{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T06:08:24Z","timestamp":1788761304135,"version":"build-2803163510"},"reference-count":47,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T00:00:00Z","timestamp":1788739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Bioeng. Biotechnol."],"abstract":"<jats:sec>\n                    <jats:title>Introduction<\/jats:title>\n                    <jats:p>Investigating the stress distribution generated by orthodontic forces within the periodontal ligament (PDL) is critical for quantifying mechanical stimuli, correlating them with subsequent histological responses, and ultimately identifying evidence-based optimal force levels. This study aimed to evaluate the combined biomechanical effects of alveolar bone height loss, tooth movement type, and alveolar bone density on the initial retraction of the maxillary central incisor, and to quantify the weighting of each factor on PDL stress.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>A three-dimensional (3D) finite element model of the maxilla, dentition, PDL, and orthodontic appliances was constructed based on cone-beam computed tomography (CBCT) data. Eighty experimental conditions were established by combining five levels of alveolar bone height loss (0\u20134\u00a0mm), four tooth movement types, and four alveolar bone density levels (simulated via cortical bone Young\u2019s modulus: 12,500\u201327,500\u00a0MPa). A 1\u00a0N bilateral retraction force was applied. The initial displacements of the crown and root and the maximum PDL von Mises stress were calculated. Multiple linear regression was used to quantify the factor contributions.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      Alveolar bone height loss significantly increased both tooth displacement and PDL stress. Uncontrolled and controlled tipping resulted in greater sagittal retraction and root intrusion, whereas bodily and controlled root movements were associated with more distolingual rotation. However, bone density affected displacement but had no significant effect on PDL stress. The regression model (R\n                      <jats:sup>2<\/jats:sup>\n                      = 0.80) revealed that tooth movement types exerted the strongest influence on PDL stress, followed by alveolar bone height loss (\u03b2 = 0.535,\n                      <jats:italic>p<\/jats:italic>\n                      &amp;lt; 0.05). All conditions, except for 4\u00a0mm bone loss combined with uncontrolled tipping, exhibited PDL stresses below the 0.026\u00a0MPa safety threshold.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>These findings provided novel quantitative biomechanical evidence regarding the combined effects of these variables and could guide individualized force control strategies and the development of AI-assisted orthodontic decision-making systems.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.3389\/fbioe.2026.1895763","type":"journal-article","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T05:34:37Z","timestamp":1788759277000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Combined effects and weight analysis of factors affecting initial maxillary central incisor retraction: a three-dimensional finite element study"],"prefix":"10.3389","volume":"14","author":[{"given":"Feng","family":"Feng","sequence":"first","affiliation":[{"name":"Department of Stomatology, Qingdao Hospital, University of Health and Rehabilitation Sciences (Qingdao Municipal Hospital)","place":["Qingdao, Shandong, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bin","family":"Xing","sequence":"additional","affiliation":[{"name":"Department of Stomatology, Qingdao Women and Children\u2019s Hospital, Qingdao University","place":["Qingdao, Shandong, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yucheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Orthodontics, Qingdao University Affiliated Hospital","place":["Qingdao, Shandong, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuheng","family":"Liu","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Computer Aided Design and Computer Graphics (CAD&CG), College of Computer Science and Technique, Zhejiang University","place":["Hangzhou, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yicong","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Stomatology, Qingdao Huanghai University Stomatological Hospital","place":["Qingdao, Shandong, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wen","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Stomatology, Qilu Hospital (Qingdao), Cheeloo College of Medicine, Shandong University","place":["Qingdao, Shandong, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,9,7]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"212","DOI":"10.2319\/041812-325.1","article-title":"Morphometric evaluation of changes in the alveolar bone and roots of the maxillary anterior teeth before and after en masse retraction using cone-beam computed tomography","volume":"83","author":"Ahn","year":"2013","journal-title":"Angle Orthod."},{"key":"B2","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/0889-5406(88)90292-2","article-title":"The effect of orthodontic treatment on periodontal bone support in patients with advanced loss of marginal periodontium","volume":"93","author":"Artun","year":"1988","journal-title":"Am. 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