Some factors that affect the comparison between isotropic and orthotropic inhomogeneous finite element material models of femur
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 , , and 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).
References (30)
- et al.
Long-term study of bone remodeling after femoral stem: a comparison between dexa and finite element simulation
J Biomech
(2007) - et al.
A comparative study on different methods of automatic mesh generation of human femurs
Med Eng Phys
(1998) - et al.
Automated three-dimensional finite element modelling of bone: a new method
J Biomed Eng
(1990) - et al.
Elastic modulus of trabecular bone material
J Biomech
(1988) - et al.
Relations of mechanical properties to density and CT numbers in human bone
Med Eng Phys
(1995) - et al.
Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur
J Biomech
(2000) - et al.
Trabecular bone modulus–density relationships depend on anatomic site
J Biomech
(2003) - et al.
Mathematical relationships between bone density and mechanical properties: a literature review
Clin Biomech
(2008) - et al.
Computer aided stress analysis of long bones utilizing computed tomography
J Biomech
(1990) - et al.
An improved method for the automatic mapping of ct numbers onto finite element models
Med Eng Phys
(2004)
The material mapping strategy influences the accuracy of CT-based finite element models of bones: an evaluation against experimental measurements
Med Eng Phys
A modified method for assigning material properties to FE models of bones
Med Eng Phys
A continuous wave technique for the measurement of the elastic properties of cortical bone
J Biomech
Determination of orthotropic bone elastic constants using FEA and modal analysis
J Biomech
Concept and development of an orthotropic FE model of the proximal femur
J Biomech
Cited by (60)
The influence of femoral lytic tumors segmentation on autonomous finite element analysis
2024, Clinical Biomechanics3D printed patient-specific fixation plates for the treatment of slipped capital femoral epiphysis: Topology optimization vs. conventional design
2023, Journal of the Mechanical Behavior of Biomedical MaterialsLearned Gaussian quadrature for enriched solid finite elements
2023, Computer Methods in Applied Mechanics and EngineeringCraniocaudal toggling increases the risk of screw loosening in osteoporotic vertebrae
2023, Computer Methods and Programs in BiomedicineBiomechanical Analysis of Human Femur using Finite Element Method: A Review Study
2022, Materials Today: Proceedings