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SummaryObjective: To test the hypothesis that the dimension of thebracket, both in labial and in lingual orthodontics, is a relevantparameter to determine the forces acting on the teeth, and thatsome wires commonly used in labial orthodontics (0.016”-diameter SS, TMA and Nitinol) are not suitable for the firstphase of lingual treatment.Materials and methods: An ideal dental cast was bonded witheight different brackets (Damon 3MX, Ovation, Time 2,Innovation and Smart Clip Clarity on the vestibular face;STB, Adenta Time and Innovation-L on the lingual). Afterphotographic documentation, the interbracket distance was cal-culated for each type of bracket, using ImageJ software. Themean elasticity modulus of the tested wires was obtained fromthe review of the available literature. The theoretical wire loadon every tooth was calculated mathematically at three differentlevels of deflection (0.5 mm; 1.0 mm and 1.5 mm), on both thelabial and lingual sides, for all types of bracket.

Results: The lingual arch in the anterior segment is alwaysshorter than the vestibular arch. The different brackets,having different dimensions, have an influence on the inter-bracket distance, and, consequently, on the wire load. At largedeflections, superelastic NiTi expresses light and continuousforces, which are significantly lower than the other examinedalloys.

R�esum�e

Objectif : Tester l’hypoth�ese que (a) les dimensions des brac-kets sont un param�etre pertinent, en orthodontie vestibulaireet linguale, pour d�eterminer les forces agissant sur les dents et(b) que certains fils habituellement utilis�es en orthodontievestibulaire (0.016 SS, TMA et Nitinol) ne conviennent pasa la premi�ere phase de traitement vestibulaire.Mat�eriaux et m�ethodes : Sur un mod�ele dentaire id�eal, nousavons coll�e huit brackets diff�erents (Damon 3MX, Ovation,Time 2, Innovation et Smart Clip Clarity en vestibulaire ;STB, Adenta Time et Innovation-L en lingual). Apr�es prisede photos, la distance interbrackets a �et�e calcul�ee pour cha-que type de bracket utilisant le logiciel ImageJ. Le moduled’�elasticit�e moyen des fils test�es a �et�e obtenu en effectuantune revue de la litt�erature disponible. Au moyen de calculsmath�ematiques, nous avons d�etermin�e la charge th�eoriqueappliqu�ee par les fils sur chaque dent a trois valeurs de flexion(0,5 mm ; 1,0 mm et 1,5 mm), des cot�es lingual et vestibu-laire, pour chaque type de bracket.R�esultats : L’arcade linguale est toujours plus courte dans lesegment ant�erieur que l’arcade vestibulaire. Les diff�erentsbrackets, ayant des dimensions diff�erentes, influent sur ladistance interbrackets et, par cons�equent, sur la charge surle fil. A des degr�es de flexion importants, le Superelastic NiTiexprime des forces l�eg�eres continues qui sont significative-ment plus faibles qu’avec les autres alliages �etudi�es.

Original articleArticle original

� 2010 CEOPublished by / Edite par Elsevier Masson SAS

All rights reserved / Tous droits reserves

Wire load–deflection characteristicsrelative to different types of brackets

Comparaison des caract�eristiques de charge–flexion de fils selon diff�erents types de brackets

Luca LOMBARDOa1,*, Angela ARREGHINIa2, Kholoud AL ARDHAb,Giuseppe SCUZZOa1, Kyoto TAKEMOTOc1, Giuseppe SICILIANIa3

aDepartment of Orthodontics, University of Ferrara, Via Montebello, 31, Ferrara 44100, ItalybDubai, PO Box 212482, Dubai, United Arab Emiratesc2-5-7 Kudanminami, Chiyoda, Tokyo, 102-0074 Japan

Available online: 3 Febuary 2011 / Disponible en ligne : 3 f�evrier 2011

*Correspondence and reprints / Correspondance et tir�es a part.

e-mail address / Adresse e-mail : [email protected] (Luca Lombardo)1Member of the University of Ferrara, postgraduate school of orthodontics (professor).2Member of the University of Ferrara, postgraduate school of orthodontics (postgraduatestudent).3Member of the University of Ferrara, postgraduate school of orthodontics (chairman).

120 International Orthodontics 2011 ; 9 : 120-139doi:10.1016/j.ortho.2010.12.011


Conclusion: The initial hypothesis was supported. Because ofthe reduced interbracket distance, the adoption of superelasticwires is required in lingual mechanics and with smaller diam-eter compared to labial mechanotherapy, in particular duringthe first phases of treatment. The use of a bracket with reducedmesiodistal dimensions can contribute to reduce the load on theteeth.� 2010 CEO. Published by Elsevier Masson SAS. All rightsreserved

Key-words

·Interbracket distance.·Superelasticity.·Lingual mechanotherapy.

Introduction

Lingual orthodontics is an effective alternative to traditionalvestibular appliances, in particular for those patients whowant to preserve a pleasant smile during the whole treatmenttime. Hohoff, investigating the reasons why people chooselingual orthodontics, found that their main aim is to preservetheir professional image as they did not wish to be seen with aconspicuous metal appliance [1].

However, it is not possible to simply transfer vestibularmechanics to lingual devices because of the different condi-tions prevailing on the two surfaces [2].The main difference compared with traditional orthodontics isthe smaller interbracket distance: the labial arch is signifi-cantly longer than the lingual arch, in particular in the man-dibular anterior region [3].The commercially available lingual and vestibular bracketshave different mesiovestibular dimensions, and this influ-ences interbracket distance.The force of elastic orthodontic wires is inversely proportionalto the cube of the interbracket distance [4]. This means thateven small reductions in the arch length lead to a significantincrease in the force applied to the tooth.

For many years, dental alignment was carried out with stain-less steel (SS) wires. In 1978, for the first time, Andreasen andMorrow described the beneficial characteristics for orthodon-tic practice [5] of Nitinol, which displays elastic behaviorsimilar to SS, but with lower stiffness.

TMA was introduced in 1979 and was quickly adopted onaccount of its properties: excellent shape memory, low stiff-ness, good formability and direct welding. The coefficient offriction is significantly higher than with other alloys [6].

Conclusion : L’hypoth�ese initiale a �et�e confirm�ee. En raisonde la distance interbrackets r�eduite, les fils super-�elastiquessont n�ecessaires en m�ecanique linguale avec un diam�etreplus petit par rapport a la m�ecanique vestibulaire, surtoutpendant les premi�eres phases du traitement. L’utilisationd’un bracket avec des dimensionsm�esiodistales r�eduites peutcontribuer a diminuer la charge sur les dents.� 2010 CEO. Edite par Elsevier Masson SAS. Tous droitsreserves

Mots-cl�es

·Distance interbrackets.

·Super-�elasticit�e.·M�ecanoth�erapie linguale.

Introduction

L’orthodontie linguale offre une alternative efficace aux appa-reils vestibulaires traditionnels, surtout chez les patientsd�esirant conserver un sourire agr�eable pendant toute la dur�eedu traitement. Hohoff et al. ont �etudi�e les raisons pour les-quelles les patients choisissent l’orthodontie linguale et onttrouv�e que leur objectif principal �etait de pr�eserver leur imageprofessionnelle en �evitant de se montrer avec un appareilm�etallique clairement visible en bouche [1].N�eanmoins, il est impossible de faire un simple transfert de lam�ecanique vestibulaire a la m�ecanique linguale en raison desdiff�erentes conditions qui caract�erisent les deux faces [2].La diff�erence principale par rapport a l’orthodontie conven-tionnelle est la distance interbrackets plus r�eduite : l’arcadevestibulaire est significativement plus longue que l’arcade lin-guale, surtout dans la r�egion mandibulaire ant�erieure [3].Les brackets linguaux et vestibulaires disponibles sur lemarch�e ont des dimensions m�esiodistales diff�erentes, ce quiinflue sur la distance interbrackets.La force exerc�ee par les fils orthodontiques �elastiques estinversement proportionnelle au cube de la distance inter-brackets [4]. Il en r�esulte que meme des r�eductions minimesde la longueur d’arcade produiront une augmentation signifi-cative de la force appliqu�ee a la dent.Depuis de nombreuses ann�ees, l’alignement dentaire a �et�er�ealis�e avec des fils en acier inoxydable (SS). En 1978, pour lapremi�ere fois, Andreasen et Morrow ont d�ecrit les b�en�efices,pour la pratique orthodontique [5], du Nitinol, qui propose une�elasticit�e semblable a celle de l’acier, mais avec moins derigidit�e.Le TMA a �et�e introduit en 1979 et rapidement adopt�e enraison de ses qualit�es : excellente m�emoire de forme,rigidit�e faible, bonne formabilit�e et soudage direct. Le coeffi-cient de friction est significativement plus �elev�e qu’avecd’autres alliages [6].

