Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis

R. Savignano; R. Valentino; A. V. Razionale; A. Michelotti; S. Barone; V. D’Antò

doi:10.1155/2019/9687127

Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis

Savignano, R.;Valentino, R.;Razionale, A. V.;Michelotti, A.;Barone, S.;D’Antò, V. 2019-08-07 00:00:00 Hindawi Journal of Healthcare Engineering Volume 2019, Article ID 9687127, 9 pages https://doi.org/10.1155/2019/9687127 Research Article Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis 1 2 3 2 3 R. Savignano , R. Valentino , A. V. Razionale , A. Michelotti , S. Barone, and V. D’Anto` AirNivol s.r.l., Via Giuntini 25, 56023 Navacchio, Pisa, Italy Department of Neurosciences, Reproductive Sciences and Oral Sciences, University of Naples Federico II, Via Pansini 5, 80131 Naples, Italy Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino, 56122 Pisa, Italy Correspondence should be addressed to R. Savignano; robertosavignano@gmail.com Received 8 November 2018; Revised 6 March 2019; Accepted 18 July 2019; Published 7 August 2019 Guest Editor: Bernd Lapatki Copyright © 2019 R. Savignano et al. +is 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. Aim. To evaluate the biomechanical eﬀects of four diﬀerent auxiliary-aligner combinations for the extrusion of a maxillary central incisor and to deﬁne the most eﬀective design through ﬁnite element analysis (FEA). Materials and Methods. A full maxillary arch (14 teeth) was modelled by combining two diﬀerent imaging techniques: cone beam computed tomography and surface- structured light scan. +e appliance and auxiliary element geometries were created by exploiting computer-aided design (CAD) procedures. +e reconstructed digital models were imported within the ﬁnite element solver (Ansys 17). For the extrusion movement, the authors compared the aligner without an attachment with three auxiliary-aligner designs: a rectangular palatal attachment, a rectangular buccal attachment, and an ellipsoid buccal attachment. +e resulting force-moment (MF) system delivered by the aligner to the target tooth and the tooth displacement were calculated for each scenario. Results. +e maximum tooth displacement along the z-axis (0.07 mm) was obtained with the rectangular palatal attachment, while the minimum (0.02 mm) was obtained without any attachments. With the ellipsoid attachment, the highest undesired moments M and M were x y found. +e rectangular palatal attachment showed the highest F (2.0 N) with the lowest undesired forces (F � 0.4 N; F � − 0.2 N). z x y Conclusions. FEA demonstrated that the rectangular palatal attachment can improve the eﬀectiveness of the appliance for the extrusion of an upper central incisor. vertical plane compared to the other movements have larger 1. Introduction deviations and lower predictability [5, 6]. Previous studies +e extrusion of the anterior teeth is required to treat a reported the lowest accuracy for the extrusion movement challenging malocclusion: the anterior open bite. +is (average value 29.6%); this value was 18% for a maxillary malocclusion has a multifactorial aetiology and skeletal or central incisor and 25% for a mandibular central incisor [7]. dental components [1–3]. +e low accuracy of this movement is due to a poor grip of When aligners are used to treat open bite malocclusion, the aligner with the target tooth during the vertical pull. To the extrusion of the anterior teeth, the intrusion of the overcome these limitations, some author proposed using posterior teeth, or both orthodontic movements are required attachments or elastic from a button bonded onto the tooth’s [4]. buccal surface [7, 8]. Concerning orthodontic extrusion, previous studies Even though both ﬁxed appliances and clear aligners can about clear aligner therapy reported that movements on the move the teeth to clinically acceptable positions, there is no 2 Journal of Healthcare Engineering literature on the force magnitude that is being created by approach. At ﬁrst, a clinician acquired a patient’s upper arch aligner therapy [9]. impression using polyvinyl siloxane (PVS), which then resulted in a plaster model. By using the optical scanner Previous studies showed methodological deﬁciencies related to the sources of bias, such as the study design, DentalScan (Scan system srl, Navacchio, Italy), with a 10μm sample size, and the lack of a control group. Most of these accuracy, a digital model composed of tooth crowns and oral were retrospective studies, based on superimpositions of the soft tissues was created. initial and ﬁnal cast models [6, 7, 10]. Individual crown geometries and the gingiva were ob- Kravitz and coauthors calculated tooth movement ac- tained by a segmentation of the overall surface representing curacy by the superimposition of the virtual model of the teeth shapes and oral soft tissues. +e teeth and soft tissue predicted tooth position over the virtual model of the segmentations were performed by using noncommercial achieved tooth position obtained from posttreatment im- software developed by AirNivol (Navacchio, Italy). A pressions. To overlap the two digital models, the authors semiautomated procedure was used, which exploits the refer to the untreated teeth. By using this methodology, the curvature of the digital mouth model [18]. teeth can be superimposed within an accuracy of 0.2 and To reconstruct tooth roots and alveolar bone tissues, the 1.0 mm [7, 11, 12]. authors used a sequence of Digital Imaging and Commu- +ese methods used in previous studies to evaluate the nications in Medicine (DICOM) images obtained from the predictability of tooth movement by aligners were not ac- CBCT technique. +e patient’s dental model was then ob- curate for predicting the achievable movement in a speciﬁc tained by merging the images obtained from the CBCT patient nor do they take into account the root surface of the sensor and those obtained from the optical scanning. +e target teeth. ﬁnal digital model was made of tooth crown images In the orthodontic ﬁeld, a numerical simulation could reconstructed by the optical scans and tooth root anatomies provide quantitative and detailed data on the biomechanical obtained by CBCT imaging. response occurring during treatments [13]. In particular, +is method allowed to obtain a high resolution of the ﬁnite element analysis (FEA) represents an eﬀective tool to crowns, which is crucial to deﬁne a precise ﬁnite element analyse orthodontic features and optimize their design. model (FEM). However, very few attempts have been made to study tooth- CBCTdata were also processed to reconstruct the alveolar aligner interactions by ﬁnite element models (FEMs) bone using Amira (Visage Imaging Inc., Carlsbad, CA). [14–16]. For each slice, the regions outlined by the detected tooth +e aim of this study was to design a FEM to evaluate the contours were subtracted from the area outlined by the biomechanical eﬀects of four diﬀerent attachment-aligner extracted bone contour. Teeth shapes were excluded from conﬁgurations simulating the extrusion movement of an the alveolar bone model and replaced