1. Introduction

Skin cancer is categorized into two types of melanoma and nonmelanoma. The incidence of both melanoma and non-melanoma skin cancers has been increasing over the past decades. Currently, 132000 melanoma skin cancers and between 2 and 3 million non-melanoma skin cancers occur globally each year. The lethal rate of melanoma and non-melanoma cancers is about 7000 and 2000 respectively. Due to their relative lack of skin pigmentation Caucasian populations generally have a much higher risk of getting non-melanoma or melanoma skin cancers than dark-skinned populations [1].

Malignant melanoma infiltrates melanocytes which are responsible for melanin (skin pigments) production. It is uncommon (∼1%) and the most fatal type of skin cancer. If malignant melanoma remains untreated, it will certainly lead to the demise of the patient within five years [2]. Dermatologists commonly use a grading method known as the ABCD rule to diagnose melanoma. A, B, C, D stands for: Asymmetrical shape, irregular Border, unevenly distributed Color, large Diameter (>6 mm) respectively. It is important to note, not all melanoma lesions have the aforementioned signs. Dermatologists mainly use dermoscopes (a magnifier equipped with a light source) to visually search for ABCD symptoms in a suspicious lesion, however, this instrument fails to detect sub-surface structures essential for diagnosing cancer in the early stages. Moreover, the ABCD grading method is a qualitative, inaccurate technique that relies on subjective determination in the course of the physician’s examination. A good example of the failure of the conventional examination method is one of the benign samples which was used in this study as a reference. The dermatologist diagnosed the sample as melanoma and prescribed biopsy, whereas the pathologist diagnosed the lesion as a benign mole.

Non-melanoma skin cancer has two common types; squamous cell carcinoma (SCC) and basal cell carcinoma (BCC). Basal and squamous cells are in the epidermis layer, the most superficial layer of skin. Non-melanoma lesions mainly appear as itchy, irritated sores with raised and scaly red or yellow patches, they bleed easily and do not heal or recur after healing [3]. The incidence of BCC and SCC among all types of skin cancers is about 80% and 20% respectively [2]. The incidence rate is much lower in people having a dark complexion. Unlike melanoma, non-melanoma lesions are non-lethal as in most cases spread sluggishly. However, if the appropriate treatment is not given, there is a likelihood of cancer spreading to other parts of the body. The metastasis of non-melanoma cancer has been reported to be 0.5% for BCC and 4% for SCC [3]. Regardless of the type, the symptoms of a cancerous lesion in the early stages are unnoticeable. This may lead to procrastination in diagnosis and prompt treatment. Early detection of cancer is essential to shorten the treatment period. To sum up, traditional dermoscopes often would not help dermatologists to identify the characteristic structures of melanoma or non-melanoma lesions; because the backscattered light from deep layers within the tissue often masks those features.

Furthermore, the vast majority of skin diseases such as organoid nevus, seborrheic keratosis, etc. often look like cancerous lesions, thus biopsy is the preferred diagnostic method among dermatologists, assuring a valid diagnosis based on the pathology report. However, the biopsy is costly, invasive, and may leave the skin with unwelcomed scars. Thus, there is an urgent need for a non-invasive, reliable method for early diagnosis of skin cancer which could also discriminate between melanoma and non-melanoma lesions. During the last decade several non-invasive attempts have been done for cancer diagnosis such as laser-induced breakdown spectroscopy (LIBS) and laser-induced fluorescence (LIF) spectroscopic techniques [4–7]. On the other hand, several optical techniques are recently suggested for cancerous [8].

Recently, polarized light-based techniques have demonstrated much higher sensitivity to the alteration of tissue structures or composition and are closely associated with underlying pathology. The prominent property of polarimetry techniques in optically thick turbid media addresses the effect of multiple scattering, which effectively randomizes the photon direction, phase coherence, and polarization. Consequently, a slight fraction of the light emerging from a sample will remain polarized in particular detection geometry. Thus, polarimetry relies on measuring, quantifying, and interpreting the surviving polarized light fraction.

