author's personal copy - luca lombardo · 2018-10-03 · author's personal copy progress...

This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institution

and sharing with colleagues.

Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third party

websites are prohibited.

In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further information

regarding Elsevier’s archiving and manuscript policies areencouraged to visit:

http://www.elsevier.com/copyright

http://www.elsevier.com/copyright

Author's personal copy

progress in orthodontics 1 3 ( 2 0 1 2 ) 154–163

Available online at www.sciencedirect.com

journa l homepage: www.e lsev ier .com/ locate /p io

Original article

Three-dimensional finite-element analysis of a centrallower incisor under labial and lingual loads

Luca Lombardoa,∗, Filippo Stefanonib, Francesco Mollicac, Attoresi Laurad,Giuseppe Scuzzoe, Giuseppe Siciliani f

a Research Assistant, Department of Orthodontics, University of Ferrara, Italyb Post-doctoral Researcher, Department of Engineering, University of Ferrara, Italyc Assistant Professor, Department of Engineering, University of Ferrara, Italyd Resident, Department of Orthodontics, University of Ferrara, Italye Adjunct Professor, Department of Orthodontics, University of Ferrara, Italyf Chairman, Department of Orthodontics, University of Ferrara, Italy

a r t i c l e i n f o

Article history:

Received 8 June 2011

Accepted 28 October 2011

a b s t r a c t

Introduction: The aim was to evaluate the differences between labial and lingual application

of an orthodontic force. This was achieved using a three-dimensional CAD design software

model of a real lower incisor surrounded by a prismatic representation of the mandibular

bone. This model was subjected to various loading conditions, with finite-element analysis.

Materials and methods: Cone-beam computed tomography scanning was used to create a

three-dimensional geometric model of a lower incisor, together with its simulated periodon-

tal ligament. This model was then meshed and analysed with commercial finite-element

code. Various single and combined forces and moments were applied to each side of the sim-

ulated lower incisor at the centre of the clinical crown. To evaluate the effects of the various

forces considered, the instantaneous displacement and stress generated in the bone and

the periodontal ligament were measured, as a comparison of the labial and lingual loading

sites.

Results: Dental movement was only influenced by the side of the force application when

an intrusive component was present. The simulations showed larger displacement when

a vertical force was present at the lingual surface. In general, this movement was of the

tipping type when the combined forces were applied, while there was greater intrusion

upon application of combined forces and an anticlockwise moment to the labial surface.

Conclusions: Application of an intrusive lingual force to a lower incisor appears to generate

bodily movement, while the same intrusive labial force appears to lead to labial tipping.

Subject to further study, this should be taken into consideration when devising treatment

plans for fixed appliances.

© 2012 Società Italiana di Ortodonzia SIDO. Published by Elsevier Srl. All rights reserved.

∗ Corresponding author. Contrada Nicolizia, 92100 Licata, Agrigento, Italy.E-mail address: [email protected] (L. Lombardo).

1723-7785/$ – see front matter © 2012 Società Italiana di Ortodonzia SIDO. Published by Elsevier Srl. All rights reserved.doi:10.1016/j.pio.2011.10.005


progress in orthodontics 1 3 ( 2 0 1 2 ) 154–163 155

1. Introduction

Continuous application of an orthodontic force to a toothtriggers remodelling in the surrounding bone, which even-tually leads to tooth displacement. On a biological level,dental displacement appears to be brought about by cataboliterecruitment, as deformation of the trabecular bone generatesa change in its metabolism.1

From a biomechanical perspective, numerous studies havesought to characterise how this dental movement is broughtabout. In particular, Sandstedt2 noted that different types offorce lead to different types of dental movement, and hypoth-esised that bone tissues react differently according to whetherthey are subjected to compression or tension. Specifically,Sandstedt2 documented the formation of new tissue on theside of the tooth where the periodontal fibres were under ten-sion, whereas bone resorption occurred in the same fibres onthe side of the tooth where compression was applied. On theother hand, Ren et al.,3 explored continuous application oforthodontic forces of various intensities, and reported that therate of dental displacement over time in response to theseforces shows considerable individual variation. Therefore,according to the speed of the dental displacement, patientscan be classified as ‘fast movers’ or ‘slow movers’.4

