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Loads of continuous mechanics for uprighting the second molar on the second molar and premolar

Loads of continuous mechanics for uprighting the second molar on the second molar and premolar



American Journal of Orthodontics and Dentofacial Orthopedics, 2022-05-01, Volume 161, Issue 5, Pages 679-686, Copyright © 2021 American Association of Orthodontists


Introduction

This paper aims to evaluate the effect of tube height on uprighting a mandibular second molar with a continuous arch, specifically the main effects on the molar tube and the side effects on the second premolar bracket.

Methods

Slot brackets (0.18-in) and tubes were passively bonded from the left second molar to the right second premolar of the patient’s cast and fixed to an orthodontic force tester. A mesially tipped second molar along with its tube was positioned at 5 different heights in relation to the bracket slots of the remaining appliance: 2 mm below (group −2), 1 mm below (group −1), leveled (group 0), 1 mm above (group 1) and 2 mm above (group 2). Each group had 10 different 0.016 × 0.022-in superelastic nickel-titanium wires tied one at a time to the appliance to register the vertical forces (Fz) and tipping moments (Mx) produced at the molar tube and the premolar bracket, statistically. Analysis of variance was used to identify differences of load among the groups for wire response to the position of the tube in relation to the other brackets’ slots.

Results

As the molar tube was positioned more occlusally, Fz and Mx decreased at the molar tube from 1.31 N to 0.75 N and 13.98 N.mm to 11.84 N.mm, respectively, whereas at the premolar bracket, Fz and Mx decreased from 1.52 N to 0.88 N and 8.77 N.mm to 1.05 N.mm, respectively.

Conclusions

In all groups, the load system at the molar tube (the main effects) registered a distal tipping moment and an extrusive force, whereas at the premolar bracket, the load system (side effects) included a distal tipping moment and an intrusive force. As the tube moved occlusally, the extrusive force and the uprighting moment decreased, along with the side effects at the premolar bracket. Attempting to bond the molar tube more occlusally (within reasonable intraoral dimensions) when trying to upright a molar does not appear to be sufficient to keep a molar from extruding.

Highlights

  • Continuous mechanics did not produce an uprighting moment without an extrusive force at the molar.

  • As the molar tube was moved occlusally, the extrusive force and uprighting moment decreased.

  • A continuous wire would not upright a molar without extrusion in the clinical setup tested.

  • Increasing the molar tube's vertical position to the brackets' did not produce an intrusive force.

The permanent first molars are the teeth most susceptible to caries, leading to their early loss. Isolated early loss of first molars is a very common problem worldwide, with a prevalence of about 8%-21% for the entire population. , This probably happens because they are the first posterior teeth to erupt and because of enamel developmental defects such as molar incisor hypomineralization, with a prevalence from 2.4% to 40.2%. Failure to address the loss of the first mandibular molars can lead to mesial tipping of the second molar. This condition is not uncommon in adults seeking orthodontic treatment and is associated with occlusal interference, periodontal problems, and complications in the rehabilitation of the edentulous space.

Although several force-driven approaches can produce the load system required for the second molar’s correction (ie, uprighting and intrusion), clinicians usually opt for a shape-driven approach because of its simplicity. However, most orthodontists know that continuous arch mechanics would not be the best way to upright a second molar because it may extrude ; thus, some might find that bonding the molar tubes more occlusally would create an intrusive force. Although this may seem like a good idea on the basis of a shape-driven approach, the literature does not describe in any practical way how this would affect the load system. In addition, because the load system is static indeterminate, the movement estimates can not be easily predicted through calculations. A reliable way to evaluate the effect of modifying the tube height of a mesially tipped second molar would be to use 3-dimensional calibrated load cells attached to a patient’s cast, as has already been done in other investigations.

Therefore, this paper aimed to evaluate the 3-dimensional effect of varying the height of a tube placed on a mesially tipped second molar in relation to the second premolar.

