Determination of the bone-crystallites distribution function by x ray diffraction

Correlation between hydroxyapatite crystallite orientation and ultrasonic wave velocities in bovine cortical bone

The mineral component of bone is mainly composed of calcium phosphate, constituting 70% of total bone mass almost entirely in the form of hydroxyapatite (HAp) crystals. HAp crystals have a hexagonal system and uniaxial elastic anisotropy. The objective of this study was to investigate the effect of HAp crystallite preference on macroscopic elasticity. Ultrasonic longitudinal wave velocity and the orientation of HAp crystallites in bovine cortical bone are discussed, considering microstructure, density, and bone mineral density (BMD). Eighty cube samples of cortical bone were made from two bovine femurs. The orientation of HAp crystallites was evaluated by integrated intensity ratio of (0002) peak using an X-ray diffractometer. Ultrasonic longitudinal wave velocity was investigated with a conventional pulse system. The intensity ratio of HAp crystallites and velocity were measured in three orthogonal directions; most HAp crystallites aligned in the axial direction of the femurs. Our results demonstrate a linear correlation between velocity and intensity ratio in the axial direction. Significant correlation between velocity and BMD values was observed; however, the correlation disappeared if we focused on the identical type of microstructure. In conclusion, differences in microstructure type have an impact on density and BMD, which clearly affects the velocity. In addition, at the nanoscopic level, HAp crystallites aligned in the axial direction also affected the velocity and anisotropy.

Distribution of hydroxyapatite crystallite orientation and ultrasonic wave velocity in ring-shaped cortical bone of bovine femur

At the nanoscopic level, bone consists of calcium phosphate, which forms incomplete hydroxyapatite (HAp) crystals. The preferred orientation of the c-axis of HAp crystallites induces anisotropy and inhomogeneity of elastic properties in bone. In this study, the effect of the preferred orientation of HAp crystallites on the spatial distribution of ultrasonic wave velocity was experimentally investigated, considering bone mineral density (BMD) and microstructure. Three ring-shaped cortical bone samples were made from a 36-month-old bovine femur. Longitudinal wave velocity was measured by a conventional ultrasonic pulse system, using self-made polyvinylidene fluoride transducers. The integrated intensity of the (0002) peak obtained using X-ray diffraction was estimated to evaluate the amount of preferred orientation. The velocity distribution pattern was similar to the distribution of integrated intensity of (0002). The effect of the preferred orientation of HAp crystallites on velocity was clearly observed in the plexiform structure, despite the fact that the BMD value was almost independent of the preferred orientation of HAp crystallites. Velocity measurement of cortical bone can reveal information about HAp crystallite orientation.

Unique alignment and texture of biological apatite crystallites in typical calcified tissues analyzed by microbeam X-ray diffractometer system

Preferential orientation of biological apatite (Ap) crystallites in typical calcified tissues of rabbit ulna, rabbit skull, and monkey dentulous mandible was investigated using a microbeam X-ray diffractometer, with a beam spot of 100 microm in diameter, to clarify relationship between the Ap orientation and mechanical function. Preferential alignment of the c-axis of the biological Ap was evaluated by the relative intensity between (002) and (310) diffraction peaks. Preferential alignment of biological Ap in each calcified tissue varied depending on the shape and stress condition in vivo; that is, the c-axes of biological Ap in the rabbit ulna and the rabbit skull bone were preferentially observed as a one-dimensional orientation along the longitudinal axis and a two-dimensional orientation along the surface, respectively. Precise analysis of the preferential alignment along the skull surface showed an elliptical distribution of the c-axis of biological Ap elongating along the suture inside the skull surface of both lamina exterior and interior. The c-axis of biological Ap in a monkey dentulous mandible basically aligned along the mesiodistal direction in the flat bone, but this alignment changed along the normal direction to the flat bone surface parallel to the biting direction near the tooth, due to the force of mastication. It was concluded that the microscale measurement of biological Ap texture is one of the useful new methods for evaluating mechanical function and stress distribution in vivo in calcified tissues.

