Efficacy of a four-curve auxiliary arch at preventing maxillary central incisor linguoclination during orthodontic treatment: A finite element analysis

Efficacy of a four-curve auxiliary arch at preventing maxillary central incisor linguoclination during orthodontic treatment: 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 Efficacy of a four-curve auxiliary arch at preventing maxillary central incisor linguoclination during orthodontic treatment: A finite element analysis Pingzhu Yang, Liyun Bai, Hexuan Zhang, Yu Liu, Wenjun Zhao, Xiujie Wen, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2048265/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Mar, 2023 Read the published version in BMC Oral Health → Version 1 posted 11 You are reading this latest preprint version Abstract Background The correct torque of the incisors helps assess the effect of orthodontic treatment; however, evaluating it effectively remains a challenge. Improper anterior teeth torque angle can cause cortical bone fracture and root exposure. Methods A three-dimensional finite element model of the maxillary central incisor torque controlled by a self-made four-curvature auxiliary arch was established, And the experiments were divided to simulate four different group: (1) molar ligation group ; (2) micro-implant ligation group; (3) molar retraction group ༛(4) micro-implant retraction group༛and the retracted traction force was set at 1.15 N. The displacement of the maxillary dentition and periodontal ligament stress values were analyzed with different torque forces (0.5 N, 1 N, 1.5 N, 2 N) placed on the incisors. Results Provided the absence of a tooth extraction gap, when the four-curvature auxiliary arch was used in conjunction with absolute anchorage, the recommended force value was of < 1.5 N. when maxillary central incisor retraction, a force value of < 1 N was recommended. In the case of no-implant anchorage, whether there is tooth extraction gap or not, the recommended force value was of < 1 N. The stress on the other teeth did not exceed the value of that on the periodontal ligament. The effect of using the four-curvature on the incisors was significant. Conclusions The proposed approach may help improve treatment maxillary central incisor for poor torque and avoid cortical bone fracture and root exposure Implant anchorage Self-made four-curvature auxiliary arch Three-dimensional finite element Round stainless-steel wires Anterior teeth torque angle Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction Good torque control of the incisors helps to improve the corrective effect in orthodontic cases by affecting aesthetic outcomes and occlusal relationship stability, which is also one of the important indicators to evaluate the end of orthodontic treatment. For example, when the maxillary incisors stand upright or a tongue tilt occurs ,the root of the anterior teeth can pierce the last line of defense of the alveolar bone, eventually causing the cortical bone to rupture and leaving the root without a foothold[ 1 – 3 ]. Meanwhile, a good inclination angle of the anterior teeth can help maintain the stability of dentition occlusion. Therefore, the torque of the incisors is one of a key factor determine in orthodontic treatment outcomes [ 4 – 6 ]. Experimental studies of the movement of teeth during orthodontic treatment is based on the ability of the alveolar bone and periodontal ligament to respond to mechanical stimuli, which generate force during a loading process, the strain action causes tooth movement[ 7 – 9 ]. And orthodontic process had found that the combined action of multiple orthodontic forces can cause abnormal torque movement of the teeth. If a large periodontal stress is generated at the root apex of the teeth, tooth root absorption may occur, which is an undesirable histological reaction [ 10 ]. Stiffness refers to the amount of stress produced by unit strain variable, which is the rate of load deformation. In the study of orthodontic mechanics, there are many ways to describe the properties of arch wire. In terms of stiffness, there are three levels of concepts: material stiffness, arch wire stiffness and appliance stiffness. Arch wire stiffness refers to the inherent rigidity determined by the material, the shape of the cross section and the area of the cross section. It has nothing to do with the length or configuration design of the arch wire. It represents the bending rigidity of the arch wire, and its size depends on the material properties of the bow wire (such as elastic modulus) and cross section properties (such as the distance of inertia).Orthodontists can change the stiffness of the whole or local orthodontic appliance by selecting different materials of the arch wire, different cross section sizes, and designing different span of the arch wire and the configuration of the bend, to achieve accurate control of the orthodontic force[ 11 – 13 ]. To achieve good control of maxillary anterior teeth torque angle during the correction process, we proposed a new type of torque auxiliary bow device: self-made four-curvature auxiliary arch, which is used in the early stage of treatment (Patent No: ZL 201420113873.9)[ 14 ]. The application of this device improves the control of the maxillary anterior teeth root movement. This study aimed to establish a three-dimensional (3D) finite element model of the four-curvature to explore its effect on the torque of the maxillary anterior teeth under different stabilization conditions, and to provide a reference for further research. Previously, finite element analysis was already applied to oral medicine. This approach is associated with high precision, and thus adapt to different types of complex structures with different properties. The finite element method uses its calculated support conditions and mechanical loading mode to simulate complex mouth-jaw motion system with simple problems, and the model has repeatability[ 15 ]. This model is suitable for use in oral biomechanics research. Finite element analysis involves quantitative evaluation and intuitive and correct image expression and analysis, allowing to evaluate orthodontic force involved in initial tooth displacement, associated size and direction of teeth, tooth root and periodontal membrane characteristics, as well as alveolar bone properties under stress and strain, and periodontal membrane hydrostatic pressure values. It allows to analyze tooth movement trends and to assess the risk of periodontal membrane necrosis and root resorption[ 15 , 16 ]. From a biological point of view, the optimal orthodontic displacement value should be large enough to stimulate cell activity without blocking the blood vessels in the periodontal membrane. Heavy force can lead to the necrosis of the cells in the periodontal membrane, and the alveolar bone adjacent to the teeth may be absorbed, while light force may help prevent these outcomes. The objective of orthodontic treatment is to use direct bone resorption to generate tooth movement, although local periodontal membrane necrosis and latent resorption are unavoidable. Displacement values of the incisor were extracted from the incisor end of the crown, neck of the labial lateral incisor, neck of the palatal lateral incisor, and root tip of the palatal lateral incisor. Materials And Methods Four-curvature materials and methods A self-made four-curvature auxiliary arch which were made of stainless-steel wire with a diameter of 0.457 mm (0.018 inches). First, four-curved arms are bending, and the four-curves inclined from the distal to proximal side and reached the midpoint of the labial face and neck of the teeth. When in use, the formed base of the auxiliary bow was bent in the circumferential direction pointing to the curving process at approximately 150º(Fig. 1 -a- 1 、2). The four spatulate curving processes inclined to the palatal side and pressed at approximately 30º༈Fig. 1 -a- 1 、3༉. Two hooks were respectively bent in the distal position of the two sides of the maxillary canine and hung on the main arch wire for auxiliary arch retention༈Fig. 1 -b-4༉. When the auxiliary arch is placed on the dentition, from the maxillary central incisors through the lateral incisors and maxillary canine ༈Fig. 1 -b-4),the torque auxiliary arch was gradually placed on the teeth, and the hook was attached to the main arch wire from the inside out. There was a total of four long arch-shaped processes exerting forces. The auxiliary arch was placed upward on the arcuate wire from the bottom of the anterior denture groove. The four long arch-shaped processes reached the position of the tooth neck from far to near and close to the center of impedance (Fig. 1 -c, d). The finite element Sample Collecting A 19-year-old female volunteer without dental caries no periodontal disease, or no systemic diseases, no crowding, no spacing, normal inclination and anterior overbite, and class I molar relationship was selected for this study. She provided written informed consent to participate. Using a German astrologer's Eos Comfort multifaceted spiral CT scanner, Scanning time: 14 seconds. Single tooth images: 210. The scan ranged from the lower orbital margin to the chin. After the scanning, a total of 733 CT images were obtained, and the CT scan data were output in DICOM format. Three -dimensional geometric model A cone beam computerized tomography (CBCT) examination was performed to obtain the maxilla geometry parameters and get the complete model. The DICOM (digital imaging and communication in medicine) data of the patient’s teeth and alveolar bone were obtained, and the crosssections were converted into a three-dimensional mathematical model using MIMICS 19.0 (Materialise, Leuven, Belgium), exported to Geomagic Studio (Geomagic Company, NC, USA), and modified by Solidworks and 3-matic research. The 3D geometric parameters of the maxilla, including the cortical and cancellous bones, teeth and periodontal membrane characteristics were obtained. The bracket (0.022inch MBT system bracket ceramic bracket and buccal tube), micro-implant (2 ORMCO vectors TAS with an intra-bone length of 8 mm), stainless steel wire (0.483 mm*0.635 mm), and orthodontic wire (stainless steel wire with the diameter of 0.25 mm) were designed by SolidWorks® 12.0 (SolidWorks Corporation, Velizy-Villacoublay, France). Finally, a smooth geometric model is generated. The finite element analysis model and model grouping The micro-implants were placed on the buccal side between the second premolars and first molars on both sides of the maxilla, 5 mm from the alveolar crest. The 3D geometry parameters of the maxilla, including those of the cortical and cancellous bones, teeth, periodontal membrane, bracket, micro-implants, stainless steel wire, and back-binding wire were imported to the finite element software ANSYS 19.0(Swanson Analysis System Co, Houston, TX, USA) to biomechanical analysis and then meshed. Geometric model data were imported into the finite element analysis software for finite element calculation; the proposed model was meshed with 