International Orthodontics 2011 ; 9 : 120-139 121

Wire load–deflection characteristics relative to different types of bracketsComparaison des caract�eristiques de charge–flexion de fils selon diff�erents types de brackets


In comparative mechanical studies carried out by Drake et al.,TMA has shown greater elasticity and springback than SSmaking it appropriate in cases of severe malocclusion [7].

In recent years, superelastic NiTi wires have been introduced,in particular for the first steps of dental alignment, on accountof their particular mechanical characteristics [8]. At smalldeflections they exhibit elastic behavior. Hence, the load isproportional to the deflection. However, after a given amountof wire deformation, NiTi “martensitic transformation” occursas the shape of the crystals changes and the wire developssuperelastic mechanical properties. As the deflectionincreases, the stress value remains fairly constant. This char-acteristic of the alloy is referred to as the “martensitic plateau”on the load-deflection curve [9].

A second characteristic of NiTi alloy is that the loading curveis different from the unloading curve. The difference betweenthem is called “hysteresis”. The unloading curve has greaterclinical value since it represents the forces acting on the teeth[10].

The increasing demand for lingual orthodontic treatment isforcing orthodontists to learn how to choose the appropriatetype of bracket and wire and to exert physiological forces onthe teeth without triggering root resorption [3].The aim of this study was to test the hypothesis that thedimension of the bracket, in both labial and lingual orthodon-tics, is a relevant parameter when determining the forces thatact on the teeth and that some wires commonly used in labialorthodontics are unsuitable for the first phase of lingualtreatment.

Materials and methods

To calculate the different interbracket distances when variousbrackets were used, an ideal dental cast was chosen for itscharacteristics: it featured right and left symmetrical half-arches, molar and canine Class I, normal overjet and overbite,no rotations and no diastemas.Incisors, canines and premolars were bonded on both thelabial and lingual face, with four different types of brackets,as follows (fig. 1):— Damon 3MX (Ormco): vestibular segments 1 and 3;— Innovation-L (GAC): lingual segments 1 and 3;— Ovation (GAC): vestibular segments 2 and 4;— Evolution Brackets (Adenta): lingual segments 2 and 4.In a second stage, after photographic documentation, the lin-gual brackets at segments 1 and 4 were removed (GACInnovation-L and Evolution Brackets Adenta, respectively),and STB brackets were bonded (fig. 2).Then, the dental cast was bonded as follows (fig. 3):

— Time 2 Bracket (by Micerium): segments 1 and 3;

Dans les �etudes m�ecaniques comparatives r�ealis�ees parDrake et al., le TMA a montr�e une �elasticit�e et un retour�elastique sup�erieurs au SS, ce qui le rend utile dans les casde malocclusions s�ev�eres [7].Ces derni�eres ann�ees, les fils super-�elastiques en NiTi ont �et�eintroduits, surtout utilis�es lors des premiers stades de l’aligne-ment dentaire, en raison de leurs caract�eristiquesm�ecaniquesparticuli�eres [8]. A de faibles flexions, ils ont un comportement�elastique. En cons�equence, la charge est proportionnelle a laflexion. Cependant, apr�es un certain degr�e de d�eformation, lefil en NiTi subit une « transformation martensitique » secaract�erisant par un changement de forme des cristaux et led�eveloppement de propri�et�es m�ecaniques super-�elastiques.Avec l’augmentation de la flexion, la valeur de la contraintereste assez constante, d�ecrivant ainsi ce qui est appel�e le« palier martensitique » sur la courbe charge–flexion [9].Une seconde caract�eristique de l’alliage NiTi concerne lacourbe de charge, qui se diff�erencie de la courbe de d�echarge.La diff�erence entre les deux courbes s’appelle l’hyst�er�ese. Lacourbe de d�echarge a plus d’int�eret dans le contexte cliniquepuisqu’elle repr�esente les forces qui s’exercent sur les dents[10].La demande accrue de traitement orthodontique lingual obligeles orthodontistes a apprendre a choisir les types de bracketset de fils appropri�es afin d’exercer des forces physiologiquessur les dents sans provoquer de r�esorptions radiculaires [3].L’objectif de cette �etude �etait de tester l’hypoth�ese selonlaquelle, d’une part, la dimension du bracket, en techniquelinguale comme en technique vestibulaire, constitue un para-m�etre pertinent pour d�eterminer les forces agissant sur lesdents et, d’autre part, certains fils tr�es utilis�es en orthodontievestibulaire ne conviennent pas a la premi�ere phase d’untraitement en lingual.

Mat�eriaux et m�ethodes

Pour calculer les diff�erentes distances interbrackets desdivers brackets utilis�es, nous avons choisi un mod�ele dentaireid�eal en raison de ses caract�eristiques : h�emi-arcades droiteet gauche sym�etriques, absence de rotations et de diast�emes.

Les incisives, canines et pr�emolaires ont �et�e coll�ees sur lesdeux faces, vestibulaire et linguale, avec quatre types debrackets diff�erents, et de la mani�ere suivante (fig. 1) :— Damon 3MX (Ormco) : secteurs vestibulaires 1 et 3 ;— Innovation-L (GAC) : secteurs linguaux 1 et 3 ;— Ovation (GAC) : secteurs vestibulaires 2 et 4 ;— Evolution Brackets (Adenta) : secteurs linguaux 2 et 4.Dans un deuxi�eme temps, apr�es prise de photographies, lesbrackets linguaux des secteurs 1 et 4 ont �et�e d�epos�es (GACInnovation-L et Evolution Brackets Adenta, respectivement) etdes brackets STB ont �et�e coll�es (fig. 2).Ensuite, le mod�ele dentaire a �et�e coll�e avec les prescriptionssuivantes (fig. 3) :— Time 2 Bracket (Micerium) : secteurs 1 et 3 ;

122 International Orthodontics 2011 ; 9 : 120-139

Luca LOMBARDO et al.


— Innovation (GAC): segments 2 and 4.Finally, Time 2 Brackets were removed and Smart Clip Clarity(3 M Unitek) were bonded at segments 2 and 4 (fig. 4).Six types of brackets used in this work were self-ligating (fouron the labial side and two on the lingual) and two were tradi-tional (one on the labial side and one on the lingual).The bonded casts were photographed with a gauge to calculatethe proportions. Then, the digital images were analyzed withImageJ software (National Institute of Health).

— Innovation (GAC) : secteurs 2 et 4.Enfin, les Time 2 Brackets ont �et�e d�epos�es et des Smart ClipClarity (3MUnitek) ont �et�e coll�es sur les secteurs 2 et 4 (fig. 4).Six types de brackets utilis�es dans cette �etude �etaient auto-ligaturants (quatre en vestibulaire et deux en lingual) et deux�etaient traditionnels (un en vestibulaire et un en lingual).Les mod�eles coll�es �etaient photographi�es avec une jauge afinde calculer les proportions. Ensuite, les images num�eris�eesont �et�e analys�ees avec le logiciel ImageJ (National Institute ofHealth).

[(Fig._1)TD$FIG]

Fig. 1: a-b: typodont bonded with: Damon 3MX (by Ormco) in vestibular segments 1 and 3;Innovation-L (by GAC) in lingual segments 1 and 3; Ovation (by GAC) in vestibular segments 2and 4; Evolution brackets (by Adenta) in lingual segments 2 and 4.Fig. 1 : a-b : typodont coll�e avec : Damon 3MX (Ormco) sur les secteurs vestibulaires 1 et 3 ;

Innovation-L (GAC) sur les secteurs linguaux 1 et 3 ; Ovation (GAC) sur les secteurs vestibu-

laires 2 et 4 ; Evolution Brackets (Adenta) sur les secteurs linguaux 2 et 4.

[(Fig._2)TD$FIG]

Fig. 2: a-b: typodont bonded with: Damon 3MX (by Ormco) in vestibular segments 1 and 3;Innovation-L (by GAC) in lingual segment 3; Ovation (by GAC) in vestibular segments 2 and 4;Evolution brackets (by Adenta) in lingual segment 2; STB brackets in lingual segments 1and 4.Fig. 2 : a-b : typodont coll�e avec : Damon 3MX (Ormco) sur les secteurs vestibulaires 1 et 3 ;

Innovation-L (GAC) sur le secteur lingual 3 ; Ovation (GAC) sur les secteurs vestibulaires 2 et 4 ;

Evolution Brackets (Adenta) sur le secteur lingual 2 ; brackets STB sur les secteurs linguaux 1 et

4.




