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Biomechanical Effect of Orthodontic Treatment of Canine Retraction by Using Metallic Orthodontic Mini-Implant (OMI) Covered with Various Angles of Revolving Cap

Biomechanical Effect of Orthodontic Treatment of Canine Retraction by Using Metallic Orthodontic... Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 9952392, 8 pages https://doi.org/10.1155/2021/9952392 Research Article Biomechanical Effect of Orthodontic Treatment of Canine Retraction by Using Metallic Orthodontic Mini-Implant (OMI) Covered with Various Angles of Revolving Cap 1 1,2 3 1,4 Kuson Tuntiwong, Jui-Ting Hsu, Shih-Guang Yang, Jian-Hong Yu , 1,2 and Heng-Li Huang School of Dentistry, China Medical University, Taichung 40402, Taiwan Department of Bioinformatics and Medical Engineering, Asia University, Taichung 41354, Taiwan Master Program for Biomedical Engineering, China Medical University, Taichung 40402, Taiwan Department of Dentistry, China Medical University Hospital, Taichung 40402, Taiwan Correspondence should be addressed to Jian-Hong Yu; kenkoyu@mail.cmu.edu.tw and Heng-Li Huang; hlhuang@mail.cmu.edu.tw Received 30 March 2021; Accepted 21 June 2021; Published 12 July 2021 Academic Editor: Antonio Pérez-González Copyright © 2021 Kuson Tuntiwong 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. Objective. This study evaluated the biomechanical effects of a metallic orthodontic mini-implant (OMI) covered with various types of angled revolving cap on the peri-OMI bone and the canine periodontal ligament (PDL) by finite element (FE) analyses. Materials and Methods. Three-dimensional FE models included comprised cortical bone and cancellous bone of the maxilla, and the OMIs were created. The forces (0.98 N) pulled in both the canine hook and the revolving cap, pulling towards each other in both directions as loading conditions. The upper surface of the maxilla was fixed as a boundary condition. Results. The bone stresses were increasing in the models by using OMI covered with a revolving cap as compared with that in the conventional model (in which only the OMI was placed). However, no obvious differences in bone stresses were observed among the models with various types of angled revolving cap. The minimum principal strain in the canine PDL was highest for condition 180T, followed by condition 180L. However, the maximum differences in the values between each experimental model and the conventional model were around 5%. Conclusion. This study showed no obvious effects in decreasing or increasing stress/strain in bone and PDL by using various types of angled revolving cap covered metallic mini-implant in orthodontic treatment of canine retraction. 1. Introduction ward and the tooth angulation should be made parallel to the same tooth. Orthodontic treatment is applied in dentistry for malocclu- Most cases of orthodontic treatment first involve premo- lar extraction followed by canine retraction (CR). An anchor- sion, which includes tooth crowding, protrusion, and spac- ing. Malalignment and crowding are reportedly present in age is required for such treatment, which refers to the almost 15% of adolescents, and affected adults can have resistance to reaction forces provided by other teeth, palate, extremely irregular incisors [1]. Tooth extraction is often head, or neck (via extraoral forces) [2], and an orthodontic necessary for treating malalignment and crowding. Two tis- mini-implant (OMI) is commonly used [3]. The ideal force for translating a canine is typically 150–200 gf. The availabil- sues have major effects on orthodontic tooth movement: the periodontal ligament (PDL) and alveolar bone. For cases ity of a reliable anchorage during space closure is important of Class II or Class I bimaxillary protrusion, normally, the when performing CR after premolar extraction. OMIs are anterior part of the maxillary teeth should be pulled back- suitable for facilitating orthodontic tooth movement due to 2 Applied Bionics and Biomechanics (a) (b) (c) Figure 1: Solid models of the (a) canine, second premolar, and first molar and (b) canine PDL. (c) The PDF was 0.25 mm thick. tom Sensation 16, Siemens Medical Solutions, Forchheim, their biocompatibility, small size, and placement utility [4, 5]. The placement of an OMI between the roots of the maxillary Germany). Adjacent images were separated by 1 mm. The second premolar and first molar for retracting a canine is coordinate data were used by CAD software (SolidWorks aimed at avoiding forward movement of the posterior seg- 2007, SolidWorks, Concord, MA, USA) to generate a three- ments of the maxillary arch. However, an OMI can only be dimensional solid model of the left maxilla. The PDL tissue placed between teeth with sufficient bone density and root was modeled as a thin enclosure around the dental root with clearance [4]. an average thickness of approximately 0.25 mm [9] One limitation of the maxilla is that the maxillary sinus is (Figure 1). The cortical bone was modeled as being 2 mm an important vital structure. The revolving cap can be used thick, with underlying cancellous bone. The maxilla was cut with the OMIs and allows forces to be applied to the cap at in half and had manipulated alveolar sockets, and a model diverse angulations and is particularly advantageous since of the tooth was also created. an OMI cannot be inserted or position changes by an OMI A model of a 10 mm long OMI with a diameter of 1.6 are greatly restricted in many positions close to vital struc- mm was constructed manually using CAD software (Solid- tures. The revolving cap was constructed from a medical- Works 2007). The OMI was angled 60 from the alveolar grade plastic (polycarbonate) material. ridge between the roots of the second premolar and the first The mechanics of orthodontic tooth movement due to molar on the buccal side, and