Introduction
Our aim was to compare the load systems produced by rectangular loops and continuous arch mechanics on intrusion of a maxillary second molar.
Methods
An orthodontic appliance was passively bonded from second molar to second molar on a patient’s model fixed to an orthodontic force tester. The second molars were extruded by 3 mm, and 2 mechanics systems were compared: beta-titanium rectangular loops and super-elastic nickel-titanium continuous arch. Vertical (Fz) and mesial (Fy) forces, and tipping moments around the buccal axis (Mx) at the tubes were collected at every 0.5 mm of deactivation. Repeated measures analysis of variance was used to detect differences between mechanics. The net Mx was also estimated at the center of resistance of each molar.
Results
Significant differences were found between the mechanics at the tubes, except for the Mx in the first molar, and more importantly, at the centers of resistance of the molars: Fz forces were greater in the continuous arch than in the rectangular loops, which, on the other hand, produced lower Fy forces than the continuous arch. In the second molar, net Mx was low initially and changed with deactivation. In the continuous arch, net Mx decreased from –3.6 N.mm of mesial crown tipping to clinically insignificant levels after 2 mm of deactivation. In the first molar, net Mx was lower on the rectangular loop than on the continuous arch during the first 2 mm of deactivation and became similar in the last millimeter of deactivation. Additionally, the net Mx decreased with deactivation with both mechanics.
Conclusions
Both mechanics can intrude the second molars. Although the rectangular loop produced less tipping in large deflections, the continuous arch was a better approach when less intrusion was required.
Highlights
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A continuous arch will intrude and tip a 3-mm extruded second molar.
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A rectangular loop can intrude a 3-mm extruded second molar without significant tipping.
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A continuous arch can intrude a 0.5-mm extruded second molar without side effects.
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Side effects should be controlled for the first molar in both mechanics.
Maxillary second molars may be malpositioned for several reasons: dental loss, ectopic eruption, agenesis, inadequate mechanics, and incorrect positioning of tubes. All may lead to their extrusion, which can complicate the orthodontic treatment because intruding second molars is a difficult problem. Because it is an unsupported cantilever, the posterior terminal portion of an orthodontic archwire has high flexibility, which complicates the correction of the last tooth connected to the appliance—ie, an extruded second molar. Moreover, the absence of a distal fulcrum makes it almost impossible for the archwire to be used as a shape-driven approach to guide those distal-end teeth to their correct positions.
In this situation, the step geometry between the tube of an extruded second molar and the tube of a well-positioned first molar produces a characteristic deflection of the archwire, which causes a crown-mesial (forward) tipping tendency of both molars to equilibrate the vertical forces acting on the tubes. This has already been demonstrated in computer simulations of 2 brackets in that similar position, suggesting that continuous arch mechanics could not produce intrusion of a second molar without tipping the crown mesially along with the first molar.
One solution to this problem is to use a rectangular loop, changing the insertion of the wire from going through the mesial of the second molar tube to the distal. As has been shown analytically and practically, this loop can disassociate the tipping moments from the vertical force, producing a different force system from the one inevitably produced by continuous arch mechanics. Thus, according to the orthodontist’s desire, a vertical force can be produced along a crown-distal, crown-mesial, or even an absent tipping moment, allowing intrusion of a second molar without tipping it.
There is little information available on how to use the rectangular loop in a systematical way, even though it is known that a pure force without moments can be produced in the center of its “box” with a high reactive moment at its opposite end. Moreover, it has been shown that its dimensions and activations may change the load system, and that it may be used with or without preactivation. However, the literature fails to show any comparison of these rectangular loops with continuous arch mechanics in simulations with exact oral dimensions and brackets bonded to all teeth.
The orthodontic force tester is an orthodontic measurement system that allows nano-load cells to be connected to specific teeth of a patient’s model and to acquire the tridimensional force system applied to them. This system has been used in recent years to describe and compare several orthodontic mechanics in a way that was not possible before, when the patients’ characteristics could not be replicated and simulated. Therefore, the aim of this study was to compare the load system produced by a preactivated rectangular loop continuous vs a nickel-titanium wire for the intrusion of a second molar.
Material and methods
A maxillary arch acrylic resin model of an orthodontic patient had the first molars banded with 0.018-in slot triple tubes (Roth prescription; Ormco, Glendora, Calif), while the remaining teeth had 0.018-in brackets and tubes (Opal Orthodontics, Sandy, Utah) of the same prescription passively bonded with epoxy glue (J-B Weld, Sulphur Springs, Tex) using a 0.017 × 0.025-in stainless steel wire as a guide ( Fig 1 ). The model was secured into an orthodontic force tester, and the left first and second molars were bonded to the 2 load cells (multi-axis force/torque Nano 17; ATI Industrial Automation, APEX, NC) of the orthodontic force tester, which has amplitude of measurements of 0-20 N and 0-100 N-mm. The molars were separated from the model, and the second molar was moved 3 mm vertically using an adapted precision rod and a digital dial (Mitutoyo, Aurora, Ill.) to the orthodontic force tester ( Fig 2 ). A custom modification of the ATI transducer software (Department of Mechanical Engineering, Indiana University-Purdue University, Indianapolis, Ind) registered the moment/force ratios produced when a force was applied to the tubes and away from the load cells’ origin (center of the load cell). This allowed the insertion of those offset values into the software’s calibration and the transference of the origin of the measurements 3 dimensionally to the center of the tube of each molar, with the x-axis and z-axis perpendicular to the center of the tubes ( Fig 3 ). The software also allowed rotational calibration of the origin of the measurements in all 3 dimensions.