by the separated upper central incisor. segmented teeth models. +erefore, each tooth could be independently manipulated within the orthodontic model, thus providing an eﬀective tool for orthodontic simulations 2. Materials and Methods and treatment planning processes [19]. +e computer aided engineering (CAE) workﬂow, used to Periodontal dental ligament (PDL) tissues cannot be analyse the biomechanics of the diﬀerent aligner conﬁgu- easily visualized and reconstructed by using CBCT because rations, was designed according to the following steps: the slice thickness is similar to or even greater than the ligament space, which was about 0.2 mm [20]. (1) Digital reconstruction of patient’s anatomical tissues For this reason, the PDL geometry was modelled by (2) Design of aligner and auxiliary elements detecting the interface area between bone and tooth models. +e PDL was simpliﬁed, neglecting its variable thickness, (3) Deﬁnition of the ﬁnite element model and modelled as a 0.2 mm uniform thick layer [16, 21]. A (4) Mechanical proprieties assignment shell of 0.2 mm thickness was added to the external surface (5) Deﬁnition of boundary conditions of each tooth; the shell volume was then subtracted from the (6) Finite element analysis alveolar bone to deﬁne the PDL volume [22]. Figure 1 summarizes the described workﬂow. 2.2. Design of Aligner and Auxiliary Elements. For the 2.1. Digital Reconstruction of Patient’s Anatomical Tissues. simulation of the extrusion movement of an upper central +e digital anatomical model representing all patients’ tis- incisor, in this study, the authors compared four diﬀerent sues was obtained by using a computational and engineering attachment-aligner conﬁgurations. A standard aligner framework described by Barone et al. [17]. without auxiliaries was compared to aligners designed with An upper full-arch digital model was reconstructed by three diﬀerent attachment shapes and positions: combining two diﬀerent imaging techniques: cone beam (i) Rectangular palatal attachment (2.0 mm height × computed tomography (CBCT) and surface-structured light 4.0 mm width × 1.5 mm depth) scanning. All visible dental and oral soft tissues were digitalized by (ii) Rectangular buccal attachment (2.0 mm height × using an optical scanner based on a coded structured light 4.0 mm width × 1.5 mm depth) Journal of Healthcare Engineering 3 (a) Optical scan + CBCT (b) Merging (c) (d) (e) Finite element model (f ) Finite element analysis (g) Figure 1: +e patient’s anatomical structure (a) are digitalized through optical scanning and CBCT (b). Afterwards, the two datasets are merged to create highly accurate reconstructed teeth (c). Meanwhile, attachment (d) and aligner (e) are designed through CAD operations. All the digital volumes are meshed into FEM (f), and the diﬀerent conﬁgurations are simulated and analysed (g). (iii) Ellipsoid buccal attachment (2.5 mm height × All bodies were meshed by using solid elements (quadratic 4.0 mm width × 1.5 mm depth) 10 node tetrahedral elements). For this study, a full maxillary arch composed of 14 teeth was modelled. +e mesh was +e attachments were placed with the central point of constituted by approximately 900000 nodes and 480000 their base surface located 1 mm above the clinical crown elements. In particular, the aligner was meshed with ap- center in the z-axis direction. proximately 240000 nodes and 140000 elements, with slight CAD procedures were used to create the aligner and diﬀerences due to the attachment shape. +e PDL of the attachment shapes as described by Barone et al. [14]. +e central incisor was meshed with 40000 nodes and 22000 aligner was supposed to have a uniform 0.7 mm thickness as elements. +e mean size used for these models was 0.5 mm. done in previous studies [15, 16], which originates from the +e size of the elements has been chosen in accordance with mean thickness of the thermoplastic material disk (0.75 mm previous studies [14, 15, 19], considering that the main thick) before the thermoforming process [23]. purpose of this work is to compare eﬀects of diﬀerent auxiliaries on tooth movement. +e geometrical discrepancies between teeth and ap- 2.3. Deﬁnition of the Finite Element Model. +e recon- structed digital models were imported within the ﬁnite el- pliance, which result in an initial mismatch between the bodies, are the main responsible for the simulation’s results. ement modeler, Ansys 17 (Ansys, Inc., Canonsburg, PA). ® 4 Journal of Healthcare Engineering Table 1: Mechanical properties assigned to each body. +erefore, the meshing process must be precise to preserve the ideal expected tooth movement within a certain toler- Young’s modulus (MPa) Poisson’s ratio ance range. Tooth 20000 0.3 Bone 13800 0.3 Aligner 2050 0.3 2.4. Mechanical Proprieties Assignment. +e mechanical Attachment 20000 0.3 behavior of the alveolar bone, teeth, attachments, and aligner PDL 0.059 0.49 was described by using a linear elastic model as deﬁned by Barone et al. [14]. Moreover, the teeth and bone were supposed to be made adhesion between contact surfaces with corresponding from a homogeneous material, without discerning in the nodes that cannot separate from each other. Moreover, the enamel, pulp, and dentin for the teeth and the cortical and absence of a mutual sliding or separation can be assumed. cancellous for the bone. +e bone extremities were ﬁxed in all directions. +is assumption does not seem to aﬀect the simulation results as reported in previous studies [20, 24, 25] because of 2.6. Finite Element Analysis. +e initial mismatch between the higher stiﬀness of the tooth and bone compared with the target tooth and the appliance was generated as described PDL tissues. by Barone et al. [14], translating the target tooth, the at- It is diﬃcult to analyse in vivo the ligament’s mechanical tachment, and the related PDL and bone by 0.15 mm in the behavior because of the small size of this structure (thick- opposite direction, compared with the expected movement, ness � 0.2 mm). +erefore, most of the scientiﬁc literature as shown in Figure 2. has investigated the mechanical properties of the PDL +e nonlinear problem was solved by using the through experimental analyses, and several biomechanical Newton–Raphson residuals method based on the force and models were developed to describe PDL properties: linear moment convergence values. elastic, bilinear elastic, viscoelastic, hyperelastic, and mul- During the Newton–Raphson iterations, the contact tiphase [26]. However, the complex nonlinear response of penetration was checked with respect to a maximum al- the PDL does not need to be addressed while performing an lowable penetration tolerance value, which was deﬁned as analysis of the ﬁrst phase of the orthodontic reaction as in 0.01 mm. +e standard aligner led to the minimum initial the present study [13]. It is diﬃcult to analyse in vivo the penetration of 0.15 mm; therefore, a tolerance value of ligament’s mechanical behavior because of the small size of 0.01 mm was lower than 10% of the initial geometrical this structure (thickness � 0.2 mm). +erefore, most