Tridimensional finite element analysis of teeth movement induced by different headgear forces

Maruo et al. Progress in Orthodontics (2016) 17:18 DOI 10.1186/s40510-016-0130-4 RESEARCH Open Access Tridimensional finite element analysis of teeth movement induced by different headgear forces Ivan Toshio Maruo1, Hiroshi Maruo2, Armando Yukio Saga1, Dauro Douglas de Oliveira3, Marco André Argenta4 and Orlando Motohiro Tanaka5,6* Abstract Background: This study aimed to simulate the actions of low-pull (LP), high-pull (HP), and combined pull (CP) headgears (HGs) and to analyze tooth movement tendencies through finite element analysis. Methods: Tomographic slices of a human maxilla with complete permanent dentition were processed by reconstruction software, and the triangular surface mesh was converted into non-uniform rational B-spline (NURBS) curves. An HG facial bow was also modulated in 3D. The teeth and bone were considered to have isotropic and linear behavior, whereas the periodontal ligament was considered to have non-linear and hyperelastic behavior. Data regarding the application points, directions and magnitudes of forces were obtained from the literature and from a dolichofacial patient with class II, division 1 malocclusion, who was treated with a CP HG. Results: The CP HG promoted 37.1 to 41.1 %, and the HP HG promoted 19.1 to 31.9 % of LP distalization. The HP HG presented the highest intrusion, and the LP HG presented the highest extrusion of the first molar. The LP HG contracted the distal side, and the HP and CP HGs contracted the lingual and distobuccal roots of the second molar to a lesser degree. Conclusions: The LP HG promotes the greatest distalization, followed by the CP and HP HGs; the LP HG causes greater extrusion of the first molar, and the HP HG causes greater intrusion of the first molar. The LP HG causes greater contraction of the second molar than the HP HG. Keywords: Extraoral traction appliances, Finite element analysis, Tooth movement Background Although dental distalizers and skeletal temporary anchorage devices are available, the headgear (HG) appliance is an effective treatment for class II malocclusions in growing patients [1] and is utilized by more than half of orthodontists [2]. HG can be utilized with low (or cervical) pull (LP) [3], high (or parietal) pull (HP) [4], or combined (cervical and parietal) pull (CP) [5]. While unilateral forces of 250 to 500 gf promote orthopedic-orthodontic effects (i.e., * Correspondence: 5 Graduate Program in Orthodontics, Pontifícia Universidade Católica do Paraná, School of Life Sciences, R. Imaculada Conceição, 1155 Curitiba, Brazil 6 Post-Doctoral fellowship at The Center for Advanced Dental Education, Saint Louis University, Saint Louis, MO, USA Full list of author information is available at the end of the article restrain maxillary growth), weaker forces induce exclusively orthodontic effects [6]. The concepts of applied mechanics can be used to study dental movement induced by HGs [7]. However, as this methodology does not account for the biological properties of the periodontal ligament, teeth and bone, its results are limited. Cephalometric clinical studies [4, 5, 8], which compare initial and final results and facilitate patient follow-up using medical records, are useful but also have limitations. As their samples consist of growing patients, it is difficult to isolate appliance effects from inherent craniofacial growth, as well as to distinguish orthopedic from orthodontic effects. In addition, there is the possibility of error when performing radiographs, cephalometric tracings, and measurements [9]. © 2016 The Author(s). Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Maruo et al. Progress in Orthodontics (2016) 17:18 In an attempt to overcome these limitations, finite element analysis (FEA) may be used. FEA is used to predict stress effects on mini-implants and surrounding bone [10], to determine the stresses in bracket-cement-enamel systems [11], to assess the effects of rapid maxillary expansion on the airway flow rate [12], and to evaluate the effects of orthodontic devices on tooth displacement trends. FEA also [13] provides information about the distributions and vector directions of the principal stresses on the periodontal ligament [14–16] and along bone structures [17–19]. By applying FEA, it is possible to shape and analyze dentomaxillofacial structures by dividing complex structures into smaller sections called elements, in which physical properties are applied to dictate an object’s response to an external stimulus, such as orthodontic force [20]. Although the orthopedic effects of different pulls of HGs have been studied through FEA [21], their orthodontic effects in complete permanent dentition have not received the same attention. Thus, the objectives of this study were to simulate the actions of LP, HP, and CB HGs and to analyze teeth movement tendencies using FEA. Methods Teeth and maxilla modeling This study was approved by the Research Ethics Committee of Pontifical Catholic University of Paraná. A dry human skull with complete permanent dentition (except for the absence of third molars) and without caries or restorations was obtained from the Anatomy Department of (omitted). To construct the geometry, the maxilla region below the palatine plane and anterior to the pterygopalatine fossae of the skull was precisely reconstructed based on tomographic images obtained by cone beam computerized tomography (Classic i-CAT®, Imaging Sciences, Hatfield, PA) at 120 kVp, 0.5 mm nominal focal point size, 14 bits of grayscale dynamic range, and 0.4 mm voxel size, producing 256 slices with 0.25 mm thickness, and converted into exportable DICOM files. Tomographic slices were processed by digital technology, delimiting cortical and cancellous bone and the enamel, dentin, and pulp layers. These limits were utilized to generate 3D geometry by using an assisted design program (Simpleware®, Innovation Centre, Exeter, UK). The generated solid was exported to the Solidworks® program (Dessault Systèmes Solidworks Corp., Concord, MA) to convert the surface mesh into non-uniform rational B-spline (NURBS) curves. This conversion allowed better manipulation and control of generated curves and surfaces. These data were exported to ANSYS® v. 12.1 (Swanson Analysis System Inc., Canonsburg, PA). The centers of resistance of the first and second molars were assumed to be at the trifurcation of the roots [7]. The centers of resistance of the other teeth were Page 2 of 9 assumed to be at a point 0.4 times the distance from the alveolar crest to the apex [7]. Each tooth was divided into pulp, dentine, and enamel, and the alveol (...truncated)