Author Correction: Dentinogenic effects of extracted dentin matrix components digested with matrix metalloproteinases

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Migration assay. Pulp cell migration plays a critical role in repair and regeneration 22 . In the present study, two different experimental approaches were used to study migration. The horizontal scratch wound assay allowed direct visualization of the effects of 1 µg/ml of DMCs treated with MMP-1, -3, or -9 on promotion of cell migration; there was a significant difference, compared with 1 µg/ml of incubated DMCs without the addition of MMPs (p < 0.05) (Fig. 3B,D,F). Control medium (α-minimum essential medium (MEM) containing 1% fetal bovine serum (FBS)) was used as a negative control. Trans-well assays showed significant chemotactic effects of 1 µg/ ml of DMCs treated with MMP-1, -3, -9, or -20, compared with an experimental control and negative control (p < 0.05) (Fig. 3E). No significant differences were observed in 1 µg/ml of DMCs digested by MMP-2, -8 or -13 samples, nor were differences observed at lower concentrations (0.01-0.1 µg/ml) of MMP-treated DMCs ( Supplementary Fig. 5). Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control and showed no effect in the migration assay. One microgram per millilitre of DMCs treated with MMP-1, -3, or -9 promoted horizontal migration, compared with 1 µg/ml of incubated DMCs without the addition of MMPs (p < 0.05). The trans-well assay demonstrated the significant chemotactic effects of 1 µg/ml of DMCs treated with MMP-1, -3, -9, or -20, compared with the experimental and negative controls (p < 0.05). Significant differences were not observed with 1 µg/ml DMCs treated with other MMPs, MMPs incubated alone or at lower concentrations (0.01-0.1 µg/ml) of the above-mentioned MMPs. Groups with similar lower-case letters (i.e., a and b) are not significantly different. Data represent five independent experiments. Proliferation assay. Pulp cell proliferation was promoted by 1 µg/ml of DMCs treated with MMP-1, -8, -9, or -13, compared with DMCs incubated without MMPs (experimental control) and α-MEM containing 1% FBS (negative control) (p < 0.05) (Fig. 4). However, 1 µg/ml of DMCs treated with MMPs-2, -3, or -20, as well as lower concentrations (0.01-0.1 µg/ml) of MMP-treated DMCs, did not significantly promote cell proliferation ( Supplementary Fig. 6). Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control and showed no effect in the proliferation assay. ALP activity. On day 7, primary pulp cells incubated with 1 µg/ml of DMCs treated with MMP-1 or MMP-20 showed higher alkaline phosphatase (ALP) activities, compared with incubated DMCs without MMPs (experimental control) and α-MEM containing 1% FBS (negative control) (p < 0.05) (Fig. 5). One microgram per millilitre of DMCs treated with MMP-2, -8, -9, or -13 did not promote ALP activity in pulp cell cultures by day 7, compared with controls. On day 14, DMCs treated with MMP-9 and -13 also stimulated pulp cell ALP activity, similar to MMP-1 and -20 (p < 0.05) (Fig. 5). Significant differences were not observed in 1 µg/ml of DMCs treated with MMP-2 or MMP-8, or at lower concentrations (0.01-0.1 µg/ml) of MMP-treated DMCs ( Supplementary Figs 7 and 8). Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control and showed no effect in the ALP activity assay.

Evaluation of tertiary dentin formation by direct pulp capping in vivo.
To evaluate whether DMCs treated with MMPs were able to stimulate tertiary dentin formation, a direct pulp capping experiment, which is a standard method in the dental field, was performed 5,6 . Representative micro-CT images of tertiary dentin 28 days after pulp capping by using 1 µg/ml of DMCs treated with MMP-1  Fig. 7I. Tertiary dentin formation induced by 1 µg/ml of DMCs treated with MMP-1, -9, -13, or -20 was enhanced, compared with DMCs treated with other MMPs, or without MMP treatment (p < 0.05). MMP-20-treated DMCs induced hard tissue formation with fewer defects, compared with tertiary dentin induced by MMP-1, -9, or -13, which showed larger defects or a void space beneath the pulp-capping material. As a reference, representative micro-CT and histological images of tertiary dentin 28 days after pulp capping with MTA and incubation with MMP-1, MMP-2, MMP-3, MMP-8, MMP-9, MMP-13, or MMP-20 alone are shown in Supplementary Fig. 11; MTA induced highly dense tertiary dentin without significant defects.