The interbracket distance was taken as the distance from thedistal edge of the bracket on the mesial tooth to the mesialedge of the bracket on the distal tooth (i.e. to calculate thestress on tooth 12, the measurement was taken from the distaledge of bracket 1.1 and the mesial edge of the bracket on 13).Based on the observed interbracket distance, we calculatedthe hypothetical force produced by an ideal wire on a mis-aligned tooth, at three different levels of deflection in thehorizontal plane: 0.5 mm, 1.0 mm, 1.5 mm.Four round 0.016 wires were used to calculate the load. Themodulus of elasticity of the most widely used orthodontic wireswas taken from the studies by Miura et al. [11] and Verstryngeet al. [6]:— SS: 17–20 � 103 kg/mm2;— Nitinol: 5–6 � 103 kg/mm2;

La distance interbrackets adopt�ee �etait la distance entre lebord distal du bracket de la dent m�esiale et le bord m�esial dubracket de la dent distale (c.-a-d. pour calculer la contraintesur la 12, lamesure �etait prise entre le bord distal du bracket dela 11 et le bord m�esial du bracket de la 13).Nous basant sur la distance interbrackets observ�ee, nousavons calcul�e la force hypoth�etique produite par un fil id�ealsur une dent id�eale en malposition a trois niveaux de flexiondans le plan horizontal : 0,5 mm ; 1,0 mm et 1,5 mm.Quatre fils ronds 0,016 ont �et�e utilis�es pour calculer la charge.Lemodule d’�elasticit�e des fils orthodontiques les plus utilis�es a�et�e emprunt�e aux �etudes de Miura et al. [11] et de Verstryngeet al. [6] :— SS : 17–20 � 103 kg/mm2 ;— Nitinol : 5–6 � 103 kg/mm2 ;

[(Fig._3)TD$FIG]

Fig. 3: a-b: typodont bonded with: Time 2 bracket (by Micerium) in segments 1 and 3;Innovation (by GAC) in segments 2 and 4.Fig. 3 : a-b : typodont coll�e avec : Time 2 bracket (Micerium) sur les secteurs 1 et 3 ; Innovation

(GAC) sur les secteurs 2 et 4.

[(Fig._4)TD$FIG]

Fig. 4: a-b: typodont bonded with: Smart Clip Clarity (by 3M Unitek) in segments 2 and 4;Time 2 bracket (by Micerium) in segments 1 and 3.Fig. 4 : a-b : typodont coll�e avec : Smart Clip Clarity (3MUnitek) sur les secteurs 2 et 4 ; Time 2

Bracket (Micerium) sur les secteurs 1 et 3.




— TMA: 6.5 – 10 � 103 kg/mm2;— Japanese NiTi: 3.8 � 103 kg/mm2.SS, TMA and Nitinol are elastic wires. The Japanese NiTitested byMiura et al. [11] is superelastic, so the Ym parameterwas found for every interbracket distance. Ym is the level ofdeflection at which the wire changes its behavior from elasticto superelastic. It is different for every interbracket distance.This value is needed to choose the mathematical formulae touse at the different levels of deflection.

To calculate the stress acting on a single tooth at differentdeflections, the following mathematical formulae were used[9].For elastic wires:

F ¼ 192 IEY

L3

With:— E: modulus of elasticity— I: moment of inertia: pD4/64— D: diameter of the wire: 0.016 = 0.41 mm— L: interbracket distance— Y: deflection in the horizontal planeThis mathematical relationship is also valid for superelasticwires in the elastic range (the linear part of the curve).However, for the superelastic plateau, a different formula isrequired [9]:

F ¼ 16 IEU

LD

U is an alloy parameter which can be estimated using a three-point bending test to identify the point of martensitic trans-formation Ym. The following formula is then applied [9]:

U ¼ 12 DYm

L2

Results

The interbracket distances with the different types of bracketsare reported in Tables I–VIII.Note that the vestibular distance is always greater than thelingual. The only exception is the maxillary canine-secondpremolar distance where the vestibular side is bonded withSmart Clip Clarity brackets and the lingual with STB brackets.The interbracket distance is modified significantly by changesin the type of bracket.

In the vestibular segment, the maxillary teeth bonded withTime 2 brackets showed a longer interbracket distance com-pared to those bonded with other brackets in the study, fol-lowed closely by Damon 3MX. The maxillary interbracketdistance for Innovation GAC was longer than that forOvation GAC.

— TMA : 6,5–10 � 103 kg/mm2 ;— NiTi japonais : 3,8 � 103 kg/mm2.SS, TMA et Nitinol sont des fils �elastiques. Le NiTi japonaistest�e par Miura et al. [11] est super-�elastique. Ainsi, le para-m�etre Ym a �et�e retrouv�e pour chaque distance interbrackets.Ym est le niveau de d�eflexion auquel le comportement du fil setransforme d’�elastique en super-�elastique. Il est diff�erent pourchaque distance interbrackets. Cette valeur est essentiellepour choisir les formules math�ematiques a adopter aux diff�e-rents niveaux de flexion.Pour calculer la contrainte s’exercant sur une dent uniquea des flexions diff�erentes, nous avons utilis�e les formulesmath�ematiques suivantes [9].Pour les fils �elastiques :

F ¼ 192 IEY

L3

avec :— E : module d’�elasticit�e— I : moment d’inertie : pD4/64— D : diam�etre du fil : 0,016 = 0,41 mm— L : distance interbrackets— Y : flexion dans le plan horizontalCette �equation est �egalement valable pour les fils super-�elastiques dans la gamme �elastique (la partie lin�eaire de lacourbe). Cependant, pour le plateau super-�elastique, une for-mule diff�erente est n�ecessaire [9] :

F ¼ 16 IEU

LD

U est un param�etre d’alliage qui peut etre calcul�e en utilisantun test de pliage en trois points pour identifier le point detransformation martensitique Ym. Dans ce cas, la formulesuivante est employ�ee [9] :

U ¼ 12 DYm

L2

R�esultats

Les distances interbrackets des diff�erents types de bracketssont donn�ees dans les Tableaux I–VIII.Notez que la distance vestibulaire est toujours plus grande quela distance linguale. La seule exception est la distance canine– deuxi�eme pr�emolaire maxillaire ou la face vestibulaire estcoll�ee avec des brackets Smart Clip Clarity et la face lingualeavec des brackets STB. La distance interbrackets est modifi�eede facon significative avec les changements de type debracket.Dans le secteur vestibulaire, les dentsmaxillaires coll�ees avecdes brackets Time 2 avaient une distance interbrackets plusgrande que celles coll�ees avec d’autres brackets dans l’�etude,suivis de pr�es par les Damon 3MX. La distance interbracketsdes Innovation GAC �etait plus grande que pour les OvationGAC.




In the mandibular arch, the anterior and posterior segmentsmust be distinguished. In the central incisor-canine space, alonger interbracket distance is observed with Time 2 bracket,followed by Damon, Innovation and Ovation. In the posteriorregion of the arch, the Ovation and Innovation brackets wereobserved to have a longer interbracket distance, followed byDamon 3MX and Time 2 brackets. The Smart Clip Claritybrackets had the longest mesiodistal dimension in both the

A l’arcade mandibulaire, il faut distinguer entre les secteursant�erieurs et post�erieurs. Dans l’espace incisive centrale–canine, nous avons observ�e une distance interbrackets plusgrande avec les Time 2 Bracket, suivis des brackets Damon,Innovation et Ovation. Dans la r�egion post�erieure de l’arcade,ce sont les brackets Ovation et Innovation qui avaient la dis-tance interbrackets la plus importante suivis des Damon 3X etdes Time 2. Les boıtiers Smart Clip Clarity avaient la

Table IEvolution Brackets Adenta interbracket distances (lingualsegments 2 and 4).

Tableau IEvolution Brackets (Adenta) : distances interbrackets(secteurs linguaux 2 et 4).

21–23 8.90

22–24 9.74

23–25 11.52

41–43 6.31

42–44 7.39

43–45 10.33

Table IIInnovation-L GAC interbracket distances (lingual segments 1and 3).

Tableau IIInnovation-L (GAC) : distances interbrackets (secteurslinguaux 1 et 3).

11–13 8.63

12–14 9.25

13–15 11.28

31–33 6.79

32–34 7.70

33–35 10.52

Table IIIDamon 3MX Ormco interbracket distances (vestibularsegments 1 and 3).

Tableau IIIDamon 3MX (Ormco) : distances interbrackets (secteursvestibulaires 1 et 3).

11–13 16.19

12–14 15.26

13–15 12.67

31–33 12.48

32–34 14.14

33–35 12.73




mandibular and the maxillary arch, and therefore the shortestinterbracket distance among the samples analyzed.

