ORIGINAL
ARTICLE/ARTICOLO
ORIGINALE
Conditioning
of
root
canal
anatomy
on
static
and
dynamics
of
nickel-titanium
rotary
instruments
Condizionamento
dell’anatomia
canalare
sulla
statica
e
la
dinamica
degli
strumenti
rotanti
in
Nichel-Titanio
Italo
Di
Giuseppe
a,*
,
Davide
Di
Giuseppe
b,
Vito
Antonio
Malagnino
c,
Enrico
Paolo
Silla
d,
Francesco
Somma
da
PrivatePractitionerinRome,Italy
bMechanicalEngineerinRome,Italy c
DepartmentofEndodontics,SchoolofDentistry,UniversityofChieti‘‘G.D’Annunzio’’,Chieti,Italy
dFacolta` diMedicinaeChirurgia,Universita` CattolicadelSacroCuore,LargoFrancescoVito,1,00168Roma
(RM),Italy
Received10July2015;accepted28July2015 Availableonline4October2015
KEYWORDS
Ni-Tirotaryinstruments; Rotarytranslation; Roughness; Torque;
Torsionalstress.
Abstract
Aim: Aimofthisstudyistoanalyzetherealmovement,influencedbyanatomicaldifficulties,of nickel-titaniumrotaryinstrumentswithinrootcanalsystems;thentheobjectiveistopointout thephysicalandgeometricalcharacteristicsofanidealinstrument,abletoovercomethemost complexanatomies.
Methodology: Atfirst,observationofthebehaviorofnickel-titaniumrotaryinstrumentswithin rootcanalsystemsandoftheinfluenceonthemofrootcanalanatomy.Then,attempttoavoid theanatomical obstructions exploiting,withmanualrotation, theadvantagesof azero/low torque.
PeerreviewunderresponsibilityofSocieta` ItalianadiEndodonzia.
* Correspondingauthorat:ItaloDiGiuseppe,LargoMarescialloDiaz,10—00135Roma,Italy.Tel.:+39063336787;fax:+39063330093. E-mail:studiodigiuseppe2@virgilio.it(I.DiGiuseppe).
Availableonlineatwww.sciencedirect.com
ScienceDirect
jo ur na l h o m ep a ge : w w w.e ls e v i er.c o m / lo c at e /gi e
http://dx.doi.org/10.1016/j.gien.2015.08.004
Introduction
Anatomicalcomplexitiessubmitnickel-titanium(Ni-Ti)rotary instrumentstostressesthatoftenunderminetheirstructural integrity.Despite an extraordinarydevelopment ofNi-Ti in more than 20 years of utilization, the increased risk of a separationremainsasignificantproblemformanyclinicians.1 Manyvariablemightcontributetothisfracture,butthetwo maincausesarecyclicfatigueandtorsionalfatigue,bothof whichmightcontributetofracture,dependingoncanal cur-vature,instrumentgeometryandmanufacturingmethod.2—4 Torsionalfractureoccurswhenaninstrumenttiporanother partoftheinstrumentislockedinacanal,whiletheshank continues to rotate and the elastic limit of the metal is exceeded1,5;instrumentsfracturedby fatigue donotbind inthecanalbuttheyrotatefreelyaroundacurve,generating tension/compressioncyclesatthepointofmaximumflexure until fracture occurs.6 Manyfracture simulation studies on Ni-Tiinstrumentshavebeenconductedseparatelyfromcyclic fatigueandtorsionalfailuretests.7,8Onlyafewstudieshave triedtocorrelatethesetwofactors offracture.9—12
Theendodontichandpieceimparts totheinstruments a rotarymotionaroundanaxis(axisofthehandpiece).When theapicalportionofaninstrumentisinsertedintoa curva-ture,thisportionwillrotatearoundanewanddifferentaxis (axisofthecanalafterthecurvature);thisrotationalmotion aroundanewaxisistheresultoftwoactions;thefirstdueto thestructural continuity oftheinstrument whichtendsto transfer,toitsportioninsertedintothecurvature,thesame rotarymotionimprintedbytheendodontichandpiecetothe portionofinstrumentindirectcontactwiththeendodontic
handpiece itself (rotation motion around the axis of the handpiece);thesecondduetotherootcanalwalls,which, opposingthepenetrationoftheinstrumentinsertedintothe curvature,exertonitpressingforces(thisportionof instru-ment, in fact, attempts to rotate around the axis of the handpiece,but‘‘slams’’onrootcanalwalls).Theresultantof these two actions will rotate the portion of instrument insertedintothecurvaturearound anew axis(axisofthe canalafterthecurvature).Toappreciatethisrotationaround anewanddifferentaxis,arotaryinstrumentcanbeputin rotationonaglassplate,inordertosimulateatruerotation ina rootcanal with ahigh degreeof curvature;a rotary-translation of the bent portion of the instrument can be observed;this would be impossible to value ifroot canal wallswerepresent.1
Evenwhenonthehandpieceisnotsetanytorque,once theinstrumentisinsertedintherootcanal,onitactforces (conditioningoftherootcanalwalls)thatflexitandgiveit thesamerootcanal’sshape.