Material and methods

An impression of the mandibular arch of an untreated patient who lost a right first molar and had a mesially tipped second molar was poured in acrylic resin. All teeth received 0.018-in slot MBT prescription brackets and tubes (Opal Orthodontics, Sandy, Utah) except for the second right premolar, which received a self-ligating bracket of the same prescription and slot size (Speed system Orthodontics, Cambridge, Ontario, Canada). The brackets were passively bonded with J-B Kwik epoxy glue (JB Weld Co, Sulfur Springs, Tex) to the same plane and parallel to the occlusal plane with the aid of 0.017 × 0.025-in a stainless steel archwire. (Highland Metals Inc, San Jose, Calif). The right second molar was the only tooth that received an active appliance: its tube was bonded according to its angulation, approximately a 40° angle in relationship to the wire used to make the remaining brackets passive but at the same height. Throughout this manuscript, we call the mentioned wire a guidewire to reference the tube’s height.

Using J-B Kwik glue, the cast was fixed to an orthodontics force tester (OFT) (Department of Mechanical Engineering, Purdue University, Indianapolis, Ind) table, whereas 2 load cells, (Multi-Axis Force/Nano 17 Torque, Industrial Automation, Apex, Ind) with a 0-20 N and 0-100 N.mm range, were glued to the mandibular right second molar and second premolar. These 2 teeth were then separated from the cast attached to the OFT table. ( Fig 1 ). A customized software (Mechanical Engineering Department Purdue University) made it possible to transfer the forces and moments measured by the load cell to the center of the bracket of the second premolar and the center of the tube of the second molar ( Fig 2 ).

Resin cast of the patient's mandibular arch used in this study. To register the load systems independently, the second premolar and second molar need to be cut from the cast and bonded to 2 OFT load cells while the cast remains fixed to the table. The figure also shows the white sensor of the thermometer used to control the temperature. The molar tube is positioned at a 40° in relation to the remaining brackets.
Fig 1
Resin cast of the patient's mandibular arch used in this study. To register the load systems independently, the second premolar and second molar need to be cut from the cast and bonded to 2 OFT load cells while the cast remains fixed to the table. The figure also shows the white sensor of the thermometer used to control the temperature. The molar tube is positioned at a 40° in relation to the remaining brackets.

The OFT customized software transferred the origin of the coordinate plane to the center of the second premolar bracket and the center of the second molar tube. In the premolar, the x-axis was directed buccally (normal to the crown and pointing toward the cheek), the y-axis distally (tangent to the center point of the bracket and pointing toward the molar), and the z-axis apically (perpendicular to the x-y plane and pointing toward the root. In the molar, the x-axis was directed buccally (normal to the crown and pointing toward the cheek), the y-axis mesially (tangent to the center point of the tube and pointing toward the premolar), and the z-axis apically (perpendicular to the x-y plane and pointing toward the root. Positive data depicts intrusion on Fz and crown distal tipping on Mx.
Fig 2
The OFT customized software transferred the origin of the coordinate plane to the center of the second premolar bracket and the center of the second molar tube. In the premolar, the x-axis was directed buccally (normal to the crown and pointing toward the cheek), the y-axis distally (tangent to the center point of the bracket and pointing toward the molar), and the z-axis apically (perpendicular to the x-y plane and pointing toward the root. In the molar, the x-axis was directed buccally (normal to the crown and pointing toward the cheek), the y-axis mesially (tangent to the center point of the tube and pointing toward the premolar), and the z-axis apically (perpendicular to the x-y plane and pointing toward the root. Positive data depicts intrusion on Fz and crown distal tipping on Mx.

