Comparative effects of temporary anchorage devices combined with various auxiliary attachments on maxillary molar mesialization with clear aligners: a finite element analysis

Comparative effects of temporary anchorage devices combined with various auxiliary attachments on maxillary molar mesialization with clear aligners: a 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 Comparative effects of temporary anchorage devices combined with various auxiliary attachments on maxillary molar mesialization with clear aligners: a finite element analysis Feiyu wang, Yuxin Fan, Mingyuan Liu, Qingnan Mou, Ying Yang, Jianbo Gao, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7374655/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Apr, 2026 Read the published version in BMC Oral Health → Version 1 posted 14 You are reading this latest preprint version Abstract Background This study investigated the biomechanics of maxillary dentition, specifically displacement patterns, midline deviation, and stress distribution during first molar mesialization using the clear aligners (CA) assisted by temporary anchorage devices (TADs) combined with different auxiliary attachments, including lingual buttons, aligner-based angel buttons and power arms. Methods Finite element models of the clear aligner (CA), micro-implants, maxillary teeth, periodontal ligament (PDL), and alveolar bone were constructed. Four finite element models were simulated: Model A (CA alone, control); Model B (CA with micro-implants connected to aligner-based angel buttons); Model C (CA with micro-implants connected to lingual buttons on the first molar); and Model D (CA with micro-implants connected to power arms on the buccal surface of the first molar). The simulations evaluated three-dimensional tooth displacement, midline deviation, tipping angles, and PDL hydrostatic pressure of the maxillary dentition. Results Mesialization of the first molar using CA alone resulted in mesiolingual tipping and intrusion, while anchorage teeth experienced distobuccal or distolingual tipping and extrusion. Midline deviation tended toward the edentulous side due to reciprocal forces. Auxiliary force systems generally improved the efficiency of molar mesial movement and reduced anchorage tooth displacement compared to the control. Aligner-based angel buttons showed the most effective anchorage stability and minimal midline deviation. Lingual buttons produced the largest mesial movement of the first molar, with pronounced tipping and uneven PDL stress. Power arms showed the most bodily movement of the first molar and relatively uniform PDL stress, although anchorage control was less pronounced than that of aligner-based angel buttons. Conclusion The combined use of micro-implants and auxiliary devices demonstrated distinct effects on the first molar mesialization and anchorage teeth stability. Notably, aligner-based angel buttons provided the most effective anchorage control and the least midline deviation, while power arms resulted in the most bodily movement of the first molar. Clear aligners Finite element analysis Micro-impants Molar mesialization Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Background Clear aligner therapy (CAT) has gained significant popularity among both patients and orthodontists, primarily due to its enhanced comfort, superior aesthetics, and the ability to deliver a personalized and removable treatment approach [ 1 , 2 ]. As the demand for CAT continues to rise, the importance of accurately predicting orthodontic forces becomes increasingly critical [ 3 ]. Precise force prediction not only facilitates controlled and effective tooth movement, but also contributes to treatment efficiency, improving patient satisfaction, and the achievement of optimal clinical outcomes. The absence of the second premolar is commonly observed in clinical practice, often resulting from factors such as severe dental caries or advanced periodontal disease. The alternative treatments for the missing second premolars include prosthodontic treatment [ 4 ] and space closure through orthodontic treatment which involves the mesial movement of the molars [ 5 ]. Moreover, premolars are also the preferred extraction sites when necessary in orthodontics. For patients with mild dental crowding and a well-balanced facial profile, extraction of the second premolars is often considered a favorable option [ 6 ]. In such cases, space closure is typically achieved through the mesial movement of molars. However, it is well recognized that clear aligner (CA) has limitations in effectively controlling mesial tooth movement—especially when large mesial displacement of molars is required. Without proper anchorage or auxiliary mechanics, molars tend to exhibit uncontrolled movement, such as mesial tipping and rotation [ 7 ]. In addition, anchorage loss is unavoidable due to the reciprocal forces generated on the anchorage teeth during molar mesialization, posing a challenge for correction in the later treatment stages [ 8 ]. Therefore, maintaining proper control of anchorage and molar movement during CAT becomes a critical factor for achieving successful orthodontic outcomes. Simon’s research has reported that the accuracy of molar distalization with clear aligners ranges from 85.5–87% [ 9 ], demonstrating the clinical viability of this movement. In contrast, mesial movement of molars—the counterpart of distalization—remains a considerable challenge in CAT. This is largely due to the biomechanical limitations of aligners in generating controlled mesial forces, especially over long distances [ 10 ]. Mesial movement is often achieved by shortening the aligner to exert pressure on the posterior teeth; however, this approach often results in uncontrolled inclination Moreover, existing studies primarily focus on molar ditalization, and evidence regarding the predictability and effectiveness of mesial movement of maxillary molars remains limited and inconclusive. Further clinical research and biomechanical evaluations are essential to improve our understanding of aligner-driven mesialization and to develop more effective strategies for achieving stable and controlled tooth movement in such cases. Finite element analysis (FEA) is a robust and noninvasive computational technique used to approximate the mechanical behavior of complex geometries subjected to external forces with high accuracy. By discretizing complex structures into finite elements and solving mathematical models, FEA enables the prediction of stress, deformation, and failure points with high precision [ 11 ]. Using 3D modeling and simulation, it predicts tooth movement and aligner performance, enabling personalized treatment plans for optimal results [ 12 , 13 ]. Few finite element (FE) studies have systematically investigated the biomechanics of clear aligner-mediated molar mesial movement. The work by Lyu [ 14 ] established a foundational model simulating mandibular molar displacement using aligners with auxiliary attachments. However, their study was limited to examining only molar displacement trends in auxiliary device-based orthodontics, excluding micro-implants. Therefore, establishing finite element (FE) models is essential. to accurately simulate the biomechanics involved in micro-implants assisted molar mesialization. These models serve as a critical tool for predicting tooth movement and evaluating stress distribution under complex force systems. In this study, we focused on CAT incorporating micro-implants and auxiliary appliances to support maxillary molar mesialization. To our knowledge, this is the first study to systematically analyze and quantify the orthodontic tooth movements in molar mesialization with temporary anchorage devices and auxiliary devices through FE modeling, The objective is to evaluate the displacement patterns and stress distribution in the maxillary dentition during first molar mesialization, and to provide clinical guidance for treatment planning, including the selection of traction methods and tooth movement strategies. Materials and methods Three-dimensional(3D) model reconstruction Imaging data from cone beam computed tomography (CBCT) were collected from a healthy young female with ideal occlusion and normal facial morphology. To simulate a clinical extraction scenario, the right maxillary second premolar was digitally removed to create a post-extraction model. The DICOM images were input into Mimics 21.0 (Materialise NV, Belgium) to create the initial geometry., where threshold-based segmentation techniques were employed to accurately isolate the maxillary and individual teeth components. Following segmentation, the preliminary 3D reconstructions were refined and smoothed using Geomagic Studio 2021 (3D Systems, North Carolina, USA) to eliminate noise and surface irregularities. The anatomical components, including the alveolar bone, periodontal ligament (PDL), and dentition, were then designed and assembled in SolidWorks 2024 (Dassault Systèmes, France) (Fig. 1 ). The PDL was modeled as a uniform layer 0.25 mm thick by offsetting the external surfaces of the tooth roots [ 15 ], reflecting its average physiological thickness and biomechanical properties. To enhance aligner retention and simulate clinical practice, attachments were incorporated into the model. Vertical rectangular attachments(2mm*3mm*1mm) were placed on the buccal surfaces of premolars and canines. Horizontal rectangular attachments(3mm*2mm*1mm) were applied to the buccal surfaces of the maxillary molars to provide additional control during molar mesialization.The buttons (3 mm in diameter at the base and 1 mm in height) were placed on the first molar and the aligner. Power arms (3 mm in diameter at the base and 8 mm in height) were placed on the first molar. A micro-implant (diameter:1.5mm, height:8mm) representing skeletal anchorage, was integrated into the model to assist in molar protraction, positioned between the maxillary canine and the first premolar at a 60°angle to the occlusal plane, following established clinical guidelines for optimal biomechanical force application [ 16 ]. Table 1 Material properties Material Young’s modulus (MPa) Poisson’s ratio Teeth 1.96×10 4 0.3 Bone 1.37×10 4 0.3 PDL 0.67 0.45 Attachment 1.25×10 4 0.36 Clear Aligner 5.28×10 2 0.36 Buttons 1.14×10 5 0.35 Micro-implants 1.14×10 5 0.35 The refined anatomical model and CA were loaded into ANSYS Workbench 2024 (Pennsylvania, USA) to construct a detailed FE model for biomechanical analysis. The model components including the dentition, attachments, orthodontic button, PDL, and micro-implants were all defined as homogeneous, isotropic, and linearly elastic materials, consistent with parameters reported in previous literature [ 17 , 18 ] (see Table 1 for specific material properties). To evaluate the biomechanical impact of diverse auxiliary designs during maxillary molar mesialization with CA, four distinct FE models were developed (Fig. 2 ): Model A (Control group): Simulated molar mesialization using CA alone, without any anchorage reinforcement or auxiliary devices. This group served as the baseline for comparison. Model B (Aligner-based angel button group): An angled button was incorporated into the labial surface of the first molar on the CA to enable the application of elastic forces by attaching external elastics to a micro-implant. Model C (Lingual button group): Included a standardized lingual button bonded to the buccal surface of the first molar. The button-tooth interface was modeled as a rigid bond to simulate clinical composite resin bonding. Model D (Power arm group): Included a standardized power arm structure bonded to the buccal surface of the first molar. The connection between the power arm and the tooth surface was simulated as a rigid bond. Each model was subjected to identical boundary conditions and loading protocols to enable accurate comparison of force transmission, stress distribution, and predicted tooth displacement patterns under varying auxiliary mechanics. Boundary conditions A fixed support was applied to the superior portion of the maxillary to stabilize the finite element model during orthodontic force simulation, with all translational and rotational degrees of freedom fully constrained. This constraint effectively prevented undesired movement or deformation of the maxillary base during the application of orthodontic loading, thereby preserving the structural integrity of the model throughout the simulation process. Additionally, tie contact relationships were established between biologically bonded or continuous anatomical structures to simulate perfect bonding with no relative motion. These included the interfaces between the tooth and the PDL, the PDL and the alveolar bone, the alveolar bone and the micro-implant, as well as between the orthodontic attachment, the lingual button, and the tooth surface. These tie constraints allowed for accurate transmission of force and stress across the different tissue types. For components that exhibit contact under force with potential sliding, surface-to-surface contact elements were defined. A frictional coefficient of 0.2 was applied to both the interface between the CA and the attachments, as well as the CA and the tooth surfaces [ 19 ]. The frictional contact settings allowed for realistic modeling of aligner displacement and force dissipation during tooth movement. Table 2 Nodes and elements Node no. Element no. Model A 819,903 1,624,312 Model B 844,085 1,670,167 Model C 852,797 1,683,491 Model D 851,934 1,682,678 Loading methods and coordinate system A static loading condition was adopted for the FE simulation to replicate the force system applied during each step of molar mesialization with clear aligners. The mesial displacement of the maxillary first molar was simulated in incremental steps of 0.25 mm, corresponding to a single aligner activation cycle in