of the mismatch. +is value was determined by considering that scientiﬁc literature has investigated the mechanical prop- higher values signiﬁcantly aﬀect the results, while lower erties of the PDL through experimental analyses, and several values increase convergence time without entailing signiﬁ- biomechanical models were developed to describe PDL cant changes in the results. properties: linear elastic, bilinear elastic, viscoelastic, For each simulation, the resulting force system delivered hyperelastic, and multiphase [26]. However, the complex by the aligner to the target tooth and the tooth displacement nonlinear response of the PDL does not need to be addressed and rotation were calculated. +e force system was calcu- while performing an analysis of the ﬁrst phase of the or- lated at the tooth’s center of resistance (C ), which was RES thodontic reaction as in the present study [13]. calculated according to the method described by Viecilli +e removable appliances were modelled as made of a et al. [28]. Computational time resulted in about 6 hours for polyethylene terephthalate glycol-modiﬁed (PETG) ther- each simulation, using a workstation based on Intel Xeon moplastic disc with linear elastic mechanical response CPU E3-1245 v3@3.40 GHz and 16 GB RAM. [15, 16]. +e auxiliary attachments were supposed to be made of 3. Results and Discussion the same tooth material. Table 1 summarizes the material properties assigned to +e FEA results were analysed for each conﬁguration by each body. comparing forces and moments delivered to the tooth and measured at its C (Table 2) and the amount and direction RES 2.5. Deﬁnition of Boundary Conditions. Contact interface of orthodontic movement (Table 3). between the teeth and aligner, which represents the most Table 2 shows how the ellipsoid buccal attachment important contact surface since it is responsible for the generated the maximum tooth displacement (0.092 mm), loading condition, was set as frictionless. +is is a reasonable but in this aligner conﬁguration, we have also found the choice due to the existent dissimilarity between the appli- highest undesired moments represented by mesiodistal and ance’s thermoplastic material and the dental biological tis- buccopalatal tipping (M � 2.9 N·mm; M � − 1.9 N·mm). x y sue, taking into account the presence of saliva. +e rectangular palatal attachment showed the highest force Moreover, previous studies demonstrated that friction along the extrusion axis (2 N) with lower undesired loads. does not aﬀect the results signiﬁcantly [27]. Table 3 and Figure 3 show that the maximum tooth Teeth and respective PDLs were joined by a bonded displacement along the z-axis was obtained with the rect- contact; bonded contacts were considered also between the angular palatal attachment, which showed 0.07 mm of bone and PDL. A bonded contact corresponds to a perfect translation compared to 0.06 mm obtained with the ellipsoid Journal of Healthcare Engineering 5 Initial movement (0.15 mm) RES Figure 2: C and translation imposed on the target tooth to create the initial penetration between the tooth and aligner. RES Table 2: Maximum displacement and loads delivered to the tooth by the diﬀerent aligners. Standard Rectangular palatal Rectangular buccal Ellipsoid buccal aligner attachment attachment attachment Maximum tooth 0.079 0.088 0.086 0.092 displacement (mm) F (N) 0.0 0.4 0.7 0.8 F (N) 0.0 − 0.2 0.4 0.3 F (N) 0.4 2.0 1.3 1.3 M (N mm) 1.5 − 1.7 2.8 2.9 M (N mm) 1.8 0.6 − 1.7 − 1.9 M (N mm) − 2.8 − 1.9 1.0 0.7 “F” represents the force in each direction, and “M” denotes the moment along each direction. Table 3: Translation and rotation movements of the target tooth in the four diﬀerent conﬁgurations. Expected Standard Rectangular palatal Rectangular Ellipsoid movement aligner attachment buccal attachment buccal attachment Rotation x ( ) 0 0.1 − 0.09 0.15 0.15 Rotation y ( ) 0 − 0.13 − 0.17 − 0.11 − 0.18 Rotation z ( ) 0 − 0.55 − 0.41 − 0.01 − 0.11 Translation x (mm) 0 0 0 0 0 Translation y (mm) 0 0 0.01 0.01 0.01 Translation z (mm) 0.15 0.02 0.07 0.06 0.06 and rectangular buccal attachments. +e lowest tooth dis- numeric-based decision to design the aligners. +erefore, the placement was obtained with the standard aligner conﬁg- clinical choice for the rectangular palatal attachment would uration without attachments. +e standard aligner led to the be justiﬁed by the numerical results obtained by FEA. lowest desired translation on the z-axis, while it led to the Few previous studies analysed tooth movements achieved by aligners by using FEM. +ese works calculated highest undesired movement, with a rotation of − 0.55 around the z-axis. the force system delivered by the thermoplastic appliance to Figure 4 shows the total displacement for each the target tooth, and they compared diﬀerent aligner con- conﬁguration. ﬁgurations to identify the most eﬃcient one through a FEA +e analysis of the FEA results provided interesting [16, 29, 30]. +ese studies referred to diﬀerent tooth information that could improve the design phase of or- movements, like canine distalization or the mesial move- thodontic aligners. +e resulting parameters of the force ment of an upper molar [29, 30]. FEA results demonstrated system helped to compare the advantages and disadvantages that the diﬀerent design conﬁgurations have a strong in- for each conﬁguration. +e results analysis allowed for a ﬂuence on the loads delivered to the target tooth. No studies 6 Journal of Healthcare Engineering Rotation deviations (°) Translation deviations (mm) 0.6 0.15 0.4 0.1 0.2 0.05 0 0 Rot x Rot y Rot z Transl x Transl y Transl z Standard aligner Rectangular buccal Standard aligner Rectangular buccal attachment attachment Rectangular palatal Rectangular palatal attachment attachment Ellipsoid buccal Ellipsoid buccal attachment attachment (a) (b) Figure 3: Graphical representation of rotation (a) and translation (b) deviations (absolute values) for each scenario, compared with the expected tooth movement. Rectangular Rectangular Ellipsoid Standard palatal buccal buccal aligner Displacement (mm) attachment attachment attachment 0.092 Frontal 0.082 view 0.072 0.052 0.042 0.032 Lateral view 0.022 0.011 Figure 4: Colormap of tooth displacement for each scenario. analysed the extrusion movement of an upper central incisor delivered to the tooth by the aligners, but not of the quality of by using the FEA before. the delivered loads. +e analysis of the FEM results could be performed by For this reason, the analysis gets more consistent when considering three resulting outcomes: referring to the force systems measured at the C . It can be RES (i) Force system delivered to the tooth and measured at noticed that the rectangular palatal attachment led to the its C highest force along the extrusion axis (2.0 N) with lower RES undesired moments. +e other conﬁgurations brought load (ii) Tooth translation and rotation for each spatial axis values lower than those with the rectangular palatal at- (iii) Colormap of tooth displacement tachment and to higher undesired moments. Table 2 