Coupe glénoïdienne, latéralisation effective et glène fonctionnelle : application aux glènes B2 dans un espace courbe contraint (Glenoid cut, effective lateralization and functional glenoid: application to B2 glenoids in a constrained curved space)

Glenoid cut, effective lateralization and functional glenoid:application to B2 glenoids in a constrained curved space Total shoulder arthroplasty is still most often planned within an implicit Euclidean framework: neutral CT scans, reference planes, target version and inclination, and millimetres of “lateralization” defined at the implant level. In advanced B2 glenoids, this paradigm reaches its limits: anatomically acceptable reconstructions can coexist with uncertain functional recentering, apprehension and eccentric trajectories of the humeral head. Within a broader view of the shoulder as a constrained curved space, the glenoid is no longer treated as a flat support to be restored anatomically, but as a curved functional surface on which the head rolls and glides under capsulo-ligamentous and subacromial constraints. The instantaneous center of rotation (ICR) is mobile and traces a small trajectory on this surface; in a well-centered shoulder, it remains confined within an asymmetric “drop-shaped” functional area P₀–P₄. This paper proposes:– a shift from “lateralization as a free implant parameter” to an effective lateralization L(C) induced by the glenoid cut C, defined as a geometric consequence of the prosthetic glenoid surface S_proth^C;– the notion of a functional glenoid in B2 morphology, where the quality of recentering is assessed through the behaviour of the ICR trajectory γ_C(t) within a droplet-shaped functional area rather than through isolated angles or distances;– a recentering functional J(C) combining the time spent by the ICR in a central target region (P₀–P₂) and the proximity to glenoid edges in higher-demand positions (P₃–P₄), intended as a bridge between glenoid cut planning and the clinical experience of “well-centered” or “apprehensive” prosthetic shoulders;– a speculative perspective on asymmetric “droplet glenoids”, whose articular surface would be derived from the functional area P₀–P₄ instead of from an abstract anatomical average. As with the clinical algorithm for shoulder stiffness in a constrained curved space, this work is meant as a conceptual and methodological framework rather than a validated protocol. No clinical or experimental dataset is provided at this stage. The proposed quantities (γ_C(t), J(C), L(C)) are intended to structure future studies (dynamic imaging, IMU-based tracking, retrospective series of B2 arthroplasties assisted by AI) and to offer a more functionally realistic language than the purely Euclidean model for decision-making between anatomic and reverse configurations in B2 glenoids.