This is particularly important when planning orthodon-tic treatment that involves fixed appliances. Indeed, followingmany more recent advances in the field, clinicians now haveaccess to a wide variety of high-quality techniques. In particu-lar, the growing emphasis on aesthetics means that the lingualtechnique has reached a similar level of application anddevelopment as the more conventional labial orthodontics. Inaddition to their relative unobtrusiveness, lingual appliancesobviate the need for etching the labial enamel, and the dis-placement of each tooth can be observed more clearly, withrespect to the labial technique.5,6 However, the typical greatervariability in tooth anatomy on the lingual side of the dentalarch can make the positioning of the bracket difficult,7 whichcan have a profound influence on the biomechanics of thislingual approach. In this respect, the main difference betweenthe labial and lingual techniques is the distance between thepoint of application of the force that is transmitted throughthe bracket and the centre of resistance of the tooth.7 Conse-quently, the displacement and stress induced in bone by thesetwo techniques will also differ, and these need to be evalu-ated so that useful comparisons can be made between thesetechniques.

Although biomechanical forces are relatively difficult tomeasure directly, analysis using the finite-element method(FEM) can provide useful estimates. Indeed, as an example, theFEM has already been successfully used to evaluate the stateof stress generated by palatal miniscrews, to determine theirideal implantation sites.8 Furthermore, the FEM approach hasbeen used to provide a convincing evaluation of the stress dis-tribution in tooth roots, the periodontal ligament,9–15 and thetrabecular bone upon the application of different loads.16–25

However, to the best of our knowledge, no FEM studieshave been carried out on lower incisors to compare the effectsof such forces on lingual and labial bracket-placement sites.Despite this, some studies have assumed that there are indeed

differences here.7–26 We therefore designed a FEM geometricmodel of a lower incisor, its supporting trabecular bone, andits surrounding periodontal ligament, to evaluate and com-pare the biomechanical responses to forces mimicking thosegenerated by both lingually and labially positioned brackets.To create this workable model, we used an actual ex-vivo lowerincisor, with cone-beam computed tomography scanning ofits anatomy to obtain a digital three-dimensional rendering.To obviate interference from the actual soft tissues, the sur-rounding bone was generated using three-dimensional CADdesign software. This model was subjected to FEM simulationsto evaluate the effects of loads that would be generated bya bracket positioned on each side of the crown of the lowerincisor.

Initially, each force was analysed individually, to bettercompare the effects for the two sides of the force application.Subsequently, however, to better approximate the complexreality of bracket loading conditions, combinations of severalsimultaneous forces were analysed. We thus report here onthe considerations relating to the mechanical effects of eachtype of simulated treatment.

2. Materials and methods

A whole lower incisor that was sterile and devoid of carieswas mounted on a wax support and scanned by cone-beamcomputed tomography using a NewTom 3G (QR Srl, Verona,Italy). The following settings were applied: 110 kV, 0.50 mA,12-inch field-of-view, and 5.4-second exposure time. Accord-ing to the manufacturer specifications, the voxel was anisometric cube with an edge length of 0.3 mm. To maintainoptimum image clarity and to minimise interference producedby the surrounding soft tissues, an experimental model waschosen for this initial investigation, rather than a real patient.

Mimics (Materialise, Leuven, Belgium) and SolidWorks CAD(DS SolidWorks Corp., Massachusetts, USA) three-dimensionaldesign software were used to create a solid model of the lowerincisor from the cone-beam computed tomography images.The CAD software was also used to construct a simulated pris-matic bony region of 20 × 15 × 10 mm around the lower incisorcomprising both the trabecular and cortical bone, as well asthe periodontal ligament and alveolus. The compact bone andthe periodontal ligament layers were designed to be irregularin shape, so as to conform to the shape of the lower incisor.The compact bone layer was 0.5 mm thick on average, whilethe periodontal ligament layer had a thickness ranging from0.1 mm to 0.5 mm. The lower incisor was placed virtually inthe alveolar cavity, with an angle of 110◦ created with respectto the occlusal plane, to reflect a typical clinical case. The geo-metric model was then imported into the ANSYS Workbenchplatform (ANSYS, Inc., Canonsburg, Pennsylvania, U.S.A.) forthe FEM simulations (Fig. 1).25

Due to the irregular geometry, the geometric model wasdiscretised with non-linear tetrahedral elements, each ofwhich had ten nodes (i.e. the TET10 element). The mesh wasrefined at the points where gradients were expected (e.g. atthe material interfaces) and was left coarse elsewhere, toavoid unnecessary use of computation time. The final meshhad a total of 35,684 elements and 67,133 nodes. All of the


156 progress in orthodontics 1 3 ( 2 0 1 2 ) 154–163

Fig. 1 – The geometric model. The different colours correspond to the tissues simulated, i.e. cortical bone (yellow),trabecular bone (green), periodontal ligament (dark grey) and dentine (light grey). Z is the labiolingual axis.