shows Table 2 shows that the highest maximum tooth dis- that the force delivered to the tooth along the z-axis (F ) placement (0.092 mm) was obtained with the ellipsoid increased by 5 times, from 0.4 N to 2.0 N, after adding the buccal attachment, while the lowest (0.079 mm) was ob- rectangular palatal to the standard aligner. However, the tained with the standard aligner. +e maximum tooth aligner with the ellipsoid and rectangular buccal attachments displacement does not provide exhaustive information for brought a lower F (1.3 N) and higher undesired moments analyzing the eﬀective tooth movement because it lacks (M and M ) and forces (F and F ). x y x y information about the movement direction. It can be +e amount of tooth translation and rotation in each considered an indicator of the amount of force and moment direction, shown in Table 3 and in Figure 3, conﬁrms the Journal of Healthcare Engineering 7 previous analysis. +e palatal rectangular attachments led to possible to the C on each axis to avoid undesired RES the highest translation along the z-axis (0.07 mm), while it is moments. clear that the standard aligner does not satisfy clinical ex- According to our research, the design of an aligner pectations, leading to a minimum translation along the z- treatment should be split into two parts: the deﬁnition of the axis of only 0.02 mm. expected movement and the choice of the best auxiliary +e rectangular palatal attachment delivered the highest element for each speciﬁc movement. F (2 N), which is approximately 50% more thanF measured +e aim was to demonstrate how an auxiliary element’s z z for the other attachment conﬁgurations. However, the features aﬀect the interaction between the aligner and target amount of translation along the z-axis increased only by tooth. Results demonstrated that attachments are crucial for 0.01 mm, from 0.06 mm to 0.07 mm. +is result suggests that improving the eﬀectiveness of the extrusion movement. In there are other variables that should be considered in the particular, the rectangular palatal attachment can improve analysis. the eﬀectiveness of the appliance better than the rectangular +e attachment location seems to aﬀect its eﬀectiveness buccal attachment and the ellipsoidal buccal attachment. more than its shape. +e rectangular and ellipsoid buccal Further studies should be carried on, accounting for less attachments led to very similar results; however, placing the idealized conditions. In particular, it could be useful to use a rectangular attachment on the lingual surface improved the real thermoformed aligner with nonuniform thickness, and outcome signiﬁcantly. the results should be compared to those obtained with a +is result can be related to the diﬀerent angles between uniform aligner to evaluate the eﬀect of this simpliﬁcation. the attachment active surface and the tooth. Moreover, the present study analysed the ﬁrst eﬀect of Further studies should investigate also the eﬀect of the the orthodontic appliance, thus assuming linear elastic attachment positioning criteria on the tooth movement, mechanical behavior for all bodies. focusing on the amount of active surface of the attachment. A more complete FEA could be carried on by using FEA allows also for a graphical analysis, as shown in nonlinear mechanical response for PDL and aligners. Figure 4. CAE proved to be useful for analyzing aligner behavior +e expected extrusion should be represented by a and providing information to enhance their design. +e monocromatic colormap in Figure 4, meaning a pure paper showed how it could improve the knowledge of tooth- translation of the tooth along the z-axis. appliance interaction in orthodontics. +erefore, the best colormap in Figure 3 is represented by the most uniform colour distribution. +e rectangular 4. Conclusions vestibular attachment and the ellipsoidal vestibular attach- ment conﬁgurations are characterized by an evident colour Considering the results obtained through the FEA, we can modiﬁcation from green to red on the x and y axes. conclude the following: +erefore, the tooth movement is largely represented by (i) +e extrusion of an upper central incisor cannot be undesired movement. +is consideration could be clearer by achieved without any attachment. noticing that the palatal rectangular attachment colormap is (ii) +e shape and position of the attachments aﬀect the mostly uniform. +e standard aligner is clearly the worst conﬁguration expected orthodontic movement. In this case, the also when considering the map of displacement. +e col- rectangular palatal attachment proved to be the best ormap shows a large blue circle, which approximately conﬁguration to improve the eﬀectiveness of the represents the tooth’s center of rotation (C ). +erefore, appliance for the extrusion movement of an upper ROT central incisor. instead of a pure translation along the z-axis, this conﬁg- uration generated mainly a rotation around C . ROT (iii) +e attachment position, which inﬂuences the area +e results show that the rectangular and the ellipsoidal of its active surface for the speciﬁc movement, buccal attachments provided similar results on the force showed a stronger inﬂuence on the outcome system delivered to the tooth. compared to its shape. Comparing the results obtained with the buccal and (iv) +e analysis of the force system delivered by the palatal rectangular attachment, it is noticeable that M de- aligner to the tooth should not only focus on the creased to 0.6 N·mm compared with − 1.7 N·mm and desired loads but also the eﬀect of undesired loads − 1.9 N·mm obtained with the buccal rectangular and buccal should be properly taken into account, as it is a ellipsoidal attachment, respectively. +is eﬀect can be determinant when selecting the proper appliance explained by analyzing the distance between the attachment conﬁguration. and C on the x-axis in the 3 conﬁgurations. It is known RES (v) +e developed model can well simulate the initial that higher distances on the x-axis and z-axis between the phase of an orthodontic treatment and can be used, force application and the C generate higher M . RES y during the treatment design process, for the opti- +e extrusion movement requires a force system without mization of aligner features in order to obtain a any moment and only one force (F ). +erefore, the most more predictable orthodontic treatment. eﬀective conﬁguration should provide the aligner with the maximum contact surface on the xy plane to deliver F . (vi) Further studies should analyse the eﬀect of non- Meanwhile, the contact surface should be located as close as linear mechanical behavior of PDL and aligner and 8 Journal of Healthcare Engineering and meta-analysis,” Orthodontics and Craniofacial Research, their variable thickness. Moreover, it would be vol. 20, no. 3, pp. 127–133, 2017. useful to investigate the eﬀect of multiple attach- [10] G. Djeu, C. Shelton, and A. 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Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2019 R. Savignano 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.
