Wire load-deflection characteristics relative to different types of brackets

Ó 2010 CEO Published by / E´dite´ par Elsevier Masson SAS All rights reserved / Tous droits re´serve´s

Original article Article original

Wire load–deflection characteristics relative to different types of brackets
ristiques de charge– Comparaison des caracte
rents types de brackets flexion de fils selon diffe Luca LOMBARDOa1,*, Angela ARREGHINIa2, Kholoud AL ARDHAb, Giuseppe SCUZZOa1, Kyoto TAKEMOTOc1, Giuseppe SICILIANIa3 a

Department of Orthodontics, University of Ferrara, Via Montebello, 31, Ferrara 44100, Italy Dubai, PO Box 212482, Dubai, United Arab Emirates c 2-5-7 Kudanminami, Chiyoda, Tokyo, 102-0074 Japan b

Available online: 3 Febuary 2011 / Disponible en ligne : 3 fe
vrier 2011

Summary


sume
Re

Objective: To test the hypothesis that the dimension of the bracket, both in labial and in lingual orthodontics, is a relevant parameter to determine the forces acting on the teeth, and that some wires commonly used in labial orthodontics (0.016”diameter SS, TMA and Nitinol) are not suitable for the first phase of lingual treatment. Materials and methods: An ideal dental cast was bonded with eight 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). After photographic documentation, the interbracket distance was calculated for each type of bracket, using ImageJ software. The mean elasticity modulus of the tested wires was obtained from the review of the available literature. The theoretical wire load on every tooth was calculated mathematically at three different levels of deflection (0.5 mm; 1.0 mm and 1.5 mm), on both the labial and lingual sides, for all types of bracket.

 que (a) les dimensions des bracObjectif : Tester l’hypothese  pertinent, en orthodontie vestibulaire kets sont un parametre
et linguale, pour determiner les forces agissant sur les dents et
en orthodontie (b) que certains fils habituellement utilises vestibulaire (0.016 SS, TMA et Nitinol) ne conviennent pas  phase de traitement vestibulaire. a` la premiere

 dentaire ideal,
nous Materiaux et methodes : Sur un modele
avons colle
huit brackets differents (Damon 3MX, Ovation, Time 2, Innovation et Smart Clip Clarity en vestibulaire ;  prise STB, Adenta Time et Innovation-L en lingual). Apres
e
calculee
pour chade photos, la distance interbrackets a et que type de bracket utilisant le logiciel ImageJ. Le module

a et
e
obtenu en effectuant d’elasticit e
moyen des fils testes
une revue de la litterature disponible. Au moyen de calculs


mathematiques, nous avons determin e
la charge theorique
par les fils sur chaque dent a` trois valeurs de flexion appliquee ^ es
lingual et vestibu(0,5 mm ; 1,0 mm et 1,5 mm), des cot laire, pour chaque type de bracket.
Resultats : L’arcade linguale est toujours plus courte dans le

segment anterieur que l’arcade vestibulaire. Les differents
brackets, ayant des dimensions differentes, influent sur la
distance interbrackets et, par consequent, sur la charge sur
de flexion importants, le Superelastic NiTi le fil. A` des degres
eres  exprime des forces leg continues qui sont significative

ment plus faibles qu’avec les autres alliages etudi es.

Results: The lingual arch in the anterior segment is always shorter than the vestibular arch. The different brackets, having different dimensions, have an influence on the interbracket distance, and, consequently, on the wire load. At large deflections, superelastic NiTi expresses light and continuous forces, which are significantly lower than the other examined alloys.

Correspondence and reprints / Correspondance et tire
s a` part. e-mail address / Adresse e-mail : [email protected] (Luca Lombardo) 1 Member of the University of Ferrara, postgraduate school of orthodontics (professor). 2 Member of the University of Ferrara, postgraduate school of orthodontics (postgraduate student). 3 Member of the University of Ferrara, postgraduate school of orthodontics (chairman). *

120

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

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

Conclusion: The initial hypothesis was supported. Because of the reduced interbracket distance, the adoption of superelastic wires is required in lingual mechanics and with smaller diameter compared to labial mechanotherapy, in particular during the first phases of treatment. The use of a bracket with reduced mesiodistal dimensions can contribute to reduce the load on the teeth. Ó 2010 CEO. Published by Elsevier Masson SAS. All rights reserved

 initiale a et
e
confirmee.
En raison Conclusion : L’hypothese

de la distance interbrackets reduite, les fils super-elastiques

 sont necessaires en mecanique linguale avec un diametre
plus petit par rapport a` la mecanique vestibulaire, surtout  pendant les premieres phases du traitement. L’utilisation

d’un bracket avec des dimensions mesiodistales reduites peut contribuer a` diminuer la charge sur les dents. Ó 2010 CEO. E´dite´ par Elsevier Masson SAS. Tous droits re´serve´s

Key-words


s Mots-cle

·· ·

Interbracket distance. Superelasticity. Lingual mechanotherapy.

·· ·

Distance interbrackets.
lasticite
. Super-e
canothe
rapie linguale. Me

Introduction

Introduction

Lingual orthodontics is an effective alternative to traditional vestibular appliances, in particular for those patients who want to preserve a pleasant smile during the whole treatment time. Hohoff, investigating the reasons why people choose lingual orthodontics, found that their main aim is to preserve their professional image as they did not wish to be seen with a conspicuous metal appliance [1].

