Laser Polarimetry of Biological Tissues: Computer Algorithms for Data Processing in Forensic Age Determination of Injuries 9819917336, 9789819917334

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SpringerBriefs in Applied Sciences and Technology Zhengbin Hu · I. L. Bezhenar · O. Y. Vanchulyak · A. G. Ushenko · Yu. A. Ushenko · Mykhailo P. Gorsky · Igor Meglinski

Laser Polarimetry of Biological Tissues Computer Algorithms for Data Processing in Forensic Age Determination of Injuries

SpringerBriefs in Applied Sciences and Technology

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Zhengbin Hu · I. L. Bezhenar · O. Y. Vanchulyak · A. G. Ushenko · Yu. A. Ushenko · Mykhailo P. Gorsky · Igor Meglinski

Laser Polarimetry of Biological Tissues Computer Algorithms for Data Processing in Forensic Age Determination of Injuries

Zhengbin Hu School of Computer Science Hubei University of Technology Wuhan, China O. Y. Vanchulyak Bukovinian State Medical University Chernivtsi, Ukraine Yu. A. Ushenko Chernivtsi National University Chernivtsi, Ukraine

I. L. Bezhenar Bukovinian State Medical University Chernivtsi, Ukraine A. G. Ushenko Chernivtsi National University Chernivtsi, Ukraine Mykhailo P. Gorsky Chernivtsi National University Chernivtsi, Ukraine

Igor Meglinski School of Engineering and Applied Science Aston University Birmingham, UK

ISSN 2191-530X ISSN 2191-5318 (electronic) SpringerBriefs in Applied Sciences and Technology ISBN 978-981-99-1733-4 ISBN 978-981-99-1734-1 (eBook) https://doi.org/10.1007/978-981-99-1734-1 © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Acknowledgement

This work received funding from: National Research Foundation of Ukraine, Grant 2020.02/0061 and Scholarship of the Supreme Council for Young Scientists— Doctors of Sciences.

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Contents

1 Analysis of Modern Aspects of Determination of Lifetime and Injuries Prescriptions in Forensic Medicine . . . . . . . . . . . . . . . . . . . . 1.1 Modern Aspects of Determination of Lifetime and Injuries Prescriptions in Forensic Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Optical Polarization and Correlation Methods of the Diagnostics of Phase-Inhomogeneous Biological Structures in Medicine . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Materials and Methods of Research in Laser Polarimetry Data Processing of Biological Tissues for Forensic Determining the Age of Injury . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Morphological Structure of Human Skin . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Epidermis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Derma or Skin Itself . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Amorphous Skin Substance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Modelling of the Human Skin Layer as a Transformer of Laser Radiation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 The Formation of the Distribution of Azimuths and Ellipticities of Polarization and Phase Shifts of the Laser Image of Histological Sections of the Skin . . . . . 2.2.2 The Formation of Intensity Distributions of Laser Images of Histological Sections of the Skin . . . . . . . . . . . . . . . 2.2.3 The Formation of Distributions of the Degree of Depolarization of Laser Radiation Scattered by Histological Sections of the Skin . . . . . . . . . . . . . . . . . . . . . 2.3 The Experimental Scheme of Polarimetric Studies . . . . . . . . . . . . . . . . 2.3.1 Method of Measuring Polarization and Phase Parameters of the Laser Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Statistical and Correlation Approaches in the Analysis of Laser Images of Skin Derma [22–32] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.5 Fractal Approach in the Analysis of the Polarization Properties of Laser Images of Skin Histological Sections [22–32] . . . . . . . . . . . . 23 2.6 Experimental Illustrations of the Polarization Structure of Laser Images of Histological Sections of Human Skin . . . . . . . . . . . . . . . . . . 23 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 Determination of the Lifetime and Post-mortal Nature and Temporal Dynamics of the Formation of Skin Abrasions . . . . . . . . 3.1 Study of the Statistical Structure of the Intensity Distribution of Laser Images of Histological Sections of Skin Abrasions . . . . . . . . 3.2 Analysis of the Statistical Structure of the Power Spectra of Intensity of Laser Images of Histological Sections of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Investigation of the Temporal Dynamics of Changes in the Statistical Parameters of the Intensity Distributions of Laser Images of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Study of Two-Dimensional Polarization Maps of the Skin for Differentiation of Lifetime and Post-mortal Nature and Temporal Dynamics of Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Study of Two-Dimensional Distributions of Azimuths of Polarization of Laser Images of the Skin with Lifetime and Post-mortal Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Study of the Temporal Dynamics of Changes in the Average and Dispersion of the Coordinate Distributions of the Azimuths of Polarization of Laser Images of Skin Abrasions . . . . . . . . . . . . . . . . 4.3 Study of Two-Dimensional Distributions of Ellipticity of Polarization of Laser Images of Skin with Lifetime and Post-mortal Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Investigation of the Temporal Dynamics of Changes in the Average and Dispersion of the Coordinate Distribution of the Ellipticity of Polarization of Laser Images of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Correlation Analysis of Coordinate Distributions of the Azimuth of Polarization of the Laser Images of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Spatial-Frequency Analysis of Coordinate Distributions of Azimuths of Polarization of Laser Images of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Correlation Analysis of Coordinate Distributions of Ellipticity of Polarization of Laser Images of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.5.4 Spatial-Frequency Analysis of Coordinate Distributions of Ellipticity of Polarization of Laser Images of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5 Study of the Evolution of Phase Images of the Skin for Differentiation of the Lifetime and Post-mortal Skin Abrasions and the Time of Their Appearance . . . . . . . . . . . . . . . . . . . . . . 5.1 Investigation of the Temporal Dynamics of Changes of Phase Shifts Between Orthogonal Components of the Amplitude of Laser Radiation Scattered by Skin Abrasions . . . . . . . . . . . . . . . . . . 5.2 Correlation and Spatial-Frequency Structure of Phase Images of Histological Sections of Abrasions of the Skin of Biomannequin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Spatial-Frequency Analysis of a Temporary Change in the Coordinate Phase Distributions of Laser Images of Skin Abrasions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Abbreviations and Conventions

A ACF BMI BT CCD MI P TDE (mn) μm px I I (X ) I (x, y) M1 , M2 PSD T ΩI

E α0 *β δ(x, y) Ø λ Θ θ

Analyzer Autocorrelation functions Blunt mechanical injury Biological tissues Digital camera Mechanical injury Polarizer Time of death estimation Number of rows (m) and columns (n) of pixels ( px) digital camera Micrometer (10−6 m) Single pixel of the camcorder Laser intensity Light section of the intensity of microscopic images Coordinate intensity distribution of laser images of histological skin sections Average and dispersion of the distributions of intensity of laser images of skin dermis Power spectrum of the coordinate distribution of the intensity of laser images of histological sections of the skin dermis Time (in hours) Dispersion of the distribution of extremes of the power spectrum of the coordinate distribution of the intensity of laser images of histological sections of the skin Electric tension vector Polarization azimuth Ellipticity Phase shift and coordinate phase modulation Collimated laser beam Laser wavelength Angle of rotation of a polarized light beam Angle of rotation of the plane of transmission of the laser beam radiation xi

xii

ri ΔX L L¯

Abbreviations and Conventions

Coordinate in the plane of the laser image Full range of change in the coordinates of the distribution of azimuth or polarization ellipticity Half-width of the autocorrelation function Relative (normalized to the maximum) half-width of the autocorrelation function

Chapter 1

Analysis of Modern Aspects of Determination of Lifetime and Injuries Prescriptions in Forensic Medicine

1.1 Modern Aspects of Determination of Lifetime and Injuries Prescriptions in Forensic Medicine Historically, optical methods for studying the structure of biological tissues, which can be used to diagnose its damages, can be divided into three main areas [1–12]: • spectrophotometric methods based on the analysis of spatial or temporal changes in the intensity of the radiation field scattered by biological tissues; • polarization methods based on the use and analysis of the degree of polarization and the values of the azimuth and ellipticity of the polarization of electromagnetic waves in one of the points of the field of scattered radiation; • correlation methods based on the analysis of phase distributions between orthogonal components of the amplitude of the polarization components of light vibrations at various points of the object field. The real object fields of biological tissues, including their images, are characteristically a change in the whole complex of their parameters, both photometric, polarization, and correlation characteristics. Thus, further progress in the diagnostic tasks of forensic medicine may be associated with the development of new methods for the analysis and processing of polarization-inhomogeneous images of biological tissues that have undergone lifetime or after fatal traumatic injury. Consequently, the relevance of the monograph is due to the need to develop objective criteria for determining the lifetime and post-mortality and prescription of abrasion at different time intervals based on new approaches to the analysis of laser images of human biological tissues, methods of photometric, polarization, and phase diagnostics of their structure. The purpose of the monograph is to develop objective criteria for differentiating lifetime or post-mortal abrasions and establishing the prescription of their application at different time intervals according to laser photometry, polarimetry, and phasemetry © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Hu et al., Laser Polarimetry of Biological Tissues, SpringerBriefs in Applied Sciences and Technology, https://doi.org/10.1007/978-981-99-1734-1_1

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of human skin based on statistical and spatial-frequency analysis of laser images of histological sections of the dermal layer.

