Development and Calibration of Biochemical Models for Testing Dental Restorations

Abstract

Currently, resin composites are the most popular materials for dental restoration in clinical practice. Although the properties of such materials have been improved significantly, together with better clinical techniques used for their placement, early restoration failure still occurs too frequently. As clinical studies take years to complete, and new resin composites are being produced at ever increasing pace, laboratory assessment using accelerated but representative tests is necessary. The main types of failure in resin-composite restoration are tooth/restoration fracture and secondary caries, which are caused by a combination of mechanical and biochemical challenges. In this study, a biofilm model (S. mutans) and a chemical model (lactic acid buffer) for producing artificial caries in bovine dentin are developed and calibrated against in situ data. Using a power law relationship between the demineralization depth and challenge duration, scale factors that convert the in vitro durations to the equivalent clinical durations are determined for different pH values for each model. The scale factors will allow the synchronization of biochemical and mechanical challenges in terms of their rates of action to potentially test resin-composite restoration in an accelerated but clinically representative manner.

Graphical Abstract

1. Introduction

Resin-based composite is widely used as a dental restorative material in clinics currently. It has replaced traditional amalgam as the most common material for direct restoration due to its superior esthetics and comparable clinical performance. However, the survival rate of resin-composite restoration is still under debate. Some early long-term clinical studies showed better survival rates for amalgam than for resin-composite restoration [1–2], which was supported by some recent review work [3–4]. However, other studies indicated that the evidence supporting the higher failure rates of resin-composite restoration was not sufficiently strong [5]. In fact, Opdam et al. [6] reported better 5-year and 10-year survival rates for resin-composite restoration than for amalgam restoration. A more recent 24-month clinical trial also showed no significant difference in failure rate between the two materials [7]. This increased resin-composite restoration survival rate could be due to better performing resin-composite and adhesive materials and improved skills of the clinicians. Opdam et al. [6] also reported that failure of dental restoration was mainly due to secondary caries (34%), endodontic treatment (12%), and tooth fracture (13%). In a 5-year clinical study on the survival of posterior bulk-filled resin composite restorations [8], tooth fracture and secondary caries were again reported as the main reasons for failure. Indeed, secondary caries has often been reported as a major cause for restoration failure [6][8–11]. In [9], restoration fracture was also reported as a major type of failure.

It has been reported that bacteria tend to accumulate more on resin-composite than on amalgam [12], which indicates that secondary caries can be more prominent around resin-composite restorations. Adhesive materials can also play an important role in the development of secondary caries. In an in-vitro study using biofilms [13], a significant decrease in secondary caries was reported when an adhesive containing a bacterial inhibitor was used. In another study, Opdam et al. [14] concluded that patients’ caries risk played a significant role in restoration survival. In the high-risk group, amalgam and resin-composite restorations showed similar performances. For the low-risk group and when both risk groups were considered together, resin-composite restoration had a higher survival rate. In a practice-based study of 31,472 restorations that lasted for 2.7 yrs [15], the mean annual failure rate was concluded as 7.8% at 2 yrs.

The high failure rate of resin-composite restoration means that new restorative materials are still being developed in order to improve their performance. Currently, the most reliable way of assessing the longevity of a restorative material is through clinical trials. However, these are time-consuming and expensive. By the time a clinical trial is completed, the material may already be superseded by other new materials. Thus, laboratory-based yet clinically representative accelerated testing needs to be developed to reduce the time and cost required to test dental materials. Accelerated mechanical testing using machines that can accurately simulate the chewing motion at elevated frequency has been developed and calibrated against wear data collected clinically from dental restorations [16–19]. Thus, the equivalent clinical duration represented by a certain number of mechanical cycles made by these machines, i.e. the scale factor, can be determined. For example, a scale factor of one year per 300,000 cycles has been determined from resin-composite samples subjected to a contact duration of 0.2 s per cycle and a peak force of 13 N [19]. However, mechanical loading can only produce degradation, bulk or interfacial, that leads to fracture. In order to reproduce another main failure mode in resin-composite restorations, i.e. secondary caries, in the laboratory, biochemical challenge must be added to the mechanical challenge. In a study that combined mechanical and biofilm challenges, Khvostenko et al. [20] reported that cyclic mechanical loading promoted the penetration of bacteria through gaps at the tooth-restoration interface. Carrera et al. [21] investigated the effects of applying sequentially mechanical and biochemical challenges on the fracture strength of resin-composite restorations. They found that combining the two challenges could reduce the fracture strength more than either challenge could when acting alone. Thus, both cyclic mechanical loading and biochemical challenge are indispensable in testing dental restoration. However, the latter must also be calibrated against clinical data so that, when applied together, the two are synchronized in terms of their effects with respect to time. Otherwise, the challenges would be out of synch and the rates and proportions of the different modes of failure cannot be correctly predicted.

