{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T23:01:24Z","timestamp":1772233284712,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T00:00:00Z","timestamp":1766966400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T00:00:00Z","timestamp":1766966400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Japan Society for the Promotion of Science (JSPS) KAKENHI","award":["24K20086"],"award-info":[{"award-number":["24K20086"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Prog Orthod."],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>This study aimed to evaluate the effect of external force applied from mini-screws to the aligner during space closure in extraction cases, and to determine the optimal loading conditions to prevent lingual crown tipping of the incisor and mesial tipping of the molar using the finite element (FE) method.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methodology<\/jats:title>\n                    <jats:p>A three-dimensional FE model of the maxillary dentition with extraction of first premolars was constructed, and three different loading conditions were designed. The aligner was activated for 0.25\u00a0mm of incisor retraction without using mini-screws, with application of 0, 100, 200, or 300 cN of distal force through mini-screws placed in the posterior region, or with application of 0, 100, 200, 300, or 400 cN of intrusive force through mini-screws placed in the anterior region, in addition to the application of 300 cN of distal force.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>As the magnitude of distal force increased, the degree of mesial tipping of the first molar gradually decreased, becoming almost zero with nearly 300 cN of distal force. As the magnitude of intrusive force increased in addition to the application of 300 cN of distal force, the degree of lingual crown tipping of the central incisor gradually decreased, becoming almost zero with nearly 400 cN of intrusive force.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>Application of 300 cN of distal force to the aligner from mini-screws placed in the posterior region could completely prevent mesial tipping of the molar and anchorage loss during anterior retraction. Application of 400 cN of intrusive force from mini-screws placed in the anterior region could prevent lingual crown tipping of the incisor, thus providing better torque control for the incisors.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1186\/s40510-025-00601-2","type":"journal-article","created":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T11:34:39Z","timestamp":1767008079000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Biomechanical effect of combined use of mini-screws and aligners in preventing uncontrolled tipping of the incisor and mesial tipping of the molar: a three-dimensional finite element study"],"prefix":"10.1186","volume":"26","author":[{"given":"Runa","family":"Yamaguchi-Higuchi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ryo","family":"Hamanaka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroya","family":"Komaki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toshiro","family":"Emori","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun-ya","family":"Tominaga","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yui","family":"Horiguchi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sayaka","family":"Iwata","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kazuhiro","family":"Ogawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arina","family":"Kitaura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noriaki","family":"Yoshida","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,12,29]]},"reference":[{"issue":"5","key":"601_CR1","doi-asserted-by":"publisher","first-page":"881","DOI":"10.2319\/061614-436.1","volume":"85","author":"G Rossini","year":"2015","unstructured":"Rossini G, Parrini S, Castroflorio T, Deregibus A, Debernardi CL. Efficacy of clear aligners in controlling orthodontic tooth movement: A systematic review. Angle Orthod. 2015;85(5):881\u20139.","journal-title":"Angle Orthod"},{"issue":"6","key":"601_CR2","doi-asserted-by":"publisher","first-page":"275","DOI":"10.4041\/kjod.2015.45.6.275","volume":"45","author":"XJ Zhang","year":"2015","unstructured":"Zhang XJ, He L, Guo HM, Tian J, Bai YX, Li S. Integrated three-dimensional digital assessment of accuracy of anterior tooth movement using clear aligners. Korean J Orthod. 