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ickel-Titanium (NiTi) Arch Wires:he Clinical Significance of Super Elasticity

ikolaos Pandis and Christoph P. Bourauel

The introduction of nickel-titanium (NiTi) wires has revolutionized the field

of orthodontics by delivering light continuous forces over a wider range of

displacements than the traditional stainless-steel wires. Over the years

improvements in NiTi wire manufacturing and composition have been in-

troduced; however, the claimed wire capabilities are not always easy to

verify in the clinical setting. We aim at presenting an overview of the use and

applications of NiTi alloys in orthodontics. The implications of the metallur-

gical and mechanical properties and intraoral aging of the wires in their

clinical application is discussed. Finally, time variants of orthodontic therapy

duration with the use of NiTi and alternative arch wires are presented, and

the clinical implication of superelasticity is analyzed. (Semin Orthod 2010;16:

249-257.) © 2010 Elsevier Inc. All rights reserved.

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t was recognized early on that application oflight continuous mechanical orthodontic

orces translates into optimal tooth move-ent.1,2 Manufacturing of materials and systems

hat can provide ideal forces, decreased patientonitoring, and longer intervals between visitsas been the focus of the orthodontic profes-ion.

Achievement of the aforementioned objec-ives depends heavily on the mechanical proper-ies of the wires used in treatment. Kapila andachdeva3 suggested that the ideal orthodonticire should combine low stiffness, good form-bility and high-energy storage, and large springack. Brantley et al4 added to the foregoingharacteristics biocompatibility, low surface fric-ion, and the capability to be welded or soldered.

It has been shown5 that a low load/deflectionatio of an orthodontic wire provides desirableorce and good control of force magnitude. Theact that NiTi wires possess those characteristics,mong others, has made their use almost univer-

Private Practice in Orthodontics, Corfu, Greece; Department ofrosthetic Dentistry, Preclinical Education and Materials Sciences,chool of Dentistry, University of Bonn, Bonn, Germany.

Address correspondence to Nikolaos Pandis, 29 P. Zafiropouloutreet, Corfu 49100, Greece. E-mail: npandis@yahoo.com

© 2010 Elsevier Inc. All rights reserved.1073-8746/10/1604-0$30.00/0

idoi:10.1053/j.sodo.2010.06.003

Seminars in Orthodontics, Vol 16, No

al. NiTi alloys are used in the greater biomedi-al materials area and in dentistry are used inrthodontics, endodontics, and prosthodontics.

Here, we aim to present an overview of these and applications of NiTi alloys in orthodon-ics, analyze the metallurgical structure, andummarize the phase transformation character-stics of these wires. Recent evidence on thentraoral aging pattern of these materials willlso be presented and the possible consequencesn their clinical application. Finally, the impli-ation of the metallurgical and mechanicalroperties of the wires in their clinical applica-ion is discussed in the light of recent evidence,hich explore the time variants of orthodontic

herapy duration using NiTi and alternativerchwires.

ntraoral Aging of NiTi Alloys

enerally, it has been shown that the intraoralxposure of NiTi wires affects the topographynd structure of the alloy surface creating pittingr crevice corrosion or formation of integu-ents.6 Retrieved NiTi orthodontic wires show

he formation of a proteinaceous biofilm, con-isting mainly of alcohol, amides and carbonate,aCl, KCl, and Ca–P crystalline precipitates.6

linically, this corrosion results in a slight

ncrease of the Ni ion concentration in the pa-

2494 (December), 2010: pp 249-257

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ient’s saliva (Fig 1); however, significant corro-ion defects on the surfaces of roughly 50% ofhe wires can only be identified after an ex-remely long intraoral exposure time of 24 weeksFig 2).7,8

At the wire edge opposing that engaged to theracket, cracks and crevices were observed possiblyaused by the presence of tensile forces producedrom the wire engagement. These force inducedhanges in the microstructure of the alloy involv-ng a reduction in grain size at the compressedocations that extend beyond the outer layer ofhe alloy. Changes in grain size have been doc-mented in the NiTi metallurgy as stress-in-uced martensite where the martensitic transforma-

ion occurs below the transition temperature rangehen external stress is applied.9 The effects of the

ntraoral use of NiTi alloys via temperaturehanges, which causes repetitive-phase transfor-ations, or via the cyclic mechanical loading,hich is attributed to the masticatory forces ini-

iating stress-induced martensite, may be ex-ressed as an alteration in grain size. Phase

ransformation, ie, the martensitic transforma-ion, occurs above the transition temperatureange when external stress is applied9; however,he clinical effect of this intraoral phase trans-ormation on superelasticity is not known.

