Gradient thickness in clear aligner gingival for incisor torque control in extraction cases simulated by finite element analysis

Gradient thickness in clear aligner gingival for incisor torque control in extraction cases simulated by finite element analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Gradient thickness in clear aligner gingival for incisor torque control in extraction cases simulated by finite element analysis Fujia Kang, Yifei Xu, Juan Wang, Yibao Li, Kun Qi, Menghong Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6211683/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Objectives: The objective of this study was to analyze the impact of gradient thickness of clear aligners(CAs) on incisors during retraction in extraction cases. Materials and methods: A three dimensional(3D) finite element model was constructed including maxilla, dentition, periodontal ligaments(PDLs) and CAs. The gingival-side thickness of the CAs was set as 0.8, 0.9, 1.0, 1.1, and 1.2 mm respectively. The occlusion-side thickness was adjusted to maintain the average thickness at 0.75 mm. Incisor retraction was simulated, after which, the total and segmental displacement as well as stress distribution were calculated. Results: In all groups, the incisors exhibited lingual tipping and extrusion, while the canines and premolars demonstrated mesial tipping. With the increase in the gingival-side thickness of the CAs, the maximum displacement and apical reverse movement of the incisors were reduced, accompanied by the labial and apical movement of the rotation center. Concurrently, the retraction and extrusion of incisors decreased. The stress distribution in PDLs of incisors became more uniform. Conclusions: The gradient thickness CA can reduce the extrusion and apical reverse movement, produce uniform stress distribution in PDLs, and shift the rotation center labially and apically. This proposal can be a promising strategy for torque control of incisors and prevention of root resorption. clear aligner extraction cases incisor retraction finite element analysis gradient thickness torque control Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Clear Aligners(CAs) have gained widespread popularity due to their aesthetic and comfort features( 1 ). The traditional CA manufacturing process, thermoforming, encompasses the stages of thermal softening and vacuum forming( 2 , 3 ). The film for CAs stretches and becomes thinner at protruding areas such as cusps and incisal edges. Conversely, it accumulates and thickens at fossa areas( 4 , 5 ). Since the clinical crown height of anterior teeth typically exceeds that of posterior teeth, the average thickness of CAs in the anterior region is consequently less, which is unfavorable for incisor control, especially during retraction in extraction cases. Considering that force application in CAs is up to its deformation and rebound( 6 , 7 ), theoretically, increased thickness can contribute to enhanced tooth movement control and treatment outcomes( 8 ). With the development of 3D printing technology and materials( 9 ), direct 3D printing of CAs has become possible( 10 ), and therefore the 'design-as-intended' can be realized, as illustrated in Fig. 1 . This inspires the improvement of treatment outcomes by innovation in the designs of CAs. The roller coaster effect during anterior retraction might be the main concern when the CAs are applied in extraction cases( 11 ), which is characterized by lingual tipping and extrusion of incisors, mesial tipping of canines, and all of the above-mentioned effects result in deep overbite, when the occlusal interference in anterior teeth region impedes incisors retraction, and thus mesial tipping of molars occurs. This phenomenon can be attributed by insufficient material strength and root control of CAs( 12 ). With an aim to endow CAs additional force on incisor roots, power ridges were put forward( 13 ). However, extensive application of power ridges increases the risk of CA debonding. A novel strategy is proposed in this study, that is a model of gradient thickness CAs, characterized by a continuous linear gradient increase in thickness from the occlusion-side to the gingival-side, which can be manufactured by the direct 3D printing technique. Therefore, we conducted an finite element study to analyze the impact of gradient thickness CAs on displacement of teeth and PDL stress distribution during incisor retraction in extraction cases. Material and methods Data collection The research was approved by the Ethics Committee of XXXX with the assigned identification number KY-QT-20240063. We selected patients from those who had previously undergone orthodontic treatment. The inclusion criteria include: mild dental crowding, protruding profile, permanent dentition, normal dental numbers and morphology as well as treatment plan involved the extraction of the maxillary and mandibular first premolars. We collected the pretreatment information including cone-beam computed tomography (CBCT) images utilizing the Planmeca Pro Max 3D system (Planmeca, Finland) and intraoral scanning data using the iTero® Element™ scanner (Align Technology, USA) of the patient. 3D model construction The CBCT data were imported into the Mimics software (Mimics Research v21.0, Materialise, Belgium) for subsequent processing. Employing the threshold segmentation and region growing techniques, we created mask layers for the maxilla and the upper dentition. The model files generated were then imported into the 3-Matic software (3-Matic Research v13.0, Materialise, Belgium) for advanced manipulation. Virtual extraction of the first premolars was performed, followed by manual realigning of the remaining teeth to establish a 0.5 mm gap between the canines and lateral incisors. According to previous studies, the PDLs were modeled with a 0.2 mm offset from the tooth roots( 14 , 15 ). The tooth movement step was set at 0.2 mm( 16 ) along the occlusal plane. The target dentition was constructed by completing the retraction of the incisors, and a CA model was generated by offsetting the crown surface of the target dentition. Based on varying thickness designs of the CA, a standard thickness of 0.75 mm( 17 , 18 ) was designated as the control group (Group 0). Subsequently, the gingival-side thickness of the CA was incrementally increased to achieve maximum thicknesses of 0.8, 0.9, 1.0, 1.1, and 1.2 mm. The thinned thickness was positioned at the cutting edge of the CAs, which was calculated by maximum thickness to maintain an average thickness of 0.75 mm, thereby controlling for variables, as depicted in Fig. 2 . Setting of material parameters and conditions Material parameters were derived from prior literature( 15 , 19 – 21 ), as depicted in the Table 1 . We established 'bonded' contact interfaces between the roots and the PDLs, as well as between the PDLs and the alveolar bone. Frictional contact is defined as having normal separation and tangential slip by frictional coefficient. 'Frictional' contact was defined between the external surface of the crown and the internal surface of the CA, with a friction coefficient of 0.2, according to values reported in the literature( 20 , 22 ). The upper surface of the maxilla was set as 'fixed'. To simulate the process of deformation and rebound of CA and apply mechanical loading, a 'two-step method' was utilized: initially, the incisors were moved from their target positions(post-retraction) to initial positions(pre-retraction), leading to deformation of the CAs; subsequently, stress results of CAs from the first step were applied to the dentition in its initial position, which was designed to simulate the rebound of CAs. Table 1 Material properties of the FEA model Young's modulus (MPa) Poisson's ratio Teeth 19,600 0.3 Alveolar bone 13,700 0.3 PDL 0.68 0.45 CA 528 0.36 Finite element simulation and result analysis The process of incisors retraction with gradient-thickness CA was simulated in Ansys Workbench(Ansys, USA). The comprehensive results encompass displacement of teeth and stress in PDLs. The total and directional displacement of teeth as well as Von-Mises equivalent stress in PDLs were extracted for analysis. Results Overall movement patterns of tooth in individual groups. The qualitative and quantitative thickness data of gradient-thickness CA were shown in Fig. 3 A, by which the successful model construction was confirmed. With the thickness of gingival side increased from 0.75mm to 1.20mm, the thickness of occlusion side decreased from 0.75mm to 0.60mm and the average thickness was maintained at 0.75mm. The qualitative overall dentition displacement was depicted in Fig. 3 B. During the retraction of incisors, in all groups, the central and lateral incisors showed lingual tipping and extrusion, with the root apices moved labially. The canines and second premolars exhibited mesial tipping, accompanied by minimal movement of the root apices. The first and second molars remained relatively stable. The maximum displacement was noted at the incisal edge of the lateral incisor (2.09× 10 − 1 mm in Group 0 and 1.87× 10 − 1 mm in Group 5), while the minimum was observed at the second molar (2.05× 10 − 2 mm in Group 0 and 1.82× 10 − 2 mm in Group 5). Notably, the displacement of lateral incisors of all groups were greater than that of central incisors. With the increase of gingival-side thickness of CAs from Group 0 to Group 5, the maximum displacement of the incisors decreased, whereas the decreasing trend of the lateral incisors was less significant than that of central incisors. Specifically, the maximum displacement of the lateral incisors was decreased from 2.09 × 10 − 1 mm(Group 0) to 1.87 × 10 − 2 mm(Group 5), and the maximum displacement of central incisors, decreased from 1.85 × 10 − 1 mm(Group 0) to 1.44 × 10 − 2 mm(Group 5), as shown in Table 2 . Table 2 Dentition displacement analysis (Unit[mm]) Group 0 Group 1 Group 2 Group 3 Group 4 Group 5 Central Incisor 1.85E-01 1.73E-01 1.72E-01 1.68E-01 1.63E-01 1.44E-01 Lateral Incisor 2.09E-01 1.95E-01 1.91E-01 1.87E-01 1.87E-01 1.87E-01 Canine 1.10E-01 1.10E-01 1.21E-01 1.15E-01 1.23E-01 1.13E-01 The Second Premolar 6.29E-02 7.24E-02 6.54E-02 6.01E-02 6.04E-02 5.90E-02 The First Molar 3.78E-02 3.56E-02 4.08E-02 3.19E-02 2.22E-02 2.56E-02 The Second Molar 2.05E-02 2.46E-02 2.08E-02 3.52E-02 1.85E-02 1.82E-02 Comparative analysis of directional tooth movement To