Influence of size and taper of artificial canals on the trajectoryof NiTi rotary instruments in cyclic fatigue studiesGianluca Plotino, DDS, PhD,a Nicola M. Grande, DDS, PhD,a Ciro Mazza, DDS,b

Renata Petrovic, MSc, PhD,c Luca Testarelli, DDS,a and Gianluca Gambarini, MD, DDS,a

Rome, Italy, and Belgrade, SerbiaUNIVERSITY “LA SAPIENZA,” CATHOLIC UNIVERSITY OF THE SACRED HEART, AND UNIVERSITY OFBELGRADE

Objective. The aim of this study was to investigate the influence of the shape of 3 different artificial canals on thetrajectory followed by different nickel-titanium rotary instruments.Study design. Ten ProFile and Mtwo instruments, tip sizes 20 and 25, taper .06, were tested in 3 simulated root canalswith an angle of curvature of 60° and radius of curvature of 5 mm but with different shapes. Geometric analysis of thetrajectory that each instrument followed inside the 3 different artificial canals was performed on digital images,determining 3 parameters: angle and radius of the curvature and the position of the center of the curvature. Meanvalues were then calculated for each instrument size in all of the artificial canals. Data were analysed using 1-wayanalysis of variance, Holm t test, and Student t test to determine any statistical difference (P � .05).Results. In all instrument sizes, a statistically significant difference was noted among the artificial canals for the radiusand angle of curvature. No statistically significant difference was noted between instruments of the same size for theradius and angle of curvature and the position of the center of the curve when measured in the canal constructed onthe dimension of the instruments.Conclusions. Different instruments follow different trajectories in artificial canals constructed with the sameparameters of curvature but different shapes, depending on their different bending properties. All of the instrumentsrespected the established parameters of curvature only when the artificial canal is designed on the dimension of the

instruments. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2010;109:e60-e66)

Fractured rotary nickel-titanium (NiTi) instrumentshave been classified into failure as a result of cyclicflexural fatigue or of torsional failure,1 or a combina-tion of both.2 Cyclically fatigued instruments show nomacroscopic evidence of plastic deformation, but in-struments that fracture as a result of torsional overloaddemonstrate variable deformation, such as instrument un-winding, straightening, reverse winding, and twisting.1

Torsional fracture occurs when an instrument tip is lockedin a canal while the shank continues to rotate, thereby exert-ing sufficient torque to fracture the tip. This also may happenwhen the instrument rotation at the tip is slowed substantiallyin relation to cross-sectional diameters.3

Nickel-titanium instruments rotating around a curva-ture for a prolonged period of time are subjected torepeated tensile and compressive stresses such that during

aDepartment of Endodontics, University “La Sapienza, Rome, Italy.”bDepartment of Endodontics, Catholic University of the SacredHeart, Rome, Italy.cDepartment of Restorative Dentistry and Endodontics, School ofDentistry, University of Belgrade, Serbia.Received for publication Jun 27, 2009; returned for revision Aug 3,2009; accepted for publication Aug 5, 2009.1079-2104/$ - see front matter© 2010 Published by Mosby, Inc.

doi:10.1016/j.tripleo.2009.08.009

e60

each rotation the inner surface of the instrument is com-pressed and the outer surface is under tension. This resultsin work hardening within the metal and initiation of cracksleading to eventual cyclic flexural fatigue.4

The American National Standards Institute/Ameri-can Dental Association specification no. 285 prescribestests to measure strength under torsion and flexibility ofstainless steel hand files. Unfortunately, no universallyaccepted test exists to measure cyclic fatigue resistanceof NiTi rotary files. An ideal model would involveinstrumentation of curved canals in natural teeth. How-ever, in such tests a tooth can be used only once and thetrajectory of the root canal changes during instrumen-tation, making it impossible to standardize experimen-tal conditions. As a result, several devices and methodshave been used to investigate in vitro the cyclic fatiguefracture resistance of NiTi rotary endodontic instru-ments.6-15 These devices permit the instruments to ro-tate until fracture using different geometric curvaturefeatures. Resistance of rotary instruments to cyclic fa-tigue decreases with increasing instrument diameters, spe-cifically with core dimensions.10 Moreover, increased se-verity of angle and radius of the curve, around which theinstrument rotates, decreases instrument life span invitro and clinically.10 If the test apparatus does not