Table 1 – Material properties.

Material Young’s Modulus[MPa]

PoissonCoefficient

Dentine 19600 0.31Cortical bone 13700 0.3Trabecular bone 1370 0.3Periodontal ligament 0.667 0.45

materials were considered isotropic and linearly elastic, withtheir respective properties as reported in Table 1.

For the boundary conditions, the lower and lateral surfacesof the simulated bone region holding the lower incisor werekept fixed, and the various orthodontic loads were applied tothe surfaces of the lower incisor as nodal forces. The point ofapplication of each force was designed to coincide with thecentre of the exposed coronal surface, first on the labial side,and then on the lingual side. The application site was chosenon a purely anatomical basis, without taking variables such asthe type of bracket or the slot size into consideration.

To evaluate the effects of single forces, different types ofload were applied. It should also be noted that the complete

loading on a tooth will also depend on the position of the adja-cent teeth, and therefore will differ from patient to patient.

Each single force that was applied was assumed to havea modulus of 0.3 N (ca. 30 gf). This was based on Proffit andFields,27 where the ideal force for tipping, rotation, intrusionor extrusion is given as ca. 35 g for a monoradicular tooth.

Five cases were considered for each force that was applied,which included different directions and orientations (Fig. 2):labiolingual (case 1) and linguolabial (case 2) directions; mesial(case 3) and distal (case 4) rotations; and intrusion (case 5). Thesame force modulus and direction were considered in eachcase, with the only variable being the point of application.

Combinations of several forces acting together were alsoconsidered. Here, the intrusive component was added to boththe linguolabial and labiolingual forces, to provide two addi-tional loading conditions (cases 6 and 7), which were appliedto the labial and lingual sides in turn (Fig. 3). In these cases,the resultant force had a modulus of 0.42 N (42 gf) and wasdirected at an angle of 45◦ with respect to the occlusal plane.

A complex system of forces was also applied to the lowerincisor. As considered by Liang et al.,24 a labiolingual force of

Fig. 2 – Forces applied to the lingual and labial sides of a lower incisor: 1) labiolingual; 2) linguolabial; 3) mesial rotation;4) distal rotation; 5) intrusion.



Fig. 3 – Combination of the single forces considered previously: 6) linguolabial + intrusion; 7) labiolingual + intrusion.

1 N (100 gf), an intrusive force of 0.64 N (64 gf), and an anti-clockwise moment of 0.5 N mm were used (Fig. 4), which wereapplied to both the labial and lingual sides (case 8).

To quantify the dental movement in response to theseforces, the instantaneous displacement of the lower incisorin the labiolingual direction was considered, i.e. the dis-placement immediately after the loading was applied. It isimportant to notice that this is different from the final dis-placement of the tooth, as it occurs before the remodellingof the surrounding bone tissue and it will necessarily bemuch smaller. Nevertheless, we hypothesised in this initialstudy that although different in magnitude, this immediatedisplacement will be proportional to the final displacement,thereby allowing considerations for the total movement ofthe lower incisor and comparisons of the various loadingconditions.

As the state of stress that would be generated in the lig-ament and the surrounding bone by the movement of thelower incisor is a determining factor for bone remodelling,the stress in the labiolingual direction was also evaluated. Thebenchmark value of 3.3 kPa, which corresponds to a pressureof 25 mmHg, is given in all the figures, as this is believed to be

essential for the triggering of the processes of bone remod-elling. Indeed, the well-known theory of Schwarz,28 whichconfirmed the discoveries of Sandstedt,2 defined the optimalforce as that which causes pressure variations in the periodon-tal ligament without occluding the capillaries. As the capillarypressure is from 20 gf/cm2 to 26 gf/cm2, this is considered tobe optimal. However, it should be noted that Ren et al.,3 couldnot define an optimal orthodontic force in their study of theapplication of continuous forces of various intensities.