Previously, several studies have focused on light depolarization in biological tissues, Jacques et al. demonstrated the use of polarized light for superficial tissue imaging; based on collecting two polarization images through aligned and crossed polarizers and then computing the degree of linear polarization. The image contrast was significantly improved by the subtraction of the two images, thus revealing superficial structures [9]. Moreover, the polarization based imaging techniques are reported in several articles [10–13]. Vitkin et al. reported in vivo study such that the light diffusively scattered by human skin retain significant polarization in exact backscattering directions, and the degree of polarization increases with absorption [14]. In 2000, Smith et al. used the Mueller matrix imaging polarimetry technique to study melanoma and Lupus lesions. They found a high contrast between melanoma moles and surrounding tissues according to the depolarization image. This indicates that melanoma lesions depolarize light less than the surrounding normal tissue. Unlike melanoma, the Lupus lesions are invisible in the depolarization image, but they alter the orientation of linear retardance [15,16]. In 2002 Liu et al. employed the same imaging technique to investigate the normal rat skin. Looking at the diattenuation image, they noticed a high contrast of the vascularization compared to the surrounding structure [17]. In 2021 Louie et al. construct an optical polarimetry probe for in-vivo skin cancer detection. Employing the degree of polarization relation (DOP), they found out melanoma notably preserves the initial polarization [18,19]. In 2021 Pham et al. investigated polarization characteristics of SCC, BCC and melanoma and founded, the phase retardance and linear dichroism (D) of the cancerous samples are significantly lower than those of the healthy control samples [20].

In the diagnostic method of Mueller matrix polarimetry, by measuring the elements of the Mueller matrix of human benign and cancerous skin specimens, and its polar decomposition, the polarization parameters are extracted, including retardance, diattenuation, and depolarization. Those are key parameters for an accurate diagnosis of skin cancer. Currently, the absolute diagnosis of malignant melanoma, SCC, and, BCC lesions mostly rely on biopsy and pathology reports, which is a lengthy and invasive method. Hence, we have proposed a novel, reliable alternative method to identify promptly those skin cancers. This research elucidates the correlation between the three polarimetric parameters and malignancy, besides its type. The polarimetry technique is a vehicle to differentiate the cancerous skin tissues from the benign nevus by examining the corresponding decomposition parameters. In fact, the melanoma/non-melanoma lesions are difficult to diagnose even by the elaborate pathologist due to their inherent pathological similarity and the present non-invasive technique would contribute to differentiate these lesions in lieu of traditional biopsy.

2. Theory

2.1 Stokes vector and Mueller matrix

A Stokes 4 × 1 vector, is a mathematical representation of the polarization state of light. It can be represented as a set of six intensity measurements recorded through a set of various polarizing filters, as shown below:

A 4 × 4 Mueller matrix is a mathematical description of how an optical sample interacts or transforms the polarization state of an incident light beam. In essence, the Mueller matrix can be thought of as the “optical fingerprint” of a sample. This matrix operates directly on an input or incident Stokes vector, thus resulting in an output 4 × 1 Stokes vector that describes the polarization state of the light leaving the sample. This is described mathematically by the following equation:

The Mueller matrix of a sample is experimentally measured through the application of various incident polarization states and then by analyzing the state of polarization of the light leaving the sample. Since a Mueller matrix contains 16 elements, reconstruction of the Mueller matrix requires at least 16 independent polarization measurements. Mueller matrix is reconstructed with at least 16 polarization measurements as represented by the following equation:

2.2 Mueller matrix decomposition

A Mueller matrix encodes a significant amount of information about the sample it describes. Often this information is not apparent by simple observation; however, through the application of decomposition techniques certain polarization-sensitive data are obtained to aid in sample characterization. In this investigation, we focus on three quantitative measurements of diattenuation, retardance, and depolarization. The diattenuation addresses the polarization-dependent attenuation of light. The retardance is defined as the ability of the polarization sample to change the phase of the electrical vectors of light. The depolarization power indicates the depolarizing ability of the sample. These parameters are obtained through the polar decomposition of the acquired Mueller matrix acquisition using a technique originally proposed by Lu and Chipman [21].

