**3. Results**

Scanning electron microscopy (SEM) analysis of the NiTi alloy endodontic rotary files did not detect any structural alterations or accumulated organic matter. Additionally, due to the laser machining process used to make them, the manufacturing lines were parallel to each other and perpendicular to the longitudinal axis of the files. The distance and width between these manufacturing lines were indicators of the precision and intensity of the laser machining manufacturing process. The laser machining process also resulted in tubular porosity that was observed in the files. Additionally, tubular porosity was visible in all of the NiTi alloy endodontic rotary files as a result of the combination of other chemical elements with the Ti alloys (Figure 2).

**Figure 2.** (**A**) SEM images of the full-length NiTi alloy endodontic rotary files (Ref.: IRE 02506, D, Endogal, Galician Endodontics Company, Lugo, Spain) at ×30, (**B**) and specifically of the end of the file at ×600 and ( **C**) the surface of the file at ×600.

EDX micro-analysis of the NiTi alloy endodontic rotary files was performed at three different locations at 20 kV, enabling a thorough and precise analysis of the composition of the NiTi alloy endodontic rotary files. Through EDX micro-analysis at 20 kV, the NiTi alloy endodontic rotary files were found to comprise Ti (37.59–34.52 wt.%) and Ni (34.19–38.81 wt.%), although O and C were also observed (Figure 3).

**Figure 3.** EDX micro-analysis of the NiTi alloy endodontic rotary files at locations (**A**) 1, (**B**) 2, and (**C**) 3.

Table 1 and Figure 4 show the mean and SD values of the time to failure (in seconds) across all study groups.


**Table 1.** Descriptive analysis of time to failure (seconds).

a,b,c,d,e Statistically significant differences among groups (*p* < 0.05).

The ANOVA analysis found there were differences of statistical significance among all of the study groups with regard to the time to failure (*p* < 0.001) (Figure 5). The results of the time to failure could be applied to the "number of cycles to failure" since all of the NiTi endodontic files were used at a frequency of 60 pecks per minute within the dynamic cyclic fatigue device.

The Weibull statistics scale distribution parameter (η) identified differences of statistical significance among all of the study groups with regard to the time to failure (*p* < 0.001) (Table 2, Figure 5). The Weibull statistics shape distribution parameter (β) revealed differences grea<sup>t</sup> enough to be statistically significant with regard to time to failure between the 200 rpm and 400 rpm+ groups (*p* = 0.0236), the 500 rpm and 350 rpm+ groups (*p* = 0.0003), the 350 rpm+ and 400 rpm+ groups (*p* = 0.0154), the 350 rpm and 500 rpm groups (*p* = 0.0152), and the 200 rpm and 500 rpm groups (*p* = 0.0005). However, there were not enough differences observed in the time to failure between the 350 rpm and 400 rpm+ groups (*p* = 0.2283), the 500 rpm and 400 rpm groups (*p* = 0.1908), the 200 rpm and 350 rpm+ groups (*p* = 0.08925), the 350 rpm and 350 rpm+ groups (*p* = 0.2492), and the 200 rpm and 350 rpm groups (*p* = 0.3123) to be statistically significant (Table 2, Figure 5). In short, the NiTi alloy endodontic rotary systems exhibited very predictable behavior, as it took about the same amount of time for the majority of the endodontic rotary files within each study group to reach the point of failure. The more gradual slope seen when using the NiTi endodontic rotary files at 350 rpm+ would indicate that this behavior is easier to predict than other kinematics. The NiTi alloy endodontic rotary files at 350 rpm+ were shown to be the most resistant to cyclic fatigue, followed by the NiTi alloy endodontic rotary files at 400 rpm+, 200 rpm, 350 rpm, and 500 rpm.

**Figure 4.** Box plot of time to failure. The median value of the respective study groups is represented by the horizontal line in each box. ♦—Box plot mean value. O—Extrema value.


