Variability of slot size in orthodontic brackets

Abstract Objective The accuracy of the information incorporated into brackets is a determining factor for the efficacy of torque applied to teeth. The aim of this study was to compare the dimensions of a bracket's slots with the nominal values announced by the manufacturer. Materials and methods A total of 730 maxillary right central brackets manufactured by seven companies (Dentsply Gac, American Orthodontics, Rocky Mountain Orthodontics, GC Orthodontics, 3M Unitek, and Dentaurum) were studied. The sample included 0.018 × 0.025 and 0.022 × 0.028 in., metal and ceramic, conventional and self‐ligating brackets. Images were obtained with an Olympus BX51 optical microscope. Slot dimensions were measured at the base and at the face on both mesial and distal sides using ImageJ software. Data were analyzed using Wilcoxon, sign tests, two‐ and three‐way ANOVA, and Tukey's tests. Intraclass correlation coefficient was employed to assess the intraobserver and interobserver variability. The threshold for statistical significance was p ≤ .05. Results Statistical analysis showed that the slot dimensions of 90% to 97% of studied brackets were significantly different from nominal values. In general, slot size was oversized, with a face size larger than the base size. Comparison between mesial and distal sides showed that up to 45% of the brackets were significantly asymmetrical. The manufacturer had a significant effect for base and face widths (p = .0001) and for length (p = .003). Conclusion This study shows that a large proportion of measured brackets displays dimensional inaccuracies when compared with stated values. Clinically, the slot oversize and the divergence of slot walls cause an increase of wire‐slot play, inducing a loss of torque control. Practitioners cannot fully trust the precision of used appliances and should be aware that adjustments could be needed in the finishing stages of the treatment.


| INTRODUCTION
The use of straight-wire techniques implies the insertion of successive straight archwires of increasing cross-sections, ending with a full-size arch. The last archwire is expected to fill entirely the bracket slot, allowing then a complete expression of the brackets information.
Contrary to those expectations, the bracket/wire play was proved not to correspond to the theoretical values, showing a systematical increase (Archambault et al., 2009;Arreghini, Lombardo, Mollica, & Siciliani, 2014;Dalstra, Eriksen, Bergamini, & Melsen, 2015). This excess of play is multifactorial. Among these factors, we can point the mode of ligation, the type of material composing the bracket, and the manufacturing imprecision.
The last but not least of the factors causing an increase of play consists in the structural inaccuracies of brackets and archwires, which seem to be due to manufacturing processes. Gioka and Eliades reported in their systematic review that slot surfaces showed microstructural defects and striations (Gioka & Eliades, 2004). Those irregularities appear to be caused by milling processes, and the rough surface generated would prevent the wire from being fully inserted in the bracket slot. Such an obstacle could also be caused by molding processes, as they expose the bracket to shrinkage, but also to a bevel of the slot corners (Major, Carey, Nobes, & Major, 2010). In order to avoid the lack of insertion of the wire into the slot, manufacturers appear to have taken measures such as enlarging the slots and slimming the archwires. It was also shown that a lack of slot wall parallelism could be added to this loss of dimensional accuracy, thus aggravating the bracket/wire play (Cash, Good, Curtis, & McDonald, 2004).
This study had the aim of studying the dimensional precision of a wide sample of marketed bracket series in regards to slot width and length, parallelism of walls, and symmetry between mesial and distal sides.

| MATERIALS AND METHODS
A total of 730 maxillary right central brackets were provided by seven companies (Dentsply GAC, Bohemia, NY; American Orthodontics, Sheboygan, WI; Ormco, Glendora, CA; Rocky Mountain Orthodontics, Denver, CO; GC Orthodontics, Breckerfeld, Germany; 3M Unitek, Monrovia, CA; and Dentaurum, Ispringen, Germany). All brackets were preinformed, 0.018 × 0.025 or 0.022 × 0.028 in., metal or ceramic, conventional or self-ligating. Self-ligating bracket clips were either passive or active. In accordance with these criteria, 73 different series (with the same batch) of brackets were put together, and a sample of 10 brackets of each series was randomly selected.
Bracket slot images were obtained using a calibrated Olympus BX51 optical microscope.
Each bracket slot was measured at base and at face, using ImageJ software (National Institute of Health). To prevent the bias due to the roundness of the slot angles, the measurement was done at a distance of 100 μm from the slot base. For the same reasons, the faces were measured at 610 μm ( Figure 1a). In cases where the slot was not long enough, the dimensions were taken as far as possible from the base.
Slot length was evaluated for the self-ligating brackets. This length was measured as the shortest distance between the slot base and the clip ( Figure 1b).
All measurements were rounded off at to the nearest micron.
F I G U R E 1 (a) Side view of a bracket, displaying base and face width measurements (d1, distance between slot base and base measurement; d2, distance between slot base and face measurement); (b) Side view of a selfligating bracket (d3, slot length measurement) Width and length sizes were compared with those announced by the manufacturers. Bracket symmetry, slot walls parallelism, and intraseries reproducibility were also analyzed.
Wilcoxon signed-rank test and sign test were used to compare matched samples or repeated measurements on a single sample. Data were analyzed using two-and three-way ANOVA and Tukey's tests (p < .05).
A hundred bracket slot images were analyzed independently and randomly by two blinded examiners. The intraobserver and interobserver variability was assessed using the intraclass correlation coefficient. An intraclass correlation coefficient score close to 1 states that the correlation is strong.
Statistical analyses were performed using SPSS ® v. 25.0 software (IBM Corporation, Armonk, NY). A p value <.05 was considered as statistically significant.

