Finite Element Analysis of Incisor Retraction with Clear Aligners

Cone beam computed tomography (CBCT) data (HiRes3D-Plus; Largev, Beijing, China) were acquired from a healthy volunteer with well-aligned dentition and normal axial inclination of the upper anterior teeth. As shown in Fig. 1a, three dimensions base models of the maxillary dentition with extracted first premolar were established using MIMICS 20.0 (Materialise, Leuven, Belgium). GEOMAGIC Studio 2014 (Raindrop GEOMAGIC, North Carolina, USA) was used to optimize the basic model and create a surface model structure. With the help of NX1911 software (Siemens, German), the outer surface of the maxillary teeth roots was extended outward by 0.25 mm to generate a preliminary model for PDLs. The maxillary was also moved inward by 1.3 mm to generate a bone cortex and cancellous structure. Vertical rectangular attachments (3 mm height, 2 mm width, and 1 mm thickness) were designed for all teeth other than the central incisor and the lateral incisor. The maxillary crown and attachment were extended outward by 0.5 mm to simulate the thickness of the appliance, and each tooth was treated as an independent component. All components were imported into ANSYS Workbench 2019 (Ansys, Pennsylvania, USA) to generate a 3D finite element model for finite element analysis.Fig. 1

Three-dimensional finite element model for incisor retraction in a case involving 1st premolar extraction. a Maxillary arch with 1st premolar removal with attachments on the vestibular surfaces of the crowns and a geometric model of the clear aligner. b Different axial inclinations of the upper central incisor (U1-SN = 105°; U1-SN = 110°). c The position and size of the power ridge

All structures were assumed as linear elastic isotropic and homogeneous materials. Their mechanical properties were obtained from previous studies [2 (link), 11 (link)] and are shown in Table 1. It was worthy of note that most scholars still agreed that it was reasonable to study tooth movement tendency even if the PDL was assigned linear material properties in FEA [7 (link), 12 (link), 13 (link)]. Bonding was established at the following interfaces: ligament bone, tooth ligament, and tooth attachments. No separation conditions were constructed among tooth interfaces. Frictionless conditions were established on contact interfaces between the aligner and tooth crown surfaces and attachments. The establishment of frictionless conditions created a nonlinear connection; this meant that this was a nonlinear study.Table 1

Properties of the materials considered in this study

Material	Young’s modulus, MPa	Poisson ratio
Alveolar bone	1.37 × 103	0.3
Tooth	1.96 × 104	0.3
PDL	6.9 × 10−1	0.45
Aligner	816	0.36
Attachment	12.5 × 103	0.36