Mechanical properties of loops depend on many factors like loop design, wire materials, wire dimension, and gable bend. Earlier, the loops were made from stainless steel (SS) wires, but increased stiffness of SS wires required the use of additional length that was achieved by increasing the height of loop. This was uncomfortable for the patient at times. Hence, TMA (Beta Titanium) wires with reduced modulus of elasticity, stiffness, and load deflection rate have become the wire of choice for fabricating the loops.
The most important mechanical characteristic of a loop which determines the type of tooth movement is the moment/force ratio (M/F ratio) [12, 13]. As TMA wires exert lesser force than SS wires for the same amount of activation, hence, M/F ratio will be more in loops fabricated by TMA wires. Higher dimension TMA wires used in prescribed slot result in lesser amount of play and better torque expression that is further reinforced by gable bends given anteriorly in loops. This results in increased counterbalancing moment, hence better M/F ratios with higher dimension wires. This justifies the use of TMA wires of higher dimension in 0.18 slot over SS wires in the present study. According to the orthodontic literature, M/F ratio of 5:1 produces uncontrolled tipping, ratio of 7:1 produces controlled tipping, ratio of 10:1 produces bodily movement, and ratios greater than 10:1 produces root movement in labial orthodontics .
The result obtained in this study showed T-loop exerted less force, and thereby increased M/F ratio as compared to closed helical loop on 1 mm activation.
Initially, the FEM studies by Liang et al.  and Mascarenhas et al.  in 2014 concentrated on retraction of single tooth in lingual orthodontics and observed more of lingual tipping in lingual orthodontics. Similarly in a previous FEM study by Lombardo et al. , loss of torque control during retraction in extraction patients is more likely to occur in lingual orthodontics than in labial using sliding mechanics.
Several studies had been conducted to assess biomechanical properties of the loops, used for anterior retraction in labial orthodontics, but no such attempt had been done so far in lingual orthodontics. In 2006, Safavi et al.  conducted a study to compare biomechanical characteristics of T-loop, vertical helical loop, L-loop, and opus loop of 0.016 × 0.022 wire of stainless steel but did not consider the modeling of brackets (whether lingual or labial) or tooth along with the root or the compensatory curvatures. They obtained higher force in their study as they did not consider placement of wire in the brackets. Hence, the moment obtained by them was also higher and was not truly representative of moment obtained during orthodontics tooth movement. The M/F ratio of T-loop (13.4) was also higher in their study because of the difference in the loop design and length, difference in the material used for fabricating the loop (made of stainless steel), degree of compensatory curvatures, and importantly the fact that their study was on labial orthodontics. Such higher M/F ratios at anterior end in their study are representative of root movement that is difficult to attain on 1 mm activation in reality.
Yet another study has been conducted by Patel et al.  in labial orthodontics comparing the biomechanical properties of T-loops, mushroom loops, teardrop loop, and keyhole loop of 0.019 × 0.025 TMA on 2 mm activation at 4 tooth nodes (incisors, canine, premolar, and molar tooth node). They used the tooth and the bracket to determine the interbracket distance; later, they excluded both tooth and brackets and just considered the wire for study. M/F ratio showed variable values. This could probably be due to difference in the range of activation, measuring the force at tooth nodes instead of anterior and posterior end of loop as used in present study.
Amongst the various variations in position, amount of deflection, height, length, and width of T-loop in a study by Chaudary et al.  in 2013, the biomechanical properties of T-loop of height 7 mm made of 0.017 × 0.025 TMA placed in the center of extraction space showed variable results in terms of force and M/F ratio.
Techalertpaisarn et al.  conducted a study in 2013, assessing the mechanical properties of opus closing loops, L-loops, and T-loops at a distance of 2, 4, 6, 8, and 10 mm from premolar brackets with a interbracket distance of 12 mm and on application of 100 and 200 g of horizontal force. The authors stressed on the importance of the shape of loop to adjust its mechanical properties. Loop height affects M/F ratio, i.e., as loop height increased, M/F ratio increased, but no loop can attain M/F ratio greater than its height. Even Burstone and Koenig reported that height matters more than length of the loop . In this present study, the M/F ratio of T-loop in both the conditions is lesser than the loop height, i.e. 7 mm in the present study, and the same was true for closed helical loop.
Techalertpeisarn et al.  also conducted another FEM study in 2016 to compare the mechanical properties of T-loop force system with and without vertical step fabricated on 0.016 × 0.022 stainless steel wire. They have used 0.018 slot bracket and measured the M/F ratio at canine and premolar brackets. They observed the M/F ratio increased on increasing loop height and length from 8 to 10 mm, increasing the inter bracket distance from 6, 9, to 12, increasing the vertical step, and decreasing the force of activation.
Various authors had used different techniques to determine the biomechanical properties of loop during tooth retraction, besides FEM [6, 26,27,28]. In 2016, Srivastava et al.  used Loop software program (dHal) to calculate force and moment and their ratios at various positions and for various activations for a standard design of T-loop and found comparable results.
In another study by Kum et al. , M/F ratio of 3 closing loops U-, T-, and X-loop was measured during activation and deactivation using force and moment transducers in labial orthodontics. They found lesser values of M/F ratio, as they did not incorporate any gable bend in the legs of the loop.
Although FEM methods allow the evaluation of detailed behavior of different types of loops in terms of force, moment, displacements, and stress by simulating a clinical condition of tying loops to the brackets and activating it, this approach has its own limitations. FEM does not allow us to study the changes in the force system or the stress pattern as the wire deactivates or as 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 angulation, vertical position, and loop activation will change gradually. These changes will alter the loop conditions and thus potentially the mechanical properties. Even the linear properties of PDL are taken to be isotropic in FEM studies whereas the histological changes in PDL on application of orthodontic force can alter its material properties [10, 22, 30].
Despite of these limitations of FEM analysis, the result of this study indicates that T-loop showed more M/F ratio than closed helical loop at 30° of compensatory curvature (Table 4). These results can be applied in different clinical situations when using lingual technique where chances of lingual tipping are always more in comparison to labial technique. When severely proclined incisors have to be retracted in lingual orthodontics, then T-loop or closed helical loop can be used, and as the teeth uprights, there will be gradual decay of force, thereby increasing the M/F ratio at anterior end. When torque has to be preserved from beginning in anterior segment during retraction, T-loop with better M/F ratios can be preferred over closed helical loop. In future, FEM studies can be conducted to assess the mechanical properties of different loops in different lingual bracket systems or the effect of loop shape, size, and position on retraction in lingual orthodontics can be done. As there is no published data for the numerical values of M/F ratio for various tooth movements in lingual orthodontics, the same can be determined in the future.
The horizon of further studies can be expanded to include the assessment of mechanical properties of loop under changing condition as the teeth moves to newer position during retraction and results of FEM approach must be correlated with clinical experiments to validate its findings.