These data represent six independent experiments. Representative histological images of haematoxylin and eosin (HE)-stained teeth, 28 days after pulp capping, highlighted the positive effects of treatment with 1 µg/ml of MMP-treated DMCs (Fig. 8). One microgram per millilitre of DMCs treated with MMP-1 (Fig. 8A), MMP-9 ( Fig. 8E), MMP-13 ( Fig. 8F), or MMP-20 ( Fig. 8G) stimulated pulp tissue repair, compared with 1 µg/ml DMCs treated with other MMPs, based on the coverage of the exposed pulp by a tertiary dentin bridge (p < 0.05) (Tables 1 and 2). Tubular structure and defects or continuous nature of tertiary dentin are commonly used to assess quality of tertiary dentin. According to these criteria, the tubular regularity of tertiary dentin formation stimulated by 1 µg/ml of DMCs treated with MMP-1, -9, -13, and -20 was superior to the formation stimulated by MMP-2, -3, or -8, as well as 1 µg/ml of DMCs without addition of MMPs (experimental control) or PBS (negative control) (p < 0.05). In particular, 1 µg/ml of DMCs treated with MMP-20 resulted in increased tertiary dentin formation and enhanced tubular structure (Fig. 8I), compared with DMCs treated with other MMPs (p < 0.05). Representative histological images of HE-stained teeth, 28 days after pulp capping with MTA are shown (Supplemental Fig. 10). Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control and showed no effect on the direct pulp capping (Supplemental Fig. 10).

Discussion
Traditional direct pulp capping materials, such as Ca (OH) 2 or MTA, have a 60%-80% success rate, as reported in clinical studies 4,23,24 . However, these materials were developed on a more empirical basis, rather than through specific understanding of the wound-healing mechanisms of the dentin-pulp complex. Recent studies have aimed to introduce bio-mimicked tissue healing with growth factors as a direct pulp-capping material [25][26][27] . However, limited effects have been observed regarding the healing of wounded pulp tissues as the wound healing mechanisms of the dentin-pulp complex remain not entirely clear.
MMPs are calcium-and zinc-dependent, host-derived enzymes 28 that can hydrolyse ECM components 29 . ECM integrity is affected by MMPs and TIMPs, which play critical roles during matrix remodelling [9][10][11] . Several MMPs have been reported to be sequestered in mineralized dentin 30 , and recent studies revealed that host-derived MMPs contribute to the breakdown of collagenous matrices during dental caries 30 . Conversely, MMPs have been reported to be involved in wound healing processes, such as cell growth, cell migration, tissue remodelling and angiogenesis 31,32 . We also previously reported upregulated MMP gene expression after pulp injury 8 and MMPs have been detected in the dentin matrix in an inactive state 33,34 . The distribution of MMP molecules has been reported at deeper sites within the dentin, where they exhibit gradients of activity [35][36][37] . The presence of these molecules within the dentin-pulp complex enable them to activate DMCs released by bacterial acids or restorative materials. These activated molecules may subsequently act in biological defence and repair processes within the tooth. Therefore, in the present study, we focused on MMPs that might facilitate matrix remodelling of dental pulp tissues or digested DMCs which promote wound healing 21,37 . Dentin is a major component of the tooth and covers the dental pulp. It is considered to be part of the ECM of the combined dentin-pulp complex, rather than being a distinct tissue, as it originates from the same mesenchymal tissue 38,39 . However, the complete range of functions of dentin is still under investigation. During caries progression, dentin is demineralized by acids secreted by caries-associated bacteria, and DMCs may be digested enzymatically during this process 40 . Therefore, we investigated the effects of digested DMCs on wound healing of the dentin-pulp complex both in vitro and in vivo.
Protein analysis by SDS-PAGE showed DMCs were digested with MMPs-1, -2, -3, -8, -9, -13, and -20. The resultant protein profiles differed among MMPs (Fig. 1), which was as expected because of their differing substrate specificities. Generally, MMP-1 has been considered as a collagenase and MMP-2 is reported as a gelatinase. However, MMP-1 is also able to degrade proteoglycans 41 and MMP-2 reportedly can degrade and activate the DMP-1 protein, which is a key dentin matrix signalling protein 42 . In addition, non-canonical substrates have been identified as targets of these MMPs 41 . Similarly, MMP20 has been recognized as enamelysin and cleaves enamel-related proteins; however, further substrates could exist. Recently, MMP20 was reported to associate with the activation of DSPP, which is a member of the small integrin-binding ligand, N-linked glycoprotein (SIBLING) family 43 . Several previous reports have demonstrated that various proteins from the SIBLING family, along with several growth factors, are present in DMCs [44][45][46][47] . Therefore, DMCs may contain SIBLING substrates for MMPs.