1.2 Optical Polarization and Correlation Methods of the Diagnostics of Phase-Inhomogeneous Biological Structures in Medicine Over the past decades, significant successes have been achieved in medical diagnostic technologies that are used to determine anatomical changes at the organ level. A set of methods has been developed—magnetic resonance imaging and spectroscopy, Xray computed tomography, and ultrasound, which allow non-invasive study of the human body. Recently, various optical methods, such as elastic and Raman scattering, absorption, and fluorescence, have been used to substantiate accurate diagnoses of various diseases by studying non-invasively the human body tissues, in situ. One of the most common applications of biomedical optics is the non-invasive or minimally invasive detection of pre-malignant or early malignant changes in the epithelium, the cell layer, and lining the inner surfaces of the human body. Dysplasia is limited to the epithelial layer and is characterized by a rapid increase in cells, the appearance of altered cell nuclei, and a change in the architectonics of tissues. In many cases, the tissue affected by dysplasia is flat and does not differ from the adjacent healthy tissue. In some cases, agreement with the diagnosis of the researcher may be 50%. Historically, optical methods for studying the structure of biological tissues (BT) can be divided into three groups [1–12]: • spectrophotometric methods based on the analysis of spatial or temporal changes in the intensity of the radiation field scattered by BT; • polarization methods based on the analysis of the degree of polarization of the scattered radiation field; • correlation methods based on the analysis of the autocorrelation functions of light vibrations at various points of the object field. For real object fields of BT, including their images, characteristically there is a change in both their photometric, polarization, and correlation characteristics. In future, our review will be devoted to precisely these three main directions of optical diagnostics of phase-inhomogeneous objects and media. Spectrophotometric studies of the properties of biological tissues are carried out by directly measuring the parameters of scattering and absorption of optical radiation. Monte Carlo simulation method based on the two-stream Kubelka–Munk model and its three-, four-, and seven-stream modifications found wider application among spectrophotometric diagnostic methods.

1.2 Optical Polarization and Correlation Methods of the Diagnostics …

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Such modelling is effective in the problems of laser sensing of biological tissue. For example, a four-stream model describes two scattered (object) laser beams propagating towards each other (Kubelka–Munk model) and two parallel laser beams— one incident and one reflected from the back of the sample. The seven-stream model allows one to represent and calculate in three-dimensional space the intensity distribution of the field of scattered laser radiation propagating in an infinite medium. The indicated spectrophotometric Monte Carlo methods are universal and are characterized by high accuracy. However, this method with the rapid development of computer software requires considerable time. In parallel with the classical diagnostic methods of optics of biological tissues, polarization methods are developed based on the account of the transverse direction of scattered electromagnetic waves [13–15]. The novelty of such diagnostic methods is that they expand the data on the intensity distribution with information on the coordinate or spatial distributions of the azimuths of the ellipticity of the polarization of the field of scattered radiation. The use of lasers in solving the problems of optics of biological tissues and media has made it urgent to study new types of optical fields characterized by a simultaneous change (distribution) of photometric, polarization, and phase characteristics. An important step in the development of optical diagnostics of biological objects and media [16–25] was the combination of polarization, phase, and correlation approaches to the analysis of fields scattered by laser radiation. The basis for the formation of a new direction in biomedical diagnostics has become methods of laser polarimetry, combining traditional methods of polarimetry with new methods of correlation analysis of the structure of laser images of biological tissues [26–28]. The theoretical basis of laser polarimetry is a two-component amorphouscrystalline model of the optical properties of biological tissue, according to which optical-anisotropic fibrillar birefringent structures (trabeculae, osteons of bone tissue, muscle tissue, collagen dermal layer of the skin, etc.) are capable of converting the polarization structure of laser radiation. As a result of a complex of studies in this area, a diagnostic relationship was established between the azimuths and ellipticities of the polarization of the laser object field with the directions of the optical axes and phase shifts of birefringent fibrillar protein (collagen, elastin, myosin) networks of human biological tissues. An important stage in the development of laser polarimetry was the use of statistical analysis of laser fields scattered by biological tissues of various morphological structures and physiological states. This approach made it possible to develop new methods for diagnosing the physiological state of human biological tissues. Subsequently, the main polarization relationships between the signs of the processes of pathological changes in biological tissues at an early stage of their occurrence and the increase in the dispersion of the azimuths of polarization were established. The correlation approach to the analysis of polarization-inhomogeneous laser images turned out to be effective in the problems of optical diagnosis of human biological tissues. It was shown that a decrease in the dispersion of the directions of the optical axes of protein fibrils is manifested in the formation of the oscillating component of the autocorrelation function of laser images of biological tissues.

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It is shown that the dispersion of the distribution of extrema of the values of the autocorrelation function can be used as a diagnostic sign of the physiological state of biological tissues [29–31]. A new information step in non-contact diagnostics of the structure of human biological tissues is the statistical and correlation analysis of two-dimensional distributions of azimuths and ellipticity of polarization (polarization maps) of their images. The relationship between the set of statistical moments of the first–fourth order characterizing the orientation-phase structure of the fibrillar architectonics of human biological tissues and the combination of the corresponding statistical moments of the two-dimensional distributions of the azimuth and ellipticity of light oscillations of their polarization maps is revealed. On this basis, it was shown that an increase in the asymmetry and excess of the azimuth distributions and ellipticity of polarization maps is associated with an increase in the dispersion of the directions of the optical axes of anisotropic fibrils of biological tissues; inverse processes correspond to an increase in the dispersion of phase shifts introduced by optical-anisotropic architectonic networks [32–40]. Over the past five years, methods and means of laser polarimetry have begun to be implemented in the field of forensic science. A new approach to solving the urgent problem is proposed and justified—the establishment of a set of differential criteria for objectively determining the prescription of the onset of death by a complex of polarizing, matrix, statistical, and correlation parameters of laser images of biological tissues of various morphological structures. In the research cycle, the problems are associated with finding out the possibility of using laser polarimetric analysis of histological sections to identify changes in the BT of a human corpse after death. On this basis, the dynamics of changes in the parameters of the Jones matrix characterize the polarization properties of histological sections of BT of the human body, for different intervals after the death period. The relationships between changes in histological sections of tissues, which are described by the Jones polarization matrix, and the polarization parameters of their laser images depending on the TDE were revealed. It was found that when using polarization indices of BT laser images, the time range of the TDE installation, due to the features after the death changes of the latter, ranges from 1–4 h for brain tissue to 1–48 h for muscle tissue. The studied set of methods for laser analysis of BT polarization images is the basis for differentiating the determination of TDE by selective analysis of various types of tissues, namely for “long-term” diagnostics, polarimetry of structured BT (muscle tissue, skin dermis) is required, and “short-term” one or two tissues parenchymal organs or brain. The achieved level of diagnostic techniques based on laser polarimetry of biological tissues reliably substantiates the development of new promising methods related to the possibilities of objective differentiation of lifetime and post-mortal injuries of biological tissues of the human body and the prescription of their application.

References

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19. H. Zhengbing, S. Gnatyuk, T. Okhrimenko, S. Tynymbayev, M. Iavich, High-speed and secure PRNG for cryptographic applications. Int. J. Comp. Netw. Inf. Secur. (IJCNIS) 12(3), 1–10 (2020). https://doi.org/10.5815/ijcnis.2020.03.01 20. H. Zhengbing, I. Dychka, M. Onai, Y. Zhykin, Blind payment protocol for payment channel networks. Int. J. Comp. Netw. Inf. Secur. (IJCNIS) 11(6), 22–28 (2019). https://doi.org/10. 5815/ijcnis.2019.06.03 21. H. Zhengbing, Y. Khokhlachova, V. Sydorenko, I. Opirskyy, Method for optimization of information security systems behavior under conditions of influences. Int. J. Intell. Syst. Appl. (IJISA) 9(12), 46–58 (2017). https://doi.org/10.5815/ijisa.2017.12.05 22. H. Zhengbing, S.V. Mashtalir, O.K. Tyshchenko, M.I. Stolbovyi, Video shots’ matching via various length of multidimensional time sequences. Int. J. Intell. Syst. Appl. (IJISA) 9(11), 10–16 (2017). https://doi.org/10.5815/ijisa.2017.11.02 23. V. Prysyazhnyuk, Y. Ushenko, A. Dubolazov, A. Ushenko, V. Ushenko, Polarization-dependent laser autofluorescence of the polycrystalline networks of blood plasma films in the task of liver pathology differentiation. Appl. Opt. 55(12), B126–B132 (2016) 24. A. Ushenko, O. Dubolazov, V. Ushenko, O. Novakovskaya, O. Olar, Fourier polarimetry of human skin in the tasks of differentiation of benign and malignant formations. Appl. Opt. 55(12), B56–B60 (2016) 25. Y. Ushenko, V. Bachynsky, O. Vanchulyak, A. Dubolazov, M. Garazdyuk, V. Ushenko, Jonesmatrix mapping of complex degree of mutual anisotropy of birefringent protein networks during the differentiation of myocardium necrotic changes. Appl. Opt. 55(12), B113–B119 (2016) 26. O. Dubolazov, V. Ushenko, L. Trifoniuk, Y. Ushenko, V. Zhytaryuk, O. Prydiy, M. Grytsyuk, L. Kushnerik, I. Meglinskiy, Methods and means of 3D diffuse Mueller-matrix tomography of depolarizing optically anisotropic biological layers. Proc. SPIE 10396, 103962P (2017) 27. A. Ushenko, A. Dubolazov, V. Ushenko, O. Novakovskaya, Statistical analysis of polarizationinhomogeneous Fourier spectra of laser radiation scattered by human skin in the tasks of differentiation of benign and malignant formations. J. Biomed. Opt. 21(7), 071110 (2016) 28. Y. Ushenko, G. Koval, A. Ushenko, O. Dubolazov, V. Ushenko, O. Novakovskaia, Muellermatrix of laser-induced autofluorescence of polycrystalline films of dried peritoneal fluid in diagnostics of endometriosis. J. Biomed. Opt. 21(7), 071116 (2016) 29. A. Dubolazov, N. Pashkovskaya, Y. Ushenko, Y. Marchuk, V. Ushenko, O. Novakovskaya, Birefringence images of polycrystalline films of human urine in early diagnostics of kidney pathology. Appl. Opt. 55(12), B85–B90 (2016) 30. M. Garazdyuk, V. Bachinskyi, O. Vanchulyak, A. Ushenko, O. Dubolazov, M. Gorsky, Polarization-phase images of liquor polycrystalline films in determining time of death. Appl. Opt. 55(12), B67–B71 (2016) 31. A. Ushenko, A. Dubolazov, V. Ushenko, Y. Ushenko, M. Sakhnovskiy, O. Olar, Methods and means of laser polarimetry microscopy of optically anisotropic biological layers. Proc. SPIE 9971, 99712B (2016) 32. A. Ushenko, A. Dubolazov, V. Ushenko, Y. Ushenko, L. Kushnerick, O. Olar, N. Pashkovskaya, Y. Marchuk, Mueller-matrix differentiation of fibrillar networks of biological tissues with different phase and amplitude anisotropy. Proc. SPIE 9971, 99712K (2016) 33. O. Dubolazov, A. Ushenko, Y. Ushenko, M. Sakhnovskiy, P. Grygoryshyn, N. Pavlyukovich, O. Pavlyukovich, V. Bachynskiy, S. Pavlov, V. Mishalov, Z. Omiotek, O. Mamyrbaev, Laser Müller matrix diagnostics of changes in the optical anisotropy of biological tissues, in Information Technology in Medical Diagnostics II—Proceedings of the International Scientific Internet Conference on Computer Graphics and Image Processing and 48th International Scientific and Practical Conference on Application of Lasers in Medicine and Biology, vol. 2018 (2019), pp. 195–203 34. M. Borovkova, M. Peyvasteh, O. Dubolazov, Y. Ushenko, V. Ushenko, A. Bykov, S. Deby, J. Rehbinder, T. Novikova, I. Meglinski, Complementary analysis of Mueller-matrix images of optically anisotropic highly scattering biological tissues. J. Eur. Opt. Soc. 14(1), 20 (2018)