The microscopic evaluation of NiTi alloyires has revealed material loss and variousodes of corrosion, such as delamination, crev-

ce, and pitting corrosion on the surfaces en-

igure 1. Nickel ion concentration in the patients’aliva during treatment with a fixed appliance: (1)efore start of orthodontic treatment, (2) after place-ent of bands and brackets, (3) 2 weeks later and

efore placing the nickel titanium (NiTi) archwires,4) immediatelly after insertion of the NiTi archwires,

p5) 4 and (6) 8 weeks after insertion of the wires.

aged to the bracket slots. In addition, retrievedires engaged to the brackets exhibited signifi-ant grain size alterations compared with thetched reference wires.

Important differences also were observed inhe surface profile morphology of the longitudi-ally-sectioned and polished wires relative to thes-received specimens. Surface regions engagedo the bracket slot showed surfaces demonstrat-ng excessive wear, while characteristic patternsf delamination were observed. Those alter-tions may be assigned to compressive forcesnduced by wire activation through ligation, pos-ible frictional damage produced inside the slot,nd plowing during sliding of NiTi alloy wire ontainless-steel bracket slot. NiTi and beta-tita-ium (�-Ti) wire alloys are most likely to present

his effect because of the surfaces roughnesshey possess due the wire drawing process.

linical Implications of the Superelasticroperties and Aging of NiTi Alloys

iTi wires have excellent spring-back and de-iver the lightest force with the widest elasticange among the alloys used in orthodontics;owever, these wires are comparably more ex-ensive, have poor formability, and cannot beoldered or welded,4 and they exhibit high arch-ire-bracket friction compared with beta-tita-ium because of the rough wire surfaces thatrise from the high titanium content. However,he limited clinical evidence currently availables not supportive of a difference in the durationf treatment in patients treated with NiTi alloys

igure 2. Traces of corrosion on the surfaces of re-rieved NiTi wires. The percentage of wires thathowed corrosion defects after a certain intraoral ex-osure time is stated.

ossessing distinctively different surface charac-

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251Nickel-Titanium (NiTi) Arch Wires

eristics, ie, ion-bombarded NiTi and conven-ional NiTi.10

It is possible to use greater dimension NiTi archires in the early stages of treatment to accomplisharious tasks simultaneously, such as correction ofotation, tipping, leveling, and torquing. The su-erelastic and shape-memory nickel-titanium wiresre particularly useful where large deflections areecessary for malpositioned teeth, whereas super-lastic nickel-titanium coil springs, originally devel-ped for orthodontics by Miura et al,11 have alsoound wide applicability. The force generated byhe coil spring depends upon the dimensionalharacteristics of the austenite final transforma-ion temperature of the spring. These springs, byxerting continuous light forces over a very wideange, provide the clinician with an excellent ve-icle for optimal tooth movement under the ap-ropriate clinical conditions with little clinician

ntervention. However, it has been found that theorce delivery of the superelastic coil springs cane substantially affected by small changes in tem-erature.4

Conclusive evidence is lacking regarding in-raoral aging, as discussed in the previous sec-ion, which involves severe surface and structurallterations of the wires, on the martensite-aus-enite phase transformation characteristics. In aecent study investigating the phase transforma-ion of NiTi endodontic rotary files, the authorseported that files exposed to clinically simu-ated procedures presented similar percentagef phase transformation to that found for thes-received products.12 However, extrapolatingrom the aforementioned study to orthodonticrch wires may be inappropriate because of themportant differences in use and application;hus, further research on this issue is requiredefore a definitive consensus is reached.