it was positioned 1 mm from remodeling were investigated using finite element (FE) anal- the PDL. This location eliminated interference from adjacent ysis [6]. This technique is popular in orthodontics since it roots and was based on the local root anatomy. A subtrac- can reveal internal strains and resolve significantly indefi- tion operation was performed to create a hole for the OMI nite force systems. [7, 8]. Numerous studies have attempted in the maxillary model. The 0.018 in standard nontorqued, to improve the modeling of biological structures, with that nonangulated, edgewise orthodontic canine brackets; molar of Cattaneo et al. probably the most important for different tube; OMI; and revolving cap were modeled manually based PDL assumptions [7]. Those authors found that making on a typical clinical treatment process. The reconstructed different assumptions about the PDL markedly influences maxilla, canine, second premolar, first molar, PDL, brackets, the resulting stress in the ligament. However, modeling OMI, and revolving cap were all modeled using CAD soft- approaches are still necessary since in vivo studies remain ware (SolidWorks 2007) (Table 1). insufficient for investigating biomechanical effects such as All models were combined using Boolean operations, stress and strain in PDL. and files containing the models in IGES format were then Therefore, this study used computer-aided design (CAD) imported into ANSYS Workbench (Swanson Analysis, and FE analysis to evaluate the effects of various loading sys- Huston, PA, USA) to generate the FE model (Figure 2) tems on the maxillary bone and PDL in cases of CR per- using 10-node tetrahedral h-elements. Homologous, isotro- formed using a revolving cap. The objectives of this study pic, and linearly elastic material properties were used for also included determining the effects of applying forces in all models except for the PDL, which was included as a various directions by angulating the revolving cap and evalu- bilinear elastic material [10–13]. The material properties ated the maximum and minimum principal strains in the assigned to the FE models are listed in Table 2. In the maxillary canine PDL as well as the equivalent (von Mises) simplified model, a 0.98 N (100 gf) couple force was stress in the maxillary bones to fully characterize the biome- applied as the loading condition either towards the canine chanics of orthodontic CR. hook or towards the revolving cap (Table 1). The mesio- distal surfaces of the maxilla bone were constrained to zero displacement in the x, y, and z directions as a bound- 2. Materials and Methods ary condition. A fixed boundary condition assigned to the A series of computed tomography images of the maxilla of an upper sectioned surface of the maxillary bone as shown in orthodontic patient was obtained from the left upper teeth Figure 3 completed the simulation of natural anatomic (canine, second premolar, and first molar) and PDL (Soma- constraints. Applied Bionics and Biomechanics 3 Table 1: The simulations involved ten models with different positions of the revolving cap and loading types (red arrows). Model Position of force Loading condition 0T 0L 45T 45L 90T 90L 135T 135L 180T 180L 4 Applied Bionics and Biomechanics 0.00 10.00 (a) 0.00 20.00 (mm) X 10.00 (b) Figure 2: (a) The upper view and (b) frontal view of the FE model in this study. Table 2: Material properties used in the FE model. [10–13]. Young’s modulus Material Poisson’s ratio (MPa) Tooth 1:8×10 0.30 E =0:15 PDL (bilinear) 0.30 E =0:6 2 0.00 40.00 (mm) 20.00 Cancellous bone 460 0.30 1:49 × 10 Cortical bone 0.30 Figure 3: The boundary condition set at the upper surface of the maxilla. Bracket and tube 2:3×10 0.30 OMI (stainless steel) 2:3×10 0.30 2:75 × 10 and 180 . A traction force was applied at two locations on Revolving cap (polycarbonate) 0.38 the cap for each of these angles: (1) at the top of the cap (“T” suffix) or low down the cap (“L” suffix). Hence, a total of 10 sets of FE models was analyzed: 0T, 0L, 45T, 45L, An FE analysis produces an approximate rather than an 90T, 90L, 135T, 135L, 180T, and 180L (Table 1). exact solution. Therefore, the convergence of the FE models was tested to verify the mesh quality, with a maximum ele- 3. Results ment size of 2.0 mm set for meshing in all FE models used in this study. Orthodontic forces were simulated according 3.1. Equivalent (von Mises) Stress in the Maxilla. Distinct to normal clinical practice. The loading conditions consisted stresses were evident in the cortical bone only in the peri- of the following different angulations of the revolving cap OMI bone and not in the adjacent areas around the socket ° ° ° ° that was placed to cover the head of OMI: 0 ,45 ,90 , 135 , of the teeth. The results indicate that condition 0T (37.6 Applied Bionics and Biomechanics 5 Max. (control) (0T) (45T) (90T) (135T) (180T) (0L) (45L) (90L) (135L) (180L) Figure 4: von Mises stress distributions for CR in the conventional model (control) and the experimental models. Areas with high stresses are indicated in red. Max 6e-6 (control) 5e-6 4e-6 3e-6 (0T) (45T) (90T) (135T) (180T) 2e-6 1e-6 (0L ) (45L) (90L) (135L ) (180L ) Figure 5: Distributions of the maximum principal strain for CR in the conventional model (control) and the experimental models. Areas with −6 high tensile strains are indicated in red. (e‐6 indicates 1 ∗ 10 ). MPa) induced the highest equivalent (von Mises) stress in the marked differences in the stresses were observed between bone. Moreover, conditions 180L (34.1 MPa), 90T (32.9 the conventional model and conditions 0L, 45L, 90L, 135T, MPa), 180T (32.2 MPa), 45T (28.9 MPa), 0 L (27.4 MPa), and 135L (Figure 4). 