3. Results

The maximum instantaneous displacement vectors causedby the application of forces to the lower incisor in cases 1-5were in the direction of the forces themselves, and these arereported in Table 2. These values were very similar in cases 1-4,irrespective of the application site (lingual or labial), whilethere was a marked difference in case 5, although the valuesare very small in all cases.

Considering case 1, Figure 5 shows the comparison ofthe dental displacement in the labiolingual direction upon

Fig. 4 – Complex system of forces applied to the incisor (Case 8): a) linguolabial, intrusion and anticlockwise momentapplied to the labial surface; b) labiolingual, intrusion and anticlockwise moment applied to the lingual surface.



Table 2 – Absolute values for the maximumdisplacement in the direction of the force applied in thescenarios considered.

Maximum displacement in the directionof the force applied [�m]

Labial application Lingual application

Case 1 0.15 0.15Case 2 0.15 0.15Case 3 0.25 0.26Case 4 0.25 0.26Case 5 0.08 0.04

Fig. 5 – Displacement [mm] in a labiolingual direction inCase 1. Left: Labial application. Right: Lingual application.

application of the single force to the labial or lingual sidesof the lower incisor. The normal stress in the same direction(�Z) in the alveolar region for the same case 1 is shown inFigure 6. In both of these analyses, the lower incisor displace-ment is concentrated in the crown of the lower incisor, withvirtually none in the apical region, which indicates a tippingmovement. Moreover, Figure 6 shows a trend in the stress gen-erated that conforms to this type of dental movement, i.e. it

shows two regions of compression, in the upper and lowerthirds of the apical region.

In the interest of brevity, the results obtained for cases 2-4are not reported individually, as they all showed maximumdisplacement as localised at the incisal border of the crown ofthe lower incisor, with far lower, and almost negligible, valuesat the apex. Thus, the fulcrum of the displacement is again atthe apex, in proximity to the centre of displacement, and thisalso causes a rotational, i.e. tipping, movement in these cases.Likewise, the tensional states are analogous, irrespective ofthe side of the force application to the lower incisor.

Interestingly, the results for case 5, i.e. intrusion, reveala different distribution between the two sides of application(Fig. 7). Indeed, when the force was applied labially, the trendwas similar to that reported for case 1, albeit to a lesser extent.However, the lingual application resulted in the displacementof the upper and lower thirds of the lower incisor in thesame direction as the force, while the central portion of thelower incisor moved in the opposite direction. In this case,the displacement trend in the direction of the force applied(downwards) can provide useful information about the den-tal displacement. Indeed, the labial force application led toregional differences in the downwards movements, which issuggestive of tipping. However, upon lingual application, onlytwo areas were displaced, and to very limited degrees, therebyindicating that this lingual application of the force inducesonly limited bodily intrusion.

Figure 8 shows a comparison of the stress states in case5, upon labial (Fig. 8, left) and lingual (Fig. 8, right) applica-tion of the force. When the force was applied labially, zones ofcompression were evident in the upper and lower thirds of theapical region of the lower incisor, confirming its tipping. Thelingual application of the force, on the other hand, generateda more generalised compression throughout the alveolar areaof the lower incisor, thereby indicating bodily intrusion.

For the cases with combined forces, Figure 9 shows theimmediate displacement of the lower incisor for case 6. Whenthe forces were applied to the labial side of the lower incisor,the displacement was greater, thereby leading to more pro-nounced rotation. Figure 10 shows the stress states in alabiolingual direction in the bony region for the lower incisor.In both cases, the stress trends are very similar, although

Fig. 6 – Stress (�Z) in a labiolingual direction [MPa] in Case 1. Left: Labial application. Right: Lingual application.



Fig. 7 – Tooth displacement [mm] in labiolingual (Z, above)and downward (Y, below) directions upon application of theforce on the labial (left) and lingual (right) sides.

larger regions of compression are seen when the force isapplied lingually; here, rotation was impeded by the anatom-ical features that blocked the movement of the lower incisor,thereby generating greater stress in the surrounding areas.

Fig. 9 – Displacement in a labiolingual direction [mm] inCase 6. Left: Labial application. Right: Lingual application.

Figure 11 shows the instantaneous displacement of thelower incisor for case 7. Here, the displacement indicateda tipping movement, irrespective of the side of application,although it was seen to be greater for the lingual force appli-cation. This is confirmed by the trend in stress shown inFigure 12, where there are larger regions of stress when theforces were applied labially and the displacement of the lowerincisor was impeded.

