Polarization-phase mapping and reconstruction of biological tissue architectonics during diagnosis of pathological lesions

Specific features of the formation of local and statistical polarization structures of laser radiation scattered in phase-inhomogeneous layers (PIL) of biological tissue (BT) were studied. The distribution of azimuth and eccentricity of boundary field polarization was found to correlate with the orientation-phase structure of multifractal PIL. A method of polarization phase reconstruction of BT architectonics was suggested.     

Polarization-based visualization of multifractal structures for the diagnostics of pathological changes in biological tissues

The dynamics of the changes in the statistical polarization structure of coherent images of biological tissues are studied for the visualization process of their optically anisotropic (collagen) structure.     

Laser probing of biological tissues and the polarization selection of their images

Problems of increasing the signal-to-noise ratio in coherent images obtained in laser polarization probing of optically anisotropic architectonics of the morphological structure of biological tissues are discussed. Possibilities of polarization selection and contrast enhancement of such images screened by other biological tissues are analyzed.     

Polarization contrast enhancement of images of biological tissues under the conditions of multiple scattering

The concept of laser polarization probing of biological tissues under the conditions of scattering of high multiplicities is analyzed and approbated experimentally. The effect of the degree of depolarization of the scattered background on the signal-to-noise ratio in coherent images of an optically anisotropic architectonic of the morphological structure of a biological tissue and of the polarization correction of the probing beam on the contrast enhancement of these images are considered.     

Laser polarimetry of polarization-phase statistical moments of the object field of optically anisotropic scattering layers

Issues related to the direct polarization-interference measurements of the second and higher statistical moments of the random object field of a phase-inhomogeneous layer are considered. The relation between the statistical parameters of the surface and volume structure of the object and the statistics of the vector laser field is determined. The results of analytical modeling are compared with direct experimental measurements.     

Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation

Chaos game representation (CGR) is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima (WTMM) method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonucleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.     

Correlation characteristics of optical coherence tomography images of turbid media with statistically inhomogeneous optical parameters

Noisy structure of optical coherence tomography (OCT) images of turbid medium contains information about spatial variations of its optical parameters. We propose analytical model of statistical characteristics of OCT signal fluctuations from turbid medium with spatially inhomogeneous coefficients of absorption and backscattering. Analytically predicted correlation characteristics of OCT signal from spatially inhomogeneous medium are in good agreement with the results of correlation analysis of OCT images of different biological tissues. The proposed model can be efficiently applied for quantitative evaluation of statistical properties of absorption and backscattering fluctuations basing on correlation characteristics of OCT images.     

Propagation of stochastic electromagnetic vortex beams through the turbulent biological tissues

The general analytical expression of the stochastic electromagnetic vortex beams through turbulent biological tissues is derived based on the fractal model. The statistical properties, including the spectral density, the spectral degree of coherence and the spectral degree of polarization are investigated in detail. It can be found that the normalized spectral density of the stochastic electromagnetic vortex beams with higher topological charge is less influenced by turbulence than that with lower topological charge. In addition, the change of the degree of polarization versus propagation distance of the anisotropic vortex beams in biological tissues differs from that of the isotropic vortex beams. The findings might be useful in the investigation of the structures of biological tissues and operation of communication and sensing systems involving biological tissues turbulence channels.     

Investigating the nanostructured gold thin films using the multifractal analysis

The atomic force microscopy images representing the surface morphology of the nanostructured gold thin films of thickness of 20, 50 and 200 nm, respectively, were investigated using the multifractal analysis. The interface width and growth exponent corresponding to films of different thicknesses were estimated. The surfaces having greater roughness give rise to larger nonlinearity and wider width of the multifractal spectrum. The statistical tests confirm that the gold thin film surfaces under investigation are multifractal in nature.     

Correlation processing and wavelet analysis of polarization images of biological tissues

Methods of polarization filtering, correlation processing, and wavelet analysis of coherent images of physiologically normal and necrotically changed (myocardium infarct) muscular tissues are considered. A technique of early optical diagnostics of the appearance of these biological objects and the course of their degenerative-dystrophic changes is proposed.     

Investigation of the fractal features of the polarization reversal processes in ferroelectric crystals under injection conditions

The features of polarization reversal processes of ferroelectric crystals are analyzed under the condition that electron beams of a scanning electron microscope are injected into the subsurface layer of a sample. The proposed mathematical model describes the dynamics of the polarization switching of a ferroelectric crystal using the injection contact technique. The simulation relies on the basic principles of scale invariance in domain structure evolution. The polarization switching current of ferroelectric crystals is investigated as the dynamic characteristic of a finite medium exhibiting fractal behavior. The application of fractal and multifractal analysis of a time series enables us to calculate the fractal dimension of the polarization reversal process under injection conditions.     

Spectral-morphological analysis of acoustical images of biological tissues and composite structures: II. Test classification of acoustomicroscopic images

Results of numerical classification of different structure types in acoustomicroscopic images of real biological tissues and composite structures are reported. The classification is based on the Bayesian statistical hypothesis testing method. General realizations of this method in the form of the spatial-spectrum and spectral-morphological approaches are considered. The spatial-spectrum approach cannot discriminate between morphologically different structures with statistically identical power spectra. This disadvantage is eliminated in the spectral-morphological approach, which uses information on the spectral properties of the structure type being classified, as well as on the particular form of its characteristic features. The general approaches and their particular realizations (Bartlett’s and Pisarenko’s methods) are compared as applied to practical problems.     