In the lingual segment, with respect to the other tested brack-ets, the STB had a greater interbracket distance for both themaxillary and the mandibular arch.The segment of maxillary arch bonded with Evolution bracketshad a greater interbracket distance than the section bonded

dimension m�esiodistale la plus grande aux deux arcades et,par cons�equent, la distance interbrackets la plus courte parmiles �echantillons �etudi�es.Dans la zone linguale, les brackets STB avaient une distanceinterbrackets plus grande par rapport aux autres bracketstest�es aux deux arcades.Le secteur de l’arcade maxillaire coll�e avec des bracketsEvolution avait une distance interbrackets plus grande que

Table IVOvation GAC interbracket distances (vestibular segments 2and 4).

Tableau IVOvation (GAC) : distances interbrackets (secteursvestibulaires 2 et 4).

21–23 14.80

22–24 14.23

23–25 12.18

41–43 10.83

42–44 14.02

43–45 13.21

Table VSTB interbracket distances (lingual segments 1 and 4).

Tableau VSTB : distances interbrackets (secteurs linguaux 1 et 4).

11–13 9.42

12–14 10.06

13–15 12.13

41–43 7.36

42–44 7.83

43–45 11.31

Table VITime 2Micerium interbracket distance (vestibular segments 1and 3).

Tableau VITime 2 (Micerium) : distance interbrackets (secteursvestibulaires 1 et 3).

11–13 16.42

12–14 15.61

13–15 13.24

31–33 12.61

32–34 13.71

33–35 12.99




with Innovation-L. Conversely, in the mandible, a shorterinterbracket distance was found with Evolution compared toInnovation-L.The ratio of the vestibular to the lingual interbracket distancefor every tooth and for every pair of brackets is reported inTable IX.Considering the same tooth, the type of brackets significantlyinfluenced the ratio of the vestibular to lingual interbracketdistance, which ranged from a minimum value of 0.95 to amaximum of 1.99. The former was the maxillary canine-sec-ond premolar space, bonded with Smart Clip Clarity on thevestibular side and with STB on the lingual. The second wasthe mandibular central incisor-canine, bonded with vestibularTime 2 brackets and lingual Evolution brackets.

Given that the load of an orthodontic wire is inversely propor-tional to the cube of the interbracket distance, the result wasthat, for the same wire diameter, lingual appliances providedforces which were up to 7.88 times greater than labialappliances.The single stress values applied on the teeth bonded with thedifferent brackets are reported in Tables X–XVII.

celui coll�e avec Innovation-L. Inversement, a la mandibule,nous avons trouv�e une distance interbrackets plus courte avecEvolution par rapport a Innovation-L.Le rapport vestibulaire/lingual de la distance interbrackets estdonn�e dans le Tableau IX.

Quelle que soit la dent, le type de bracket a eu un impactsignificatif sur le rapport vestibulaire/lingual de la distanceinterbrackets qui variait entre une valeur minimale de 0,95 etune valeur maximale de 1,99. La premi�ere correspondaita l’espace entre la canine et la deuxi�eme pr�emolaire maxil-laires, coll�ees avec des brackets Smart Clip Clarity du cot�evestibulaire et avec des STB du cot�e lingual. La secondecorrespondait a l’espace entre l’incisive centrale et la caninemandibulaires coll�ees avec des brackets Time 2 vestibulaireset des brackets linguaux Evolution.�Etant donn�e que la charge d’un fil orthodontique est inverse-ment proportionnelle au cube de la distance interbrackets, ilressort que, pour le meme diam�etre de fil, les appareils lin-guaux exercaient des forces qui �etaient jusqu’a 7,88 fois plusgrandes que les appareils vestibulaires.Les valeurs de la meme contrainte appliqu�ee aux dents col-l�ees avec les diff�erents brackets sont rapport�ees dans lesTableaux X–XVII.

Table VIIInnovation GAC interbracket distance (vestibular segments 2and 4).

Tableau VIIInnovation (GAC) : distance interbrackets (secteursvestibulaires 2 et 4).

21–23 15.41

22–24 14.73

23–25 12.61

41–43 11.85

42–44 14.43

43–45 12.66

Table VIIISmart Clip Clarity (3M Unitek) interbracket distance(vestibular segments 2 and 4).

Tableau VIIISmart Clip Clarity (3M Unitek) : distance interbrackets(secteurs vestibulaires 2 et 4).

21–23 14.36

22–24 13.95

23–25 11.42

41–43 10.68

42–44 12.89

43–45 11.85




Table IXRatio of the vestibular to the lingual interbracket distance, forevery pair of brackets.

Tableau IXRapport vestibulaire/lingual de la distance interbrackets pourchaque paire de brackets.

Adenta Time GAC Innovation-L STB

Damon 3MX

1–3 Mx 1.82 1.88 1.71

2–4 Mx 1.57 1.65 1.52

3–5 Mx 1.10 1.12 1.04

1–3 Md 1.98 1.84 1.70

2–4 Md 1.91 1.84 1.80

3–5 Md 1.23 1.21 1.12

Ovation

1–3 Mx 1.66 1.65 1.57

2–4 Mx 1.46 1.54 1.41

3–5 Mx 1.06 1.08 1.01

1–3 Md 1.72 1.59 1.47

2–4 Md 1.90 1.82 1.79

3–5 Md 1.28 1.25 1.17

Time 2

1–3 Mx 1.84 1.90 1.74

2–4 Mx 1.60 1.69 1.55

3–5 Mx 1.15 1.17 1.09

1–3 Md 1.99 1.86 1.71

2–4 Md 1.86 1.78 1.75

3–5 Md 1.26 1.23 1.15

Innovation

1–3 Mx 1.73 1.79 1.64

2–4 Mx 1.51 1.59 1.46

3–5 Mx 1.09 1.12 1.04

1–3 Md 1.88 1.75 1.61

2–4 Md 1.95 1.87 1.84

3–5 Md 1.22 1.20 1.12

Smart Clip Clarity

1–3 Mx 1.61 1.66 1.52

2–4 Mx 1.43 1.51 1.39

3–5– Mx 1.01 1.02 0.95

1–3– Md 1.69 1.57 1.45

2–4– Md 1.74 1.67 1.64

3–5– Md 1.15 1.13 1.41




Among the elastic wires (SS, TMA, Nitinol), the load increasedproportionally to the deflection (0.5 mm, 1.0 mm, 1.5 mm) andit increased with the modulus of elasticity. SS had the highestYoung’s absolute value (17–20 � 103 kg/mm2), followed byTMA (6.5–10 � 103 kg/mm2) and Nitinol (5–6 � 103 kg/mm2).Superelastic Japanese NiTi has a lower modulus of elasticitycompared to the other wires considered. Consequently, even atsmall deflections, in the elastic interval, it provides lighterforces than the other wires.

Parmi les fils �elastiques (SS, TMA, Nitinol), la charge augmen-tait proportionnellement a la flexion (0,5 mm ; 1,0 mm, 1,5mm) et augmentait avec le module d’�elasticit�e. L’acier avaitla valeur absolue de Young la plus �elev�ee (17–20 � 103 kg/mm2), suivi du TMA (6,5–10 � 103 kg/mm2) et du Nitinol(5–6 � 103 kg/mm2).Le NiTi japonais super-�elastique avait un module d’�elasticit�eplus faible compar�e aux autres fils �etudi�es. Par cons�equent,meme a des d�eflexions peu importantes, dans l’intervalled’�elasticit�e, il d�elivrait des forces plus l�eg�eres que les autres fils.

Table XLoad of the different wires (g), with the minimum andmaximum E value. Evolution Adenta Bracket (lingual,segments 2 and 4).

Tableau XCharge des diff�erents fils (g), avec la valeur E minimale etmaximale des diff�erents fils (g). Evolution Adental Bracket(secteurs linguaux 2 et 4).

