Biomechanical effect of dual-dimensional archwire on controlled movement of anterior teeth compared with rectangular archwire: A finite element study

Introduction

This study aimed to determine and compare the effectiveness of the use of the dual-dimensional archwire and conventional rectangular archwire on tooth movement patterns when combined with various lengths of power arms.

Methods

Displacements of the maxillary central incisor and the deformation of the wire section were calculated when applying retraction forces from different lengths of power arms using the finite element method.

Results

Torque control of the incisor could be carried out more effectively when using the dual-dimensional archwire combined with long power arms than with the rectangular archwire. The use of the dual-dimensional archwire produced bodily movement of the central incisor at height levels of the power arm between 8 and 10 mm and lingual root tipping at the level of 10 mm.

Conclusions

The use of the dual-dimensional archwire provided better-controlled movement of the incisor, including bodily movement or root movement, than the rectangular archwire.

Highlights

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Biomechanical features of dual-dimensional and rectangular archwire were compared.
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The dual-dimensional archwire provided better torque control of the incisor.
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The dual-dimensional archwire showed greater mesiolingual molar rotation.
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The dual-dimensional archwire produced less frictional resistance.
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The use of the dual-dimensional archwire could shorten the treatment time.

In orthodontic treatment, there has been wide use of sliding mechanics to perform space closure after the extraction of premolars for the correction of crowding or maxillary and mandibular protrusion. The advantage of sliding mechanics is that the height level of the retraction force with respect to the center of resistance (CR) of a tooth can be freely adjusted by attaching various lengths of power arms onto the archwire, depending on the patient. In other words, combining sliding mechanics with power arms has the potential to produce preprogrammed force systems for achieving controlled movement of the anterior teeth. During space closure, torque control of the anterior teeth is quite important to avoid side effects such as the bowing effect and uncontrolled tipping of the incisors, which causes a gummy smile, bite deepening, and prolonged treatment time. ^, ^,

However, several disadvantages have been noted with sliding mechanics. One of the most critical drawbacks is that the friction generated at the interface between the archwire and brackets could interfere with efficient tooth movement. A previous study suggested that the use of the rectangular archwire is likely to increase contact forces and friction, which could substantially affect the tooth movement pattern. Hamanaka et al have also reported that, as the space was closed, the amount of friction produced in the molar region had a tendency to increase, which would prevent the teeth from moving efficiently and consequently prolong the total treatment time. The amount of friction can be reduced by using an archwire with a smaller cross-section, such as a round one, which could make it difficult to achieve better torque control of the anterior tooth. ^, ^, To overcome such a shortcoming, a dual-dimensional archwire has been developed. The cross-section of the dual-dimensional archwire is a rectangle in the anterior portion to maintain the effectiveness of anterior torque control and round in the posterior portion to increase play between the archwire and brackets, thereby reducing friction ( Fig 1 ).

Although several studies have been performed to investigate various biomechanical factors affecting tooth movement in sliding mechanics, such as the length or location of power arms and archwire dimension, the effectiveness of the use of the dual-dimensional archwire during space closure has not yet been fully clarified. This study aimed to investigate and compare the biomechanical effects of the dual-dimensional archwire and conventional rectangular archwire when combined with various lengths of power arms on patterns of tooth movement by performing analyses of long-term tooth movement by means of the finite element (FE) method and to verify the hypothesis that the use of the dual-dimensional archwire could reduce the friction and shorten the treatment time.

Material and methods

The methodology for the construction of the 3-dimensional (3D) FE model and numeric simulation for long-term orthodontic movement was described in detail in the previously published article. A brief description is provided below. Moreover, 3D images of a maxillary dentition were taken using a multi-image microcomputed tomography scanner (3DX; J. Morita, Kyoto, Japan) with a voxel size of 80 μm from a dry skull. A 3D FE model of the left half dentition was constructed using 3D image processing and editing software (Mimics 10.02; Materialise Software, Leuven, Belgium) and outputted to FE preprocessing and postprocessing software (Patran 2012.1; MSC Software, Los Angeles, Calif) for FE analysis, assuming that the dentition was symmetrical.

