Surrogate-based positioning optimization of hip prostheses for minimal stress shielding

The stress shielding phenomenon causes undesirable changes in stress distribution in the bones in which implants are implanted. This phenomenon leads to a gradual decrease in bone density in the vicinity of the implant and ultimately loosening. To improve the endurance of the prosthesis and postpone the revision surgery the prosthesis should be designed and positioned in such a way that the post-implant stress distribution within the bones is as close to the natural distribution as possible.

We formulate the problem of achieving a near-normal stress distribution as a constrained optimization problem in which the difference between pre- and post-implant stress distributions constitutes the loss function and five positional and dimensional parameters, including Femoral Anteversion, Neck Shaft Angle, Femoral Head Offset, Cup Version, and Cup Inclination comprise the set of design variables. Finite Elements (FE) analysis is used to obtain the stress distribution in bones before and after the implantation. To create a FE model, first a three-dimensional model of the patient's hip is created using CT images. The model is then subjected to the loads obtained from the patient's gait analysis, and the Stress Shielding Index (SSI) is calculated at critical points of the bones before and after the implantation. The difference between pre- and post-implant SSI values defines the cost function. To reduce the computational cost of numerous cost function evaluations a surrogate model (a 5 × 1 MLP neural network) is employed to predict the value of the cost function. Design Of Experiments (DOE) is used to sample the hyperspace of the design variables and generate training, test and validation data. The optimization problem is solved using Genetic Algorithms and the results are compared with the results of the best set of initial samples.

Results from the proposed approach show a significant reduction in the difference between pre- and post-implant stress distributions and a 12 % reduction in the Stress Shielding Index.