Introduction
Theoretical background
Experimental approach
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birefringence (\( L{B}_{0,90};\kern0.5em L{B}_{45,135};\kern0.5em C{B}_{\otimes, \oplus } \)):
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dichroism (\( L{D}_{0,90};\kern0.5em L{D}_{45,135};\kern0.5em C{D}_{\otimes, \oplus } \)):
Brief description of the facilities
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brain tissue-geometric thickness l = 60μm; coefficient of attenuation (extinction) τ = 0.21; degree of depolarization of laser radiation Λ = 43%;
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rectal wall tissue-l = 60μm; τ = 0.32; Λ = 58%;
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tissue samples of the vaginal wall-l = 60μm; τ = 0.26 ÷ 0.29; Λ = 47 % − 52%.
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birefringent spatially structured fibrillar nerve fiber networks of brain tissue (fragment (a));
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“islands” of optically active birefringent fibers of loose connective tissue of the rectum wall (fragment (b));
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optically anisotropic fibers of loose connective tissue and
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ibrillar myosin nets of healthy (fragment (c)) and pathologically altered (fragment (d)) vaginal wall.
Results and discussion
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determination of the magnitude and ranges of the changes in the statistical moments of the first to fourth orders Zi = 1; 2; 3; 4, which characterize the distributions\( {\displaystyle \begin{array}{l}L{B}_{0,90};L{B}_{45;135};C{B}_{\otimes, \oplus };\\ {}L{D}_{0,90};L{D}_{45;135};C{D}_{\otimes, \oplus}\end{array}} \)(Tables 1 and 2);
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comparative analysis of the diagnostic efficiency of our method and the traditional methods of direct polarization and Mueller matrix mapping (Table 5).
Zi | LB0; 90 | LB45; 135 | CB⊗; ⊕ | LD0; 90 | LD45; 135 | CD⊗; ⊕ |
---|---|---|---|---|---|---|
Z1 | 0.015 | 0.025 | 0.01 | 0.074 | 0.085 | 0.065 |
Z2 | 0.03 | 0.04 | 0.02 | 0.087 | 0.07 | 0.06 |
Z3 | 0.11* | 0.21 | 0.17* | 0.82* | 0.57 | 1.37* |
Z4 | 0.18* | 0.27 | 0.23* | 1.12* | 0.33 | 1.76* |
Zi | LB0; 90 | LB45; 135 | CB⊗; ⊕ | LD0; 90 | LD45; 135 | CD⊗; ⊕ |
---|---|---|---|---|---|---|
Z1 | 0.011 | 0.017 | 0.015 | 0.055 | 0.05 | 0.025 |
Z2 | 0.02 | 0.025 | 0.02 | 0.048 | 0.06 | 0.04 |
Z3 | 0.38* | 0.24* | 0.41 | 0.52* | 0.18* | 0.97 |
Z4 | 0.44* | 0.32* | 0.53 | 0.88* | 0.34* | 0.58 |
Zi | LB0, 90 | Ac, % | LB45; 135 | Ac, % | CB⊗, ⊕ | Ac, % | |||
---|---|---|---|---|---|---|---|---|---|
Z1 | 0.04 ± 0.003 | 0.03 ± 0.002 | 74 | 0.045 ± 0.003 | 0.033 ± 0.002 | 78 | 0.025 ± 0.002 | 0.028 ± 0.002 | 60 |
Z2 | 0.06 ± 0.004 | 0.045 ± 0.003 | 76 | 0.055 ± 0.004 | 0.04 ± 0.003 | 80 | 0.021 ± 0.001 | 0.031 ± 0.002 | 66 |
Z3 | 0.31 ± 0.017* | 0.48 ± 0.029* | 82* | 0.43 ± 0.027* | 0.87 ± 0.052* | 88* | 0.32 ± 0.018* | 0.51 ± 0.029* | 84* |
Z4 | 0.44 ± 0.027* | 0.69 ± 0.041* | 86* | 0.62 ± 0.039* | 0.96 ± 0.062* | 86* | 0.38 ± 0.022* | 0.62 ± 0.036* | 88* |
Zi | LD0, 90 | Ac, % | LD45; 135 | Ac, % | CD⊗, ⊕ | Ac, % | |||
---|---|---|---|---|---|---|---|---|---|
Z1 | 0.08 ± 0.005 | 0.065 ± 0.004 | 72 | 0.07 ± 0.004 | 0.05 ± 0.003 | 82 | 0.065 ± 0.004 | 0.046 ± 0.003 | 78 |
Z2 | 0.09 ± 0.006 | 0.07 ± 0.004 | 78 | 0.09 ± 0.006 | 0.06 ± 0.004 | 86 | 0.075 ± 0.005 | 0.057 ± 0.004 | 76 |
Z3 | 0.48 ± 0.028* | 0.92 ± 0.0049* | 90* | 0.41 ± 0.025* | 0.24 ± 0.014* | 94* | 0.29 ± 0.017* | 0.12 ± 0.007* | 92* |
Z4 | 0.34 ± 0.019* | 0.76 ± 0.042* | 94* | 0.32 ± 0.019* | 0.18 ± 0.011* | 92* | 0.36 ± 0.021* | 0.15 ± 0.008* | 90* |
Zi | {α; β} | {Mik} | (LB0, 90; LB45; 135; CB⊗, ⊕) | (LD0, 90; LD45; 135; CD⊗, ⊕) |
---|---|---|---|---|
Z1 | 54–60% | 58–62% | 60–78% | 72–82% |
Z2 | 55–62% | 60–64% | 66–80% | 76–86% |
Z3 | 63–65% | 65–69% | 82–88%* | 90–94%* |
Z4 | 61–67% | 64–68% | 86–88%* | 90–94%* |
Differential matrices of the first order of spatially structured fibrillar networks