L’orthodontie linguale offre une alternative efficace aux appareils vestibulaires traditionnels, surtout chez les patients
sirant conserver un sourire agre
able pendant toute la dure
e de
tudie
les raisons pour lesdu traitement. Hohoff et al. ont e quelles les patients choisissent l’orthodontie linguale et ont
que leur objectif principal e
tait de pre
server leur image trouve
vitant de se montrer avec un appareil professionnelle en e
tallique clairement visible en bouche [1]. me
anmoins, il est impossible de faire un simple transfert de la Ne
canique vestibulaire a` la me
canique linguale en raison des me
rentes conditions qui caracte
risent les deux faces [2]. diffe
rence principale par rapport a` l’orthodontie convenLa diffe
duite : l’arcade tionnelle est la distance interbrackets plus re vestibulaire est significativement plus longue que l’arcade lin
gion mandibulaire ante
rieure [3]. guale, surtout dans la re Les brackets linguaux et vestibulaires disponibles sur le
ont des dimensions me
siodistales diffe
rentes, ce qui marche influe sur la distance interbrackets.
e par les fils orthodontiques e
lastiques est La force exerce inversement proportionnelle au cube de la distance inter
sulte que me ^me des re
ductions minimes brackets [4]. Il en re de la longueur d’arcade produiront une augmentation signifi
e a` la dent. cative de la force applique
es, l’alignement dentaire a e
te
Depuis de nombreuses anne
alise
avec des fils en acier inoxydable (SS). En 1978, pour la re re fois, Andreasen et Morrow ont de
crit les be
ne
fices, premie pour la pratique orthodontique [5], du Nitinol, qui propose une
lasticite
semblable a` celle de l’acier, mais avec moins de e
. rigidite
te
introduit en 1979 et rapidement adopte
en Le TMA a e
s : excellente me
moire de forme, raison de ses qualite
faible, bonne formabilite
et soudage direct. Le coeffirigidite
leve
qu’avec cient de friction est significativement plus e d’autres alliages [6].

However, it is not possible to simply transfer vestibular mechanics to lingual devices because of the different conditions prevailing on the two surfaces [2]. The main difference compared with traditional orthodontics is the smaller interbracket distance: the labial arch is significantly longer than the lingual arch, in particular in the mandibular anterior region [3]. The commercially available lingual and vestibular brackets have different mesiovestibular dimensions, and this influences interbracket distance. The force of elastic orthodontic wires is inversely proportional to the cube of the interbracket distance [4]. This means that even small reductions in the arch length lead to a significant increase in the force applied to the tooth. For many years, dental alignment was carried out with stainless steel (SS) wires. In 1978, for the first time, Andreasen and Morrow described the beneficial characteristics for orthodontic practice [5] of Nitinol, which displays elastic behavior similar to SS, but with lower stiffness. TMA was introduced in 1979 and was quickly adopted on account of its properties: excellent shape memory, low stiffness, good formability and direct welding. The coefficient of friction is significantly higher than with other alloys [6].

International Orthodontics 2011 ; 9 : 120-139

121

Luca LOMBARDO et al.

In comparative mechanical studies carried out by Drake et al., TMA has shown greater elasticity and springback than SS making 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 account of their particular mechanical characteristics [8]. At small deflections they exhibit elastic behavior. Hence, the load is proportional to the deflection. However, after a given amount of wire deformation, NiTi “martensitic transformation” occurs as the shape of the crystals changes and the wire develops superelastic mechanical properties. As the deflection increases, the stress value remains fairly constant. This characteristic 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 curve is different from the unloading curve. The difference between them is called “hysteresis”. The unloading curve has greater clinical value since it represents the forces acting on the teeth [10]. The increasing demand for lingual orthodontic treatment is forcing orthodontists to learn how to choose the appropriate type of bracket and wire and to exert physiological forces on the teeth without triggering root resorption [3]. The aim of this study was to test the hypothesis that the dimension of the bracket, in both labial and lingual orthodontics, is a relevant parameter when determining the forces that act on the teeth and that some wires commonly used in labial orthodontics are unsuitable for the first phase of lingual treatment.


tudes me
caniques comparatives re
alise
es par Dans les e
une e
lasticite
et un retour Drake et al., le TMA a montre
lastique supe
rieurs au SS, ce qui le rend utile dans les cas e
ve res [7]. de malocclusions se res anne
es, les fils super-e
lastiques en NiTi ont e
te
Ces dernie
s lors des premiers stades de l’aligneintroduits, surtout utilise
ristiques me
caniques ment dentaire, en raison de leurs caracte ` de faibles flexions, ils ont un comportement res [8]. A particulie
lastique. En conse
quence, la charge est proportionnelle a` la e s un certain degre
de de
formation, le flexion. Cependant, apre fil en NiTi subit une « transformation martensitique » se
risant par un changement de forme des cristaux et le caracte
veloppement de proprie
te
s me
caniques super-e
lastiques. de Avec l’augmentation de la flexion, la valeur de la contrainte
crivant ainsi ce qui est appele
le reste assez constante, de « palier martensitique » sur la courbe charge–flexion [9].
ristique de l’alliage NiTi concerne la Une seconde caracte
rencie de la courbe de de
charge. courbe de charge, qui se diffe
rence entre les deux courbes s’appelle l’hyste
re se. La La diffe
charge a plus d’inte
re ^ t dans le contexte clinique courbe de de
sente les forces qui s’exercent sur les dents puisqu’elle repre [10]. La demande accrue de traitement orthodontique lingual oblige les orthodontistes a` apprendre a` choisir les types de brackets
s afin d’exercer des forces physiologiques et de fils approprie
sorptions radiculaires [3]. sur les dents sans provoquer de re
tude e
tait de tester l’hypothe se selon L’objectif de cette e laquelle, d’une part, la dimension du bracket, en technique linguale comme en technique vestibulaire, constitue un paratre pertinent pour de
terminer les forces agissant sur les me s utilise
s en orthodontie dents et, d’autre part, certains fils tre re phase d’un vestibulaire ne conviennent pas a` la premie traitement en lingual.