ISSN: 2040-2295
eISSN: 2040-2309
DOI: 10.1155/2019/9687127
Publisher site: See Article on Publisher Site

Abstract

Hindawi Journal of Healthcare Engineering Volume 2019, Article ID 9687127, 9 pages https://doi.org/10.1155/2019/9687127 Research Article Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis 1 2 3 2 3 R. Savignano , R. Valentino , A. V. Razionale , A. Michelotti , S. Barone, and V. D’Anto` AirNivol s.r.l., Via Giuntini 25, 56023 Navacchio, Pisa, Italy Department of Neurosciences, Reproductive Sciences and Oral Sciences, University of Naples Federico II, Via Pansini 5, 80131 Naples, Italy Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino, 56122 Pisa, Italy Correspondence should be addressed to R. Savignano; robertosavignano@gmail.com Received 8 November 2018; Revised 6 March 2019; Accepted 18 July 2019; Published 7 August 2019 Guest Editor: Bernd Lapatki Copyright © 2019 R. Savignano et al. +is 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. Aim. To evaluate the biomechanical eﬀects of four diﬀerent auxiliary-aligner combinations for the extrusion of a maxillary central incisor and to deﬁne the most eﬀective design through ﬁnite element analysis (FEA). Materials and Methods. A full maxillary arch (14 teeth) was modelled by combining two diﬀerent imaging techniques: cone beam computed tomography and surface- structured light scan. +e appliance and auxiliary element geometries were created by exploiting computer-aided design (CAD) procedures. +e reconstructed digital models were imported within the ﬁnite element solver (Ansys 17). For the extrusion movement, the authors compared the aligner without an attachment with three auxiliary-aligner designs: a rectangular palatal attachment, a rectangular buccal attachment, and an ellipsoid buccal attachment. +e resulting force-moment (MF) system delivered by the aligner to the target tooth and the tooth displacement were calculated for each scenario. Results. +e maximum tooth displacement along the z-axis (0.07 mm) was obtained with the rectangular palatal attachment, while the minimum (0.02 mm) was obtained without any attachments. With the ellipsoid attachment, the highest undesired moments M and M were x y found. +e rectangular palatal attachment showed the highest F (2.0 N) with the lowest undesired forces (F � 0.4 N; F � − 0.2 N). z x y Conclusions. FEA demonstrated that the rectangular palatal attachment can improve the eﬀectiveness of the appliance for the extrusion of an upper central incisor. vertical plane compared to the other movements have larger 1. Introduction deviations and lower predictability [5, 6]. Previous studies +e extrusion of the anterior teeth is required to treat a reported the lowest accuracy for the extrusion movement challenging malocclusion: the anterior open bite. +is (average value 29.6%); this value was 18% for a maxillary malocclusion has a multifactorial aetiology and skeletal or central incisor and 25% for a mandibular central incisor [7]. dental components [1–3]. +e low accuracy of this movement is due to a poor grip of When aligners are used to treat open bite malocclusion, the aligner with the target tooth during the vertical pull. To the extrusion of the anterior teeth, the intrusion of the overcome these limitations, some author proposed using posterior teeth, or both orthodontic movements are required attachments or elastic from a button bonded onto the tooth’s [4]. buccal surface [7, 8]. Concerning orthodontic extrusion, previous studies Even though both ﬁxed appliances and clear aligners can about clear aligner therapy reported that movements on the move the teeth to clinically acceptable positions, there is no 2 Journal of Healthcare Engineering literature on the force magnitude that is being created by approach. At ﬁrst, a clinician acquired a patient’s upper arch aligner therapy [9]. impression using polyvinyl siloxane (PVS), which then resulted in a plaster model. By using the optical scanner Previous studies showed methodological deﬁciencies related to the sources of bias, such as the study design, DentalScan (Scan system srl, Navacchio, Italy), with a 10μm sample size, and the lack of a control group. Most of these accuracy, a digital model composed of tooth crowns and oral were retrospective studies, based on superimpositions of the soft tissues was created. initial and ﬁnal cast models [6, 7, 10]. Individual crown geometries and the gingiva were ob- Kravitz and coauthors calculated tooth movement ac- tained by a segmentation of the overall surface representing curacy by the superimposition of the virtual model of the teeth shapes and oral soft tissues. +e teeth and soft tissue predicted tooth position over the virtual model of the segmentations were performed by using noncommercial achieved tooth position obtained from posttreatment im- software developed by AirNivol (Navacchio, Italy). A pressions. To overlap the two digital models, the authors semiautomated procedure was used, which exploits the refer to the untreated teeth. By using this methodology, the curvature of the digital mouth model [18]. teeth can be superimposed within an accuracy of 0.2 and To reconstruct tooth roots and alveolar bone tissues, the 1.0 mm [7, 11, 12]. authors used a sequence of Digital Imaging and Commu- +ese methods used in previous studies to evaluate the nications in Medicine (DICOM) images obtained from the predictability of tooth movement by aligners were not ac- CBCT technique. +e patient’s dental model was then ob- curate for predicting the achievable movement in a speciﬁc tained by merging the images obtained from the CBCT patient nor do they take into account the root surface of the sensor and those obtained from the optical scanning. +e target teeth. ﬁnal digital model was made of tooth crown images In the orthodontic ﬁeld, a numerical simulation could reconstructed by the optical scans and tooth root anatomies provide quantitative and detailed data on the biomechanical obtained by CBCT imaging. response occurring during treatments [13]. In particular, +is method allowed to obtain a high resolution of the ﬁnite element analysis (FEA) represents an eﬀective tool to crowns, which is crucial to deﬁne a precise ﬁnite element analyse orthodontic features and optimize their design. model (FEM). However, very few attempts have been made to study tooth- CBCTdata were also processed to reconstruct the alveolar aligner interactions by ﬁnite element models (FEMs) bone using Amira (Visage Imaging Inc., Carlsbad, CA). [14–16]. For each slice, the regions outlined by the detected tooth +e aim of this study was to design a FEM to evaluate the contours were subtracted from the area outlined by the biomechanical eﬀects of four diﬀerent attachment-aligner extracted bone contour. Teeth shapes were excluded from conﬁgurations simulating the extrusion movement of an the alveolar bone model and replaced by the separated upper central incisor. segmented teeth models. +erefore, each tooth could be independently manipulated within the orthodontic model, thus providing an eﬀective tool for orthodontic simulations 2. Materials and Methods and treatment planning processes [19]. +e computer aided engineering (CAE) workﬂow, used to Periodontal dental ligament (PDL) tissues cannot be analyse the biomechanics of the diﬀerent aligner conﬁgu- easily visualized and reconstructed by using CBCT because rations, was designed according to the following steps: the slice thickness is similar to or even greater than the ligament space, which was about 0.2 mm [20]. (1) Digital reconstruction of patient’s anatomical tissues For this reason, the PDL geometry was modelled by (2) Design of aligner and auxiliary elements detecting the interface area between bone and tooth models. +e PDL was simpliﬁed, neglecting its variable thickness, (3) Deﬁnition of the ﬁnite element model and modelled as a 0.2 mm uniform thick layer [16, 21]. A (4) Mechanical proprieties assignment shell of 0.2 mm thickness was added to the external surface (5) Deﬁnition of boundary conditions of each tooth; the shell volume was then subtracted from the (6) Finite element analysis alveolar bone to deﬁne the PDL volume [22]. Figure 1 summarizes the described workﬂow. 