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Comparative Numerical Analysis between Two Types of Orthodontic Wire for the Lingual Technique, Using the Finite Element Method

Comparative Numerical Analysis between Two Types of Orthodontic Wire for the Lingual Technique,... Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 6658039, 15 pages https://doi.org/10.1155/2021/6658039 Research Article Comparative Numerical Analysis between Two Types of Orthodontic Wire for the Lingual Technique, Using the Finite Element Method 1 2 Rosa Alicia Hernández-Vázquez , Rodrigo Arturo Marquet-Rivera , 2 2 Octavio Alejandro Mastache-Miranda , Angel Javier Vázquez-López , 2 2 Salvador Cruz-López , and Juan Alejandro Vázquez-Feijoo Universidad Politécnica del Valle de México, Departamento de Mecatrónica, Av. Mexiquense s/n Esquina Av. Universidad Politécnica, Col. Villa Esmeralda, Tultitlán, C.P. 54910 Estado de México, Mexico Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica, Sección de Estudios de Posgrado e Investigación, Unidad Profesional Adolfo López Mateos “Zacatenco”, Avenida Instituto Politécnico Nacional s/n, Edificio 5, 2do. Piso, Col. Lindavista, C.P. 07320 Ciudad de México, Mexico Correspondence should be addressed to Rosa Alicia Hernández-Vázquez; ra.hernandez.vazquez@gmail.com and Rodrigo Arturo Marquet-Rivera; r.marquet.rivera@gmail.com Received 30 November 2020; Revised 21 January 2021; Accepted 10 March 2021; Published 26 March 2021 Academic Editor: Donato Romano Copyright © 2021 Rosa Alicia Hernández-Vázquez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the lingual orthodontic technique, there are two paradigms regarding the type of wire used. Regardless of the material or gauge, some orthodontists choose to use the straight wire and resin and bond it to the surface of the tooth; they call it compensations. Other orthodontists prefer to bend the wire, giving it a mushroom shape. There is no specific indication for the use of each type of wire, so orthodontists use them according to their criteria. The present study establishes the bases so that it is possible to find the indications for each type of wire. A clinical trial of a lingual orthodontic patient was used. To carry out the comparative study, a straight arch was placed in his right arch and a mushroom arch in the left arch. Using 3D imaging, a high-biofidelity biomodel of the patient’s mandible was generated, with which the FEM analysis was performed, which allowed comparing the reactions of the mandibular bone and appliances with the different arches. It was found that, on the side with the straight arch, there were greater deformations, and in the mushroom arch, there were greater stresses. With this, it is possible to find which clinical cases in each type of wire are indicated. 1. Introduction who, despite the visibility of the brackets, consider it a sign of high social level [1]. Orthodontic treatments are generally requested by patients, That is why orthodontic treatment is helpful to achieve that aesthetic that is believed necessary for life in society. for aesthetic reasons, considering that the smile and front teeth are socially associated as a fundamental part of a per- But this is only one of its benefits; although it is true that aes- son’s appearance, development, and social status. The impor- thetics are fundamental in social demands, orthodontic treat- tance of its correct occlusion in its physiological function is ment fulfills an important function, in which it returns and the least considered. These are reasons why parents worry improves a better functioning of the stomatognathic system. Mainly, the orthodontic treatment is aimed at bringing the about their children getting this benefit, so not long ago orthodontics was considered an exclusive treatment for chil- teeth to their ideal position (or as close as possible) by dren and teenagers. In countries like Mexico in many cases, remodeling the alveolar bone and thus improving facial aes- these treatments are well accepted mainly by teenagers, thetics, and it also allows increasing the physiological life of 2 Applied Bionics and Biomechanics Figure 1: Contributions of orthodontics to better prosthetic treatments. Orthodontics verticalizes the position of the inclined teeth that will serve as pillars for the prosthesis, improving its support. (a) (b) Figure 2: Standardized arches for the lingual technique: (a) mushroom shape and (b) straight. The choice of the type of arch is according to the criteria and experience of the orthodontist. the teeth, since it locates them in a position of equilibrium Orthodontic forces Micro-osteoperforation with respect to the surrounding forces and receiving the F forces of mastication in the vertical and axial directions [2]. Inflammation Osteoclasts Osteoblasts In addition, orthodontics establishes interactions with other areas of dentistry that allow better treatments. An Cytokines example of this interaction is the one that is established between the prosthesis and oral rehabilitation when the Bone remodeling replacement of teeth is necessary. Orthodontic treatment Fibroblasts IL-18 can be indicated to give the best conditions to the prosthesis IL-6 (abutment parallelism, occlusion balance, anterior guide, Tooth movement TNF canine guide, etc.) (Figure 1). This in turn improves the chewing, digestive, nutritional, and respiratory function, as Figure 3: Mechanotransduction of the bone by the action of well as the patient’saffective, psychological, and emotional orthodontic forces. When the orthodontic forces produce the aspects [3]. movement of the dental organ, on the side towards which these As already mentioned, today, orthodontic treatment in forces are directed, they cause the osteoclasts to activate, adults is common. However, they tend to have greater resis- producing osteolysis of the bone. In the same way, on the opposite side, the osteoblasts are activated, producing bone osteogenesis. tance to treatment. They have lower tolerance to pain, and they demand to know more about the interventions they should undergo, time, cost, duration and frequency of extracellular matrix that surrounds them. The experimental appointments, and how to evaluate the effectiveness of the orthodontic movements in rats induce dynamic changes in treatment, in other words, the results [4]. But mainly, unlike the nerve fibers and the density of the pulp blood vessels, teenagers, they do not like to wear visible brackets, whether which correspond to the sequence of changes observed in metallic or aesthetic. For this reason, invisible aesthetic both the periodontal ligament and the alveolar bone [6]. orthodontics meets the expectations of this type of patient. These forces are generated by the bracket and directed The technique with lingual appliances has been in develop- through the wires or arches. In the case of the lingual tech- ment for approximately 25 years, and with the experience nique, there are two types of arches that are commonly used: of the cases treated, a completely protocolized technique the straight and mushroom-shaped arcs. On this aspect, it is has been conceived [5] (Figure 2). worth mentioning that there is still no accepted consensus or Orthodontic tooth movement is a physical phenomenon well-founded research, which has allowed establishing the in which the mechanical forces applied to the tooth are trans- criteria that allow selecting the one indicated for each specific lated into biological events that occur in the cells and the case (Figure 3). There is a publication that mentions that Applied Bionics and Biomechanics 3 Finite Nodes elements Figure 4: Finite elements of low biofidelity models. The low biofidelity of the biomodels causes the results to be far from those obtained in reality. Figure 5: First biomodels of dental organs. orthodontists consider that the mushroom-shaped arch serves to compensate for the morphology of the lingual faces of the teeth when there is dental crowding. However, this through various CAM/CAD-type computational systems leads to complicated biomechanics in some cases, as it (Figure 5) [16]. requires precise bending, which often results in discomfort Simulation and analysis consist of the study of the bio- model that represents the biological element, in real situa- for the patient. In addition, they require many bends, which depend on the ability of the orthodontist to shape them pre- tions in terms of its function and the agents that act on cisely, which entails more work for him and time to prepare. them. This simulation refers to the fact that, in the computer With the straight arch, orthodontists believe