International Journal of Health & Allied Sciences

: 2019  |  Volume : 8  |  Issue : 2  |  Page : 92--97

Stress assessment of mandibular incisor intrusion during initial leveling in continuous arch system with different archwire shapes of superelastic nickel-titanium: A three-dimensional finite element study

Pornpat Theerasopon1, Weerachai Kosuwan2, Chairat Charoemratrote1,  
1 Department of Preventive Dentistry, Faculty of Dentistry, Prince of Songkla University, Hat Yai, Songkhla, Thailand
2 Department of Orthopedics, Faculty of Medicine, Khon Kaen University, Khon Kaen, Thailand

Correspondence Address:
Dr. Chairat Charoemratrote
Department of Preventive Dentistry, Faculty of Dentistry, Prince of Songkla University, Hat Yai, Songkhla 90110


INTRODUCTION: Orthodontic leveling of mandibular teeth with deep curve of Spee usually creates an intrusive force on mandibular incisors with labial tipping. After placing an archwire, a deactivation force causes tooth movement within the periodontal space which induces the first step and is the first signal for further remodeling processes. This study aimed to investigate stress distribution and types of mandibular incisor movement after initial leveling with different nickel-titanium (Ni-Ti) archwires using finite element analysis. MATERIALS AND METHODS: A three-dimensional finite element model of well-aligned mandibular teeth with a deep curve of Spee was created to investigate intrusive force on mandibular incisors within the periodontal ligament (PDL) space. Round, square, and rectangular superelastic Ni-Ti archwires of 0.016” in height were tested to compare stress magnitude and the pattern of distribution on the root surface and PDL as well as the pattern of tooth displacement between the archwires. RESULTS: Intrusive force by an archwire within the PDL space caused the highest stress at both labial and lingual cervical roots, but much higher stress was found at the labial than the lingual cervical roots. The highest labial stress was more cervical than lingual in all models. Round wires showed much higher stress than either square- or rectangular-shaped archwires. Displacement in the labial direction of round wires moved the farthest, whereas square and rectangular wires showed less labial displacement. CONCLUSIONS: Lower incisor intrusion with round wires produced more stress at the labial cervical root and tipped more labially compared to square and rectangular archwires.

How to cite this article:
Theerasopon P, Kosuwan W, Charoemratrote C. Stress assessment of mandibular incisor intrusion during initial leveling in continuous arch system with different archwire shapes of superelastic nickel-titanium: A three-dimensional finite element study.Int J Health Allied Sci 2019;8:92-97

How to cite this URL:
Theerasopon P, Kosuwan W, Charoemratrote C. Stress assessment of mandibular incisor intrusion during initial leveling in continuous arch system with different archwire shapes of superelastic nickel-titanium: A three-dimensional finite element study. Int J Health Allied Sci [serial online] 2019 [cited 2019 May 23 ];8:92-97
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Mechanical force is one kind of stimulus which can induce cellular activities in dental and paradental tissues[1],[2] that leads to a cascade of modeling and remodeling processes, which is the reason an orthodontic force can move a tooth. Immediately after orthodontic force application, a tooth initially moves within its periodontal space which evokes compression and tension. Therefore, this initial displacement is the first signal for further orthodontic tooth movement.

The curve of Spee[3] is a naturally occurring phenomenon defined as the depth of occlusal curvature in mandibular teeth,[4] and a flat curve is one key to successful orthodontic treatment.[5] Thus, if Spee's curvature persists, the archwire will deflect vertically by the superiorly positioned mandibular incisor teeth, and immediately after deactivation of the archwire, an intrusive force at the mandibular incisor teeth begins. A previous study reported that an intrusive force at the labial brackets of the mandibular incisors caused high stress at the labial cervical root and apical root apex areas,[6] which evinced labial tipping. This kind of tooth movement was markedly observed in mandibular incisors from the initial phase of orthodontic treatment for leveling and aligning the teeth.[7],[8]

