2.1.

Experimental Setup

Figure 1 shows the schematic diagram of the experimental setup for combined PTR and LUM monitoring. A semiconductor laser diode with wavelength 660 nm and maximum power 130 mW was used as a radiation source (Opnext, HL6545 MG). A laser diode controller (Thorlabs, LDC202B) triggered by a software lock-in amplifier (National Instruments, NI6221) modulated the laser current. The modulated laser beam was focused on the surface of a tooth sample with the aid of lenses (Thorlabs, LMR1) as indicated in Fig. 1. The modulated PTR response of the tooth sample was focused by two off-axis paraboloidal mirrors and was collected by the HgCdZnTe [mercury cadmium telluride (MCT)] detector (VIGO, PVI-2TE-5) as indicated with arrows in Fig. 1. The HgCdZnTe detector was optimized for the maximum performance at the optimal wavelength of 5 μm. This is in the mid-infrared spectral range. The LUM response was focused onto a photodetector (Thorlabs, PDA36A). A cut-on optical colored filter (cut-on wavelength 715 nm, Edmund Optics) was placed in front of the photodetector to block unwanted laser light reflected or back-scattered by the tooth. Collected PTR-LUM signals were digitized and stored using a software lock-in amplifier (National Instruments, NI6221) and Labview software.

Fig. 1

Schematic diagram of the experimental setup for combined PTR and LUM: a solid arrow indicates the direction of the incident laser light focused on to the sample tooth, a coarse dashed arrow indicates the direction of the LUM signal collected with the photodetector; and fine dashed arrows indicate the direction of the PTR signal collected with the MCT detector.

2.2.

Sample Preparation

2.2.1.

Materials adjacent to a vertically sectioned tooth sample

An extracted human tooth was vertically sectioned in half using a diamond-tipped cutter. One of the two half teeth was mounted on a Lego block with the aid of plastic epoxy. Using the heavily filled large particle composite restoration material Heliomolar (IvoclarVivadent) shade A3, a small structure of a composite restoration was built on a separate Lego block against the sectioned vertical wall of the half-tooth sample as shown in Fig. 2. The composite restoration material was packed and light-cured every 2 mm of thickness according to the manufacturer’s instructions. The prepared sample was stored in a humid container to prevent it from dehydration that can cause structural damage. Structures with glass and mirror were also prepared to test the effects of transmitted and reflected laser radiation through the vertical surface on the PTR and LUM signals.

Fig. 2

A vertically sectioned half-tooth sample mounted on a Lego block with a composite restoration block built on a Lego block against the vertically sectioned wall of the tooth sample. PTR-LUM scans commenced near the interfacial edge indicated as a dot and moved up to 2 mm away from the edge in the direction of an arrow.

2.3.

PTR-LUM Scanning Procedures

There were two types of PTR-LUM scans conducted throughout the study: a frequency scan and a line scan. The frequency scan was performed at a fixed position on the tooth surface to examine the frequency dependence of PTR and LUM signals from 2 to 200 Hz. Measurements were made at one frequency starting from 2 Hz, and the frequency was automatically increased using Labview software. Four frequency values were used for most of the experiments throughout the study: 2, 6, 15, and 200 Hz. Four frequencies were used to save the measurement time and thereby prevent the tooth samples from over-dehydration. A preliminary pilot study showed that four frequencies are sufficient to define the frequency dependence of the signal. There was at least a 15-s delay between measurements at each frequency in order to allow the signals to stabilize upon frequency change. Changing the frequency allowed one to examine various depths beneath the tooth surface.^17–19

Line scans were performed to measure PTR and LUM signals along a spatial coordinate on the tooth surface at a fixed frequency and they were conducted along a line on the tooth sample starting from the sectioned edge and moving away from the tooth-restoration interface. The micrometer stage where the tooth sample was placed was adjusted to move to the next measurement position. After each change of measurement position, there was a 15-s delay time for signal stabilization.

2.3.2.

Development of artificial wall lesions—Case 1: demineralization of the entire sectioned tooth wall

Both enamel and dentin were affected when demineralizing the entire sectioned surface of the tooth (Fig. 3). Measurement locations were carefully chosen in each sample, since the thickness of enamel varies from enamel to root. Moreover, the thickness of enamel varied between samples. In each case, the measurement line was chosen such that the thickness of the enamel layer was approximately 1 mm. Before a scan, each sample was taken out of the humid container, rinsed thoroughly with running tap water for more than 20 s, and excessive water was removed. Then the sample was placed on a three-axis micrometer sample stage, and the laser was focused onto the sample tooth by adjusting the three-axis micrometer stage. Scanning was done for only 1 h ($\sim 20\min$ for warm up and $\sim 40\min$ for scanning) to avoid dehydration of the tooth sample.²⁰ Line and frequency scans were conducted at several stages of demineralization: before demineralization and after 1, 2, 3, 5, 7, 10, and 14 days demineralization. The composite restoration was not in place during these scans.