Materials and methods


riaux et me
thodes Mate

To calculate the different interbracket distances when various brackets were used, an ideal dental cast was chosen for its characteristics: it featured right and left symmetrical halfarches, molar and canine Class I, normal overjet and overbite, no rotations and no diastemas. Incisors, canines and premolars were bonded on both the labial 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 lingual brackets at segments 1 and 4 were removed (GAC Innovation-L and Evolution Brackets Adenta, respectively), and STB brackets were bonded (fig. 2). Then, the dental cast was bonded as follows (fig. 3):


rentes distances interbrackets des Pour calculer les diffe
s, nous avons choisi un mode le dentaire divers brackets utilise
al en raison de ses caracte
ristiques : he
mi-arcades droite ide
triques, absence de rotations et de diaste mes. et gauche syme

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

122


molaires ont e
te
colle
es sur les Les incisives, canines et pre deux faces, vestibulaire et linguale, avec quatre types de
rents, et de la manie re suivante (fig. 1) : brackets diffe — 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. me temps, apre s prise de photographies, les Dans un deuxie
te
de
pose
s (GAC brackets linguaux des secteurs 1 et 4 ont e Innovation-L et Evolution Brackets Adenta, respectivement) et
te
colle
s (fig. 2). des brackets STB ont e le dentaire a e
te
colle
avec les prescriptions Ensuite, le mode suivantes (fig. 3) : — Time 2 Bracket (Micerium) : secteurs 1 et 3 ;

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

[(Fig._1)TD$IG]

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 2 and 4; Evolution brackets (by Adenta) in lingual segments 2 and 4.
avec : Damon 3MX (Ormco) sur les secteurs vestibulaires 1 et 3 ; Fig. 1 : a-b : typodont colle Innovation-L (GAC) sur les secteurs linguaux 1 et 3 ; Ovation (GAC) sur les secteurs vestibulaires 2 et 4 ; Evolution Brackets (Adenta) sur les secteurs linguaux 2 et 4.

[(Fig._2)TD$IG]

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 1 and 4.
avec : Damon 3MX (Ormco) sur les secteurs vestibulaires 1 et 3 ; Fig. 2 : a-b : typodont colle 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.

— 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 (four on the labial side and two on the lingual) and two were traditional (one on the labial side and one on the lingual). The bonded casts were photographed with a gauge to calculate the proportions. Then, the digital images were analyzed with ImageJ software (National Institute of Health).

International Orthodontics 2011 ; 9 : 120-139

— Innovation (GAC) : secteurs 2 et 4.
te
de
pose
s et des Smart Clip Enfin, les Time 2 Brackets ont e
te
colle
s sur les secteurs 2 et 4 (fig. 4). Clarity (3M Unitek) ont e
s dans cette e
tude e
taient autoSix types de brackets utilise ligaturants (quatre en vestibulaire et deux en lingual) et deux
taient traditionnels (un en vestibulaire et un en lingual). e les colle
s e
taient photographie
s avec une jauge afin Les mode
rise
es de calculer les proportions. Ensuite, les images nume
te
analyse
es avec le logiciel ImageJ (National Institute of ont e Health).

123

Luca LOMBARDO et al.

[(Fig._3)TD$IG]

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.
avec : Time 2 bracket (Micerium) sur les secteurs 1 et 3 ; Innovation Fig. 3 : a-b : typodont colle (GAC) sur les secteurs 2 et 4.

[(Fig._4)TD$IG]

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.
avec : Smart Clip Clarity (3M Unitek) sur les secteurs 2 et 4 ; Time 2 Fig. 4 : a-b : typodont colle Bracket (Micerium) sur les secteurs 1 et 3.

The interbracket distance was taken as the distance from the distal edge of the bracket on the mesial tooth to the mesial edge of the bracket on the distal tooth (i.e. to calculate the stress on tooth 12, the measurement was taken from the distal edge of bracket 1.1 and the mesial edge of the bracket on 13). Based on the observed interbracket distance, we calculated the hypothetical force produced by an ideal wire on a misaligned tooth, at three different levels of deflection in the horizontal plane: 0.5 mm, 1.0 mm, 1.5 mm. Four round 0.016 wires were used to calculate the load. The modulus of elasticity of the most widely used orthodontic wires was taken from the studies by Miura et al. [11] and Verstrynge et al. [6]: — SS: 17–20
103 kg/mm2; — Nitinol: 5–6
103 kg/mm2; 124


e e
tait la distance entre le La distance interbrackets adopte
siale et le bord me
sial du bord distal du bracket de la dent me bracket de la dent distale (c.-a`-d. pour calculer la contrainte
tait prise entre le bord distal du bracket de sur la 12, la mesure e
sial du bracket de la 13). la 11 et le bord me
e, nous Nous basant sur la distance interbrackets observe
la force hypothe
tique produite par un fil ide
al avons calcule
ale en malposition a` trois niveaux de flexion sur une dent ide dans le plan horizontal : 0,5 mm ; 1,0 mm et 1,5 mm.
te
utilise
s pour calculer la charge. Quatre fils ronds 0,016 ont e
lasticite
des fils orthodontiques les plus utilise
s a Le module d’e
te
emprunte
aux e
tudes de Miura et al. [11] et de Verstrynge e et al. [6] : — SS : 17–20
103 kg/mm2 ; — Nitinol : 5–6
103 kg/mm2 ;

