Three-Dimensional Finite Element Analysis of Retracting Mandibular Anterior Teeth with Labial Fixed Appliances in Different Force Application and Traction Points

Three-Dimensional Finite Element Analysis of Retracting Mandibular Anterior Teeth with Labial Fixed Appliances in Different Force Application and Traction Points | 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 Three-Dimensional Finite Element Analysis of Retracting Mandibular Anterior Teeth with Labial Fixed Appliances in Different Force Application and Traction Points Li Yang, Yuanyuan Wang, Xi Zhao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7834509/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Objective This study aimed to employ three-dimensional finite element analysis (3D-FEA) to investigate the effects of varying microscrew implantation points and traction hook heights on the biomechanical behavior and movement of mandibular anterior teeth during retraction. Methods An adult patient requiring the extraction of maxillary and mandibular first premolars was selected from the Orthodontics Department of Urumqi Stomatological Hospital, which provided ethical approval for this study. Various models of 3D-FEA were constructed, differentiated by microscrew position and traction hook height. Finite element analysis was utilized to calculate stress levels in the alveolar bone, brackets, archwires, and the displacement responses of teeth under different force delivery conditions. Results The length of the anterior traction hook was positively correlated with the displacement magnitude of mandibular lateral incisors and canines. When the same traction hook was applied under different anchorage conditions, the maximum tooth movement in each group exhibited a comparable trend. Compared with the other two groups (mini-implant anchorage groups), Group A1 (47th tooth anchorage group) showed statistically significant displacement of the 47th tooth. The equivalent stress of the periodontal ligament (PDL) remained stable, whereas the alveolar bone stress attained a maximum when mini-screws were placed between the first and second molars (consistent with anatomical sequencing). With increasing height of the anterior traction hook, the bracket stress in Groups A1 and A2 increased incrementally; furthermore, this increase in traction hook height enhanced the control over vertical movement in Group A2. Conclusion The clinical application of microscrews as anchorage is theoretically supported, emphasizing that optimizing force application parameters and selecting appropriate anchorage sites are crucial for effective mandibular anterior tooth retraction. This research provides a foundational rationale for optimizing future orthodontic treatment strategies. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Extraction orthodontics is one of the most widely practiced methods for correcting dental protrusion and improving convex facial profiles. It necessitates robust anchorage to facilitate extensive anterior tooth retraction, thereby correcting the lateral profile. Key challenges in extraction orthodontics include maintaining normal torque of incisors, controlling overall anterior retraction, and preventing overbite deepening during treatment. Microscrew implants, which are strategically embedded within the jawbone, provide "absolute anchorage" and enable effective anterior retraction by minimizing movement inefficiencies. Prior studies have established that microscrews can securely anchor orthodontic appliances, allowing for greater utilization of extraction spaces for anterior retraction [ 1 – 2 ]. Their clinical application has expanded widely. The regulation of anterior tooth movement is determined by the alignment of force direction and the center of resistance of the teeth [ 3 ]. Bodily translation occurs when the line of force passes through the root's center of resistance; conversely, inclined movements may result from misalignment. The center of resistance is dynamic, influenced by various factors including dental and periodontal conditions. The use of traction hooks can effectively adjust the force application point relative to the center of resistance, thereby promoting bodily movements. Shifts in microscrew implantation locations and traction hook heights affect the entire biomechanical system, leading to altered patterns of tooth movement. The establishment of the force direction-tooth movement relationship provides insights for selecting appropriate microscrew locations and heights for safe and effective tooth movement. Kojima et al. [ 4 ] demonstrated that an 8 mm long traction arm positioned high enhances the bodily movement of anterior teeth. Lee et al. [ 5 ] highlighted that microscrews placed between buccal premolars improve both intrusion and retraction of anterior teeth. Previous research predominantly focused on maxillary anterior teeth [ 6 ], yet the mandibular arch's denser bone structure presents unique challenges, such as lingual tipping of anterior crowns during treatment. This study employed three-dimensional finite element analysis (3D-FEA) to compare the displacement of mandibular anterior teeth under different systems of force application and traction heights, contributing to an in-depth understanding of the biomechanical characteristics involved in labial fixed orthodontic treatment following tooth extraction. Materials and Methods Study Subject A permanent dentition adult patient with bimaxillary protrusion requiring the extraction of first mandibular and maxillary premolars was selected from the Urumqi Stomatological Hospital Orthodontics Department. Urumqi Stomatological Hospital provided ethical approval for this study. Inclusion Criteria: 1. Adult patients with maxillary and mandibular protrusive facial deformity. 2. Patients primarily concerned with improving their convex facial profile and who accepted the extraction treatment plan. 3. Symmetrical facial and dental arch shape; mesofacial type; labial protrusion evident on lateral view. 4. Complete permanent dentition, with labial inclination of anterior teeth and no periodontal or dental anomalies. 5. Good medical history, lacking systemic medication within the past six months. 6. Normal alveolar bone tissue. 7. Patients who understood the study's purposes and provided consent. Model Establishment Preprocessing and CBCT Data Acquisition The patient's skull was scanned using a CBCT device in the Radiology Department of Urumqi Stomatological Hospital. The scanning range extended from the infraorbital margin to the mental region. Settings included an axial step of 0.250 mm, 120 kV voltage, 5 mA current, and 26.9 s exposure time. High-resolution digital data was saved in DICOM format, reconstructed using Mimics Medical software. Teeth 34 and 44 were removed to simulate first premolar extractions. Periodontal Ligament (PDL) Modeling Due to the invisibility of the PDL in X-ray scans, the PDL was modeled at a uniform thickness of 0.2 mm. The teeth were isotropically expanded by 0.2 mm, with the original tooth volume removed to create the PDL model. Design of Orthodontic Components Labial fixed appliances, traction hooks, and microscrew implants were designed using SOLIDWORKS 2020 software. To optimize calculation time, labial fixed appliances were treated as tetrahedral elements anchored to the teeth. Archwires were designed in AutoCAD and SOLIDWORKS 2020 for optimal adaptation. The utilized archwire for the labial technique measured 0.018×0.025 inches stainless steel. The archwires were posteriorly positioned in brackets with a friction coefficient of 0.0. Traction hooks were strategically placed halfway on the archwire, between the lateral incisors and canines. Additional traction hooks were implemented on the canine brackets to facilitate direct force application. Eight-millimeter-long microscrew implants were placed on the buccal surfaces between the second premolar and first molar, and between the first molar and second molar, based on Poggio et al.'s assessment of these zones as microscrew-safe in 2006. Furthermore, the position of the second molar was simulated as an anchorage tooth for mandibular anterior retraction, with a traction appliance built on the buccal tube of the second molar, allowing