## 2 Materials and Methods
### Image Processing  
Images before and after instrumentation were repositioned in all three planes of space using the DataViewer software (ver. 1.5.6.2; Bruker X-ray, Kontich, Belgium). These images were imported into CTAn software (ver. 1.20.3.0; Bruker X-ray, Kontich, Belgium) and DataViewer to calculate canal volume, surface area, non-instrumented area, transportation, STL model preparation, and the thickness of the dentin in the danger zone.  
Changes in volume and surface area were determined by subtracting the values before and after instrumentation using the CTAn software. The software was used to determine the region of interest (ROI). Furthermore, by adjusting the values of brightness and opacity, it is possible to remove \"unwanted\" voxels before calculating the final volume of the pulp and the canal cavity. Therefore, the software allows to obtain the desired volume, and the changes in volume and surface area can be compared between pre- and post-instrumentation [20]. CTVol software (ver. 2.3.2.0; Bruker X-ray, Kontich, Belgium) was used for the visualization of the STL models. The STL models were obtained with CTAn software by selecting the ROIs that include the root canals and adjusting the threshold to select the air in the canal for the preparation of the models.  
The percentage of the non-instrumented area was calculated according to the study by [PERSON] et al. [20] calculated using CTAn software as the percentage of the number of static voxel surfaces to the total number of surface voxels from the fitted 3D model before and after root canal preparation.  
Canal transportation, the shortest distances from the orifice to the root tip before and after instrumentation, were measured in the mesial and distal directions using the DataViewer software. Then, using these data, the amount of transportation was obtained for each canal with the formula  
\[\text{The amount of transportation}=(\text{m1}-\text{m2})-(\text{d1}-\text{d2}), \tag{1}\]  
This formula was previously used in the study of [PERSON] et al. [18]. In this formula, m1 represents the shortest distance from the mesial border of the root to the non-instrumented mesial margin, m2 represents the shortest distance from the mesial border of the root to the mesial margin of the instrumented canal, d1 represents the shortest distance from the distal border of the root to the non-instrumented distal margin, and d2 represents the shortest distance from the distal border of the root to the distal margin of the instrumented canal.  
A value for canal transportation equal to 0 means no transportation. If the transportation value is negative, it indicates transportation in the distal direction, and if it is positive, it indicates mesial transportation. In Figure 4, images from the DataViewer software, where the measurement of the transportation amount is made, are displayed.  
Figure 4 shows the measurement of the transportation. The transportation was measured using the Dataviewer software. In Figure 4, red lines show the shortest distances between borders and margins.  
To measure the thickness of dentin in the danger zone area after canal preparation, sections were created from the images obtained from DataViewer software. In these slices, the thickness of the canal wall was measured in the axial plane. To assess changes in dentin thickness, the shortest distance from the instrumented and non-instrumented canal inner wall to the corresponding outer wall of the canal was measured. Radii of curvature were measured for all the samples, and the mean value for this measurement was 6.52 \(\pm\) 1.49 mm using the method from [PERSON] et al.'s study [21]. All images were evaluated and measured by a single observer with 12 years of Micro-CT experience, and all measurements were made twice by the same observer.