Background: Retraction in lingual orthodontics has biomechanical differences when compared to labial orthodontics, which is not yet established. Thus, we have intended to compare the biomechanical characteristics of closed helical loop and T-loop on 1 mm activation with 30° of compensatory curvatures during retraction in lingual orthodontics. Methods: STb lingual brackets were indirectly bonded to maxillary typhodont model that was scanned to obtain FEM model. Closed helical loop (2 × 7 mm) and T-loop (6 × 2 × 7 mm) of 0.016″ ×0.016″ TMA wire were modeled without preactivation bends. Preactivation bends at 30° were given in the software. Boundary conditions were set. The force (F) and moment (M) of both the loops were determined on 1 mm activation, using ANSYS software. M/F ratio was also calculated for both the loops. Results: T-loop exerted less force, thus increased M/F ratio as compared to closed helical loop on 1 mm activation. Conclusions: When torque has to be preserved in the anterior segment during retraction in lingual orthodontics, T-loop can be preferred over closed helical loop. Keywords: Lingual orthodontics, T-loop, Closed helical loop, FEM, M/F ratio Background application is lingual to CRes [3–5]. Hence, to overcome Retraction or space closure after extraction in labial as this, torque loss and bowing effect certain degrees of well as lingual orthodontics can be done either by fric- compensatory curves in addition to what is given in tion/sliding mechanics or frictionless/loop mechanics. labial technique are incorporated in the archwire to gen- The drawback of sliding mechanics in terms of overcom- erate counterbalancing moments [6, 7]. ing the amount of friction generated between the In contemporary labial orthodontics, many closing bracket and the wire interface , before bringing effect- loops are being used for retraction such as a vertical ive tooth movement, can be avoided in frictionless/loop closing loop, teardrop loops, T-loops, L-loops, mush- mechanics. room loops, opus loops, keyhole loop, and open-vertical Lingual orthodontics provides complete solution for loop [8–11] whereas in lingual technique, closed helical patient’s esthetic concern. Lingual technique has bio- loop, L-loop, or T-loop is commonly used for space clos- mechanical differences from the labial technique due to ure . the difference in point of application of force and its dis- To estimate the efficacy of any loop in a clinical situ- tance from center of resistance (CRes) of the tooth . ation, it is important to determine its biomechanical There is tendency for retroclination of anterior teeth characteristics like force, moment, and moment to force during retraction in lingual orthodontics as site of force ratio [13, 14]. The biomechanics of tooth movement is based on the moment of force (MF) applied on the bracket which is generated due to application of force * Correspondence: firstname.lastname@example.org Department of Orthodontics and Dentofacial Orthopedics, Babu Banarasi Das away from the center of resistance (CRes) (MF = Force × College of Dental Sciences (BBDCODS), Lucknow, India © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Chacko et al. Progress in Orthodontics (2018) 19:14 Page 2 of 8 perpendicular distance of the bracket from CRes). M/F ratio obtained as a ratio between counterbalancing mo- ment (M ) given to negate the unwanted effect of MF and the force. This ratio determines the type of tooth movement possible like M/F ratio of 7:1 denotes tipping movement and 10:1 is seen in bodily and 12:1 in root movement. The efficacy of the loops in the labial technique has been extensively researched in the last few decades [8– 11]; however, there is no literature about the application of these loops in the lingual technique till date. Closed helical loop was simple in its design, and T-loop provided better torque control in anterior teeth in a clinical study Fig. 1 Typhodont with lingually bonded brackets and buccal tube cited in book by Takemoto . Hence, it was decided to determine biomechanical properties of T-loop and closed helical loop in the present study. and T-loop of 6 mm length, 2 mm width, and 7 mm Quantitative determination of the biomechanical char- height for this study. Both the loops were placed at the acteristics of loops is not possible clinically; however, center of extraction space. these mechanical properties can be determined by newer The assembled physical typhodontic model was 3D and precise examination tools, i.e., finite element scanned at Advance CAD