SS min SS max TMA min TMA max Nitinol min Nitinol max NiTi Giapp

21–23 Ym = 0.45

Ya = 3200 Ya = 3629 Ya = 1221 Ya = 1878 Ya = 942 Ya = 1128 Ya = 640

Yb = 6400 Yb = 7258 Yb = 2442 Yb = 3757 Yb = 1885 Yb = 2257 Yb = 640

Yc = 9600 Yc = 10887 Yc = 3663 Yc = 5635 Yc = 2827 Yc = 3385 Yc = 640

22–24 Ym = 0.54

Ya = 2435 Ya = 2864 Ya = 949 Ya = 1429 Ya = 717 Ya = 858 Ya = 543

Yb = 4870 Yb = 5728 Yb = 1858 Yb = 2858 Yb = 1434 Yb = 1717 Yb = 585

Yc = 7305 Yc = 8592 Yc = 2937 Yc = 4287 Yc = 2151 Yc = 2575 Yc = 585

23–25 Ym = 0.76

Ya = 1464 Ya = 1722 Ya = 558 Ya = 859 Ya = 431 Ya = 516 Ya = 326

Yb = 2928 Yb = 3444 Yb = 1117 Yb = 1718 Yb = 862 Yb = 1032 Yb = 494

Yc = 4392 Yc = 5166 Yc = 1675 Yc = 2577 Yc = 1293 Yc = 1548 Yc = 494

41–43 Ym = 0.23

Ya = 8960 Ya = 10540 Ya = 3420 Ya = 5260 Ya = 2640 Ya = 3160 Ya = 903

Yb = 17920 Yb = 21080 Yb = 6840 Yb = 10520 Yb = 5280 Yb = 6320 Yb = 903

Yc = 26880 Yc = 31620 Yc = 10260 Yc = 15780 Yc = 7920 Yc = 9480 Yc = 903

42–44 Ym = 0.31

Ya = 5600 Ya = 6587 Ya = 2137 Ya = 3287 Ya = 1650 Ya = 1975 Ya = 771

Yb = 11200 Yb = 13175 Yb = 4275 Yb = 6575 Yb = 3300 Yb = 3950 Yb = 771

Yc = 16800 Yc = 19762 Yc = 6412 Yc = 9862 Yc = 4950 Yc = 5925 Yc = 771

43–45 Ym = 0.6

Ya = 2036 Ya = 2395 Ya = 777 Ya = 1195 Ya = 600 Ya = 718 Ya = 460

Yb = 4072 Yb = 4790 Yb = 1554 Yb = 2390 Yb = 1200 Yb = 1436 Yb = 556

Yc = 6108 Yc = 7185 Yc = 2331 Yc = 3585 Yc = 1800 Yc = 2154 Yc = 556




The superelastic transition point Ym changes with the differ-ent interbracket distances: on the dental cast in the study, theminimum value was 0.23 mm, corresponding to the shortestinterbracket distance (lingual Evolution, between 41 and 43),and its maximum value was 1.54 mm (vestibular Smart ClipClarity, between 11 and 13). This superelastic wire providedlower forces than the other wires, in particular with reducedinterbracket distance.

Le point de transition super-�elastique Ym varie selon lesdiff�erentes distances inter-�elastiques : sur le mod�ele dentairedans cette �etude, la valeur minimale �etait de 0,23 mm, cor-respondant a la distance interbrackets la plus courte(Evolution lingual entre 41 et 43). La valeur maximale �etaitde 1,54 mm (Smart Clip Clarity vestibulaire entre 11 et 13).Ce fil super-�elastique d�elivrait des forces plus l�eg�eres que lesautres fils, en particulier dans le cas de distances interbrack-ets r�eduites.

Table XILoad of the different wires (g), with the minimum andmaximum E value. Innovation- L GAC brackets (lingualsegments 1 and 3).

Tableau XICharge des diff�erents fils (g), avec la valeur E minimale etmaximale. Brackets Innovation-L GAC (secteurs linguaux 1et 3).


11–13 Ym = 0.42

Ya = 3500 Ya = 4117 Ya = 1335 Ya = 2054 Ya = 1031 Ya = 1234 Ya = 660

Yb = 7000 Yb = 8234 Yb = 2671 Yb = 4109 Yb = 2062 Yb = 2468 Yb = 660

Yc = 10500 Yc = 12351 Yc = 4006 Yc = 6163 Yc = 3093 Yc = 3702 Yc = 660

12–14 Ym = 0.49

Ya = 2835 Ya = 3335 Ya = 1082 Ya = 1664 Ya = 835 Ya = 1000 Ya = 616

Yb = 5670 Yb = 6670 Yb = 2164 Yb = 3329 Yb = 1670 Yb = 2000 Yb = 616

Yc = 8505 Yc = 10005 Yc = 3246 Yc = 4993 Yc = 2505 Yc = 3000 Yc = 616

13–15 Ym = 0.72

Ya = 1566 Ya = 1842 Ya = 597 Ya = 919 Ya = 461 Ya = 552 Ya = 349

Yb = 3132 Yb = 3685 Yb = 1195 Yb = 1839 Yb = 923 Yb = 1104 Yb = 505

Yc = 4698 Yc = 5527 Yc = 1792 Yc = 2758 Yc = 1384 Yc = 1656 Yc = 505

31–33 Ym = 0.26

Ya = 7225 Ya = 8500 Ya = 2758 Ya = 4241 Ya = 2129 Ya = 2548 Ya = 839

Yb = 14450 Yb = 17000 Yb = 5516 Yb = 8483 Yb = 4258 Yb = 5096 Yb = 839

Yc = 21675 Yc = 25500 Yc = 8274 Yc = 12724 Yc = 6387 Yc = 7644 Yc = 839

32–34 Ym = 0.34

Ya = 4870 Ya = 5728 Ya = 1858 Ya = 2858 Ya = 1434 Ya = 1717 Ya = 746

Yb = 9740 Yb = 11456 Yb = 3717 Yb = 5717 Yb = 2869 Yb = 3434 Yb = 746

Yc = 14610 Yc = 17184 Yc = 5575 Yc = 8575 Yc = 4303 Yc = 5151 Yc = 746

33–35 Ym = 0.63

Ya = 1931 Ya = 2271 Ya = 737 Ya = 1133 Ya = 569 Ya = 681 Ya = 435

Yb = 3862 Yb = 4542 Yb = 1474 Yb = 2267 Yb = 1138 Yb = 1362 Yb = 546

Yc = 5793 Yc = 6813 Yc = 2211 Yc = 3400 Yc = 1707 Yc = 2043 Yc = 546




Discussion

The results of this study demonstrate the importance of inter-bracket distance in determining the load of a wire on a singletooth.According to the study by Schudy and Schudy [12], the deflec-tion of an orthodontic wire is directly proportional to theinterbracket distance and inversely proportional to the wirecross-section. The delivered force increases with decreasingtooth size. Hence, the decrease in interbracket space. As aresult, to reduce wire stress on the teeth, orthodontists must

Discussion

Les r�esultats de cette �etude soulignent l’importance de ladistance interbrackets pour d�eterminer la charge d�elivr�eepar un fil a une dent donn�ee.En accord avec l’�etude de Schudy et Schudy [12], la flexiond’un fil orthodontique est directement proportionnelle a la dis-tance interbrackets et inversement proportionnelle a la sectiondu fil. La force d�elivr�ee augmente avec la diminution de la taillede la dent. D’ou la diminution de l’espace interbrackets. Parcons�equent, pour r�eduire la contrainte impos�ee par le fil aux

Table XIILoad of the different wires (g), with the minimum andmaximum E value. Damon 3MX Ormco brackets (vestibularsegments 1 and 3).

Tableau XIICharge des diff�erents fils (g), avec la valeur E minimale etmaximale. Brackets Damon 3MX (Ormco) (secteursvestibulaires 1 et 3).


11–13 Ym = 1.49

Ya = 528 Ya = 621 Ya = 201 Ya = 310 Ya = 155 Ya = 186 Ya = 117

Yb = 1056 Yb = 1242 Yb = 403 Yb = 620 Yb = 311 Yb = 372 Yb = 235

Yc = 1584 Yc = 1863 Yc = 604 Yc = 930 Yc = 466 Yc = 558 Yc = 352

12–14 Tm = 1.33

Ya = 640 Ya = 742 Ya = 241 Ya = 370 Ya = 186 Ya = 211 Ya = 141

Yb = 1280 Yb = 1484 Yb = 482 Yb = 740 Yb = 372 Yb = 422 Yb = 282

Yc = 1920 Yc = 2226 Yc = 723 Yc = 1110 Yc = 558 Yc = 633 Yc = 373

13–15 Ym = 0.91

Ya = 1103 Ya = 1298 Ya = 421 Ya = 647 Ya = 325 Ya = 389 Ya = 246

Yb = 2206 Yb = 2596 Yb = 842 Yb = 1295 Yb = 650 Yb = 778 Yb = 450

Yc = 3309 Yc = 3894 Yc = 1263 Yc = 1942 Yc = 975 Yc = 1167 Yc = 450

31–33 Ym = 0.89

Ya = 1125 Ya = 1324 Ya = 429 Ya = 660 Ya = 331 Ya = 397 Ya = 251

Yb = 2250 Yb = 2648 Yb = 859 Yb = 1321 Yb = 663 Yb = 794 Yb = 456

Yc = 3375 Yc = 3972 Yc = 1288 Yc = 1981 Yc = 994 Yc = 1191 Yc = 456

32–34 Ym = 1.14

Ya = 794 Ya = 934 Ya = 303 Ya = 466 Ya = 234 Ya = 280 Ya = 177

Yb = 1588 Yb = 1868 Yb = 606 Yb = 932 Yb = 468 Yb = 560 Yb = 354

Yc = 2382 Yc = 2802 Yc = 909 Yc = 1398 Yc = 702 Yc = 840 Yc = 403

33–35 Ym = 0.92

Ya = 1087 Ya = 1279 Ya = 415 Ya = 638 Ya = 320 Ya = 383 Ya = 243

Yb = 2174 Yb = 2558 Yb = 830 Yb = 1276 Yb = 640 Yb = 766 Yb = 448

Yc = 3261 Yc = 3837 Yc = 1245 Yc = 1914 Yc = 960 Yc = 1149 Yc = 448




use elastic wires with a smaller cross-section, and also brack-ets with relatively small dimensions. The type of bracketbecomes a relevant parameter when lingual mechanics isused, as can be seen from the comparison of the eight typesof tested appliances.

