Mechanical testing of cancellous bone from the femoral head: Experimental errors due to off-axis measurements
Introduction
Cancellous bone is a porous material that presents various structural anisotropies depending on the specific anatomical site (Feldkamp et al., 1989; Gibson, 1985, Gibson, 2005). The tissue structure has been shown to range from nearly transverse isotropic (e.g. human vertebra) to orthotropic (e.g. human calcaneus) (Majumdar et al., 1998).
A mathematical model to describe the structure of cancellous bone in two dimensions, using images from a scanning electron microscope, was proposed by Whitehouse (1974). He found that the polar diagram representing the measured mean intercept lengths (MIL) in different directions is an ellipse. Harrigan and Mann (1984) extended this model to three dimensions, introducing the use of a second rank symmetric tensor to describe the degree of orientation in orthotropic materials. Cowin (1985) expanded the use of tensors, showing that there is a theoretical relationship between the fourth rank elasticity tensor of a porous, anisotropic, linear-elastic material and a second-rank symmetric tensor. The latter, referred to as the ‘fabric’ tensor characterises the arrangement of the microstructural components of the material. Several studies (Odgaard et al., 1997; Wang et al., 2004; Zysset et al., 1998) have been done to confirm the theory of Cowin (1985). In those studies, the three-dimensional structure of cancellous bone specimens was obtained by means of micro-tomographic images. The structural anisotropy was expressed in terms of a fabric tensor. From this tensor the structural main directions were calculated. The mechanical principal directions were estimated with finite element simulations. The structural main directions predicted well the mechanical principal directions with differences of only a few degrees (from 1.4° to 3.8°).
Several experimental studies have been performed to assess the mechanical behaviour in three orthogonal directions of cancellous bone (Augat et al., 1998; Ciarelli et al., 1991; Goulet et al., 1994; Majumdar et al., 1998). Those studies confirmed an orthotropic or transversely isotropic behaviour of the cancellous bone. However, little effort has been made to experimentally investigate the effect of the load direction with respect to the main trabecular direction (MTD), hereafter called ‘off-axis angle’, on the measurement of the mechanical behaviour of cancellous bone. A theoretical study (Turner and Cowin, 1988), to estimate the error induced by off-axis measurements on the elastic properties of bone, showed that mechanical behaviour of cancellous bone is affected by the testing direction. A power relationship was found between the off-axis angle and the percentage error of the elastic properties. The mean error in the measured Young's modulus with an off-axis angle of 10° was calculated to be 9.5%. To the authors’ knowledge, only one experimental study (Birnbaum et al., 2001) has been done to evaluate the effect of testing cancellous bone off-axis. Birnbaum et al. (2001) found no significant difference between the maximum compressive strength, when testing the cancellous bone of the femoral head extracted along the postulated primary compressive group, which was identified on the basis of the local anatomy of the femur, and at an off-axis angle of 45°. There is thus a disagreement between theoretical predictions and experimental results about the importance of testing cancellous bone in the MTD.
The aim of this study was to verify if the alignment of cancellous bone specimens with the MTD has a significant effect on the measured Young's modulus and compressive strength.
Section snippets
Samples
Ten heads were cut from human femurs obtained from the International Institute for the Advancement of Medicine (IIAM, Jessup, PA, USA). The heads were stored in a 70% ethanol solution for at least four weeks before testing to prevent the transmission of infectious diseases during laboratory handling. It has been demonstrated that this treatment has no effect on the elastic properties of cancellous bone but only on the viscoelastic properties (hysteresis energy and loss tangent), which increase (
Results
All results from the tests for the two groups are summarised in Table 1. No statistical significant difference was found between the two groups in BV/TV and age. Instead, as expected, a significant difference was found between the off-axis angles (p<0.001).
The tissue structure and quality of the two groups were not different since no statistically significant differences were found between calculated histomorphometric parameters (SMI, Tb.Th, and Tb.Sp), hardness or ash density of the bone
Discussion
The aim of this study was to confirm or decline the importance of controlling the direction when testing cancellous bone. In this study tissue samples extracted from the femoral head were tested. Young's modulus and ultimate stress of 10 specimens extracted with an inclination of 20° to the MTD were compared with 10 specimens aligned with the MTD. There were no significant differences in trabecular structure and tissue quality between the two groups, as demonstrated by histomorphometric
Acknowledgements
This work was partially supported by the European Community (project number: IST-2004-026932; project title: Living Human Digital Library; acronym: LHDL).
The authors wish to thank Roberta Fognani, Dennis Triezenberg, Wouter Raatjes and Riccardo Sforza for the technical support; Luigi Lena for the artwork; Manuela De Clerico for the statistics.
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