## 2 Materials and Methods  
Fifteen endodontic NiTi instruments were used in this study. They were divided in three groups, each one with an equal number of instruments (\(n=5\)), (Figure 1):  
* **Group Endostar** consists of E3 Endostar (Endostar, Poldert Co. Ltd., Warsaw, Poland) instruments. * **Group Reciproc** consists of Reciproc R25 (VDW, Munchen, Germany) instruments. * **Group Protaper** consists of Protaper Next X2 (Dentsply Maillefer, Ballaigues, Switzerland) instruments. For the sample size calculus, we conducted a power analysis test with GPower3.1 application using a \"Laplace\" Parent Distribution, 0.05 level of significance, 80% power and 1 as an allocation ratio. Each type of instrument has different shapes of their cross-section (Figure 1a), as well as different movements performed in the root canal. Thus, instruments of Groups Endostar and Protaper use a continuous rotational movement, while instruments of Group Reciproc use a reciprocating movement. Before preparing the simulated root canals, to establish the testing configuration, all instruments were measured with a Mitutoyo digital caliper with a 0.02 mm accuracy and with a Mitutoyo micrometer with a 0.01 mm accuracy (Mitutoyo America, Aurora, IL, USA), to determine the total length and tip diameter, respectively. This approach is based on the fact that, as studied in the literature, assuring repeatability is an issue in the manufacturing of orthodontic wires [25]. In addition, the initial lengths are important to determine the distance from the tip after fracture. Figure 1: The three investigated types of NiTi rotary instruments before torsional fracture: (**a**) measurements of their dimensions; (**b**) instruments introduced in the simulated root canals. Notations: Endostar, Reciproc, and Protaper stand for the three considered groups. In general, the tip diameter plays an important role in clinical root access, while the total length determines the access in deep root canals and also the flexibility of the instrument. Their values are presented in Figure 2. The length \(L_{1}\) and the tip size \(\Phi\) of the instruments are specific for each manufacturer; the deviations of individual instruments are in the range of hundredths of a millimeter, within the accuracy of the measuring systems. Seventy-five simulated root canals were used for this study [26]. Each of the studied instruments was used to prepare five simulated root canals according to the manufacturer's indications (Figure 1b). Thus, each instrument was subjected to wearing in real-life conditions that (however may) surpass normal endodontic procedures, as such procedures usually imply changing the instrument after even a single preparation, to avoid fracturing it in the next canal. Following this five-times preparation procedure of each instrument, the torsional stress was measured on each of the five instruments from the three groups using the Mecmesin Vortex \(i\) machine (Mecmesin Ltd., Slinford, UK) equipped with a loading cell 0 to 10 Nm (\(\pm\)0.5%), under the following conditions: total number of samples, 15; loading velocity, 2\({}^{\circ}\)/s; regarding the machine control, the maximum angular displacement was equal to 350\({}^{\circ}\); regarding the fixing of a sample, the driving part of the instrument was placed in the chuck and the tip was placed between its parallel jaws (Figure 3). Figure 3: The configuration of the torsion test. Figure 2: Dimensions of the considered NiTi rotary instruments: (**a**) full length \(L_{1}\) (mm) and (**b**) tip diameter \(\Phi\) (mm). Notations: Endostar, Reciproc, and Protaper stand for the three considered groups. Each sample instrument was inserted 2 to 3 mm deep in the parallel jaws, using a template spacer, while the driving end was hold in the chuck by inserting the full cylindrical tail of the instrument. This distance was selected as representing the most common section to fail (i.e., for the instrument tip to get stuck inside a root canal) in clinical practice, because of the anatomical characteristics of teeth.