Pressingforcesexertedbyrootcanalwalls,ifononehand deviate the axis of rotation of the portion on instrument insertedinthecurvature,ontheothercausetheincreasing offrictionforcesthatopposetherotationandthe advance-mentof the instrument.In vivo, whenthe curvatures are morethanone,this phenomenon happensat everycurve. Pressingforces(frictionalforces),increase,uptotheresult oftheinabilitytorotateand/oradvancetheendodonticfile. Today we have particularly efficient instruments that, cutting a lot, advance until reaching the apical foramen
PAROLECHIAVE
Roto-traslazione; Rugosita`; Stresstorsionale; Strumentirotantiin Ni-Ti;
Torque.
Results: Giventhat, in someroot canals theseverityof thecurvesprevents instrumentsto advancein rotation,weobtainedsignificantresults bymanuallyadvancing androtatingNiTi rotaryinstruments.
Conclusions: Therefore, in some cases, we would need an instrument that can reconcile efficiencywithareductionofmassandtorque;theidealinstrumentshouldhaveaverycontained workingpart,combiningefficiencywiththedecreaseofmassand,consequently,oftorsional stressestoo.
ß2015Societa` ItalianadiEndodonzia.ProductionandhostingbyElsevierB.V.Allrightsreserved.
Riassunto
Obiettivi: obiettivodiquestostudioe` diregistrareilrealemovimentodeglistrumenti, condi-zionato dalle difficolta` anatomiche,all’interno dei sistemiendocanalari, per poi tentare di evidenziare le caratteristiche fisiche e geometriche dello strumento ideale, impegnato ad affrontareleanatomiepiu` complesse.
MaterialieMetodi: inunprimomomento:osservazionedelcomportamentodellelime endo-dontiche meccaniche in Ni-Ti all’interno dei sistemi canalari e del condizionamento che l’anatomiacanalareha sudiesse.In seguito:tentativodieludere l’impedimentoanatomico sfruttando,conlarotazionemanuale,ivantaggidiuntorquenullo-basso.
Risultati: premesso chein alcunicanali la severita` delle curve impedisceagli strumenti di avanzarein rotazione, sisono ottenuti risultati significativifacendo avanzare e ruotare gli strumentimanualmente.
Conclusioni: allalucediquesteconsiderazioni,inalcunicasiavremmobisognodiunostrumento chepossaconciliarel’efficienzaconunadiminuzionedimassaetorque.L’idealesarebbetrovare unostrumentocon partelavorantemoltocontenutaecheconiughi,quindi,l’efficienza alla diminuzionedellamassaediconseguenzaanchedellostresstorsionale.
ß 2015Societa` ItalianadiEndodonzia.Production and hosting byElsevierB.V.Tutti idiritti riservati.
(easily, mostof the time). Therefore, the problem of the torsionisremovedandinstrumentsseemstobreakonlyfor accumulationofcyclicfatigue. Infact,studieshavefound cyclicfatiguetobetheprimarycauseofinstrumentfracture. It accounted for 50—90% of the mechanical failures.13 However, it is unlikely that cyclic fatigue can occur if a rotating instrument does not significantly contact canal walls. Consequently, cyclic fatigue is not necessarily the main reason for instrument failure.1 These considerations bring renewed emphasis on torsional stress as cause of fracture:thereistorsion,moreorlesssignificant,whenever thereisacurvature.However,theunderlyingphysical prin-ciples of rotary root canal instrumentation are not fully understood nor researched; likewise, there is no concise normforcyclicfatiguetests.1
TheaimofthisstudyistohighlightthebehaviorofNi-Ti rotaryfilesinsiderootcanalsandbringbacktheattentionon torsionalstress,partiallyforgottensincethecuttingability allowsinstrumentstorapidlyadvanceandgaintheapex.
