2.1.

Adhesive/Dentin Interface Specimen Preparation

Specimen preparation was done at the University of Missouri, Kansas City (UMKC), School of Dentistry. Six extracted human molars were collected at the Oral Surgery Clinic at UMKC. Based on a protocol approved by the UMKC adult health sciences institutional review board, the teeth were collected after the patient’s informed consent. The teeth were then stored in separate vials containing 0.9% normal saline and 0.002% sodium azide and stored at $4°\mathrm{C}$ . The specimen preparation has been described in greater detail in some earlier publications.^{11, 12, 21}

First, dentin disks were formed by cutting off the roots at the cementum enamel junction by using a water-cooled low-speed diamond saw obtained from Buehler Limited (Lake Bluff, Illinois). The occlusal one-third of the crown was sectioned perpendicular to the long axis of the tooth. Using 600-grit silicon carbide under water, a uniform smear layer was created on these fractions. The dentin was then etched with 35% phosphoric acid for $15\mathrm{s}$ . Single bond (SB) adhesive was applied to the etched dentin according to the manufacturer’s instructions and polymerized for $30\mathrm{s}$ using a visible light source (Spectrum Light, Dentsply, Milford, Delaware). The “wet bonding” technique was used throughout the bonding procedure.^{6, 22} The specimens were stored for a minimum of $24\mathrm{h}$ in water at $25°\mathrm{C}$ before further sectioning. The treated dentin surfaces were sectioned perpendicular and parallel to the surface using a water-cooled low-speed diamond saw. The final dimension of the slab was $10\mathrm{mm}$ long, $2\mathrm{mm}$ thick, and $1.5\mathrm{mm}$ wide.

2.2.

Data Acquisition

The Jasco NRS 2000 micro-Raman spectrometer (Jasco Incorporated, Easton, (Maryland) used an argon ion laser beam $\left(514.5\mathrm{nm}\right)$ focused through an $60\times$ Olympus Plan Neofluor water-immersion objective [numerical aperture (NA) 1.2] to a $\sim 1.5\text{-}\mathrm{\mu }\mathrm{m}$ beam diameter. Raman back-scattered light was collected through the objective and resolved with a monochromator. The spectra were recorded with a software-controlled charge-coupled device (CCD) array. The CCD array goes from left to right across a row of the specimen and the same way in the next row. Laser power was approximately $3\mathrm{mW}$ . An imaging system and high-resolution monitor were used to visually identify the points at which the Raman spectra are collected. The Raman shift was calibrated using the known peaks of silicon and neon.

The adhesive/dentin specimen was placed at the focus of a $60\times$ water immersion objective and covered with distilled water in preparation for micro-Raman spectroscopic analysis. Spectra were acquired at positions corresponding to $1\text{-}\mathrm{\mu }\mathrm{m}$ intervals across the adhesive/dentin interface using the computer controlled $x\text{-}y\text{-}z$ stage with minimum step width of $50\mathrm{nm}$ . Spectra were obtained at a spectral resolution of $\sim 6{\mathrm{cm}}^{-1}$ over the spectral region of 875 to $1785{\mathrm{cm}}^{-1}$ and with an integration time of $60\mathrm{s}$ .

2.3.

Data Preprocessing

The Raman spectra collected are often contaminated with various interfering signals. The sources of interference include fluorescence and stretching of spectral intensity amplitudes. The amplitude stretching could be due to specimen inclination, variation in specimen thickness, and absolute intensity of light. To eliminate interfering signals and bring the spectra to a common platform of comparison, certain preprocessing operations are performed. Data preprocessing was carried out by use of procedures written in the laboratory, in MatLab (The Mathworks, Natick, (Massachusetts). As in referenced literature,²³ a baseline correction is used to get rid of the fluorescence spectra. A third-degree polynomial baseline fit has been subtracted out of each spectrum for this purpose.

