Abstract
Introduction
Finite element (FE) models are commonly used to analyse the mechanical behaviour of the bone under different conditions. They provide detail information but they can be numerically expensive and this limits their use in cases where large or numerous simulations are required. On the other hand, 2D models show less computational cost but the precision of results depends on the approach used for the simplification. Three 2D approaches are commonly used: models without side-plate (WOSP)[1]; models with variable thickness side-plate and constant cortical thickness (SPCT)[2]; models with side-plate and variable cortical thickness (SPVT)[3]. The aim of this study is to determine which 2D approach reproduces best the FE results obtained with a 3D model involving hip stems.
Methods
The 2D models were generated by the intersection of the 3D model with the stem symmetry plane. Three approaches were considered to assure 3D-2D correspondence: 1) consider variable thickness for the cortical elements so that their transversal area moment of inertia equals the cross-sectional area moment of inertia from the 3D model (model WOSP); 2) include an additional side-plate with variable thickness to match the area moment of inertia from the 3D model, and consider constant thickness for the cortical bone elements (model SPCT); 3) include the side-plate but consider variable thickness for the cortical bone elements, derived from the 3D model (model SPVT). In all cases, the cancellous bone and stem elements had variable thickness computed so that their transversal area moment of inertia was equal to the cross-sectional area moment of inertia measured in the 3D model. This was done at different levels (Fig.1), providing a thickness distribution for the 2D elements. FE analyses were carried out for the static loading condition simulating stair climbing[4]. All materials were defined as linear isotropic and homogeneous. The post-operative situation where bone ingrowth is achieved was considered, resulting in bonded contact between the bone and the implant. The comparison between the 2D and 3D models was done based on three physical quantities: the Von Mises stresses (σVM); the strain energy density (U) and the interfacial shear stress (t) along the stem-bone interface.
Results
Fig.2 shows the σVM, U and t distributions for the 3D model and in the three 2D models. In general, the values for the three physical quantities were under estimated in all 2D models although the differences were small. However, the maximum values of σVM and U were larger in the 2D models than in the 3D model, whereas maximum t values were under estimated.
Discussion
It is possible to use 2D simplifications based on the stem symmetry plane to perform FE analyses when large number of simulations is needed or when the computational cost needs to be limited. In this way, a side-plate with variable thickness should be considered to obtain close results to the 3D model, while cortical bone thickness can be kept constant and cancellous bone thickness is varied.
For figures/tables, please contact authors directly.