clinical practice. All geometric models were discretized using 10-node tetrahedral (solid187) elements, which offer higher accuracy in capturing stress-strain behavior in complex anatomical structures. Table 2 presents the nodes and linear elements for each model. To enhance computational efficiency while maintaining numerical precision, region-specific mesh densities were applied based on the structural complexity and mechanical sensitivity of each component. The element sizes were defined as follows: 0.15 mm for the PDL, 0.20 mm for the dentition, orthodontic attachments, and appliances, 0.25 mm for the maxillary bone [ 18 , 19 ]. These mesh settings were optimized through a convergence test to balance computational cost and solution accuracy. A right-handed local coordinate system was established at the center of each tooth’s clinical crown for three-dimensional displacement analysis [ 20 ]. In this system, the X-axis represented the mesiodistal direction, the Y-axis corresponded to the buccolingual (or labiolingual) direction, and the Z-axis indicated the occlusogingival (or coronoapical) direction (Fig. 3 ). Displacement vectors were recorded with the mesial, palatal, and gingival directions defined as positive (+) values, allowing for the precise evaluation of individual tooth movement patterns in response to orthodontic force application. Midline deviation was determined using the global coordinate system by selecting the midpoint of the incisal edges between the maxillary central incisors (teeth 11 and 21) To analyze the first molar displacement trends, we measured the average displacement values from four cusp landmarks (mesiobuccal, distobuccal, and two palatal cusps) and three root apex points(mesiobuccal, distobuccal, and palatal roots) of the first molar, representing crown and root movement respectively.The difference in X-axis displacement between the crown and root was used to assess sagittal tipping tendency. The rotation angles θ of the first molar in the standard anatomical plane(XZ) are defined in Eq. ( 2 ), as illustrated in Fig. 3 D, the parameter α denoted the rotational change of the tooth, expressed in radians, and could be calculated using the given equation. The mesial movement efficiency was calculated as the proportion of the intended 0.25 mm movement that resulted in actual molar mesialization, as shown in Eq. ( 3 ). Anchorage teeth distalization, undesired tipping and rotation, occupied the remaining percentage. Results The whole dentiton displacement Figure 4 illustrated the force loading system exerted by CA. Model A was using CA alone. Model B applied elastic force to the aligner's angled button. Model C delivered the elastic force directly to the first molar via a lingual button, while model D exerted the force on a power arm bonded to the buccal surface of the first molar. As the first molar shifted mesially, an opposing force was exerted on the anchorage teeth, causing them to move in the reverse direction. The use of auxiliary devices and micro-implants helped reduce anchorage loss. Figure 5 depicted the resultant displacement trends across the maxillary dentition. When the first molar moved mesially, the anchorage teeth moved in the opposite direction, and the anterior teeth moved in the disto-palatal direction. Across all experimental models, Model C, featuring an lingual button on the the first molar with 200 g of traction force, showed the maximal displacement at 0.1501 mm. In contrast, Model A without micro-implants anchorage demonstrated minimal displacement of only 0.1269 mm. Figure 6 demonstrated the efficiency of tooth movement contributing to first molar mesialization at a 0.25 mm distance. In model A, the first molar exhibited 44.12% mesial movement, while the second molar and first premolar moved distally by 22.00% and 23.20%, respectively. The remaining 10.68% consisted of other unwanted movements. With the assistance of micro-implants, Models B, C and D resulted in a higher efficiency of first molar mesialization compared with model A. Among them, the increment in Model B was the smallest, while that in model C was the largest. Models B, C and D also had more proportion of undesired movements, compared with model A. Moreover,the incorporation of micro-implants in models B, C, and D led to a reduction in the distal displacement of the second molar and first premolar compared to model A. Additionally, model B exhibited a lower proportion of distalization than models C and D. These results suggested that micro-implants could improve the first molar mesialization (especially lingual button bonded on the tooth), and reduce the second molar and first premolar distalization (especially angle buttons), but also had more undesired movement (especially angle buttons). Furthermore, with increasing traction force, the proportion of effective molar mesialization showed a gradual rise, indicating improved efficiency of targeted tooth movement. However, this was accompanied by a simultaneous increase in the proportion of unintended movements, including tipping and rotation, suggesting that excessive force may compromise the quality of control and lead to less predictable outcomes. Three-dimensional displacement of the first molar The displacement patterns of the first molar varied considerably among the four models, as illustrated in Fig. 7 and Table 3 . All models exhibited that the first molar primarily moved mesially, with lingual or buccal movement and intrusion. The magnitude of displacement showed a positive correlation with the intensity of the applied force in model B, C and D. Due to the assistance of the micro-implant, the mesial movement of the first molar in models B, C and D was all increased compared to model A. The increment in model B was the smallest, whereas model C exhibited the largest. The use of the micro-implant also reduced the mesial tipping tendency of the first molar, with model D showing the least tipping and model B the most. Moreover, the first molar experienced lingual movement and intrusion during mesial movement with clear aligners alone. With the assistance of the micro-implant, the lingual movement decreased and the intrusion of the first molar increased. Among the three models with auxiliary devices, the lingual movement in model C was the smallest, while B displayed slight buccal movement. The first molar exhibited the greatest intrusion in Model C, whereas the least amount of intrusion was observed in Model D. Three-dimensional displacement of the second molar and first premolar The second molar mainly exhibited distal displacement and tipping, with slight buccal movement and extrusion during the mesial movement of the first molar (Fig. 7 and Table 3 ). In model A, where no additional anchorage was provided, the second molar showed the most pronounced distal tipping (-0.229°), as well as the largest distal displacement, buccal movement and extrusion. With the assistance of the micro-implant, the second molar exhibited reduced distal inclination, buccal displacement, and extrusion. These reductions were most pronounced in model B and least evident in model D. These results suggested that all three auxiliary-supported models effectively reduced undesired second molar movement, with model B providing the greatest stability, followed by model C and model D. The first premolar also mainly showed a distal displacement and tipping, and accompanied with a little lingual movement and extrusion. In model A, the premolar experienced the greatest distal movement and distal tipping (-0.243°), along with the largest lingual movement and extrusion. With the assistance of the micro-implant, distal tipping, lingual displacement, and extrusion of the first premolar were reduced. These changes were most significant in model B and least pronounced in model D. The results indicated that all three models supported by auxiliaries effectively minimized unwanted premolar movement, with model B offering the highest stability, followed by models C and D. Table 3 Proclination angle of the molar and premolar in X-axis (+, mesial; -distal) The first molar The second molar The first premolar Model A 0.831° −0.229° −0.243° Model B 100g 0.512° −0.088° −0.092° 150g 0.536° −0.094° −0.103° 200g 0.557° −0.112° −0.109° Model C 100g 0.714° −0.101° −0.114° 150g 0.743° −0.117° −0.127° 200g 0.784° −0.133° −0.150° Model D 100g 0.266° −0.120° −0.139° 150g 0.273° −0.125° −0.143° 200g 0.289° −0.132° −0.151° Three-dimensional displacement of the anterior teeth and midline deviation The anterior teeth exhibited a tendency to move toward distolingual tipping and extrusion (Fig. 8 ), resulting in anterior teeth retraction and midline deviation to the side of edentulous space in all models. Compared to model A, all undesired anterior tooth movement (distal tipping, lingual tipping and extrusion) was reduced in models B, C, and D, with model B showing the least amount of anterior teeth displacement. Model D has slightly more undesired anterior tooth movement than model C. Moreover, the midline deviated to edentulous space in all models. In model A, the anterior segment showed the most pronounced distal displacement, with an average of 0.0483 mm at the midline deviation of approximately toward the traction side. In model B, the deviation of midline was the least, measuring only 0.0137 mm, indicating excellent anchorage preservation and minimal reciprocal movement. Model D had slightly more midline deviation than model C. Hydrostatic stress distribution in PDL The PDL hydrostatic pressure was evaluated using the dentition as the unit of analysis to better reflect the biomechanical response under different loading conditions (Fig. 9 ). As for the first molar in model A, the highest hydrostatic pressure within the PDL was mainly localized in the mesial cervical region and the furcation area. Moreover, the degree of uneven force distribution varied across the four models. Among them, Models A and C exhibited the most uneven stress distribution, whereas Model D showed the most uniform pattern. Simultaneously, the micro-implant raised the PDL hydrostatic pressure. Compared to Model A, the maximum PDL pressure in Models C, B, and D was increased. Meanwhile, model C had the most PDL pressure because it is subjected to direct traction force and its mechanical distribution is uneven. As for the second molar, the maximum hydrostatic pressure in the PDL was primarily concentrated in the distal cervical region, and it was lower than that observed in the first molar. Compared to model A, models B, C, and D exhibited significantly reduced PDL hydrostatic stress. Notably, under increasing force (from 100 g to 200 g), the stress distribution remained stable, indicating better loading management and a reduced risk of tissue overload. Discussion Despite the growing popularity of CA in orthodontic treatment, molar mesialization using this approach presents several limitations. Due to the limited mechanical force that CA can deliver, achieving bodily movement of molars is challenging, often resulting in uncontrolled tipping and undesired movements such as lingual inclination and mesial tipping [ 21 ]. Additionally, the lack of rigid anchorage in CAT may lead to reciprocal movements of adjacent teeth, reducing the overall efficiency of molar mesialization. These limitations highlight the need for adjunctive strategies, such as skeletal anchorage or force-modulating auxiliaries devices, to improve the predictability and effectiveness of molar mesialization with CA. A recent research has reviewed that CA with a modified lever arm (MLA) reduced undesigned mesial tipping and rotation, optimized molar mesialization biomechanics [ 14 ]. However, current research on molar mesialization using CA combined auxiliary devices with micro-implants remains little. Unlike previous finite element studies that focused on single anchorage control or individual auxiliary devices, this work directly compared the biomechanical effects of multiple auxiliaries—including aligner-based angle buttons, lingual buttons, and power arms—combined with temporary anchorage devices. To the best of our knowledge, this is the first comparative approach to provide a comprehensive understanding of how different force delivery systems influence molar mesialization and anchorage control in clear aligner therapy. Our study demonstrated that when using clear aligners to move the first molar mesially, the main tooth movement was the mesialization of the first molar, followed by the distalization of the second molar and the first premolar. At the same time, other movements such as the retraction of the anterior teeth and the tipping movement of the tooth also occurred. Micro-implants could enhance the mesialization efficiency and intrusion amount of the first molar, reduced its mesial inclination, and also minimized the distal movement and lingual inclination of the anchoring teeth. These findings suggested that the use of micro-implants enhanced the efficiency of molar mesialization with clear aligners and helped stabilize the anchorage teeth. In addition, treatment designs that counteracted mesial tipping and lingual displacement of the molars were necessary. The tooth movement will be influenced by the direction of the traction force and the position of the resistance center [ 22 ]. Gandhi et al [ 23 ] identified the center of resistance of maxillary first molars is located apical and distal to the root trifurcation. As the center of rotation gets closer to the center of resistance, the molar demonstrates more parallel movement and less unwanted tipping/rotation [ 24 ]. In our study, the angle button connected to the CA, the lingual button and the power arm bonded on the first molar all affected the mesialization efficiency of the first molar and the type of tooth movement. For the angle button, since it was directly connected to the CA, it not only increased the