Effect of power arm length combined with additional anterior torque on the axial orientation of the maxillary incisors during en-masse retraction: A finite element analysis

Introduction

This study aimed to clarify the effect of power arm length combined with additional torque incorporated into the archwire on the controlled movement of the anterior teeth using the finite element method.

Methods

An adult patient requiring medium anchorage after extraction of the maxillary first premolars was selected for this study. The power arms were placed between the lateral incisor and the canine at 3 levels: 3 mm, 6 mm, and 9 mm. A 150 g of retraction force was applied from each height of the anterior hook to the first molar tube, with 0°, 5°, and 10° of applied lingual root torque on the incisors.

Results

A 3-mm hook with 10° of applied torque, a 6-mm hook with 5° of applied torque, or a 9-mm hook with no extra torque constituted the best combinations targeted at controlling the inclination of incisors during retraction. Extrusion and distal tipping of the canine were observed. Moreover, mesial tipping and mesiopalatal rotation of the molar were unavoidable. Finally, intercanine and intermolar widths were decreased.

Conclusions

Adding extra torque on the incisors or using high torque brackets is recommended for patients with maxillary first premolar extraction.

Highlights

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Anterior hook height and torque, boss impact incisor tipping during retraction.
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Without torque control, the amount of retraction will be increased.
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When medium anchorage is needed, mesial tip and mesiopalatal rotation of the molars will occur.

Nowadays, maxillary first premolar extractions are well accepted in the treatment of patients with malocclusion that require the retraction of anterior teeth, such as severe crowding, bimaxillary protrusion, Class II malocclusion, convex facial profile, as well as those with borderline relationships.

Most orthodontists throughout the world are now adopting sliding mechanics for space closure. The latter occurs when brackets slide along a stiff archwire to achieve anterior retraction. Hence, controlling anterior tooth movement during this treatment phase is quintessential to avoid the lingual tipping of incisors.

It is important to estimate the location of the center of resistance (CR) of the anterior teeth during sliding mechanics. The relationship between the force system acting on the tooth and the CR determines the type of tooth movement. Van den Bulcke et al found that the CR shifted apically as the number of anterior teeth in the dental units increased. Hence, the greatest shift was in the 6-tooth unit after the integration of the canines into the incisor segment.

The true translation movement of incisors during sliding mechanics will occur if the force passes through the CR. Accordingly, using long anterior retraction hooks (ARH) attached to the archwire enables the orthodontist to achieve a controlled movement of the anterior teeth. It has been proved that placing the power arm between the lateral incisor and the canine allows for better control during retraction. Through the use of the finite element method, numerous studies in the literature have evaluated the relationship between the length of the ARH and the movement of the incisors during sliding mechanics. ^,

The finite element method was introduced in dental biomechanical research in 1973, and since then, it has been widely applied in the analysis of stress and strain fields as well as of tooth displacement when subjected to simulated forces. By creating models for biomechanical studies, this method was shown to be highly reliable, with results closely mimicking histologic observations and clinical reality.

The preadjusted bracket systems used in our clinical practice do not provide an effective and sufficient crown and root position control in all 3 space planes. To overcome the issue of play, an additional lingual root torque must thus be added to the maxillary incisors during sliding mechanics. The effective torque will equal the bracket torque and incorporated wire torque minus torsional play.

To our knowledge, none of the previous studies have determined the effect of the anterior torque on the axial orientation of the maxillary incisors during sliding mechanics. This is an important clinical feature that can facilitate the control of incisor inclination in extraction.

Material and methods

One adult patient was selected as the subject of this study. The selection criteria were complete maxillary permanent dentition, good alignment, maxillary alveolar protrusion, no restorations, no dental fractures or caries, and no periodontal disease. A cone-beam computed tomography was obtained from the archive of the Department of Radiology of the Saint Joseph University of Beirut, using the NewTom VGi machine (Newtom, Verona, Italy) at these settings: 110 kVp, 6.14 mA, 0.125-mm voxel size, 3.6-second scan time, and field view of 24 × 19 cm). The study was approved by the Ethics Committee of the University of Saint Joseph of Beirut (USJ-2021-175). The digital imaging and communication in medicine files were then imported into the Blue Sky Plan software (BlueSky Plan, Grayslake, Ill) to generate the external surface of the bone and teeth using the gray scale threshold technique. Teeth 14 and 24 were deleted to simulate the extraction of the first premolars.

The x-ray imaging process cannot detect the periodontal ligament (PDL); thus, modeling was carried out with the Autodesk Meshmixer (version 3.3; Autodesk, San Rafael, Calif). The PDL was deemed to be of a uniform thickness of 0.2 mm, so teeth were expanded by 0.2 mm uniformly, and then, the initial teeth were subtracted to get the PDL. Both the brackets and the power arms were also modeled with the Meshmixer software. To reduce the calculation time, brackets were considered hexahedral elements connected to the teeth, with a 0.022 × 0.028-in slot size. The bracket torque prescription was 17° for the central incisor and 10° for the lateral incisor. These values were taken from the Victory Series Low Profile Bracket System (3M Unitek, MBT prescription).

The 0.019 × 0.025-in stainless steel archwire was drawn with AutoCAD (Autodesk) using the 3-dimensional (3D) coordinates of the brackets for a perfect fit. The consecutive interaction surfaces between the archwire and the slot were not parallel to each other and the movement direction because the archwire was discretized into linear elements. This process induces frictional forces inside the bracket slot during sliding, even if a frictionless property was used. The 6 anterior teeth were tied with an 8-figure stainless steel ligature (diameter, 0.010-in) to minimize the relative movement.