2015;45(6):275\u201381.","journal-title":"Korean J Orthod"},{"key":"601_CR3","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.ajodo.2007.05.018","volume":"135","author":"ND Kravitz","year":"2009","unstructured":"Kravitz ND, Kusnoto B, BeGole E, Obrez A, Agran B. How well does invisalign work? A prospective clinical study evaluating the efficacy Oftooth movement with invisalign. Am J Orthod Dentofac Orthop. 2009;135:27\u201335.","journal-title":"Am J Orthod Dentofac Orthop"},{"key":"601_CR4","doi-asserted-by":"publisher","first-page":"19","DOI":"10.2319\/122115-875.1","volume":"87","author":"JP Houle","year":"2017","unstructured":"Houle JP, Piedade L, TodescanR PFH Jr. The predictabilityof transverse changes with invisalign. Angle Orthod. 2017;87:19\u201324.","journal-title":"Angle Orthod"},{"key":"601_CR5","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1186\/s12903-018-0695-z","volume":"19","author":"Y Ke","year":"2019","unstructured":"Ke Y, Zhu Y, Zhu M. A comparison of treatment effectiveness between clear aligner and fixed appliance therapies. BMC Oral Health. 2019;19:24.","journal-title":"BMC Oral Health"},{"key":"601_CR6","doi-asserted-by":"publisher","first-page":"e275","DOI":"10.1016\/j.ajodo.2020.10.018","volume":"159","author":"M Al-Balaa","year":"2021","unstructured":"Al-Balaa M, Li H, Ma Mohamed A, Xia L, Liu W, Chen Y, et al. Predicted and actual outcome of anterior intrusion with invisalign assessed with cone-beam computed tomography. Am J Orthod Dentofac Orthop. 2021;159:e275\u201380.","journal-title":"Am J Orthod Dentofac Orthop"},{"key":"601_CR7","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1186\/s40510-018-0255-8","volume":"20","author":"J Kawamura","year":"2019","unstructured":"Kawamura J, Tamaya N. A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with Miniscrew sliding mechanics. Prog Orthod. 2019;20:3.","journal-title":"Prog Orthod"},{"key":"601_CR8","doi-asserted-by":"crossref","unstructured":"Venugopal A, Manzano P, Rengalakshmi S. A novel temporary anchorage device aided sectional mechanics for simultaneous orthodontic retraction and intrusion. Case Rep Dent. 2020; 2020:5213936.","DOI":"10.1155\/2020\/5213936"},{"key":"601_CR9","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.ajodo.2021.02.020","volume":"162","author":"L Liu","year":"2022","unstructured":"Liu L, Song Q, Zhou J, Kuang Q, Yan X, Zhang X, et al. The effects of aligner overtreatment on torque control and intrusion of incisors for anterior Retraction with clear aligners: a finite-element study. Am J Orthod Dentofac Orthop. 2022;162:33\u201341.","journal-title":"Am J Orthod Dentofac Orthop"},{"key":"601_CR10","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1111\/ocr.12353","volume":"23","author":"L Robertson","year":"2020","unstructured":"Robertson L, Kaur H, Fagundes NCF, Romanyk D, Major P, Flores Mir C. Effectiveness of clear aligner therapy for orthodontic treatment: a systematic review. Orthod Craniofac Res. 2020;23:133\u201342.","journal-title":"Orthod Craniofac Res"},{"key":"601_CR11","first-page":"200","volume-title":"The Biomechanical foundation of clinical orthodontics","author":"CJ Burstone","year":"1981","unstructured":"Burstone CJ, Koenig HA. The Biomechanical foundation of clinical orthodontics. Volume 178. Chicago: Quintessence Publishing; 1981. p. 200. 185."},{"issue":"5","key":"601_CR12","doi-asserted-by":"publisher","first-page":"679","DOI":"10.2319\/090418-646.1","volume":"89","author":"FF Dai","year":"2019","unstructured":"Dai FF, Xu TM, Shu G. Comparison of achieved and predicted tooth movement of maxillary first molars and central incisors: first premolar extraction treatment with invisalign. Angle Orthod. 2019;89(5):679\u201387.","journal-title":"Angle Orthod"},{"issue":"6","key":"601_CR13","doi-asserted-by":"publisher","first-page":"794","DOI":"10.2319\/120420-982.1","volume":"91","author":"L Liu","year":"2021","unstructured":"Liu L, Zhan Q, Zhou J, Kuang Q, Yan X, Zhang X, et al. Effectiveness of an anterior mini-screw in achieving incisor intrusion and palatal root torque for anterior Retraction with clear aligners. Angle Orthod. 