that not only is program, the biomodel is capable of reproducing or emulat- it easier and faster to work with this arch but also the ing the function performed by the biological structure. In addition, the biomodel can also simulate the biological mushroom-shaped system presents some difficulties in its construction [7]. So, orthodontists use them, according to response to agents outside it (pathologies, prostheses, forces, their criteria. devices, etc.). Knowing the magnitudes of the appropriate forces for In the medical and dental area, the use of the FEM is rel- each case is of utmost importance to minimize undesirable atively new; it is not quite common for the generality of doc- tors and dentists to handle this type of research methodology. reactions both in the dental organ and in its tissues that make it up and other surrounding tissues [8]. One way to obtain Its application is a good tool to be able to predict and calcu- the calculation and the reactions of the forces that occur is late, among many other applications in the various areas of through analysis using the finite element method (FEM). dentistry, the results of the orthodontic forces applied in a This numerical method simulates a real physical phenome- treatment and in this way provide patients with better treat- ment plans. In this way, it is possible to meet the expectations non, through a geometric model, discretizing or dividing it into small parts called finite elements. These allow modeling of patients, especially adults. structures with complex geometries which are divided into Specifically, in the lingual technique as already men- these small parts, in the form of triangles, squares, or tetrahe- tioned, there are two types of arches or wires that are used: dral whose vertices are joined to form nodes (Figure 4). In mushroom-shaped or straight. The selection of the caliber depends on the stage of the treatment. However, the choice each of these nodes, the solution to the study variables is located through the equations that govern the phenomenon of the arch shape depends on the criteria of the orthodontist, analyzed (elasticity, stresses, deformations, and elongations, since there is no specific indication for each arch shape, in among others). The number of finite elements that structure relation to the type of patient or case. the geometry determines the precision of the analysis and The present work shows through the application of this method the analysis of the types of arches used for lingual simulation of reality and therefore the results [9]. A fundamental part for carrying out this type of simula- orthodontics. The objective is to find a numerical support tion and analysis is the geometric model that is used. In the that serves as a basis to establish, in a more objective way, case of biological structures, these models that will represent which cases in each of the different wires should be used, the tissue or organ are called biomodel, which is the virtual depending on the stresses and reactions in the bone, the den- tal organs, and the wire itself. three-dimensional representation of the biological structure [10–12]. The quality of this biomodel turns out to be funda- mental for the analysis by FEM, since the biofidelity that it 2. Materials and Methods has [13–15] will allow the generation of the quantity and quality of the appropriate finite elements. For the numerical analysis that was carried out in the present Initially, the biomodels were no more than representa- work, a clinical case belonging to the CONRICYT Torre tions of the structures through geometric figures that were Médica Metropolitana, in its Orthodontic Research Depart- far from representing their morphology and morphometry. ment under the DDS MS Alfredo Gilbert Reisman, was used. Currently, 3D imagenology (magnetic resonance, standard This is a 29-year-old male patient who required lingual computed tomography, and cone-beam tomography) is pos- orthodontic treatment. His Ricketts analysis shows that he sible to generate these biomodels with high biofidelity, has a severe dolico facial pattern with bone class II. The 4 Applied Bionics and Biomechanics 90.8° 81.4° 67.1 115.2° 9.3° 64.5 35.7 132.2 45.0 83.4° 88.1 81.2° 148.4° 18.4 107.7° 47.4° 55.8 29.8 10.1 3.8 117.0° 90.3° 4.2 –1.0 7.6 2.8 57.9° 85.8 29.5° 7.2 137.7° 21.3 41.6° 30.8 62.5 56.7 13.7 13.8 1.7% Figure 6: Radiographic study (cranial lateral radiography and orthopantomography) and cephalometry (Ricketts analysis, Jarabak analysis, and soft profile analysis) of the patient, necessary for the diagnosis of the patient. Figure 7: High-biofidelity biomodel of the patient, generated from the latest generation tomography, necessary to perform the numerical analysis. molar relationship shows class I dental and canine class II craniofacial region. This new imaging modality offers accu- dental relationship. The upper molar position is in class III rate and high-quality three-dimensional representations of with labial protrusion. In the Roth-Jarabak analysis, mandib- the elements present in the maxillofacial complex. Unlike ular retrognathism is indicated. The diagnosis is skeletal and conventional tomography that shows consecutive slices, the dental class II with open bite (Figure 6). data obtained by a DVT and processed by the computer cre- For the generation of the high-biofidelity biomodel, ates a reconstruction of the studied volume. which is necessary to perform the numerical analysis, three- dimensional imaging of the patient was used. From Cranial 2.1. FEM Analysis Considerations. To carry out this study, Digital Volumetric Tomography (DVT) with the Cone- the biomodel of the patient’s mandible was generated from Beam Computed Tomography (CBTC) system, DICOM his cone-beam tomography (Figure 7). The biomodel gen- images are obtained that allow 3D reconstruction. This sys- erated is shaped up of five different materials: dental organ, tem is used to obtain images in tissues that are difficult to cortical bone, bracket, steel wire (stainless steel), and resin visualize. It is widely used in medicine and dentistry in the or adhesive. Applied Bionics and Biomechanics 5 Figure 8: Discretization of the patient’s biomodel with brackets and wires in place, prior to performing the numerical analysis. 1.2 N. The ANSYS® computer program was used to perform Table 1: Characteristics of the biomodel. the numerical analysis (Figure 9). Tissue Biomodel 3. Results Mesh Tetrahedral solid elements [12, 17–25] Meshing Semicontrolled Once the simulation and the numerical analysis had been Mesh quality High-order quadratic elements performed, the total deformations and the normal and von Nodes 2178470 Mises stresses that occurred in the complete system (mandib- Elements 1377416 ular bone, dental organs, brackets, and wire), the mandibular bone, and the wire were obtained, with both types of arch (mushroom-shaped and straight), obtaining the following. Table 2: Mechanical properties used in the analysis. In the complete system (Figure 10), it is observed that the maximum deformations (0.011 mm) occur in the dental pro- Tissue Young’s modulus (GPa) Poisson’s ratio cess, in the mandibular border zone. Mainly to the left side Enamel 70 0.30 where the mushroom arch was placed, the minimum defor- Dentin 18.3 0.30 mations equal to 0 mm are found, in both condyles from Cortical bone 15 0.32 the neck to their upper edge. Steel 193 0.29 In the deformations in the analyses that only consider the mandibular bone (Figure 11), the results and the reactions Resin 12.4 0.30 are practically the same as those obtained in the complete system. After obtaining the biomodel, it was corrected and solid- Specifically, in the wire (Figure 12), it is shown that the ified using CAM/CAD-type computer programs, to be sub- maximum deformations (0.009 mm) occur in the anterior jected to analysis. Once this was done, the controlled teeth area, mainly towards the right side where the arch is discretization of the same was carried out (Figure 8), obtain- straight. Minimum deformations (0.007 mm) occur on both ing a total of 1377416 elements and 2178470 nodes. It has sides (straight and mushroom-shaped), in the molar area. high-order tetrahedral elements (Table 1). This is similar to the results and reactions presented by the The characteristics of the biomodel are described in deformation in the complete system and in the mandibular Table 1, and the mechanical properties of the tissues are bone; only the distribution shows slight variations. described in Table 2. In the results of normal stresses and their reactions, the To carry out the simulation, the tissues are considered