135L (23.5 MPa), 45L (23.4 MPa), 135T (23.1 MPa), and 90L (22.5 MPa) are implied. The stress was lowest in the con- 3.2. Maximum Principal Elastic Strain in the Canine PDL. ventional model (22.1 MPa). The areas with high compres- The principal strain in the canine PDL was highest when sive stresses (indicated as red areas in the figures) around traction forces were applied. Regions exhibiting compressive the uppermost OMI thread hole were much larger in condi- and tensile normal strains could be identified in the PDL. tions 180T and 180L than in the conventional model. No However, the magnitude of the tensile strain was significantly 6 Applied Bionics and Biomechanics –2e-6 0.000 4.000 (mm) 0.000 0.000 0.000 4.000 (mm) –2.5e-6 4.000 (mm) 0.000 4.000 (mm) 4.000 (mm) 0.000 4.000 (mm) 2.000 2.000 2.000 2.000 2.000 2.000 Control 0T 45T 90T 135T 180T –3.125e-6 –3.75e-6 –4e-6 –5e-6 0.000 0.000 4.000 (mm) 4.000 (mm) 0.000 4.000 (mm) 0.000 4.000 (mm) 0.000 4.000 (mm) 2.000 2.000 2.000 2.000 2.000 0L 45L 90L 135L 180L Figure 6: Distributions of the minimum principal strain for CR in the conventional model (control) and the experimental models. Areas with −6 high compressive strains are indicated in blue. (e‐6 presents 1 ∗ 10 ). higher than that of the compressive strain. All dominant revolving cap to overcome some of the limitations associated principal strains were clearly evident at the mesiolabial mar- with using an OMI. The biomechanical performance when gin of the PDL, with no marked differences in the strain dis- using various orthodontic loading directions with an OMI tribution between the models (Figure 5). The strain was the and a revolving cap anchorage in the case of orthodontic highest in condition 0L (14.9 μstrain), followed by conditions CR was investigated. The maximum and minimum principal 0T (14.8 μstrain), 45L and 90L (14.7 μstrain), and 45T, 90T, strains in the canine PDL were examined to determine differ- 135T, and 135L (14.6 μstrain). The maximum strain in the ences in CR. The von Mises stress was examined in the peri- conventional model was 14.3 μstrain. The peak strain was OMI cortical bone [14], which may be related to the risk of lower in conditions 180L (14.2 μstrain) and 180T (13.9 bone resorption. A revolving cap is a supplementary device μstrain) than in the conventional model. The difference in used in CR to overcome limitations in the positioning of the values between each experimental model and the conven- the OMI. tional model did not exceed 5%. This study found that the values of tensile strain (maxi- mum principal strain) in the canine PDL in all models did 3.3. Minimum Principal Elastic Strain in the Canine PDL. not differ by more than 5% from those in the conventional The principal strain in the canine PDL was the lowest when model when a revolving cap was located on the OMI between compressive forces were applied. An area of compressive the second premolar and the first molar. During orthodontic strain was clearly evident at the mesiolabial margin of the treatment, the revolving cap can be easily managed in PDL and on the distal surface of the inner PDL. The mini- cases of maxillary pneumatization. Moreover, the minimum mum strain peaked at condition 180T (−7.5 μstrain), principal strain is usually a compressive strain, and the com- followed by condition 180L (−7.6 μstrain); both of these pression at the canine PDL margin was on the inner mesiola- values were higher than those in the conventional model. bial surface, which indicates the occurrence of tipping. The The minimum strain was −7.9 μstrain for conditions 0L, minimum principal strain in the canine PDL for an angula- 45L, and 90L and −7.8 μstrain for conditions 0T, 90T, tion of 180 relative to the revolving cap resulted in the 135T, and 135L. The minimum strain in the conventional desired orthodontic movement. model and condition 45T was −7.7 μstrain. When translation The von Mises stresses in the peri-OMI bone of the max- occurred, an area of compression started to appear on the illa was highest for condition 0T (37.6 MPa) and varied distal surface of the inner PDL in the direction of the applied between 22 and 34 MPa in the conventional model as well force. A blue area appeared on the distal surface of the inner as in the other experimental models when the revolving cap PDL for conditions 180T and 180L, which was almost per- was located on the OMI between the second premolar and fectly aligned with the initial canine translation (Figure 6). the first molar. Stress values from 34 to 48 MPa will induce The maximum differences in the values between each exper- bone resorption, following the studies of Qian et al. and imental model and the conventional group were around 5%. Frost, which means using a revolving cap in condition 0T is not recommended [15, 16]. There is considerable interest among both patients and 4. Discussion orthodontists in using OMIs to move teeth due to their OMIs are often used to induce tooth translation in the dental advantages over both conventional methods and the use of extraoral devices. It is relatively straightforward to use clinic. This study has introduced the innovation of utilizing a Applied Bionics and Biomechanics 7 a revolving cap to cover the OMI to facilitate tooth move- Authors’ Contributions ment and hence also the translational mechanics phase of Kuson Tuntiwong and Jui-Ting Hsu are equal contributors. orthodontic treatment. This study showed that covering mini-implants by a revolving cap increased the peri-OMI Acknowledgments bone stress. In addition to the risk of pathologic bone resorption, there is also a possibility of crestal bone resorp- This research was supported by the China Medical Univer- tion based on the high stress values induced in the peri- sity, Taiwan (CMU109-MF-77). OMI bone when using the revolving cap under an angula- tion of 0 . This is probably due to the distance from the References original force to the revolving cap area, which would result in higher bone stress. Fortunately, a revolving cap at an [1] W. Proffit and H. Field, Malocclusion and dentofacial defor- angulation of 0 is not used frequently in orthodontic mity in contemporary society, in Contemporary Orthodontics, treatments. Mosby, St. Louis, MO, 1993. This study was subject to a variety of limitations, includ- [2] D. Roberts-Harry and J. Sandy, “Orthodontics. Part 9: anchor- ing the inherent ones that apply in any modeling study. A age control and distal movement,” British Dental Journal, model can only produce results as accurate as the set of vol. 196, no. 5, pp. 255–263, 2004. assumptions that were used to create it, including boundary [3] H.