Subsequently, we performed SDS-PAGE analysis and confirmed that DMCs extracted with EDTA could react and respond to the MMP molecules. These results suggested that MMPs may hydrolyse or facilitate dentin decomposition, consistent with the findings from these previous studies 48 .
Next, we examined the effects of DMCs digested with MMPs on the functions of primary pulp cells in vitro. DMCs digested with some MMPs promoted angiogenesis, migration, proliferation, migration, osteogenic    Fig. 7I. Quantification of tertiary dentin formation induced 1 µg/ml of DMCs treated with MMP-1, -9, -13, or -20 facilitated hard tissue formation, compared with 1 µg/ml of DMCs treated with other MMPs or incubated DMCs without MMP. One microgram per millilitre of DMCs treated with MMP-20 induced a significantly thicker tertiary dentin beneath pulp capping materials. One microgram per millilitre of DMCs treated with MMP-1, -9, and -13 induced tertiary dentin with some defect or void space beneath pulp capping materials. These data represent six independent experiments. C = cavity, D = dentin, P = pulp. White arrow = dentin bridge. this variation also agrees with previous reports 49 . Indeed, whilst we observed that DMCs digested with MMPs up-regulated some pulp cell responses in vitro (as described above) which associate with the wound healing response in the pulp tissue, it was however important to directly investigate whether MMP-digested DMCs invoked tissue healing responses in vivo, by using a direct pulp capping approach. Such an approach enables the evaluation of a more complete and simulated form of dental tissue repair and may also identify translational opportunities. Thus, we investigated the effects of digested DMCs on wound healing in pulp tissue by using direct pulp capping in vivo. The result of micro-CT analysis of hard tissue formation indicated that DMCs digested with MMP-20 induced highly condensed tertiary dentin beneath the pulp-capping materials applied (Fig. 7H,I) and histological images from the same specimen showed appropriate tubular dentin morphology (Fig. 8I). In contrast, DMCs digested with other MMPs induced tertiary dentin with more defects and void structures (Fig. 7A,E,F;  Tables 1 and 2). These results suggest that MMP20 may play an essential role in the pulpal healing process, compared with other MMPs in vivo.
Given that wound healing in vivo is affected by a variety of complex and interacting factors, the results of in vitro experiments might not always mirror the in vivo processes. Furthermore, the source of MMPs in vivo is unclear and could be derived from variety of sources and locations, such as resident cells within the pulp and/ or the inflammatory infiltrate. A further potential explanation for the differences observed in vivo and in vitro may be due to the presence of other environmental factors, as it has been shown that ECM digested with several enzymes stimulated different actions, according to the environment studied 50 .
Most reports concerning MMP-20 have found that this enzyme appears to be predominantly expressed within the tooth 51,52 . Indeed, during tooth development, MMP-20 may contribute to enamel formation by digesting enamel-related proteins 53 . Additionally, MMP-20 is present in the dentin matrix and is expressed by odontoblasts in mature teeth and activated by dental caries progression 17 . Others have reported that MMP-20 is present in carious dentin compared with sound dentin 33 . More specifically these reports relate to the localization of MMP20 in the dentin-pulp complex; however, there appear to be no reports of its biological role in this location. Data from the present study indicate that MMP-20 might be involved in a specific pulpal repair system enabling tertiary dentin formation.
For in vitro and in vivo experiments, MMP molecules alone were also used to investigate their direct effects; however, no direct effects on pulp cell function or pulpal tissue repair were observed. This outcome is likely due to the MMP molecule exerting no direct effect on these responses, or the inability to generate sufficient substrates in this environment due to the target molecules being embedded within the mineralized ECM. In addition, the most effective ratio of MMPs and DMCs is unknown. The concentration of MMPs in this study may not reflect the true biological environment as is present in dental caries. However, this study does indicate a potential role for MMP molecules in modifying or improving the local healing response of the dentin-pulp complex, via its action on DMCs. This model may therefore provide novel insight enabling the future elucidation of the mechanism involved in pulpal healing.
