Effects of stress relaxation in beta-titanium cantilevers used in orthodontic mechanics

ABSTRACT Objective: This study evaluated the force decay and design shape changes caused by stress relaxation in two different orthodontic cantilever configurations. Methods: Eighty cantilevers made of 0.017 x 0.025-in beta-titanium wires were standardized in a passive position, using real scale templates, and randomly divided into two groups (n = 40): Type 1 and Type 2. Each group received a different design (Type 1 with three bends, and Type 2 with two bends), and both were divided in four subgroups (n = 10) according to the evaluation periods: G1 = 24h, G2 = 1 week, G3 = 4 weeks, and G4 = 8 weeks. Mechanical tests were performed immediately after preactivation and at the end of each period, to evaluate force decay. The cantilevers were also scanned and the angles of the bends were measured to assess shape changes. Results: Cantilever forces decayed over time. Type 1 - G1 showed less force decay than Type 2 (10.83 cN vs 17.87 cN). Type 1 cantilevers showed significant force decay only when G4 was compared to G1 (9.05 cN), G2 (11.73 cN), and G3 (9.78 cN). Type 2 cantilevers presented differences when G1 was compared to G2 (9.57 cN) and G3 (7.89 cN). Regarding to the cantilever angle closest to the bracket insertion, Type 1 cantilevers showed significant decrease for G2 (1.58°) and G4 (1.52°). Conclusions: Cantilevers’ design and proximity of the bends influenced force decay pattern overtime. Type 1 cantilevers presented more stable design at the first weeks than Type 2.


INTRODUCTION
Orthodontic tooth movement is the result of force application on a tooth. Primarily, orthodontists generate forces using archwires, springs, and elastics. The role of the orthodontic wire is to act as a spring and/or a guide, and cantilevers appear as a versatile tool for orthodontics.
Cantilevers can be a simple straight wire or a wire with a special shape. Anchored at only one end, a cantilever is a beam with which the orthodontist can easily and accurately predict tooth movement. [1][2][3] By producing effects on the tooth in all three planes, controlling and individualizing the forces applied, cantilevers can be applied to provide intrusion or extrusion of one or several teeth simultaneously. They can also perform tractions, uprightings, retractions, and early corrections of the deep curve of Spee. [1][2][3][4][5][6] Because of their formability and springback characteristics, titanium-molybdenum alloys, also called β-titanium, are often used for the manufacturing of cantilevers. [1][2][3][4][5][7][8][9][10] This alloy in straight-wire applications can be deflected 105 percent more than stainless steel without permanent deformation, and its stiffness makes it ideal in applications where less force is required but a lower modulus of elasticity would be inadequate to develop the required force magnitudes. 11 Therefore, the use of β-titanium alloys enables the construction of cantilevers with simpler designs, saving time during the clinical procedures. Jacob HB, Gonzaga AS, Trinh B, Le ET, English JD -Effects of stress relaxation in beta-titanium cantilevers used in orthodontic mechanics 5 Despite their wide use, the best interval between activation is difficult to determine. The choice of the design of the segmented arch, material, and the way that it is bent has direct influence on how forces decay through time during clinical use. [7][8][9][10] The shape of the cantilever as well as its activation are individual choices of each orthodontist, and often the simpler shapes are more frequently used. However, the impact of a cantilever's design on the delivery of forces is a variable that is more frequently studied in more complex designs, and there is a lack of evidence for those with simpler designs, as well as which is the best form of use during orthodontic treatment. Therefore, the present study aims to compare the force decay and design shape changes caused by stress relaxation, as well as to determine the ideal time interval of reactivation, between two different cantilevers' activation types.

MATERIAL AND METHODS
Eighty cantilevers, made of 0.017 x 0.025-in beta-titanium wires  for Type 1 and Type 2 cantilevers. B) Preactivation template for the Type 1 cantilever. C) Preactivation template for the Type 2 cantilever. Jacob HB, Gonzaga AS, Trinh B, Le ET, English JD -Effects of stress relaxation in beta-titanium cantilevers used in orthodontic mechanics A B Figure 2: Loop software simulation of tension concentration areas for: A) Type 1 cantilever and B) Type 2 cantilever. The gradient of colors change from red, which means maximum tension concentration, to blue, which represents the minimum tension concentration.
Afterward, the cantilevers were randomly divided into two groups (n = 40) and submitted to two different preactivations designs: Type 1, with an extra bend for activation (angle α); and Type 2 (Fig 2).
Then, using a template generated by the Loop software in a 1:1 scale for standardization, the Type 1 cantilevers and the Type 2 cantilevers were preactivated 10 mm using the Marcotte plier. The amount of activation was chosen to provide enough moment for molar uprighting due to the cantilever length; 13 in addition, the amount of activation could be used for intrusion of the mandibular anterior teeth. 14,15 According to the software, Immediately after the cantilevers were preactivated (baseline), they were tested using a tabletop universal testing machine   After being scanned, the cantilevers were maintained active (simulating the clinical activation) in a custom-made device (Fig 3). The device was composed of a plastic sign-holder with brackets and tubes (0.018-in slot) from the SPEED System (Strite Industries, Ontario, Canada) carefully bonded with Loctite Super Glue (Loctite, Westlake, OH) at a distance of 28 mm. Jacob HB, Gonzaga AS, Trinh B, Le ET, English JD -Effects of stress relaxation in beta-titanium cantilevers used in orthodontic mechanics A 10 mm 0.016 x 0.022-in stainless steel wire was inserted on the brackets, and the cantilevers were hooked onto it. The bonding was organized in two rows of ten pairs, separated by design type at each side of the sign-holder, and kept ordered throughout the experiment. The cantilevers were prepared, stored, and tested at room temperature (set at 23°C). After performing mechanical test for each group, the cantilevers were scanned and the angles were measured by the same operator, in order to assess the permanent deformation of the structure (Fig 4).