-S. Park, S.-M. Bae, H.-M. Kyung, and J.-H. Sung, “Micro- conditions, loading conditions, and material properties. The implant anchorage for treatment of skeletal class I bialveolar boundary conditions of the present model included that the protrusion,” Journal of Clinical Orthodontics, vol. 35, no. 7, pp. 417–422, 2001. top surface of the maxilla was fixed. The loading conditions included applying load over the revolving cap covering [4] H. H. Ammar, P. Ngan, R. J. Crout, V. H. Mucino, and O. M. Mukdadi, “Three-dimensional modeling and finite element OMI, which was placed between the second premolar and analysis in treatment planning for orthodontic tooth move- the first molar sites. The position of the OMI was set between ment,” American Journal of Orthodontics and Dentofacial the root of the second premolar and the first molar. There- Orthopedics, vol. 139, no. 1, pp. e59–e71, 2011. fore, the present findings might not apply to other positions [5] M. A. Papadopoulos and F. Tarawneh, “The use of miniscrew of OMIs and revolving caps. implants for temporary skeletal anchorage in orthodontics: a comprehensive review,” Oral Surgery, Oral Medicine, Oral 5. Conclusions Pathology, Oral Radiology, and Endodontics, vol. 103, no. 5, pp. e6–e15, 2007. Within the limitations as described above, the findings of this [6] S. Mohammed and H. Desai, “Basic concepts of finite element study can be summarized as follows: analysis and its applications in dentistry: an overview,” Journal of Oral Hygiene & Health, vol. 2, p. 156, 2014. (1) No obvious effects in decreasing bone stress were [7] P. Cattaneo, M. Dalstra, and B. Melsen, “The finite element observed in all models by using mini-implant method: a tool to study orthodontic tooth movement,” Journal (OMI) covered with various angles of the revolving of Dental Research, vol. 84, no. 5, pp. 428–433, 2005. cap. However, the stress around the top of the OMI [8] M. Poppe, C. Bourauel, and A. Jäger, “Determination of the thread hole was greatly increased in conditions elasticity parameters of the human periodontal ligament and 180T and 180L compared with the conventional the location of the center of resistance of single-rooted teeth,” model. No obvious differences in the stress in the Journal of Orofacial Orthopedics, vol. 63, no. 5, pp. 358–370, peri-OMI bone were found between the conventional model and conditions 0L, 45L, 90L, 135T, and 135L [9] E. D. Coolidge, “The thickness of the human periodontal membrane,” Journal of the American Dental Association (2) All dominant principal strains were clearly evident at (1939), vol. 24, no. 8, pp. 1260–1270, 1937. the mesiolabial margin of the PDL. However, the [10] Z. Liao, J. Chen, W. Li, M. A. Darendeliler, M. Swain, and highest strain in each experimental model did not Q. Li, “Biomechanical investigation into the role of the peri- differ by more than 5% from that in the conventional odontal ligament in optimising orthodontic force: a finite ele- model. It looks like there are no obvious effects in ment case study,” Archives of Oral Biology, vol. 66, pp. 98– decreasing or increasing the strain in PDL by using 107, 2016. the revolving cap in orthodontic treatment of canine [11] A. Kawarizadeh, C. Bourauel, and A. Jäger, “Experimental and retraction numerical determination of initial tooth mobility and material properties of the periodontal ligament in rat molar speci- Data Availability mens,” European Journal of Orthodontics, vol. 25, no. 6, pp. 569–578, 2003. The underlying data can be found through the authors. Any- [12] T.-S. Lin, F.-D. Tsai, C.-Y. Chen, and L.-W. Lin, “Factorial body who is interested in the data can email the authors analysis of variables affecting bone stress adjacent to the ortho- directly. dontic anchorage mini-implant with finite element analysis,” American Journal of Orthodontics and Dentofacial Orthope- dics, vol. 143, no. 2, pp. 182–189, 2013. Conflicts of Interest [13] M. S. M. Lande, A. Desai, A. Verma, and A. Gaur, “Stress anal- The authors declare that they have no conflicts of interest. ysis of polycarbonate spur gears for sugarcane juice machine 8 Applied Bionics and Biomechanics using FEA,” International Journal on Recent Technologies in Mechanical and Electrical Engineering (IJRMEE), vol. 2, no. 10, pp. 14–19, 2015. [14] M. Motoyoshi, S. Ueno, K. Okazaki, and N. Shimizu, “Bone stress for a mini-implant close to the roots of adjacent teeth - 3D finite element analysis,” International Journal of Oral and Maxillofacial Surgery, vol. 38, no. 4, pp. 363–368, 2009. [15] L. Qian, M. Todo, Y. Matsushita, and K. Koyano, “Finite ele- ment analysis of bone resorption around dental implant,” Journal of Biomechanical Science and Engineering, vol. 4, no. 3, pp. 365–376, 2009. [16] H. M. Frost, “Perspectives: bone's mechanical usage windows,” Bone and Mineral, vol. 19, no. 3, pp. 257–271, 1992. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Bionics and Biomechanics Hindawi Publishing Corporation

Biomechanical Effect of Orthodontic Treatment of Canine Retraction by Using Metallic Orthodontic Mini-Implant (OMI) Covered with Various Angles of Revolving Cap

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Copyright © 2021 Kuson Tuntiwong 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.
