A New Perspective in Rotation Correction; 3D Analysis During FEM

A New Perspective in Rotation Correction; 3D Analysis During FEM | 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 Article A New Perspective in Rotation Correction; 3D Analysis During FEM Hannaneh Ghadirian, Allahyar Geramy, Maryam Sobhani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8725262/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Introduction: The main goal of this study was to assess the vertical reaction of a lower right canine after being derotated by a couple of forces in a finite element setup. Method and material: Eight 3D models of canine with different root forms and length were designed, including: ellipsoid and triangular in occlusal aspect (cross-section), U-shaped and conical root forms from buccal aspect and then all of the 4 roots forms were designed in two length including long and short. A couple of two 0.25 N forces were applied in lingual side, and the amount of vertical displacement was measured. Result: The highest extrusion was obtained in the mesial of the short triangular root (0.000045981 mm), and the least extrusion also occurred in the mesial of the long ellipsoid root (0.000001014 mm). The highest intrusion occurred in the distal of the short conical (-0.00003843 mm), and the lowest intrusion occurred in the distal of the long ellipsoid root (-0.00000015641 mm). In the short ellipsoid root and the short U-shaped root, intrusion was observed on both the mesial and distal sides. Also, unlike other root shapes, the tooth with long U-shaped root extruded distally and intruded mesially. Conclusion: Different vertical displacements occur according to different root shapes and length after being derotated by a couple of forces. Health sciences/Anatomy Physical sciences/Engineering Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Introduction Our efforts, as a clinician to treat a maloccusoion, and reach a stable occlusion according to Andrews, have ups and downs and pass through different stages( 1 ). Aligning is not achieved completely unless all rotations are corrected. A suitable arch form can be achieved only after all contacts have been firmly established ( 2 ). Rotation corrections, apart from their force system for treatment, are a challenging situation for clinicians. Multi-rooted teeth, which need a considerable amount of bone to be resorbed and appositioned and single-rooted ones with few bone modifications in their process, all have a point in common: the force system contains a moment. It is out of the scope of this article to enter the space problems encountered during the correction. When a couple is applied in a plane ( eg , XZ), it is not expected to bring about any side effects in the other plane (YZ plane). It is unlikely that orthodontic movements, especially rotation correction, will be performed without side effects; therefore, side effects should be recognized and controlled( 3 ). One of the effects observed in laboratory and clinical studies is unwanted intrusive movements during derotation in orthodontic treatment using clear aligner treatment (CAT)( 4 ). For example, a finite element study has shown that during derotation of maxillary canine rotation with CAT, a significant intrusive movement is observed, which is 3.7 times greater in the absence of attachments than in the case with attachments ( 5 ). The study by Elkloy et al. showed intrusive movement in both mesial and distal rotations of the maxillary central incisor during rotation correction ( 6 ). The generation of intrusive force can be explained by the application of unequal forces; the two contact points of the tooth and aligner in the mesial and distal regions generate a force system that includes both a vertical and a horizontal component, thus generating both a rotational moment and an intrusive force ( 6 ). The forces are clearly intrusive because of the occlusal surface orientation ( 7 ). This unwanted undesirable intrusive effect can be reduced with appropriate attachment design, orienting the active surface at an angle in which the normal component of the force transmitted by the aligner will express an extrusive tendency.( 7 ) Since these factors such as occlusal surface orientation are not contribute in fixed orthodontic treatment, it is expected that the rotation correction will take place without affecting the vertical dimension. While there are many studies about the side effects of other orthodontic movements, such as tipping, torque, and translation ( 8 , 9 ), the side effects of rotation movement, which is an integral part of orthodontic treatment, have not been well studied. There are also many studies investigating three-dimensional changes in rotation movement in CAT ( 5 , 6 , 10 – 13 ), but no study has investigated the pure rotation movement of the tooth and its vertical displacement. Any side effects of rotation correction of a tooth in the vertical axis (Y axis) after applying a couple in the lingual side of its crown (XZ Plane) need to be inspected in detail to reach an acceptable answer. The main goal of this study was to assess the vertical reaction of a lower right canine after being derotated by a couple of forces. Its root length (short and long), root cross-section (ellipsoid and triangular), and root form when viewed buccally (bluntd and conical) were evaluated using finite element method/analysis (FEM/A). The stress distribution in complex structures can be analyzed using FEM, which uses their properties to produce accurate geometric modeling and stress-strain pattern analysis ( 14 ). Method and material Preparation of models and material properties: This study was conducted at the Department of Orthodontics, Tehran University of Medical Sciences. To analyse the rotation correction, a model of the mandibular arch, periodontal ligament (with thickness 0.25 mm), cancellous and cortical bone, and eight 3D models of canine with different root forms and length were designed in SolidWorks 2023 (SolidWorks, Concord, MA, USA) based on Wheeler’s dental anatomy ( 15 ) (Fig. 1 ). Different root shapes including ellipsoid (a smaller mesio-distal dimension for the root) and triangular root