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35. V.G. Kolobrodov, Q.A. Nguyen, G.S. Tymchik, The problems of designing coherent spectrum analyzers, in Proceedings of SPIE, 2013, vol. 9066, p. Article number 90660N, 11th International Conference on Correlation Optics18 September 2013 through 21 September 2013, Code 103970 36. V.A. Ostafiev, S.P. Sakhno, S.V. Ostafiev, G.S. Tymchik, Laser diffraction method of surface roughness measurement. J. Mater. Process. Technol. N63, 871–874 (1997) 37. I. Chyzh, V. Kolobrodov, A. Molodyk, V. Mykytenko, G. Tymchik, R. Romaniuk, P. Kisała, A. Kalizhanova, B. Yeraliyeva, Energy resolution of dual-channel opto-electronic surveillance system, in Proceedings Volume 11581, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2020; 115810K (2020), Wilga, Poland. https:// doi.org/10.1117/12.2580338 38. V.H. Kolobrodov, V.I. Mykytenko, G.S. Tymchik, Polarization model of thermal contrast observation objects. Thermotlectricity 1, 36–49 (2020) 39. V.H. Kolobrodov, M.S. Kolobrodov, G.S. Tymchik, A.S. Vasyura, P. Komada, Z. Azeshova, The output signal of a digital optoelectronic processor, in Proceedings SPIE 10808, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018, 108080W (1 October 2018) 40. G.S. Tymchik, V.I. Skytsyuk, T.R. Klotchko, H. Bezsmertna, W. Wójcik, S. Luganskaya, Z. Orazbekov, A. Iskakova, Diagnosis abnormalities of limb movement in disorders of the nervous system, in Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2017, 2017/8/7, pp. 104453S–104453S-11. https://doi.org/10.1117/12. 228100

Chapter 2

Materials and Methods of Research in Laser Polarimetry Data Processing of Biological Tissues for Forensic Determining the Age of Injury

Objects of research are1076 histological sections of the skin of biomanekens, which were 269 corpses of males and females aged 18–60 years old. Skin samples were taken from regional regions of the same type (neck, chest, back, shoulder girdle) of bodies of biomanekens without concomitant pathology of haematopoiesis or skin integument (both damaged and intact). The causes of death were mainly open and closed skeletal bone fractures with damage to internal organs, cases of mechanical asphyxia, and arrogant deaths from coronary heart disease. In cases where death occurred on the background of severe blood loss or a significant increase in the level of ethyl alcohol in the blood of the victims (more than 3%), samples were not taken to exclude non-standard reactive changes in soft tissues. The lifetime abrasions caused in the early period of time before the onset of death were strangulated grooves of corpses, and the cause of death of which was mechanical asphyxiation with compression of the neck loop. At the same time, the duration of skin injury before death did not exceed 10 min. After fatal injuries were obtained by tightening the loop on the neck of biomanekens with the same initial data. When deciding on the prescription of getting lifetime injuries, skin samples were taken from abrasion sites of biomanekens, the time of receipt, and onset of death of which was reliably known. In all expert cases, in the accompanying documents (medical records of the inpatient, directions, and resolutions of the judicially investigative authorities), bodily injuries and the onset of death were clearly recorded. When establishing the deadlines for causing bodily harm in the period after death, a series of experimental studies were carried out on biomanekens with similar initial data and a precisely defined time of death, by causing abrasions of the same areas by tangentially sliding (at an angle of 15–450 ) by impacts with blunt solid objects with angular, limited surfaces (1 to 180 h after the death period). All seized skin fragments, namely lifetime and post-mortem simulated abrasions, as well as the corresponding control—the intact skin was dried in a thermostat at a temperature of 37 °C for 5 h to achieve the conditions of lifetime loss of moisture from the abrasion site. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Hu et al., Laser Polarimetry of Biological Tissues, SpringerBriefs in Applied Sciences and Technology, https://doi.org/10.1007/978-981-99-1734-1_2

9

10

2 Materials and Methods of Research in Laser Polarimetry Data …

Table 2.1 General characteristics of the studied material Damage

Cases

Sections

Control

12

48

4

192

Lifetime

121

484

4

1936

Post-mortal

124

496

4

1984

12

48

4

192

269

1076

4

4304

Strangulation Total

Methods

Number of studies

Histological sections were made on a cryostat-microtome, after which studies of their polarization properties were carried out. Comparison groups were lifetime abrasions with intact skin (control), post-mortal abrasion with intact skin (control), and lifetime abrasions with post-mortal abrasion. In addition, we analysed the statistical significance of the differences in indicators for both lifetime and post-mortal abrasions at different lifetime and post-mortal time intervals. When analysing changes in the studied indicators, both qualitative and quantitative changes were taken into account (Table 2.1). Table 2.2 shows the amount of test material studied, lifetime and post-mortal abrasions, the number of methods used, and the total number of studies performed.

2.1 Morphological Structure of Human Skin 2.1.1 Epidermis The epidermis is a surface layer of the skin, built from a multilayer epithelium, in which continuous movement of cells passes from the basal layer to the surface of the stratum corneum. In the process of their upward movement, poorly differentiated germ cells undergo a series of structural and biochemical changes and finally turn into horn cells [1]. Thus, the shape and essence of cells at each level of the epidermis are not the same; each next cell comes from the previous one and reflects only a separate, short-lived phase of cell life. Since the path that each epidermal cell travels under normal conditions is the same, the same cell shapes come across at the same level, and as a result, continuous connections of homogeneous cells or layers are formed that give the epidermis a picture of a heterogeneous histological building. Five layers are distinguished in the epidermis (Fig. 2.1), which are arranged from bottom to top in this sequence [2]: • basal (main) or germ layer; • layer of prickly cells;

2.1 Morphological Structure of Human Skin

11

Table 2.2 The number of studied abrasions of expert and experimental material Lifetime abrasions Number of cases

Time intervals The number of sections made

Post-mortal abrasions Number of cases

The number of sections made

5

20

1

4

16

4

16

4

2

8

4

16

6

4

16

3

12

8

4

16

3

12

10

4

16

3

12

12

4

16

4

16

16

4

16

4

16

18

4

16

4

16

20

4

16

4

16

24

4

16

4

16

30

4

16

3

12

36

4

16

4

16

40

4

16

4

16

42

4

16

3

12

48

4

16

3

12

50

4

16

2

8

52

4

16

2

8

54

5

20

2

8

60

3

12 12

2

8

66

3

2

8

70

2

8

2

8

72

2

8 12

3

12

76

3

2

8

78

2

8

2

8

80

2

8

2

8

90

3

12

3

12

96

3

12

4

16

100

3

12

2

8

110

2

8

4

16

112

3

12

4

16

120

3

12

4

16

124

4

16

4

16

130

3

12

4

16

144

2

8 (continued)

12

2 Materials and Methods of Research in Laser Polarimetry Data …

Table 2.2 (continued) Lifetime abrasions Number of cases

Total

Time intervals The number of sections made

Post-mortal abrasions Number of cases

The number of sections made

4

16

148

3

12

4

16

160

3

12

4

16

172

121

484

4

16

124

496

Fig. 2.1 The epidermis of the skin of the palm of a 17-year-old guy. 140× magnification

• a layer of keratohyalin or granular cells. Three layers taken together make up the malpighian layer of the epidermis; • eleidin or shiny layer; • stratum corneum. The lower surface of the epidermis is uneven and wavy. Dipping the epidermis into the dermis is called outgrowths. In some of them, throughout the life, the excretory ducts of the sweat glands are located and, accordingly, on the surface of the skin— ridges with the mouths of the sweat glands. The widest outgrowths seem to be the bottom for small grooves of a thin skin pattern, and, at worst, in addition to these outgrowths, the epidermis up to 20–25 years of age creates more and more outgrowths to increase its lower surface and thereby bring its cells closer to the vessels of the dermis and to create a stronger bond between the epidermis and dermis. Under normal conditions, the shape of the last outgrowths is predominantly conical. Thus, three types of outgrowths are distinguished in the epidermis: some of

