2.1.

Stokes–Mueller Matrix Decomposition Method for Extracting Optical Parameters

Based on previous studies, we applied the analytical technique of Pham and Lo^28–30 to extract nine effective parameters, including the LB orientation angle ($\alpha$), the LB phase retardance ($\beta$), the CB optical rotation angle ($\gamma$), the LD orientation angle (${\theta }_d$), the linear dichroism ($D$), the circular dichroism ($R$), the degrees of linear depolarization ($e_1$ and $e_2$), the degree of circular depolarization ($e_3$), and the depolarization index ($\mathrm{\Delta }$), of healthy and skin cancer samples.

For a biomedical sample, the output Stokes vector, $S_c$, has the form

Noticeably, full details of the experimental procedure used to extract the various parameters are mentioned in Refs. 2829.–30. To sum up, the LB orientation angle ($\alpha$), phase retardance ($\beta$), optical rotation angle ($\gamma$), LD orientation angle (${\theta }_d$), linear dichroism ($D$), circular dichroism ($R$), linear depolarization $(e_1,e_2)$, and circular depolarization ($e_3$) can be extracted using Stokes–Mueller technique from Refs. 2829.–30. Notably, this methodology does not require the alignment of the principal birefringence axes and diattenuation axes. Although only four different input polarization lights, namely three linear polarization lights (i.e., ${\widehat{S}}_{0\mathrm{deg}}$, ${\widehat{S}}_{45\mathrm{deg}}$, and ${\widehat{S}}_{90\mathrm{deg}}$) and one circular polarization lights (i.e., ${\widehat{S}}_{\mathrm{RHC}}$), are enough for obtaining all elements of Mueller matrix, the extra two input polarization states (i.e., ${\widehat{S}}_{135\mathrm{deg}}$ and ${\widehat{S}}_{\mathrm{LHC}}$) further improve the experimental results. Moreover, the ability of the analytical model for extracting all the optical parameters of interest over the measurement ranges was verified using an analytical simulation and error analysis technique. Thus, the analytical model yielded accurate results even when the output Stokes parameters had errors in the range of $\pm 0.005$, or the samples had the minimum measurement of birefringence or dichroism.^28–30

2.2.

Experimental Setup

The polarized light system included a helium–neon laser (wavelength of 632.8 nm, power $<5\mathrm{mW}$), a quarter-wave plate, polarizers, and a Stokes polarimeter to characterize the LB, LD, CB, CD, L-Dep, and C-Dep properties of turbid media. In performing the experiments, the input light was provided by a frequency-stable He–Ne laser (HNLS008R, Thorlabs Co.) with a central wavelength of 633 nm. Also, a polarizer (GTH5M, Thorlabs Co.) and a quarter-wave plate (QWP0-63304-4-R10, CVI Co.) were used to produce four linear polarization lights (0 deg, 45 deg, 90 deg, and 135 deg) and two circular polarization lights (right-handed and left-handed). Finally, a neutral density filter (NDC-100-2, ONSET Co.) was used to ensure that each of the input polarization lights had the equal intensities. The output Stokes parameters were computed from the intensity measurements obtained using a commercial Stokes polarimeter (PAX5710, Thorlabs Co.) at a sampling rate of 33.33 samples per second. A minimum of 1024 data points was obtained for each sample. Of these data points, 100 points were chosen and used to calculate the mean value of each effective parameter. Figure 1 shows the installation of the system. The samples were placed between the polarizer and detector by being fixed to a side stand. It is noted that the error analysis of the proposed system was performed and described in detail in Ref. 29. The analytical model yields accurate results even when the output Stokes parameters have errors in the range $-0.005$ to $+0.005$ or the samples have very low values of birefringence or dichroism.²⁹ Furthermore, the reliability of the proposed system was evaluated using different optical samples, namely a quarter-wave plate (QWP0-633-04-4-R10, CVI Co.); a half-wave plate (QWP0-633-04-2-R10, CVI Co.), a polarizer (GTH5M, Thorlabs Co.); a baked polarizer (LLC2-82-18S, OPTIMAX Co.); a polarization controller; a composite sample comprising a quarter-wave plate, a half-wave plate, and a polarizer; and a depolarizer (DEQ-1N in ONSET Co.).^28,29

Fig. 1

Schematic illustration of a model of measurement.

3.1.

Materials

7,12-dimethylbenz[a]anthracene (DMBA) ($\ge 95\%$) and croton oil were purchased from Sigma–Aldrich Co. (Germany), meanwhile Hematoxylin and Eosin stain were bought from Sigma–Aldrich Co.. Ethanol, xylene, and acetic acid ($\mathrm{CH}3\mathrm{COOH}\ge 99.5\%$) were purchased from Xilong, China.

3.2.

Experimental Animals

We performed the experiment on 17 healthy male Swiss albino mice (25 to 30 g) purchased from Institute of Vaccine and Medical Biology of Nha Trang city, IVAC (Vietnam). Mice were individually housed per cage and were acclimatized to a 12-h light–dark cycle for at least one week before each experiment. The animals had free access to food pellets (IVAC, Vietnam) and water ad libitum. One day before the treatment, the dorsal skin of mice was shaved for an $\sim 2\mathrm{cm}\times 2\mathrm{cm}$ area. All experimental protocols were conducted under the agreement of the scientific committee, specialty of Pharmacology and Clinical Pharmacy, Faculty of Pharmacy, University of Medicine and Pharmacy at the Ho Chi Minh City, Vietnam (Number 03-2016/QĐ-SĐHD).

3.3.