To correct fluctuations in the intensity amplitudes, signal normalization is performed using a standard normal variate (SNV) at every pixel in the specimen. This is a standard preprocessing technique used in earlier literature.²³ The SNV is given as

The disadvantage of the SNV is that if the intensity amplitude fluctuations are due to real concentration differences, these concentration differences will be masked, thus limiting quantitative analysis. This admission does not detract from the results of this study, since chemical and structural classification, not quantification, is attempted. After data normalization, we applied the PCA to extract significant features and then use fuzzy c-means clustering to identify chemically important constitutes. There are multi-variant statistical approaches, which are well suited for hyperspectral data analysis.

2.4.

Principal Component Analysis

PCA is a widely used statistical technique to compress and denoise large datasets.¹³ The principal components represent the best set of axes that can be used to view the data. The data are uncorrelated in the new set of axes as opposed to the old one. This shows an important characteristic of the principal components in that they form a basis for the data. Therefore, it is easy to make out patterns in the data. Further, the principal components of the data are arranged in decreasing order of their contribution to the variance. Hence, we can select those components that contribute the most to the variance. There are several algorithms to perform principal component analysis. The algorithm using the noniterative partial least squares (NIPALS) algorithm has been used in the current study, as it performs only the required number of principal components desired. The NIPALS algorithm gives the scores and principal components (PCs) out of the 2-D dataset $X$ . The NIPALS algorithm is based on the fact that the dataset $X$ can be expressed in terms of linearly independent components.

A random vector $t$ from $X$ is chosen as the initial assumption for the first (most important in terms of contribution to variance) principal component. The corresponding score is calculated based on the principle that it is the projection of $t$ on $X$ , or the vector of covariances of $t$ with the other spectra using Eq. 2.

After obtaining the first principal component $t$ and the corresponding set of scores $p$ , $t{p}^{\prime }$ is now the contribution of principal component 1 to the data and is subtracted from the data.

The 2-D matrix $X$ considered in this study is the matrix consisting of the vector spectra. Therefore the PCs $t$ represent “spectra.” The principal components are not true spectra, since they also contain negative intensities. They are linear combinations of true spectra and as such are not expected to be similar to the pure component spectra.¹³ Since the principal component spectra now form the basis spectra for the data, the scores of these principal components represent the data. Hence, these scores can be used in future calculations in place of the data. The PCs can be scrutinized based on the equivalence to the pure component spectra. If they are equivalent, then the correlated scores can be represented as 2-D images, which usually correlate to chemical images.

To determine whether the principal component obtained is noise or represents minute variation within the spectral data, a simple visual evaluation of the variation among the PCs²⁴ is performed. There should be a distinct difference between the PCs that associate with signal as opposed to those associating with noise. Usually, the number of principal components is much smaller than the number of spectra in the data. In this work, the number of principal components to be used to describe the data was decided by looking at the plots of the first few components.

2.5.

Fuzzy C-Means Clustering

Cluster analysis is an unsupervised statistical method of grouping the data, without a priori knowledge of its nature, purely based on its mathematical attributes. It is a particularly useful technique to characterize hyperspectral data. Moreover, it has been applied quite often in the analysis of medical data.²⁵ There are many types of clustering algorithms available in the literature like k-means, fuzzy c-means, hierarchical, etc. Fuzzy c-means clustering was chosen over k-means because of its capability to assign pixels to different clusters.

The hyperspectral data in our case are the set of scores $p$ taken at each pixel. Initially, the membership function $U$ is initialized as random numbers.

Using the centroids obtained, the new set of membership functions is calculated as

Using this new set of distance values and the centroids calculated from the earlier set of membership functions, the dissimilarity function between the old set of membership functions and the new set of centroids is calculated as

The membership functions $u_{ij}$ here describe the contributions of each centroid score set $c_{iq}$ to a particular pixel $j$ . Each centroid score set can be converted into the corresponding centroid spectrum using Eq. 10.

Fig. 1

The color graph ranging from 0 to 255. (Color online only.)

3.1.