Diattenuation can be acquired directly through the algebraic calculation of the elements in the Mueller matrix shown by,

The normalized diattenuation vector is given by,

The Mueller matrix of an optical sample can be decomposed in the form of the equation,

The diattenuation matrix can be found by the means of the following equations regardless of whether the Mueller matrix is depolarizing or non-depolarizing

Then the product of retardance and depolarizing matrices can be obtained as:

Further, these above matrices can be defined as:

Here, ${\vec{P}_\varDelta } = \frac{{\vec{P} - m\vec{D}}}{{1 - {D^2}}}$ and the polarizance vector $\vec{P} = \frac{1}{{{m_{00}}}}{[{{m_{10}}\;{m_{20}}\;{m_{30}}} ]^T}$.

According to (9) and (10), the retardance matrix ${M_R}$ can be determined and the retardance$\; R\; $can be acquired by:

Lastly, the depolarization power $\varDelta $ is defined by

It should be noted, that all the above equations are held valid only if $m^{\prime}$ is non-singular [22].

3. Methods and materials

3.1 Mueller matrix measurement setup

Figure 2 depicts the experimental setup for measuring the Mueller matrix of the sample in a back-scattering configuration. The light source used in the setup is a He-Ne laser manufactured by Melles Griot at $632.8\; nm$ and 2 mW stable power laser. It is coherent, and is vertically polarized. A sample with an unknown Mueller matrix has 16 unknown elements. Consequently, the minimum number of trials to suffice the Mueller matrix determination reaches 16. The experimental setup includes two different branches: polarization state generator and polarization state analyzer which are abbreviated as PSG and PSA respectively. In the PSG branch, firstly a linear polarizer P1 is placed to transmit the vertically-polarized light. The linearly polarized direction is changed from vertical to other directions by the use of a half-wave HW plate, situated after P1. By rotating the HW, the horizontal (H) and linear $+ {45^o}$ (P) polarization states are generated. The quarter-wave plate QW1 is placed afterward to generate the right circular polarization state (R). Then the scattered light from the sample enters the PSA branch. The latter collects the scattered light via the lens L with the focal distance of $10\; cm$, at ${20^o}$ off-axis from the exact back-scattering direction, and gets analyzed via the combination of the second quarter-wave plate QW2 and linear polarizer P2. A photodiode sensor model 818-SL manufactured by Newport company is employed at the end to detect the output light. To sum up, 4 different polarization states (stokes vectors) are produced in the PSG branch; including horizontal (H), vertical (V), linear $+ {45^o}$ (P), right circular (R) polarization; then in the (PSA) branch, 4 sets of measurements are carried out on the scattered light to determine what fraction of the initial polarization has survived afterward. Consequently, there will be 16 polarization combinations including VV, VH, VP, VR, HH, HV, HP, HR, PV, PH, PP, PR, RV, RH, RP, and RR, via all these measurements it is possible to reconstruct the Mueller matrix of the sample using the matrix in Eq.3. Before collecting any sample data, the precision of the system has been tested after calibration. This was accomplished by recording the Mueller matrix from a known optical component. Here a mirror is examined. Comparing Eq. 16 with the theoretical value given by Eq.17, the maximum relative error for all elements is assessed to be around the acceptable level of 2%. Fig. 1 illustrates a typical Muller matrix and the corresponding vectors as show in Code 1 (Ref. [34]).

 

Fig. 1. 4 × 4 Mueller matrix of the sample.

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Fig. 2. Schematic of polarimetry setup to obtain Mueller matrix elements.

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3.2 Sample preparation

The selected patients are Tehran inhabitants and Caucasoid with tanned complexion. Formalin-preserved skin tissues with $0.3 - 1.5mm$ thickness have been obtained from the Razi dermatology hospital, Tehran, Iran. The 632.8nm-wavelength laser penetrates through the skin as far as 2 mm. The rear part of sample is covered with a thin layer of transparent wax and the laser beam traverses through specimen and wax thickness and air after all. Thus, the partial reflection from the wax-air interface is similar for all samples. A series of systematic experiments have been carried out on 8 samples of melanoma (Clark level III, no ulceration) specimens, 8 basal cell carcinoma (BCC) specimen and 8 squamous cell carcinoma (SCC) specimens as well as 8 benign nevi. Subsequently 3 different measurements on 3 sites of a sample were carried out as if 24 datasets are collected for each lesion type. This study has been accomplished in 3 years and a half of follow-up.

