Skin cancer represents one of the most common type of cancer in the world. It develops, normally, at the epidermis (the outer layer) of the human skin. Cutaneous melanoma (CM) represents the most serious melanoma form of human skin cancer [
21]. Nodular basal cell carcinoma (NBCC) and squamous cell carcinoma (SCC) define the forms of non-melanoma. They occur more frequently and spread at a slower rate than CM melanoma.
Salomatina et al. [
24] and Garcia-Uribe et al. [
25] proposed different optical properties of normal and cancerous human skin. In vivo characterizations have been employed in their works, and analyses of pigmented skin lesions have been considered using oblique incidence diffuse reflectance spectrometry [
25]. In our present work, the main optical properties of non-melanoma and melanoma type skin carcinomas are taken from [
24,
25]. Firstly, malignancy in human skin start as a thin layer of carcinoma situated in the basal layer of the living epidermis, as explained in [
21]. Then, the malignancy spreads into the living epidermis. In the third phase, it enters the stratum corneum, and appears as a tumor at the skin’s outer-surface.
Anderson and Parrish [
26] presented an optical characterization of normal and malignant human skins in the range of 600–1300 nm wavelengths. This range of wavelength has a special potential for the optical discovery of skin abnormalities. The thickness, absorption coefficient, scattering coefficient and anisotropic factor of a normal skin model at 520 and 840 nm are presented in
Table 1 [
21,
27,
28,
29], while the same properties corresponding to a wavelength of 785 nm are summarized in
Table 2 [
21,
27,
28]. The optical properties of a skin lesion at 785 nm are also displayed in
Table 3.
In this section, human skin with and without malignancies is numerically studied after having been exposed to a low-power short-pulse (ultrafast) laser (
Figure 1 and
Figure 2). The incident laser pulse
Ic(
t) obeys Equation (4), and the same thicknesses for both layers (i.e., the epidermis and the dermis) are used as those by Wang et al. [
30] and Bhowmik et al. [
21]. The thicknesses of the hypodermis (the subcutaneous) and muscular layers and their refractive indices,
n, are obtained from the works of Bhowmik et al. [
21] and Bashkatov et al. [
27,
28]. Thus, the total thickness in the collimated x-direction of the human skin layers is 8.0 mm. In our study, three-dimensional skin layers, with dimensions 8 × 100 × 100 mm
3, are simulated. The total optical thickness
at a wavelength of 785 nm (
Table 2) is obtained from its integration along the total thickness of the skin as follows [
21]:
The incident laser pulse
Ic(t) has a Gaussian’s profile, as plotted in
Figure 3. Temporal deviations of transmittance and reflectance signals are examined for three-dimensional skins. All computations are done using 400 × 21 × 21 control volumes and 80 control angles (i.e., the FT8). Only the predictions of the CLAM scheme are analyzed. For all cases, a time step size
ps has been applied, and thus this step size is much less than the pulse width (i.e., (
tp)). The incident angle of the ultrafast laser is taken as normal to the irradiated boundary (i.e.,
θc = 0.0°) (
Figure 3). For all results, both transmittance and reflectance signals have been normalized according to their corresponding highest values in each corresponding case.
3.1. Human Skin without Malignancies
In this section, the influence of the pulse width
tp on the normalized reflectance and the transmittance for normal human skin is analyzed according to the properties described below as well as without malignancies (
Figure 4 and
Figure 5). Four pulse widths are considered for a single pulse:
tp = 1 ns, 100 ps, 10 ps and 1 ps. In addition, signals reported by Bhowmik et al. [
21] are plotted for a one-dimensional case so that we may compare our present three-dimensional results using the FTn FVM to those given by the discrete ordinates method utilized in [
21]. In order to analyze the signals properly, we depict the results using the CLAM scheme only. In fact, for fine spatial grids, the results obtained using the STEP scheme, which are not shown here, closely match those reported using the CLAM scheme.