comparison of biomechanical characteristics. Model Parameter Setting To evaluate the biomechanical effects of varying hook heights and microscrew locations, multiple model versions were constructed. The traction hooks were positioned at 2 mm, 7 mm, and 11 mm heights, with bracket heights of 0 mm (direct force to the canine) and 5 mm. The microscrew was situated 7 mm from the alveolar crest, and traction on the second molar was set at 2 mm (direct force to the second molar's buccal tube) and 7 mm. Meshing of all components was executed in Meshmixer, targeting an element edge length of 1 mm for bones and 0.5 mm for teeth and PDL. Stereolithography files were imported into Workbench 2023, resulting in 16 models. The final model comprised 249,188 elements and 466,654 nodes. For boundary conditions, the translational degrees of freedom on the opposite side of the model were fixed. Material properties for bones, teeth, PDL, brackets, archwires, power arms, and microscrew implants were established as homogeneous, isotropic, and linearly elastic. Young's modulus and Poisson's ratio for materials are detailed in Table 1 . Various interfaces were bound, including alveolar bone-PDL, teeth-PDL, brackets-tooth, microscrew-jawbone, archwire-tooth, and traction hooks-archwires. The global coordinate system defined the y-axis as vertical (crownward positive), the x-axis as mesiodistal (mesial positive), and the z-axis as buccopalatal (labial-buccal positive). Protocol for Force Application Sites of Force Placement: Second molar: Traction applied at 2 mm and 7 mm heights. 2. Microscrew implants: Two microscrews placed 7 mm from the alveolar crest between the second premolar and first molar, and between the first molar and second molar. These microscrews served as force-bearing points. Force-bearing Points (buccal traction hooks on anterior teeth): 1. Positioned in the archwire's midpoint between lateral incisors and canines at 2 mm, 7 mm, and 11 mm heights. 2. Located on the canine bracket at 0 mm and 5 mm heights. A retraction force of 1.96 N was computed from force application points to bearing points. Various combinations of anchorages and hook heights were established, totaling 16 conditions (see Table 2 and Fig. 1 ). Each condition's maximum equivalent stress on bone, tooth, PDL, bracket, archwire, power arm, and microscrew implants, as well as initial tooth displacement, were quantified. The model was considered symmetrical; thus, only results from the right side were noted, with the left side assumed to be symmetrical. Table 1 Elastic Moduli and Poisson's Ratios of Various Materials Material Name Elastic Modulus (MPa) Poisson's Ratio Tooth 18600 0.30 Alveolar Bone 13700 0.30 Periodontal Ligament 0.689 0.45 Bracket 209000 0.30 Archwire/Traction Hook 193000 0.30 Table 2 Parameters of Oral Orthodontic Traction Conditions Condition Group Anchorage Traction Hook Force A1-1 Dental anchorage Traction arm of buccal tube on tooth 47 2 mm from archwire Traction hook between teeth 42 and 43 2 mm from archwire 1.96N A1-2 7 mm from archwire A1-3 11 mm from archwire A1-4 7 mm from archwire 2 mm from archwire A1-5 7 mm from archwire A1-6 11 mm from archwire A2-7 Microscrew implant anchorage Between teeth 45 and 46 7 mm from alveolar crest Traction hook between teeth 42 and 43 2 mm from archwire A2-8 7 mm from archwire A2-9 11 mm from archwire A2-10 Between teeth 46 and 47 2 mm from archwire A2-11 7 mm from archwire A2-12 11 mm from archwire A3-13 Microscrew implant anchorage Between teeth 45 and 46 7 mm from alveolar crest Traction hook on bracket of tooth 43 0 mm from archwire A3-14 5 mm from archwire A3-15 Between teeth 46 and 47 0 mm from archwire A3-16 5 mm from archwire Results Tooth Displacement Characteristics Under consistent traction hook conditions, the maximum tooth displacement across groups shared a uniform tendency under different anchorage conditions. Additionally, towing tooth 43 displacement exhibited a positive correlation with anterior traction hook length. Group A1 (anchorage using tooth 47) revealed a significant displacement of tooth 47 compared to the other microscrew anchorage groups, demonstrating minimal variability within Group A1. This suggested notable anchorage loss when utilizing tooth 47 for anterior retraction. From Groups A1 and A2, it was observed that across all anchorage sites, maximum displacement of tooth 41 was minimized with an anterior traction hook height set to 7 mm (Fig. 2 ). In Group A1, irrespective of posterior traction arm height, lower anterior traction hook heights correlated with greater lingual inclination of the anterior tooth crown. At a 2 mm posterior traction arm and an 11 mm anterior traction hook, the crown of tooth 42 exhibited undesirable movements, characterized by mesiolabial rotation about the long axis, while the crown of tooth 41 showed labial inclination, likely as an adjustment to localized archwire bending (Fig. 4 ). Groups A1-5 and A1-6 exhibited similar anterior movement patterns; however, maximum anterior tooth displacements varied significantly. Comparable stresses for brackets, archwires, PDL, and alveolar bone showed considerable distinctions. Furthermore, teeth 41 and 42 exhibited movement approaching ideal bodily dynamics (Fig. 4 ). In Group A2, as anterior traction hook heights were increased to 7 mm and 11 mm, crowns of teeth 41 and 42 displayed a tendency towards labial movement. Teeth 41 and 42 rotated around their long axes—attributable to local archwire deformation. At the 11 mm height, notable labial tipping and rotational movements were observed in teeth 41 and 42, due to both the center of resistance of anterior teeth and localized archwire bending. Group A2-8 illustrated improved vertical control of teeth 41 and 42 when maintained at the same point of traction (Fig. 4 ). In Group A3, where the anterior traction hook was fixed on the canine bracket, tooth 43 demonstrated primarily rotational movement, whereas teeth 42 and 41 exhibited compound movements (including distal inclination and labial inclination). Increasing anterior traction hook heights intensified labial inclination movement, potentially due to dog rotation induced by traction force and local archwire deflection, resulting in complex movements of teeth 42 and 41 (Fig. 4 ). Stress Distribution Patterns Equivalent stress in the PDL exhibited relative stability, positively correlating with anterior traction hook lengths, peaking at 0.117 MPa in Group A1-6. Alveolar bone equivalent stress rose significantly with microscrew anchorage, achieving maximum stress when the microscrew was positioned between the first and second molars, confirming that the application of microscrews substantially amplifies the surrounding bone stress (Fig. 3 ). Subsequent to microscrew loading, bracket equivalent stress remained low—most notably in Group A3, which was contrary to anticipated outcomes. In contrast, Groups A1 and A2 showed increases in bracket stress relative to traction hook heights. Archwire equivalent stress reached its peak at 719.54 MPa in Groups A1-3, while Group A3 presented low archwire stress (Fig. 3 ). Stress analysis in Group A3 revealed that anterior bracket stress concentrated within the slot, distinct from the patterns observed in the other two groups. In Group A3, stress concentration on brackets associated with teeth 41 and 42 occurred at their base. Meanwhile, stress concentration on the bracket of tooth 43 became evident in the traction hook region as height increased (Fig. 5 ). Discussion The essence of orthodontic treatment involves orchestrating controlled tooth movement via precise biomechanical control, effective anchorage design, and optimizing force application parameters—key determinants of orthodontic success. Finite element analysis serves a critical role in exploring various orthodontic strategies. For instance, Jiang et al. [ 9 ] constructed a 3D-FEA model for clear aligner treatment post-first premolar extraction, illustrating anterior and posterior tooth displacement patterns and the complexity of tooth movement during clear aligner therapy. Utilizing 3D-FEA to systematically investigate mechanics behind mandibular anterior retraction post-first premolar extraction, the findings align closely with conventional