The mandibular incisor region was found to be the area of most frequent bone dehiscence and gingival recession[9],[10],[11],[12],[13] because of its anatomical limitation of alveolar bone boundary, especially in the antero–posterior dimension. Both animal and clinical studies found a positive relationship of alveolar bone loss or gingival recession after mandibular incisor proclination, which is the concern,[10],[14],[15],[16],[17],[18] but certain effects of orthodontic forces and biomechanical loading on periodontal tissues are difficult to evaluate quantitatively from both in vitro and in vivo studies and even in clinical studies. Moreover, in the continuous archwire system, the force and moment exertion on each tooth is much difficult to forecast.[19],[20]

To understand the biomechanical response after various orthodontic force applications, a precise method for numerical analysis should be used. The combination of engineering resources and medical research can make this process possible using a three-dimensional (3D) computerized model to simulate a bio-structural model as a finite number of elements. It can gauge the quantitative mechanical stress acting on a biological structure using a mechanical engineering process under the assigned material properties,[21] which is known as finite element analysis (FEA). FEA is widely used in orthodontic research because it is an accurate and noninvasive approach, but it can also provide concealed data, such as stress distribution, which is a limitation in other study methods.[22]

The aim of this study was to compare the magnitude, location of stress distribution in the root and periodontal tissue, and the pattern of tooth movement on the lower incisors among differently shaped continuous archwires during leveling of the curve of Spee. In the current study, the archwires consisted of 0.016” round and square archwires and 0.016” × 0.022” rectangular superelastic nickel-titanium (Ni-Ti) archwires. Tooth movement was simulated within its periodontal space by an intrusive force at the mandibular incisors in an integral finite element model in a mandible with all teeth and periodontal ligaments (PDLs).

 Materials and Methods

A finite element model of the mandibular jaw with all teeth, PDLs, and alveolar bone was constructed using cone beam computed tomography images of a participant who provided informed consent. The study was approved by the Human Research Ethics Committee, Faculty of Dentistry, Prince of Songkla University, Thailand. A 3D surface model of the mandible with the lower teeth was transferred to generate a 3D solid model using SolidWorks version 2015 software (DS SolidWorks Corp., Waltham, MA, USA). Brackets of the lower incisors, canines, and premolars for ten mandibular teeth, buccal tubes of the right and left mandibular first molars and archwires were constructed as computer-aided design (CAD) models using PowerShape software version 2013 (PowerShape, Delcam Co. Ltd., Birmingham, UK). The CAD model was meshed as a finite element model and analyzed by ANSYS software version 14.5 (ANSYS Inc., Canonsburg, PA, USA).

The finite element model of the mandibular teeth revealed a good alignment and presented a deep 4-mm curve of Spee [Figure 1]. All roots were covered with periodontal tissues as the interface between the alveolar bone socket and root surface which were assumed to be 0.2 mm of equal width.[23],[24] The right and left orthodontic buccal tubes of the first molars and the brackets of the incisors, canines, and premolars were attached to each tooth at the center of the crown. Standard edge-wise brackets with no torque and no angulation brackets were made of stainless steel material with slot dimensions of 0.018” × 0.025”. The properties of the materials are summarized in [Table 1].{Figure 1}{Table 1}

Archwires in this study were made of superelastic Ni-Ti material and were passively placed into the bracket slots. Three types of 0.016” archwires were constructed that consisted of 0.016” round-shaped wire, 0.016” × 0.016” square-shaped wire, and 0.016” × 0.022” rectangular-shaped wire.

All materials used in this study were assumed to be homogeneous, isotropic, and linearly elastic. The specific elastic material properties were Young's modulus and Poisson's ratio for all materials in this study [Table 1].[25],[26] The final meshing model contained 195,792 tetrahedral elements and 356,810 nodes.

The following three models for analysis depended on the archwire shapes:

Model 1: Mandibular teeth with 0.016” Ni-Ti archwireModel 2: Mandibular teeth with 0.016” × 0.016” Ni-Ti archwireModel 3: Mandibular teeth with 0.016” × 0.022” Ni-Ti archwire.

The analyzing procedure was assumed to be a static structure. Areas on both sides of the mandibular coronoid process and anterior chin were set as nonmovable parts, whereas the other parts could move. The interfaces between the bracket slots and archwires were movable with a friction coefficient of 0.28.[27] An intrusive movement in the apical direction of 0.2 mm from archwire deflection was applied to simulate the initial displacement of all the lower incisor teeth. The right mandibular incisors in each model were evaluated by assuming no differences between the right and left incisors.

