The use of patient imaging data in this research was in accordance with institutional ethical standards, following informed consent and approval by the Ethical Committee of the Shanghai Xuhui District Dental Center, Shanghai, China. CBCT data of a healthy adult’s dentition (with ANB angle of 4.8°, average growth pattern, Angle Class I molar relationship, and mild anterior crowding) with a slice thickness of 0.625 mm (GE Healthcare, Buckinghamshire, England) was imported into Mimics software (Version 18.0, Materialise, Leuven, Belgium) for 3 days reconstruction.

As illustrated in Figure 1a, CA with a thickness of 0.5 mm was designed on the reconstructed dentition model with the distal movement of canines (3) by 0.2 mm to provide orthodontic force. Attachments were adhered in the middle of the buccal surfaces of canines (3) and second premolars (5), and the attachment designs were categorized into 3 types: vertical wedge-shaped attachment (V), overhanging attachment (OH), and no attachment (NA). As shown in Figure 1b, vertical wedge-shaped attachments were designed with the wedge surface oriented towards the occlusal direction; OH attachments were designed with 6 mm extension towards gingiva.

CA trimline designs were divided into 4 types: (A) regular CA with unextended scalloped trimline; (B) CA with scalloped trimline and 5 mm buccal extension for gingival coverage at teeth 3∼5; (C) CA with scalloped trimline and 5 mm buccal extension for gingival coverage at teeth 2∼6; (D) CA with scalloped trimline and 5 mm buccolingual extension for gingival coverage at teeth 2∼6.

In total, 12 groups of models comprising 3 attachment types and 4 CA trimline designs were created and analyzed in this study, as shown in Table 1 and Figure 1c.

The reconstructed maxilla and dentition were then imported into 3-Matic Medical software (Version 9.0, Materialise, Leuven, Belgium) for further processing. Both first premolars (4) were removed to simulate subtractive tooth extraction. Alveolar bone was divided into cortical bone and cancellous bone, with 2 mm thickness of cortical bone. The alveolar bone was expanded outward by 2 mm to simulate the gingiva, and the space between the teeth and alveolar bone was expanded by 0.2 mm to simulate the PDL, according to typical parameters in existing orthodontic FEA studies (Canales et al., 2013; Cao et al., 2023; Çifter and Saraç, 2011).

3D reconstructed models of maxilla, dentition, gingiva, PDL, CA, and attachment in STL format were imported into the Geomagic software (3D-SYSTEM, United States) for surface smoothing, eliminating any potential geometric imperfections and noise. Subsequently, the output file was exported as IGES format and imported into Hypermesh software (Altair, United States) for preprocessing, including geometry repair, component organization, convergence experiment and shell meshing, material parameter setting, contact definition, and the application of boundary conditions. A symmetric dentition model with respect to the sagittal plane was adopted for analysis, with results ultimately presented as unilateral dentition.

The material parameters used in this study were obtained from material suppliers and literature (Seo et al., 2021; Canales et al., 2013; Sarrafpour et al., 2013), as detailed in Table 2. PDL was modeled using a visco-hyperelastic-damage constitutive model (Wu et al., 2022; Natali et al., 2008). To reduce computational complexity while maintaining accuracy, the teeth were modeled as rigid bodies, as prior studies have demonstrated that the difference in predicted displacement between rigid-body and fully elastic models was less than 3%, and that tooth deformation under orthodontic forces was negligible compared to overall movement (Tamaya et al., 2021; Hamanaka et al., 2017; Kim et al., 2025).

The interaction between CA and teeth was achieved via an interference fit, applying normal hard contact and tangential frictional sliding conditions, and a friction coefficient of 0.2. Tie constraints were applied between PDL and teeth, the outer layer of PDL and alveolar bone, alveolar bone and gingiva, teeth and gingiva (Natali et al., 2008; Hahn et al., 2009; Ortún-Terrazas et al., 2020; Huang et al., 2023; Goktas et al., 2011). The symmetrical model with respect to the sagittal plane was subjected to symmetrical displacement constraints.

