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Clinical Oral Investigations https://doi.org/10.1007/s00784-019-03016-6 ORIGINAL ARTICLE The effect of Alexander, Gianelly, Roth, and MBT bracket systems on anterior retraction: a 3-dimensional finite element study Mauro Cozzani 1 & Donia Sadri 2 & Ludovica Nucci 3 & Parsa Jamilian 4 & Amir Parham Pirhadirad 5 & Abdolreza Jamilian 6 Received: 8 November 2018 / Accepted: 10 July 2019 # Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract Objectives The aims of this study were to compare the effect of 4 bracket systems including Alexander, Roth, MBT, and Gianelly on upper anterior retraction and to quantify the amount of torque loss ratio in sliding mechanics by help of a 3-dimensional (3D) finite element method. Method and materials 3D FEM models were constructed in order to simulate anterior incisor retraction in first premolar extraction case. Displacement, stress, and strain on the incisal edge and apex of maxillary central incisor were calculated when 1-, 2-, and 3-N retraction forces were applied. Torque loss ratio was calculated by measuring the displacement of the teeth at crown tip and root apex in all 4 bracket systems on upper central incisor. Results Uncontrolled lingual crown tipping of the incisor was observed in all bracket systems. The crown moved lingually by 9.5 μm and the root labially by 4.5 μm in MBT system with 3-N retraction force. The amount of crown movement was 8 μm and the root displacement was 4 μm in Gianelly system with the same retraction force. Torque loss ratio was 1.46 in Alexander and Gianelly with 3N retraction force. However, the amount of torque loss ratio was 1.47 in MBT and Roth with the same retraction force. Conclusions and clinical Relevance Uncontrolled tipping was the least in Gianelly and was the highest in MBT. The amount of torque loss ratio was the lowest in Gianelly and Alexander systems and the amount of torque loss ratio was the highest in MBT system. Keywords Finite element analysis . Torque . Orthodontic brackets . Upper anterior segment . Biomechanics Introduction Retraction of the upper anterior dental segment is one of the main stages for correction of malocclusion. Anterior retraction * Donia Sadri [email protected] Mauro Cozzani [email protected] can be achieved using one of the two methods, either closing loops (frictionless mechanics) or sliding mechanics (frictional mechanics). Various studies have been carried out to evaluate the numerous biomechanical factors affecting tooth 2 Department of Oral and Maxillofacial Pathology, Faculty of Dentistry, Tehran Medical Sciences, Islamic Azad University, Tehran, Iran 3 Dental School, Multidisciplinary Department of Medical-Surgical and Dental Specialties, University of Campania Luigi Vanvitelli, Naples, Italy 4 International Baccalaureate Program, Danube International School, Vienna, Austria 5 Department of Bio Medical Engineering, Faculty of Bio Medical Engineering, Science and Research Branch, Cranio Maxillofacial Research Center, Islamic Azad University, Tehran, Iran 6 Department of Orthodontics, Faculty of Dentistry, Cranio Maxillofacial Research Center, Tehran Medical Sciences, Islamic Azad University, Tehran, Iran Ludovica Nucci [email protected] Parsa Jamilian [email protected] Amir Parham Pirhadirad [email protected] Abdolreza Jamilian [email protected] 1 Istituto Giuseppe Cozzani, La Spezia, Italy Clin Oral Invest Table 1 The material parameters used in the FE model Material Young’s modulus (MPa) Poisson’s ratio Tooth 20000 0.3 PDL 0.05 0.3 Alveolar bone Composite 2000 14200 0.3 0.3 Bracket Arch wire 200000 200000 0.3 0.3 movement in sliding mechanics, such as center of resistance of upper incisors, center of resistance of anterior arch segment, the amount of retraction force, friction, and flexural rigidity of the arch wire [1–8]. Torque loss is an important side effect of incisor retraction. It is very critical and important to maintain torque during anterior retraction, for which the point of force application plays a vital role . Different bracket systems with different prescriptions have been developed and are being employed in order to achieve the most appropriate torque in upper incisors. Nevertheless, the effect of various bracket systems and arch wire on anterior tooth movement in sliding mechanics has not been fully understood. The objectives of this study were to determine the effect of 4 bracket systems including Alexander, Gianelly, Roth, and MBT and arch wire dimension on anterior tooth movement and also to quantify the amount of torque loss during anterior retraction by means of a 3-dimensional finite element (3D FEM) model. Material