**Table 2.** Weibull statistics for the time to failure across the study groups.

**Figure 5.** Weibull probability plot displaying time to failure across study groups.

## **4. Discussion**

The findings of the present study do not accept the null hypothesis (H0), which postulates that rotational speed does not affect the dynamic fatigue resistance of NiTi alloy endodontic rotary files.

The present study used the same NiTi alloy endodontic instruments in rotary and reciprocating kinematic motion since the manufacturer reported that the geometrical design of the NiTi alloy endodontic files allows for its use in both kinematic movements; therefore, manufacturers recommend its use with both continuous and reciprocating rotations. Furthermore, other instrumentation systems can be used with continuous or reciprocating rotation, and it is necessary to have a motor in which the angles can be adjusted. Clear examples can be found in the studies of Yared 2008 [22] and De Deus 2010 [17], where they used instruments that cut clockwise in a reciprocating mode.

Previous studies have analyzed the effects of rotational speed on the number of cycles to fracture of rotary NiTi instruments. Lopes et al. subjected ProTaper Universal instruments F3 and F4 to 300 and 600 rpm; however, the speed values selected were too distant, a cylindrical tube was used as the artificial root canal, and the fracture detection of the NiTi alloy endodontic rotary files was subjective and therefore imprecise. Furthermore, they did not carry out any additional measurement methods [23]. Additionally, some reviews have been conducted with the aim of analyzing the mechanical and metallurgical behavior of endodontic instruments under different testing conditions and methodologies [24–26].

The results derived from the present study indicate that the resistance of NiTi alloy endodontic rotary files to cyclic fatigue is inversely proportional to the rotational speed. In addition, reciprocating movements were shown to be more resistant to cyclic fatigue when compared with continuous rotational movements. Moreover, the results derived from the

present study present a direct application to the clinical setting, since the reciprocating systems provided higher resistance to cyclic fatigue, followed by the lower values of rotational speed. Therefore, clinicians should choose reciprocating motion systems or reduce the rotational speed of the endodontic torque-controlled motor if the NiTi endodontic rotary or reciprocating file is expected to experience high cyclic fatigue, particularly in root canal systems with a pronounced angle and/or curvature radius.

Specification #28 of the American Dental Association/American National Standards Institute (ADA/ANSI) outlines tests used to measure how flexible stainless steel hand files are, as well as their strength under torsion. These same tests were also adopted under ISO 3630/1, which is meant for instruments with a 0.02 ISO taper. Currently, there are still no specifications or international standards with regard to testing the resistance of endodontic rotary instruments to cyclic fatigue [27]. The ideal model would entail curved canals being instrumented in natural teeth. That being said, each tooth can only be used once with these tests, and instrumentation causes changes to the shape of the root canal, rendering it impossible to establish standardized experimental conditions. Therefore, various methods and devices have been used to analyze the in vitro resistance of NiTi rotary endodontic instruments to cyclic fatigue fractures [28]. Cyclic fatigue is considered a dynamic event itself since the movement of the NiTi alloy endodontic rotary or reciprocating instruments inside the root canal system gives it dynamism. Cyclic fatigue tests have been carried out in a static model under well-controlled experimental conditions; however, the novel pecking movement of the endodontic handpiece of the present cyclic fatigue device provides an additional dynamic movement more representative of the in-and-out motion made by the operator. That being said, studies have shown that the number of cycles to failure is significantly higher in the dynamic model, regardless of the brand or manufacturing processes [29–31]. In the static testing model, there is no up-and-down movement applied to the instrument, causing stresses to accumulate at a fixed point. With the dynamic model, however, these stresses are spread out along the full length of the instrument, thereby increasing its cyclic fatigue resistance [23]. Furthermore, researchers have found that the up-and-down motion should not exceed 1, 2, or 3 mm/s in the dynamic testing model so as to simulate clinical conditions [24]. An automatic detection system can be used to identify the precise point of failure of endodontic rotary files [19]. Given this, the present study used an anatomically based artificial root canal design in accordance with Schneider's method [20], using a 60◦ curvature angle and radius of 5 mm, and modifying the geometry to adapt to the NiTi endodontic rotary files used in this study [11].