2021;91(6):794\u2013803.","journal-title":"Angle Orthod"},{"key":"601_CR14","doi-asserted-by":"publisher","unstructured":"Lin L, Chang CH, Roberts E. Bimaxillary protrusion and gummy smile treated with clear aligners: closing premolar extraction spaces with bone screw anchorage. APOS Trends Orthod. https:\/\/doi.org\/10.25259\/apos_45_2020","DOI":"10.25259\/apos_45_2020"},{"issue":"2","key":"601_CR15","doi-asserted-by":"publisher","first-page":"247","DOI":"10.2319\/020719-86.1","volume":"90","author":"A Cortona","year":"2020","unstructured":"Cortona A, Rossini G, Parrini S, Deregibus A, Castroflorio T. Clear aligner orthodontic therapy of rotated mandibular round-shaped teeth: a finite element study. Angle Orthod. 2020;90(2):247\u201354.","journal-title":"Angle Orthod"},{"issue":"3","key":"601_CR16","doi-asserted-by":"publisher","first-page":"454","DOI":"10.2319\/050714-330.1","volume":"85","author":"JP Gomez","year":"2015","unstructured":"Gomez JP, Pe\u00f1a FM, Mart\u00ednez 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;85(3):454\u201360.","journal-title":"Angle Orthod"},{"key":"601_CR17","doi-asserted-by":"publisher","first-page":"10156","DOI":"10.1038\/s41598-020-67273-2","volume":"10","author":"T Jiang","year":"2020","unstructured":"Jiang T, Wu RY, Wang JK, Wang HH, Tang GH. Clear aligners for maxillary anterior enmasse retraction: a 3D finite element study. Sci Rep. 2020;10:10156.","journal-title":"Sci Rep"},{"key":"601_CR18","first-page":"210","volume":"18","author":"Y Kojima","year":"1999","unstructured":"Kojima Y, Takano M, Fukui H, Mizutani M, Hasegawa J. A simple method for calculating the initial tooth mobility and stress distribution in the periodontal ligament. J Jpn Soc Dent Mat Device. 1999;18:210\u20136.","journal-title":"J Jpn Soc Dent Mat Device"},{"key":"601_CR19","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1016\/j.ajodo.2017.03.021","volume":"152","author":"R .Hamanaka","year":"2017","unstructured":".Hamanaka R, Yamaoka S, Anh TN, Tominaga JY, Koga Y, Yoshida N. Numeric simulation model for long-term orthodontic tooth movement with contact boundary conditions using the finite element method. Am J Orthod Dentfacial Orthop. 2017;152:601\u201312.","journal-title":"Am J Orthod Dentfacial Orthop"},{"key":"601_CR20","doi-asserted-by":"publisher","first-page":"1642","DOI":"10.1299\/kikaia.65.1642","volume":"65","author":"Y Kojima","year":"1999","unstructured":"Kojima Y, Hasegawa J, Fukui H. Stress distribution in periodontal tissue at initial tooth mobility. JSMET. 1999;65:1642\u20137.","journal-title":"JSMET"},{"issue":"5","key":"601_CR21","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1016\/j.ajodo.2004.12.007","volume":"127","author":"Y Kojima","year":"2005","unstructured":"Kojima Y, Fukui H. Numerical simulation of canine Retraction by sliding mechanics. Am J Orthod Dentofac Orthop. 2005;127(5):542\u201351.","journal-title":"Am J Orthod Dentofac Orthop"},{"key":"601_CR22","first-page":"40","volume":"21","author":"Y .Kojima","year":"2002","unstructured":".Kojima Y, Fukui H. A numerical analysis of tooth movement by orthodontic forces. J Jpn Soc Dent Mat Device. 2002;21:40\u20138.","journal-title":"J Jpn Soc Dent Mat Device"},{"issue":"6","key":"601_CR23","doi-asserted-by":"publisher","first-page":"811","DOI":"10.1093\/ejo\/cjs103","volume":"35","author":"K Papadopoulou","year":"2013","unstructured":"Papadopoulou K, Hasan I, Keilig L, Reimann S, Eliades T, J\u00e4ger A, et al. Biomechanical time dependency of the periodontal ligament: a combined experimental and numerical approach. Eur J Orthod. 2013;35(6):811\u20138.","journal-title":"Eur J Orthod"},{"issue":"1","key":"601_CR24","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1093\/ejo\/cjr134","volume":"36","author":"K Papadopoulou","year":"2014","unstructured":"Papadopoulou K, Keilig L, Eliades T, Krause R, J\u00e4ger A, Bourauel C. The time-dependent Biomechanical behaviour of the periodontal ligament - an in vitro experimental study in minipig mandibular two-rooted premolars. Eur J Orthod. 2014;36(1):9\u201315.","journal-title":"Eur J Orthod"},{"key":"601_CR25","doi-asserted-by":"publisher","first-page":"e328","DOI":"10.1016\/j.ajodo.2022.09.008","volume":"162","author":"D Wang","year":"2022","unstructured":"Wang D, Akbari A, Jiang F, Liu Y, Chen J. The effects of different types of periodontal ligament material models on stresses computed using finite element models. Am J Orthod Dentofac Orthop. 