Materials
and
methods
As already mentioned, pressing forces generate frictional forces, which oppose the relative motion of rotation and advancementoftheendodonticinstruments.Thesefrictional forcesaremuchstrongerthanthegreateraretheforcesthat pressonesurfaceontheotherandthegreateristheroughness ofthetwosurfacesincontact.Formulaofslidingfrictionforce: Fa¼mFp
whereFaistheforceoffriction,misthecoefficientoffriction (static or dynamic) which is directly proportional to the roughnessofsurfacesincontact;Fpisthepressingforce.
Therelationships,whichdescribetheforcesactingonthe instrumentaccordingwiththecurvaturethatitassumesinits variouspointsareexpressedbelow,where:EistheYoung’s modulusofthematerial,Iisitsmomentofinertia,P istheforce thatexertthewalls,xisthedistancebetweenthepointof applicationofforceandanypointXoftheinstrument,d2v/dx2
isthecurvature(thatistheinverseoftheradiusofcurvature) atapointx,M(x)istheflexingmomentatapointx(i.e.the forcePperthearmx),v(x)isthedisplacementcomparedto the’axisofthehandpieceofapointxoftheinstrument,theta (x)istheanglebetweentheaxisoftheinstrumentandthe axisofthehandpieceatapointX.Fig.1showsasectionof theinstrument,forcesexertedbywallsareradial.
Flexingmomentinx: Mx¼Px d2vðxÞ dx2 ¼ Px EI dvðxÞ dx ¼ Px2 2EIþC1 vðxÞ¼Px 3 6EIþC1xþC2
Inthepointofloadapplication: v0¼1PL 3 3EI u0¼1PL 2 2EI
Formulas showthat in a point X of the instrument the curvature-shape, taken by theinstrument, is greater how muchistheforce(P)exertedbyrootcanalwalls.
Weobserve thatendodonticinstrumentsmadeof parti-cular Ni-Ti alloys (more ‘‘malleable’’ after thermal and mechanicaltreatments),afterarotationinarootcanalwith particularlyseverecurvatures,appeardeformedbytorsion after the impact with canal walls. A ‘‘softer’’ instrument whentakescontactwithrootcanalwallsduringtherotation tendsto deform, losing‘‘roughness’’; so ithascertainly a greaterabilitytoadvance,butasmallercuttingcapacity.As well, alessmalleable instrument,which doesnot tendto deformincontactwith rootcanalwalls,willbemore effi-cient,butwillaccumulaterapidlytorsionfatigue. Endodon-ticinstruments withsuperiorcuttingabilityanduntreated Ni-Ti alloys (harder),non-deformable in contact with root canalwalls,inanaloganglesundergosmallerdeformations and,inonesense,lessreportthepresenceofnatural tor-sionalstress.Thelatteraremorecleansing,thefirstdeform andmakeminorcleansing,burnishingbutlesscutting,root canalwalls:sotheinstrumentwillreachtheapicalforamen, butorganicandinorganicdebriswillbecoatedonthewalls. Infact,weknowthatthemostefficientcleaningisobtained bythecuttingactionoftheendodonticinstruments.14
We noticedthatinsome complexrootcanal anatomies
(Figs. 2 and 3), inside of which, in mechanical rotation,
endodonticfilesappeartoberejectedand,inmanual rota-tion,theycouldcovertheentirecanallength.Byusingrotary Ni-Ti instruments manually, we apply minimum values of torqueandangular acceleration, oftenallowingthe endo-donticfiletoovercometheanatomicalobstacle(Figs.4—6). Withmanualrotationthechangeofaxisofrotationstartsina less abrupt and moregradual way. The light push toward apicaldirection,contextualtomanualrotation,compatibly
withsizeandroughnessoftheinstrument(asamatteroflow roughnessandsmallsizes,weusedMTwo-Sweden&Martina, Padova,Italy),willanticipatetherotary-translationand,at the same time, the generated impact on root canal’s walls; this impact produces frictions, which prevents the instrument from advancing. In addition, many authors reportedthatreductioninoperationalspeedcouldprevent taper locking, deformation and fracturing of Ni-Ti instru-ments15—17duringclinicalpractice.
