**1. Introduction**

The introduction of nickel–titanium alloy (NiTi) in the manufacturing of root canal instruments entailed a grea<sup>t</sup> revolution in the field of endodontics, as these endodontic files decreased the iatrogenic complications [1,2]. However, the failure of endodontic rotary files is still a concern, despite the continuous mechanical and chemical improvements in the NiTi alloy endodontic rotary instruments made by manufacturers to reduce the incidence of complications during root canal treatment [3]. Nevertheless, the incidence of fracture of NiTi endodontic rotary files ranges from 0.09% to 5% [4,5]. The failure of NiTi endodontic rotary files occurs when fatigue resistance is overcome by torsional stress, flexural bending (cyclic) stress, or a combination of the two [6]. Specifically, torsional fatigue occurs when the tip of the endodontic file becomes blocked in the root canal while the instrument continues rotating [7], and flexural bending fatigue occurs by the alternating application of compressive and tensile stress cycles on a curved root canal, leading to overcoming plastic deformation and the subsequent failure of the endodontic rotary instrument [6,8].

**Citation:** Faus-Llácer, V.; Hamoud-Kharrat, N.; Marhuenda Ramos, M.T.; Faus-Matoses, I.; Zubizarreta-Macho, Á.; Ruiz Sánchez, C.; Faus-Matoses, V. Influence of the Geometrical Cross-Section Design on the Dynamic Cyclic Fatigue Resistance of NiTi Endodontic Rotary Files—An In Vitro Study. *J. Clin. Med.* **2021**, *10*, 4713. https://doi.org/ 10.3390/jcm10204713

Academic Editors: Massimo Amato, Giuseppe Pantaleo and Alfredo Iandolo

Received: 6 September 2021 Accepted: 11 October 2021 Published: 14 October 2021

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**Copyright:** © 2021 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/).

In addition, the unexpected failure of the NiTi alloy endodontic rotary instruments might condition the outcome of the root canal treatment by blocking the advancement of disinfecting agents beyond the fractured instrument [9–11], which may lead to subsequent pulp necrosis and the formation of periapical lesions [12] or decrease the success rate of root canal treatment of teeth with periapical pathology [13]. Therefore, several reports have been conducted to analyze the influence of both the NiTi alloy and the geometrical parameters on the torsional and flexural bending resistance of endodontic rotary instruments to prevent the incidence of failure of endodontic rotary instruments. Both the chemical composition and crystalline structure of the NiTi alloy have been widely found to highly influence the fatigue resistance of endodontic rotary files, in particular, the endodontic rotary systems, composed of a higher concentration of the martensitic phase and manufactured by electropolishing, ion implantation, cryogenic treatment, and heat treatments, improve the mechanical behavior of NiTi endodontic rotary files, increasing their cyclic fatigue resistance [14]. However, some geometrical factors have also been reported to influence the instrument's performance, including the taper and apical diameter [15], cross-section design [16,17], flute length, helix angle, and pitch [18]. Unfortunately, the independent assessment of each factor associated with flexural bending fatigue may be difficult in a clinical setting due to the heterogeneous anatomy of the root canal system; thus, controlled experimental studies have been conducted to independently analyze each variable using custom-made cyclic fatigue devices [15].

The aim of this study was to analyze and compare the influence of the geometrical cross-section design on the dynamic cyclic fatigue resistance of NiTi endodontic rotary files, with a null hypothesis (H0) stating that the geometry of the cross-section design would not affect the resistance of NiTi endodontic rotary files to dynamic cyclic fatigue.