This study developed biofilm and chemical models for inducing biochemical challenges to resin-composite restoration in an accelerated manner. The models were developed in a Center for Disease Control (CDC) reactor by following a previous work [22] to produce environments that could induce different rates of dentin demineralization. The data collected from these models were then compared against in-situ data published by Hara et al. [23] to establish the scale factors that convert laboratory durations to equivalent clinical durations under the different conditions considered.

2. Materials and Methods

2.1. Dentin disc preparation

Dentin samples were collected from the incisor roots of 3-year old cows. After soft-tissue removal, the bovine teeth were rinsed with de-ionized water and stored in 0.5% Chloramine-T at 4 °C before use. By following the previously reported procedures [24], the crown and root tip (around 2–3 mm from the tip end) were removed from each tooth by a low-speed diamond saw (Isomet, Buehler, Lake Bluff, IL, USA). The separated root was then trimmed to a cylinder of 5 mm in diameter and the root canal was enlarged to 2 mm in diameter. After that, the hollow dentin cylinder was sliced into 2-mm thick rings with the same low-speed diamond saw. These dentin rings were stored in distilled water at 4 °C overnight before experiments. The top, bottom, and outer wall surfaces of the rings were covered with nail varnish (Revlon, Inc., New York, NY, USA) before subjecting them to low-pH challenge. Thus, only the inner canal wall was exposed to the low-pH environment.

2.2. In-vitro biofilm challenge

2.2.1. Center for Disease Control (CDC) biofilm reactor

In this part of the experiments, a single species biofilm model was used. A previous study confirmed that a low-pH chemical model could produce similar demineralization and reduced bond strength at the dentin-composite interface as multi-species oral biofilms [24]. It is therefore reasonable to assume that acid-producing single-species biofilm models will have similar degradative effects. Thus, S. mutans (ATCC®, 700610^TM, Manassas, VA, USA) were inoculated on Mitis Salivarius agar plates (BD Difco^TM, Sparks, MD, USA) and incubated under 5% CO₂ at 37 °C. After colonization, the S. mutans were cultured in Brain-Heart Infusion (BHI) liquid medium (BD BBL^TM, Sparks, MD, USA) with a target optical density of 0.2 measured at 600 nm wavelength (OD₆₀₀) under the same conditions. The optical density was measured using a Beckman DU-64 spectrophotometer (Beckman Coulter Inc., USA). The typical bacterial count of the OD₆₀₀ ≈ 0.2 medium was 1.79 × 10⁻⁷ CFU/ml. The bacteria-containing BHI liquid medium with an OD₆₀₀ ≈ 0.2 was then diluted by a factor of 1:10 before being used as the medium for biofilm challenge.

