MATHEMATICAL OPTIMIZATION OF ELASTIC PROPERTIES - APPLICATION TO CEMENTLESS HIP STEM DESIGN

The designer of a cementless hip stem in total hip replacement must fi nd a balance between two conflicting demands. On the one hand, a stiff stem shields the surrounding bone from mechanical loading (stress shi elding), which may lead to bone loss, particularly around the proximal part of the stem. Reducing the stem stiffness decreases the amount of stress shielding and hence the amount of bone loss. However, this mea sure inevitably promotes higher proximal interface stresses and thereb y increases the risk of proximal interface failure. The designer's tas k therefore is to optimize the stem stiffness in order to find the bes t compromise in the conflict. Yet, a better compromise might be found when the stem material was nonhomogeneous, in other words when an arbi trary distribution of the elastic properties inside the stern was allo wed. The number of conceivable designs would increase enormously, maki ng the designer's task almost impossible. In the present paper, we dev elop a numerical design optimization method to determine the optimal s tiffness characteristics for a hip stern. A finite element program is coupled with a numerical optimization method, thus producing a design optimization scheme. The scheme minimizes the probability for interfac e failure while limiting the amount of bone loss, by adapting the para meters describing the nonhomogeneous elastic modulus distribution. As an example, a simplified model of a hip stern is made, whose modulus d istribution is optimized. Assuming equal long-term bone loss, the maxi mum interface stress can be reduced by over 50 percent when compared t o a homogeneous flexible stem, thus demonstrating the value of the new approach.