{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T22:21:31Z","timestamp":1777414891475,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T00:00:00Z","timestamp":1774396800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCM"],"abstract":"<jats:p>Background\/Objectives: This finite element analysis (FEA) assessed stress distribution in the tooth and dentin within an intact periodontium under 4 N of force and five orthodontic movements (intrusion, extrusion, rotation, tipping, and translation), using four failure criteria commonly used in numerical dental studies. Secondly, differences between brittle- and ductile-like failure criteria were found, and the most accurate criterion was determined. Additionally, movements more prone to inducing external orthodontic root resorption were assessed. Methods: Using nine 3D models of the second lower premolar, 180 numerical simulations were performed. The models were anatomically accurate based on CBCT scans. FEA employed the brittle-like Maximum Principal (MaxP), Minimum Principal (MinP), and ductile-like Von Mises (VM) and Tresca (T). Results: The results showed that tipping was less prone to external orthodontic root resorption than translation, extrusion, intrusion, and rotation, which showed areas of high stress concentration in the cervical third of the root. High-stress areas were visible only when the dentin-pulp-NVB components were separately analyzed, and not when the entire tooth structure was assessed. Only by correlating the qualitative with the quantitative results could the difference between brittle-like and ductile-like failure criteria be seen. Conclusions: In total, 4 N of applied orthodontic force can induce limited islands of external orthodontic root resorption (intrusion\u2013extrusion on the vestibular side, rotation\u2013translation on the lingual and distal\u2013lingual sides). The ductile-like failure criteria maintained the accuracy of the results across all FEA simulations, while the brittle-like criteria showed various quantitative and qualitative inconsistencies.<\/jats:p>","DOI":"10.3390\/jcm15072503","type":"journal-article","created":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T09:11:14Z","timestamp":1774429874000},"page":"2503","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Orthodontically Induced External Root Resorption: A Finite Element Analysis"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8043-2310","authenticated-orcid":false,"given":"Radu-Andrei","family":"Moga","sequence":"first","affiliation":[{"name":"Department of Odontology, Endodontics and Oral Pathology, School of Dental Medicine, University of Medicine and Pharmacy Iuliu Hatieganu, Str. Motilor 33, 400001 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristian Doru","family":"Olteanu","sequence":"additional","affiliation":[{"name":"Department of Orthodontics, School of Dental Medicine, University of Medicine and Pharmacy Iuliu Hatieganu, Str. Avram Iancu 31, 400083 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ada Gabriela","family":"Delean","sequence":"additional","affiliation":[{"name":"Department of Odontology, Endodontics and Oral Pathology, School of Dental Medicine, University of Medicine and Pharmacy Iuliu Hatieganu, Str. Motilor 33, 400001 Cluj-Napoca, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Akg\u00fcn, H., and Kalyoncuo\u011flu, E. (2025). Mechanical behavior of external root resorption cavities restored with different materials: A 3D-FEA study. BMC Oral Health, 25.","DOI":"10.1186\/s12903-025-05458-9"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1111\/aej.12962","article-title":"Finite Element Analysis of Stress Distribution in Various Sizes Internal Root Resorption Cavities Filled With Different Materials","volume":"51","author":"Aktas","year":"2025","journal-title":"Aust. Endod. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"984","DOI":"10.1007\/s10266-024-01029-6","article-title":"Stress distribution in restored mandibular molars with external cervical resorption: A finite element analysis","volume":"113","author":"Aslan","year":"2025","journal-title":"Odontology"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3872","DOI":"10.4103\/jfmpc.jfmpc_802_20","article-title":"External apical root resorption in orthodontic patients: Molecular and genetic basis","volume":"9","author":"Kalra","year":"2020","journal-title":"J. Fam. Med. Prim. Care"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"100","DOI":"10.34172\/joddd.2021.017","article-title":"External apical root resorption after orthodontic treatment: Incidence, severity and risk factors","volume":"15","author":"Bayir","year":"2021","journal-title":"J. Dent. Res. Dent. Clin. Dent. Prospect."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhang, X., Zhou, H., Liao, X., and Liu, Y. (2022). The influence of bracket torque on external apical root resorption in bimaxillary protrusion patients: A retrospective study. BMC Oral Health, 22.","DOI":"10.1186\/s12903-022-02042-3"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"320.e1","DOI":"10.1016\/j.ajodo.2008.05.014","article-title":"Physical properties of root cementum: Part 13. Repair of root resorption 4 and 8 weeks after the application of continuous light and heavy forces for 4 weeks: A microcomputed-tomography study","volume":"136","author":"Cheng","year":"2009","journal-title":"Am. J. Orthod. Dentofac. Orthop."