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

— TMA: 6.5 – 10
103 kg/mm2; — Japanese NiTi: 3.8
103 kg/mm2. SS, TMA and Nitinol are elastic wires. The Japanese NiTi tested by Miura et al. [11] is superelastic, so the Ym parameter was found for every interbracket distance. Ym is the level of deflection at which the wire changes its behavior from elastic to superelastic. It is different for every interbracket distance. This value is needed to choose the mathematical formulae to use at the different levels of deflection. To calculate the stress acting on a single tooth at different deflections, the following mathematical formulae were used [9]. For elastic wires: F¼

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 plane This mathematical relationship is also valid for superelastic wires in the elastic range (the linear part of the curve). However, for the superelastic plateau, a different formula is required [9]: F¼

16 IEU LD

U is an alloy parameter which can be estimated using a threepoint bending test to identify the point of martensitic transformation Ym. The following formula is then applied [9]: U¼

12 DY m L2

— TMA : 6,5–10
103 kg/mm2 ; — NiTi japonais : 3,8
103 kg/mm2.
lastiques. Le NiTi japonais SS, TMA et Nitinol sont des fils e
par Miura et al. [11] est super-e
lastique. Ainsi, le parateste tre Ym a e
te
retrouve
pour chaque distance interbrackets. me
flexion auquel le comportement du fil se Ym est le niveau de de
lastique en super-e
lastique. Il est diffe
rent pour transforme d’e chaque distance interbrackets. Cette valeur est essentielle
matiques a` adopter aux diffe
pour choisir les formules mathe rents niveaux de flexion. Pour calculer la contrainte s’exer¸cant sur une dent unique
rentes, nous avons utilise
les formules a` des flexions diffe
matiques suivantes [9]. mathe
lastiques : Pour les fils e

F¼

192 IEY L3

avec :
lasticite
— E : module d’e — I : moment d’inertie : pD4/64 tre du fil : 0,016 = 0,41 mm — D : diame — L : distance interbrackets — Y : flexion dans le plan horizontal
quation est e
galement valable pour les fils superCette e
lastiques dans la gamme e
lastique (la partie line
aire de la e
lastique, une forcourbe). Cependant, pour le plateau super-e
rente est ne
cessaire [9] : mule diffe

F¼

16 IEU LD

tre d’alliage qui peut e ^tre calcule
en utilisant U est un parame un test de pliage en trois points pour identifier le point de transformation martensitique Ym. Dans ce cas, la formule
e [9] : suivante est employe

U¼

12 DY m L2

Results


sultats Re

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


rents types de brackets Les distances interbrackets des diffe
es dans les Tableaux I–VIII. sont donne Notez que la distance vestibulaire est toujours plus grande que la distance linguale. La seule exception est la distance canine me pre
molaire maxillaire ou` la face vestibulaire est – deuxie
e avec des brackets Smart Clip Clarity et la face linguale colle
e avec des brackets STB. La distance interbrackets est modifie de fa¸con significative avec les changements de type de bracket.
es avec Dans le secteur vestibulaire, les dents maxillaires colle des brackets Time 2 avaient une distance interbrackets plus
es avec d’autres brackets dans l’e
tude, grande que celles colle s par les Damon 3MX. La distance interbrackets suivis de pre
tait plus grande que pour les Ovation des Innovation GAC e GAC.

In the vestibular segment, the maxillary teeth bonded with Time 2 brackets showed a longer interbracket distance compared to those bonded with other brackets in the study, followed closely by Damon 3MX. The maxillary interbracket distance for Innovation GAC was longer than that for Ovation GAC.

International Orthodontics 2011 ; 9 : 120-139

125

Luca LOMBARDO et al.

Table I

Tableau I

Evolution Brackets Adenta interbracket distances (lingual segments 2 and 4).

Evolution 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 II

Tableau II

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

Innovation-L (GAC) : distances interbrackets (secteurs linguaux 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 III

Tableau III

Damon 3MX Ormco interbracket distances (vestibular segments 1 and 3).

Damon 3MX (Ormco) : distances interbrackets (secteurs vestibulaires 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

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

126

` l’arcade mandibulaire, il faut distinguer entre les secteurs A
rieurs et poste
rieurs. Dans l’espace incisive centrale– ante
une distance interbrackets plus canine, nous avons observe grande avec les Time 2 Bracket, suivis des brackets Damon,
gion poste
rieure de l’arcade, Innovation et Ovation. Dans la re ce sont les brackets Ovation et Innovation qui avaient la distance interbrackets la plus importante suivis des Damon 3X et des Time 2. Les boıˆtiers Smart Clip Clarity avaient la

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

Table IV

Tableau IV

Ovation GAC interbracket distances (vestibular segments 2 and 4).

Ovation (GAC) : distances interbrackets (secteurs vestibulaires 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 V

Tableau V

STB interbracket distances (lingual segments 1 and 4).

STB : 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 VI

Tableau VI

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

Time 2 (Micerium) : distance interbrackets (secteurs vestibulaires 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

mandibular and the maxillary arch, and therefore the shortest interbracket distance among the samples analyzed. In the lingual segment, with respect to the other tested brackets, the STB had a greater interbracket distance for both the maxillary and the mandibular arch. The segment of maxillary arch bonded with Evolution brackets had a greater interbracket distance than the section bonded

International Orthodontics 2011 ; 9 : 120-139


siodistale la plus grande aux deux arcades et, dimension me
quent, la distance interbrackets la plus courte parmi par conse
chantillons e
tudie
s. les e Dans la zone linguale, les brackets STB avaient une distance interbrackets plus grande par rapport aux autres brackets
s aux deux arcades. teste
avec des brackets Le secteur de l’arcade maxillaire colle Evolution avait une distance interbrackets plus grande que

127

Luca LOMBARDO et al.