elucidate the directional tooth movement patterns, we divided the incisors into six equal sections from the incisal edges to the root apices and was named as Level 0 to Level 5 as shown in Fig. 4 . Sagittal and vertical displacements of each section were shown in Table 3 – 6 and plotted as histograms shown in Fig. 5 . The nodes of the incisors with a sagittal displacement less than 1×10 − 3 mm were identified, which were fitted to a spatial straight line using the least square method, representing the rotation axis of the incisors in the sagittal plane. In the sagittal view from Group 0 to Group 5, the position of the rotation axis moved apically and labially. Moreover, the retraction of the right central incisor at the Level 1 decreased from 1.41×10 − 1 mm in Group 0 to 1.17×10 − 1 mm in Group 5, and at the Level 2 from 1.02×10 − 1 mm in Group 0 to 9.89×10 − 2 mm in Group 5. Whereas the decreasing trend at the Level 3 and Level 4 became less significant. At the Level 5 and Level 6 region, there was a decreasing tendency of labial movement. In the vertical view, from Group 0 to Group 5, the extrusion movement of the central incisor at Level 1 decreased, while the extrusion in Level 6 decreased. Overall, as the gingival-side thickness of the CA increased and the occlusion-side thickness decreased. the incisor's retraction and extrusion movement decreased. Table 3 Directional displacement of right lateral incisor (Unit[mm]) Group 0 Group 1 Group 2 Group 3 Group 4 Group 5 Sagittal displacement of right lateral incisor Level 1 1.78E-01 1.75E-01 1.64E-01 1.63E-01 1.65E-01 1.59E-01 Level 2 1.39E-01 1.30E-01 1.32E-01 1.26E-01 1.26E-01 1.28E-01 Level 3 9.81E-02 9.23E-02 8.79E-02 9.00E-02 8.60E-02 9.01E-02 Level 4 5.90E-02 5.44E-02 5.01E-02 4.96E-02 4.71E-02 5.96E-02 Level 5 1.97E-02 1.67E-02 1.30E-02 1.33E-02 1.85E-02 2.16E-02 Level 6 -1.92E-02 -2.01E-02 -1.58E-02 -2.27E-02 -1.64E-02 -2.13E-02 Average 8.87E-02 8.63E-02 7.97E-02 8.01E-02 8.52E-02 8.30E-02 Vertical displacement of right lateral incisor Level 1 -3.08E-02 -2.96E-02 -3.18E-02 -2.86E-02 -2.70E-02 -2.54E-02 Level 2 -1.66E-02 -1.30E-02 -2.08E-02 -1.62E-02 -1.09E-02 -1.11E-02 Level 3 -2.78E-03 -2.05E-03 -4.37E-03 -2.69E-03 -2.50E-03 1.64E-03 Level 4 3.12E-03 9.41E-03 6.34E-03 8.15E-03 7.89E-03 1.56E-02 Level 5 1.54E-02 2.09E-02 1.89E-02 1.99E-02 1.83E-02 2.61E-02 Level 6 2.70E-02 3.25E-02 3.19E-02 3.25E-02 2.99E-02 3.83E-02 Average -1.22E-03 -3.37E-04 -2.82E-03 -4.96E-04 -1.48E-03 3.66E-03 Table 4 Directional displacement of right central incisor (Unit[mm]) Group 0 Group 1 Group 2 Group 3 Group 4 Group 5 Sagittal displacement of right central incisor Level 1 1.41E-01 1.34E-01 1.31E-01 1.22E-01 1.23E-01 1.17E-01 Level 2 1.02E-01 1.01E-01 9.77E-02 9.29E-02 9.44E-02 8.98E-02 Level 3 6.46E-02 7.00E-02 6.64E-02 6.41E-02 6.30E-02 6.37E-02 Level 4 4.09E-02 4.02E-02 3.66E-02 3.54E-02 3.09E-02 3.73E-02 Level 5 4.10E-03 8.19E-03 5.21E-03 6.20E-03 5.00E-03 9.81E-03 Level 6 -3.57E-02 -3.16E-02 -3.23E-02 -2.67E-02 -1.95E-02 -1.78E-02 Average 7.13E-02 6.79E-02 6.55E-02 6.43E-02 6.05E-02 6.44E-02 Vertical displacement of right central incisor Level 1 -5.56E-02 -5.10E-02 -5.16E-02 -4.57E-02 -4.83E-02 -3.86E-02 Level 2 -3.57E-02 -3.46E-02 -3.59E-02 -3.22E-02 -3.45E-02 -2.55E-02 Level 3 -2.29E-02 -2.15E-02 -2.06E-02 -1.90E-02 -1.80E-02 -1.33E-02 Level 4 -8.67E-03 -6.08E-03 -5.05E-03 -4.95E-03 -1.88E-03 -2.84E-04 Level 5 3.70E-03 5.48E-03 5.10E-03 5.11E-03 9.31E-03 9.46E-03 Level 6 1.19E-02 1.39E-02 1.34E-02 1.13E-02 1.70E-02 1.44E-02 Average -2.54E-02 -2.08E-02 -2.17E-02 -2.00E-02 -1.84E-02 -1.46E-02 Table 5 Directional displacement of left central incisor (Unit[mm]) Group 0 Group 1 Group 2 Group 3 Group 4 Group 5 Sagittal displacement of left central incisor Level 1 1.38E-01 1.26E-01 1.20E-01 1.14E-01 1.17E-01 1.08E-01 Level 2 9.88E-02 9.39E-02 8.92E-02 8.27E-02 8.61E-02 8.15E-02 Level 3 6.45E-02 6.05E-02 6.18E-02 5.46E-02 5.75E-02 5.84E-02 Level 4 3.02E-02 2.53E-02 3.12E-02 2.59E-02 2.96E-02 3.37E-02 Level 5 -2.07E-03 -3.55E-03 -3.21E-03 -1.83E-03 1.39E-03 5.44E-03 Level 6 -3.59E-02 -3.88E-02 -3.31E-02 -2.68E-02 -2.64E-02 -2.13E-02 Average 6.54E-02 6.33E-02 5.53E-02 5.54E-02 5.63E-02 5.33E-02 Vertical displacement of left central incisor Level 1 -5.64E-02 -5.48E-02 -5.05E-02 -4.44E-02 -4.23E-02 -3.39E-02 Level 2 -3.74E-02 -3.77E-02 -3.66E-02 -2.89E-02 -2.72E-02 -2.64E-02 Level 3 -2.36E-02 -2.25E-02 -2.32E-02 -1.89E-02 -1.79E-02 -2.04E-02 Level 4 -6.44E-03 -3.60E-03 -8.85E-03 -4.86E-03 -3.47E-03 -9.21E-04 Level 5 5.55E-03 8.64E-03 3.75E-03 5.69E-03 7.17E-03 6.82E-03 Level 6 1.00E-02 1.41E-02 1.52E-02 1.49E-02 1.71E-02 1.79E-02 Average -2.36E-02 -2.19E-02 -2.13E-02 -1.84E-02 -1.59E-02 -1.64E-02 Table 6 Directional displacement of left lateral incisor (Unit[mm]) Group 0 Group 1 Group 2 Group 3 Group 4 Group 5 Sagittal displacement of left lateral incisor Level 1 1.92E-01 1.85E-01 1.79E-01 1.75E-01 1.81E-01 1.75E-01 Level 2 1.49E-01 1.48E-01 1.39E-01 1.43E-01 1.39E-01 1.43E-01 Level 3 1.05E-01 9.72E-02 9.39E-02 1.00E-01 9.39E-02 9.65E-02 Level 4 5.77E-02 4.65E-02 4.95E-02 5.09E-02 4.62E-02 4.92E-02 Level 5 9.27E-03 -3.98E-04 8.16E-03 5.37E-03 6.22E-03 1.36E-02 Level 6 -3.89E-02 -3.59E-02 -2.85E-02 -3.41E-02 -3.50E-02 -3.09E-02 Average 9.08E-02 9.47E-02 8.98E-02 9.31E-02 8.77E-02 9.14E-02 Vertical displacement of left lateral incisor Level 1 -3.87E-02 -3.48E-02 -2.93E-02 -3.50E-02 -3.10E-02 -3.04E-02 Level 2 -2.62E-02 -2.07E-02 -1.82E-02 -1.91E-02 -1.84E-02 -1.63E-02 Level 3 -9.05E-03 -9.63E-04 1.86E-04 -2.69E-03 -1.86E-03 5.73E-05 Level 4 3.59E-03 1.06E-02 1.10E-02 8.32E-03 8.20E-03 1.01E-02 Level 5 1.75E-02 2.38E-02 2.11E-02 2.41E-02 2.02E-02 2.36E-02 Level 6 3.36E-02 3.46E-02 3.37E-02 3.61E-02 3.30E-02 3.56E-02 Average -6.56E-03 -2.90E-03 -7.14E-04 -3.54E-03 -2.72E-03 1.13E-03 Von Mises equivalent stress distribution of the incisors PDLs The stress distribution in the PDLs was shown in the Fig. 6 A, with the color gradient from red to blue representing decrease in stress. Stress concentration phenomena were observed at the cervical areas in all groups. The stress distribution patterns on the PDLs were similar for the corresponding teeth on the left and side. The average stress value was 0.071Mpa for the right lateral incisors, and 0.047Mpa for right central incisor. From Group 0 to Group 5, the stress distribution become more uniform, and both the maximum stress and the average stress values become smaller. As shown in Fig. 6 B, the maximum stress of the right lateral incisor was 0.36, 0.32 0.35, 0.34, 0.33 and 0.32Mpa respectively, and the values for right central incisor were 0.27, 0.20, 0.22, 0.20, 0.19 and 0.16Mpa respectively. The average stress of the right lateral incisor was 0.087, 0.080, 0.088, 0.083, 0.080 and 0.071Mpa respectively, and the values for right central incisor were 0.059, 0.054, 0.053, 0.050, 0.055 and 0.047Mpa respectively. Discussion In this study, we proposed the model of CA with gradient thickness for the first time. And according to the finite element analysis, increased gingival-side and decreased occlusion-side thickness of CAs can decrease extrusion and tipping movement of incisors during retraction, and meanwhile achieve less Von Mises equivalent stress with more uniform distribution on PDLs, as depicted in Graphical Abstract. Challenges in torque and vertical control of the anterior teeth by CAs in extraction cases has been reported by numerous studies. Dai( 23 ) demonstrated that the central incisors tipped more lingually than predicted, with an achieved lingual crown torque of -14.43° ± 7.34 compared to a predicted value at -9.27° ± 9.09, furthermore, the central incisors exhibited more extrusion(-1.68 mm ± 1.02) than predicted(-1.18 mm ± 1.60). Likewise, compared with fixed appliance, the maxillary central incisors in the Invisalign group demonstrated significantly more lingual tipping and a greater increase in overbite( 24 ). The deficiency of CAs in torque control can be explained by the difficulties in applying a force couple system on the round surface of CAs compared to fixed appliances. Additionally, the elasticity of removable aligners inevitably limits the mechanical strength of the CAs, and as a result the root control of CAs is constrained. In this situation, the design of variable thickness of CAs become a promising key to this clinical issue. The association between the thickness of CAs and treatment outcomes has been demonstrated. Jeong-Hee found that the 0.75 mm-thick CAs resulted in 6% and 0.03% higher principal stresses in the PDLs and more teeth movement than that of the same treatment using a 0.05 mm-thick aligner( 25 ). In another study( 26 ), it was confirmed that the stress on the PDLs of incisors distributed more evenly with the 0.75mm-thick aligners than that of 0.5mm-thick ones after torque compensation with power ridge, and the torque control effects were more significant with 0.75 mm-thick aligners. Based on these previous findings, it can be safely concluded that thicker aligners benefit tooth movement and stress distribution. However, there has been no research on CAs with gradient thickness so far. In this study, this novel approach, a differential design in the thickness of CAs, was presented during incisors retraction. With the increase of gingival-side thickness of the CAs, the force for the lingual movement on the cervical and root of the incisors was intensified, thus leading the rotation center to shift apically and labially, which is consistent with previous studies( 27 ). Due to the apical movement of the rotation center, the distance between the apices and rotation center decreased, and unfavorable reverse movement of the root apices decreased. Meanwhile, as the undesired tipping movement of the incisors was reduced, the displacement differences among the segments of incisors was decreased. Consequently, the extrusion was decreased and the vertical control was improved. In summary, the outcomes above theoretically explained by the movement of rotation center confirmed the feasibility of the gradient thickness of the CA. Apart from the efficient tooth movement, the lower stress on the PDLs with more uniformly distribution was also achieved by gradient thickness in the gingival side. In this experiment, the stress on the PDLs gradually decreased from Group 1 to Group 5, which may be attributed to the decreased reverse movement of the root apices. The stress on PDLs of lateral incisors