This study focuses on the topographic structure of optical anisotropy maps (theziograms) of dehydrated blood plasma films (facies) to identify and utilize markers for diagnosing self-similarity (multifractality) in the birefringence parameters of supramolecular protein networks. The research is based on the Jones-matrix analytical framework, which describes the formation of polarization-structural speckle fields in polycrystalline blood plasma facies. In the proposed model, algorithms were developed to relate the real and imaginary parts of the complex elements of the Jones matrix to the theziograms of linear and circular birefringence. To experimentally implement these algorithms, a novel optical technology was introduced for polarization-interference registration and phase scanning of the laser speckle field of blood plasma facies. The laser-based Jones-matrix layer-by-layer theziography relies on polarization filtration and the digital recording of interference patterns from microscopic images of blood plasma facies. This process includes digital 2D Fourier reconstruction and phase-by-phase scanning of the object field of complex amplitudes, enabling the acquisition of phase sections of laser polarization-structural speckle field components scattered with varying multiplicities. Jones-matrix images of supramolecular networks, along with their corresponding theziograms of linear and circular birefringence, were obtained for each phase plane. The experimental data derived from laser layer-by-layer Jones-matrix theziography were quantitatively analyzed using two complementary approaches: statistical analysis (central moments of the 1st to 4th orders) and multifractal analysis (spectra of fractal dimension distributions). As a result, the most sensitive markers—namely asymmetry and kurtosis—were identified, highlighting changes in the statistical and scale self-similar structures of the theziograms of linear and circular birefringence in blood plasma facies. The practical aspect of this work is to evaluate the diagnostic potential of the Jones-matrix theziography method for identifying and differentiating changes in the birefringence of supramolecular networks in blood plasma facies caused by the long-term effects of COVID-19. For this purpose, a control group (healthy donors) and three experimental groups of patients, confirmed to have had COVID-19 one-to-three years prior, were formed. Within the framework of evidence-based medicine, the operational characteristics of the method—sensitivity, specificity, and accuracy—were assessed. The method demonstrated excellent accuracy in the differential diagnosis of the long-term effects of COVID-19. This was achieved by statistically analyzing the spectra of fractal dimensions of Jones-matrix theziograms reconstructed in the phase plane of single scattering within the volume of blood plasma facies.

The article describes a technique for digital holographic reconstruction of complex amplitude fields in diffuse blood facies using laser polarization-interference phase scanning to isolate a single scattered component of the object field. This method serves as the basis for developing algorithms for Mueller-matrix reconstruction of linear and circular birefringence parameters in the polycrystalline architectonics of blood facies. Statistical (central moments of the 1st-4th orders) and multifractal analyses (fractal dimension spectra) are applied to study the optical anisotropy maps of polycrystalline networks during blood dehydration. The study explores a practical application in the differential diagnosis of blood loss volume, identifying higher-order central moments (skewness, kurtosis) as sensitive markers. The method achieved a maximum accuracy of 92.9% in differentiating blood loss volume.

A new polarization-interference biomedical diagnostic three-dimensional (3D) Jones-matrix technology with digital Fourier reconstruction of layered maps of optical anisotropy (thesiograms) of dehydrated films (facies) of biological fluids of human organs is presented and experimentally tested. An original model of layered phase scanning of polycrystalline architectonics of supramolecular networks of biological fluid facies is proposed for the purpose of theoretical justification and prognostic use of the obtained results. On its basis, algorithms of Jones-matrix reconstruction of thesiograms of birefringence and dichroism of facies of synovial fluid, bile and blood are found. As a result, layered thesiograms of linear and circular birefringence and dichroism of facies with different spatial-angular architectonics of supramolecular networks are experimentally obtained for the first time. Within the framework of statistical analysis of experimental data, new objective markers (asymmetry and excess of optical anisotropy parameter distributions) for diagnostics of pathological changes in the optical anisotropy of biological fluid facies were defined and clinically tested. As a result, an excellent level of balanced accuracy of the developed polarization-interference Jones-matrix method of layer-by-layer reconstruction of thesiograms of polycrystalline supramolecular networks in differential diagnostics of bile facies (cholelithiasis), synovial fluid (reactive synovitis-septic arthritis) and whole blood (follicular adenoma-papillary thyroid cancer) was achieved.

A 3D phase scanning method was applied to study blood plasma facies, generating layered polarization maps of the object field. The most sensitive parameters to changes in birefringence distribution were identified. Multifractal analysis using wavelet transforms and fractal dimension spectra provided specific insights into the scale self-similarity of the polarization maps. The multifractal spectra of ellipticity distributions were algorithmically derived, revealing that the third- and fourth-order statistical moments were most sensitive to changes in the supramolecular networks of the facies. These findings were successfully applied to differentiate post-COVID-19 effects with high accuracy.

