**1. Introduction**

Chemical disinfection and mechanical instrumentation of the root canal system are crucial in the prevention of apical periodontitis that arises due to treatment, or to cure it if already established [1]. However, the failure of nickel–titanium (NiTi) alloy endodontic rotatory files remains a major dilemma for endodontists during root canal treatment, despite the NiTi alloy undergoing continuous chemical and mechanical enhancements by manufacturers so as to help prevent complications during endodontic therapy [2]. The fracture of NiTi alloy endodontic rotary files can be caused by torsional fatigue, cyclic fatigue, or some combination thereof [3]. Torsional failure happens when the end of a NiTi alloy endodontic rotary file has become trapped on one of the root canal walls while the instrument is still rotating, causing the file to fracture once the elasticity of the material has been exceeded [4,5]. Flexural bending fatigue is caused by the repeated application of

**Citation:** Faus-Matoses, V.; Faus-Llácer, V.; Ruiz-Sánchez, C.; Jaramillo-Vásconez, S.; Faus-Matoses, I.;Martín-Biedma, B.;

Zubizarreta-Macho, Á. Effect of Rotational Speed on the Resistance of NiTi Alloy Endodontic Rotary Files to Cyclic Fatigue—An In Vitro Study. *J. Clin. Med.* **2022**, *11*, 3143. https:// doi.org/10.3390/jcm11113143

Academic Editors: Massimo Amato, Giuseppe Pantaleo, Alfredo Iandolo and Gianrico Spagnuolo

Received: 2 May 2022 Accepted: 30 May 2022 Published: 31 May 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

compression and traction cycles that the NiTi alloy endodontic rotary file experiences at the site of maximum curvature of the root canal; these stresses subsequently lead to plastic deformation, which can result in unexpected file fracture [3,6].

Several studies have reported that a fractured fragment of the NiTi alloy endodontic rotary file may block the curved canal, negatively affecting the treatment outcome, as disinfecting agents can no longer reach the infected root canal areas [1,7,8]. Additionally, root canal systems that have not been properly disinfected may have a lower likelihood of healing in teeth with periapical lesions [9].

Several additional factors have been linked to the fracture of NiTi alloy endodontic rotary files, including instruments with a cross-section design [10], taper and apical diameter [11], flute length, pitch, and helix angle [12]. In addition, the dynamics of the instrument, such as torque [13] and canal geometry [8], as well as the manufacturing process, whether electropolishing, heat treatment, or ion implantation [14], can influence the risk of fracture.

It remains unclear whether or not rotational speed affects the resistance to cyclic fatigue of NiTi alloy endodontic rotary files. Yared et al. and Martín et al. have found that rotational speed does indeed influence the prevalence of fracture in NiTi alloy endodontic rotary files [15,16]. However, Pruett et al. showed that rotational speed had no significant impact on the risk of fracture of NiTi alloy endodontic rotary files [8]. Additionally, some studies have reported that reciprocating motion may overextend the cyclic fatigue life of NiTi alloy endodontic files in comparison to continuous motion [17,18].

The present study aims to evaluate and assess the effect of the rotational speed of NiTi alloy endodontic rotary files on their resistance to dynamic cyclic fatigue, with a null hypothesis (H0) postulating that rotational speed has no effect on how resistant NiTi alloy endodontic rotary files are to dynamic cyclic fatigue.

#### **2. Materials and Methods**

#### *2.1. Study Design*

One hundred and fifty (150) sterile, brand new endodontic rotary files with a parallelogram cross-section design, 6% taper, and 250 μm apical diameter (Ref.: IRE 02506, D, Endogal, Galician Endodontics Company, Lugo, Spain) were randomly distributed among different study groups: Group A: continuous rotational speed at 200 rpm (200 rpm) (*n* = 30); Group B: continuous rotational speed at 350 rpm (350 rpm) (*n* = 30); Group C: continuous rotational speed at 500 rpm (500 rpm) (*n* = 30); Group D: reciprocating movement at 350 rp m with 120◦ counterclockwise and 30◦ clockwise motion (350 rpm+) (*n* = 30); and Group E: reciprocating movement at 400 rpm with 120◦ counterclockwise and 30◦ clockwise motion (400 rpm+) (*n* = 30). The final total of experimental units included was 150, with these being assigned to one of the five study groups in keeping with the proportions determined by the researchers. The power was set at 80% and testing the null hypothesis H0 resulted in an effect size of 0.606. A single-factor ANOVA test for independent samples was used to make equal the mean values of the five groups, and the significance level was set at 5%. A microscope (OPMI pico, Zeiss, Oberkochen, Germany) was used to examine all NiTi alloy endodontic rotary files (Ref.: IRE 02506, D, Endogal, Galician Endodontics Company, Lugo, Spain) prior to use, with no files discarded. Between January and July 2022, this controlled experiment was conducted at the Department of Stomatology of the Faculty of Medicine and Dentistry at the University of Valencia (Valencia, Spain).