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"20190108","DOI":"10.1098\/rsif.2019.0108","article-title":"In vivo effects of different orthodontic loading on root resorption and correlation with mechanobiological stimulus in periodontal ligament","volume":"16","author":"Zhong","year":"2019","journal-title":"J. R. Soc. Interface"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1111\/edt.12868","article-title":"Effects of different treatment modalities on biomechanical behavior of maxillary incisors with external invasive cervical resorption at different progression levels","volume":"39","year":"2023","journal-title":"Dent. Traumatol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1080\/10255842.2021.2017904","article-title":"An analysis of the optimal intrusion force of the maxillary central incisor with root horizontal resorption using the finite element method and curve fitting","volume":"25","author":"Zhang","year":"2022","journal-title":"Comput. Methods Biomech. Biomed. Engin"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1111\/iej.13715","article-title":"Present status and future directions: Root resorption","volume":"55","author":"Patel","year":"2022","journal-title":"Int. Endod. J."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Deng, Y., Sun, Y., and Xu, T. (2018). Evaluation of root resorption after comprehensive orthodontic treatment using cone beam computed tomography (CBCT): A meta-analysis. BMC Oral Health, 18.","DOI":"10.1186\/s12903-018-0579-2"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Moga, R.A., Olteanu, C.D., Botez, M.D., and Buru, S.M. (2023). Assessment of the Orthodontic External Resorption in Periodontal Breakdown-A Finite Elements Analysis (Part I). Healthcare, 11.","DOI":"10.3390\/healthcare11101447"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Moga, R.A., Delean, A.G., Buru, S.M., Botez, M.D., and Olteanu, C.D. (2023). Orthodontic Internal Resorption Assessment in Periodontal Breakdown-A Finite Elements Analysis (Part II). Healthcare, 11.","DOI":"10.3390\/healthcare11192622"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Moga, R.-A., Olteanu, C.D., and Delean, A.G. (2024). The Amount of Orthodontic Force Reaching the Dental Pulp and Neuro-Vascular Bundle During Orthodontic Movements in the Intact Periodontium. Medicina, 60.","DOI":"10.3390\/medicina60122045"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Moga, R.-A., Olteanu, C.D., and Delean, A.G. (2024). The Importance of Boundary Conditions and Failure Criterion in Finite Element Analysis Accuracy\u2014A Comparative Assessment of Periodontal Ligament Biomechanical Behavior. Appl. Sci., 14.","DOI":"10.3390\/app14083370"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Moga, R.-A., Olteanu, C.D., and Delean, A.G. (2024). Periodontal Breakdown, Orthodontic Movements and Pulpal Ischemia Correlations\u2014A Comparison Between Five Study Methods. J. Clin. Med., 13.","DOI":"10.3390\/jcm13237062"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.ajodo.2003.11.026","article-title":"Physical properties of root cementum: Part 5. Volumetric analysis of root resorption craters after application of light and heavy orthodontic forces","volume":"127","author":"Chan","year":"2005","journal-title":"Am. J. Orthod. Dentofac. Orthop."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhao, D., Xue, K., Meng, J., Hu, M., Bi, F., and Tan, X. (2023). Orthodontically induced external apical root resorption considerations of root-filled teeth vs vital pulp teeth: A systematic review and meta-analysis. BMC Oral Health, 23.","DOI":"10.1186\/s12903-023-02982-4"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1007\/s00784-020-03467-2","article-title":"Numerical simulation of optimal range of rotational moment for the mandibular lateral incisor, canine and first premolar based on biomechanical responses of periodontal ligaments: A case study","volume":"25","author":"Wu","year":"2021","journal-title":"Clin. Oral Investig."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1294","DOI":"10.1080\/10255842.2019.1661390","article-title":"Investigation of effective intrusion and extrusion force for maxillary canine using finite element analysis","volume":"22","author":"Wu","year":"2019","journal-title":"Comput. Methods Biomech. Biomed. Engin."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1631\/jzus.B1700195","article-title":"A biomechanical case study on the optimal orthodontic force on the maxillary canine tooth based on finite element analysis","volume":"7","author":"Wu","year":"2018","journal-title":"J. Zhejiang Univ. Sci. B"},{"key":"ref_23","first-page":"103","article-title":"Root Resorption in Orthodontics","volume":"29","year":"2016","journal-title":"Turk. J. Orthod."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.cmpb.2008.09.004","article-title":"Correspondences of hydrostatic pressure in periodontal ligament with regions of root resorption: A clinical and a finite element study of the same human teeth","volume":"93","author":"Hohmann","year":"2009","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"653","DOI":"10.2319\/060806-234","article-title":"Periodontal ligament hydrostatic pressure with areas of root resorption after application of a continuous torque moment","volume":"77","author":"Hohmann","year":"2007","journal-title":"Angle Orthod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"12671","DOI":"10.1038\/s41598-022-16480-0","article-title":"Finite element and in vitro study on biomechanical behavior of endodontically treated premolars restored with direct or indirect composite restorations","volume":"12","author":"Comba","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1758736014520809","DOI":"10.1177\/1758736014520809","article-title":"Comparison of mechanical property and role between enamel and dentin in the human teeth","volume":"5","author":"Chun","year":"2014","journal-title":"J. Dent. Biomech."