The principles of the use of fractal analysis in the problems of polarization mapping of microscopic images of biological preparations are considered. Myocardial tissue of the deceased with various pathological and necrotic changes was selected as the object of study. A model of the polycrystalline structure of such an object is proposed. Obtained maps of the ellipticity of the polarization of microscopic images of such an object. Within the framework of fractal analysis, the statistical moments of the 1st - 4th orders were found, which characterize the distribution of the logarithmic dependences of the power spectra of polarization ellipticity maps. The criteria for differentiation of various pathological states of myocardial tissue are determined.
This report contains the results of approbations of the polarization correlometry method (PCM) – statistical mapping of biological tissues fractal structure (myocardium and brain - “fibrillar optically anisotropic networks” and the wall of the rectum - “island optically anisotropic structures”) and liquids (polycrystalline films of synovial fluid - a superposition of “structured and island networks of biological crystals").
The results of the multifunctional Stokes polarimetric mapping of the manifestations of phase and amplitude anisotropy of histological sections of the internal organs of rats are presented. The methods of statistical analysis of vector-parametric images are used. Criteria for the differentiation of pathological conditions are obtained.
A theoretical basis for the method of polarization-phase mapping of optically thin polycrystalline films of human biological fluids is given. The coordinate distributions of the magnitude of the phase shifts and the polarization-inhomogeneous microscopic images of polycrystalline films of the synovial fluid of the human joint are investigated. In the framework of the statistical (statistical moments of 1st-4th order), correlation (dispersion and kurtosis characterizing autocorrelation functions) and fractal (dispersion, characterizing the logarithmic dependencies of power spectra) approaches, objective criteria for the distribution of local contrast values are established. The possibility of differentiation of weak changes in the optical anisotropy of synovial fluid films in patients with different severity of the pathology of the knee joint has been determined. Comparative studies of the accuracy of this method and the traditional method of polarization mapping.
This work is aimed at generalizing the methods of laser polarimetry in the case of depolarizing optically anisotropic biological layers. A method of differential polarization mapping for reproducing Mueller-matrix images of fluctuations of linear and circular birefringence and dichroism of diffuse layers of biological tissues of various morphological structures is proposed and substantiated. The coordinate distributions of the elements of a second-order differential matrix of histological sections of brain tissue with a spatially structured optically anisotropic fibrillar network and parenchymal tissue of the rectum wall with an "island" polycrystalline structure were determined. Within the framework of the statistical analysis of polarization-reproduced Müller-matrix images of phase and amplitude anisotropy fluctuations, a significant sensitivity of statistical moments of the third and fourth orders to the changes in the polycrystalline structure of the depolarizing layers of biological tissues was observed.
The method of azimuthally invariant 3D Muller-matrix mapping of distributions of phase and amplitude anisotropy parameters of partially depolarizing layers of biological tissues of different morphological structures is proposed and substantiated. In the volume of biological samples, the coordinate distributions of the magnitude of the set of Mullermatrix invariants (MMI) histological sections of the myocardium tissue with a spatially structured optical anisotropic fibrillary network, as well as parenchymal tissue of the rat liver with an islet polycrystalline structure, were obtained. The "phase" dependences of the magnitude of the statistical moments of the 1 st - 4 th orders, which characterize the distributions of the MMI values of polarization manifestations of the parameters of linear and circular birefringence and dichroism of the polycrystalline component of different types of biological tissues, are determined. A comparative study was made of the possibilities of differentiation of changes in the parameters of optical anisotropy using traditional 2D and 3D Muller-matrix mapping methods. The optimal conditions for the differentiation of polycrystalline structures of biological tissues - the range of phase sections and the most sensitive parameters - are the statistical moments of the 3rd and 4th orders that characterize the distributions of MMI associated with the polarization manifestations of linear birefringence and dichroism of different types of optically anisotropic structures.
An optical model of the polycrystalline structure of the human blood film is proposed as a superposition of completely polarized and depolarized components. Analytical algorithms for describing the polarization manifestations of such components are found. A new technique for laser sounding of blood films and detection of polarization-inhomogeneous fields by means of variations in the states of polarization of the reference wave is developed. The algorithm of digital holographic reconstruction of distributions of complex amplitudes of the polarization-inhomogeneous object field of polycrystalline films of blood is used. Layered maps of the distribution of azimuth and ellipticity of polarization of the object field of polycrystalline films of blood were obtained and analyzed. 3D distributions of the linear and circular birefringence and dichroism of such films are determined. Sensitivity, specificity and balanced accuracy of the method of digital polarization-holographic 3D reconstruction of the polycrystalline structure of blood films are determined. Statistical analysis of polarization maps of the polycrystalline structure of blood films revealed objective criteria for the diagnosis of breast cancer.
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