was higher than that of central incisors, which may be explained by the smaller PDL area of lateral incisors compared to that of the central incisors( 28 , 29 ). During retraction of incisors, the incisal edge moves towards the lingual side, while the root apex moves to the opposite direction. Since the amount of root displacement is often positively related to its stress( 30 – 33 ), increased displacement of root apex and incisal edge leads to increased and uneven stress distribution in PDLs. Based on the results in this study, reduced reverse movement of the root apex alleviates stress and its concentration, and therefore contributes to decreased tooth root resorption. Commercially available CAs are mainly produced by thermoforming process, which is composed of cast printing, thermal softening, vacuum forming and trimming. Apart from the effects on material properties due to heat generation and high labor cost in this process, the inhomogeneous thickness in CAs has become the significant drawback of this conventional technique( 34 ). With the emerging of direct 3D printing technique, the computer-aided digitally designed CAs for personalized treatment become feasible( 35 ). Furthermore, the appropriate thickness design assisted by FEA method, which simulates comprehensive responses of complex dental biomechanics, provides predictive capabilities for tooth movement and PDL stress distribution. More importantly, certain materials for direct 3D printing of CAs including Tera Harz TC85( 36 ), Dental LT( 37 ) and LuxCreo, which produce highly precise CAs with smooth edges, make this advanced technique applicable. Further comprehensive data of CA necessitates the conduct of additional in vitro mechanical testing and in vivo clinical assessments. Consequently, ongoing efforts are imperative to advance CA treatment. Conclusions Based on finite element analysis, increased thickness in CA gingival side improves torque and vertical control of the anterior teeth during retraction in extraction cases. Moreover, less apical reverse movement and more evenly stress distribution achieved by this strategy contribute to decreased risk of root resorption. Therefore, increased thickness in CA gingival side can be a promising and practical proposal for extraction cases by invisible treatment. Declarations Ethics approval and consent to participate This study was approved by the Ethics Committee of Stomatological Hospital of Xi'an Jiaotong University (KY-QT-20240063). According to the Declaration of Helsinki, written patient informed consent was obtained from the subject. The authors confirmed that all the methods were performed in accordance with the relevant guidelines and regulations. Consent for publication Not applicable. Competing interests The authors declare that they have no competing interests. Funding This work was supported and funded by the Xi'an Science and Technology Plan Project(2023JH-YXYB-0211). Author Contribution Fujia Kang conceived, designed and conducted the study, analyzed the results and drafted the manuscript. Yifei Xu, Juan Wang, Yibao Li contributed to perform the analyses and arranged the charts and tables. Kun Qi, Menghong Li reviewed the article and provided the instruction. All authors read and approved the final manuscript Acknowledgements Not applicable. Data Availability The data that support the findings of this study are available from the corresponding author and the first author upon reasonable request. References Bichu YM, Alwafi A, Liu X, Andrews J, Ludwig B, Bichu AY, et al. Advances in orthodontic clear aligner materials. Bioact Mater. 2023;22:384–403. Bhate M, Nagesh S. 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Guo R, Lam XY, Zhang L, Li W, Lin Y. Biomechanical analysis of miniscrew-assisted molar distalization with clear aligners: a three-dimensional finite element study. Eur J Orthod. 2024;46(1). Cortona A, Rossini G, Parrini S, Deregibus A, Castroflorio T. Clear aligner orthodontic therapy of rotated mandibular round-shaped teeth: A finite element study. Angle Orthod. 2020;90(2):247–54. Hong K, Kim WH, Eghan-Acquah E, Lee JH, Lee BK, Kim B. Efficient Design of a Clear Aligner Attachment to Induce Bodily Tooth Movement in Orthodontic Treatment Using Finite Element Analysis. Mater (Basel). 2021;14(17). Liu X, Cheng Y, Qin W, Fang S, Wang W, Ma Y, et al. Effects of upper-molar distalization using clear aligners in combination with Class II elastics: a three-dimensional finite element analysis. BMC Oral Health. 2022;22(1):546. Lin F, Ordinola-Zapata R, Fok ASL, Lee R. Influence of minimally invasive endodontic access cavities and bonding status of resin composites on the mechanical property of endodontically-treated teeth: A finite element study. Dent Mater. 2022;38(2):242–50. Cheng Y, Gao J, Fang S, Wang W, Ma Y, Jin Z. Torque movement of the upper anterior teeth using a clear aligner in cases of extraction: a finite element study. Prog Orthod. 2022;23(1):26. Dai FF, Xu TM, Shu G. Comparison of achieved and predicted tooth movement of maxillary first molars and central incisors: First premolar extraction treatment with Invisalign. Angle Orthod. 2019;89(5):679–87. Song JH, Lee JH, Joo BH, Choi YJ, Chung CJ, Kim KH. Treatment outcome comparison of Invisalign vs fixed appliance treatment in first premolar extraction patients. Am J Orthod Dentofac Orthop. 2024;165(4):399–413. Seo JH, Eghan-Acquah E, Kim MS, Lee JH, Jeong YH, Jung TG et al. Comparative Analysis of Stress in the Periodontal Ligament and Center of Rotation in the Tooth after Orthodontic Treatment Depending on Clear Aligner Thickness-Finite Element Analysis Study. Mater (Basel). 2021;14(2). Cheng Y, Liu X, Chen X, Li X, Fang S, Wang W, et al. The three-dimensional displacement tendency of teeth depending on incisor torque compensation with clear aligners of different thicknesses in cases of extraction: a finite element study. BMC Oral Health. 2022;22(1):499. Wang YG, Zhu GY, Liu JQ, Wang YF, Zhao ZH. Dynamic biomechanical changes of clear aligners during extraction space closure: Finite element analysis. Am J Orthod Dentofac Orthop. 2024;165(3):272–84. e3. Li Y, Jacox LA, Little SH, Ko CC. Orthodontic tooth movement: The biology and clinical implications. Kaohsiung J Med Sci. 2018;34(4):207–14. Ovy EG, Romanyk DL, Flores Mir C, Westover L. Modelling and evaluating periodontal ligament mechanical behaviour and properties: A scoping review of current approaches and limitations. Orthod Craniofac Res. 2022;25(2):199–211. Kirschneck C, Meier M, Bauer K, Proff P, Fanghanel J. Meloxicam medication reduces orthodontically induced dental root resorption and tooth movement velocity: a combined in vivo and in vitro study of dental-periodontal cells and tissue. Cell Tissue Res. 2017;368(1):61–78. Feller L, Khammissa RA, Schechter I, Moodley A, Thomadakis G, Lemmer J. Periodontal Biological Events Associated with Orthodontic Tooth Movement: The Biomechanics of the Cytoskeleton and the Extracellular Matrix. ScientificWorldJournal. 2015;2015:894123. Feller L, Khammissa RA, Schechter I, Thomadakis G, Fourie J, Lemmer J. Biological Events in Periodontal Ligament and Alveolar Bone Associated with Application of Orthodontic Forces. ScientificWorldJournal. 2015;2015:876509. Kim SY, Kim BS, Kim H, Cho SY. Occlusal stress distribution and remaining crack propagation of a cracked tooth treated with different materials and designs: 3D finite element analysis. Dent Mater. 2021;37(4):731–40. Jindal P, Worcester F, Siena FL, Forbes C, Juneja M, Breedon P. Mechanical behaviour of 3D printed vs thermoformed clear dental aligner materials under non-linear compressive loading using FEM. J Mech Behav Biomed Mater. 2020;112:104045. Maspero C, Tartaglia GM. 3D Printing of Clear Orthodontic Aligners: Where We Are and Where We Are Going. Mater (Basel). 2020;13(22). Simunovic L, Cekalovic Agovic S, Maric AJ, Bacic I, Klaric E, Uribe F et al. Color and Chemical Stability of 3D-Printed and Thermoformed Polyurethane-Based Aligners. Polym (Basel). 2024;16(8). Paradowska-Stolarz A, Wezgowiec J, Malysa A, Wieckiewicz M. Effects of Polishing and Artificial Aging on Mechanical Properties of Dental LT Clear((R)) Resin. J Funct Biomater. 2023;14(6). Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6211683","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":444598723,"identity":"1cf9de35-21f9-4398-b10a-f256b79af6df","order_by":0,"name":"Fujia Kang","email":"","orcid":"","institution":"Stomatological Hospital of Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Fujia","middleName":"","lastName":"Kang","suffix":""},{"id":444598724,"identity":"af565724-2ccc-4ac9-9cb9-b8460b00a837","order_by":1,"name":"Yifei Xu","email":"","orcid":"","institution":"Air Force Medical University","correspondingAuthor":false,"prefix":"","firstName":"Yifei","middleName":"","lastName":"Xu","suffix":""},{"id":444598725,"identity":"7694de65-9c57-4a8b-846f-447c8bcf96e1","order_by":2,"name":"Juan Wang","email":"","orcid":"","institution":"Stomatological Hospital of Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Juan","middleName":"","lastName":"Wang","suffix":""},{"id":444598726,"identity":"190147bf-7da8-42e6-9f1e-6c163e202694","order_by":3,"name":"Yibao Li","email":"","orcid":"","institution":"Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Yibao","middleName":"","lastName":"Li","suffix":""},{"id":444598727,"identity":"96740c6e-f375-46c3-9e69-94d2fd936a09","order_by":4,"name":"Kun Qi","email":"","orcid":"","institution":"Stomatological Hospital of Xi'an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Kun","middleName":"","lastName":"Qi","suffix":""},{"id":444598728,"identity":"56f918ba-0080-4c8e-853e-247aa82e0976","order_by":5,"name":"Menghong Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIiWNgGAWjYBACPmYwdQCImQ8wSIA5Cfi1sCG0sCUwSCQQo4UBroXHAKqakBZ27sTHBb/uyJnzr/kmYfnjMAM/e44Bw88d+BzGu9l4Zt8zY8sZbzcbSCQcZpDseWPA2HsGr5Zt0rw9hxM33Di78QFIi8GNHANmxja8Wrb/hmg58+AASIs9EVq2MfP8AGo538MIsUWCsJbN0rwNh40NbrAZG0ikpfNInHlWcLAXjxZ+/rMbP/P8OSxncP7wM2kJG2s5/vbkjQ9+4tECBmBnAKORGRj7PCCBAwQ0AMEfkH0HGBg/EFY6CkbBKBgFIxAAAAM7UPpsNYKnAAAAAElFTkSuQmCC","orcid":"","institution":"Stomatological Hospital of Xi'an Jiaotong University","correspondingAuthor":true,"prefix":"","firstName":"Menghong","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2025-03-12 11:38:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6211683/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6211683/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81017935,"identity":"55949b89-67db-4d95-90d3-a26b3bb8881d","added_by":"auto","created_at":"2025-04-21 09:13:04","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":227109,"visible":true,"origin":"","legend":"\u003cp\u003ethermoforming and direct 3D printing of CAs.