The information on mechanical properties ofhe nickel-titanium arch wires that have beenreviously discussed, and specifically on super-lasticity, refer mostly to in vitro observations,13

hereas clinical studies in which investigatorsompared the rate of tooth movement duringreatment by using different archwire alloyshowed no significant differences among super-lastic, nonsuperelastic NiTi wires, and multi-tranded stainless-steel wires.14 Other research-rs have proposed that superelasticity bears littler no clinical importance for torque applica-

ions, because at least 45° of activation was re- a

uired to show deactivation plateau.15 Finally,hree-point bending studies showed that super-lastic wires required at least 2 mm of deflectiono exhibit a plateau region.16

It is encouraging that recent studies on me-hanical behavior of NiTi alloys presented sig-ificant progress in materials characteristics and

hus in the stability and clinical applicability ofuperelasticity.17-19 The development of Interna-ional Standardization Organization (ISO) stan-ards for Orthodontic wires20 has facilitated aoherent and uniform approach in testing sev-ral mechanical properties of wires; however,iomechanical setups, which are more clinicallyeaningful have greatly assisted the extrapola-

ion of clinically relevant information (Fig 3A,). Although in the study of Kayser et al18 mostf the wires showed plateau starts at deflectionss high as 1.5 mm or greater, in the study ofischer,19 plateaus started at approximately 0.5

igure 3. (A) Three-point bending test on an orth-dontic NiTi wire according to the ISO standard5,841. (B) Biomechanical testing of the wire in aimulated clinical situation. (Color version of figure is

vailable online.)

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252 Pandis and Bourauel

m (Fig 4) Moreover, clearly decreased forcesould be observed for the modern, superelasticires, with numerous wires having forces ofround 0.5 N at a deflection of 2 mm (Fig 5).evertheless, wires with forces up to 2 N at a-mm deflection still exist (Fig 5), indicatingignificant fluctuations of the materials charac-eristics of NiTi wires.

igure 4. Selected load/deflection curves in three-po

he differing heights on the unloading plateaus.

Support to the foregoing conclusion has beenrovided by a study revealing that many superelas-

ic wires exhibit no superelastic properties in vivo,r at least no advantage over conventional NiTiires.21 These wires required a tooth displacementf at least 1 mm to express a plateau region and aorce level at the plateau reached 500 g, a magni-ude far beyond the typical limits of orthodontic

ending. Note the variability of hysteresis curves and

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253Nickel-Titanium (NiTi) Arch Wires

orce application, whereas others have estimated aaximum vertical force of 390 g, by simulating 1

nd 2 mm crowding with 20° angulation.22 Thus,n vivo studies revealed no superelastic behavior ofuperelastic NiTi wires and no differences onooth migration in cases treated with these wiresompared with the therapeutic results of the con-entional NiTi wires.

Pandis et al23 comparatively explored man-ibular arch alignment efficiency between NiTind CuNiTi wires. Sixty patients were includedn this single-center, single-operator, double-lind randomized trial. All patients were bondedith the In-Ovation-R self-ligating bracket (GAC,ohemia, NY) of 0.022-inch slot and the amountf crowding of the lower anterior dentition wasssessed by the use of the irregularity index. Theatients were randomly allocated into two groups:

he 0.016-inch CuNiTi 35°C (ORMCO, Glendora,A) group, and the 0.016-inch NiTi (Modern-rch, Wyomissing, PA) group (Figs 6A, B and 7A,). This study revealed no difference in mandibu-

ar alignment during the first 6 months of treat-ent between the ORMCO copper NiTi (CuNiTi)

hermoactive arch wires and ModernArch NiTiires, whereas increased irregularity resulted in

onger treatment periods (Fig 8A, B; Table 1). Theact that no differences were observed in vivo be-ween the arch wires may be attributed to mechan-cal and biological reasons.

