Technical noteCritical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur
Introduction
In order to simulate the reactions of bone to physiological and non-physiological load conditions multiple computer-aided finite element models of the proximal femur have been generated since the mid-1970s (Andriacchi et al., 1976; Svensson et al., 1977; Rohlmann et al (1980), Rohlmann et al (1982), Rohlmann et al (1983); Huiskes et al., 1989). Although many previous studies had clearly demonstrated the anisotropic behaviour of bone (Dempster and Liddicoat, 1952; Bargren et al., 1974; Martens et al., 1983; Goulet et al., 1994), all FE-simulations that have been developed so far have assumed isotropic material properties without exception.
Besides the numerical problems of anisotropic simulation of bone remodelling (Beaupré et al., 1990; Jacobs et al., 1997), the main reason for this exclusive assumption of isotropic conditions in bony FE-models has been the lack of a comprehensive data bank incorporating the material properties of bone as a function of the orthotropic load directions.
Therefore, it was the aim of this study to summarize the present knowledge in the literature about the direction-dependent material properties of cortical and cancellous femoral bone. In addition, we tried to answer the question whether these data are sufficient to develop and feed anisotropic FE-models of the proximal femur.
Section snippets
Materials and methods
A survey of more than 300 published studies which investigated experimentally the following material properties of human cadaverous femurs were analyzed:
- 1.
Young's modulus
- 2.
Compressive strength, tensile strength and torsional strength
- 3.
Shear modulus
- 4.
Poisson's ratio
- 5.
Viscoelastic behaviour
As inclusion criteria of this evaluation all investigations had to be carried out on freshly extracted cadaverous femurs, in a moist environment and at body temperature. Additionally, studies were also accepted where
Young's modulus
The Young's modulus of cortical bone is a function of density. For this reason, cortical bone must be considered an inhomogeneous material (Rauber, 1896; Knese et al., 1956; Schmitt, 1968). Fig. 1 shows differences of Young's modulus of cortical bone between 33% (at low apparent densities; 1.5 g/cm3) and 62% (at high apparent densities; 2 g/cm3) higher in the axial than in the transverse load directions.
Similar results have been found in the case of cancellous bone (Fig. 2). Here, apparent
Discussion
Although over the last 25 years multiple investigations were performed to determine the material properties of the proximal femur, definitive statements about the real in vivo behaviour of cortical and cancellous femoral bone are still impossible. This is mainly due to restrictions in ascertaining in vivo conditions in experimental work.
For constructing finite element models of bony structures, the apparent density-dependent characterization of material properties appears to be the most
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