biomechanical theory, establishing a quantitative framework for optimizing clinical treatment planning. Initially, Group A1's severe anchorage loss during retraction with tooth 47 underscores the challenges of maintaining stable dental anchorage in extensive retraction scenarios—consistent with the biomechanical constraints experienced by dentition under mechanical loading [ 10 – 12 ]. This insight emphasizes the importance of selecting appropriate anchorage teeth and examining force direction in intense retraction strategies. Furthermore, the mesiolingual rotation observed in tooth 47 within Group A1 arises from force application that does not intersect with the anchorage tooth's center of resistance, producing moments that affect crown alignment [ 13 – 14 ]. Differing from earlier studies [ 15 ], the current research utilized a friction coefficient of 0 to isolate the effects of archwire sliding friction on incisor retraction, which revealed minimal movement of tooth 47 in the microscrew anchorage groups and concentrated alveolar bone stress around the implant—successfully minimizing force loss due to elastic deformation [ 16 ]. Consequently, this work substantiates the theoretical framework supporting the clinical use of microscrews in orthodontics and offers guidance for future selection and application practices. The application of microscrews, combined with elongated anterior traction devices, enhances torque control in pursuit of bodily movement. Nevertheless, torque loss frequently occurs in clinical settings, strongly associated with traction arm length, microscrew position, archwire elastic deformation, bracket placement, and archwire-bracket interaction. Literature indicates that reducing archwire dimensions increases bracket play, prompting elastic deformation that can induce lingual tipping and extrusion of incisors [ 17 ].However, for archwires with the same shape, the larger the cross-sectional area, the smaller the clearance, and in turn the smaller the movement magnitude of the mandibular dentition[ 18 ]. In this study, the use of a 0.018×0.025 inch archwire alongside a 7 mm anterior traction height allowed tooth 43 to demonstrate bodily movement. In contrast, at an 11 mm height, considerable labial movements in teeth 41 and 42 were noted, supporting that aligning the line of force with the center of resistance minimizes additional moments and encourages bodily movements [ 19 – 20 ].However, other studies have proposed that when an 8.323 mm force application arm is used on the archwire or mandibular canine for retracting anterior teeth, due to the rotational effect generated by the effort arm and the archwire deformation effect, an undesirable tooth movement path will be induced[ 21 ]. Furthermore, studies highlight that extending the traction arm induces torsional forces at the anterior region of the archwire, influencing incisor torque expression [ 22 – 23 ]. Research indicates that a traction arm measuring a minimum of 14 mm is necessary when deploying a 0.019×0.025 inch archwire to facilitate bodily movement of anterior teeth [ 24 ]. Thus, in this study, an 11 mm arm paired with a 0.018×0.025 inch archwire resulted in distinct labial movement tendencies of anterior crowns, providing compelling evidence supporting the clinical application of microscrews and anterior traction appliances. Moreover, when retracting anterior teeth with high-positioned traction arms, alignment near the center of resistance enhances bodily movement [ 25 – 26 ]. Finding a positive correlation between force arm length and maximal displacement of tooth 43 suggests that increased force arm length yields greater moments. Unexpectedly, escalating anterior traction hook height resulted in nonuniform stress distribution on tooth 43. While overall stress was relatively low, the canine, acting as a fulcrum, faced the highest risk of stress concentration within the PDL area near the tooth neck, potentially leading to local overload and subsequent tissue damage or complications. This observation aligns with findings from prior research emphasizing the necessity of managing canine torque to mitigate periodontal harm. This study's limitations stem from the finite element model's inability to simulate PDL viscoelasticity. Given the dynamic and nonlinear factors involved in tooth movement, future model optimization could incorporate viscoelastic material properties to represent periodontal responses under force loading accurately. Additionally, dynamic bone remodeling—absent in this model—should be validated through animal studies to assess long-term treatment outcomes. These investigational areas will enhance the empirical foundation for orthodontic science and practice. In summary, this paper elucidates the influence of varying force application conditions on the biomechanical responses of anterior tooth retraction, reaffirming that choosing an effective anchorage system and optimizing force application parameters are pivotal for successful orthodontic outcomes. The findings provide valuable recommendations for clinical orthodontists, facilitating more precise treatment planning and increasing overall efficiency in extraction orthodontics. Conclusion Anchorage Selection: Microscrew anchorage positioned from the first molar to second premolar is recommended to optimize treatment outcomes. Force Application Parameters: A traction arm height of 7 mm is optimal for anterior retraction, minimizing unwanted rotation and inclination. Archwire Specifications: Where friction conditions allow, employing a thicker archwire is advised to enhance anterior tooth torque control and reduce archwire-bracket play. Declarations Funding This work was supported by the Natural Science Foundation of the Xinjiang Uygur Autonomous Region (Grant No.: 2024D01A30). Ethics approval and consent to participate The study was approved by the Ethics Committee of Urumqi Stomatological Hospital (Approval No.: WKY-LS-2024–025), and written informed consent was obtained from the only participant involved in the study. And we will do our best to protect the rights and privacy of the subjects, and there is no conflict of interest in the content and results of the study. Consent for publication Not applicable. Competing interests The authors declare no competing interests. Author Contribution L. Y. and X.Z.designed The experiment. L.Y. and Y. W. analyzed the experimental results of the three-dimensional (3D) finite element experiment. L.Y. and Y. W. wrote the manuscript. All authors contributed to the preparation and editing of the manuscript for intellectual content. Data Availability The datasets generated and/or analyzed during the current study are not publicly available due to privacy and ethical concerns but are available from the corresponding author on reasonable request. References Xu Y, Xie J. Comparison of the effects of mini-implant and traditional anchorage on patients with maxillary dentoalveolar protrusion[J]. Angle Orthod. 2017;87(2):320–7. Upadhyay M. Yadav S,Nanda R.Biomechanics of incisor retraction with mini-implant anchorage[J]. J Orthod 2014,41(1):15–23. Song JW, Lim JK, Lee KJ et al. Finite element analysis of maxillary incisor displacement during en-masse retraction according to orthodonticmini-implant position[J]. Korean J Orthod 2016,46(4):242–52. Kawamura J, Tamaya N. A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics[J]. Prog Orthod. 2019;20:3. Lee KJ, Park YC, Hwang CJ, et al. 