Maxillary posterior intrusion mechanics with mini-implant ...orthodontic treatments became established, the need for patient cooperation became obsolete, and side ... latinal aspect;

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Maxillary posterior intrusion mechanics withmini-implant anchorage evaluated with the finiteelement method

Muhsin Ciftera and M€uyesser Saracb

Istanbul, Turkey

FromIstanbaResebProfeThe aucts oSuppoT-830Reprintistry,yahooSubm0889-Copyrdoi:10

Introduction: The goal of this study was to evaluate the effects of 3 maxillary posterior intrusion mechanics withmini-implant anchorage by using the finite element method.Methods: Finite element models were generated byassembling the images obtained by computed tomography and a laser surface scanner. For each posterior den-tal segment, a 300-g force was applied and distributed to the mini-implants in proportion to their calculated rootsurface areas. Results: The most balanced intrusion and the most uniform stress distribution were obtained byconcurrent force applications from the vestibular and palatinal sides. In the models with transpalatal arches andbuccal force application, vestibular tipping movement and overall stress values were prominent. In all models,increased stress values were identified at the apical region of the first premolar roots and at the apical regionof the first molar mesial root. Conclusions: The results of this study suggest that the apical region of the firstpremolar roots and the apical region of the first molar mesial root should be considered to be prone to resorptionduring posterior intrusion treatment. Posterior intrusion systems with force application from counterbalancingsites lead to a more uniform stress distribution and balanced intrusion than the mechanics with a transpalatalarch. For a balanced intrusion, root surface areas should be considered when determining the appropriateforces. (Am J Orthod Dentofacial Orthop 2011;140:e233-e241)

Intrusion of the posterior teeth is regarded as a diffi-cult orthodontic tooth movement. Several factors,such as magnitude and direction of the forces and

orientation of the anchorage units, should be consideredduring posterior intrusion to prevent undesirable move-ment and root resorption.1,2 In most studies, it wasreported that traditional posterior intrusion mechanicssuch as bite-blocks and fixed appliances with verticalelastics and multi-loop archwire therapy often havelimited intrusion and side effects from insufficientanchorage.3-6 Once temporary anchorage devices inorthodontic treatments became established, the needfor patient cooperation became obsolete, and side

the Department of Orthodontics, Faculty of Dentistry, Istanbul University,ul, Turkey.arch assistant.ssor and head.uthors report no commercial, proprietary, or financial interest in the prod-r companies described in this article.rted by the Research Support Unit of Istanbul University, project number/02062006.t requests to: Muhsin Cifter, Department of Orthodontics, Faculty of Den-Istanbul University, Capa, 34093, Istanbul, Turkey; e-mail, [email protected], February 2011; revised and accepted, June 2011.5406/$36.00ight � 2011 by the American Association of Orthodontists..1016/j.ajodo.2011.06.019

effects on the surrounding tissues were reducedsignificantly. The posterior intrusion methodology withtemporary anchorage devices has also eliminated theneed for orthognathic surgery for some borderlineopen-bite patients.7,8 Kuroda et al9 used titanium screwanchorage to treat open bites and stated that theirresults were similar to those obtained by 2-jaw orthog-nathic surgery. Sherwood et al7 aimed to treat anterioropen bites by intruding the molars with titaniummini-plate anchorage; as a result, they accomplishedtrue molar intrusion in adults. They stated that anterioropen bites can be treated by posterior intrusion, result-ing in reduced anterior vertical face height, a decreasedmandibular plane angle, and counterclockwise rotationof the mandible.

Many studies have reported on the application andclinical efficiency of posterior intrusion mechanics; how-ever, studies about biomechanical effects such as stress,strain, and displacements on the teeth and the surround-ing tissues are limited.10 Since in-vivo studies are notquite sufficient in assessing biomechanical effects suchas stress and strain, finite element analysis, a commonmethod in engineering, became a valuable option forevaluation of biomechanical factors in orthodontics.Briefly, finite element analysis is a numeric methodwith which stress, strain, and deformation of structures

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Fig 1. Model 1: A, vestibular aspect with force distribution in proportion to the root surface area; B, pa-latinal aspect; C, detailed view showing the variable cortical bone thickness and the microimplants.

e234 Cifter and Sarac

with complex geometries can be studied in various load-ing and boundary conditions. Its philosophy is based ondividing complicated structures into manageable pieces,called elements, that can be easily defined with differen-tial equations. These finite numbers of elements are thenassembled to form an approximate mathematic model ofthe structure.

