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Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors.

ABSTRACT: Numerical models commonly account for elastic inhomogeneity in cortical bone using power-law scaling relationships with various measures of tissue density, but limited experimental data exists for anatomic variation in elastic anisotropy. A recent study revealed anatomic variation in the magnitude and anisotropy of elastic constants along the entire femoral diaphysis of a single human femur (Espinoza Orías et al., 2009). The objective of this study was to confirm these trends across multiple donors while also considering possible confounding effects of the anatomic quadrant, apparent tissue density, donor age, and gender. Cortical bone specimens were sampled from the whole femora of 9 human donors at 20%, 50%, and 80% of the total femur length. Elastic constants from the main diagonal of the reduced fourth-order tensor were measured on hydrated specimens using ultrasonic wave propagation. The tissue exhibited orthotropy overall and at each location along the length of the diaphysis (p < 0.0001). Elastic anisotropy increased from the mid-diaphysis toward the epiphyses (p < 0.05). The increased elastic anisotropy was primarily caused by a decreased radial elastic constant (C(11)) from the mid-diaphysis toward the epiphyses (p < 0.05), since differences in the circumferential (C(22)) and longitudinal (C(33)) elastic constants were not statistically significant (p > 0.29). Anatomic variation in intracortical porosity may account for these trends, but requires further investigation. The apparent tissue density was positively correlated with the magnitude of each elastic constant (p < 0.0001, R(2) > 0.46), as expected, but was only weakly correlated with C(33)/C(11) (p < 0.05, R(2) = 0.04) and not significantly correlated with C(33)/C(22) and C(11)/C(22).

SUBMITTER: Rudy DJ

PROVIDER: S-EPMC3111152 | biostudies-literature | 2011 Jun

REPOSITORIES: biostudies-literature

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Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors.

Rudy David J DJ Deuerling Justin M JM Espinoza Orías Alejandro A AA Roeder Ryan K RK

Journal of biomechanics 20110502 9

Numerical models commonly account for elastic inhomogeneity in cortical bone using power-law scaling relationships with various measures of tissue density, but limited experimental data exists for anatomic variation in elastic anisotropy. A recent study revealed anatomic variation in the magnitude and anisotropy of elastic constants along the entire femoral diaphysis of a single human femur (Espinoza Orías et al., 2009). The objective of this study was to confirm these trends across multiple don ...[more]

PMID: 21543070

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Project description:Knowledge of the nature of the elastic symmetry of trabecular bone is fundamental to the study of bone adaptation and failure. Previous studies have classified human vertebral trabecular bone as orthotropic or transversely isotropic but have typically obtained samples from only selected regions of the centrum. In this study, the elastic symmetry of human vertebral trabecular bone was characterized using microfinite element (?FE) analyses performed on 1019 cubic regions of side length equal to 5 mm, obtained via thorough sampling of the centrums of 18 human L1 vertebrae (age?=?81.17?±?7.7?yr; eight males and ten females). An optimization procedure was used to find the closest orthotropic representation of the resulting stiffness tensor for each cube. The orthotropic elastic constants and orientation of the principal elastic axes were then recorded for each cube and were compared to the constants predicted from Cowin's fabric-based constitutive model (Cowin, 1985, "The Relationship Between the Elasticity Tensor and the Fabric Tensor," Mech. Mater., 4(2), pp. 137-147.) and the orientation of the principal axes of the fabric tensor, respectively. Deviations from orthotropy were quantified by the "orthotropic error" (van Rietbergen et al., 1996, "Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture," J. Biomech., 29(12), pp. 1653-1657), and deviations from transverse isotropy were determined by statistical comparison of the secondary and tertiary elastic moduli. The orthotropic error was greater than 50% for nearly half of the cubes, and the secondary and tertiary moduli differed from one another (p?<?0.0001). Both the orthotropic error and the difference between secondary and tertiary moduli decreased with increasing bone volume fraction (BV/TV; p???0.007). Considering only the cubes with an orthotropic error less than 50%, only moderate correlations were observed between the fabric-based and the ?FE-computed elastic moduli (R2???0.337; p?<?0.0001). These results indicate that when using a criterion of 5?mm for a representative volume element (RVE), transverse isotropy or orthotropy cannot be assumed for elderly human vertebral trabecular bone. Particularly at low values of BV/TV, this criterion does not ensure applicability of theories of continuous media. In light of the very sparse and inhomogeneous microstructure found in the specimens analyzed in this study, further work is needed to establish guidelines for selecting a RVE within the aged vertebral centrum.