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The asymmetric structure of the histograms of distributions of the linear and circular dichroism (LD0; 90; LD45; 135; CD⊗; ⊕) parameters (fragments (4)–(6) and, conversely, sufficiently symmetrical bell-shaped structure of histograms of distributions of the linear and circular birefringence (LB0; 90; LB45; 135; CB⊗; ⊕) parameters (fragments (1)–(3)). From the physical point of view, these facts can be related to the different multiplicities of the “non-absorbing” (phase anisotropy—“q-acts”) and “absorbing” (amplitude anisotropy—“k-acts”) interaction of laser radiation with optically anisotropic structures of biological tissue of brain—q ≻ ≻ k. This difference is also determined by the fact that in the red «section of the spectrum, the probability of absorption is significantly lower than that of Fresnel transformations of laser waves by birefringent refractive collagen fibrils formed by optically active protein molecules. Due to the influence of these two factors in accordance with the central boundary theorem [44], the average values of the linear (LB0; 90; LB45; 135) and circular (CB⊗; ⊕) birefringence appear to be almost normally distributed. On the contrary, the values of the linear (LD0; 90; LD45; 135) and circular (CD⊗; ⊕) dichroism parameters of collagen networks are distributed asymmetrically.
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The predominance of the mechanisms of linear birefringence and dichroism (average values and range of histogram variation presented in fragments (4), (5)) over optical activity and circular dichroism (fragment (6))—\( {\displaystyle \begin{array}{l}L{B}_{0,90};L{B}_{45;135}>C{B}_{\otimes, \oplus };\\ {}L{D}_{0,90};L{D}_{45;135}>C{D}_{\otimes, \oplus}\end{array}} \)is due to the “developed” fibrillar structure of brain tissue.
Differential matrices of the first order of “islet” polycrystalline structures of parenchymatous tissue
Differential diagnosis of pathological changes in the polycrystalline structure of partially depolarizing layers of biological tissues
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in the operatively extracted (prolapse of the genitalia) wall of the vagina it were visually determined areas of healthy and pathologically altered tissue;
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two groups of samples were formed: histological sections of tissue from such areas;
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by means of histological method (“gold standard”) for each sample, its state was determined—“norm” (group1, 32 samples) or “pathology” (group 2, 32 samples);
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within the limits of each group of samples with the verified diagnosis, the average values (\( {\overline{Z}}_{i=1;2;3;4} \)) and standard deviations (±2σ) of the magnitude of the statistical moments that characterize the distributions\( \left(\begin{array}{l}L{B}_{0,90};L{B}_{45;135};C{B}_{\otimes, \oplus };\\ {}L{D}_{0,90};L{D}_{45;135};C{D}_{\otimes, \oplus}\end{array}\right) \) were calculated;
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the parameter Zi was considered statistically reliable if its average value \( {{\overline{Z}}^{(1)}}_i \) in group 1 does not coincide with the value \( {{\overline{Z}}^{(2)}}_i\pm 2\sigma \) in group 2 and vice versa;
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on this basis, the parameters \( {Z}_{i=1;2;3;4}^{\ast } \)of objective differentiation of the samples of both groups were determined.
Comparative studies of the diagnostic efficiency of direct polarization, Mueller matrix, and differential matrix mapping
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Polarization mapping {α, β} is not applicable (Ac < 70%) for differential diagnosis of the vagina wall with genital prolapse.
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Accuracy of differential diagnosis by direct Mueller matrix mapping {Mik} method reaches satisfactory (Ac = 71–72%) level.
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Efficiency of differential matrix mapping lies within good (Ac > 80%) and excellent quality (Ac > 90%) (Table 5) (highlighted in gray).