Figure 2 Initial RX, showing the necessity of a root canal treatmenton1.7.ApparentresorptionofDBroot.
Figure3 CB-CTimageshowingtheS-shaped anatomyof DB root.
Figure4 FinalRX,fillingofrootcanalsystemof1.7.
Figure5 CB-CTimagesshowinghowtheS-shapedanatomyof DBroot has been entirely cleaned,shaped (with Ni-Ti rotary instrumentsusedinmanualrotation),thenfilled.
Figure6 3Dimageofthefilledrootcanalsystems.
Inthisothercase(Fig.7),wecanseehowinarootcanal withhighdegreeofcurvatureintheapicalone-third(Fig.8), whichpreventstheengine-driveninstrumentstoadvancein rotation, as said, by manual rotation the entire working lengthcanbeshaped(Figs.9and10).
Results
So, we need to contain friction forces; to do thiswe can modify the characteristics of endodontic instruments,
decreasing their roughness or reducing pressing forces betweentheinstrumentandrootcanalwalls.Forexample, weshouldstudyinstrumentswithaverycontainedworking part and significantly reduced cutting efficiency in the coronalportion,inordertodecreaseroughnessofitssections incontact.Thisinstrumentcouldbeusedafterapreliminary enlargementwithconventionalrotaryinstruments,brought in proximity ofthe anatomical complication.As seen, the geometricaldesignisanimportantdeterminantbecauseof the effect on the torsional andbending properties of the instrument.19 In fact, the mechanical properties of the instrumentsareclearlyinfluencedbytheirgeometrical con-figurations,whichincludethecross-sectional shape(which determinethebendingandtorsionalinertia),taper,helical angleandpitch.20
However,fromtheabove,anotherfundamentalelement that we can modify to reduce the friction is to decrease pressingforces,forexample,byreducingthetorqueonthe endodonticmotor. In fact,the higheris thetorque setat the orifice of root canal (torque set on the endodontic motor),the greateris the reaction(andthus thepressing force)thatwereceivefromthecanalwalls:thus,decreasing themomentumonthehandpiece,theintensityoffrictional forceswillbereduced.
T¼ fb
whereTisthetorque,fistheintensityofthepairofforces applied from the handpiece to the instrument, and b is the armor the distance betweenthe twoforces. Hence, reducing T,forthe same arm, decreases the intensity of the forces applied from the handpiece and, therefore, decreasestheintensity ofpressing forces.Theamountof torquegeneratedclearlydependsonthesizeofthecontact areasbetweentheinstrumentsandthecanalwalls,aswas demonstrated.21
Ni-Tiengine-filesoperatebywayofcontinuousrotation inthe rootcanal and,assuch,aresubjectedto unidirec-tionaltorque(assumingnostalling).2Thevalueoftorsional (shear)stressvariesdependingonthecanalsize,22,23 hard-nessofthedentinetobecut,24andtheuseofalubricant.25 The cross-sectional configuration is also an important determinant ofthe distribution of stresses onthe instru-ment.26
Insomecases,therefore,theonlywaytoadvanceisto reducetorque,buttheminimumvalueoftorqueselectable in most endodonticmotor is 1N/m;a low value,but not negligible in absolute and still too high for circumvent theanatomicalimpediment.Friction,therefore,decrease eitherreducingthetorqueoftheendodonticmotor,orby making a less wrinkled endodontic instrument (limiting/ containingitsworkingpart),insuchawaythatitsportion locatedatthepointofmaximumcurvature,takesminimum contacts with root canal walls (better zero contacts), simulating what occurs in vitro with cyclicfatigue tests. Todate,severaltorque-controlledlow-speedmotorshave beenintroducedtohelpreducetheincidenceofseparation when using rotary instruments.1 The efficacyand clinical rationaleforusingthesetorque-controlledmotorshasbeen describedrecentlyinacasereport.27
Oneoftheeffectsoftherealmovementofrotary endo-donticinstrumentsintorootcanalsystemsisthatthefilewill goacrossalongerwaythanthatofasteelfile,used,atfirst,
Figure8 Mesialrootcanalsystem’shighdegreeofcurvature.
