Validation of finite-element-simulated orthodontic forces produced by thermoplastic aligners: Effect of aligner geometry and creep.

PURPOSE: Finite element (FE) models for determining the orthodontic forces delivered by clear aligners often lack validation. The aim of this study was to develop and validate accurate FE models for clear aligners, considering the small but important geometrical variations from the thermoforming process and the creep behavior of the aligner material. METHODS AND MATERIALS: The tooth misalignment considered was a 2.4° torque aberration (rotation about the mesial-distal axis at the level of the center of resistance) of the maxillary left central incisor. FE models were created from Micro-CT scans of a model dental arch and five nominally identical aligners with the aforementioned misfit. Fitting of the aligners onto the dental arch was simulated using Abaqus's Interference Fit function, followed by surface-to-surface frictional interaction. Stress relaxation of the aligner material was measured using double-cantilever beam bending and modeled with a Prony series. The assembled FE models were validated by comparing the predicted forces and moments delivered to the maxillary left central incisor with experimental data, obtained with a custom-built but fully calibrated apparatus. RESULTS: Good agreement between prediction and measurement was obtained for both the short- and long-term forces and moments. In the short-term, i.e., after 30 s, the dominant force in the labial-lingual direction had a maximum difference of 2.9% between experiment and simulation, and the dominant moment about the mesial-distal axis had a maximum difference of 8.3%. In the long-term, i.e., after 4 h, the experimental and numerical forces had a maximum difference of 8.4%. There were statistically significant differences in the forces delivered among the nominally identical aligners, which were predicted by the geometrically accurate FE models and attributed to the variations in the points of contact between the aligners and the dental arch. The decay in force applied was affected by both the viscoelastic material behavior and friction between the aligner and arch. CONCLUSION: For accurate prediction of the forces and moments delivered by thermoplastic aligners, FE models that can accurately capture the point contacts between the aligners and the underlying teeth are essential. Stress relaxation of the aligners could be adequately modeled using the Prony series to represent the temporal changes of their elastic modulus.

Validation of finite element models for orthodontic aligners.

PURPOSE: Clear thermoplastic aligners have become popular in orthodontics, but the biomechanics of these devices is not well understood. Neither is the tooth movement induced by such devices. The aim of this study was to develop and validate finite element (FE) models for clear thermoplastic teeth aligners for orthodontic force prediction. METHODS AND MATERIALS: FE models were created from Micro-CT scans of an aligner and a model arch of teeth with one of the incisors tipped buccal-lingually by 2.4°. The models were uniformly meshed with 0.3-mm long elements. Linear-elastic mechanical properties provided by the material manufacturers were used. Fitting of the two components was simulated using Abaqus's interference fit, followed by frictional surface-to-surface interaction. The assembled FE model was validated by comparing its prediction for the teeth-aligner gaps and aligner surface strains with experimental data. The experimental teeth-aligner gaps were obtained from the Micro-CT scans whereas the aligner surface strains were measured using a 2-camera digital image correlation (DIC) system. RESULTS: Good agreement between prediction and measurement was obtained for both the teeth-aligner gaps and aligner surface strains. The linear regression between prediction and measurement for teeth-aligner gaps sampled at different positions had a R2 value of 0.99. The mean difference between prediction and measurement for the aligner surface strains (von Mises) over 1544 nodes on the labial side and 1929 nodes on the lingual side was 0.07% and 0.01%, respectively, both being lower than the mean background noise. CONCLUSION: A FE model for clear thermoplastic teeth aligners has been successfully developed and validated. The model can therefore be used with confidence to predict the forces and moments applied to teeth by the aligners, thus improving our understanding of the biomechanics of such devices and the tooth movement they induce.

A parametric study of acetabular cup design variables using finite element analysis and statistical design of experiments.

To isolate the primary variables influencing acetabular cup and interface stresses, we performed an evaluation of cup loading and cup support variables, using a Statistical Design of Experiments (SDOE) approach. We developed three-dimensional finite element (FEM) models of the pelvis and adjacent bone. Cup support variables included fixation mechanism (cemented or noncemented), amount of bone support, and presence of metal backing. Cup loading variables included head size and cup thickness, cup/head friction, and conformity between the cup and head. Interaction between and among variables was determined using SDOE techniques. Of the variables tested, conformity, head size, and backing emerged as significant influences on stresses. Since initially nonconforming surfaces would be expected to wear into conforming surfaces, conformity is not expected to be a clinically significant variable. This indicates that head size should be tightly toleranced during manufacturing, and that small changes in head size can have a disproportionate influence on the stress environment. In addition, attention should be paid to the use of nonmetal backed cups, in limiting cup/bone interface stresses. No combination of secondary variables could compensate for, or override the effect of, the primary variables. Based on the results using the SDOE approach, adaptive FEM models simulating the wear process may be able to limit their parameters to head size and cup backing.