**3. Results**

We considered the characteristic average normalized Raman spectra of surface formations on teeth with this disease (Figure 2). This is often the reason for this disease.

**Figure 2.** The average Raman spectra, normalized to the average intensity of the studied samples. d—above-gum dental calculus and e—under-gum dental calculus.

Figure 2 shows that the Raman spectra of the under-gum and above-gum calculi have certain spectral features that are apparently related to different periods of disease formation. In the initial stage of dental calculus formation, the above-gum calcareous deposits are composed primarily of organic components, as can be seen from the more intense lines in the ranges of 1550–1565 cm<sup>−</sup><sup>1</sup> (Amide II) and 1600–1665 cm<sup>−</sup><sup>1</sup> (Amide I) and the less intense line at 956 cm<sup>−</sup><sup>1</sup> (PO4<sup>3</sup>− (ν1), hydroxyapatite), compared with the under-gum calculus spectrum. At the same time, the under-gum calculus spectrum is characterized by the explicit intensity of the lines of mineral components (PO4<sup>3</sup>− (ν1), hydroxyapatite).

Figures 3 and 4 show the averaged spectra of the tissues of teeth with periodontitis and healthy teeth from the in vitro study (Figure 3) and the in vivo study (Figure 4).

**Figure 3.** The average Raman spectra, normalized to the average intensity, for two groups of samples studied in vitro: a—enamel, b—denti and c—cementum. I = healthy, while II = diagnosed with periodontitis.

**Figure 4.** The average Raman spectra, normalized to the average intensity, of two in vivo studied groups of teeth of the volunteer: Ia—healthy enamel and IIa—enamel of the teeth with periodontitis.

The analysis of the healthy tooth tissues and the tissues of teeth with periodontitis showed that the main spectral features of tissues of teeth with periodontitis are changes in the intensity of organic compound lines at 852, 873 cm<sup>−</sup><sup>1</sup> (C–C stretching, proline, and hydroxyproline (collagen assignment)) [20], 1664 (Amide I), 1242 (Amide III) [21], and 1446 cm<sup>−</sup><sup>1</sup> (lipids and proteins) [22], as well as changes in the intensity of the lines of mineral compounds of the teeth at 956 cm<sup>−</sup><sup>1</sup> (P–O symmetrical valence fluctuation PO4<sup>3</sup>− (ν1)) [23].

The comparative analysis shown in Figures 2–4 highlights many spectral changes in all tissues of teeth with periodontitis. These changes mainly occur in the same Raman lines as those related to calculus.

These spectral features are likely to be related to biochemical processes that take place during the formation of surface deposits during periodontitis (e.g., dental calculus and plaques), which affect all tooth tissues. The etiology of calculus formation is related to the mechanism of mineralization of the tooth surface deposits that consist of hydrocarbons and proteins (30% of each), as well as about 15% of lipids. The other components are extracellular bacterial products (plaques), remnants of their cytoplasm, and cell membranes (extracellular polysaccharides) [17].

To make the received Raman spectra more informative, a nonlinear regressive analysis of the Raman spectra was conducted, including an investigation of their spectral line decomposition. Figure 5 shows the results of decomposition of the spectral contours on the sum of distribution of the Gaussian lines. The Gaussian test function is described by the formula in [24].

The composition of the spectral lines was determined by literature analysis and multi-iteration modeling of 392 Raman spectra using MagicPlotPro 2.5.1 software. When modeling the spectral contours at the lines used as a template, the position x0 and the width of the line (HWHM—half width at half) *dx* were fixed. Only the intensity of the line was selected when modeling. This allowed us to achieve highly stable results when modeling the contours. The amplitude of the lines *a*, which depended on the values of the independent regressors *dx* and *x0*, as defined in the initial terms of the analysis, was used as a criterion variable.

