Comparative analysis of torsional and bending behavior through finiteelement models of five Nickel-Titanium endodontic instruments

Transcription

1 Submitted to Journal of Endodontics, July 2009 Comparative analysis of torsional and bending behavior through finiteelement models of five Nickel-Titanium endodontic instruments Valérie Chevalier *, Reza Arbab-Chirani *, Shabnam Arbab-Chirani and Sylvain Calloch * CHU-Service d Odontologie/UEB-UFR d Odontologie, Brest, France Laboratoire Brestois de Mécanique et des Systèmes, UEB-ENSIETA, Brest, France Laboratoire de Traitement de l Information Médicale, INERSM-U650, Brest, France Laboratoire Brestois de Mécanique et des Systèmes, UEB-ENIB, Plouzané, France * Centre Hospitalier Universitaire-Service d Odontologie, 5 avenue Foch, 29200, Brest /Université Européenne de Bretagne-Faculté d Odontologie, 22 rue Camille Desmoulins, 29238, Brest Cedex 3, France Laboratoire Brestois de Mécanique et des Systèmes, Université Européenne de Bretagne-Ecole Nationale Supérieure d Ingénieurs des Etudes et Techniques d Armement, 2 rue François Verny, Brest Laboratoire de Traitement de l Information Médicale, INERSM U650, 5 avenue Foch, 29200, Brest Laboratoire Brestois de Mécanique et des Systèmes, Université Européenne de Bretagne-Ecole Nationale d Ingénieurs de Brest, Technopôle Iroise 29238, Plouzané, France Correspondence: Reza Arbab-Chirani, DDS, PhD, UFR d Odontologie de Brest, 22 rue Camille Desmoulins, Brest Cedex 3, France. (Tel.: Fax: arbab@univ-brest.fr)

2 Abstract Hypothesis To develop a numerical model to compare the mechanical behavior of five existing endodontic instruments under bending and torsion. Methods A numerical study has been carried out. At first, the geometry of each instrument was meshed with a finite element code. Then, the two most representative clinical loadings in practice, i.e. bending and torsion have been studied with an ad hoc model for the superelasticity of Ni-Ti. Then, the results obtained under these conditions have been compared. Major findings Mechanical properties of different endodontic rotary files were evaluated by numerical simulation. These instruments did not have the same behavior during simulated shaping. Results of the present study showed that the five instruments of 0.06 taper had different levels of torque and bending stress. Conclusions The use of a 3-D finite elements approach, in order to carry out studies about the geometry of endodontic files and their mechanical properties, appears to be relevant. Keywords Nickel-Titanium, finite element analysis, comparison of rotary instruments, endodontic preparation, bending and torsion, behavior model.

3 Introduction Since a few years, Nickel-Titanium (Ni-Ti) endodontic instruments, which are much more flexible in bending than traditional stainless steel instruments (1), are used to facilitate and improve treatment of curved root canals. This extreme flexibility is due to a feature in the mechanical behavior of Ni-Ti Shape Memory Alloys (SMA): the superelasticity. The two main characteristics of the SMA superelastic behavior are a typical hysteretic behavior and the absence of residual strain after a total strain of 6% to 8% (2). The initial form of the material is the austenite phase; when it is loaded beyond a certain stress level and at a constant temperature greater than the characteristic temperature of the Martensite Start (M s ), the austenite phase transforms into a martensite phase. This martensitic transformation is reversible during unloading (3). An increasing number of Ni-Ti instrument systems are currently available (4). These files have unique design properties in terms of cross-sectional shape with radial lands or sharp cutting edges, constant or variable pitch (5), progressive or constant taper, etc. However, whatever the instrument may be, intracanal separation can occur (6). Some authors suggest that instrument separation can be caused by fatigue which occurs under repetition of bending stresses in curved canals (7-9). Other authors relate it to torsion (10, 11). It may jeopardize the outcome of the endodontic treatment (12). This is the reason why it remains important to study the resistance of these different endodontic instruments under bending and torsion. A traditional approach consists in experimental studies. However, numerical modeling and analysis have constituted a complementary way to study mechanical behavior of existing or even future files. To our knowledge, only few studies have dealt with numerical analysis of the mechanical behavior of several Ni-Ti endodontic instruments. The behavior models used in these investigations consisted of either elastic (13-15), or elasto-plastic model (16-18) which are not appropriate for superelasticity of SMA. This is confirmed in a very recent paper, where the model used is more suited to SMA (19). Moreover, some of the comparative studies ignored the taper of the root canal files (13-16). The aim of present investigation was to compare numerically the bending and torsional resistance of five existing instruments with the equivalent size (Hero, HeroShaper, ProFile, ProTaper, Mtwo) by using an ad hoc behavior model for superelasticity of SMA (20).

