Mechanical testing of cancellous bone from the femoral head: Experimental errors due to off-axis measurements

https://doi.org/10.1016/j.jbiomech.2006.11.020Get rights and content

Abstract

The aim of this study was to verify whether a misalignment between the testing direction and the trabecular main direction has a significant effect on the compressive behaviour of cancellous bone.

Ten cylindrical specimens were extracted from femoral heads with a misalignment to the trabecular main direction of approximately 20°. Each specimen was paired with a specimen extracted aligned with the main direction of the trabeculae on the basis of the closest bone volume fraction, obtaining two groups, one ‘aligned’ and one ‘misaligned’. The average off-axis angle was 6.1° and 21.6° for the ‘aligned’ and ‘misaligned’ group, respectively. The specimens underwent micro-tomographic analysis, compressive testing, micro-indentation testing and ashing.

No significant differences were found in histomorphometric parameters, hardness and ash density between the two groups, whereas significant differences were found in Young's modulus and ultimate stress: both parameters, measured for the ‘misaligned’ group, were about 40% lower than those measured for the ‘aligned’ group.

These results demonstrate a great effect of the angle between the testing direction and the main direction of the trabecular structure on the compressive behaviour of cancellous bone. This angle should be reduced as much as possible (in the present work the average value was 6.6±3.3°), in any case measured, and always reported together with the mechanical parameters of cancellous bone.

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.

References (32)

  • F. Linde et al.

    The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens

    Journal of Biomechanics

    (1992)
  • S. Majumdar et al.

    High-resolution magnetic resonance imaging: three-dimensional trabecular bone architecture and biomechanical properties

    Bone

    (1998)
  • A. Odgaard

    Three-dimensional methods for quantification of cancellous bone architecture

    Bone

    (1997)
  • A. Odgaard et al.

    Fabric and elastic principal directions of cancellous bone are closely related

    Journal of Biomechanics

    (1997)
  • K. Birnbaum et al.

    Material properties of trabecular bone structures

    Surgical—Radiologic Anatomy

    (2001)
  • S.J. Brown et al.

    Regional differences in mechanical and material properties of femoral head cancellous bone in health and osteoarthritis

    Calcified Tissue International

    (2002)
  • Cited by (0)

    View full text