sufficiently constrain the shaft of the instrument and its

OOOOEVolume 109, Number 1 Plotino et al. e61

working part during cyclic fatigue testing, each differ-ent instrument, depending on tip size, taper, design,pitch length, and other morphologic and geometric fea-tures, will tend to regain its original straight shape andwill follow its own trajectory, thus not respecting theparameters of radius and angle of curvature and point ofmaximum curvature that must be well established whenconstructing the testing device. Furthermore, if an in-strument is not well retained in a precise trajectory,different bending properties as a result of the physicaland geometric features of the instruments may deter-mine a different trajectory inside the curvature.

If instruments of the same dimensions follow differenttrajectories in the test apparatus, a direct comparison betweeninstruments of different brands may be difficult to performand the results obtained may be unreliable and inconsistent.

The aim of the present study was to investigate theinfluence of the shape of 3 different artificial canals onthe trajectory followed by different NiTi rotary instru-ments. Shape can be considered to be composed of thevariables of degree of curvature, radius of curvature,size, and shape. In this paper, the variables of degreeand radius of curvature were constant and the size andtaper were changed.

MATERIALS AND METHODSTen ProFile NiTi rotary instruments (Dentsply

Maillefer, Ballaigues, Switzerland), tip size 20/taper.06, 10 ProFile instruments, tip size 25/taper .06, 10 MtwoNiTi rotary instruments (Sweden and Martina, Padova,Italy), tip size 20/taper .06, and 10 Mtwo instruments, tipsize 25/taper .06 were selected for this study.

Three simulated root canal with an angle of curvatureof 60° and radius of curvature of 5 mm were constructedfor each instrument size. The center of the curvature was5 mm from the tip of the instrument, the curved segmentof the canal was 5 mm in length, and the linear segmentbetween the tip of the instrument and the end point of thecurvature was 2.5 mm. The artificial canals were con-structed with 3 different shapes. They were milled instainless steel blocks with a precision milling machine.

An artificial canal (A) was constructed with a taperedshape corresponding to the dimensions of the instru-ment tested (tip size and taper), thus providing theinstrument with a suitable trajectory. To ensure theaccuracy of the size of each canal, a copper duplicate ofeach instrument was milled, increasing the original sizeof the instrument by 0.1 mm using a computer numericcontrol machining bench (Bridgeport VMC 760XP3;Hardinge Machine Tools, Leicester, U.K.) was used.The copper duplicates were constructed according tothe curvature parameters that were chosen for the study.With these negative molds the artificial canals were

made using a die-sinking electrical-discharge machin-

ing process (Agietron Hyperspark 3; AGIE, Losone,Switzerland) in a stainless steel block. The depth ofeach artificial canal was machined to the maximumdiameter of the instrument plus 0.2 mm, allowing theinstrument to rotate freely inside the artificial canal.The blocks were hardened through annealing.

A second artificial canal (B) was constructed with atapered shape but with bigger dimensions that did notmatch the instrument size and taper; the artificial canalwas machined, increasing the original size of the in-strument by 0.3 mm.

A third artificial canal (C) was constructed with acylindrical shape and inner diameter of 2 mm.

Each artificial canal was mounted on a stainless steelblock that was connected to a main frame to which amobile plastic support for the handpiece was also con-nected. The dental handpiece was mounted on a mobiledevice that allowed for precise and simple placement ofeach instrument inside the artificial canal, ensuring3-dimensional alignment and positioning of the instru-ments to the same depth.

To ensure precise positioning of the instruments in-side the artificial canal to the same depth, a round stopmade in Teflon was created to fit precisely inside theround hole that was created apically to the end point ofthe artificial canal. The artificial canal was covered witha tempered glass to prevent the instruments from slip-ping out and to allow for observation of the instrument.