Fig. 3

Vertical tooth wall showing enamel and dentin layer—PTR-LUM scans were conducted on the scanning (side) surface of the tooth where the enamel layer is approximately 1 mm thick. For frequency scans, the laser beam (excitation/probe) was focused at the interfacial edge on the tooth sample, indicated with a dot; and for line scan, the laser beam (excitation/probe) was moved along the line in the direction of the solid arrow shown in the figure.

After the last PTR-LUM measurement, following a total of 14 days of demineralization, tooth sections were cut from the zone of the line scan. The sections were microradiographed and analyzed to determine the degree of demineralization for each sample by measuring the mineral loss and lesion depth. Mineral loss and lesion depth values were determined by averaging several scans over the distance of the thin section taken from the center of the demineralized area where PTR-LUM measurements were made. The mineral loss (in vol% μm) was obtained by calculating the difference in volume percent of matter between sound and demineralized tissue integrated over the lesion depth. The mineral content plateau in deeper regions of the enamel section, representative of sound tissue, was pre-set at the 87 vol% level.²¹ The lesion depth was determined as the distance from the measured sound enamel surface to the location in the lesion where mineral content was 95% of the sound enamel mineral volume. Statistical analysis was conducted using IBM SPSS Statistics 19 software with significance level ($\alpha$) pre-chosen at 0.05. Correlation between PTR-LUM signals and TMR results was determined using Pearson’s coefficient of correlation.

3.1.

Materials Adjacent to a Vertically Sectioned Tooth Sample

Figure 4 shows results of line scans with the composite resin block, the glass, and the mirror in contact with the sectioned tooth surface. There is a signal strength dependence on the type of material placed against the vertical tooth wall for both PTR and LUM. This is consistent with the effect of vertical surface reflectivity and transmissivity on the overall measured PTR (amplitude and phase) and LUM (amplitude) signals. LUM phases are not shown as they carry no information when they are dominated by scattered light. This was shown to be the case from satellite experiments involving the scattered light from a rough metallic surface. Even under these circumstances, the LUM amplitudes in this study were very useful as they were found to be sensitive to the effects of the changing vertical wall boundary structure on the forward- (exiting) and backward-scattered light from interface materials into the body of the tooth. The shape of the PTR curves is indicative of the dominance of thermal-wave confinement within the gap, as well as between the laser beam incidence location and the vertical wall. The highest LUM signal occurred with the mirror in place (highest reflectivity) and the lowest with no material beside the tooth (zero reflectivity). Figure 4 indicates PTR and LUM sensitivity levels which support signal sensitivity to vertical wall demineralization or breakdown along the margins of the restoration.

Fig. 4

PTR-LUM line scan results collected on the side surface of the tooth with materials of different optical properties placed adjacent to the vertical wall of the half-tooth sample. Zero position on $x$-axis represents the interfacial edge of the tooth. There was no lesion on the vertical wall.

Figure 5 shows the PTR and LUM signals obtained at the interfacial edge on the side surface of the sectioned tooth (no demineralization lesion) at a fixed frequency while gradually increasing the gap size. The purpose of these measurements was to assess the effect of gap size on the PTR and LUM signals due to optical and thermal-wave confinement. PTR signals were obtained at 2 Hz and LUM signals at 20 Hz so as to optimize signal-to-noise ratio (SNR) for each channel. Measurements were taken at 100-μm increments of gap size from 0 to 1000 μm and at 500-μm increments from 1000 to 5000 μm. PTR plots show that after $\sim 100\mu \mathrm{m}$ only small changes due to thermal-wave confinement effects appear, and they indicate that gaps larger than 100 to 200 µm behave as semi-infinite. Clinically acceptable gap sizes are in the range of 119 to 160 µm.^22,23 Therefore, our PTR and LUM measurements are expected to be sensitive to the gap size in clinical practice. The PTR phase shows sensitivity within error to the presence of restorations up to $\sim 500\text{-}\mu \mathrm{m}$ gap size. However, LUM amplitude plots show that further increases in gap size clearly affect the signals up to the relatively large gap size of 4000 μm. These PTR observations are consistent with the size of the thermal diffusion length, ${\mu }_{\mathrm{th}}$, in air. Using the equation

Fig. 5

PTR-LUM signals collected at the interfacial edge on the side surface of the tooth with different gap sizes between the tooth and the composite restoration: PTR signals were obtained at 2 Hz; LUM signals were obtained at 20 Hz.