The findings of this study corroborate the findings of Kim et al., who found that the Reciproc R25 and WaveOne Primary heat-treated NiTi alloy endodontic reciprocating files were more resistant to torsion and cyclic fatigue when compared with ProTaper F2 NiTi alloy endodontic rotary files used under continuous rotation [32]. Similarly, De Deus et al. found that the ProTaper F2 NiTi alloy endodontic rotary file also exhibited significantly greater resistance to cyclic fatigue when employed using reciprocating movement rather than continuous rotational motion [17]. Furthermore, several other studies have emphasized the increase in the lifespan of NiTi alloy endodontic rotary files when using reciprocating movement as opposed to continuous rotational motion [33,34]. That being said, there are several studies that have analyzed the impact of rotational speed on how resistant NiTi alloy endodontic rotary files are to cyclic fatigue, although the findings remain controversial. Lopes et al. found that the ProFile NiTi alloy endodontic rotary instrument exhibited greater susceptibility to accidental fracture at higher rotational speeds, and they found that the total number of cycles to failure was about 30% lower in ProTaper instruments when the rotational speed was increased from 300 to 600 rpm [23]. On the other hand, Martin et al. reported that unexpected fracture of NiTi alloy endodontic rotary instruments was correlated with the rotational speed, as the ProTaper NiTi alloy endodontic rotary instrument was more susceptible to fracture at 350 rpm than at 250 or 150 rpm [16]. However, Gao et al. reported no statistically significant differences (*p* > 0.05) between files that had similar NiTi alloys and apical diameters when used at different

rotational speeds [35]. The discrepancies in these findings may be due to differing study designs, NiTi alloys, or geometrical designs of the instruments under study. Additionally, not only the asymmetric oscillatory counterclockwise motion (reciprocation motion) but also the asymmetric oscillatory clockwise motion can be used with any rotary instrument. Martins et al. evaluated the cyclic fatigue resistance of three replicate rotary instruments compared with their original brand systems using continuous rotation and optimum torque reverse kinematics. They reported that reciprocating files showed greater resistance to cyclic fatigue than continuous rotation files, and the replicas showed higher cyclic fatigue resistance than the original brand instruments and higher transition temperatures to the austenitic phase [36].

The results found by Ray et al. were corroborated by those obtained in the present study using an analysis of dynamic cyclic fatigue when employing a standardized axial movement, increasing the durability of NiTi alloy endodontic rotary instruments subjected to cyclic fatigue in comparison with the results observed in static cyclic fatigue devices [37]. Most studies comparing dynamic and static cyclic fatigue appliances have concluded endodontic rotary instruments exhibited a time to fracture roughly 20–40% longer when undergoing dynamic cyclic fatigue than the time to fracture found in studies of static cyclic fatigue, with this also being more similar to the clinical setting [38–40].

The cyclic fatigue testing was performed in a room temperature setting, according to the results by La Rosa et al., who showed that studies at body temperature impaired the cyclic fatigue resistance of most files [41]. In addition, Plotino et al. reported that the surrounding temperature affected the NiTi crystalline phase transformation, significantly decreasing the cyclic fatigue resistance at body temperature [42].

Regrettably, the limitations of this study precluded analyzing any additional kinematic movements, under both reciprocating and continuous rotation movements. Future studies ought to include more NiTi alloys, apical diameters, pitch, helix angles, manufacturing processes, and tapers. Furthermore, due to difficulties with the standardization of samples, the present study was not conducted in a clinical setting. However, the present study provided multimethod research, including SEM, EDX, and an accurate dynamic cyclic fatigue device, increasing the knowledge of the mechanical behavior of NiTi endodontic rotary files under different kinematic conditions.