| RESULTS
The comparison between slot widths and nominal values exhibited that 90% of tested brackets showed a statistically significant difference with the announced size at base, whereas 97% of the brackets were significantly different at face. The interobserver agreement was 0.96 and the intraobserver variability was 0.99 and 0.98.
Base and face widths are presented in Tables 1 and 2. At base, 11% (mesial value) to 12% (distal value) of bracket slots were significantly narrower than expected. On the opposite, 78% (distal value) to 79% (mesial value) of the slot measurements at base were significantly wider. At face, no bracket slot was significantly narrower than expected, whereas 97% were significantly wider than expected.
There was a statistically significant three-way interaction between manufacturer, ligating type, and material for base size (F = 8.365, p = .0001) and for face size (F = 2.481, p = .030). The manufacturer had a significant effect for base and face widths (p = .0001). Two-way ANOVA did not reveal an interaction between ligating type and material for base (F = 3.060, p = .080) and for face (F = 0.328, p = .567). of the self-ligating ones). At distal side, 85% of the brackets showed a statistically significant difference between the base and the face (88% for conventional brackets and 78% for self-ligating ones). Significant convergence or divergence of the slot walls was also assessed, and it was shown that 1% (distal) to 3% (mesial value) of the walls were significantly convergent, whereas 84% (distal) to 85% (mesial value) were significantly divergent. No conventional bracket showed a convergence according to the mesial side measure, and no self-ligating bracket showed a convergence according to the distal side measure.
The comparison between mesial and distal sides was made in order to evaluate bracket symmetry. It was shown that 45% of the bracket slots were asymmetrical at their bases (36% for conventional brackets and 65% for self-ligating ones), against 34% at their faces (32% for conventional brackets and 39% for self-ligating ones).
Slot length analysis was performed for active and passive selfligating brackets (Figure 1b,

| DISCUSSION
In the present study, the purpose was to select a bracket series from the entire product range of seven different manufacturers, in order to evaluate brackets with different types of ligation mode, size, and material. Results regarding this particular parameter bring out the fact that the dimensional reproducibility is very uneven within the different series, hence preventing the practitioner from relying on the repeatability of treatment outcomes.
This study highlights the dimensional inaccuracy of a large proportion of the tested bracket series. It was shown that 90% to 97% of slot width measurements differed with stated value. Those measurements generally tended toward an enlargement of the slot and a divergence of slot walls.
Bracket dimensional variations have already been a concern for several authors whose findings were in accordance with those stated in the present study. Siatkowski described slot enlargement in 1999 and then explained such variation by an error of conversion between the American imperial tooling system and the European metric tooling, causing an oversize of brackets by 4.22% (Siatkowski, 1999).
Most recent studies are more inclined to attribute these inaccuracies to imprecise manufacturing processes.
Cash et al. gathered a sample of 55 brackets of 0.022 × 0.028 in. stated dimensions, marketed by six different companies (Cash et al., 2004). They pointed out that all bracket slots were enlarged, with a maximum oversizing of +24% (Discovery Roth, Forestadent, Pforzheim, Germany). They noted that some of the slots were convergent, and some, divergent. Focusing on interseries discrepancies, we can emphasize the significance of the irregularities between different bracket series. Regarding bracket asymmetry, we notice that about a third to a half of the slots were asymmetrical. Such difference between mesial and distal sides would cause a poor control of tooth tipping, especially for brackets comprising a large mesio-distal width.
Measurement of slot length was performed for all self-ligating bracket series, with passive or active clip. Active clip in self-ligating brackets are expected to exert a pressure on the wire, and thus improving the insertion of the wire in the slot. Present outcomes reveal that mean slot length was highly uneven among the different active self-ligating bracket series, the lowest being 0.014 in (Cosmetic Empower, AO), and the higher 0.023 in. (Dinamique M, Dentaurum). This will indicate that, for some bracket series, the clip will have an action as soon as the early stages of tooth leveling, whereas for others, the practitioner will have to wait for the use of a rectangular archwire with a cross-section superior to 0.023 in. The usefulness of those active clips was already questioned by Brauchli et al. in 2011, as they stated that the spring strength was limited to 1 Nmm, which would be insufficient to produce a clinical action (Brauchli et al., 2011).
Besides the fact that dimensions are not accurate, it is relevant to note that slot inclination angles are not reliable either (Lefebvre, Olive, Saadaoui, Renaudin, & Jordana, 2018).
According to our results, we argue that, to comply with dimension regulations, improvement is required to manufacturers. Practitioners cannot fully trust the precision of the appliances available on the market and must be aware that adjustments are needed in the finishing stages of the treatment.

| CONCLUSIONS
A total of 730 maxillary right central brackets manufactured by seven companies (Dentsply Gac, American Orthodontics, Rocky Mountain Orthodontics, GC Orthodontics, 3M Unitek, and Dentaurum) were studied. A proportion of 90% to 97% of the brackets evaluated displayed a statistically significant inaccuracy with the nominal value in regards to slot width. Slots were mostly oversized, with divergent walls. Manufacturer had a significant effect for base and face widths (p = .0001) and for length (p = .003).
Clinically, such variations will increase the wire-slot play, which induces a loss of torque control. Those findings indicate that, even when using a straight wire technique, the orthodontist cannot rely only on the information incorporated into the brackets and is likely to add correction bends.