In this study, we compared the load system, vertical forces (Fz), and tipping moments (Mx), produced by 0.016 × 0.022-in superelastic nickel-titanium (NiTi) wires at the second molar tube and second premolar bracket in 5 distinct clinical situations. The groups differed on the height of the molar tube in relation to the remaining leveled brackets, which were bonded passive to a 0.017-in × 0.025-in stainless steel archwire, referred to as a guidewire. The vertical position of the tube could be adjusted by moving the molar vertically (with the tube bonded to it) using an adapted precision rod and a digital dial. (Mitutoyo, Aurora, Ill.) In the first group (group −2), the center of the molar tube was positioned 2 mm cervical to the plane of the guidewire; in the second (group −1), the center of the molar tube was positioned 1 mm cervical to the plane of the guidewire, in the third group (group 0) the center of the tube was leveled with the plane of the guidewire, in the fourth group (group 1), it was 1 mm occlusal to the plane of the guidewire and in the final group (group 2), the center of the tube was 2 mm occlusal to the plane of the guidewire. Again, this served the purpose of simulating precisely the effect of bonding the tube more occlusally or more cervically in relationship to the other brackets.

Ten 0.016 × 0.022-in superelastic NiTi archwires of the same shape and size as the guidewire (Highland Metals, Franklin, Ind) were tied to the brackets and tubes in each of the groups to register Fz and Mx at the second molar’s tube and premolar’s bracket ( Fig 3 ). To ensure data were collected at a temperature of 37°C ± 1°, the OFT was placed in a thermal polystyrene box equipped with a hot-air blower and a digital thermometer. Descriptive statistics of the data and analysis of variance with a posthoc Tukey test ( P = 0.05) were used to identify the wire response pattern, depending on the position of the molar tube in relation to the bracket plane, and to detect differences among the groups.

In the first column, pictures of all 5 groups tested show the increasing deflection of the 0.016 × 0.022-in NiTi wire inserted into the resin set up, which was always larger close to the molar tube than closer to the premolar bracket. In group −2, the molar tube was positioned 2 mm cervical to the guidewire, in group −1 the molar tube was positioned 1 mm cervical to the guidewire, in group 0, the molar tube was positioned at the same level as the guidewire, in group 1, the molar tube was positioned 1 mm occlusal to the guidewire and in group 2 the molar tube was positioned 2 mm occlusal to the guidewire. In the middle column, it can be observed that as the molar tube is positioned more occlusally in relationship to the occlusal plane, the angle of entry at that tube in relation to the premolar bracket diminishes. At the premolar tube, the angle of entry decreases to zero and changes sense. At the right column, the apparent change in the height of the tube translates into changes in the tube and bracket’s angulation which cannot be normally perceived clinically.
Fig 3
In the first column, pictures of all 5 groups tested show the increasing deflection of the 0.016 × 0.022-in NiTi wire inserted into the resin set up, which was always larger close to the molar tube than closer to the premolar bracket. In group −2, the molar tube was positioned 2 mm cervical to the guidewire, in group −1 the molar tube was positioned 1 mm cervical to the guidewire, in group 0, the molar tube was positioned at the same level as the guidewire, in group 1, the molar tube was positioned 1 mm occlusal to the guidewire and in group 2 the molar tube was positioned 2 mm occlusal to the guidewire. In the middle column, it can be observed that as the molar tube is positioned more occlusally in relationship to the occlusal plane, the angle of entry at that tube in relation to the premolar bracket diminishes. At the premolar tube, the angle of entry decreases to zero and changes sense. At the right column, the apparent change in the height of the tube translates into changes in the tube and bracket’s angulation which cannot be normally perceived clinically.

Results

At the molar tube and premolar bracket, Fz and Mx decreased from group −2 to group 2. ( Table I )

Table
Mean and SD of Fz (N) and Mx (N.mm) per group registered at the molar tube and premolar bracket as determined by ANOVA
Tooth Group −2 Group −1 Group 0 Group 1 Group 2 P
Mean SD Mean SD Mean SD Mean SD Mean SD
Molar
Fz −1.31 a 0.06 −1.15 b 0.05 −0.97 c 0.04 −0.81 d 0.05 −0.75 e 0.03 <0.001
Mx 13.98 a 0.67 13.62 a 0.71 12.6 b 0.38 11.84 c 0.73 12.21 b,c 0.32 <0.001
Premolar
Fz 1.52 a 0.04 1.35 b 0.05 1.09 c 0.07 1.03 c 0.06 0.88 d 0.04 <0.001
Mx 8.77 a 0.37 6.58 b 0.39 4.47 c 0.26 2.01 d 0.41 1.05 e 0.14 <0.001
Note. Positive values depict intrusive forces and distal crown sense tipping moments; means with different superscripted letters indicate significant differences among groups.
ANOVA , analysis of variance; SD , standard deviation.