The general FEA software ABAQUS (DASSAULT, France) was employed as the solver and processor to perform a detailed biomechanical analysis. Element sizes of the models were determined via the convergence experiment to ensure a sufficiently refined mesh for the simulation, and the applied element types, sizes and counts, and node counts were listed in Table 3. As shown in Table 3 and Figure 2, CAs were simulated using S4R shell elements and an element size of 0.2 mm. Attachments were simulated using C3D10M elements with a size of 0.2 mm. Gingiva and PDL were modeled using C3D10H elements with a size of 0.2 mm. For alveolar bone, C3D10 elements were applied, with element sizes of 0.2 mm in regions sharing nodes with gingiva and PDL (Seo et al., 2021; AlKahlan et al., 2025), and gradual transition of element sizes to 2 mm at other regions. Dentition was simulated using R3D3 elements with a size of 0.2 mm in regions sharing nodes with PDL, and gradual transition of element sizes to 0.8 mm at other regions.

The hydrostatic pressure exerted on the PDL served as an indicator of its tensile and compressive states. Exposure to tensile or compressive stress activated the internal vascular and neural elements of the PDL under their stress conditions, thereby triggering a series of biochemical reactions and activating osteoclasts and osteoblasts, which led to bone remodeling at the interface between the PDL and the alveolar bone. Typically, bone resorption occurred on the compression side, while bone formation took place on the tension side (Sarrafpour et al., 2013; Li et al., 2021).

As illustrated in the Figure 3a, it was evident that during the root control movement of canine (3) following the extraction of first premolar (4), the disto-cervical and mesio-apical areas of PDL near were subjected to compression (+), whereas the disto-apical and mesio-cervical areas were tension (−). The maximum and mean stress values for these regions were presented in Table 4. The comparison of the maximum hydrostatic pressure in the PDL was shown in Figure 3b. Under the same CA trimline design condition, the peak hydrostatic pressure in the PDL progressively increased from the no-attachment (NA) group, to the regular vertical attachment (V) group, and further to the overhanging attachment (OH) group, with the OH group exhibiting the highest pressure. Similarly, under the same attachment design condition, the peak hydrostatic pressure also increased sequentially from the conventional CA trimline (A), to the 3∼5 buccal extension (B), to the 2∼6 buccal extension (C), and to the 2∼6 buccolingual extension (D), with the D group presenting the maximum pressure. The application of regular attachments or OH attachments, as well as the buccal or lingual extended coverage of the CA, all enhanced the orthodontic force, thereby increasing the stress values in PDL. In all, the CA with 2∼6 buccolingual gingival extensions and OH attachments exhibited the highest hydrostatic pressure in PDL.

The ratio of mesio-apical to disto-cervical stress of PDL reflected the tipping extent of the tooth (Bi and Shi, 2023). In an ideal situation when the canine moved distally and translationally, both mesio-cervical and mesio-apical hydrostatic stress were tensile (with negative value or zero), and both disto-cervical and disto -apical hydrostatic stress were compressive (with positive value or zero), resulting in a zero or negative value of the ratio of mesio-apical to disto-cervical stress. Therefore, the closer the ratio of mesio-apical to disto-cervical stress was to zero or negative value, the closer the tooth movement was to distal translation. In this study, the ratios of mesio-apical to disto-cervical stress in PDL of canine in different groups were shown in Figure 4, calculated with maximum stress value (Figure 4a) or mean value (Figure 4b). With the same CA trimline design, the ratios progressively decreased from no-attachment (NA) group, to regular vertical attachment (V) group, and further to OH attachment group, with the OH group exhibiting the lowest ratio, indicating OH attachment was the most effective for achieving bodily tooth movement among the three attachment designs. Similarly, with the same attachment design, the ratios decreased sequentially from the conventional CA trimline (A), to the 3∼5 buccal extension (B), to the 2∼6 buccal extension (C), and to the 2∼6 buccolingual extension (D), with the D group presenting the minimum ratio. It could be concluded that the CA with 2∼6 buccolingual gingival extensions and OH attachments represented the optimal configuration for facilitating translational canine movement.