Univariate Analysis

Univariate analysis results are presented first so that they can be compared and contrasted with the multivariate analysis. There are three major components in this specimen: adhesive, dentin, and the adhesive/dentin interface. The representative spectra of these three components are extracted from the specimen and shown in Fig. 2 . The SB adhesive is a bonding agent containing both hydrophilic hydroxylethyl methacrylate (HEMA) and hydrophobic bisphenol A diglycidyl methacrylate (BisGMA) components.¹¹ The intense peaks related to the SB adhesive occur at $1720{\mathrm{cm}}^{-1}$ (carbonyl), $1609{\mathrm{cm}}^{-1}$ (phenyl $\mathrm{C}\mathrm{C}$ ), $1453{\mathrm{cm}}^{-1}$ ( ${\mathrm{CH}}_2$ def), and $1113{\mathrm{cm}}^{-1}$ $\left(\mathrm{C}\text{-}\mathrm{O}\text{-}\mathrm{C}\right)$ . These peaks are related to methacrylate monomers in the bonding agent. Particularly, the peaks at 1609 and $1113{\mathrm{cm}}^{-1}$ are related to the BisGMA monomer. In the dentin spectrum, the peaks related to collagen occur at $1667{\mathrm{cm}}^{-1}$ (amide 1), and $1245{\mathrm{cm}}^{-1}$ (amide 3); the peak related to mineral occurs at $961{\mathrm{cm}}^{-1}$ (P-O). The spectrum of the interface shows the contribution from the adhesive and dentin [Fig. 2c], indicating adhesive has penetrated into the partially demineralized dentin layer.

Fig. 2

Three fundamental spectra present in the specimen, that of the (a) interface, (b) dentin, and (c) adhesive, in that order.

The simplest approach of micro-Raman spectral data analysis is the display of specific functional group intensities related to the chemical components of the specimen as a function of position. The univariate intensity maps of the Raman shift values of 961, 1113, 1453, and $1667{\mathrm{cm}}^{-1}$ , respectively, are shown in Fig. 3 (the related light image of the adhesive/dentin interface can be seen in Ref. 11). The intensities at these positions are used to display the distributions of the phosphate mineral, BisGMA monomer, SB adhesive (both BisGMA and HEMA), and collagen as a function of position across the adhesive/dentin interface. Black represents the lowest intensity, while red represents the highest. By comparing the spectra shown in Fig. 2, it can be seen that the peaks at 961 and $1113{\mathrm{cm}}^{-1}$ do not overlap with other peaks, and that they can be considered to be “unique” peaks for chemical mapping of mineral phosphate and BisGMA. The univariate images based on these two parameters provide reliable information on the spatial distribution of the mineral and BisGMA monomer. However, it is noted that the ${\mathrm{CH}}_2$ peak $\left(1453{\mathrm{cm}}^{-1}\right)$ of the adhesive overlaps with the ${\mathrm{CH}}_2$ peak of the collagen. Hence, the univariate image does not give an accurate picture of the description of either adhesive or collagen without spectral subtraction. By the same reasoning, it is observed that Fig. 3b shows high intensity of ${\mathrm{CH}}_2$ in the interface region due to the summing up of the peaks of adhesive as well as collagen. Also, the amide 1 region more or less overlaps the carbonyl and $\mathrm{C}\mathrm{C}$ region of the adhesive. Therefore, these images too cannot be used directly for composition interpretation. In summary, the univariate imaging approach does not always precisely identify functional group distribution due to interference from neighboring peaks.

Fig. 3

The pseudo color representations of the distributions of (a) phosphate mineral, (b) adhesive, (c) BisGMA monomer, and (d) amide 1 in the specimen. (Color online only.)

3.2.

Principal Component Analysis

To evaluate the number of components that can be detected in the mapped spectra data, PCA was applied. The first six principal components from the PCA on the Raman data $X$ are shown in Fig. 4 . It is shown that the first three or four components are the ones that contribute to the part of the spectrum comprising the dentin and/or adhesive. The other principal components could either represent minor changes in the chemical structure or could indicate cosmic or other noise. Since it is difficult to ascertain whether a component represents noise or chemical structure change, different numbers of components are tested for results. An important point to be noted is that principal components can sometimes have negative values for their intensities. It is observed that they sometimes are combinations of positive and negative spectra. Hence, the components have to be considered with both the positive and negative signs. As described previously, the scores of these principal components can be used as the basis for the Raman data rather than the intensities at different Raman shift values.