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Hindawi Applied Bionics and Biomechanics Volume 2021, Article ID 9952392, 8 pages https://doi.org/10.1155/2021/9952392 Research Article Biomechanical Effect of Orthodontic Treatment of Canine Retraction by Using Metallic Orthodontic Mini-Implant (OMI) Covered with Various Angles of Revolving Cap 1 1,2 3 1,4 Kuson Tuntiwong, Jui-Ting Hsu, Shih-Guang Yang, Jian-Hong Yu , 1,2 and Heng-Li Huang School of Dentistry, China Medical University, Taichung 40402, Taiwan Department of Bioinformatics and Medical Engineering, Asia University, Taichung 41354, Taiwan Master Program for Biomedical Engineering, China Medical University, Taichung 40402, Taiwan Department of Dentistry, China Medical University Hospital, Taichung 40402, Taiwan Correspondence should be addressed to Jian-Hong Yu; kenkoyu@mail.cmu.edu.tw and Heng-Li Huang; hlhuang@mail.cmu.edu.tw Received 30 March 2021; Accepted 21 June 2021; Published 12 July 2021 Academic Editor: Antonio Pérez-González Copyright © 2021 Kuson Tuntiwong 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. Objective. This study evaluated the biomechanical effects of a metallic orthodontic mini-implant (OMI) covered with various types of angled revolving cap on the peri-OMI bone and the canine periodontal ligament (PDL) by finite element (FE) analyses. Materials and Methods. Three-dimensional FE models included comprised cortical bone and cancellous bone of the maxilla, and the OMIs were created. The forces (0.98 N) pulled in both the canine hook and the revolving cap, pulling towards each other in both directions as loading conditions. The upper surface of the maxilla was fixed as a boundary condition. Results. The bone stresses were increasing in the models by using OMI covered with a revolving cap as compared with that in the conventional model (in which only the OMI was placed). However, no obvious differences in bone stresses were observed among the models with various types of angled revolving cap. The minimum principal strain in the canine PDL was highest for condition 180T, followed by condition 180L. However, the maximum differences in the values between each experimental model and the conventional model were around 5%. Conclusion. This study showed no obvious effects in decreasing or increasing stress/strain in bone and PDL by using various types of angled revolving cap covered metallic mini-implant in orthodontic treatment of canine retraction. 1. Introduction ward and the tooth angulation should be made parallel to the same tooth. Orthodontic treatment is applied in dentistry for malocclu- Most cases of orthodontic treatment first involve premo- lar extraction followed by canine retraction (CR). An anchor- sion, which includes tooth crowding, protrusion, and spac- ing. Malalignment and crowding are reportedly present in age is required for such treatment, which refers to the almost 15% of adolescents, and affected adults can have resistance to reaction forces provided by other teeth, palate, extremely irregular incisors [1]. Tooth extraction is often head, or neck (via extraoral forces) [2], and an orthodontic necessary for treating malalignment and crowding. Two tis- mini-implant (OMI) is commonly used [3]. The ideal force for translating a canine is typically 150–200 gf. The availabil- sues have major effects on orthodontic tooth movement: the periodontal ligament (PDL) and alveolar bone. For cases ity of a reliable anchorage during space closure is important of Class II or Class I bimaxillary protrusion, normally, the when performing CR after premolar extraction. OMIs are anterior part of the maxillary teeth should be pulled back- suitable for facilitating orthodontic tooth movement due to 2 Applied Bionics and Biomechanics (a) (b) (c) Figure 1: Solid models of the (a) canine, second premolar, and first molar and (b) canine PDL. (c) The PDF was 0.25 mm thick. tom Sensation 16, Siemens Medical Solutions, Forchheim, their biocompatibility, small size, and placement utility [4, 5]. The placement of an OMI between the roots of the maxillary Germany). Adjacent images were separated by 1 mm. The second premolar and first molar for retracting a canine is coordinate data were used by CAD software (SolidWorks aimed at avoiding forward movement of the posterior seg- 2007, SolidWorks, Concord, MA, USA) to generate a three- ments of the maxillary arch. However, an OMI can only be dimensional solid model of the left maxilla. The PDL tissue placed between teeth with sufficient bone density and root was modeled as a thin enclosure around the dental root with clearance [4]. an average thickness of approximately 0.25 mm [9] One limitation of the maxilla is that the maxillary sinus is (Figure 1). The cortical bone was modeled as being 2 mm an important vital structure. The revolving cap can be used thick, with underlying cancellous bone. The maxilla was cut with the OMIs and allows forces to be applied to the cap at in half and had manipulated alveolar sockets, and a model diverse angulations and is particularly advantageous since of the tooth was also created. an OMI cannot be inserted or position changes by an OMI A model of a 10 mm long OMI with a diameter of 1.6 are greatly restricted in many positions close to vital struc- mm was constructed manually using CAD software (Solid- tures. The revolving cap was constructed from a medical- Works 2007). The OMI was angled 60 from the alveolar grade plastic (polycarbonate) material. ridge between the roots of the second premolar and the first The mechanics of orthodontic tooth movement due to molar on the buccal side, and it was positioned 1 mm from remodeling were investigated using finite element (FE) anal- the PDL. This location eliminated