Multi-Scale Analysis of Dentinal Matrix Micromechanical Properties

Objectives: (1) To develop a multi-scale poroelastic model that relates the micrometer and the millimeter scale properties of dentin, and (2) to obtain the elastic properties of the dentinal matrix utilizing the developed model in order to understand how the dentin anisotropy is affected by the presence of water. Methods: Resonant ultrasound spectroscopy has been used recently to measure the elastic constants of millimeter sized samples of dry and wet dentin. These measurements indicate that the wet dentin is transversely isotropic, with higher stiffness perpendicular to the tubule direction, while dry dentin is isotropic. A multi-scale model is developed to analyze these measurements and derive elastic moduli of dentinal matrix at micro-scales. The multi-scale model is based upon Hill's volume averaging method, and “concentration” tensors obtained through the self consistent technique. Results: The dentinal matrix is found to be mildly transverse isotropic with higher stiffness in the direction perpendicular to the tubule [in GPa: c11=39.68, c33=36.97, c12=15.48, c13=15.44, c44=11.48, assuming a mid-coronal porosity of 2.5%]. The predicted wet dentin properties are found to be transverse isotropic, and the predicted values of the wet dentin elasticity tensor are similar to the measured value in the literature [in GPa: c11=42.90, c33=36.52, c12=20.90, c13=14.71, c44=11.48]. However, this anisotropy is due to the pore pressures developed under undrained conditions during ultrasonic wave propagation. Conclusions: The anisotropic nature of dentinal matrix predicted by the multi-scale model is in agreement with the morphological features, such as the orientation of the collagen fibrils in the peri-tubular and inter-tubular dentin and the anisotropic nature of the hydroxyapatite crystals reported in the literature. The anisotropy of the wet dentin measured using resonant ultrasound method may be partially explained by the pore pressures developed during ultrasonic wave propagation. Supported in part: NIH/NIDCR DE014392