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-6211683/v1/6139420b5e3cc8854fcc1bf1.png"},{"id":81018662,"identity":"5fec898d-860e-4387-8db5-adc6fc0265d1","added_by":"auto","created_at":"2025-04-21 09:21:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":736649,"visible":true,"origin":"","legend":"\u003cp\u003eModel construction and grouping\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-6211683/v1/0bf1cd92a091553a2a3222ad.png"},{"id":81017951,"identity":"15080c0f-357d-44c3-8e87-3a88811a2204","added_by":"auto","created_at":"2025-04-21 09:13:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":278063,"visible":true,"origin":"","legend":"\u003cp\u003eQualitative and quantitative analysis of CAs thickness (A) and dentition displacement (B)\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6211683/v1/e9c1d50eea54cb27f1d4243e.png"},{"id":81017936,"identity":"b147c746-1d02-4377-ab3b-c12c1ad97d9d","added_by":"auto","created_at":"2025-04-21 09:13:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":34540,"visible":true,"origin":"","legend":"\u003cp\u003eSegmentation methods for incisors\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-6211683/v1/9761661410b7e896a2ff231e.png"},{"id":81017942,"identity":"bf4a0089-409c-4068-94b2-4ed3b401e24d","added_by":"auto","created_at":"2025-04-21 09:13:04","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":426024,"visible":true,"origin":"","legend":"\u003cp\u003eDirectional displacement of central and lateral incisors. (A) The rotation axis positioning of incisors. (B) The Sagittal displacement of incisors. (C) The vertical displacement of incisors.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-6211683/v1/e8ea39cd4ed545f3db220fdb.png"},{"id":81021114,"identity":"cc7ad789-f95b-40d1-bcd7-d71ec814bdb5","added_by":"auto","created_at":"2025-04-21 09:45:04","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":335471,"visible":true,"origin":"","legend":"\u003cp\u003eVon Mises equivalent stress distribution in the PDLs(A) and quantitative analysis(B)\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-6211683/v1/0a5f27462a1fa476988a92ea.png"},{"id":87845756,"identity":"b0d59c88-93ea-4690-b2f1-c90f097ef602","added_by":"auto","created_at":"2025-07-29 15:02:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3011522,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6211683/v1/12420ae9-6c48-471a-a75c-87b1e6e8fab9.pdf"},{"id":81019805,"identity":"7e57fca3-a3f0-4388-a95a-f324f646cc21","added_by":"auto","created_at":"2025-04-21 09:29:04","extension":"bmp","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":5872554,"visible":true,"origin":"","legend":"","description":"","filename":"abstract.bmp","url":"https://assets-eu.researchsquare.com/files/rs-6211683/v1/b019c521ea5d4a89785d64a6.bmp"}],"financialInterests":"No competing interests reported.","formattedTitle":"Gradient thickness in clear aligner gingival for incisor torque control in extraction cases simulated by finite element analysis","fulltext":[{"header":"Introduction","content":"\u003cp\u003eClear Aligners(CAs) have gained widespread popularity due to their aesthetic and comfort features(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e). The traditional CA manufacturing process, thermoforming, encompasses the stages of thermal softening and vacuum forming(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e). The film for CAs stretches and becomes thinner at protruding areas such as cusps and incisal edges. Conversely, it accumulates and thickens at fossa areas(\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e). Since the clinical crown height of anterior teeth typically exceeds that of posterior teeth, the average thickness of CAs in the anterior region is consequently less, which is unfavorable for incisor control, especially during retraction in extraction cases. Considering that force application in CAs is up to its deformation and rebound(\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e), theoretically, increased thickness can contribute to enhanced tooth movement control and treatment outcomes(\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e). With the development of 3D printing technology and materials(\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e), direct 3D printing of CAs has become possible(\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e), and therefore the 'design-as-intended' can be realized, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. This inspires the improvement of treatment outcomes by innovation in the designs of CAs.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe roller coaster effect during anterior retraction might be the main concern when the CAs are applied in extraction cases(\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e), which is characterized by lingual tipping and extrusion of incisors, mesial tipping of canines, and all of the above-mentioned effects result in deep overbite, when the occlusal interference in anterior teeth region impedes incisors retraction, and thus mesial tipping of molars occurs. This phenomenon can be attributed by insufficient material strength and root control of CAs(\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e). With an aim to endow CAs additional force on incisor roots, power ridges were put forward(\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e). However, extensive application of power ridges increases the risk of CA debonding. A novel strategy is proposed in this study, that is a model of gradient thickness CAs, characterized by a continuous linear gradient increase in thickness from the occlusion-side to the gingival-side, which can be manufactured by the direct 3D printing technique.\u003c/p\u003e \u003cp\u003eTherefore, we conducted an finite element study to analyze the impact of gradient thickness CAs on displacement of teeth and PDL stress distribution during incisor retraction in extraction cases.\u003c/p\u003e"},{"header":"Material and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eData collection\u003c/h2\u003e \u003cp\u003eThe research was approved by the Ethics Committee of XXXX with the assigned identification number KY-QT-20240063. We selected patients from those who had previously undergone orthodontic treatment. The inclusion criteria include: mild dental crowding, protruding profile, permanent dentition, normal dental numbers and morphology as well as treatment plan involved the extraction of the maxillary and mandibular first premolars. We collected the pretreatment information including cone-beam computed tomography (CBCT) images utilizing the Planmeca Pro Max 3D system (Planmeca, Finland) and intraoral scanning data using the iTero\u0026reg; Element\u0026trade; scanner (Align Technology, USA) of the patient.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003e3D model construction\u003c/h3\u003e\n\u003cp\u003eThe CBCT data were imported into the Mimics software (Mimics Research v21.0, Materialise, Belgium) for subsequent processing. Employing the threshold segmentation and region growing techniques, we created mask layers for the maxilla and the upper dentition. The model files generated were then imported into the 3-Matic software (3-Matic Research v13.0, Materialise, Belgium) for advanced manipulation. Virtual extraction of the first premolars was performed, followed by manual realigning of the remaining teeth to establish a 0.5 mm gap between the canines and lateral incisors. According to previous studies, the PDLs were modeled with a 0.2 mm offset from the tooth roots(\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e). The tooth movement step was set at 0.2 mm(\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e) along the occlusal plane. The target dentition was constructed by completing the retraction of the incisors, and a CA model was generated by offsetting the crown surface of the target dentition. Based on varying thickness designs of the CA, a standard thickness of 0.75 mm(\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e) was designated as the control group (Group 0). Subsequently, the gingival-side thickness of the CA was incrementally increased to achieve maximum thicknesses of 0.8, 0.9, 1.0, 1.1, and 1.2 mm. The thinned thickness was positioned at the cutting edge of the CAs, which was calculated by maximum thickness to maintain an average thickness of 0.75 mm, thereby controlling for variables, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eSetting of material parameters and conditions\u003c/h3\u003e\n\u003cp\u003eMaterial parameters were derived from prior literature(\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e), as depicted in the Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. We established 'bonded' contact interfaces between the roots and the PDLs, as well as between the PDLs and the alveolar bone. Frictional contact is defined as having normal separation and tangential slip by frictional coefficient. 'Frictional' contact was defined between the external surface of the crown and the internal surface of the CA, with a friction coefficient of 0.2, according to values reported in the literature(\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e). The upper surface of the maxilla was set as 'fixed'. To simulate the process of deformation and rebound of CA and apply mechanical loading, a 'two-step method' was utilized: initially, the incisors were moved from their target positions(post-retraction) to initial positions(pre-retraction), leading to deformation of the CAs; subsequently, stress results of CAs from the first step were applied to the dentition in its initial position, which was designed to simulate the rebound of CAs.