2022;162:e328\u201336.","journal-title":"Am J Orthod Dentofac Orthop"},{"key":"601_CR26","doi-asserted-by":"publisher","first-page":"566","DOI":"10.2319\/120121-879.1","volume":"93","author":"J Kawamura","year":"2023","unstructured":"Kawamura J, Ojima K, Nanda R. Effect of attachment type on distal bodily movement of the maxillary canine in aligner orthodontics: a finite element study. Angle Orthod. 2023;93:566\u201371.","journal-title":"Angle Orthod"},{"key":"601_CR27","doi-asserted-by":"publisher","first-page":"1075097","DOI":"10.1155\/2019\/1075097","volume":"2019","author":"Y Yokoi","year":"2019","unstructured":"Yokoi Y, Usui Y, Kawamura J, Uozumi T, Arai A, Okafuji N. Effects of attachment of plastic aligner in closing of diastema of maxillary dentition by finite element method. J Healthc Eng. 2019;2019:1075097.","journal-title":"J Healthc Eng"},{"issue":"1","key":"601_CR28","doi-asserted-by":"publisher","first-page":"10156","DOI":"10.1038\/s41598-020-67273-2","volume":"10","author":"T Jiang","year":"2020","unstructured":"Jiang T, Wu RY, Tang GH, Wang JK, Wang HH. Clear aligners for maxillary anterior En masse retraction: a 3D finite element study. Sci Rep. 2020;10(1):10156.","journal-title":"Sci Rep"},{"key":"601_CR29","doi-asserted-by":"crossref","unstructured":"Ahmad W, Xiong J, Xia Z. The mechanical effect of aligner\u2019s thickness and material properties in invisible orthodontics: A quantitative finite element study. Dent Mater J. 2025.","DOI":"10.4012\/dmj.2024-085"},{"issue":"1","key":"601_CR30","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1186\/s40510-023-00493-0","volume":"24","author":"J Gao","year":"2023","unstructured":"Gao 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;24(1):43.","journal-title":"Prog Orthod"},{"issue":"2","key":"601_CR31","doi-asserted-by":"publisher","first-page":"381","DOI":"10.2319\/0003-3219(2008)078[0381:TCPA]2.0.CO;2","volume":"78","author":"N Brezniak","year":"2008","unstructured":"Brezniak N. The clear plastic appliance. Angle Orthod. 2008;78(2):381\u20132.","journal-title":"Angle Orthod"},{"issue":"6","key":"601_CR32","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1016\/j.ajodo.2006.06.025","volume":"133","author":"DK Baldwin","year":"2008","unstructured":"Baldwin DK, King G, Ramsay DS, Huang G, Bollen AM. Activation time and material stiffness of sequential removable orthodontic appliances. Part 3: premolar extraction patients. Am J Orthod Dentofac Orthop. 2008;133(6):837\u201345.","journal-title":"Am J Orthod Dentofac Orthop"},{"issue":"1","key":"601_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1472-6831-14-68","volume":"14","author":"M Simon","year":"2014","unstructured":"Simon M, Keilig L, Schwarze J, Jung BA, Bourauel C. Treatment outcome and efficacy of an aligner technique - regarding incisor torque, premolar derotation and molar distalization. BMC Oral Health. 2014;14(1):1\u20137.","journal-title":"BMC Oral Health"},{"issue":"1","key":"601_CR34","doi-asserted-by":"publisher","first-page":"11","DOI":"10.2319\/113015-813.1","volume":"87","author":"L Lombardo","year":"2017","unstructured":"Lombardo L, Martines E, Mazzanti V, Arreghini A, Mollica F, Siciliani G. Stress relaxation properties of four orthodontic aligner materials: a 24-hour in vitro study. Angle Orthod. 2017;87(1):11\u20138.","journal-title":"Angle Orthod"},{"issue":"3","key":"601_CR35","doi-asserted-by":"publisher","first-page":"e3141","DOI":"10.1016\/j.ajodo.2009.01.023","volume":"136","author":"HS Park","year":"2009","unstructured":"Park HS, Lee SK, Kwon TG. Density of alveolar and basal bones in the maxilla and mandible. Am J Orthod Dentofac Orthop. 2009;136(3):e3141\u201331412.","journal-title":"Am J Orthod Dentofac Orthop"},{"issue":"5","key":"601_CR36","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1016\/j.ajodo.2012.05.016","volume":"142","author":"SN Papageorgiou","year":"2012","unstructured":"Papageorgiou SN, Zogakis IP, Papadopoulos MA. Failure rates and associated risk factors of orthodontic Miniscrew implants: a meta-analysis. Am J Orthod Dentofac Orthop. 