forms in occlusal aspect (cross section), and bluntd (normal root form) and conical root forms in buccal aspect were designed (Fig. 2 ). All of these 4 root shapes were designed in both long (16 mm) and short root lengths (20% reduction in root length) (Fig. 3). Two force vectors in forming a couple were applied in lingual side: ( 1 ) in the distolingual surface with the labial direction and ( 2 ) in the mesiolingual surface with the lingual direction. To apply the force correctly, two perfectly symmetrical prominences were designed as points of force application on the lingual side of the crown (Fig. 4 ). Boundary conditions and loading: The models were meshed in ANSYS Workbench 2021 R1 (Ansys Inc., Southpointe, Canonsburg, PA, USA). The mechanical properties were defined based on previous studies ( 16 , 17 )(Table 1 ). In the coordinate system, the X axis represents the coronal plane, with the positive direction towards the mesial. The Y axis represents the vertical plane, the positive direction to occlusal, and the Z axis represents the sagittal plane, the positive direction to buccal. A path of nodes (49 nodes) was defined in the lingual surface of the canine crown (starting from the distal point to the mesial) (Fig. 4 ). A couple of two 0.25 N forces were applied, and the amount of vertical displacement was measured as positive numbers (extrusion) and negative numbers (intrusion). The maximum von Mises stress (SEQV) was also measured and compared on each model. Figure 3: A: long ellipsoid root B: short ellipsoid root Table 1 The mechanical properties of the material used in the models Young’s Modulus Poisson’s Ratio Spongy Bone 13.400 0.38 Cortical Bone 34.000 0.26 Tooth 20.300 0.26 PDL 0.667 0.49 Result Root forms from the occlusal aspect : In comparing the Triangular and ellipsoid roots, the highest amount of intrusion was obtained in the distal of the short triangular root (-0.000032902 mm), and the highest extrusion was obtained in the mesial of the same root form (0.000045981 mm). (Table 2 ) Table 2 Vertical displacement of the mesial and distal of the crown in ellipsoid and triangular root forms. L: long, S: short. Triangle L Triangle S ellipsoid Root L ellipsoid Root S Distal -0.000020781 -0.000032902 -0.00000015641 -0.00000021072 Mesial 0.00002876 0.000045981 0.000001014 -0.0000021191 Root forms from buccal aspect: In comparing the U-shaped and conical roots, the highest amount of intrusion was obtained in the distal of the short conical root (-0.000001511mm), and the highest extrusion was obtained in the mesial of the same root form (0.000022248 mm). (Table 3 ) Table 3 Vertical displacement in the mesial and distal of the crown in U-shaped and conical root forms. L: long, S: short. U-shaped L U-shaped S conical L conical S Distal 0.0000010529 -0.000001511 -0.000023011 -0.00003843 Mesial -0.0000027854 -0.0000065055 0.000022248 0.000030083 Long root forms: In comparing the types of the long root shapes, the highest amount of intrusion was obtained in the distal of the conical root (-0.000023011 mm), and the highest extrusion was obtained in the mesial of the Triangular root (0.00002876 mm). The displacement in the ellipsoid root and the U-shaped root was significantly less (Fig. 5 ). Short root forms: In comparing the short root shapes, the highest intrusion was obtained in the distal of the conical root (-0.00003843), and the highest extrusion was obtained in the mesial of the Triangular root (0.000045981) (Fig. 6 ). The displacement in the ellipsoid root and the U-shaped root was significantly less. Among 8 models the highest extrusion was obtained in the mesial of the short triangular root and the short conical root, respectively. The least extrusion also occurred in the mesial of the long ellipsoid root. The ratio of tooth displacement with different forms is given in Fig. 7 . The highest intrusion occurred in the distal of the short conical and the short triangular roots, respectively. The lowest intrusion also occurred in the distal of the long ellipsoid root. In the short ellipsoid root and the short U-shaped root, intrusion was observed on both the mesial and distal sides. Also, unlike other root shapes, the tooth with a long U-shaped root extruded distally and intruded mesially. The comparison of the maximum von Mises stress is shown in Table 4. The results showed that the highest stress is in the short conical root, and the lowest one in the long ellipsoid root. Figure 8 shows the exact values of the stress. Table 4: Maximum PDL SEQV.. L: long, S: short. PDL Max. SEQV ellipsoid root L 0.0041715 ellipsoid root S 0.0049775 Triangular L 0.0062608 Triangular S 0.007131 U root L 0.006151 U root S 0.0071835 V root L 0.0072575 V root S 0.009898 Discussion A couple, when analyzed biomechanically, has a moment nature. Moments are expected to produce rotation. Rotation is expected to be produced without a reaction out of the plane of the couple. In this study, a couple of forces were applied in the occlusal plane. Detecting a vertical reaction was interesting. Different vertical displacements are observed in its mesial and distal surfaces when the tooth rotated mesially in and distally out, which vary according to the root anatomy. Teeth with triangular and conical roots, especially with shorter roots, will have the most vertical displacement, and U-shaped and ellipsoid roots, especially with long roots, will have the least vertical displacement. Thus, the most extrusion occurred in the mesial of triangular roots and the least extrusion occurred in the mesial of ellipsoid roots. The most intrusion occurred in the distal of tooth with conical roots, and the least intrusion occurred in the distal of ellipsoid roots. Teeth with the short ellipsoid roots and the short U-shaped roots experienced little intrusion without any extrusion. One of the side effects observed in treatment with clear aligners is unintended intrusion movement, which can be explained by the tooth-aligner contact and the orientation of the occlusal surface (6). Given that these factors are not present in fixed appliance orthodontics, pure rotation is expected to occur. However, as observed in this study, displacement in the