interference from adjacent ysis [6]. This technique is popular in orthodontics since it roots and was based on the local root anatomy. A subtrac- can reveal internal strains and resolve significantly indefi- tion operation was performed to create a hole for the OMI nite force systems. [7, 8]. Numerous studies have attempted in the maxillary model. The 0.018 in standard nontorqued, to improve the modeling of biological structures, with that nonangulated, edgewise orthodontic canine brackets; molar of Cattaneo et al. probably the most important for different tube; OMI; and revolving cap were modeled manually based PDL assumptions [7]. Those authors found that making on a typical clinical treatment process. The reconstructed different assumptions about the PDL markedly influences maxilla, canine, second premolar, first molar, PDL, brackets, the resulting stress in the ligament. However, modeling OMI, and revolving cap were all modeled using CAD soft- approaches are still necessary since in vivo studies remain ware (SolidWorks 2007) (Table 1). insufficient for investigating biomechanical effects such as All models were combined using Boolean operations, stress and strain in PDL. and files containing the models in IGES format were then Therefore, this study used computer-aided design (CAD) imported into ANSYS Workbench (Swanson Analysis, and FE analysis to evaluate the effects of various loading sys- Huston, PA, USA) to generate the FE model (Figure 2) tems on the maxillary bone and PDL in cases of CR per- using 10-node tetrahedral h-elements. Homologous, isotro- formed using a revolving cap. The objectives of this study pic, and linearly elastic material properties were used for also included determining the effects of applying forces in all models except for the PDL, which was included as a various directions by angulating the revolving cap and evalu- bilinear elastic material [10–13]. The material properties ated the maximum and minimum principal strains in the assigned to the FE models are listed in Table 2. In the maxillary canine PDL as well as the equivalent (von Mises) simplified model, a 0.98 N (100 gf) couple force was stress in the maxillary bones to fully characterize the biome- applied as the loading condition either towards the canine chanics of orthodontic CR. hook or towards the revolving cap (Table 1). The mesio- distal surfaces of the maxilla bone were constrained to zero displacement in the x, y, and z directions as a bound- 2. Materials and Methods ary condition. A fixed boundary condition assigned to the A series of computed tomography images of the maxilla of an upper sectioned surface of the maxillary bone as shown in orthodontic patient was obtained from the left upper teeth Figure 3 completed the simulation of natural anatomic (canine, second premolar, and first molar) and PDL (Soma- constraints. Applied Bionics and Biomechanics 3 Table 1: The simulations involved ten models with different positions of the revolving cap and loading types (red arrows). Model Position of force Loading condition 0T 0L 45T 45L 90T 90L 135T 135L 180T 180L 4 Applied Bionics and Biomechanics 0.00 10.00 (a) 0.00 20.00 (mm) X 10.00 (b) Figure 2: (a) The upper view and (b) frontal view of the FE model in this study. Table 2: Material properties used in the FE model. [10–13]. Young’s modulus Material Poisson’s ratio (MPa) Tooth 1:8×10 0.30 E =0:15 PDL (bilinear) 0.30 E =0:6 2 0.00 40.00 (mm) 20.00 Cancellous bone 460 0.30 1:49 × 10 Cortical bone 0.30 Figure 3: The boundary condition set at the upper surface of the maxilla. Bracket and tube 2:3×10 0.30 OMI (stainless steel) 2:3×10 0.30 2:75 × 10 and 180 . A traction force was applied at two locations on Revolving cap (polycarbonate) 0.38 the cap for each of these angles: (1) at the top of the cap (“T” suffix) or low down the cap (“L” suffix). Hence, a total of 10 sets of FE models was analyzed: 0T, 0L, 45T, 45L, An FE analysis produces an approximate rather than an 90T, 90L, 135T, 135L, 180T, and 180L (Table 1). exact solution. Therefore, the convergence of the FE models was tested to verify the mesh quality, with a maximum ele- 3. Results ment size of 2.0 mm set for meshing in all FE models used in this study. Orthodontic forces were simulated according 3.1. Equivalent (von Mises) Stress in the Maxilla. Distinct to normal clinical practice. The loading conditions consisted stresses were evident in the cortical bone only in the peri- of the following different angulations of the revolving cap OMI bone and not in the adjacent areas around the socket ° ° ° ° that was placed to cover the head of OMI: 0 ,45 ,90 , 135 , of the teeth. The results indicate that condition 0T (37.6 Applied Bionics and Biomechanics 5 Max. (control) (0T) (45T) (90T) (135T) (180T) (0L) (45L) (90L) (135L) (180L) Figure 4: von Mises stress distributions for CR in the conventional model (control) and the experimental models. Areas with high stresses are indicated in red. Max 6e-6 (control) 5e-6 4e-6 3e-6 (0T) (45T) (90T) (135T) (180T) 2e-6 1e-6 (0L ) (45L) (90L) (135L ) (180L ) Figure 5: Distributions of the maximum principal strain for CR in the conventional model (control) and the experimental models. Areas with −6 high tensile strains are indicated in red. (e‐6 indicates 1 ∗ 10 ). MPa) induced the highest equivalent (von Mises) stress in the marked differences in the stresses were observed between bone. Moreover, conditions 180L (34.1 MPa), 90T (32.9 the conventional model and conditions 0L, 45L, 90L, 135T, MPa), 180T (32.2 MPa), 45T (28.9 MPa), 0 L (27.4 MPa), and 135L (Figure 4). 