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Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 15 Jan, 2026 Reviewers agreed at journal 29 Dec, 2025 Reviews received at journal 28 Dec, 2025 Reviewers agreed at journal 16 Dec, 2025 Reviewers invited by journal 08 Dec, 2025 Editor invited by journal 20 Nov, 2025 Editor assigned by journal 17 Nov, 2025 Submission checks completed at journal 17 Nov, 2025 First submitted to journal 11 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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16:40:26","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":29310,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/c83051de2c8457cf92716f79.png"},{"id":98047992,"identity":"f95306da-e415-45e2-b12f-692187ff25e0","added_by":"auto","created_at":"2025-12-12 08:31:28","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":166029,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/88062753e88811bf7bc18465.png"},{"id":98047995,"identity":"63deb80b-7922-40fb-86a2-9cd7fa5c7281","added_by":"auto","created_at":"2025-12-12 08:31:28","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":28522,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/da6cb9faf580310265976ad2.png"},{"id":98047993,"identity":"3eba06d8-257f-4813-b1e0-fc3dc628dc3c","added_by":"auto","created_at":"2025-12-12 08:31:28","extension":"xml","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":72639,"visible":true,"origin":"","legend":"","description":"","filename":"7c70ce66e1b9445192bdb1a95e02b41d1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/5a5190c835105ba0c770b88e.xml"},{"id":98047994,"identity":"0f0026a4-6e09-47e1-a807-9eb62fc9f163","added_by":"auto","created_at":"2025-12-12 08:31:28","extension":"html","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":79971,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/49c9e39f6ecca4d3952297bd.html"},{"id":98427531,"identity":"ac0652a1-d849-442b-a2ce-9c0747e0055a","added_by":"auto","created_at":"2025-12-17 16:40:37","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":349312,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic Diagram of Condition Group Classification\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/17c5aaba42be1fc028b62a9a.png"},{"id":98425927,"identity":"c3939a91-d823-4447-a822-74963ff8f073","added_by":"auto","created_at":"2025-12-17 16:35:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":68221,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum Displacement Diagram of the Right Mandibular Teeth (Unit: mm)\u003c/p\u003e\n\u003cp\u003eFor ease of observation, the maximum displacement values of all teeth were magnified by a factor of 10⁵ for mapping. Figure 2 shows the maximum displacement of the right mandibular teeth in Group A1, Group A2, and Group A3 respectively。\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/e8b23b256b1eb6dd6b2695f6.png"},{"id":98047981,"identity":"1988f014-2eec-4e5a-82d0-6927958d446a","added_by":"auto","created_at":"2025-12-12 08:31:28","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":71373,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic Diagram of Effective Stress Values of Periodontal Ligament, Alveolar Bone, Archwire, and Bracket in Each Group\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/ac854170eb8e3fcca97652ee.png"},{"id":98425909,"identity":"31be58a6-7c26-45ff-87da-f8fc3fd5ef4c","added_by":"auto","created_at":"2025-12-17 16:35:20","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":832459,"visible":true,"origin":"","legend":"\u003cp\u003eDisplacement Trend Diagram of the Right Mandibular Teeth\u003c/p\u003e\n\u003cp\u003e(a)Movement trends of teeth 41, 42, 43, and 47 in each group, observed from the occlusal view;\u003c/p\u003e\n\u003cp\u003e(b)Movement trends of teeth 41, 42, and 43 in each group, observed from the mesiodistal view;\u003c/p\u003e\n\u003cp\u003e(c) Movement trends of tooth 47 in each group, observed from the buccal view.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/c86d199a44b17ecf9afb651c.png"},{"id":98047990,"identity":"f5cf82fa-7772-4bf6-87db-2031deb25f18","added_by":"auto","created_at":"2025-12-12 08:31:28","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":140341,"visible":true,"origin":"","legend":"\u003cp\u003eStress Distribution Diagram of Anterior Teeth Brackets in Group A3\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/e63934609b168a23d26121ca.png"},{"id":98444543,"identity":"934b9065-5d87-4028-9270-62f8511fbd74","added_by":"auto","created_at":"2025-12-17 17:16:20","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2327534,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7834509/v1/1f9f6817-300e-4e21-b497-8f7947581f8f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Three-Dimensional Finite Element Analysis of Retracting Mandibular Anterior Teeth with Labial Fixed Appliances in Different Force Application and Traction Points","fulltext":[{"header":"Introduction","content":"\u003cp\u003eExtraction orthodontics is one of the most widely practiced methods for correcting dental protrusion and improving convex facial profiles. It necessitates robust anchorage to facilitate extensive anterior tooth retraction, thereby correcting the lateral profile. Key challenges in extraction orthodontics include maintaining normal torque of incisors, controlling overall anterior retraction, and preventing overbite deepening during treatment. Microscrew implants, which are strategically embedded within the jawbone, provide \"absolute anchorage\" and enable effective anterior retraction by minimizing movement inefficiencies.\u003c/p\u003e\u003cp\u003ePrior studies have established that microscrews can securely anchor orthodontic appliances, allowing for greater utilization of extraction spaces for anterior retraction [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Their clinical application has expanded widely. The regulation of anterior tooth movement is determined by the alignment of force direction and the center of resistance of the teeth [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Bodily translation occurs when the line of force passes through the root's center of resistance; conversely, inclined movements may result from misalignment. The center of resistance is dynamic, influenced by various factors including dental and periodontal conditions. The use of traction hooks can effectively adjust the force application point relative to the center of resistance, thereby promoting bodily movements.\u003c/p\u003e\u003cp\u003eShifts in microscrew implantation locations and traction hook heights affect the entire biomechanical system, leading to altered patterns of tooth movement. The establishment of the force direction-tooth movement relationship provides insights for selecting appropriate microscrew locations and heights for safe and effective tooth movement.\u003c/p\u003e\u003cp\u003eKojima et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] demonstrated that an 8 mm long traction arm positioned high enhances the bodily movement of anterior teeth. Lee et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] highlighted that microscrews placed between buccal premolars improve both intrusion and retraction of anterior teeth. Previous research predominantly focused on maxillary anterior teeth [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], yet the mandibular arch's denser bone structure presents unique challenges, such as lingual tipping of anterior crowns during treatment.\u003c/p\u003e\u003cp\u003eThis study employed three-dimensional finite element analysis (3D-FEA) to compare the displacement of mandibular anterior teeth under different systems of force application and traction heights, contributing to an in-depth understanding of the biomechanical characteristics involved in labial fixed orthodontic treatment following tooth extraction.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cp\u003eStudy Subject\u003c/p\u003e\n\u003cp\u003eA permanent dentition adult patient with bimaxillary protrusion requiring the extraction of first mandibular and maxillary premolars was selected from the Urumqi Stomatological Hospital Orthodontics Department. Urumqi Stomatological Hospital provided ethical approval for this study.\u003c/p\u003e\n\u003cp\u003eInclusion Criteria:\u003c/p\u003e\n\u003cp\u003e\u003cspan\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e1. Adult patients with maxillary and mandibular protrusive facial deformity.\u003c/p\u003e\u003cspan\u003e\n \u003cp\u003e2. Patients primarily concerned with improving their convex facial profile and who accepted the extraction treatment plan.\u003c/p\u003e\n\u003c/span\u003e\u003cspan\u003e\n \u003cp\u003e3. Symmetrical facial and dental arch shape; mesofacial type; labial protrusion evident on lateral view.\u003c/p\u003e\n\u003c/span\u003e\u003cspan\u003e\n \u003cp\u003e4. Complete permanent dentition, with labial inclination of anterior teeth and no periodontal or dental anomalies.