The meshing all the components was done in Meshmixer with a 1-mm target edge length for the bone and 0.5 mm for the teeth and PDL. The resulting stereolithography files were imported into Abaqus (version 6.13; Dassault Systems Simulia Corp, Minneapolis, Minn) and assembled to create the 3D finite element model ( Fig 1 ).

After meshing the geometric field, the nodal displacement of the tooth was evaluated according to the 3 planes of space (ie, x, y, and z) representing movements in the horizontal, sagittal, and vertical planes, respectively. A positive value indicates the mesial x-axis, posterior y-axis, and upward z-axis.

The final model consisted of 1,001,748 elements and 191,133 nodes. As for the boundary conditions, the translational degrees of freedom on the upper side of the model were blocked. Material properties were defined for bone, teeth, PDL, brackets, archwire, power arms, and 8-figure ligatures. They were assumed to be homogeneous and isotropic linear elastic materials. Young’s modulus and Poisson ratio are defined in Table I .

Table I

Material properties

Material	Young’s Modulus (MPa)	Poisson’s ratio
Bone	2000	0.30
Teeth	20,000	0.30
PDL	0.68	0.49
Archwire, brackets, power arms, figure 8 ligature (stainless steel)	200,000	0.30

The power arms were placed between the lateral incisor and the canine at 3 levels: 3 mm, 6 mm, and 9 mm. A 150 g of retraction force was applied from each height of the anterior hook to the first molar tube to simulate en-masse retraction of the 6 anterior teeth with a nickel-titanium closed coil spring. With each level of traction, 0°, 5°, and 10ۣ° of applied lingual root torque were incorporated into the archwire into the incisor segment. En-masse retraction in our study means retracting the 6 anterior teeth (the incisors and the canines) after extracting the maxillary first premolars.

The simulation was conducted because the play between the archwire and the brackets exists as it influences the effective torque on each tooth. The theoretical torque loss illustrated in Figure 2 differed from the torque loss in this study because manufacturers tend to enlarge the size of the slots and decrease the section of the archwires relative to the reported size. The Victory Series slot used in our study was oversized by 6%. The net effective torque on each tooth was introduced in the finite element model as a physical moment represented by a couple of forces.

A total of 9 models were obtained after the modification of both the length of the power arm and the applied torque. The names of the models were based on these 2 variables. For instance, H6T5 means that the height of the anterior hook was 6 mm, and the applied torque on the incisors was 5°.

The displacement of the original nodes was measured to evaluate the effects of applied torsional forces to achieve tooth movement. The stress produced in the PDL of the anterior region was also calculated. Assuming the model’s symmetry, we only analyzed the results on the right side.

Results

The evaluation of initial tooth movement in the anterior region displayed the following results. In the sagittal plane, lingual crown tipping of the central and lateral incisor was produced in the models H3T0, H3T5, and H6T0 ( Tables II and III ). As the height of the retraction force on the power arm was raised apically from the bracket slot level, a backward displacement of the roots was observed. The apex of the central incisor in model H9T0 started to move slightly backward, but it was accompanied by a greater retraction of the crown, thus also leading to the lingual tipping of the tooth ( Table IV ). The previous results are confirmed by the negative values of the rotation of the incisors around the x-axis, which explains the generation of a clockwise rotation of the anterior teeth around the occlusal plane ( Figs 3 and 4 ).

Table II

Displacement of the incisors according to the applied anterior torque when the length of the hook was 3 mm

Model, tooth, and node	Displacement (10 ⁻⁴mm)
Model, tooth, and node	X	Y	Z
H3T0
11
Occlusal	2	29	−11
Apical	0	−4	9
12
Occlusal	18	30	−13
Apical	−1	1	5
H3T5
11
Occlusal	4	11	0
Apical	−1	3	4
12
Occlusal	23	22	−9
Apical	−1	2	5
H3T10
11
Occlusal	6	−9	12
Apical	−2	11	0
12
Occlusal	24	4	2
Apical	−1	4	3

Table III

T Displacement of the incisors according to the applied anterior torque when the length of the hook was 6 mm

Model, tooth, and node	Displacement (10 ⁻⁴mm)
Model, tooth, and node	X	Y	Z
H6T0
11
Occlusal	3	19	−3
Apical	−1	1	8
12
Occlusal	23	15	−3
Apical	−1	4	5
H6T5
11
Occlusal	6	1	8
Apical	−1	7	4
12
Occlusal	28	7	1
Apical	−1	5	5
H6T10
11
Occlusal	8	−19	20
Apical	−2	15	0
12
Occlusal	29	−11	12
Apical	−1	7	4

Table IV

Displacement of the incisors according to the applied anterior torque when the length of the hook was 9 mm

Model, tooth, and node	Displacement (10 ⁻⁴mm)
Model, tooth, and node	X	Y	Z
H9T0
11
Occlusal	5	9	5
Apical	−1	5	7
12
Occlusal	29	−1	7
Apical	−1	7	5
H9T5
11
Occlusal	8	−9	15
Apical	−2	11	3
12
Occlusal	34	−9	12
Apical	−2	8	5
H9T10
11
Occlusal	10	−29	28
Apical	−3	19	−1
12
Occlusal	34	−27	22
Apical	−1	10	4