Figure 13 shows the immediate displacement of the lowerincisor in case 8. The movements observed, which apparentlyincluded tipping, were very similar. Figure 14 shows the stressstate in the labiolingual direction in the bony region, whichreveals compression of the entire area due to the intrusionof the lower incisor following the labial force application, andan apparent rotation when the force was applied lingually, asseen by the zones of compression.

4. Discussion

The objective of the present initial study was to compare thebiomechanical responses to labial and lingual application of




Fig. 10 – Stress (�Z) in a labiolingual direction [MPa] in Scenario 6. Left: Labial application. Right: Lingual application.







an orthodontic force on a lower incisor. To this end, we eval-uated the instantaneous displacement of the lower incisorthrough the FEM. To complete the picture, the stress distribu-tion within the surrounding bony support was also calculated,to identify regions of tension and compression. As thesemeasurements in actual patients would be hampered by thevariability in their tissue responses and by the dental anatomyitself, a bespoke three-dimensional FEM model was createdthat featured both the lower incisor and the alveolus.

To perform the FEM analysis, some simplifying assump-tions were made. In this respect, perhaps the most criticalpoint is that the result of the FEM simulations is not the finaldisplacement of the lower incisor at the end of the orthodon-tic treatment, but rather the immediate displacement afterthe application of the forces. It is clear that the final toothdisplacement depends heavily on the remodelling phenom-ena that occur within the bone tissue that supports the lowerincisor, but these were not considered in the present study.Indeed, these are still considered to be unresolved issues inbiomechanics. Although precise quantification of the finalmovements of the lower incisor cannot be obtained with thepresent approach, useful comparisons under the various load-ing conditions can be drawn on the assumption that the finallower incisor displacement is proportional to this initial dis-placement.

Secondly, the simulated lower incisor was embedded in abone block that is just a rough representation of an authen-tic alveolar site, even though it was designed according to thematerial properties of the trabecular and cortical portions, andof the periodontal ligament. This approach clearly simplifiesthe numerical analysis, as the geometry is easier. However, itdoes not consider the possible interactions between differentteeth during this orthodontic treatment, which will undoubt-edly be an important factor. Nonetheless, it must be borne inmind that the stress state in an elastic solid that is loadedin a relatively small region (like the bone tissue holding thelower incisor in our analysis) decays with distance accordingto the cube of the distance.29 We therefore assumed that thedimensions of the simulated bone block were large enough toprovide significant results, within certain limits.

Finally, all of the materials were assumed to be linearlyelastic, thereby simplifying the numerical analysis. Whilesuch a hypothesis may be appropriate for bone, dentine andenamel, the periodontal ligament, as a soft tissue, should beconsidered a non-linear, perhaps even viscoelastic, material.Nevertheless, for the purpose of the present initial analysis,the hypothesis of linearity appears to be reasonable due tothe small strains in the periodontal ligament which neverexceeded 0.07% to 0.10%.

When this model underwent various simulations to high-light the differences according to the side of application ofthe force to the lower incisor, the findings showed substan-tial differences in four of the cases. For the cases in whichsingle forces were applied (cases 1-5), the only differenceswere noted for an intrusive force (i.e. case 5): there was amore bodily dental displacement when the force was appliedto the lingual surface of the lower incisor. This confirmsthe findings documented in the literature, and particularlythose reported of Ryoon et al.,30 in their prospective clinicalstudy: i.e. intrusion of the lower incisors is more effectivewhen the lingual mechanics are exploited. Furthermore, inthe same study,30 and in agreement with Schudy et al.,31 itwas confirmed that the correction of labial overbite usingcontinuous wire occurs through the extrusion of the pos-terior sectors and the labial displacement of the incisors,with minimal incisor intrusion. This demonstrates that theapplication of a force with an intrusive component to the lin-gual surface of an incisor will bring it closer to the centre ofresistance.

Different displacements did, however, result from labialand lingual application of the combined forces to the lowerincisor. Indeed, with the loading towards the exterior in case6, this resulted in greater rotation when the combined forcewas applied labially to the lower incisor, while in case 7, withthe loading towards the interior, there was greater rotationwhen the combined force was applied lingually to the lowerincisor.