Fig. 4

Principal components of Raman spectral data in decreasing order of their contribution to the variance.

The score of the first principal component shown in Fig. 5a represents the partially demineralized dentin in the specimen. The partially demineralized dentin is visible in the region from about 10 to $15\mathrm{\mu }\mathrm{m}$ in the $x$ direction. The regions from about 5 to $10\mathrm{\mu }\mathrm{m}$ in the $x$ direction represent the demineralization of dentin in the specimen resulting from acid etching. The region beyond $15\mathrm{\mu }\mathrm{m}$ represents dentin that is still in the mineralized form. Earlier work⁷ used the ratio of $961∕1454{\mathrm{cm}}^{-1}$ to arrive at the distribution of demineralization. However, the subtraction process necessitates the subtraction of the ${\mathrm{CH}}_2$ from the adhesive before taking the ratio. Also, principal component analysis shows us that there are two components, namely, partially demineralized dentin and mineralized dentin. This separation of components is difficult to obtain by univariate methods.

Fig. 5

The scores of the six principal components used in describing the specimen.

Figure 5b represents the score of the second principal component, which shows the complementary relationship between the adhesive and the mineral distribution. It represents adhesive in a negative sense and mineral in a positive one. The mineral distribution is seen to correspond closely with that obtained from the univariate imaging shown in Fig. 3a. We note that the adhesive infiltrates those regions of the interface that are void of mineral. Looking at score 2 in a negative sense helps us to note the decrease in concentration of the adhesive as it penetrates into the demineralized dentin. This result is consistent with that obtained using univariate peak ratio methods.^{11, 21} It is noted that the adhesive distribution as determined by the earlier methods required the subtraction of the ${\mathrm{CH}}_2$ peak of the collagen from the ${\mathrm{CH}}_2$ peak of the adhesive.^{11, 21}

As shown in Fig. 5c, score 3 describes the distribution of the collagen in the interface region. This distribution is difficult to obtain by univariate methods, because the amide 1 and 3 peaks of collagen overlap the vibrational peaks of the adhesive.²⁶ The thickness of the demineralized layer as well the extent of penetration of the adhesive is critical to the effectiveness of the bond between the dentin and adhesive. These characteristics, i.e., depth of dentin demineralization and adhesive infiltration, are directly obtained, noise free from the principal component analysis results, as they are independent spectral results. It is thus seen that principal component scores extract the spectral information in independent sets in decreasing order of their importance. The latter components are perceived to be either the minor changes in the chemical structure or noise, and their scores are therefore not considered here in extracting information. Other methods such as clustering will be considered for further detailed analysis.

The spectral components detected from the PC analysis are not spectra of pure components but rather linear combinations of pure spectra. The scores of the PCA represent the distribution of linearly independent components that are either complementary or supplementary linear combinations of pure components. Hence, rather than the set of Raman shift values, the principal components can be used as the set of basis vectors to represent the hyperspectral dataset. Correspondingly, the scores of these principal components are their contributions at every pixel and can be used in place of intensity values in fuzzy c-means clustering analysis.

3.3.

Fuzzy C-Means Clustering

Cluster analysis separates the group of spectra into clusters with clear similarities within each cluster and distinctions between the clusters. Figure 6a shows the first image where the data has been split into three clusters. The regions are identified by observation of the cluster centroid spectra shown in the same figure. This is a low level of resolving the data, where it can be seen that the specimen is divided into three major components: the adhesive, the interface, and the dentin. Different regions have different spectra clusters. The demineralized collagen matrix region is obtained directly without having to subtract out the ${\mathrm{CH}}_2$ peak of the adhesive. From the comparison of the interface spectrum with the adhesive spectrum [shown in Fig. 6a], the BisGMA monomer concentration is readily observed to be lesser in the interface region as compared to the other SB adhesive components (mostly HEMA) concentration.

Fig. 6

The clustered images show the division of the specimen into chemically distinct regions.