mesialization efficiency of the first molars, but also had the strongest protection of the anchorage tooth. The lingual button bonded to the first molar not only significantly increased mesialization efficiency, but also had the greatest effect on its intrusion and mesial inclination. The power arm which could apply force closer to the center of resistance not only increased the mesialization amount of the first molars, but also significantly reduced its mesial inclination, and this was consistent with the fundings of the Hong et al [ 25 ]. The alignment between the maxillary dental midline and facial midline plays a pivotal role in facial esthetics [ 26 , 27 ]. In cases of unilateral tooth loss requiring molar mesialization, the reactive forces generated during molar mesialization often lead to a shift of the anterior teeth toward the edentulous side, resulting in midline deviation. Our study showed that when micro-implants were employed to deliver external forces, these undesired reactive effects could be effectively counteracted. Specifically, when using the aligner based angle button, the traction force from the mini-implant was distributed through the entire aligner system. This integration allowed for better force dissipation and anchorage control, thereby minimizing its influence on the dental midline. The magnitude and location of PDL hydrostatic pressure are related to the type of tooth movement, and direction and magnitude of force [ 28 , 29 ]. In this study, the PDL hydrostatic stress of the first molar was mainly concentrated at the mesial cervical and furcation regions, demonstrating that tooth movement in all models was mainly tipping movement, which was consistent with the findings of Jain’s research [ 30 ]. Our research also showed that the use of micro-implants not only increased the PDL hydrostatic stress on the first molar, but also affected the uniformity of the stress distribution in the PDL. Similar results were also observed in studies on the molar distalization [ 31 ]. Furthermore, if the traction force applied by the micro-implant directly acted on the lingual button bonded to the buccal regions of the first molar, it significantly increased the tipping movement, as well as the stress levels at the mesial cervical and furcation regions. However, using the power arm, since it was close to the resistance center of the first molar, the degree of tooth inclination decreased, and the unevenness of the stress distribution in the PDL also reduced. Excessive stress in the PDL can lead to risks such as root resorption and tooth loosening [ 32 , 33 ]. Therefore, during molar mesialization, using power arm bonded on the tooth or angle buttons connected to the aligner appliance is more beneficial for dental health. Nevertheless, this study had several limitations that should be taken into consideration when interpreting the results. The finite element model was constructed based on the CBCT data of a single patient, which may not adequately capture individual anatomical variations such as differences in root morphology, bone density, and periodontal ligament characteristics. Additionally, the simulation environment differed from actual clinical conditions; material properties of biological tissues were modeled as linear, isotropic, and uniform, which did not fully reflect the complex biomechanical behavior of oral structures. Futhermore, the forces generated by clear aligners and elastics were also simplified as static, constant loads, without accounting for changes due to oral function, patient compliance, or time-dependent effects. These simplifications may influence the accuracy of the predicted tooth movements, particularly in long-term clinical scenarios. While FEA served as a valuable technique for understanding biomechanical patterns, it remained a static, idealized model that did not simulate biological responses such as bone remodeling or tissue adaptation, and thus, its results should be interpreted as theoretical trends rather than precise clinical outcomes. Therefore, further clinical studies are necessary to validate and refine these findings before they can be widely applied in practice. Conclusion This finite element study aimed to analyze the biomechanical efficiency of molar mesialization and other tooth movements combined with CA. The findings showed that when only a clear aligner was used to move the first molar mesially, the mesialized tooth exhibited mesiolingual tipping and intrusion, while the anchorage teeth underwent distobuccal or distolingual tipping and extrusion. The midline deviated toward the side of the missing tooth as a result of reciprocal forces. Micro-implants could increase the effective contribution to molar mesialization, reduce mesiolingual tipping of the first molar, stabilize the anchorage teeth, minimize midline deviation, and optimize the distribution of PDL hydrostatic stress in the first molar. Meanwhile, with the assistance of the power arm, the first molar tended to exhibit bodily movement, and resulted in the most uniform distribution of PDL hydrostatic stress in the first molar.The use of angel buttons connected to the aligners maximized the stability of the anchorage teeth and minimized the midline deviation. Additionally, although the lingual button bonded to the first molar significantly increased its mesial movement, it also led to mesiolingual tipping and the most uneven distribution of PDL hydrostatic stress. The results provide valuable guidance for clinical decision-making on the use of micro-implants and selection of auxiliary attachments in clear aligner-based molar mesialization. Abbreviations CA :Clear aligner CAT Clear aligner therapy PDL Periodontal ligament FEA Finite element analysis CBCT Cone beam computed tomography Declarations Ethics approval and consent to participate This study was approved by the Ethics Committee of Hospital of Stomatology, Xi’an Jiaotong University, with the ethical review number (11[2022]NO.051).Informed consent was obtained from the participant, all methods were performed in accordance with the Declaration of Helsinki. Consent for publication Not applicable Competing interests The authors declare no competing interests Funding This study was supported by The National Natural Science Foundation of China (82370909); Author Contribution FW was responsible for conceptualization, methodology, finite element modeling, data analysis, and drafting the original manuscript. YF contributed to software development, data curation, and formal analysis. ML assisted with formal analysis and investigation. QM contributed to resource acquisition, investigation, and data management. YY was involved in data visualization and supported manuscript review and editing. PP , YH and JG jointly supervised the study and were involved in conceptualization, validation, critical manuscript revision, and funding acquisition. Acknowledgements Not applicable Data Availability The data supporting this study are available from the corresponding author upon reasonable request. References Cardoso PC, Espinosa DG, Mecenas P, Flores-Mir C, Normando D. Pain level between clear aligners and fixed appliances: a systematic review. Prog Orthod. 2020;21:3. https://doi.org/10.1186/s40510-019-0303-z . Rossini G, Parrini S, Castroflorio T, Deregibus A, Debernardi CL. Efficacy of clear aligners in controlling orthodontic tooth movement: a systematic review. Angle Orthod. 2015;85:881–9. https://doi.org/10.2319/061614-436.1 . Tartaglia GM, Mapelli A, Maspero C, Santaniello T, Serafin M, Farronato M, et al. Direct 3D printing of clear orthodontic aligners: Current state and future possibilities. Mater (Basel). 2021;14:1799. https://doi.org/10.3390/ma14071799 . Kokich VG, Kokich VO. Congenitally missing mandibular second premolars: clinical options. Am J Orthod Dentofac Orthop. 2006;130:437–44. https://doi.org/10.1016/j.ajodo.2006.05.025 . Williams R, Park JH, Chae J-M, Vaden JL. The congenitally missing second premolar: Space closure. A viable option. Am J Orthod Dentofac Orthop. 2020;157:571–e58316. https://doi.org/10.1016/j.ajodo.2019.10.015 . Elias KG, Sivamurthy G, Bearn DR. Extraction vs nonextraction orthodontic treatment: a systematic review and meta-analysis. Angle Orthod. 2024;94:83–106. https://doi.org/10.2319/021123-98.1 . Yang Y, Yang R, Liu L, Zhang X, Jiang Q, Fan Q, et al. The effects of aligner anchorage preparation on mandibular first molars during premolar-extraction space closure with clear aligners: A finite element study. Am J Orthod Dentofac Orthop. 2023;164:226–38. https://doi.org/10.1016/j.ajodo.2022.12.013 . Ren L, Liu L, Wu Z, Shan D, Pu L, Gao Y, et al. The predictability of orthodontic tooth movements through clear aligner among first-premolar extraction patients: a multivariate analysis. Prog Orthod. 2022;23:52. https://doi.org/10.1186/s40510-022-00447-y . Simon M, Keilig L, Schwarze J, Jung BA, Bourauel C. Treatment outcome and efficacy of an aligner technique–regarding incisor torque, premolar derotation and molar distalization. BMC Oral Health. 2014;14:68. https://doi.org/10.1186/1472-6831-14-68 . Long H, Wu Z, Yan X, Wang Q, Liu L, Wang Y, et al. An objective system for appraising clear aligner treatment difficulty: clear aligner treatment complexity assessment tool (CAT-CAT). BMC Oral Health. 2020;20:312. https://doi.org/10.1186/s12903-020-01300-6 . Zhu G-Y, Zhang B, Yao K, Lu W-X, Peng J-J, Shen Y, et al. Finite element analysis of the biomechanical effect of clear aligners in extraction space closure under different anchorage controls. Am J Orthod Dentofac Orthop. 2023;163:628–e64411. https://doi.org/10.1016/j.ajodo.2022.02.018 . Cattaneo PM, Cornelis MA. Orthodontic tooth movement studied by finite element analysis: An update. What can we learn from these simulations? Curr Osteoporos Rep. 2021;19:175–81. https://doi.org/10.1007/s11914-021-00664-0 . Murakami N, Wakabayashi N. Finite element contact analysis as a critical technique in dental biomechanics: a review. J Prosthodont Res. 2014;58:92–101. https://doi.org/10.1016/j.jpor.2014.03.001 . Lyu X, Cao X, Chen L, Liu Y, Li H, Hu C, et al. Accumulated biomechanical effects of mandibular molar mesialization using clear aligners with auxiliary devices: an iterative finite element analysis. Prog Orthod. 2023;24:13. https://doi.org/10.1186/s40510-023-00462-7 . Cai Y, Yang X, He B, Yao J. Finite element method analysis of the periodontal ligament in mandibular canine movement with transparent tooth correction treatment. BMC Oral Health. 2015;15:106. https://doi.org/10.1186/s12903-015-0091-x . Liu X, Wu J, Cheng Y, Gao J, Wen Y, Zhang Y, et al. Effective contribution ratio of the molar during sequential distalization using clear aligners and micro-implant anchorage: a finite element study. Prog Orthod. 2023;24:35. https://doi.org/10.1186/s40510-023-00485-0 . Daqiq O, Gareb B, Spijkervet FKL, Wubs FW, Roossien CC, van Minnen B. Finite element analysis of the human mandible: a systematic review with meta-analysis of the essential input parameters. Sci Rep. 2025;15:19582. https://doi.org/10.1038/s41598-025-03959-9 . Jiang T, Wu RY, Wang JK, Wang HH, Tang GH. Clear aligners for maxillary anterior en masse retraction: a 3D finite element study. Sci Rep. 2020;10:10156. https://doi.org/10.1038/s41598-020-67273-2 . He X, Zhuang W-H, Zhang D-L. A three-dimensional finite element analysis: Maxillary dentition distalization with the aid of microimplant in lingual orthodontics. Int J Gen Med. 2021;14:8455–61. https://doi.org/10.2147/IJGM.S337212 . 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;22:499. https://doi.org/10.1186/s12903-022-02521-7 . Dai F-F, Xu T-M, 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;89:679–87. https://doi.org/10.2319/090418-646.1 . Yoshida N, Jost-Brinkmann PG, Koga Y, Mimaki N, Kobayashi K. Experimental evaluation of initial tooth displacement, center of resistance, and center of rotation under the influence of an orthodontic force. Am J Orthod Dentofac Orthop. 2001;120:190–7. https://doi.org/10.1067/mod.2001.115036 . Gandhi V, Luu B, Dresner R, Pierce D, Upadhyay M. Where is the center of resistance of a maxillary first molar? A 3-dimensional finite element analysis. Am J Orthod Dentofac Orthop. 2021;160:442–e4501. https://doi.org/10.1016/j.ajodo.2020.04.033 . Tanne K, Koenig HA, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofac Orthop. 1988;94:426–31. https://doi.org/10.1016/0889-5406(88)90133-3 . Hong K, Kim W-H, Eghan-Acquah E, Lee J-H, Lee B-K, Kim B. Efficient design of a clear aligner attachment to induce bodily tooth movement in orthodontic treatment using finite element analysis. Materials. 2021;14(17):4926. https://doi.org/10.3390/ma14174926 . Wang X, Long J, Mei M, Huang J, Chen Y, Zhou Y, et al. Acceptable deviation of labial tubercle and anterior tooth midlines relative to facial midline in smile aesthetics: A retrospective observational study. Med (Baltim). 2022;101:e30983. https://doi.org/10.1097/MD.0000000000030983 . Korkut B, Ograk I, Murat N, Ntovas P, Tuter Bayraktar E, Senol AA, et al. Effect of Midline deviation and crown width disproportion on perception of smile esthetics. J Esthet Restor Dent. 2025. https://doi.org/10.1111/jerd.13492 . Nogueira AVB, Marcantonio CC, de Molon RS, Leguizamón NDP, Silva RCL, Deschner J, et al. Experimental models of orthodontic tooth movement and their effects on periodontal tissues remodelling. Arch Oral Biol. 2021;130:105216. https://doi.org/10.1016/j.archoralbio.2021.105216 . Nazeri A, Castillo JA Jr, Ghaffari-Rafi A. Impact of molar distalization with clear aligners on periodontal ligament stress and root resorption risk: A systematic review of 3D finite element analysis studies. Dent J. 2025;13. https://doi.org/10.3390/dj13020065 . Jain A, Prasantha GS, Mathew S, Sabrish S. Analysis of stress in periodontium associated with orthodontic tooth movement: a three dimensional finite element analysis. Comput Methods Biomech Biomed Engin. 