Multiscale Design and Multiobjective Optimization of Orthopaedic Cellular Hip Implants

Abstract

A multiscale design and multiobjective optimization procedure is developed to design a new type of graded cellular hip implant. We assume that the prosthesis design domain is occupied by a unit cell representing the building block of the implant. An optimization strategy seeks the best geometric parameters of the unit cell to minimize bone resorption and interface failure, two conflicting objective functions. Using the asymptotic homogenization method, the microstructure of the implant is replaced by a homogeneous medium with an effective constitutive tensor. This tensor is used to construct the stiffness matrix for the finite element modeling (FEM) solver that calculates the value of each objective function at each iteration. As an example, a 2D finite element model of a left implanted femur is developed. The relative density of the lattice material is the variable of the multiobjective optimization, which is solved through the non-dominated sorting genetic algorithm II (NSGA-II). The set of optimum relative density distributions is determined to minimize concurrently interface stress distribution and bone loss mass. The results show that the amount of bone resorption and the maximum value of interface stress can be reduced by over 70% and 50%, respectively, when compared to current fully dense titanium stem.