Multiscale modelling and diffraction-based characterization of elastic behaviour of human dentine.

Human dentine is a hierarchical mineralized tissue with a two-level composite structure, with tubules being the prominent structural feature at a microlevel, and collagen fibres decorated with hydroxyapatite (HAp) crystallite platelets dominating the nanoscale. Few studies have focused on this two-level structure of human dentine, where the response to mechanical loading is thought to be affected not only by the tubule volume fraction at the microscale, but also by the shape and orientation distribution of mineral crystallites, and their nanoscale spatial arrangement and alignment. In this paper, in situ elastic strain evolution within HAp in dentine subjected to uniaxial compressive loading along both longitudinal and transverse directions was characterized simultaneously by two synchrotron X-ray scattering techniques: small- and wide-angle X-ray scattering (SAXS and WAXS, respectively). WAXS allows the evaluation of the apparent modulus linking the external load to the internal HAp crystallite strain, while the nanoscale HAp distribution and arrangement can be quantified by SAXS. We proposed an improved multiscale Eshelby inclusion model that takes into account the two-level hierarchical structure, and validated it with a multidirectional experimental strain evaluation. The agreement between the simulation and measurement indicates that the multiscale hierarchical model developed here accurately reflects the structural arrangement and mechanical response of human dentine. This study benefits the comprehensive understanding of the mechanical behaviour of hierarchical biomaterials. The knowledge of the mechanical properties related to the hierarchical structure is essential for the understanding and predicting the effects of structural alterations that may occur due to disease or treatment on the performance of dental tissues and their artificial replacements.