Figure 4 and
Figure 5 show that the results of both normalized transmittance and reflectance reproduce the incident ultrafast laser, although their peak magnitudes are different. Also, the present three-dimensional signals have the same shapes as those for the one-dimensional case of [
21]. For the same pulse width, the transmittance is greatly decreased (
Figure 4) by comparison to the reflectance (
Figure 5). In fact, for
tp = 1 ns, the peak values of the normalized transmittance and reflectance are 1.8 × 10
−2 and 0.41, respectively. It is shown that the decrease of the pulse width decreases the peak magnitude of the transmittance signals (
Figure 4). This can be explained by the fact that large pulse widths require more thermal energy (heat) input to the skin, thus creating the trend obtained at higher peak amplitudes for a larger pulse width. Both peak magnitudes and temporal differences of the reflectance are small for the lower value of
tp (
Figure 5). The cascading effect becomes visible only for the lowest laser pulse width (i.e.,
tp = 1 ps) (
Figure 5). The consecutive augmentation in the reflectance’s peak magnitude is more important for
tp = 1 ps.
The photons travel the skin at the speed of light within this medium,
cmed =
c/
n, and thus those that are not scattered in the tissue require a time of
t =
Lx/
cmed = 37.33 ps to reach the boundary opposite to the laser source (i.e., the boundary at x =
Lx). Thus, the transmittance is different from zero only after this time (
Figure 4); however, the reflectance, at boundary x = 0, reveals much before this point (
Figure 5). In fact, when the laser light enters the skin at the boundary x = 0, the attenuation and diffusion of the intensity start immediately, and so an increase of the reflectance signal at this collimated boundary is obtained.
Figure 4 shows that the transmittance signals are very weak. In addition, in real medical applications, any malignancy in human skin is taken into account except for some cells of the affected tissues that are surgically removed and analyzed due to an amplified opacity of bone and skin. These bons and skin are obstacles to laser light and thus prevent transmittance signals from reaching the other side of the body. While transmittances are negligible in the case of malignancy, the reflectance profiles will remain present. In the next sections, only reflectance signals for malignancies in human skin are studied.
To examine the transmittance and reflectance profiles correctly, we illustrate the predictions of a laser pulse with a width of tp = 1 ps only. These predictions are easily distinguishable at smaller pulse widths, so for the evaluation objective solutions for 1 ps are discussed.
In comparison with the referenced solutions of [
21], the average absolute relative error does not exceed 1.8% and 4.2% for the FT8 and FT6 schemes, respectively (
Table 4). As can be seen in
Table 5, an acceptable margin of error of less than 1.8% is observable for a spatial discretization of 400 × 21 × 21. Thus, an excellent agreement between the present results and the ones found in the literature [
21] is achieved when the FT8 scheme and a spatial discretization of 400 × 21 × 21 are applied.
3.2. Human Skin with Malignancies
Skin cancer, which includes melanoma, basal cell carcinoma and squamous cell carcinoma, frequently starts as precancerous lesions. It grows through several intermediate phases and can present as new growths or precancerous lesions, whereafter it establishes itself as a tumor on the outer surface of the skin. Firstly, it is seen in the basal layer (with a thickness of around 10 μm), then it similarly develops on the other parts of neighboring cells of the epidermis layer. The neighboring medium contains the living epidermis (with a thickness of around 70 μm) and the papillary dermis (with a thickness of around 80 μm), as studied by Bhowmik et al. [
21].
In the present work, consideration is given to a tool for the early detection of skin cancer, and the two intermediate phases of the development of cancer in human skin are analyzed. At first, the predictions are delivered for cases where the cancer appears only in the basal layer, and normal other layers of the human skin are conspired (
Figure 6). Then, predictions are discussed for cases where the cancer develops similarly on both sides of the basal layer (i.e., the rest of the living epidermis, with a thickness of 70 μm) and the papillary dermis (with thickness: 80 μm), producing a 160-μm total thickness of the affected skin tissue (
Figure 7).
Figure 6 presents temporal variations in the reflectance at x = 0 for the first case where the cancer is developed only in the basal layer (thickness: 10 μm) in consideration of the three main types of malignancies (i.e., cutaneous melanoma (CM), nodular basal cell carcinoma (NBCC) and squamous cell carcinoma (SCC)). These skin malignancies differ in their optical properties, as tabulated in
Table 3.