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMaterial properties of the FEA model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYoung's modulus (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoisson's ratio\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTeeth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19,600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAlveolar bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e13,700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e528\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e\n\u003ch3\u003eFinite element simulation and result analysis\u003c/h3\u003e\n\u003cp\u003eThe process of incisors retraction with gradient-thickness CA was simulated in Ansys Workbench(Ansys, USA). The comprehensive results encompass displacement of teeth and stress in PDLs. The total and directional displacement of teeth as well as Von-Mises equivalent stress in PDLs were extracted for analysis.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e \u003cb\u003eOverall movement patterns of tooth in individual groups.\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe qualitative and quantitative thickness data of gradient-thickness CA were shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA, by which the successful model construction was confirmed. With the thickness of gingival side increased from 0.75mm to 1.20mm, the thickness of occlusion side decreased from 0.75mm to 0.60mm and the average thickness was maintained at 0.75mm. The qualitative overall dentition displacement was depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB. During the retraction of incisors, in all groups, the central and lateral incisors showed lingual tipping and extrusion, with the root apices moved labially. The canines and second premolars exhibited mesial tipping, accompanied by minimal movement of the root apices. The first and second molars remained relatively stable. The maximum displacement was noted at the incisal edge of the lateral incisor (2.09\u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003emm in Group 0 and 1.87\u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003emm in Group 5), while the minimum was observed at the second molar (2.05\u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003emm in Group 0 and 1.82\u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003emm in Group 5). Notably, the displacement of lateral incisors of all groups were greater than that of central incisors. With the increase of gingival-side thickness of CAs from Group 0 to Group 5, the maximum displacement of the incisors decreased, whereas the decreasing trend of the lateral incisors was less significant than that of central incisors. Specifically, the maximum displacement of the lateral incisors was decreased from 2.09 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e mm(Group 0) to 1.87 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e mm(Group 5), and the maximum displacement of central incisors, decreased from 1.85 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e mm(Group 0) to 1.44 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e mm(Group 5), as shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDentition displacement analysis (Unit[mm])\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup 0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGroup 3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGroup 4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGroup 5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCentral Incisor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.85E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.73E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.72E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.68E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.63E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.44E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLateral Incisor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.09E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.95E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.91E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.87E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.87E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.87E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCanine\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.10E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.10E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.21E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.15E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.23E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.13E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe Second Premolar\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.29E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.24E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.54E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.01E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.04E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.90E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe First Molar\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.78E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.56E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.08E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.19E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.22E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.56E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe Second Molar\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.05E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.46E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.08E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.52E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.85E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.82E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eComparative analysis of directional tooth movement\u003c/h2\u003e \u003cp\u003eTo elucidate the directional tooth movement patterns, we divided the incisors into six equal sections from the incisal edges to the root apices and was named as Level 0 to Level 5 as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Sagittal and vertical displacements of each section were shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and plotted as histograms shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The nodes of the incisors with a sagittal displacement less than 1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003emm were identified, which were fitted to a spatial straight line using the least square method, representing the rotation axis of the incisors in the sagittal plane. In the sagittal view from Group 0 to Group 5, the position of the rotation axis moved apically and labially. Moreover, the retraction of the right central incisor at the Level 1 decreased from 1.41\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e mm in Group 0 to 1.17\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e mm in Group 5, and at the Level 2 from 1.02\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e mm in Group 0 to 9.89\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e mm in Group 5. Whereas the decreasing trend at the Level 3 and Level 4 became less significant. At the Level 5 and Level 6 region, there was a decreasing tendency of labial movement. In the vertical view, from Group 0 to Group 5, the extrusion movement of the central incisor at Level 1 decreased, while the extrusion in Level 6 decreased. Overall, as the gingival-side thickness of the CA increased and the occlusion-side thickness decreased. the incisor's retraction and extrusion movement decreased.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDirectional displacement of right lateral incisor (Unit[mm])\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup 0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGroup 3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGroup 4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGroup 5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eSagittal displacement of right lateral incisor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.78E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.75E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.64E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.63E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.65E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.59E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.39E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.30E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.32E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.26E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.26E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.28E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.81E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.23E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.79E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.00E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.60E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.01E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.90E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.44E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.01E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.96E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.71E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.96E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.97E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.67E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.30E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.33E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.85E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.16E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.92E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.01E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.58E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.27E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.64E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.13E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.87E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.63E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.97E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.01E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.52E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8.30E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eVertical displacement of right lateral