Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue
Introduction
The mechanical properties of trabecular bone depend on volume fraction, architecture, and trabecular tissue material properties. Characterization of the latter and its role in trabecular bone mechanical behavior has potential clinical and biological importance. Clinically, knowledge of the elastic and failure properties of trabecular tissue could be used to investigate the effects of drug treatments, aging, and disease at the tissue level. Biologically, these properties, and their relation to cortical tissue properties, could provide insight into general structure-function relationships for bone. Tissue-level elastic and yield properties are also required as input for both computational (Niebur et al., 2000; Silva and Gibson, 1997; van Rietbergen et al., 1995; Yeh and Keaveny, 1999) and analytical (Gibson, 1985) models, and therefore represent an important basis for micro-mechanical analysis of trabecular bone.
Although the tissue-level elastic properties of trabecular bone have been reported in numerous studies (Table 1; also see Guo, 2001 for a more detailed review), because of technical challenges, there remain substantial discrepancies in these data and there are almost no data available for tissue-level failure properties. An alternative approach to direct mechanical testing at the tissue level is to use high-resolution finite element models, derived from micro-computed tomography (micro-CT) scans, together with specimen-specific experimental data at the whole specimen (apparent) level to calibrate “effective” elastic properties of the tissue (van Rietbergen et al., 1995). Most of these types of studies have used compression testing with platens to provide the calibration data. However, because of the associated end-artifacts (Jacobs et al., 1999; Keaveny et al., 1997; Odgaard and Linde, 1991), such studies have reported low values of calibrated effective tissue moduli (Hou et al., 1998; Ladd et al., 1998) when compared to the experimental studies (Rho et al., 1997; Turner et al., 1999; Zysset et al., 1999) that used ultrasound and nanoindentation or the finite element-experimental studies (Niebur et al., 2000) that used testing protocols that minimized end-artifacts at the apparent level. Regarding failure properties, by using a combination of nonlinear, high-resolution finite element analyses and apparent-level mechanical tests (Niebur et al., 2000), it was found that the tissue-level tension-compression strength asymmetry for bovine trabecular bone was close to values reported for bovine cortical bone (Burstein et al., 1976; Reilly and Burstein, 1975). However, except for the fatigue strength of micro-beam specimens (Choi and Goldstein, 1992), no studies have reported failure properties for human trabecular tissue.
In any study comparing trabecular tissue mechanical properties to those of cortical tissue, porosity, orientation, anatomic site, degree of mineralization, and age need to be controlled. Focusing on a cohort of specimens from elderly human femora, addressing longitudinal behavior, and accounting for vascular porosity effects, our goal was to test the hypothesis that trabecular and cortical tissue have similar elastic and yield properties. Using an approach that included high-resolution finite element analysis and various types of mechanical testing, our specific objectives were to: (1) determine the effective tissue-level elastic modulus and tissue tensile and compressive yield strains for human femoral neck trabecular bone; and (2) compare these properties with cortical tissue elastic and yield properties obtained from tension testing, using tissue from a similar cohort of donors. While this study is complementary to others on tissue-level elastic properties (Rho et al., 1999; Turner et al., 1999; Zysset et al., 1999), it is novel in its focus on yield behavior.
Section snippets
Trabecular bone
Twelve human trabecular bone specimens from 11 cadavers (six male, five female; mean age 65.5±9.1 yr, age range 51–85) were studied. The two specimens obtained from the same donor were taken from similar locations in the right and left femoral neck. Eight-millimeter diameter, 32-mm long (nominally) specimens were extracted from the femoral neck, aligned with their principal trabecular orientation as determined by contact radiographs (Keaveny et al., 1994; Morgan and Keaveny, 2001). Specimens
Results
The mean (±S.D.) value of the effective trabecular tissue modulus calibrated for the 12 trabecular bone specimens was 18.0±2.8 GPa, ranging from 12.1 to 22.2 GPa. Linear regression analysis indicated that this parameter did not depend on the measured volume fraction (p>0.99), apparent modulus (p>0.34), or apparent density (p>0.94, Fig. 3a).
The mean values (±S.D.) of the calibrated trabecular tissue tensile and compressive yield strains were 0.41±0.04% and 0.83±0.15%, respectively, and the
Discussion
Trabecular and cortical tissue properties are of great interest in the etiology of osteoporosis since it is widely speculated that this aspect of bone “quality” does affect fracture risk (Heaney, 1993). Considering that elastic and strength properties at the apparent (whole specimen) level for cortical vs. trabecular bone can vary by orders of magnitude, cortical tissue and trabecular tissue have remarkably similar elastic and (yield) strain properties. The tensile-compressive asymmetry in
Acknowledgements
This study was supported by grants from the National Institutes of Health (AR43784; AR41481), the National Science Foundation (BES-9625030), and the National Partnership for Advanced Computational Infrastructure (UCB254; UCB266). Cadaveric tissue was obtained from NDRI and UCSF Department of Anatomy. We would like to thank Dr. Sharmila Majumdar, Andrew Burghardt, Jacob Pollock, Margaretha Winata, Arul Krishnan, and Michael Y. Yu for their technical assistance.
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