ProFile and Mtwo instruments were tested within the3 different artificial canals.

Geometric analysis of the trajectory that each instru-ment followed inside the 3 different artificial canalswas performed on digital images, determining 3 param-eters: angle and radius of the curvature described bythe instruments as measured following Pruett et al.6

and the position of the center of the curvature de-scribed by the instruments.

A first straight line (PQ) was drawn along the longaxis of the coronal straight portion of the instrument. Asecond line (TS) was drawn along the long axis of theapical straight portion of the instrument. There was apoint on each of these lines at which the instrumentdeviated to begin (Q) or end (S) the curvature. Thecurved portion of the instrument was represented by asegment of a circle (C) with tangents at these points.The most precise circumference that lay on the trajec-tory of the instrument was geometrically determinedusing the osculating circumference method.16 The os-culating circle of a curve at a given point is the circlethat best approximates the curve at that point, and it isunique. This method was chosen because the curvaturefollowed by an instrument not constrained in a precisetrajectory is not a precise circumference, but a plain

curve with a different equation. In these cases, this is

OOOOEe62 Plotino et al. January 2010

the most accurate method to define a curvature by theparameters of radius and angle of a circumference. It ispossible to determine the osculating circle passing through3 points of a curve. The points that were chosen on thetrajectory of the instruments were the beginning (Q) andthe end (S) of the curve and a point B that was chosen asthe center of mass of the triangle resulting from the pointsQ, S, and R, which was the point where the straightcoronal and apical portions of the instrument met. Theangle of curvature was defined as the number of de-grees on the arc of the circle between the beginning andend points of the curvature; the radius of the circle wasdefined as the radius of the canal curvature in millime-ters. The center of the curve was calculated measuringthe length of the segments TS and BS (Fig. 1).

The calculation of the radius and angle of curvatureand of the center of the curvature determined by theosculating circumference method was repeated for eachinstrument analyzed in each different artificial canals(Figs. 2-5). Mean values were then calculated for eachinstrument size in all of the artificial canals.

To determine any statistical difference among the arti-ficial canals A, B, and C for all of the instruments and

Fig. 1. The osculating circumference method to determinethe geometrical parameters of the trajectory of the instrument.

parameters of the curvature measured, the data were sub-

jected to a 1-way analysis of variance (ANOVA). Whenthe overall F test indicated a significant difference, themultiple-comparisons Holm t test procedure was per-formed to identify the mean that differed from the others.Moreover, to determine any statistical significance be-tween instruments of the same size and taper (ProFile20/.06 vs. Mtwo 20/.06 and ProFile 25/.06 vs. Mtwo25/.06), data obtained were subjected to a Student t test.Significance was determined at the 95% confidence level.

RESULTSMean values and standard deviations of the radius

and angle of curvature described by the instruments inthe different artificial canals and the position of thecenter of curvature are presented in Table I.

In all instrument sizes a statistically significant differ-ence (ANOVA: P � .001) was noted among artificialcanals A, B, and C for the radius and angle of curvature.A proportional statistically significant increase in the ra-dius of the curvature (Holm t test: P � .05) and a propor-tional statistically significant decrease in the angle of curva-ture (Holm t test: P � .05) occurred in canal B comparedwith canal A and in canal C compared with canal B.

Considering the position of the center of the curva-ture for the ProFile 20/.06, there was no statisticallysignificant difference between canal A and canal C(Holm t test: P � .05), whereas there was statisticaldifference between canal B and canal C and betweencanal A and canal B (Holm t test: P � .05). For Mtwo20/.06 instruments, there was statistically significantdifference among canals A, B, and C (Holm t test: P �.05). For ProFile and Mtwo 25/.06 instruments, therewere no statistically significant differences among ca-nal A, B, and C (ANOVA: P � .05).