2.1 Morphological Structure of Human Skin

13

them are associated with the leading ducts of the sweat glands, others are associated with skin grooves, and due to the third, mainly the epidermis increases its lower surface. Germ layer. Over a long epidermis, the germ layer is represented by only one row of cells that have a cylindrical shape, and their orientation is perpendicular to the skin surface, so they are located on their own membrane in the form of a “front garden”. The upper surface of the cylindrical cells is not flat, but domed. A layer of prickly cells is located above the germ cells, and its thickness is second only to the stratum corneum and strictly follows after the thickness of the epidermis as a whole. Even in one place of the skin, the thickness of the prickly layer varies: between the outgrowths it is much less than in the region of outgrowth. This layer consists of several rows of cells, 16 above the papillae, and 7–15 in the region of outgrowths. Cells at different levels of the layer have an uneven shape: the lowest of them approach cubic, the highest—flattened—polygonal. The bulk of the cells has a polygonal shape. The cells do not fit tightly to each other, there are gaps between them (Fig. 2.2), through which bridges are thrown from cell to cell. Intercellular clefts and bridges in this layer are more pronounced than in other layers of the epidermis. Bridges depart from the corners and lateral surfaces of each cell, and therefore, if you make a cut in the middle of the bridges and thus isolate the cell, then it seems that the latter has numerous prickles—that is why, they called the layer prickly. The intercellular bridge, as in the basal layer, in radiation spectroscopy is a fibril that passes from one cell to another in the form of small bundles. Fig. 2.2 Intercellular fissures between the cells of the malpighian layer of the skin of the palm of a 30-year-old woman. 280× magnification

14

2 Materials and Methods of Research in Laser Polarimetry Data …

Research in an electron microscope, according to some authors, also showed that the bridges are composed of tonofibrils and do not have a shell. As the cell advances, the tonofibrils, which occupy a place in the protoplasm of prickly, granular cells and in bridges, gradually lose their filamentous structure, turning into a heavy homogeneous structure. Stratum corneum—the most powerful outer layer of the epidermis. Its thickness in various parts of the skin varies widely. It was built from keratinized plates. There are no nuclei in these cells. In the lower and middle parts of the stratum corneum, the cells are firmly interconnected; on the surface, they exfoliate in the form of scales.

2.1.2 Derma or Skin Itself Derma is a connective tissue built from collagen, elastic and argyrophil fibres, an amorphous core substance, and collagen elements. The bulk of the derma is fibrous tissue and, in general, collagen fibres [3–5]. The sebaceous and sweat glands, hair roots, their bulbs and follicles, muscles, blood and lymph vessels, and nerves are embedded in the derma. In the dermis, two layers are distinguished: papillary and reticular. They are not clearly divided among themselves (Fig. 2.3). The papilla of the dermis located between the outgrowths of the epidermis is called the papillary layer. Fig. 2.3 The papillary and reticular layer of the skin of the guy’s chest. 140× magnification

2.2 Modelling of the Human Skin Layer as a Transformer of Laser Radiation …

15

This layer of unequal thickness in different areas of the skin. It is most pronounced in areas with a thickened epidermis: on the palms, soles, the back surface of the hands, the plantar surface of the feet, and the transitional border of the lips. In its structure, the papillary layer differs from the reticular layer by the absence of large bundles of collagen fibres in it, their other relative positions, a large amount of intermediate substance, and cellular elements. In the papilla of the dermis, collagen and elastic fibres are more often single or make up small bundles and are located mainly perpendicular to the skin surface. Under the papillae, small bundles of collagen fibres take mainly a direction parallel to the skin surface. In the mesh layer, bundles of collagen fibres, intersecting each other, go in different directions, forming a dense network, which became the reason to call the lower and middle part of the dermis the mesh layer. The lower the surface of the skin, the larger the bundles of collagen fibres. The largest of them penetrate between the fat particles of the hypodermis and are woven into the subcutaneous fascia, which attaches skin to it. Collagen fibres 2– 10 µm thick are bundles of various sizes and are surrounded by an amorphous basic substance. They make up more than 98% of the connective tissue of the dermis and are characterized by great strength, but low elasticity. The strength of the skin is mainly due to the presence of collagen fibres in it. Each fibre has a fibrillar structure. The diameter of individual fibrils is 0.1 µm. The main protein basis of collagen fibres is collagen—a complex protein, which is classified as scleroproteins.

2.1.3 Amorphous Skin Substance In the broad sense of the word, the intermediate or basic substance is a combination of fibres and an amorphous substance, and the latter surrounds the fibres and cells of the connective tissue. In a narrower sense, under amorphous skin substance is understood to mean a structureless substance saturated with tissue substance that surrounds collagen, argentophilic and elastic fibres, and connecting cells. In the dermis and the connecting layers of the hypodermis, the amorphous basic substance has the form of a thin unstructured film located between the fibres and their bundles.

2.2 Modelling of the Human Skin Layer as a Transformer of Laser Radiation Parameters The morphological structure of human skin is considered by us for further modelling of its properties. Imagine a layer of connective tissue in the form of a two-component matrix consisting of an isotropic external (rough layer of the epithelium) and

16

2 Materials and Methods of Research in Laser Polarimetry Data …

anisotropic internal (birefringent collagen network and a saturated by capillary blood network) components [6–12]. Schematically, such a structure is shown in Fig. 2.4. This model illustrates the capabilities of the complex of methods of laser polarimetry of biological tissues for solving the urgent task of forensic medicine— the development and justification of an objective determination of the type (lifetime or post-mortal) of skin damage and fixing the time of injury by statistical and correlation analysis of the parameters of laser images of histological sections of tissue of biomanekens (Fig. 2.5). To this end, we consider in more detail the mechanisms by which a layer of skin transforms the main parameters of laser radiation. Fig. 2.4 A model of the human skin layer as a two-component structure that converts the parameters of laser radiation: 1—rough surface of the epithelium; 2—collagen mesh layer; 3—mesh capillary vessels

Fig. 2.5 A model of a layer of damaged human skin as an optically anisotropic structure that converts the parameters of laser radiation: 1—rough surface of the epithelium; 2—collagen mesh layer; 3—a grid of damaged capillary vessels; 4—shaped blood cells that extend beyond the boundaries of blood vessels as a result of haemorrhages

2.2 Modelling of the Human Skin Layer as a Transformer of Laser Radiation …

17

2.2.1 The Formation of the Distribution of Azimuths and Ellipticities of Polarization and Phase Shifts of the Laser Image of Histological Sections of the Skin It was preliminarily established that during the passage of polarized laser radiation with a polarization azimuth α0 (Fig. 2.6a) through birefringent collagen skin structures, the angle (azimuth α) of the plane of oscillation of the electric tension vector (E) of the laser wave changes (Fig. 2.6b). In addition, the trajectory of the vector E changes and an elliptically polarized wave is formed which is characterized by azimuth α and ellipticity β (Fig. 2.6b). It is known that the specific values of the azimuth αi and ellipticity βi of polarization at each point (with coordinates (x, y)) of the image of the dermal layer of human skin are determined by the laying direction and the thickness of the collagen fibre. Based on this, the laser image of such a histological section represents the coordinate distribution of random azimuths and polarization ellipticity (Fig. 2.7). The

Fig. 2.6 Model scheme for the formation of a polarized state of a laser beam by collagen fibre

18

2 Materials and Methods of Research in Laser Polarimetry Data …

Fig. 2.7 Polarization structure of a laser image of a histological section of the dermal layer of human skin

latter, in turn, represent an “imprint” of the orientational and geometric structure of the collagen network of the dermis of the skin. Thus, the study of the polarization structure of laser images of histological sections of human skin is informative in the study of the morphological structure of collagen networks and can be promising in the diagnosis and differentiation of the type of traumatic injuries of a person. In addition to polarization modulation of laser radiation in the dermal layer of the skin of the dermis, coordinate phase modulation δ(x, y) occurs, due to the different propagation velocities of the orthogonal components of the amplitude E x , E y in the birefringent material of collagen beams (Fig. 2.8). Thus, the study of phase shifts in laser images of histological sections of human skin is an additional method for the objective diagnosis of the coordinate distribution of the optical anisotropy of their collagen networks.

Fig. 2.8 Analysis of the formation of the phase structure of a laser image of a histological section of the dermal layer of human skin

2.2 Modelling of the Human Skin Layer as a Transformer of Laser Radiation …

19

It is known that the anisotropy of any substance, including organic, depends on its mechanical, traumatic stress. Thus, the phasemetry of laser images of histological sections of biological tissues is an effective method for studying not only their birefringent extracellular matrices, but can also be an effective method for monitoring such changes under the influence of various kinds of traumatic factors.

2.2.2 The Formation of Intensity Distributions of Laser Images of Histological Sections of the Skin All images of histological sections of biological tissues are coordinate-distributed intensity values I (x, y) that can be directly recorded by a photodetector or a photosensitive digital camera. Each point of the laser image is characterized by its own polarization (Fig. 2.7). It is known that the intensity (I0 ) of light with azimuth α and ellipticity β when passing through a polarizing filter changes in accordance with the Malus law. [ ] I = I0 cos2 (α + θ ) + tg2 β sin2 (α + θ )

(2.1)

Schematically, the process of formation of the intensity distribution is illustrated in Fig. 2.9. Thus, the study of the intensity distribution in laser images of histological sections of human skin is a direct experimental method for the objective diagnosis of the coordinate distribution of polarization states due to the optical anisotropy of their collagen networks. In other words, studies of changes in the coordinate distributions of the intensity of histological sections of the skin can be the basis for differentiating the type of damage or the time of its application.

