Evaluation of stress on the periodontium induced by a fixed retraction screw appliance and an active tie-back: A 3-dimensional finite element study

INTRODUCTION

Orthodontic space closure has always been a challenge for the orthodontist. In fixed appliances it is achieved either by segmental retraction i.e., two step, involving canine retraction followed by incisor retraction^[1,2] or single step, en-masse sliding technique involving retraction of all six anteriors at a time.^[3,4]

With the advent of pre adjusted edgewise appliances, sliding mechanics has become the more preferred method and is accomplished using elastomeric chain, nickel titanium coil springs, active tie backs, intra-oral elastics, etc.^[5,6]

Quinn and Yoshikawa^[7] proposed four possible hypotheses for the relation between force magnitude and the rate of orthodontic tooth movement. The concept of optimum force levels for orthodontic tooth movement states that it should be just high enough to stimulate cellular activity without completely occluding blood vessels in the periodontal ligament (PDL).^[8,9] Otherwise a hyalinized avascular necrotic area is formed, resulting in slow treatment progress and increased treatment time.^[8] Most of the authors have thus recommended a force of 100-200 g during retraction irrespective of the technique.^[10] All the above options have produced space closure of the magnitude of 0.5-1 mm/month.^[6]

In sliding mechanics, friction occurs at the wire-bracket interface.^[11] Studies have been carried out to evaluate frictional forces produced by various wire and bracket combinations.^[12,13] Friction dissipates some of the applied force and decreases the rate of the tooth movement. Application of high magnitude force, in an attempt to overcome the friction, might increase the movement of the anchor teeth, and the belief has been that friction is detrimental to anchorage.^[14] Studies have revealed that friction has no significant effect on the movement ratio of canine and anchor teeth, in two step retraction.^[15,16]

Another important component is the frequency of applied force that has been neglected completely. Studies on rapid canine distraction have shown that repetitive activation expresses a favorable cellular response leading to rapid tooth movement.^[17,18] With every activation, there is an up-regulation of the various factors (interleukins [IL], prostaglandins etc.) associated with the remodeling process within the PDL.^[19,20] Research has proved that multiple cycles of change in force magnitude are significant in that bone and cartilage cells respond more readily to rapid oscillation in force magnitude than to a constant force.^[20,21]

Recently, an alternative method of space closure has been proposed using an active retraction screw device (hycon device).^[21] It consists of a retraction screw which allows precise closing activations at a relatively high force level, but over a short distance allowing reactivation more frequently for a more physiologic space closure.

In the present study, 3-dimensional finite element modeling (3D FEM) method was used to investigate the response of the maxillary anterior teeth to forces delivered by two retraction devices hycon appliance and active tie back in 3D, the stress developed in the periodontium and the amount of tooth movement achieved.

MATERIALS AND METHODS

The present analytical model was developed from a dried adult human skull with intact maxillary teeth and without any gross defects or discontinuity in the anatomy. Computed tomographic scan images of the maxillary dentition and supporting structures were made in the axial direction at 2 mm intervals in the horizontal plane. The dental and skeletal components were traced on acetate paper enlarged 140 times to the original skull size. This was traced onto a graph paper for digitization of x, y and z co-ordinates by using Microsoft Image Pro-plus software (Media Cybernetics, Inc., Rockville, MD, USA) (Image-Pro Plus image analysis software makes it easy to acquire images, count, measure and classify objects, and automate the work). These tracings were later imported into the AutoCAD engineering software version 2004 (Autodesk Inc., SanRafael, CA, USA) for modeling of the maxillary dentition with periodontium and bone which was saved in integrated graphics exchange system (.iges) format.

Finite element model generation was achieved with Altair Hypermesh version 7 (Altair Engineering Inc. Troy, Mich, USA) by converting the. .iges into .hm (hypermesh binary database files) format. The model was later converted into mesh diagram, boundary conditions applied and equation resolved using FEM and post-processing software (FEMAP - is CAD-independent Windows-native pre- and post-processor for advanced engineering finite element analysis) (SIEMENS: NEi Nastran Software Inc., Westminister, CA) run on a personal computer using the graphic accelerator.