Considering each of the 3 different artificial canals,no statistically significant difference (Student t test:P � 1.000) was noted between instruments of the samesize for the radius and angle of curvature and theposition of the center of the curve when measured in thecanal A. A statistically significant difference (P � .001)was noted between instruments of the same size in bothartificial canals B and C.

DISCUSSIONThe impact of torsional fracture, metal fatigue, or

fracture of NiTi rotary instruments due to a combina-tion of torsional stress and accumulation of fatigue isstill debated. Material fatigue appears to be an impor-tant reason for the separation of rotary instrumentsduring clinical use. Peng et al.17 classified most of thefractured instruments analyzed as flexural failure, im-plying fatigue to be the predominant mechanism for thematerial failure. In a related study, Cheung et al.18

reported that the great majority (93%) of instruments

, end o

OOOOEVolume 109, Number 1 Plotino et al. e63

appeared to have failed because of flexural fatigue. Fa-tigue failure accounting for the majority of broken instru-ments might be explained as follows. First, fatigue-crackgrowth rates in NiTi alloys have been reported to be

Fig. 2. Trajectory of the ProFile instrument of tip size 20, tapeof mass of the triangle resulting from the points Q, R, and S;straight coronal and apical portions of the instrument met; S

Fig. 3. Trajectory of the ProFile instrument of tip size 25,Abbreviations as in Fig. 2.

significantly greater than in other metals of similar

strength.19 Thus, once a microcrack is initiated, it canquickly propagate to cause catastrophic failure.

In comparison, Sattapan et al.1 reported that torsionalfracture occurred in 55.7% of all fractured files,

n artificial canals A (left), B (middle), and C (right). B, centerbeginning of instrument trajectory curve; R, point where thef instrument trajectory curve.

.06, in artificial canals A (left), B (middle), and C (right).

r .06, iC, ; Q,

taper

whereas flexural fatigue occurred in 44.3%. These re-

OOOOEe64 Plotino et al. January 2010

sults indicated that torsional failure, which may becaused by using too much apical force during instru-mentation, occurred more frequently than flexural fa-tigue, which may result from use in curved canals.Alapati et al.20 hypothesized that the clinical fracture ofNiTi rotary instruments was largely caused by a single

Fig. 4. Trajectory of the Mtwo instrument of tip size 20, tapas in Fig. 2.

Fig. 5. Trajectory of the Mtwo instrument of tip size 25,Abbreviations as in Fig. 2.

overload incident (causing ductile fracture) during in-

strumentation rather than the result of significant alloyfatigue after a large number of loading cycles. Cheunget al.18 have questioned the macroscopic or lateral viewexamination of a separated file used in these studies,suggesting that fractography techniques are required.

The results of the present study indicate that the

in canals A (left), B (middle), and C (right). Abbreviations

06, in artificial canals A (left), B (middle), and C (right).

er .06,

taper .

trajectory followed by an instrument in an artificial

OOOOEVolume 109, Number 1 Plotino et al. e65

canal depends on the shape of the canal, even if theywere designed with the same geometric parameters.

When the artificial canal was constructed precisely onthe dimensions of each instrument (canal A), all the in-struments were well constrained inside a precise trajec-tory, and even instruments with different design main-tained the parameters of curvature established for theartificial canal. In contrast, when an instrument is not wellconstrained by the artificial canal in a precise trajectory,because the canal is not precisely shaped on its dimension,each instrument may follow its own trajectory inside thecanal even if the parameters of the curve are well established.

Considering each instrument size, the results of the presentstudy indicate that a proportional increase in the radius of thecurvature and a proportional reduction in the angle ofcurvature occurred in canal B and in canal C comparedwith the artificial canal constructed on the size of theinstruments (canal A). For this reason, the file follows acurvature that is less severe than that established on theartificial canal. Furthermore, with less adaptation of theinstrument to the artificial canal, more variation was seenin the parameters of the curvature investigated.

Considering each different artificial canal, no differencewas noted among all of the the instruments when mea-sured in canal A. They followed the same trajectory, asestablished by the parameters of canal itself (radius andangle of curvature and position of the center of the curve).