Technology Pvt. Ltd., Pune, method (FEM). FEM is a computer simulation technique using Rexcan III 3D White light Scanner manufactured used to analyze stress distribution in objects . It gen- by SOLUTIONIX, Korea (2012), without preactivation erates a three-dimensional model with the freedom to bends. The CAD modeling was carried out by software simulate and study orthodontic force systems in all the named Solidwork CAD software 2014. The geometric anatomical dimensions making it possible to study sta- model was constructed of the tooth with the bonded tistically indeterminate system. The FEM principle is brackets in Geomagic Modelling Software, 3D Systems, based on the division of a complex structure into smaller Inc., USA (2014). The roots of the teeth were fabricated sections called elements in which physical properties, according to the dimensions cited in the textbook titled such as the modulus of elasticity, are applied to indicate “Ash’ Dental Anatomy, Physiology and Occlusion” by the object response against an external stimulus such as Wheeler’s (Fig. 2). Various material properties  an orthodontic force. Considering all this, the aim of this prescribed for the elements of the jaw such as tooth, study was to evaluate and compare the force, moment, PDL, and alveolar bone were assigned to the geometric and moment to force ratio between closed helical loop model to obtain the final FEM model (Table 1). and T-loop at 1 mm activation in lingual orthodontics Now, the mesh model was created by Altair hyper- using finite element method. mesh software (Altair Engineering, Inc.) after the nodal connectivity and equivalence was completed. The model Methods of the archwire with loop was simulated separately by This comparative in-vitro study was conducted by our the 3D Hex Mesh software, CoreTech System Co., Ltd. department, in collaboration with FEA Solutions, Mumbai. As this study was done only on the maxillary arch, a commercially available typhodont model of maxillary dentition in normal occlusion was selected where the 1st bicuspid was removed to simulate the extraction space needed for retraction of anterior teeth. The STb lingual brackets and molar tube with 0.18 slot, manufactured and marketed by Ormco Corporation, were selected, and transfer tray was fabricated using bracket placement de- vice (BPD) and torque angulation device (TAD) at lab for lingual orthodontics (Fig. 1). This transfer tray was used to bond the brackets and molar tube on typhodont. 0.016″ × 0.016″ preformed titanium molybdenum alloy (TMA; ORMCO product) wires were used to fabri- Fig. 2 Root simulated in the software cate closed helical loop of 2 mm width and 7 mm height Chacko et al. Progress in Orthodontics (2018) 19:14 Page 3 of 8 Table 1 Material properties of various anatomical structures Components Density (g/mm ) Young’s modulus (GPa) Poisson’s ratio (μ) Teeth 1.7–06 2.03 + 04 0.3 Periodontal ligament (PDL) 1.7–06 0.667 0.49 Alveolar bone 1.7–06 1.37 + 04 0.38 (Figs. 3 and 4). The specific material properties of The center of resistance of upper 6 anterior teeth was stainless steel and TMA were assigned to brackets and taken 13.5 mm apical and 12.0 mm posterior from the archwire respectively (Table 2). Preactivation bends, i.e., incisal tip of the central incisors, and the center of anti-bowing curve (to prevent transverse bowing) and resistance of posterior segment comprising of the 2nd compensatory curves in the posterior segment, were premolar and 1st molar was taken mesial to the furca- standardized to 30°. tion of the 1st molar on its mesiobuccal root [20, 21]. Fig. 3 Loops simulated by 3D Hex Mesh software. a Closed helical loop. b T-loop Chacko et al. Progress in Orthodontics (2018) 19:14 Page 4 of 8 Fig. 4 Perpendicular distance (d) from CRes to the line of action of force This was used to determine the moment (Fig. 5). The steel (SS) wires, but increased stiffness of SS wires re- boundary conditions were set so that the terminal node quired the use of additional length that was achieved by in the anterior segment was restrained in X and Y axis increasing the height of loop. This was uncomfortable (i.e., it was not able to move and rotate in X and Y axis), for the patient at times. Hence, TMA (Beta Titanium) only the rotation along the Z axis was allowed. The ter- wires with reduced modulus of elasticity, stiffness, and minal node of the posterior segment was restrained in a load deflection rate have become the wire of choice for similar way to the anterior segment, except that it was free fabricating the