incisor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3.08E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.96E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-3.18E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.86E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.70E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.54E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.66E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.30E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.08E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.62E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.09E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.11E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.78E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.05E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-4.37E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.69E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.50E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.64E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.12E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.41E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.34E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.15E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.89E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.56E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.54E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.09E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.89E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.99E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.83E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.61E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.70E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.25E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.19E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.25E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.99E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.83E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.22E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.37E-04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.82E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-4.96E-04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.48E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.66E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDirectional displacement of right central incisor (Unit[mm])\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup 0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGroup 3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGroup 4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGroup 5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eSagittal displacement of right central incisor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.41E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.34E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.31E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.22E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.23E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.17E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.02E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.01E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9.77E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.29E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.44E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8.98E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.46E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.00E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.64E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.41E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.30E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.37E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.09E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.02E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.66E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.54E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.09E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.73E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.10E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.19E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.21E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.20E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.00E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.81E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3.57E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.16E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-3.23E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.67E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.95E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.78E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7.13E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.79E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.55E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.43E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.05E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.44E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eVertical displacement of right central incisor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-5.56E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-5.10E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-5.16E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-4.57E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-4.83E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-3.86E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3.57E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.46E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-3.59E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-3.22E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.45E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.55E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.29E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.15E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.06E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.90E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.80E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.33E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-8.67E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-6.08E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-5.05E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-4.95E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.88E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.84E-04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.70E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.48E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.10E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.11E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.31E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.46E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.19E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.39E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.34E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.13E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.70E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.44E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.54E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.08E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.17E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.00E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.84E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.46E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDirectional displacement of left central incisor (Unit[mm])\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup 0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGroup 3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGroup 4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGroup 5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eSagittal displacement of left central incisor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.38E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.26E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.20E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.14E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.17E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.08E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.88E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.39E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.92E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.27E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.61E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8.15E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.45E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.05E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.18E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.46E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.75E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.84E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.02E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.53E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.12E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.59E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.96E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.37E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.07E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.55E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-3.21E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.83E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.39E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.44E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3.59E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.88E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-3.31E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.68E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.64E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.13E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.54E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.33E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.53E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.54E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e5.63E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.33E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eVertical