# Quantitative Assessment Methods of Early Enamel Caries with Optical Coherence Tomography: A Review
## 4 Quantitative Assessment Methods of Early Enamel Caries with OCT
### 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:  
\[I(z)\propto\exp(-2\mu_{t}z) \tag{2}\]  
where \(I\) is the OCT signal intensity, \(\mu_{t}\) is the attenuation coefficient, and \(z\) is the depth beneath the tooth surface. [PERSON] et al. [66] reported that attenuation coefficients for sound areas of the samples were the smallest, ranging from 0.08 to 0.29 mm\({}^{-1}\), increasing to a range of 1.34 to 3.4 mm\({}^{-1}\) after demineralization, and decreasing after remineralization with mean values of 0.81 and 0.85 mm\({}^{-1}\). Moreover, there was a strong linear regression (r = \(-0.97\)) between the \(\mu_{t}\) 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]. [PERSON] 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 \(\mu_{t}\) determined by OCT was more sensitive to alterations than fluorescence measured by QLF. [PERSON] et al. [69] verified that the attenuation coefficient could be employed for the \begin{table}
\begin{tabular}{c c c c} \hline
**Reference** & **OCT System** & **Sample Preparation** & **Reflectivity Result (dB\(\times\upmu\)m)** \\ \hline \multirow{6}{*}{[PERSON] et al. [61]} & \multirow{6}{*}{850-nm TD-OCT.} & Sample number: 15 bovine teeth for in vitro detection & \\  & & Solution: pH 4.5 & \(R_{\times}\) for 1 to 3 days: \\  & & demineralization solution & 54.0 \(\pm\) 11.27, 71.87 \(\pm\) 4.79, \\ \cline{2-3}  & & Method: demineralization for 3 days & 86.64 \(\pm\) 7.57 \\ \hline \multirow{6}{*}{[PERSON] et al. [63]} & \multirow{6}{*}{850-nm TD-OCT, axial/lateral resolution 16/10 \(\upmu\)m.} & Sample number: 15 bovine incisor teeth for \\  & & in vitro detection & Reflectivity of \\ \cline{1-1} \cline{2-3}  & & Solution: pH 4.5 & \(\upmu\)mineralization for 0, 24, 48, \\ \cline{1-1} \cline{2-3}  & & demineralization solution & 72 h: 31.86 \(\pm\) 9.30, \\ \cline{1-1} \cline{2-3}  & & Method: 3 windows for each & 14.45 \(\pm\) 5.47, 8.66 \(\pm\) 1.96, \\ \cline{1-1} \cline{2-3}  & & teeth. Demineralization for 24, & 4.32 \(\pm\) 2.72 \\ \cline{1-1} \cline{2-3}  & & 48, 72 h, respectively. & \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._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 [PERSON] et al. 's work [PERSON] et al. (2018); [PERSON] et al. (2018). The mean attenuation coefficient was 1.35 mm\({}^{-1}\) for sound enamel and 0.77 mm\({}^{-1}\) for caries lesions [PERSON] et al. (2018). 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. [PERSON] et al. 's study used the 1310-nm SS-OCT system, while [PERSON] 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.  
The Beer-Lambert equation used in the methods is based on a single scattering model.