following was obtained. The normal stresses on the X axis materials that present a linear-elastic behavior and whose in the complete system (Figure 13) show that the maximum internal structure is isotropic and homogeneous. Regarding stresses (3.11 MPa) are presented on the left side, where the border conditions, these were established around the man- arc has a mushroom shape. These stresses are in tension dibular condyles. Therefore, the displacements and rotations and are located in the upper right angle of the central incisor in the directions of the X, Y, and Z axes were restricted, in the bracket. The minimum stresses (-2.22 MPa) occur on the anatomical region corresponding to the mandibular con- right side (straight arch) and are compressive stresses dis- dyles. The applied force corresponds to those established by posed at the junction of the wire with the canine bracket. Jarabak as optimal forces [26], being distributed as follows: Figure 14 shows that the maximum stresses in the Y axis incisors and canines, 0.2 N; premolars, 0.5 N; and molars, (-5.20 MPa) are presented on the left side, on the mushroom- 6 Applied Bionics and Biomechanics B F Movement restriction UX = UY = UZ = 0 E Rot X = Rot Y = Rot Z = 0 Forces applied on the wire H D G F B Figure 9: Boundary conditions and forces applied to the wire according to their actual application to brackets and teeth. The red arrows indicate the direction of the forces generated in the wire, in each dental organ. Max Min Y X 0 0.002 0.005 0.007 0.010 0.001 0.003 0.006 0.008 0.011 (mm) Figure 10: Total deformation occurring in the complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum deformations, and the blue marker indicates the minor deformations. shaped wire, specifically at the union of the canine bracket (straight arch), in the alveolar process of the first premolar with the wire, which are in compression. The minimum in its proximal area. stresses (3.73 MPa) that are in tension are located on the right Figure 17 shows the maximum stresses on the Y axis in side, where the arch is straight, at the junction of the wire the mandibular bone (-0.81 MPa). They are in compression and occur on the left side (mushroom-shaped wire), in the with the canine bracket. Figure 15 shows that the maximum and minimum alveolar process of the first molar, in its distal area. The min- stresses on the Z axis are located on the left side, where the imum stresses (0.78 MPa) are in tension, on the right side arc is in the mushroom shape. Maximum stresses (straight arch), in the alveolar process of the first premolar, (-4.49 MPa) are present in compression at the union of the in its proximal area. Figure 18 shows that the maximum stresses on the Z axis wire with the lateral incisor bracket. The minimum stresses (2.74 MPa) are tensile stresses and are settled at the junction in the mandibular bone are in tension (1.05 MPa) and the of the wire with the central incisor bracket. minimum (-0.73 MPa) in compression. Both appear on the Figure 16 shows that the maximum stresses on the X axis left side (mushroom-shaped wire), in the furcation crotch in the mandibular bone (0.48 MPa) are in tension and appear area of the first molar. The maximum stresses are towards on the left side (mushroom-shaped wire), in the furcation the distal are and the minimum towards the proximal are. crotch area of the first molar. The minimum stresses Figure 19(a) shows the stresses on the X axis in the wire. (-0.30 MPa) are in compression and occur on the right side The maximum stresses (1.93 MPa) which are in tension are Applied Bionics and Biomechanics 7 0 0.002 0.005 0.007 0.010 0.001 0.003 0.006 0.008 0.011 (mm) Figure 11: Total deformation that occurs in the mandibular bone. The red marker indicates the maximum deformations, and the blue marker indicates the minor deformations. compression (-3.09 MPa) are observed in the molar area on the right side, where the mushroom arch is located. The minimum stresses (3.73 MPa) are in tension and are around the right side. Finally, Figure 20 shows von Mises stresses throughout the system. The maximum values (7.64 MPa) are found on the right side (straight arch), at the junction of the wire and the canine bracket. In Figure 21, the maximum von Mises stresses (1.34 MPa) in the mandibular bone are presented on the left side (mushroom-shaped wire), in the alveolar pro- cess of the first molar, in its distal area. Figure 22 shows that the maximum von Mises stresses in the wire (6.77 MPa) occur in the area where the mushroom-shaped wire is located in the first premolar. 4. Discussion In the present work, the results and reactions obtained in the 0.007 0.0075 0.008 0.0085 0.009 0.0073 0.0078 0.0083 0.0088 0.0092 (mm) displacements, normal stresses, and von Mises stresses that occur in what was named the complete system (bone mandib- Figure 12: Total deformation that occurs in the wire. The red ular, dental organs, brackets, and wire) were analyzed. These marker indicates the maximum deformations, and the blue marker results were compared with those found in the mandibular indicates the minor deformations. bone separately and in the wire, which is mushroom-shaped on the left side and straight on the right side. This allowed located on the right side where the mushroom arch is finding the following. located, between the canine and the 1st premolar. The min- The deformations were increased on the side where the imum stresses (-1.75 MPa) are in compression, and they are straight wire is located, in the three entities analyzed located in the central zone. Figure 19(b) shows the Y axis (Figure 23). stresses in the wire. The maximum stresses (-0.46 MPa) are Figure 24 shows the stresses generated on the X axis. On shown on the right side where the mushroom arch is the contrary to the deformations, the stresses are greater on located, between the canine and the 1st premolar, which the side where the wire has a mushroom shape, this result are in compression. The minimum stresses (3.37 MPa) are being consistent in the three entities analyzed (the complete in tension and are around the right side, where the arch system, mandibular bone, and wire). The same happens in is straight. Figure 19(c) shows the normal stresses on the the forces that are generated on the Y axis and the Z axis Z axis in the wire. The maximums stresses which are in (Figures 25 and 26). 8 Applied Bionics and Biomechanics X X –2.22 –1.03 0.14 1.33 2.51 –1.63 –0.44 0.73 1.92 3.11 (MPa) Figure 13: Normal stresses in the X complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Y Y X X X Y 3.73 1.74 –0.24 –2.22 –4.21 2.74 0.75 –1.23 –3.22 –5.20 (MPa) Figure 14: Normal stresses in the Y complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Applied Bionics and Biomechanics 9 Y X X X 2.74 1.38 –0.47 –2.08 –3.69 1.94 0.33 –1.27 –2.88 –4.49 (MPa) Figure 15: Normal stresses in the Z complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. X Y X –0.30 –0.13 0.04 0.22 0.39 –0.21 –0.04 0.13 0.30 0.48 (MPa) Figure 16: Normal stresses in X, mandibular bone. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. 10 Applied Bionics and Biomechanics Z Z Y X X Y Z X Y 0.78 0.43 0.07 –0.27 –0.63 0.61 0.25 –0.10 –0.45 –0.81 (MPa) Figure 17: Normal stresses in Y, mandibular bone. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Z Z X Y Y Z Y X X Y –0.73 –0.33 0.06 0.45 0.85 –0.53 –0.13 0.25 0.65 1.05 (MPa) Figure 18: Normal stresses in Z, mandibular bone. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Applied Bionics and Biomechanics 11 Min Max –1.75 –0.93 –0.11 0.70 1.52 3.37 1.99 0.26 –1.46 –3.20 –1.34 –0.52 0.29 1.11 1.93 (MPa) 2.86 1.13 –0.60 –2.33 –4.06 (MPa) (a) (b) 2.59 1.32 0.06 –1.20 –2.46 1.96 0.69 –0.56 –1.83 –3.09 (MPa) (c) Figure 19: Normal stresses in the wire: (a) X axis; (b) Y axis; (c) Z axis. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. this shape, stress concentrators are being generated, due to In the case of von Mises stresses (Figure 27), like defor- mations, the highest values are presented on the side where its geometry. This concentration is transmitted to the bone the straight wire is located, this result being consistent in and other adjacent elements, a situation that does not occur the three entities analyzed (the complete system, the mandib- in the straight wire. As there are no such stress concentrators, ular bone, and the wire). only deformations of the agents and loads to which the wire is subjected are presented, and therefore, the stresses gener- Both the deformations and the von Mises stresses are greater when using the straight arch. This is consistent since ated and transmitted are lower. the von Mises criterion is the most conservative and is related According to this, it is possible to affirm that, when using to the strain energy. That is why it is logical that the results of a straight wire, less stresses will be generated that act on the these two analyses are congruent. bone and dental organs than if a mushroom-shaped wire is On the other hand, the stresses generated in the used. This is, at least, for this case study. Although this is a mushroom-shaped wire are greater than those of the straight very subdued first approximation to reality, further studies wire, and these stresses are transmitted to the mandibular of this type still need to be carried out. These studies should bone and the brackets and wires. The areas where the maxi- include a greater number of study subjects and make a mum stresses occur in the mushroom wire correspond to greater limitation of the variables, which could be done by the places where the geometry of the mushroom is formed trying to ensure that the study subjects have similar charac- (where the bends of the wire are made for the conformation teristics (higher control of the inclusion and exclusion cri- of the mushroom). By bending the wire so that it acquires teria) and that the study is carried out with complete 12 Applied Bionics and Biomechanics Z Z Y X Y X -6 1.27×10 1.69 3.39 5.09 6.79 0.84 2.54 4.24 5.94 7.64 (MPa) Figure 20: von Mises stresses on the complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. arches. It is worth mentioning that this study is the first of treatment. Some of these efforts are located in anatomical others where the aspects are considered. areas of importance to consider during orthodontic treat- This is not to say that the present study does not establish ment. These areas were stresses within the alveolus of the first a good starting point. On the contrary, this study establishes molar, in the furcation area and in the alveolar ridge. the bases where it is observed that biomechanically, there are Considering that lingual orthodontics is mostly used by differences between using a straight wire or a mushroom- adults, the condition that these stresses exert on the alveolar shaped wire, as well as the possible repercussions that could and supporting bone is an important point to consider. Adult be generated. As already mentioned, there is no documented patients may represent some conditions or habits that com- support for the orthodontist to decide which is better or promise periodontal health: osteopenia, osteoporosis in the which cases in each one are indicated. With studies of this case of women or metabolic and systemic diseases, smoking, type, the consensus not yet reached can be achieved, with and poor brushing techniques due to lack of time, which can proven scientific bases, rather than through personal prefer- affect the supporting tissues. ences or empirical knowledge. In addition, it demonstrates On the other hand, although with the straight arch the the usefulness of using the finite element method in dental stresses are much lower, the deformations are also aspects research, as a tool that could reduce the time and number to consider. The deformation of the wire can cause them to of study subjects. deactivate, or their action is not adequate. Above all, when patients do not attend their check-up appointments with the necessary regularity, which is known, it can also generate 5. Conclusions undesirable movements that later have to be corrected when Based on the previous discussions, it was possible to reach the they go to their appointment and that delay the treatment time or have to consider other circumstances in addition to following conclusions. the initial treatment plan. The straight wire transmits less stress than a mushroom- shaped wire, which would be important to consider since This is clear for orthodontists: greater stress on bone and anatomical areas and greater damage to supporting tissues; such stresses could lead to undesirable movements during Applied Bionics and Biomechanics 13 Z Z X X X Y 0.29 0.59 0.89 1.19 0.14 0.44 0.74 1.04 1.34 (MPa) Figure 21: von Mises stresses on the mandibular bone. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Total deformations 0.6 0.4 0.2 Complete system Mandible Wire arch Straight wire arch Mushroom arch wire Figure 23: Total deformations (mm). The graph shows a comparison between the deformations that were generated in each of the analyzed sections: complete system (mandibular bone, 0.00 1.50 3.01 4.51 6.02 dental organs, brackets, and wires) and separately the mandible 0.75 2.25 3.76 5.26 6.77 (MPa) and the two different types of arches or wires. Figure 22: von Mises stresses on the wire. The red marker indicates Normal stresses on the X axis the maximum stresses, and the blue marker indicates the minor stresses. therefore, in patients with periodontal conditions, it can cause problems (this depends on age, sex, diet, dentition, Complete system Mandible Wire arch health status, etc.). The mushroom arch causes greater Mushroom arch wire stresses on bone and anatomical areas, which could contrain- Straight wire arch dicate its use in this type of patient. A deformation of the wires demonstrates that there is no Figure 24: Normal stresses in the X axis (MPa). The graph shows a control in the mechanobiology and mechanotransduction of comparison between the stresses in the X axis that were generated in orthodontic movement. For patients who do not come regularly, each of the analyzed sections: complete system (mandibular bone, this canbeaproblem.Thestraightarchsuffers from greater dental organs, brackets, and wires) and separately the mandible deformations, which would contraindicate its use in these cases. and the two different types of arches or wires. 14 Applied Bionics and Biomechanics Normal stresses on the Y axis preparation of this work. The authors also thank CONRI- 1.5 CYT Torre Médica Metropolitana, Orthodontic Research 1 Department, and DDS MS Alfredo Gilbert for their partici- pation in the clinical phase. 0.5 Complete system Mandible Wire arch References Mushroom arch wire Straight wire arch [1] L. G. Selna, H. T. Shillingburg, and P. A. Kerr, “Finite element analysis of dental structures? Axisymmetric and plane stress Figure 25: Normal stresses in the Y axis (MPa). The graph shows a idealizations,” Journal of Biomedical Materials Research, comparison between the stresses in the Y axis that were generated in vol. 9, no. 2, pp. 237–252, 1975. each of the analyzed sections: complete system (mandibular bone, [2] Y. A. Valerievich, Z. V. Valerievich, Z. A. Nikolaevich, and dental organs, brackets, and wires) and separately the mandible N. I. Valerievna, “Determination of biomechanical character- and the two different types of arches or wires. istics of dentine and dental enamel in vitro,” European Science Review, vol. 5, no. 1, pp. 101–103, 2016. Normal stresses on the Z axis [3] T. Mitsiadis and D. Graf, “Cell fate determination during tooth development and regeneration,” Embryo Today, vol. 87, no. 3, pp. 199–211, 2009. [4] S. Pabari, D. R. Moles, and S. J. Cunningham, “Assessment of motivation and psychological characteristics of adult ortho- Complete system Mandible Wire arch dontic patients,” American Journal of Orthodontics and Dento- facial Orthopedics, vol. 140, no. 6, pp. e263–e272, 2011. Mushroom arch wire Straight wire arch [5] M. Nascimento, D. Dilbone, P. Pereira, S. Geraldeli, A. Delgado, and W. Duarte, “Abfraction lesions: etiology, diag- Figure 26: Normal stresses in the Z axis (MPa). The graph shows a nosis, and treatment options,” Clinical, Cosmetic and Investi- comparison between the stresses in the Z axis that were generated in gational Dentistry, vol. 8, no. 1, pp. 79–87, 2016. each of the analyzed sections: complete system (mandibular bone, [6] W. C. Lee and W. S. Eakle, “Possible role of tensile stress in the dental organs, brackets, and wires) and separately the mandible etiology of cervical erosive lesions of teeth,” The Journal of and the two different types of arches or wires. Prosthetic Dentistry, vol. 52, no. 3, pp. 374–380, 1984. [7] B. Owen, G. Gullion, G. Heo, J. P. Carey, P. W. Major, and von Mises stresses D. L. Romanyk, “Measurement of forces and moments around 8 the maxillary arch for treatment of a simulated lingual incisor and high canine malocclusion using straight and mushroom archwires in fixed lingual appliances,” European Journal of Orthodontics, vol. 39, no. 6, pp. 665–672, 2017. [8] S. K. Abass and J. K. Hartsfield Jr., “Orthodontics and external X axis Y axis Z axis apical root resorption,” Seminars in Orthodontics, vol. 