135L (23.5 MPa), 45L (23.4 MPa), 135T (23.1 MPa), and 90L (22.5 MPa) are implied. The stress was lowest in the con- 3.2. Maximum Principal Elastic Strain in the Canine PDL. ventional model (22.1 MPa). The areas with high compres- The principal strain in the canine PDL was highest when sive stresses (indicated as red areas in the figures) around traction forces were applied. Regions exhibiting compressive the uppermost OMI thread hole were much larger in condi- and tensile normal strains could be identified in the PDL. tions 180T and 180L than in the conventional model. No However, the magnitude of the tensile strain was significantly 6 Applied Bionics and Biomechanics –2e-6 0.000 4.000 (mm) 0.000 0.000 0.000 4.000 (mm) –2.5e-6 4.000 (mm) 0.000 4.000 (mm) 4.000 (mm) 0.000 4.000 (mm) 2.000 2.000 2.000 2.000 2.000 2.000 Control 0T 45T 90T 135T 180T –3.125e-6 –3.75e-6 –4e-6 –5e-6 0.000 0.000 4.000 (mm) 4.000 (mm) 0.000 4.000 (mm) 0.000 4.000 (mm) 0.000 4.000 (mm) 2.000 2.000 2.000 2.000 2.000 0L 45L 90L 135L 180L Figure 6: Distributions of the minimum principal strain for CR in the conventional model (control) and the experimental models. Areas with −6 high compressive strains are indicated in blue. (e‐6 presents 1 ∗ 10 ). higher than that of the compressive strain. All dominant revolving cap to overcome some of the limitations associated principal strains were clearly evident at the mesiolabial mar- with using an OMI. The biomechanical performance when gin of the PDL, with no marked differences in the strain dis- using various orthodontic loading directions with an OMI tribution between the models (Figure 5). The strain was the and a revolving cap anchorage in the case of orthodontic highest in condition 0L (14.9 μstrain), followed by conditions CR was investigated. The maximum and minimum principal 0T (14.8 μstrain), 45L and 90L (14.7 μstrain), and 45T, 90T, strains in the canine PDL were examined to determine differ- 135T, and 135L (14.6 μstrain). The maximum strain in the ences in CR. The von Mises stress was examined in the peri- conventional model was 14.3 μstrain. The peak strain was OMI cortical bone [14], which may be related to the risk of lower in conditions 180L (14.2 μstrain) and 180T (13.9 bone resorption. A revolving cap is a supplementary device μstrain) than in the conventional model. The difference in used in CR to overcome limitations in the positioning of the values between each experimental model and the conven- the OMI. tional model did not exceed 5%. This study found that the values of tensile strain (maxi- mum principal strain) in the canine PDL in all models did 3.3. Minimum Principal Elastic Strain in the Canine PDL. not differ by more than 5% from those in the conventional The principal strain in the canine PDL was the lowest when model when a revolving cap was located on the OMI between compressive forces were applied. An area of compressive the second premolar and the first molar. During orthodontic strain was clearly evident at the mesiolabial margin of the treatment, the revolving cap can be easily managed in PDL and on the distal surface of the inner PDL. The mini- cases of maxillary pneumatization. Moreover, the minimum mum strain peaked at condition 180T (−7.5 μstrain), principal strain is usually a compressive strain, and the com- followed by condition 180L (−7.6 μstrain); both of these pression at the canine PDL margin was on the inner mesiola- values were higher than those in the conventional model. bial surface, which indicates the occurrence of tipping. The The minimum strain was −7.9 μstrain for conditions 0L, minimum principal strain in the canine PDL for an angula- 45L, and 90L and −7.8 μstrain for conditions 0T, 90T, tion of 180 relative to the revolving cap resulted in the 135T, and 135L. The minimum strain in the conventional desired orthodontic movement. model and condition 45T was −7.7 μstrain. When translation The von Mises stresses in the peri-OMI bone of the max- occurred, an area of compression started to appear on the illa was highest for condition 0T (37.6 MPa) and varied distal surface of the inner PDL in the direction of the applied between 22 and 34 MPa in the conventional model as well force. A blue area appeared on the distal surface of the inner as in the other experimental models when the revolving cap PDL for conditions 180T and 180L, which was almost per- was located on the OMI between the second premolar and fectly aligned with the initial canine translation (Figure 6). the first molar. Stress values from 34 to 48 MPa will induce The maximum differences in the values between each exper- bone resorption, following the studies of Qian et al. and imental model and the conventional group were around 5%. Frost, which means using a revolving cap in condition 0T is not recommended [15, 16]. There is considerable interest among both patients and 4. Discussion orthodontists in using OMIs to move teeth due to their OMIs are often used to induce tooth translation in the dental advantages over both conventional methods and the use of extraoral devices. It is relatively straightforward to use clinic. This study has introduced the innovation of utilizing a Applied Bionics and Biomechanics 7 a revolving cap to cover the OMI to facilitate tooth move- Authors’ Contributions ment and hence also the translational mechanics phase of Kuson Tuntiwong and Jui-Ting Hsu are equal contributors. orthodontic treatment. This study showed that covering mini-implants by a revolving cap increased the peri-OMI Acknowledgments bone stress. In addition to the risk of pathologic bone resorption, there is also a possibility of crestal bone resorp- This research was supported by the China Medical Univer- tion based on the high stress values induced in the peri- sity, Taiwan (CMU109-MF-77). OMI bone when using the revolving cap under an angula- tion of 0 . This is probably due to the distance from the References original force to the revolving cap area, which would result in higher bone stress. Fortunately, a revolving cap at an [1] W. Proffit and H. Field, Malocclusion and dentofacial defor- angulation of 0 is not used frequently in orthodontic mity in contemporary society, in Contemporary Orthodontics, treatments. Mosby, St. Louis, MO, 1993. This study was subject to a variety of limitations, includ- [2] D. Roberts-Harry and J. Sandy, “Orthodontics. Part 9: anchor- ing the inherent ones that apply in any modeling study. A age control and distal movement,” British Dental Journal, model can only produce results as accurate as the set of vol. 196, no. 5, pp. 255–263, 2004. assumptions that were used to create it, including boundary [3] H.