As it was discussed earlier, intraoral agingmposes significant morphologic and structurallterations, including destruction of the struc-ural integrity of NiTi wire, delamination, forma-ion of craters, and increased porosity precipita-ion of calcium and phosphorus complexes,rising from the calcification of adsorbed integ-

igure 5. Forces on the unloading plateau in threeoint bending. (Color version of figure is availablenline.)

ment.6 (

Although several studies have highlighted thelterations of wires in vivo, the sole evidence on theffect of intraoral conditions on transformation ofopper NiTi (CuNiTi) wires derives from a recenttudy, in which the authors assessed the differen-ial scanning calorimetric parameters of intraorallyxposed and as-received wires.24 This investigationeported no difference between as-received andlinically retrieved wires in key variables related toransformation, except for a significant reductionn heating enthalpy associated with the martensite-o-austenite transition in the 27°C CuNiTi archires. Therefore, the hypothesis assigning the lackf difference between NiTi and CuNiTi specimensannot be assigned to intraoral conditions, whichffect the phase transformation variables of theatter.

Although the foregoing discussion shows thatsed wires can present transformation character-

igure 6. (A) Mandibular arch on the day of bondingtted with CuNiTi 0.016-inch wire. (B) Degree oflignment at 180 days with CuNiTi 0.016-inch wire.

Color version of figure is available online.)

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254 Pandis and Bourauel

stics within the range of their as-received coun-erparts, studies have shown exceptional temper-ture sensitivity for superelastic NiTi wires. Thus,lterations in mouth temperature could cause atress fluctuation in nickel-titanium wires duringrthodontic treatment. Iijima et al25 investigatedhe effects of temperature changes on mechan-cal properties of the wires by examining theesponse of NiTi wires at constant temperaturend stepwise temperature changes from 37° to0°C and back to 37°C and from 37° to 2°C andack to 37°C. It was determined that the loadxpressed by the superelastic nickel-titaniumires increased with heating and decreased withooling, phenomena attributed to a change inhe critical stress for martensite transformationnduced by temperature fluctuations. Interest-ngly, in the stepwise temperature changes oneating, the load measured at body temperatures the final step was much higher than that

igure 7. (A) Mandibular arch on the day of bondingtted with NiTi 0.016-inch wire. (B) Degree of align-ent at 180 days with NiTi 0.016-inch wire. (Color

ersion of figure is available online.)

easured at body temperature initially; that im- fi

lies that perhaps sequential heating-cooling cy-les of clinically applied NiTi wires may result inreater load expression at mouth temperature.lso, it has been shown that the effects on theire vary depending on whether cooling/heat-

ng is applied during the activation or deactiva-ion phases. Cooling induces transient effects on

wire in its deactivation phase, but prolongedffects when the wire was tested in the activationhase. In contrast, the effect of short-term heat-

ng was transient when the wire was tested in thectivation phase, but prolonged when the wireas tested in the deactivation phase.26

Evidence indicating the association of me-hanical properties of superelastic NiTi wires onemperature changes; have also been presentedy others by the use of a different approach.eling and Odegaard27 have reported that

ome true shape memory wires continued toxert sub-baseline bending force after short-erm application of cold water, and this effectemained even after 30 minutes of postexposureestitution. In addition, it has been indicatedhat annulling of this effect required a temper-ture increase to about 50°C through intake of aot drink.28 Therefore, despite the lack of signif-

cant phase transformational changes noted afterse, the temperature dependence of thermoactiveires may differ from their behavior in vivo.

An alternative hypothesis, which may be for-ulated to explain the observations of the Pan-

is23 study, pertains to the differences of loadingonditions between the laboratory conditionsnd the oral cavity. In general, loading of theiTi arch wire arising from its engagement into

he bracket slot walls, presents a much differentattern than free NiTi wire segments subjected to

hree-point, or cantilever bending. The uniqueharacter of loading during engagement is due tohe presence of free play or slack between therchwire and the slot.29 Such a pattern cannote simulated in laboratory configurations anday differentiate the performance of the mate-

ial. As a result, the simplified in vitro mechan-cal testing of NiTi wires may preclude the ex-ression of the actual clinical performance ofiTi arch wires. The use of self-ligating appli-

nces that may minimize the variability of thengagement by eliminating the variation causedy elastomeric ligation has not been shown toave an effect on NiTi wire performance. This

nding may imply that the free play caused by

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255Nickel-Titanium (NiTi) Arch Wires