loops. to move along the horizontal leg of the posterior segment. The most important mechanical characteristic of a loop This simulated the movement of the wire sliding through which determines the type of tooth movement is the mo- a molar tube. The loops were activated by the displace- ment/force ratio (M/F ratio) [12, 13]. As TMA wires exert ment of the distal end by 1 mm for both the loops, and lesser force than SS wires for the same amount of activa- the force and moments were obtained at both anterior tion, hence, M/F ratio will be more in loops fabricated by and posterior end using the ANSYS software by Swanson TMA wires. Higher dimension TMA wires used in pre- Analysis Systems, Inc. (SASI) (Fig. 6a and b). scribed slot result in lesser amount of play and better torque expression that is further reinforced by gable bends Results given anteriorly in loops. This results in increased coun- Nodes and elements are listed in Table 3 for this FEM terbalancing moment, hence better M/F ratios with higher study. Force reaction (F) and moment (M) was more in dimension wires. This justifies the use of TMA wires of closed helical loop than in T-loop on 1 mm activation at higher dimension in 0.18 slot over SS wires in the present 30° of compensatory curvature in posterior segment study. According to the orthodontic literature, M/F ratio (Table 4). of 5:1 produces uncontrolled tipping, ratio of 7:1 produces M/F ratio was more for T-loop than for closed helical controlled tipping, ratio of 10:1 produces bodily move- loop (Table 4). ment, and ratios greater than 10:1 produces root move- ment in labial orthodontics . Discussion The result obtained in this study showed T-loop Mechanical properties of loops depend on many factors exerted less force, and thereby increased M/F ratio as like loop design, wire materials, wire dimension, and compared to closed helical loop on 1 mm activation. gable bend. Earlier, the loops were made from stainless Initially, the FEM studies by Liang et al.  and Mascarenhas et al.  in 2014 concentrated on retrac- tion of single tooth in lingual orthodontics and observed Table 2 Material properties of wire and brackets more of lingual tipping in lingual orthodontics. Similarly Components Young’s modulus Poisson’s ratio in a previous FEM study by Lombardo et al. , loss of (GPa) (μ) torque control during retraction in extraction patients is TMA (ORMCO) 66 0.3 more likely to occur in lingual orthodontics than in la- Stainless steel brackets 168 0.3 bial using sliding mechanics. Chacko et al. Progress in Orthodontics (2018) 19:14 Page 5 of 8 Fig. 5 FEM model. a T-loop. b Closed helical loop Several studies had been conducted to assess biomech- characteristics of T-loop, vertical helical loop, L-loop, anical properties of the loops, used for anterior retrac- and opus loop of 0.016 × 0.022 wire of stainless steel but tion in labial orthodontics, but no such attempt had did not consider the modeling of brackets (whether lin- been done so far in lingual orthodontics. In 2006, Safavi gual or labial) or tooth along with the root or the com- et al.  conducted a study to compare biomechanical pensatory curvatures. They obtained higher force in Fig. 6 a Activation of T-loop. b Activation of closed helical loop Chacko et al. Progress in Orthodontics (2018) 19:14 Page 6 of 8 Table 3 Nodes and elements in FEM model and 10 mm from premolar brackets with a interbracket distance of 12 mm and on application of 100 and 200 g Components No. of nodes No. of elements of horizontal force. The authors stressed on the import- Teeth 172,888 798,462 ance of the shape of loop to adjust its mechanical prop- Periodontal ligament 20,429 30,211 erties. Loop height affects M/F ratio, i.e., as loop height Alveolar bone 16,684 817,296 increased, M/F ratio increased, but no loop can attain Brackets 24,006 94,038 M/F ratio greater than its height. Even Burstone and Archwire 6597 2928 Koenig reported that height matters more than length of the loop . In this present study, the M/F ratio of T- their study as they did not consider placement of wire in loop in both the conditions is lesser than the loop the brackets. Hence, the moment obtained by them was height, i.e. 7 mm in the present study, and the same was also higher and was not truly representative of moment true for closed helical loop. obtained during orthodontics tooth movement. The M/F Techalertpeisarn et al.  also conducted another ratio of T-loop (13.4) was also higher in their study be- FEM study in 2016 to compare the mechanical proper- cause of the