2012;142(5):577\u201395.","journal-title":"Am J Orthod Dentofac Orthop"},{"issue":"6","key":"601_CR37","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1002\/ca.20671","volume":"21","author":"JE Lim","year":"2008","unstructured":"Lim JE, Lim WH, Chun YS. Quantitative evaluation of cortical bone thickness and root proximity at maxillary interradicular sites for orthodontic mini-implant placement. Clin Anat. 2008;21(6):486\u201391.","journal-title":"Clin Anat"},{"issue":"24","key":"601_CR38","doi-asserted-by":"publisher","first-page":"7697","DOI":"10.3390\/jcm13247697","volume":"13","author":"M Santmart\u00ed-Oliver","year":"2024","unstructured":"Santmart\u00ed-Oliver M, Jorba-Garc\u00eda A, Moya-Mart\u00ednez T, de-la-Rosa-Gay C, Camps-Font O. Safety and accuracy of guided interradicular Miniscrew insertion: a systematic review and meta-analysis. J Clin Med. 2024;13(24):7697.","journal-title":"J Clin Med"},{"issue":"4 Suppl 1","key":"601_CR39","first-page":"13","volume":"81","author":"L Zhang","year":"2019","unstructured":"Zhang L, Lin Y, Guo R, Huang Y, Xu B, Li W, Li W. Comparison of direct and indirect mini-implant anchorage in adults with maxillary protrusion: a randomized controlled trial. Indian J Pharm Sci. 2019;81(4 Suppl 1):13\u201320.","journal-title":"Indian J Pharm Sci"},{"issue":"5","key":"601_CR40","doi-asserted-by":"publisher","first-page":"628","DOI":"10.1016\/j.ajodo.2022.02.018","volume":"163","author":"GY Zhu","year":"2023","unstructured":"Zhu GY, Zhang B, Yao K, Lu WX, Peng JJ, Shen Y, Zhao ZH. Finite element analysis of the Biomechanical effect of clear aligners in extraction space closure under different anchorage controls. Am J Orthod Dentofac Orthop. 2023;163(5):628\u2013e64411. https:\/\/doi.org\/10.1016\/j.ajodo.2022.02.018.","journal-title":"Am J Orthod Dentofac Orthop"},{"key":"601_CR41","first-page":"265","volume":"14","author":"TF Mulligan","year":"1980","unstructured":"Mulligan TF. Common sense mechanics. Part 7. J Clin Orthod: JCO. 1980;14:265.","journal-title":"J Clin Orthod: JCO"},{"issue":"4","key":"601_CR42","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s00056-021-00327-w","volume":"83","author":"B Golkhani","year":"2022","unstructured":"Golkhani B, Weber A, Keilig L, Reimann S, Bourauel C. Variation of the modulus of elasticity of aligner foil sheet materials due to thermoforming. J Orofac Orthop. 2022;83(4):233\u201343.","journal-title":"J Orofac Orthop"},{"issue":"2","key":"601_CR43","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3390\/dj8020047","volume":"8","author":"F Tamburrino","year":"2020","unstructured":"Tamburrino F, D\u2019Ant\u00f2 V, Bucci R, Alessandri-Bonetti G, Barone S, Razionale AV. Mechanical properties of thermoplastic polymers for aligner manufacturing: in vitro study. Dent J. 2020;8(2):1\u201310.","journal-title":"Dent J"},{"key":"601_CR44","doi-asserted-by":"crossref","unstructured":"Yang S, Cheng Y. A novel Mechanics-Based design for overcorrection in clear aligner orthodontics via finite element analysis. Bioengineering 2025;12(2).","DOI":"10.3390\/bioengineering12020110"},{"key":"601_CR45","doi-asserted-by":"crossref","unstructured":"Elshazly TM, Keilig L, Nang D, Golkhani B, Weber A, Elattar H, Talaat S, Bourauel C. Effect of thermomechanical aging on force system of orthodontic aligners made of different thermoformed materials: an in vitro study. J Orofac Orthop. 2024;337\u201346.","DOI":"10.1007\/s00056-024-00527-0"},{"issue":"1","key":"601_CR46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0002-9416(76)90257-8","volume":"70","author":"C Burstone","year":"1976","unstructured":"Burstone C, Koenig H. Optimizing anterior and canine Retraction. Am J Orthod. 1976;70(1):1\u201319.","journal-title":"Am J Orthod"},{"key":"601_CR47","first-page":"592","volume-title":"Contemporary orthodontics","author":"WR Proffit","year":"2007","unstructured":"Proffit WR. Closure of extraction space. In: Proffit WR, Fields HW, Sarver DM, editors. Contemporary orthodontics. 4th ed. St. Louis: Mosby Elsevier; 2007. pp. 592\u2013601.","edition":"4"}],"container-title":["Progress in Orthodontics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40510-025-00601-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s40510-025-00601-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40510-025-00601-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T12:01:47Z","timestamp":1767009707000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s40510-025-00601-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,29]]},"references-count":47,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["601"],"URL":"https:\/\/doi.org\/10.1186\/s40510-025-00601-2","relation":{},"ISSN":["2196-1042"],"issn-type":[{"value":"2196-1042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,29]]},"assertion":[{"value":"28 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 December 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"54"}}