13, Straight wire arch no. 4, pp. 246–256, 2007. Mushroom arch wire [9] L. F. Zeola, F. A. Pereira, A. C. Machado et al., “Effects of non- carious cervical lesion size, occlusal loading and restoration on Figure 27: von Mises stresses (MPa). The graph shows a biomechanical behaviour of premolar teeth,” Australian Den- comparison between von Mises stresses that were generated in tal Journal, vol. 61, no. 4, pp. 408–417, 2016. each of the analyzed sections: complete system (mandibular bone, dental organs, brackets, and wires) and separately the mandible [10] A. M. El-Marakby, F. A. Al-Sabri, S. A. Alharbi, S. M. Hala- and the two different types of arches or wires. wani, and M. T. B. Yousef, “Noncarious cervical lesions as abfraction: etiology, diagnosis, and treatment modalities of lesions: a review article,” Dentistry, vol. 7, no. 438, pp. 1–6, Data Availability All data generated or analyzed during this study are included [11] A. Rand, M. Stiesch, M. Eisenburger, and A. Greuling, “The in this published article. effect of direct and indirect force transmission on peri- implant bone stress–a contact finite element analysis,” Com- puter Methods in Biomechanics and Biomedical Engineering, Conflicts of Interest vol. 20, no. 10, pp. 1132–1139, 2017. [12] T. R. Shyagali and D. Aghera, “Evaluation of the stress gener- The authors declare no conflict of interest. ation on the cortical bone and the palatal micro-implant com- plex during the implant-supported en masse retraction in lingual orthodontic technique using the FEM: Original Acknowledgments research,” Journal of Dental Research, Dental Clinics, Dental The authors thank Instituto Politécnico Nacional, Consejo Prospects, vol. 13, no. 3, pp. 192–199, 2019. Nacional de Ciencia y Tecnología, and Universidad Politéc- [13] R. Uhlir, V. Mayo, P. H. Lin et al., “Biomechanical characteri- nica del Valle de México for the support provided in the zation of the periodontal ligament: orthodontic tooth Applied Bionics and Biomechanics 15 [25] A. Hasegawa, A. Shinya, Y. Nakasone, L. V. Lassila, P. K. Val- movement,” The Angle Orthodontist, vol. 87, no. 2, pp. 183– 192, 2016. littu, and A. Shinya, “Development of 3D CAD/FEM analysis system for natural teeth and jaw bone constructed from X- [14] E. Bramanti, G. Cervino, F. Lauritano et al., “FEM and von ray CT images,” International Journal of Biomaterials, Mises analysis on prosthetic crowns structural elements: vol. 2010, Article ID 659802, 7 pages, 2010. evaluation of different applied materials,” The Scientific [26] E. H. Hixon, H. Atikian, G. E. Callow, H. W. McDonald, and World Journal, vol. 2017, no. 2017, Article ID 1029574, 7 pages, 2017. R. J. Tacy, “Optimal force, differential force, and anchorage,” American Journal of Orthodontics, vol. 55, no. 5, pp. 437– [15] E. Carrera, D. 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Desiate, “Finite element method (FEM), mechanobiol- ogy and biomimetic scaffolds in bone tissue engineering,” International Journal of Biological Sciences, vol. 7, no. 1, pp. 112–132, 2011. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Bionics and Biomechanics Hindawi Publishing Corporation

Comparative Numerical Analysis between Two Types of Orthodontic Wire for the Lingual Technique, Using the Finite Element Method

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Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 6658039, 15 pages https://doi.org/10.1155/2021/6658039 Research Article Comparative Numerical Analysis between Two Types of Orthodontic Wire for the Lingual Technique, Using the Finite Element Method 1 2 Rosa Alicia Hernández-Vázquez , Rodrigo Arturo Marquet-Rivera , 2 2 Octavio Alejandro Mastache-Miranda , Angel Javier Vázquez-López , 2 2 Salvador Cruz-López , and Juan Alejandro Vázquez-Feijoo Universidad Politécnica del Valle de México, Departamento de Mecatrónica, Av. Mexiquense s/n Esquina Av. Universidad Politécnica, Col. Villa Esmeralda, Tultitlán, C.P. 54910 Estado de México, Mexico Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica, Sección de Estudios de Posgrado e Investigación, Unidad Profesional Adolfo López Mateos “Zacatenco”, Avenida Instituto Politécnico Nacional s/n, Edificio 5, 2do. Piso, Col. Lindavista, C.P. 07320 Ciudad de México, Mexico Correspondence should be addressed to Rosa Alicia Hernández-Vázquez; ra.hernandez.vazquez@gmail.com and Rodrigo Arturo Marquet-Rivera; r.marquet.rivera@gmail.com Received 30 November 2020; Revised 21 January 2021; Accepted 10 March 2021; Published 26 March 2021 Academic Editor: Donato Romano Copyright © 2021 Rosa Alicia Hernández-Vázquez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the lingual orthodontic technique, there are two paradigms regarding the type of wire used. Regardless of the material or gauge, some orthodontists choose to use the straight wire and resin and bond it to the surface of the tooth; they call it compensations. Other orthodontists prefer to bend the wire, giving it a mushroom shape. There is no specific indication for the use of each type of wire, so orthodontists use them according to their criteria. The present study establishes the bases so that it is possible to find the indications for each type of wire. A clinical trial of a lingual orthodontic patient was used. To carry out the comparative study, a straight arch was placed in his right arch and a mushroom arch in the left arch. Using 3D imaging, a high-biofidelity biomodel of the patient’s mandible was generated, with which the FEM analysis was performed, which allowed comparing the reactions of the mandibular bone and appliances with the different arches. It was found that, on the side with the straight arch, there were greater deformations, and in the mushroom arch, there were greater stresses. With this, it is possible to find which clinical cases in each type of wire are indicated. 1. Introduction who, despite the visibility of the brackets, consider it a sign of high social level [1]. Orthodontic treatments are generally requested by patients, That is why orthodontic treatment is helpful to achieve that aesthetic that is believed necessary for life in society. for aesthetic reasons, considering that the smile and front teeth are socially associated as a fundamental part of a per- But this is only one of its benefits; although it is true that aes- son’s appearance, development, and social status. The impor- thetics are fundamental in social demands, orthodontic treat- tance of its correct occlusion in its physiological function is ment fulfills an important function, in which it returns and the least considered. These are reasons why parents worry improves a better functioning of the stomatognathic system. Mainly, the orthodontic treatment is aimed at bringing the about their children getting this benefit, so not long ago orthodontics was considered an exclusive treatment for chil- teeth to their ideal position (or as close as possible) by dren and teenagers. In countries like Mexico in many cases, remodeling the alveolar bone and thus improving facial aes- these treatments are well accepted mainly by teenagers, thetics, and it also allows increasing the physiological life of 2 Applied Bionics and Biomechanics Figure 1: Contributions of orthodontics to better prosthetic treatments. Orthodontics verticalizes the position of the inclined teeth that will serve as pillars for the prosthesis, improving its support. (a) (b) Figure 2: Standardized arches for the lingual technique: (a) mushroom shape and (b) straight. The choice of the type of arch is according to the criteria and experience of the orthodontist. the teeth, since it locates them in a position of equilibrium Orthodontic forces Micro-osteoperforation with respect to the surrounding forces and receiving the F forces of mastication in the vertical and axial directions [2]. Inflammation Osteoclasts Osteoblasts In addition, orthodontics establishes interactions with other areas of dentistry that allow better treatments. An Cytokines example of this interaction is the one that is established between the prosthesis and oral rehabilitation when the Bone remodeling replacement of teeth is necessary. Orthodontic treatment Fibroblasts IL-18 can be indicated to give the best conditions to the prosthesis IL-6 (abutment parallelism, occlusion balance, anterior guide, Tooth movement TNF canine guide, etc.) (Figure 1). This in turn improves the chewing, digestive, nutritional, and respiratory function, as Figure 3: Mechanotransduction of the bone by the action of well as the patient’saffective, psychological, and emotional orthodontic forces. When the orthodontic forces produce the aspects [3]. movement