{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:01Z","timestamp":1760239981584,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,11]],"date-time":"2019-02-11T00:00:00Z","timestamp":1549843200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The objective of the present paper is to describe all the anatomical considerations surrounding the nasopalatine foramen by relating them to the study of bone structure density via an accurate fractal dimension analysis in that area. We consecutively selected a sample of 130 patients, all of them with cone beam computed tomography (CBCT) images performed for treatment needs. We chose a specific window (ROI), which coincides with an axial cut at the level of the anterior nasal spine. Different anthropometric measurements were analyzed and a novel fractal dimension analysis was performed. Our sample consisted of 130 patients and was divided into two groups: group one (consisting of 65 subjects without loss of teeth) and group two (consisting of 65 patients with the absence of some teeth). In the sample, 52.31% were women (68 people). Mann\u2013Whitney tests were applied to obtain the statistical results. The mean age of the patients in that sample was     53.67     years with a standard deviation of     8.20     years. We conclude that fractal dimension, a mathematical invariant, behaves symmetrically for binary images from the CBCT scanners of each subject of our sample of study. We also conclude that there were no significant differences between all the anthropometric measures used neither in the subjects themselves nor in the different groups. Therefore, some patterns of symmetry were appreciated at a complete range of levels.<\/jats:p>","DOI":"10.3390\/sym11020202","type":"journal-article","created":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T03:18:20Z","timestamp":1549941500000},"page":"202","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7773-8957","authenticated-orcid":false,"given":"Michael M.","family":"Bornstein","sequence":"first","affiliation":[{"name":"Department of Applied Oral Sciences of the Faculty of Dentistry, University of Hong Kong, Hong Kong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuel","family":"Fern\u00e1ndez-Mart\u00ednez","sequence":"additional","affiliation":[{"name":"University Center of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Murcia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2788-809X","authenticated-orcid":false,"given":"Juan L. G.","family":"Guirao","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada y Estad\u00edstica, Universidad Polit\u00e9cnica de Cartagena, Hospital de Marina, 30203 Cartagena, Regi\u00f3n de Murcia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco J.","family":"G\u00f3mez-Garc\u00eda","sequence":"additional","affiliation":[{"name":"Department of Dermatology, Stomatology, Radiology and Physical Medicine, Morales Meseguer General Universitary Hospital, Avda. Marqu\u00e9s de los V\u00e9lez, 30008 Murcia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yolanda","family":"Guerrero-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Department of Dermatology, Stomatology, Radiology and Physical Medicine, Morales Meseguer General Universitary Hospital, Avda. Marqu\u00e9s de los V\u00e9lez, 30008 Murcia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3314-8613","authenticated-orcid":false,"given":"P\u00eda","family":"L\u00f3pez-Jornet","sequence":"additional","affiliation":[{"name":"Department of Dermatology, Stomatology, Radiology and Physical Medicine, Morales Meseguer General Universitary Hospital, Avda. Marqu\u00e9s de los V\u00e9lez, 30008 Murcia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,11]]},"reference":[{"key":"ref_1","unstructured":"G\u00f3mez de Ferraris, M.E., and Campos Mu\u00f1oz, A. (2009). Histolog\u00eda, Embriolog\u00eda e Ingenier\u00eda Tisular Bucodental, Panamericana."},{"key":"ref_2","unstructured":"Velayos Santana, J.L. (2007). Anatom\u00eda de la Cabeza para Odont\u00f3logos, Panamericana."},{"key":"ref_3","unstructured":"L\u00f3pez Mu\u00f1iz, A., Hern\u00e1ndez Gonz\u00e1lez, L.C., del Valle Soto, M., Su\u00e1rez Garnacho, S., Carbajo P\u00e9rez, E., and Junceda Moreno, J. (2008). Anatom\u00eda Topogr\u00e1fica Humana, Ediciones de la Universidad de Oviedo."},{"key":"ref_4","first-page":"229","article-title":"Preservaci\u00f3n del reborde alveolar. Por qu\u00e9 y cu\u00e1ndo","volume":"17","author":"Griffin","year":"2007","journal-title":"Periodoncia y Osteointegraci\u00f3n"},{"key":"ref_5","unstructured":"Chimenos Kustner, E., Ribera Uribe, M., and L\u00f3pez L\u00f3pez, J. (2012). Gerodontolog\u00eda, Sociedad Espa\u00f1ola de Gerodontolog\u00eda."},{"key":"ref_6","unstructured":"Misch, C.E. (2008). Contemporary Implant Dentistry, Mosby Elsevier."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"794","DOI":"10.4329\/wjr.v6.i10.794","article-title":"Recent advances in imaging technologies in dentistry","volume":"6","author":"Shah","year":"2014","journal-title":"World J. Radiol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1111\/j.1600-0501.2010.02010.x","article-title":"Morphology of the nasopalatine canal and dental implant surgery: A radiographic analysis of 100 consecutive patients using limited cone beam computed tomography","volume":"22","author":"Bornstein","year":"2011","journal-title":"Clin. Oral Implants Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1111\/j.1600-051X.2009.01429.x","article-title":"Macro- and micro-anatomical, histological and computed tomography scan characterization of the nasopalatine canal","volume":"36","author":"Liang","year":"2009","journal-title":"J. Clin. Periodontol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"527","DOI":"10.5603\/FM.a2018.0013","article-title":"Evaluation of anatomical and morphological characteristics of the nasopalatine canal in a Turkish population by cone beam computed tomography","volume":"77","author":"Hakbilen","year":"2018","journal-title":"Folia Morphol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/0030-4220(92)90222-C","article-title":"Fractal dimension from radiographs of peridental alveolar bone","volume":"74","author":"Ruttimann","year":"1992","journal-title":"Oral Surg. Oral Med. Oral Pathol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"423","DOI":"10.21042\/AMNS.2016.2.00036","article-title":"Applied mathematics and nonlinear sciences in the war on cancer","volume":"1","author":"Fitzpatrick","year":"2016","journal-title":"Appl. Math. Nonlinear Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"375","DOI":"10.21042\/AMNS.2018.2.00029","article-title":"Optimal control problems for differential equations applied to tumor growth: State of the art","volume":"3","author":"Rojas","year":"2018","journal-title":"Appl. Math. Nonlinear Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4533","DOI":"10.3233\/JIFS-169772","article-title":"An intelligent system to study the fractal dimension of trabecular bones","volume":"35","year":"2018","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"437","DOI":"10.21042\/AMNS.2016.2.00037","article-title":"A survey on fractal dimension for fractal structures","volume":"1","year":"2016","journal-title":"Appl. Math. Nonlinear Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/202\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:31:09Z","timestamp":1760185869000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,11]]},"references-count":15,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["sym11020202"],"URL":"https:\/\/doi.org\/10.3390\/sym11020202","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,2,11]]}}}