Elsevier

Journal of Biomechanics

Volume 34, Issue 12, December 2001, Pages 1649-1654
Journal of Biomechanics

Technical note
Finite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions

https://doi.org/10.1016/S0021-9290(01)00155-5Get rights and content

Abstract

Strong correspondence between the uniaxial apparent strength and stiffness of cancellous bone allows the use of stiffness as a predictor of bone strength. Measured values of mechanical properties in cancellous bone can be different between experiments due to different experimental conditions. In the current study, bone volume fraction, experimentally determined and finite element (FE) predicted stiffness were examined as predictors of cancellous bone ultimate strength in two different groups each of which was tested using a different end constraint. It is demonstrated that, although always significant, the relationships of strength with bone volume fraction and experimentally determined stiffness are different between test groups. Apparent stiffness, estimated by FE modeling, predicts the ultimate strength of human cancellous bone consistently for all examined experimental protocols.

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 σuEexp relationship was different between the toe and non-toe specimens of the Glued group (p<0.01), whereas σuEFEM 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.

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