Spectral-morphological analysis of acoustical images of biological tissues and composite structures: I. Statistical approach

The problem of classifying images of different biological tissues and composite structures is solved using the spectral and morphological analysis based on the Bayesian method for statistical hypothesis verification. The basis functions are constructed from a learning set. The spectral approach and its particular realizations in the form of Bartlett’s and Pisarenko’s methods adapted to the problem are considered. An extension of the spectral approach to the more general spectral-morphological classification is proposed. The latter takes into account the spatial-spectrum features of the structure types to be classified, as well as their morphological features, which manifest themselves in a correlation between the expansion coefficients. The characteristic properties of the spectral and spectral-morphological approaches are discussed using numerical classification examples. The method is generalized to the classification of multiparameter images of structures, which may be represented, for example, by the distributions of the sound velocity, density, absorption, and values of the nonlinear parameter.     

New enhancement of infrared image based on human visual system

Infrared images are firstly analyzed using the multifractal theory so that the singularity of each pixel can be extracted from the images. The multifractal spectrum is then estimated, which can reflect overall characteristic of an infrared image. Thus the edge and texture of an infrared image can be accurately extracted based on the singularity of each pixel and the multifractal spectrum. Finally the edge pixels are classified and enhanced in accordance with the sensitivity of human visual system to the edge profile of an infrared image. The experimental results obtained by this approach are compared with those obtained by other methods. It is found that the proposed approach can be used to highlight the edge area of an infrared image to make an infrared image more suitable for observation by human eyes.     

Polarization-Sensitive Spectral Interferometric Optical Coherence Tomography for Human Skin Imaging

Polarization-sensitive spectral interferometric optical coherence tomography (PS-SI-OCT) is designed for imaging of the inner structure of a biological tissue with polarization properties corresponding to Müller matrix elements. With arbitrary polarization state of incident and reference light, the change of polarization state can be acquired, and the axial structure of the tissue is measured by single detection of the power spectrum, superposition of object and reference light. Using with this OCT system, a cross-sectional Müller matrix images of human skin can be observed.     

Azimuth-invariant mueller-matrix differentiation of the optical anisotropy of biological tissues

A Mueller-matrix model is proposed for analysis of the optical anisotropy of protein networks of optically thin nondepolarizing layers of biological tissues with allowance for birefringence and dichroism. The model is used to construct algorithms for reconstruction of coordinate distributions of phase shifts and coefficient of linear dichroism. Objective criteria for differentiation of benign and malignant tissues of female genitals are formulated in the framework of the statistical analysis of such distributions. Approaches of evidence-based medicine are used to determine the working characteristics (sensitivity, specificity, and accuracy) of the Mueller-matrix method for the reconstruction of the parameters of optical anisotropy and show its efficiency in the differentiation of benign and malignant tumors.     

Analysis of the spatial distribution of detector sensitivity in a multilayer randomly inhomogeneous medium with strong light scattering and absorption by the Monte Carlo method

The spatial distribution of sensitivity in the domain of detection of a fiber-optic sensor used for spectrophotometric studies of skin and other biological tissues is studied. The method and results of modeling the propagation of optical radiation in multilayer randomly inhomogeneous media with strong light scattering and absorption are presented. Owing to the small distances between the source and detector (100–800 μm), the propagation of radiation in the medium under study is modeled by the Monte Carlo method combining the calculation of true paths and the use of statistical weights. For the same reason, we represent the surface and interfaces of layers of skin as rough randomly periodic surfaces corresponding to the actual structure of human skin. The method presented can be recommended as a means for the optimum selection of an arrangement for radiation incoupling and outcoupling.     

Biological ferroelectricity uncovered in aortic walls by piezoresponse force microscopy

Many biological tissues are piezoelectric and pyroelectric with spontaneous polarization. Ferroelectricity, however, has not been reported in soft biological tissues yet. Using piezoresponse force microscopy, we discover that the porcine aortic walls are not only piezoelectric, but also ferroelectric, with the piezoelectric coefficient in the order of 1 pm/V and coercive voltage approximately 10 V. Through detailed switching spectroscopy mapping and relaxation studies, we also find that the polarization of the aortic walls is internally biased outward, and the inward polarization switched by a negative voltage is unstable, reversing spontaneously to the more stable outward orientation shortly after the switching voltage is removed. The discovery of ferroelectricity in soft biological tissues adds an important dimension to their biophysical properties, and could have physiological implications as well.     

Multifractal Structure of Intermittency in a Developed Ionospheric Turbulence

We present the results of studying the multifractal structure of intermittency in a developed ionospheric turbulence during special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005–2006. It is shown, in particular, that the determination of multidimensional structural functions of the energy fluctuations of received signals permits one to obtain the necessary information on multifractal spectra of the studied process of radio-wave scattering in the ionosphere. Experimental data on multifractal spectra of slow fluctuations in the received-signal energy under conditions of a developed small-scale turbulence are compared with the existing concept of the radio-wave scattering within the framework of the statistical theory of radio-wave propagation in the ionosphere. It is inferred that under conditions of a developed ionospheric turbulence, the multifractal structure of the intermittency of slow fluctuations in the received-signal energy is a consequence of the intermittency of small-scale fluctuations in the electron number density of the ionospheric plasma on relatively large spatial scales of about several ten kilometers. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 6, pp. 485–493, June 2008.