4-noded tetrahedral like elements. Material properties were set as follows: the mandible was set as heterogeneous and anisotropic linear elastic material, and the periodontal membrane was set as heterogeneous and anisotropic nonlinear elastic material. Teeth, brackets, arch wires, back-binding wire, and traction hooks were set as continuous, homogeneous, and isotropic linear elastic materials (Fig. 2 ). The elastic modulus and Poisson's ratio of different materials are shown in Table 1[ 17 – 19 ], details on the FEM model can be found in previous references. The skull of individual patients with normal occlusion was scanned by CBCT, and the data were imported into Mimics software for 3D reconstruction of jaw. The reverse engineering software Geomagic was used to remove noise and trim edge morphology, and a single jaw bone solid and smooth solid model of teeth was generated after automatic surface optimization. CAD software was used to bracket, arch wire, four-curve auxiliary arch and micro-implant, and the solid model was combined in SolidWorks software to obtain the geometric model of maxilla-group teeth-bracket-arch wire-micro-implant-four-curve auxiliary arch system, the Gaussian curvature is calculated in the model, make the points as even as possible. In ANSYS software, the solid model was meshed, material attributes were set, contact relations were set, and the load was calculated. To simulate intraoral conditions, the model was attached between the tooth root and periodontal membrane, periodontal membrane and alveolar bone, tooth and bracket, and micro-implant and maxillary. The orthodontic wire and bracket, and four-curvature auxiliary arch and tooth were set as contact connections, with the friction coefficient of 0.3. Frictionless connection was set between the teeth. Four types of models were established based on the states without and with an extraction gap, including molar ligation, micro-implant ligation, no-implant in maxillary central incisor adduction group, and micro-implant in maxillary central incisor adduction models (Fig. 3 ); Different torque force values (0.5 N, 1 N, 1.5 N, 2 N) were applied to the cervical of the incisors buccal side. The total number of elements and nodes are listed in Table 2. The calculation results indicate the direction of the symmetry axis whereby the X-axis is horizontal and transverse is positive. The Y-axis is sagittal and forward is positive. The Z-axis is vertical and the up axis is positive. The origin of the three-dimensional coordinate system is set as the mesial contact point of the central incisor. The bottom of alveolar bone was taken as the fixed constraint surface, and the displacement and rotation in the X, Y and Z directions were constrained in Table 3. Self-made four-curvature application to clinical cases All clinical procedures were approved by the Ethical Committee of Army Medical University and performed in accordance with the applicable guidelines. On July 8, 2015, a 24-year-old female was transferred to the stomatology department of the Military Medical Center requiring a correction to the incisor protrusion. The patient had received orthodontic treatment (8 premolars were extracted) in a local dental clinic 1 year before and treatment fails, the failure of anterior root control resulted in the incisors lingual inclination. CBCT showed that the anterior tooth root was already outside the alveolar bone, resulting in bone fenestration. With the use of teeth will lead to functions failure and all the incisors loose or fall out. (Fig. 4-a). The self-made four-curvature was used to rotate the maxillary incisors, and the torque correction effect of the incisors was obvious. The use of the four-curvature auxiliary arch not only improved the torque of the front teeth, but also reduced the risk of root exposure to soft tissue, which effectively improved the soft tissue profile. After the correction of the four-curvature auxiliary arch, the root of the maxillary incisors entered the central position of the maxilla from the outside of the bone cortex, as to avoid the occurrence of maxillary fenestrations and bone fractures, so that cortical bones do not appear cracks continuous. And the four-curvature auxiliary arch did not cause the absorption of the anterior tooth root, therefore, there is no need to worry about the risk of root resorption in clinical application, so it can be safely used in orthodontic treatment and improve the torque of the incisors. (Fig. 4-b) Results Stress value of periodontal membrane As for incisor, the maximum stress value of the periodontal membrane occured in the cervical of the buccal side, and the stress value in the apical part far less than 2.6 × 10-2MPa [ 20 ]in the all groups. Otherwise, with increase of torque force value, the stress value of the periodontal membrane increased. The periodontal membrane stress value in the cervical of the incisors buccal side in group 1a, 1b, 2a, 2b, 3a, 3b, 3c, 4a and 4b below 2.6 × 10-2MPa, and the tooth movement was relatively safe (Fig. 5 ). As for molar, the molar was not subjected to force loading in the ligation group. When the adduction traction was 1.15N and the self-made four-curvature auxiliary arch was loaded with different torque forces, the periodontal membrane stress value of the first molar did not exceed 2.6 × 10-2MPa(Fig. 5 – 7 ). Displacement of the maxillary central incisor In the molar ligation group and micro-implant ligation group (Fig. 5 – 6 ), the crown of the upper incisors were almost no moves towards the lips while the root of the tooth moves towards the palate under the torque force. With the torque force value increased, displacement value of the cut end, root end and the difference of cut end to the root tip increased. The use of micro-implants increases the torque angle of the crown and reduces the displacement difference between the cut end and the root tip. As shown in Fig. 4– 6 , slight tendency of movement in non-implant in maxillary anterior teeth adduction group (2 groups). With the loading of the force value of the four-curvature auxiliary arch, the molar displacement is basically the same, so the torque force exerted by the four-curvature will not affect the movement trend of the remaining teeth. The results of clinical After the treatment of the four-curve auxiliary arch, the root of the anterior teeth had completely into the maxillary alveolar bone, the cortical bone to rupture and leaving the root without a foothold phenomenon disappeared, the anterior teeth did not have excessive lip lateral tilt, and the whole Upper and lower dentition had good occlusion. No root resorption occurred during the whole treatment process. Changes to soft and hard tissues before and after treatment were evalated, the treatment resulted in an ideal chin shape and good facial balance (Fig 8,9) Discussion At first, the accuracy of 3D finite element analysis results is affected by some factors, such as the similarity of the built geometric models, the size and number of element grids, material properties, contact relations, setting of load conditions, etc. Errors in any link may cause differences between the calculated results and the real results. Secondly, the three-dimensional finite element analysis method only calculates the instantaneous displacement and the stress and strain of the periodontal membrane under the stress of the teeth. However, the movement of orthodontic teeth requires the continuous loading of the force and the reconstruction of alveolar bone, and Movement of the oral and dental junction system is complex and changeable, and the force of the teeth is not ideal and single. Therefore, the results of the finite element analysis method can provide biomechanical guidance for clinical practice, but it needs to be combined with clinical practice to comprehensively consider, in order to achieve more in-depth and scientific research results. Finally, there are some differences between the finite element and the actual curvature of the oral cavity, which cannot simulate the state of the force. Orthodontic treatment requires various devices, which differ in their modes of action and associated oral biomechanics. The use of the finite element method allows to compare different types of devices and to provide guidance for choosing the most suitable one. Orthodontic treatment involves the use of force, which is applied to the Maxillary and mandibular dentition; therefore, a 3D finite element method model may help clinicians better understand these mechanisms and optimize treatment. The solid model involves brackets and arch wires, which differ from the elements used on conventional models that involve a direct application of a loading force. In addition to this approach is close to approximation of the clinical picture than the previously used models. The force is applied by loading the arch wires and is then transferred to the posterior teeth by the brackets, allowing to observe tooth movement and force characteristics. The finite element method has been used in the field of orthodontic biomechanics. A previous study had reported that the force of 2.6 × 10 -2 MPa is the maximum stress value that may be applied to the periodontal membrane and this limit is safe and effective in orthodontic treatment [21]. Outside of it, periodontal ischemia may occur, leading to irreversible necrosis of the surrounding tissue. In the present study, tooth stress response was represented by different colors; the stress value of the periodontal membrane was represented by a yellow box when it was of <2.6 × 10 -2 MPa and a green box with gradually deepened color [22]. This color-coding supports an intuitive interpretation of the stress response distribution [23, 24]. In this experiment 0.022 bracket was used to place 0.019*0.025 SS wire in the groove, so 0.001 inch has a clearance Angle of 3.77°. The resulting gap Angle changes the torque Angle of the incisor during the stress process (incisal and occlusal） surface cannot be kept stationary), resulting in the incisal and occlusal surface displacement in the opposite direction. Although the incisal and occlusal surface was displaced due to uncontrollable factors in the experiment, the data showed that the displacement of the root was much larger than that of incisor and occlusal surface displacement, so making the root of the incisor enter the central maxilla, The results showed that incisors were not tilted move too much, and the root control effect is obvious. Given no tooth extraction gap and a gradual increase of the torque force, the displacement of the root tip and incisor occlusal end gradually increased. When the molar of the Maxillary was anchored, the moment force exceeded 1 N when the periodontal membrane analysis exceeds the maximum stress value of the periodontal membrane. Therefore, provided the molar is refastened, the torque force value of ≤1 N is safe and effective. When the Maxillary micro-implant was used as absolute anchorage, the periodontal membrane stress value exceeded the desirable range when the self-made four-curvature auxiliary