1 November 2005 Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state
Author Affiliations +
J. of Biomedical Optics, 10(6), 060502 (2005). doi:10.1117/1.2149844
Abstract
This is the first attempt devoted to the 1st–4th order statistic analysis of the complex degree of mutual polarization of biological tissues coherent images. The ensemble of diagnostic criteria (skewness and kurtosis of two-dimensional distributions of complex degree of mutual polarization) of pathological changes of muscular and connective (skin derma) tissues is defined.
Angelsky, Ushenko, and Ushenko: Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state

1.

Introduction

Real object fields scattered on biological tissue (BT) possess a change of both polarization and correlation characteristics.1 For analyzing these fields a new methodological approach is proposed2, 3, 4, 5, 6 based on the analysis of complex degree of mutual polarization (CDMP) V2(ri,ri+1) of BT speckle image, determined by its magnitude V2(ri,ri+1) and optical-geometric phase difference β between the oscillations in the points ri and ri+1 6:

1

V2(ri,ri+1)=V2(ri,ri+1)exp(iβ),
where

2

V2(ri,ri+1)=({[I(0)(ri+1)I(0)(ri)]12[I(90)(ri+1)I(90)(ri)]12}2+4[I(0)(ri+1)I(90)(ri+1)I(0)(ri)I(90)(ri)]12cos(δi+1δi))(I(ri+1)I(ri))
Here I(0)(ri) ; I(90)(ri) are arrays of the BT image intensities measured for passing axis orientation of the analyzer corresponding to the angles Θ=0deg and Θ=90deg ; δi+1δi is the phase difference between the orthogonal components of oscillations E(0)(ri) , E(90)(ri) and E(0)(ri+1) , E(90)(rr+1) in the points with the corresponding coordinates ri+1 and ri in the image plane.

From the physical point of view the CDMP 2-D distributions V2[I(0)(ri+1,ri);I(90)(ri+1,ri);δi+1,δi,β] characterize the degree of correlation between the states of the field polarization in its different points. Naturally this degree of correlation is determined by optical and structural characteristics of the object such as anisotropy, birefringence, etc. Pathological changes of BT are accompanied by the transformation of such a structure.7, 8 Thus the analysis of physiologically normal and pathologically changed BT by means of 2-D distributions of CDMP proves to be important.

The parameter equal to that of visibility of interference pattern (which is formed by the beams with the polarization under consideration) was the base of metrological estimation of polarization interconnection in various points of the field.6 Decomposition into two mutually-orthogonal, linearly-polarized states with the corresponding oscillations phase shift δ1 , δ2 was used for representing the arbitrary type of polarization. The measured visibility is a sum of additive partial visibilities of interference patterns formed by mutually parallel linear polarization components of two beams.9 The phase difference of oscillations in the orthogonally-polarized components forming two systems of interference beams, i.e., (δi+1δi) will show in relative shift of the interference pattern. This will also influence the resulting visibility of the whole interference pattern.

In this situation only the first of all CDMP phase components, ( δi+1δiδi+1,i and β ), has the diagnostic meaning. It is univocally interrelated with azimuths α(ri+1;ri) and ellipticities γ(ri+1;ri) distributions of polarization images by the following relation1:

3

δi+1,i=arctg{tg2γ(ri+1)[sin2α(ri+1)]1}arctg{tg2γ(ri)[sin2α(ri)]1}.
Sensitivity of the measuring polarization parameters is 1 . The phase β of CDMP defines only the shift of the resulting interference pattern as a whole in the registration plane. It is not diagnostically important in this case.

The optical scheme for experimental measuring of CDMP of BT images is presented in Fig. 1 . Illumination was realized by a collimated (=104μm) He–Ne laser beam ( λ=0.6328μm , W=5.0mW ). The polarization illuminator consisted of two quarter-wave plates and a polarizer forming an illuminating beam with the range of azimuth 0degα0180deg and with the range of polarization ellipticity 0degγ090deg . BT polarization images were projected onto the plane of a light-sensitive area (800×600pixels) of a CCD camera by means of a microscope objective. The CCD camera provided a measuring range of structural BT elements for the scales 22000μm . The polarization analysis of BT images was realized by using a polarizer. By rotating passage axis Θ of the analyzer within Θ=0deg180deg one can define arrays of α(ri),γ(ri) .

Fig. 1

Experimental setup. 1—He–Ne laser; 2—collimator; 3, 5, 8—quarter-wave plates; 4, 9—polarizer and analyzer, respectively; 6—object of investigation; 7—micro-objective; 10—CCD camera; 11—personal computer.