displacement of left central incisor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-5.64E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-5.48E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-5.05E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-4.44E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-4.23E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-3.39E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3.74E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.77E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-3.66E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.89E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.72E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.64E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.36E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.25E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.32E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.89E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.79E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-2.04E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-6.44E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.60E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-8.85E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-4.86E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.47E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-9.21E-04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.55E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.64E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.75E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.69E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.17E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e6.82E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.00E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.41E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.52E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.49E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.71E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.79E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.36E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.19E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.13E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.84E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.59E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.64E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDirectional displacement of left lateral incisor (Unit[mm])\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGroup 0\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup 1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eGroup 2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGroup 3\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eGroup 4\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eGroup 5\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eSagittal displacement of left lateral incisor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.92E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.85E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.79E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.75E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.81E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.75E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.49E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.48E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.39E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.43E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.39E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.43E-01\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.05E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.72E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9.39E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.00E-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9.39E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.65E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.77E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.65E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.95E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.09E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4.62E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e4.92E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.27E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.98E-04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.16E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.37E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6.22E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.36E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3.89E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.59E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.85E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-3.41E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.50E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-3.09E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.08E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.47E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8.98E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9.31E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.77E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9.14E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003eVertical displacement of left lateral incisor\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-3.87E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-3.48E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-2.93E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-3.50E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-3.10E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-3.04E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-2.62E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.07E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.82E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1.91E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.84E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.63E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-9.05E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-9.63E-04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.86E-04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-2.69E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.86E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.73E-05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.59E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.06E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.10E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8.32E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e8.20E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.01E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.75E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.38E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.11E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.41E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.02E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.36E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLevel 6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.36E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.46E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.37E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.61E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.30E-02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.56E-02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-6.56E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-2.90E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-7.14E-04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-3.54E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.72E-03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.13E-03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eVon Mises equivalent stress distribution of the incisors PDLs\u003c/h3\u003e\n\u003cp\u003eThe stress distribution in the PDLs was shown in the Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eA, with the color gradient from red to blue representing decrease in stress. Stress concentration phenomena were observed at the cervical areas in all groups. The stress distribution patterns on the PDLs were similar for the corresponding teeth on the left and side. The average stress value was 0.071Mpa for the right lateral incisors, and 0.047Mpa for right central incisor. From Group 0 to Group 5, the stress distribution become more uniform, and both the maximum stress and the average stress values become smaller. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eB, the maximum stress of the right lateral incisor was 0.36, 0.32 0.35, 0.34, 0.33 and 0.32Mpa respectively, and the values for right central incisor were 0.27, 0.20, 0.22, 0.20, 0.19 and 0.16Mpa respectively. The average stress of the right lateral incisor was 0.087, 0.080, 0.088, 0.083, 0.080 and 0.071Mpa respectively, and the values for right central incisor were 0.059, 0.054, 0.053, 0.050, 0.055 and 0.047Mpa respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this study, we proposed the model of CA with gradient thickness for the first time. And according to the finite element analysis, increased gingival-side and decreased occlusion-side thickness of CAs can decrease extrusion and tipping movement of incisors during retraction, and meanwhile achieve less Von Mises equivalent stress with more uniform distribution on PDLs, as depicted in Graphical Abstract.