arch force value exceeded 1.5 N. When a tooth extraction gap was not closed, given the gradual increase of the torque force, the displacement of the root tip and incisor occlusal end gradually increased. When a tooth extraction gap was closed, the periodontal membrane stress value exceeded the desirable limit when the torque force exceeded 1 N, suggesting that the values of 1 N exceeded the periodontal membrane stress value, suggesting the force value of 1 N may be safe and effective when the molar is reattached. When the torque force was applied to the maxillary incisors, the stress to the periodontal membrane of each part concentrated at the cervical of the labial side and tongue of the tooth. When the values of the stress to the periodontal membrane exceeded those to the tooth root tip, absorption at the tooth root tip was not caused affected in the use of the four-curvature auxiliary arch. Under different stable anchorage methods, the stress at the cervical of the labial teeth changed. In the remaining cases, the force of <1 N was recommended. The displacement of other teeth and the periodontal membrane stress response were not affected when the four-curvature auxiliary arch force was loaded. With the load of torque force, the periodontal membrane stress at the other teeth did not exceed the maximum periodontal membrane stress2.6 × 10 -2 MPa. [25] . The four-curvature affected the torque force value of the maxillary incisors. In the whole finite element method of maxillary incisors, the tooth cervical is the force center in the process of controlling the torque of the anterior teeth with the self-made four-curvature auxiliary arch. In the first group, the second model, the buccal tube was set to contact the hook while the micro-implant was set to bond, which created conditions comparable to those observed with a hard back. Meanwhile, in the third and fourth groups, the tooth extraction clearance adduction traction value was 1.15 N, resulting in the buccal tube and micro implant adduction traction values of 1.15 N. As the only spring element in finite element analysis in ANSYS software is set expression, the third and fourth group models of adduction tooth extraction traction were displayed as a tension spring. Overall, the 3D finite element simulation model was representative of the phenomena observed in clinical practice [26, 27]. This study aimed to explore the periodontal membrane stress response and tooth displacement changes of the maxillary dentition when the torque force of the maxillary incisors was controlled by the four-curvature auxiliary arch. The secondary aim of this study was to examine changes to the torque force of the incisors using different anchoring methods to provide theoretical basis for clinical practice[28, 29]. The present study involved 16 conditions, with and without tooth extraction space, and with stable resistance in different modes. Torque force was applied to the analysis of tooth displacement and periodontal membrane changes; the present findings provide preliminary insights into the use of the self-made four-curvature auxiliary arch, which may enable the application of the torque force while preventing root absorption and other adverse reactions. The other 3 groups that the four-curvature auxiliary arch torque force may not exceed 1 N when the auxiliary arch is used; when the arch is used with absolute anchorage, the recommended force may not exceed 1.5 N, given no tooth extraction gap. No absorption was observed when the four-curvature auxiliary arch was used for torque control of the incisors root, suggesting that this method is safe and effective, given specific parameters [29, 30]. The case patient initially presented at the stomatology department with anterior tooth tilting laterally to the tongue, missing eight premolars, and incomplete closure of the tooth extraction gap. During treatment, the torque of the incisors teeth laterally inclining to the tongue was significantly improved after the use of miniature implants and the four-curvature auxiliary arch; Accordingly, the impact of the four-curvature auxiliary arch was easily observed. Initially, the root of the incisors was located outside the labial cortex of the maxillary alveolar bone. However, it was adjusted to the center of the maxillary alveolar bone with the use of the four-curvature auxiliary arch. No root resorption occurred during the whole treatment process. The treatment resulted in an ideal chin shape and good facial balance. Changes to soft and hard tissues before and after treatment were evaluated. The micro-implant provided independent absolute anchorage during treatment, which supported the biomechanics of orthodontics. The present report shows that the use of a micro-implant combined with the four-curvature auxiliary arch device may help achieve desirable outcomes in orthodontic treatment, including the correction of poor or excessive torque loss in the upper incisors Conclusion This experiment, the more unit nodes are divided, the closer the property and parameter changes of the material are to the real situation. This modeling method can better simulate the complex oral environment and make the result closer to the real oral environment system. The proposed approach may help improve treatment for excessive torque loss in anterior teeth and avoid improper anterior teeth torque angle can cause cortical bone fracture and root exposure provide theoretical basis for clinical practice provide theoretical basis. Consider the slot dimensions and wire size also effect overall torque expression the change, it's also computed in the model of root displacement, but it didn’t affect the effect of the auxiliary arch auxiliary arch. The disadvantages in this experiment of the esthetic and hygiene maintenance issues, but it's unavoidable to orthodontic fixation treatment. Declarations Compliance with Ethical Standard Ethical approval and consent to participate The patient has signed informed consent confirms volunteered all of information/images subjects for my clinical treatment in stomatology to the Army Specialty Medical Center stomatology department as a research approach and published them in journals all information and images subjects for publication of identifying in an online open-access publication. Consent for publication The patient has signed informed consent confirms volunteered all of information/images subjects for my clinical treatment in stomatology to the Army Specialty Medical Center stomatology department as a research approach and published them in journals all information and images subjects for publication of identifying in an online open-access publication. Data declaration All data generated or analysed during this study are included in this published article [and its supplementary information files]. Funding This work was supported by the Chongqing Natural Science Foundation of China (no.cstc2021jcyj-msxmX0475 & no.cstc2021jcyj-msxmX0466), the Youth Development Project of Army Military Medical University (no. 2018XQN014), the Clinical Innovation Project of Army University (no.2019XLC2014). Competing interests All the authors declare that they have no competing interest. Ethical approval All clinical procedures were approved by the Ethical Committee of Army Medical University and performed in accordance with the applicable guidelines. All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki. Informed consent was obtained from all individual participants included in the study. Informed consent Informed consent was obtained from all individual participants included in the study. Authors' contributions Rui-Liu and Xiu-Jie Wen made equal Corresponding author to this study; Rui-Liu was provided funding support; Xiu-Jie Wen provides an important reference for the rationality of experimental design; Ping-Zhu Yang wrote the manuscript and treated the patient; Ping-Zhu Yang,Li-Yun Bai, and He-xuan Zhang provided advice on possible treatment strategies and gave valuable comments regarding important intellectual content of the manuscript; Wen-Jun Zhao was Language changes have contributed. Yu Liu is a supporter of 3D finite element technology. Acknowledgments The authors thanks of the Participants who were involved in this study. References C C-A, LE A-G, YA R-C, GA R-M, G F-C, HL D-DS, A A-DC: Changes in maxillary incisor inclination and position after traction of unilateral vs bilateral maxillary impacted canines in nonextraction treatment: A cone-beam computed tomography study . 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V M, P H, D KJS: Finite element analysis of slot wall deformation in stainless steel and titanium orthodontic brackets during simulated palatal root torque . American journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics 2018, 153 (4):481-488. SN P, L K, V V-R, T E, C B: Torque differences due to the material variation of the orthodontic appliance: a finite element study . Progress in orthodontics 2017, 18 (1):6. M S, L K, J S, BA J, C B: Forces and moments generated by removable thermoplastic aligners: incisor torque, premolar derotation, and molar distalization . American journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics 2014, 145 (6):728-736. NJ M, AN W, ML J, J M: A stress analysis of the periodontal ligament under various orthodontic loadings . European journal of orthodontics 1991, 13 (3):231-242. Shokrani P, Hashemi A, Shirin MB, Oskui IZ: Effect of Geometric Dimensions and Material Models of the Periodontal Ligament in Orthodontic Tooth Movement . Orthodontics and Craniofacial Research 2020. A B, Y S, F G, L T, V S: New finite element study protocol: Clinical simulation of orthodontic tooth movement . International orthodontics 2017, 15 (2):165-179. HH A, P N, RJ C, VH M, OM M: Three-dimensional modeling and finite element analysis in treatment planning for orthodontic tooth movement . American journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics 2011, 139 (1):e59-71. Tables Table 1 to 3 is available in the Supplementary Files section. Additional Declarations No competing interests reported. Supplementary Files Table1Mechanicalproperties.png Table2.Thenumberofelementsandnodes.png Table3Modelgroup.png Theoriginaldata.docx Cite Share Download PDF Status: Published Journal Publication published 11 Mar, 2023 Read the published version in BMC Oral Health → Version 1 posted Editorial decision: Major revision 09 Nov, 2022 Reviews received at journal 18 Oct, 2022 Reviews received at journal 17 Oct, 2022 Reviewers agreed at journal 11 Oct, 2022 Reviewers agreed at journal 11 Oct, 2022 Reviewers agreed at journal 11 Oct, 2022 Reviewers invited by journal 11 Oct, 2022 Editor assigned by journal 11 Oct, 2022 Editor invited by journal 28 Sep, 2022 Submission checks completed at journal 28 Sep, 2022 First submitted to journal 09 Sep, 2022 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. 