In group −2, the archwires produced an extrusive Fz of 1.31 N and a distal crown Mx of 13.98 N.mm at the molar tube. At the second premolar bracket, they produced an intrusive Fz of 1.52 N and a distal crown Mx of 8.77 N.mm. ( Table I and Fig 4 , A )

Mean of Fz and Mx registered for each of the groups tested. A, group -2; B, group -1; C, group 0; D, group 1; and E, group 2. The black dotted line represents the extension of the wire used to bond the anterior brackets passively.
Fig 4
Mean of Fz and Mx registered for each of the groups tested. A, group -2; B, group -1; C, group 0; D, group 1; and E, group 2. The black dotted line represents the extension of the wire used to bond the anterior brackets passively.

In group −1, the archwires produced an extrusive Fz of 1.15N and a distal crown Mx of 13.62 N.mm at the molar tube. Although at the second premolar bracket, they produced an intrusive Fz of 1.35 N and a distal crown Mx of 6.58 N.mm ( Table I and Fig 4 , B ).

In group 0, the archwires produced an extrusive Fz of 0.97 N and a distal crown Mx of 12.6 N.mm at the molar tube. Although at the second premolar bracket, the archwires produced an intrusive Fz of 1.09 N and a distal crown Mx of 4.47 N.mm ( Table I and Fig 4 , C ).

In group 1, an extrusive Fz of 0.81 N and a distal crown Mx of 11.84 N.mm were produced at the molar tube, whereas the second premolar bracket, an intrusive Fz of 1.03 N and the distal crown Mx of 2.01 N.mm were produced. ( Table I and Fig 4 , D

Finally, in group 2, the archwire produced an extrusive Fz of 0.75 N and a distal crown Mx of 12.21 N.mm at the molar tube. At the second premolar bracket, the archwire produced an intrusive Fz of 0.88N and a distal crown Mx of 1.05 N.mm. ( Table I and Fig 4 , E )

Discussion

The specific continuous arch mechanics tested in this manuscript did not produce an uprighting moment without an extrusive force at the molar tube. The direction of the moment and the force were associated with the lever direction produced by the archwire. In other words, the direction of the moment was consistent with the direction of the applied force when the archwire is inserted into the molar tube and then inserted into the anterior brackets; thus, a second-order moment is formed tending to tilt the molar in the distal crown direction. This situation only happened because the molar tube had the larger angle of entry (ie, angulation between the passive archwire and the bracket or tube), thus dictating the direction of the associated equilibrium vertical forces. There is a direct relationship between the angle of entry and the moment in the archwire on activation. The larger angle of entry was detected not only by the larger moment registered at the tube but could also have been perceived visually by a greater deflection of the archwire next to the molar tube. ( Fig 3 ) Our results are in consonance, from a mechanical point of view to a recent paper on the intrusion of tipped second molars. Because both experiments focused on the load system produced only at the brackets ( Fig 5 ), the geometry between the brackets does not change even though these investigations were carried out in opposing arches. However, the different results on the second molars’ tubes are explained by the different angle of entry of the wire onto them and the smaller interbracket distance (which also alters the angle of entry) ( Fig 5 ). In our study, the second molar tube had a larger angle of entry, thus generating extrusion at that tube and intrusion at the premolar bracket, whereas in the mentioned study, the angle of entry was larger at the first molar tube, causing extrusive forces in this tube, rather than at the second molar tube. Therefore, it seems that any continuous wire used to upright molars causes extrusive forces in those very same teeth when attached to anterior teeth, regardless of whether the wire is straight or if there is an addition of loops. However, this will only hold if the larger angle of entry will be at the molar tube, which can be very easily detected by clinicians by observing the deflection of the archwire. The literature has shown interesting devices used for molar uprighting , following the same mechanical rationale. Molars can be uprighted and subjected to extrusive force if their angle on entry is larger than that of the supporting teeth, or they could be intruded with an adjunct device if their angle of entry is smaller. However, the latter will produce a smaller tipping moment in the molar than the side effects in the reactive supporting teeth.

