## 3 Results
### Representative Mechanical Characteristics
#### 3.1.2 Modulus of Elasticity of Whole Specimen  
Based on the fitted model, summarized in Appendix B and Table A2, vary the estimated values of modulus of elasticity around the overall median value 47.22 GPa. More specifically, the model-based median value of the modulus of elasticity in a particular specimen is between 42.26 and 51.08 GPa. This range reflects variability among specimens. Similarly, as in the case of the hardness, the value of modulus of elasticity was also significantly (\(p<0.0001\)) lower at the uppermost part of the samples (the row closest to the surface, approximately 70 \(\upmu\)m). Regardless the thickness of the root canal wall, this decrease was approximately by 24%. The value of modulus of elasticity was significantly (\(p<0.0001\)) lower in locations closest to the root canal wall for the thinnest root canal wall (0.8 mm). The decrease was with respect to the value in the inner part of the sample by 27%. Unlike the case of the hardness, a slight effect of the root canal wall proximity was also significant for the thicknesses 1.2 and 1.6 mm. The decrease of the modulus of elasticity value was approximately by 10%, compared to the center of the sample. These features are also visible in Figure 3.  
The Range of Influence of Root Canal Wall Thickness on Mechanical Properties of MTA--Effect of Wall Thickness on Hardness Spatial Dependence  
At the second stage of the research, the effect of distance from the internal surface of the root canal wall was of the main interest. For a dataset, based on more detailed measurements of three samples with wall thicknesses 0.8 mm (\"Thin\"), 1.2 mm (\"Medium\"), and 1.6 mm (\"Thick\"), a simple linear model was employed for a detailed interpretation. Introduction of the proper model allowed to (statistically) estimate the appropriated values of median for hardness and reduced modulus. Based on the estimated model, summarized in Appendix C and Table A3, the hardness measured in the center part of the sample with thick root canal wall was systematically about 28% higher than hardness in the center of samples with thin and medium root canal wall. Moreover, the values of hardness in the center of the latter two samples were comparable. More specifically, the estimated median values were at the uppermost layer of the samples 1.11 GPa and 0.87 GPa for the thick and thin or medium walls, respectively. While the hardness did not change significantly with changing proximity to the wall in the case of the thick root canal wall (boxplots C/0-C/13 in Figure 4), an effect of the root canal wall proximity was present for the thinner canal walls. In both cases of the 0.8 mm and 1.2 mm wall, the hardness remained constant within the central matrices, when, in the peripheral  
Figure 3: Boxplots of (log-)modulus of elasticity measured on specimens with different root canal wall thickness (0.8, 1.2, and 1.6 mm) and in different distance from the center of a specimen (0-center, 3-periphery). ones, it decreased with the horizontal distance from the center of the sample towards the root canal wall. For the 1.2 mm wall, the decrease was observable within the whole peripheral matrices (i.e., the last seven indentation points B/7-B/13 in Figure 4, approximately 190 \(\upmu\)m), when, with each 20 \(\upmu\)m, the hardness decreased approximately by 13%. By the 0.8 mm wall was the decrease significant for the last five of the most peripheral indentation points A/9-A/13 in Figure 4 (approximately 150 \(\upmu\)m) and was more dramatic, while each 20 \(\upmu\)m decreases the hardness approximately by 21%. Finally, the hardness slightly changed with the vertical distance from the surface. Despite the wall thickness and the horizontal location of the measurement, the value decreased by approximately 2% with each 20 \(\upmu\)m of depth.