of the dental organ, on the side towards which these As already mentioned, today, orthodontic treatment in forces are directed, they cause the osteoclasts to activate, adults is common. However, they tend to have greater resis- producing osteolysis of the bone. In the same way, on the opposite side, the osteoblasts are activated, producing bone osteogenesis. tance to treatment. They have lower tolerance to pain, and they demand to know more about the interventions they should undergo, time, cost, duration and frequency of extracellular matrix that surrounds them. The experimental appointments, and how to evaluate the effectiveness of the orthodontic movements in rats induce dynamic changes in treatment, in other words, the results [4]. But mainly, unlike the nerve fibers and the density of the pulp blood vessels, teenagers, they do not like to wear visible brackets, whether which correspond to the sequence of changes observed in metallic or aesthetic. For this reason, invisible aesthetic both the periodontal ligament and the alveolar bone [6]. orthodontics meets the expectations of this type of patient. These forces are generated by the bracket and directed The technique with lingual appliances has been in develop- through the wires or arches. In the case of the lingual tech- ment for approximately 25 years, and with the experience nique, there are two types of arches that are commonly used: of the cases treated, a completely protocolized technique the straight and mushroom-shaped arcs. On this aspect, it is has been conceived [5] (Figure 2). worth mentioning that there is still no accepted consensus or Orthodontic tooth movement is a physical phenomenon well-founded research, which has allowed establishing the in which the mechanical forces applied to the tooth are trans- criteria that allow selecting the one indicated for each specific lated into biological events that occur in the cells and the case (Figure 3). There is a publication that mentions that Applied Bionics and Biomechanics 3 Finite Nodes elements Figure 4: Finite elements of low biofidelity models. The low biofidelity of the biomodels causes the results to be far from those obtained in reality. Figure 5: First biomodels of dental organs. orthodontists consider that the mushroom-shaped arch serves to compensate for the morphology of the lingual faces of the teeth when there is dental crowding. However, this through various CAM/CAD-type computational systems leads to complicated biomechanics in some cases, as it (Figure 5) [16]. requires precise bending, which often results in discomfort Simulation and analysis consist of the study of the bio- model that represents the biological element, in real situa- for the patient. In addition, they require many bends, which depend on the ability of the orthodontist to shape them pre- tions in terms of its function and the agents that act on cisely, which entails more work for him and time to prepare. them. This simulation refers to the fact that, in the computer With the straight arch, orthodontists believe that not only is program, the biomodel is capable of reproducing or emulat- it easier and faster to work with this arch but also the ing the function performed by the biological structure. In addition, the biomodel can also simulate the biological mushroom-shaped system presents some difficulties in its construction [7]. So, orthodontists use them, according to response to agents outside it (pathologies, prostheses, forces, their criteria. devices, etc.). Knowing the magnitudes of the appropriate forces for In the medical and dental area, the use of the FEM is rel- each case is of utmost importance to minimize undesirable atively new; it is not quite common for the generality of doc- tors and dentists to handle this type of research methodology. reactions both in the dental organ and in its tissues that make it up and other surrounding tissues [8]. One way to obtain Its application is a good tool to be able to predict and calcu- the calculation and the reactions of the forces that occur is late, among many other applications in the various areas of through analysis using the finite element method (FEM). dentistry, the results of the orthodontic forces applied in a This numerical method simulates a real physical phenome- treatment and in this way provide patients with better treat- ment plans. In this way, it is possible to meet the expectations non, through a geometric model, discretizing or dividing it into small parts called finite elements. These allow modeling of patients, especially adults. structures with complex geometries which are divided into Specifically, in the lingual technique as already men- these small parts, in the form of triangles, squares, or tetrahe- tioned, there are two types of arches or wires that are used: dral whose vertices are joined to form nodes (Figure 4). In mushroom-shaped or straight. The selection of the caliber depends on the stage of the treatment. However, the choice each of these nodes, the solution to the study variables is located through the equations that govern the phenomenon of the arch shape depends on the criteria of the orthodontist, analyzed (elasticity, stresses, deformations, and elongations, since there is no specific indication for each arch shape, in among others). The number of finite elements that structure relation to the type of patient or case. the geometry determines the precision of the analysis and The present work shows through the application of this method the analysis of the types of arches used for lingual simulation of reality and therefore the results [9]. A fundamental part for carrying out this type of simula- orthodontics. The objective is to find a numerical support tion and analysis is the geometric model that is used. In the that serves as a basis to establish, in a more objective way, case of biological structures, these models that will represent which cases in each of the different wires should be used, the tissue or organ are called biomodel, which is the virtual depending on the stresses and reactions in the bone, the den- tal organs, and the wire itself. three-dimensional representation of the biological structure [10–12]. The quality of this biomodel turns out to be funda- mental for the analysis by FEM, since the biofidelity that it 2. Materials and Methods has [13–15] will allow the generation of the quantity and quality of the appropriate finite elements. For the numerical analysis that was carried out in the present Initially, the biomodels were no more than representa- work, a clinical case belonging to the CONRICYT Torre tions of the structures through geometric figures that were Médica Metropolitana, in its Orthodontic Research Depart- far from representing their morphology and morphometry. ment under the DDS MS Alfredo Gilbert Reisman, was used. Currently, 3D imagenology (magnetic resonance, standard This is a 29-year-old male patient who required lingual computed tomography, and cone-beam tomography) is pos- orthodontic treatment. His Ricketts analysis shows that he sible to generate these biomodels with high biofidelity, has a severe dolico facial pattern with bone class II. The 4 Applied Bionics and Biomechanics 90.8° 81.4° 67.1 115.2° 9.3° 64.5 35.7 132.2 45.0 83.4° 88.1 81.2° 148.4° 18.4 107.7° 47.4° 55.8 29.8 10.1 3.8 117.0° 90.3° 4.2 –1.0 7.6 2.8 57.9° 85.8 29.5° 7.2 137.7° 21.3 41.6° 30.8 62.5 56.7 13.7 13.8 1.7% Figure 6: Radiographic study (cranial lateral radiography and orthopantomography) and cephalometry (Ricketts analysis, Jarabak analysis, and soft profile analysis) of the patient, necessary for the diagnosis of the patient. Figure 7: High-biofidelity biomodel of the patient, generated from the latest generation tomography, necessary to perform the numerical analysis. molar relationship shows class I dental and canine class II craniofacial region. This new imaging modality offers accu- dental relationship. The upper molar position is in class III rate and high-quality three-dimensional representations of with labial protrusion. In the Roth-Jarabak analysis, mandib- the elements present in the maxillofacial complex. Unlike ular retrognathism is indicated. The diagnosis is skeletal and conventional tomography that shows consecutive slices, the dental class II with open bite (Figure 6). data obtained by a DVT and processed by the computer cre- For the generation of the high-biofidelity biomodel, ates a reconstruction of the studied volume. which is necessary to perform the numerical analysis, three- dimensional imaging of the patient was used. From Cranial 2.1. FEM Analysis Considerations. To carry out this study, Digital Volumetric Tomography (DVT) with the Cone- the biomodel of the patient’s mandible was generated from Beam Computed Tomography (CBTC) system, DICOM his cone-beam tomography (Figure 7). The biomodel gen- images are obtained that allow 3D reconstruction. This sys- erated is shaped up of five different materials: dental organ, tem is used to obtain images in tissues that are difficult to cortical bone, bracket, steel wire (stainless steel), and resin visualize. It is widely used in medicine and dentistry in the or adhesive. Applied Bionics and Biomechanics 5 Figure 8: Discretization of the patient’s biomodel with brackets and wires in place, prior to performing the numerical analysis. 