vertical dimension is inevitable. These changes seem to be related to tooth morphology and crown and root dimensions., Savignano et al. in their study showed that the way the tooth moves and its axis of resistance depend on the morphology of the crown and root, as well as the force system(18). Choy et al. also in their study about the effect of root shape on stress distribution in PDL showed that the short conical root are more prone to tipping (19). Various studies have confirmed the effect of root shape on the distribution of mechanical forces in the PDL, which indicates its effect on the amount and type of tooth movement (14,15). The center of resistance of each tooth also varies depending on the number of roots, the height of the alveolar crest, and the shape and length of the root (22). In fixed orthodontic treatment, controlling the thickness of the wire can be one of the effective factors in reducing unwanted vertical movements. Kwamura et al. showed that in the retraction of anterior teeth to close the extraction space, when the wire size is reduced, lingual tipping of the teeth occurs due to increased play and elastic deformity of the arch wire, and this tipping leads to incisor extrusion(23). This study also showed that the Maximum PDL SEQV is highest in the short conical root and lowest in the long ellipsoid roots. In general, the Maximum PDL SEQV was lower in long roots than the short roots with a similar shape. Therefore, it seems that if the root anatomy is in a way that provides more surface for force distribution, the Maximum PDL SEQV will be lower. In the study of Gao et al., the von Mises stress of the root during upper molar distalization using clear aligners, the lateral tooth was identified as the stress concentration site, because it has the lowest root surface in maxilla (24). In the present study, the effect of rotation on the generation of vertical displacement in different root shapes was investigated. Teeth with triangular and conical roots, especially with shorter roots, will have the greatest vertical displacement, and teeth with U-shaped and ellipsoid roots, especially with longer roots, will have the least vertical displacement. The maximum von Mises stress is greatest in the short conical root and least in the long ellipsoid root. Although finite element analyses can be a basis for understanding the effects of force application on different models, there are also limitations. The results of these models cannot be directly applied to clinical situations, and future clinical studies with similar models are recommended. The reason for these shortcomings is that finite element analyses cannot fully simulate the oral environment, and factors such as biological organisms, muscle function, and saliva may alter the clinical outcomes of orthodontic treatments. In addition, these analyses do not reflect the long-term outcomes of treatments. Despite all these limitations, finite element analyses can reduce the sample size and costs of future clinical studies(25). Conclusions Teeth with triangular and conical roots, especially with shorter roots, will have the greatest vertical displacement. Teeth with U-shaped and ellipsoid roots, especially with the long roots, will have the least vertical displacement. The short ellipsoid root and the short U-shaped root had little introgression without extrusion. Maximum PDL SEQV was lower in the long roots than the short roots of similar shape. Maximum PDL SEQV was highest in the short conical root and lowest in the long ellipsoid root. Declarations Aknowledgements: None Conflict of Interest Statement: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Funding sources: Not applicanble. References Andrews LF. The six keys to normal occlusion. Am J Orthod. 1972 Sep;62(3):296–309. Sander C, Sander FM, Sander FG. The Derotation of Premolars and Canines with NiTi Elements. Journal of Orofacial Orthopedics / Fortschritte der Kieferorthopädie. 2006 Mar;67(2):117–26. Sander C, Sander FM, Sander FG. The Derotation of Premolars and Canines with NiTi Elements. 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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-8725262","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":588032305,"identity":"fe57a33f-294d-4f1c-a6ef-b2dc37d59754","order_by":0,"name":"Hannaneh Ghadirian","email":"","orcid":"","institution":"Tehran University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Hannaneh","middleName":"","lastName":"Ghadirian","suffix":""},{"id":588032306,"identity":"27462a9f-97d7-41e5-b9e3-0f9801c7f53e","order_by":1,"name":"Allahyar Geramy","email":"","orcid":"","institution":"Tehran University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Allahyar","middleName":"","lastName":"Geramy","suffix":""},{"id":588032307,"identity":"f04c91fd-29fe-4413-9de5-bbc3ccdaddf0","order_by":2,"name":"Maryam Sobhani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYJACZsYGBgY2diDBYIAQ5SGshecAWIsE8VoYJBLAHAl8KsFAt4H94ePCHXZ5fJJvH378UcBQZ3Dt+AOGHzUMMuYN2LWYHeAxNp55JrmYTTrdWEIC6DCD2zkGjD3HGHhkDuDUwibN28ac2CadBlQO0cLAwNvAwIPLiWYH2J8BtdQntkkeY/6RANaS/oDxL14tDGZALYcT2yTY2CQOgLUkGDDjtwXkl7bjiW08aWyWDQYSkjOBfjksc0wCn8OAIdZWnTi//RjzzR9/bPj5bqc/fPimxsYeZ3DLP0DhQtQdICZ+RsEoGAWjYBTgBgCVdEx9apbVuwAAAABJRU5ErkJggg==","orcid":"","institution":"Tehran University of Medical Sciences","correspondingAuthor":true,"prefix":"","firstName":"Maryam","middleName":"","lastName":"Sobhani","suffix":""}],"badges":[],"createdAt":"2026-01-28 21:53:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8725262/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8725262/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102486337,"identity":"8b2fbc13-2b20-4022-91aa-303f77fac8b4","added_by":"auto","created_at":"2026-02-12 07:43:21","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":184530,"visible":true,"origin":"","legend":"\u003cp\u003emeshed model. A: buccal aspect B: lingual aspect\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8725262/v1/4786daed06c54386e15e8d19.png"},{"id":102486334,"identity":"7fe9d424-8c42-4508-98b5-b40d55a29b48","added_by":"auto","created_at":"2026-02-12 07:43:21","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":545388,"visible":true,"origin":"","legend":"\u003cp\u003eRoot forms: A: ellipsoid root. B: Triangular root. C: U-shaped root. 