2021;24:1841–53. https://doi.org/10.1080/10255842.2021.1925255 . Tang X, Wang M, Hu X, Zheng L, Yang C. The effects of palatal anchorage device on molar distalization with clear aligner: Three-dimensional finite element analysis. Am J Orthod Dentofac Orthop. 2025. https://doi.org/10.1016/j.ajodo.2025.04.012 . Hohmann A, Kober C, Young P, Dorow C, Geiger M, Boryor A, et al. Influence of different modeling strategies for the periodontal ligament on finite element simulation results. Am J Orthod Dentofac Orthop. 2011;139:775–83. https://doi.org/10.1016/j.ajodo.2009.11.014 . Qian L, Todo M, Morita Y, Matsushita Y, Koyano K. Deformation analysis of the periodontium considering the viscoelasticity of the periodontal ligament. Dent Mater. 2009;25:1285–92. https://doi.org/10.1016/j.dental.2009.03.014 . 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-7374655","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":513675902,"identity":"67582830-5aad-4354-8071-35cff25835dd","order_by":0,"name":"Feiyu wang","email":"","orcid":"","institution":"Key laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi’an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Feiyu","middleName":"","lastName":"wang","suffix":""},{"id":513675903,"identity":"5078cb44-ab6d-4c72-bbd2-f7ab75a2c383","order_by":1,"name":"Yuxin Fan","email":"","orcid":"","institution":"Shaanxi Key Laboratory of Intelligent Robots, Xi’an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Yuxin","middleName":"","lastName":"Fan","suffix":""},{"id":513675904,"identity":"2d2fe3ec-e68b-4069-a7e4-afea5616a842","order_by":2,"name":"Mingyuan Liu","email":"","orcid":"","institution":"Key laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi’an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Mingyuan","middleName":"","lastName":"Liu","suffix":""},{"id":513675905,"identity":"b48283c2-166a-4abd-989d-d798da4c5037","order_by":3,"name":"Qingnan Mou","email":"","orcid":"","institution":"Key laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi’an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Qingnan","middleName":"","lastName":"Mou","suffix":""},{"id":513675906,"identity":"efa0d3d2-2e3c-4c53-b16f-1eabf31abc8a","order_by":4,"name":"Ying Yang","email":"","orcid":"","institution":"Key laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi’an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Ying","middleName":"","lastName":"Yang","suffix":""},{"id":513675907,"identity":"281cf990-c0c1-43ee-979f-445fda7b12b8","order_by":5,"name":"Jianbo Gao","email":"","orcid":"","institution":"Department of Orthopaedics, Xijing Hospital, Fourth Military Medical University","correspondingAuthor":false,"prefix":"","firstName":"Jianbo","middleName":"","lastName":"Gao","suffix":""},{"id":513675908,"identity":"ebe37d66-0ae6-4635-8a54-47f6ac2984ae","order_by":6,"name":"Yuxia Hou","email":"","orcid":"","institution":"Key laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi’an Jiaotong University","correspondingAuthor":false,"prefix":"","firstName":"Yuxia","middleName":"","lastName":"Hou","suffix":""},{"id":513675909,"identity":"46dda17c-7bef-45f6-8b50-60325edfb9b0","order_by":7,"name":"Panjun Pu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYBACNvaG9B8fDP7L2bc3HyBOCx/PgQeSMwqYjQ14jiUQp0VOIvGBNMcH5kQDiRwDIh3GkJxgzGDAlmDOc+bjjTcMdnK6DQS1HEtILjDgybNs791sOYch2djsACEtjD0Jh2cYSBQznDm7TZqH4UDiNoJamPk/NvMYGCQ23Mh5RqQWoGeYeQwSEjfcyGEjUgsPQxrjDIMDxpI9x4wt5xgQ4Rf5+Q/SGD78OSDHz9788MabCjs5glpQgAQPkVGDrIVUHaNgFIyCUTAiAAArCEKQ5BgMWwAAAABJRU5ErkJggg==","orcid":"","institution":"Key laboratory of Shaanxi Province for Craniofacial Precision Medicine Research, College of Stomatology, Xi’an Jiaotong University","correspondingAuthor":true,"prefix":"","firstName":"Panjun","middleName":"","lastName":"Pu","suffix":""}],"badges":[],"createdAt":"2025-08-14 14:08:36","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7374655/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7374655/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s12903-026-08187-9","type":"published","date":"2026-04-01T15:59:18+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":91315627,"identity":"c79f5cdb-87e8-49f5-9f48-3a8d9b1e35bb","added_by":"auto","created_at":"2025-09-15 08:10:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":3446439,"visible":true,"origin":"","legend":"\u003cp\u003eStructural elements of the model\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/19d618c818c1eec7fe61d272.png"},{"id":91315645,"identity":"45541809-a816-4063-b58a-c359738d5f32","added_by":"auto","created_at":"2025-09-15 08:10:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":3486938,"visible":true,"origin":"","legend":"\u003cp\u003eSubmodels and groups. Model (A, B, C and D) was used to simulate the mesialization of the first molar by 0.25mm distance. Model A was control group. Model B represented aligner-based angel buttons combined with micro-implants. Model C was using lingual button in combination with micro-implant. Model D represented power arms combined with micro-implants.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/6b4cce8208482130bb31c0da.png"},{"id":91315662,"identity":"d84e48fe-4989-4152-99f9-86160ad5a431","added_by":"auto","created_at":"2025-09-15 08:10:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":6908256,"visible":true,"origin":"","legend":"\u003cp\u003eMesh setup, coordinate systems, and tipping angle measurement. A. Mesh setup; B. Global coordinate system; C. Local coordinate system; D. Tipping angle measurement.\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/ae74f5dec6c97631908939a1.png"},{"id":91315673,"identity":"14b7edbc-f0b6-4f28-b552-ec90e84212cd","added_by":"auto","created_at":"2025-09-15 08:10:39","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":9649539,"visible":true,"origin":"","legend":"\u003cp\u003eThe force loading system. Mesial movement of the first molar generated reciprocal forces on adjacent teeth, which manifested as distal displacement of the second molar and distalization of the premolars and anterior teeth toward the edentulous area, accompanied by palatal inclination.\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/fa51c195e874de8aa7583d78.png"},{"id":91315641,"identity":"6c7e60ed-5877-497f-9983-603d11e7c16f","added_by":"auto","created_at":"2025-09-15 08:10:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":8471542,"visible":true,"origin":"","legend":"\u003cp\u003eTotal displacement of the maxillary dentition in Four models. Model A (control, without anchorage reinforcement), model B (micro-implants connected to the tooth via an angle button), model C (micro-implants connected to a button which was bonded on the first molar), model D (micro-implants connected to a power arm which was bonded on the first molar). Displacement directions across the entire maxillary arch are illustrated using vector diagrams. Bar charts present the magnitude of total displacement for each model under different levels of traction force (mm). In this system, the x-axis corresponds to the coronal plane (positive to the left, negative to the right), the y-axis aligns with the sagittal plane (positive toward the posterior, negative toward the anterior), and the z-axis aligns with the vertical plane (positive in the superior direction, negative in the inferior direction).\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/7955d791b5964f0e0e78a169.png"},{"id":91315634,"identity":"be20d1eb-1fd6-4c02-8e74-6ed8d9ee0976","added_by":"auto","created_at":"2025-09-15 08:10:36","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":3974552,"visible":true,"origin":"","legend":"\u003cp\u003eThe ratio of effective teeth displacement contributing to a 0.25 mm distalization of the first molar. The pie graphs present the distribution of first molar mesialization, distal movement of the anchorage teeth, and other undesired movements, mainly tipping and rotation. A, model A; B, model B; C, model C; D, model D. E. The contribution ratio of the first molar mesialization among the four models under varying traction forces. F.The distalization contribution of the second molar in the four models subjected to varying traction forces. G The distalization contribution of the first premolar in the four models subjected to varying traction forces. H The proportion of other undesired tooth movement among the four models under varying traction forces.\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/41798b8e38710e6770432829.png"},{"id":91315636,"identity":"3c645f5c-1f44-4e75-8646-67b72ee480af","added_by":"auto","created_at":"2025-09-15 08:10:36","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":7432450,"visible":true,"origin":"","legend":"\u003cp\u003eThree-dimensional displacement patterns of the molars and premolar according to the local coordinate system. In the color maps, red indicates regions of maximum displacement, while blue denotes areas of minimum displacement. The histograms display displacement values along the x-, y-, and z-axis (mm). A local coordinate system is established for each tooth, where positive x-axis values correspond to the mesial direction, positive y-axis values indicate the palatal direction, positive Z-axis values indicate the gingival direction.\u003c/p\u003e","description":"","filename":"Figure7.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/0af3d3714374ab516dbd9aa3.png"},{"id":91315795,"identity":"d5d986fc-b747-4edc-a1d1-da082fb677cb","added_by":"auto","created_at":"2025-09-15 08:18:37","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":6277134,"visible":true,"origin":"","legend":"\u003cp\u003eDisplacement patterns of maxillary anterior anchorage teeth. The three-dimensional displacement values for each model under different traction forces (g) are shown in histograms, referenced to a local coordinate system (X axis: mesial; Y axis: palatal; Z axis: gingival). Furthermore, Midline deviations across the groups are shown in the histograms using the global coordinate system, with positive values indicating shifts to the patient’s right and negative to the left (relative to the anterior teeth midline).\u003c/p\u003e","description":"","filename":"Figure8.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/a90bb1248f30e0161bde6e32.png"},{"id":91315649,"identity":"fc6783fa-3153-4374-9fbf-476b160b4dc0","added_by":"auto","created_at":"2025-09-15 08:10:37","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":5320143,"visible":true,"origin":"","legend":"\u003cp\u003eHydrostatic stress distribution in the PDL. Color maps illustrate the buccal and occlusal views of the PDL across the entire dentition and molar region. Histograms depict compressive pressures of the first molar’s PDL hydrostatic stress (MPa).\u003c/p\u003e","description":"","filename":"Figure9.png","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/0b6d95284a5a812832aa53b7.png"},{"id":106343735,"identity":"bcbc1805-d403-473b-9611-b6a574647edd","added_by":"auto","created_at":"2026-04-07 16:08:27","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":63215979,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7374655/v1/89aa5cef-bfbe-4ccd-ba56-2a275e651757.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Comparative effects of temporary anchorage devices combined with various auxiliary attachments on maxillary molar mesialization with clear aligners: a finite element analysis","fulltext":[{"header":"Background","content":"\u003cp\u003eClear aligner therapy (CAT) has gained significant popularity among both patients and orthodontists, primarily due to its enhanced comfort, superior aesthetics, and the ability to deliver a personalized and removable treatment approach [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. As the demand for CAT continues to rise, the importance of accurately predicting orthodontic forces becomes increasingly critical [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Precise force prediction not only facilitates controlled and effective tooth movement, but also contributes to treatment efficiency, improving patient satisfaction, and the achievement of optimal clinical outcomes.\u003c/p\u003e\u003cp\u003eThe absence of the second premolar is commonly observed in clinical practice, often resulting from factors such as severe dental caries or advanced periodontal disease. The alternative treatments for the missing second premolars include prosthodontic treatment [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] and space closure through orthodontic treatment which involves the mesial movement of the molars [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Moreover, premolars are also the preferred extraction sites when necessary in orthodontics. For patients with mild dental crowding and a well-balanced facial profile, extraction of the second premolars is often considered a favorable option [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. In such cases, space closure is typically achieved through the mesial movement of molars. However, it is well recognized that clear aligner (CA) has limitations in effectively controlling mesial tooth movement\u0026mdash;especially when large mesial displacement of molars is required. Without proper anchorage or auxiliary mechanics, molars tend to exhibit uncontrolled movement, such as mesial tipping and rotation [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. In addition, anchorage loss is unavoidable due to the reciprocal forces generated on the anchorage teeth during molar mesialization, posing a challenge for correction in the later treatment stages [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Therefore, maintaining proper control of anchorage and molar movement during CAT becomes a critical factor for achieving successful orthodontic outcomes.