\u003c/p\u003e\n\u003c/span\u003e\u003cspan\u003e\n \u003cp\u003e5. Good medical history, lacking systemic medication within the past six months.\u003c/p\u003e\n\u003c/span\u003e\u003cspan\u003e\n \u003cp\u003e6. Normal alveolar bone tissue.\u003c/p\u003e\n\u003c/span\u003e\u003cspan\u003e\n \u003cp\u003e7. Patients who understood the study\u0026apos;s purposes and provided consent.\u003c/p\u003e\n\u003c/span\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eModel Establishment\u003c/p\u003e\n\u003cp\u003ePreprocessing and CBCT Data Acquisition\u003c/p\u003e\n\u003cp\u003eThe patient\u0026apos;s skull was scanned using a CBCT device in the Radiology Department of Urumqi Stomatological Hospital. The scanning range extended from the infraorbital margin to the mental region. Settings included an axial step of 0.250 mm, 120 kV voltage, 5 mA current, and 26.9 s exposure time. High-resolution digital data was saved in DICOM format, reconstructed using Mimics Medical software.\u003c/p\u003e\n\u003cp\u003eTeeth 34 and 44 were removed to simulate first premolar extractions.\u003c/p\u003e\n\u003cp\u003ePeriodontal Ligament (PDL) Modeling\u003c/p\u003e\n\u003cp\u003eDue to the invisibility of the PDL in X-ray scans, the PDL was modeled at a uniform thickness of 0.2 mm. The teeth were isotropically expanded by 0.2 mm, with the original tooth volume removed to create the PDL model.\u003c/p\u003e\n\u003cp\u003eDesign of Orthodontic Components\u003c/p\u003e\n\u003cp\u003eLabial fixed appliances, traction hooks, and microscrew implants were designed using SOLIDWORKS 2020 software. To optimize calculation time, labial fixed appliances were treated as tetrahedral elements anchored to the teeth. Archwires were designed in AutoCAD and SOLIDWORKS 2020 for optimal adaptation. The utilized archwire for the labial technique measured 0.018\u0026times;0.025 inches stainless steel. The archwires were posteriorly positioned in brackets with a friction coefficient of 0.0. Traction hooks were strategically placed halfway on the archwire, between the lateral incisors and canines. Additional traction hooks were implemented on the canine brackets to facilitate direct force application.\u003c/p\u003e\n\u003cp\u003eEight-millimeter-long microscrew implants were placed on the buccal surfaces between the second premolar and first molar, and between the first molar and second molar, based on Poggio et al.\u0026apos;s assessment of these zones as microscrew-safe in 2006. Furthermore, the position of the second molar was simulated as an anchorage tooth for mandibular anterior retraction, with a traction appliance built on the buccal tube of the second molar, allowing comparison of biomechanical characteristics.\u003c/p\u003e\n\u003cp\u003eModel Parameter Setting\u003c/p\u003e\n\u003cp\u003eTo evaluate the biomechanical effects of varying hook heights and microscrew locations, multiple model versions were constructed. The traction hooks were positioned at 2 mm, 7 mm, and 11 mm heights, with bracket heights of 0 mm (direct force to the canine) and 5 mm. The microscrew was situated 7 mm from the alveolar crest, and traction on the second molar was set at 2 mm (direct force to the second molar\u0026apos;s buccal tube) and 7 mm.\u003c/p\u003e\n\u003cp\u003eMeshing of all components was executed in Meshmixer, targeting an element edge length of 1 mm for bones and 0.5 mm for teeth and PDL. Stereolithography files were imported into Workbench 2023, resulting in 16 models. The final model comprised 249,188 elements and 466,654 nodes. For boundary conditions, the translational degrees of freedom on the opposite side of the model were fixed. Material properties for bones, teeth, PDL, brackets, archwires, power arms, and microscrew implants were established as homogeneous, isotropic, and linearly elastic. Young\u0026apos;s modulus and Poisson\u0026apos;s ratio for materials are detailed in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. Various interfaces were bound, including alveolar bone-PDL, teeth-PDL, brackets-tooth, microscrew-jawbone, archwire-tooth, and traction hooks-archwires. The global coordinate system defined the y-axis as vertical (crownward positive), the x-axis as mesiodistal (mesial positive), and the z-axis as buccopalatal (labial-buccal positive).\u003c/p\u003e\n\u003cp\u003eProtocol for Force Application\u003c/p\u003e\n\u003cp\u003eSites of Force Placement:\u003c/p\u003e\n\u003col\u003e\n \u003cli\u003e\u003cspan\u003eSecond molar: Traction applied at 2 mm and 7 mm heights.\u003cbr\u003e\u003c/span\u003e\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003e2. Microscrew implants: Two microscrews placed 7 mm from the alveolar crest between the second premolar and first molar, and between the first molar and second molar. These microscrews served as force-bearing points.\u003c/p\u003e\n\u003cp\u003eForce-bearing Points (buccal traction hooks on anterior teeth):\u003c/p\u003e\n\u003cp\u003e\u003cspan\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e1. Positioned in the archwire\u0026apos;s midpoint between lateral incisors and canines at 2 mm, 7 mm, and 11 mm heights.\u003c/p\u003e\u003cspan\u003e\n \u003cp\u003e2. Located on the canine bracket at 0 mm and 5 mm heights.\u003c/p\u003e\n\u003c/span\u003e\n\u003cp\u003e\u003c/p\u003e\n\u003cp\u003eA retraction force of 1.96 N was computed from force application points to bearing points. Various combinations of anchorages and hook heights were established, totaling 16 conditions (see Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Each condition\u0026apos;s maximum equivalent stress on bone, tooth, PDL, bracket, archwire, power arm, and microscrew implants, as well as initial tooth displacement, were quantified. The model was considered symmetrical; thus, only results from the right side were noted, with the left side assumed to be symmetrical.\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\u003eElastic Moduli and Poisson\u0026apos;s Ratios of Various Materials\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 Name\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eElastic Modulus (MPa)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePoisson\u0026apos;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\u003eTooth\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e18600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAlveolar Bone\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13700\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ePeriodontal Ligament\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.689\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\u003eBracket\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e209000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eArchwire/Traction Hook\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e193000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cdiv align=\"left\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003ctable id=\"Tab2\" border=\"1\" class=\"fr-table-selection-hover\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eParameters of Oral Orthodontic Traction Conditions\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCondition Group\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eAnchorage\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003eTraction Hook\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eForce\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\u003eA1-1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eDental anchorage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eTraction arm of buccal tube on tooth 47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003e2 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eTraction hook between teeth 42 and 43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"16\"\u003e\n \u003cp\u003e1.96N\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA1-2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA1-3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA1-4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003e7 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA1-5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA1-6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA2-7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eMicroscrew