1.2 N. The ANSYS® computer program was used to perform Table 1: Characteristics of the biomodel. the numerical analysis (Figure 9). Tissue Biomodel 3. Results Mesh Tetrahedral solid elements [12, 17–25] Meshing Semicontrolled Once the simulation and the numerical analysis had been Mesh quality High-order quadratic elements performed, the total deformations and the normal and von Nodes 2178470 Mises stresses that occurred in the complete system (mandib- Elements 1377416 ular bone, dental organs, brackets, and wire), the mandibular bone, and the wire were obtained, with both types of arch (mushroom-shaped and straight), obtaining the following. Table 2: Mechanical properties used in the analysis. In the complete system (Figure 10), it is observed that the maximum deformations (0.011 mm) occur in the dental pro- Tissue Young’s modulus (GPa) Poisson’s ratio cess, in the mandibular border zone. Mainly to the left side Enamel 70 0.30 where the mushroom arch was placed, the minimum defor- Dentin 18.3 0.30 mations equal to 0 mm are found, in both condyles from Cortical bone 15 0.32 the neck to their upper edge. Steel 193 0.29 In the deformations in the analyses that only consider the mandibular bone (Figure 11), the results and the reactions Resin 12.4 0.30 are practically the same as those obtained in the complete system. After obtaining the biomodel, it was corrected and solid- Specifically, in the wire (Figure 12), it is shown that the ified using CAM/CAD-type computer programs, to be sub- maximum deformations (0.009 mm) occur in the anterior jected to analysis. Once this was done, the controlled teeth area, mainly towards the right side where the arch is discretization of the same was carried out (Figure 8), obtain- straight. Minimum deformations (0.007 mm) occur on both ing a total of 1377416 elements and 2178470 nodes. It has sides (straight and mushroom-shaped), in the molar area. high-order tetrahedral elements (Table 1). This is similar to the results and reactions presented by the The characteristics of the biomodel are described in deformation in the complete system and in the mandibular Table 1, and the mechanical properties of the tissues are bone; only the distribution shows slight variations. described in Table 2. In the results of normal stresses and their reactions, the To carry out the simulation, the tissues are considered following was obtained. The normal stresses on the X axis materials that present a linear-elastic behavior and whose in the complete system (Figure 13) show that the maximum internal structure is isotropic and homogeneous. Regarding stresses (3.11 MPa) are presented on the left side, where the border conditions, these were established around the man- arc has a mushroom shape. These stresses are in tension dibular condyles. Therefore, the displacements and rotations and are located in the upper right angle of the central incisor in the directions of the X, Y, and Z axes were restricted, in the bracket. The minimum stresses (-2.22 MPa) occur on the anatomical region corresponding to the mandibular con- right side (straight arch) and are compressive stresses dis- dyles. The applied force corresponds to those established by posed at the junction of the wire with the canine bracket. Jarabak as optimal forces [26], being distributed as follows: Figure 14 shows that the maximum stresses in the Y axis incisors and canines, 0.2 N; premolars, 0.5 N; and molars, (-5.20 MPa) are presented on the left side, on the mushroom- 6 Applied Bionics and Biomechanics B F Movement restriction UX = UY = UZ = 0 E Rot X = Rot Y = Rot Z = 0 Forces applied on the wire H D G F B Figure 9: Boundary conditions and forces applied to the wire according to their actual application to brackets and teeth. The red arrows indicate the direction of the forces generated in the wire, in each dental organ. Max Min Y X 0 0.002 0.005 0.007 0.010 0.001 0.003 0.006 0.008 0.011 (mm) Figure 10: Total deformation occurring in the complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum deformations, and the blue marker indicates the minor deformations. shaped wire, specifically at the union of the canine bracket (straight arch), in the alveolar process of the first premolar with the wire, which are in compression. The minimum in its proximal area. stresses (3.73 MPa) that are in tension are located on the right Figure 17 shows the maximum stresses on the Y axis in side, where the arch is straight, at the junction of the wire the mandibular bone (-0.81 MPa). They are in compression and occur on the left side (mushroom-shaped wire), in the with the canine bracket. Figure 15 shows that the maximum and minimum alveolar process of the first molar, in its distal area. The min- stresses on the Z axis are located on the left side, where the imum stresses (0.78 MPa) are in tension, on the right side arc is in the mushroom shape. Maximum stresses (straight arch), in the alveolar process of the first premolar, (-4.49 MPa) are present in compression at the union of the in its proximal area. Figure 18 shows that the maximum stresses on the Z axis wire with the lateral incisor bracket. The minimum stresses (2.74 MPa) are tensile stresses and are settled at the junction in the mandibular bone are in tension (1.05 MPa) and the of the wire with the central incisor bracket. minimum (-0.73 MPa) in compression. Both appear on the Figure 16 shows that the maximum stresses on the X axis left side (mushroom-shaped wire), in the furcation crotch in the mandibular bone (0.48 MPa) are in tension and appear area of the first molar. The maximum stresses are towards on the left side (mushroom-shaped wire), in the furcation the distal are and the minimum towards the proximal are. crotch area of the first molar. The minimum stresses Figure 19(a) shows the stresses on the X axis in the wire. (-0.30 MPa) are in compression and occur on the right side The maximum stresses (1.93 MPa) which are in tension are Applied Bionics and Biomechanics 7 0 0.002 0.005 0.007 0.010 0.001 0.003 0.006 0.008 0.011 (mm) Figure 11: Total deformation that occurs in the mandibular bone. The red marker indicates the maximum deformations, and the blue marker indicates the minor deformations. compression (-3.09 MPa) are observed in the molar area on the right side, where the mushroom arch is located. The minimum stresses (3.73 MPa) are in tension and are around the right side. Finally, Figure 20 shows von Mises stresses throughout the system. The maximum values (7.64 MPa) are found on the right side (straight arch), at the junction of the wire and the canine bracket. In Figure 21, the maximum von Mises stresses (1.34 MPa) in the mandibular bone are presented on the left side (mushroom-shaped wire), in the alveolar pro- cess of the first molar, in its distal area. Figure 22 shows that the maximum von Mises stresses in the wire (6.77 MPa) occur in the area where the mushroom-shaped wire is located in the first premolar. 4. Discussion In the present work, the results and reactions obtained in the 0.007 0.0075 0.008 0.0085 0.009 0.0073 0.0078 0.0083 0.0088 0.0092 (mm) displacements, normal stresses, and von Mises stresses that occur in what was named the complete system (bone mandib- Figure 12: Total deformation that occurs in the wire. The red ular, dental organs, brackets, and wire) were analyzed. These marker indicates the maximum deformations, and the blue marker results were compared with those found in the mandibular indicates the minor deformations. bone separately and in the wire, which is mushroom-shaped on the left side and straight on the right side. This allowed located on the right side where the mushroom arch is finding the following. located, between the canine and the 1st premolar. The min- The deformations were increased on the side where the imum stresses (-1.75 MPa) are in compression, and they are straight wire is located, in the three entities analyzed located in the central zone. Figure 19(b) shows the Y axis (Figure 23). stresses in the wire. The maximum stresses (-0.46 MPa) are Figure 24 shows the stresses generated on the X axis. On shown on the right side where the mushroom arch is the contrary to the deformations, the stresses are greater on located, between the canine and the 1st premolar, which the side where the wire has a mushroom shape, this result are in compression. The minimum stresses (3.37 MPa) are being consistent in the three entities analyzed (the complete in tension and are around the right side, where the arch system, mandibular bone, and wire). The same happens in is straight. Figure 19(c) shows the normal stresses on the the forces that are generated on the Y axis and the Z axis Z axis in the wire. The maximums stresses which are in (Figures 25 and 26). 