\u003c/p\u003e\u003cp\u003eSimon\u0026rsquo;s research has reported that the accuracy of molar distalization with clear aligners ranges from 85.5\u0026ndash;87% [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], demonstrating the clinical viability of this movement. In contrast, mesial movement of molars\u0026mdash;the counterpart of distalization\u0026mdash;remains a considerable challenge in CAT. This is largely due to the biomechanical limitations of aligners in generating controlled mesial forces, especially over long distances [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Mesial movement is often achieved by shortening the aligner to exert pressure on the posterior teeth; however, this approach often results in uncontrolled inclination Moreover, existing studies primarily focus on molar ditalization, and evidence regarding the predictability and effectiveness of mesial movement of maxillary molars remains limited and inconclusive. Further clinical research and biomechanical evaluations are essential to improve our understanding of aligner-driven mesialization and to develop more effective strategies for achieving stable and controlled tooth movement in such cases.\u003c/p\u003e\u003cp\u003eFinite element analysis (FEA) is a robust and noninvasive computational technique used to approximate the mechanical behavior of complex geometries subjected to external forces with high accuracy. By discretizing complex structures into finite elements and solving mathematical models, FEA enables the prediction of stress, deformation, and failure points with high precision [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Using 3D modeling and simulation, it predicts tooth movement and aligner performance, enabling personalized treatment plans for optimal results [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Few finite element (FE) studies have systematically investigated the biomechanics of clear aligner-mediated molar mesial movement. The work by Lyu [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] established a foundational model simulating mandibular molar displacement using aligners with auxiliary attachments. However, their study was limited to examining only molar displacement trends in auxiliary device-based orthodontics, excluding micro-implants. Therefore, establishing finite element (FE) models is essential. to accurately simulate the biomechanics involved in micro-implants assisted molar mesialization. These models serve as a critical tool for predicting tooth movement and evaluating stress distribution under complex force systems. In this study, we focused on CAT incorporating micro-implants and auxiliary appliances to support maxillary molar mesialization.\u003c/p\u003e\u003cp\u003eTo our knowledge, this is the first study to systematically analyze and quantify the orthodontic tooth movements in molar mesialization with temporary anchorage devices and auxiliary devices through FE modeling, The objective is to evaluate the displacement patterns and stress distribution in the maxillary dentition during first molar mesialization, and to provide clinical guidance for treatment planning, including the selection of traction methods and tooth movement strategies.\u003c/p\u003e"},{"header":"Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eThree-dimensional(3D) model reconstruction\u003c/h2\u003e\n \u003cp\u003eImaging data from cone beam computed tomography (CBCT) were collected from a healthy young female with ideal occlusion and normal facial morphology. To simulate a clinical extraction scenario, the right maxillary second premolar was digitally removed to create a post-extraction model. The DICOM images were input into Mimics 21.0 (Materialise NV, Belgium) to create the initial geometry., where threshold-based segmentation techniques were employed to accurately isolate the maxillary and individual teeth components.\u003c/p\u003e\n \u003cp\u003eFollowing segmentation, the preliminary 3D reconstructions were refined and smoothed using Geomagic Studio 2021 (3D Systems, North Carolina, USA) to eliminate noise and surface irregularities. The anatomical components, including the alveolar bone, periodontal ligament (PDL), and dentition, were then designed and assembled in SolidWorks 2024 (Dassault Syst\u0026egrave;mes, France) (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). The PDL was modeled as a uniform layer 0.25 mm thick by offsetting the external surfaces of the tooth roots [\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e], reflecting its average physiological thickness and biomechanical properties.\u003c/p\u003e\n \u003cp\u003eTo enhance aligner retention and simulate clinical practice, attachments were incorporated into the model. Vertical rectangular attachments(2mm*3mm*1mm) were placed on the buccal surfaces of premolars and canines. Horizontal rectangular attachments(3mm*2mm*1mm) were applied to the buccal surfaces of the maxillary molars to provide additional control during molar mesialization.The buttons (3 mm in diameter at the base and 1 mm in height) were placed on the first molar and the aligner. Power arms (3 mm in diameter at the base and 8 mm in height) were placed on the first molar. A micro-implant (diameter:1.5mm, height:8mm) representing skeletal anchorage, was integrated into the model to assist in molar protraction, positioned between the maxillary canine and the first premolar at a 60\u0026deg;angle to the occlusal plane, following established clinical guidelines for optimal biomechanical force application [\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eMaterial properties\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eYoung\u0026rsquo;s modulus (MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePoisson\u0026rsquo;s ratio\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTeeth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.96\u0026times;10\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.37\u0026times;10\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePDL\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.45\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAttachment\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.25\u0026times;10\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.36\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eClear Aligner\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.28\u0026times;10\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.36\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eButtons\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.14\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMicro-implants\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.14\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eThe refined anatomical model and CA were loaded into ANSYS Workbench 2024 (Pennsylvania, USA) to construct a detailed FE model for biomechanical analysis. The model components including the dentition, attachments, orthodontic button, PDL, and micro-implants were all defined as homogeneous, isotropic, and linearly elastic materials, consistent with parameters reported in previous literature [\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e] (see Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e for specific material properties).\u003c/p\u003e\n \u003cp\u003eTo evaluate the biomechanical impact of diverse auxiliary designs during maxillary molar mesialization with CA, four distinct FE models were developed (Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e):\u003c/p\u003e\n \u003cp\u003eModel A (Control group): Simulated molar mesialization using CA alone, without any anchorage reinforcement or auxiliary devices. This group served as the baseline for comparison.\u003c/p\u003e\n \u003cp\u003eModel B (Aligner-based angel button group): An angled button was incorporated into the labial surface of the first molar on the CA to enable the application of elastic forces by attaching external elastics to a micro-implant.\u003c/p\u003e\n \u003cp\u003eModel C (Lingual button group): Included a standardized lingual button bonded to the buccal surface of the first molar. The button-tooth interface was modeled as a rigid bond to simulate clinical composite resin bonding.\u003c/p\u003e\n \u003cp\u003eModel D (Power arm group): Included a standardized power arm structure bonded to the buccal surface of the first molar. The connection between the power arm and the tooth surface was simulated as a rigid bond.\u003c/p\u003e\n \u003cp\u003eEach model was subjected to identical boundary conditions and loading protocols to enable accurate comparison of force transmission, stress distribution, and predicted tooth displacement patterns under varying auxiliary mechanics.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eBoundary conditions\u003c/h3\u003e\n\u003cp\u003eA fixed support was applied to the superior portion of the maxillary to stabilize the finite element model during orthodontic force simulation, with all translational and rotational degrees of freedom fully constrained. This constraint effectively prevented undesired movement or deformation of the maxillary base during the application of orthodontic loading, thereby preserving the structural integrity of the model throughout the simulation process. Additionally, tie contact relationships were established between biologically bonded or continuous anatomical structures to simulate perfect bonding with no relative motion. These included the interfaces between the tooth and the PDL, the PDL and the alveolar bone, the alveolar bone and the micro-implant, as well as between the orthodontic attachment, the lingual button, and the tooth surface. These tie constraints allowed for accurate transmission of force and stress across the different tissue types.\u003c/p\u003e\n\u003cp\u003eFor components that exhibit contact under force with potential sliding, surface-to-surface contact elements were defined. A frictional coefficient of 0.2 was applied to both the interface between the CA and the attachments, as well as the CA and the tooth surfaces [\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]. The frictional contact settings allowed for realistic modeling of aligner displacement and force dissipation during tooth movement.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eNodes and elements\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNode no.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eElement no.\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eModel A\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e819,903\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1,624,312\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eModel B\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e844,085\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1,670,167\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eModel C\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e852,797\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1,683,491\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eModel D\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e851,934\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1,682,678\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003ch3\u003eLoading methods and coordinate system\u003c/h3\u003e\n\u003cp\u003eA static loading condition was adopted for the FE simulation to replicate the force system applied during each step of molar mesialization with clear aligners. The mesial displacement of the maxillary first molar was simulated in incremental steps of 0.25 mm, corresponding to a single aligner activation cycle in clinical practice.\u003c/p\u003e\n\u003cp\u003eAll geometric models were discretized using 10-node tetrahedral (solid187) elements, which offer higher accuracy in capturing stress-strain behavior in complex anatomical structures. Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e presents the nodes and linear elements for each model. To enhance computational efficiency while maintaining numerical precision, region-specific mesh densities were applied based on the structural complexity and mechanical sensitivity of each component. The element sizes were defined as follows: 0.15 mm for the PDL, 0.20 mm for the dentition, orthodontic attachments, and appliances, 0.25 mm for the maxillary bone [\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]. These mesh settings were optimized through a convergence test to balance computational cost and solution accuracy.\u003c/p\u003e\n\u003cp\u003eA right-handed local coordinate system was established at the center of each tooth\u0026rsquo;s clinical crown for three-dimensional displacement analysis [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e]. In this system, the X-axis represented the mesiodistal direction, the Y-axis corresponded to the buccolingual (or labiolingual) direction, and the Z-axis indicated the occlusogingival (or coronoapical) direction (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). Displacement vectors were recorded with the mesial, palatal, and gingival directions defined as positive (+) values, allowing for the precise evaluation of individual tooth movement patterns in response to orthodontic force application. Midline deviation was determined using the global coordinate system by selecting the midpoint of the incisal edges between the maxillary central incisors (teeth 11 and 21)\u003c/p\u003e\n\u003cp\u003eTo analyze the first molar displacement trends, we measured the average displacement values from four cusp landmarks (mesiobuccal, distobuccal, and two palatal cusps) and three root apex points(mesiobuccal, distobuccal, and palatal roots) of the first molar, representing crown and root movement respectively.The difference in X-axis displacement between the crown and root was used to assess sagittal tipping tendency. The rotation angles \u0026theta; of the first molar in the standard anatomical plane(XZ) are defined in Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e), as illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eD, the parameter \u0026alpha; denoted the rotational change of the tooth, expressed in radians, and could be calculated using the given equation.