Micromechanics of bone strength and fracture

The mechanical properties of bone were modeled in the context of a filled polymeric composite containing a collagenous matrix and a hydroxyapatite filler. The longitudinal and transverse moduli of cortical bone as a composite with perfect alignment of filler particles were calculated to be 34.5 and 5.3 GPa, respectively. When considering that particle orientation is arranged within a distribution about the long axis, moduli close to the experimentally measured values are achieved. The calculated tensile strength of 1.7 GPa is higher than the experimental values, which may be attributable to intrinsic sample flaws and biological heterogeneity. The mode of tensile failure in this model is particle-matrix debonding, which may explain fatigue or stress fractures. Overall, the filled composite model of bone helps explain the roles of mineralization fraction, particle shape and orientation, and other attributes of the constituent phases in understanding the tensile properties. The fundamentals of bone behavior in compression are less well understood. It is proposed that incorporation of an inorganic phase in bone was teleologically necessary for vertebrates to achieve adequate levels of compressive strength.

Orientation of bone mineral and its role in the anisotropic mechanical properties of bone--transverse anisotropy

An orientation of hydroxyapatite (HAP) crystals in bovine femur mineral was investigated by means of X-ray pole figure analysis (XPFA). It was found that the c-axis of HAP generally orients parallel to the longitudinal axis of bone (bone axis) and a significant amount of c-axis was oriented in other directions, in particular, perpendicular to the bone axis. Comparing these results with those of the small angle X-ray scattering (SAXS) investigation by Matsushima et al. (Jap. J. appl. Phys. 21, 186-189, 1982) at least two types of morphology of bone mineral were found; rod like bone mineral having the c-axis of HAP crystal parallel to the longitudinal axis of the rod and that having the c-axis not parallel, in a particular case, perpendicular to its longitudinal axis. Transverse anisotropy in mechanical properties of bone was reproduced by the estimation of Young's moduli by using the structural results mainly from XPFA. It is concluded that the anisotropy in mechanical properties of bone is well explained by taking account of the non-longitudinal (off-bone) axial distribution of orientation of bone mineral.

Determination of mineral-organic bonding effectiveness in bone--theoretical considerations

It is postulated that the effectiveness of bonding between the mineral and organic phases could be an important influence on the behavior of bone with respect to its mechanical properties, metabolic activity, and aging effects associated with these factors. Changes in bonding effectiveness might also be related to the etiology of osteoporosis. If this hypothesis is correct, it would be of interest to determine the amount of debonding present in bone. An analysis that employs both macromechanical and micromechanical composite theory is performed to show how this quantity could be calculated. The approach taken is first to determine the elastic moduli of a characteristic volume from bulk elastic properties of bone and the mineral crystallite orientation distribution. Voigt and Reuss type averages are used to obtain upper and lower bounds. Modifications of the Halpin-Tsai equations that apply to chopped fiber composites are then used to calculate the amount of debonding between the phases in the characteristic volume. All of the parameters employed in the theory are measurable using established techniques. To apply the theory quantitatively the following information must be known: 1) the density and elastic moduli of the bone (and its phases), and 2) the mineral orientation distribution.

An X-ray diffraction investigation of age-related changes in the crystal structure of bone apatite

Evidence relating to the existence of crystalline bone mineral in vivo is considered, and bone apatite crystal structure investigated using an x-ray powder diffraction technique. Specimens of femoral compacta excised post-mortem from male and female subjects ranging from 3 1/2 years to 87 years of age have been studied. Values of the ratio c/a of bone apatite crystal cell axes for females are significantly higher (p less than 0.05) than for males. Moreover, significant change of c/a with age is observed for males (p = 0.0005) but not for females (p = 0.30). Differences in c/a are interpreted as indicating substitution of constituent ions in the bone apatite crystals.