## 4 Discussion  
The present investigation analyzed the influence of conventional or heat-treated NiTi alloys of five commercially available NiTi endodontic instruments. Stress and strain distributions during rotation in two selected dentine canal models, simulating a sound dentine (18 GPa) or a highly mineralized dentine canal (42 GPa), were considered. The root canal model used in this study was characterized by a specific design with a curve approximately at the medium-apical third, as used in different studies for fatigue test evaluation [22; 23; 24; 25; 26; 27; 28], granting the opportunity to compare the results and information. In the present study, instruments with a conicity of 4% were tested in a canal model with the same conicity, while instruments with 6% conicity were tested in the canal model of 6% in order to simulate similar conditions and to provide a comparable friction surface. This was an innovative approach, addressing a drawback of previous mechanical studies in which all instruments were tested in the same metallic canal model. Another innovative approach is represented by the volume measurement of the instruments. The volume is in relationship with the design, conicity and geometrical features. The instrument with a higher volume may \"fill\" the root canal space and increase stress and friction along the dentine canal. Specifically, using this canal model, the FEA demonstrated a well-defined peak of stress in the same location in the correspondence of canal curvature for all instruments (approximately at 7 mm from the apex/tip of the instrument). This peak was extremely abrupt for conventional alloys with very high von Mises stress level distributions (see  
Figure 8: Von Mises stress distribution and propagation in the dentine with the two different values of dentine elastic modulus (18 or 42 GPa). Figure 7) and, in particular, in the most rigid and curved dentine canal models. The null hypothesis was consequently rejected. Endodontic rotary instruments are normally subjected, in a curved canal, to both compressive and tensile stresses: the concave portion of the instrument is under compression while the external portion is under tension [38]. In this study, all the heat-treated alloy instruments showed distinctly lower von Mises stress and strain values in both straight and curved regions of the different dentine root canals than the conventional ones. These data were also confirmed by the analyses on the endodontic cross sections, as reported in Figure 6, where in a section plane, the highest von Mises stress magnitudes for each instrument according to the elastic modulus of the root canal model (18 or 42 GPa) was summarized. Regarding the different instruments Hyflex CM and One Curve showed the best mechanical rotating behaviors. Recent in vitro investigations [39] confirmed, from a mechanical viewpoint, the influence of different heat treatments on the torsional and cyclic fatigue resistance of rotary instruments. The cross section was reported as being one of the most important variables in von Mises stress distributions for conventional alloy instruments [1; 31]. F360 and F6 Skytaper are both conventional based NiTi alloys (Table 1). In particular, F360 has an S-shaped cross-section, while F6 skytaper has a quadrangular cross section. These instruments exhibited the highest stress magnitude (298.01 and 253.41 MPa respectively) in high mineralized dentine canals, irrespective of their cross section. Heat treatment allows for a higher presence of martensitic and R phases in NiTi instruments at room and body temperature, lowering their elastic moduli, improving the instrument flexibility and, as consequence, also improving the von Mises stress and strain patterns in simulated clinical conditions [9; 10]. Other investigated instruments include those based on heat-treated NiTi alloys. One Curve was characterized by a variable asymmetrical cross-section, which becomes S-shaped near the top of the shaft and then more triangular at the tip.