Ten rectangular loops were made with a 0.017 × 0.025-in beta-titanium (TMA; Ormco) wire on a custom-made template in the Loop software (dHAL Software; Athens, Greece) and printed in a 1:1 ratio, to standardize the loops. A photograph of the system was inserted into the software in scale, and the loops were drawn passively, with dimensions of 8 × 10 mm, ensuring that the center of the second molar tube was in the center of the box of the loop ( Fig 4 ). The bent loops were inserted in the model and adjusted until they were passive, using the measurement indication on the orthodontic force tester software.
Because the loops were built passively, they needed to be preactivated. Preactivation is the shape modification (eg, a group of bends) made into the loops to modify their shapes to make them active, before placing them into the orthodontic appliance. The vertical preactivation of the loops was performed using a second template, also made by the Loop software, which can estimate wire deflections and freeze the acquired design for a shape-type preactivation. The virtual tube of the second molar was positioned 3 mm vertically without angulation ( Fig 4 , B ) into a level position, and the loop (which was built passively to the extruded molar) was activated. The deformation of the loop was frozen by the software, and this preactivated loop shape was printed in a 1:1 ratio. The real loops had their passive shapes modified into this new preactivated shape and subjected to stress relief through trial activations until their new shapes were stabilized. Felt tip pen marks were made on the loops to ensure centralization of the second molar tube in the center of the loop box on engagement in the maloclusion simulation model ( Fig 5 , A and B ).
The loops were inserted into the molar tubes with the second molar tube centralized in the box of the loop. The vertical (Fz) and horizontal (Fy) forces and the tipping moments (Mx) were recorded by the orthodontic force tester software at every 0.5 mm of deactivation until the second molar leveled (from 3-0 mm extrusion). The precise vertical movement of the second molar was allowed by the rod coupled to the orthodontic force tester, which moved only in the vertical direction by the precision gear rotation and digital dial.
The second mechanics system for intrusion of the second molar was the continuous arch. Ten 0.014-in super-elastic nickel-titanium arches (Highland Metals, Franklin, Ind) were inserted into the brackets and tubes, from second molar to second molar, and secured in place with elastic ligatures ( Fig 5 , C ). Unlike the loops, the wires did not require preactivation because they were not made passive to the maloclusion. They were manufactured and already active once inserted into the unlevelled brackets. The second molar was also extruded by 3 mm. Force and moment (Fz, Fy, and Mx) values were also recorded at every 0.5 mm of deactivation until full alignment was reached (0 mm). Because nickel-titanium wires were being evaluated, all mechanical tests were performed at 37°C ± 1°C.
The data were compared with software (version 16.0; SPSS, Chicago, Ill). Four repeated-measures analysis of variance tests, with a significance level of 5%, were used to detect differences in the moments and forces produced between the loop and continuous arch mechanics in both first and second molars.
The center of resistance location was used to calculate the net Mx, which is relevant to understanding the final rotation direction of each molar and was calculated according to the axes of resistance methodology proposed by Viecilli et al. Therefore, to estimate the molar’s center of resistance, previously published finite element models were used. As previously described, the center of resistance for a movement was defined as the intersection of the orthogonal projections of the 2 axes of resistance perpendicular to the desired force direction. The number, displacement, and coordinates of the node that defines 1 axis of rotation were recorded with an initial couple load of 3 N-mm. The moment vector determined the direction of each axis. Peak periodontal ligament principal strains were under about 7.5% in all directions with this load, thus justifying the periodontal ligament’s linear properties at E = 0.05 MPa. Cross-product matrix calculations were performed by inputting nodal coordinates and the final moment value, to output the necessary nodal forces to obtain a moment vector parallel to each coordinate system axis to the tooth. A moment of a couple parallel to the x direction, for example, causes a rotation axis that generates nodal displacement on the y and z directions. This couple-derived axis of rotation was then used as 1 of the 3 axes of resistance. The same procedure was performed for the other axes. We further approximated the coordinates of the node that defined each axis by iterative refinement of the mesh around the node with the lowest displacements in the plane of movement, until the position varied within ±0.05 mm.
Even though Fz and Fx measured by the load cells were the same at the bracket and at the estimated centers of resistance of the molars, they will influence the Mx measured by the load cell at the brackets, producing at the center of resistance a net Mx that will be actually the one felt by the molars. This (net) Mx produced at the centers of resistance of the molars was calculated using the following formulas.
For the second molar, net Mx (at the center of resistance) = Fy*(−8.32) + Fz*(−1.34) + Mx (at the tube).