Figure 6 shows that, for normal skin, the peak magnitude of the reflectance is obtained at time t = 3.85 ps. However, the peak of magnitudes in the existence of CM, NBCC and SCC malignancies in the basal layer manifest a little ahead of the normal tissue (at 0.06, 0.15 and 0.17 ps, respectively). In addition, these peak magnitudes of reflectance are less than that of the normal skin. By comparison to the last peak magnitude cited for the normal skin, the differences are 0.00154, 0.0016 and 0.002 for CM, NBCC and SCC, respectively (
Figure 6).
In the second case, where the cancer has spread similarly on both sides of the basal layer (consisting of the living epidermis and papillary dermis) up to a total thickness of 160 μm,
Figure 7 shows the temporal signals of the reflectance for human skin for CM, NBCC and SCC. Variances in the peak magnitudes between the normal skin and the skin with CM, NBCC and SCC malignancies are clearer than they are in the previous case (i.e., where these three types of malignancies are only located in the basal layer (
Figure 6)). For the CM, NBCC and SCC malignancies, these variances are 0.026, 0.0305 and 0.0351, respectively. Thus, the difference is approximately 16 times more than the same difference for the first case where the malignancy exists only in the basal layer (
Figure 6). Similarly, this difference is also important in the decaying region (
Figure 7).
It is notable that the CM, NBCC and SCC malignancies decrease the absorption coefficient and scattering coefficient, as shown in
Table 1 and
Table 3. The emission phenomena is negligible in the case of a skin subjected to ultrafast lasers, whereas it is the scattering that gives in to the reflectance, as described above. Thus, decreasing scattering in the skin produces low magnitudes of reflectance. In addition, when this disease develops in the rest of the living epidermis as well as papillary dermis (as in the second case), the laser light scatters in additional cells (160 μm) of the human tissues, so that the reflectance decreases even more.
The results show that the CM malignancy has the peak magnitude in human skin when compared against the two other malignancies, due its superior scattering coefficient (the scattering coefficients are 9.185, 8.140 and 6.680 for the skin with CM, NBCC and SCC (
Table 3), respectively). It can be seen in
Figure 8,
Figure 9,
Figure 10 and
Figure 11 that for all cases of human skin with and without malignancies, the peak magnitudes occur near the cut-off time of input laser light (3 ps).
3.3. Parametric Analysis
In this section, the effects of two main parameters are analyzed in detail: laser wavelengths, and the variations of different growth phases of cutaneous melanoma on the radiation of ultrafast laser interactions within human skin.
3.3.1. Effects of Laser Light Wavelength
In the present work, only three different laser wavelengths (520, 785 and 840 nm) are considered.
Table 1 shows the absorption coefficient, the scattering coefficient and the anisotropic factor of the human skin at 785 nm.
Table 2 summarizes these properties at 520 and 840 nm. Additionally, three laser pulse widths (1, 10 and 25 ps) are analyzed.
Figure 8 and
Figure 9 show the temporal transmittance and reflectance signals from normal skin subjected to a laser at these three different wavelengths and three laser pulse widths. The increase of the laser wavelength decreases the magnitudes of these two signals due to the decrease in the optical thickness of skin when the laser wavelength varies from
λ = 840 nm to
λ = 785 nm.
In addition, laser diffuses to a greater distance at higher wavelengths at lower wavelengths, which can be shown in the difference in magnitude of the transmittance (
Figure 8).
In the case of the much smaller wavelength (
λ = 520 nm), no transmittance signals appear at the boundary opposite to the laser source (i.e., the boundary at x =
Lx (
Figure 8)). This is principally due to the attenuation of the light, which decreases with an increase of the laser wavelength, as shown in
Table 1 and
Table 2. Furthermore, the human skin is optically thick at the smaller wavelength of
λ = 520 nm, so no transmittance can reach the boundary opposite the laser source. On the other hand, the reflectance signals at x = 0, from the human skin subjected to laser light at the smaller wavelength of
λ = 520 nm, display an augmentation in the peak magnitude in comparison to the larger wavelengths of 785 and 840 nm when the laser width is 1 ps (
Figure 9). For small wavelengths, most of the scattered light at the skin-surface is reflected from the stratum corneum by the laser pulse below 6 ps. Therefore, the peak magnitude of the reflectance profiles of the smaller laser wavelength (
λ = 520 nm) occurs before those at larger laser wavelengths (
λ = 785 and 840 nm), as shown in
Figure 8, although
Figure 9 reveals that this trend in the reflectance signals is reversed for the laser pulse widths of 10 and 25 ps.