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L: long, S: short.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8725262/v1/db55d606e5f0f4fceb27bba9.png"},{"id":102486343,"identity":"42b32ecf-8ff6-4a52-81dc-37fa6e0a4955","added_by":"auto","created_at":"2026-02-12 07:43:26","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":41599,"visible":true,"origin":"","legend":"\u003cp\u003eVertical displacement in rotation correction in the short roots. L: long, S: short.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8725262/v1/8e08b0dc1c32259a9cb5e5b5.png"},{"id":102486315,"identity":"bade7812-0a76-4168-bbd3-d9a31b069d9d","added_by":"auto","created_at":"2026-02-12 07:43:21","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":39388,"visible":true,"origin":"","legend":"\u003cp\u003eThe ratio of vertical displacement in mesial and distal of the crown. L: long, S: short.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8725262/v1/3e9884a3afcc7aca8f77b571.png"},{"id":102486344,"identity":"740bf4e7-b675-41e7-898d-81a44a6b5cd0","added_by":"auto","created_at":"2026-02-12 07:43:27","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":28238,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum PDL SEQV. . L: long, S: short.\u003c/p\u003e\n\u003cp\u003eximum PDL SEQV\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8725262/v1/05a75dcd152401fcd3926615.png"},{"id":106851507,"identity":"83f91ef8-4b8f-4c0f-8b57-1f727287917d","added_by":"auto","created_at":"2026-04-14 06:27:35","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1608666,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8725262/v1/c75de699-06bf-42d0-93db-6dd0e3473bbb.pdf"},{"id":102486333,"identity":"737fc18f-a9ba-4373-9f56-7699bb93cd27","added_by":"auto","created_at":"2026-02-12 07:43:21","extension":"xlsx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":421031,"visible":true,"origin":"","legend":"","description":"","filename":"Data.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-8725262/v1/cb0cb08a4808561d6d576d36.xlsx"}],"financialInterests":"No competing interests reported.","formattedTitle":"A New Perspective in Rotation Correction; 3D Analysis During FEM","fulltext":[{"header":"Introduction","content":"\u003cp\u003eOur efforts, as a clinician to treat a maloccusoion, and reach a stable occlusion according to Andrews, have ups and downs and pass through different stages(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e). Aligning is not achieved completely unless all rotations are corrected. A suitable arch form can be achieved only after all contacts have been firmly established (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e). Rotation corrections, apart from their force system for treatment, are a challenging situation for clinicians. Multi-rooted teeth, which need a considerable amount of bone to be resorbed and appositioned and single-rooted ones with few bone modifications in their process, all have a point in common: the force system contains a moment. It is out of the scope of this article to enter the space problems encountered during the correction. When a couple is applied in a plane (\u003cem\u003eeg\u003c/em\u003e, XZ), it is not expected to bring about any side effects in the other plane (YZ plane). It is unlikely that orthodontic movements, especially rotation correction, will be performed without side effects; therefore, side effects should be recognized and controlled(\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOne of the effects observed in laboratory and clinical studies is unwanted intrusive movements during derotation in orthodontic treatment using clear aligner treatment (CAT)(\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e). For example, a finite element study has shown that during derotation of maxillary canine rotation with CAT, a significant intrusive movement is observed, which is 3.7 times greater in the absence of attachments than in the case with attachments (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e). The study by Elkloy et al. showed intrusive movement in both mesial and distal rotations of the maxillary central incisor during rotation correction (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). The generation of intrusive force can be explained by the application of unequal forces; the two contact points of the tooth and aligner in the mesial and distal regions generate a force system that includes both a vertical and a horizontal component, thus generating both a rotational moment and an intrusive force (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). The forces are clearly intrusive because of the occlusal surface orientation (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e). This unwanted undesirable intrusive effect can be reduced with appropriate attachment design, orienting the active surface at an angle in which the normal component of the force transmitted by the aligner will express an extrusive tendency.(\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e) Since these factors such as occlusal surface orientation are not contribute in fixed orthodontic treatment, it is expected that the rotation correction will take place without affecting the vertical dimension. While there are many studies about the side effects of other orthodontic movements, such as tipping, torque, and translation (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e), the side effects of rotation movement, which is an integral part of orthodontic treatment, have not been well studied. There are also many studies investigating three-dimensional changes in rotation movement in CAT (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan additionalcitationids=\"CR11 CR12\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e), but no study has investigated the pure rotation movement of the tooth and its vertical displacement.