Figure9 FinalRX.
todetermineworkinglength.Somuchsothat,ifwereferthe workinglengthmeasuredwithanhandfileonarotaryfile, once it isrotating,when therubber stopper,representing the established working length, arrives in correspondence ofthechosenpointofreference,theapexlocatoroftendoes notconfirmthisdata;butitwillbenecessaryanothersmall advancement to get the real workinglength. Thisprocess wouldbeparticularly valuable as muchsevere willbethe curves that rotary instrument has to face and much less root canal system will be relatively straight and wide its transverse diameter; reason why we would need always apexlocatorto beconnectedto therotary fileduringroot canalshaping.
Discussion
SinceweknowtherealmovementofNi-Tirotaryfileinroot canals,wecannowunderstandtheimportanceoftorsional stressandcontrolledtorqueforclinicpractice.Infact,inthe clinicalsituation,because ofthediversity ofcanal dimen-sions,Ni-Tirotary instruments maybesubjectto torsional stress of varying degrees, especially at the early stage of canalenlargement.28
Weknowthatcyclicfatiguetestsareperformedwithout torque:inthiscase,theinstrumentdoesnotkeepcontact withcanalwalls.Infact,incyclicfatiguetests29fileswere rotatedfreelywithouttipbinding,whichlimitsthestresson thefilestothatproducedbyflexuralstress.Moreover, tor-sionalorlateralloadingoftheinstrumentasmaybe experi-encedintheclinicalsituationisnotreproducedinmuchtest method.30 Furthermore, the few documented studies on torsional moments and forces exerted during actual canal preparationwerecarriedoutusingstraightcanals.1
Clinically,cyclicfatiguefracture seemsto bemore pre-valentincurvedrootcanals,whereastorsionalfailuremight occureveninastraightcanal.3,31Althoughbothfailuremodes probably occur simultaneously during rootcanal shaping,32 mostlaboratorystudiesofinstrumentseparationhavebeen conductedseparatelyeitherforcyclicfatigueresistanceor torsionalfailure,3,7,18,31,33—35probablyforconvenienceorfor better control of the loading condition. There were rare studiesthatcorrelatedthesetwoaspectsoffracture.28
Invivo,assoonastherotaryfiletakescontactwiththewalls ofacurvature,becauseofthefrictionthatcomesfromthe pressingforces,ittwistsandstrugglestoadvance:theprogress oftherotationwillbestronglyslowed.Ifwerelyonlyonthe resultsofcyclicfatiguetests,wecoulduseanewendodontic instrument respecting thetime limitsthatare providedby manufacturers.However,invivo,thatdatacouldpointout onlytheflexibilityoftheinstrument,butthosetimesarenot respectedbecausewehavetoconsider,inadditiontosimple rotatingbending,alsotorsionalfatigue,thatcannotbe eval-uated in vitro. Therefore, we have to take special care because,inparticularsituations,wecouldhavesuddenand unexpectedbreakagethatweactuallyhadto expect:Ni-Ti rotaryfilesaresusceptibletofracture,especiallywhenthey areusedincurvedrootcanalsincontinuousrotation.34
Particularly,whenanendodonticinstrumenthastofacea 908curvature,thetorquesetontheendodontichandpieceis equaltothatofresistance,sotheinstrumentcannotadvance becausethepropulsionitreceivesisequalandoppositeto theforce,thatpreventsitsprogression.
Ateverycurvature,in fact,themostapicalpartofthe instrument, as seen, changes its axis of rotation and its rotation become a rotatory-translation that, because of thepresenceofrootcanalwalls,turnsintotorsion. There-fore,weshouldtalkaboutaccumulationoftorsionalfatigue, becausetheinstrumentsaresubjecttotorsionalforces,that aregreaterthemoreextensiveandnumerousaretheangles ofthecurvature.Inaddition,moresharpaninstrumentis, thegreaterareitscontactswithrootcanalwalls,moreitwill be subject to torsional stresses, thus to accumulation of torsional fatigue. The endodontic instrument is subjected totorsion, itsprogression slowsdownand,becauseofthe accumulationoffatigue(cyclicandtorsional),itcanundergo breakage.