difference in the loop design and length, dif- ties of T-loop force system with and without vertical ference in the material used for fabricating the loop step fabricated on 0.016 × 0.022 stainless steel wire. They (made of stainless steel), degree of compensatory curva- have used 0.018 slot bracket and measured the M/F ratio tures, and importantly the fact that their study was on at canine and premolar brackets. They observed the M/F labial orthodontics. Such higher M/F ratios at anterior ratio increased on increasing loop height and length end in their study are representative of root movement from 8 to 10 mm, increasing the inter bracket distance that is difficult to attain on 1 mm activation in reality. from 6, 9, to 12, increasing the vertical step, and de- Yet another study has been conducted by Patel et al. creasing the force of activation.  in labial orthodontics comparing the biomechanical Various authors had used different techniques to de- properties of T-loops, mushroom loops, teardrop loop, termine the biomechanical properties of loop during and keyhole loop of 0.019 × 0.025 TMA on 2 mm activa- tooth retraction, besides FEM [6, 26–28]. In 2016, Sri- tion at 4 tooth nodes (incisors, canine, premolar, and vastava et al.  used Loop software program (dHal) to molar tooth node). They used the tooth and the bracket calculate force and moment and their ratios at various to determine the interbracket distance; later, they positions and for various activations for a standard de- excluded both tooth and brackets and just considered sign of T-loop and found comparable results. the wire for study. M/F ratio showed variable values. In another study by Kum et al. , M/F ratio of 3 This could probably be due to difference in the range of closing loops U-, T-, and X-loop was measured during activation, measuring the force at tooth nodes instead of activation and deactivation using force and moment anterior and posterior end of loop as used in present transducers in labial orthodontics. They found lesser study. values of M/F ratio, as they did not incorporate any Amongst the various variations in position, amount of gable bend in the legs of the loop. deflection, height, length, and width of T-loop in a study Although FEM methods allow the evaluation of de- by Chaudary et al.  in 2013, the biomechanical prop- tailed behavior of different types of loops in terms of erties of T-loop of height 7 mm made of 0.017 × 0.025 force, moment, displacements, and stress by simulating TMA placed in the center of extraction space showed a clinical condition of tying loops to the brackets and ac- variable results in terms of force and M/F ratio. tivating it, this approach has its own limitations. FEM Techalertpaisarn et al.  conducted a study in 2013, does not allow us to study the changes in the force sys- assessing the mechanical properties of opus closing tem or the stress pattern as the wire deactivates or as loops, L-loops, and T-loops at a distance of 2, 4, 6, 8, the tooth moves under the influence of the forces. When teeth or groups of teeth move to new positions during orthodontic treatment, interbracket distance, bracket an- Table 4 Force (F), moments (M), and M/F ratio on 1 mm gulation, vertical position, and loop activation will activation of T-loop and closed helical loop with compensatory change gradually. These changes will alter the loop con- curvature ditions and thus potentially the mechanical properties. Loops Nodes F (g) Moment M/F (g mm) Even the linear properties of PDL are taken to be iso- tropic in FEM studies whereas the histological changes T-loop Anterior 105.6 407.62 3.86:1 in PDL on application of orthodontic force can alter its Posterior 72.29 96.87 1.34:1 material properties [10, 22, 30]. Closed helical loop Anterior 143.2 461.11 3.22:1 Despite of these limitations of FEM analysis, the result Posterior 100.1 102.11 1.02:1 of this study indicates that T-loop showed more M/F Chacko et al. Progress in Orthodontics (2018) 19:14 Page 7 of 8 ratio than closed helical loop at 30° of compensatory Received: 21 February 2018 Accepted: 13 April 2018 curvature (Table 4). These results can be applied in dif- ferent clinical situations when using lingual technique References where chances of lingual tipping are always more in 1. Sivakumar A, Valiathan A. An intra-arch retraction mechanics—a contemporary comparison to labial technique. When severely proclined review. 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Published: May 28, 2018
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