Development of a density-based topology optimization of homogenized lattice structures for individualized hip endoprostheses and validation using micro-FE

Abstract

Prosthetic implants, particularly hip endoprostheses, often lead to stress shielding because of a mismatch in compliance between the bone and the implant material, adversely affecting the implant's longevity and effectiveness. Therefore, this work aimed to demonstrate a computationally efficient method for density-based topology optimization of homogenized lattice structures in a patient-specific hip endoprosthesis. Thus, the root mean square error (RMSE) of the stress deviations between the physiological femur model and the optimized total hip arthroplasty (THA) model compared to an unoptimized-THA model could be reduced by 81 % and 66 % in Gruen zone (GZ) 6 and 7. However, the method relies on homogenized finite element (FE) models that only use a simplified representation of the microstructural geometry of the bone and implant. The topology-optimized hip endoprosthesis with graded lattice structures was synthesized using algorithmic design and analyzed in a virtual implanted state using micro-finite element (micro-FE) analysis to validate the optimization method. Homogenized FE and micro-FE models were compared based on averaged von Mises stresses in multiple regions of interest. A strong correlation (CCC > 0.97) was observed, indicating that optimizing homogenized lattice structures yields reliable outcomes. The graded implant was additively manufactured to ensure the topology-optimized result's feasibility.

Keywords: Additive manufacturing; Individualized hip endoprosthesis; Lattice structures; Micro-FE; Topology optimization.

Figure 1

Presentation of the study as a program flow chart with the individual phases: (a) selection of the CT scan and reconstruction of the physiological bone, (b) the density-based topology optimization of the hip endoprosthesis, (c) the synthesis results of the endoprosthesis with graded lattice structure for additive manufacturing, (d) the simulation method comparison of the physiological hFE model and physiological $\mu$FE model, and (e) the simulation method comparison of the optimized-THA hFE model and optimized-THA $\mu$FE model.

Figure 2

Design space of topology optimization: (a) representation of the radius of the strut as a function of relative density and unit cell volume, (b) only the inner region of the implant is topology optimized for stability reasons and filled with graded lattice structures.

Figure 3

The synthesis process of the implant with a graded lattice structure, starting from (a) the individualized endoprosthesis as a complete implant, (b) the definition of the design space with the inner area, which is optimized, and the outer edge area, which is filled with lattice structures of a constant density. Subsequently, the volumes are filled with unit cell boxes, (c) as a grid of unit cells of the outer edge area and (d) as a cube representation of unit cells of the inner area, and in (e)–(f) the unit cells are filled with struts as well as thickened. In the last step (g), the volumes are combined, and the topology-optimized implant is finalized.

Figure 4

Stresses in the different femur models: (a) physiological hFE model, (b) unoptimized-THA hFE model (with implant bed and corresponding GZ), (c) optimized-THA hFE model (with implant bed).

Figure 5

Boxplot representation for the von Mises stresses of the physiological hFE model, unoptimized-THA hFE model, optimized-THA hFE model in the GZ (a) 1, (b) 3, (c) 6, (d) 7.

Figure 6

Stress deviations in the postoperative condition between (a) ${\mathrm{\Delta }}_{\text{THA-hFE}}$ and (b) ${\mathrm{\Delta }}_{\text{optimized-THA-hFE}}$ with corresponding RMSE values of the respective GZ.

Figure 7

The result of the endoprosthesis with graded lattice structures in five section views as (a) an additive manufactured model, (b) CAD model, (c) density distribution of the topology optimization, and (d) histogram of the relative densities.

Figure 8

Verification of the additive manufacturing quality in the lower part of the endoprosthesis as (a) reconstruction of the microCT scan, (b) nominal-actual comparison between real part (gray) and CAD model (color), and (c) an optical microscope image to evaluate the shape fidelity of the inner struts.

Figure 9

Results of the different simulation methods, (a) physiological hFEA, (b) physiological $\mu$FEA, (c) optimized-THA hFEA, (d) optimized-THA $\mu$FEA.

Figure 10

Correlation analysis and calculation of Lin’s CCC to validate simulation results in (a) physiological hFEA and $\mu$FEA and in (b) with optimized-THA hFEA and $\mu$FEA.