As an example, the Meuller matrix in Eq. (1)8 belongs to one of the melanoma samples. It is decomposed to three depolarization, retardance and diattenuation matrices. Consequently, the depolarization (Δ=0.7633), retardance (R=2.8557) and diattenuation (D=0.0570) parameters is extracted.

2.4.4 Results and discussion

Mueller matrices recorded from malignant and normal samples are decomposed in the MATLAB program to obtain the relevant polarization parameters. Figure 3 illustrates results for the retrieved polarization parameters including average depolarization, retardance, and diattenuation values, alongside the corresponding standard deviation.

 

Fig. 3. (a) Diattenuation (b) Depolarization (c) Retardance for Melanoma, squamous cell carcinoma, basal cell carcinoma, and benign nevus as reference.

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Table 1 as well as Fig. 3 (a, b, c) all indicate that the melanoma specimen in comparison to other samples, exhibits the lowest diattenuation $({D = 0.0670} )$, and retardance $({R = 2.8790} )$. In terms of diattenuation and depolarization power, the benign nevus shows the highest diattenuation $({D = 0.1017} )$ and depolarization (Δ=0.7563) and also retardance, however, the difference in their depolarization parameter is statistically insignificant for the non-melanoma lesions. The effect of wax on the depolarization coefficient is inevitable such that Fig. 3 (b) could only differentiate benign nevus from cancerous lesions. There is no choice to eliminate the depolarizing wax effect. The glycerol optical clearing, angular reflectance and high resolution photographs are several vehicles to improve the present findings.

Table 1. Mean values of diattenuation, depolarization, and retardance for melanoma and non-melanoma cancers and healthy lesions as well as typical p value and confidence levels in favor of melanoma/benign nevus lesions

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In fact, the normal and cancerous tissues exhibit different behaviors facing the polarized light. Two prominent transformations take place for cells during the process of malignancy.

The first transformation that a cell undergoes during malignancy is the elevation of the nuclear-to-cytoplasmic (N:C) ratio. Typically, a high N:C ratio is a sign of cellular atypia and malignancy. In cytopathology, the N:C ratio acts as a diagnostic feature because specimens are often comprised of single cells lacking the architecture of whole tissue samples. Figure 4(a) and Fig. 4(b) displays schemes of a normal cell against a malignant cell. The latter has a larger N:C ratio [23].

 

Fig. 4. (a) a normal cell with a lower N:C ratio. (b) a malignant cell with a high N:C ratio. Note that this keeps the illuminating light’s polarization more than that of normal tissue. (c) skin tissue with healthy collagen fibers (d) cancerous lesions alongside collagen destruction.

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It is worth explaining the structure of the cell briefly. The average human skin cell is about 40 micrometers in diameter [24] which is within the Mie scattering regime [25]. Cell possesses a hard nucleus. It is approximately 5 to 10 times stiffer than the surrounding cytoskeleton, characterizing the absorption peak at 250 nm. The nucleus is surrounded by cytoplasm, which consists of ∼80% water and its main component is cytosol – a gel-like substance. Various cytoplasmic inclusions exist in the cytoplasm including the organelles, a collection of mitochondria, lysosomes, and peroxisomes. From an optical perspective, the cytoplasm with its substructures provides an anisotropic medium. Comparing the nucleus and cytoplasm, the cytoplasm is the more highly scattering part and it significantly contributes to the depolarizing property of the whole cell. Figure 4(a) represents a normal cell having a lower nucleus to cell ratio in terms of volume, so the illuminating light enters the cytoplasm and is scattered by organelles multiple times, consequently gets depolarized after leaving the cell. Conversely, Fig. 4(b) shows that in a cancerous cell the abnormal majority of the cell’s volume is occupied by the nucleus. Thus, the incoming light preferentially gets backscattered by the large and stiff nucleus [26,27].