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igure 8. (A) Kaplan–Meier failure estimation plot showing the variation of treatment duration by type of wire.-axis gives proportion of patients still in treatment (not aligned) at different times (days on x-axis); failureertains to event, which here indicates completion of alignment. By drawing line perpendicular to x axis at given

ime value, proportion of patients not completed for each crowding group (moderate or severe) is extrapolatedrom corresponding value given in y axis. Note persistence of similarity of alignment completion pattern untilay 120. The frequent crossing-over of the blue and red lines indicates no difference in time to alignmentfailure) between wire types. After day 120, the lines begin to diverge showing a preference for NiTi; however,aplan–Meier plots are less reliable on the right side because the lines represent smaller sample sizes.30 (B)aplan–Meier failure estimation plot shows the variation of treatment duration with severity of crowding. Y-axisives proportion of patients still in treatment (not aligned) at different times (days on x-axis), failure meansvent which here indicates completion of alignment. By drawing line perpendicular to x-axis at given time value,roportion of patients not completed for each crowding group (moderate or severe) is extrapolated fromorresponding value given in y axis. Note persistence of alignment completion pattern through entire treatmenteriod: severe crowding has higher percentage of incomplete patients compared with moderate crowding at any

reatment time. (Color version of figure is available online.)

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256 Pandis and Bourauel

he difference of wire/bracket slot size may be aactor even if the stress relaxation of elastomericigatures is excluded.

onclusions

n conclusion, metallurgical and testing of NiTiires may facilitate useful information on keyroperties of NiTi wires. However, when used toxtrapolate evidence on the clinical perfor-ance of NiTi wires, these studies fail to provide

eliable data. In addition, the authors of clinicalrials indicate a lack of an effect of superelasticityn the crowding alleviation in vivo, an effect thatan be attributed to the free play of bracket andire inside the slot walls, as well as potentialging of the involved elements (bracket, archires). More clinical trials are necessary to elu-idate the mechanism underlying these observa-ions which question the clinical meaning of initro evidence.

eferences1. Reitan K: Tissue behavior during orthodontic tooth

movement. Am J Orthod 45:881-900, 19602. Smith R, Storey E: The importance of force in orthodon-

tics. Aust Dent J 56:291-304, 19523. Kapila S, Sachdeva R: Mechanical properties and clinical

applications of orthodontic wires. Am J Orthod Dento-fac Orthop 96:100-109, 1989

4. Brantley WA, Webb CS, Soto U, et al: X-ray diffractionanalyses of copper Ni–Ti orthodontic wires. J Dent Res76:401, 1997

5. Burstone CJ, Qin B, Morton JY: Chinese NiTi wire-a neworthodontic alloy. Am J Orthod 87:445-452, 1985

6. Eliades T, Eliades G, Athanasiou A, et al: Surface char-acterization of retrieved NiTi orthodontic archwires. EurJ Orthod 22:317-326, 2000

7. Petoumenou E, Kislyuk M, Hoederath H, et al: Corro-sion susceptibility and nickel release of nickel titaniumwires during clinical application. J Orofac Orthop 69:

able 1. Treatment Time to Alignment Characteristi

Totaln Successfully Aligned

WiretypeCuNiTi 30 19NiTi 30 22

IrregularitySevere (�5 mm) 29 16Moderate (�5 mm) 31 25

dapted with permission from Pandis et al.23

411-423, 2008

8. Petoumenou E, Arndt M, Keilig L, et al: Nickel concentra-tion in the saliva of patients with nickel-titanium orthodonticappliances. Am J Orthod Dentofac Orthop 135:59-65, 2009

9. Weyman CM: Shape memory alloys. Mater Resour SocBull 18:49-56, 1993

0. Kula K, Phillips C, Gibilaro A, et al: Effect of ion implantationof TMA archwires on the rate of orthodontic sliding spaceclosure. Am J Orthod Dentofac Orthop 114:577-581, 1998

1. Miura F, Mogi M, Ohura Y, et al: The super-elasticproperty of the Japanese NiTi alloy wire for use in orth-odontics. Am J Orthod 90:1-10, 1986

