## 2 Materials and Methods
### Micro-CT Scans and Analysis  
The specimens were scanned with high-resolution micro-CT equipment, SkyScan 1272 (Bruker-microCT, Kontich, Belgium). The following system settings were used for the scanning process: a voltage of 100 kV, a current of 100 mA, a 0.4 rotation step, and a 1406 ms exposure time. The procedure was performed at an isotropic resolution of 6 \(\upmu\)m using a 0.11 mm copper filter. The teeth were placed in closed Eppendorf tubes with a moist cotton piece at the bottom to prevent dentin desiccation during the 90 min scan. Images of the specimens were reconstructed using a ring artifact reduction factor of 2 and beam hardening correction of around 5% with NRecon v. 1.7.4.2 software (Bruker Micro-CT).  
CTAn (version 1.20.8) and CTVol software (v. 2.3.2.0; Bruker Micro-CT, SkyScan, Belgium) were used for the three-dimensional (3D) reconstruction, quantification of the root-end cavity and filling material volume, the calculation of the material porosity, and the relevant volumetric analysis. The 3 mm thick apical portion of the resected root was chosen as the region of interest (ROI). In order to measure the volume of the gap at the root dentin-to-filling material interface, the volume of interest (VOI) was determined as a cylindrical area with a length of 3 mm that included only the root-end cavity.  
Porosity was determined by segmentation within the ROI. Grayscale thresholds were defined semi-automatically in order to separate the different \"phases\": root dentin, cavity borders, material, interfacial gaps, and inner pores. Due to the heterogeneous structure of the filling material and the large absorption difference between the dots in the cement and the rest of the 3D image, the grayscale range was so selected that the dots were slightly overexposed. Densities ranging from 80 to 255 were specified for the filling material and 80-255 for the voids (pores). The established threshold gray level thus enabled the detection of pores inside the VOI that were smaller than 5 \(\upmu\)m. A binarizing method (i.e., black-and-white images) was also applied for images in the VOI in order to facilitate the quantification process. Micro-CT scans, image reconstructions, and volumetric measurements were performed by one experienced operator.  
The cavity volume (Vc) and the root-end filling material volume (Vm) were measured in mm\({}^{3}\). Then the following parameters were calculated: (1) the volume of the interfacial gaps and voids present in the material-to-dentin wall interface, defined as open porosityvolume for brevity (OPV); and (2) the volume of micropores within the material, defined as closed porosity volume (CPV). The quantities of both the internal and interfacial porosity fractions were measured separately and as the total amount (TPV). They were calculated as absolute values in mm\({}^{3}\) and relative values in percentages.  
To assess the volume of interfacial open pores (OPV), the sum of the filling material volume (Vm) itself, including closed pores (CPV), was subtracted from the cavity volume (Vc). Then the total porosity volume was calculated as a sum of OPV and CPV. Subsequently, the relative values of those parameters (OPV% and CPV%) were computed using the following formulas (Equations (1) and (2)):  
\[\mathbf{OPV\%}=\frac{OPV}{Vc}\times 100 \tag{1}\]  
and  
\[\mathbf{CPV\%}=\frac{CPV}{Vm+CPV}\times 100 \tag{2}\]  
Ultimately, the sums of OPV + CPV and OPV% + CPV% were utilized to calculate the total porosity volume and percentage.