The crucial role of periodontal ligament's Poisson's ratio and tension-compression asymmetric moduli on the evaluation of tooth displacement and stress state of periodontal ligament.

The hydrostatic stress in the periodontal ligament (PDL) evaluated by finite element analysis is considered an important indicator for determining an appropriate orthodontic force. The computed result of the hydrostatic stress strongly depends on the PDL material model used in the orthodontic simulation. This study aims to investigate the effects of PDL Poisson's ratio and tension-compression asymmetric moduli on both the simulated tooth displacement and the PDL hydrostatic stress. Three tension-compression symmetric and two asymmetric PDL constitutive models were selected to simulate the tensile and compressive behavior of a PDL specimen under uniaxial loading, and the resulting numerical results were compared with the in-vitro PDL experimental results reported in the literature. Subsequently, a tooth model was established, and the selected constitutive models and parameters were employed to assess the hydrostatic stress state in the PDL under two distinct loading conditions. The simulated results indicate that PDL Poisson's ratio and tension-compression asymmetry exert substantial influences on the simulated PDL hydrostatic stress. Conversely, the elastic modulus exhibits minimal impact on the PDL stress state under the identical loading conditions. Furthermore, the PDL models with tension-compression asymmetric moduli and appropriate Poisson's ratio yield more realistic hydrostatic stress. Hence, it is imperative to employ suitable Poisson's ratio and tension-compression asymmetric moduli for the purpose of characterizing the biomechanical response of the PDL in orthodontic simulations.

Anchorage effects of ligation and direct occlusion in orthodontics: A finite element analysis.

BACKGROUND AND OBJECTIVE: During orthodontic treatment, the figure-of-eight ligature and the physiological occlusion play an important role in providing anchorage effects. However, their effects on reaction forces of tooth and stress state in periodontal ligament (PDL) have not been quantitatively evaluated yet. In this study, we presented a finite element analysis process for simulating posterior molar ligature and direct occlusion during orthodontics in order to quantitatively assess their anchorage effects. METHODS: A high precision 3D biomechanical model containing upper and lower teeth, PDL, brackets and archwire was generated from the images of computed tomographic scan and sophisticated modelling procedures. The orthodontic treatment of closing the extraction gap was simulated via the finite element method to evaluate the biomechanical response of the molars under the conditions with or without ligation. The simulations were divided into experimental and control groups. In the experimental group, orthodontic force of 1 N was first applied, then direct occlusal forces of 3 and 10 N were applied on each opposite tooth. While in the control group, occlusal forces were applied without orthodontic treatment. The tooth displacement, the stress state in the PDL and the directions of the resultant forces on each tooth were evaluated. RESULTS: In the case of molars ligated, the maximum hydrostatic stress in the molars' PDL decreases by 60%. When an initial tooth displacement of several microns occurs in response to an orthodontic force, the direction of the occlusal force changes simultaneously. Even a moderate occlusal force (3 N per tooth) can almost completely offset the mesial forces on the maxillary teeth, thus to provide effective anchorage effect for the orthodontics. CONCLUSIONS: The proposed method is effective for simulating ligation and direct occlusion. Figure-of-eight ligature can effectively disperse orthodontic forces on the posterior teeth, while a good original occlusal relationship provides considerable anchorage effects in orthodontics.