The main contributions of our study were to compareand evaluate the stress and displacement effects of 3maxillary posterior intrusion mechanics with mini-implant anchorage by using the finite element method.The intrusive forces simulated in this study were as-signed in proportion to the calculated root surface areas.

MATERIAL AND METHODS

A computer-aided designmodel of themaxillary bonewas generated by using 3- dimensional Doctor software(version 4.0; Able Software, Lexington, Mass). For thisprocess, computed tomography images taken fromamaxillary bone at 0.625-mm intervals in the axial direc-tion were assembled perpendicular to the occlusal plane.The premolars and molars were modeled manually assuggested by Wheeler11 with 3ds Max software (Auto-desk, San Rafael, Calif). Each tooth was located in themaxillary model according to the Roth12 prescriptionand aligned with reference to a maxillary mediumTru-Arch form (Ormco, Orange, Calif). Periodontal mem-brane, cortical bone, and alveolar bone layers were alldefined by using the 3ds Max software. The periodontalmembrane was assumed to have a thickness of 0.25 mmevenly. The thickness of the cortical bone was 2 mm atthe palatinal alveolar bone and decreased from 2 to1 mm from the top of the alveolar bone to the nasal floorof the vestibular alveolar bone (Fig 1, C).13,14 Thecomputer-aided design model of 0.018 3 0.025-inbrackets, bands, and archwires with the same dimensionswere generated with a laser surface scanner (NextEngine,Santa Monica, Calif) and 3ds Max software. Bracketswere attached to the teeth so that the midpoint ofthe brackets overlapped the midpoint of the facial-

November 2011 � Vol 140 � Issue 5 American

palatinal surface of the crowns. Mini-implants weremodeled manually with the 3ds Max software.

In the first model, the posterior teeth were connectedby full-dimension segmental archwires from thevestibular and palatal sides. Mini-implants were placedbetween the roots of the first and second premolarsand the first and second molars from both vestibularand palatinal sides (Fig 1).

In the second model, the posterior teeth were con-nected from the vestibular side, and the mini-implantswere placed from the same side between the roots ofthe first and second premolars and the first and secondmolars. In this model, to balance the moments producedin the vestibular direction, transpalatal arches witha diameter of 1.4 mm were constructed connecting thefirst premolars and the first molars (Fig 2).

In the third model, as in the second model, the pos-terior teeth were connected from the vestibular side, andthe mini-implants were placed from the same side be-tween the roots of the first and second molars. In thismodel, only 1 transpalatal arch connecting the firstmolars was modeled (Fig 3).

In accordance with the clinical applications, transpa-latal arches were adapted evenly 5 mm from the palatalbone to achieve clearance for the intrusion movement.In clinical applications, to minimize tipping movements,a rigid connection should be preferred at the transpalatalarch-band interface. Accordingly, to simulate a weldedconnection, the transpalatal arch-band interface wasconsidered a fully bonded surface.

Finite element models were generated by importingsolid models into ALGOR software (Autodesk). Three-dimensional discretemesh generations of the solidmodelswere realized by using hexahedral “brick” and tetrahedralelements. The total numbers of elements used in the finiteelement models were 94,630, 203,150, and 198,600 forthe first, second, and third models, respectively. By thisprocess, convergence analyses of finite element methodmodels were completed. All nodes, except for the con-strained ones, had 3 translational degrees of freedom

Journal of Orthodontics and Dentofacial Orthopedics

Fig 2. Model 2: A, vestibular aspect with force distribution in proportion to the root surface area;B, diagonal aspect showing the double transpalatal arch with 1.4 mm diameter for intersegmentalconnection.

