetic resonance images of a healthy shoulder. From the images, the 3D geometry of the muscles, tendons and bones was acquired. A finite element mesh was constructed using hexahedral elements. The 3D trajectories of the muscle fibers were approximated and mapped onto the finite element mesh. A hyperelastic, transversely-isotropic material model was used to represent the nonlinear stress-strain relationship of muscle. Bone motions were prescribed and the resulting muscle deformations were simulated using Nike3D, an implicit finite element solver.

To characterize muscle contributions to joint motion, we calculated moment arms for each modeled muscle fiber. The moment arm indicates the mechanical advantage of activating a fiber and its potential contribution to the resulting joint moment. We found that 3D finite element models predicted substantial variability in moment arms across fibers within each muscle, which is not generally represented in line segment models. We also discovered that for muscles with large attachment regions, such as deltoid, the line segment models under constrained the muscle paths in some cases. As a result, line segment based moment arms changed more with joint rotation than moment arms predicted by the 3D models.

Glenohumeral instability is a common clinical problem which is difficult to treat. To better understand the mechanics of instability we used the model to investigate the role of the muscles in stabilizing the glenohumeral joint. This was done by simulating an imposed 1 cm translational displacement of the humeral head in the anterior-posterior and superior-inferior directions relative to the glenoid. We found that at the neutral position, the anterior deltoid provides the largest potential to resist anterior translation. This counters the conclusions of conventional line segment based models, and is the result of compression generated by muscle contact, which must be considered when characterizing the ability of muscle to resist joint translation.

This dissertation provides a new computational method for analyzing shoulder mechanics, and demonstrates the importance of 3D analysis when investigating the complex function of shoulder muscles.