*4.3. Quantitative Assessment Based on Attenuation Coefficient*

The attenuation coefficient is the sum of the absorption coefficient and scattering coefficient [35]. The attenuation characteristics of sound and carious enamel are different because of the alteration in optical properties of the teeth after demineralization. Hence, the attenuation coefficient can be used to quantify early enamel caries. Attenuation coefficients can be obtained by fitting the normalized A-scan signal with the Beer-Lambert law equation [65] as follows:

$$I(z) \approx \exp(-2\mu\_l z) \tag{2}$$

where *I* is the OCT signal intensity, *μ<sup>t</sup>* is the attenuation coefficient, and *z* is the depth beneath the tooth surface.

Mandurah et al. [66] reported that attenuation coefficients for sound areas of the samples were the smallest, ranging from 0.08 to 0.29 mm<sup>−</sup>1, increasing to a range of 1.34 to 3.4 mm−<sup>1</sup> after demineralization, and decreasing after remineralization with mean values of 0.81 and 0.85 mm<sup>−</sup>1. Moreover, there was a strong linear regression (r = −0.97) between the *μ<sup>t</sup>* measured by OCT and integrated nanohardness (INH) measured by a nanoindentation device. Hardness has been recognized as a measure of hard tissue's mineral density for a long time [67]. Maia et al. [68] studied morphological alterations between sound enamel and artificial white spot lesions in human teeth using OCT and QLF. The attenuation coefficient increases of enamel lesions ranged between 27.8% and 62.5%, while fluorescence intensity reduction ranged between 11.9% and 34.2%. Therefore, it was demonstrated that *μ<sup>t</sup>* determined by OCT was more sensitive to alterations than fluorescence measured by QLF. Cara et al. [69] verified that the attenuation coefficient could be employed for the initial lesion to effectively discriminate between sound and demineralized enamel with 0.93 sensitivity and 0.96 specificity.

A weaker attenuation of the OCT signal in enamel lesions was observed in Popescu et al.'s work [70,71]. The mean attenuation coefficient was 1.35 mm−<sup>1</sup> for sound enamel and 0.77 mm−<sup>1</sup> for caries lesions [70]. They attributed the results to the high porosity of demineralized enamel. One possible reason for the contradictory results of the studies mentioned above is the use of different wavelengths. Mandurah et al.'s study used the 1310-nm SS-OCT system, while Popescu et al.'s study used the 850-nm OCT system. The optical properties of enamel at the two wavelength ranges are different. A summary of the above research results is shown in Table 3.

**Table 3.** Results of quantifying enamel caries with the attenuation coefficient.


The Beer-Lambert equation used in the methods is based on a single scattering model. The single scattering model only considers single scattering, while the demineralization of caries enhances the effect of multiple scattering. This leads to bias of the obtained attenuation coefficients. In addition, reliably extracting attenuation coefficients from OCT signals can be affected by noise. These features diminish the utility of employing the attenuation coefficient as a marker for early enamel caries detection.

#### *4.4. Quantitative Assessment Based on Degree of Polarization*

Demineralized enamel results in rapid depolarization of polarized light in the NIR due to increased scattering [72], which has been confirmed by PS-OCT measurements [73]. Polarization imaging can provide higher contrast images of early enamel caries. Since OCT is an interferometric imaging method, only the contribution of fully polarized light can be measured. Thus, the degree of polarization within a single speckle is always equal to 1. However, when depolarized, the polarization state of the adjacent speckles is uncorrelated. Therefore, the degree of polarization uniformity (DOPU) has been proposed to assess carious lesions [74]. DOPU can be derived by an averaging of Stokes vectors over adjacent speckles, as follows:

$$\text{DOPU} = \sqrt{Q\_{mcan}^2 + lI\_{mean}^2 + V\_{mean}^2} \tag{3}$$

where *Qmean*, *Umean* and *Vmean* are the mean values of the Stokes vector elements within a certain evaluation kernel. It can be seen that the value of DOPU depends on the number of speckles in the chosen kernel.

The combination of the DOPU algorithm and PS-OCT was first applied to detect carious lesions by Golde et al. [74], and has been used for ophthalmologic research [75]. They measured three tooth samples with different proximal lesions, and the significant DOPU contrast provided better identification of lesions in comparison with reflectivity images. Furthermore, the effect of different DOPU evaluation kernel sizes on the resulting contrast was investigated. In a following study, they improved the DOPU algorithm by noise-immune processing, and adopted this approach to examine two tooth samples with stains and occlusal lesions [76]. Then, the research group measured the DOPU of bovine enamel at different stages of demineralization by using PS-OCT, and compared it with lesion depth obtained from PLM measurements [77]. The results showed that there was no depolarization in sound enamel, but an increased depolarization after 15 days of demineralization, corresponding to a decrease in DOPU. There was a high linear correlation (*R*<sup>2</sup> = 0.7118) between the DOPU and measured lesion depth with PLM, as shown in Figure 2. The summary of the above research results is shown in Table 4.

**Figure 2.** Correlation between the calculated mean DOP by PS-OCT and determined lesion depths by PLM. This figure was adapted from [77].

While the above results indicate the feasibility of assessing the demineralization stage by DOPU, there is a need to investigate the validity of DOPU at various polarization changes and the correlation between DOPU and mineral loss measured by TMR for further studies.


