Stiffness Homogenization of Damaged Teeth Repaired by Resin Injection
Résumé
Caries are the most common human pathology. Teeth are made of pulp, dentin and enamel. Dentin has a complex fabric, made of tubules [dimensions] surrounded by interwoven collagen fibers. In sane dentin, collagen fibers contain hydroxyapatite minerals. Caries can be cured by demineralizing the dentin collagen matrix and then injecting a resin composite to substitute for the damaged dentin. The main weakness with this reparation technique stems from adhesion deficiencies between the dentin which stays in place and the injected resin. This research work aims to model the elastic properties of dentin repaired by resin injection, for various adhesion scenarios. As a first approach, it is assumed that dentin structure is periodic. The unit cell contains a portion of tubule surrounded by a matrix made of collagen fibers [typical dimensions of the unit cell]. Resin is assumed to penetrate the collagen matrix in the vicinity of the tubule. Thus, three zones are modeled: (a) the tubule (full of resin), (b) a porous matrix of collagen fibers containing resin, (c) a matrix of collagen fibers with void pores. Dentin stiffness homogenization is performed in two stages: 1. The self-consistent method is used to homogenize the properties of the matrix made of collagen fibers. Two computations are performed, for the zone with void inter-fiber space (demineralized dentin), and for the zone where the inter-fiber space has the elastic properties of resin (peri-tubular dentin after injection), 2. The elasticity tensor of the unit cell is homogenized by considering the tubule as an inclusion with the elastic properties of the composite resin. The dimensions of the unit cell are fixed [dimensions]. Several cell geometries are studied, depending on the resin penetration distance in the collagen matrix. Two cases are studied to model the interface between the tubule and the dentin matrix: (a) perfect bonding, and (b) traction free boundary conditions. The proposed homogenization scheme is used to compute the elastic moduli of dentin repaired by injection and predict repaired dentin behavior during an axial compression test. The computational results are compared to experimental data obtained in the same loading conditions. Options to model resin adhesion at the interface between the tubule and the collagen matrix are discussed.