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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-2048265","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":140218282,"identity":"14ade182-6678-4766-89ea-f59aecd3d19d","order_by":0,"name":"Pingzhu Yang","email":"","orcid":"","institution":"Army Medical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Pingzhu","middleName":"","lastName":"Yang","suffix":""},{"id":140218283,"identity":"fe528188-fa60-4123-a23d-f02c1559f34b","order_by":1,"name":"Liyun Bai","email":"","orcid":"","institution":"Army Medical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Liyun","middleName":"","lastName":"Bai","suffix":""},{"id":140218284,"identity":"4443b5b9-e6d0-4a1e-86f4-1a219fd366ec","order_by":2,"name":"Hexuan Zhang","email":"","orcid":"","institution":"Army Medical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hexuan","middleName":"","lastName":"Zhang","suffix":""},{"id":140218285,"identity":"e59aa112-b878-4dd8-b40f-9f9788a5fa6c","order_by":3,"name":"Yu Liu","email":"","orcid":"","institution":"ChuangNeng Technology (ChongQing) co. LTD","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yu","middleName":"","lastName":"Liu","suffix":""},{"id":140218286,"identity":"33e7d07d-b63f-4bc8-9aab-bc08cffd0ede","order_by":4,"name":"Wenjun Zhao","email":"","orcid":"","institution":"Army Medical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Wenjun","middleName":"","lastName":"Zhao","suffix":""},{"id":140218287,"identity":"b471e2be-46fc-4509-b086-0d42f41a5501","order_by":5,"name":"Xiujie Wen","email":"","orcid":"","institution":"Southwest Medical University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xiujie","middleName":"","lastName":"Wen","suffix":""},{"id":140218288,"identity":"5427d8ca-0b1d-4eae-a2a9-69006eeab1bd","order_by":6,"name":"Rui Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIie3PIQvCQBTA8TsGZzmWnyjbV9hxIH6cu6JlWiwGkQfCTHaD+DHMJleGeSadgsliMyy4KTa5zWa4P1x48H7cHSE22z+2LY4ipM3KQY3B82sQiooE/E2SrhRYh5CCvAYajfXrXlNuvIhPpzznLgyukK1BUXSyc2ogzWSvUUfFw6DfAb2BYYMwKUMDCdJQoMaS9FhJRhQ5axnJ8SZQ5R+yAo3bKpLygrAPwRqkmYRiqSPJGb86XbUDKWYVf3HjJLg/cs/z5z16eEymnt+YZRcT+ZLz27rNZrPZvvQE3m1GF6OvGYgAAAAASUVORK5CYII=","orcid":"","institution":"Army Medical University","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Rui","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2022-09-09 09:14:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2048265/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2048265/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s12903-023-02833-2","type":"published","date":"2023-03-11T19:31:05+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":27289535,"identity":"251632ac-9e36-4297-98d8-2680435355bf","added_by":"auto","created_at":"2022-10-03 18:50:30","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":962976,"visible":true,"origin":"","legend":"\u003cp\u003eFour-curvature of the process\u003c/p\u003e","description":"","filename":"Fig1Fourcurvatureoftheprocess.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/eb298492f484e2ac0e3d7b5b.png"},{"id":27289536,"identity":"0c3598c1-711f-4d66-b985-377f792fa64f","added_by":"auto","created_at":"2022-10-03 18:50:30","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":285722,"visible":true,"origin":"","legend":"\u003cp\u003eFinite element smooth model\u003c/p\u003e","description":"","filename":"Fig2Finiteelementsmoothmodel.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/47b06fd1fdf01f46ae9553fe.png"},{"id":27288791,"identity":"b031f4aa-0653-4318-bea6-ae956381207b","added_by":"auto","created_at":"2022-10-03 18:40:30","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":187364,"visible":true,"origin":"","legend":"\u003cp\u003eFour kinds of 3D FE models\u003c/p\u003e\n\u003cp\u003ea: molar ligation group\u003c/p\u003e\n\u003cp\u003eb: micro-implant ligation group.\u003c/p\u003e\n\u003cp\u003ec: micro-implant retraction group\u003c/p\u003e\n\u003cp\u003ed: micro-implant ligation group\u003c/p\u003e","description":"","filename":"Fig3Fourkindsof3DFEmodels.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/6d9460b2ef8471d638cce804.png"},{"id":27289417,"identity":"53f27e45-fe69-4f83-be73-47960b7748b2","added_by":"auto","created_at":"2022-10-03 18:45:31","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":599179,"visible":true,"origin":"","legend":"\u003cp\u003eintraoral photographs \u0026amp; CBCT before and during treatment\u003c/p\u003e","description":"","filename":"Fig4intraoralphotographsCBCT.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/e6a7e55002cece42ec313090.png"},{"id":27288798,"identity":"8d5be0d0-e60b-44b8-aac7-a87f36dfdd48","added_by":"auto","created_at":"2022-10-03 18:40:31","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":29406234,"visible":true,"origin":"","legend":"\u003cp\u003eDisplacement distribution\u003c/p\u003e","description":"","filename":"Fig5Displacementdistribution.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/65558ce23f4683b7084475df.png"},{"id":27289420,"identity":"5b279313-3e89-4282-9b48-41910d970e81","added_by":"auto","created_at":"2022-10-03 18:45:31","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":26646361,"visible":true,"origin":"","legend":"\u003cp\u003eperiodontal membrane\u003c/p\u003e","description":"","filename":"Fig6periodontalmembrane.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/5ca6d4d86d68e43f0dda6dc9.png"},{"id":27289419,"identity":"93f93b02-b279-4907-97eb-d855e985ae1b","added_by":"auto","created_at":"2022-10-03 18:45:31","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":108702,"visible":true,"origin":"","legend":"\u003cp\u003eContrast incisor diagram\u003c/p\u003e\n\u003cp\u003ea Contrast incisor end displacement;\u003c/p\u003e\n\u003cp\u003eb Contrast incisor root tip;\u003c/p\u003e\n\u003cp\u003ec Contrast incisor occlusal end tip;\u003c/p\u003e\n\u003cp\u003ed Contrast incisor stress value of periodontal membrane (max);\u003c/p\u003e\n\u003cp\u003ee Contrast incisor stress value of periodontal membrane (mix).\u003c/p\u003e\n\u003cp\u003e(1 molar ligation group ； 2 micro-implant ligation group ; 3 molar retraction group ；4 micro-implant retraction group ；)\u003c/p\u003e","description":"","filename":"Fig7Contrastincisor.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/a4d53d2fdc1610e1436cb54f.png"},{"id":27288796,"identity":"72025a1e-c5ba-4281-aa6c-700bb2f63efc","added_by":"auto","created_at":"2022-10-03 18:40:31","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":407136,"visible":true,"origin":"","legend":"\u003cp\u003eintraoral photographs \u0026amp; CBCT Treatment of complete\u003c/p\u003e","description":"","filename":"Fig8intraoralphotographsCBCT.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/13a12d72466990a9aa29d5ff.png"},{"id":27288794,"identity":"098c4151-9878-4684-9025-012fb0a75762","added_by":"auto","created_at":"2022-10-03 18:40:31","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":373652,"visible":true,"origin":"","legend":"\u003cp\u003eCBCT show tooth root torque change \u0026amp; Root length \u0026amp; Lateral photographs\u003c/p\u003e","description":"","filename":"Fig9CBCTshowtoothroottorque.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/6de30c8095070fb10393b979.png"},{"id":44721848,"identity":"7f83ddd3-7f4a-4c36-98cc-053f5fb5ad4f","added_by":"auto","created_at":"2023-10-16 19:40:13","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6806275,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/396ce159-d6d9-47b8-8144-320258518862.pdf"},{"id":27288787,"identity":"db1bff01-352a-49d8-871e-aa991ce3b698","added_by":"auto","created_at":"2022-10-03 18:40:30","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":52023,"visible":true,"origin":"","legend":"","description":"","filename":"Table1Mechanicalproperties.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/7ca71a93b1f98870bbff49f2.png"},{"id":27289589,"identity":"ca207468-04bf-4d7a-8c54-d0261fbd1a9a","added_by":"auto","created_at":"2022-10-03 18:55:30","extension":"png","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":41227,"visible":true,"origin":"","legend":"","description":"","filename":"Table2.Thenumberofelementsandnodes.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/10be9691d3b763f30f67247f.png"},{"id":27289414,"identity":"04a83aba-6292-4627-9ed5-cc296ea4704b","added_by":"auto","created_at":"2022-10-03 18:45:30","extension":"png","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":46137,"visible":true,"origin":"","legend":"","description":"","filename":"Table3Modelgroup.png","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/cef2b305674437d773d266de.png"},{"id":27288799,"identity":"892cb206-5366-43e5-8972-6ee2bcc63411","added_by":"auto","created_at":"2022-10-03 18:40:31","extension":"docx","order_by":4,"title":"","display":"","copyAsset":false,"role":"supplement","size":13910938,"visible":true,"origin":"","legend":"","description":"","filename":"Theoriginaldata.docx","url":"https://assets-eu.researchsquare.com/files/rs-2048265/v1/6b9734881de3bc72831d2297.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Efficacy of a four-curve auxiliary arch at preventing maxillary central incisor linguoclination during orthodontic treatment: A finite element analysis","fulltext":[{"header":"Introduction","content":"\u003cp\u003eGood torque control of the incisors helps to improve the corrective effect in orthodontic cases by affecting aesthetic outcomes and occlusal relationship stability, which is also one of the important indicators to evaluate the end of orthodontic treatment. For example, when the maxillary incisors stand upright or a tongue tilt occurs ,the root of the anterior teeth can pierce the last line of defense of the alveolar bone, eventually causing the cortical bone to rupture and leaving the root without a foothold[\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Meanwhile, a good inclination angle of the anterior teeth can help maintain the stability of dentition occlusion. Therefore, the torque of the incisors is one of a key factor determine in orthodontic treatment outcomes [\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Experimental studies of the movement of teeth during orthodontic treatment is based on the ability of the alveolar bone and periodontal ligament to respond to mechanical stimuli, which generate force during a loading process, the strain action causes tooth movement[\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. And orthodontic process had found that the combined action of multiple orthodontic forces can cause abnormal torque movement of the teeth. If a large periodontal stress is generated at the root apex of the teeth, tooth root absorption may occur, which is an undesirable histological reaction [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eStiffness refers to the amount of stress produced by unit strain variable, which is the rate of load deformation. In the study of orthodontic mechanics, there are many ways to describe the properties of arch wire. In terms of stiffness, there are three levels of concepts: material stiffness, arch wire stiffness and appliance stiffness. Arch wire stiffness refers to the inherent rigidity determined by the material, the shape of the cross section and the area of the cross section. It has nothing to do with the length or configuration design of the arch wire. It represents the bending rigidity of the arch wire, and its size depends on the material properties of the bow wire (such as elastic modulus) and cross section properties (such as the distance of inertia).Orthodontists can change the stiffness of the whole or local orthodontic appliance by selecting different materials of the arch wire, different cross section sizes, and designing different span of the arch wire and the configuration of the bend, to achieve accurate control of the orthodontic force[\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. To achieve good control of maxillary anterior teeth torque angle during the correction process, we proposed a new type of torque auxiliary bow device: self-made four-curvature auxiliary arch, which is used in the early stage of treatment (Patent No: ZL 201420113873.9)[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The application of this device improves the control of the maxillary anterior teeth root movement. This study aimed to establish a three-dimensional (3D) finite element model of the four-curvature to explore its effect on the torque of the maxillary anterior teeth under different stabilization conditions, and to provide a reference for further research.