In contrast, when measured in canals B and C, dif-ferent instruments of the same size followed trajectorieswith radius and angle of curvature that were different

Table I. Mean values and standard deviation of theradius and angle of curvature described by the instru-ments in the different artificial canals and the positionof the centre of curvature

Artificial canal* Radius Angle Center

ProFile 20/.06 A 5 mmb 60°c 5 mma

B 5.5 mm 52° 5.6 mmC 6.5 mm 46° 4.8 mma

Mtwo 20/.06 A 5 mmb 60°c 5 mma

B 5.8 mm 56° 4.7 mmC 7.2 mm 52° 5.3 mm

ProFile 25/.06 A 5 mmd 60°e 5 mma

B 6.3 mm 51° 5.3 mma

C 7 mm 40° 5 mma

Mtwo 25/.06 A 5 mmd 60°e 5 mma

B 5.7 mm 54° 5 mma

C 6.5 mm 44° 5.3 mma

*A: tapered shape corresponding to the dimensions of the instrument;B: tapered shape as in canal A with the size increased by 0.3 mm; C:cylindrical shape and inner diameter of 2 mm.a-eSame letter between parentheses means no statistically significantdifference.

from that established on the artificial canal. A statisti-

cally significant difference (P � .05) was noted be-tween the 2 different instruments in both canal B andcanal C. This demonstrates that if the artificial canal isnot constructed on the shape of the instrument, differentinstruments do not follow the curvature established,and each instrument may follow a different trajectorydepending on its characteristics. In fact, the stiffness ofeach instrument determined by its design may deter-mine different trajectories inside the same curvature,because of different bending properties. For this reason,it is difficult to compare the results of different instru-ments tested on the same artificial canal if the device is notconstructed on the dimension of each instrument size.

Considering the position of the center of the curva-ture measured for each instrument in the different arti-ficial canals, the values obtained were not consistentwith the variation registered for the other parametersanalyzed. This could be due to the approximation of theosculating circumference method to calculate the pa-rameters of a curvature followed by an instrument notconstrained in a precise trajectory. In this case, thecurvature followed by the instrument is not a circum-ference, but a plain curve with a different equation, andthe osculating circumference method represents themost precise method to define a curvature by the pa-rameters of radius and angle of a circumference.16 Thiscalculation is not precise, because the points that de-termine the curvature are approximated and chosen bythe investigator and may be not well repeatable. Forthis reason, by using a precise artificial root canal, theinstrument follows exactly a circular trajectory andthere is not the need of an approximation to calculateand verify the parameters of the curvature. To constructartificial canals on the dimensions of the instruments tobe tested is of importance to reduce the influence of thisvariable on the outcome of these studies.

In earlier studies, there has been no mention of the“fit” of the instrument in the tube or groove. Only 1study calculated the radius of the curvature followed bythe instruments tested for fatigue on digital photographsusing image analyzer software best-fitting a circle tocoincide without crossing the midline of the curvedinstruments for as great a distance as possible.13

Because the instrument is likely to be fitting loosely, thedescription of the radius of curvature in those studies islikely to be overstated; that is, the file was actually bentless severely than reported. Furthermore, each differentinstrument that fits loosely inside the device may follow amore or less severe curvature depending on the stiffness ofthe file. That would explain the wide variation in thereported fatigue life. The large scatter generally encoun-tered in various forms of fatigue tests would add to thevariation in the result.13 To limit this problem, Cheung

and Darvell13 constrained the instrument into a curvature

OOOOEe66 Plotino et al. January 2010

using 3 stainless-steel pins. It has been reported in a3-point bending test of NiTi wires that such constraintsproduce a curvature that is circular.21 Those authors af-firmed that although this cannot actually be true, theapproximation should be reasonable. Unfortunately, NiTiendodontic files are tapered and with different cross-sec-tional design. The different bending properties of thedifferent files and the different bending properties be-tween the coronal and apical portion of the same file maydetermine different trajectories between the pins if the fileis not constrained precisely.

