Parametric Design Optimisation of Proximal Humerus Plates Based on Finite Element Method

Abstract

Optimal treatment of proximal humerus fractures remains controversial. Locking plates offer theoretical advantages but are associated with complications in the clinic. This study aimed to perform parametric design optimisation of proximal humerus plates to enhance their mechanical performance. A finite element (FE) model was developed that simulated a two-part proximal humerus fracture that had been treated with a Spatial Subchondral Support (S3) plate and subjected to varus bending. The FE model was validated against in vitro biomechanical test results. The predicted load required to apply 5 mm cantilever varus bending was only 0.728% lower. The FE model was then used to conduct a parametric optimisation study to determine the orientations of inferomedial plate screws that would yield minimum fracture gap change (i.e. optimal stability). The feasible design space was automatically identified by imposing clinically relevant constraints, and the creation process of each FE model for the design optimisation was automated. Consequently, 538 FE models were generated, from which the obtained optimal model had 4.686% lower fracture gap change (0.156 mm) than that of the manufacturer's standard plate. Whereas its screws were oriented towards the inferomedial region and within the range of neck-shaft angle of a healthy subject. The methodology presented in this study promises future applications in patient-specific design optimisation of implants for other regions of the human body.

Keywords: Constrained optimisation; Finite element method; Parametric design; Proximal humerus fractures.

Figure 1

Assembly of humerus and plate in the FE model and selection of the head boundary condition surface and the shaft surface to apply varus displacement (red arrow).

Figure 2

Position-based zoning of head screws of the S3 proximal humerus plate.

Figure 3

Experimental setup for varus bending tests of the S3 plate, with a load (red arrow) applied on the humeral shaft in a cantilever fashion.

Figure 4

Visual representation of (a) fracture gap change calculation, (b) divergence angle θ_d and height angle θ_h of screws 4 and 5, along with screws’ midpoint (large black dot) and their midline (dashed grey line) and (c) the bone region (green) surrounding screw 10’s axis (black line) selected for stress calculations.

Figure 5

Overall workflow of the parametric optimisation study, starting from the selection of the design parameters and the object function, followed by the FE automation in Abaqus CAE (red), feasible region implementation in Geomagic Wrap (blue) and Mimics (green) and finally the creation of all 538 FE models and selection of the optimal model.

Figure 6

Load–displacement relationship predicted by the FE model compared with the in vitro biomechanical measurement data (mean ± SD).

Figure 7

von Mises stress (MPa) distribution across the plate (a), humeral head (b) and humeral shaft (c), in the standard FE model under 5 mm varus displacement, with their respective points of maximum stress shown with red arrows.

Figure 8

Contour plots showing the percentage changes in the fracture gap change (ΔG) for each of the 538 feasible height and divergence angle combinations, when subjected to 5 mm (a), 2 mm (b) and 10 mm (c) of varus displacement. Percentage changes for each loading condition are calculated with respect to the baseline values from its standard model.

Figure 9

Contour plots showing the percentage changes in the peak load (F₅, F₂, F₁₀) for each of the 538 feasible height and divergence angle combinations, when subjected to 5 mm (a), 2 mm (b) and 10 mm (c) of varus displacement. Percentage changes for each loading condition are calculated with respect to the baseline values from its standard model.

Figure 10

Contour plots showing the percentage changes in the mean von Mises stress in the bone region 5 mm around screw 10, for each of the 538 feasible height and divergence angle combinations, when subjected to 5 mm (a), 2 mm (b) and 10 mm (c) of varus displacement. Percentage changes for each loading condition are calculated with respect to the baseline values from its standard model.

Figure 11

Contour plots showing the percentage changes in the maximum von Mises stress in the bone region 5 mm around screw 10, for each of the 538 feasible height and divergence angle combinations, when subjected to 5 mm (a), 2 mm (b) and 10 mm (c) of varus displacement. Percentage changes for each loading condition are calculated with respect to the baseline values from its standard model.

Figure 12

Frontal (a) and sagittal (b) view of the superimposition of the manufacturer’s standard plate (blue, screws 4 and 5 highlighted in green) and the optimal plate design found by the FE-based optimisation (grey).

Figure 13

Contour plots showing the percentage changes in the fracture gap change (a), F₅ (b), mean (c) and maximum (d) von Mises stress in the bone region 5 mm around screw 10, for each of the 25 combinations of percentage lengths of screw 4 and 5. Percentage changes for each loading condition are calculated with respect to the baseline values from the 5 mm standard model.