Shape Optimization of Cementless Hip Prosthesis Souptick Chanda, Sanjay Gupta*, D.K. Pratihar Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721 302, West Bengal, India. The shape and geometry of femoral implant influence peri-prosthetic bone remodelling and implant-bone interface stresses, which are primary causes of aseptic loosening in cementless THA. Development of a shape optimization scheme is necessary to achieve a trade-off between these two conflicting objectives. The objective of this study was to develop a novel multi-objective shape optimization scheme for cementless femoral implant by integrating finite element (FE) analysis and a multi-objective Genetic Algorithm (GA). INTRODUCTION MATERIALS AND METHOD RESULTS AND DISCUSSION The present optimization scheme comprised of a parametric implant model generator, a script for virtual implantation, an automatic mesh generator, an FE analysis script and finally an optimization controller. A total of eighteen geometric parameters was introduced as design variables (Fig. 1). All the design variables had lower and upper bounds and geometric constraints in order to achieve clinically admissible shapes [1]. The initial design of the stem was similar to a generic design of a collarless TriLock (DePuy) prosthesis having stem-length 113 mm (Fig. 2). The generation of three-dimensional (3-D) Finite Element (FE) models of the intact and implanted femurs and allocation of bone material properties were based on CT-scan data of a 31 year-old male patient (Fig. 3). The results predicted by the two objective functions were found to be contradictory; a reduction in the proximal bone resorption was accompanied by a greater chance of interface failure (Fig. 5). The resorbed proximal BMF was found to be between 23-27% for the Optimal Stem Geometries (OSGs) as compared to ~39% for the initial design (Fig. 5). The three OSGs with nature of key sections are shown in Fig. 6. The OSGs demonstrated better load transfer proximally with less chances of distal debonding (Fig. 7). Overall, an average reduction of ~68% in peak FL value was observed for OSGs compared to that for the initial stem (Fig. 8). The adaptive bone remodelling was also found to be less for the OSGs as compared to the initial stem (Fig. 9) and, further with remodelling, the chances of interface debonding increased only marginally. Figure 1. Parameterization and design variables. OSG-1 OSG-2 OSG-3 Figure 6. Three OSGs with nature of four key transverse sections. OSG-1 OSG-2 OSG-3 initial P A P: Posterior A: Anterior Figure 2. Initial design (TriLock). Figure 3. FE model of implanted femur. A multi-objective genetic algorithm, namely NSGA-II was used as the optimization tool. The optimization controller (NSGA-II) initialized new values for the design variables in order to generate new implant geometry. Thereafter, the new implant model was virtually implanted into the resected femur model generated from the CT scan dataset, following standard surgical guidelines. The STL file of implanted femur was meshed using an automatic mesh generator and thereafter, the FE model was analyzed in ANSYS to calculate objective function values. These values of the objective functions were fed back to the optimization controller for strategizing new set of design variables and the cycle was repeated (Fig. 4). Optimization scheme: Optimization Module (NSGA-II) Optimized implant geometry(s) Objective Function Evaluation FE Analysis (ANSYS) Auto-Meshing Implantation Implant Modelling CT Image Processor CT-scan data of femur 3-D femur model Implanted 3-D data FE mesh Results f1 f2 New design variables 3-D implant Generation not exceeded Material Property Evaluation Figure 5. Pareto-optimal front with three OSGs. Figure 7. Distribution of FL values: initial design vs three OSGs. OSG-1 OSG-2 OSG-3 initial Figure 4. Flowchart of the optimization framework The objective function, considered in the study to assess the effect of implant-induced bone resorption, was expressed in terms of percentage resorption of Bone Mass Fraction (BMF) in immediate post-operative case [2]. Since bone resorption predominantly occurs in the proximal part of the femur [3], the calculations for BMF were confined to the bone elements located in the proximal femur (intact and implanted) upto the lesser trochanter. The calculation for the BMF was based on the adaptive bone remodelling theory [4]. Formulation of the other objective function related to interface stresses was based on the multi-axial failure theory known as Hoffman’s criterion [5]. This theory relates the interface stresses with the strength of the bone element adjacent to the interface and ascertains the area with likely chances of debonding by evaluating local failure values (FL)[2,6]. OSG-1 OSG-2 OSG-3 initial Objective function formulation: Figure 8. Probability plot of FL values: initial design vs OSGs. Figure 9. Adaptive bone density changes : initial vs OSGs. CONCLUSION A novel 3-D multi-objective shape optimization scheme has been proposed for cementless femoral implant design. The study deals with most number of design parameters (18) in an attempt to flexibly characterize the implant shape. It was evident from the results that the objective functions were contradictory in nature. The optimal implant designs reduced the chances of interface debonding by evolving changes in geometric profile and yielded favourable proximal load transfer, thereby inducing less proximal bone resorption. The adaptive bone remodelling was found to be minimal for the optimally designed implants and, further with remodelling, the chances of interface debonding increased only marginally. It appears therefore, that the GA is an effective shape optimization tool and the proposed method can serve as a major step towards customized implant design. Minimize Objective 1 (f1) Minimize Objective 2 (f2) subject to a2 – a1 ≥ 0, b2 – b1 ≥ 0, a4 – a2 ≥ 0, b3 – b2 ≥ 0, a6 –a4 ≥ 0, b4 – b3 ≥ 0,a3 – a2 – 4.5 ≥ 0, a5 – a3 – 4.5 ≥ 0, a5 – a3 – 7.0 ≤ 0 and a2 + a5 – 2.0 × a3 ≥ 0 Implant material selected: Ti-alloy (E=110 GPa) REFERENCES [1] Ruben et al. 2007, Struct. Multidisc. Optim., 34:261-75; [2] Kuiper 1993, PhD-thesis, Nijmegen; [3] Huiskes et al. 1992, Clin. Orthop. Relat. Res., 274:124-34; [4] Weinans et al. 1993, J. Orthop. Res., 11:500-13; [5] Hoffman 1967, J. Compos. Mater., 1:200-6; [6] Khanoki and Passini 2012, J. Biomech. Eng., 134:031004. ACKNOWLEDGEMENT *Email (Sanjay Gupta, IIT Kharagpur): sangupta@mech.iitkgp.ernet.in The authors wish to thank University of Southampton, UK, for providing the CT-scan dataset of the femur.