Comparison between our results in (group 2) and Shintcovsk et al. 10 Both studies have a geometry close to Class IV, differing only with the tube with the larger angle of entry for the wire (θ B ). In our study, θ B is in the second molar tube, whereas in Shintcovskt al it is in the first molar tube. A, Images of both clinical setups. B, Geometry between brackets in the clinical perspective view. C, Geometry between brackets in perspective relative to a plane passing through both brackets’ centers. D, Load systems. E, Ratio between the moments produced.
Fig 5
Comparison between our results in (group 2) and Shintcovsk et al. Both studies have a geometry close to Class IV, differing only with the tube with the larger angle of entry for the wire (θ B ). In our study, θ B is in the second molar tube, whereas in Shintcovskt al it is in the first molar tube. A, Images of both clinical setups. B, Geometry between brackets in the clinical perspective view. C, Geometry between brackets in perspective relative to a plane passing through both brackets’ centers. D, Load systems. E, Ratio between the moments produced.

As the molar tube was placed more occlusally in relation to the other brackets, the extrusive force decreased. In this investigation, the molar was moved with the tube using the precision rod to simulate the effect of bonding the tube more occlusally or more cervically to the other brackets. Moving the tooth vertically is highly more precise than rebonding the tube. Although the results showed an expected trend of decreased vertical force as the tube was moved occlusally, the extrusive force was still existent (0.75 N or 76 g of force) even when the molar tube was 2 mm more occlusally than the remaining brackets. Although tubes on second molars must usually be positioned in the middle of the band in the occlusal-gingival dimension to avoid gingival or occlusal interference, it is not realistic to move the tube >2 mm because of the crown’s dimensions. Thus, it seems that in the clinical situation tested, it is not possible to avoid an extrusive force on the molar when trying to upright it. This is due to the geometry of 40 o mesially tipped tube to the remaining brackets and the limited difference in height allowed by intraoral anatomy. In this paper, we used an OFT to measure the load system produced in the second premolar bracket and the second molar tube, although we have a complete set of brackets in the mechanics. A different approach to estimating the load system produced in those 2 attachments would be to simplify the problem as a 2-dimensional 2 brackets problem, making it easier to analyze the problem or design a solution. Using the knowledge of Class geometries of 2 brackets described by Burstone could show similar results to the ones found by our investigation. However, the 2-brackets Class geometries described in an 0.016-in stainless steel wire, might not match the ones produced in a 2-brackets system with NiTi wires or in a complete set of brackets system. In addition, we believe that measuring a load system experimentally will produce more realistic results than doing it analytically.

The uprighting moment produced by the archwire was favorable to molar correction in all situations tested, and it was always larger than the reactive moment measured at the premolar bracket. Both moments were always in the same direction and were surprisingly low (<13.99 N.mm or <1427 g of force.mm) compared with the 2000-3000 g of force.mm usually suggested for molar uprighting. , Clinically speaking, these moments might not be enough to upright the molar, and the teeth may end up being majorly subjected to the undesirable vertical forces produced. Possible solutions to increase the moments produced could include the rebonding of the molar tube into a more angulated position and/or an increase of the archwire cross-sectional area, moving to a larger archwire. However, neither of these solutions would be adequate because both would proportionally increase the extrusive force, albeit for distinct reasons. Modifying the position of the molar tube further would increase the angle of entry of the archwire while changing the alloy or increasing the wire’s cross-sectional area would increase its stiffness.