Figure 5 presented the heatmap of tooth movement in vector diagram. In all groups, distal inclination of canine was observed, accompanied with labial tipping of incisors and mesial inclination of molars, as an outcome of normal anchorage effect. As evidenced by the upper limits of the heatmap scale, the trend in tooth displacement aligned with the prior findings for PDL hydrostatic pressure, following the pattern OH > V > NA and D > C > B > A.

Figure 6 presented the heatmap of tooth movement with contour, where the point of minimum displacement (the center of blue region) represented the center of rotation of canine (Seo et al., 2021). Distances from root apex and tooth cusp to the rotational center were respectively designated as d1 and d2. The smaller the ratio of d1/d2, the closer the rotational center was to the root apex. And a ratio of zero indicated translational movement of the tooth. The ratios of d1/d2 in different groups were shown in Figure 7a. The ratio of mesio-apical to disto-occlusal displacement of canine (Figure 7b; Table 5) also reflected the degree of root control. The smaller the ratio, the closer the tooth movement was to distal translation (Liu L. et al., 2022).

With the same CA trimline design, the ratios of d1/d2 progressively decreased from no-attachment (NA) group, to regular vertical attachment (V) group, and further to OH attachment group, with the OH group reaching the minimum value. Similarly, with the same attachment design, the ratios of d1/d2 decreased sequentially from the conventional CA trimline (A), to the 3∼5 buccal extension (B), to the 2∼6 buccal extension (C), and to the 2∼6 buccolingual extension (D), with the D group presenting the minimum ratio. In all, D-OH group exhibited the smallest ratio of d1/d2. A similar trend was observed regarding the ratio of mesio-apical to disto-occlusal displacement of canine (Figure 7b; Table 5).

The CA with extended buccal and lingual gingival coverage and OH attachments effectively reduced the ratio of d1/d2 to 0.461, which was beneficial for controlling tooth rotation and reducing the inclination of tooth during translational movement. Findings in this study were consistent with previous reports (Elshazly et al., 2023; Elshazly et al., 2022) suggesting that extending the gingival coverage of CA benefited root control movement.

The deformation of the CA was shown in Figure 8. The maximum deformation occurred at the labial side of lateral incisor in groups without attachments (NA), which was attributed to the compression caused by anchorage effect that endowed the mesial movement of canine, resulting in a labial protrusion. With attachments on 3 and 5, maximum deformation occurred around the attachment on canine, deformation of CA at the lateral incisor was reduced, and the deformation at the buccal side of molars became more pronounced. As evidenced by the upper limits of the heatmap scale, introduction of attachments reduced the overall maximum deformation of CA, indicating more evenly distributed orthodontic force. With buccal extended coverage on 2∼6, the overall maximum deformation of CA increased, while with buccolingual extended coverage on 2∼6, the overall maximum deformation of CA decreased except for the OH attachment group (D-OH). The buccolingual extension exerted a slight torsion along the dental arch curve towards the mesial direction. Moreover, upon increasing the lingual and gingival coverage, and the maximum deformation of the CA shifted to the lingual gingival extension under the first molar, resulting in a decrease in deformation of molar crowns and enhancing the retention of CA, thereby avoiding the occurrence of attachment debonding.

Figure 9 indicated that an increase in maximum Von-Mises stress value was observed in CAs with no attachment (NA) as the gingival coverage enlarged (D > C > B > A). Comparing A-V with A-NA, the maximum Von-Mises stress values increased after the addition of a regular vertical attachment (V), while buccal extension of CA (B-V and C-V) resulted in decreased maximum Von-Mises stress to the level of A-N. Using regular vertical attachment (V), buccolingual extension (D-V) exhibited slightly increased stress compared to buccal extension (B-V and C-V). Notably, using OH attachment, there was no significant difference in the maximum Von-Mises stress values with or without extended gingival coverage, indicating the OH attachment could minimize stress concentration in CA. The membrane material employed in this simulation was PETG, with a yield strength of 45 MPa. All designs of CA met the material strength requirements, ensuring that no plastic deformation occurred during the wearing process.