4 Materials and Methods Geometry Five instruments with the same tip diameter of 0.20 mm and an average taper around 0.06 have been modeled. The geometries of these files, Hero (20/.06) (Micro-Mega, Besançon, France), HeroShaper (20/.06) (Micro-Mega), ProFile (20/.06) (Dentsply-Maillefer, Ballaigues, Switzerland), Mtwo (20/.06) (Dentsply-Maillefer) and ProTaper F1 (20/.055 to.07) (Dentsply-Maillefer) were generated according to the information provided by the manufacturers and according to literature (18, 19). In order to obtain more details, all the instruments were observed by an optical microscope. All these instruments were numerically created using the Castem software (Commissariat Energie Atomique, Saclay, France) based on the finite element method. The geometric models took into account the form of the crosssection, the taper (constant or progressive), the length and the pitch (constant or progressive) of each instrument. Mechanical loadings To take into account the use conditions of the instrument, two different loading paths, i.e. bending and torsion were numerically applied to the meshing generated by Castem. The handle of the instruments was kept fixed throughout the different simulations. The bending has been simulated by moving the tip of each instrument up to f = 3.8 mm in the cross-section plane. The torsion has been simulated by applying, to each instrument tip, a rotation of θ = 22 around the file axis. Ni-Ti behavior model All the simulations have been carried out with an ad-hoc model for superelasticity of SMA (20) which has been implemented in Castem. The Ni-Ti material parameters which are necessary for the mechanical behavior models have been deduced from a loading-unloading tensile test (Zwick machine, Ulm, Germany) up to 7.5% axial strain. It has been realized on a wire used to manufacture endodontic instruments. The mechanical parameters were as following: Young s modulus = MPa, Transformation Yield stress = 505 MPa, Hardening modulus = 333 MPa, Hysteresis size = 250 MPa, Maximal transformation strain = 6% and Poisson s ratio = 0.3.

5 Results Simulated geometry of each instrument was obtained (Fig. 1A). The experimental stress-strain curves and the numerical curves were also obtained and compared (Fig. 1B). The first part of the results concerns the numerical study of the five files in the case of bending (Fig. 2A). Figure 2B illustrates the evolution of the generated bending effort versus the imposed displacement obtained by simulations. The graphs highlight that the level of bending (3.8 mm) in use in our simulations appears to be sufficient to get a non-linear response for all the instruments except ProFile (Fig. 2B). It can be mentioned that the instruments which develop the greater level of bending effort are ProTaper, HeroShaper and Hero, respectively. The instruments ProFile and Mtwo develop a low level of bending effort. Figure 2C shows more details of the results obtained on the different files at the maximal bending. We can see the stress distribution and strain level through the deformed geometry. These simulations highlight that, during bending, the maximal stress level is situated in the curved part of each instrument (Fig. 2C). Stress generated by torsion was also evaluated (Fig. 3A). Figure 3B describes the evolution of the generated torque as a function of the imposed torsion angle (θ = 22 ). It shows that except one file (Mtwo), all other instruments develop a non-linear response based on martensitic transformation. The instruments with the greatest level of torque are in descending order ProTaper, HeroShaper, Hero, ProFile and Mtwo (Fig. 3B). The equivalent stress in the instruments of maximal torsion can be evaluated (Fig. 3C). In order to have a better visualization of the results under torsion, a zoom of the tip-half of the instruments has been realized. It shows also that under torsion, the maximal stress is localized at the tip of the instrument.

6 Hero Taper : 6% 16.0 Ø HeroShaper Taper : 6% 11.0 Ø ProFile Taper : 6% 16.0 Ø Mtwo A Taper : 6% Ø 0.2 ProTaper Taper : 5.5% 12.5 Taper : 7% Ø B Figure 1 Figure 1. (A) The Finite element meshing of five endodontic instruments: Hero (6%, 0.2mm), HeroShaper (6%, 0.2mm), ProFile (6%, 0.2mm), Mtwo (6%, 0.2mm) and ProTaper F1 (5.5%-7%, 0.2mm). (B) Comparison of experimental results ( ) and simulation ones ( ) obtained by a tensile test on a Ni-Ti wire with the superelastic numerical model.

