The relative influence of apatite crystal orientations and intracortical porosity on the elastic anisotropy of human cortical bone.

Elastic anisotropy exhibits spatial inhomogeneity in human cortical bone, but the structural origins of anatomic variation are not well understood. In this study, the elastic anisotropy of human cortical bone was predicted using a specimen-specific multiscale model that investigated the relative influence of apatite crystal orientations and intracortical porosity. The elastic anisotropy of cortical bone specimens from the diaphysis of human femora was measured by ultrasonic wave propagation as the ratio of elastic constants in the longitudinal/radial (L/R) and longitudinal/circumferential (L/C) anatomic specimen axes. Experimental measurements of elastic constants exhibited orthotropy, with greater anisotropy in the L/R plane compared to the L/C plane. Model predictions included (1) a micromechanical model accounting for the effects of apatite crystal orientations, (2) a voxel-based finite element model accounting for the effects of intracortical porosity, and (3) a combined model accounting for both effects. The combined model provided the most accurate predictions of elastic anisotropy in both the L/R and L/C plane, with less than 10% mean error. The micromechanical model alone was able to accurately predict elastic anisotropy in the L/C plane, but predicted transverse isotropy. The finite element model alone grossly underestimated elastic anisotropy in both the L/R and L/C planes, but was able to predict orthotropy. Therefore, the results of this study suggest that the dominant and less variable transverse isotropy of human cortical bone, reflected by L/C, is governed primarily by apatite crystal orientations, while the more subtle and variable orthotropy, reflected by the difference between L/R and L/C, is governed primarily by intracortical porosity. Moreover, the combined model may be useful to investigate other structure-function relationships or in place of current numerical models, for example, in the study of bone adaptation and metabolic bone disease.

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

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).

Improved accuracy of cortical bone mineralization measured by polychromatic microcomputed tomography using a novel high mineral density composite calibration phantom.

PURPOSE: Microcomputed tomography (micro-CT) is increasingly used as a nondestructive alternative to ashing for measuring bone mineral content. Phantoms are utilized to calibrate the measured x-ray attenuation to discrete levels of mineral density, typically including levels up to 1000 mg HA/cm3, which encompasses levels of bone mineral density (BMD) observed in trabecular bone. However, levels of BMD observed in cortical bone and levels of tissue mineral density (TMD) in both cortical and trabecular bone typically exceed 1000 mg HA/cm3, requiring extrapolation of the calibration regression, which may result in error. Therefore, the objectives of this study were to investigate (1) the relationship between x-ray attenuation and an expanded range of hydroxyapatite (HA) density in a less attenuating polymer matrix and (2) the effects of the calibration on the accuracy of subsequent measurements of mineralization in human cortical bone specimens. METHODS: A novel HA-polymer composite phantom was prepared comprising a less attenuating polymer phase (polyethylene) and an expanded range of HA density (0-1860 mg HA/cm3) inclusive of characteristic levels of BMD in cortical bone or TMD in cortical and trabecular bone. The BMD and TMD of cortical bone specimens measured using the new HA-polymer calibration phantom were compared to measurements using a conventional HA-polymer phantom comprising 0-800 mg HA/cm3 and the corresponding ash density measurements on the same specimens. RESULTS: The HA-polymer composite phantom exhibited a nonlinear relationship between x-ray attenuation and HA density, rather than the linear relationship typically employed a priori, and obviated the need for extrapolation, when calibrating the measured x-ray attenuation to high levels of mineral density. The BMD and TMD of cortical bone specimens measured using the conventional phantom was significantly lower than the measured ash density by 19% (p < 0.001, ANCOVA) and 33% (p < 0.05, Tukey's HSD), on average, respectively. The BMD and TMD of cortical bone specimens measured using the HA-polymer phantom with an expanded range of HA density was significantly lower than the measured ash density by 8% (p < 0.001, ANCOVA) and 10% (p < 0.05, Tukey's HSD), on average, respectively. CONCLUSIONS: The new HA-polymer calibration phantom with a less attenuating polymer and an expanded range of HA density resulted in a more accurate measurement of micro-CT equivalent BMD and TMD in human cortical bone specimens compared to a conventional phantom, as verified by ash density measurements on the same specimens.

Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone.

The anisotropic elastic constants of human cortical bone were predicted using a specimen-specific micromechanical model that accounted for structural parameters across multiple length scales. At the nano-scale, the elastic constants of the mineralized collagen fibril were estimated from measured volume fractions of the constituent phases, namely apatite crystals and Type I collagen. The elastic constants of the extracellular matrix (ECM) were predicted using the measured orientation distribution function (ODF) for the apatite crystals to average the contribution of misoriented mineralized collagen fibrils. Finally, the elastic constants of cortical bone tissue were determined by accounting for the measured volume fraction of Haversian porosity within the ECM. Model predictions using the measured apatite crystal ODF were not statistically different from experimental measurements for both the magnitude and anisotropy of elastic constants. In contrast, model predictions using common idealized assumptions of perfectly aligned or randomly oriented apatite crystals were significantly different from the experimental measurements. A sensitivity analysis indicated that the apatite crystal volume fraction and ODF were the most influential structural parameters affecting model predictions of the magnitude and anisotropy, respectively, of elastic constants.

Anatomic variation in the elastic anisotropy of cortical bone tissue in the human femur.

Experimental investigations for anatomic variation in the magnitude and anisotropy of elastic constants in human femoral cortical bone tissue have typically focused on a limited number of convenient sites near the mid-diaphysis. However, the proximal and distal ends of the diaphysis are more clinically relevant to common orthopaedic procedures and interesting mechanobiology. Therefore, the objective of this study was to measure anatomic variation in the elastic anisotropy and inhomogeneity of human cortical bone tissue along the entire length (15%-85% of the total femur length), and around the periphery (anterior, medial, posterior and lateral quadrants) of the femoral diaphysis, using ultrasonic wave propagation in the three orthogonal specimen axes. The elastic symmetry of tissue in the distal and extreme proximal portions of the diaphysis (15%-45% and 75%-85% of the total femur length, respectively) was, at most, orthotropic. In contrast, the elastic symmetry of tissue near the mid- and proximal mid-diaphysis (50%-70% of the total femur length) was reasonably approximated as transversely isotropic. The magnitudes of elastic constants generally reached maxima near the mid- and proximal mid-diaphysis in the lateral and medial quadrants, and decreased toward the epiphyses, as well as the posterior and anterior quadrants. The elastic anisotropy ratio in the longitudinal and radial anatomic axes showed the opposite trends. These variations were significantly correlated with the apparent tissue density, as expected. In summary, the human femur exhibited statistically significant anatomic variation in elastic anisotropy, which may have important implications for whole bone numerical models and mechanobiology.