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This research is aimed to investigate the reliability of Mueller-matrix differentiation of birefringence change of optically thick layers of biological liquid crystals at the early stages of the change in their physiological state. This is performed by measuring the set of skewness and kurtosis values of Mueller matrix image of the phase element

Among many methods of optical diagnostics of organic phase-inhomogeneous object a new technique—laser polarimetry [

To analyze this polarimetric information the following model approach was elaborated [

all the variety of human BT can be represented as four main types—connective, muscle, epithelial, and nerve tissues;

morphological structure of any BT type is regarded as a 2-component amorphous-crystalline structure;

the crystalline component or extracellular matrix is an architectonic net consisting of coaxial cylindrical protein (collagen, myosin, elastin, etc.) fibrils;

optically, the protein fibrils possess the properties of uniaxial birefringent crystals;

interaction of laser radiation with the BT layer is considered in the single scattering approximation, when the attenuation factor corresponds to

Specifically, the above mentioned model was used for finding and substantiating the interconnections between the ensemble of statistic moments of the 1st–4th orders that characterize the orientation-phase structure (distribution of optical axes and phase shifts of protein fibrils networks directions) of birefringent BT architectonics and that of 2D distributions of the elements of the corresponding Mueller matrix [

However, such techniques do not take into account the coordinate heterogeneity of orientation-phase structure of protein crystals nets of the BT layer as well as the order of scattering in its depth. Thus it is important to investigate the distribution of statistic moments of the 1st–4th orders that characterize the 2D elements of Mueller matrix not only in the section of the probing laser beam but also within the whole BT layer of various optical thickness and physiological state.

For this we shall consider the potentiality of matrix modeling of polarization properties of optically thick BT layer.

Let us represent the layer of such a biological object as the set of successively located optical thin partial layers (Figure

On the analysis of modeling polarization properties of anisotropic component of optically thick biological tissue.

Polarization properties of birefringent nets of every other BT layer are described by the Mueller matrix

Mueller matrix

for finite number (

for “infinite” (

Here

Mueller matrix of optically thick BT is determined by multiplication of partial matrix operators:

To make it simpler (without decreasing the analysis depth) further we shall consider only a 2-layered BT:

In the expanded form the matrix operator elements (

The analysis of relations (

The analysis of relations (

Thus, it is important to elaborate approximated statistical methods of experimental solution of such diagnostic task.

Generally speaking, the increase of optical thickness of biological layer results in multiple scattering regime in its volume. Such process appeared in formation of integral depolarization of laser field and results in averaging within angular aperture of photodetector of azimuth and ellipticity random values of fully polarized isolated speckles [

The histological sections of different geometrical (optical) thickness were used as the objects of investigation. The technique of obtaining of such objects is convenient: biological tissue is freezing to nitrogen temperature with the following obtaining, by means of medical microtome, the histological sections (from 10

Conventional optical scheme of polarimeter for measuring 2D distributions of the BT Mueller matrix elements is presented in Figure

Optical scheme of polarimeter, where 1: He-Ne laser; 2: collimator; 3: stationary quarter-wave plate; 5, 8: mechanically movable quarter-wave plates; 4, 9: polarizer and analyzer correspondingly; 6: object of investigation; 7: microobjective; 10: CCD camera; 11: PC.

Histological sections of BT were illuminated by a parallel beam of He-Ne laser (

The technique of measuring the ensemble (

the plane of BT histological sections (

within each of 50 areas (

for every local array

the histograms

The following histological sections of different types of rat’s tissues were investigated—connection tissue, muscular tissue, epithelial tissue, and nervous tissue. All these tissues have common optical peculiarity—the presence of birefringent network of protein fibrils [

Distributions

The choice of matrix element

The series of Figures

Coordinate and 3D distribution of the values of phase matrix element

Coordinate and 3D distribution of the values of phase matrix element

The following can be seen from the data obtained:

2D distributions of matrix elements

for the sample of healthy muscle tissue (Figure

The structure of 2D distributions of elements

Thus, phase elements

Secondly, the inflammation process is accompanied by the increase of birefringence

The histograms of distribution

Histograms of the set of skewness

The analysis of experimentally measured histograms

the change ranges of the values of skewness

extreme values of skewness in the distribution

extreme values of kurtosis in the distribution

Thus, it can be stated that for single differentiation of physiological state of optically thin layers of muscle tissue it is enough to measure the 2D phase matrix element

The series of Figures

Coordinate and 3D distribution of the values of phase matrix element

Coordinate and 3D distribution of the values of phase matrix element

It can be seen from the data obtained the following:

for the samples of the healthy and inflamed muscle tissue the same range of values change (from −0,55 to 0,55) is typical in the distribution of matrix elements

comparative visual analysis of coordinate distributions of matrix elements

Similarity of the distribution structure

Figure

Histograms of the set of skewness

The analysis of experimental data showed the following:

the skewness

histograms

extreme values of kurtosis

Thus for realization of Mueller-matrix differentiation of optically thick BT layers at early stages of changing their physiological state the measurement of distributions of the kurtosis

The Mueller-matrix approach in diagnostics and differentiation of the biological crystals networks appears to be effective for optically thick histological sections layers of human tissues (skin derma, tissues of women reproductive sphere, parenchymatous tissues) also.