Fig 3. Model 3: A, vestibular aspect with force distribution in proportion to the root surface area; B, pa-latinal aspect showing 1 transpalatal arch with 1.4 mm diameter for intersegmental connection.

Table I. Mechanical properties

Young’s modulus (MPa) Poisson’s ratioAlveolar bone 1370 0.3Cortical bone 13700 0.26Periodontal membrane 0.6668 0.49Teeth 19613.3 0.15Stainless steel 200000 0.3

Cifter and Sarac e235

(x, vestibulopalatinal; y,mesiodistal; z, vertical). Boundaryconditions were assigned to the nodes on the floor of thenasal cavity as zero displacement in all directions. Me-chanical properties of the materials in the models were as-signed as shown in Table I.15,16 All materials in the finiteelement analysis were assumed to be homogeneous,isotropic, and linearly elastic. Bracket-tooth, bracket-archwire, and bone-implant interfaces were defined asfully bonded surfaces.

For all models, finite element analysis was realized byapplying a total of 300 gf to each dental segment. Dis-tributions of the forces were calculated in proportionto the root surface areas determined by the 3ds Maxsoftware (Figs 1-3). The root surface area ratio of themolars to the premolars was calculated as 1.936 androunded to 2; the ratio of the vestibular roots alongthe segment to the palatinal roots was calculated as1.36 and rounded to 1.5.

By using the finite element method, the initial verti-cal displacement of the posterior teeth and the VonMises stress distribution along the root surface wereevaluated. To determine tipping movements precisely,vertical displacements of the nodes, having the same co-ordinates in each model at the root apexes and the cusptips, were assessed, and superimpositions were used.

American Journal of Orthodontics and Dentofacial Orthoped

RESULTS

Among all models, the lowest stress magnitudes wereproduced in the first model (Fig 4, A). The maximumVon Mises stress was 0.07855 N per square millimeter.The apical third of the first premolar roots and thesame region of the first molar mesial root showed thehighest stress magnitudes. Trifurcation areas of the firstmolar and regions adjacent to the force application sitesalso showed relatively high stress values.

In the second model, the maximum Von Mises stresswas 0.49114 N per square millimeter (Fig 5, A). Thisvalue was about 6.3 times higher than the maximumstress value in the first model. Increased stress valueswere observed at the apical third of the first premolarroots. The palatal surfaces of the first molar and first

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Fig 4. Model 1: A, Von Mises stress distribution (N/mm2) along the root surfaces; B, vertical displace-ment of the roots (mm).

Fig 5. Model 2: A, Von Mises stress distribution (N/mm2) along the root surfaces; B, vertical displace-ment of the roots (mm); negative vertical displacement values indicate extrusion movement.


premolar roots and regions adjacent to the force applica-tion sites also showed increased stress magnitudes.

The third model had the highest maximum VonMisesstress value among all models, with 0.52708 N persquare millimeter, which was approximately 6.7 timeshigher than the first model (Fig 6, A). Increased stress


values were identified at the first molar roots, especiallyon the vestibular surfaces and at the apical third of thefirst premolar roots.

In the first model, themaximum intrusion values wereidentified at the second molar mesial root (Fig 4, B).Intrusion values calculated for the vestibular roots were


Fig 6. Model 3: A, Von Mises stress distribution (N/mm2) along the root surfaces; B, vertical displace-ment of the roots (mm); negative displacement values indicate extrusion movement.

