**4. Discussion**

The results obtained in the present study reject the null hypothesis (H0) that stated that the geometry of the cross-section design would not affect the resistance of NiTi endodontic rotary files to dynamic cyclic fatigue.

The results derived in the present study reported that Mtwo NiTi alloy endodontic rotary files with double S-shaped cross-section showed higher resistance to dynamic cyclic fatigue than T Pro E1 austenite phase NiTi alloy endodontic rotary files with rectangular cross-sections, T Pro E2 austenite phase NiTi alloy endodontic rotary files with convex triangular cross-sections, and T Pro E4 austenite phase NiTi alloy endodontic rotary files with triangular cross-sections. The results can be summarized in that with the increase in the mass and the contact points between the instrument surface and the dentin walls of the root canal, the cyclic fatigue resistance of the NiTi endodontic rotary files decreases. This can also influence the flexibility of the NiTi endodontic rotary files and lead the instrument to cause excessive root canal dentine removal, apical transportation [22], root perforations, and fractures [4,23,24].

The persistent bacterial load present in the root canal system after endodontic therapy has been highlighted as a relevant etiologic factor in the endodontic failure and secondary endodontic infections [25]; moreover, Sjögren established a relationship between the bacterial load reduction during the root canal treatment and the prognosis of the endodontic therapy, and reported that negative microbiological cultures obtained from the root canal system led to an endodontic success rate close to 94%, whereas positive cultures reduced the success rate to 68% [26]. This is the reason that the cyclic fatigue resistance of NiTi endodontic rotary files has been widely analyzed.

The design of the anatomical-based artificial root canal used in the present study was based on the method described by Schneider [21], selecting a 5 mm radius and 60◦ curvature angle and adapting the geometry to the NiTi endodontic rotary files included in this study. Previous studies have shown that the fatigue resistance of endodontic rotary files decreases as the angle of curvature increases and the radius of curvature decreases [10,27,28], since the stress accumulation on the endodontic rotary file is inversely proportional to the radius of curvature of the canal. As a result, in more abrupt root canals, there is an augmentation of the torsion and flexural bending fatigue that ultimately results in instrument fracture [10,21]. Moreover, clinical or even ex vivo experimental studies would be desirable to reproduce clinical conditions and extrapolate the cyclic fatigue results to the clinical setting; however, the difficulty to homogenize the radius, curvature angle, apical diameter, hardness, and cross-section of the root canals can bias the study by introducing more variables [28]. Therefore, custom-made static and dynamic cyclic fatigue devices have been developed to independently analyze the influence of the variable under study; unfortunately, there is neither a norm that regulates the characteristics of the custom-made cyclic fatigue devices nor an international standard for testing the cyclic fatigue behavior of NiTi endodontic rotary instruments with taper higher than 2% [29].

Static and dynamic testing devices have been used to analyze the cyclic fatigue. In the static cyclic fatigue testing models, the NiTi endodontic files are rotated until fracture occurs and the tension–compression cycles are concentrated in the maximum curvature angle of the root canal, resulting in microstructural alterations in the file and subsequent failure. Therefore, dynamic cyclic fatigue testing devices are preferable to better reproduce the clinical conditions, especially the pecking motion of the NiTi endodontic rotary files. Thus, this study used a dynamic cyclic fatigue testing model, an anatomical-based artificial root canal and an automatic detection system to objectively and accurately identify failures of endodontic rotary files [28,30,31].

Previous studies have analyzed the influence of cross-section design on the mechanical behavior of the NiTi endodontic rotary files. Sekar et al. analyzed the role of the crosssection on the cyclic fatigue resistance of NiTi endodontic rotary files under continuous and reciprocation motion and reported that the 25.06 Mtwo rotary files were significantly more resistant to failure than Revo-S SU and One Shape files in both continuous (*p* < 0.001) and reciprocating motion (*p* < 0.001) [17]. These findings are consistent with the results of our study, which concluded that the double S-shaped cross-section of Mtwo NiTi endodontic files showed higher cyclic fatigue resistance than the rectangular cross-section of T Pro E1 NiTi endodontic files, the convex triangular cross-section of T Pro E2 NiTi endodontic files, and the triangular cross-section of T Pro E4 NiTi endodontic files. In addition, de Menezes et al. reported that ProDesign endodontic rotary files with a modified double S-shaped cross-section design presented a significantly higher (*p* < 0.05) number of cycles to failure (910.37 ± 472.10) than Wave One Gold endodontic reciprocating files with a parallelogram cross-section design (264.76 ± 305.42) in artificial root canals with a 60◦ curvature and 5 mm radius of curvature [32]. Moreover, Adiguzel et al. showed that XP-endo Shaper endodontic rotary files with triangular cross-sections design presented a significantly higher (*p* < 0.05) number of cycles to failure (3064.0 ± 248.1) than HyFlex CM endodontic rotary files with a variable cross-section design (from triangular to trapezoidal and quadratic) (1120.5 ± 106.1) in artificial root canals with a 60◦ curvature and 3 mm radius of curvature [33]; however, Uygun et al. showed that HyFlex EDM endodontic rotary files with a variable cross-section design (from triangular to trapezoidal and quadratic) presented a significantly higher (*p* < 0.05) number of cycles to failure (1710.42 ± 114.89) than Vortex Blue endodontic rotary files with a convex triangular cross-section design

(548.39 ± 77.64), ProTaper Gold endodontic rotary files with a convex triangular crosssection design (600.83 ± 66.49), and One Curve endodontic rotary files with a variable cross-section design (from double S-shaped to triangular) (959.58 ± 61.18) in artificial root canals with a 60◦ curvature and 3 mm radius of curvature [34].

Unfortunately, the limitations of the present study prevented the analysis of more cross-section designs to standardize the NiTi alloy, apical diameter, pitch, helix angle, manufacturing process, speed, and taper. In addition, the study was not developed in a clinical environment due to the difficulty in standardizing the sample.
