A New Method of Mueller-Matrix Diagnostics and Differentiation of Early Oncological Changes of the Skin Derma

The paper deals with investigation of the processes of laser radiation transformation by biological crystals networks using the singular optics techniques. The results obtained showed a distinct correlation between the points of “characteristic” values of coordinate distributions of Mueller matrix (Mik = 0, ± 1) elements and polarization singularities (Land C-points) of laser transformation of biological crystals networks with the following possibility of Mueller-matrix selection of polarization singularity. The technique of Mueller-matrix diagnostics of pathological changes of skin derma is proposed.


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A new approach to description of the BT laser images based on the analysis of coordinate distributions of polarization singularities became developed the above-mentioned statistical [13][14][15][16][17][18][19][20][21][22].Linearly (L-points) and circularly (Cpoints) polarized states of light oscillations belong to them.For L-points the direction of the electric-intensity vector's rotation is indefinite (singular).For a C-point, the polarization azimuth of the electric intensity vector is indefinite.
Investigation of laser images of the connective tissue layers revealed a developed network of polarization singularities [23][24][25][26], which was quantitatively estimated in the form of distribution of the amount of L-and C-points.By means of the analysis of the given distribution's statistical moments of the 1st-4th orders (the technique of polarization mapping) the criteria of diagnostics of oncological changes of uterus neck tissue were found.
It should be pointed out that singular approach is predominantly realized out of the analysis of the mechanisms of forming polarizationally heterogeneous laser images of BT by an extracellular matrix.Thus, development of laser polarimetry techniques based on determination of singular interconnections "object-field" in order to find new methods of diagnostics of transformation of the BT extracellular matrix orientation-phase structure connected with precancer changes of their physiological state is very important.
To solve such a problem, we should revert to the analysis of optical properties of biological crystals' nets, comprehensively described by the Mueller matrix though within a singular approach.

A Brief Theory of the Mueller Matrixes Approach in the Analysis of the Biological Tissue Birefringent Nets Polarization Properties
The use of the fourth parameter of the Stokes vector appears to be a suitable and widely applied means of such singularities representation According to analysis of (1) and ( 2), one can see the interconnection between the polarization singular states and certain (characteristic) values of orientation ρ * and phase δ * parameters of the BT crystals' nets of the extracellular matrix ρ * = 0 0 ; ±45 0 90 0 ; As it can be seen, relations (3) are the necessary terms for forming polarization singular states of the laser beam (L-(δ = 0 • , 180 • ) and C-(δ = ±90 • ) points) by optically coaxial birefringent crystal.

Considering expressions (1)-(3) the characteristic values M *
ik were defined that determine the L-and C-points in laser image of the extracellular matrix of the BT layer: (i) the values M 44 = 0 and V 4 = ±1 determine the complete set of ± C-points (δ = ±90 • ); (ii) the complete set of L-points (δ = 0 • ) of the laser image is caused by the terms M 22 = M 33 = M 44 = 1 and V 4 = 0.
Mueller-matrix analysis enables to perform the sampling of polarization singularities of the laser image, formed by biological crystals with orthogonally oriented (δ = 0 • , 90 (ii) "orthogonal" L 0;90 -and L 45;135 -points Thus, measuring the coordinate distributions of the characteristic values (M * ik = 0, ±1) of the BT Mueller matrix elements enables not only to foresee the scenario (M * ik → V * 4 ) of forming the ensemble of polarization singularities (V 4 = 0, ±1) of its image, but also to additionally realize their differentiation, conditioned by the specificity of orientation structure of biological crystals.The optical thin (the absorption coefficient τ < 0, 1) BT histological sections were used as the objects of investigation.In this situation, one has a single scattering regime of laser radiation scattered by BT network and the narrowband scattering indicatrix is formed (95% of energy is  concentrated within the angle cone ΔΩ ≤ 15 0 ).Therefore, the speckle background formation in the BT histological section image due to scattering on optical elements is insignificant.

The Scheme and Methods of Experimental Investigations
At the first stage the interconnections (M * ik → V * 4 ) of matrix and polarization singularities were investigated on the example of histological section of healthy skin derma layer.
Figure 2 represents coordinate distributions of matrix elements M 44,24,34 (m×n) of histological section of skin derma and the fourth parameter V 4 (m × n) of its image's Stokes vector with the characteristic values 0, ±1 plotted on them (within the marked 100 pix × 100 pix sampling plot).
It can be seen from the data obtained that there is direct correlation between the coordinate (k, Analytically substantiated and experimentally proven interconnections between the matrix and polarization singularities were used as the basis for Mueller-matrix singular diagnostics of oncological changes of the tissues of women's reproductive sphere.