\u003c/p\u003e \u003cp\u003eAny side effects of rotation correction of a tooth in the vertical axis (Y axis) after applying a couple in the lingual side of its crown (XZ Plane) need to be inspected in detail to reach an acceptable answer. The main goal of this study was to assess the vertical reaction of a lower right canine after being derotated by a couple of forces. Its root length (short and long), root cross-section (ellipsoid and triangular), and root form when viewed buccally (bluntd and conical) were evaluated using finite element method/analysis (FEM/A).\u003c/p\u003e \u003cp\u003eThe stress distribution in complex structures can be analyzed using FEM, which uses their properties to produce accurate geometric modeling and stress-strain pattern analysis (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e).\u003c/p\u003e"},{"header":"Method and material","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003ePreparation of models and material properties:\u003c/h2\u003e \u003cp\u003eThis study was conducted at the Department of Orthodontics, Tehran University of Medical Sciences. To analyse the rotation correction, a model of the mandibular arch, periodontal ligament (with thickness 0.25 mm), cancellous and cortical bone, and eight 3D models of canine with different root forms and length were designed in SolidWorks 2023 (SolidWorks, Concord, MA, USA) based on Wheeler\u0026rsquo;s dental anatomy (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDifferent root shapes including ellipsoid (a smaller mesio-distal dimension for the root) and triangular root forms in occlusal aspect (cross section), and bluntd (normal root form) and conical root forms in buccal aspect were designed (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). All of these 4 root shapes were designed in both long (16 mm) and short root lengths (20% reduction in root length) (Fig.\u0026nbsp;3).\u003c/p\u003e \u003cp\u003eTwo force vectors in forming a couple were applied in lingual side: (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) in the distolingual surface with the labial direction and (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) in the mesiolingual surface with the lingual direction. To apply the force correctly, two perfectly symmetrical prominences were designed as points of force application on the lingual side of the crown (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eBoundary conditions and loading:\u003c/h3\u003e\n\u003cp\u003eThe models were meshed in ANSYS Workbench 2021 R1 (Ansys Inc., Southpointe, Canonsburg, PA, USA). The mechanical properties were defined based on previous studies (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e)(Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In the coordinate system, the X axis represents the coronal plane, with the positive direction towards the mesial. The Y axis represents the vertical plane, the positive direction to occlusal, and the Z axis represents the sagittal plane, the positive direction to buccal.\u003c/p\u003e \u003cp\u003eA path of nodes (49 nodes) was defined in the lingual surface of the canine crown (starting from the distal point to the mesial) (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e ). A couple of two 0.25 N forces were applied, and the amount of vertical displacement was measured as positive numbers (extrusion) and negative numbers (intrusion). The maximum von Mises stress (SEQV) was also measured and compared on each model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure 3: A: long ellipsoid root B: short ellipsoid root\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe mechanical properties of the material used in the models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYoung\u0026rsquo;s Modulus\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePoisson\u0026rsquo;s Ratio\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpongy Bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e13.400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCortical Bone\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e34.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTooth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.667\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Result","content":"\u003cp\u003e\u003cstrong\u003eRoot forms from the occlusal aspect\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eIn comparing the Triangular and ellipsoid roots, the highest amount of intrusion was obtained in the distal of the short triangular root (-0.000032902 mm), and the highest extrusion was obtained in the mesial of the same root form (0.000045981 mm). (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e)\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eVertical displacement of the mesial and distal of the crown in ellipsoid and triangular root forms. L: long, S: short.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTriangle L\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTriangle S\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eellipsoid Root L\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eellipsoid Root S\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDistal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.000020781\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.000032902\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.00000015641\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.00000021072\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMesial\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00002876\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.000045981\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.000001014\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.0000021191\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003ch3\u003eRoot forms from buccal aspect:\u003c/h3\u003e\n\u003cp\u003eIn comparing the U-shaped and conical roots, the highest amount of intrusion was obtained in the distal of the short conical root (-0.000001511mm), and the highest extrusion was obtained in the mesial of the same root form (0.000022248 mm). (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e)\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eVertical displacement in the mesial and distal of the crown in U-shaped and conical root forms. L: long, S: short.