To observe further detail in the specimen, the number of clusters is increased successively and the details are shown in Fig. 6b. In addition to the details observed in three clusters, a separate region where there is more mineral concentration and correspondingly, a lesser concentration of adhesive penetration, can be seen. This can be observed from the comparison of the spectra of the two new clusters obtained [Fig. 6b]. The new cluster region can be correlated with score 1 in Fig. 5a, where the region with higher mineral concentration corresponds closely with the cluster that has a lesser concentration of the adhesive. Also, it is observed that adhesive penetration is not consistent with dentin demineralization. Comparison of Fig. 6c to the partially demineralized zone observed in score 2 [Fig. 5b] shows that the partially demineralized zone to the right of the interface beyond $12\mathrm{\mu }\mathrm{m}$ shows almost no adhesive infiltration.

From Fig. 6c, in addition to the earlier clusters formed, the adhesive can be seen to be split into two regions in which the lower region has a slightly lesser concentration. The centroid of the new cluster is observed to have a slightly lower BisGMA content compared to the entire adhesive cluster. Using the clustering method, the chemically and structurally altered regions in the adhesive layer are clearly seen. The alterations are almost impossible to see using univariate methods. This information is very important for understanding the quality and durability of the adhesive/dentin interface.

From Fig. 6d, in addition to the information obtained from five clusters, we can now see still greater detail in the interface region. The new cluster formed indicates the penetration of the adhesive through the interface. This cluster is observed to be particularly rich in BisGMA monomer, compared to the hybrid layer. The BisGMA monomer has therefore not penetrated very well into the interface, but has spread around it. These results match the univariate image shown in Fig. 3c. These results agree well with the previous results.¹¹ The new cluster centroid also indicates the presence of layers with lesser concentration of adhesive that has penetrated through the demineralized dentin matrix.

Further clustering results in the formation of duplicate clusters, and inclusion of more principal components is not found to produce significant changes in the clusters. Hence, the number of clusters as well as factors is fixed at six. A minimum number of clusters divide the specimen into regions of different chemical makeup, while further clusters tend to reveal differences in the concentrations of the chemical constituents present within basic clusters.

In this study, both univariate and multivariate methods were used to extract information from 2-D Raman imaging data. Univariate methods bring out the distribution of functional groups that are taken to represent particular constituents in the specimen. For example, to study mineral distribution, adhesive resins, BisGMA monomer, and collagen, $961{\mathrm{cm}}^{-1}$ (P-O), $1453{\mathrm{cm}}^{-1}$ $\left({\mathrm{CH}}_2\right)$ , $1113{\mathrm{cm}}^{-1}$ $\left(\mathrm{C}\text{-}\mathrm{O}\text{-}\mathrm{C}\right)$ , and $1667{\mathrm{cm}}^{-1}$ (amide) are used, respectively. However, the peaks represented by these groups sometimes overlap and are sometimes inadequate to separate out chemically different regions. Apart from this, it is difficult to separate out regions at successively greater resolutions. For example, it becomes difficult to separate out the zone of partially demineralized dentin from fully demineralized dentin.

These results can be obtained without such a-priori knowledge and spectral manipulation by using multivariate methods, namely, PCA and fuzzy c-means clustering as demonstrated in this work. From the score images of the principal components, the distributions of partially demineralized dentin, adhesive, and mineral distribution, as well as collagen fiber arrangement, were observed. The fuzzy c-means clustered images of the specimen indicated results like the unequal distribution of the two monomers—HEMA and BisGMA—and the mismatch between the extent of demineralization and adhesive penetration. While five clusters showed the penetration of the adhesive into the collagen fiber network, six clusters further split the specimen into regions that show the difference in monomer concentrations and penetration over the specimen. Since the wet bonding technique was used, relative hydrophobic BisGMA could not penetrate as well as hydrophilic HEMA, as observed from the relevant cluster centroids in all the cluster sets. Similar results were observed using univariate methods. However, while using pseudo color representation of fuzzy clustered scores as demonstrated in this work, all the zones can be observed on the same image, rendering the interpretation easy. Also, separation of chemical spectra distinct to each chemical is inherent in the algorithm, and digital subtraction of spectra is not required.