Table VII

Tableau VII

Innovation GAC interbracket distance (vestibular segments 2 and 4).

Innovation (GAC) : distance interbrackets (secteurs vestibulaires 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 VIII

Tableau VIII

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

Smart 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

with Innovation-L. Conversely, in the mandible, a shorter interbracket distance was found with Evolution compared to Innovation-L. The ratio of the vestibular to the lingual interbracket distance for every tooth and for every pair of brackets is reported in Table IX. Considering the same tooth, the type of brackets significantly influenced the ratio of the vestibular to lingual interbracket distance, which ranged from a minimum value of 0.95 to a maximum of 1.99. The former was the maxillary canine-second premolar space, bonded with Smart Clip Clarity on the vestibular side and with STB on the lingual. The second was the mandibular central incisor-canine, bonded with vestibular Time 2 brackets and lingual Evolution brackets. Given that the load of an orthodontic wire is inversely proportional to the cube of the interbracket distance, the result was that, for the same wire diameter, lingual appliances provided forces which were up to 7.88 times greater than labial appliances. The single stress values applied on the teeth bonded with the different brackets are reported in Tables X–XVII.

128


avec Innovation-L. Inversement, a` la mandibule, celui colle
une distance interbrackets plus courte avec nous avons trouve Evolution par rapport a` Innovation-L. Le rapport vestibulaire/lingual de la distance interbrackets est
dans le Tableau IX. donne Quelle que soit la dent, le type de bracket a eu un impact significatif sur le rapport vestibulaire/lingual de la distance interbrackets qui variait entre une valeur minimale de 0,95 et re correspondait une valeur maximale de 1,99. La premie me pre
molaire maxila` l’espace entre la canine et la deuxie
es avec des brackets Smart Clip Clarity du co ^ te
laires, colle ^ te
lingual. La seconde vestibulaire et avec des STB du co correspondait a` l’espace entre l’incisive centrale et la canine
es avec des brackets Time 2 vestibulaires mandibulaires colle et des brackets linguaux Evolution.

que la charge d’un fil orthodontique est inverseEtant donne ment proportionnelle au cube de la distance interbrackets, il ^me diame tre de fil, les appareils linressort que, pour le me
taient jusqu’a` 7,88 fois plus guaux exer¸caient des forces qui e grandes que les appareils vestibulaires. ^me contrainte applique
e aux dents colLes valeurs de la me
es avec les diffe
rents brackets sont rapporte
es dans les le Tableaux X–XVII.

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

Table IX

Tableau IX

Ratio of the vestibular to the lingual interbracket distance, for every pair of brackets.

Rapport vestibulaire/lingual de la distance interbrackets pour chaque paire de brackets.

Adenta Time

GAC Innovation-L

STB

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

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

1–3 Mx

1.84

1.90

1.74

2–4 Mx

1.60

1.69

1.55

Damon 3MX

Ovation

Time 2

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

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

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

Innovation

Smart Clip Clarity

International Orthodontics 2011 ; 9 : 120-139

129

Luca LOMBARDO et al.

Table X

Tableau X

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

SS min

SS max

TMA min


rents fils (g), avec la valeur E minimale et Charge des diffe
rents fils (g). Evolution Adental Bracket maximale des diffe (secteurs linguaux 2 et 4).

TMA max

Nitinol min

Nitinol max

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

Among the elastic wires (SS, TMA, Nitinol), the load increased proportionally to the deflection (0.5 mm, 1.0 mm, 1.5 mm) and it increased with the modulus of elasticity. SS had the highest Young’s absolute value (17–20
103 kg/mm2), followed by TMA (6.5–10
103 kg/mm2) and Nitinol (5–6
103 kg/ mm2). Superelastic Japanese NiTi has a lower modulus of elasticity compared to the other wires considered. Consequently, even at small deflections, in the elastic interval, it provides lighter forces than the other wires.

130

NiTi Giapp


lastiques (SS, TMA, Nitinol), la charge augmenParmi les fils e tait proportionnellement a` la flexion (0,5 mm ; 1,0 mm, 1,5
lasticite
. L’acier avait mm) et augmentait avec le module d’e
leve
e (17–20
103 kg/ la valeur absolue de Young la plus e mm2), suivi du TMA (6,5–10
103 kg/mm2) et du Nitinol (5–6
103 kg/mm2).
lastique avait un module d’e
lasticite
Le NiTi japonais super-e
aux autres fils e
tudie
s. Par conse
quent, plus faible compare ^me a` des de
flexions peu importantes, dans l’intervalle me
lasticite
, il de
livrait des forces plus le
ge  res que les autres fils. d’e

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

Table XI

Tableau XI

Load of the different wires (g), with the minimum and maximum E value. Innovation- L GAC brackets (lingual segments 1 and 3).

SS min

SS max

TMA min


rents fils (g), avec la valeur E minimale et Charge des diffe maximale. Brackets Innovation-L GAC (secteurs linguaux 1 et 3).

TMA max

Nitinol min

Nitinol max

11–13

NiTi Giapp 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

The superelastic transition point Ym changes with the different interbracket distances: on the dental cast in the study, the minimum value was 0.23 mm, corresponding to the shortest interbracket distance (lingual Evolution, between 41 and 43), and its maximum value was 1.54 mm (vestibular Smart Clip Clarity, between 11 and 13). This superelastic wire provided lower forces than the other wires, in particular with reduced interbracket distance.

