Translational stiffness of the replaced shoulder joint

Results after a total shoulder arthroplasty in rheumatoid patients are poor, indicated by loosening of especially the glenoid component, bad joint functionality and the possibility of a joint dislocation. The failure mechanisms behind this are multiple, including patient, surgical and design factors. These results must be improved. At present, the optimal geometrical prosthesis component design, focused on joint conformity and constraint, still has to be investigated.

Proper understanding of the effect of geometrical design parameters on the theoretical relationship between joint translations and joint forces may contribute to improved designs. The main objective of this study is to theoretically describe this relationship and to investigate the joint translational stiffness, which can be used to investigate the effect of design parameters on joint motion. Joint translational stiffness is the gradient of the subluxation force with respect to the humeral head displacement.

For this static analysis a potential field is introduced, as the result of a joint compressive force (muscle forces) and a subluxation force (external forces). The positive and negative stiffness during articulation inside and subluxation outside the glenoid cavity, lead to stable and unstable equilibrium joint positions, respectively. A most lateral position of the humeral head centre coincides with a zero subluxation force; at this position the humerus is dislocated and a restoring force is needed to relocate the humeral head.

Joint conformity and compression force influence the joint translational stiffness during articulation inside the glenoid cavity, whereas during articulating outside the glenoid cavity this is influenced by the joint compression force and humeral radius of curvature. The glenoid radius of curvature influences the contact point and, in combination with the glenoid superior–inferior chord length, it also influences the constraintness angle, which influences the maximum allowable subluxation load to prevent a joint dislocation. This constraintness angle together with the joint conformity also influences maximum joint translations before articulation outside the glenoid cavity. Furthermore, the sign of the joint translational stiffness determines the stability of shoulder motion, which is stable and unstable if this stiffness is positive and negative, respectively.