The von Mises stress would be generated at the root surface and PDL from the archwire displacement on the bracket of the right mandibular central incisor. The linear relationship within the elastic limit of materials of stress and strain was described using the Hooke's law.[28]

For evaluation of the stress distribution, the levels of maximum stress at each labial and lingual side of the tooth surface in each model were constructed using forty equal horizontal rectangular boxes from the incisal edge to the root apex as the tooth rotated vertically to its long axis [Figure 2]. The first box was located at the incisal edge of the tooth, and the number of boxes that presented the maximum von Mises stress would be collected. To know the pattern of tooth movement, the Z-axis displacement in each model was reported as an incisal edge that moved in the antero–posterior direction and was compared between each model. A positive value indicated that the incisal edge was labially displaced.{Figure 2}


Stress distribution and incisal edge displacement in the antero–posterior dimension were derived from all the three finite element models after a clinical simulation of an initial 0.2-mm intrusion at the mandibular incisors. The results of the analysis are summarized in [Table 2]. The locations of the distributed stress were evaluated using forty equal horizontal rectangular boxes from the incisal edge to the root apex. The areas with the highest von Mises stress in all models were found at the same sites which were labial cervical root areas at the 18th box that was approximately at the alveolar crest, whereas the maximum stress at the lingual side was also found at the cervical third of the root area, but the locations were below the level of the alveolar crestal bone. Comparisons between each model of 0.016” archwire found that the highest von Mises stress was 2.598 MPa. However, the 0.016” square wire model and 0.016” rectangular wire model found much lower von Mises stress values of 0.343 and 0.372 MPa, respectively. For lingual side, stress from the round wire model was 1.694 MPa which was higher than that of the square wire and rectangular wire models of 0.208 and 0.200 MPa, respectively. Periodontal tissues of the right mandibular incisors in each model presented areas of maximum stress similar to their roots at the cervical regions at the labial and lingual surfaces.{Table 2}

The initial displacement caused the incisal edge of the mandibular central incisors in all models to be displaced in the labial direction (Z-axis). The 0.016” round wire model found the highest displacement of 5.47 × 10−3 mm, whereas the 0.016” × 0.016” Ni-Ti wire model and the 0.016” × 0.022” Ni-Ti wire model found incisal edge displacement of 0.72 × 10−3 mm and 0.80 × 10−3 mm, respectively. Movement in the vertical dimension (Y-axis) indicated that the farthest amount of intrusion was found in the 0.016” round archwire model, whereas those of square and rectangular models were similar. However, the amount of displacement in the Y-axis of each model found little change.


Mandibular tooth leveling using the continuous archwire technique can effectively reduce overbite by lower incisor intrusion with flaring and some molar extrusion.[29] Those results coincided with the results of the current study which found much higher stress at the labial cervical area of the root than the lingual surface in all models. Stress distribution was found to have the maximum stress at the labial sides which was more cervical than lingual, which represented the type of tooth movement after mandibular incisor intrusion at the labial brackets by continuous archwire deflection. This effect resulted from the application of a biomechanical force that did not pass through the center of resistance of the teeth. Yan et al.[6] confirmed this effect using a finite element model of a mandibular incisor to study stress distribution after an intrusive force application at the labial crown. They found the highest von Mises stress at the labial cervical root area. Furthermore, a study by Lombardo et al.[30] found labial displacement of the lower incisor after an intrusive force applied at the labial surface. The results of both studies coincided with the results of the current study. However, this study constructed all mandibular teeth with a continuous archwire system and force that was applied through the archwire to simulate the real clinical situation in which the Ni-Ti archwire would deflect from the curve of Spee for leveling.

