2.1.1.

Specimen preparation

Four freshly extracted noncarious mandibular central incisor teeth were collected and stored in phosphate buffered saline (PBS) solution ( $0.1\mathrm{M}$ phosphate buffer, pH 7.2). These specimens were transilluminated so that teeth with cracks or extraction damage could be excluded. Specimens were prepared by grinding the mesial and distal sides of the teeth specimens on wet emery paper of grit size 400, 800, and 1000, under constant irrigation to obtain midline buccolingual plane-sided, slab-shaped sections ( $2.5\pm 0.2\mathrm{mm}$ thicknesses) of the teeth. These specimens represented the entire faciolingual bulk of the dentine and contained the pulp chamber and the root canal in the core region (Fig. 1 ).

Fig. 1

Schematic diagram to highlight the region of the tooth used as a specimen.

2.1.2.

Experiments

Moiré methods utilize diffraction gratings as a deformation sensing element. In moiré interferometry, a grating replicated specimen (specimen grating) was interrogated using a virtual reference grating formed by the interference of two mutually coherent beams incident on the specimen plane at a fixed angle. Moiré fringes result from the interference between the deformed specimen grating and the virtual reference grating. These fringes represent contours of in-plane displacement fields and were analyzed using image processing software as discussed previously.^{4, 16} In order to prepare the specimen grating, a high-frequency cross-grating $(f=1200\text{lines}∕\mathrm{mm})$ was replicated on a buccolingual surface of the tooth using epoxy adhesive at room temperature. The replication was done in such a way that the grating lines were parallel and perpendicular to the long axis of the tooth. The distance between the adjacent grating lines is referred to as the pitch of the grating, which in this case was $0.833\mu \mathrm{m}$ .

The moiré interferometer consisted of two mutually coherent light beams from a diode laser $(\lambda =670\mathrm{nm})$ that were incident on the specimen grating at an oblique angle and generated a virtual reference grating of $2400\text{lines}∕\mathrm{mm}$ [corresponding to a pitch $\left(P\right)$ of $0.417\mu \mathrm{m}$ ]. This virtual reference grating interacted with the deformed specimen grating to produce the moiré fringe patterns. A high-resolution charge-coupled device (CCD) camera with a spatial resolution of $753\left(\mathrm{H}\right)\times 244\left(\mathrm{V}\right)\text{pixels}$ was used to digitize and record the fringe patterns obtained for further analysis (Fig. 2 ). Moiré fringes represent contours of displacement components in the direction perpendicular to the lines of the grating.¹⁶ During experiments, (1) the fully hydrated specimen grating was positioned in the moiré interferometer and the real-time dehydration-induced surface deformations along the $x$ axis, known as the $U$ field and that along the $y$ axis, known as the $V$ field were recorded for a period of $12\mathrm{h}$ . Similarly, (2) a $72\text{-}\mathrm{h}$ prior dehydrated specimen grating was positioned in the moiré interferometer and the real-time hydration-induced surface displacements along the $x$ and $y$ axes were recorded. The acquired digital moiré fringe patterns were used to determine the in-plane normal strains along different regions of interest on the cervical portion of the root dentine as shown in Fig. 3 . Further details about the moiré interferometry and the calculations of normal stains are presented elsewhere.^{17, 18}

Fig. 2

Schematic diagram of the digital moiré interferometer.

Fig. 3

Shows a typical (a) $V$ -field and (b) $U$ -field moiré fringe patterns and the calculation of normal strain from the region of interest.

2.2.1.

Specimen preparation

Twelve freshly extracted single-rooted teeth were collected and stored in PBS solution. These teeth were transilluminated so that teeth with cracks or extraction damage could be excluded. Specimens were prepared by grinding the mesial and distal sides of the teeth specimens on wet emery paper of grit size 400, 800, and 1000, under constant irrigation resulting in the formation of midline buccolingual plane-sided, slab-shaped sections ( $2.5\pm 0.2\text{-}\mathrm{mm}$ thick). All the specimens had a thin layer of enamel on the coronal aspect, cementum on facial and lingual sides, and pulp chamber in the center (Fig. 1). The ground surface was polished to a final finish on an automatic polisher with $3\text{-}\mu \mathrm{m}$ particle size diamond paste. These tooth specimens were used for the gravimetric experiments.

2.2.2.