In his 1987 study, Moran [2] found that the mean ratio of thevestibular-to-lingual interbracket distance in anterior seg-ments is 1.47. Thus, the forces delivered on the lingual sideare about three times greater than on the labial side. Thisfinding is confirmed by the measurements taken in our work:

dents, le praticien doit utiliser des fils �elastiques avec un dia-m�etre r�eduit de meme que des brackets avec des dimensionsrelativement petites. Le type de bracket utilis�e devient un para-m�etre pertinent lorsqu’une m�ecanique linguale est adopt�ee,comme le fait apparaıtre une comparaison des huit types dedispositifs test�es.Dans son �etude datant de 1987, Moran [2] a trouv�e que lerapport vestibulolingual moyen pour la distance interbracketsdans les segments ant�erieurs �etait de 1,47. Ainsi, les forcesexerc�ees du cot�e lingual sont trois fois plus importantes quedu cot�e vestibulaire. Ce r�esultat est confirm�e par les mesures

Table XIIILoad of the different wires (g), with the minimum andmaximum E value. Ovation GAC brackets (vestibularsegments 2 and 4).

Tableau XIIICharge des diff�erents fils (g), avec la valeur E minimale etmaximale. Brackets Ovation GAC (secteurs vestibulaires 2et 4).


21–23 Ym = 1.25

Ya = 691 Ya = 813 Ya = 263 Ya = 406 Ya = 203 Ya = 243 Ya = 154

Yb = 1382 Yb = 1626 Yb = 527 Yb = 812 Yb = 407 Yb = 487 Yb = 308

Yc = 2073 Yc = 2439 Yc = 790 Yc = 1218 Yc = 610 Yc = 730 Yc = 385

22–24 Ym = 1.15

Ya = 777 Ya = 914 Ya = 297 Ya = 456 Ya = 229 Ya = 274 Ya = 173

Yb = 1555 Yb = 1829 Yb = 594 Yb = 913 Yb = 458 Yb = 548 Yb = 347

Yc = 2332 Yc = 2743 Yc = 891 Yc = 1369 Yc = 687 Yc = 822 Yc = 400

23–25 Ym = 0.84

Ya = 1237 Ya = 1456 Ya = 472 Ya = 726 Ya = 364 Ya = 436 Ya = 279

Yb = 2475 Yb = 2912 Yb = 944 Yb = 1453 Yb = 729 Yb = 872 Yb = 472

Yc = 3712 Yc = 4368 Yc = 1416 Yc = 2179 Yc = 1093 Yc = 1308 Yc = 472

41–43 Ym = 0.67

Ya = 1764 Ya = 2074 Ya = 673 Ya = 1035 Ya = 519 Ya = 622 Ya = 393

Yb = 3528 Yb = 4149 Yb = 1346 Yb = 2070 Yb = 1039 Yb = 1244 Yb = 526

Yc = 5292 Yc = 6223 Yc = 2019 Yc = 3105 Yc = 1558 Yc = 1866 Yc = 526

42–44 Ym = 1.12

Ya = 814 Ya = 958 Ya = 310 Ya = 478 Ya = 240 Ya = 287 Ya = 182

Yb = 1629 Yb = 1916 Yb = 621 Yb = 956 Yb = 480 Yb = 574 Yb = 364

Yc = 2443 Yc = 2874 Yc = 931 Yc = 1434 Yc = 720 Yc = 861 Yc = 406

43–35 Ym = 0.99

Ya = 974 Ya = 1145 Ya = 371 Ya = 571 Ya = 286 Ya = 343 Ya = 217

Yb = 1948 Yb = 2291 Yb = 743 Yb = 1143 Yb = 573 Yb = 686 Yb = 431

Yc = 2922 Yc = 3436 Yc = 1114 Yc = 1714 Yc = 859 Yc = 1029 Yc = 431




the values we found ranged from a minimum of 0.95 to amaximum of 1.99. In the posterior regions of the arch, theforces on the lingual side are comparable with those on thevestibular side, because of the similar interbracket dis-tance. In only one space (maxillary canine-second premo-lar), the vestibular interbracket distance was found to besmaller than the lingual one, when comparing the largervestibular bracket (Smart Clip Clarity) with the shorterlingual one (STB). Otherwise, the forces can be up to7.88 times larger where the interbracket distance is smal-ler, in particular when relatively large lingual brackets areused.

relev�ees dans notre �etude : les valeurs que nous avonstrouv�ees allaient de 0,95 a un maximum de 1,99. Dans lesr�egions post�erieures de l’arcade, les forces du cot�e lingualsont semblables a celles retrouv�ees du cot�e vestibulaire enraison de la similarit�e entre les distances interbrackets respec-tives. Pour un espace seulement (canine – deuxi�eme pr�emo-laire maxillaires), nous avons observ�e une distance inter-brackets plus petite du cot�e vestibulaire par rapport au cot�elingual lorsque nous avons compar�e le bracket vestibulaire leplus grand (Smart Clip Clarity) avec le bracket lingual le plus�etroit (STB). Autrement, les forces peuvent etre jusqu’a7,88 fois plus importantes avec une distance interbracketsr�eduite, en particulier lorsque les brackets linguaux utilis�essont assez larges.

Table XIVLoad of the different wires (g), with the minimal and maximumE value. STB brackets (lingual segments 1 and 4).

Tableau XIVCharge des diff�erents fils (g), avec la valeur E minimale etmaximale. Brackets STB (secteurs linguaux 1 et 4).


11–13 Ym = 0.51

Ya = 2698 Ya = 3175 Ya = 1030 Ya = 1584 Ya = 795 Ya = 915 Ya = 608

Yb = 5396 Yb = 6350 Yb = 2060 Yb = 3168 Yb = 1590 Yb = 1831 Yb = 610

Yc = 8094 Yc = 9525 Yc = 3090 Yc = 4752 Yc = 2385 Yc = 2746 Yc = 610

12–14 Ym = 0.58

Ya = 2196 Ya = 2583 Ya = 838 Ya = 1289 Ya = 647 Ya = 774 Ya = 495

Yb = 4392 Yb = 5166 Yb = 1676 Yb = 2578 Yb = 1294 Yb = 1549 Yb = 571

Yc = 6588 Yc = 7749 Yc = 2514 Yc = 3867 Yc = 1941 Yc = 2322 Yc = 571

13–15 Ym = 0.84

Ya = 1258 Ya = 1480 Ya = 480 Ya = 738 Ya = 370 Ya = 443 Ya = 283

Yb = 2516 Yb = 2960 Yb = 960 Yb = 1477 Yb = 741 Yb = 887 Yb = 474

Yc = 3774 Yc = 4440 Yc = 1440 Yc = 2215 Yc = 1111 Yc = 1330 Yc = 474

41–43 Ym = 0.31

Ya = 5600 Ya = 6587 Ya = 2137 Ya = 3287 Ya = 1650 Ya = 1975 Ya = 781

Yb = 11200 Yb = 13175 Yb = 4275 Yb = 6575 Yb = 3300 Yb = 3950 Yb = 781

Yc = 16800 Yc = 19762 Yc = 6412 Yc = 9862 Yc = 4950 Yc = 5925 Yc = 781

42–44 Ym = 0.35

Ya = 4666 Ya = 5490 Ya = 1781 Ya = 2740 Ya = 1375 Ya = 1645 Ya = 734

Yb = 9332 Yb = 10980 Yb = 3562 Yb = 5480 Yb = 2750 Yb = 3291 Yb = 734

Yc = 13998 Yc = 16470 Yc = 5343 Yc = 8220 Yc = 4125 Yc = 4936 Yc = 734

43–45 Ym = 0.73

Ya = 1545 Ya = 1817 Ya = 590 Ya = 907 Ya = 455 Ya = 544 Ya = 348

Yb = 3090 Yb = 3634 Yb = 1180 Yb = 1814 Yb = 910 Yb = 1089 Yb = 508

Yc = 4635 Yc = 5451 Yc = 1770 Yc = 2721 Yc = 1365 Yc = 1633 Yc = 508




The inverse relationship between the load of a wire and thecube of the interbracket distance explains why the stressincreases significantly with small reductions in distance.SS, TMA and Nitinol wires display a linear relationshipbetween stress and strain, as described by Hooke’s law [4].Even if TMA and Nitinol have a lower absolute elasticity valuewith respect to SS, at large deflections, the delivered force isvery high. Consequently, they are not appropriate for the firststages of dental alignment and for lingual mechanotherapy[13].The widespread use of superelastic alloys in orthodonticsoffers new and major treatment possibilities. They are wires