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eU-shaped L\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eU-shaped S\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003econical L\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003econical S\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDistal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0000010529\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.000001511\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.000023011\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.00003843\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMesial\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.0000027854\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.0000065055\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.000022248\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.000030083\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003ch3\u003eLong root forms:\u003c/h3\u003e\n\u003cp\u003eIn comparing the types of the long root shapes, the highest amount of intrusion was obtained in the distal of the conical root (-0.000023011 mm), and the highest extrusion was obtained in the mesial of the Triangular root (0.00002876 mm). The displacement in the ellipsoid root and the U-shaped root was significantly less (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003eShort root forms:\u003c/h2\u003e\n \u003cp\u003eIn comparing the short root shapes, the highest intrusion was obtained in the distal of the conical root (-0.00003843), and the highest extrusion was obtained in the mesial of the Triangular root (0.000045981) (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e). The displacement in the ellipsoid root and the U-shaped root was significantly less.\u003c/p\u003e\n \u003cp\u003eAmong 8 models the highest extrusion was obtained in the mesial of the short triangular root and the short conical root, respectively. The least extrusion also occurred in the mesial of the long ellipsoid root. The ratio of tooth displacement with different forms is given in Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003eThe highest intrusion occurred in the distal of the short conical and the short triangular roots, respectively. The lowest intrusion also occurred in the distal of the long ellipsoid root. In the short ellipsoid root and the short U-shaped root, intrusion was observed on both the mesial and distal sides. Also, unlike other root shapes, the tooth with a long U-shaped root extruded distally and intruded mesially.\u003c/p\u003e\n \u003cp\u003eThe comparison of the maximum von Mises stress is shown in Table 4. The results showed that the highest stress is in the short conical root, and the lowest one in the long ellipsoid root. Figure \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e shows the exact values of the stress.\u003c/p\u003e\n \u003cp\u003eTable 4: Maximum PDL SEQV.. L: long, S: short.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Taba\" border=\"1\"\u003e\n \u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\n \u003cp\u003ePDL Max. SEQV\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eellipsoid root L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0041715\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eellipsoid root S\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0049775\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTriangular L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0062608\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTriangular S\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.007131\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eU root L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.006151\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eU root S\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0071835\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eV root L\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0072575\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eV root S\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.009898\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eA couple, when analyzed biomechanically, has a moment nature. Moments are expected to produce rotation. Rotation is expected to be produced without a reaction out of the plane of the couple. In this study, a couple of forces were applied in the occlusal plane. Detecting a vertical reaction was interesting. Different vertical displacements are observed in its mesial and distal surfaces when the tooth rotated mesially in and distally out, which vary according to the root anatomy. Teeth with triangular and conical roots, especially with shorter roots, will have the most vertical displacement, and U-shaped and ellipsoid roots, especially with long roots, will have the least vertical displacement. Thus, the most extrusion occurred in the mesial of triangular roots and the least extrusion occurred in the mesial of ellipsoid roots. The most intrusion occurred in the distal of tooth with conical roots, and the least intrusion occurred in the distal of ellipsoid roots. Teeth with the short ellipsoid roots and the short U-shaped roots experienced little intrusion without any extrusion.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp;One of the side effects observed in treatment with clear aligners is unintended intrusion movement, which can be explained by the tooth-aligner contact and the orientation of the occlusal surface (6). Given that these factors are not present in fixed appliance orthodontics, pure rotation is expected to occur. However, as observed in this study, displacement in the vertical dimension is inevitable. These changes seem to be related to tooth morphology and crown and root dimensions., Savignano et al. in their study showed that the way the tooth moves and its axis of resistance depend on the morphology of the crown and root, as well as the force system(18). Choy et al. also in their study about the effect of root shape on stress distribution in PDL showed that the short conical root are more prone to tipping (19). Various studies have confirmed the effect of root shape on the distribution of mechanical forces in the PDL, which indicates its effect on the amount and type of tooth movement (14,15). The center of resistance of each tooth also varies depending on the number of roots, the height of the alveolar crest, and the shape and length of the root (22).