Some factors that affect the comparison between isotropic and orthotropic inhomogeneous finite element material models of femur

https://doi.org/10.1016/j.medengphy.2010.01.004Get rights and content

Abstract

The objective of this study was to investigate whether there were significant differences between isotropic and orthotropic inhomogeneous material models of femur by taking into account the effects of some factors, such as comparative parameters, loading conditions and mesh refinement. Three femoral meshes of increasing refinement levels were assigned isotropic and orthotropic material properties. Then six different loading conditions were separately applied to each material model. Based on the analysis results of Von Mises stress and nodal displacement, eight regions of interest in femur were selected to compare the differences between isotropic and orthotropic material models. The results showed that marked differences for Von Mises stress (maximum 13.25%) and nodal displacement (maximum 15.04%) appeared in the regions where the maximum absolute Von Mises stress and the maximum absolute nodal displacement did not occur. It was observed that the comparison results were significantly different under different loading cases. The mesh refinement had a great influence on the comparison results, especially for the Von Mises stresses in the regions of the femoral neck. Therefore, it can be concluded that the differences between two material property assignments are significant, at least in some local regions.

Introduction

The finite element (FE) method has been widely used to investigate the mechanical behavior of bone tissue [1]. Accurate FE simulation depends on not only the exact model obtained via three-dimensional reconstruction, but also the realistic material properties assigned to the model. It is well known that CT images can provide accurate information on bone geometry based on the high contrast between the bone tissue and the surrounding soft tissue [2], [3]. Once the FE mesh models are generated from the CT data, it is essential to define material properties for the models. Fortunately, material properties can also be obtained from the CT data because the relationships between Hounsfield unit (HU), bone density and mechanical property have been established [4], [5], [6], [7], [8], [9]. Thus, the process of assigning material properties into FE mesh models can be completed using appropriate algorithms.

Most studies done in this area were based on the assumption that bone material was isotropic and only inhomogeneous distribution of material properties was taken into account. The CT data (related to the tissue density), which can be regarded as a three-dimensional scalar field sampled over a regular grid, and the FE mesh, which is generated from the same CT data, are perfectly aligned in space. The only problem, then, is how to properly map the material properties that are derived from the CT dataset into the FE mesh. Many approaches have been proposed to perform this task and the algorithms have been improved [10], [11], [12], [13], [14]. However, bone material is factually considered as being anisotropic rather than isotropic [15]. Therefore, the inhomogeneous isotropic material models, in theory, are inaccurate because the isotropic material properties cannot reflect the actual structure and mechanical behavior of bone.

Some researchers tried to develop orthotropic material models that need nine independent elastic constants and the principal orientations of orthotropy, to realistically simulate bone material properties [16]. When expressions of orthotropic elastic constants are introduced in many studies, the most crucial problem is how to define the orientations of orthotropy based on the anatomic structure of bone. Some invasive methods that implemented cutting or grinding schemes were used to manually assign the principal axes of orthotropy to FE models [17], [18].

Recently, comparisons were made between isotropic and orthotropic material models. After comparing isotropic material property assignment with orthotropic assignment on femoral FE models, it was concluded that the differences were small and bone was a weak orthotropic material [19]. Nevertheless, the orthotropic orientations of cortical and cancellous bone over the entire femoral model were defined with the same global coordinate system. This definition of the orthotropic orientations does not fit the real anatomic structures in femur, especially in the femoral neck where the principal orientations are distinct from those in the femoral stem. The results, therefore, were distorted [20]. Another study overcame above mentioned shortcomings by manually defining the orthotropic orientations based on the real anatomical structures of femur [18]. The conclusion indicated that no significant difference between isotropic and orthotropic material models existed for global FE analysis. The comparisons in these studies were merely limited to the maximum Von Mises stress or the maximum nodal displacement. Hence, what differences are in other parts of femur remains a problem. In addition, only one or two loading conditions applied on the femoral models were taken into account. From what have been discussed above, it is reasonable to believe that many factors may affect the comparative results between isotropic and orthotropic FE models.

The first objective of our study was to investigate whether comparative results would be influenced by factors such as comparative parameters, loading conditions and mesh refinement. The second objective was to find out if there were marked differences between isotropic and orthotropic material models in FE analysis in regards to the same factors.

Section snippets

CT data and finite element meshes

The CT dataset of a right femur was obtained from a public database, which was created by the VAKHUM project (http://www.ulb.ac.be/project/vakhum/index.html). The CT data are in standard DICOM formats.

The FE meshes of the right femur, which were generated from the corresponding CT dataset above, were also from the VAKHUM project. All of the meshes are made of linear hexahedral elements. In order to investigate the effect of mesh refinement on comparative results, three meshes of increasing

Material properties of isotropic and orthotropic models

M1, M2 and M3 were each assigned both isotropic and orthotropic inhomogeneous material properties. As a result, there were six different kinds of material models (three isotropic and three orthotropic). The distribution of material properties for these models are summarized in Table 1. For orthotropic material models, principal material orientations were also defined (Fig. 4).

Differences of FE analysis results between isotropic and orthotropic models

For Von Mises stress, most of the values of Δσ5, Δσ6, Δσ7 and Δσ8 for all loading conditions were lower than 1% (Table 2

Discussion

Material property assignment is a fundamental step for FE analysis of biological structures. Isotropic and orthotropic mapping algorithms have been developed, however, whether there are great differences in computational results between using isotropic and orthotropic models remains a problem as many factors may affect the comparative results. Therefore, this work was aimed to investigate the differences between an isotropic material model and an orthotropic material model by taking into

Conflict of interest statement

None declared.

Acknowledgement

This study was supported by the National Natural Science Foundation of China (no. 30700165 and no. 10872061).

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