Analysis of the characteristics of slot design affecting resistance to sliding during active archwire configurations

In the modern straight-wire mechanics, the sliding of the wire through brackets and tubes is fundamental in achieving the alignment of the dental arch[1]. A range from 12% to 60% of the orthodontic forces applied is expected to be lost due to resistance to sliding (RS)[2], reducing the amount of forces exerted by fixed appliance. This wide range of variability reduces the predictability of the applied forces; for this reason, a better understanding of the RS is mandatory in order to apply predictable amount of forces.

The RS between bracket and wire depends mainly on classical friction (FR), in which the type of wire engaging system is influential, and binding (BI)[2]. FR is proportional to the normal force (FN), acting perpendicular to the direction of movement on the contact surface and depends on the coefficient of friction (μ) of a specific material according to the formula: FR = μ FN[3]. BI represents the force produced when the wire first contacts both opposing edges of the slot and is governed by the angular relationship between bracket slot and wire[4]. BI is encountered throughout the treatment, i.e., during arch alignment and leveling, space closure, or the finishing phase when the torque control is required for a correct tridimensional position of dental roots[5], and it is influenced by the wire stiffness[6]. Factors such as bracket type[7, 8], type and method of ligation[9, 10], bracket and arch-wire alloy[11, 12], surface characteristics[11, 13], wire-slot angulation[3, 14, 15], arch-wire size[15, 16], and section[16, 17] were found to affect the RS.

To the best of our knowledge, there are no studies evaluating how specific characteristics of slot design, such as the mesio-distal slot width and slot depth, influence the RS.

The aim of this study was to evaluate the effect of the abovementioned slot design characteristics on the RS recorded testing five different low-friction brackets.

The brackets tested can be listed in decreasing order of mesio-distal width and depth of the slot, respectively: In-Ovation, Damon II, Quick, Time 2, and Synergy; and Synergy, Quick, Time 2, Damon II, and In-Ovation (Table 2).

In the straight-wire biomechanics, the biological response of the orthodontic movement is limited by the friction generated during the sliding of the wire[23]. Studies have shown that approximately 50% of the force applied to reach the orthodontic dental movement is spent to overcome the frictional resistances[24] causing an inconsistent application of forces on the tooth. Minimizing the causes of RS may both speed tooth movement and increase its predictability.

In this study, we analyzed how the different slot designs of five low-friction brackets could affect the RS in two different experimental models (i.e., vertical and horizontal bracket displacements). The brackets chosen for this study were all reduced friction brackets; testing these brackets represents a great advantage because it is possible to reduce the experimental error constituted by the classical friction when a study aims to investigate the mechanical conditions governed by the binding.

Previous reports demonstrated that an increase of mesio-distal slot width, during vertical displacement of brackets, affects the BI by (a) reducing the interbracket distance, which increases the stiffness of the wire and (b) reducing the contact angle (θ c)[4]. Both of these phenomena increase the forces of binding and consequently the RS. In this study, we found a significant positive correlation between the mesio-distal slot width and frictional values when Time 2 bracket was excluded (Table 5). This finding suggests that wider mesio-distal slot dimensions cause higher frictional forces within brackets that are vertically displaced. According to these findings, clinicians should select brackets presenting a reduced mesio-distal width in order to minimize the RS.

The Time 2 bracket did not comply with this correlation; although it featured a reduced mesio-distal width, it showed higher levels of RS (1.50 N) compared with the other tested brackets (Table 3). The clear angle at the mesial and distal slot edges of Time 2, which is a specific feature of this bracket, could be responsible for this finding. Indeed, when the wire contacts both opposing edges of the slot (active configuration), the presence of clear edges could increase the binding of the wire and consequently the RS[25]. Therefore, bracket slot design featuring chamfered slot edges (Figure 4) could be an important requisite for a low-friction bracket system. The undersized vertical slot dimension of Time 2 (Table 2) could also contribute significantly to this finding.

The Quick bracket showed lower values of RS among the low-friction brackets tested in this setting. The oversized vertical slot dimension of this bracket (Table 2) along with the presence of chamfered slot edges could explain this result.

In horizontal bracket displacement, no significant correlation was found between RS and both slot depth and mesio-distal slot dimensions (Table 6); this result could be explained considering that the binding forces are influenced simultaneously by the abovementioned variables of slot design. These two variables affect each other, vary in an unrelated way among the brackets tested, and could explain the absence of any significant correlation.

The Quick bracket was found to express the lower values of RS among the evaluated self-ligating brackets despite that it did not feature the wider slot depth; it presented, instead, the shorter mesio-distal slot width, which allowed to a greater clearance of the wire within the horizontally displaced brackets.

In self-ligating brackets, the slot depth is also related to the type of wire engaging system[26, 27] such as active, interactive, and passive that can influence the RS expressed when the brackets are horizontally displaced. In this study, the In-Ovation bracket, which featured a sloped clip, showed higher values of RS compared to the Damon II, which is a passive self-ligating bracket (Table 4). Our finding is in agreement with Kim et al.[28] who reported that the interaction wire/clip of active self-ligating brackets was responsible for higher values of RS found in comparison with passive self-ligating brackets even when the degree of malocclusion increased.

The Synergy bracket showed, in absolute, the lesser values of RS (0.68 N). This could be attributed to the behavior of the elastomeric module which caused an augmentation of the critical angle (θ c) by accommodating the deflection of the wire (Figure 2).

On the contrary, Time 2 was found to express the higher values of RS (1.35 N) despite that it featured a reduced mesio-distal slot width (Table 2); this bracket was the only one that did not present chamfered edges at the extremities of the clip and the base of the slot. This characteristic could be responsible for the higher binding between the wire and the clip itself, increasing the RS values, as suggested by other authors[23].

In vitro studies are reported to be unable to simulate exactly the in vivo conditions;[29, 30] however, the in vitro settings are fundamental for the qualitative assessment of the singular variable that affect the overall resistance to slide.

The bracket slot design is a fundamental aspect affecting the RS generated at the wire/bracket interface.

In the presence of brackets vertically displaced, the RS is directly influenced by the mesio-distal slot width. Furthermore, the absence of chamfered edges of the slot contributes to increase the RS.

In order to select the proper low-friction bracket system, clinicians should consider some characteristics of slot design such as mesio-distal slot dimension and the presence of chamfered slot edges of the bracket slot.