International Orthodontics 2011 ; 9 : 120-139


lastique Ym varie selon les Le point de transition super-e
rentes distances inter-e
lastiques : sur le mode le dentaire diffe
tude, la valeur minimale e
tait de 0,23 mm, cordans cette e respondant a` la distance interbrackets la plus courte
tait (Evolution lingual entre 41 et 43). La valeur maximale e de 1,54 mm (Smart Clip Clarity vestibulaire entre 11 et 13).
lastique de
livrait des forces plus le
ge  res que les Ce fil super-e autres fils, en particulier dans le cas de distances interbrack
duites. ets re

131

Luca LOMBARDO et al.

Table XII

Tableau XII

Load of the different wires (g), with the minimum and maximum E value. Damon 3MX Ormco brackets (vestibular segments 1 and 3).

SS min

SS max

TMA min


rents fils (g), avec la valeur E minimale et Charge des diffe maximale. Brackets Damon 3MX (Ormco) (secteurs vestibulaires 1 et 3).

TMA max

Nitinol min

Nitinol max

11–13

NiTi Giapp 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

Discussion

Discussion

The results of this study demonstrate the importance of interbracket distance in determining the load of a wire on a single tooth. According to the study by Schudy and Schudy [12], the deflection of an orthodontic wire is directly proportional to the interbracket distance and inversely proportional to the wire cross-section. The delivered force increases with decreasing tooth size. Hence, the decrease in interbracket space. As a result, to reduce wire stress on the teeth, orthodontists must


sultats de cette e
tude soulignent l’importance de la Les re
terminer la charge de
livre
e distance interbrackets pour de
e. par un fil a` une dent donne
tude de Schudy et Schudy [12], la flexion En accord avec l’e d’un fil orthodontique est directement proportionnelle a` la distance interbrackets et inversement proportionnelle a` la section
livre
e augmente avec la diminution de la taille du fil. La force de de la dent. D’ou` la diminution de l’espace interbrackets. Par
quent, pour re
duire la contrainte impose
e par le fil aux conse

132

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

Table XIII

Tableau XIII

Load of the different wires (g), with the minimum and maximum E value. Ovation GAC brackets (vestibular segments 2 and 4).

SS min

SS max

TMA min


rents fils (g), avec la valeur E minimale et Charge des diffe maximale. Brackets Ovation GAC (secteurs vestibulaires 2 et 4).

TMA max

Nitinol min

Nitinol max

21–23

NiTi Giapp 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

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

Ya = 393

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

use elastic wires with a smaller cross-section, and also brackets with relatively small dimensions. The type of bracket becomes a relevant parameter when lingual mechanics is used, as can be seen from the comparison of the eight types of tested appliances. In his 1987 study, Moran [2] found that the mean ratio of the vestibular-to-lingual interbracket distance in anterior segments is 1.47. Thus, the forces delivered on the lingual side are about three times greater than on the labial side. This finding is confirmed by the measurements taken in our work:

International Orthodontics 2011 ; 9 : 120-139


lastiques avec un diadents, le praticien doit utiliser des fils e tre re
duit de me ^me que des brackets avec des dimensions me
devient un pararelativement petites. Le type de bracket utilise tre pertinent lorsqu’une me
canique linguale est adopte
e, me comme le fait apparaıˆtre une comparaison des huit types de
s. dispositifs teste
tude datant de 1987, Moran [2] a trouve
que le Dans son e rapport vestibulolingual moyen pour la distance interbrackets
rieurs e
tait de 1,47. Ainsi, les forces dans les segments ante
es du co ^ te
lingual sont trois fois plus importantes que exerce ^ te
vestibulaire. Ce re
sultat est confirme
par les mesures du co

133

Luca LOMBARDO et al.

Table XIV

Tableau XIV

Load of the different wires (g), with the minimal and maximum E value. STB brackets (lingual segments 1 and 4).

SS min

SS max

TMA min


rents fils (g), avec la valeur E minimale et Charge des diffe maximale. Brackets STB (secteurs linguaux 1 et 4).

TMA max

Nitinol min

Nitinol max

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

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

12–14

Ym = 0.58

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 values we found ranged from a minimum of 0.95 to a maximum of 1.99. In the posterior regions of the arch, the forces on the lingual side are comparable with those on the vestibular side, because of the similar interbracket distance. In only one space (maxillary canine-second premolar), the vestibular interbracket distance was found to be smaller than the lingual one, when comparing the larger vestibular bracket (Smart Clip Clarity) with the shorter lingual one (STB). Otherwise, the forces can be up to 7.88 times larger where the interbracket distance is smaller, in particular when relatively large lingual brackets are used.

134

NiTi Giapp


es dans notre e
tude : les valeurs que nous avons releve
es allaient de 0,95 a` un maximum de 1,99. Dans les trouve
gions poste
rieures de l’arcade, les forces du co ^ te
lingual re
es du co ^te
vestibulaire en sont semblables a` celles retrouve
entre les distances interbrackets respecraison de la similarite me pre
motives. Pour un espace seulement (canine – deuxie
une distance interlaire maxillaires), nous avons observe ^te
vestibulaire par rapport au co ^ te
brackets plus petite du co
le bracket vestibulaire le lingual lorsque nous avons compare plus grand (Smart Clip Clarity) avec le bracket lingual le plus
troit (STB). Autrement, les forces peuvent e ^tre jusqu’a` e 7,88 fois plus importantes avec une distance interbrackets
duite, en particulier lorsque les brackets linguaux utilise
s re sont assez larges.