\u003c/p\u003e \u003cp\u003ePreviously, finite element analysis was already applied to oral medicine. This approach is associated with high precision, and thus adapt to different types of complex structures with different properties. The finite element method uses its calculated support conditions and mechanical loading mode to simulate complex mouth-jaw motion system with simple problems, and the model has repeatability[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. This model is suitable for use in oral biomechanics research. Finite element analysis involves quantitative evaluation and intuitive and correct image expression and analysis, allowing to evaluate orthodontic force involved in initial tooth displacement, associated size and direction of teeth, tooth root and periodontal membrane characteristics, as well as alveolar bone properties under stress and strain, and periodontal membrane hydrostatic pressure values. It allows to analyze tooth movement trends and to assess the risk of periodontal membrane necrosis and root resorption[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFrom a biological point of view, the optimal orthodontic displacement value should be large enough to stimulate cell activity without blocking the blood vessels in the periodontal membrane. Heavy force can lead to the necrosis of the cells in the periodontal membrane, and the alveolar bone adjacent to the teeth may be absorbed, while light force may help prevent these outcomes. The objective of orthodontic treatment is to use direct bone resorption to generate tooth movement, although local periodontal membrane necrosis and latent resorption are unavoidable. Displacement values of the incisor were extracted from the incisor end of the crown, neck of the labial lateral incisor, neck of the palatal lateral incisor, and root tip of the palatal lateral incisor.\u003c/p\u003e"},{"header":"Materials And Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e\u003cspan type=\"BoldItalic\" class=\"BoldItalic\" name=\"Emphasis\"\u003eFour-curvature materials and methods\u003c/span\u003e\u003c/h2\u003e \u003cp\u003eA self-made four-curvature auxiliary arch which were made of stainless-steel wire with a diameter of 0.457 mm (0.018 inches). First, four-curved arms are bending, and the four-curves inclined from the distal to proximal side and reached the midpoint of the labial face and neck of the teeth. When in use, the formed base of the auxiliary bow was bent in the circumferential direction pointing to the curving process at approximately 150\u0026ordm;(Fig.\u0026nbsp;\u0026lt;link rid=\"fig1\"\u0026gt;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u0026lt;/link\u0026gt;\u003c/span\u003e-a-\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e、2). The four spatulate curving processes inclined to the palatal side and pressed at approximately 30\u0026ordm;༈Fig.\u0026nbsp;\u0026lt;link rid=\"fig1\"\u0026gt;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u0026lt;/link\u0026gt;\u003c/span\u003e-a-\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e、3༉. Two hooks were respectively bent in the distal position of the two sides of the maxillary canine and hung on the main arch wire for auxiliary arch retention༈Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e-b-4༉. When the auxiliary arch is placed on the dentition, from the maxillary central incisors through the lateral incisors and maxillary canine ༈Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e-b-4),the torque auxiliary arch was gradually placed on the teeth, and the hook was attached to the main arch wire from the inside out. There was a total of four long arch-shaped processes exerting forces. The auxiliary arch was placed upward on the arcuate wire from the bottom of the anterior denture groove. The four long arch-shaped processes reached the position of the tooth neck from far to near and close to the center of impedance (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e-c, d).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eThe finite element Sample Collecting\u003c/h2\u003e \u003cp\u003eA 19-year-old female volunteer without dental caries no periodontal disease, or no systemic diseases, no crowding, no spacing, normal inclination and anterior overbite, and class I molar relationship was selected for this study. She provided written informed consent to participate. Using a German astrologer's Eos Comfort multifaceted spiral CT scanner, Scanning time: 14 seconds. Single tooth images: 210. The scan ranged from the lower orbital margin to the chin. After the scanning, a total of 733 CT images were obtained, and the CT scan data were output in DICOM format.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eThree -dimensional geometric model\u003c/h2\u003e \u003cp\u003eA cone beam computerized tomography (CBCT) examination was performed to obtain the maxilla geometry parameters and get the complete model. The DICOM (digital imaging and communication in medicine) data of the patient\u0026rsquo;s teeth and alveolar bone were obtained, and the crosssections were converted into a three-dimensional mathematical model using MIMICS 19.0 (Materialise, Leuven, Belgium), exported to Geomagic Studio (Geomagic Company, NC, USA), and modified by Solidworks and 3-matic research. The 3D geometric parameters of the maxilla, including the cortical and cancellous bones, teeth and periodontal membrane characteristics were obtained. The bracket (0.022inch MBT system bracket ceramic bracket and buccal tube), micro-implant (2 ORMCO vectors TAS with an intra-bone length of 8 mm), stainless steel wire (0.483 mm*0.635 mm), and orthodontic wire (stainless steel wire with the diameter of 0.25 mm) were designed by SolidWorks\u0026reg; 12.0 (SolidWorks Corporation, Velizy-Villacoublay, France). Finally, a smooth geometric model is generated.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eThe finite element analysis model and model grouping\u003c/h2\u003e \u003cp\u003eThe micro-implants were placed on the buccal side between the second premolars and first molars on both sides of the maxilla, 5 mm from the alveolar crest. The 3D geometry parameters of the maxilla, including those of the cortical and cancellous bones, teeth, periodontal membrane, bracket, micro-implants, stainless steel wire, and back-binding wire were imported to the finite element software ANSYS 19.0(Swanson Analysis System Co, Houston, TX, USA) to biomechanical analysis and then meshed. Geometric model data were imported into the finite element analysis software for finite element calculation; the proposed model was meshed with 4-noded tetrahedral like elements. Material properties were set as follows: the mandible was set as heterogeneous and anisotropic linear elastic material, and the periodontal membrane was set as heterogeneous and anisotropic nonlinear elastic material. Teeth, brackets, arch wires, back-binding wire, and traction hooks were set as continuous, homogeneous, and isotropic linear elastic materials (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The elastic modulus and Poisson's ratio of different materials are shown in Table\u0026nbsp;1[\u003cspan additionalcitationids=\"CR18\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], details on the FEM model can be found in previous references.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe skull of individual patients with normal occlusion was scanned by CBCT, and the data were imported into Mimics software for 3D reconstruction of jaw. The reverse engineering software Geomagic was used to remove noise and trim edge morphology, and a single jaw bone solid and smooth solid model of teeth was generated after automatic surface optimization. CAD software was used to bracket, arch wire, four-curve auxiliary arch and micro-implant, and the solid model was combined in SolidWorks software to obtain the geometric model of maxilla-group teeth-bracket-arch wire-micro-implant-four-curve auxiliary arch system, the Gaussian curvature is calculated in the model, make the points as even as possible. In ANSYS software, the solid model was meshed, material attributes were set, contact relations were set, and the load was calculated.\u003c/p\u003e \u003cp\u003eTo simulate intraoral conditions, the model was attached between the tooth root and periodontal membrane, periodontal membrane and alveolar bone, tooth and bracket, and micro-implant and maxillary. The orthodontic wire and bracket, and four-curvature auxiliary arch and tooth were set as contact connections, with the friction coefficient of 0.3. Frictionless connection was set between the teeth. Four types of models were established based on the states without and with an extraction gap, including molar ligation, micro-implant ligation, no-implant in maxillary central incisor adduction group, and micro-implant in maxillary central incisor adduction models (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e); Different torque force values (0.5 N, 1 N, 1.5 N, 2 N) were applied to the cervical of the incisors buccal side. The total number of elements and nodes are listed in Table\u0026nbsp;2. The calculation results indicate the direction of the symmetry axis whereby the X-axis is horizontal and transverse is positive. The Y-axis is sagittal and forward is positive. The Z-axis is vertical and the up axis is positive. The origin of the three-dimensional coordinate system is set as the mesial contact point of the central incisor. The bottom of alveolar bone was taken as the fixed constraint surface, and the displacement and rotation in the X, Y and Z directions were constrained in Table\u0026nbsp;3.