The position of each tooth was then adjusted to minimize the interproximal space between adjacent teeth. The first premolar was extracted on the assumption that the case model was diagnosed as having a maxillary protrusion. The extraction space was set to be 4 mm, considering the consumption of space during the initial leveling.

The periodontal ligament with a thickness of 0.2 mm was constructed on the root surface of each tooth, and Young’s modulus of 0.05 MPa and Poisson’s ratio of 0.3 were assigned. For fixed appliances, a 0.022 × 0.028-in slot bracket and 2 types of stainless steel archwire models were created, namely, the dual-dimensional archwire, whose cross-section was 0.019 × 0.025-in in the anterior portion corresponding to the central and lateral incisors and 0.019-in in the posterior portion, and the conventional rectangular archwire, whose cross-section was 0.019 × 0.025-in ( Fig 2 ). Models of 2 archwires, brackets, and power arms were constructed using 8-node hexahedral elements with Young’s modulus of 204 GPa and a Poisson’s ratio of 0.3.

Power arms of various lengths (4, 6, 8, and 10 mm) were attached to the archwire corresponding to the middle point between the lateral incisor and canine from the height of the archwire. En-masse retraction was performed by applying the retraction force of 1.5 N from the hook on the second molar tube to the power arm ( Fig 2 ). Long-term orthodontic tooth movement was analyzed using the bone remodeling algorithm and the sequential analysis of initial displacement. All FE analyses were performed using the Marc version 2014.1 FE package (MSC software).

Contact boundary conditions were prescribed so that each tooth, bracket, and archwire could be in contact with each other. The displacement of the archwire in the transverse direction was constrained at the midsagittal plane. The coefficient of friction between the bracket slot and archwire was assumed to be 0.1. The frictional resistance produced at the interface between the archwire and the bracket and tube was analyzed. The number of remodeling steps required to close the extraction space was also calculated. The position of the CR of each tooth was determined according to the method previously reported by Hamanaka et al.

Results

Figure 3 shows the degree of labiolingual tipping as a function of the amount of translational displacement at the CR of the central incisor in the lingual direction when the power arm length was set at 4, 6, 8, and 10 mm. Positive signs indicate lingual crown tipping, and negative signs indicate lingual root tipping. There was no significant difference in the degree of lingual crown tipping between the dual-dimensional archwire (anterior: 0.019 × 0.025-in rectangular; posterior: 0.019-in round) and the conventional rectangular archwire (0.019 × 0.025-in) with the power arm of 4 mm. However, when the power arm length increased beyond 6 mm, the degree of lingual crown tipping with the dual-dimensional archwire was smaller than that with the rectangular archwire when retracted from the same power arm height. As the power arm length increased, the degree of lingual crown tipping of the central incisor decreased with both archwires, and the discrepancy in the tipping degree between the 2 archwires increased. Finally, the incisor showed lingual root tipping with the dual-dimensional archwire combined with the 10 mm power arm.

Figure 4 shows how the central incisor moved and how the anterior portions of the archwire and the power arm were deformed before and after space closure, viewed from the sagittal plane. Positions of the tooth, archwire, and power arm after completion of space closure are indicated in red for the dual-dimensional archwire and green for the rectangular archwire. The amounts of tooth displacement and the deformation of the archwire and power arm were magnified twice for a better understanding, focusing on the displacement of the central incisor in association with the deformation of the wire section to visualize the effect of power arm length on incisor movement. The degree of inclination of the power arm was larger with the dual-dimensional archwire than with the rectangular archwire.

Table I shows the amounts of displacement for the incisal edge and root apex of the central incisor in the lingual direction. The central incisor showed lingual crown tipping, in which the amount of displacement of the incisal edge was larger than that of the root apex in the lingual direction, except when using the dual-dimensional archwire with a 10 mm power arm, which caused lingual root tipping, in which the amount of lingual displacement of the root apex was larger than that of the incisal edge. The displacement of the root apex was substantially larger with the dual-dimensional archwire than with the rectangular archwire when the power arm height was raised beyond 6 mm.

Table I

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