The presented results are from the multifractal analysis of the polarization-correlation maps of the modulus |𝑆𝐾4 12|(𝑚 × 𝑛) of the fourth parameter of the two-point Stokes vector in microscopic images of histological sections of biological tissues with fibrous (skin dermis) and parenchymal (spleen) architectural structures of the polycrystalline component.

The results of diagnostic application of vector-parametric polarization mapping and polarization-interference phase scanning with digital holographic reconstruction of layer-wise polarization maps of azimuth and ellipticity of phase nonuniform object fields of soft tissue layers are presented for the differential diagnosis of necrotic and pathological changes in optically anisotropic polycrystalline components of myocardium - "ischemic heart disease (IHD) - acute coronary insufficiency (ACI)". All investigations within representative groups of histological sections were performed using circularly polarized laser beam illumination, ensuring azimuthal invariance and reliability of group polarization measurements. Integral and layer-wise maps, as well as histograms of distributions of random variables of azimuth and ellipticity of polarization in microscopic images of histological sections of human organ tissues with various types of pathology, are presented. Systematized tables of statistical moments of 1st-4th orders characterizing the maps of azimuth and ellipticity of polarization in microscopic images of histological sections of human organ tissues with various types of pathology are provided. A set of the most sensitive diagnostic markers, which are statistical parameters most responsive to changes in the polycrystalline structure of biological tissues, has been identified.

The fundamental component of the work contains a summary of the theoretical foundations of the algorithms of the scale-self-similar approach for the analysis of digital Mueller-matrix images of birefringent architectonics of biological tissues. The theoretical consideration of multifractal analysis and determination of singularity spectra of fractal dimensions of coordinate distributions of matrix elements (Mueller-matrix images - MMI) of biological tissue preparations is based on the method of maxima of amplitude modules of the wavelet transform (WTMM). The applied part of the work is devoted to the comparison of diagnostic capabilities for determining the prescription of mechanical brain injury using algorithms of statistical (central statistical moments of the 1st - 4th orders), fractal (approximating curves to logarithmic dependences of power spectra) and multifractal (WTMM) analysis of MMI linear birefringence of fibrillar networks of neurons of nervous tissue. Excellent (~95%) accuracy of differential diagnosis of the prescription of mechanical injury has been achieved.

Abstract This study introduces a novel approach in the realm of liquid biopsies, employing a 3D Mueller-matrix (MM) image reconstruction technique to analyze dehydrated blood smear polycrystalline structures. Our research centers on exploiting the unique optical anisotropy properties of blood proteins, which undergo structural alterations at the quaternary and tertiary levels in the early stages of diseases such as cancer. These alterations manifest as distinct patterns in the polycrystalline microstructure of dried blood droplets, offering a minimally invasive yet highly effective method for early disease detection. We utilized a groundbreaking 3D MM mapping technique, integrated with digital holographic reconstruction, to perform a detailed layer-by-layer analysis of partially depolarizing dry blood smears. This method allows us to extract critical optical anisotropy parameters, enabling the differentiation of blood films from healthy individuals and prostate cancer patients. Our technique uniquely combines polarization-holographic and differential MM methodologies to spatially characterize the 3D polycrystalline structures within blood films. A key advancement in our study is the quantitative evaluation of optical anisotropy maps using statistical moments (first to fourth orders) of linear and circular birefringence and dichroism distributions. This analysis provides a comprehensive characterization of the mean, variance, skewness, and kurtosis of these distributions, crucial for identifying significant differences between healthy and cancerous samples. Our findings demonstrate an exceptional accuracy rate of over $$90\%$$ 90 % for the early diagnosis and staging of cancer, surpassing existing screening methods. This high level of precision and the non-invasive nature of our technique mark a significant advancement in the field of liquid biopsies. It holds immense potential for revolutionizing cancer diagnosis, early detection, patient stratification, and monitoring, thereby greatly enhancing patient care and treatment outcomes. In conclusion, our study contributes a pioneering technique to the liquid biopsy domain, aligning with the ongoing quest for non-invasive, reliable, and efficient diagnostic methods. It opens new avenues for cancer diagnosis and monitoring, representing a substantial leap forward in personalized medicine and oncology.

Optical methods for diagnosing various polycrystalline objects (layers of solid and soft matter) and visualizing their structure occupy a prominent place due to their high informativeness and the possibility of multifunctional (photometric, spectral, polarimetric, and correlation) monitoring of the investigated environment. However, there is currently no unified methodological approach to diagnose such structures. In studies of solid matter layers, methods of speckle optics, Fourier optics, correlation optics, and other branches of classical optics prevail. The main fundamental directions of such research are the results of theoretical and experimental studies of photon transport in soft matter layers, specifically biological tissues. Polarimetric research has formed a separate direction in the field of optical studies of biological tissues. The analysis of the polarization characteristics of scattered radiation allows obtaining qualitatively new results about the morphological and physiological state of biological tissues, including cataracts of the lens, glucose concentration in tissues of diabetic patients, and malignant changes.