Sucrose solution was added to the S. mutans-containing BHI liquid medium to lower its pH via the production of organic acids by the bacteria as they metabolized the sucrose. By adjusting the concentration of sucrose added, media of different initial pH values, i.e. 4.5, 5.0, and 5.5, could be produced. However, activity of the bacteria caused the pH of the medium to drop over time, especially those with pH > 4.5. Thus, the pH of media with target values of 5.0 and 5.5 needed to be adjusted manually by adding BHI medium (~pH 6.9) periodically. The pH and sucrose concentrations employed in the biofilm model are listed in Table 1. As it was hard to maintain the pH for long periods with the biofilm model due to the reason mentioned above, the longest duration for all the three pH values was 3 days. The biofilm challenge was performed with 400 ml of the medium in the CDC reactor (BioSurface Technologies, Bozeman, MT, USA) in which a baffled stir bar provided a constant shear flow. The temperature of the medium was maintained at 37 °C by a heating plate (Fisherbrand^TM Isotemp^TM CAT# 1130049shp, Fisher Scientific). The pH was measured continuously throughout the test by a pH electrode (Accumet, CAT# 13-620-130, Fisher Scientific) paired with a digital pH meter (Accumet Excel XL15, Fisher Scientific) and recorded every 15 minutes. Full description of the experimental setup using the CDC reactor could be found in a previous study [22].

Table 1.

pH and sucrose concentrations employed in the biofilm model

pH	Sucrose Concentration
4.5	1%
5.0	0.2%
5.5	0.05%

The speed of fluid flow and the resulting shear stresses in a CDC bioreactor may not be identical to those in the oral environment, but this bioreactor has been shown to be able to produce oral biofilms that preserve over 60% of the species identified [22]. In addition, the CDC bioreactor can produce a controllable homogeneous environment for all the specimens contained within it. This makes measurement and data analysis straightforward.

There were 2 runs and 4 replicates per run for each combination of pH and duration. The total sample size for each combination of pH and duration was therefore 8. Durations for each pH were 1, 2 and 3 days.

2.2.2. Bacterial penetration

To see whether the bacteria would penetrate the dentin rings through the dentinal tubules, S. mutans labeled with green fluorescence protein (GFP) [25] was used for the biofilm challenge in a separate test. The fluorescent S. mutans was cultured in BHI liquid medium and diluted as described above. Again, different concentrations of sucrose were used to adjust the pH of the medium (Table 1). The pH of the medium was measured using pH-indicator strips (CAT# 1095420001, MColorpHast™, EMD Millipore). For simplicity, the dentin rings were placed within the wells of a 24-well plate and incubated in a 5% CO₂ incubator maintained at 37 °C. Each dentin disc was challenged with 2 mL of the medium, which was replaced every 24 hrs. The sample size for each combination of pH and duration was 3. The rings thus tested were imaged with a fluorescence microscope to estimate the depth of bacterial penetration.

2.3. Chemical challenge

As mentioned above, a previous study confirmed that a low-pH chemical model could produce similar demineralization and reduced bond strength at the dentin-composite interface as multi-species oral biofilms [24]. Thus, in this part of the experiments, the dentin rings were challenged with a lactic-acid buffer solution (0.1 M lactic acid, 2.2 mM CaCl₂, 2.2 mM K₂HPO₄) at pH 4.5, 5.0, and 5.5 for various durations (see Table 2). The pH of the buffer solution was adjusted by adding 1 M sodium hydroxide (NaOH) or 1 M hydrogen chloride (HCl) solution. The chemical challenge was also performed in the CDC reactor with 400 ml of the lactic-acid buffer solution. Again, the baffled stir bar provided a continuous shear flow and the temperature was maintained at 37 °C by the heating plate. The pH value of the lactic acid buffer solution was continuously monitored with the pH electrode and pH meter described above.

Table 2.

pH and durations employed with the chemical model

pH	1Day	2Days	3Days	7Days	14Days
4.5	√	√	√
5.0	√		√	√
5.5	√			√	√

Same as the biofilm model with the CDC reactor, 8 dentin rings were used for each combination of pH and duration (2 runs per combination and 4 rings per run).

2.4. X-ray microtomography (μ-CT) characterization

X-ray micro-computed tomography was used to determine the depth of dentin demineralization. This non-destructive characterization method allowed us to analyze the extent of demineralization in three dimensions longitudinally, giving more representative results with less scatter from inter-specimen variations.