060502_1_040506jbo1.jpg

2.

Characteristics of the Objects of Investigation

“Optically thin” ( τd0.1 , “extinction” of radiation by a layer of thickness d ) frozen histological sections of muscular (MT) and skin derma (SD) of human tissue have been investigated. Such samples quite completely represent the main groups of the structured tissues.10 The following groups of pathology (muscular dystrophy, SD psoriasis) have been considered. The samples of physiologically normal BT (group “A”) and the samples of “conventionally” normal BT, histological sections, taken in the areas which do not correspond to localization of pathological changes in architectonics (group “B”) have been used [Figs. 2 (a1), (e1), (a2), and (e2)]. From the optical point of view pathological changes of BT structure on the early stages are accompanied by the decrease of the protein fibrils anisotropy substance forming their architectonic nets.1, 7, 8

Fig. 2

The CDMP magnitude [(c1), (g1), (c2), (g2)] of MT and SD samples correspondingly. Parts (c1) and (c2) correspond to normal samples, parts (g1) and (g2) to pathologically changed ones. The phase difference between the orthogonal components of polarization is depicted in parts (b1), (f1), (b2), and (f2). Histological images of physiologically normal and pathologically changed samples are presented in parts (a1), (a2) and (e1), (e2) correspondingly. Parts (d1), (h1), (d2), (h2) correspond to statistical distribution of CDMP magnitude.

060502_1_040506jbo2.jpg

The technique of freezing the thin layers of BT to “nitrogen” temperatures provided practically complete identity with their morphological structure both in vivo and in vitro.11 From the medical point of view the samples of groups “A” and “B” are practically indistinguishable. Traditional histochemical investigations show no differences in their physiological state.11

3.

Experimental Data Analysis and Discussion

Figure 2 represents coordinate distributions of phase δi+1,i [(b1), (f1), (b2), (f2)] and magnitude V2(Δri) [(c1), (g1), (c2), (g2)] with [(d1), (h1), (d2), (h2)] histograms of physiologically normal and pathologically changed BT coherent images. The analysis of obtained data about coordinate and statistic structure of 2-D distributions of the CDMP parameter of BT speckle images shows that distributions V2(Δri) of coherent images of all types of physiologically normal BT are rather close in their structure—mainly formed by the areas [Fig. 2(c1), (c2)] with maximally correlated state of polarization V2(Δri)1 . Distributions V2(Δri) of coherent images of the pathologically changed BT samples are formed by the areas for which the value of CDMP changes within wide limits (0V2(Δri)1) [Fig. 2(g1), (g2)]. Corresponding histograms Q[V2(Δri)] contain the ensemble of equiprobable extrema for the whole range the CDMP value changes of coherent images.

The results of comparative analysis of statistic moments of the 1st–4th orders of the V2(Δri) value of coherent images of the groups of physiologically normal (MV2*;σV2*;AV2*;EV2*) and pathologically changed (MV2;σV2;AV2;EV2) BT of all types are presented in Table 1 .

Table 1

1st–4th order statistics of CDMP of BT coherent images.

MT (37 samples)SD (34 samples)
Statistic momentsNormalPathologyNormalPathology
MV2 0.18±6% 0.96±9% 0.24±8% 0.35±10%
σV2 0.11±5% 0.67±10% 0.18±7% 0.41±9%
AV2 67.4±11% 589.7±16% 89.3±9% 436.217%±
EV2 324.2±16% 1451.3±22% 174.9±13% 981.7±21%

It can be seen that the values of statistic moments of CDMP images of physiologically normal and pathologically changed BT are sufficiently different. These differences (up to 1 order) are the most pronounced for the 3rd and 4th statistic moments.

4.

Conclusion

The results of this investigation can be applied in clinical practice in the following ways:

  • in vitro: by the use of BT biopsy technique (if it is possible);

  • in vivo: by the use of the suggested technique of 2-D analysis of BT images CDMP obtained by means of the techniques of polarization-sensitive optical coherent tomography.12, 13

References

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© (2005) Society of Photo-Optical Instrumentation Engineers (SPIE)
Oleg V. Angelsky, Alexander G. Ushenko, Yevheniya G. Ushenko, "Complex degree of mutual polarization of biological tissue coherent images for the diagnostics of their physiological state," Journal of Biomedical Optics 10(6), 060502 (1 November 2005). http://dx.doi.org/10.1117/1.2149844
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Polarization

Tissues

Biological research

Diagnostics

Statistical analysis

Tissue optics

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