Traditional methods of imaging Muller-matrix polarimetry ensure obtaining large arrays of experimental data in the form of 16 Muller-matrix images. Processing and comparative analysis of the received information is quite time-consuming and requires a long time. A new algorithmic polarization-singular approach to the analysis of coordinate distributions of matrix elements (Mueller-matrix maps) of polycrystalline birefringent structure of biological tissues is considered. A Mueller-matrix model for describing the optical anisotropy of biological layers is proposed. Analytical correlations between polarization-singular states of the object field and characteristic values of Mueller-matrix images of birefringence soft tissue objects were found. The proposed algorithmic polarization-singular theory is experimentally verified. Examples of polarization singularities networks of Mueller-matrix maps of histological preparations of real tissues of female reproductive sphere are given. Diagnostic possibilities of the developed polarization-singular algorithms in diagnostics and differentiation of the stages of extragenital endometriosis are illustrated. Another area of biomedical diagnostics has been successfully tested: polarization-singular criteria for forensic Mueller-matrix determination of the age of myocardial injury of the deceased have been defined.

Significance:The interference-holographic method of phase scanning of fields of scattered laser radiation is proposed. The effectiveness of this method for the selection of variously dispersed components is demonstrated. This method made it possible to obtain polarization maps of biological tissues at a high level of depolarized background. The scale-selective analysis of such maps was used to determine necrotic changes in the optically anisotropic architectonics of biological tissues. Objective:Development and experimental approbation of layered phase polarimetry of repeatedly scattered fields in diffuse layers of biological tissues. Application of scale-selective processing of the found coordinate distributions of polarization states in various phase sections of object fields. Determination of criteria (markers) for histological differential diagnosis of the causes of necrotic changes in optical anisotropy of biological tissues. Approach:We used a synthesis of three instrumental and analytical methods. Polarization-interference registration of laser radiation scattered by a sample of biological tissue. Digital holographic reconstruction and layered phase scanning of distributions of complex amplitudes of the object field. Analytical determination of polarization maps of various phase cross-sections of repeatedly scattered radiation. Application of wavelet analysis of the distributions of polarization states in the phase plane of a single scattered component of an object field. Determination of criteria (markers) for differential diagnosis of necrotic changes in biological tissues with different morphological structure. Two cases are considered. The first case is the myocardium of those who died as a result of coronary heart disease and acute coronary insufficiency. The second case is lung tissue samples of deceased with bronchial asthma and fibrosis. Results:A method of polarization-interference mapping of diffuse object fields of biological tissues has been developed and experimentally implemented. With the help of digital holographic reconstruction of the distributions of complex amplitudes, polarization maps in various phase sections of a diffuse object field are found. The wavelet analysis of azimuth and ellipticity distributions of polarization in the phase plane of a single scattered component of laser radiation is used. Scenarios for changing the amplitude of the wavelet coefficients for different scales of the scanning salt-like MHAT function are determined. Statistical moments of the first to fourth orders are determined for the distributions of the amplitudes of the wavelet coefficients of the azimuth maps and the ellipticity of polarization. As a result, diagnostic markers of necrotic changes in the myocardium and lung tissue were determined. The statistical criteria found are the basis for determining the accuracy of their differential diagnosis of various necrotic states of biological tissues. Conclusions:Necrotic changes caused by "coronary artery disease-acute coronary insufficiency" and "asthma-pulmonary fibrosis" were demonstrated by the method of wavelet differentiation with polarization interference with excellent accuracy.

The presented results concern the diagnostic application of vector-parameter polarization mapping and polarization-interference phase scanning applied to layered azimuths and ellipticity polarization maps obtained with the help of digital holographic reproduction for phase-inhomogeneous tissue layers in the female reproductive system. The differential diagnosis of the pathological changes in optically anisotropic polycrystalline tissue components, specifically “benign (fibroids) and precancerous (endometriosis),” was investigated. All studies within the representative groups of the histological samples were conducted using circularly polarized laser radiation, ensuring azimuthal invariance and polarization measurement reliability. Integral and layered maps and polarization azimuths and ellipticity random variable distribution histograms were obtained from the microscopic images of histological sections from the female reproductive system tumors. Systematized tables present statistical moments which characterize azimuths and ellipticity polarization maps for fibroids and endometriosis tissues. It is shown that the statistical parameters (diagnostic markers) are the most sensitive to benign and precancerous changes in the female reproductive system tissues. The results of information analysis, including the accuracy determination of the diagnostic vector-parameter polarization and polarization-interference methods for detecting and differentiating the samples of fibroids and precancerous endometriosis tissues in the female reproductive system, are presented.