The different MMPs may also function at different doses; therefore, future studies are needed to determine optimal doses required. As MMPs have been reported to directly upregulate dental pulp through protease-activated receptors 54,55 , further investigation is also necessary to address this. In addition, other enzymes (e.g., serine or cysteine proteinases) are present in the dentin matrix 56 and these proteinases may further degrade DMCs 57 . Thus, the effects of other endogenous enzymes during repair of the dentin-pulp complex should be examined.
Based on our findings, host-derived MMP may be involved in the wound healing process of the dentin-pulp complex (Fig. 9). During caries progression, initially enamel and then dentin is decalcified by bacterial acids and the organic dentin matrix is exposed (Fig. 9A). Subsequently, the dentin matrix is digested with MMPs,

Grade
Dentin bridge formation 0 No dentin bridge formation 1 Slight dentin bridge formation (dentin bridge formation covers 1/3 of exposed pulp) 2 Incomplete dentin bridge formation (dentin bridge formation covers 2/3 of exposed pulp) 3 Complete dentin bridge formation (dentin bridge formation completely covers exposed pulp) Table 1. Criteria used for histological analysis of tertiary dentinogenesis.  which may be present endogenously (Fig. 9B), and dental pulp cells are activated by these MMP-digested DMCs (Fig. 9C). DMCs digested with MMP-1, -9, -13, and -20 facilitated wound healing of the dentin-pulp complex in our system (Fig. 9D). To our knowledge, this study is the first to examine the wound healing potential of the dentin-pulp complex by using DMCs digested with MMP-1, -2, -3, -8, -9, -13, and -20; the data identify a significant role for MMP-20 in mature teeth. Further studies are necessary to analyse the components generated by digested DMCs and identify which molecules are critical for wound healing of this tissue.

Methods
Preparation of DMCs digested with MMPs. Human dentin specimens were prepared from extracted sound non-carious teeth (erupted, permanent dentition) collected from patients of both genders and all ages (generally 16-40 years) attending the Oral Surgery Department at Birmingham Dental Hospital (Birmingham, UK). Informed consent was obtained from all subjects. The protocols and all experimental procedures were approved by and performed in accordance with the relevant guidelines and regulations of the ethics approval of the University of Birmingham School of Dentistry Tooth Bank (Ethics approval no. 90/H0405/33) as described in a previous report 58 . Briefly, after the tooth was extracted, pulp tissue and enamel were removed from the tooth by using dental instruments. The remaining dentin was pulverized into a powder by using a percussion mill (Spex 6700 Freezer/ Mill, Glen Creston Ltd, Stanmore, UK), then cooled with liquid nitrogen and filtered through a 60-μm mesh sieve. Powdered dentin was treated with a 10% (w/v) EDTA solution containing proteinase inhibitors, 10 mM N-ethylmaleimide (Sigma-Aldrich, Dorset, UK), and 5 mM phenylmethylsulfonyl fluoride (Sigma-Aldrich) for 14 days with agitation at 4 °C. The extraction solution was changed daily after centrifuging at 3,000 rcf for 10 min and the supernatant was collected. The pooled extraction supernatants were dialysed extensively against distilled water for 7 days and lyophilized by using a freeze dryer (Modulyo, London, UK). A dialysis membrane with a Figure 9. Proposed model for wound healing in pulp tissue following dental caries. Dentin decalcification initially releases matrix metalloproteinases (MMPs) from the dentin matrix during caries progression (A). The dentin matrix is then digested with MMPs (B). Dental pulp cells are subsequently activated by digested dentin matrix components (DMCs) (C). DMCs digested by MMPs, particularly MMP-20, stimulate wound healing in the dentin-pulp complex (D). molecular weight cut-off of approximately 12,000 kDa was used to maintain consistency among dentin matrix preparations 59,60 . The lyophilized powder was collected as intact DMCs.