and methods A 3D model of maxilla was prepared according to the method described by Tominaga et al. . The image of 12 maxillary teeth including incisors, canines, and premolars, first and second molars, was constructed by a cone beam computed tomography (CBCT) scanner (GE Medical Systems, HiSpeed QX/i, Milwaukee, WI, USA). These data were exported to 3D Table 2 Configuration of Alexander, Roth, MBT, and Gianelly systems Wire Bracket Slot Prescription Central incisor Lateral incisor Cuspid 2nd premolar 1st molar image processing software (Mimics Innovation Suite 188.8.131.525 Research (Materialise, Leuven, Belgium). The 3D solid model along with alveolar bone, bracket design, and wire was formed and exported to a 3D FEM program (ABAQUS 6.10 software) using FE analysis preprocess and postprocess software (Dassault systems). Periodontal ligament was considered as a uniform structure with 0.2-mm width at all points. Bilateral maxillary first premolars were not constructed. Canines were replaced in the tooth space of first premolars. FE was designed in order to simulate anterior incisor retraction in first premolar extraction case. Young’s modulus and Poisson’s ratio for the tooth, periodontal ligament, alveolar bone, composite, bracket, and arch wire were inserted according to Tominaga et al. . Each bracket prescription was created by the same software and according to the manufacturer’s guidelines on the incorporated tip and torque. These material parameters are shown in Table 1. A FE mesh was constructed to make a node-to-node connection between tooth, periodontal ligament, and alveolar bone. A FE mesh of the wire was also generated separately to allow the wire to slide through the bracket slots. The elements used to recreate the materials were linear tetrahedral type defined by C3D4. Four 3D solid models, including Alexander, Roth, MBT, were designed to allow the sliding of the wire through the 4 bracket systems with the following prescriptions which are shown in Table 2 in accordance with the manufacturer’s instructions. Force application and incisor retraction The FE model was restricted in 6 degrees of freedom at the bottom of the alveolar bone to avoid sliding movement of the entire model and the coefficient of friction between the wire and the brackets was set at 0.2. Under these conditions, horizontal retraction forces of 1, 2, and 3 N were applied on each end of arch wire respectively . FEM analysis was performed using a 3D FE program (ABAQUS 6.10 software). The incisal edge and the apex of maxillary central incisor were selected as the region of interest in this research and the values for maximum stress, strain, and displacement were calculated 0.018 × 0.022 0.018 × 0.025(Ant) 0.017 × 0.025 0.018 × 0.025 0.019 × 0.025 0.022 × 0.028 0.022 × 0.028(Post) Gianelly Torque Tip 12 5 8 9 0 7 0 0 0 0 Alexander Torque 15 9 −3 −8 − 10 Roth Torque 12 8 0 −7 − 14 Tip 5 9 10 4 −6 Tip 5 9 11 0 0 MBT Torque 17 10 0 −7 − 14 Tip 4 8 8 0 0 Clin Oral Invest Table 3 The maximum amount of stress (Pa), displacement (μm), and strain on the maxillary central incisor with 1- until 3-N retraction force Newton brand Gianelly (bidimensional) Alexander Roth MBT 1 2 3 S D E S D E S D E 1.355 × 10−1 1.946 × 10−1 1.399 × 10−1 1.396 × 10−1 2.6 2.9 3.1 3.1 6.752 × 10−7 9.642 × 10−7 6.981 × 10−7 6.971 × 10−7 2.711 × 10−1 3.892 × 10−1 2.798 × 10−1 2.793 × 10−1 5.2 5.9 6.3 6.3 1.35 × 10−6 1.928 × 10−6 1.39 × 10−6 1.394 × 10−6 4.066 × 10−1 5.838 × 10−1 4.197 × 10−1 4.189 × 10−1 7.9 8.8 9.4 9.4 2.025 × 10−6 2.893 × 10−6 2.095 × 10−6 2.092 × 10−6 in each bracket systems for each retraction force in 4 bracket systems. In this study, linear solver was used and for a better understanding the teeth movement, all of the displacements were magnified 56 times, and the displacements of the central incisor were focused on. Displacement, von Misses stresses, and strain on the incisal edge and root apex of upper central incisor in 4 bracket systems were compared. The torque loss ratio was calculated by measuring the difference between the initial displacement of crown tip and root apex, if both the crown tip and root apex moved equally, it showed the translation, i.e., the bodily movement. The torque loss ratio was also calculated by adding the distance between the initial displacement of crown tip and root apex, if both the crown tip and root apex moved unequally which shows uncontrolled tipping. Then this amount was divided to the amount of crown movement in order to obtain torque loss ratio [9, 12]. Results After analyzing models, the amount of displacement, von Misses stresses, and strain were calculated for incisal edge and root apex of central maxillary