Extrusion of lower second premolars with Nuvola® clear aligners: a time-dependent finite element framework for assessing displacement efficiency and contact force trends

Context: Predicting a patient-specific clear aligner (CA) therapy outcome is challenging, especially when exploring the connection between aligner-to-tooth contact force transmission and tooth displacement. The periodontal ligament (PDL) response is fundamental in this interaction and, when simulated in a virtual environment, requires realistic approximations. This study evaluated extrusion efficiency and contact force trends in lower second premolars, using various attachment configurations. The PDL position was updated between multiple Nuvola® aligners during treatment. Simulations were run in FEBio. Methodology: In a finite element method (FEM) framework, three differently shaped attachments (horizontal rectangular, Nuvola®-drop and beveled) were applied on second premolars, with a retention group on adjacent teeth. Six aligners were designed to achieve a 0.15mm extrusion each (14 days of use) while the PDL was modeled as a coupled hyper-viscoelastic material and repositioned after each aligner use in an iterative scheme. Displacement efficiency was calculated by means of four metrics, and contact forces were another output. Results: Contact force trends in time showed highest initial peak and residual with the rectangular attachment, without significantly increasing efficiency as compared to the other attachments. They exhibited values in the range of 5 - 35 gf (∼= 0.05 - 0.35 N), in accordance with in vitro tests in literature. Angle-dependent efficiency metrics with penalty factors gave realistic results, with rough values in the range of 40-70%, depending on tooth, attachment and metric. Contact forces recorded a decrease during single aligner use, reflecting the PDL viscoelastic relaxation and progressive aligner adaptation. Conclusions: An appropriate PDL model was essential to predict teeth movement efficiency and contact force trends during CA therapy. Attachment designs strongly influenced force magnitudes, while it had a limited influence on the extrusion efficiency when compared to each other; however, all designs have shown a significant improvement in terms of efficiency with respect to no-attachment cases. Also, the retention group induced a more symmetric response of the two premolars. Future studies could implement patient-specific PDL properties calibration and integrate FEM tools to orthodontic setup software, increasing predictability of an actual treatment outcome and supporting aligner design optimization.