The complete geometry is defined as an assemblage of discrete pieces called elements, which are connected to adjacent elements with the help of nodes, which joins them in all directions [Figure 1]. The total number of elements and nodes created were 45037 and 225400 respectively.

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Figure 1

Completed finite element model of maxillary dentition with the periodontal ligament and alveolar bone

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The material data used in this study were defined according to experimental data obtained from previous studies^[22,23] [Table 1]. The FEM model was restrained in the inferior portion so that the teeth moved through the periodontium and bone without interference. The final FEM model was constructed in such a way that the dimensions of skull and teeth matched average anatomical values. The maxillary dentition was consolidated into a separate unit consisting of all teeth except for 1^st premolar [Figure 1], thus simulated the clinical scenario of therapeutic 1^st premolar extraction. The forces generated by hycon device and active tie back were 400 g and 200 g respectively applied along the arch wire in the horizontal direction so as to simulate the retraction of maxillary anterior teeth with hycon device and active tie backs as in the 1^st premolar extraction case [Figures 2 and 3]. The stresses on the periodontium were evaluated at three levels: The cervix, mid root and at the apex. The stresses were further evaluated on the labial, lingual, mesial and distal aspect at each level on all the teeth.

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Figure 2

Clinical and numerical simulation of anterior segmental retraction with hycon

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Figure 3

Clinical and numerical simulation of anterior segmental retraction with active tie backs

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RESULTS

The biomechanical changes evaluated included stresses (compressive and tensile) — as principal stresses (maximum, moderate and minimum), Von Mises stress and displacements.

Von Mises is a theoretical measure of stress used to estimate yield failure criteria in ductile materials and is also popular in fatigue strength calculations (where it is signed positive or negative according to the dominant Principal stress), whilst Principal stress is a more “real” and directly measurable stress.

Only maximum principal stresses were used to describe the results as the moderated and minimal stresses produced negligible changes.

Maximum principal stress distribution

The pattern of stress distribution differed in various aspects (labial, lingual, mesial and distal) and at different levels (cervix, midroot and apex) of all maxillary teeth [Table 2]. This variation in stress distribution was induced by the retraction devices-hycon device (410 g) and active tie back on the numerically simulated 3D FEM model of maxillary dentition [Figures 4 and 5].

Table 2 Stresses on periodontium produced by retraction screw device and active tie backs

Teeth	Central		Lateral		Canine		2nd premolar		1st molar		2nd molar
	410 g	200 g	410 g	200 g	410 g	200 g	410 g	200 g	410 g	200 g	410 g	200 g
Cervix
Labial	0.008885	0.00223	0.09422	0.048	0.4919	0.2945	0.08309	0.04245	0.03954	0.01977	0.01049	0.00695
Lingual	−0.00526	−0.00288	−0.01039	−0.00533	−0.01419	−0.0071	−0.1758	−0.0679	−0.04024	−0.0284	−0.0417	−0.03895
Mesial	0.001292	0.000646	0.01128	0.00564	0.2789	0.1345	−0.02284	−0.01142	−0.1596	−0.0724	−0.02189	−0.01495
Distal	−0.01379	−0.0071	−0.01779	−0.00869	−0.0254	−0.0138	0.3746	0.1873	0.05012	0.02506	0.04335	0.021675
Middle
Labial	0.00729	0.003845	0.02951	0.0215	0.02228	0.0166	0.01266	0.00656	0.01468	0.00734	0.008851	0.004426
Lingual	−0.00361	−0.0019	−0.00505	−0.00267	−0.01384	−0.00692	−0.02996	−0.015	−0.01513	−0.00648	−0.00619	−0.0031
Mesial	0.001942	0.000997	0.01117	0.00545	0.0217	0.0135	−0.01666	−0.00833	−0.02663	−0.0151	−0.01152	−0.00576
Distal	−0.0073	−0.0038	−0.02159	−0.012	−0.01476	−0.00788	0.02845	0.0179	0.01331	0.006655	0.003845	0.001883
Apex	−0.00414	−0.00202	−0.01199	−0.00585	−0.0111	−0.00572	−0.01196	−0.00583	−0.00953	−0.00477	−0.00357	−0.00139