Mueller-Matrix Diagnostics and Differentiation of Pathological Changes of the Skin Derma
Three groups of histological sections of the main tissue of skin derma-were used as the objects of investigation: (i) biopsy of the sound tissue of skin derma (type "A"-Figure 3   (iii) biopsy of the skin derma in cancer state (type "C"-Figure 3(c)).To determine the criteria of Mueller-matrix diagnostics of skin derma oncological state and differentiation of its severity degree the following technique was used: (i) coordinate networks of characteristic values of matrix elements M * 44,24,34 (m×n) = 0, ±1 were scanned in the direction x ≡ 1, . . ., m with the step Δx = 1 pixel; (ii) within the obtained sampling (1 pix × n pix ) (k= 1,2,...,m ) for coordinate distribution of the element M 44 (m×n) the total amount (N (k) ) of characteristic points (0, ±1), which set the complete ensemble of singular points was calculated and the dependencies N(x) ≡ (N (1) , N (2) , . . ., N (m) ) were determined; (iii) distributions of the number of "orthogonal" singular L-and ±C-points were determined according to the terms (4) and ( 5); + N L M 24,42 = 0 , (iv) statistical moments of the 1st-4th orders of the obtained distributions of N(x) amount of singularities were calculated according to the algorithms Figures 4, 5, and 6 show the networks of characteristic values M * 44,24,34 (m × n) of coordinate distributions of matrix elements M 44,24,34 (m × n) of histological sections of skin derma of "A", "B", "C"-types.
Figure 7 illustrates the distributions of the number of characteristic values N(x), N 0,90 (x), N 45,135 (x) of skin derma tissues of "A" (left column), "B" (central column), "C" (right column) types.The comparative analysis of the data obtained shows that (i) coordinate distributions of the elements M 44,24,34 (m× n) of Mueller matrix of skin derma tissue of all types is characterized by individual (according to quantitative and topological structure) networks of characteristic points (Figures 4-6);

Advances in Optical Technologies
(ii) total amount of ±C-points (M * 44 (m × n) = 0) sequentially increases for the samples of skin derma of "A", "B", "C" types (Figures 4(a The obtained results can be connected with the increase of birefringence (Δn ≈ 1.5 × 10 −2 ) of collagen fibrils of pathologically changes skin derma of "B"-and "C"-types.Besides, at early stages (precancer) the directions of the growth of newly formed fibrils are being formed.At cancer states such pathologically changed fibrils form specifically oriented network of biological crystals.
In terms of physics, such morphological processes are manifested in the increase of probability of forming the ±C- points (skin derma samples of "B" and "C"-types), as well as in appearance of asymmetry between ranges of dependences values N 0,90 (x) and N 45,135 (x), which characterize the number of orthogonal L-and C-points.

Conclusions
Correlation between the coordinate locations of characteristic points of 2D elements of Mueller matrix of optically thin layer of biological tissue and the network of L-and C-points in its laser image is defined.The potentiality of Muellermatrix sampling of polarization singularities formed by biological crystals with orthogonally oriented (ρ = 0 • , 90 • and ρ = 45 • , 135 • ) optical axes is shown.The efficiency of Mueller-matrix diagnostics not only for oncological changes of skin derma tissue but also for differentiating their severity degree is demonstrated.

Figure 1
Figure1shows traditional optical scheme of polarimeter for measuring due to Gerrard technique[27] of Stokes parameters and elements of Mueller matrix of the BT histological sections.The parallel (Ø = 10 4 μm) beam of He-Ne laser (λ = 0.6328 μm, W = 5.0 μW) was used as an illuminator.Polarization illuminator consists of quarter-wave plates 3, 5 and polarizer 4, and it sequentially forms a series of linearly polarized (I 0 , I 45 , I 90 , I 135 ) with azimuths 0 • , 90 • , 45 • , 135 • , and right-hand (I ⊗ ) and left-hand (I ⊕ ) circularly polarized probing BT laser beams.The BT images made by microobjective (4×) 7 were projected into the plane of a light-sensitive plate (m × n = 800 × 600 pixels) of CCD-camera 10.Polarization analysis of the BT images was performed by means of polarizer 9 and quarter-wave plate 8.The optical thin (the absorption coefficient τ < 0, 1) BT histological sections were used as the objects of investigation.In this situation, one has a single scattering regime of laser radiation scattered by BT network and the narrowband scattering indicatrix is formed (95% of energy is
)-6(a)); (iii) dependencies N 0,90 (x) of the number of characteristic values of matrix elements (8) and (9) for the samples of skin derma tissue of all types are similar in their structure (Figures 7(d), 7(e) and 7(f)); (iv) distributions N 45,135 (x) for the samples of skin derma tissue of "B"-type are characterized by sufficient increase (by 2-3 times) of the number of characteristic values in comparison with similar dependencies N 0,90 (x) (Figures 7(e) and 7(h)).