\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"EquationNumber\"\u003e\u003cimg 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\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eThe mesial movement efficiency was calculated as the proportion of the intended 0.25 mm movement that resulted in actual molar mesialization, as shown in Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). Anchorage teeth distalization, undesired tipping and rotation, occupied the remaining percentage.\u003c/p\u003e\n\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n \u003cdiv class=\"EquationNumber\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 546px;\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003eThe whole dentiton displacement\u003c/h2\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e illustrated the force loading system exerted by CA. Model A was using CA alone. Model B applied elastic force to the aligner's angled button. Model C delivered the elastic force directly to the first molar via a lingual button, while model D exerted the force on a power arm bonded to the buccal surface of the first molar. As the first molar shifted mesially, an opposing force was exerted on the anchorage teeth, causing them to move in the reverse direction. The use of auxiliary devices and micro-implants helped reduce anchorage loss. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e depicted the resultant displacement trends across the maxillary dentition. When the first molar moved mesially, the anchorage teeth moved in the opposite direction, and the anterior teeth moved in the disto-palatal direction. Across all experimental models, Model C, featuring an lingual button on the the first molar with 200 g of traction force, showed the maximal displacement at 0.1501 mm. In contrast, Model A without micro-implants anchorage demonstrated minimal displacement of only 0.1269 mm.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e demonstrated the efficiency of tooth movement contributing to first molar mesialization at a 0.25 mm distance. In model A, the first molar exhibited 44.12% mesial movement, while the second molar and first premolar moved distally by 22.00% and 23.20%, respectively. The remaining 10.68% consisted of other unwanted movements. With the assistance of micro-implants, Models B, C and D resulted in a higher efficiency of first molar mesialization compared with model A. Among them, the increment in Model B was the smallest, while that in model C was the largest. Models B, C and D also had more proportion of undesired movements, compared with model A. Moreover,the incorporation of micro-implants in models B, C, and D led to a reduction in the distal displacement of the second molar and first premolar compared to model A. Additionally, model B exhibited a lower proportion of distalization than models C and D. These results suggested that micro-implants could improve the first molar mesialization (especially lingual button bonded on the tooth), and reduce the second molar and first premolar distalization (especially angle buttons), but also had more undesired movement (especially angle buttons). Furthermore, with increasing traction force, the proportion of effective molar mesialization showed a gradual rise, indicating improved efficiency of targeted tooth movement. However, this was accompanied by a simultaneous increase in the proportion of unintended movements, including tipping and rotation, suggesting that excessive force may compromise the quality of control and lead to less predictable outcomes.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eThree-dimensional displacement of the first molar\u003c/h2\u003e\u003cp\u003eThe displacement patterns of the first molar varied considerably among the four models, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. All models exhibited that the first molar primarily moved mesially, with lingual or buccal movement and intrusion. The magnitude of displacement showed a positive correlation with the intensity of the applied force in model B, C and D. Due to the assistance of the micro-implant, the mesial movement of the first molar in models B, C and D was all increased compared to model A. The increment in model B was the smallest, whereas model C exhibited the largest. The use of the micro-implant also reduced the mesial tipping tendency of the first molar, with model D showing the least tipping and model B the most. Moreover, the first molar experienced lingual movement and intrusion during mesial movement with clear aligners alone. With the assistance of the micro-implant, the lingual movement decreased and the intrusion of the first molar increased. Among the three models with auxiliary devices, the lingual movement in model C was the smallest, while B displayed slight buccal movement. The first molar exhibited the greatest intrusion in Model C, whereas the least amount of intrusion was observed in Model D.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eThree-dimensional displacement of the second molar and first premolar\u003c/h3\u003e\n\u003cp\u003eThe second molar mainly exhibited distal displacement and tipping, with slight buccal movement and extrusion during the mesial movement of the first molar (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). In model A, where no additional anchorage was provided, the second molar showed the most pronounced distal tipping (-0.229\u0026deg;), as well as the largest distal displacement, buccal movement and extrusion. With the assistance of the micro-implant, the second molar exhibited reduced distal inclination, buccal displacement, and extrusion. These reductions were most pronounced in model B and least evident in model D. These results suggested that all three auxiliary-supported models effectively reduced undesired second molar movement, with model B providing the greatest stability, followed by model C and model D.\u003c/p\u003e\u003cp\u003eThe first premolar also mainly showed a distal displacement and tipping, and accompanied with a little lingual movement and extrusion. In model A, the premolar experienced the greatest distal movement and distal tipping (-0.243\u0026deg;), along with the largest lingual movement and extrusion. With the assistance of the micro-implant, distal tipping, lingual displacement, and extrusion of the first premolar were reduced. These changes were most significant in model B and least pronounced in model D. The results indicated that all three models supported by auxiliaries effectively minimized unwanted premolar movement, with model B offering the highest stability, followed by models C and D.\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\u003eProclination angle of the molar and premolar in X-axis (+, mesial; -distal)\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\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\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eThe first molar\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eThe second molar\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eThe first premolar\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003eModel A\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.831\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.229\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.243\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eModel B\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.512\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.088\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.092\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e150g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.536\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.094\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.103\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e200g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.557\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.112\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.109\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eModel C\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.714\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.101\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.114\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e150g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.743\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.117\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.127\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e200g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.784\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.133\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.150\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eModel D\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.266\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.120\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.139\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e150g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.273\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.125\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.143\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e200g\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.289\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;0.132\u0026deg;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;0.151\u0026deg;\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\u003eThree-dimensional displacement of the anterior teeth and midline deviation\u003c/h3\u003e\n\u003cp\u003eThe anterior teeth exhibited a tendency to move toward distolingual tipping and extrusion (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e), resulting in anterior teeth retraction and midline deviation to the side of edentulous space in all models. Compared to model A, all undesired anterior tooth movement (distal tipping, lingual tipping and extrusion) was reduced in models B, C, and D, with model B showing the least amount of anterior teeth displacement. Model D has slightly more undesired anterior tooth movement than model C.\u003c/p\u003e\u003cp\u003eMoreover, the midline deviated to edentulous space in all models. In model A, the anterior segment showed the most pronounced distal displacement, with an average of 0.0483 mm at the midline deviation of approximately toward the traction side. In model B, the deviation of midline was the least, measuring only 0.0137 mm, indicating excellent anchorage preservation and minimal reciprocal movement. Model D had slightly more midline deviation than model C.\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eHydrostatic stress distribution in PDL\u003c/h2\u003e\u003cp\u003eThe PDL hydrostatic pressure was evaluated using the dentition as the unit of analysis to better reflect the biomechanical response under different loading conditions (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e). As for the first molar in model A, the highest hydrostatic pressure within the PDL was mainly localized in the mesial cervical region and the furcation area. Moreover, the degree of uneven force distribution varied across the four models. Among them, Models A and C exhibited the most uneven stress distribution, whereas Model D showed the most uniform pattern. Simultaneously, the micro-implant raised the PDL hydrostatic pressure. Compared to Model A, the maximum PDL pressure in Models C, B, and D was increased. Meanwhile, model C had the most PDL pressure because it is subjected to direct traction force and its mechanical distribution is uneven.\u003c/p\u003e\u003cp\u003eAs for the second molar, the maximum hydrostatic pressure in the PDL was primarily concentrated in the distal cervical region, and it was lower than that observed in the first molar. Compared to model A, models B, C, and D exhibited significantly reduced PDL hydrostatic stress. Notably, under increasing force (from 100 g to 200 g), the stress distribution remained stable, indicating better loading management and a reduced risk of tissue overload.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eDespite the growing popularity of CA in orthodontic treatment, molar mesialization using this approach presents several limitations. Due to the limited mechanical force that CA can deliver, achieving bodily movement of molars is challenging, often resulting in uncontrolled tipping and undesired movements such as lingual inclination and mesial tipping [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Additionally, the lack of rigid anchorage in CAT may lead to reciprocal movements of adjacent teeth, reducing the overall efficiency of molar mesialization. These limitations highlight the need for adjunctive strategies, such as skeletal anchorage or force-modulating auxiliaries devices, to improve the predictability and effectiveness of molar mesialization with CA. A recent research has reviewed that CA with a modified lever arm (MLA) reduced undesigned mesial tipping and rotation, optimized molar mesialization biomechanics [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. However, current research on molar mesialization using CA combined auxiliary devices with micro-implants remains little. Unlike previous finite element studies that focused on single anchorage control or individual auxiliary devices, this work directly compared the biomechanical effects of multiple auxiliaries\u0026mdash;including aligner-based angle buttons, lingual buttons, and power arms\u0026mdash;combined with temporary anchorage devices. To the best of our knowledge, this is the first comparative approach to provide a comprehensive understanding of how different force delivery systems influence molar mesialization and anchorage control in clear aligner therapy.