We aimed developing and experimentally validating methods for 3D scale-selective polarimetry of multiply scattered fields in diffuse myocardium layers for mechanical myocardial injury prescription histological differential diagnostics. We used the synthesis of diffuse object field polarization-interference registration and polarization-inhomogeneous field digital holographic reconstruction and layer-by-layer complex amplitudes distributions The method for selection single and diffuse object field multiply scattered components polarization maps is proposed. The conditions for eliminating the distorting influence of a depolarized background high level are found. On the basis of еру object field single scattered component polarization maps a large-scale selective wavelet analysis the criteria (markers) for mechanical myocardial injury different prescription diagnosis was determinate. Excellent accuracy mechanical injury myocardium necrotic changes with different duration using polarization-interference wavelet differentiation were achieved.

The polarization-based optical interference approach is expanded for an express differentiation between prostate adenocarcinoma with different grades and Gleason scores. The approach is founded on evaluation of local contrast of polarized interference patterns originated by a superposition of reference laser beam and interference of light transmitted through the tissue sample placed in the image plane. The observed polarization-based optical interference patterns are linked directly to the morphology of the biological tissue under investigation. The polarization patterns obtained for three sets of histological sections of the prostate tumour biopsy samples are further processed with the statistical moments of 1st to 4th order. The developed approach is implemented for assessment of histological sections of the prostate tumour tissues with high, moderately and poorly differentiated adenocarcinoma. The application of the developed polarization-based optical interference approach demonstrates a high (> 90%) level of accuracy.

A new local-topological approach to describe the spatial and angular distributions of polarization parameters of multiply scattered optically anisotropic biological layers of laser fields is considered. A new analytical parameter to describe the local polarization structure of a set of points of coherent object fields, the degree of local depolarization (DLD), is introduced for the first time. The experimental scheme and the technique of measuring coordinate distributions (maps) of DLD The new method of local polarimetry was experimentally tested on histological specimens of biopsy sections of operatively extracted breast tumors. The measured DLD maps were processed using statistical, autocorrelation and scale-sampling approaches. Markers for differential diagnosis of benign (fibroadenoma) and malignant (sarcoma) breast tumors were defined.

Statistical analysis of coordinate distributions of random intensity values in the points of digital images of histological slices of skin dermis with different degrees and causes of lesions was performed. From the point of view of forensic medicine, the possibility of diagnosing and delimiting the surfaces (both damaged and not damaged) of biological tissues into statistical and fractal images of the intensity distribution of their images is promising.

The relationship between the changes in the birefringence of fibrillar biological crystallites and the distribution of the values of the Mueller-matrix images of histological sections of biological tissues was revealed. On this basis, the effectiveness of a statistical analysis of the distribution of the values of the phase Mueller-matrix image of a birefringent protein network in differentiating optically thin histological sections of a benign and malignant uterine wall biopsy was demonstrated for the first time. The Fourier-stokes method of polarimetry of the spatial frequency spectra of laser images was developed, based on cross-correlation analysis of polarization maps with the determination of a set of statistical moments of the 1st–4th orders characterizing the distribution of orthogonal (in two mutually perpendicular scanning directions) autocorrelation functions and logarithmic dependences of power spectra of coordinate distributions of azimuth and polarization ellipticity. Based on this, the differentiation of pathological conditions of biological tissues (histological sections of a biopsy of a benign and malignant tumor of the rectum) in the Fourier plane.

Experimental investigations of the coordinate distributions of the values of the elements of the Mueller matrices of histological sections of biological tissues were carried out at the location of the Stokes polarimeter. As the main information arrays, we will use the data of analytical modeling a set of values of azimuthally independent Mueller-matrix invariants (MMI). The analysis of the magnitudes of the statistical moments of the first and fourth orders characterizing the distribution of values MMI revealed the maximum average and dispersion values for the Mueller-matrix images of invariants associated with the influence of linear birefringence. The results obtained suggest a fairly high level of balanced accuracy of azimuthally independent Mueller-matrix mapping in the differentiation of changes in the optical anisotropy of benign and malignant tumors of human organs. According to the criteria of evidence-based medicine, the parameter $$R\left( {M_{44} ,\;\Delta M} \right)\ 70\%$$ meets satisfactory quality and $$R\left( {M_{14} ,\;M_{41} } \right)\ 80\%$$ meets good quality. Mueller-matrix mapping of blood-filled biological tissues has proven effective in the differential diagnosis of inflammatory processes of appendicitis tissue—balanced accuracy $$Ac = 78\% - 83\%$$ ).