FORCE ANALYSIS
Intraobserver systematic errors of the two measurement moments did not show significant differences. The differences between the first and second measurement ranged from <0. Jacob HB, Gonzaga AS, Trinh B, Le ET, English JD -Effects of stress relaxation in beta-titanium cantilevers used in orthodontic mechanics 12 Although there was a significant decrease of force among all groups in both Type 1 cantilevers and Type 2 cantilevers, only the 1-day period evaluation showed significant difference between the two cantilevers design (    angles during the experiment (Table 4). Angle 1 showed significant opening in G2 (-1.58°) and in G4 (-1.52°). Angle 2 had significant closure in G3 (0.82°), and angle α showed significant opening in G2 (-0.85°). Regarding Type 2 cantilevers, Angles 1 and 2 changed significantly through time (Table 5). Angle 1 showed a progressive opening, with significant differences at G1 (-0.74°), G2 (-0.88°) and G4 (-1.42°); while Angle 2 showed a progressive closing, with significant differences at G2 (0.70°), G3 (0.69°) and G4 (0.97°).
Comparing groups, Type 1 angle's changes were different through time for Angles 1 and 2 (Table 6), while Type 2 cantilevers did not present differences between groups for either angle (Table 7). Angle 1 of the Type 1 cantilever showed significant differences among four out of six comparisons.   The changes were significant for G2 in comparison to G1 (1.04°) and G3 (-1.52°), and for G3 x G4 (1.47°), while the difference between changes at G2 and G4 was minimal (-0.06°). Angle 2 showed that changes after 1 week (G2) were significant when compared to G3 (-1.75°) and G4 (-1.77°), and angle α did not express changes among groups. Sharpness and proximity of bends influence force decay. Type 1 cantilever design presents three concentrated bends in one end, and Type 2 cantilever design presents only two, and the changes of forces could be explained by the differences between the cantilevers' designs and its tension concentration areas (Fig 2).
The different designs led to more force decay within eight weeks, and/or stress-relaxation, as previously reported by the literature using "T" loop shape designs. 7,9,10 Normally, the orthodontist schedules the patient's appointments from four to eight weeks apart, and based on this study, the Type 1 cantilevers showed a more stable design than Type 2, due to amount of force decreasing in the first few weeks. The effect of stress relaxation was gradual in Type 1 cantilevers, occurring majorly after 4 weeks. The deformation presented during the first 24 hours in the Type 1 cantilever decreased the force level in approximately 29%, whereas the Type 2 cantilever decreased the force level in approximately 42%. Then, the reactivation could be performed after 4 weeks to maintain these optimal forces producing a more constant force levels. Although these results suggest that reactivation of cantilevers could be done up to 8 weeks, it is important to consider the permanent deformation that beta-titanium wires suffer as a function of time when exposed to long periods of deflection. 7,9,10,16,17,21 Clinically, a force decay of 20 cN has a great influence over tooth movement. Light forces are used for intrusion and it is recommended approximately 60cN to intrude all mandibular incisors. 14 If the force decay to 25 cN (20cN less than the applied initially), the intrusion of the mandibular incisors would not be performed.
Another clinical situation is related to the moment generate by the applied force. In order to efficiently upright one molar, it is necessary to produce a moment with magnitude of approximately 1100 cN-mm. 13 Considering a cantilever length of 25 mm, a vertical force of approximately 45 cN is required at the point of force application. A decay of 20 cN over the initial 45 cN will not provide enough force to generate the ideal moment.
The results of this study need to be cautiously interpreted.
Performing further tests to confirm this information, such as the measurement of forces over time after reactivation of the same cantilevers and clinical research (in vivo) of stress relaxation of cantilevers during the orthodontic treatment, is necessary to corroborate the findings of the present study. In addition, to better understand the cantilevers' behavior, X-ray diffraction test should be used to analyze the changes on the surface characteristics of the crystallographic structure.