7 A f = 3.8 mm f = 3.8 B C Hero HeroShaper Mtwo ProFile Pro Taper F1

8 A θ = 22 B C Hero HeroShaper Mtwo ProFile Pro Taper F1 Figure 3

9 Figure 2. Simulation results of bending. (A) Simulation of bending f = 3.8 mm, (B) Correlation between bending stress and deflection, (C) Stress distribution in the five instruments under bending. Figure 3. Simulation results of torsion. (A) Simulation of torsion = 22, (B) Correlation between torque and angle of torsion, (C) Stress distribution in the five instruments under torsion. Discussion Flexibility and resistance are properties expected from an ideal root canal file (21, 22). However, it is important to note that no instrument can be considered as ideal for all clinical cases. Sattapan et al. observed clinically used endodontic Ni-Ti rotary instruments. They showed that flexural fatigue occurred in 44.3% whereas torsional failure occurred in 55.7% of them (10). Evaluation of the endodontic files mechanical properties can allow improving their clinical use and minimizing blockage and separation risks. Analysis of mechanical aspects of these instruments can be undertaken by either experimental or numerical method by an adequate mathematical model. To go further in the numerical study of Ni-Ti instruments, the present investigation considers the mechanical behavior under bending and torsion of five existing instruments of equivalent size. The experimental stress-strain curves and the numerical curves were obtained and showed a very good correlation (Fig. 1B). It illustrates the good ability of the superelastic model, used in this study, to correctly reproduce the hysteretic mechanical behavior of Ni-Ti SMA, with no residual strain. To our knowledge, these five instruments have never been compared all together. Even though it is difficult to find and compare systems with total similar geometrical characteristics, the present study compares endodontic files with the same diameter and an equivalent average taper, but with a variety of cross-sectional shapes. Indeed, many authors have proven that the behavior under bending and thus, the resistance to cyclic fatigue is influenced by the diameter (12) and the taper of the files (23, 24). Moreover, the torque in the instruments and consequently, the fracture under torsion are also conditioned by the same parameters (10, 21). That is why most of the comparative investigations deal with instruments of the same diameter and equivalent taper (4, 18, 25). Ni-Ti files have higher elastic flexibility and a superior resistance to torsional fracture than manuals endodontic instruments (22). However, all of the rotary Ni-Ti instruments do

10 not have the same mechanical properties. Results of the present study confirm this observation and show the instruments with the greatest level of torque and bending stress are in descending order ProTaper, HeroShaper, Hero, ProFile and Mtwo. According to manufacturer s recommendations, Hero and HeroShaper (20/.06) are not designated to prepare apical canal portion whereas the three other files can be normally used to prepare until the working length. This different clinical protocol can explain that Hero and HeroShaper are more rigid than ProFile and Mtwo (20/.06). The high level of stiffness of the ProTaper F1 (20/.055 to.07) may be explained in that this progressive taper instrument is more solicited by the imposed loading in the.07 tapered portion than.055. There is no research reported in the current endodontic literature that specifically compares the mechanical properities of the five instruments evaluated in the presented study. However, previous numerical and experimental studies have been conducted to test the torque, resistance to fracture and the flexibility of nickel-titanium rotary files (4, 8, 13-15, 18, 22, 25-27). In experimental investigations, authors have studied flexibility and resistance of some files by evaluating the cyclic fatigue of those (4, 8, 22, 26). From the results of these studies, the correlation between mechanical behavior and cross-sectional area and length of pitch was demonstrated. In numerical field, some attempts have been made to compare different endodontic files and their mechanical properties, especially by means of bending moment evaluation (13-15, 18, 25). Globally, these experimental and mathematical modeling data are consistent with the results under bending for the different instruments of the present study. Our results under torsion are more debated in comparison with literature. However, they are consistent with the graphs presented in the studies of Kim et al. concerning ProFile and ProTaper on one hand, and Mtwo and HeroShaper on the other hand (18, 25). The clinical significance of the difference of mechanical behavior among endodontic systems can only be determined by means of numerous numerical and experimental evaluations and long-term clinical studies. However, it is important to note that the clinical use of Ni-Ti rotary instruments for shaping curved canals reduces their fatigue resistance, especially for stiff files (24, 26). Thus, the stiffest Ni-Ti rotary files with.06 taper should not be used for apical enlargement of severe curved canals but should be retained for less curved canals. However, concerning this study, one could deplore the lack of experimental validation. In a near future, the development of an experimental bending set-up for Ni-Ti instrument should allow us to compare the results of our simulations under bending conditions with

11 experimental data obtained by recording the bending effort versus the displacement. The same procedure will be further developed under torsion conditions. Such comparisons of numerical results against experimental ones are essential to validate the method based on a finite element approach. In our opinion, after validation of this step, the numerical simulations with a well-adapted behavior model should facilitate the comparison of the mechanical behavior of existing files. They can also ease the design of new Ni-Ti instruments while reducing the time required for testing and marketing. Such an accurate predictive analysis should permit designers to easily vary parameters (geometrical features, use of different Ni-Ti materials or steels, ) in order to better understand the behavior of a given instrument, assess the risk of failure and predict its life-time prior to the building a prototype. In conclusion, within the limitations of the present study, the use of a 3-D finite elements approach, in order to carry out studies about the geometry of commercially available files and their mechanical properties, appears to be relevant. The results of this study suggested that the five studied endodontic files had different behavior in mechanical point of view. Further numerical and experimental investigations are needed to evaluate the mechanical behavior of different endodontic Ni-Ti instruments and their clinical benefits and eventual negative consequences. Acknowledgments This study is a part of the MAFESMA project, \Tools for modeling, design and control of smart structural systems based on shape memory alloys". It has been supported by ANR (the French National Agency for Research).

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