Fig. 2.9 Analysis of the formation of the intensity distribution of the laser image of a histological section of the dermal layer of human skin

20

2 Materials and Methods of Research in Laser Polarimetry Data …

2.2.3 The Formation of Distributions of the Degree of Depolarization of Laser Radiation Scattered by Histological Sections of the Skin During the passage of the laser beam through the surface and inner layers of the skin (Fig. 2.4), it is repeatedly scattered by inhomogeneous structures of the epidermis and dermis. As a result of each such act, there is a transformation of polarization states (Figs. 2.6, 2.7) and phases (Fig. 2.8). Therefore, at each point of the corresponding laser image, a large number of differently polarized waves are superimposed (Fig. 2.10). The result of this overlap is the depolarization or averaging of the polarization states of local beams. It is known that the greater the scattering ratio, the higher the depolarization. In biomedical optics, one of the most scattering media is blood. This scattering effect in the blood capillary network can be used to diagnose the type and time differentiation of traumatic injuries of human skin.

2.3 The Experimental Scheme of Polarimetric Studies Figure 2.11 shows the optical scheme of the study of laser images [12–21] of histological sections of human skin. The object of study was irradiated with a collimated beam (Ø = 104 µm) of a He–Ne laser (1), at λ = 0.6328 µm. Using a polarizing illuminator (quarter-wave plates (3, 5) and a polarizer (4)), various states of polarization of the illuminating beam were formed. Polarization images of biological tissues were formed in the plane of the photosensitive area of the CCD camera (10) using a microlens (7). The resolution of camera

Fig. 2.10 Analysis of the formation of depolarization of the laser image of histological sections of the skin

2.3 The Experimental Scheme of Polarimetric Studies

21

Fig. 2.11 The optical scheme of the polarimeter, where 1 is a He–Ne laser; 2—collimator; 3, 5, 8— quarter-wave plates; 4, 9—polarizer and analyser, respectively; 6—object of study; 7—microlens; 10—CCD camera; 11—personal computer

is sufficient for measurements in the wide range of sizes of structural elements of human tissues (2–2000 µm).

2.3.1 Method of Measuring Polarization and Phase Parameters of the Laser Images We used the classical methods of measuring such parameters introduced earlier. The sequence of actions consisted of the following algorithm: 1. Using the rotation of the analyser’s transmission axis (A) within 0°–180°, the arrays of the minimum and maximum intensity levels ⎛ ⎞⎛ ⎞ r1 , . . . rm r1 , . . . rm I ⎝ · · · ⎠⎝ · · · ⎠ of skin histological sections for each indirn , . . . rm rn , . . . rm max min vidual pixel (mn) of the CCD camera and the corresponding rotation angles ⎛ ⎞⎛ ⎛ ⎞ ⎞ r1 , . . . rm r1 , . . . rm Θ⎝ · · · ⎠⎝ I ⎝ · · · ⎠ ≡ min()⎠ were determined. rn , . . . rm rn , . . . rm 2. The coordinate distributions (polarization maps) of polarization states in the image plane of skin histological sections were calculated using such ratios: ⎞ r1 , . . . rm ( π) α ⎝ · · · ⎠ = Θ I (ri ) ≡ min() 2 rn , . . . rm ⎛ ⎞ r1 , . . . rm I (ri )min β ⎝ · · · ⎠ = arctg I (ri )max . rn , . . . rm ⎛

(2.2)

3. The phase shifts between the orthogonal components of the laser wave amplitude at the image point ri of skin histological sections were calculated using the following ratio:

22

2 Materials and Methods of Research in Laser Polarimetry Data …

] [ tg2β(ri ) Δ(ri ) = arctg tgα(ri )

(2.3)

4. The value of the degree of depolarization of laser radiation at the image point of skin histological sections was calculated using the following ratio: Δ=

2Imin Iminmax

(2.4)

2.4 Statistical and Correlation Approaches in the Analysis of Laser Images of Skin Derma [22–32] As the main analytical tool for assessing the distributions of random variables (z) characterizing images (azimuths (α) and ellipticity (β) of polarization of light vibrations, phase shifts (δ), and degree of depolarization (Δ) of skin histological sections, we used the statistical moments of the first (M1 ) and second (M2 ) orders that were calculated by the following algorithms: 1 (Δz 1 + Δz 2 + · · · + Δz N ); N / ) 1( 2 Δz 1 + Δz 22 + · · · + Δz 2N , M2 = N M1 =

(2.5)

(2.6)

where N —total number of pixels of a digital camera. One of the most famous and effective approaches in the analysis (estimation) of the coordinate structure of distributions z(x, y) is their autocorrelation comparison using the following function K(Δx, Δy): 1 K(Δx, Δy) = lim x → 0 X 0 Y0 y→0

∫x ∫ y [z(x, y)][z(x − Δx, y − Δy)]dxdy. 0

(2.7)

0

Here, (Δx, Δy) are the “steps” with which the coordinates (x, y) of the distributions of the optical parameters z(x, y) of the images of histological sections of the investigated biological tissues of the bodies are changed.

2.6 Experimental Illustrations of the Polarization Structure of Laser Images …

23

2.5 Fractal Approach in the Analysis of the Polarization Properties of Laser Images of Skin Histological Sections [22–32] A fractal analysis of estimating a set of random variables () characterizing microscopic images of the skin was performed using the “MATLAB-6” program with a known sequence of actions. First, the autocorrelation functions K (Δx, Δy) were calculated and the Log dependences of their power spectra log P S D were found, which were approximated by the least squares method in the curves ϕ(z). The classification of coordinate distributions of parameters (z), which characterize laser images of histological sections of the skin, was carried out in accordance with the following criteria: • Coordinate distributions of the parameters z(x, y) are considered fractal (selfsimilar), provided the curves are linear ϕ(z). • Sets z(x, y) are stochastic if there are several constant angles of curves ϕ(z). • Sets z(x, y) are random in the absence of stable slopes of the curves ϕ(z).

2.6 Experimental Illustrations of the Polarization Structure of Laser Images of Histological Sections of Human Skin This section presents the results of a study of the polarization structure of laser images of some samples of human skin, illustrating the adequacy of universal modelling of objects such as a two-component amorphous-anisotropic structure. As samples of an experimental study, histological sections of the skin of two types were selected: • intact skin; • traumatically damaged (blunt objects) skin. In the series of Fig. 2.12, Fig. 2.13 shows laser images of these samples obtained for different orientations of the transmission plane of the polarizer-analyser: θ = 0° (“a”), 45° (“b”), and 90° (“c”). A comparative analysis of laser images of histological sections of samples of both skin types obtained under different polarization conditions of the experiment revealed a significant dependence of the coordinate intensity distributions. Such a transformation may be related to the polarization inhomogeneity of the studied images. As a result, when passing through the analyser of differently polarized (α, β) sections of the laser image, their intensity (Fig. 2.9) changes differently in accordance with relation (2.1), which characterizes the degree of transmission of intensity I (α, β) depending on the angle of rotation of the transmission plane θ . In addition, it is seen that traumatically damaged skin is characterized by a significantly higher level of image bleaching (Fig. 2.13c) in the crossed polarizer and analyser, which may be

24

2 Materials and Methods of Research in Laser Polarimetry Data …

Fig. 2.12 Polarization structure of laser images of intact skin: a 0°, b 45°, c 90°

Fig. 2.13 Polarization structure of laser images of injured skin: a 0°, b 45°, c 90°

associated with an increase in the level of anisotropy (collagen bundles) and the degree of depolarization (haemorrhage). The revealed structural feature of laser images of histological sections of the skin of different conditions is the basis for the development of a set of objective diagnostic methods for the lifetime or post-mortal nature of damage, as well as the prescription of its appearance.

References 1. V. Tuchin, L. Wang, D. Zimnjakov, Optical Polarization in Biomedical Applications (Springer, New York, USA, 2006) 2. R. Chipman, Polarimetry, in ed. by M. Bass, Handbook of Optics: Vol I—Geometrical and Physical Optics, Polarized Light, Components and Instruments (McGraw-Hill Professional, New York, 2010), pp. 22.1–22.37 3. N. Ghosh, M. Wood, A. Vitkin, Polarized light assessment of complex turbid media such as biological tissues via Mueller matrix decomposition, in ed. by V. Tuchin, Handbook of