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

Table XV

Tableau XV

Load of the different wires (g), with the minimum and maximum E value. Time 2 Micerium brackets (vestibular segments 1 and 3).

SS min

SS max

TMA min


rents fils (g), avec la valeur E minimale et Charge des diffe maximale. Brackets Time 2 (Micerium) (secteurs vestibulaires 1 et 3).

TMA max

Nitinol min

Nitinol max

11–13

NiTi Giapp 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

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

International Orthodontics 2011 ; 9 : 120-139


e entre la charge du fil et le cube de la La relation inverse distance interbrackets explique l’augmentation significative
ductions de distance. de la contrainte avec de petites re Selon la loi de Hooke [4], les fils SS, TMA et Nitinol montrent
aire entre la contrainte et la flexion. Me ^me si le une relation line
lasticite
absolue plus faible TMA et le Nitinol ont une valeur d’e par rapport au SS, a` des niveaux de flexion importants, la force
e est tre s e
leve
e, les rendant inapproprie
s pour les exerce res phases de l’alignement dentaire ainsi qu’en premie
canothe
rapie linguale [13]. me
quente des alliages super-e
lastiques ouvre de L’utilisation fre
s de traitement importantes. Ces fils ont nouvelles possibilite

135

Luca LOMBARDO et al.

Table XVI

Tableau XVI

Load of the different wires (g), with the minimum and maximum E value. Innovation GAC brackets (vestibular segments 2 and 4).

SS min

SS max

TMA min


rents fils (g), avec la valeur E minimale et Charge des diffe maximale. Brackets Innovation (GAC) (secteurs vestibulaires 2 et 4).

TMA max

Nitinol min

Nitinol max

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

which exhibit elastic behavior at small deflections, so that the load is proportional to the deflection. At large deformations, above a specific value, the elastic deformation is non-linear and the stress remains almost constant. The shorter the interbracket distance, the lower the value of the deflections at which the martensitic transformation occurs [10]. Muraviev et al. [9] obtained a mathematical formula for the calculation of the stress that a superelastic wire of known diameter provides in the martensitic plateau. For simplicity,

136

NiTi Giapp


lastique a` des niveaux de flexion faibles, un comportement e de telle sorte que la charge est proportionnelle a` la
formation. En cas de de
formations importantes, de
rieures a` une valeur spe
cifique, la de
formation e
lastique supe
aire et la contrainte reste presque constante. Plus n’est pas line la distance interbrackets est courte, plus faible sera la valeur de flexion a` laquelle se produit la transformation martensitique [10].
labore
une formule mathe
matique pour Muraviev et al. [9] ont e calculer la contrainte fournie sur le palier martensitique par un
lastique de diame tre connu. Pour plus de simplicite
, fil super-e

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

Table XVII

Tableau XVII

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

SS min

SS max

TMA min


rents fils (g), avec la valeur E minimale et Charge des diffe maximale. Brackets Smart Clip Clarity (3M Unitek) (secteurs vestibulaires 2 et 4).

TMA max

Nitinol min

Nitinol max

21–23

NiTi Giapp 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

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

Ya = 417

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

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

International Orthodontics 2011 ; 9 : 120-139


re
e comme e
tant constante, me ^me si cette force est conside
ge rement le long du palier. elle diminue le
les proprie
te
s me
caniques du fil NiTi Miura et al. [11] ont teste
lastique avec un test de pliage en trois points. Apre s super-e
la courbe de contrainte–flexion, il identifiait le avoir dessine point de flexion de la transformation martensitique Ym. Celui
duire tous les parame tres pour calculer la ci lui permettait de de
orique du fil. force the
les fils e
lastiques et superLorsque nous avons compare
lastiques, le NiTi japonais exer¸cait une contrainte infe
rieure, e ^me a` des niveaux de flexion peu importants, puisque sa me
rieure a` celle du SS, du TMA valeur de Young absolue est infe
livre a` des degre
s de flexion et du Nitinol. Les forces qu’il de

137

Luca LOMBARDO et al.

by SS. This means that superelastic wire proprieties are useful on the vestibular side in cases of large deflections, and on the lingual side, even for small deflections, because of the reduced interbracket distance. It is noteworthy that the force values reported in the tables belong to the loading curve. The stress acting on the teeth is described by the unloading curve. The difference between the two curves increases as the hysteresis increases [4]. Miura et al. [11] report that, for the Japanese NiTi wire they tested, the unloading curve was about half the loading curve. The values we calculated in this study are theoretical since several of the wire parameters, such as the point of martensitic transformation, were obtained in vitro using three-point bending tests, in ideal and controlled conditions. As reported by Wilkinson et al. [14], wire performances can differ significantly if the experimental model is changed. It must be borne in mind that the friction between the teeth and in the wireligation-bracket complex can drastically modify the level of stress delivered to the teeth [14]. Using elastomeric ligation, Kasuya et al. [8] demonstrated that the friction is so great that the behavior of superelastic wire is modified and its properties diminished. Conversely, laboratory tests show that self-ligating brackets enhance the superelastic proprieties of the wire [8]. Although approximate and theoretical, the loading values we found nevertheless highlight the importance of making an appropriate choice of brackets and wire characteristics, in particular if lingual mechanics is chosen.