The samples tested in the CDC reactor were scanned with a μ-CT machine (HMX-XT 225 X-tek System, Nikon Metrology, Inc., Brighton, MI, USA) using the following parameters: 90 kV voltage, 57 μA current, 708 ms exposure time, 720 projections, and 4 frames/projection. A 0.5-mm thick aluminum filter was used during scanning. Additionally, the magnification was ×38.9, and the resolution was 5.14 μm. Reconstruction of the samples was done using CT Pro 3D XT 3.1.11 (Nikon Metrology, Inc., Brighton, MI, USA). Image analysis and determination of demineralization depth were performed on 16-bit unsigned DICOM files using VGSTUDIO MAX 3.1 (Volume Graphics GmbH, Heidelberg, Germany). Samples were kept in de-ionized water at 4 °C before scanning. Each scan took approximately 35 min.

In this study, the mean total demineralization depth was calculated.

2.5. Mean Total Demineralization Depth

Both the mean $\left(\overline{G}\right)$ and standard deviation (σ) of the gray values of the background (the inner-hole region of the dentin ring) and those of sound dentin were calculated. In a well reconstructed 3D image that has been corrected for beam hardening, the histogram of grey values within a region of uniform material follows roughly the standard normal distribution (Figure 1(a)). As 99.7% of the values in a normal distribution are within 3σ of the mean, regions with grey values greater than $\overline{G}-3\sigma$ of sound dentin were considered to be sound dentin. Similarly, regions with grey values lower than $\overline{G}+3\sigma$ of the background were considered to belong to the background. These limiting or threshold grey values were used to determine the volume (V) of the inner hole of the dentin disk before and after demineralization. Assuming the loss of minerals was uniform circumferentially, i.e. the inner hole remaining cylindrical, an effective radius (r) was calculated for the inner hole before and after demineralization using the equation

$$V=\pi r^{2}h$$ (1)

where h is the disk’s thickness.

Figure 1.

Determination of the mean total demineralization determination depth. (a) An example of Gaussian fit of the background (inner-hole region) grey value histogram of a dentin disc sample. (b) The region of interest isolated from a dentin disc used for demineralization depth calculation. (c) Schematic diagram showing the effective radius of the inner-hole. (d) Top view of a dentin disc where the background was isolated by applying a threshold of $\overline{G}+3\sigma$. (e) Zoo-min view of the background-dentin boundary. (f) Zoom-in view of the demineralized dentin-sound dentin boundary. (g) Top view of the dentin disc where the sound dentin was isolated by applying a threshold of $\overline{G}-3\sigma$.

The mean demineralization depth was the difference between the inner-hole radii calculated before and after demineralization.

2.6. Empirical model for demineralization depth

The power law was applied to describe the relationship between the demineralization depth (δ) and the duration (t), i.e.

$$\delta =k*t^a$$ (2)

where k and a are constants. Their values were determined from the linearized logarithmic relationship between (δ) and t, i.e.

$$\text{ln}\left(\delta \right)=\text{ln}\left(k\right)+a*\text{ln}\left(t\right)$$ (3)

using the method of least square.

2.7. Scanning electron microscopy (SEM)

After μ-CT scanning, samples challenged by biofilm in the CDC reactor were dehydrated through critical point drying. The dehydrated rings were then cut along a diameter by hitting them with a surgical blade using a hammer to expose the dentinal tubules. Images of the exposed tubules were taken by using an environmental SEM (TM3000, Hitachi-High Technology, Japan) to ascertain whether bacterial penetration had occurred.

2.8. Fluorescence imaging

Dentin rings challenged by the fluorescent S. mutans were sectioned along a diameter to have the tubules exposed. Fluorescence images were taken of the cut surface to estimate the depth of bacterial penetration. The fluorescence microscope used (DM6 B, Leica Microsystem Inc.) was paired with a CCD camera (DFC3000 G, Leica Microsystem Inc.) and a LED light source (pE-300, CoolLED Ltd.). Bacterial penetration depth was measured from the fluorescence images by using ImageJ (ImageJ 1.52h, National Institutes of Health, USA). Measurements were made at ten randomly selected locations for each sample.

2.9. Statistical analysis

As samples were collected from two runs of the experiments, the independent t-test was used to compare the demineralization depth between the two runs in order to justify combining the two sets of data. The F-test was used to compare the rate-controlling parameters between the biofilm model and the chemical model. The level of significance was set at α = 0.05 for both tests.

