{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T03:02:13Z","timestamp":1789614133360,"version":"build-2803163510"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T00:00:00Z","timestamp":1789516800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T00:00:00Z","timestamp":1789516800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["J of Oral Rehabilitation"],"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Mandibular protrusion is traditionally described using a single sagittal angular parameter, which does not capture directional variation along the protrusive trajectory.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Objective<\/jats:title>\n                    <jats:p>To develop a rule\u2010based geometric framework for analysing directional organisation of mandibular protrusion and characterising directional variation of protrusive trajectories.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>Sixty\u2010four protrusive trajectories were analysed using Global Protrusive Dynamics (GPD). Internal points of maximum directional deflection were identified within proportional search windows (25\u201350\u201325), defining four trajectory segments (S0\u2013S4). Segmental directional angles were calculated for condylar and incisal trajectories. Robustness was assessed using independent procedures.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Segmental analysis revealed non\u2010uniform directional variation along the protrusive trajectory. Significant differences were observed between early (S1) and late (S4) trajectory segments, with large effect sizes. Median segmental directional angles showed progressive reduction along the condylar pathway. The incisal\u2013condylar relationship also varied across segments. These patterns were consistent across workflows and stable under sensitivity analyses.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>Mandibular protrusion can be described as a structured spatial trajectory characterised by segment\u2010dependent directional variation rather than a single sagittal inclination. The GPD framework provides a reproducible geometric approach for describing protrusive trajectory organisation and may support future longitudinal comparison of trajectory patterns under different functional conditions.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1111\/joor.70309","type":"journal-article","created":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T02:17:04Z","timestamp":1789611424000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Segmental Geometry of Protrusive Trajectories"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-4254-442X","authenticated-orcid":false,"given":"Eduardo","family":"Crespo Bonnet","sequence":"first","affiliation":[{"name":"Private Clinical Practice in Occlusion and Temporomandibular Disorders  Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5318-1779","authenticated-orcid":false,"given":"Alejandro","family":"Mart\u00ednez Garc\u00eda","sequence":"additional","affiliation":[{"name":"Albacete Research Institute of Informatics  Albacete Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-7246-2215","authenticated-orcid":false,"given":"Eduardo","family":"Crespo S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Private Dental Practice  Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1968-7108","authenticated-orcid":false,"given":"Enrique","family":"Arias\u2010Ant\u00fanez","sequence":"additional","affiliation":[{"name":"Department of Computing Systems University of Castilla\u2010La Mancha  Ciudad Real Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2757-6619","authenticated-orcid":false,"given":"Rub\u00e9n","family":"Agust\u00edn\u2010Panadero","sequence":"additional","affiliation":[{"name":"Department of Stomatology, Faculty of Medicine and Dentistry Universitat De Val\u00e8ncia (UV)  Val\u00e8ncia Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,16]]},"reference":[{"key":"e_1_2_11_2_1","first-page":"1757","article-title":"Biomechanics of the Jaw System","volume":"76","author":"Koolstra J. H.","year":"1997","journal-title":"Journal of Dental Research"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1177\/00220345000790080701"},{"key":"e_1_2_11_4_1","first-page":"963","article-title":"Measurement of Normal and Pathological Mandibular and Temporomandibular Joint Kinematics: A Systematic Review","volume":"47","author":"Minagi S.","year":"2020","journal-title":"Journal of Oral Rehabilitation"},{"key":"e_1_2_11_5_1","first-page":"1","article-title":"The Problem of Articulation","volume":"52","author":"Gysi A.","year":"1910","journal-title":"Dental Cosmos"},{"key":"e_1_2_11_6_1","first-page":"620","article-title":"A Research Report on Articulator Design","volume":"5","author":"McCollum B. B.","year":"1955","journal-title":"Journal of Prosthetic Dentistry"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1096-8644(199805)106:1<35::AID-AJPA3>3.0.CO;2-C"},{"key":"e_1_2_11_8_1","first-page":"10","article-title":"The Dynamic Mechanical Viscoelastic Properties of the Temporomandibular Joint Disc","volume":"95","author":"Ghazanfari S.","year":"2019","journal-title":"Journal of the Mechanical Behavior of Biomedical Materials"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmbbm.2021.104522"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1259\/dmfr.20190464"},{"key":"e_1_2_11_11_1","volume-title":"The Masticatory Organ: Functions and Dysfunctions","author":"Slavicek R.","year":"2002"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jdent.2024.105534"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1259\/dmfr.20180162"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2021.106299"},{"key":"e_1_2_11_15_1","first-page":"481","article-title":"Measurements of Sagittal Condylar Inclination: Intraindividual Variations","volume":"40","author":"\u010cimi\u0107 S.","year":"2022","journal-title":"Cranio"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.prosdent.2024.05.014"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.3389\/fdmed.2025.1654118"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.3390\/jcm13185567"},{"key":"e_1_2_11_19_1","first-page":"49","article-title":"Kinematic and Kinetic Patterns in Human Gait: Variability and Compensating Effects","volume":"16","author":"Winter D. A.","year":"1983","journal-title":"Journal of Biomechanics"}],"container-title":["Journal of Oral Rehabilitation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/joor.70309","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/joor.70309","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/joor.70309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T02:17:06Z","timestamp":1789611426000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/joor.70309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,16]]},"references-count":18,"alternative-id":["10.1111\/joor.70309"],"URL":"https:\/\/doi.org\/10.1111\/joor.70309","archive":["Portico"],"relation":{},"ISSN":["0305-182X","1365-2842"],"issn-type":[{"value":"0305-182X","type":"print"},{"value":"1365-2842","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,16]]},"assertion":[{"value":"2026-04-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-08-22","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"joor.70309"}}