leve
s sont assez constantes et significativement moins e
leve
es que celles ge
ne
re
es par le SS. Cela signifie que les e
te
s du fil super-e
lastique utilise
en vestibulaire sont proprie
sence de flexions importantes, ainsi que du co ^ te
utiles en pre ^me en cas de flexions mineures, en raison de la lingual, me
duite. distance interbrackets re Il est important de noter que les valeurs des forces fournies dans les tableaux se rapportent a` la courbe de charge. La
e sur les dents est de
crite par la courbe de contrainte place
charge. La diffe
rence entre les deux courbes augmente de
re se [4]. avec l’augmentation de l’hyste Miura et al. [11] rapportent que, sur le fil NiTi japonais qu’ils ont
, la courbe de de
charge e
tait approximativement la moitie
teste de la courbe de charge.
es dans cette e
tude sont the
oriques puisLes valeurs calcule tres de fil, tel que le point de transque plusieurs des parame
taient obtenus in vitro en utilisant formation martensitique, e des tests de pliage en trois points, dans des conditions de ^ le ide
ales. Comme l’ont constate
Wilkinson et al. [14], contro les performances des fils peuvent varier de fa¸con significative le expe
rimental. On doit tenir en cas de changement de mode compte du fait que la friction entre les dents et dans le s complexe fil–ligature–bracket peut modifier de fa¸con tre
rable le niveau de contrainte s’exer¸cant sur les dents conside
lastome
riques, Kasuya e al. [8] [14]. Utilisant des ligatures e
que la friction est tellement e
leve
e que le comporont montre
lastique s’en trouve modifie
de telle sorte tement du fil super-e
te
s diminuent. Inversement, des tests de que ses proprie
montre
que les brackets auto-ligaturants laboratoire ont de
liorent les proprie
te
s super-e
lastiques du fil [8]. ame
oriques et approximatives, les valeurs de charge Quoique the
es nous aident a` comprendre a` quel que nous avons trouve
livre
es, point il est important, en ce qui concerne les forces de
ristiques des fils, de bien choisir ses brackets et les caracte surtout lors d’un traitement en technique linguale.

Conclusions

Conclusions

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

se de de
part a e
te
confirme
e par l’e
tude : Notre hypothe
a un impact pertinent sur la dis— le type de bracket utilise
quence, sur les forces tance interbrackets et, en conse
livre
es aux dents ; de
lastiques utilise
s habituellement en technique ves— les fils e tibulaire (0,016 SS, Nitinol et TMA) ne conviennent pas en re phase du orthodontie linguale, surtout pendant la premie
ne rent ; traitement en raison des forces excessives qu’ils ge
lastiques sont les fils de choix dans les cas — les fils super-e
ve re et pour la me
canique linguale, en d’encombrement se
a` de
livrer des forces le
ge  res et raison de leur capacite
s de flexion importants. continues avec des degre

Conflict of interest statement


re ^t Conflit d’inte

None.

Aucun.

138

International Orthodontics 2011 ; 9 : 120-139

Wire load–deflection characteristics relative to different types of brackets


ristiques de charge–flexion de fils selon diffe
rents types de brackets Comparaison des caracte

References/Re
fe
rences 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Hohoff A, Wiechmann D, Fillion D, Stamm T, Lippold C, Ehmer U. Evaluation of the parameters underlying the decision by adult patients to opt for lingual therapy: an international comparison. J Orofac Orthop 2003;64(2):135–44. Moran KI. Relative wire stiffness due to lingual versus labial interbracket distance. Am J Orthod Dentofac Orthop 1987;92:24-32. Fuck LM, Wiechmann D, Drescher D. Comparison of the initial orthodontic force systems produced by a new lingual bracket system and a straight-wire appliance. J Orofac Orthop 2005;66:363–76. Garrec P, Jordan L. Stiffness in bending of a superelastic NiTi orthodontic wire as a function of cross-sectional dimension. Angle Orthod 2004;74:691–6. Andreasen GF, Morrow RE. Laboratory and clinical analysis of Nitinol wire. Am J Orthod 1978;73:142–51. Verstrynge A, Van Humbeeck J, Willems G. In-vitro evaluation of the material characteristics of stainless steel and beta-titanium orthodontic wires. Am J Orthod Dentofac Orthop 2006;130:460–70. Drake SR, Wayne DM, et al. Mechanical properties of orthodontic wires in tension, bending and torsion. Am J Orthod 1982;82:206–10. Kasuya S, Nagasaka S, Hanyuda A, Ishimura S, Hirashita A. The effect of ligation on the load deflection characteristics of nickel titanium orthodontic wire. Eur J Orthod 2007;29 (6):578–82 [Epub 2007 Sep 14]. Muraviev SE, Ospanova GB, Shlyakhova MY. Estimation of force produced by nickeltitanium superelastic archwires at large deflection. Am J Orthod Dentofac Orthop 2001;119:604–9. Bartzela TN, Senn C, Wichelhaus A. Load-deflection characteristics of superelastic NickelTitanium wires. Angl Orthod 2007;6:991–8. Miura F, Mogi M, et al. The super-elastic property of the Japanese NiTi alloy wire for use in orthodontics. Am J Orthod Dentofac Orthop 1986;90:1-10. Schudy GF, Schudy FF. Interbracket space and interbracket distance: critical factors in clinical orthodontics. Am J Orthod Dentofac Orthop 1989;96:281–94. Satoh K, Osawa H, Yoshizawa M, Nakano H, Hirasawa T, Kihira K, et al. Mechanical properties of several nickel-titanium alloy wires in three-point bending test. Am J Orthod Dentofac Orthop 1999;115:390–5. Wilkinson PD, Dysart PS, Hood JA, Herbison GP. Load-deflection characteristics of superelastic nickel-titanium orthodontic wires. Am J Orthod Dentofac Orthop 2002;121:483–95.

International Orthodontics 2011 ; 9 : 120-139

139