-S. Park, S.-M. Bae, H.-M. Kyung, and J.-H. Sung, “Micro- conditions, loading conditions, and material properties. The implant anchorage for treatment of skeletal class I bialveolar boundary conditions of the present model included that the protrusion,” Journal of Clinical Orthodontics, vol. 35, no. 7, pp. 417–422, 2001. top surface of the maxilla was fixed. The loading conditions included applying load over the revolving cap covering [4] H. H. Ammar, P. Ngan, R. J. Crout, V. H. Mucino, and O. M. Mukdadi, “Three-dimensional modeling and finite element OMI, which was placed between the second premolar and analysis in treatment planning for orthodontic tooth move- the first molar sites. The position of the OMI was set between ment,” American Journal of Orthodontics and Dentofacial the root of the second premolar and the first molar. There- Orthopedics, vol. 139, no. 1, pp. e59–e71, 2011. fore, the present findings might not apply to other positions [5] M. A. Papadopoulos and F. Tarawneh, “The use of miniscrew of OMIs and revolving caps. implants for temporary skeletal anchorage in orthodontics: a comprehensive review,” Oral Surgery, Oral Medicine, Oral 5. Conclusions Pathology, Oral Radiology, and Endodontics, vol. 103, no. 5, pp. e6–e15, 2007. Within the limitations as described above, the findings of this [6] S. Mohammed and H. Desai, “Basic concepts of finite element study can be summarized as follows: analysis and its applications in dentistry: an overview,” Journal of Oral Hygiene & Health, vol. 2, p. 156, 2014. (1) No obvious effects in decreasing bone stress were [7] P. Cattaneo, M. Dalstra, and B. Melsen, “The finite element observed in all models by using mini-implant method: a tool to study orthodontic tooth movement,” Journal (OMI) covered with various angles of the revolving of Dental Research, vol. 84, no. 5, pp. 428–433, 2005. cap. However, the stress around the top of the OMI [8] M. Poppe, C. Bourauel, and A. Jäger, “Determination of the thread hole was greatly increased in conditions elasticity parameters of the human periodontal ligament and 180T and 180L compared with the conventional the location of the center of resistance of single-rooted teeth,” model. No obvious differences in the stress in the Journal of Orofacial Orthopedics, vol. 63, no. 5, pp. 358–370, peri-OMI bone were found between the conventional model and conditions 0L, 45L, 90L, 135T, and 135L [9] E. D. Coolidge, “The thickness of the human periodontal membrane,” Journal of the American Dental Association (2) All dominant principal strains were clearly evident at (1939), vol. 24, no. 8, pp. 1260–1270, 1937. the mesiolabial margin of the PDL. However, the [10] Z. Liao, J. Chen, W. Li, M. A. Darendeliler, M. Swain, and highest strain in each experimental model did not Q. Li, “Biomechanical investigation into the role of the peri- differ by more than 5% from that in the conventional odontal ligament in optimising orthodontic force: a finite ele- model. It looks like there are no obvious effects in ment case study,” Archives of Oral Biology, vol. 66, pp. 98– decreasing or increasing the strain in PDL by using 107, 2016. the revolving cap in orthodontic treatment of canine [11] A. Kawarizadeh, C. Bourauel, and A. Jäger, “Experimental and retraction numerical determination of initial tooth mobility and material properties of the periodontal ligament in rat molar speci- Data Availability mens,” European Journal of Orthodontics, vol. 25, no. 6, pp. 569–578, 2003. The underlying data can be found through the authors. Any- [12] T.-S. Lin, F.-D. Tsai, C.-Y. Chen, and L.-W. Lin, “Factorial body who is interested in the data can email the authors analysis of variables affecting bone stress adjacent to the ortho- directly. dontic anchorage mini-implant with finite element analysis,” American Journal of Orthodontics and Dentofacial Orthope- dics, vol. 143, no. 2, pp. 182–189, 2013. Conflicts of Interest [13] M. S. M. Lande, A. Desai, A. Verma, and A. Gaur, “Stress anal- The authors declare that they have no conflicts of interest. ysis of polycarbonate spur gears for sugarcane juice machine 8 Applied Bionics and Biomechanics using FEA,” International Journal on Recent Technologies in Mechanical and Electrical Engineering (IJRMEE), vol. 2, no. 10, pp. 14–19, 2015. [14] M. Motoyoshi, S. Ueno, K. Okazaki, and N. Shimizu, “Bone stress for a mini-implant close to the roots of adjacent teeth - 3D finite element analysis,” International Journal of Oral and Maxillofacial Surgery, vol. 38, no. 4, pp. 363–368, 2009. [15] L. Qian, M. Todo, Y. Matsushita, and K. Koyano, “Finite ele- ment analysis of bone resorption around dental implant,” Journal of Biomechanical Science and Engineering, vol. 4, no. 3, pp. 365–376, 2009. [16] H. M. Frost, “Perspectives: bone's mechanical usage windows,” Bone and Mineral, vol. 19, no. 3, pp. 257–271, 1992.

Journal

Applied Bionics and BiomechanicsHindawi Publishing Corporation

Published: Jul 12, 2021

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