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Photonics for Biomedical Science (CRC Press, Taylor & Francis Group, London, 2010), pp. 253–282 S. Jacques, Polarized light imaging of biological tissues, in Handbook of Biomedical Optics. ed. by D. Boas, C. Pitris, N. Ramanujam (CRC Press, Boca Raton, London, New York, 2011), pp.649–669 N. Ghosh, Tissue polarimetry: concepts, challenges, applications, and outlook. J. Biomed. Opt. 16(11), 110801 (2011) M. Swami, H. Patel, P. Gupta, Conversion of 3×3 Mueller matrix to 4×4 Mueller matrix for non-depolarizing samples. Opt. Commun. 286, 18–22 (2013) V. Ushenko, O. Vanchuliak, M. Sakhnovskiy, O. Dubolazov, P. Grygoryshyn, I. Soltys, O. Olar, System of Mueller matrix polarization correlometry of biological polycrystalline layers. Proc. SPIE 10352, 103520U (2017) V. Ushenko, O. Vanchuliak, M. Sakhnovskiy, O. Dubolazov, P. Grygoryshyn, I. Soltys, O. Olar, A. Antoniv, Polarization-interference mapping of biological fluids polycrystalline films in differentiation of weak changes of optical anisotropy. Proc. SPIE 10396, 103962O (2017) O. Dubolazov, L. Trifonyuk, Y. Marchuk, Y. Ushenko, V. Zhytaryuk, O. Prydiy, L. Kushnerik, I. Meglinskiy, Two-point Stokes vector parameters of object field for diagnosis and differentiation of optically anisotropic biological tissues. Proc. SPIE 10352, 103520V (2017) L. Trifonyuk, O. Dubolazov, Y. Ushenko, V. Zhytaryuk, O. Prydiy, M. Grytsyuk, L. Kushnerik, I. Meglinskiy, I. Savka, New opportunities of differential diagnosis of biological tissues polycrystalline structure using methods of Stokes correlometry mapping of polarization inhomogeneous images. Proc. SPIE 10396, 103962R (2017) O. Dubolazov, V. Ushenko, L. Trifoniuk, Y. Ushenko, V. Zhytaryuk, O. Prydiy, M. Grytsyuk, L. Kushnerik, I. Meglinskiy, Methods and means of 3D diffuse Mueller-matrix tomography of depolarizing optically anisotropic biological layers. Proc. SPIE 10396, 103962P (2017) A. Ushenko, A. Dubolazov, V. Ushenko, O. Novakovskaya, Statistical analysis of polarizationinhomogeneous Fourier spectra of laser radiation scattered by human skin in the tasks of differentiation of benign and malignant formations. J. Biomed. Opt. 21(7), 071110 (2016) Y. Ushenko, G. Koval, A. Ushenko, O. Dubolazov, V. Ushenko, O. Novakovskaia, Muellermatrix of laser-induced autofluorescence of polycrystalline films of dried peritoneal fluid in diagnostics of endometriosis. J. Biomed. Opt. 21(7), 071116 (2016) V. Prysyazhnyuk, Y. Ushenko, A. Dubolazov, A. Ushenko, V. Ushenko, Polarization-dependent laser autofluorescence of the polycrystalline networks of blood plasma films in the task of liver pathology differentiation. Appl. Opt. 55(12), B126–B132 (2016) A. Ushenko, O. Dubolazov, V. Ushenko, O. Novakovskaya, O. Olar, Fourier polarimetry of human skin in the tasks of differentiation of benign and malignant formations. Appl. Opt. 55(12), B56–B60 (2016) Y. Ushenko, V. Bachynsky, O. Vanchulyak, A. Dubolazov, M. Garazdyuk, V. Ushenko, Jonesmatrix mapping of complex degree of mutual anisotropy of birefringent protein networks during the differentiation of myocardium necrotic changes. Appl. Opt. 55(12), B113–B119 (2016) V.G. Kolobrodov, Q.A. Nguyen, G.S. Tymchik, The problems of designing coherent spectrum analyzers, in Proceedings of SPIE, 2013, vol. 9066, p. Article number 90660N, 11th International Conference on Correlation Optics18 September 2013 through 21 September 2013, Code 103970. V.A. Ostafiev, S.P. Sakhno, S.V. Ostafiev, G.S. Tymchik, Laser diffraction method of surface roughness measurement. J. Mater. Process. Technol. N63, 871–874 (1997) I. Chyzh, V. Kolobrodov, A. Molodyk, V. Mykytenko, G. Tymchik, R. Romaniuk, P. Kisała, A. Kalizhanova, B. Yeraliyeva, Energy resolution of dual-channel opto-electronic surveillance system, in Proceedings Volume 11581, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2020; 115810K, Wilga, Poland (2020). https:// doi.org/10.1117/12.2580338 V.H. Kolobrodov, V.I. Mykytenko, G.S. Tymchik, Polarization model of thermal contrast observation objects. Thermotlectricity 1, 36–49 (2020)

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21. V.H. Kolobrodov, M.S. Kolobrodov, G.S. Tymchik, A.S. Vasyura, P. Komada, Z. Azeshova, The output signal of a digital optoelectronic processor, in Proceedings SPIE 10808, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018, 108080W (1 October 2018). 22. G.S. Tymchik, V.I. Skytsyuk, T.R. Klotchko, H. Bezsmertna, W. Wójcik, S. Luganskaya, Z. Orazbekov, A. Iskakova, Diagnosis abnormalities of limb movement in disorders of the nervous system, in Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2017, 2017/8/7, pp. 104453S–104453S-11. https://doi.org/10.1117/12. 228100 23. H. Zhengbing, M. Ivashchenko, L. Lyushenko, D. Klyushnyk, Artificial neural network training criterion formulation using error continuous domain. Int. J. Mod. Educ. Comp. Sci. (IJMECS) 13(3), 13–22 (2021). https://doi.org/10.5815/ijmecs.2021.03.02 24. H. Zhengbing, I. Tereikovskyi, D. Chernyshev, L. Tereikovska, O. Tereikovskyi, D. Wang, Procedure for processing biometric parameters based on wavelet transformations. Int. J. Mod. Educ. Comp. Sci. (IJMECS) 13(2), 11–22 (2021). https://doi.org/10.5815/ijmecs.2021.02.02 25. H. Zhengbing, R. Odarchenko, S. Gnatyuk, M. Zaliskyi, A. Chaplits, S. Bondar, V. Borovik, Statistical techniques for detecting cyberattacks on computer networks based on an analysis of abnormal traffic behavior. Int. J. Comp. Netw. Inf. Secur. (IJCNIS) 12(6), 1–13 (2020). https:// doi.org/10.5815/ijcnis.2020.06.01 26. H. Zhengbing, S. Gnatyuk, T. Okhrimenko, S. Tynymbayev, M. Iavich, High-speed and secure PRNG for cryptographic applications. Int. J. Comp. Netw. Inf. Secur. (IJCNIS) 12(3), 1–10 (2020). https://doi.org/10.5815/ijcnis.2020.03.01 27. H. Zhengbing, I. Dychka, M. Onai, Y. Zhykin, Blind payment protocol for payment channel networks. Int. J. Comp. Netw. Inf. Secur. (IJCNIS) 11(6), 22–28 (2019). https://doi.org/10. 5815/ijcnis.2019.06.03 28. H. Zhengbing, Y. Khokhlachova, V. Sydorenko, I. Opirskyy, Method for optimization of information security systems behavior under conditions of influences. Int. J. Intell. Syst. Appl. (IJISA) 9(12), 46–58 (2017). https://doi.org/10.5815/ijisa.2017.12.05 29. H. Zhengbing, S.V. Mashtalir, O.K. Tyshchenko, M.I. Stolbovyi, Video shots’ matching via various length of multidimensional time sequences. Int. J. Intell. Syst. Appl. (IJISA) 9(11), 10–16 (2017). https://doi.org/10.5815/ijisa.2017.11.02 30. H. Zhengbing, I.A. Tereykovskiy, L.O. Tereykovska, V.V. Pogorelov, Determination of structural parameters of multilayer perceptron designed to estimate parameters of technical systems. Int. J. Intell. Syst. Appl. (IJISA) 9(10), 57–62 (2017). https://doi.org/10.5815/ijisa.2017.10.07 31. H. Zhengbing, Y.V. Bodyanskiy, N.Y. Kulishova, O.K. Tyshchenko, A multidimensional extended neo-fuzzy neuron for facial expression recognition. Int. J. Intell. Syst. Appl. (IJISA) 9(9), 29–36 (2017). https://doi.org/10.5815/ijisa.2017.09.04 32. H. Zhengbing, I. Dychka, Y. Sulema, Y. Radchenko, Graphical data steganographic protection method based on bits correspondence scheme. Int. J. Intell. Syst. Appl. (IJISA) 9(8), 34–40 (2017). https://doi.org/10.5815/ijisa.2017.08.04

Chapter 3

Determination of the Lifetime and Post-mortal Nature and Temporal Dynamics of the Formation of Skin Abrasions

The urgent task of forensic medicine is determination the fact of lifetime or postmortal damage of the biological tissues of a person. A new perspective direction in solving this problem is the use of modern methods of statistical analysis of microscopic images of biological tissues [1–18]. The achieved level of the obtained images of the structure of human biological tissues objectively necessitates the development of new methods for their processing and analysis. Currently, methods based on the estimation of statistical moments of scalar parameters—intensity distributions prevail [19–31]. Along with statistical approaches over the past 5–10 years, methods of fractal analysis of self-similarity of the geometric structure of biological tissues have begun to be used in optical diagnostics. 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.

3.1 Study of the Statistical Structure of the Intensity Distribution of Laser Images of Histological Sections of Skin Abrasions As the objects of study used histological sections of human skin, which are made in compliance with the conditions set forth in Chap. 2, namely: • with intact skin (Fig. 3.1a); • with lifetime abrasion (Fig. 3.1b); • with post-mortal abrasion (Fig. 3.1c).

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Hu et al., Laser Polarimetry of Biological Tissues, SpringerBriefs in Applied Sciences and Technology, https://doi.org/10.1007/978-981-99-1734-1_3

27

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3 Determination of the Lifetime and Post-mortal Nature and Temporal …

Fig. 3.1 Laser images of histological sections of human skin: a intact skin; b lifetime abrasion; c post-mortal abrasion

In the series of Figs. 3.2, 3.3 and 3.4, it shows scaled-up samples of the intensity distribution of laser images of histological sections of human skin of all types and their three-dimensional reconstruction. A comparative visual analysis of laser images of skin histological sections postmortal abrasions with intact skin (Figs. 3.1, 3.2, 3.3 and 3.4) practically does not reveal significant differences. A comparative visual analysis of three-dimensional reconstructions indicates that there is a difference between the reconstruction of the intensity distribution of the laser image of the histological section of intact skin and lifetimely damaged skin. As a result of this, an objective analytical comparison of the intensity distributions of laser images of human skin is relevant.