3. Results

3.1. pH measurements

Figure 2 shows example pH measurements for the chemical and biofilm models. The time-averaged value and standard deviation of the pH for each group are listed in Table 3. In both models, the actual pH showed fluctuations over time, but the time-averaged values were within 4% of the target values. The fluctuations in pH were larger in the biofilm model than in the chemical model, except at pH 4.5 where a very stable value could be seen in the biofilm model.

Figure 2.

pH data over test duration for (a) biofilm model and (b) chemical model

Table 3.

The mean and standard deviation (SD) of pH for the biofilm and chemical models

Target pH	Actual Mean pH (SD)
	Biofilm Model	Chemical Model
4.50	4.55 (0.027)	4.52 (0.036)
5.00	5.02 (0.13)	5.01 (0.011)
5.50	5.70 (0.15)	5.47 (0.052)

3.2. Demineralization depth

To determine if the data collected from the two runs could be merged, the independent t-test was used to compare the demineralization depth between the two runs. The p values for all the combinations of pH and duration are shown in Table 4 for both models. As all the p values are over 0.05, the data collected from the 2 runs could be merged for model development.

Table 4.

Results from independent t-test of the 2 runs of experiments

	t-Test of Biofilm Model
	pH 4.5			pH 5.0			pH 5.5
	1 Day	2 Days	3 Days	1 Day	2 Days	3 Days	1 Day	2 Days	3 Days
p	0.49041	0.55956	0.53867	0.08272	0.19326	0.24593	0.53619	0.26275	0.18139
	t-Test of Chemical Model
	pH 4.5			pH 5.0			pH 5.5
	1 Day	2 Days	3 Days	1 Day	3 Days	7 Days	1 Day	7 Days	14 Days
p	0.56360	0.54793	0.34868	0.92323	0.20747	0.69933	0.57169	0.0682	0.40759

The demineralization depth calculated from the μ-CT images is plotted against the duration in Figure 3 for both models. The mean demineralization depth (31.1 ± 17.6 μm) of bovine dentin obtained from in-situ tests over 14 days [23] is also included in the plots for comparison.

Figure 3.

Relationships between demineralization depth and duration for (a) biofilm challenge and (b) chemical challenge.

In both models, the demineralization depth increased monotonically with the duration for all the pH values. With the same duration, the lower the pH, the deeper the demineralization. The data suggest that the time-average pH for the in-situ condition was likely over 5.5.

3.3. Bacterial penetration into dentinal tubules

A sample fluorescent image (×10 magnification) of bacteria penetrating into a dentin disc is shown in Figure 4, from which the depth of bacterial penetration was measured. The measurement results are shown in Figure 4(b) as a function of time and pH. In general, the longer the duration, the deeper the bacteria penetrated into the dentinal tubules. However, the depth of penetration appeared to plateau with time, especially under the higher pH values. For the same duration, the lower the pH, the deeper the bacteria penetrated.

Figure 4.

(a) Fluorescent image showing penetration of protein-labeled S. mutans into bovine dentin disc. (b) Penetration depth as a function of time and pH. (c) SEM image showing the presence of bacteria on dentin disc surface and within the tubules.

Figure 4(c) shows an SEM image of the longitudinal section of a dentin disc subjected to biofilm challenge. Presence of bacteria on the disc surface and within the tubules can be clearly seen, with the amount of bacteria reducing with increasing depth.

3.4. Curve fitting for the two models

The linearized logarithmic relationships between δ and t as described by Eq. 3 are shown in Figure 5. The parameters for the assumed power law are given for each group in Table 5. It can be seen that k increased significantly with reducing pH, whereas the value of a appeared to be insensitive to the pH or the model used. The R² values listed in Table 4 were obtained by linear regression for the linearized plots in Fig. 5 using the mean value for each duration.

Figure 5.

Linear regression of ln(δ) vs. ln(t) data for (a) biofilm model and (b) chemical model.