In the specific setup studied, as the molar tube was placed more occlusally to the other brackets, the intrusion force and tipping moment (crown distal/root forward sense) on the premolar bracket decreased. Because in this specific setup, the premolar is in a good position, these loads are considered side effects of the mechanics. The loads shown at the premolar bracket are relatively counterintuitive because one might believe that the premolar would experience more extrusive force if the molar tube is bonded more occlusally. There are fewer side effects in the premolar because of a change in the angle of entry between the molar and premolar, and this changes the load system, as has already been demonstrated. Therefore, if a mistake in the position of the brackets should occur, it is preferable to have the molar tube more occlusally than cervically.

In the specific situation tested, it appears that the use of a continuous wire to upright a molar without extruding is not clinically feasible. Because of equilibrium, as the molar tube was moved occlusally, the decreased extrusion force caused the desired uprighting moment produced in the molar tube to become lower (9.34 N.mm) than the conventionally accepted value for an efficient correction (20-30 N.mm). , In this investigation, we could have moved the molar tube occlusally to determine how far the height difference would be to produce an intrusive force. We have not done so because we have considered that bonding a molar tube even further occlusally would not be clinically viable. However, we made a regression line using the experimental data and have forecasted, using the line equation, that the molar tube would have to be bonded 6.7 mm occlusal to the remaining brackets for the archwire to produce zero extrusive force ( Fig 6 ). This would not be possible. Step bends and v-bends could be placed in the archwire to change the force system, but it is very hard to precisely place v-bends. Moreover, because the load system is statically undetermined, it is very hard to add up the load system given by the tube and bracket geometry to the load system produced by the bend: that would have to be measured by load cells. In addition, although a precisely placed bend in a continuous arch could produce the load system to upright and intrude a second molar, there would be a high cost of a large reactive net moment in the anterior region, which would be larger than the active moment at the molar because of equilibrium.

Graph depicting the extrusive force registered at the molar tube in relation to the position of the molar tube (zero value means the tube is leveled with the remaining brackets). The full blue line regard experimental data, whereas the dotted blue line regard estimates. The regression line explains 98% of the values. These data are specific to the situation tested by this investigation.
Fig 6
Graph depicting the extrusive force registered at the molar tube in relation to the position of the molar tube (zero value means the tube is leveled with the remaining brackets). The full blue line regard experimental data, whereas the dotted blue line regard estimates. The regression line explains 98% of the values. These data are specific to the situation tested by this investigation.

There are other strategies in the literature for uprighting molars, such as cantilevers, double cantilevers, and root correction loops, although all of them have their own drawbacks. While the cantilever increases the uprighting moment because of its increased length, allows a choice to where in the archwire to dissipate the reactive force and does not produce a reactive couple anteriorly, it still produces an extrusive force on the molar. This extrusion can lead to premature contact, impaired functionality, and discomfort to the patient. The double cantilever, similarly to a root spring, or even a precisely placed bend in a continuous arch, could upright and intrude a second molar, but as already mentioned, at the cost of a large reactive net moment in the anterior region, as a side effect. The main issue with these uprighting methods is that all derive from a vertical force to produce an uprighting moment, which may need to be controlled.

Possible solutions for the problem of uprighting a molar without extruding it and without reactive side effects of the mechanics on the anterior segment can be found using indirect skeletal anchorage, such as inserting a miniscrew between the premolars and attaching it to the second premolar or inserting the device directly into the miniscrew or even into 2 anterior miniscrews. Another option is to invert the lever direction to distal, which makes the vertical force of activation of the same moment becomes intrusive in the molar and anchored in a miniscrew inserted in the retromolar region, improving its predictable because it is a statically determined force system. In addition, using another skeletal anchorage biomechanical strategy, and one of the most reported, is to use the moment of a force, instead of a moment of a couple, with the miniscrew in the retromolar area and using an elastic force between the molar’s distal crest and the miniscrew. Thus, the line of action of the elastic traction force passes above the center of resistance located approximately in the furcation region, which generates an uprighting moment. In patients with anatomic limitations for retromolar miniscrew insertion, it can be inserted in the anterior region. A spring can push the molar, assuming a force action line above the center of resistance. This spring alternatively can be anchored to the premolars, which are often migrated distally in this situation, to correct the Class II sagittal relationship, which may be convenient.

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