Table II. Vertical displacement of the nodes at the root apices (mm)

Model 1 Model 2 Model 3I. Premolar buccal 14.9 3 10�4 17.4 3 10�4 18.6 3 10�4

I. Premolar palatinal 13.6 310�4 4.9 3 10�4 3 3 10�4

II. Premolar 14.3 3 10�4 17.6 3 10�4 24.5 3 10�4

I. Molar mesiobuccal 14.3 3 10�4 28.5 3 10�4 47.4 3 10�4

I. Molar distobuccal 15 3 10�4 33.8 3 10�4 58.2 3 10�4

I. Molar palatinal 13.4 3 10�4 7.7 3 10�4 6.6 3 10�4

II. Molar mesiobuccal 15.1 3 10�4 36.1 3 10�4 12.7 3 10�4

II. Molar distobuccal 12.8 3 10�4 30.5 3 10�4 6.9 3 10�4

II. Molar palatinal 12.5 3 10�4 3.2 3 10�4 �1.8 3 10�4

Positive values indicate intrusion; negative values indicate extrusion.


slightly higher than those of the palatinal roots (Table II).This slight vestibular tipping of the teeth can also berealized from the slight variation of intrusion betweenthe vestibular and palatinal cusps (Fig 7, Table III). Inthe anteroposterior direction, there was no significanttipping or bowing of the dental segment (Fig 7).

In the second model, maximum intrusion movementsoccurred at the first and second molar vestibular roots(Fig 5, B; Table II). Intrusion of the vestibular rootswas considerably higher than at the palatinal roots(Fig 8). In contrast to the intrusion at the palatinal roots,extrusion was evident at the palatinal cusps, as the resultof the prominent vestibular tipping movement of thedental segment (Table III).

In the third model, maximum intrusion was evident atthe first molar vestibular roots, and intrusion values


decreased progressively from the first molar to the ante-rior and posterior of the dental segment (Figs 6,B, and 9).All roots along the dental segment, other than the secondmolar palatinal root, showed intrusion (Table II). As in thesecond model, also in this model, the vestibular rootsshowed considerably more intrusion than did the palati-nal roots. The third model experienced the greatestvestibular tipping movement among all models and,hence, the greatest extrusion at the palatinal cusps(Figs 6, B, and 9) was observed in this model.

DISCUSSION

Intrusion of the posterior teeth has been a difficult is-sue in orthodontics because of the lack of anchorage.Temporary anchorage devices have allowed cliniciansto gain anchorage frommany different sites for balanced


Fig 7. Model 1: A, superimposition denoting the vertical displacement identified at the crowns (blue,before; pink, after); B, vertical displacement identified at the roots; C, displacement in the vestibulopa-latinal direction.

Table III. Vertical displacement of the nodes at the cusp tips (mm)

Model 1 Model 2 Model 3I. Premolar buccal 14 3 10�4 5.8 3 10�4 4 3 10�4

I. Premolar palatinal 12.7 3 10�4 �6.7 3 10�4 �11.6 3 10�4

II. Premolar buccal 14.2 3 10�4 12.7 3 10�4 15.7 3 10�4

II. Premolar palatinal 13 3 10�4 �0.6 3 10�4 �6.7 3 10�4

I. Molar mesiobuccal 13.4 3 10�4 12.4 3 10�4 17.5 3 10�4

I. Molar distobuccal 14 3 10�4 13.7 3 10�4 22.6 3 10�4

I. Molar mesiopalatinal 12.6 3 10�4 �5.7 3 10�4 �10.2 3 10�4

I. Molar distopalatinal 13.1 3 10�4 �4.1 3 10�4 �9.2 3 10�4

II. Molar mesiobuccal 16 3 10�4 15.3 3 10�4 3.4 3 10�4

II. Molar distobuccal 13.2 3 10�4 10.3 3 10�4 1 3 10�4

II. Molar mesiopalatinal 14.4 3 10�4 �11.4 3 10�4 �10.3 3 10�4

II. Molar distopalatinal 11.2 3 10�4 �21.7 3 10�4 �13.6 3 10�4

Positive values indicate intrusion; negative values indicate extrusion.


intrusion with minimal side effects. But there are stillunclear data concerning the biomechanical issues.

This finite element method study was carried out toevaluate the effects of various posterior intrusion me-chanics with mini-implant anchorage. In finite elementmethod studies, the reliability of the results dependson the accuracy of the models. In this study, to maximizethe similarity of the models with the maxilla, modelswere generated from computed tomography imagestaken at 0.625-mm intervals. In addition, variable max-illary cortical bone thicknesses were generatedmanually;this is an important parameter in tooth movement.Another parameter affecting the precision of the finiteelement analysis is the numbers of elements and nodescomprising the models. Therefore, in our study, weused elements as small as 1.1 mm to enhance thenumber of nodes in the critical regions where stressand displacements were evaluated.