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eSelf-made four-curvature application to clinical cases\u003c/h2\u003e \u003cp\u003eAll clinical procedures were approved by the Ethical Committee of Army Medical University and performed in accordance with the applicable guidelines. On July 8, 2015, a 24-year-old female was transferred to the stomatology department of the Military Medical Center requiring a correction to the incisor protrusion. The patient had received orthodontic treatment (8 premolars were extracted) in a local dental clinic 1 year before and treatment fails, the failure of anterior root control resulted in the incisors lingual inclination. CBCT showed that the anterior tooth root was already outside the alveolar bone, resulting in bone fenestration. With the use of teeth will lead to functions failure and all the incisors loose or fall out. (Fig.\u0026nbsp;4-a). The self-made four-curvature was used to rotate the maxillary incisors, and the torque correction effect of the incisors was obvious. The use of the four-curvature auxiliary arch not only improved the torque of the front teeth, but also reduced the risk of root exposure to soft tissue, which effectively improved the soft tissue profile. After the correction of the four-curvature auxiliary arch, the root of the maxillary incisors entered the central position of the maxilla from the outside of the bone cortex, as to avoid the occurrence of maxillary fenestrations and bone fractures, so that cortical bones do not appear cracks continuous. And the four-curvature auxiliary arch did not cause the absorption of the anterior tooth root, therefore, there is no need to worry about the risk of root resorption in clinical application, so it can be safely used in orthodontic treatment and improve the torque of the incisors. (Fig.\u0026nbsp;4-b)\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eStress value of periodontal membrane\u003c/h2\u003e \u003cp\u003eAs for incisor, the maximum stress value of the periodontal membrane occured in the cervical of the buccal side, and the stress value in the apical part far less than 2.6 \u0026times; 10-2MPa [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]in the all groups. Otherwise, with increase of torque force value, the stress value of the periodontal membrane increased. The periodontal membrane stress value in the cervical of the incisors buccal side in group 1a, 1b, 2a, 2b, 3a, 3b, 3c, 4a and 4b below 2.6 \u0026times; 10-2MPa, and the tooth movement was relatively safe (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs for molar, the molar was not subjected to force loading in the ligation group. When the adduction traction was 1.15N and the self-made four-curvature auxiliary arch was loaded with different torque forces, the periodontal membrane stress value of the first molar did not exceed 2.6 \u0026times; 10-2MPa(Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e7\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eDisplacement of the maxillary central incisor\u003c/h2\u003e \u003cp\u003eIn the molar ligation group and micro-implant ligation group (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), the crown of the upper incisors were almost no moves towards the lips while the root of the tooth moves towards the palate under the torque force. With the torque force value increased, displacement value of the cut end, root end and the difference of cut end to the root tip increased. The use of micro-implants increases the torque angle of the crown and reduces the displacement difference between the cut end and the root tip.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;4\u0026ndash;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, slight tendency of movement in non-implant in maxillary anterior teeth adduction group (2 groups). With the loading of the force value of the four-curvature auxiliary arch, the molar displacement is basically the same, so the torque force exerted by the four-curvature will not affect the movement trend of the remaining teeth.\u003c/p\u003e \u003c/div\u003e \u003cp\u003e\u003cstrong\u003eThe results of clinical\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAfter the treatment of the four-curve auxiliary arch, the root of the anterior teeth had completely into the maxillary alveolar bone, the cortical bone to rupture and leaving the root without a foothold phenomenon disappeared, the anterior teeth did not have excessive lip lateral tilt, and the whole Upper and lower dentition had good occlusion. No root resorption occurred during the whole treatment process. Changes to soft and hard tissues before and after treatment were evalated, the treatment resulted in an ideal chin shape and good facial balance (Fig 8,9)\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eAt first, the accuracy of 3D finite element analysis results is affected by some factors, such as the similarity of the built geometric models, the size and number of element grids, material properties, contact relations, setting of load conditions, etc. Errors in any link may cause differences between the calculated results and the real results. Secondly, the three-dimensional finite element analysis method only calculates the instantaneous displacement and the stress and strain of the periodontal membrane under the stress of the teeth. However, the movement of orthodontic teeth requires the continuous loading of the force and the reconstruction of alveolar bone, and Movement of the oral and dental junction system is complex and changeable, and the force of the teeth is not ideal and single. Therefore, the results of the finite element analysis method can provide biomechanical guidance for clinical practice, but it needs to be combined with clinical practice to comprehensively consider, in order to achieve more in-depth and scientific research results. Finally, there are some differences between the finite element and the actual curvature of the oral cavity, which cannot simulate the state of the force. \u003c/p\u003e\n\u003cp\u003eOrthodontic treatment requires various devices, which differ in their modes of action and associated oral biomechanics. The use of the finite element method allows to compare different types of devices and to provide guidance for choosing the most suitable one. Orthodontic treatment involves the use of force, which is applied to the Maxillary and mandibular dentition; therefore, a 3D finite element method model may help clinicians better understand these mechanisms and optimize treatment. The solid model involves brackets and arch wires, which differ from the elements used on conventional models that involve a direct application of a loading force. In addition to this approach is close to approximation of the clinical picture than the previously used models. The force is applied by loading the arch wires and is then transferred to the posterior teeth by the brackets, allowing to observe tooth movement and force characteristics. The finite element method has been used in the field of orthodontic biomechanics.\u003c/p\u003e\n\u003cp\u003eA previous study had reported that the force of 2.6 \u0026times; 10\u003csup\u003e-2 \u003c/sup\u003eMPa is the maximum stress value that may be applied to the periodontal membrane and this limit is safe and effective in orthodontic treatment [21]. Outside of it, periodontal ischemia may occur, leading to irreversible necrosis of the surrounding tissue.\u003c/p\u003e\n\u003cp\u003eIn the present study, tooth stress response was represented by different colors; the stress value of the periodontal membrane was represented by a yellow box when it was of \u0026lt;2.6 \u0026times; 10\u003csup\u003e-2 \u003c/sup\u003eMPa and a green box with gradually deepened color [22]. This color-coding supports an intuitive interpretation of the stress response distribution [23, 24]. \u003c/p\u003e\n\u003cp\u003eIn this experiment 0.022 bracket was used to place 0.019*0.025 SS wire in the groove, so 0.001 inch has a clearance Angle of 3.77\u0026deg;. The resulting gap Angle changes the torque Angle of the incisor during the stress process (incisal and occlusal） surface cannot be kept stationary), resulting in the incisal and occlusal surface displacement in the opposite direction. Although the incisal and occlusal surface was displaced due to uncontrollable factors in the experiment, the data showed that the displacement of the root was much larger than that of incisor and occlusal surface displacement, so making the root of the incisor enter the central maxilla, The results showed that incisors were not tilted move too much, and the root control effect is obvious.\u003c/p\u003e\n\u003cp\u003eGiven no tooth extraction gap and a gradual increase of the torque force, the displacement of the root tip and incisor occlusal end gradually increased. When the molar of the Maxillary was anchored, the moment force exceeded 1 N when the periodontal membrane analysis exceeds the maximum stress value of the periodontal membrane. Therefore, provided the molar is refastened, the torque force value of \u0026le;1 N is safe and effective. When the Maxillary micro-implant was used as absolute anchorage, the periodontal membrane stress value exceeded the desirable range when the self-made four-curvature auxiliary arch force value exceeded 1.5 N.\u003c/p\u003e\n\u003cp\u003eWhen a tooth extraction gap was not closed, given the gradual increase of the torque force, the displacement of the root tip and incisor occlusal end gradually increased. When a tooth extraction gap was closed, the periodontal membrane stress value exceeded the desirable limit when the torque force exceeded 1 N, suggesting that the values of \u0026lt;1 N may be safe and effective in this context. When the micro-implant ligation, the moment force value of \u0026gt;1 N exceeded the periodontal membrane stress value, suggesting the force value of 1 N may be safe and effective when the molar is reattached.\u003c/p\u003e\n\u003cp\u003eWhen the torque force was applied to the maxillary incisors, the stress to the periodontal membrane of each part concentrated at the cervical of the labial side and tongue of the tooth. When the values of the stress to the periodontal membrane exceeded those to the tooth root tip, absorption at the tooth root tip was not caused affected in the use of the four-curvature auxiliary arch. Under different stable anchorage methods, the stress at the cervical of the labial teeth changed. In the remaining cases, the force of \u0026lt;1 N was recommended. The displacement of other teeth and the periodontal membrane stress response were not affected when the four-curvature auxiliary arch force was loaded. With the load of torque force, the periodontal membrane stress at the other teeth did not exceed the maximum periodontal membrane stress2.6 \u0026times; 10\u003csup\u003e-2 \u003c/sup\u003eMPa. [25] .