The results of another study22 have demonstratedthat even small variations in the parameters of thecurvature followed by an instrument subjected to flex-ural fatigue resulted in a significant influence on theresults of the cyclic fatigue test. For this reason, it isdifficult to compare the results of different instrumentstested on the same artificial canal if the device is notconstructed on the dimension of each instrument size. Ifinstruments of the same dimensions follow differenttrajectories in the test apparatus, the results obtainedmay be biased by the different parameters of the cur-vature followed by the instruments.

Cyclic fatigue tests are laboratory studies in whichthe variable investigated is the resistance of an instru-ment to fracture because of the accumulation of metalfatigue determined by the tension/compression cyclesat the point of maximum flexure. This condition is farfrom the clinical setting, in which the fracture occursdue to several factors that act together in the same mo-ment. This represents a pure mechanical test to extrapolateonly 1 characteristic of the instruments. The need for astandardization in cyclic fatigue tests is mandatory toobtain consistent results to compare the cyclic fatigueresistance of the different instruments.

Further studies are need to investigate how the re-duced severity of the curve followed by instrumentsthat do not fit well in an artificial canal may influencethe outcome of cyclic fatigue studies.

CONCLUSIONSDifferent instruments follow different trajectories in

artificial canals constructed with the same parametersof curvature but different shapes (size and taper) de-pending on their different bending properties. All theinstruments respected the established parameters ofcurvature only when the artificial canal was designedon the dimension of the instruments.

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nickel-titanium files after clinical use. J Endod 2000;26:161-5.2. Serene TP, Adams JD, Saxena A. Nickel-titanium instruments. Appli-

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5. ANSI/ADA. Specification no. 28-2002. Root canal files and reamers,type K for hand use. Chicago: American Dental Association; 2002.

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12. Plotino G, Grande NM, Sorci E, Malagnino VA, Somma F.Influence of a brushing working motion on the fatigue life ofNiTi rotary instruments. Int Endod J 2007;40:45-51.

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14. Zinelis S, Darabara M, Takase T, Ogane K, Papadimitriou GD.The effect of thermal treatment on the resistance of nickel-titanium rotary files. Oral Surg Oral Med Oral Pathol Oral RadiolEndod 2007;103:843-7.

15. Gambarini G, Grande NM, Plotino G, Somma F, Garala M, DeLuca M, Testarelli L. Fatigue resistance of engine-driven rotarynickel-titanium instruments produced by new manufacturingmethods. J Endod 2008;34:1003-5.

16. Gray A. Osculating circles to plane curves. In: Gray A. Moderndifferential geometry of curves and surfaces with Mathematica.2nd ed. Boca Raton (FL): CRC Press; 1997. p. 111-5.

17. Peng B, Shen Y, Cheung GSP, Xia TJ. Defects in ProTaper S1instruments after clinical use: longitudinal examination IntEndod J 2005;38:550-7.

18. Cheung GS, Peng B, Bian Z, Shen Y, Darvell BW. Defects inProTaper S1 instruments after clinical use: fractographic exam-ination. Int Endod J 2005;38:802-9.

19. Dauskardt RH, Duerig TW, Ritchie RO. Effect of in situ phasetransformation on fatigue-crack propagation in titanium-nickelshape-memory alloys. In: Proceedings of Materials ResearchSociety International Meeting on Advanced Materials, vol. 9;Pittsburgh: Materials Research Society; 1989; pp 243-9.

20. Alapati SB, Brantley WA, Svec TA, Powers JM, Nusstein JM,Daehn GS. SEM observations of nickel-titanium rotary endodonticinstruments that fractured during clinical Use. J Endod 2005;31:40-3.

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22. Plotino G, Grande NM, Cordaro M, Testarelli L, Gambarini G.Influence of the shape of artificial canals on the fatigue resistance ofNiTi rotary instruments. Int Endod J [in press].

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Dr. Gianluca PlotinoVia Eleonora Duse 2200197 RomeItaly

gplotino@fastwebnet.it