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

#### *2.1. Study Design*

Forty (40) sterile and non-used NiTi alloy endodontic rotary instruments were used in this in vitro study. A controlled experimental trial was performed at the Department of Stomatology of the Faculty of Medicine and Dentistry at the University of Valencia (Valencia, Spain), between March and July 2021. The NiTi endodontic rotary files were selected and categorized into the following study groups: A: double S-shaped cross-section with 250 μm apical diameter and 6% taper conventional NiTi alloy endodontic rotary files mainly consisting of austenite phase at body temperature [19] (Ref.: 0236 025 025, Mtwo, VDW, Munich, Germany) (*n* = 10) (Mtwo); B: rectangular cross-section with 200 μm apical diameter and 4% taper austenite phase NiTi alloy endodontic rotary files (Ref.: 20010103, T Pro E1, Perfect Endo, Shenzhen Perfect Medical Instruments, Shanwei City, China) (*n* = 10) (T Pro E1); C: convex triangular cross-section with 250 μm apical diameter and 4% taper austenite phase NiTi alloy endodontic rotary file (Ref.: 20010103, T Pro E2, Perfect Endo, Shenzhen Perfect Medical Instruments, Shanwei City, China) (*n* = 10) (T Pro E2); and D: triangular cross-section with 250 μm apical diameter and 6% taper austenite phase NiTi alloy endodontic rotary file (Ref.: 20010103, T Pro E4, Perfect Endo, Shenzhen Perfect Medical Instruments, Shanwei City, China) (*n* = 10) (T Pro E4). All endodontic rotary files were manufactured in austenitic phase with an austenite finish ( *A*f), and the temperatures of the Mtwo, T Pro E1, T Pro E2, and T Pro E4 were approximately 15 ◦C [19], 15 ◦C, 20 ◦C, and 20 ◦C, respectively. The *A*f temperatures of T Pro E1, T Pro E2, and T Pro E4 were provided by the manufacturer.

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

All NiTi endodontic rotary files were initially analyzed under scanning electron microscopy (SEM) (HITACHI S-4800, Fukuoka, Japan) at ×30 and ×600 in the Central Support Service for Experimental Research of the University of Valencia (Burjassot, Spain) under the following exposure parameters: acceleration voltage: 20 kV, magnification from 100× to 6500×, and a resolution between −1.0 nm at 15 kV and 2.0 nm at 1 kV, to perform

a surface characterization to discard further surface defects in its manufacture and analyze and compare the geometrical design of the NiTi endodontic rotary files (Figure 1).

**Figure 1.** (**A**) SEM analysis of the Mtwo NiTi alloy endodontic rotary file, (**B**) T Pro E1 Gold-Wire NiTi alloy endodontic rotary file, (**C**) T Pro E2 Gold-Wire NiTi alloy endodontic rotary file, and (**D**) T Pro E4 Gold-Wire NiTi alloy endodontic rotary file.

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

Additionally, an energy-dispersive X-ray spectroscopy (EDX) analysis was performed on all NiTi endodontic rotary files in the Central Support Service for Experimental Research of the University of Valencia (Burjassot, Spain) under the following exposure parameters: acceleration voltage: 20 kV; magnification: from 100× to 6500×; and a resolution between −1.0 nm at 15 kV and 2.0 nm at 1 kV, in order to analyze the elemental composition of the chemical elements of the NiTi endodontic rotary files used in the static fatigue tests, by means of the atomic weight percent measurement, at three randomized locations (Figure 2).

**Figure 2.** (**A**) EDX micro-analysis of the Mtwo NiTi alloy endodontic rotary file, (**B**) T Pro E1 austenite phase NiTi alloy endodontic rotary file, (**C**) T Pro E2 austenite phase NiTi alloy endodontic rotary file, and (**D**) T Pro E4 austenite phase NiTi alloy endodontic rotary file.

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

Dynamic cyclic fatigue tests were performed using the previously described custommade device (utility model patent number ES1219520) [20]. The structure of the dynamic cyclic fatigue test device was designed by computer aided design/computer aided engineering (CAD/CAE) 2D/3D software (Midas FX+®, Brunleys, Milton Keynes, UK) and created using 3D printing (ProJet® 6000 3D Systems©, Rock Hill, SC, USA) (Figure 3).

