Two-Level Homogenization Model for Sound and Caries Affected Dentin Elasticity

Methods: Elastic modulus of a second primary molar specimen exhibiting sound and caries-affected regions has been measured recently at ~100 µm resolution using SAM. The mineral mass fraction of the same sample was also obtained using backscattered electron microscopy (BSEM) and analyzed to obtain composition and mass density at the same location and lateral resolution as the SAM measurements. To investigate the relationship between elasticity and composition, a two-level homogenization model was developed. In level-1, a 3-component system formed by collagen/water/mineral is analyzed using rule of mixtures to obtain bounds of dentinal matrix elastic constants. In level-2, the dentinal matrix elastic constants are incorporated in a self-consistent porous media model to obtain the elastic constants at ~100 µm resolution.

Results: The experimental results exhibited a weak correlation between elastic modulus and composition. At certain density and mineral volume fraction, the elastic modulus variation was found to be as large as five times. Using the 2-level homogenization model we are able to show that the elastic moduli at a given composition can be predicted within tight bounds.

Conclusions: The homogenization model provides a reasonable approach to elastic moduli prediction of dentin within well defined upper and lower bounds. These methods do not provide exact predictions for the elastic moduli and these calculations suggest that additional interaction must be considered for better prediction methods.

Supported in part: NIH/NIDCR DE014392, 1K23DE/HD00468