3.2.

Development of Artificial Wall Lesions—Case 1: Demineralization of the Entire Sectioned Tooth Wall

Figure 6 shows the line scan results obtained after each period of demineralization on entire vertical sectioned wall with one representative tooth sample. The PTR amplitude plots show a decrease upon demineralization, although the trend is not monotonic. LUM signals also decrease with demineralization. The non-monotonic temporal behavior of the PTR signal line scans is very interesting as it is consistent with other PTR observations in our laboratory involving demineralization of intact (whole) dental enamel surfaces using the same gel. It appears that the state of demineralization of the vertical wall follows similar trends as intact outer dental enamel surfaces and the PTR signal is controlled by wall demineralization processes, as expected. In PTR amplitude plots in Fig. 6 note the thermal-wave interference pattern between laser beam position and vertical wall for distances $<250\mu \mathrm{m}$ in the untreated and treated sample. Before demineralization, the PTR amplitudes at locations adjacent to the vertical wall edge rapidly increased as expected from a thermal standing wave formed due to coherent thermal-wave accumulation at the wall interfering (i.e., superposed) with the forward diffusing wave; however, this phenomenon started to disappear with more days of demineralization as the sharp vertical enamel—air interface gave way to a less structured demineralized layer which scrambled a portion of the superposition between forward diffusing and interface-accumulated thermal waves.

Fig. 6

PTR-LUM line scan results obtained after each period of demineralization of the entire sectioned tooth wall.

Frequency scans were conducted with the same samples after each demineralization period at two measurement locations on the side (buccal) surface of the tooth: at the edge and 2 mm away from the edge. Figure 7 shows PTR amplitude, PTR phase, and LUM amplitude. PTR amplitudes decrease and PTR phases increase with more days of demineralization. It is important to note that the effect of vertical surface demineralization on the PTR signal can be measured up to 2 mm away from the interface in both amplitudes and phases and up to 15 Hz or more. These distances are too large compared to the relevant thermal diffusion length (a few hundred micrometers). This is consistent with strongly back-scattered light following interaction with the vertical wall which changes the optical field distribution in the bulk of the tooth, thereby contributing to the generation of a photothermal field component at locations away from the interface. At $f>15\mathrm{Hz}$, the PTR amplitudes become less sensitive to the condition of the vertical wall, as expected from the $f^{1/2}$ dependence of the thermal diffusion length, Eq. (1). However, the phases remarkably retain their sensitivity to the wall condition even for $f$ $\sim 200\mathrm{Hz}$. On the other hand, LUM signal amplitudes are less sensitive to demineralization especially close to the edge.

Fig. 7

Frequency scan PTR amplitude, PTR phase, and LUM amplitude obtained after each period of demineralization of the entire sectioned tooth wall, collected at different measurement locations on the side surface of the tooth: at the edge and 2 mm away from the edge.

TMR analysis was performed on each sample to determine the amount of mineral loss and lesion depth after 14 days of demineralization. PTR-LUM signals at two stages of demineralization were used to define one set of independent variables for the calculation of the correlation coefficients: before demineralization and after a total of 14 days of demineralization. For PTR and LUM amplitudes, “14 days demineralization data” were divided by the “before demineralization data” and expressed as percentage signal amplitude change for each sample. For PTR phase, “14 days of demineralization data” were subtracted from the “before demineralization data” to calculate phase shift for each sample. These values were correlated to the values of the mineral loss and lesion depth. There were statistically significant correlations between the PTR amplitude and the mineral loss ($r=0.941$; $p<0.05$), and the LUM amplitude and the lesion depth ($r=-0.998$; $p<0.001$). There was no significant correlation between neither mineral loss and PTR phase/LUM amplitude nor lesion depth and PTR amplitude/phase. A reason could be that the samples experienced a relatively low degree of demineralization. Previous studies conducted in our laboratory used tooth samples demineralized with the same demineralization gel.¹⁹ Their typical mineral loss was more than 1000 vol% µm, and lesion depth was deeper than $\sim 60\mu \mathrm{m}$. The mineral loss and lesion depth values of the samples used for this study were $255\pm 41.53$ vol% µm and $13.6\pm 3.01\mu \mathrm{m}$, respectively, which indicates that the samples used for this study experienced a much lower degree of demineralization. It was expected to have a lower degree of demineralization in this study because a small quantity of the demineralization gel was used over a larger area, so the gel gets saturated within a short time by the elements diffusing out of the tooth tissue, and this retards the demineralization process. A higher degree of sample demineralization could have resulted in more drastic changes of PTR-LUM signals and in more statistically significant correlation coefficient values.