implant anchorage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eBetween teeth 45 and 46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e7 mm from alveolar crest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eTraction hook between teeth 42 and 43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA2-8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA2-9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA2-10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eBetween teeth 46 and 47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA2-11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA2-12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA3-13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eMicroscrew implant anchorage\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eBetween teeth 45 and 46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003e7 mm from alveolar crest\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"4\"\u003e\n \u003cp\u003eTraction hook on bracket of tooth 43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA3-14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA3-15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eBetween teeth 46 and 47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA3-16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5 mm from archwire\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eTooth Displacement Characteristics\u003c/p\u003e\u003cp\u003eUnder consistent traction hook conditions, the maximum tooth displacement across groups shared a uniform tendency under different anchorage conditions. Additionally, towing tooth 43 displacement exhibited a positive correlation with anterior traction hook length.\u003c/p\u003e\u003cp\u003eGroup A1 (anchorage using tooth 47) revealed a significant displacement of tooth 47 compared to the other microscrew anchorage groups, demonstrating minimal variability within Group A1. This suggested notable anchorage loss when utilizing tooth 47 for anterior retraction.\u003c/p\u003e\u003cp\u003eFrom Groups A1 and A2, it was observed that across all anchorage sites, maximum displacement of tooth 41 was minimized with an anterior traction hook height set to 7 mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In Group A1, irrespective of posterior traction arm height, lower anterior traction hook heights correlated with greater lingual inclination of the anterior tooth crown. At a 2 mm posterior traction arm and an 11 mm anterior traction hook, the crown of tooth 42 exhibited undesirable movements, characterized by mesiolabial rotation about the long axis, while the crown of tooth 41 showed labial inclination, likely as an adjustment to localized archwire bending (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eGroups A1-5 and A1-6 exhibited similar anterior movement patterns; however, maximum anterior tooth displacements varied significantly. Comparable stresses for brackets, archwires, PDL, and alveolar bone showed considerable distinctions. Furthermore, teeth 41 and 42 exhibited movement approaching ideal bodily dynamics (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn Group A2, as anterior traction hook heights were increased to 7 mm and 11 mm, crowns of teeth 41 and 42 displayed a tendency towards labial movement. Teeth 41 and 42 rotated around their long axes\u0026mdash;attributable to local archwire deformation. At the 11 mm height, notable labial tipping and rotational movements were observed in teeth 41 and 42, due to both the center of resistance of anterior teeth and localized archwire bending. Group A2-8 illustrated improved vertical control of teeth 41 and 42 when maintained at the same point of traction (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn Group A3, where the anterior traction hook was fixed on the canine bracket, tooth 43 demonstrated primarily rotational movement, whereas teeth 42 and 41 exhibited compound movements (including distal inclination and labial inclination). Increasing anterior traction hook heights intensified labial inclination movement, potentially due to dog rotation induced by traction force and local archwire deflection, resulting in complex movements of teeth 42 and 41 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eStress Distribution Patterns\u003c/p\u003e\u003cp\u003eEquivalent stress in the PDL exhibited relative stability, positively correlating with anterior traction hook lengths, peaking at 0.117 MPa in Group A1-6. Alveolar bone equivalent stress rose significantly with microscrew anchorage, achieving maximum stress when the microscrew was positioned between the first and second molars, confirming that the application of microscrews substantially amplifies the surrounding bone stress (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eSubsequent to microscrew loading, bracket equivalent stress remained low\u0026mdash;most notably in Group A3, which was contrary to anticipated outcomes. In contrast, Groups A1 and A2 showed increases in bracket stress relative to traction hook heights. Archwire equivalent stress reached its peak at 719.54 MPa in Groups A1-3, while Group A3 presented low archwire stress (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eStress analysis in Group A3 revealed that anterior bracket stress concentrated within the slot, distinct from the patterns observed in the other two groups. In Group A3, stress concentration on brackets associated with teeth 41 and 42 occurred at their base. Meanwhile, stress concentration on the bracket of tooth 43 became evident in the traction hook region as height increased (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe essence of orthodontic treatment involves orchestrating controlled tooth movement via precise biomechanical control, effective anchorage design, and optimizing force application parameters\u0026mdash;key determinants of orthodontic success. Finite element analysis serves a critical role in exploring various orthodontic strategies. For instance, Jiang et al. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] constructed a 3D-FEA model for clear aligner treatment post-first premolar extraction, illustrating anterior and posterior tooth displacement patterns and the complexity of tooth movement during clear aligner therapy.\u003c/p\u003e\u003cp\u003eUtilizing 3D-FEA to systematically investigate mechanics behind mandibular anterior retraction post-first premolar extraction, the findings align closely with conventional biomechanical theory, establishing a quantitative framework for optimizing clinical treatment planning.\u003c/p\u003e\u003cp\u003eInitially, Group A1's severe anchorage loss during retraction with tooth 47 underscores the challenges of maintaining stable dental anchorage in extensive retraction scenarios\u0026mdash;consistent with the biomechanical constraints experienced by dentition under mechanical loading [\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThis insight emphasizes the importance of selecting appropriate anchorage teeth and examining force direction in intense retraction strategies. Furthermore, the mesiolingual rotation observed in tooth 47 within Group A1 arises from force application that does not intersect with the anchorage tooth's center of resistance, producing moments that affect crown alignment [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eDiffering from earlier studies [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], the current research utilized a friction coefficient of 0 to isolate the effects of archwire sliding friction on incisor retraction, which revealed minimal movement of tooth 47 in the microscrew anchorage groups and concentrated alveolar bone stress around the implant\u0026mdash;successfully minimizing force loss due to elastic deformation [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eConsequently, this work substantiates the theoretical framework supporting the clinical use of microscrews in orthodontics and offers guidance for future selection and application practices. The application of microscrews, combined with elongated anterior traction devices, enhances torque control in pursuit of bodily movement. Nevertheless, torque loss frequently occurs in clinical settings, strongly associated with traction arm length, microscrew position, archwire elastic deformation, bracket placement, and archwire-bracket interaction.