8 Applied Bionics and Biomechanics X X –2.22 –1.03 0.14 1.33 2.51 –1.63 –0.44 0.73 1.92 3.11 (MPa) Figure 13: Normal stresses in the X complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Y Y X X X Y 3.73 1.74 –0.24 –2.22 –4.21 2.74 0.75 –1.23 –3.22 –5.20 (MPa) Figure 14: Normal stresses in the Y complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Applied Bionics and Biomechanics 9 Y X X X 2.74 1.38 –0.47 –2.08 –3.69 1.94 0.33 –1.27 –2.88 –4.49 (MPa) Figure 15: Normal stresses in the Z complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. X Y X –0.30 –0.13 0.04 0.22 0.39 –0.21 –0.04 0.13 0.30 0.48 (MPa) Figure 16: Normal stresses in X, mandibular bone. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. 10 Applied Bionics and Biomechanics Z Z Y X X Y Z X Y 0.78 0.43 0.07 –0.27 –0.63 0.61 0.25 –0.10 –0.45 –0.81 (MPa) Figure 17: Normal stresses in Y, mandibular bone. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Z Z X Y Y Z Y X X Y –0.73 –0.33 0.06 0.45 0.85 –0.53 –0.13 0.25 0.65 1.05 (MPa) Figure 18: Normal stresses in Z, mandibular bone. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Applied Bionics and Biomechanics 11 Min Max –1.75 –0.93 –0.11 0.70 1.52 3.37 1.99 0.26 –1.46 –3.20 –1.34 –0.52 0.29 1.11 1.93 (MPa) 2.86 1.13 –0.60 –2.33 –4.06 (MPa) (a) (b) 2.59 1.32 0.06 –1.20 –2.46 1.96 0.69 –0.56 –1.83 –3.09 (MPa) (c) Figure 19: Normal stresses in the wire: (a) X axis; (b) Y axis; (c) Z axis. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. this shape, stress concentrators are being generated, due to In the case of von Mises stresses (Figure 27), like defor- mations, the highest values are presented on the side where its geometry. This concentration is transmitted to the bone the straight wire is located, this result being consistent in and other adjacent elements, a situation that does not occur the three entities analyzed (the complete system, the mandib- in the straight wire. As there are no such stress concentrators, ular bone, and the wire). only deformations of the agents and loads to which the wire is subjected are presented, and therefore, the stresses gener- Both the deformations and the von Mises stresses are greater when using the straight arch. This is consistent since ated and transmitted are lower. the von Mises criterion is the most conservative and is related According to this, it is possible to affirm that, when using to the strain energy. That is why it is logical that the results of a straight wire, less stresses will be generated that act on the these two analyses are congruent. bone and dental organs than if a mushroom-shaped wire is On the other hand, the stresses generated in the used. This is, at least, for this case study. Although this is a mushroom-shaped wire are greater than those of the straight very subdued first approximation to reality, further studies wire, and these stresses are transmitted to the mandibular of this type still need to be carried out. These studies should bone and the brackets and wires. The areas where the maxi- include a greater number of study subjects and make a mum stresses occur in the mushroom wire correspond to greater limitation of the variables, which could be done by the places where the geometry of the mushroom is formed trying to ensure that the study subjects have similar charac- (where the bends of the wire are made for the conformation teristics (higher control of the inclusion and exclusion cri- of the mushroom). By bending the wire so that it acquires teria) and that the study is carried out with complete 12 Applied Bionics and Biomechanics Z Z Y X Y X -6 1.27×10 1.69 3.39 5.09 6.79 0.84 2.54 4.24 5.94 7.64 (MPa) Figure 20: von Mises stresses on the complete system (mandibular bone, dental organs, brackets, and wires). The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. arches. It is worth mentioning that this study is the first of treatment. Some of these efforts are located in anatomical others where the aspects are considered. areas of importance to consider during orthodontic treat- This is not to say that the present study does not establish ment. These areas were stresses within the alveolus of the first a good starting point. On the contrary, this study establishes molar, in the furcation area and in the alveolar ridge. the bases where it is observed that biomechanically, there are Considering that lingual orthodontics is mostly used by differences between using a straight wire or a mushroom- adults, the condition that these stresses exert on the alveolar shaped wire, as well as the possible repercussions that could and supporting bone is an important point to consider. Adult be generated. As already mentioned, there is no documented patients may represent some conditions or habits that com- support for the orthodontist to decide which is better or promise periodontal health: osteopenia, osteoporosis in the which cases in each one are indicated. With studies of this case of women or metabolic and systemic diseases, smoking, type, the consensus not yet reached can be achieved, with and poor brushing techniques due to lack of time, which can proven scientific bases, rather than through personal prefer- affect the supporting tissues. ences or empirical knowledge. In addition, it demonstrates On the other hand, although with the straight arch the the usefulness of using the finite element method in dental stresses are much lower, the deformations are also aspects research, as a tool that could reduce the time and number to consider. The deformation of the wire can cause them to of study subjects. deactivate, or their action is not adequate. Above all, when patients do not attend their check-up appointments with the necessary regularity, which is known, it can also generate 5. Conclusions undesirable movements that later have to be corrected when Based on the previous discussions, it was possible to reach the they go to their appointment and that delay the treatment time or have to consider other circumstances in addition to following conclusions. the initial treatment plan. The straight wire transmits less stress than a mushroom- shaped wire, which would be important to consider since This is clear for orthodontists: greater stress on bone and anatomical areas and greater damage to supporting tissues; such stresses could lead to undesirable movements during Applied Bionics and Biomechanics 13 Z Z X X X Y 0.29 0.59 0.89 1.19 0.14 0.44 0.74 1.04 1.34 (MPa) Figure 21: von Mises stresses on the mandibular bone. The red marker indicates the maximum stresses, and the blue marker indicates the minor stresses. Total deformations 0.6 0.4 0.2 Complete system Mandible Wire arch Straight wire arch Mushroom arch wire Figure 23: Total deformations (mm). The graph shows a comparison between the deformations that were generated in each of the analyzed sections: complete system (mandibular bone, 0.00 1.50 3.01 4.51 6.02 dental organs, brackets, and wires) and separately the mandible 0.75 2.25 3.76 5.26 6.77 (MPa) and the two different types of arches or wires. Figure 22: von Mises stresses on the wire. The red marker indicates Normal stresses on the X axis the maximum stresses, and the blue marker indicates the minor stresses. therefore, in patients with periodontal conditions, it can cause problems (this depends on age, sex, diet, dentition, Complete system Mandible Wire arch health status, etc.). The mushroom arch causes greater Mushroom arch wire stresses on bone and anatomical areas, which could contrain- Straight wire arch dicate its use in this type of patient. A deformation of the wires demonstrates that there is no Figure 24: Normal stresses in the X axis (MPa). 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Applied Bionics and BiomechanicsHindawi Publishing Corporation

Published: Mar 26, 2021

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