\u003c/p\u003e\n\u003cp\u003eThe four-curvature affected the torque force value of the maxillary incisors. In the whole finite element method of maxillary incisors, the tooth cervical is the force center in the process of controlling the torque of the anterior teeth with the self-made four-curvature auxiliary arch. In the first group, the second model, the buccal tube was set to contact the hook while the micro-implant was set to bond, which created conditions comparable to those observed with a hard back. Meanwhile, in the third and fourth groups, the tooth extraction clearance adduction traction value was 1.15 N, resulting in the buccal tube and micro implant adduction traction values of 1.15 N. As the only spring element in finite element analysis in ANSYS software is set expression, the third and fourth group models of adduction tooth extraction traction were displayed as a tension spring. Overall, the 3D finite element simulation model was representative of the phenomena observed in clinical practice [26, 27].\u003c/p\u003e\n\u003cp\u003eThis study aimed to explore the periodontal membrane stress response and tooth displacement changes of the maxillary dentition when the torque force of the maxillary incisors was controlled by the four-curvature auxiliary arch. The secondary aim of this study was to examine changes to the torque force of the incisors using different anchoring methods to provide theoretical basis for clinical practice[28, 29]. The present study involved 16 conditions, with and without tooth extraction space, and with stable resistance in different modes. Torque force was applied to the analysis of tooth displacement and periodontal membrane changes; the present findings provide preliminary insights into the use of the self-made four-curvature auxiliary arch, which may enable the application of the torque force while preventing root absorption and other adverse reactions. The other 3 groups that the four-curvature auxiliary arch torque force may not exceed 1 N when the auxiliary arch is used; when the arch is used with absolute anchorage, the recommended force may not exceed 1.5 N, given no tooth extraction gap. No absorption was observed when the four-curvature auxiliary arch was used for torque control of the incisors root, suggesting that this method is safe and effective, given specific parameters [29, 30].\u003c/p\u003e\n\u003cp\u003eThe case patient initially presented at the stomatology department with anterior tooth tilting laterally to the tongue, missing eight premolars, and incomplete closure of the tooth extraction gap. During treatment, the torque of the incisors teeth laterally inclining to the tongue was significantly improved after the use of miniature implants and the four-curvature auxiliary arch; Accordingly, the impact of the four-curvature auxiliary arch was easily observed. Initially, the root of the incisors was located outside the labial cortex of the maxillary alveolar bone. However, it was adjusted to the center of the maxillary alveolar bone with the use of the four-curvature auxiliary arch. No root resorption occurred during the whole treatment process. The treatment resulted in an ideal chin shape and good facial balance. Changes to soft and hard tissues before and after treatment were evaluated. The micro-implant provided independent absolute anchorage during treatment, which supported the biomechanics of orthodontics. The present report shows that the use of a micro-implant combined with the four-curvature auxiliary arch device may help achieve desirable outcomes in orthodontic treatment, including the correction of poor or excessive torque loss in the upper incisors\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis experiment, the more unit nodes are divided, the closer the property and parameter changes of the material are to the real situation. This modeling method can better simulate the complex oral environment and make the result closer to the real oral environment system. The proposed approach may help improve treatment for excessive torque loss in anterior teeth and avoid improper anterior teeth torque angle can cause cortical bone fracture and root exposure provide theoretical basis for clinical practice provide theoretical basis. Consider the slot dimensions and wire size also effect overall torque expression the change, it's also computed in the model of root displacement, but it didn\u0026rsquo;t affect the effect of the auxiliary arch auxiliary arch. The disadvantages in this experiment of the esthetic and hygiene maintenance issues, but it's unavoidable to orthodontic fixation treatment.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCompliance with Ethical Standard\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;Ethical approval and consent to participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe patient has signed informed consent confirms volunteered all of information/images subjects for my clinical treatment in stomatology to the Army Specialty Medical Center stomatology department as a research approach and published them in journals all information and images subjects for publication of identifying in an online open-access publication.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe patient has signed informed consent confirms volunteered all of information/images subjects for my clinical treatment in stomatology to the Army Specialty Medical Center stomatology department as a research approach and published them in journals all information and images subjects for publication of identifying in an online open-access publication.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data generated or analysed during this study are included in this published article [and its supplementary information files].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Chongqing Natural Science Foundation of China (no.cstc2021jcyj-msxmX0475 \u0026amp; no.cstc2021jcyj-msxmX0466), the Youth Development Project of Army Military Medical University (no. 2018XQN014), the Clinical Innovation Project of Army University (no.2019XLC2014).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll the authors declare that they have no competing interest.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eEthical approval\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll clinical procedures were approved by the Ethical Committee of Army Medical University and performed in accordance with the applicable guidelines. All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki. Informed consent was obtained from all individual participants included in the study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInformed consent\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eInformed consent was obtained from all individual participants included in the study.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eRui-Liu and Xiu-Jie Wen made equal Corresponding author to this study; Rui-Liu was provided funding support; Xiu-Jie Wen provides an important reference for the rationality of experimental design; Ping-Zhu Yang wrote the manuscript and treated the patient; Ping-Zhu Yang,Li-Yun Bai, and He-xuan Zhang provided advice on possible treatment strategies and gave valuable comments regarding important intellectual content of the manuscript; Wen-Jun Zhao was Language changes have contributed. Yu Liu is a supporter of 3D finite element technology.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors thanks of the Participants who were involved in this study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eC C-A, LE A-G, YA R-C, GA R-M, G F-C, HL D-DS, A A-DC: \u003cstrong\u003eChanges in maxillary incisor inclination and position after traction of unilateral vs bilateral maxillary impacted canines in nonextraction treatment: A cone-beam computed tomography study\u003c/strong\u003e. \u003cem\u003eAmerican journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics \u003c/em\u003e2019, \u003cstrong\u003e156\u003c/strong\u003e(6):767-778.\u003c/li\u003e\n\u003cli\u003eC B, J X, H S, C J, H J, R H: \u003cstrong\u003eFactors affecting treatment duration of labial inversely impacted maxillary central incisors\u003c/strong\u003e. \u003cem\u003eAmerican journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics \u003c/em\u003e2018, \u003cstrong\u003e153\u003c/strong\u003e(5):708-715.\u003c/li\u003e\n\u003cli\u003eJE L, CY J, Y K, YA K, Y K, JB P: \u003cstrong\u003eAnalysis of Alveolar Bone Morphology of the Maxillary Central and Lateral Incisors with Normal Occlusion\u003c/strong\u003e. \u003cem\u003eMedicina (Kaunas, Lithuania) \u003c/em\u003e2019, \u003cstrong\u003e55\u003c/strong\u003e(9).\u003c/li\u003e\n\u003cli\u003eH ZN, M O, MH K, S T: \u003cstrong\u003eEsthetic evaluation of incisor inclination in smiling profiles with respect to mandibular position\u003c/strong\u003e. \u003cem\u003eAmerican journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics \u003c/em\u003e2015, \u003cstrong\u003e148\u003c/strong\u003e(3):387-395.\u003c/li\u003e\n\u003cli\u003eA L, M M, P A, LH G: \u003cstrong\u003eTransverse and torque dental changes after passive self-ligating fixed therapy: A two-year follow-up study\u003c/strong\u003e. \u003cem\u003eAmerican journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics \u003c/em\u003e2019, \u003cstrong\u003e156\u003c/strong\u003e(1):94-103.\u003c/li\u003e\n\u003cli\u003eRen X, Li J, Zhao Y, Li H, Lei L: \u003cstrong\u003eTorque expression by active and passive self-ligating brackets in patients with four premolar extractions: A retrospective study\u003c/strong\u003e. \u003cem\u003eOrthodontics \u0026amp; craniofacial research \u003c/em\u003e2020.\u003c/li\u003e\n\u003cli\u003eCS P, HS Y, JY C, SS M, KJ L: \u003cstrong\u003eEffect of archwire stiffness and friction on maxillary posterior segment displacement during anterior segment retraction: A three-dimensional finite element analysis\u003c/strong\u003e. \u003cem\u003eKorean journal of orthodontics \u003c/em\u003e2019, \u003cstrong\u003e49\u003c/strong\u003e(6):393-403.\u003c/li\u003e\n\u003cli\u003eRH A, MQ M, AM A-T, A I: \u003cstrong\u003eOptimal force magnitude loaded to orthodontic microimplants: A finite element analysis\u003c/strong\u003e. \u003cem\u003eThe Angle orthodontist \u003c/em\u003e2016, \u003cstrong\u003e86\u003c/strong\u003e(2):221-226.\u003c/li\u003e\n\u003cli\u003eB DL, B L, JA L, L C, R M, J H: \u003cstrong\u003eInsertion torque values and success rates for paramedian insertion of orthodontic mini-implants : A retrospective study\u003c/strong\u003e. \u003cem\u003eJournal of orofacial orthopedics = Fortschritte der Kieferorthopadie : Organ/official journal Deutsche Gesellschaft fur Kieferorthopadie \u003c/em\u003e2018, \u003cstrong\u003e79\u003c/strong\u003e(2):109-115.\u003c/li\u003e\n\u003cli\u003eD VP, R TC, L HdS, F AM, FC T, PE GC: \u003cstrong\u003eTorque value accuracy of preadjusted metal brackets for upper and lower incisors\u003c/strong\u003e. \u003cem\u003eMinerva stomatologica \u003c/em\u003e2019, \u003cstrong\u003e68\u003c/strong\u003e(1):31-35.\u003c/li\u003e\n\u003cli\u003eCattaneo PM, Cornelis MA: \u003cstrong\u003eOrthodontic Tooth Movement Studied by Finite Element Analysis: an Update. What Can We Learn from These Simulations?