**Figure 5.** Spectral contour distribution of the enamel samples. The blue line is the original spectrum.

The average value of the coefficient of determination for the initial result spectrum in the range of 780–1780 cm<sup>−</sup><sup>1</sup> was R<sup>2</sup> = 0.998, the relative spectral line intensity assessment error *a* was less than 8%, the average standard deviation of the coordinate of a line *x0* was 1.4 cm<sup>−</sup>1, and the average standard deviation of the width of the Gaussian line (HWHM) *dx* was 2.3 cm<sup>−</sup>1.

For the relative quantitative analysis of the component composition, the relative coefficient *k* was introduced, where the Raman line of amide *I* ~1664 cm<sup>−</sup><sup>1</sup> was used as a denominator:

$$k\_i = \frac{I\_i}{I\_{1664}},\tag{1}$$

where *Ii* represents the values of intensity of the spectral lines of the analyzed components.

The analysis of the received data was done with IBM SPSS Statistics software through linear discriminant analysis (LDA).

The analysis of the relationships among groups with a pathology or relation to a certain tooth tissue is shown in Figure 6. It can be seen that most of the dispersion between the studied groups of samples can be described by the LD-1 function (58.5%). The common sampling size was 392 Raman spectra. The discriminant function LD-2 was able to describe 29.1% of the dispersion. This function has the physical meaning of the relationship of tooth tissue to the healthy group or to the group with periodontitis.

Positive values of LD-1 were found to mainly characterize the Raman spectra received from the enamel samples, and vice versa; the negative values characterized the samples of cementum, dentine, and dental calculus. The areas of the groups showed intersections, which influenced the rate of correctly classified subjects. The LD-1 function has the physical meaning of the difference between spectral compositions of tooth tissues. Positive values of LD-2 characterized the Raman spectra of the tooth tissue with periodontitis, and the negative values characterized the Raman spectra of healthy tooth tissue.

**Figure 6.** Chart of values showing the linear discriminant functions of the tooth tissue samples. a—enamel, b—dentin, and c—cementum. I = healthy tissue, II = tissue diagnosed with periodontitis.

Figures 6 and 7 show that the difference between healthy tissues and tissues with periodontitis can be described by the LD-2 function. It can be noted that the spectral composition of dental calculus showed similar changes to the spectra of dentin and cementum, which confirms the earlier hypothesis that calculus influences the internal structures of tooth tissue.

**Figure 7.** The values of factor structure coefficients for the tooth tissue samples.

High relative intensity values were observed for the lines ~1446 (CH2 scissoring and CH3 bending fluctuations of lipids and proteins), ~852 (C–C stretching benzene ring of proline), and ~873 cm<sup>−</sup><sup>1</sup> (C–C stretching benzene ring of hydroxyproline), with the rest of the lines having low spectral lines. These values characterize the tooth tissues—dentin, cementum with periodontitis, as well as calculus—compared with enamel, which indicates the di fferences in the organic–mineral compositions of these tissues.

Study of the changes in the enamel of teeth with periodontitis was further carried out. Figures 8 and 9 show a comparison of the LDA results of the enamel of healthy teeth and teeth with periodontitis. Sixty-seven spectra of the enamel of teeth with periodontitis and 43 Raman spectra of the enamel of healthy teeth were analyzed. The discriminant function LD-1 was able to describe 100% of the dispersion. Positive LD-1 values characterized the Raman spectra of the healthy enamel samples (the average LD-1 value of the group was 1.95, and the standard deviation was 0.912), and vice versa; negative values characterized the Raman spectra of the group of pathologic enamel samples (the average LD-1 value of the group was −1.25, and the standard deviation was 1.052). The areas of the groups had a minor intersection in the range of LD-1 = (−0.25; 2.25).

**Figure 8.** Chart of the linear discriminant function values of the enamel samples. The red line is the enamel of teeth with periodontitis (damaged enamel), and the blue line is the enamel of healthy teeth.

**Figure 9.** The values of factor structure coe fficients for the enamel samples. Negative values are highlighted in red and positive values are highlighted in blue.

Figure 9 shows the coe fficients of the factor structure matrix, with a correlation between the variables in the model and the discriminant function. In the analysis, these correlation coe fficients were considered to be the factor loadings of the variables for each discriminant function.