Angiogenesis assay. To evaluate the angiogenic effects of DMCs treated with MMPs, an endothelial tube formation assay was performed with the Angiogenesis Kit (Kurabo, Osaka, Japan). Human umbilical vein endothelial cells were co-cultured with human fibroblasts as a feeder layer containing 0.01-1 µg/ml of MMP-treated DMCs or incubated DMCs without MMP as an experimental control in angiogenesis induction medium (Kurabo). After incubation for 11 days, cells were fixed with 70% (v/v) ethanol for 30 min, then immunostaining with CD31 (mouse anti-human CD31, Kurabo) to visualize endothelial cells of blood vessels. The acquired images were analysed by using Angiogenesis Image Analyzer V.2.0.5 (Kurabo) software to quantify the newly formed tubular formation, including vessel number, branch length and branch point in blood vessel-like structures (n = 3). Angiogenesis induction medium containing 20 μM/L of suramin was used as a negative control and recombinant human VEGF (2 ng/ml) was used as a positive control. The exact mechanism of suramin as an inhibitor of angiogenesis is not known; however, its non-specific interactions with numerous growth factors and angiogenic factors, such as basic fibroblast growth factor (b-FGF), platelet-derived growth factor, transforming growth factor, and VEGF, have been shown 62 . VEGF, as a promoter of angiogenesis, has been reported to regulate intracellular functions and activities by binding to receptors 63 . Each MMP molecule incubated alone (0.01-1 µg/ ml) was used as an additional control.
Migration assessment by wound scratch assay. An in vitro wound scratch healing model was used to investigate cell migration. Rat primary pulp cells (5 × 10 4 cells) were seeded onto 6-well cell culture dishes (Becton Dickinson and Company, Franklin Lake, NJ, USA) containing α-MEM supplemented with 10% FBS. When cells became sub-confluent, the medium was changed to α-MEM supplemented with 1% (v/v) FBS and cells were cultured for an additional 24 h. Then, 10 µg/ml of mitomycin-C (Calbiochem, San Diego, CA, USA) was applied to the medium for 30 min to remove the effect of proliferation and determine more specifically the role of migration in closure of the scratch wound by the cells. The experimental approach used here is based on previous studies, which have explored the roles of proliferation and migration in the wound closure assays 64 . An artificial scratch wound was created by disrupting the monolayer using a sterile plastic pipette tip. Medium containing 0.01-1 µg/ml of MMP-treated DMCs or incubated DMCs without MMP as an experimental control were then added and cells were cultured for 36 h to allow migration into the wounded area. Cells not treated with DMCs served as a negative control. Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control. Eight points were randomly selected to assess migration; the distances of the cells from the edge of the scratch wound were averaged and statistically evaluated by microscopic observation (Fig. 3A) and compared with controls by using ImageJ software (Version 1.47, National Institutes of Health, Bethesda, MD, USA).
Migration assessment by trans-well assay. Cell migration (chemotaxis) was also evaluated by using a Boyden chamber (membrane pore size = 8 µm) (Cytoselect®, Cell Biolabs, San Diego, CA, USA) 65  for 30 min. Then, CyQuant® GR dye (Cell Biolabs) was added to the lower chamber for fluorescent staining of migratory cells. Migration was quantified by using a microplate reader (ARVO MX, PerkinElmer, Waltham, MA, USA) at 485 nm/535 nm fluorescence intensity (n = 8 for each group). Cells not treated with DMCs in the lower chamber served as a negative control. Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control.
Cell proliferation assay. To evaluate the effects of MMP-treated DMCs on the growth of rat primary pulp cells, the WST-1 assay was performed. Rat primary pulp cells (1.0 × 10 4 cells) were cultured in α-MEM supplemented with digested DMCs (0.01-1.0 µg/ml) or incubated DMCs without MMP (0.01-1.0 µg/ml) as an experimental control for 5 days. Then, WST-1 reagent (Roche, Basel, Switzerland) was added and cells were incubated for 2 h. The fluorescence at 450 nm was measured using a microplate reader (ARVO MX) to evaluate cell proliferation (n = 6 for each group). Cells not treated with DMCs served as negative controls. Each MMP molecule incubated alone (0.01-1 µg/ml) was used as additional control. ALP activity. Alkaline phosphatase (ALP) activity was measured to investigate the effects of digested DMCs on pulp cell differentiation 66 . Rat primary pulp cells were cultured with 0.01-1 µg/ml MMP-treated DMCs or incubated DMCs without MMP as an experimental control in α-MEM supplemented with 10 mM β-glycerophosphate (Sigma-Aldrich), 50 µg/ml ascorbic acid (Sigma-Aldrich), and 10% (v/v) FBS (differentiation induction medium) at a density of 2.0 × 10 4 cells/well. After 7-or 14-day incubation, ALP activity was measured with the Alkaline Phosphate Substrate Kit (Bio-Rad Laboratories, Hercules, CA, USA) according to the manufacturer's instructions. Cells not treated with DMCs served as negative controls (n = 6 for each group). Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control.