Experiments

During experiments, twelve tooth specimens were allowed to dehydrate at $21°\mathrm{C}$ and 60% relative humidity for $72\mathrm{h}$ . The rate of weight loss due to dehydration was monitored gravimetrically. The gravimetric measurements were recorded every $15\min$ for the first $8\mathrm{h}$ and subsequently after 24, 48, and $72\mathrm{h}$ intervals. The twelve samples subjected to dehydration were later divided into two groups of equal numbers. Group 1 was subjected to rehydration at $21°\mathrm{C}$ , and group 2 was subjected to desiccation at $105°\mathrm{C}$ .^{7, 8, 19} The weight gain during the rehydration process (group 1) and the weight loss due to desiccation (group 2) were recorded every $15\min$ for the first $8\mathrm{h}$ and after 24, 48, and $72\mathrm{h}$ intervals.

2.3.1.

Specimen preparation

Nine freshly extracted mandibular single-rooted teeth were collected and midline buccolingual plane-sided, slab-shaped sections ( $2.5\pm 0.2\text{-}\mathrm{mm}$ thickness) were prepared by grinding the specimens on wet emery paper of grit size 400, 800, and 1000. The enamel and cementum portions of these specimens were trimmed off using a tapering fissure diamond bur (Shofu, ISO no. 017).

2.3.2.

Experiments

These specimens were divided into three equal groups for this study. The specimens in group 1 were subjected to room temperature dehydration at $21°\mathrm{C}$ (60% relative humidity) for $72\mathrm{h}$ . The specimens in group 2 were subjected to desiccation at $105°\mathrm{C}$ for $72\mathrm{h}$ , (7, 8, 19) while specimens in group 3 were kept fully hydrated. The dentine specimens in group 1, group 2, and group 3 were pulverized to fine powder in a mechanical grinder. Total time spent in grinding one group was less than a minute. The fine powder was immediately transferred to a NMR tube and was tested by NMR spectroscopy. The NMR measurements were carried out with a $300\text{-}\mathrm{MHz}$ Bruker ACF-300 (Bruker Analytik, GmbH, Rheinstetten, Germany), equipped with a BVT-3000 temperature controlled unit. A dedicated 1-H probe was used. Line width was used to measure the area under the curve. Spectra were collected with a radio frequency of $300.13\mathrm{MHz}$ , and 16 $\mathbf{K}$ data points were sampled in $3.4\mathrm{s}$ , corresponding to a spectral width of $2.4\mathrm{kHz}$ . During each measurement, 250 scans were used to record the data.

3.1.1.

Dehydration-induced strains in dentine structure

Figure 4a shows the strain distribution pattern in the dentine (in the direction perpendicular to the dentinal tubules) during dehydration. The fourth-order polynomial trend line was used to fit the data. Notice that the $R^2$ value is 0.9876 for inner dentine data and 0.9941 for outer dentine data, which is a good fit of the line to the data. The $U$ -field moiré analysis (strain in the direction perpendicular to the dentinal tubules) showed a generalized increase in strains in dentine with dehydration. This dehydration-induced strain response occurred in three stages. In the initial stage, there was no obvious increase in strains with dehydration (stage 1). This stage (stage 1) lasted for the first $4\mathrm{h}$ , and subsequently, there was a rapid increase in strains with dehydration (stage 2). The stage 2 lasted until $9\mathrm{h}$ of dehydration. The outer dentine (or peripheral dentine adjacent to the cementum) produced higher and earlier strains in these stages. After $9\mathrm{h}$ , both inner (core dentine adjacent to the root canal lumen) and the outer dentine tended to behave uniformly with minor increase in strains with dehydration (stage 3).

Fig. 4

(a) Dehydration-induced strains at the region of interest (direction perpendicular to the dentinal tubules) in the dentine structure. (b) Dehydration-induced strains at the region of interest (direction parallel to the dentinal tubules) in the dentine structure. (c) Rehydration-induced strains at the region of interest (direction perpendicular to the dentinal tubules) in the dentine structure. (d) Rehydration-induced strains at the region of interest (direction parallel to the dentinal tubules) in the dentine structure.

Figure 4b shows the strain distribution pattern in the inner and the outer dentine (in the direction parallel to the dentinal tubules) during dehydration. The fourth-order polynomial trend line was used to fit the data. Notice that the $R^2$ value is 0.9889 for outer dentine data and 0.9871 for inner dentine data, which is a good fit of the line to the data. The $V$ -field moiré analysis (strains in the direction parallel to the dentinal tubules) also showed an increase in strains with dehydration in three stages. There was no obvious increase in strains for the first hour of dehydration (stage 1), which was followed by a rapid increase in strains with dehydration until about $10\mathrm{h}$ (stage 2). During this period, the outer dentine exhibited higher strain than the inner dentine. There was only a minor increase in strains after $10\mathrm{h}$ of dehydration (stage 3).