Two-Stage Chemical Carcinogenesis Protocol

The cutaneous tumors were initiated on 12 mice by a single application on the dorsal shaved skin $50\mu \mathrm{L}$ of a 0.2% DMBA solution prepared in acetone (equivalent to $100\mu \mathrm{g}$ DMBA per mouse). Two weeks later, $50\mu \mathrm{L}$ of a 2% croton oil solution prepared in acetone (equivalent to 1 mg croton oil per mouse) was topically applied two times weekly until the end of the experiment. At the 20th week, mice were euthanized by ${\mathrm{CO}}_2$ asphyxiation, and skin samples were then isolated and fixed in 10% formalin. Tissues were embedded in paraffin wax for further experiment.

3.4.

Optical Characterization

The samples were sectioned with microtome with the thickness of $5\mu \mathrm{m}$ and embedded on Quartz slides. The slides were then analyzed using the polarized light system mentioned above.

3.5.

Histopathological Analysis

Cancerous tissue samples were sectioned with microtome with the thickness of $5\mu \mathrm{m}$ and stained with Haematoxylin and Eosin (H&E) stain. Stained slides were observed under a light microscope for histopathological analysis.

4.1.

Histopathological Validation of Pathology

Figure 2 shows the histopathological results of nonmelanoma-induced mice. To be specific, there is the existence of abnormal squamous cells and the invasion of those cells from the epidermis to the dermis (yellow arrow). In Figs. 2(a), 2(c), and 2(e), keratin accumulates and appears as keratin pearls (red arrow). Furthermore, the thickness of the epidermis increases massively, and no borderline between epidermis and dermis has shown. These characteristics validate our induction of nonmelanoma skin cancer (squamous cell carcinoma) on mice.

Fig. 2

Histopathological results of nonmelanoma-induced mice. (a) and (b) Sample 1, (c) and (d) sample 15, e and (f) sample 9, and (g) and (h) sample 10.

4.2.

Optical Properties of Nonmelanoma Tumors

The results of nine effective properties of nonmelanoma skin cancer in mice are shown in Fig. 3. Most of the optical characteristics extracted from 12 subjects show similarity, except orientation angle of LD (${\theta }_S$) and optical rotation of CB (${\gamma }_S$). Specifically, in Fig. 3(a), orientation angles of LB (${\alpha }_S$) are all close to 82 deg, whereas phase retardations of LB (${\beta }_S$) are around 0.9 deg. Also, in Figs. 3(b) and 3(d), measured linear dichroisms ($D_S$) are nearly 0.06, whereas measured circular dichroisms ($R_S$) are almost $-0.006$. Figure 3(e) shows that all of the linear depolarization ($e_{1S}$ and $e_{2S}$) and circular depolarization are close to 0.99, 0.96, and 1, respectively. However, depolarization indices calculated from ($e_{1S}$, $e_{2S}$, and $e_{3S}$) show slight variation ranging from 0.20 to 0.28. Noticeably, in Figs. 3(b) and 3(c), most of the subjects showed properties of the orientation angle of LD (${\theta }_S$) at almost 20 deg, and the optical rotation angle of CB (${\gamma }_S$) varied among the mice ranging from 0.025 deg to 0.08 deg.

Fig. 3

Effective properties of (a) orientation angles of LB (${\alpha }_S$) and phase retardations of LB (${\beta }_S$); (b) orientation angle of LD (${\theta }_S$) and linear dichroism ($D_S$); (c) optical rotation of CB (${\gamma }_S$); (d) circular dichroism ($R_S$); (e) depolarization ($e_{1S}$, $e_{2S}$, and $e_{3S}$); and (f) depolarization index of squamous cell skin cancer in mice.

Table 1 shows the values of optical properties for the control samples and nonmelanoma skin cancer. The values were the average, and the standard deviation from 6 measurement points on each of 72 samples extracted from 12 cancer subjects and each of 30 samples extracted from 5 normal subjects are calculated as shown in Table 1.

Table 1

Optical properties of normal and squamous cell skin cancer in mice.

The detailed results of major effective properties including phase retardance and orientation angle of LB, optical rotation angle of CB, LD, and depolarization index comparing healthy tissue and squamous cell skin cancer in mice are shown in Figs. 4Fig. 5–6. Birefringence, LD, and depolarization index are the representatives of three fundamental polarization properties of the medium: retardance, diattenuation, and depolarization, respectively.

Fig. 4

LB properties of healthy and squamous cell skin cancer in mice (a) orientation angles of LB (${\alpha }_S$) and (b) phase retardations of LB (${\beta }_S$).

Fig. 5

CB properties of healthy and squamous cell skin cancer in mice.

Fig. 6

LD of squamous cell skin cancer in mice.

Figure 4 shows that the values of measured orientation angle and phase retardance of LB in mice with squamous cell skin cancer are significantly lower than in normal mice, where the figures of $\alpha$ and $\beta$ among normal mice are around 145 deg and 1.26 deg; the ones in cancer mice are $\sim 82.6\mathrm{deg}$ and 0.9 deg, respectively. As shown in Fig. 5, the tendency of CB is similar with that of LB. The optical rotation angles of CB, $\gamma$, of normal samples fluctuate around 0.88 deg while that of cancerous samples is close to 0.05 deg. Remarkably, there is a normal skin sample with high $\gamma$ and large standard deviation. The results of LD are in the same tendency with birefringence as shown in Fig. 6. The $D$ of control samples is slightly below 0.13 deg, whereas those of cancer mice fluctuate around 0.06 deg. The trend for the depolarization index of healthy and cancer mice is opposite as shown in Fig. 7. The values in 12 samples of cancer mice fluctuate around 0.015, whereas normal skin tissues have more depolarization (around 0.011). Wide error bars that appear in several subjects indicate the measured values are relatively dispersed. In general, the five parameters analyzed have provided a significant distinction between squamous cell skin cancer and healthy skin in mice.

Fig. 7

Depolarization index of healthy and squamous cell skin cancer in mice.