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Symmetry 2019, 11(2), 202;

On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

Department of Applied Oral Sciences of the Faculty of Dentistry, University of Hong Kong, Hong Kong, China
University Center of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Murcia, Spain
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203 Cartagena, Región de Murcia, Spain
Department of Dermatology, Stomatology, Radiology and Physical Medicine, Morales Meseguer General Universitary Hospital, Avda. Marqués de los Vélez, 30008 Murcia, Spain
Author to whom correspondence should be addressed.
Received: 17 December 2018 / Revised: 1 February 2019 / Accepted: 3 February 2019 / Published: 11 February 2019
(This article belongs to the Special Issue New Trends in Dynamics)
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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–Whitney 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. View Full-Text
Keywords: fractal dimension; nasopalatine foramen; cone beam computed tomography fractal dimension; nasopalatine foramen; cone beam computed tomography

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Bornstein, M.M.; Fernández-Martínez, M.; Guirao, J.L.G.; Gómez-García, F.J.; Guerrero-Sánchez, Y.; López-Jornet, P. On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis. Symmetry 2019, 11, 202.

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