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; In fixed orthodontic treatment, controlling the thickness of the wire can be one of the effective factors in reducing unwanted vertical movements. Kwamura et al. showed that in the retraction of anterior teeth to close the extraction space, when the wire size is reduced, lingual tipping of the teeth occurs due to increased play and elastic deformity of the arch wire, and this tipping leads to incisor extrusion(23). This study also showed that the Maximum PDL SEQV is highest in the short conical root and lowest in the long ellipsoid roots. In general, the Maximum PDL SEQV was lower in long roots than the short roots with a similar shape. Therefore, it seems that if the root anatomy is in a way that provides more surface for force distribution, the Maximum PDL SEQV will be lower. In the study of Gao et al., the von Mises stress of the root during upper molar distalization using clear aligners, the lateral tooth was identified as the stress concentration site, because it has the lowest root surface in maxilla (24).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; In the present study, the effect of rotation on the generation of vertical displacement in different root shapes was investigated. Teeth with triangular and conical roots, especially with shorter roots, will have the greatest vertical displacement, and teeth with U-shaped and ellipsoid roots, especially with longer roots, will have the least vertical displacement. The maximum von Mises stress is greatest in the short conical root and least in the long ellipsoid root.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; Although finite element analyses can be a basis for understanding the effects of force application on different models, there are also limitations. The results of these models cannot be directly applied to clinical situations, and future clinical studies with similar models\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003eare recommended. The reason for these shortcomings is that finite element analyses cannot fully simulate the oral environment, and factors such as biological organisms, muscle function, and saliva may alter the clinical outcomes of orthodontic treatments. In addition, these analyses do not reflect the long-term outcomes of treatments. Despite all these limitations, finite element analyses can reduce the sample size and costs of future clinical studies(25).\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cul\u003e\n \u003cli\u003eTeeth with triangular and conical roots, especially with shorter roots, will have the greatest vertical displacement.\u003c/li\u003e\n \u003cli\u003eTeeth with U-shaped and ellipsoid roots, especially with the long roots, will have the least vertical displacement.\u003c/li\u003e\n \u003cli\u003eThe short ellipsoid root and the short U-shaped root had little introgression without extrusion.\u003c/li\u003e\n \u003cli\u003eMaximum PDL SEQV was lower in the long roots than the short roots of similar shape.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eMaximum PDL SEQV was highest in the short conical root and lowest in the long ellipsoid root.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"Declarations","content":"\u003cul\u003e\n \u003cli\u003e\u003cstrong\u003eAknowledgements:\u0026nbsp;\u003c/strong\u003eNone\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eConflict of Interest Statement:\u0026nbsp;\u003c/strong\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eFunding sources:\u003c/strong\u003e Not applicanble.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAndrews LF. The six keys to normal occlusion. Am J Orthod. 1972 Sep;62(3):296\u0026ndash;309.\u003c/li\u003e\n \u003cli\u003eSander C, Sander FM, Sander FG. The Derotation of Premolars and Canines with NiTi Elements. Journal of Orofacial Orthopedics / Fortschritte der Kieferorthop\u0026auml;die. 2006 Mar;67(2):117\u0026ndash;26.\u003c/li\u003e\n \u003cli\u003eSander C, Sander FM, Sander FG. The Derotation of Premolars and Canines with NiTi Elements. Journal of Orofacial Orthopedics / Fortschritte der Kieferorthop\u0026auml;die. 2006 Mar;67(2):117\u0026ndash;26.\u003c/li\u003e\n \u003cli\u003eElkholy F, Mikhaiel B, Schmidt F, Lapatki BG. Mechanical load exerted by PET-G aligners during mesial and distal derotation of a mandibular canine. Journal of Orofacial Orthopedics / Fortschritte der Kieferorthop\u0026auml;die. 2017 Sep 29;78(5):361\u0026ndash;70.\u003c/li\u003e\n \u003cli\u003eGomez JP, Pe\u0026ntilde;a FM, Mart\u0026iacute;nez V, Giraldo DC, Cardona CI. Initial force systems during bodily tooth movement with plastic aligners and composite attachments: A three-dimensional finite element analysis. Angle Orthod. 2015 May 1;85(3):454\u0026ndash;60.\u003c/li\u003e\n \u003cli\u003eElkholy F, Schmidt F, J\u0026auml;ger R, Lapatki BG. Forces and moments applied during derotation of a maxillary central incisor with thinner aligners: An in-vitro study. American Journal of Orthodontics and Dentofacial Orthopedics. 2017 Feb;151(2):407\u0026ndash;15.\u003c/li\u003e\n \u003cli\u003eRavindra Nanda, Tommaso Castroflorio, Francesco Garino, Kenji Ojima. Principles and Biomechanics of Aligner Treatment. 1st ed. 2021.\u003c/li\u003e\n \u003cli\u003eCaruso S, Nota A, Ehsani S, Maddalone E, Ojima K, Tecco S. Impact of molar teeth distalization with clear aligners on occlusal vertical dimension: a retrospective study. BMC Oral Health. 2019 Dec 13;19(1):182.\u003c/li\u003e\n \u003cli\u003eSu H, Zhuang Z, Han B, Xu T, Chen G. Vertical changes in the hard tissues after space closure by miniscrew sliding mechanics: a three-dimensional modality analysis. Head Face Med. 2023 Dec 4;19(1):52.\u003c/li\u003e\n \u003cli\u003eHahn W, Fialka-Fricke J, Dathe H, Fricke-Zech S, Zapf A, Gruber R, et al. Initial forces generated by three types of thermoplastic appliances on an upper central incisor during tipping. The European Journal of Orthodontics. 