Project description:ObjectiveThis study used microcomputed tomography (micro-CT) to evaluate the effects of ovariectomy on the trabecular bone microarchitecture and cortical bone morphology in the femoral neck and mandible of female rats.Materials and methodsTwelve female Wister rats were divided into two groups: the control and ovariectomized groups. The rats in the ovariectomized group received ovariectomy at 8 weeks of age; all the rats were sacrificed at 20 weeks of age, and their mandibles and femurs were removed and scanned using micro-CT. Four microstructural trabecular bone parameters were measured for the region below the first mandibular molar and the femoral neck region: bone volume fraction (BV/TV), trabecular thickness (TbTh), trabecular separation (TbSp), and trabecular number (TbN). In addition, four cortical bone parameters were measured for the femoral neck region: total cross-sectional area (TtAr), cortical area (CtAr), cortical bone area fraction (CtAr/TtAr), and cortical thickness (CtTh). The CtTh at the masseteric ridge was used to assess the cortical bone morphology in the mandible. The trabecular bone microarchitecture and cortical bone morphology in the femoral necks and mandibles of the control group were compared with those of the ovariectomized group. Furthermore, Spearman's correlation (rs) was conducted to analyze the correlation between the osteoporosis conditions of the mandible and femoral neck.ResultsRegarding the trabecular bone microarchitectural parameters, the BV/TV of the trabecular bone microarchitecture in the femoral necks of the control group (61.199±11.288%, median ± interquartile range) was significantly greater than that of the ovariectomized group (40.329±5.153%). Similarly, the BV/TV of the trabecular bone microarchitecture in the mandibles of the control group (51.704±6.253%) was significantly greater than that of the ovariectomized group (38.486±9.111%). Furthermore, the TbSp of the femoral necks in the ovariectomized group (0.185±0.066 mm) was significantly greater than that in the control group (0.130±0.026mm). Similarly, the TbSp of the mandibles in the ovariectomized group (0.322±0.047mm) was significantly greater than that in the control group (0.285±0.041mm). However, the TbTh and TbN trends for the mandibles and femoral necks were inconsistent between the control and ovariectomized groups. Regarding the cortical bone morphology parameters, the TtAr of the femoral necks in the ovariectomized group was significantly smaller than that in the control group. There was no significant difference in the TtAr, CtAr, or CtTh of the femoral necks between the control and ovariectomized groups, and no significant difference in the CtTh of the mandibles between the control and ovariectomized groups. Moreover, the BV/TV and TbSp of the mandibles were highly correlated with those of the femurs (rs = 0.874 and rs = 0.755 for BV/TV and TbSp, respectively). Nevertheless, the TbTh, TbN, and CtTh of the mandibles were not correlated with those of the femoral necks.ConclusionAfter the rats were ovariectomized, osteoporosis of the trabecular bone microarchitecture occurred in their femurs and mandibles; however, ovariectomy did not influence the cortical bone morphology. In addition, the parametric values of the trabecular bone microarchitecture in the femoral necks were highly correlated with those of the trabecular bone microarchitecture in the mandibles.

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Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors.

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Anatomic variation in the elastic inhomogeneity and anisotropy of human femoral cortical bone tissue is consistent across multiple donors.

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