Technical noteFinite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions
Introduction
Cancellous bone is the primary load bearing structure in vertebrae (Silva and Gibson, 1997; Overaker et al., 1999). An accurate prediction of cancellous bone strength has been of interest for a better ability to diagnose higher fracture risk and a better understanding of underlying mechanisms by which bone strength is affected. An important experimental observation for achieving this goal is that bone strength is highly correlated with bone stiffness (Brown and Ferguson, 1980; Goulet et al., 1994; Keaveny et al., 1994; Hou et al., 1998). Moreover, the relationship is expected to be similar between different bones (Fyhrie and Vashishth, 2000). However, experimentally determined mechanical properties of cancellous bone are sensitive to testing conditions which may result in different relationships of strength with stiffness, although they are all statistically significant, as seen in results from previous studies. A good number of these studies from human cancellous bone were tabulated by Linde et al. (1992) previously. The effect of specimen geometry, size, aspect ratio, constraints and measurement technique on the measured mechanical properties of cancellous bone have been studied (Linde and Hvid, 1989; Linde et al., 1992; Keaveny et al (1993), Keaveny et al (1997); Zhu et al., 1994). Among these, end constraints seem to be the source of greatest errors in measurements of strains, therefore, cancellous bone stiffness (Linde and Hvid, 1989; Keaveny et al (1993), Keaveny et al (1997)). Theoretically, the ultimate strength may also be affected by the use of different end supports (Gu et al., 2001), however, it is not expected to be the case for cancellous bone (Linde et al., 1992; Wenzel et al., 1993).
A standardized non-invasive method for the prediction of apparent stiffness would prove useful for predicting the ultimate strength of cancellous bone. Large scale finite element modeling (LS-FE), used in conjunction with 3D micro computed tomography (μCT) imaging, is an effective method for predicting stress distributions and mechanical properties of cancellous bone (Fyhrie and Hou, 1995; Hou et al., 1998; Ladd et al., 1998; Van Rietbergen et al., 1999; Fyhrie et al., 2000). Furthermore, finite element (FE) predicted apparent stiffness is highly correlated with the ultimate strength of vertebral cancellous bone (Hou et al., 1998). As FE predicted stiffness is free of experimental artifacts and ultimate strength is expected to be less sensitive to end constraints, it is expected that the relationship between ultimate strength and the FE predicted stiffness of cancellous bone will be more consistent than the relationship of strength with other experimental predictors for specimens tested with different end conditions.
The objective of this study was to test whether the ultimate strength vs. FE predicted stiffness relationship would be affected by different end conditions used in mechanical testing. Bone volume fraction, which is commonly used as a predictor of bone mechanical properties, also highly correlates with bone strength. Whether the relationship between bone volume and strength can be unified was also tested for comparison with stiffness.
Section snippets
Materials and methods
Cylindrical human vertebral cancellous bone specimens, 8 mm in diameter and 9.5 mm in height, cut in the infero-superior direction from the 12th thoracic vertebra (T12), one from each of 23 individuals (Platens group: aged 23–91 yr with mean±standard deviation=58.1±18.5 yr) using an 8 mm diameter diamond abrasive coring tool (Felker, Cerritos, CA) were utilized in previous studies (Hou et al., 1998; Fyhrie et al., 2000). Thirty-five additional specimens were prepared similarly, as many as possible
Results
Despite the use of a gluing technique for the “Glued” group, there was a toe region on the stress–strain curve for some specimens (Fig. 1). After careful examination of the mechanical testing data, 23 experiments were accepted as valid (with no toe region) for Glued group. Further analysis of the relationships between strength and BV/TV, EFEM and Eexp revealed that the σu−Eexp relationship was different between the toe and non-toe specimens of the Glued group (p<0.01), whereas σu−EFEM and σu
Discussion
The ultimate strength of cancellous bone that was mechanically tested with different experimental conditions was correlated to experimentally determined stiffness, bone volume fraction and stiffness predicted by FE analysis performed with the same end conditions (frictionless interface) for both groups. The results indicate that the relationship of strength with experimental stiffness and bone volume fraction is different between test groups whereas the relationship of strength with FE
Acknowledgments
This work was supported by NIH AR40776. The authors thank Dr. Deepak Vashishth for his assistance with mechanical testing and Dr. Fu Hou for his assistance with generating the Platens group data.
References (28)
- et al.
Femoral strength is better predicted by finite element models than QCT and DXA
Journal of Biomechanics
(1999) - et al.
Bone stiffness predicts strength similarly for human vertebral cancellous bone in compression and for cortical bone in tension
Bone
(2000) - et al.
Human vertebral cancellous bone surface distribution
Bone
(1995) - et al.
The relationship between the structural and orthogonal compressive properties of trabecular bone
Journal of Biomechanics
(1994) - et al.
Human vertebral body apparent and hard tissue stiffness
Journal of Biomechanics
(1998) - et al.
NACOB presentation to ASB young scientist award: postdoctoral. The impact of boundary conditions and mesh size on the accuracy of cancellous bone tissue modulus determination using large-scale finite-element modeling. North American congress on biomechanics
Journal of Biomechanics
(1999) - et al.
Theoretical analysis of the experimental artifact in trabecular bone compressive modulus
Journal of Biomechanics
(1993) - et al.
Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus
Journal of Biomechanics
(1994) - et al.
The effect of constraint on the mechanical behaviour of trabecular bone specimens
Journal of Biomechanics
(1989) - et al.
The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens
Journal of Biomechanics
(1992)
Modeling the mechanical behavior of vertebral trabecular boneeffects of age-related changes in microstructure
Bone
Finite element analysis of trabecular bone structurea comparison of image-based meshing techniques
Journal of Biomechanics
A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models
Journal of Biomechanics
Effects of specimen load-bearing and free surface layers on the compressive mechanical properties of cellular materials
Journal of Biomechanics
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