2009 Dec 1;31(6):625\u0026ndash;31.\u003c/li\u003e\n \u003cli\u003eHahn W, Zapf A, Dathe H, Fialka-Fricke J, Fricke-Zech S, Gruber R, et al. Torquing an upper central incisor with aligners--acting forces and biomechanical principles. The European Journal of Orthodontics. 2010 Dec 1;32(6):607\u0026ndash;13.\u003c/li\u003e\n \u003cli\u003eElkholy F, Panchaphongsaphak T, Kilic F, Schmidt F, Lapatki BG. Forces and moments delivered by PET-G aligners to an upper central incisor for labial and palatal translation. Journal of Orofacial Orthopedics / Fortschritte der Kieferorthop\u0026auml;die. 2015 Nov 9;76(6):460\u0026ndash;75.\u003c/li\u003e\n \u003cli\u003eHahn W, Engelke B, Jung K, Dathe H, Kramer FJ, R\u0026ouml;dig T, et al. The influence of occlusal forces on force delivery properties of aligners during rotation of an upper central incisor. Angle Orthod. 2011 Nov;81(6):1057\u0026ndash;63.\u003c/li\u003e\n \u003cli\u003eLERTCHIRAKARN V, PALAMARA J, MESSER H. Finite Element Analysis and Strain-gauge Studies of Vertical Root Fracture. J Endod. 2003 Aug;29(8):529\u0026ndash;34.\u003c/li\u003e\n \u003cli\u003eStanley J. Nelson. Wheeler\u0026rsquo;s Dental anatomy, physiology and occlusion. 11th ed. 2015.\u003c/li\u003e\n \u003cli\u003eNassar N, Geramy A, Kmeid R, Nassif NB, Medawar L, Sayegh P, et al. \u003cem\u003eEn masse\u003c/em\u003e maxillary dentition distalization with clear aligners using infrazygomatic mini-implants: A finite element study. Korean J Orthod. 2025 May 25;55(3):183\u0026ndash;92.\u003c/li\u003e\n \u003cli\u003eGeramy A, Safari F. Effect of clear aligner type on maxillary full-arch intrusion: 3D analysis using finite element method. BMC Oral Health. 2024 Feb 13;24(1):231.\u003c/li\u003e\n \u003cli\u003eSavignano R, Viecilli RF, Oyoyo U. Three-dimensional nonlinear prediction of tooth movement from the force system and root morphology. Angle Orthod. 2020 Nov 1;90(6):811\u0026ndash;22.\u003c/li\u003e\n \u003cli\u003eChoy K, Pae EK, Park Y, Kim KH, Burstone CJ. Effect of root and bone morphology on the stress distribution in the periodontal ligament. American Journal of Orthodontics and Dentofacial Orthopedics. 2000 Jan;117(1):98\u0026ndash;105.\u003c/li\u003e\n \u003cli\u003eKamble RH, Lohkare S, Hararey P V., Mundada RD. Stress distribution pattern in a root of maxillary central incisor having various root morphologies. Angle Orthod. 2012 Sep;82(5):799\u0026ndash;805.\u003c/li\u003e\n \u003cli\u003eChoy K, Kim KH, Burstone CJ. Initial changes of centres of rotation of the anterior segment in response to horizontal forces. The European Journal of Orthodontics. 2006 Oct 1;28(5):471\u0026ndash;4.\u003c/li\u003e\n \u003cli\u003eGeramy A. Alveolar bone resorption and the center of resistance modification (3-D analysis by means of the finite element method). American Journal of Orthodontics and Dentofacial Orthopedics. 2000 Apr;117(4):399\u0026ndash;405.\u003c/li\u003e\n \u003cli\u003eKawamura J, Tamaya N. A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics. Prog Orthod. 2019 Dec 21;20(1):3.\u003c/li\u003e\n \u003cli\u003eGao J, Guo D, Zhang X, Cheng Y, Zhang H, Xu Y, et al. Biomechanical effects of different staging and attachment designs in maxillary molar distalization with clear aligner: a finite element study. Prog Orthod. 2023 Dec 4;24(1):43.\u003c/li\u003e\n \u003cli\u003eGeramy A, Ebrahimi S. Evaluation of different models of intrusive force application and temporary anchorage device (TAD) placement in total arch intrusion using clear aligners; a finite element analysis. BMC Oral Health. 2023 Oct 10;23(1):740.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8725262/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8725262/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eIntroduction: \u003c/strong\u003eThe main goal of this study was to assess the vertical reaction of a lower right canine after being derotated by a couple of forces in a finite element setup.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethod and material: \u003c/strong\u003eEight 3D models of canine with different root forms and length were designed, including: ellipsoid and triangular in occlusal aspect (cross-section), U-shaped and conical root forms from buccal aspect and then all of the 4 roots forms were designed in two length including long and short. A couple of two 0.25 N forces were applied in lingual side, and the amount of vertical displacement was measured.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResult: \u003c/strong\u003e\u0026nbsp;The highest extrusion was obtained in the mesial of the short triangular root (0.000045981 mm), and the least extrusion also occurred in the mesial of the long ellipsoid root (0.000001014 mm). The highest intrusion occurred in the distal of the short conical (-0.00003843 mm), and the lowest intrusion occurred in the distal of the long ellipsoid root (-0.00000015641 mm). In the short ellipsoid root and the short U-shaped root, intrusion was observed on both the mesial and distal sides. Also, unlike other root shapes, the tooth with long U-shaped root extruded distally and intruded mesially.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusion:\u003c/strong\u003e Different vertical displacements occur according to different root shapes and length after being derotated by a couple of forces.\u003c/p\u003e","manuscriptTitle":"A New Perspective in Rotation Correction; 3D Analysis During FEM","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-12 07:42:34","doi":"10.21203/rs.3.rs-8725262/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"92729077-2a38-4096-aaa9-8e3bd18a0a04","owner":[],"postedDate":"February 12th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":62554056,"name":"Health sciences/Anatomy"},{"id":62554057,"name":"Physical sciences/Engineering"}],"tags":[],"updatedAt":"2026-04-14T06:27:08+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-12 07:42:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8725262","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8725262","identity":"rs-8725262","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}