2.2. Design of Aligner and Auxiliary Elements. For the 2.1. Digital Reconstruction of Patient’s Anatomical Tissues. simulation of the extrusion movement of an upper central +e digital anatomical model representing all patients’ tis- incisor, in this study, the authors compared four diﬀerent sues was obtained by using a computational and engineering attachment-aligner conﬁgurations. A standard aligner framework described by Barone et al. [17]. without auxiliaries was compared to aligners designed with An upper full-arch digital model was reconstructed by three diﬀerent attachment shapes and positions: combining two diﬀerent imaging techniques: cone beam (i) Rectangular palatal attachment (2.0 mm height × computed tomography (CBCT) and surface-structured light 4.0 mm width × 1.5 mm depth) scanning. All visible dental and oral soft tissues were digitalized by (ii) Rectangular buccal attachment (2.0 mm height × using an optical scanner based on a coded structured light 4.0 mm width × 1.5 mm depth) Journal of Healthcare Engineering 3 (a) Optical scan + CBCT (b) Merging (c) (d) (e) Finite element model (f ) Finite element analysis (g) Figure 1: +e patient’s anatomical structure (a) are digitalized through optical scanning and CBCT (b). Afterwards, the two datasets are merged to create highly accurate reconstructed teeth (c). Meanwhile, attachment (d) and aligner (e) are designed through CAD operations. All the digital volumes are meshed into FEM (f), and the diﬀerent conﬁgurations are simulated and analysed (g). (iii) Ellipsoid buccal attachment (2.5 mm height × All bodies were meshed by using solid elements (quadratic 4.0 mm width × 1.5 mm depth) 10 node tetrahedral elements). For this study, a full maxillary arch composed of 14 teeth was modelled. +e mesh was +e attachments were placed with the central point of constituted by approximately 900000 nodes and 480000 their base surface located 1 mm above the clinical crown elements. In particular, the aligner was meshed with ap- center in the z-axis direction. proximately 240000 nodes and 140000 elements, with slight CAD procedures were used to create the aligner and diﬀerences due to the attachment shape. +e PDL of the attachment shapes as described by Barone et al. [14]. +e central incisor was meshed with 40000 nodes and 22000 aligner was supposed to have a uniform 0.7 mm thickness as elements. +e mean size used for these models was 0.5 mm. done in previous studies [15, 16], which originates from the +e size of the elements has been chosen in accordance with mean thickness of the thermoplastic material disk (0.75 mm previous studies [14, 15, 19], considering that the main thick) before the thermoforming process [23]. purpose of this work is to compare eﬀects of diﬀerent auxiliaries on tooth movement. +e geometrical discrepancies between teeth and ap- 2.3. Deﬁnition of the Finite Element Model. +e recon- structed digital models were imported within the ﬁnite el- pliance, which result in an initial mismatch between the bodies, are the main responsible for the simulation’s results. ement modeler, Ansys 17 (Ansys, Inc., Canonsburg, PA). ® 4 Journal of Healthcare Engineering Table 1: Mechanical properties assigned to each body. +erefore, the meshing process must be precise to preserve the ideal expected tooth movement within a certain toler- Young’s modulus (MPa) Poisson’s ratio ance range. Tooth 20000 0.3 Bone 13800 0.3 Aligner 2050 0.3 2.4. Mechanical Proprieties Assignment. +e mechanical Attachment 20000 0.3 behavior of the alveolar bone, teeth, attachments, and aligner PDL 0.059 0.49 was described by using a linear elastic model as deﬁned by Barone et al. [14]. Moreover, the teeth and bone were supposed to be made adhesion between contact surfaces with corresponding from a homogeneous material, without discerning in the nodes that cannot separate from each other. Moreover, the enamel, pulp, and dentin for the teeth and the cortical and absence of a mutual sliding or separation can be assumed. cancellous for the bone. +e bone extremities were ﬁxed in all directions. +is assumption does not seem to aﬀect the simulation results as reported in previous studies [20, 24, 25] because of 2.6. Finite Element Analysis. +e initial mismatch between the higher stiﬀness of the tooth and bone compared with the target tooth and the appliance was generated as described PDL tissues. by Barone et al. [14], translating the target tooth, the at- It is diﬃcult to analyse in vivo the ligament’s mechanical tachment, and the related PDL and bone by 0.15 mm in the behavior because of the small size of this structure (thick- opposite direction, compared with the expected movement, ness � 0.2 mm). +erefore, most of the scientiﬁc literature as shown in Figure 2. has investigated the mechanical properties of the PDL +e nonlinear problem was solved by using the through experimental analyses, and several biomechanical Newton–Raphson residuals method based on the force and models were developed to describe PDL properties: linear moment convergence values. elastic, bilinear elastic, viscoelastic, hyperelastic, and mul- During the Newton–Raphson iterations, the contact tiphase [26]. However, the complex nonlinear response of penetration was checked with respect to a maximum al- the PDL does not need to be addressed while performing an lowable penetration tolerance value, which was deﬁned as analysis of the ﬁrst phase of the orthodontic reaction as in 0.01 mm. +e standard aligner led to the minimum initial the present study [13]. It is diﬃcult to analyse in vivo the penetration of 0.15 mm; therefore, a tolerance value of ligament’s mechanical behavior because of the small size of 0.01 mm was lower than 10% of the initial geometrical this structure (thickness � 0.2 mm). +erefore, most of the mismatch. +is value was determined by considering that scientiﬁc literature has investigated the mechanical prop- higher values signiﬁcantly aﬀect the results, while lower erties of the PDL through experimental analyses, and several values increase convergence time without entailing signiﬁ- biomechanical models were developed to describe PDL cant changes in the results. properties: linear elastic, bilinear elastic, viscoelastic, For each simulation, the resulting force system delivered hyperelastic, and multiphase [26]. However, the complex by the aligner to the target tooth and the tooth displacement nonlinear response of the PDL does not need to be addressed and rotation were calculated. +e force system was calcu- while performing an analysis of the ﬁrst phase of the or- lated at the tooth’s center of resistance (C ), which was RES thodontic reaction as in the present study [13]. calculated according to the method described by Viecilli +e removable appliances were modelled as made of a et al. [28]. Computational time resulted in about 6 hours for polyethylene terephthalate glycol-modiﬁed (PETG) ther- each simulation, using a workstation based on Intel Xeon moplastic disc with linear elastic mechanical