\u003c/p\u003e\u003cp\u003eLiterature indicates that reducing archwire dimensions increases bracket play, prompting elastic deformation that can induce lingual tipping and extrusion of incisors [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].However, for archwires with the same shape, the larger the cross-sectional area, the smaller the clearance, and in turn the smaller the movement magnitude of the mandibular dentition[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. In this study, the use of a 0.018\u0026times;0.025 inch archwire alongside a 7 mm anterior traction height allowed tooth 43 to demonstrate bodily movement. In contrast, at an 11 mm height, considerable labial movements in teeth 41 and 42 were noted, supporting that aligning the line of force with the center of resistance minimizes additional moments and encourages bodily movements [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].However, other studies have proposed that when an 8.323 mm force application arm is used on the archwire or mandibular canine for retracting anterior teeth, due to the rotational effect generated by the effort arm and the archwire deformation effect, an undesirable tooth movement path will be induced[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eFurthermore, studies highlight that extending the traction arm induces torsional forces at the anterior region of the archwire, influencing incisor torque expression [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Research indicates that a traction arm measuring a minimum of 14 mm is necessary when deploying a 0.019\u0026times;0.025 inch archwire to facilitate bodily movement of anterior teeth [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThus, in this study, an 11 mm arm paired with a 0.018\u0026times;0.025 inch archwire resulted in distinct labial movement tendencies of anterior crowns, providing compelling evidence supporting the clinical application of microscrews and anterior traction appliances. Moreover, when retracting anterior teeth with high-positioned traction arms, alignment near the center of resistance enhances bodily movement [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eFinding a positive correlation between force arm length and maximal displacement of tooth 43 suggests that increased force arm length yields greater moments. Unexpectedly, escalating anterior traction hook height resulted in nonuniform stress distribution on tooth 43. While overall stress was relatively low, the canine, acting as a fulcrum, faced the highest risk of stress concentration within the PDL area near the tooth neck, potentially leading to local overload and subsequent tissue damage or complications. This observation aligns with findings from prior research emphasizing the necessity of managing canine torque to mitigate periodontal harm.\u003c/p\u003e\u003cp\u003eThis study's limitations stem from the finite element model's inability to simulate PDL viscoelasticity. Given the dynamic and nonlinear factors involved in tooth movement, future model optimization could incorporate viscoelastic material properties to represent periodontal responses under force loading accurately. Additionally, dynamic bone remodeling\u0026mdash;absent in this model\u0026mdash;should be validated through animal studies to assess long-term treatment outcomes.\u003c/p\u003e\u003cp\u003eThese investigational areas will enhance the empirical foundation for orthodontic science and practice.\u003c/p\u003e\u003cp\u003eIn summary, this paper elucidates the influence of varying force application conditions on the biomechanical responses of anterior tooth retraction, reaffirming that choosing an effective anchorage system and optimizing force application parameters are pivotal for successful orthodontic outcomes. The findings provide valuable recommendations for clinical orthodontists, facilitating more precise treatment planning and increasing overall efficiency in extraction orthodontics.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eAnchorage Selection: Microscrew anchorage positioned from the first molar to second premolar is recommended to optimize treatment outcomes.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eForce Application Parameters: A traction arm height of 7 mm is optimal for anterior retraction, minimizing unwanted rotation and inclination.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eArchwire Specifications: Where friction conditions allow, employing a thicker archwire is advised to enhance anterior tooth torque control and reduce archwire-bracket play.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis work was supported by the Natural Science Foundation of the Xinjiang Uygur Autonomous Region (Grant No.: 2024D01A30).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study was approved by the Ethics Committee of Urumqi Stomatological Hospital (Approval No.: WKY-LS-2024\u0026ndash;025), and written informed consent was obtained from the only participant involved in the study. And we will do our best to protect the rights and privacy of the subjects, and there is no conflict of interest in the content and results of the study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eL. Y. and X.Z.designed The experiment. L.Y. and Y. W. analyzed the experimental results of the three-dimensional (3D) finite element experiment. L.Y. and Y. W. wrote the manuscript. All authors contributed to the preparation and editing of the manuscript for intellectual content.\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eThe datasets generated and/or analyzed during the current study are not publicly available due to privacy and ethical concerns but are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eXu Y, Xie J. Comparison of the effects of mini-implant and traditional anchorage on patients with maxillary dentoalveolar protrusion[J]. Angle Orthod. 2017;87(2):320\u0026ndash;7.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eUpadhyay M. Yadav S,Nanda R.Biomechanics of incisor retraction with mini-implant anchorage[J]. J Orthod 2014,41(1):15\u0026ndash;23.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSong JW, Lim JK, Lee KJ et al. Finite element analysis of maxillary incisor displacement during en-masse retraction according to orthodonticmini-implant position[J]. Korean J Orthod 2016,46(4):242\u0026ndash;52.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKawamura J, Tamaya N. A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics[J]. Prog Orthod. 2019;20:3.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLee KJ, Park YC, Hwang CJ, et al. Displacement pattern of the maxillary arch depending on mini-screw position in sliding mechanic[J]. Am J Orthod Dentofac Orthop. 2011;140(2):224\u0026ndash;32.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMontasser ZM, Scribante A, Zampetti P, Montasser MA. En-masse maxillary anterior retraction to close the extraction space with fixed orthodontic appliances: A systematic review. Int Orthod. 2025;23(3):101004.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKojima Y. Kawamura J,Fukui H.Finite element analysis of the effect of force directions on tooth movement in extraction space closure with miniscrew sliding mechanics[J]. Am J Orthod Dentofac Orthop 2012,142(4):501\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHedayati Z. Mehrdad Shomali.Maxillary anterior en masse retraction using different antero-posterior position of miniscrew:a 3D finite element study[J]. Prog Orthodont. 2016;17(1):31.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJiang X, et al. Three-dimensional finite element analysis of tooth displacement patterns during maxillary anterior teeth retraction with clear aligners after extraction of the first premolars [J]. Angle Orthod. 2019;89(4):529\u0026ndash;37.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSi M, Hao Z, Fan H, et al. Maxillary Protraction: A Bibliometric Analysis. Int Dent J. 2023;73(6):873\u0026ndash;80.