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Background There is still a lack of knowledge regarding the permeability and configuration of infected root dentin. The aim of this ex vivo study was to compare the dentin penetrability of healthy teeth and necrotic teeth with apical periodontitis by evaluating the penetration of sodium hypochlorite (NaOCl) and to analyze the histopathological features of root dentin. Methods Forty-eight molars were collected and divided into two groups. The clinical diagnosis for one group was pulp necrosis with apical periodontitis and the pulp and periapex were normal in the other group. Forty-eight straight roots were divided into two groups: infected and healthy. First, all root canals were stained with 2% methylene blue to visualize penetration after standard root canal instrumentation and irrigation. Transverse sections were obtained, and the dye penetration parameters were measured. The cross sections were processed to 20–30 μm and stained with hematoxylin and eosin for observation of the histopathological changes in the root dentin. Results The maximum penetration depth, median penetration depth and penetration percentage of NaOCl solutions, in infected root canals were significantly lower than those in healthy root canals. The histopathological analysis showed that the frequency of reparative dentin formation in infected root canals was significantly greater than that in healthy root canals. Conclusions The dentin penetrability of teeth with necrotic teeth and apical periodontitis was more superficial during root canal irrigation than that of healthy teeth. The histopathological changes in infected radicular dentin, namely the formation of reparative dentin, might be associated with the lower permeability of dentin tubules in human teeth with apical periodontitis.

The strength failure of brittle materials under complex stress is an important problem. Herein, we propose a novel three-parameter twin τ2 strength theory considering the influence of hydrostatic pressure and normal stress on the principal shear-stress surface, derive a mathematical expression for the strength theory, and compare the theoretical predictions under several stress states with existing experimental data. The results show that different ultimate stress ratios, α and β, correspond to different strength theories for brittle materials. The principal stress σ1 increases gradually with an increase in σ2 (=σ3) under the stress state σ1 > σ2 = σ3; σ1 (=σ2) increases gradually with an increase in σ3 under the stress state σ1 = σ2 > σ3. Furthermore, the biaxial compressive strength is considerably higher than the uniaxial compressive strength under the biaxial compressive stress for σ1 > 0, σ2 > 0, and σ3 = 0. When σ3 is fixed and σ2 is relatively small under the stress states of σ1 > 0, σ2 > 0, and σ3 > 0, the maximum principal stress σ1 increases with the increasing σ2. When σ2 is relatively large and as σ1 gradually decreases with the increasing σ2, the effect law of intermediate principal stress σ2 is obtained.