## 4 Discussion
### Congruency/Fitting of the Artificial Root Canals to Instruments  
In nearly all studies reported in the endodontic literature concerning cyclic fatigue, instruments were set into rotation/reciprocation in glass or metal tubes, grooved blocks, or metal blocks. Only a minority of the studies mentioned fitting of the instrument in the artificial canal or tube; hence, congruency remains unclear. As [PERSON] et al. highlighted, the so-called \"free space\" between the canal wall and the instrument, also termed the shape of the artificial tube, is crucial for the load of the endodontic instruments, because trajectories differ due to different shapes [43]. It can be assumed that the impact of the radius of curvature on the obtained results may have been overestimated in many studies. This may represent a reason for the huge variability in the results of identical instrumentstested under different experimental conditions [22]. A lower fit results in a lower curvature of the endodontic file and a lower load onto the instrument (Figure 7). The manufacturing tolerance of endodontic instruments allowed by the ISO standard is \(\pm\)0.02 mm [23]. Therefore, the dimension in the narrowest canal was set within these tolerances at 0.02 mm bigger than the instrument size. The subsequent diameters of the artificial canals were larger at +0.05 mm and +0.10 mm. A parallel tube with a diameter of 1.25 mm served as a control. The present results clearly demonstrated a significant difference between the narrowest size of the artificial canal (instrument size +0.02 mm) and the +0.05 mm and +0.10 mm canal sizes. (Table 1). The cyclic fatigue resistance of instruments was significantly reduced in the matching artificial canal (same conicity as the instrumented tested; diameter +0.02 mm), whereas the length of the fractured fragments did not differ compared to the subsequent artificial canal sizes. No significant differences occurred between the 0.05 mm and 0.10 mm groups with respect to any of the evaluated parameters (\(p>0.05\)). Only the parallel tube showed significant differences regarding all values examined (\(p<0.05\)). This raises the question whether the sizes of the artificial canals should be set at the manufacturing tolerance level as preset in the ISO specification (i.e., \(\pm\)0.02 mm) or even up to 0.10 mm larger. However, the instrument tolerances were valid in both directions, i.e., larger and thinner compared to the given sizes. This may allow a kind of range in matching congruency (Table 2). Differences between the instrument sizes and the tube were smallest in the matching tube and did not exceed a factor of 1.17. Whereas, in the +0.05 mm and +0.10 mm groups, the factors were between 1.10-1.30 and 1.30-1.52, respectively, the parallel tube offered a 4.40- to 5.20-fold increase in diameter. Nevertheless, when looking at the standard deviations of time and cycles to fracture (Table 1), only in the matching size group did these values not exceed the 10% level of the mean values; therefore, the deviations were relatively the smallest and the results seem to be the most reliable. Figure 7: Straightening of the instrument due to increasing diameter of the artificial root canal. From left to right: parallel tube with a diameter of 1.25 mm (green), instrument size +0.10 mm (red), instrument size +0.05 mm (orange), matching tube = instrument size +0.02 mm (blue). Nevertheless, a major limitation of the present study is the fact that only instruments with a size # 25 were investigated. It is important to consider that the relative increase in the diameters decreases with increasing instrument size (Table 2); for example, an instrument with a size # 15 would have ranges of 0-31%, 17-54%, 47-95%, and 706-923% in the different artificial canals representing identical artificial canal sizes adapted to the instrument. Thus, the importance of congruence and minimum free space between the artificial canal and the endodontic instrument seems desirable to achieve a better guidance of the instruments during testing.