La relation invers�ee entre la charge du fil et le cube de ladistance interbrackets explique l’augmentation significativede la contrainte avec de petites r�eductions de distance.Selon la loi de Hooke [4], les fils SS, TMA et Nitinol montrentune relation lin�eaire entre la contrainte et la flexion. Meme si leTMA et le Nitinol ont une valeur d’�elasticit�e absolue plus faiblepar rapport auSS, a des niveaux de flexion importants, la forceexerc�ee est tr�es �elev�ee, les rendant inappropri�es pour lespremi�eres phases de l’alignement dentaire ainsi qu’enm�ecanoth�erapie linguale [13].L’utilisation fr�equente des alliages super-�elastiques ouvre denouvelles possibilit�es de traitement importantes. Ces fils ont

Table XVLoad of the different wires (g), with the minimum andmaximum E value. Time 2 Micerium brackets (vestibularsegments 1 and 3).

Tableau XVCharge des diff�erents fils (g), avec la valeur E minimale etmaximale. Brackets Time 2 (Micerium) (secteurs vestibulaires1 et 3).


11–13 Ym = 1.54

Ya = 505 Ya = 595 Ya = 193 Ya = 297 Ya = 149 Ya = 178 Ya = 114

Yb = 1011 Yb = 1190 Yb = 386 Yb = 594 Yb = 298 Yb = 357 Yb = 228

Yc = 1516 Yc = 1785 Yc = 579 Yc = 891 Yc = 447 Yc = 535 Yc = 342

12–14 Ym = 1.39

Ya = 589 Ya = 693 Ya = 225 Ya = 346 Ya = 173 Ya = 208 Ya = 133

Yb = 1179 Yb = 1386 Yb = 450 Yb = 692 Yb = 347 Yb = 416 Yb = 266

Yc = 1768 Yc = 2079 Yc = 675 Yc = 1038 Yc = 520 Yc = 624 Yc = 368

13–15 Ym = 1.00

Ya = 965 Ya = 1136 Ya = 368 Ya = 567 Ya = 284 Ya = 340 Ya = 217

Yb = 1931 Yb = 2272 Yb = 737 Yb = 1134 Yb = 569 Yb = 681 Yb = 435

Yc = 2896 Yc = 3408 Yc = 1105 Yc = 1701 Yc = 853 Yc = 1021 Yc = 434

31–33 Ym = 0.91

Ya = 1114 Ya = 1311 Ya = 425 Ya = 654 Ya = 328 Ya = 393 Ya = 251

Yb = 2228 Yb = 2622 Yb = 850 Yb = 1308 Yb = 657 Yb = 786 Yb = 456

Yc = 3342 Yc = 3933 Yc = 1275 Yc = 1962 Yc = 982 Yc = 1179 Yc = 456

32–34 Ym = 1.07

Ya = 868 Ya = 1021 Ya = 331 Ya = 509 Ya = 256 Ya = 306 Ya = 195

Yb = 1736 Yb = 2042 Yb = 663 Yb = 1019 Yb = 512 Yb = 612 Yb = 391

Yc = 2604 Yc = 3063 Yc = 994 Yc = 1528 Yc = 768 Yc = 918 Yc = 419

33–35 Ym = 0.96

Ya = 1023 Ya = 1403 Ya = 390 Ya = 600 Ya = 301 Ya = 360 Ya = 230

Yb = 2046 Yb = 2406 Yb = 780 Yb = 1200 Yb = 603 Yb = 721 Yb = 443

Yc = 3069 Yc = 4209 Yc = 1170 Yc = 1800 Yc = 904 Yc = 1081 Yc = 443




which exhibit elastic behavior at small deflections, so that theload is proportional to the deflection. At large deformations,above a specific value, the elastic deformation is non-linearand the stress remains almost constant. The shorter the inter-bracket distance, the lower the value of the deflections atwhich the martensitic transformation occurs [10].

Muraviev et al. [9] obtained a mathematical formula for thecalculation of the stress that a superelastic wire of knowndiameter provides in the martensitic plateau. For simplicity,

un comportement �elastique a des niveaux de flexion faibles,de telle sorte que la charge est proportionnelle a lad�eformation. En cas de d�eformations importantes,sup�erieures a une valeur sp�ecifique, la d�eformation �elastiquen’est pas lin�eaire et la contrainte reste presque constante. Plusla distance interbrackets est courte, plus faible sera la valeurde flexion a laquelle se produit la transformationmartensitique[10].Muravievet al. [9] ont �elabor�e une formulemath�ematique pourcalculer la contrainte fournie sur le palier martensitique par unfil super-�elastique de diam�etre connu. Pour plus de simplicit�e,

Table XVILoad of the different wires (g), with the minimum andmaximum E value. Innovation GAC brackets (vestibularsegments 2 and 4).

Tableau XVICharge des diff�erents fils (g), avec la valeur E minimale etmaximale. Brackets Innovation (GAC) (secteurs vestibulaires2 et 4).


21–23 Ym = 1.35

Ya = 612 Ya = 720 Ya = 233 Ya = 359 Ya = 180 Ya = 216 Ya = 138

Yb = 1224 Yb = 1440 Yb = 467 Yb = 718 Yb = 360 Yb = 432 Yb = 276

Yc = 1836 Yc = 2160 Yc = 700 Yc = 1077 Yc = 540 Yc = 648 Yc = 373

22–24 Ym = 1.24

Ya = 700 Ya = 823 Ya = 267 Ya = 411 Ya = 206 Ya = 247 Ya = 158

Yb = 1400 Yb = 1647 Yb = 534 Yb = 822 Yb = 412 Yb = 494 Yb = 316

Yc = 2100 Yc = 2470 Yc = 801 Yc = 1233 Yc = 618 Yc = 741 Yc = 390

23–25 Ym = 0.91

Ya = 1114 Ya = 1311 Ya = 425 Ya = 652 Ya = 328 Ya = 393 Ya = 251

Yb = 2228 Yb = 2622 Yb = 850 Yb = 1304 Yb = 657 Yb = 786 Yb = 456

Yc = 3342 Yc = 3933 Yc = 1275 Yc = 1956 Yc = 985 Yc = 1179 Yc = 456

41–43 Ym = 0.80

Ya = 1349 Ya = 1587 Ya = 534 Ya = 792 Ya = 397 Ya = 476 Ya = 304

Yb = 2698 Yb = 3174 Yb = 1068 Yb = 1584 Yb = 795 Yb = 952 Yb = 485

Yc = 4047 Yc = 4761 Yc = 1602 Yc = 2376 Yc = 1192 Yc = 1428 Yc = 485

42–44 Ym = 1.19

Ya = 746 Ya = 878 Ya = 285 Ya = 438 Ya = 220 Ya = 263 Ya = 168

Yb = 1493 Yb = 1756 Yb = 570 Yb = 876 Yb = 440 Yb = 527 Yb = 336

Yc = 2239 Yc = 2634 Yc = 855 Yc = 1314 Yc = 660 Yc = 790 Yc = 398

43–45 Ym = 0.91

Ya = 1103 Ya = 1298 Ya = 421 Ya = 648 Ya = 325 Ya = 389 Ya = 249

Yb = 2206 Yb = 2596 Yb = 842 Yb = 1296 Yb = 650 Yb = 778 Yb = 454

Yc = 3309 Yc = 3894 Yc = 1263 Yc = 1944 Yc = 975 Yc = 1167 Yc = 454




this force is considered to be constant, even if it increasesslightly along the plateau.Miura et al. [11] tested the mechanical proprieties of a super-elastic NiTi wire with a three-point bending test. After drawingthe load-deflection curve, he identified the deflection point ofmartensitic transformation Ym. This allowed him to extract allthe parameters for the calculation of the theoretical force ofthe wire.When we compared elastic and superelastic wires, JapaneseNiTi was shown to exert lower stress, even at small deflections,since its Young’s absolute value is lower than that of SS, TMAand Nitinol. The forces it provides at large deflections arefairly constant, and significantly lower than those generated

cette force est consid�er�ee comme �etant constante, meme sielle diminue l�eg�erement le long du palier.Miura et al. [11] ont test�e les propri�et�es m�ecaniques du fil NiTisuper-�elastique avec un test de pliage en trois points. Apr�esavoir dessin�e la courbe de contrainte–flexion, il identifiait lepoint de flexion de la transformation martensitique Ym. Celui-ci lui permettait de d�eduire tous les param�etres pour calculer laforce th�eorique du fil.Lorsque nous avons compar�e les fils �elastiques et super-�elastiques, le NiTi japonais exercait une contrainte inf�erieure,meme a des niveaux de flexion peu importants, puisque savaleur de Young absolue est inf�erieure a celle du SS, du TMAet du Nitinol. Les forces qu’il d�elivre a des degr�es de flexion

Table XVIILoad of the different wires (g), with the minimum andmaximum E value. Smart Clip Clarity 3M Unitek brackets(vestibular segments 2 and 4).