incisors in four bracket systems. The peak values of displacement micrometer (μm), stresses (Pa), and strain on incisal edge of maxillary central incisor are shown under continuous retraction forces of 1, 2, and 3 N for 4 bracket systems including Alexander, Roth, MBT, and Gianelly (bidimensional technique) in Table 3. Full FE model including force vectors and further boundary conditions can be seen in Fig. 1. This study showed that the amount of incisal edge displacement and apex root movement were increased by enhancing the retraction force from 1 to 3 N Figs. 2, 3, and 4. The amount of incisal edge displacement and apex movement were increased from 1 to 3 N of retraction forces in Gianelly, Alexander, Roth, and MBT respectively. Gianelly had uncontrolled tipping, with 8 μm of crown movement and 4 μm of root apex in the direction of force application with 3 N of retraction forces. MBT had uncontrolled tipping, with 3 μm of crown movement and 4.5 μm of root apex in the direction of force application with 3 N of retraction forces. Gianelly had the lowest uncontrolled tipping and MBT had the highest tipping in all 1–3 N of retraction forces on the apex and incisal edge Figures 2, 3, 4, and 5.. In this study, all of the teeth had uncontrolled tipping; in other words, crown and root apex moved unequally; therefore, the torque loss ratio was calculated by adding the distance between the initial displacement of crown tip and root apex. Then this amount was divided to the amount of crown movement. The amount of torque loss ratio in all bracket systems with 1, 2, and 3 N of retraction force was seen in Fig. 6. It shows the torque loss ratio was 1.464 and 1.465 with 3-N retraction force in Alexander and Gianelly respectively and it was equally the same. However, MBT had the highest torque loss ratio and this amount was 1.478 with the same retraction force. Figures 7 and 8 show incisor displacement in MBT and Gianelly with 3 N of retraction force respectively. Discussion Fig. 1 Full FE model including force vectors and further boundary conditions One of the major challenges is to clarify the complexities involved in the response of teeth to the forces and the moments during anterior retraction. Finite element analysis was Clin Oral Invest Fig. 2 The amount of incisal edge of central maxillary incisor movement with 1- until 3-N retraction force in 4 bracket systems selected for the current study because of the complexity of the clinical design, variability in dental differences, multiplicity of elements needed to be matched, individual response to force applied, and the potential effect of other variables. Moreover, FE is nearest that one possibly can get in simulating the oral environment in vitro and the actual displacement, stress, and strain can be measured [9, 13]. This model simulates a first premolar extraction case. The canines were retracted individually in place of first bicuspid extraction cases and then anterior retraction was started to simulate the real condition on clinical situation. In this study, three levels of force (1, 2, 3 N) were applied because different techniques utilize different level of force for en masse and/or incisor retraction. – – Gianelly (bidimensional technique) utilizes a sliding mechanic: 3 N applied with a superelastic NiTi coil for incisor retraction; Alexander utilizes a .018 × .025 closing loop for incisor retraction: We estimated on the incisors a force at the activation around 3 N and a decay to 1 N during the deactivation period; Fig. 3 The amount of apex root movement of central maxillary incisor with 1- until 3-N retraction force in 4 bracket systems – – MBT utilizes a sliding mechanic: an Alastik module with 1 N for en masse retraction. We estimated a force of 1 N on the incisors; Roth utilized a double keyhole loop in a .019 × .025 wire for en masse retraction, more recently, a sliding mechanic with 1.5 N applied with a NiTi superelastic coil: We estimated, for this set-up, a force of 1 N on the incisor. This study showed that each bracket system has a significant impact on anterior tooth retraction in sliding mechanics. In this study, sliding method was used for anterior retraction and in sliding mechanics, friction occurs at the interference between bracket slot and arch wire. The amount of incisal edge displacement and apex movement were increased by enhancing the force. The minimum displacement on incisal edge of upper central incisor was found in Gianelly system and the maximum displacement was shown in MBT system. The results of our study revealed that the anterior teeth exhibited various amount of uncontrolled tipping. Uncontrolled tipping was observed as there