In all models, increased Von Mises stress values wereobserved in the apical region of the first premolar rootsand at the apical region of the first molar mesial root.


This observation can be attributed to the small surfacearea and geometric shape of these regions. Denoted sitesshould be considered highly prone to root resorption,according to several clinical studies.17-19 Even thoughtotal root surface areas and the applied forces were thesame, the produced stresses will alter if the toothgeometries are different. Since stress is the cause ofthe biomechanical response rather than the appliedforce, root geometries should also be considered whendetermining orthodontic force magnitudes.15,20

Another common finding related to stress distribu-tion was the increase in stress magnitudes adjacent tothe force application sites. The smallest increase in stresswas identified in the first model, and the greatest in-crease was observed in the third model. This findingfor the first model was due to the simultaneous multipleforce applications from different sites; this led touniform stress distributions among all 3 models.

In the pilot study conducted with the first model, evenintrusive forces (75 gf from each mini-implant) were ap-plied to the anterior, posterior, vestibular, and palatinal





sides of the posterior dental segment; as a result, severeanterior and palatinal tipping was observed. This behaviorsupports several clinical studies undertaken for this type ofprocedure.2,21 One explanation for this behavior wasdue to the variable distribution of root surface areasalong the dental segment; this led to uneven stressdistributions and various tipping movements. Therefore,in the final study, we have calculated the intrusive forcesaccording to the root surface area ratios. As a result, theapplied forces according to the selected root surfacearea ratios gave a virtually uniform intrusion movement,which was particularly evident in the first model.Nonetheless, it should be considered that the distri-bution of root surface areas is not the only variable fora balanced intrusion. Variations in tooth morphologiesand root angles, inclination differences of the vestibularand palatinal slopes of the alveolar bone, andanisotropic and nonlinear properties of the tissues alsocan have significant effects on the stress distributionand the path of the intrusion movement.


The most balanced intrusion was identified in thefirst model, with only a slight vestibular tipping move-ment observed. One reason for this slight vestibular tip-ping might be the assumption made for the root surfacearea ratio of the vestibular roots to the palatinal roots,calculated as 1.36 and rounded to 1.5. However, as men-tioned previously, several factors other than root surfacearea ratios can influence the intrusion movement. At thisstage, it could be considered that the most salutary fea-ture of the mechanics used in the first model is the abilityto clinically change the properties of the forces appliedthrough 4 different aspects. This leads to virtually fullcontrol over the movement of the dental segment duringtreatment. However, particularly if intrusion of bothright and left segments is considered, 4 mini-implantsfor each segment will be too much for a patient. Thus,although the mechanics used in the first model are bio-mechanically ideal, clinical application can be difficult.

In the second and the third models, a transpalatalarch was used to balance the produced moments and



inhibit vestibular tipping movements. Compared withthe first model, the vestibular tipping movements inthe second and third models were more prominent; thesecaused extrusion of the palatinal cusps. In clinical situa-tions, extrusion of the palatinal cusps can create inter-ferences between the antagonist teeth and lead toa decreased overbite. However, the static finite elementanalysis used in this study only simulated the initialtooth movement in the periodontal membrane becauseof the extremely large difference between Young’s mod-ulus of the periodontal membrane and the bone layers.In clinical situations, if a transpalatal arch with sufficientresistance is used, it will exhibit its uprighting effectthrough a long-term process of bone remodeling, andmost of the initial interferences will disappear withtime by intrusion of the palatinal cusps. The other sideeffect of the vestibular tipping movement identified inthe second and third models was the increase in overallstress magnitudes, which clinically increase the probabil-ity of root resorption.18,22 Thus, in most open-bite pa-tients, it is crucial to prevent vestibular tipping duringposterior intrusion. With simultaneous force applicationfrom the vestibular and palatinal sides, this can easily becontrolled. However, through mechanics with vestibularforce application and a transpalatal arch, the horizontalcomponent of the forces at each segment should beintersegmentally balanced. For this process to havea sufficient force transition between the segments, theresistance of the transpalatal arch should be adequate,and the connection between the transpalatal arch andthe teeth should be rigid. In the second and third models,prominent vestibular tipping was due to insufficient re-sistance of the transpalatal arch. Clinically, with similarforce levels, a thicker transpalatal arch would lead tobetter stress distribution and better vestibular tippingcontrol. In this study, the connection between the teethand the transpalatal arch was considered to be fullybonded. In clinical applications, a welded or solderedconnection would be appropriate to prevent any rota-tional movement at this junction.