Finally, for consideration of the most complex case inwhich the lower incisor was subjected to forces and momentsacting in labiolingual, downwards and anticlockwise



directions, the labial application mainly caused a bodilyretrusive movement of the lower incisor, whereas the lin-gual application generated tipping, with an apical centre ofresistance.

Among others, Liang et al.,24 also reached the same con-clusions. i.e. that bodily (translatory) displacement of a toothis favoured by the application of the force to the labial side.

5. Conclusions

In the present study, various FEM simulations were usedto evaluate the differences in the mechanical responses tovarious types of force-loading conditions. These conditionsparallel the application of an orthodontic bracket on the lin-gual or labial side of an anatomical system that comprisesa lower incisor and its corresponding alveolar region. Theresults were the following:– When single forces are applied to the lower incisor, a tip-

ping displacement is generated, irrespective of the point ofapplication, except when an intrusive force is applied to thelingual side.

– When combined linguolabial and intrusive forces areapplied to the lower incisor, it is displaced in a labial direc-tion, irrespective of the side of application.

– When combined labiolingual and intrusive forces areapplied to the lower incisor, the tooth displacement isessentially reminiscent of tipping, irrespective of the side ofapplication. This finding is confirmed by the trend in stressobserved around the dental surface.

– For a plausible system of forces acting on a lower incisor,bodily retrusion occurs when the force is applied labially,whereas a force applied lingually creates a tipping move-ment of the lower incisor that is accompanied by a greaterloss of torque.The intrusion of lower incisors is one of the most com-

mon movements in fixed appliance orthodontics. This is used,for example, during bite opening or for the flattening of thecurve of Spee. The present FEM simulation demonstrates thatlingual orthodontic appliances are more efficient than labialappliances for bodily intrusion of a lower incisor.

Conflict of interest

The authors have no conflicts of interest.

Riassunto

Obiettivi: Lo scopo di questo studio è di valutare le differenze mec-caniche nell’applicazione di una forza ortodontica sulla superficievestibolare o linguale di uno stesso dente. Lo studio è stato realizzatomediante un software di design CAD tridimensionale con il quale èstato creato un modello di un incisivo inferiore circondato dalla rap-presentazione prismatica dell’osso mandibolare. Questo modello èstato soggetto a vari condizioni di carico con l’analisi a modelli finiti(FEM).Materiali e metodi: Un’acquisizione mediante tomografia volumet-rica è stata usata per creare un modello geometrico tridimensionaledi un incisivo inferiore, insieme al suo legamento parodontale. Varieforze singole (orizzontali, verticali e laterali) e momenti (orizzontali

e verticali; orizzontali, verticali e antiorari) sono stati applicatidurante diverse simulazioni al centro della corona clinica della super-ficie vestibolare e linguale dell’ incisivo inferiore. Per valutare glieffetti delle varie forze considerate, sono stati considerati la dislo-cazione immediata e gli stress generati nell’osso e nel legamentoparodontale.Risultati: Il movimento dentale era influenzato dalla superficie diapplicazione della forza solo quando erano presenti forze intrusive.Le simulazioni hanno evidenziato movimenti più grandi quando laforza verticale era applicata sul lato linguale. In genere, il movimentoera di tipping quando erano applicate forze combinate, mentre c’erapiù intrusione in seguito all’applicazione di forze combinate e di unmomento antiorario sulla superficie vestibolare.Conclusioni: L’applicazione di una forza intrusiva su un incisivoinferiore sembra generare un movimento corporeo, mentre la stessaforza intrusiva applicata sulla superficie vestibolare determina tip-ping. Questo dovrebbe essere preso in considerazione ogni volta cheviene fatto un piano di trattamento che prevede l’impiego di apparec-chiature fisse.