was more of crown movement than of a root apex in the direction of force application. MBT had more of crown movement (9.5 μm) than of a root Clin Oral Invest Fig. 4 The amount of incisal edge of central maxillary incisor with 1- until 3-N retraction force in 4 bracket systems Fig. 5 The amount of apex root movement of central maxillary incisor with 1- until 3-N retraction force in 4 bracket systems apex displacement (4.5 μm) in the sagittal plane which results in maximum uncontrolled tipping with 3 N of retraction force. The amount of uncontrolled tipping was increased from Gianelly, Alexander, and Roth to MBT respectively in all retraction forces Figs. 3 and 4. There were some differences in the amount of uncontrolled tipping between the four bracket systems during anterior retraction. This finding is due to this fact that the play between arch wire and bracket slot was greater in MBT than Gianelly. The existence of play between Fig. 6 The amount of torque loss on the central maxillary incisor with 1- until 3-N retraction force in 4 bracket systems bracket slot and arch wire should be considered to predict the tooth movement. Similarly, Tominaga  found that the play between the wire and the bracket slot has an excessive impact on the anterior tooth movement. FE simulations clarified the type of tooth movement in 4 bracket systems, although friction arises at the bracket arch wire interface in sliding mechanics. Many measurements of the friction force have been carried out for various combinations of brackets and arch wires. The friction dissipates some Clin Oral Invest Fig. 7 Anterior retraction after 3 N of retraction force in MBT system of the force and reduces the speed of tooth movement [5, 6, 15, 16]. The torque loss was calculated by adding the distance between the initial displacement of crown tip and root apex, if both the crown tip and root apex moved unequally. Then this amount was divided to the amount of crown movement. In this study, the crown of upper incisors had uncontrolled tipping; in other words, crown tip and root moved unequally. Figure 6 shows the amount of torque loss ratio in 4 bracket systems with 1 until 3 N of retraction force. The amount of torque loss ratio was the lowest one in Gianelly and Alexander Fig. 8 Anterior retraction after 3 N of retraction force in Gianelly system systems and they were almost the same. The amount of torque loss was highest in MBT. FEM is a suitable method, but it has its limitations. It cannot perfectly represent the human skull and the result of the current research is only valid for patients with similar root lengths, root angulations, root morphology, bone density, crown sizes etc. It is necessary to consider anatomic parameters that is why a clinical study is needed to confirm these findings from this FE study. The results only represent the very initial response of the system to the force application (THE crown moved lingually Clin Oral Invest by 9.5 μm in MBT system with 3-N retraction force.) and not the actual process of gap closure, where other factors (especially rigidity of the different arch wire dimensions) may also play a role in torque control (a negative curve of spee as a result of a less rigid arch wire during gap closure will also result in loss of torque of the incisors). It should, also, be taken into consideration that brackets and wires’ nominal values differ from real measures; moreover, real measures are different from company to company . 5. 6. 7. Conclusion & The amount of incisal edge and root movement were increased by enhancing the amount of force from 1 to 3 N of retraction force in all bracket systems. Gianelly had the lowest displacement on the incisal edge and root apex of upper central incisor in 1, 2, and 3 N of retraction force and MBT had the highest movement on the incisal edge and root apex of the same tooth in the same retraction forces. Uncontrolled tipping was the least in Gianelly and was the highest one in MBT. Gianelly and Alexander systems had the lowest torque loss ratio and MBT had the highest one. & & & 8. 9. 10. 11. Acknowledgments The authors wish to express appreciation to support of the American Orthodontics (USA) and Dentaurum Company (Germany) for supporting the bracket geometry basis for the FE models. 12. Compliance with ethical standards 13. Conflict of interest The authors declare that they have no conflict of interest. 14. Ethical approval This article does not contain any studies with human participants or animals performed by any of the authors. Informed consent For this type of study, formal consent is not required. 15. References 1. 2. 3. 4. 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