Table 5.

pH-dependent constants for power law used to describe relationship between demineralization depth and duration

Biofilm Model
pH	Linear Regression R2	k	95% Confidence Interval of ln(k)	a	95% Confidence Interval of a	$\overline{a}$
4.5	0.719	146.5	0.292	0.42	0.381	0.41
5.0	0.997	82.0	0.389	0.42	0.518
5.5	0.975	56.7	0.409	0.43	0.545
Chemical Model
pH	Linear Regression R2	k	95% Confidence Interval of ln(k)	a	95% Confidence Interval of a
4.5	0.946	135.0	0.272	0.39	0.363
5.0	0.933	82.8	0.381	0.37	0.295
5.5	0.992	56.7	0.436	0.44	0.274

The same power law was used to describe the in-situ data. As a seemed to be independent of pH, the mean value $\overline{a}=0.41$ obtained by pooling results from all the groups was used to determine the value of k for the in-situ data. The value of k thus obtained is 10.53.

The rate-controlling parameters of the two models were compared using the F-test. The resulting p values (Table 6) indicate that there was no statistically significant difference between the biofilm model and the chemical model in terms of the rate of dentin demineralization they induced.

Table 6.

Results from comparing the rate-controlling parameters between the biofilm model and the chemical model using the F-test

pH	p
4.5	0.22512
5.0	0.90147
5.5	0.99971

3.5. Calibration of chemical and biofilm models using in-situ data

Using the parameters derived for the in-situ data, the durations required for developing different demineralization depths in bovine dentin in-situ can be calculated. These are listed in Table 7. The durations required for the same demineralization depths using the in-vitro models are also listed. As can be seen, the two in vitro models can significantly accelerate the demineralization process. They are also very similar in action, with the biofilm model producing a slightly faster rate of demineralization. The difference in duration required between the biofilm and chemical models increases with decreasing pH and increasing demineralization depth.

Table 7.

Durations needed to produce different demineralization depths by in-vitro and in-situ models

Demineralization Depth (μm)	Duration by Biofilm Model (Days)			Duration by Chemical Model (Days)			Duration by In-situ Model (Days)
	pH 4.5	5.0	5.5	4.5	5.0	5.5
50	<0.5	<0.5	0.75	<0.5	<0.5	0.75	44.5
100	<0.5	1.6	3.7	<1	1.7	3.7	241
150	1	4	9.5	1.3	5	9.3	648
200	2	9	18	2.7	11	18	1306

From Eq. (1), assuming a to be a constant, we can write for a certain demineralization depth

$$k_{iv}{t}_{iv}^a=k_{is}{t}_{is}^a,$$ (4)

where the subscripts iv and is stand for in vitro and in situ conditions, respectively. Rearranging Eq. (4) gives

$$t_{iv}={\left(\frac{k_{is}}{k_{iv}}\right)}^{1/a}{t}_{is}.$$ (5)

Thus, given a particular clinical duration, the time required for the laboratory test to produce the same demineralization effect using an in vitro model can be estimated using Eq. (5) above.

4. Discussion

Bovine teeth are often used as a substitute for human teeth in laboratory research due to the former’s easier access. The justification for this substitution has been investigated extensively. For example, the behaviors of dentin from bovine and human teeth under demineralization, erosion, abrasion, and adhesion tests [23][26,27] have been compared. According to these studies, the type of teeth and the position where dentin is collected need to be considered, as there are differences in the size and spatial density of the dentinal tubules between human and bovine dentin [28]. Nevertheless, the chemical composition [29] and microstructure [30] of human and bovine dentin were found to be similar. In particular, comparable caries progression rate for bovine and human dentin has been reported based on in-situ data [23]. Soares et al. also concluded that bovine teeth are a reliable substitute for human teeth in bond strength studies through their review work [31]. Thus, the use of bovine dentin derived from the same type of and same position of teeth (incisor roots) to generate data for calibrating the biochemical models presented in this study is justified.

