Advancing Musculoskeletal Shoulder Modeling: Reflecting Glenohumeral Translation with Bony, Ligamentous, and Muscular Stability Constraints

Johanna Menze ^1,2* Eleonora Croci ^3,4 Michael Skipper Andersen ⁵ Hanspeter Hess ⁶ Morten Enemark Lund ⁷ Enrico De Pieri ^4,8 Matthias A. Zumstein ⁹ Stephen J. Ferguson ⁸ Andreas Marc Müller ³ Annegret Mündermann ^3,4 Kate Gerber ¹⁰

• ¹ School of Biomedical and Precision Engineering, University of Bern, Bern, Switzerland
• ² Institute for Biomechanics, ETH Zurich, Zurich, Switzerland
• ³ Department of Orthopedics and Traumatology, University Hospital of Basel, Basel, Basel-Stadt, Switzerland
• ⁴ Department of Biomedical Engineering, University of Basel, Basel, Switzerland
• ⁵ Center for Mathematical Modeling of Knee Osteoarthritis, Department of Materials and Production, Aalborg University, Aalborg, Denmark
• ⁶ School of Biomedical and Precision Engineering, Univesity of Bern, Bern, Switzerland
• ⁷ AnyBody Technology (Denmark), Aalborg, Denmark
• ⁸ Institute for Biomechanics, Department of Health Sciences and Technology, ETH Zurich, Zürich, Zürich, Switzerland
• ⁹ Department of Shoulder, Elbow and Sports Orthopedics, Sonnenhof Orthopaedic Centre KLG, Bern, Bern, Switzerland
• ¹⁰ School for Biomedical and Precision Engineering, University of Bern, Bern, Bern, Switzerland

Glenohumeral (GH) stability is a delicate interplay between bony congruence, muscle contraction, and ligamentous or capsular stability that can be disrupted by pathologies such as rotator cuff tears. We aimed to develop an advanced musculoskeletal shoulder model that incorporates subject-specific glenohumeral joint contact, active and passive muscle stability, and mechanical properties of ligaments to calculate GH translation using force-dependent kinematics (FDK). We hypothesized that inferior-superior GH translation computed using this model are consistent with in vivo GH translation measured by dynamic uniplanar fluoroscopy in healthy shoulders and in shoulders with partial or full RC tears, and that muscle and joint forces computed using the FDK shoulder model are higher than those of the default shoulder model.The AnyBody ShoulderArm model was extended to compute GH translation using FDK, considering joint constraints due to bone congruence and to labrum, ligament and muscle stabilization. The inferior-superior GH translations computed using the FDK model were compared with the translations measured using dynamic uniplanar fluoroscopy in healthy shoulders and shoulders with partial and full RC tears during 0 to 30° abduction-adduction cycles with 0 to 3 kg of handheld weight. The FDK model simulations revealed a decrease in median inferior-superior translations, from 2.8 to 1.8 mm with increasing handheld weight (0 to 3 kg) which was higher than those observed in fluoroscopic imaging (1.4 mm and 1.1 mm at 0 and 2 kg handheld weight). FDK model simulations in abduction with no additional handheld weight revealed greater variations in glenohumeral translations in shoulders with full RC tear. Compressive joint forces and muscle forces were higher in the FDK model than in the default shoulder model, particularly in the infraspinatus in the healthy model and in the deltoid in the full RC tear model. Distinct differences in muscle and joint forces between the FDK and the default shoulder models confirm that unconstrained translational degrees of freedom of the glenohumeral joint are important to advance knowledge of the biomechanical principles of the shoulder. Computed inferior-superior GH translations were greater than in vivo measured GH translations, suggesting that joint stability, particularly through muscle recruitment, could be underestimated.