3.3.

Development of Artificial Wall Lesions—Case 2: Localized Demineralization and Remineralization

Figure 8 shows the vertical wall of one representative sample after 1 day of localized demineralization. It is clearly shown that a white spot was created at the top right corner of the vertical wall (indicated with an arrow in the figure) even after 1 day of demineralization, which indicates that demineralization actually occurred and made a physical change to the sample. Figure 9 shows PTR-LUM amplitude and phase signals at several measurement locations (at the edge and at 100 μm, 200 μm, and 2 mm away from the edge) upon progressive demineralization and subsequent remineralization. This figure shows that PTR amplitude decreases upon demineralization. Following remineralization there appears a delayed upward PTR amplitude trend accompanied by a slight downward LUM amplitude trend. The PTR phase exhibits slight increases. It is likely that these trends are due to the changing interface structure at the exposed spot which controls a fraction of the amount of back-reflected and back-scattered light into the tooth bulk. It is clearly seen that even after 1 day of demineralization, the PTR amplitude decreased well beyond the error bar. The timing of signal change is consistent with the fact that a white spot was created even after 1 day of demineralization as shown in Fig. 8. The PTR phase also changed beyond the error bar only after approximately 2 days of demineralization, but the amount of change with respect to the error bar was less than the PTR amplitude. The LUM amplitude changed beyond the error bar after 3 days of demineralization; however, the amount of PTR amplitude change after each demineralization was much larger than that of the LUM amplitude. These results indicate that PTR is more sensitive to demineralization than LUM. Signal changes due to remineralization of all channels were generally moderate compared to demineralization, presumably due to the slower remineralization rate. The PTR amplitude was sensitive only after 1 week of remineralization. PTR phase changed beyond the error bar after 3 weeks of remineralization. LUM amplitude changed beyond the error bar after 2 weeks of remineralization.

Fig. 8

Vertical wall of one representative sample after 1 day of demineralization on a localized spot. A white spot was created at the top right corner indicated with an arrow.

Fig. 9

PTR-LUM scans at fixed positions after each period of demineralization and remineralization of the localized spot. Demineralization occurred from day 1 to 14; remineralization occurred from day 15 to day 56.

Figures 10 and 11 show line- and frequency-scan results of the same sample, respectively. PTR amplitude signals exhibit a slightly decreasing trend in the first 14 days of progressive demineralization and a reversal, a slightly increasing trend, upon the onset of the subsequent remineralization. Also, the PTR phase keeps increasing during both demineralization and remineralization. LUM amplitude signals exhibit a decreasing pattern at excitation/probe distances larger than 200 μm away from the edge for both demineralization and remineralization; however, in locations close to the edge (up to $\sim 200\mu \mathrm{m}$), the figures show that LUM signals slightly decrease upon demineralization and slightly increase during the subsequent remineralization. This is consistent with the trends of Fig. 9 and implies that probing closer to the vertical surface which undergoes localized demineralization and remineralization enhances LUM and PTR sensitivity to these processes. However, PTR sensitivity to local conditions on the upper (scanned outer enamel) surface may control the relative signals at the scanned locations. All PTR frequency scans of Fig. 11 converge above 100 Hz, i.e., they become less sensitive or outright insensitive to the condition of the vertical wall, as expected when the decreasing thermal diffusion length [computed as 37.6 μm at 100 Hz using Eq. (1) and thermal diffusivity of enamel ${\alpha }_E=4.445\times {10}^{-7}{\mathrm{m}}^2/\mathrm{s}$ (Refs. 24 and 25)] does not reach the vertical wall (thermally thick condition) to undergo wall-condition-dependent confinement for each probe location indicated in the figures.

Fig. 10

Line scan data obtained after each period of demineralization and remineralization of the localized spot. PTR signals were obtained at 2 Hz and LUM signals were obtained at 200 Hz.

Fig. 11

Frequency scan PTR amplitude, PTR phase, and LUM amplitude data obtained after each period of demineralization and remineralization of the localized spot. Measurements were taken at different locations on the side surface of tooth: at the edge and 2 mm away from the edge.

Furthermore, there were no expected significant contribution changes to the PTR signal from vertical wall back-scattering during localized demineralization, as the large majority of wall sites remained unaltered. This is unlike the full-wall demineralization process which was seen to affect the PTR signal as far away as 2 mm from the wall (Fig. 6).