2. Brantley WA: Orthodontic wires, in Brantley WA, EliadesT (eds): Orthodontic Materials: Scientific and ClinicalAspects. Stuttgard, Germany, Thieme, 2001

3. Gioka C, Eliades T: Superelasticity of NiTi alloys: metal-lurgical structure and clinical implications. Hel. OrthodRev 5:111-127, 2002

4. Cobb HW III, Kula KS, Phillips C, et al: Efficiency ofmulti-strand steel, superelastic Ni–Ti and ion-implantedNiTi archwires for initial alignment. Clin Orthod Res 1:12-19,1998

5. Meling TR, Odegaard J: The effect of short-term tem-perature changes on the mechanical properties of rect-angular nickel titanium archwires tested in torsion. An-gle Orthod 68:369-376, 1998

6. Tonner RIM, Waters NE: The characteristics of super-elastic Ni–Ti wires in three-point bending. part I: Theeffect of temperature. Eur J Orthod 16:409-419, 1994

7. Kayser D: Comparison of mechanical properties of orth-odontic nickel-titanium wires. Doctoral Thesis, Univer-sity of Bonn, 2001

8. Kayser D, Bourauel C, Braumann B, et al: mechanischereigenschaften orthodontischer nickel-Titan-Drähte. BiomedTechnol 47:334-342, 2002

9. Fischer C: Materials science and biomechanichal analysis ofcurrent NiTi wires. Doctoral Thesis, University of Bonn, 2009

0. ISO 15841. Dentistry—Wires for use in orthodontics.ISO 15841, 2006

1. Segner D, Ibe D: Properties of superelastic wires andtheir relevance to orthodontic treatment. Eur J Orthod17:395-402, 1995

2. Schumacher HA, Bourauel C, Drescher D: Deaktivier-ungsverhalten und Effektivität verschiedener orthodon-tischer Nivellierungsbögen—eine dynamische analyseder Kraftsysteme. Fortsch Kiefer 53:273-285, 1992

3. Pandis N, Polychronopoulou A, Eliades T: Alleviation of

Wire System and Crowding Severity (in days)

an Time tonment, Days Min, Days Median, Days Max, Days

129.4 32 142.5 195.0121.4 28 116.5 190.0

138.5 32 152.0 190.0113.1 28 104.0 195.0

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mandibular anterior crowding with copper-nickel-titanium

2

2

2

2

2

2

3

257Nickel-Titanium (NiTi) Arch Wires

vs nickel-titanium wires: a double-blind randomized controltrial. Am J Orthod Dentofac Orthop 136:e1-e7, 2009

4. Biermann MC, Berzins DW, Bradley TG: Thermal analysisof as-received and clinically retrieved copper-nickel-titaniumorthodontic archwires. Angle Orthod 207 77:499-503, 2007

5. Iijima M, Ohno H, Kawashima I, et al: Mechanical behaviorat different temperatures and stresses for superelastic nick-el-titanium orthodontic wires having different transforma-tion temperatures. Dent Mater 18:88-93, 2002

6. Meling TR, Odegaard J: The effect of short-term tem-perature changes on superelastic nickel-titanium arch-wires activated in orthodontic bending. Am J Orthod

Dentofac Orthop 119:263-273, 2001

7. Meling TR, Odegaard J: On the variability if cross-sec-tional dimensions and torsional properties of rectangu-lar nickel-titanium arch wires. Am J Orthod DentofacOrthop 113:546-557, 1998

8. Airoldi G, Riva G, Vanelli M, et al: Oral environmenttemperature changes induced by cold/hot liquid intake.Am J Orthod Dentofac Ortop 112:58-63, 1997

9. Sebanc J, Brantley WA, Pincsak JJ, et al: Variability ofeffective root torque as a function of edge bevel onorthodontic arch wires. Am J Orthod 86:43-51, 1984

0. Pocock SJ, Clayton TC, Altman DG: Survival plots oftime-to-event outcomes in clinical trials: good practice

and pitfalls. Lancet 359:1686-1689, 2002