The highest stress magnitudes and the most severevestibular tipping movements were observed in the thirdmodel, having 1 transpalatal arch. Also for this model,application of the total intrusive force from 1 pointcaused a bowing effect in the vertical direction. The firstand second molars tipped distally and mesially, respec-tively, from the bowing effect. The reason for this initialdisplacement in the periodontal membrane was theinsufficient resistance of the vestibular arch. But, aspreviously described, the movement of the teeth differswith bone remodeling by time. In clinical situations,sufficient time is needed to allow the full-dimensionarchwires to compensate for the initial tipping of the


molars. Nonetheless, second-order antitip bends canalso be used to prevent tipping movements at the firstand second molars. In this study, an 0.018-in systemwas simulated with full-dimension archwires. Ifa 0.022-in system or a stiff cap splint were used, the ini-tial intrusion and the stress distribution along the seg-ments could be more homogeneous; thus, the initialbowing of the segment would be minimized.

In most open-bite patients, to obtain an ideal occlu-sion, intrusion of the posterior segment is needed moreat the molars than at the premolars because of the hingemovement of the mandible and the excessive eruption ofthe molars.23 With separate force applications from pre-molar and molar sites, such as those in the first and sec-ond models, it is possible to prescribe intrusion amounts,thereby adjusting the mesiodistal cant of the segments.

Because of individual variations, it is essential to useunique mechanics and force systems for each patient.Evenwith perfectmechanics and exact force systems, afterthe initial tooth movement, the biomechanical effect ofthe force system changes, and modifications arerequired during treatment. In this study, static finiteelement analysis only simulated the initial tooth move-ment in the periodontal membrane and the initial stressdistribution along the root surfaces. During the treatmentcycle, ongoingmovements and stresses can differ becauseof the changes in force systems and biologic responses.Other limitations of this study were the constant valuesused for the physical properties of the tissues, whichwouldnormally alter clinically through the histologic process,and the assumption that the periodontal membrane washomogeneous, isotropic, and uniform in thickness. Theselimitations can cause differences between clinical applica-tions and simulation studies. Also, because of individualvariations, it is impossible to simulate an exact mathe-matic model to validate each case. However, similaritiesbetween the results of this study and clinical studieswith parallel mechanics show that the finite elementmodels generated were accurate enough to simulateclinical conditions.2,23,24

CONCLUSIONS

1. The apical region of the first premolar roots and theapical region of the first molar mesial root experi-enced increased stress levels; thus, these sites shouldbe considered to be prone to resorption.

2. To obtain a balanced intrusion, root surface areashould be considered when determining the appro-priate forces.

3. Segmental posterior intrusion mechanics with forceapplications from counterbalancing sides (anterior-posterior, vestibular-palatine) lead to a more



uniform stress distribution and balanced intrusionthan the mechanics with a transpalatal arch.

Ideally, the results gained through finite elementanalysis should be integrated with clinical experiencesto maximize accuracy.

We thank Ata Mu�gan, Istanbul Technical University,Faculty of Mechanical Engineering, for his guidingcomments.

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Maxillary posterior intrusion mechanics with mini-implant ...orthodontic treatments became established, the need for patient cooperation became obsolete, and side ... latinal aspect;

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