The custom-made artificial root canals were performed with a 60◦ curvature according to Schneider's measuring technique [21] and 3 mm radius of curvature using CAD/CAE 2D/3D software for inverse engineering technology. The artificial root canal was created from stainless steel using electrical discharge machining (EDM) molybdenum wire-cut technology (Cocchiola S.A., Buenos Aires, Argentina). This process ensured intimate contact between the NiTi endodontic reciprocating files and the artificial root canal walls. The artificial root canal was positioned on its support, and failure of the endodontic rotary instrument was detected using a Light-Dependent Resistor (LDR) sensor (Ref.: C000025, Arduino LLC®, Ivrea, Italy) located at the apex of the artificial root canal. The LDR sensor quantifies the continuous light source emitted by a high-brightness white Light-Emitting Diode (LED) (20000 mcd) (Ref.: 12.675/5/b/c/20k, Batuled, Coslada, Spain), which is located opposite the artificial root canal. The light signals emitted by the LED sensor were detected by the LDR (Ref.: C000025, Arduino LLC®) sensor with a frequency of 50 ms to accurately identify the precise time of failure.

**Figure 3.** (**A**) Front, (**B**) back, (**C**) right, and (**D**) left surfaces of the dynamic cyclic fatigue device.

The direction and speed of the movement generated by the brushed DC gear motor (Ref.: 1589, Pololu® Corporation, Las Vegas, NV, USA) and controlled by the driver (Ref.: DRV8835, Pololu® Corporation, Las Vegas, NV, USA) were transferred to the artificial root canal support through a roller bearing system (Ref.: MR104ZZ, FAG, Schaeffler Herzogenaurach, Germany). The artificial root canal support moved in a pure axial motion using a lineal guide (Ref.: HGH35C 10249-1 001 MA, HIWIN Technologies Corp. Taichung, Taiwan). All the NiTi endodontic rotary files were used with a 6:1 reduction handpiece (X-Smart plus, Dentsply Maillefer, Baillagues, Switzerland) and torque-controlled motor. Mtwo NiTi alloy endodontic rotary files (Ref.: 0236 025 025, Mtwo, VDW, Munich, Germany) were used at 250 rpm and 2.3 N/cm torque, T Pro E1 austenite phase NiTi alloy endodontic rotary files (Ref.: 20010103, T Pro E1, Perfect Endo, Shenzhen Perfect Medical Instruments, Shanwei City, China) were used at 250 rpm and 2 N/cm torque, T Pro E2 austenite phase NiTi alloy endodontic rotary files (Ref.: 20010103, T Pro E1, Perfect Endo, Shenzhen Perfect Medical Instruments, Shanwei City, China) were used at 250 rpm and 2 N/cm torque, and T Pro E4 austenite phase NiTi alloy endodontic rotary files (Ref.: 20010103, T Pro E1, Perfect Endo, Shenzhen Perfect Medical Instruments, Shanwei City, China) were used at 250 rpm and 2 N/cm torque, according to the manufacturer's instructions.

All NiTi endodontic files were used in the dynamic cyclic fatigue device at a frequency of 60 pecking movements/min according to a previous study [20]. To reduce the friction between the rotating files and the artificial canal walls, special high-flow synthetic oil designed for the lubrication of mechanical parts (Singer All-Purpose Oil; Singer Corp., Barcelona, Spain) was applied.

All NiTi endodontic rotary files were used until fracture occurred. The time to failure and the number of cycles to failure were measured and recorded.

#### *2.5. Statistical Tests*

Statistical analysis of all the variables was carried out using SAS 9.4 (SAS Institute Inc., Cary, NC, USA). Descriptive statistics are expressed as the mean and standard deviation

(SD) for quantitative variables. Comparative analysis was performed by comparing the time to failure (in seconds) and the number of cycles to failure using the ANOVA test. For the comparisons, the *p*-values were adjusted using the Tukey method to correct the type I error. In addition, Weibull characteristic strength and Weibull modulus were calculated. The statistical significance was set at *p* < 0.05.
