Validation of subject-specific automated p-FE analysis of the proximal femur
Introduction
Accurate methods for predicting and monitoring in vivo bone strength are of major importance in clinical applications. Subject-specific finite element (FE) modeling is becoming a commonly used tool for the numerical analysis of the biomechanical response of human bones. The use of subject-specific FE models in clinical practice requires a high level of automation and an accurate evaluation of the numerical errors. Geometry and material parameters are two key components when addressing subject-specific FE models of bones and both can be estimated from quantitative CT (QCT) data. Generation of a FE model requires extensive processing of QCT data. Because CT-based simulations are to be used in vivo, the surrounding of the bone may influence the model generation and the influence on the results must be carefully examined. For example, Keyak and Falkinstein (2003) examined whether FE models generated from CT scans in situ and in vitro yield comparable predictions of proximal femoral fracture load. Their conclusion is that substantially different predicted fracture loads are noticed.
The influence of material assignment strategy to FE models was investigated e.g. in Helgason et al., 2008, Schileo et al., 2007, Taddei et al., 2007, Peng et al., 2006. In Taddei et al. (2007) two methods were compared to experimental measurements, the first used a classical strategy of calculating Young's modulus from an average element density, the second calculated the average of Young's modulus that was directly derived from each CT slice. The results showed that the two strategies produced two distributions of material properties that were statistically different. Strain predictions showed that the second method is in a better agreement with the experimental results. In Helgason et al. (2008) a comparison was made between two different methods for assigning material properties to FE models. A modified material assignment strategy allowing for spatial variation of Young's modulus within the elements was presented and compared to a more conventional strategy, whereby constant material properties are assigned to each element. The first method performs better when strain prediction is of interest. Limited number of studies have been dedicated to systematic validation of subject-specific FE models of femoral bones by comparison to experiments. A good accuracy in the prediction of strain levels was reported in recent works by Helgason et al. (2008) and Bessho et al. (2007) (displacements were not reported). Conventional h-version FE methods (h-FEM) were used in most FE studies (see e.g. Keyak et al., 1990, Cody et al., 1999, Schileo et al., 2007) with inhomogeneous distribution of material properties obtained by assigning constant distinct values to different elements—this caused the material properties to become mesh dependent (Taddei et al., 2007). Furthermore, same relation between Young's modulus and bone density is considered both in the trabecular and cortical subregions although many studies report on different relations in the cortical and trabecular regions (Carter and Hayes, 1977, Cody et al., 2000, Wirtz et al., 2000).
In Yosibash et al. (2007a) a p-FE method was suggested, and an inhomogeneous Young's modulus was represented by smooth functions, independent of the mesh, having different relations in the cortical and trabecular subregions. Herein, we further validate and improve the method presented in Yosibash et al. (2007a) and examine it under different CT scan conditions. The material assignment strategy is reinvestigated to evaluate the numerical errors inherent in it. In Yosibash et al. (2007a) two experiments on fresh frozen human femurs (30 year old male and 21 year old female) were conducted and observations were used for the validation of the FE model. Herein, a fresh frozen femur of a 54 year old female is scanned by two separate QCT scans. In the first (wet CT) the bone was immersed in water to simulate in vivo condition and to reduce beam hardening effects. In the second scan (dry CT) the bone was exposed to air. Thereafter the proximal femur was loaded (in vitro experiments) by a quasi-static force of 1000 N. The data from the two QCT scans were used to determine the geometrical representation of the femur and determination of its material properties, followed by generation of p-FE models. These were subjected to boundary conditions so to mimic the experiment conditions. We compared displacements and strains computed using the wet CT model with the ones obtained from the dry CT model. Young's modulus representation strategy was reinvestigated by two different methods, directly extracted from the CT data using weighted point average (WPA) and by several continuous spatial functions describing the inhomogeneous bone density with monotonic increase in polynomial degree. Experimental observations were used to validate FE results.
Section snippets
Methods
A fresh frozen femur of a 54 year old female donor was deep-frozen shortly after death. The bone was checked to be free of skeletal diseases as described in Yosibash et al. (2007a). After defrosting, soft tissue was removed from the bone and was degreased with ethanol. The proximal femur was cut and fixed concentric into a cylindrical sleeve by six bolts and a PMMA substrate and scanned in two different environments. QCT scans were performed using a Phillips Brilliance 16 CT (Eindhoven,
FE model verification—different CT conditions
The geometrical representation and Young's modulus assignment are the main keys for constructing a FE model. The boundary detection algorithm was found to be insensitive to the wet or dry CT scans and produce almost the same geometry of the bone. Fig. 6 presents the boundary tracing results for the two different CT scans and demonstrate its accuracy at several slices. The main advantage of using is its generality. Calibration phantoms enable same material evaluation for the wet and dry
Discussion
This study was preformed to validate and improve the methods presented in Yosibash et al. (2007a) with the aim of generating reliable FE models of the proximal femur using subject specific QCT data. We denote by reliable subject specific FE models these which satisfy three conditions: (a) They were verified, i.e. the numerical errors are under control. This means that the relative error in energy norm of the overall model is guaranteed to be small and the data of interest (strains and
Conflict of interest statement
None of the authors have any conflict of interest to declare that could bias the presented work.
Acknowledgment
The authors thank Dr. Arie Bussiba for his assistance in the experiments.
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