Torsionaloverloadisanimportantcauseoffailureforan endodontic instrument and should never be forgotten or underestimated. Therefore, it is easy to understand the importance to study a technique or an endodontic instru-ment,whichcanrelatethisphenomenon andallowa safe endodontictreatmentaccordingtorootcanalanatomy.
Conclusions
Wehaveseenhowanatomicalcomplexitiesmakevery intri-catetherealmovementofrotaryinstrumentsintorootcanal systems.Besides,wehaveseenthatthemechanicalrotation isactuallyarotary-translation.
Thatisthereasonwhy,insomecases,wewouldneedan endodonticinstrumentthatcanreconcileefficiencywitha reductionofworkingpartandtorque.Theidealwouldbeto findaninstrument:
Withfew,minimalradialcontactpointsandworkingpart limitedtothefinishingtouchandnegotiationofapical one-third.
Verysharpinordertokeepdownthevalueoftorque.
Conflict
of
interest
Theauthorshavenoconflictofinteresttodeclare.
References
1.Peters OA,Barbakow F. Dynamictorque andapical forces of ProFile.04 rotary instruments during preparation of curved canals.IntEndodJ2002;35(4):379—89.
2.KimTO,CheungGS, LeeJM, KimBM,HurB, KimHC.Stress distributionofthreeNiTirotaryfilesunderbendingandtorsional conditionsusingamathematicanalysis.IntEndodJ2009;42(1): 14—21.
3.PruettJ,ClementD,CarnesDJ.Cyclicfatiguetestingof nickel-titaniumendodonticinstruments.JEndod1997;23:77—85.
4.KimHC,YumJ,HurB,CheungGS.Cyclicfatigueandfracture characteristics of ground and twisted nickel-titanium rotary files.JEndod2010;36:147—52.
5.ParashosP,MesserHH.RotaryNiTiinstrumentsfractureandits consequences.JEndod2006;32:1031—43.
6.Pedulla` E, GrandeNM, Plotino G, Gambarini G, Rapisarda E. Influenceofcontinuousorreciprocatingmotiononcyclicfatigue resistance of 4 different nickel-titanium rotary instruments. JEndod2013;39:258—61.
7.YumJ,CheungGSP,ParkJK,HurB,KimHC.Torsionalstrength andtoughnessofnickel-titaniumrotaryfiles.JEndod2011;37: 382—6.
8.Pedulla` E,PlotinoG, GrandeNM, PappalardoA,Rapisarda E. Cyclicfatigueresistanceoffournickel-titaniumrotary instru-ments:acomparativestudy.AnnStomatol2012;3:59—63.
9.Bahia MG, Melo MC, Buono VT. Influence of cyclic torsional loadingonthefatigueresistanceofK3instruments.IntEndod J2008;41:883—91.
10.KimJY,CheungGS,ParkSH,KoDC,KimJW,KimHC.Effectfrom cyclicfatigueofnickel-titaniumrotaryfilesontorsional resis-tance.JEndod2012;38:527—30.
11.CheungGS,OhSH,HaJH,KimSK,ParkSH,KimHC.Effectof torsionalloadingofnickel-titaniuminstrumentsoncyclicfatigue resistance.JEndod2013;39:1593—7.
12.CampbellL,ShenY,ZhouHM,HaapasaloM.Effectoffatigueon torsional failureofnickel-titaniumcontrolledmemory instru-ments.JEndod2014;40:562—5.
13.ParashosP,GordonI,MesserHH.Factorsinfluencingdefectsof rotarynickeltitaniumfilesafterclinicaluse.JEndod2004;30: 722—5.
14.Dobo´-NagyC,Serba´nT,Szabo´ J,NagyG,Madle´naM.A compar-isonoftheshapingcharacteristicsoftwonickel-titanium endo-dontichandinstruments.IntEndodJ2002;35:283—8.
15.Yared GM,BouDagher FE, MachtouP. Influenceof rotational speed, torque and operator’s proficiency on ProFilefailures. IntEndodJ2001;34:47—53.
16.MartinB,ZeladaG,VarelaP,BahilloJG,Maga´n F,AhnS,etal. Factorsinfluencingthefractureofnickel-titaniumrotary instru-ments.IntEndodJ2003;36:262—6.