#### *2.2. Analysis with Scanning Electron Microscopy*

A scanning electron microscope (SEM) (HITACHI S-4800, Fukuoka, Japan) was used at ×30 and ×600 for the initial inspection of the NiTi alloy endodontic rotary files (Ref.: IRE 02506, D, Endogal, Galician Endodontics Company, Lugo, Spain). This analysis was conducted at the Central Support Service for Experimental Research of the University of Valencia in Burjassot, Spain. The analysis was carried out with the following exposure parameters: 20 kV acceleration voltage; magnification from 100× to 6500×; and resolution

ranging from −1.0 nm at 15 kV to 2.0 nm at 1 kV. Researchers did this to evaluate the surface characteristics and ensure there were no manufacturing surface defects.

#### *2.3. Analysis with Energy-Dispersive X-ray Spectroscopy*

In addition, energy-dispersive X-ray spectroscopy (EDX) was also used to analyze all the NiTi alloy endodontic rotary files (Ref.: IRE 02506, D, Endogal, Galician Endodontics Company, Lugo, Spain). This was conducted at the Central Support Service for Experimental Research at the University of Valencia in Burjassot, Spain. This inspection used these exposure parameters: 20 kV acceleration voltage; magnification from 100× to 6500×; and resolution ranging from −1.0 nm at 15 kV to 2.0 nm at 1 kV. These parameters were used to assess the elemental makeup of the chemicals in the files used to test their resistance to static fatigue. The researchers also evaluated the atomic weight percent, taking measurements from three different sections (apical third, medium third, and coronal third of the NiTi alloy endodontic files).

#### *2.4. Experimental Model Simulating Dynamic Cyclic Fatigue*

The researchers conducted tests of resistance to dynamic cyclic fatigue at room temperature (20 ◦C) to evaluate the mechanical behavior of the instruments, according to Martins et al. [19], using the aforementioned customized device (Utility Model Patent No. ES1219520) [20]. CAD/CAE 2D/3D software (Midas FX+®, Brunleys, Milton Keynes, UK) was used to design the structure of the device, which was subsequently created with 3D-printing software (ProJet® 6000 3D Systems©, Rock Hill, SC, USA) (Figure 1).

**Figure 1.** (**A**) Front, (**B**) back, ( **C**) right, and ( **D**) left sides of the dynamic cyclic fatigue device.

The customized artificial root canals were performed using Schneider's measuring technique, with a curvature of 60◦ [21] and a 5 mm curvature radius. The inverse engineering software used for this purpose was CAD/CAE 2D/3D. Molybdenum wire-cut technology (Cocchiola S.A., Buenos Aires, Argentina) was used with electrical discharge machining (EDM) to create the artificial root canal from stainless steel. Researchers also ensured that the NiTi files were flush with the walls of the artificial root canal. This newly created artificial canal was then positioned on its support, and a light-dependent resistor (LDR) sensor (Ref.: C000025, Arduino LLC®, Ivrea, Italy) placed at the apex of the canal was used to identify any failures in the endodontic rotary instruments (Ref.: IRE 02506, D, Endogal, Galician Endodontics Company, Lugo, Spain). This device works by measuring the light source continuously generated by a very strong white LED (20,000 mcd) (Ref.: 12.675/5/b/c/20k, Batuled, Coslada, Spain). The LED was positioned opposite the artificial root canal. An LED LDR sensor (Ref.: C000025, Arduino LLC®) at 50 ms was used to interpret the LED signals so as to identify the precise time of failure.

A roller bearing system (Ref.: MR104ZZ, FAG, Schaeffler Herzogenaurach, Herzogenaurach, Germany) was used to apply the movement direction and speed indicated by the operator (Ref.: DRV8835, Pololu® Corporation, Las Vegas, NV, USA) and created by the brushed DC gear motor (Ref.: 1589, Pololu® Corporation, Las Vegas, NV, USA) to the artificial support. The support was maneuvered in an exclusively axial motion with the help of a linear guide (Ref.: HGH35C 10249-1 001 MA, HIWIN Technologies Corp. Taichung, Taiwan). A torque-controlled motor and 6:1 reduction handpiece (X-Smart plus, Dentsply Maillefer, Baillagues, Switzerland) were used in conjunction with the NiTi endodontic rotary files.

A frequency of 60 pecks per minute was used for the NiTi endodontic files within the dynamic cyclic fatigue device, following the parameters of a prior study [19]. Researchers also applied a high-flow synthetic oil (Singer All-Purpose Oil; Singer Corp., Barcelona, Spain) to help prevent friction between the NiTi endodontic files and the walls of the artificial root canal; this oil is specifically formulated for the lubrication of mechanical parts.

The files were all used until failure. The researchers recorded and evaluated both the length of time and the number of cycles the files took to fracture.

#### *2.5. Statistical Tests*

Statistical analysis of all variables was performed using SAS 9.4 (SAS Institute Inc., Cary, NC, USA). The mean value and SD were used to express the descriptive statistics of the quantitative variables. The researchers then used an ANOVA test to perform a comparative analysis of the number of cycles to failure and the time to failure (in seconds). In 2-to-2 comparisons, the Tukey method was used to determine the *p*-values and correct any Type I errors. The researchers also calculated the Weibull modulus and Weibull characteristic strength. Statistical significance was defined as *p* < 0.05.