\u003c/p\u003e \u003cp\u003eChallenges in torque and vertical control of the anterior teeth by CAs in extraction cases has been reported by numerous studies. Dai(\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e) demonstrated that the central incisors tipped more lingually than predicted, with an achieved lingual crown torque of -14.43\u0026deg; \u0026plusmn; 7.34 compared to a predicted value at -9.27\u0026deg; \u0026plusmn; 9.09, furthermore, the central incisors exhibited more extrusion(-1.68 mm\u0026thinsp;\u0026plusmn;\u0026thinsp;1.02) than predicted(-1.18 mm\u0026thinsp;\u0026plusmn;\u0026thinsp;1.60). Likewise, compared with fixed appliance, the maxillary central incisors in the Invisalign group demonstrated significantly more lingual tipping and a greater increase in overbite(\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e). The deficiency of CAs in torque control can be explained by the difficulties in applying a force couple system on the round surface of CAs compared to fixed appliances. Additionally, the elasticity of removable aligners inevitably limits the mechanical strength of the CAs, and as a result the root control of CAs is constrained. In this situation, the design of variable thickness of CAs become a promising key to this clinical issue.\u003c/p\u003e \u003cp\u003eThe association between the thickness of CAs and treatment outcomes has been demonstrated. Jeong-Hee found that the 0.75 mm-thick CAs resulted in 6% and 0.03% higher principal stresses in the PDLs and more teeth movement than that of the same treatment using a 0.05 mm-thick aligner(\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). In another study(\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e), it was confirmed that the stress on the PDLs of incisors distributed more evenly with the 0.75mm-thick aligners than that of 0.5mm-thick ones after torque compensation with power ridge, and the torque control effects were more significant with 0.75 mm-thick aligners. Based on these previous findings, it can be safely concluded that thicker aligners benefit tooth movement and stress distribution. However, there has been no research on CAs with gradient thickness so far. In this study, this novel approach, a differential design in the thickness of CAs, was presented during incisors retraction. With the increase of gingival-side thickness of the CAs, the force for the lingual movement on the cervical and root of the incisors was intensified, thus leading the rotation center to shift apically and labially, which is consistent with previous studies(\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e). Due to the apical movement of the rotation center, the distance between the apices and rotation center decreased, and unfavorable reverse movement of the root apices decreased. Meanwhile, as the undesired tipping movement of the incisors was reduced, the displacement differences among the segments of incisors was decreased. Consequently, the extrusion was decreased and the vertical control was improved. In summary, the outcomes above theoretically explained by the movement of rotation center confirmed the feasibility of the gradient thickness of the CA.\u003c/p\u003e \u003cp\u003eApart from the efficient tooth movement, the lower stress on the PDLs with more uniformly distribution was also achieved by gradient thickness in the gingival side. In this experiment, the stress on the PDLs gradually decreased from Group 1 to Group 5, which may be attributed to the decreased reverse movement of the root apices. The stress on PDLs of lateral incisors was higher than that of central incisors, which may be explained by the smaller PDL area of lateral incisors compared to that of the central incisors(\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e). During retraction of incisors, the incisal edge moves towards the lingual side, while the root apex moves to the opposite direction. Since the amount of root displacement is often positively related to its stress(\u003cspan additionalcitationids=\"CR31 CR32\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e), increased displacement of root apex and incisal edge leads to increased and uneven stress distribution in PDLs. Based on the results in this study, reduced reverse movement of the root apex alleviates stress and its concentration, and therefore contributes to decreased tooth root resorption.\u003c/p\u003e \u003cp\u003eCommercially available CAs are mainly produced by thermoforming process, which is composed of cast printing, thermal softening, vacuum forming and trimming. Apart from the effects on material properties due to heat generation and high labor cost in this process, the inhomogeneous thickness in CAs has become the significant drawback of this conventional technique(\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e). With the emerging of direct 3D printing technique, the computer-aided digitally designed CAs for personalized treatment become feasible(\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e). Furthermore, the appropriate thickness design assisted by FEA method, which simulates comprehensive responses of complex dental biomechanics, provides predictive capabilities for tooth movement and PDL stress distribution. More importantly, certain materials for direct 3D printing of CAs including Tera Harz TC85(\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e), Dental LT(\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e) and LuxCreo, which produce highly precise CAs with smooth edges, make this advanced technique applicable.\u003c/p\u003e \u003cp\u003eFurther comprehensive data of CA necessitates the conduct of additional in vitro mechanical testing and in vivo clinical assessments. Consequently, ongoing efforts are imperative to advance CA treatment.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eBased on finite element analysis, increased thickness in CA gingival side improves torque and vertical control of the anterior teeth during retraction in extraction cases. Moreover, less apical reverse movement and more evenly stress distribution achieved by this strategy contribute to decreased risk of root resorption. Therefore, increased thickness in CA gingival side can be a promising and practical proposal for extraction cases by invisible treatment.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eEthics approval and consent to participate\u003c/h2\u003e \u003cp\u003eThis study was approved by the Ethics Committee of Stomatological Hospital of Xi'an Jiaotong University (KY-QT-20240063). According to the Declaration of Helsinki, written patient informed consent was obtained from the subject. The authors confirmed that all the methods were performed in accordance with the relevant guidelines and regulations.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent for publication\u003c/strong\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis work was supported and funded by the Xi'an Science and Technology Plan Project(2023JH-YXYB-0211).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eFujia Kang conceived, designed and conducted the study, analyzed the results and drafted the manuscript. Yifei Xu, Juan Wang, Yibao Li contributed to perform the analyses and arranged the charts and tables. Kun Qi, Menghong Li reviewed the article and provided the instruction. All authors read and approved the final manuscript\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eNot applicable.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data that support the findings of this study are available from the corresponding author and the first author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBichu YM, Alwafi A, Liu X, Andrews J, Ludwig B, Bichu AY, et al. Advances in orthodontic clear aligner materials. Bioact Mater. 2023;22:384\u0026ndash;403.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBhate M, Nagesh S. Assessment of the Effect of Thermoforming Process and Simulated Aging on the Mechanical Properties of Clear Aligner Material. Cureus. 2024;16(7):e64933.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePalone M, Longo M, Arveda N, Nacucchi M, Pascalis F, Spedicato GA, et al. 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Effects of Polishing and Artificial Aging on Mechanical Properties of Dental LT Clear((R)) Resin. J Funct Biomater. 2023;14(6).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"clear aligner, extraction cases, incisor retraction, finite element analysis, gradient thickness, torque control","lastPublishedDoi":"10.21203/rs.3.rs-6211683/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6211683/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eObjectives:\u003c/strong\u003eThe objective of this study was to analyze the impact of gradient thickness of clear aligners(CAs) on incisors during retraction in extraction cases.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMaterials and methods: \u003c/strong\u003eA three dimensional(3D) finite element model was constructed including maxilla, dentition, periodontal ligaments(PDLs) and CAs. The gingival-side thickness of the CAs was set as 0.8, 0.9, 1.0, 1.1, and 1.2 mm respectively. The occlusion-side thickness was adjusted to maintain the average thickness at 0.75 mm. Incisor retraction was simulated, after which, the total and segmental displacement as well as stress distribution were calculated.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e In all groups, the incisors exhibited lingual tipping and extrusion, while the canines and premolars demonstrated mesial tipping. With the increase in the gingival-side thickness of the CAs, the maximum displacement and apical reverse movement of the incisors were reduced, accompanied by the labial and apical movement of the rotation center. Concurrently, the retraction and extrusion of incisors decreased. The stress distribution in PDLs of incisors became more uniform.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusions: \u003c/strong\u003eThe gradient thickness CA can reduce the extrusion and apical reverse movement, produce uniform stress distribution in PDLs, and shift the rotation center labially and apically. This proposal can be a promising strategy for torque control of incisors and prevention of root resorption.\u003c/p\u003e","manuscriptTitle":"Gradient thickness in clear aligner gingival for incisor torque control in extraction cases simulated by finite element analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-21 09:12:59","doi":"10.21203/rs.3.rs-6211683/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"497aaf59-62fd-43e4-b276-0f297ab462e3","owner":[],"postedDate":"April 21st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-29T14:54:04+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-21 09:12:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6211683","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6211683","identity":"rs-6211683","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}