},{"key":"ref_28","first-page":"e71238","article-title":"Evaluating the Restoration of External Root Resorption Under Biomechanical Stress: A Finite Element Analysis","volume":"16","author":"Celebi","year":"2024","journal-title":"Cureus"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"D\u00fczg\u00fcn, S., Esim, E., Aslan, T., and Avc\u0131, A.T.E. (2025). Finite element analysis of stress in mandibular molars repaired after fractured instrument removal. BMC Oral Health, 25.","DOI":"10.1186\/s12903-025-05464-x"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"103903","DOI":"10.1016\/j.identj.2025.103903","article-title":"Thermal Behaviour of Teeth With Internal Root Resorption During Obturation and Enhancing Thermal Simulations: A Finite-Element Analysis","volume":"75","author":"Kabakci","year":"2025","journal-title":"Int. Dent. J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1841","DOI":"10.1080\/10255842.2021.1925255","article-title":"Analysis of stress in periodontium associated with orthodontic tooth movement: A three dimensional finite element analysis","volume":"24","author":"Jain","year":"2021","journal-title":"Comput. Methods Biomech. Biomed. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.jobcr.2024.04.012","article-title":"Stress distribution in endodontically treated external cervical resorption lesions restored with MTA and biodentine\u2014A finite element analysis","volume":"14","author":"Manaktala","year":"2024","journal-title":"J. Oral Biol. Craniofacial Res."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Rodrigues Fonseca Tavares, A., Aurelio de Carvalho, M., Cardoso Lazari-Carvalho, P., Rodrigues de Ara\u00fajo Estrela, L., Santos de Freitas Silva, B., Antoninha Del Bel Cury, A., and Rodrigues Ara\u00fajo Estrela, C. (2025). Teeth with External Apical Root Resorption Under Orthodontic Movement: An In Silico Analysis on Stress and Displacement. J. Orofac. Orthop., Available online: https:\/\/www.springermedizin.de\/teeth-with-external-apical-root-resorption-under-orthodontic-mov\/51672644.","DOI":"10.1007\/s00056-025-00620-y"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1186\/s40001-024-02228-1","article-title":"Effect of high trimline aligners on distalizing mandibular molars: A three-dimensional finite element study","volume":"29","author":"Su","year":"2024","journal-title":"Eur. J. Med. Res."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Su, R., Sun, J., Li, S., and Wang, W. (2025). Biomechanical effects of aligner trimline design and intrusion protocol on mandibular anterior teeth: A finite element study. BMC Oral Health, 25.","DOI":"10.1186\/s12903-025-07191-9"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"e495","DOI":"10.1016\/j.ajodo.2010.01.036","article-title":"Physical properties of root cementum: Part 18. The extent of root resorption after the application of light and heavy controlled rotational orthodontic forces for 4 weeks: A microcomputed tomography study","volume":"139","author":"Wu","year":"2011","journal-title":"Am. J. Orthod. Dentofac. Orthop."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.ajodo.2007.03.032","article-title":"Mechanical responses to orthodontic loading: A 3-dimensional finite element multi-tooth model","volume":"135","author":"Field","year":"2009","journal-title":"Am. J. Orthod. Dentofac. Orthop."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.joen.2023.10.007","article-title":"Evaluation of Fracture Strength after Repair of Cervical External Resorption Cavities with Different Materials","volume":"50","year":"2024","journal-title":"J. Endod."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"e1555","DOI":"10.4317\/jced.62050","article-title":"Survival of teeth with external cervical resorption after Internal and External Repair: A Systematic Review","volume":"16","author":"Sousa","year":"2024","journal-title":"J. Clin. Exp. Dent."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Yilmaz, A., Kabakci, A., and Helvacioglu Yigit, D. (2025). Impact of treatment modalities on stress distribution in maxillary incisors with varying levels of external cervical resorption: A finite element analysis. BMC Oral Health, 25.","DOI":"10.1186\/s12903-025-06562-6"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Flatten, J., Gedrange, T., Bourauel, C., Keilig, L., and Konermann, A. (2024). The Role of Bone and Root Resorption on the Biomechanical Behavior of Mandibular Anterior Teeth Subjected to Orthodontic Forces: A Finite Element Approach. Biomedicines, 12.","DOI":"10.3390\/biomedicines12091959"}],"container-title":["Journal of Clinical Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2077-0383\/15\/7\/2503\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T09:58:10Z","timestamp":1774432690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2077-0383\/15\/7\/2503"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,25]]},"references-count":41,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["jcm15072503"],"URL":"https:\/\/doi.org\/10.3390\/jcm15072503","relation":{},"ISSN":["2077-0383"],"issn-type":[{"value":"2077-0383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,25]]}}}