For the first molar, with the continuous arch mechanics, net Mx (at the center of resistance) = Fy*(−7.53) + Fz*(−0.6) + Mx (at the tube).
For the first molar, with the loop mechanics, a different vertical distance was used because the auxiliary tube was located 1.9 mm more apically (where the loop was engaged). Net Mx (at the center of resistance) = Fy*(−5.63) + Fz*(−1.34) + Mx (at the tube).
Results
The 4 analysis of variance tests of repeated measurements identified significant differences ( P <0.001) between the Mx, Fz, and Fy values produced by the rectangular loops and the continuous arch in both molar tubes, except for the Mx values in the first molar tube ( P = 0.232) that were similar between mechanics.
In the second molar tube, the rectangular loops produced an insignificant Mx initially, whereas the continuous arch produced −7.9 N-mm. Throughout deactivation, Mx remained either very low or insignificant (0.5 and 0 mm) for the rectangular loop; for the continuous arch, Mx dropped linearly ( Table I ). In the first molar tube, the rectangular loop produced a Mx of −9.5 N-mm at the 3-mm activation, whereas the continuous arch produced −8.8 N-mm. In both mechanics, Mx dropped linearly with deactivation ( Table I ).
| Mechanics | 3.0 mm | 2.5 mm | 2.0 mm | 1.5 mm | 1.0 mm | 0.5 mm | 0.0 mm | |
|---|---|---|---|---|---|---|---|---|
| Second molars | Rectangular loop | −<.01 (.06) ∗ | −.14 (.21) | −.30 (.22) | −.34 (.27) | −.28 (.28) | −.13 (.33) ∗ | .18 (.33) ∗ |
| Continuous arch | −7.87 (.26) | −6.51 (.22) | −5.01 (.19) | −2.93 (.14) | −.96 (.10) | .11 (.18) ∗ | .14 (.20) | |
| First molars | Rectangular loop | −9.55 (1.0) | −7.17 (.99) | −5.15 (.91) | −3.12 (.85) | −1.19 (.79) | .30 (.60) ∗ | .36 (.48) |
| Continuous arch | −8.85 (.76) | −7.28 (.36) | −5.13 (.29) | −2.22 (.33) | −.36 (.28) | .19 (.31) | .33 (.37) |
In the second molar tube, the rectangular loops produced an initial intrusive Fz of 0.94 N, and the continuous wire produced 1.5 N ( Fig 6 ). Forces dropped in both mechanics, with deactivation linearly ( Table II ). In the first molar tube, the rectangular loop produced an extrusive Fz of −0.96 N initially, whereas the continuous arch yielded a Fz of −1.5 N. Similarly to what happened in the second molar, the forces dropped linearly with deactivation in both mechanics ( Table II ).
| Mechanics | 3.0 mm | 2.5 mm | 2.0 mm | 1.5 mm | 1.0 mm | 0.5 mm | 0.0 mm | |
|---|---|---|---|---|---|---|---|---|
| Second molars | Rectangular loop | −.94 (.11) | −.72 (.10) | −.52 (.09) | −.33 (.08) | −.14 (.07) | <.00 (.05) ∗ | .05 (.04) |
| Continuous arch | −1.47 (.11) | −1.20 (.09) | −.88 (.07) | −.53 (.03) | −.22 (.01) | −.02 (.01) | .02 (.02) | |
| First molars | Rectangular loop | .96 (.10) | .74 (.09) | .55 (.08) | .36 (.07) | .17 (.06) | .02 (.04) ∗ | −.02 (.02) |
| Continuous arch | 1.55 (.09) | 1.31 (.08) | 1.03 (.07) | .75 (.05) | .39 (.04) | .05 (.02) | −.02 (.03) ∗ |
In the second molar tube, the rectangular loops produced mesial forces from .12 to .08 N, without significant variations with deactivation, whereas the continuous arch produced distal forces from .28 N decreasing to insignificant forces ( Table III ; Fig 7 ). In the first molar tube, however, the loops produced distal forces from −.10 N to insignificant forces, and the continuous arch produced mesial forces of .67 N initially, gradually decreasing to insignificant forces with deactivation.
| Mechanics | 3.0 mm | 2.5 mm | 2.0 mm | 1.5 mm | 1.0 mm | 0.5 mm | 0.0 mm | |
|---|---|---|---|---|---|---|---|---|
| Second molars | Rectangular loop | .12 (.09) | .11 (.06) | .09 (.06) | .08 (.07) | .09 (.07) | .11 (.08) | .11 (.08) |
| Continuous arch | −.28 (.17) | −.39 (.19) | −.55 (.19) | −.38 (.09) | −.14 (.03) | >.−01 (<.01) ∗ | >.−01 (<.01) ∗ | |
| First molars | Rectangular loop | −.07 (.09) | −.07 (.07) | −.05 (.07) | −.05 (.08) ∗ | −.07 (.09) | −.09 (.09) | −.10 (.09) |
| Continuous arch | .67 (.10) | .51 (.09) | .35 (.07) | .13 (.03) | .02 (.02) | >−.01 (<.01) ∗ | >−.01 (<.01) ∗ |
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