In this study, we noticed that square- and rectangular-shaped archwires presented lower von Mises stress than that of the round-shaped archwire caused by torque expression which reduced their tipping. Torque expression is influenced by different archwire sizes, archwires, bracket materials,[31] and bracket slot dimension.[32] This study used archwires of the same height (0.016”) for a better comparison among the different cross-section shapes. We found that the square- and rectangular-shaped archwires expressed torque effects of a lower distributed stress at the labial side and found a slightly superior level of maximum stress at the lingual side in the rectangular archwire. Displacement in the Z-direction in square- and rectangular-shaped archwires was less than that of the round-shaped wire which was assumed to have more pure intrusion and less labial crown tipping. The round-shaped archwire model found the highest amount of displacement in the Y-axis, whereas the other two models found less displacement indicated by the leveling of the curve of Spee by the round-shaped archwire that was affected mostly by the relative intrusion of the mandibular incisors by the labial tipping movement compared to archwire leveling by square-shaped or rectangular-shaped archwires.

Tipping movement is a type of orthodontic tooth movement that usually occurs.[30] Since the time when this effect was first reported, there have been many attempts to propose alternative methods to reduce labial tipping of lower incisors during intrusion. A segmented archwire proposed by Charles J. Burstone could reduce this effect, but a statistical test revealed insignificant results.[29] The orthodontic miniscrew also found high stress distribution at the labial cervical root after performing various lower anterior tooth intrusion techniques in a finite element study.[33] This study proved that the biomechanics of round wire can tip lower incisors during tooth leveling, and the torque effect from square- or rectangular-shaped archwires can reduce this flaring.

Stress distribution was observed at both labial and lingual cervical areas of the roots in all models. However, if we focus on areas of high stress, we found that the maximum stress at the labial surface was slightly higher than that of the lingual side, which confirmed labial tipping. However, stress was observed at both labial and lingual cervical areas of the roots that definitely showed intrusive movement which was possibly caused from the conical shape of the roots which are larger at the cervical level than at the apical level. This may cause the roots to move apically and subsequently touch the alveolar bone socket in the cervical areas.

The stress analysis was obtainable from a finite element model which is reproducible and available for further investigations. This study developed a virtual finite element model of the mandibular jaw with all teeth and periodontal tissue to simulate a clinical situation after archwire placement as in orthodontic practice. During leveling the curve of Spee by lower incisor intrusion, the intrusion forces in this study were deactivation forces from archwire deflection. The orthodontic forces acted on the brackets and were transferred to the teeth and periodontal tissues as von Mises stress which was evident on FEA, whereas previous studies[6],[30] applied a given intrusive force at the center of the labial crown with no bracket placement.

This study has a couple of limitations. First, the amount of archwire activation was limited in the periodontal space to prevent the root being pressed against the alveolar bone. Second, because this study used continuous archwire, the precise force that was produced cannot be known. Therefore, we used the deactivation force from the deflection of the archwire, which allows movement only in the periodontal space. The data from this study could be used in clinical applications regarding the patterns of tooth movement and the related stress distribution when leveling with a different archwire shape. The superelastic Ni-Ti archwire forces in this study were also considered as optimal forces because all of the highest levels of stress in the PDL space were lower than the capillary pulse pressure of 20–26 g/cm2.[34]

For further clinical application, tooth aligning could be introduced without leveling using either accentuated curve of Spee round archwires or sectional anterior round wire with subsequent leveling with square- or rectangular-shaped archwires. However, a clinical study needs to be conducted to prove these advantages.


The initial movement of a mandibular incisor when an intrusive force was applied caused apical displacement with labial tipping that depended on the shape of the archwire cross section. Mandibular incisor intrusion by round-shaped wire caused more tipping movement than the square- or rectangular-shaped archwires. The labial cervical areas of the teeth and periodontal tissues received more stress when leveling with round-shaped wire even with superelastic Ni-Ti archwires.


The authors wish to express a sincere thanks to Assoc. Prof. Dr. Sajee Sattayut, Chairman of the Laser in Dentistry Research Group at Khon Kaen University, for facilitating the coordination. We greatly appreciate the Graduate School of Prince of Songkla University and the Faculty of Dentistry at Prince of Songkla University for grant support.

Financial support and sponsorship

The Graduate School of Prince of Songkla University and the Faculty of Dentistry at Prince of Songkla University financially supported the study.

Conflicts of interest

There are no conflicts of interest.


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