The arrangement and orientation of the ultrastructure plays an important role for the mechanical properties of inhomogeneous and anisotropic materials, such as polymers, wood, or bone. However, there is a lack of techniques to spatially resolve and quantify the material's ultrastructure orientation in a macroscopic context. In this study, a new method is presented, which allows deriving the ultrastructural 3D orientation in a quantitative and spatially resolved manner. The proposed 3D scanning small-angle X-ray scattering (3D sSAXS) method was demonstrated on a thin trabecular bone specimen of a human vertebra. A micro-focus X-ray beam from a synchrotron radiation source was used to raster scan the sample for different rotation angles. Furthermore, a mathematical framework was developed, validated and employed to describe the relation between the SAXS data for the different rotation angles and the local 3D orientation and degree of orientation (DO) of the bone ultrastructure. The resulting local 3D orientation was visualized by a 3D orientation map using vector fields. Finally, by applying the proposed 3D scanning SAXS method on consecutive bone sections, a 3D map of the local orientation of a complete trabecular element could be reconstructed for the first time. The obtained 3D orientation map provided information on the bone ultrastructure organization and revealed links between trabecular bone microarchitecture and local bone ultrastructure. More specifically, we observed that trabecular bone ultrastructure is organized in orientation domains of tens of micrometers in size. In addition, it was observed that domains with a high DO were more likely to be found near the surface of the trabecular structure, and domains with lower DO (or transition zones) were located in-between the domains with high DO. The method reproducibility was validated by comparing the results obtained when scanning the sample under different sample tilt angles. 3D orientation maps such as the ones created using 3D scanning SAXS will help to quantify and understand structure-function relationships between bone ultrastructure and bone mechanics. Beyond that, the proposed method can also be used in other research fields such as material sciences, with the aim to locally determine the 3D orientation of material components.
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