A Three-Dimensional Model for Shape Optimization of Hip Prostheses Using a Multi-Criteria Formulation

1. Abstract In this work a multi-criteria optimization model is developed to obtain the optimal geometry of the femoral component of a hip prostheses. The objective function minimizes both the relative tangential displacement and the contact normal stress. For cementless stems, these two factors are relevant for the prostheses stability and therefore for the implant success. In fact, “small” relative displacements on the interface and “small” contact stresses are required for the biologic fixation of bone to the porous surface of the stem. Furthermore, “large” contact stresses and “large” relative displacements are causes of thigh pain. Numerical tests performed on different stems show that the relative displacement and contact stresses are related with the stem geometry. The three-dimensional optimization procedure developed in this work allows us to characterize the stem shape that minimizes the displacement and stresses individually, or both simultaneously using a multi-criteria approach. Design variables characterize successive stem sections, and are subjected to linear geometric constraints in order to obtain clinically admissible geometries. Multiple loads are also considered to incorporate several daily life activities. The set bone-stem is considered a structure in equilibrium with contact condition on interface. The contact formulation allows us to analyze different lengths of porous coating. Numerical examples are presented for a three-dimensional model of a hip stem. Results give us good indications about the relation between shape, porous coating, interface relative displacement and contact stress.