Résumé

Objectifs: Le but de cette étude a été d’évaluer toutes les dif-férences mécaniques entre l’application labiale et linguale d’uneattache orthodontique par le biais d’une simulation virtuelle quicomprend une incisive inférieure entourée de son support osseux etsoumise à de différentes conditions de charge.Matériels et méthodes: L’imagerie par tomographie volumique àfaisceau conique (CBCT) d’une incisive inférieure a été utilisée pourcréer un premier modèle géométrique tridimensionnel et ensuite unmodèle éléments finis de la dent, avec son support osseux et son li-gament alvéolo-dentaire. Des forces et des moments individuels(dans les sens horizontal, vertical et latéral) et combinés (sens hori-zontal et vertical; horizontal, vertical et antihoraire) ont été appliquésà ce modèle sur chaque côté de la dent au milieu de la couronneclinique.Résultats: Dans le but d’évaluer l’effet des différentes forces prisesen examen, le déplacement instantané dans le sens labiolingual et lestress engendré sur l’os et le ligament parodontal, suite à ce mou-vement, ont été mesurés et utilisés pour comparer les deux sites demises en charge.Conclusions: Le côté où la force a été appliquée n’a influencé le mou-vement dentaire que lorsqu’une composante intrusive était présente.Par voie de conséquence, c’est le résultat souhaité qui devra déter-miner le site de placement d’une attache. Les simulations réaliséesont mis en relief aussi un mouvement en corps supérieur lorsqu’uneforce verticale est présente sur la surface linguale. En général, cemouvement a été du type oscillatoire lorsque des forces combinéesont été appliquées; toutefois, une intrusion en corps supérieure a étéenregistrée après application de forces combinées et d’un moment deforce antihoraire sur la surface labiale.

Resumen

Objectivo: El objetivo de este estudio es valorar cualquierdiferencia mecánica entre la aplicación labial y lingual de unbracket ortodóntico, mediante la creación de un simulacro virtual quecontempla un incisivo inferior rodeado de su soporte óseo, sometién-dolo a condiciones diferentes de carga.Materiales y métodos: Realización de una imagen por tomografíade haz de cono (CBCT) en un incisivo inferior para crear, primero, un



modelo geométrico tridimensional y luego un modelo de elementosfinitos del diente, completo con su soporte óseo y ligamento periodon-tal. Fuerzas y momentos individuales (horizontal, vertical y lateral)y combinados (horizontal y vertical; horizontal, sentido antihorario)han sido aplicados a este modelo, en ambos lados del diente, en elcentro de la corona clínica.Resultados: Para valorar el efecto de las diferentes fuerzasconsideradas, fueron medidos tanto el desplazamiento instantáneo,en el sentido labiolingual, y el estrés engendrado en el hueso y elligamento periodontal, a raíz de este movimiento. Lo anterior sirviópara comparar los dos lados sometidos a carga.Conclusiones: El lado en que se aplicó la fuerza influyó en elmovimiento dentario únicamente cuando estaba presente un com-ponente intrusivo. Por consiguiente, en estos casos, el lugar decolocación del bracket debería depender del resultado que se quierelograr. Los simulacros realizados también destacaron un movimientoen cuerpo superior cuando estaba presente una fuerza vertical en lasuperficie lingual. En términos generales, este movimiento fue de tipooscilatorio cuando se aplicaron fuerzas combinadas, pero se observóuna intrusión en cuerpo superior en el caso de aplicación de fuerzascombinadas y un momento antihorario en la superficie labial.

r e f e r e n c e s

1. Proffit WR, Fields Henry Jr W. Contemporary orthodontics.4th ed. Elsevier; 2011. p. 342–3.

2. Sandstedt C. Einige beitrage zur theorie der zahnregulierung.Nord Tandl Tidsskr 1904-5 1904:236–56.

3. Ren Y, Kuijpers-Jagtman AM, Malta JC. Optimum forcemagnitude for orthodontic tooth movement: a systematicliterature review. Angle Orthod 2003;73:86–92.

4. Pilon JJ, Kuijpers-Jagtman AM, Maltha JC. The magnitude oforthodontic force and rate of bodily tooth movement, anexperimental study in beagle dogs. Am J Orthod DentofacialOrthop 1996;107:16–23.

5. Scuzzo G, Takemoto K, Takemoto Y, Takemoto A, Lombardo L.A New Lingual Straight-Wire Technique. JCO2010;XLIV:114–23.

6. Attin R, Stawarczyk B, Kecik D, Knösel M, Wiechmann D,Attin T. Shear bond strength of brackets to demineralizeenamel after different pretreatment methods. Angle Orthod2012;82(1):56–61.

7. Scuzzo G, Takemoto K. Invisible Orthodontics. 1st ed. Berlin:Quintessenz Verlags-GmbH; 2003. p. 61–95.

8. Lombardo L, Gracco A, Zampini F, Stefanoni F, Mollica F.Optimal palatal configuration for miniscrew application.Angle Orthod 2010;80:145–52.