To mimic the biochemical challenge that occurs in the oral cavity, an accelerated biofilm model and an accelerated chemical model were developed in this study. These two models could shorten the duration of testing by using a sustained low-pH condition. In order to synchronize the mechanical and biochemical challenges, the biochemical models needed to be calibrated against appropriate clinical data to determine their temporal scale factors (Table 7). A considerable amount of work has been published on the degradation of the dentin-composite interface [13,32,33]. pH cycling, thermal cycling, mechanical fatigue, enzymatic attack or long-term water storage have been used to challenge the tooth-restoration interface [34]. However, most of these are in vitro studies that cannot be used for calibration purposes. Except the dentin demineralization data [23] used in this study, there are currently no quantitative clinical data on the temporal degradation of dental tissues, restorative materials or the tooth-restoration interface under the different challenges mentioned. Until these data become available, calibration of any in-vitro accelerated models to account for such degradation processes in a clinically representative manner would be very difficult. The same can be said about the possible impact of restorative materials on the biofilms. Without such calibration and the subsequent synchronization of the different challenges in terms of their rates of action, the times of appearance and the proportions of the different failure modes cannot be correctly predicted using in vitro models.

In this study, the in-situ data on dentin demineralization used to calibrate the models were taken from Hara et al. [23]. As far as we are aware, this is the only longitudinal study available with clinical, albeit in situ, data on the rate of biochemical challenge in the oral cavity. In their study, dentin slabs cut from bovine incisor roots were fixed on acrylic palatal devices which were worn by volunteers for 14 days. During the 14 days, the devices were only removed for sucrose solution dripping (4 times per day), meal intakes (3 times per day), and cleaning with dentifrice right after mealtimes. Under such in situ conditions, the pH can return to a more neutral value for long periods when remineralization could occur. This is probably why the rate of dentin demineralization in situ was much slower. In contrast, a sustained low-pH challenge was used by our biofilm and chemical models to accelerate the demineralization process and the duration required to produce a certain demineralization depth was controlled by the pH.

It should be pointed out that the biochemical models developed in this study are not meant for producing dentin demineralization or secondary caries only; they are meant for degrading composite restorations biochemically in general. Dentin demineralization data were used to calibrate the models purely because they were the only clinical, albeit in situ, data available for calibration. Had there been clinical data on the biochemical degradation of composite restoration without the influence of other challenges, it would have been possible to use composite restorations in this study.

The collagen matrix in dentin is protected by its mineral contents and, as reported by Kleter et al. [35], the dentin organic matrix can in turn inhibit demineralization. Bacteria degrade dentin by producing organic acids to dissolve the mineral [36] as well as secreting collagenolytic proteases to damage the exposed collagen [37]. Kleter et al. [35] also reported that the reduced mineral content at low pH (4.5) might lead to increased penetration of collagenase. Thus, dentin with damaged collagen will be demineralized faster than that with intact collagen, and enzymatic degradation of dentinal collagen can accelerate with increasing loss of mineral contents. There are reports [38–40] which show that S. mutans could indeed produce collagenolytic proteases. Further, the local pH within a biofilm at the tooth surface can be lower than the bulk pH value of the surrounding medium. The biofilm model is therefore expected to be more degradative than the chemical model. Our study did indicate that the biofilm model appeared to demineralize dentin slightly faster than the chemical model, especially at pH 4.5. This is consistent with the findings of Kleter et al. [35], although the difference between our in-vitro models was not found to be statistically significant. The latter can be attributed to the relatively short durations employed in this study.

The durations required to produce a certain lesion depth (Table 7) using the accelerated biofilm and chemical models can be calculated by using Eq. (5) and the constants listed in Table 5. The difference between the two models appeared to become more significant for deeper demineralization depth or longer durations at lower pH, possibly because of the reasons given above.

In this study, the demineralization of dentin was induced mostly along the dentinal tubules which were exposed on the inner surface of the root dentin rings. Dentin demineralization can also occur perpendicularly to the dentinal tubules, but the rate of progression in this direction is expected to be much slower. Clinically, bacteria can invade the dentinal tubules [41] once the tooth-restoration interface has been breached [42]. This will move the source of biochemical challenge or production of hydrogen ions by bacteria deep into the dentin, thus accelerating the demineralization process. This assertion is supported by the fluorescent and SEM images in Fig. 4. In contrast, the chemical model relies solely on the diffusion of hydrogen ions produced in the surrounding buffer into dentin to progress demineralization – the source of hydrogen production does not move. This could be another reason for the apparently higher rates of demineralization seen with the biofilm model.

