In the initial alignment phase of orthodontic treatment using edgewise appliances, light round archwires are usually ligated to each bracket. Archwires are deflected between adjacent brackets to create orthodontic force. The magnitude of force delivered to each bracket affects the efficiency of tooth movement and the possibility of root resorption. ^, It is, therefore, crucial to understand the characteristics of the force delivered to each bracket.

In addition to interbracket distance, ^, bracket width, ^, bracket design, ^, and archwire diameter, ^, the ligation method ^{, ,} is a significant factor that affects the magnitude of force. According to a recent questionnaire study, 63% of orthodontists reported using a self-ligation bracket. Self-ligation has become widely used by orthodontists as well as conventional elastic ligation (CL).

Previous in vitro studies measured the direction and magnitude of force at the bracket only for the displaced tooth and compared these measurements among different ligation methods. Few studies have measured the force delivered not only for the displaced tooth but also adjacent teeth. However, Badawi et al recently developed an orthodontic simulator to simulate the maxillary dental arch using multiple 6-axis force sensors connected to all of the teeth of the maxillary dental arch, which are designed to measure the 3-dimensional (3D) forces delivered at each bracket. Accordingly, Fok et al ^, simulated a high maxillary canine displaced 4 mm by using the orthodontic simulator, ligated 0.014-inch round copper-nickel-titanium archwire to each bracket with self-ligation or CL, and measured the 3D forces delivered at all maxillary brackets while moving the high canine to a normal position. They found more extensive force distribution around the dental arch in CL than in self-ligation.

More recently, Tochigi et al measured the force delivered by 0.014- and 0.016-inch nickel-titanium alloy archwires by using a newly developed multisensor measuring system designed to measure the forces at each bracket attached to the mandibular teeth and compared the force magnitude at the mandibular incisors brackets between CL and self-ligation in the simulation of 2-mm mandibular lateral incisor linguoversion. They found that the force magnitude in CL was larger than that in self-ligation. However, the authors compared only the force magnitude between the ligation methods and did not analyze 3D directions of the force.

In oral biomechanical research, several studies have applied finite element models (FEM) to compare stress and torque between ligation methods; whereas other studies used a simulator. FEM is an engineering method for calculating stress and strain in all materials, including living tissue. Therefore, FEM can simulate a variety of clinical situations. However, the accuracy of FEM results greatly depends on the accuracy of the generated mesh and appropriateness of the elements used to discrete the structure. Although the use of a simulator overcomes these limitations, one great disadvantage of the simulator is that root, periodontal ligament, saliva, tooth mobility, and tooth-tooth contact cannot be simulated. ^{, ,} However, one advantage of the simulator is that bracket, archwire, and elastic modules, which are used in clinical practice, can be applied to the simulator regardless of design complexity and mechanical property.

Mandibular anterior crowding is commonly observed, and mandibular lateral incisor linguoversion, in particular, shows a major crowding pattern in orthodontic patients. In addition, it has also been reported that more apical root resorption occurs at the mandibular incisors next to the maxillary incisors.

The mesial-distal diameters of mandibular anterior teeth are usually smaller than those of maxillary anterior teeth. Therefore, in edgewise appliances, it would be assumed that the interbracket distance in the mandibular anterior tooth is the smallest among maxillary and mandibular dental arches. Because the interbracket distance ^, is another significant factor that affects the magnitude of force, it is important to investigate force applied to the mandibular anterior teeth. However, characteristics including the 3D direction and magnitude of force delivered to crowded mandibular anterior teeth have not been evaluated in great detail.

Therefore, the purpose of the present study was to compare the 3D forces delivered to the displaced tooth and its adjacent teeth between passive self-ligation (PSL) and CL in the simulation of mandibular incisor linguoversions.

Material and methods

A multisensor measuring system was used to measure the 3D forces delivered to the brackets attached to the mandibular left central incisor, lateral incisor, and canine (FDI tooth numbers 31, 32, and 33, respectively) ( Fig 1 , A ). This system consists of stainless steel blocks simulating each mandibular tooth and micrometers for adjusting the 3D position of each block. Three 6-axis force sensors were connected to 31, 32, and 33 in the present study.

The multisensor measuring system. A, Overall view of the multisensor measuring system. B, 1-mm displacement × PSL. C, 1-mm displacement × CL. D, 4-mm displacement × PSL. E, 4-mm displacement × CL.

In addition, PSL brackets made of stainless steel with a 0.022 × 0.027-inch slot (Damon Q; Ormco, Orange, Calif) and molar tubes (peerless cast buccal tube; Ormco) were welded to the labial and buccal surface of each block. We selected Damon Q in the present study because 42% of orthodontists who use self-ligation brackets reported using Damon in a recent questionnaire study.

First, a 0.019 × 0.025-inch stainless steel guide wire was fabricated to pass the bracket slot points suggested by Oda et al, which represented the position of the base of the bracket slot in relation to the tooth of Japanese normal occlusion. The guide wire was ligated to the brackets. The positions of all metal blocks were adjusted by micrometers to simulate the arch form of Japanese normal occlusion until the force delivered to each bracket reached under 0.1 N.

Then the guide wire was removed. To simulate mandibular left lateral incisor linguoversion, 32 was displaced lingually by micrometers; the position of 32 was constantly checked during displacement using a laser sensor at 0.001-mm increments.

Next, a 0.014-inch round nickel-titanium alloy archwire was ligated to each bracket. 3D forces (Fx, Fy, and Fz) delivered at 31, 32, and 33 were measured. Fx, Fy, and Fz correspond to force in the direction of the x-, y-, and z-axis, respectively. The coordinate systems were determined at 31, 32, and 33. The x-axis showed the labial-lingual direction (lingual, positive; labial, negative), the y-axis showed the mesial-distal direction (mesial, positive; distal, negative), and the z-axis showed the extrusion-intrusion direction (extrusion, positive; intrusion, negative).

One and 4 mm of lingual displacement were used in the present study ( Fig 1 , B-E ).

Two types of ligation methods were used: PSL and CL. In PSL, the archwire was ligated by closing the slide built-in brackets. In CL, an elastic shooter (Straight Shooter; TP Orthodontics, LaPorte, Ind) was used to ligate the archwire with an elastic module (Power O 110; Ormco, Glendora, Calif). To make the bracket width the same between PSL and CL, passive self-ligating brackets were also used in CL with opened slides.

In this study, 0.014-inch round nickel-titanium alloy archwires (archwire) were used. Based on Saze and Arai, 3 types of arch form, similar to the arch form of Japanese normal occlusion, were selected to reduce the force generated by the difference between the arch form of Japanese normal occlusion and archwires: (1) Damon (Damon Arch Form; Ormco), (2) VIA (VIA wires-Square; Opal Orthodontics, South Jordan, Utah), and (3) Bio-Arch V (TP Orthodontics). Five archwires from the 3 types were used for measurements. All measurements were performed in a chamber maintained at 37°C.

The sample size was estimated to have an effect size of 1.03, which was determined based on a previous study using the G-power statistical program (version 3.1; Heinrich Heine Universitat Düsseldorf Experimentelle Psychologie, Düsseldorf, Germany). Power analysis revealed that the required minimum sample size for each group was 5 to detect this effect size with 80% power and a significance level of 5%.

In the present study, forces at 31, 32, and 33 were measured at 2 amounts of displacement (1 and 4 mm), 2 ligation methods (PSL and CL), and 5 archwires from 3 types (Damon, VIA, and Bio-Arch V). In total, 60 combinations of measurement were performed.