The increase of the laser pulse width above 10 ps (i.e., for 10 and 25 ps) increases the peak magnitude of the reflectance signals at the larger wavelengths (λ = 785 and 840 nm), and these peaks become higher than the obtained value for the smaller laser wavelength (λ = 520 nm). The input heat and time for which the pulse persists at any position are increased when the pulse width is above 10 ps. Therefore, the effect of the highest radiation arriving at the laser-source border from the human skin layers with a pulse width greater than 10 ps. The higher wavelength limits the outcome of the important portion of the radiation reaching the laser-source boundary from the stratum corneum. However, for the case of λ = 520 nm, most of the light scatters from the stratum corneum, so the signals still seem ahead of those obtained for the two other higher wavelengths.
3.3.2. Effect of Different Growth Phases of Cutaneous Melanoma
Biomedical diagnosis shows that the volume of the cancerous zone increases with time. The skin cancer starts within a few cells, then grows to additional regions of the tissue, eventually reaching the phase of metastasis when it spreads to other organs of the body. Optical and thermal specifications of a skin cancer change according to its grade [
31]. Further, the scattering coefficient differs over a wide range. In the present study, the effect of different growth phases of cutaneous melanoma on the laser interaction with the skin is considered. Thus, volumes of the cancerous zones are analyzed according to the varying thicknesses of the malignant layer and their scattering coefficients. CM malignancy is the most harmful malignancy, and thus attention is given in the present work to the results from CM malignancy specifically, with only a 785-nm laser used.
3.3.3. Effect of the Volume of the Cancerous Region
The effect of the cancerous region’s volume is investigated through a consideration of human skin with CM that has spread to four different thicknesses: 10, 60, 120 and 160 μm. These thicknesses represent the spreading of CM in 10 μm of the basal layer (case 1), 30 μm of living epidermis and 30 μm of papillary dermis (case 2), 30 μm of living epidermis and 30 μm of papillary dermis (case 3) and 80 μm of living epidermis and 80 μm of papillary dermis (case 4).
Figure 10 displays the temporal variations of the normalized reflectance for these four cases. In addition, the reflectance of the normal skin is also plotted. The reflectance is shown over a period of 0 to 20 ps, which is divided into two sub-periods (0–8 and 8–20 ps) to show more of the difference between signals. It is notable that the same total thickness of human skin as in the previous studies (i.e., 8.0 mm) has been considered here. This shows that as the cancerous volume in the human skin increases, the peak magnitude of the reflectance decreases. However, an opposite trend is obtained in the decaying zone, as shown in
Figure 10. The variation in the temporal profile of the normalized reflectance thus reveals the spread of cancer in more depth.
3.3.4. Effect of the Scattering Coefficient of the Cancerous Region
Figure 11 shows the effect of the scattering coefficient of the malignancy
on the temporal reflectance profiles from human skin with CM spears in the basal layer. In the present work, four different coefficients are considered: 9.185 (the same value as the previous case), 20.00, 30.00 and 40.00 mm
−1. It is notable that because this layer is entirely full of this of this malignancy, the CM malignancy and basal layer have the same
.
The modification of the scattering coefficient of the malignancy reveals a significant variation in the peak magnitude of the reflectance, as presented in
Figure 11. This peak magnitude increases with an increase of
, and while an opposite trend is obtained in the decaying region, the effect of
is important. The normalized reflectance is higher when the scattering coefficient of the CM is higher than that for the normal human skin, although in the case of comparable scattering coefficients, the reflectance signals are practically the same. When
of the CM is smaller in comparison to its value for the normal human skin, the normalized reflectance is lower. These conclusions are explained by the fact that the reflectance is principally dominated by the scattered diffuse radiation that is received at the boundary of incidence. When
increases, the scattering increases, and thereafter a higher reflectance is obtained. The significant augmentation of the scattering character of the damaging malignant lesion has been well-verified. This can be explained by the augmentation of the size of scatterers and/or modification of the volume density of scatterers in the affected cells [
21,
27,
28].