Optimizing functionally graded tibial components for total knee replacements: a finite element analysis and multi-objective optimization study

Abstract

The optimal design of complex engineering systems requires tracing precise mathematical modeling of the system’s behavior as a function of a set of design variables to achieve the desired design. Despite the success of current tibial components of knee implants, the limited lifespan remains the main concern of these complex systems. The mismatch between the properties of engineered biomaterials and those of biological materials leads to inadequate bonding with bone and the stress-shielding effect. Exploiting a functionally graded material for the stem of the tibial component of knee implants is attractive because the properties can be designed to vary in a certain pattern, meeting the desired requirements at different regions of the knee joint system. Therefore, in this study, a Ti6Al4V/Hydroxyapatite functionally graded stem with a laminated structure underwent simulation-based multi-objective design optimization for a tibial component of the knee implant. Employing finite element analysis and response surface methodology, three material design variables (stem’s central diameter, gradient factor, and number of layers) were optimized for seven objective functions related to stress-shielding and micro-motion (including Maximum stress on the cancellous bone, maximum and mean stresses on predefined paths, the standard deviation of mean stress on paths, maximum and mean micro-motions at the bone-implant interface and the standard deviation of mean micro-motion). Then, the optimized functionally graded stem with 6 layers, a central diameter of 5.59 mm, and a gradient factor of 1.31, was compared with a Ti6Al4V stem for various responses. In stress analysis, the optimal stem demonstrated a 1.92% improvement in cancellous bone stress while it had no considerable influence on the maximum, mean, and standard deviation of stresses on paths. In micro-motion analysis, the maximum, mean, and standard deviation of mean micro-motion at the interface were enhanced by 24.31%, 39.53%, and 19.77%, respectively.