Mineralization assay. Mineralization of rat primary pulp cells was evaluated by alizarin red staining (PG Research, Tokyo, Japan). Rat primary pulp cells (5.0 × 10 4 cells) were incubated in differentiation induction medium with 0.01-1 µg/ml of MMP-treated DMCs or incubated DMCs without MMPs as an experimental control for 21 days. Then, cells were fixed in 10% neutral buffered formalin and mineralized nodules were stained with alizarin red. The bound dye was quantified with a mineralization assay kit (PG Research) by measuring absorbance at 405 nm by using a microplate reader (ARVO MX). Specimens cultured in mineralization medium that were not treated with DMCs served as negative controls (n = 6 for each group). Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control.
Direct pulp capping using rat teeth in vivo. The effects of MMP-treated DMCs on wound healing of the dentin-pulp complex were examined by direct pulp capping in 8-week-old male Wistar rats (CLEA Japan). After general anaesthesia, the pulp was exposed on the occlusal surfaces of maxillary first molars by using a #1 round carbide bur (Dentsply Maillefer, Ballaigues, Switzerland), as previously described 8,62 . The size of the cavity measured approximately 1 mm in depth and 0.4 mm in diameter. The exposed pulp tissue was rinsed with saline and dried, then directly covered with a gelatine sponge (Spongel®, Astellas Pharma Inc, Tokyo, Japan) containing 20 µl of MMP-treated DMCs (0.01-1 µg/ml), or incubated DMCs without MMP as an experimental control. ProRoot MTA (Dentsply, Tulsa, OK, USA) was used as a positive control 3,6,66 . Each MMP molecule incubated alone (0.01-1 µg/ml) was used as an additional control. The cavity was then sealed with glass ionomer cement (Fuji IX, GC, Tokyo, Japan). Specimens with a gelatine sponge containing 20 µl of PBS served as negative controls (n = 6 for each group).
Twenty-eight days after pulp capping, rats were perfused with physiological saline followed by paraformaldehyde solution (Nacalai Tesque, Kyoto, Japan). Pulp-capped teeth were removed en bloc with surrounding maxillary bone and immersed in the same fixative for an additional 24 h. The induced tertiary dentin (n = 6 in each group) was analysed by using a micro-CT scanner (R_mCT2, Rigaku, Tokyo, Japan) at settings of 90 kV and 160 µA with a scanning resolution of 20 μm intervals in individual image. After scanning, the area of induced tertiary dentin of each specimen was quantitatively analysed by using three-dimensional reconstruction images for bone (TRI/3D-BON; Ratoc System Engineering, Tokyo, Japan) with reference to previous report 67,68 . After confirming the consistency between micro-CT and histological images, image analysis was performed. Teeth were demineralized in a 10% (v/v) citric-22.5% (v/v) formic acid solution (Wako Pure Chemicals, Osaka, Japan) for 1 week at 4 °C. The specimens were prepared by the previous protocol of graded alcohol dehydration, followed by paraffin embedding, and sagittal sections were prepared at a thickness of 5 µm for HE staining 69 . Wound healing of the pulp tissue was quantified based on tertiary dentin formation, as previously described 70 . Namely, conventional histopathological methods were used to analyse six consecutive sections from each sample. Defects in tertiary dentin could be generally observed around the centre of exposed pulp area due to tertiary dentin formation that began at the periphery of the exposed pulp tissue. Subsequently, we selected and evaluated six consecutive images from the central area of the tertiary dentin to determine the quality of tertiary dentin with reference to micro-CT images, based on previously published histological criteria. The criteria for histological evaluation were derived from previous publications [71][72][73] and are shown in Table 1. For the histological evaluation, two independent observers were trained to evaluate histological features by using the designated criteria with 95% consistency referring to micro-CT images. If there was disagreement between the two observers, consensus was reached by discussion.
Statistical analysis. Significant differences were evaluated by one-way ANOVA with Tukey's post-hoc test, the Kruskal-Wallis test, or the Steel-Dwass test. P values < 0.05 were considered statistically significant.