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Figure 4

Principle stress at 410 g force using hycon device

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Figure 5

Principle stress at 200 g force using active tie backs

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The principal stress examined in the maxillary dentition demonstrated maximum amount of tensile stress on the labio-cervical and mesio-cervical aspect of canine and distocervical aspect of the 2^nd premolar [Table 2]. This was seen in both types of retraction devices used in the study [Figures 4 and 5]. Labio-cervical aspect of maxillary central and lateral incisor also experienced maximum tensile stress as compared to other aspects. The disto-cervical aspect of the 1^st and 2^nd molar experienced low tensile stress, this was contrary to the observation in the 2^nd premolar [Table 2]. Maximum compressive stresses were reported in the linguo-cervical aspect of the 2^nd premolar and mesio-cervical aspect of 1^st molar. However the apex of all teeth demonstrated minimal compressive stress [Figures 4, and 5 and Table 2]. In the maxillary anterior segment maximum compressive stress was induced in the disto-cervical and distal midroot region of central and lateral incisor, the canines however experienced maximum compressive stress in the linguo-cervical aspect [Table 2].

Displacement

The anterior and posterior segments were displaced in the backward and forward direction respectively in both types of retraction devices [Figure 6]. In the present study, the displacement produced by the hycon device was of the magnitude of 0.172-0.183 mm (0.177 mm) in the anterior segment and 0.0065-0.007822 mm (0.0071 mm) in the posteriors (anchor loss). Active tie backs produce a displacement of 0.162-0.172 mm in the anterior segment and a negligible amount of displacement in the posteriors.

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Figure 6

Displacement vector diagram

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DISCUSSION

In clinical practice, space closure is attained by the application of forces.^[5-9] It has been realized from previous studies that the stresses generated in response to these forces vary with different methods and in different patients.^[5-9,21,24] In the present study, retraction forces of 410 g with hycon device and 200 g with active tie backs were simulated and stress generated in the periodontium with these were analyzed on each tooth in all 3D of space at the cervix, midroot and apex. The maxillary 1^st premolar was excluded from the model for the stimulation of the clinical situation of retraction in therapeutic first premolar extraction. Evidence from previous frictional studies suggested lesser magnitude of friction in 0.019 × 0.025” stainless steel (SS) wire than 0.021 ×0.025” SS wire.^[25] Therefore, simulation in the present model was done with 0.019 × 0.025” SS wire.

Over the years, too much emphasis has been placed on the magnitude of forces without considering the impact of frequency of forces on the biologic system.^{[5-7,22,24,26]} Therefore, a simple retraction screw (hycon device) was chosen to facilitate precise repetitive activation to be carried out. The screw has a pitch of 0.35 mm that was determined by using the pitch gauge and by viewing and measuring it in a stereomicroscope at ×40 magnification. This was in conformation with the findings of McLaughlin et al.^[21] Space closure typically occurs anterior and posterior to the periodontal space, which has been measured at 0.25 mm. Thus when the screw is turned 360°, it produces an activation of 0.35 mm and the activation for each tooth is about 0.175 mm, which is less than the periodontal space. The manufacturer recommends activation of the device by one turn twice a week. However, it was hypothesized that 2 turns in a week would probably squeeze the PDL and would not allow sufficient time for the periodontal tissues to recover. Thus, for this study, an activation of one turn/ week was considered as a standard activation.

CONCLUSIONS

Sequential repetitive loading of the PDL using hycon screw is:

• Beneficial in achieving space closure at a much faster rate of 1.428 mm/month (96.14% of anterior segmental retraction) in comparison with 0.165 mm by active tie backs.

• With minimal deleterious effects to the periodontium as the displacement (0.177 mm/ activation) produced is well within biological limits of the periodontium in comparison with the active tie backs.