The second transformation in tissue point of view happens for collagen fibers, the most abundant birefringent component of the skin. These long fibers exhibit some net orientation through the skin [28]. From an optical perspective, birefringent materials such as collagen possesses two orthogonal fast and slow axes. Relative to these axes and light’s polarization vector, the light experiences two different refractive indices. The one which encounters greater refractive index, traverses more slowly, consequently lags the other ray in phase. Collagen contains helix-type molecule binding structures whose anisotropic alignment causes the fiber extension direction to be the slow axis and causes the cross-sectional direction to be the fast. When a cancerous tumor develops, numerous changes in collagen components take place. For example, the deposition of collagen fibers resulting from an increased number of fibroblasts, also the secretion of proteolytic enzymes in cancer invasion leads to the denaturation of the collagen fibers. Thus, the cancerous structures also alter the elastic properties of the tissue that can affect the tissue birefringence [19]. Hereby, the loss of birefringence arises from the deformation of the regular molecular binding structure and even the damage of the helix-type molecules [29,30].

It is crucial to point out that, the same anisotropy that appears in the form of birefringence (anisotropic refraction) also leads to diattenuation (anisotropic attenuation) which arises from anisotropic absorption (dichroism) and scattering of light. The intensity of polarized light that is transmitted through a diattenuating medium depends on the direction of polarization relative to the orientation of the optic axis (symmetry axis) in the medium. The transmitted light intensity becomes maximal for light polarized in a particular direction and minimal for light polarized in the corresponding orthogonal direction [31]. Moreover, it should be highlighted that retardance and diattenuation both arise from differences in refractive indices for different polarization states, and are often described in terms of ordinary and extraordinary indices and axes. Difference in the real parts of the complex refractive indices addresses retardance, whereas discrepancy in the imaginary parts indicates dichroism and diattenuation [32]. To sum up, diattenuation and retardance have a common origin. This is the main reason for their similar behavior in Fig. 3 (a) and (c). In other words, diattenuation and retardance values are in a positive correlation. Consequently, if a test does not exhibit such a correlation, it may be invalid and recommended to be repeated.

All types of skin cancer destroy the collagen fibers; however, this destruction is more severe in melanoma skin cancer. For instance, quantification of collagen fiber density from different regions around the melanoma lesion exhibits varying degrees of fiber density ranging from 0.8% in the middle of the lesion to 38% in the non-lesion area of skin. Moreover, In the melanoma lesion areas, the collagen morphology is greatly affected. They appear in very short, thin wispy fibers [33]. According to these biological facts, we elucidate why a very low level of retardance and diattenuation appear in melanoma lesions. Nevertheless, the difference between non-melanoma cancers and normal skin is subtle. Figure 4(d) depicts a model of a cancerous tumor that deforms and terminates the collagen fibers.

Considering all the aforementioned reasons, our results are in good agreement with biological facts that in the melanoma samples, the retardance and diattenuation values level down, emphasizing that the anisotropy and birefringence property of collagen fibers decrease due to the acute alteration of the collagen fiber’s structure.

To sum up, Fig. 5, a plots a diagnostic algorithm to find out whether a lesion is cancerous or benign. This also discriminates melanoma from non-melanoma lesions. Firstly, the diattenuation well differentiated malignancy from benign nevus, and secondly, the retardance/depolarization value ascertains the type of skin cancer. It is worth to note that the D, Δ, R values are dependent to skin age and complexion too. Thus, it would be better to compare the patient’s lesion of test with their healthy skin.

 

Fig. 5. (a) Algorithm and 3D scatter plot of the decomposition parameters, and 2D scatter plot for (b) benign nevus/melanoma and (c) SCC/BCC non-melanoma lesions.

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5. Conclusion

Here, benign lesion, melanoma, and nonmelanoma invitro human samples are exposed to polarized light by means of the polarimetric setup. By making use of Mueller matrix decomposition, the diattenuation, depolarization, and retardance values are obtained for the benign and cancerous specimens of interest. It is observed that the benign lesion benefits a high level of depolarization in comparison to all types of skin cancers. This difference originates in the high nucleus to cytoplasm ratio of cancerous cells; because the abnormal large nucleus impedes light penetration to the cell’s cytoplasm so the light gets backscattered promptly thus preserves its initial polarization and intensity relatively. On the other hand, the retardance/diattenuation addresses real/imaginary part of complex refraction in collagen fibers. In fact, the diattenuation and retardance of the melanoma lesions exhibit relatively low values, emphasizing the decrease of anisotropy in melanoma lesions. This mainly arises from the dramatic destruction and deformation of collagen fibers. This work can be extended in favor of in-vivo polarimetry of tissue in near future.