The fluorescent images tracking the migration of bacteria into the dentin rings showed that the depth of penetration increased with time. The lower the pH, the deeper the penetration. Bearing in mind that a higher sucrose concentration, which helped fuel bacterial activity and proliferation, was required to produce a lower pH in the biofilm model, it is perhaps not surprising to see these results. The depth of penetration appeared to plateau with time, especially at higher pH. This can be explained by the limit of sucrose diffusion into the dentinal tubules as a result of consumption by the bacteria. The lower the sucrose concentration in the surrounding medium, i.e. the higher the pH, the shorter the expected length of sucrose diffusion and the shallower the bacterial penetration. The increase in bacterial penetration depth as a function of pH mirrored that of the dentin demineralization depth. However, the latter is expected to be greater than the former as dentin demineralization can occur ahead of bacteria migration through the diffusion of hydrogen ions produced locally by the bacteria. Note that human teeth have smaller dentinal tubules than the bovine teeth used in this study. Under the same conditions, bacterial penetration in human dentin may therefore be shallower than those reported here.

It has been estimated that an average person undergoes 300,000 cycles of chewing motions in a year [19]. This can be achieved in less than two days with a chewing simulator operating at 2 Hz. Using Eq. (5) and the mean values of a and k listed in Table 5, scale factors for the different pH values were calculated and listed in Table 8. Thus, an appropriate pH value could be selected so that the biochemical challenge could be synchronized with the mechanical challenge in their rates of action.

Table 8.

Scale factors of accelerated biofilm and chemical models

	Biofilm Model			Chemical Model
pH	4.5	5.0	5.5	4.5	5.0	5.5
Scale Factor (year/day)	1.68	0.41	0.17	1.37	0.42	0.17

Each of the two models has its own pros and cons. The biofilm model is more comparable to the in-vivo oral conditions and potentially can produce degradation faster, especially at lower pH. Still, the single-species biofilm model used here may be too simplistic, as S. mutans is not the only cariogenic and collagenolytic bacterium [43]. Multiple-species biofilms would likely provide us with more clinically representative models. On the other hand, the chemical model is simpler to control and can be applied for longer periods, which would be useful if longer durations of challenge are required. Enzymes such as collagenase or esterase, which degrades Bis-GMA-containing resins, could be added to the chemical model to better mimic the actual oral environment. Using an in vitro model, Kermanshahi et al. [32] reported that dentin-composite specimens with prior incubation in solutions containing esterases exhibited more bacterial microleakage along the dentin-composite interface than the control specimens. Regardless, all models need to be validated. This will be done by testing dental restorations using models with synchronized biochemical and mechanical challenges to see if they can correctly predict the respective modes and rates of failure seen clinically. It is possible that there could be synergistic effects between the mechanical and biochemical challenges, and further calibrations may be required following validation tests using dental restorations, or when other bioreactors, such as the drip flow bioreactor, are used.

5. Conclusion

Accelerated biofilm and chemical models have been developed and calibrated in this study using clinically obtained dentin demineralization data. By selecting an appropriate pH level, the biochemical and mechanical challenges could be synchronized in their rates of action to potentially test resin-composite restorations in an accelerated yet clinically representative manner.

Statement of significance.

Although the properties of resin composites for dental restoration have been improved significantly, early restoration failure still occurs too frequently. As clinical studies take years to complete, accelerated laboratory testing is necessary. Resin-composite restoration fail mainly through fracture and secondary caries, caused by a combination of mechanical and biochemical challenges. In this study, a biofilm and a chemical model for producing artificial caries in bovine dentin are calibrated against in situ data. Using a power law relationship between demineralization depth and challenge duration, scale factors are determined for different pH for each model. The scale factors will allow the synchronization of biochemical and mechanical challenges in testing resin-composite restoration in an accelerated but clinically representative manner.