The higher the absolute value of LD-1 for the variable is, the more strongly it determined the di fference between the groups of samples in the received model of discriminant analysis. For example, the values of the introduced coe fficients k873, k956, k1000, k1039, k1044, k1067, and k1091 were higher in the group of enamel samples with periodontitis, which indicates an increase in the relative intensity of the corresponding lines in tissue with periodontitis.

The increase in the relative intensity of the lines for hydroxyapatite 956 (P–O symmetrical valence fluctuation PO4 3− (ν1)), ~1044 (PO4 3− (ν3) (P–O asymmetrical valence fluctuation)), 1067 (C–O planar valence fluctuation CO3 2− (ν1) B-type substitution), and 1091 cm<sup>−</sup><sup>1</sup> (C–O planar valence fluctuation CO3 2− (ν1) A-type substitution) may be related to the presence of a water–mineral metabolism disorder in the tissues of teeth with periodontitis, which leads to more intensive substitution of the hydroxide ion OH by apatite ions CO3 2− in the structure.

The change in the relative intensity of the lines at 1000 cm<sup>−</sup><sup>1</sup> and 1039 cm<sup>−</sup>1, corresponding to fluctuations in the phenylalanine molecule, and 873 cm<sup>−</sup><sup>1</sup> (C–C stretching, proline and hydroxyproline (collagen assignment)) are apparently related to collagen synthesis disorder, which can also be seen in osteoporotic changes of bone tissues, as we showed earlier in [25].

We also observed a reduction in the relative intensity of the lines at ~1742 (phospholipids), ~1556 (Amide II Parallel/Antiparallel β-sheet structure), 1200–1300 (Amide III), ~1418, and ~1446 cm<sup>−</sup><sup>1</sup> (CH2 scissoring and CH3 bending fluctuations of lipids and proteins) in the tissues of teeth with periodontitis compared with healthy tissues. This e ffect may have been caused by the dehydration of peptide groups of amides that are sensitive to structural changes in the molecules of collagen [26].

In [6,16], chemical and structural changes were shown in the periodontal ligament after the application of orthodontic force and gingival slit fluid in teeth with periodontitis. Violation of the ligamentous apparatus leads to the development of periodontitis and changes in tooth tissues. Raman spectroscopy analysis of enamel can be used for the early diagnosis of periodontitis.

As a result of the discriminant analysis, we built a discriminant model of the enamel of healthy teeth and the enamel of teeth with periodontitis, taking into account characteristic changes in the relative intensity of the Raman lines. The number of true positive (*TP*) results was 64, while there were 3 false negative (*FN*) results. The number of true negative (*TN*) results was 41, and there were 2 false positive (*FP*) results.

The calculated sensitivity and specificity values of the method are

$$\text{Sen} = \frac{TP}{TP + FN} = \frac{64}{64 + 3} = 95.5\% \tag{2}$$

$$Sp\mathfrak{c} = \frac{TN}{TN + FP} = \frac{41}{41 + 2} = 95.3\%. \tag{3}$$

Figure 10 shows the results of the receiver operator characteristic (ROC) analysis of the developed algorithm for diagnosing periodontitis. The discriminant adequacy of the method had an area under the curve (AUC) value of 0.983, which indicates the grea<sup>t</sup> quality of the diagnostic tool. The standard error (SE) was 0.01, and the 95% confidence interval of the AUC was in the range of 0.963–1. The optimal cut-o ff point for the presented algorithm, determined according to the condition of balance between sensitivity and specificity, was 0.55 (Figure 11). The values of sensitivity and specificity for the diagnostic model at that cut-o ff point were 95.5% and 95.3%, respectively.

**Figure 10.** Receiver operator characteristic (ROC) analysis of the algorithm for periodontitis assessment, using the Raman spectroscopy method: green line—ROC-curve, the red square is the optimal cut-off point.

**Figure 11.** The balance point between sensitivity and specificity.

Therefore, if the received spectrum of enamel is classified as the spectrum of enamel with periodontitis, it could be a reason for including the patient in the at-risk group and may determine the treatment given.