response CPU E3-1245 v3@3.40 GHz and 16 GB RAM. [15, 16]. +e auxiliary attachments were supposed to be made of 3. Results and Discussion the same tooth material. Table 1 summarizes the material properties assigned to +e FEA results were analysed for each conﬁguration by each body. comparing forces and moments delivered to the tooth and measured at its C (Table 2) and the amount and direction RES 2.5. Deﬁnition of Boundary Conditions. Contact interface of orthodontic movement (Table 3). between the teeth and aligner, which represents the most Table 2 shows how the ellipsoid buccal attachment important contact surface since it is responsible for the generated the maximum tooth displacement (0.092 mm), loading condition, was set as frictionless. +is is a reasonable but in this aligner conﬁguration, we have also found the choice due to the existent dissimilarity between the appli- highest undesired moments represented by mesiodistal and ance’s thermoplastic material and the dental biological tis- buccopalatal tipping (M � 2.9 N·mm; M � − 1.9 N·mm). x y sue, taking into account the presence of saliva. +e rectangular palatal attachment showed the highest force Moreover, previous studies demonstrated that friction along the extrusion axis (2 N) with lower undesired loads. does not aﬀect the results signiﬁcantly [27]. Table 3 and Figure 3 show that the maximum tooth Teeth and respective PDLs were joined by a bonded displacement along the z-axis was obtained with the rect- contact; bonded contacts were considered also between the angular palatal attachment, which showed 0.07 mm of bone and PDL. A bonded contact corresponds to a perfect translation compared to 0.06 mm obtained with the ellipsoid Journal of Healthcare Engineering 5 Initial movement (0.15 mm) RES Figure 2: C and translation imposed on the target tooth to create the initial penetration between the tooth and aligner. RES Table 2: Maximum displacement and loads delivered to the tooth by the diﬀerent aligners. Standard Rectangular palatal Rectangular buccal Ellipsoid buccal aligner attachment attachment attachment Maximum tooth 0.079 0.088 0.086 0.092 displacement (mm) F (N) 0.0 0.4 0.7 0.8 F (N) 0.0 − 0.2 0.4 0.3 F (N) 0.4 2.0 1.3 1.3 M (N mm) 1.5 − 1.7 2.8 2.9 M (N mm) 1.8 0.6 − 1.7 − 1.9 M (N mm) − 2.8 − 1.9 1.0 0.7 “F” represents the force in each direction, and “M” denotes the moment along each direction. Table 3: Translation and rotation movements of the target tooth in the four diﬀerent conﬁgurations. Expected Standard Rectangular palatal Rectangular Ellipsoid movement aligner attachment buccal attachment buccal attachment Rotation x ( ) 0 0.1 − 0.09 0.15 0.15 Rotation y ( ) 0 − 0.13 − 0.17 − 0.11 − 0.18 Rotation z ( ) 0 − 0.55 − 0.41 − 0.01 − 0.11 Translation x (mm) 0 0 0 0 0 Translation y (mm) 0 0 0.01 0.01 0.01 Translation z (mm) 0.15 0.02 0.07 0.06 0.06 and rectangular buccal attachments. +e lowest tooth dis- numeric-based decision to design the aligners. +erefore, the placement was obtained with the standard aligner conﬁg- clinical choice for the rectangular palatal attachment would uration without attachments. +e standard aligner led to the be justiﬁed by the numerical results obtained by FEA. lowest desired translation on the z-axis, while it led to the Few previous studies analysed tooth movements achieved by aligners by using FEM. +ese works calculated highest undesired movement, with a rotation of − 0.55 around the z-axis. the force system delivered by the thermoplastic appliance to Figure 4 shows the total displacement for each the target tooth, and they compared diﬀerent aligner con- conﬁguration. ﬁgurations to identify the most eﬃcient one through a FEA +e analysis of the FEA results provided interesting [16, 29, 30]. +ese studies referred to diﬀerent tooth information that could improve the design phase of or- movements, like canine distalization or the mesial move- thodontic aligners. +e resulting parameters of the force ment of an upper molar [29, 30]. FEA results demonstrated system helped to compare the advantages and disadvantages that the diﬀerent design conﬁgurations have a strong in- for each conﬁguration. +e results analysis allowed for a ﬂuence on the loads delivered to the target tooth. No studies 6 Journal of Healthcare Engineering Rotation deviations (°) Translation deviations (mm) 0.6 0.15 0.4 0.1 0.2 0.05 0 0 Rot x Rot y Rot z Transl x Transl y Transl z Standard aligner Rectangular buccal Standard aligner Rectangular buccal attachment attachment Rectangular palatal Rectangular palatal attachment attachment Ellipsoid buccal Ellipsoid buccal attachment attachment (a) (b) Figure 3: Graphical representation of rotation (a) and translation (b) deviations (absolute values) for each scenario, compared with the expected tooth movement. Rectangular Rectangular Ellipsoid Standard palatal buccal buccal aligner Displacement (mm) attachment attachment attachment 0.092 Frontal 0.082 view 0.072 0.052 0.042 0.032 Lateral view 0.022 0.011 Figure 4: Colormap of tooth displacement for each scenario. analysed the extrusion movement of an upper central incisor delivered to the tooth by the aligners, but not of the quality of by using the FEA before. the delivered loads. +e analysis of the FEM results could be performed by For this reason, the analysis gets more consistent when considering three resulting outcomes: referring to the force systems measured at the C . It can be RES (i) Force system delivered to the tooth and measured at noticed that the rectangular palatal attachment led to the its C highest force along the extrusion axis (2.0 N) with lower RES undesired moments. +e other conﬁgurations brought load (ii) Tooth translation and rotation for each spatial axis values lower than those with the rectangular palatal at- (iii) Colormap of tooth displacement tachment and to higher undesired moments. Table 2 shows Table 2 shows that the highest maximum tooth dis- that the force delivered to the tooth along the z-axis (F ) placement (0.092 mm) was obtained with the ellipsoid increased by 5 times, from 0.4 N to 2.0 N, after adding the buccal attachment, while the lowest (0.079 mm) was ob- rectangular palatal to the standard aligner. However, the tained with the standard aligner. +e maximum tooth aligner with the ellipsoid and rectangular buccal attachments displacement does not provide exhaustive information for brought a lower F (1.3 N) and higher undesired moments analyzing the eﬀective tooth movement because it lacks (M and M ) and forces (F and F ). x y x y information about the movement direction. It can be +e amount of tooth translation and rotation in each considered an indicator of the amount of force and moment direction, shown in Table 3 and in Figure 3, conﬁrms the Journal of Healthcare Engineering 7 previous analysis. +e palatal rectangular attachments led to possible to the C on each axis to avoid undesired RES the highest translation along the z-axis (0.07 mm), while it is moments. clear that the standard aligner does not satisfy clinical ex- According to our research, the design of an aligner pectations, leading to a minimum translation along the z- treatment should be split into two parts: the deﬁnition of the axis of only 0.02 mm. expected movement and the choice of the best auxiliary +e rectangular palatal attachment delivered the highest element for each speciﬁc movement. F (2 N), which is approximately 50% more thanF measured +e aim was to demonstrate how an auxiliary element’s z z for the other attachment conﬁgurations. However, the features aﬀect the interaction between the aligner and target amount of translation