Impact of reverse shoulder arthroplasty design and patient shoulder size on moment arms and muscle fiber lengths in shoulder abductors

Background: Reverse shoulder arthroplasty (RSA) increases the moment arm of the deltoid; however, there is limited knowledge on the accompanying changes in muscle architecture that play a role in muscle force production. The purpose of this study was to use a geo-metric shoulder model to evaluate the anterior deltoid, middle deltoid, and supraspinatus regarding (1) the differences in moment arms and muscle-tendon lengths in small, medium, and large native shoulders and (2) the impact of 3 RSA designs on moment arms, muscle fiber lengths, and force-length (F-L) curves. Methods: A geometric model of the native glenohumeral joint was developed, validated, and adjusted to represent small, medium, and large shoulders. Moment arms, muscle-tendon lengths, and normalized muscle fiber lengths were assessed for the supraspinatus, anterior deltoid, and middle deltoid from 0 degrees to 90 degrees of abduction. RSA designs were modeled and virtually implanted, including a lateralized glenosphere with an inlay 135 degrees humeral component (lateral glenoid-medial humerus [LGMH]), a medialized glenosphere with an onlay 145 degrees humeral component (medial glenoid-lateral humerus [MGLH]), and a medialized glenosphere with an inlay 155 degrees humeral component (medial glenoid-medial humerus [MGMH]). Descriptive statistics were used to compare moment arms and normalized mus-cle fiber lengths. Results: As shoulder size increased, the moment arms and muscle-tendon lengths for the anterior deltoid, middle deltoid, and supra-spinatus increased. All RSA designs achieved greater moment arms for the anterior and middle deltoid, with the MGLH design achieving the largest increase. The resting normalized muscle fiber length of the anterior and middle deltoid was substantially increased in the MGLH (1.29) and MGMH (1.24) designs, shifting the operating ranges of these muscles to the descending portions of their F-L curves, whereas the LGMH design maintained a resting deltoid fiber length (1.14) and operating range similar to the native shoulder. All RSA designs demonstrated a decrease in the native supraspinatus moment arm in early abduction, with the largest decrease in the MGLH design (-59%) and minimal decrease in the LGMH design (-14%). The supraspinatus operated on the ascending limb of its F-L curve in the native shoulder and remained on this portion of the F-L curve for all RSA designs. Conclusion: Although the MGLH design maximizes the abduction moment arm for the anterior and middle deltoid, overlengthening of the muscle may compromise deltoid muscle force production by forcing the muscle to operate on the descending portion of its F-L curve. In contrast, the LGMH design increases the abduction moment arm for the anterior and middle deltoid more modestly while allowing the muscle to operate near the plateau of its F-L curve and maximizing its force-producing potential.