\u003c/p\u003e\u003cp\u003eOur study demonstrated that when using clear aligners to move the first molar mesially, the main tooth movement was the mesialization of the first molar, followed by the distalization of the second molar and the first premolar. At the same time, other movements such as the retraction of the anterior teeth and the tipping movement of the tooth also occurred. Micro-implants could enhance the mesialization efficiency and intrusion amount of the first molar, reduced its mesial inclination, and also minimized the distal movement and lingual inclination of the anchoring teeth. These findings suggested that the use of micro-implants enhanced the efficiency of molar mesialization with clear aligners and helped stabilize the anchorage teeth. In addition, treatment designs that counteracted mesial tipping and lingual displacement of the molars were necessary.\u003c/p\u003e\u003cp\u003eThe tooth movement will be influenced by the direction of the traction force and the position of the resistance center [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Gandhi et al [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] identified the center of resistance of maxillary first molars is located apical and distal to the root trifurcation. As the center of rotation gets closer to the center of resistance, the molar demonstrates more parallel movement and less unwanted tipping/rotation [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. In our study, the angle button connected to the CA, the lingual button and the power arm bonded on the first molar all affected the mesialization efficiency of the first molar and the type of tooth movement. For the angle button, since it was directly connected to the CA, it not only increased the mesialization efficiency of the first molars, but also had the strongest protection of the anchorage tooth. The lingual button bonded to the first molar not only significantly increased mesialization efficiency, but also had the greatest effect on its intrusion and mesial inclination. The power arm which could apply force closer to the center of resistance not only increased the mesialization amount of the first molars, but also significantly reduced its mesial inclination, and this was consistent with the fundings of the Hong et al [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe alignment between the maxillary dental midline and facial midline plays a pivotal role in facial esthetics [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. In cases of unilateral tooth loss requiring molar mesialization, the reactive forces generated during molar mesialization often lead to a shift of the anterior teeth toward the edentulous side, resulting in midline deviation. Our study showed that when micro-implants were employed to deliver external forces, these undesired reactive effects could be effectively counteracted. Specifically, when using the aligner based angle button, the traction force from the mini-implant was distributed through the entire aligner system. This integration allowed for better force dissipation and anchorage control, thereby minimizing its influence on the dental midline.\u003c/p\u003e\u003cp\u003eThe magnitude and location of PDL hydrostatic pressure are related to the type of tooth movement, and direction and magnitude of force [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In this study, the PDL hydrostatic stress of the first molar was mainly concentrated at the mesial cervical and furcation regions, demonstrating that tooth movement in all models was mainly tipping movement, which was consistent with the findings of Jain\u0026rsquo;s research [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Our research also showed that the use of micro-implants not only increased the PDL hydrostatic stress on the first molar, but also affected the uniformity of the stress distribution in the PDL. Similar results were also observed in studies on the molar distalization [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Furthermore, if the traction force applied by the micro-implant directly acted on the lingual button bonded to the buccal regions of the first molar, it significantly increased the tipping movement, as well as the stress levels at the mesial cervical and furcation regions. However, using the power arm, since it was close to the resistance center of the first molar, the degree of tooth inclination decreased, and the unevenness of the stress distribution in the PDL also reduced. Excessive stress in the PDL can lead to risks such as root resorption and tooth loosening [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. Therefore, during molar mesialization, using power arm bonded on the tooth or angle buttons connected to the aligner appliance is more beneficial for dental health.\u003c/p\u003e\u003cp\u003eNevertheless, this study had several limitations that should be taken into consideration when interpreting the results. The finite element model was constructed based on the CBCT data of a single patient, which may not adequately capture individual anatomical variations such as differences in root morphology, bone density, and periodontal ligament characteristics. Additionally, the simulation environment differed from actual clinical conditions; material properties of biological tissues were modeled as linear, isotropic, and uniform, which did not fully reflect the complex biomechanical behavior of oral structures. Futhermore, the forces generated by clear aligners and elastics were also simplified as static, constant loads, without accounting for changes due to oral function, patient compliance, or time-dependent effects. These simplifications may influence the accuracy of the predicted tooth movements, particularly in long-term clinical scenarios. While FEA served as a valuable technique for understanding biomechanical patterns, it remained a static, idealized model that did not simulate biological responses such as bone remodeling or tissue adaptation, and thus, its results should be interpreted as theoretical trends rather than precise clinical outcomes. Therefore, further clinical studies are necessary to validate and refine these findings before they can be widely applied in practice.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis finite element study aimed to analyze the biomechanical efficiency of molar mesialization and other tooth movements combined with CA. The findings showed that when only a clear aligner was used to move the first molar mesially, the mesialized tooth exhibited mesiolingual tipping and intrusion, while the anchorage teeth underwent distobuccal or distolingual tipping and extrusion. The midline deviated toward the side of the missing tooth as a result of reciprocal forces. Micro-implants could increase the effective contribution to molar mesialization, reduce mesiolingual tipping of the first molar, stabilize the anchorage teeth, minimize midline deviation, and optimize the distribution of PDL hydrostatic stress in the first molar. Meanwhile, with the assistance of the power arm, the first molar tended to exhibit bodily movement, and resulted in the most uniform distribution of PDL hydrostatic stress in the first molar.The use of angel buttons connected to the aligners maximized the stability of the anchorage teeth and minimized the midline deviation. Additionally, although the lingual button bonded to the first molar significantly increased its mesial movement, it also led to mesiolingual tipping and the most uneven distribution of PDL hydrostatic stress. The results provide valuable guidance for clinical decision-making on the use of micro-implants and selection of auxiliary attachments in clear aligner-based molar mesialization.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003eCA :Clear aligner\u003c/p\u003e\n\u003cp\u003eCAT Clear aligner therapy\u003c/p\u003e\n\u003cp\u003ePDL Periodontal ligament\u003c/p\u003e\n\u003cp\u003eFEA Finite element analysis\u003c/p\u003e\n\u003cp\u003eCBCT Cone beam computed tomography\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 Hospital of Stomatology, Xi\u0026rsquo;an Jiaotong University, with the ethical review number (11[2022]NO.051).Informed consent was obtained from the participant, all methods were performed in accordance with the Declaration of Helsinki.\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\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003cp\u003eThe authors declare no competing interests\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThis study was supported by The National Natural Science Foundation of China (82370909);\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eFW was responsible for conceptualization, methodology, finite element modeling, data analysis, and drafting the original manuscript. YF contributed to software development, data curation, and formal analysis. ML assisted with formal analysis and investigation. QM contributed to resource acquisition, investigation, and data management. YY was involved in data visualization and supported manuscript review and editing. PP , YH and JG jointly supervised the study and were involved in conceptualization, validation, critical manuscript revision, and funding acquisition.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e\u003cp\u003eNot applicable\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data supporting this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eCardoso PC, Espinosa DG, Mecenas P, Flores-Mir C, Normando D. Pain level between clear aligners and fixed appliances: a systematic review. Prog Orthod. 2020;21:3. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s40510-019-0303-z\u003c/span\u003e\u003cspan address=\"10.1186/s40510-019-0303-z\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRossini G, Parrini S, Castroflorio T, Deregibus A, Debernardi CL. Efficacy of clear aligners in controlling orthodontic tooth movement: a systematic review. Angle Orthod. 2015;85:881\u0026ndash;9. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2319/061614-436.1\u003c/span\u003e\u003cspan address=\"10.2319/061614-436.1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTartaglia GM, Mapelli A, Maspero C, Santaniello T, Serafin M, Farronato M, et al. Direct 3D printing of clear orthodontic aligners: Current state and future possibilities. Mater (Basel). 2021;14:1799. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/ma14071799\u003c/span\u003e\u003cspan address=\"10.3390/ma14071799\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKokich VG, Kokich VO. Congenitally missing mandibular second premolars: clinical options. Am J Orthod Dentofac Orthop. 2006;130:437\u0026ndash;44. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ajodo.2006.05.025\u003c/span\u003e\u003cspan address=\"10.1016/j.ajodo.2006.05.025\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWilliams R, Park JH, Chae J-M, Vaden JL. The congenitally missing second premolar: Space closure. A viable option. Am J Orthod Dentofac Orthop. 2020;157:571\u0026ndash;e58316. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ajodo.2019.10.015\u003c/span\u003e\u003cspan address=\"10.1016/j.ajodo.2019.10.015\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eElias KG, Sivamurthy G, Bearn DR. Extraction vs nonextraction orthodontic treatment: a systematic review and meta-analysis. Angle Orthod. 2024;94:83\u0026ndash;106. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2319/021123-98.1\u003c/span\u003e\u003cspan address=\"10.2319/021123-98.1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYang Y, Yang R, Liu L, Zhang X, Jiang Q, Fan Q, et al. The effects of aligner anchorage preparation on mandibular first molars during premolar-extraction space closure with clear aligners: A finite element study. Am J Orthod Dentofac Orthop. 2023;164:226\u0026ndash;38. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ajodo.2022.12.013\u003c/span\u003e\u003cspan address=\"10.1016/j.ajodo.2022.12.013\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRen L, Liu L, Wu Z, Shan D, Pu L, Gao Y, et al. The predictability of orthodontic tooth movements through clear aligner among first-premolar extraction patients: a multivariate analysis. Prog Orthod. 2022;23:52. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s40510-022-00447-y\u003c/span\u003e\u003cspan address=\"10.1186/s40510-022-00447-y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSimon M, Keilig L, Schwarze J, Jung BA, Bourauel C. Treatment outcome and efficacy of an aligner technique\u0026ndash;regarding incisor torque, premolar derotation and molar distalization. BMC Oral Health. 2014;14:68. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/1472-6831-14-68\u003c/span\u003e\u003cspan address=\"10.1186/1472-6831-14-68\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLong H, Wu Z, Yan X, Wang Q, Liu L, Wang Y, et al. An objective system for appraising clear aligner treatment difficulty: clear aligner treatment complexity assessment tool (CAT-CAT). BMC Oral Health. 2020;20:312. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s12903-020-01300-6\u003c/span\u003e\u003cspan address=\"10.1186/s12903-020-01300-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhu G-Y, Zhang B, Yao K, Lu W-X, Peng J-J, Shen Y, et al. Finite element analysis of the biomechanical effect of clear aligners in extraction space closure under different anchorage controls. Am J Orthod Dentofac Orthop. 2023;163:628\u0026ndash;e64411. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ajodo.2022.02.018\u003c/span\u003e\u003cspan address=\"10.1016/j.ajodo.2022.02.018\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCattaneo PM, Cornelis MA. Orthodontic tooth movement studied by finite element analysis: An update. What can we learn from these simulations? Curr Osteoporos Rep. 2021;19:175\u0026ndash;81. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s11914-021-00664-0\u003c/span\u003e\u003cspan address=\"10.1007/s11914-021-00664-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMurakami N, Wakabayashi N. Finite element contact analysis as a critical technique in dental biomechanics: a review. J Prosthodont Res. 2014;58:92\u0026ndash;101. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jpor.2014.03.001\u003c/span\u003e\u003cspan address=\"10.1016/j.jpor.2014.03.001\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLyu X, Cao X, Chen L, Liu Y, Li H, Hu C, et al. Accumulated biomechanical effects of mandibular molar mesialization using clear aligners with auxiliary devices: an iterative finite element analysis. Prog Orthod. 2023;24:13. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s40510-023-00462-7\u003c/span\u003e\u003cspan address=\"10.1186/s40510-023-00462-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCai Y, Yang X, He B, Yao J. Finite element method analysis of the periodontal ligament in mandibular canine movement with transparent tooth correction treatment. BMC Oral Health. 2015;15:106. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s12903-015-0091-x\u003c/span\u003e\u003cspan address=\"10.1186/s12903-015-0091-x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLiu X, Wu J, Cheng Y, Gao J, Wen Y, Zhang Y, et al. Effective contribution ratio of the molar during sequential distalization using clear aligners and micro-implant anchorage: a finite element study. Prog Orthod. 2023;24:35. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s40510-023-00485-0\u003c/span\u003e\u003cspan address=\"10.1186/s40510-023-00485-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDaqiq O, Gareb B, Spijkervet FKL, Wubs FW, Roossien CC, van Minnen B. Finite element analysis of the human mandible: a systematic review with meta-analysis of the essential input parameters. Sci Rep. 2025;15:19582. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-025-03959-9\u003c/span\u003e\u003cspan address=\"10.1038/s41598-025-03959-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJiang T, Wu RY, Wang JK, Wang HH, Tang GH. Clear aligners for maxillary anterior en masse retraction: a 3D finite element study. Sci Rep. 2020;10:10156. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-020-67273-2\u003c/span\u003e\u003cspan address=\"10.1038/s41598-020-67273-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHe X, Zhuang W-H, Zhang D-L. A three-dimensional finite element analysis: Maxillary dentition distalization with the aid of microimplant in lingual orthodontics. Int J Gen Med. 2021;14:8455\u0026ndash;61. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2147/IJGM.S337212\u003c/span\u003e\u003cspan address=\"10.2147/IJGM.S337212\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCheng 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;22:499. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1186/s12903-022-02521-7\u003c/span\u003e\u003cspan address=\"10.1186/s12903-022-02521-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDai F-F, Xu T-M, 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;89:679\u0026ndash;87. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.2319/090418-646.1\u003c/span\u003e\u003cspan address=\"10.2319/090418-646.1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYoshida N, Jost-Brinkmann PG, Koga Y, Mimaki N, Kobayashi K. Experimental evaluation of initial tooth displacement, center of resistance, and center of rotation under the influence of an orthodontic force. Am J Orthod Dentofac Orthop. 2001;120:190\u0026ndash;7. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1067/mod.2001.115036\u003c/span\u003e\u003cspan address=\"10.1067/mod.2001.115036\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGandhi V, Luu B, Dresner R, Pierce D, Upadhyay M. Where is the center of resistance of a maxillary first molar? A 3-dimensional finite element analysis. Am J Orthod Dentofac Orthop. 2021;160:442\u0026ndash;e4501. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ajodo.2020.04.033\u003c/span\u003e\u003cspan address=\"10.1016/j.ajodo.2020.04.033\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTanne K, Koenig HA, Burstone CJ. Moment to force ratios and the center of rotation. Am J Orthod Dentofac Orthop. 1988;94:426\u0026ndash;31. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0889-5406(88)90133-3\u003c/span\u003e\u003cspan address=\"10.1016/0889-5406(88)90133-3\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHong K, Kim W-H, Eghan-Acquah E, Lee J-H, Lee B-K, Kim B. Efficient design of a clear aligner attachment to induce bodily tooth movement in orthodontic treatment using finite element analysis. Materials. 2021;14(17):4926. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/ma14174926\u003c/span\u003e\u003cspan address=\"10.3390/ma14174926\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang X, Long J, Mei M, Huang J, Chen Y, Zhou Y, et al. Acceptable deviation of labial tubercle and anterior tooth midlines relative to facial midline in smile aesthetics: A retrospective observational study. Med (Baltim). 2022;101:e30983. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1097/MD.0000000000030983\u003c/span\u003e\u003cspan address=\"10.1097/MD.0000000000030983\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKorkut B, Ograk I, Murat N, Ntovas P, Tuter Bayraktar E, Senol AA, et al. Effect of Midline deviation and crown width disproportion on perception of smile esthetics. J Esthet Restor Dent. 2025. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/jerd.13492\u003c/span\u003e\u003cspan address=\"10.1111/jerd.13492\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNogueira AVB, Marcantonio CC, de Molon RS, Leguizam\u0026oacute;n NDP, Silva RCL, Deschner J, et al. Experimental models of orthodontic tooth movement and their effects on periodontal tissues remodelling. Arch Oral Biol. 2021;130:105216. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.archoralbio.2021.105216\u003c/span\u003e\u003cspan address=\"10.1016/j.archoralbio.2021.105216\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNazeri A, Castillo JA Jr, Ghaffari-Rafi A. Impact of molar distalization with clear aligners on periodontal ligament stress and root resorption risk: A systematic review of 3D finite element analysis studies. Dent J. 2025;13. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/dj13020065\u003c/span\u003e\u003cspan address=\"10.3390/dj13020065\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJain A, Prasantha GS, Mathew S, Sabrish S. Analysis of stress in periodontium associated with orthodontic tooth movement: a three dimensional finite element analysis. Comput Methods Biomech Biomed Engin. 2021;24:1841\u0026ndash;53. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/10255842.2021.1925255\u003c/span\u003e\u003cspan address=\"10.1080/10255842.2021.1925255\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTang X, Wang M, Hu X, Zheng L, Yang C. The effects of palatal anchorage device on molar distalization with clear aligner: Three-dimensional finite element analysis. Am J Orthod Dentofac Orthop. 2025. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ajodo.2025.04.012\u003c/span\u003e\u003cspan address=\"10.1016/j.ajodo.2025.04.012\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHohmann A, Kober C, Young P, Dorow C, Geiger M, Boryor A, et al. Influence of different modeling strategies for the periodontal ligament on finite element simulation results. Am J Orthod Dentofac Orthop. 2011;139:775\u0026ndash;83. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ajodo.2009.11.014\u003c/span\u003e\u003cspan address=\"10.1016/j.ajodo.2009.11.014\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eQian L, Todo M, Morita Y, Matsushita Y, Koyano K. Deformation analysis of the periodontium considering the viscoelasticity of the periodontal ligament. Dent Mater. 2009;25:1285\u0026ndash;92. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.dental.2009.03.014\u003c/span\u003e\u003cspan address=\"10.1016/j.dental.2009.03.014\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-oral-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ohea","sideBox":"Learn more about [BMC Oral Health](http://bmcoralhealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ohea/default.aspx","title":"BMC Oral Health","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Clear aligners, Finite element analysis, Micro-impants, Molar mesialization","lastPublishedDoi":"10.21203/rs.3.rs-7374655/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7374655/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cb\u003eBackground\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThis study investigated the biomechanics of maxillary dentition, specifically displacement patterns, midline deviation, and stress distribution during first molar mesialization using the clear aligners (CA) assisted by temporary anchorage devices (TADs) combined with different auxiliary attachments, including lingual buttons, aligner-based angel buttons and power arms.\u003c/p\u003e\u003cp\u003e\u003cb\u003eMethods\u003c/b\u003e\u003c/p\u003e\u003cp\u003eFinite element models of the clear aligner (CA), micro-implants, maxillary teeth, periodontal ligament (PDL), and alveolar bone were constructed. Four finite element models were simulated: Model A (CA alone, control); Model B (CA with micro-implants connected to aligner-based angel buttons); Model C (CA with micro-implants connected to lingual buttons on the first molar); and Model D (CA with micro-implants connected to power arms on the buccal surface of the first molar). The simulations evaluated three-dimensional tooth displacement, midline deviation, tipping angles, and PDL hydrostatic pressure of the maxillary dentition.\u003c/p\u003e\u003cp\u003e\u003cb\u003eResults\u003c/b\u003e\u003c/p\u003e\u003cp\u003eMesialization of the first molar using CA alone resulted in mesiolingual tipping and intrusion, while anchorage teeth experienced distobuccal or distolingual tipping and extrusion. Midline deviation tended toward the edentulous side due to reciprocal forces. Auxiliary force systems generally improved the efficiency of molar mesial movement and reduced anchorage tooth displacement compared to the control. Aligner-based angel buttons showed the most effective anchorage stability and minimal midline deviation. Lingual buttons produced the largest mesial movement of the first molar, with pronounced tipping and uneven PDL stress. Power arms showed the most bodily movement of the first molar and relatively uniform PDL stress, although anchorage control was less pronounced than that of aligner-based angel buttons.\u003c/p\u003e\u003cp\u003e\u003cb\u003eConclusion\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe combined use of micro-implants and auxiliary devices demonstrated distinct effects on the first molar mesialization and anchorage teeth stability. Notably, aligner-based angel buttons provided the most effective anchorage control and the least midline deviation, while power arms resulted in the most bodily movement of the first molar.\u003c/p\u003e","manuscriptTitle":"Comparative effects of temporary anchorage devices combined with various auxiliary attachments on maxillary molar mesialization with clear aligners: a finite element analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-15 08:10:23","doi":"10.21203/rs.3.rs-7374655/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-03T08:35:08+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-02T12:42:17+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-30T16:06:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-11T12:58:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"121833555292559764456145820854128039115","date":"2025-09-11T06:09:31+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-10T06:29:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"59864044733462022570811547069840832963","date":"2025-09-09T08:17:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"141362488451913216436360313896789302629","date":"2025-09-08T11:31:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"99997476841404189745337438117967969188","date":"2025-09-08T11:16:23+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-08T10:56:16+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-08-29T16:44:58+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-28T06:34:42+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-28T06:33:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Oral Health","date":"2025-08-14T14:02:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-oral-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ohea","sideBox":"Learn more about [BMC Oral Health](http://bmcoralhealth.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/ohea/default.aspx","title":"BMC Oral Health","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"998de793-bb3c-4945-8fde-b566461e1cdb","owner":[],"postedDate":"September 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2026-04-07T16:04:00+00:00","versionOfRecord":{"articleIdentity":"rs-7374655","link":"https://doi.org/10.1186/s12903-026-08187-9","journal":{"identity":"bmc-oral-health","isVorOnly":false,"title":"BMC Oral Health"},"publishedOn":"2026-04-01 15:59:18","publishedOnDateReadable":"April 1st, 2026"},"versionCreatedAt":"2025-09-15 08:10:23","video":"","vorDoi":"10.1186/s12903-026-08187-9","vorDoiUrl":"https://doi.org/10.1186/s12903-026-08187-9","workflowStages":[]},"version":"v1","identity":"rs-7374655","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7374655","identity":"rs-7374655","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}