3.1.2.

Rehydration-induced strains in dentine structure

The $U$ -field moiré analysis (strains in the direction perpendicular to the dentinal tubules) displayed a decrease in strains with rehydration, which occurred in two stages [Fig. 4c]. The third-order polynomial trend line was used to fit the data. Notice that the $R^2$ value is 0.9752 for inner dentine data and 0.9282 for outer dentine data. This indicates a good fit of the line to the data. In the stage 1, there was a rapid decrease in strains with rehydration for the first $3\mathrm{h}$ , which was followed by a steady state in which there was only a minor decrease in strains with rehydration (stage 2). The rate of decrease in strains with rehydration was higher in the inner than the outer dentine.

The $V$ -field analysis (strains in the direction parallel to the dentinal tubules) showed strain response in the outer and inner dentine upon rehydration in three stages. Figure 4d shows the strain distribution in the inner and the outer dentine (in the direction parallel to the dentinal tubules) during rehydration. The third-order polynomial trend line was used to fit the data. Notice that the $R^2$ value is 0.8439 for inner dentine data and 0.9648 for outer dentine data. This indicates a good fit of the line to the data. It was found that there was an increase in strain immediately upon rehydration (stage 1). This stage lasted for about $4\mathrm{h}$ , and subsequently, there was a rapid decrease in strains with rehydration for about $10\mathrm{h}$ (stage 2). Beyond $10\mathrm{h}$ of rehydration, the dentine structure showed only a minor decrease in strains with rehydration (stage 3).

3.2.1.

Water loss during dehydration

Figure 5a shows the pattern of water loss in dentine when dehydrated at $21°\mathrm{C}$ (Table 1 ). The second-order polynomial trend line was used to fit the data. Notice that the $R^2$ value is 0.9344, which is a good fit of the line to the data. Gravimetric analysis of the fully hydrated dentine specimens showed that room temperature dehydration resulted in a biphasic water-loss response. An initial rapid weight-loss phase, which lasted for $\sim 2\mathrm{h}$ , followed by the slow weight-loss phase, during which the rate of water loss was minimal. These observations were consistent in all the samples (Table 1). The average weight loss due to dehydration after $72\mathrm{h}$ was 5.3% [standard deviation (SD): 0.61]. Further, it was noted that 81% of the dehydration-induced water loss occurred in the first $2\mathrm{h}$ of dehydration.

Fig. 5

(a) Dehydration-induced weight loss of the dentine specimen. (b) Desiccation-induced weight loss of the dentine specimen. (c) Rehydration-induced weight gain of the dentine specimen.

Table 1

Shows the dehydration- and dessciation-induced weight loss in the dentine specimens.

3.2.2.

Water loss during desiccation

Figure 5b shows the pattern of water loss in dentine when desiccated at $105°\mathrm{C}$ (Table 1). The second-order polynomial trend line was used to fit the data. Notice that the $R^2$ value is 0.8211, which is a good fit of the line to the data. The high-temperature desiccation also produced a biphasic response in water loss. There was a rapid water-loss phase in the first $2\mathrm{h}$ of desiccation (stage 1), following which there was a gradual water-loss phase (stage 2). Desiccation of dentine specimens at $105°\mathrm{C}$ accounted for 7.73% (SD: 0.43) weight loss in $72\mathrm{h}$ . However, the initial rapid water-loss phase or the stage 1 accounted for 86% of the total weight loss.

3.2.3.

Water regain during rehydration

Figure 5c shows the pattern of water regain in dentine when rehydrated at $21°\mathrm{C}$ . Rehydration of previously dehydrated specimens showed a 99.1% (SD: 1.1) weight gain in $2\text{weeks}$ (Table 2 ). The second-order polynomial trend line was used to fit the data. Notice that the $R^2$ value is 0.9737 and this is a good fit of the line to the data. Rehydration-induced weight gain also had a biphasic response. There was an initial rapid water-regain phase for the first $2\mathrm{h}$ of rehydration (stage 1). This phased resulted in about 96% of the water regain. The second phase showed a gradual regain of water with rehydration (stage 2).

Table 2

Shows the rehydration-induced weight gain in the previously dehydrated dentine specimens.