\u003c/strong\u003e \u003cem\u003eCurr Osteoporos Rep \u003c/em\u003e2021, \u003cstrong\u003e19\u003c/strong\u003e(2):175-181.\u003c/li\u003e\n\u003cli\u003eVilela ABF, Soares PBF, Beaini TL, Versluis A, Soares CJ: \u003cstrong\u003eSplint stiffness and extension effects on a simulated avulsed permanent incisor-A patient-specific finite element analysis\u003c/strong\u003e. \u003cem\u003eDent Traumatol \u003c/em\u003e2022, \u003cstrong\u003e38\u003c/strong\u003e(1):53-61.\u003c/li\u003e\n\u003cli\u003eXie Q, Li D: \u003cstrong\u003eThe cross-sectional effects of ribbon arch wires on Class II malocclusion intermaxillary traction: a three-dimensional finite element analysis\u003c/strong\u003e. \u003cem\u003eBMC Oral Health \u003c/em\u003e2021, \u003cstrong\u003e21\u003c/strong\u003e(1):501.\u003c/li\u003e\n\u003cli\u003eRui Liu W-BH, Ping-Zhu Yang, Lin Zhu, Yong-Quan Zhou, Xia Yu, Xiu-Jie Wen: \u003cstrong\u003e\u0026lt;Severe skeletal bimaxillary protrusion treated with micro-implants__and a self-made four-curvature torquing auxiliary_ A case report.pdf\u0026gt;\u003c/strong\u003e. \u003cem\u003eWorld J Clin Cases \u003c/em\u003e2021 January 26, \u003cstrong\u003e9\u003c/strong\u003e(3):722-735.\u003c/li\u003e\n\u003cli\u003eBill Tran DSN, Paul W Major, Jason P Carey, Dan L Romanyk \u003cstrong\u003eThe three-dimensional mechanical response of orthodontic archwires and brackets in vitro during simulated orthodontic torque\u003c/strong\u003e. \u003cem\u003eJ Mech Behav Biomed Mater \u003c/em\u003e2021, \u003cstrong\u003e114\u003c/strong\u003e.\u003c/li\u003e\n\u003cli\u003ePouyafar V, Meshkabadi R, Sadr Haghighi AH, Navid A: \u003cstrong\u003eFinite element simulation and statistical investigation of an orthodontic mini-implant\u0026apos;s stability in a novel screw design\u003c/strong\u003e. \u003cem\u003eProc Inst Mech Eng H \u003c/em\u003e2021, \u003cstrong\u003e235\u003c/strong\u003e(9):1046-1057.\u003c/li\u003e\n\u003cli\u003eVerri FR, Santiago Junior JF, Almeida DA, Verri AC, Batista VE, Lemos CA, Noritomi PY, Pellizzer EP: \u003cstrong\u003eThree-Dimensional Finite Element Analysis of Anterior Single Implant-Supported Prostheses with Different Bone Anchorages\u003c/strong\u003e. \u003cem\u003eScientificWorldJournal \u003c/em\u003e2015, \u003cstrong\u003e2015\u003c/strong\u003e:321528.\u003c/li\u003e\n\u003cli\u003eSarrafpour B, Swain M, Li Q, Zoellner H: \u003cstrong\u003eTooth eruption results from bone remodelling driven by bite forces sensed by soft tissue dental follicles: a finite element analysis\u003c/strong\u003e. \u003cem\u003ePLoS One \u003c/em\u003e2013, \u003cstrong\u003e8\u003c/strong\u003e(3):e58803.\u003c/li\u003e\n\u003cli\u003ePelsue BM, Zinelis S, Bradley TG, Berzins DW, Eliades T, Eliades G: \u003cstrong\u003eStructure, composition, and mechanical properties of Australian orthodontic wires\u003c/strong\u003e. \u003cem\u003eAngle Orthod \u003c/em\u003e2009, \u003cstrong\u003e79\u003c/strong\u003e(1):97-101.\u003c/li\u003e\n\u003cli\u003eCosgarea RAMSMBCGCR: \u003cstrong\u003eCompressive stress in periodontal ligament under orthodontic movements during periodontal breakdown\u003c/strong\u003e. \u003cem\u003eAmerican Journal of Orthodontics and Dentofacial Orthopedics \u003c/em\u003e2021, \u003cstrong\u003e159\u003c/strong\u003e( 3):E291-E299.\u003c/li\u003e\n\u003cli\u003eB Z, H S: \u003cstrong\u003eCoordinating bracket torque and incisor inclination : Part 3: Validity of bracket torque values in achieving norm inclinations\u003c/strong\u003e. \u003cem\u003eJournal of orofacial orthopedics = Fortschritte der Kieferorthopadie : Organ/official journal Deutsche Gesellschaft fur Kieferorthopadie \u003c/em\u003e2018, \u003cstrong\u003e79\u003c/strong\u003e(5):320-327.\u003c/li\u003e\n\u003cli\u003eSN P, I S, L K, R P, S A, T E, C B: \u003cstrong\u003eTorque differences according to tooth morphology and bracket placement: a finite element study\u003c/strong\u003e. \u003cem\u003eEuropean journal of orthodontics \u003c/em\u003e2017, \u003cstrong\u003e39\u003c/strong\u003e(4):411-418.\u003c/li\u003e\n\u003cli\u003eT W, K M, T F, M K, M T, S G: \u003cstrong\u003eInsertion torque and Periotest values are important factors predicting outcome after orthodontic miniscrew placement\u003c/strong\u003e. \u003cem\u003eAmerican journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics \u003c/em\u003e2017, \u003cstrong\u003e152\u003c/strong\u003e(4):483-488.\u003c/li\u003e\n\u003cli\u003eV M, P H, D KJS: \u003cstrong\u003eFinite element analysis of slot wall deformation in stainless steel and titanium orthodontic brackets during simulated palatal root torque\u003c/strong\u003e. \u003cem\u003eAmerican journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics \u003c/em\u003e2018, \u003cstrong\u003e153\u003c/strong\u003e(4):481-488.\u003c/li\u003e\n\u003cli\u003eSN P, L K, V V-R, T E, C B: \u003cstrong\u003eTorque differences due to the material variation of the orthodontic appliance: a finite element study\u003c/strong\u003e. \u003cem\u003eProgress in orthodontics \u003c/em\u003e2017, \u003cstrong\u003e18\u003c/strong\u003e(1):6.\u003c/li\u003e\n\u003cli\u003eM S, L K, J S, BA J, C B: \u003cstrong\u003eForces and moments generated by removable thermoplastic aligners: incisor torque, premolar derotation, and molar distalization\u003c/strong\u003e. \u003cem\u003eAmerican journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics \u003c/em\u003e2014, \u003cstrong\u003e145\u003c/strong\u003e(6):728-736.\u003c/li\u003e\n\u003cli\u003eNJ M, AN W, ML J, J M: \u003cstrong\u003eA stress analysis of the periodontal ligament under various orthodontic loadings\u003c/strong\u003e. \u003cem\u003eEuropean journal of orthodontics \u003c/em\u003e1991, \u003cstrong\u003e13\u003c/strong\u003e(3):231-242.\u003c/li\u003e\n\u003cli\u003eShokrani P, Hashemi A, Shirin MB, Oskui IZ: \u003cstrong\u003eEffect of Geometric Dimensions and Material Models of the Periodontal Ligament in Orthodontic Tooth Movement\u003c/strong\u003e. \u003cem\u003eOrthodontics and Craniofacial Research \u003c/em\u003e2020.\u003c/li\u003e\n\u003cli\u003eA B, Y S, F G, L T, V S: \u003cstrong\u003eNew finite element study protocol: Clinical simulation of orthodontic tooth movement\u003c/strong\u003e. \u003cem\u003eInternational orthodontics \u003c/em\u003e2017, \u003cstrong\u003e15\u003c/strong\u003e(2):165-179.\u003c/li\u003e\n\u003cli\u003eHH A, P N, RJ C, VH M, OM M: \u003cstrong\u003eThree-dimensional modeling and finite element analysis in treatment planning for orthodontic tooth movement\u003c/strong\u003e. \u003cem\u003eAmerican journal of orthodontics and dentofacial orthopedics : official publication of the American Association of Orthodontists, its constituent societies, and the American Board of Orthodontics \u003c/em\u003e2011, \u003cstrong\u003e139\u003c/strong\u003e(1):e59-71.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable 1 to 3 is available in the Supplementary Files section.\u003c/p\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":"Implant anchorage, Self-made four-curvature auxiliary arch, Three-dimensional finite element, Round stainless-steel wires, Anterior teeth torque angle","lastPublishedDoi":"10.21203/rs.3.rs-2048265/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2048265/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e \u003cp\u003eThe correct torque of the incisors helps assess the effect of orthodontic treatment; however, evaluating it effectively remains a challenge. Improper anterior teeth torque angle can cause cortical bone fracture and root exposure.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e \u003cp\u003eA three-dimensional finite element model of the maxillary central incisor torque controlled by a self-made four-curvature auxiliary arch was established, And the experiments were divided to simulate four different group: (1) molar ligation group ; (2) micro-implant ligation group; (3) molar retraction group ༛(4) micro-implant retraction group༛and the retracted traction force was set at 1.15 N. The displacement of the maxillary dentition and periodontal ligament stress values were analyzed with different torque forces (0.5 N, 1 N, 1.5 N, 2 N) placed on the incisors.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e \u003cp\u003eProvided the absence of a tooth extraction gap, when the four-curvature auxiliary arch was used in conjunction with absolute anchorage, the recommended force value was of \u0026lt;\u0026thinsp;1.5 N. when maxillary central incisor retraction, a force value of \u0026lt;\u0026thinsp;1 N was recommended. In the case of no-implant anchorage, whether there is tooth extraction gap or not, the recommended force value was of \u0026lt;\u0026thinsp;1 N. The stress on the other teeth did not exceed the value of that on the periodontal ligament. The effect of using the four-curvature on the incisors was significant.\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e \u003cp\u003eThe proposed approach may help improve treatment maxillary central incisor for poor torque and avoid cortical bone fracture and root exposure\u003c/p\u003e","manuscriptTitle":"Efficacy of a four-curve auxiliary arch at preventing maxillary central incisor linguoclination during orthodontic treatment: A finite element analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-10-03 18:40:28","doi":"10.21203/rs.3.rs-2048265/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2022-11-09T07:23:24+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-10-18T05:31:44+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2022-10-17T14:51:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"3ac51c6b-8f86-4ae3-a673-101c7c361ca7","date":"2022-10-11T23:25:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"1f2cb6b0-c58c-4e10-8b63-56c71e57ccb1","date":"2022-10-11T21:54:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"e8bce0ec-1b6e-413a-91d8-8dad6256949b","date":"2022-10-11T20:38:11+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-10-11T19:12:31+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-10-11T09:21:52+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2022-09-28T08:05:12+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2022-09-28T08:00:32+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Oral Health","date":"2022-09-09T09:10:19+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":"fc807fbc-a912-419b-ae4d-f8a2d0310904","owner":[],"postedDate":"October 3rd, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T19:37:16+00:00","versionOfRecord":{"articleIdentity":"rs-2048265","link":"https://doi.org/10.1186/s12903-023-02833-2","journal":{"identity":"bmc-oral-health","isVorOnly":false,"title":"BMC Oral Health"},"publishedOn":"2023-03-11 19:31:05","publishedOnDateReadable":"March 11th, 2023"},"versionCreatedAt":"2022-10-03 18:40:28","video":"","vorDoi":"10.1186/s12903-023-02833-2","vorDoiUrl":"https://doi.org/10.1186/s12903-023-02833-2","workflowStages":[]},"version":"v1","identity":"rs-2048265","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2048265","identity":"rs-2048265","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}