Fig. 3.2 Three-dimensional reconstruction of the intensity distribution of the laser image of the histological section of intact skin

3.1 Study of the Statistical Structure of the Intensity Distribution of Laser …

29

Fig. 3.3 Three-dimensional reconstruction of the intensity distribution of the laser image of the histological section of lifetime abrasion

Fig. 3.4 Three-dimensional reconstruction of the intensity distribution of the laser image of the histological section of abrasion obtained after death

30

3 Determination of the Lifetime and Post-mortal Nature and Temporal …

Fig. 3.5 Coordinate distribution of the image intensity I (X ) of the histological section of intact human skin

In the series of Figs. 3.5, 3.6 and 3.7 shown, the light sections I (X ) of the intensity of laser images obtained using computer sampling from a data array ⎞ ⎛ I1;1 , . . . I1;800 ⎠. ⎝ ··· I600;1 , . . . I600;800 The intensity of the image of the histological section of intact human skin is coordinately distributed between the values of 320–270, the histological section of the skin of a person with lifetime abrasion between the values of 80–45, and the histological section of the skin of a person with a post-mortal abrasion between the values of 55–35. A comparative analysis of Figs. 3.5, 3.6 and 3.7 shows that all the dependences I (X ) consist of a combination of randomly located local extrema, the presence of which can be associated with the roughness of the skin surface. On the other hand, the structure of the light sections of laser images with lifetime and post-mortal abrasions (Figs. 3.6 and 3.7) is significantly different from the dependence I (X ) obtained for intact skin (Figs. 3.5). It can be seen that the magnitude of the extrema of the local intensity values in the abrasion region is much smaller than the value I (X ) in the image of the undamaged areas. This feature can be explained by the presence of hemorrhages in the abrasion zone, which is optically manifested in the absorption of radiation. Thus, the image intensity in such places is less than in areas without internal hemorrhages.

3.1 Study of the Statistical Structure of the Intensity Distribution of Laser …

31

Fig. 3.6 Coordinate distribution of the intensity I (X ) of the image of the histological section of human skin with lifetime abrasion

Fig. 3.7 Coordinate distribution of the intensity I (X ) of the image of the histological section of the skin of a person with post-mortal abrasion

32

3 Determination of the Lifetime and Post-mortal Nature and Temporal …

Table 3.1 General statistical indicators (average and dispersion) of the intensity distributions of laser images of the skin

Statistical moments

Intact skin (n = 48)

Abrasions Lifetime (n = 532)

Post-mortal (n = 496)

Average, M1 0.71 ± 0.08

0.32 ± 0.025

0.27 ± 0.023

P1

p < 0.001

p < 0.001

P2

p > 0.05 0.16 ± 0.012

0.23 ± 0.031

P1

p < 0.001

p < 0.001

P2

p < 0.001

Dispersion, M2

0.11 ± 0.009

Remark P1 —when comparing intact skin with lifetime and after fatal injury; P2 —when comparing lifetime injury with after fatal injury

On the other hand, a qualitative comparative analysis of the dependences I (X ) obtained for the image of histological skin sections with lifetime abrasion (Fig. 3.6) and post-mortal abrasion (Fig. 3.7) did not reveal sufficiently reliable criteria for their differentiation. Subsequently, we carried out a statistical analysis of the coordinate distributions I (x, y) of laser images of histological sections of the skin of all types. The results of this analysis are shown in Table 3.1. An analysis of the average indicators of the first statistical moment M 1 of the distribution of the intensity of laser images of the skin shows that there is a statistical difference between intact skin (control) and lifetime and post-mortal abrasions. At the same time, the average value of this indicator for lifetime and post-mortal abrasions does not show the presence of a statistically significant difference. The analysis of the second statistical indicator M 2 shows the presence of a significant difference in the comparison groups between intact skin (control) and lifetime and post-mortal abrasions and between lifetime and post-mortal abrasions. An analysis of the distribution of the average and dispersion of the intensity of laser images of statistically significant groups of histological sections of intact skin, lifetime, and post-mortal abrasions of the human skin revealed that a second statistical moment (dispersion) can be used as a diagnostic criterion for differentiating the origin of traumatic injury. It was found that magnitudes of the average-statistical dispersion of the intensity of laser images of skin tissue with post-mortal abrasions exceed within 1/2 the value of a similar parameter characterizing laser images of skin with lifetime abrasions.

3.2 Analysis of the Statistical Structure of the Power Spectra of Intensity …

33

3.2 Analysis of the Statistical Structure of the Power Spectra of Intensity of Laser Images of Histological Sections of Skin Abrasions In order to obtain additional information on the possibility of objective differentiation of laser images of histological sections of intact skin, lifetime, and post-mortal abrasions of human skin, we studied the power spectra of their intensity distributions ⎛ ⎞ I1;1 , . . . I1;800 ⎝ ⎠ (see Chap. 2, Sect. 2.5). ··· I600;1 , . . . I600;800 Figures 3.8, 3.9 and 3.10 illustrate experimentally measured dependences logPSD for laser images of intact skin (Fig. 3.8), lifetime (Fig. 3.9), and post-mortal (Fig. 3.10) abrasions Each of the figures shows an element of the light section of the intensity distribution of the laser image. From the data obtained, it can be seen that the coordinate intensity distributions of the laser image of intact skin samples are characterized by a structure close to fractal—the slope of the corresponding dependences of the power spectra (see Chap. 2, Sect. 2.5) is practically unchanged (Fig. 3.8). From other expert and experimental data obtained, it can be seen that the coordinate intensity distributions of the laser image of lifetime and post-mortal abrasions are characterized by a statistical structure—there is no stable slope (see Chap. 2, Sect. 2.5) of the corresponding dependences of the power spectra of intensity distributions (Figs. 3.9 and 3.10). The results can be associated with the features of changes in the optical-geometric structure of human skin samples. Fig. 3.8 Power spectrum of the intensity of the laser image of intact skin

34

3 Determination of the Lifetime and Post-mortal Nature and Temporal …

Fig. 3.9 Power spectrum of the intensity of the laser image of lifetime abrasion

Fig. 3.10 Power spectrum of the intensity of the laser image with post-mortal abrasion

Thus, intact skin is characterized by the self-similar nature of its elements (epithelial plates and fibrils of the collagen network of the dermis). Therefore, the coordinate distribution of intensity of its laser image is also self-similar or fractal. Damage to the skin leads to the destruction of large-scale self-similarity of the geometric structure of its microstructure, and the obtained data of image of histological sections of lifetime and post-mortal abrasion can be associated with the statistical, random nature of laser radiation scattering by the inhomogeneous, and traumatized optical-geometric structure of skin samples. We performed a statistical analysis of the distributions of the extrema of the LogPSD dependencies of laser images of histological sections of the skin of all origin. The results of this analysis are shown in Table 3.2. The analysis of the data given in Table 3.2 indicates that when comparing the average data of the extrema of the power spectra of laser images of histological

3.2 Analysis of the Statistical Structure of the Power Spectra of Intensity … Table 3.2 General statistical indicators (average and dispersion) of the distributions of the extremes of the power spectra of laser images of the skin

35

Statistical moments

Intact skin (n = 48)

Abrasions Lifetime (n = 532)

Post-mortal (n = 496)

Average, M1

0.52 ± 0.06

0.64 ± 0.05

0.61 ± 0.069

P1

p < 0.001

p < 0.001

P2

p > 0.05 0.09 ± 0.024

0.12 ± 0.016

P1

p < 0.001

p < 0.001

P2

p > 0.05

Dispersion, M2

0.02 ± 0.0035

sections of lifetime abrasion with control, the difference is statistically significant. The same difference appears when comparing post-mortal abrasion with the control, and the difference between the lifetime and post-mortal abrasion is unreliable. The analysis indicators of dispersion M 2 indicate the presence of a statistical difference in the comparison groups of lifetime abrasion—control and post-mortal abrasion—control, and the difference between lifetime and post-mortal abrasion is unreliable. In order to summarize the results, we conducted a study of 1076 histological sections of intact skin, lifetime, and post-mortal abrasions. Table 3.3 shows the results of studies of 1076 histological sections of intact skin, lifetime, and post-mortal abrasions for statistically reliable indicators M1 ± 2M2 within each group of histological sections. Analyzing the statistically averaged values of the distributions of the extrema of the power spectra of the intensity of laser images of the skin, it is clear that when comparing the confidence indicator between intact skin with lifetime abrasions and post-mortal abrasion, the difference is not significant. The same difference exists when comparing damage to each other. Table 3.3 Statistically averaged values (average and dispersion) of the distributions of the extrema of the power spectra of the intensity of laser images of the skin

Statistical moments

Intact skin (n = 48)

Abrasions Lifetime (n = 532)

Post-mortal (n = 532)

Average, M1 0.47 ± 0.05

0.52 ± 0.06

0.47 ± 0.04

P1

p > 0.05

p > 0.05

P2

p > 0.05 0.10 ± 0.014

0.13 ± 0.012

P1

p < 0.001

p < 0.001

P2

p > 0.05

Dispersion, M2

0.03 ± 0.004

36

3 Determination of the Lifetime and Post-mortal Nature and Temporal …

The analysis of the second statistical moment indicates the presence of a difference between damage and control and the absence of a difference between the damage itself. Thus, it can be stated that studies of the statistical (second statistical moment) and correlation (dispersion of extremes of power spectra) structure of laser images of histological skin sections can be used to differentiate the origin (lifetime or postmortal) of abrasions. In view of the presence of qualitative differences in the studied parameters between the control and skin lesions of different origin and dissociation of average indicators with them M 1 , M 2 , we consider it appropriate to analyze the time dependence of the range of changes in the analyzed parameters.

