Deformation analysis of the periodontium considering the viscoelasticity of the periodontal ligament

Objectives: The aim of the present work was, by means of a combined experimental and numerical approach, to investigate the full-field distributions of displacement, stress and strain, and their evolution with loading in the entire fresh periodontium under an externally applied force. Methods: In situ intrusion tests were performed to identify the nonlinear, viscoelastic behavior of the periodontal ligament (PDL) of a pig mandible; a digital image correlation method was applied to examine the full-field deformation patterns in the entire periodontium. The finite element (FE) model was created based on the actual anatomic profiles of individual constituents of the tooth structure; the nonlinear and time-dependent viscoelastic properties of the PDL were input into the FE model to fit the numerical computations with the experimental measurements. Results: The nonlinear, viscoelastic behavior of the PDL was identified and characterized quantitatively. The simulation results were validated by the experiments. The results showed the tilting of tooth and the movement of cervical bone toward the mid-tooth in the studied periodontium under vertical compressive loading. Major strain was concentrated in the PDL, with the maxima near to the tooth apexes, at the tooth-root bifurcation and also at the sides of the tooth roots, and maintained a slight rise during holding of the applied displacement. High stress in the tooth was located mainly at the sides of tooth roots, in the bone it was concentrated near the apexes and the root bifurcation, and these stresses decreased gradually during the holding period. Significance: The combined approach of experiments that apply the digital image correlation method and FE analyses that take into account the nonlinear and time-dependent viscoelasticity of the PDL enables the acquisition of a full picture of detailed, realistic stress/strain fields and deformation patterns of the entire fresh periodontium, being of essence in orthodontics and dentistry.