Tableau XVIICharge des diff�erents fils (g), avec la valeur E minimale etmaximale. Brackets Smart Clip Clarity (3M Unitek) (secteursvestibulaires 2 et 4).


21–23 Ym = 1.18

Ya = 756 Ya = 890 Ya = 289 Ya = 444 Ya = 223 Ya = 267 Ya = 170

Yb = 1513 Yb = 1780 Yb = 578 Yb = 888 Yb = 446 Yb = 534 Yb = 341

Yc = 2269 Yc = 2670 Yc = 867 Yc = 1332 Yc = 669 Yc = 801 Yc = 400

22–24 Ym = 1.11

Ya = 826 Ya = 972 Ya = 315 Ya = 485 Ya = 243 Ya = 291 Ya = 186

Yb = 1653 Yb = 1945 Yb = 630 Yb = 970 Yb = 487 Yb = 583 Yb = 373

Yc = 2479 Yc = 2917 Yc = 945 Yc = 1455 Yc = 730 Yc = 874 Yc = 412

23–25 Ym = 0.76

Ya = 1454 Ya = 1711 Ya = 555 Ya = 854 Ya = 428 Ya = 513 Ya = 328

Yb = 2909 Yb = 3422 Yb = 1110 Yb = 1708 Yb = 857 Yb = 1026 Yb = 498

Yc = 4363 Yc = 5133 Yc = 1665 Yc = 2562 Yc = 1285 Yc = 1539 Yc = 498

41–43 Ym = 0.65

Ya = 1851 Ya = 2177 Ya = 706 Ya = 1087 Ya = 545 Ya = 653 Ya = 417

Yb = 3702 Yb = 4355 Yb = 1413 Yb = 2174 Yb = 1090 Yb = 1306 Yb = 538

Yc = 5553 Yc = 6532 Yc = 2119 Yc = 3261 Yc = 1635 Yc = 1959 Yc = 538

42–44 Ym = 0.95

Ya = 1046 Ya = 1231 Ya = 399 Ya = 614 Ya = 308 Ya = 369 Ya = 236

Yb = 2093 Yb = 2462 Yb = 799 Yb = 1229 Yb = 617 Yb = 738 Yb = 446

Yc = 3139 Yc = 3693 Yc = 1198 Yc = 1843 Yc = 925 Yc = 1107 Yc = 446

43–45 Ym = 0.80

Ya = 1349 Ya = 1587 Ya = 515 Ya = 792 Ya = 397 Ya = 476 Ya = 304

Yb = 2698 Yb = 3174 Yb = 1030 Yb = 1584 Yb = 795 Yb = 952 Yb = 485

Yc = 4047 Yc = 4761 Yc = 1545 Yc = 2376 Yc = 1192 Yc = 1428 Yc = 485




by SS. This means that superelastic wire proprieties are usefulon the vestibular side in cases of large deflections, and on thelingual side, even for small deflections, because of thereduced interbracket distance.

It is noteworthy that the force values reported in the tablesbelong to the loading curve. The stress acting on the teeth isdescribed by the unloading curve. The difference between thetwo curves increases as the hysteresis increases [4].

Miura et al. [11] report that, for the Japanese NiTi wire theytested, the unloading curve was about half the loading curve.

The values we calculated in this study are theoretical sinceseveral of the wire parameters, such as the point of martensitictransformation, were obtained in vitro using three-point bend-ing tests, in ideal and controlled conditions. As reported byWilkinson et al. [14], wire performances can differ signifi-cantly if the experimental model is changed. It must be bornein mind that the friction between the teeth and in the wire-ligation-bracket complex can drastically modify the level ofstress delivered to the teeth [14]. Using elastomeric ligation,Kasuya et al. [8] demonstrated that the friction is so great thatthe behavior of superelastic wire is modified and its propertiesdiminished. Conversely, laboratory tests show that self-ligat-ing brackets enhance the superelastic proprieties of the wire[8].

Although approximate and theoretical, the loading values wefound nevertheless highlight the importance of making anappropriate choice of brackets and wire characteristics, inparticular if lingual mechanics is chosen.

Conclusions

Our hypothesis was supported by the study performed:— the type of bracket has a relevant influence on the inter-bracket distance and, consequently, on the forces delivered tothe teeth;— elastic wires commonly used in the vestibular technique(0.016 SS, Nitinol and TMA) are not suitable for lingual ortho-dontics, in particular during the first phase of treatment onaccount of the excessive forces they generate;— superelastic wires are the first choice in cases of severecrowding and with lingual mechanotherapy, on account oftheir ability to deliver light, continuous forces at largedeflections.

Conflict of interest statement

None.

�elev�es sont assez constantes et significativement moins�elev�ees que celles g�en�er�ees par le SS. Cela signifie que lespropri�et�es du fil super-�elastique utilis�e en vestibulaire sontutiles en pr�esence de flexions importantes, ainsi que du cot�elingual, meme en cas de flexions mineures, en raison de ladistance interbrackets r�eduite.Il est important de noter que les valeurs des forces fourniesdans les tableaux se rapportent a la courbe de charge. Lacontrainte plac�ee sur les dents est d�ecrite par la courbe ded�echarge. La diff�erence entre les deux courbes augmenteavec l’augmentation de l’hyst�er�ese [4].Miura et al. [11] rapportent que, sur le fil NiTi japonais qu’ils onttest�e, la courbe de d�echarge �etait approximativement la moiti�ede la courbe de charge.Les valeurs calcul�ees dans cette �etude sont th�eoriques puis-que plusieurs des param�etres de fil, tel que le point de trans-formation martensitique, �etaient obtenus in vitro en utilisantdes tests de pliage en trois points, dans des conditions decontrole id�eales. Comme l’ont constat�e Wilkinson et al. [14],les performances des fils peuvent varier de facon significativeen cas de changement de mod�ele exp�erimental. On doit tenircompte du fait que la friction entre les dents et dans lecomplexe fil–ligature–bracket peut modifier de facon tr�esconsid�erable le niveau de contrainte s’exercant sur les dents[14]. Utilisant des ligatures �elastom�eriques, Kasuya e al. [8]ont montr�e que la friction est tellement �elev�ee que le compor-tement du fil super-�elastique s’en trouve modifi�e de telle sorteque ses propri�et�es diminuent. Inversement, des tests delaboratoire ont d�emontr�e que les brackets auto-ligaturantsam�eliorent les propri�et�es super-�elastiques du fil [8].Quoique th�eoriques et approximatives, les valeurs de chargeque nous avons trouv�ees nous aident a comprendre a quelpoint il est important, en ce qui concerne les forces d�elivr�ees,de bien choisir ses brackets et les caract�eristiques des fils,surtout lors d’un traitement en technique linguale.

Conclusions

Notre hypoth�ese de d�epart a �et�e confirm�ee par l’�etude :— le type de bracket utilis�e a un impact pertinent sur la dis-tance interbrackets et, en cons�equence, sur les forcesd�elivr�ees aux dents ;— les fils �elastiques utilis�es habituellement en technique ves-tibulaire (0,016 SS, Nitinol et TMA) ne conviennent pas enorthodontie linguale, surtout pendant la premi�ere phase dutraitement en raison des forces excessives qu’ils g�en�erent ;— les fils super-�elastiques sont les fils de choix dans les casd’encombrement s�ev�ere et pour la m�ecanique linguale, enraison de leur capacit�e a d�elivrer des forces l�eg�eres etcontinues avec des degr�es de flexion importants.

Conflit d’int�eret

Aucun.




References/R�ef�erences

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