along the z-axis increased only by tooth. Results demonstrated that attachments are crucial for 0.01 mm, from 0.06 mm to 0.07 mm. +is result suggests that improving the eﬀectiveness of the extrusion movement. In there are other variables that should be considered in the particular, the rectangular palatal attachment can improve analysis. the eﬀectiveness of the appliance better than the rectangular +e attachment location seems to aﬀect its eﬀectiveness buccal attachment and the ellipsoidal buccal attachment. more than its shape. +e rectangular and ellipsoid buccal Further studies should be carried on, accounting for less attachments led to very similar results; however, placing the idealized conditions. In particular, it could be useful to use a rectangular attachment on the lingual surface improved the real thermoformed aligner with nonuniform thickness, and outcome signiﬁcantly. the results should be compared to those obtained with a +is result can be related to the diﬀerent angles between uniform aligner to evaluate the eﬀect of this simpliﬁcation. the attachment active surface and the tooth. Moreover, the present study analysed the ﬁrst eﬀect of Further studies should investigate also the eﬀect of the the orthodontic appliance, thus assuming linear elastic attachment positioning criteria on the tooth movement, mechanical behavior for all bodies. focusing on the amount of active surface of the attachment. A more complete FEA could be carried on by using FEA allows also for a graphical analysis, as shown in nonlinear mechanical response for PDL and aligners. Figure 4. CAE proved to be useful for analyzing aligner behavior +e expected extrusion should be represented by a and providing information to enhance their design. +e monocromatic colormap in Figure 4, meaning a pure paper showed how it could improve the knowledge of tooth- translation of the tooth along the z-axis. appliance interaction in orthodontics. +erefore, the best colormap in Figure 3 is represented by the most uniform colour distribution. +e rectangular 4. Conclusions vestibular attachment and the ellipsoidal vestibular attach- ment conﬁgurations are characterized by an evident colour Considering the results obtained through the FEA, we can modiﬁcation from green to red on the x and y axes. conclude the following: +erefore, the tooth movement is largely represented by (i) +e extrusion of an upper central incisor cannot be undesired movement. +is consideration could be clearer by achieved without any attachment. noticing that the palatal rectangular attachment colormap is (ii) +e shape and position of the attachments aﬀect the mostly uniform. +e standard aligner is clearly the worst conﬁguration expected orthodontic movement. In this case, the also when considering the map of displacement. +e col- rectangular palatal attachment proved to be the best ormap shows a large blue circle, which approximately conﬁguration to improve the eﬀectiveness of the represents the tooth’s center of rotation (C ). +erefore, appliance for the extrusion movement of an upper ROT central incisor. instead of a pure translation along the z-axis, this conﬁg- uration generated mainly a rotation around C . ROT (iii) +e attachment position, which inﬂuences the area +e results show that the rectangular and the ellipsoidal of its active surface for the speciﬁc movement, buccal attachments provided similar results on the force showed a stronger inﬂuence on the outcome system delivered to the tooth. compared to its shape. Comparing the results obtained with the buccal and (iv) +e analysis of the force system delivered by the palatal rectangular attachment, it is noticeable that M de- aligner to the tooth should not only focus on the creased to 0.6 N·mm compared with − 1.7 N·mm and desired loads but also the eﬀect of undesired loads − 1.9 N·mm obtained with the buccal rectangular and buccal should be properly taken into account, as it is a ellipsoidal attachment, respectively. +is eﬀect can be determinant when selecting the proper appliance explained by analyzing the distance between the attachment conﬁguration. and C on the x-axis in the 3 conﬁgurations. It is known RES (v) +e developed model can well simulate the initial that higher distances on the x-axis and z-axis between the phase of an orthodontic treatment and can be used, force application and the C generate higher M . RES y during the treatment design process, for the opti- +e extrusion movement requires a force system without mization of aligner features in order to obtain a any moment and only one force (F ). +erefore, the most more predictable orthodontic treatment. eﬀective conﬁguration should provide the aligner with the maximum contact surface on the xy plane to deliver F . (vi) Further studies should analyse the eﬀect of non- Meanwhile, the contact surface should be located as close as linear mechanical behavior of PDL and aligner and 8 Journal of Healthcare Engineering and meta-analysis,” Orthodontics and Craniofacial Research, their variable thickness. Moreover, it would be vol. 20, no. 3, pp. 127–133, 2017. useful to investigate the eﬀect of multiple attach- [10] G. Djeu, C. Shelton, and A. Maganzini, “Outcome assessment ment positioning criteria. of invisalign and traditional orthodontic treatment compared with the American Board of Orthodontics objective grading Data Availability system,” American Journal of Orthodontics and Dentofacial Orthopedics, vol. 128, no. 3, pp. 292–298, 2005. No data were used to support this study. [11] R. J. Miller, E. Kuo, and W. Choi, “Validation of align technology’s treat III digital model superimposition tool and Disclosure its case application,” Orthodontics and Craniofacial Research, vol. 6, no. s1, pp. 143–149, 2003. +e authors would like to mention that a preliminary [12] C. Nguyen and J. Cheng, “+ree-dimensional superimposi- version of the method, with diﬀerent aims and results, was tion tool,” in ;e Invisalign System, O. C. Tuncay, Ed., th previously presented as a poster at the 94 congress of the Quintessence Publishing, Batavia, IL, USA, 2006. European Orthodontic Society with the title “Biomechanical [13] P. M. Cattaneo, M. Dalstra, and B. Melsen, “+e ﬁnite element eﬀects of diﬀerent auxiliary-aligner designs for the rotation method: a tool to study orthodontic tooth movement,” of an upper canine: a ﬁnite element analysis.” +e abstract is Journal of Dental Research, vol. 84, no. 5, pp. 428–433, 2005. published in “Abstracts of Lectures and Scientiﬁc Posters, [14] S. Barone, A. Paoli, A. V. Razionale, and R. Savignano, European Journal of Orthodontics, 28 September 2018.” “Computational design and engineering of polymeric or- thodontic aligners,” International Journal for Numerical Methods in Biomedical Engineering, vol. 33, no. 8, article Conflicts of Interest e2839, 2017. +e authors declare that there are no conﬂicts of interest [15] Y. Cai, X. Yang, B. He, and J. Yao, “Finite element method analysis of the periodontal ligament in mandibular canine regarding the publication of this paper. movement with transparent tooth correction treatment,” BMC Oral Health, vol. 15, no. 1, pp. 1–11, 2015. 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Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis

Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis

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Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis

Biomechanical Effects of Different Auxiliary-Aligner Designs for the Extrusion of an Upper Central Incisor: A Finite Element Analysis

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