9. McGuinness N, Wilson AN, Jones M, Middleton J,Robertson NR. Stress induced by edgewise appliances in theperiodontal ligament - a finite element study. Angle Orthod1992;62:15–21.

10. Cobo J, Argüelles J, Puente M, Vijande M. Dentoalveolar stressfrom bodily tooth movement at different levels of bone loss.Am J Orthod Dentofacial Orthop 1996;110:256–62.

11. Puente M, Galban L, Cobo J. Initial stress differences betweentipping and torque movements. A 3-dimensional finiteelement analysis. Eur J Ortod 1996;18:329–39.

12. Schneider J, Geiger M, Sander FG. Numerical experiments onlong-time orthodontic tooth movement. Am J OrthodDentofacial Orthop 2002;121:257–65.

13. Jeon P, Turley P, Ting K. Three dimensional finite elementanalysis of stress in the periodontal ligament of themaxillary first molar with simulated bone loss. Am J OrthodDentofacial Orthop 2001;119:498–504.

14. Qian H, Chen J, Katona TR. The influence of PDL principalfibers in a 3-D analysis of orthodontic tooth movement. Am JOrthod Dentofacial Orthop 2001;120:272–8.

15. Jeon PD, Turley PK, Moon HB, Ting K. Analysis of stress in theperiodontium of the maxillary first molar with a3-dimensional finite element model. Am J Orthod DentofacialOrthop 1999;115:267–74.

16. Jones ML, Hickman J, Middleton J, Knox J, Volp C. A validatefinite element method study of orthodontic tooth movementin the human subject. J Orthod 2001;28:29–38.

17. Oyama K, Motoyoshi M, Hirabayashi M, Hosoi K, Shimizu N.Effects of root morphology on stress distribution at the rootapex. Eur J Orthod 2007;29:113–7.

18. Rudolph DJ, Willes PMG, Sameshima GT. A finite elementmodel of apical force distribution from orthodontic toothmovement. Angle Orthod 2001;71:127–31.

19. Jeon PD, Turley PK, Moon HB, Ting K. Analysis of stress in theperiodontium of the maxillary first molar with a3-dimensional finite element model. Am J Orthod DentofacialOrthop 1999;115:267–74.

20. Nägerl H, Kubein-Meesenburg D. A FEM(Finite-Element-Measurement) study for the biomechanicalcomparison of labial and palatal force application on theupper incisors. Fortschr Kieferorthop 1993;54(2):76–82.

21. Brinkmann PG, Tanne K, Sakuda M, Mietcke RR. A FEM studyfor the biomechanical comparison of labial and palatal forceapplication on the upper incisors. Finite element method.Fortschr Kieferorthop 1993;54(2):76–82.

22. Cattaneo P, Dalstra M, Melsen B. The transfer of occlusalforces through the maxillary molars: a finite element study.Am J Orthod Dentofacial Orthop 2003;123:367–73.

23. Cattaneo P, Dalstra M, Melsen B. The finite element method:a tool to study orthodontic tooth movement. J Dent Res2005;84:428–33.

24. Liang W, Rong Q, Lin J, Xu B. Torque control of the maxillaryincisors in lingual and labial orthodontics: a 3-dimensionalfinite element analysis. Am J Orthod Dentofacial Orthop2009;135:316–22.

25. Mollica F, Preziosi L, Rajagopal KR. Modeling and Simulationin Science. In: Engineering and Technology - Modeling of BiologicalMaterials. Boston: Birkhäuser; 2007.

26. Siciliani G, Terranova S. Ortodonzia Linguale. Masson; 2001.ISBN: 8821425649 9788821425646.

27. Proffit WR, Fields Henry Jr W. Contemporary orthodontics.4th ed. Elsevier; 2011. p. 348.

28. Schwarz AM. Tissue changes incidental to orthodontic toothmovement. Int J Orthod Oral Surg Radiogr 1932;18:331.

29. Mal AK, Singh SJ. Deformation of elastic solids. Prentice Hall;1991.

30. Hong RK, Hong HP, Koh HS. Effect of reverse curve mushroomarchwire on lower incisors in adult patients: a prospectivestudy. Angle Orthod 2001;71:425–32.

31. Schudy FF. The control of vertical overbite in clinicalorthodontics. Angle Orthod 1968;38:19–39.

author's personal copy - luca lombardo · 2018-10-03 · author's personal copy progress...

Documents