17. LopesHP,FerreiraAA,EliasCN,MoreiraEJ,deOliveiraJC,Siqueira JrJF.Influenceofrotationalspeedonthecyclicfatigueofrotary nickel-titaniumendodonticinstruments.JEndod2009;35:1013—6.
18.LeeMH,VersluisA,KimBM,LeeCJ,HurB,KimHC.Correlation betweenexperimentalcyclicfatigueresistanceandnumerical stressanalysisfornickel-titaniumrotaryfiles.JEndod2011;37: 1152—7.
19.CampsJJ,PertotWJ,LevalloisB.Relationshipbetweenfilesize andstiffnessofnickel-titaniuminstruments.EndodDent Trau-matol1995;11:270—3.
20.Zhang Ew, Cheung GS, Zheng YF. A mathematical model for describingthemechanicalbehaviorofrootcanalinstruments. IntEndodJ2011;44:72—6.
21.Blum JY,MatctouP,MicallefJP.Locationofcontactareason rotaryProfileinstrumentsinrelationshiptotheforcesdeveloped duringmechanicalpreparationonextractedteeth.IntEndodJ 1999;32:108—14.
22. Hu¨bscherW,BarbakowF,PetersOA.Rootcanalpreparationwith FlexMaster:assessmentoftorqueandforceinrelationtocanal anatomy.IntEndodJ2003;36:883—90.
23. Peters OA, Peters CI, Schonenberg K, Barbakow F.ProTaper rotaryrootcanalpreparation:assessmentoftorqueandforce inrelationtocanalanatomy.IntEndodJ2003;36:93—9.
24. BeruttiE,ChiandussiG,GaviglioI,IbbaA.Comparativeanalysis oftorsionalandbendingstressesintwomathematicalmodels ofnickel-titaniumrotaryinstruments:ProTaperversusProFile. JEndod2003;29:15—9.
25. BoesslerC,PetersOA,ZehnderM.Impactoflubricantparameters onrotaryinstrumenttorqueandforce.JEndod2007;33:280—3.
26. TripiTR,BonaccorsoA,CondorelliGG.Cyclicfatigueofdifferent nickel-titaniumendodonticrotaryinstruments.OralSurgOral MedOralPatholOralRadiolEndod2006;102:e106—14.
27. GambariniG. Rationalefortheuseoflow-torqueendodontic motorsinroot canalinstrumentation. Endod DentTraumatol 2000;16:95—100.
28. HaJ-H,KimSK,CheungGS-P,JeongSH,BaeYC,KimH-C.Effect ofalloytipeonthelife-timeoftorsion-preloaded nickel-tita-niumendodonticinstruments.Scanning2015;37(3):172—8.
29. Haı¨kelY,SerfatyR,BatemanG,SengerB,AllemannC.Dynamic andcyclicfatigueofengine-drivenrotarynickel-titanium endo-donticinstruments.JEndod1999;25:434—40.
30. ChoOI,VersluisA,CheungGS,HaJ-H,HurB,KimH-C.Cyclic fatigue resistance tests of nickel-titanium rotary files using simulated canal and weight loading conditions. Restor Dent Endod2013;38:31—5.
31. CheungGS.Instrumentfracture:mechanisms,removalof frag-ments,andclinicaloutcomes.EndodTop2009;16:1—26.
32. WeiX,LingJ,JiangJ,HuangX,LiuL.ModesoffailureofProTaper nickel-titaniumrotaryinstrumentsafter clinicaluse.JEndod 2007;33:276—9.
33. AlapatiSB,BrantleyWA,SvecTA,PowersJM,NussteinJM,Daehn GS. SEM observations of nickel-titanium rotary endodontic instrumentsthatfracturedduringclinicaluse.JEndod2005;31: 40—3.
34. CheungGS,ShenY,DarvellBW.Effectofenvironmenton low-cyclefatigueofanickel-titaniuminstrument.JEndod2007;33: 1433—7.
35. KramkowskiTR,BahcallJ.Aninvitrocomparisonoftorsional stressandcyclicfatigueresistanceofProFileGTandProFile GT Series X rotary nickel-titanium files. J Endod 2009;35: 404—7.