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYassir YA, Nabbat SA, McIntyre GT, et al. Which anchorage device is the best during retraction of anterior teeth? An overview of systematic reviews[J]. Korean J Orthod. 2022;52(3):220\u0026ndash;35.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGarg H, Ahluwalia R, Grewal SB, Pandey SK, Mahesh A, Saini N. Stainless steel vs. titanium miniscrew implants: Evaluation of stability during retraction of maxillary and mandibular anterior teeth. J Orthod Sci. 2022;11:49.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMalhotra A, Mangla R, Dua VS, Kannan S, Arora N, Singh AK. A clinical comparative study using anchorage from mini-implants and conventional anchorage methods to retract anterior teeth. J Family Med Prim Care. 2021;10(1):468\u0026ndash;74.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSahoo SK, Chekka M, Chawla R, Nehal Naimatullah M, Kumar Misra K, Kandikatla P, Prashant MC. Comparative Study of Mini-implants versus Standard Implants in Orthodontic Anchorage for Space Closure. J Pharm Bioallied Sci. 2024;16(Suppl 3):S2458\u0026ndash;60.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXia Q, Wang W, Wang C, et al. Comparative assessment of orthodontic clear aligner versus fixed appliance for anterior retraction: a finite element study[J]. BMC Oral Health. 2024;24(1):80.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJang HJ, Roh WJ, Joo BH, Park KH, Kim SJ, Park YG. Locating the center of resistance of maxillary anterior teeth retracted by Double J Retractor with palatal miniscrews. Angle Orthod. 2010;80(6):1023\u0026ndash;8.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKawamura J, Tamaya N. A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics. Prog Orthod. 2019;20:3.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eXie Q, Li D. The cross-sectional effects of ribbon arch wires on Class II malocclusion intermaxillary traction: a three-dimensional finite element analysis. BMC Oral Health. 2021;21(1):501.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFelicita AS. Quantification of intrusive/retraction force and moment generated during en-masse retraction of maxillary anterior teeth using mini-implants: A conceptual approach. Dent Press J Orthod. 2017 Sep-Oct;22(5):47\u0026ndash;55.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eParashar A, Aileni KR, Rachala MR, Shashidhar NR, Mallikarjun V, Parik N. Torque Loss in En-Masse Retraction of Maxillary Anterior Teeth Using Miniimplants with Force Vectors at Different Levels: 3D FEM Study. J Clin Diagn Res. 2014;8(12):ZC77\u0026ndash;80.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJiang F, Roberts WE, Liu Y, Shafiee A, Chen J. Mechanical environment for lower canine T-loop retraction compared to en-masse space closure with a power-arm attached to either the canine bracket or the archwire. Angle Orthod. 2020;90(6):801\u0026ndash;10.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHamanaka R, Cantarella D, Lombardo L, Karanxha L, Del Fabbro M, Siciliani G, Yoshida N. Dual-section versus conventional archwire for en-masse retraction of anterior teeth with direct skeletal anchorage: a finite element analysis. BMC Oral Health. 2021;21(1):87.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTominaga JY, Ozaki H, Chiang PC, Sumi M, Tanaka M, Koga Y, et al. Effect of bracket slot and archwire dimensions on anterior tooth movement during space closure in sliding mechanics: a 3-dimensional finite element study. Am J Orthod Dentofac Orthop. 2014;146:166\u0026ndash;74.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWu J, Wang X, Jiang Y, Wu Z, Shen Q, Chen Y, Meng Q, Ye N. Effect of archwire plane and archwire size on anterior teeth movement in sliding mechanics in customized labial orthodontics: a 3D finite element study. BMC Oral Health. 2022;22(1):33.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLee KJ, Park YC, Hwang CJ, Kim YJ, Choi TH, Yoo HM, et al. Displacement pattern of the maxillary arch depending on miniscrew position in sliding mechanics. Am J Orthod Dentofac Orthop. 2011;140(2):224\u0026ndash;32.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhang L, Guo R, Xu B, Wang Y, Li W. Three-dimensional evaluation of maxillary tooth movement in extraction patients with three different miniscrew anchorage systems: a randomized controlled trial. Prog Orthod. 2022;23(1):46.\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":false,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-7834509/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7834509/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eObjective\u003c/h2\u003e\u003cp\u003eThis study aimed to employ three-dimensional finite element analysis (3D-FEA) to investigate the effects of varying microscrew implantation points and traction hook heights on the biomechanical behavior and movement of mandibular anterior teeth during retraction.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eAn adult patient requiring the extraction of maxillary and mandibular first premolars was selected from the Orthodontics Department of Urumqi Stomatological Hospital, which provided ethical approval for this study. Various models of 3D-FEA were constructed, differentiated by microscrew position and traction hook height. Finite element analysis was utilized to calculate stress levels in the alveolar bone, brackets, archwires, and the displacement responses of teeth under different force delivery conditions.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003eThe length of the anterior traction hook was positively correlated with the displacement magnitude of mandibular lateral incisors and canines. When the same traction hook was applied under different anchorage conditions, the maximum tooth movement in each group exhibited a comparable trend. Compared with the other two groups (mini-implant anchorage groups), Group A1 (47th tooth anchorage group) showed statistically significant displacement of the 47th tooth. The equivalent stress of the periodontal ligament (PDL) remained stable, whereas the alveolar bone stress attained a maximum when mini-screws were placed between the first and second molars (consistent with anatomical sequencing). With increasing height of the anterior traction hook, the bracket stress in Groups A1 and A2 increased incrementally; furthermore, this increase in traction hook height enhanced the control over vertical movement in Group A2.\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e\u003cp\u003eThe clinical application of microscrews as anchorage is theoretically supported, emphasizing that optimizing force application parameters and selecting appropriate anchorage sites are crucial for effective mandibular anterior tooth retraction. This research provides a foundational rationale for optimizing future orthodontic treatment strategies.\u003c/p\u003e","manuscriptTitle":"Three-Dimensional Finite Element Analysis of Retracting Mandibular Anterior Teeth with Labial Fixed Appliances in Different Force Application and Traction Points","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-12 08:31:23","doi":"10.21203/rs.3.rs-7834509/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-01-15T21:18:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"334081699241583658754397228176505529674","date":"2025-12-30T00:54:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-28T12:09:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"228492105084146067544044762458242765706","date":"2025-12-16T10:29:21+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-08T14:13:53+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-11-20T11:54:26+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-17T05:40:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-17T05:39:54+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Oral Health","date":"2025-10-11T10:39:16+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":"5fc59a03-f0f3-4b5d-9682-4e36d580ca73","owner":[],"postedDate":"December 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-12-12T08:31:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-12 08:31:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7834509","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7834509","identity":"rs-7834509","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}