**Table 4.** Results of quantifying enamel caries with degree of polarization.

### *4.5. Quantitative Assessment Based on Refractive Index*

Demineralization causes a change in the refractive index of enamel, and accurate measurement of this change can assist in the identification of early caries [32]. The refractive index of teeth can be determined with the optical path-length matching method using OCT [78]. Samples are put onto a metal plate to acquire OCT images. The depth position of the reflection surface of the metal plate before the sample is placed is *Z*0. After adding samples, the depth positions of the sample surface and the metal plate surface are *Z*<sup>1</sup> and *Z* <sup>0</sup>, respectively. The thickness of the sample is *Z*<sup>1</sup> − *Z*0. Then, the refractive index of teeth is determined by [79]:

$$m = \frac{Z\_1 - Z\_0'}{Z\_1 - Z\_0} \tag{4}$$

Hariri et al. [80] measured refractive index of sound bovine enamel, demineralized for 2 months, and remineralized for 2 months, by 1310-nm SS-OCT with an axial/lateral resolution 11/17 μm, and analyzed mineral content by TMR. The results showed that at an n range between 1.52 and 1.63, the mineral content ranged between 50 and 87 (vol.%). This indicates there were strong positive linear correlations between *n* and mineral content in both demineralized enamel (*R*<sup>2</sup> = 0.89) and remineralized enamel (*R*<sup>2</sup> = 0.86). However, this method required sectioning of the sample to measure the refractive index, which is destructive and cannot be applied in clinical practice.

#### *4.6. Quantitative Assessment Based on Scattering Coefficient*

Since the scattering properties of the enamel changes significantly after demineralization, the scattering coefficient can serve as an indicator of enamel lesion severity. A single scattering model combined with dynamic focusing can be used to determine the scattering coefficients of sound and carious enamel [81]. The OCT signal intensity is:

$$I(z) \propto \sqrt{\frac{e^{-2\mu\_s z}}{\left[1 + \left(\frac{z - z\_{cf}}{z\_R}\right)^2\right]}}\tag{5}$$

where *z* is the depth, *zc f* is the focal plane position, *zR* is Rayleigh length, and *I*(*z*) is the OCT depth profile.

Tsai et al. [81] applied acid gel to demineralize enamel and scanned the sample in vitro before and after demineralization using 850-nm SD-OCT with an axial/lateral resolution 3/4 μm. The estimated scattering coefficient is shown in Figure 3. The scattering coefficient increased with the demineralization time and leveled out at times greater than 120 s. Moreover, the average scattering coefficients were 4.60 mm−<sup>1</sup> and 8.46 mm−<sup>1</sup> for sound and carious enamel, respectively.

However, as mentioned above, the single scattering model used above is inaccurate for enamel caries. According to the optical properties of the caries lesion, it shows a significant growth in the scattering coefficient of enamel during the production of the initial lesion. Hence, if an accurate scattering coefficient is used for the quantitative assessment of early caries, early demineralization can be detected more sensitively. However, there are few studies using scattering coefficient to quantitatively evaluate early caries.

#### *4.7. Quantitative Assessment Based on the Surface Roughness of Enamel*

Acid or bacterial erosion alters the surface roughness of enamel. The root mean square of the surface roughness can be expressed as [81]:

$$R\_{\emptyset} = \sqrt{\frac{1}{n} \sum \left(z\_b - z\_t\right)^2} \tag{6}$$

where *n* is the total number of A-scans, *zt* and *zb* are the surface and underlying depth positions of lesion area in A-scan, respectively.

Tsai et al. [81] estimated the surface roughness of the demineralized enamel, as shown in Figure 4. The surface roughness of the enamel increased gradually with demineralization time, and tended to level out, varying from 5.11 μm to 31.7 μm. Although the results demonstrated that the surface roughness could be applied for the detection of early caries, there were estimation errors compared with the results of scanning electron microscopy (SEM), and the effect of artificial caries and natural caries on enamel surface roughness may be different. In addition, there are few relevant studies.

**Figure 4.** Variation of the surface roughness with demineralization time. This figure was adapted from [81] and was created with Microsoft Word (Microsoft Corp., Redmond, WA, USA).

#### *4.8. Quantitative Assessment Based on the Volume of Residual Enamel*

Demineralization caused by caries lesions changes the volume of residual enamel. Wijesinghe et al. [82] obtained cross-sectional images of sound, partially demineralized and completely demineralized teeth in vitro by using 1310-nm SD-OCT with an axial/lateral resolution 6/25 μm, and measured the volume of residual enamel with an automated calculation method based on pixel intensity. The volumetric evaluation algorithm is shown in Figure 5. For the precise selection of residual enamel, an image window is applied to the 2D OCT images, as shown in Figure 5a. Then, the pixels that satisfy the pre-determined intensity threshold range are selected as shown in Figure 5b. Finally, a 3D OCT volumetric image is obtained as shown in Figure 5c. The volume of residual enamel is determined by:

$$V\_{\text{tot}} = \left(\mathbf{N}\_1 \times l\_x \times l\_y\right) \times l\_z + \left(\mathbf{N}\_2 \times l\_x \times l\_y\right) \times l\_z + \dots + \left(\mathbf{N}\_n \times l\_x \times l\_y\right) \times l\_z \tag{7}$$

where *Ni*(*i* = 1, 2, ... , *n*) is the number of pixels in each window that satisfy the predetermined intensity cut-off points, n is the number of 2D images contained in the 3D image. *lx*, *ly* and *lz* are the pixel sizes in the x, y and z directions, respectively.

**Figure 5.** Evaluation algorithm for the volume of residual enamel. (**a**) 2D images with the applied image window; (**b**) Pixels that meet the predetermined intensity cut-off points; (**c**) 3D volumetric image. This figure was adapted from [82].

The volume of residual enamel for carious samples, partially demineralized samples and sound samples ranged from 12.26 to 28.72 mm3. The progression of dental caries is determined by detecting changes in the volume of residual enamel. When reduction in tooth volume is identified, medication can be taken immediately to inhibit the development of caries. The key in this method is the determination of threshold parameters, which requires the evaluation and standardization of volumetric information for multiple in vivo teeth to enhance accuracy.