3.3 Investigation of the Temporal Dynamics of Changes in the Statistical Parameters of the Intensity Distributions of Laser Images of Skin Abrasions Preliminarily, the data of effective diagnostics of the TDE are preliminarily presented by temporarily monitoring changes in the polarization parameters of laser images of histological sections of tissues of various organs of a human corpse. The time at which saturation of the change in the polarization parameters of the laser images of histological sections was used as a universal diagnostic approach in determining the TDE. We investigated the temporal dynamics of changes in the revealed diagnostic parameters (dispersion of intensity distributions and extremes of spectra of intensity power) of histological skin sections to differentiate the origin of abrasions. When determining the time intervals injuries in lifetime and post-mortem, histological sections were used, which were made and examined in compliance with the initial conditions set forth in the “materials and research methods” chapter. Table 3.4 shows the data of the time dependence of the range of variation of the intensity dispersion (Ω I ) of laser images of the skin (Fig. 3.1b, c, Fig. 3.3, 3.4) with various types of damage. Table 3.5 illustrates similar time dependences of the dispersion of power spectra (Ω(PSD)) of laser images of the skin dermis. Averaging was carried out on the basis of an analysis of the temporary change in the statistical parameters (Ω I , Ω(PSD)) for 360 samples of the skin dermis, which were determined for each of them individually. Analyzing the data given in Table 3.4, it can be seen that according to the rate of change in the dispersion of the intensity of laser images of lifetime damaged skin and post-mortal damaged skin, they statistically significantly differ in the intervals of abrasion 1–8 h. According to Table 3.5, relative to the time dependence of the range of variance of the dispersion of the extrema of the power spectra of the intensity of laser images of

1 n = 16

4 n=8

12 n = 12

16 n = 16

20 n = 16

24 n = 16

P

p < 0.001

p < 0.001

30 n = 16

36 n = 12

42 n= 16

48 n= 12

8 n = 16

12 n = 16

16 n = 16

20 n = 16

24 n = 16

p < 0.001

p > 0.05

p > 0.05

p > 0.05

p > 0.05

30 n = 16

36 n = 16

42 n= 16

48 n= 16

0.11 ± 0.009 0.09 ± 0.007 0.08 ± 0.006 0.06 ± 0.004 0.05 ± 0.003 0.045 ± 0.003 0.04 ± 0.002 0.02 ± 0.001

8 n = 12

ΩI 0.23 ± 0.021 0.18 ± 0.013 0.15 ± 0.011 0.11 ± 0.008 0.07 ± 0.005 0.04 ± 0.003 0.02 ± 0.0015 (post-mortal)

Abrasions

Time

0.16 ± 0.012 0.14 ± 0.01

ΩI (lifetime)

4 n = 16

1 n = 20

Abrasions

Time

Table 3.4 Temporal dependence of the range of variation in the intensity dispersion of laser images of lifetime and post-mortal abrasions

54 n= 20

54 n= 8

3.3 Investigation of the Temporal Dynamics of Changes in the Statistical … 37

12 n = 12

16 n = 16

20 n = 16

24 n = 16

30 n = 16

36 n = 12

42 n= 16

48 n= 12

Time 12 n = 16

16 n = 16

20 n = 16

24 n = 16

p > 0.05

p > 0.05

p > 0.05

p > 0.05

p > 0.05

p > 0.05

p > 0.05

8 n = 16

P

4 n=8

0.07 ± 0.008 0.06 ± 0.005 0.04 ± 0.004 0.025 ± 0.001

1 n = 16

Ω(PSD) 0.13 ± 0.011 0.11 ± 0.013 0.09 ± 0.01 (post-mortal)

Abrasions

30 n = 16

36 n = 16

42 n= 16

48 n= 16

0.10 ± 0.008 0.09 ± 0.007 0.08 ± 0.009 0.07 ± 0.006 0.06 ± 0.005 0.05 ± 0.004 0.045 ± 0.003 0.004 ± 0.004 0.035 ± 0.003 0.02 ± 0.002

8 n = 12

Ω(PSD) (lifetime)

4 n = 16

1 n = 20

Abrasions

Time

54 n= 20

54 n= 8

Table 3.5 Temporal dependence of the range of variation of the dispersion of the extrema of the power spectra of the intensity of laser images of lifetime and post-mortal abrasions

38 3 Determination of the Lifetime and Post-mortal Nature and Temporal …

3.3 Investigation of the Temporal Dynamics of Changes in the Statistical …

39

Fig. 3.11 Temporal dynamics of changes in the intensity dispersion of images of skin with lifetime—(1) and post-mortal—(2) abrasions

damaged skin and post-mortal skin damage do not show the presence of a statistically significant difference. In Fig. 3.11, it shows temporal graphical dependences of changes in the dispersion of the intensity distribution of the laser image of skin histological sections with lifetime (curve 1) and post-mortal (curve 2) abrasions. Figure 3.12 illustrates similar dependences of the temporal variation of the dispersion of the extrema of the power spectra of the intensity distribution of the laser image of skin histological sections with lifetime (curve 1) and post-mortal (curve 2) abrasions. So, according to the statistical and graphical data presented, it can be seen that: • statistical parameters of the intensity distribution of laser images of the skin and their power spectra are interrelated with the time of abrasion; • with an increase in time (T), a monotonic decrease in the dispersion (Ω I , ΩPSD ) is observed, which is associated with changes in the optical properties of the anisotropy of the skin’s collagen network and parameters (concentration, fibrin polymerization) of hemorrhages • starting from a certain time (T), the decrease in the dispersions (Ω I , ΩPSD ) is stabilized. • The study of statistical distributions of the intensity of laser images of the skin was effective in determining the time intervals when lifetime and post-mortal abrasions appear: • for the dispersion of the intensity distribution (Ω I ) from 1 to 8 h;

40

3 Determination of the Lifetime and Post-mortal Nature and Temporal …

Fig. 3.12 Temporal dynamics of changes in the dispersion of the distribution of the extrema of the power spectra of the intensity distributions of laser images of the skin with lifetime (1) and post-mortal (2) abrasions

• for (ΩPSD ) the dispersion of the distribution of the extrema of the Log–log dependences of the intensity, power spectra were not found. Thus, the effectiveness of the method for analyzing the power spectra of the intensity distributions of laser images of human skin in differentiation the temporal nature of their damage has been shown; it was found that the intensity distributions of intact skin are self-similar on a large scale; lifetime abrasions are characterized by a stochastic structure of laser images; for post-mortal abrasions of the human skin, the coordinate structure of the intensity of their images is statistical.

References 1. A. Vitkin, N. Ghosh, A. Martino, Tissue polarimetry, in Photonics: Scientific Foundations, Technology and Applications, 4th edn., ed. by D. Andrews (John Wiley & Sons Inc., Hoboken, New Jersey, 2015), pp.239–321 2. V. Tuchin, Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, 2nd edn. (SPIE Press, Bellingham, Washington, USA, 2007) 3. W. Bickel, W. Bailey, Stokes vectors, Mueller matrices, and polarized scattered light. Am. J. Phys. 53(5), 468–478 (1985) 4. V. Ushenko, O. Vanchuliak, M. Sakhnovskiy, O. Dubolazov, P. Grygoryshyn, I. Soltys, O. Olar, System of Mueller matrix polarization correlometry of biological polycrystalline layers. Proc. SPIE 10352, 103520U (2017)

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5. V. Ushenko, O. Vanchuliak, M. Sakhnovskiy, O. Dubolazov, P. Grygoryshyn, I. Soltys, O. Olar, A. Antoniv, Polarization-interference mapping of biological fluids polycrystalline films in differentiation of weak changes of optical anisotropy. Proc. SPIE 10396, 103962O (2017) 6. O. Dubolazov, L. Trifonyuk, Y. Marchuk, Y. Ushenko, V. Zhytaryuk, O. Prydiy, L. Kushnerik, I. Meglinskiy, Two-point Stokes vector parameters of object field for diagnosis and differentiation of optically anisotropic biological tissues. Proc. SPIE 10352, 103520V (2017) 7. L. Trifonyuk, O. Dubolazov, Y. Ushenko, V. Zhytaryuk, O. Prydiy, M. Grytsyuk, L. Kushnerik, I. Meglinskiy, I. Savka, New opportunities of differential diagnosis of biological tissues polycrystalline structure using methods of Stokes correlometry mapping of polarization inhomogeneous images. Proc. SPIE 10396, 103962R (2017) 8. O. Dubolazov, V. Ushenko, L. Trifoniuk, Y. Ushenko, V. Zhytaryuk, O. Prydiy, M. Grytsyuk, L. Kushnerik, I. Meglinskiy, Methods and means of 3D diffuse Mueller-matrix tomography of depolarizing optically anisotropic biological layers. Proc. SPIE 10396, 103962P (2017) 9. A. Ushenko, A. Dubolazov, V. Ushenko, O. Novakovskaya, Statistical analysis of polarizationinhomogeneous Fourier spectra of laser radiation scattered by human skin in the tasks of differentiation of benign and malignant formations. J. Biomed. Opt. 21(7), 071110 (2016) 10. Y. Ushenko, G. Koval, A. Ushenko, O. Dubolazov, V. Ushenko, O. Novakovskaia, Muellermatrix of laser-induced autofluorescence of polycrystalline films of dried peritoneal fluid in diagnostics of endometriosis. J. Biomed. Opt. 21(7), 071116 (2016) 11. V. Prysyazhnyuk, Y. Ushenko, A. Dubolazov, A. Ushenko, V. Ushenko, Polarization-dependent laser autofluorescence of the polycrystalline networks of blood plasma films in the task of liver pathology differentiation. Appl. Opt. 55(12), B126–B132 (2016) 12. A. Ushenko, O. Dubolazov, V. Ushenko, O. Novakovskaya, O. Olar, Fourier polarimetry of human skin in the tasks of differentiation of benign and malignant formations. Appl. Opt. 55(12), B56–B60 (2016) 13. Y. Ushenko, V. Bachynsky, O. Vanchulyak, A. Dubolazov, M. Garazdyuk, V. Ushenko, Jonesmatrix mapping of complex degree of mutual anisotropy of birefringent protein networks during the differentiation of myocardium necrotic changes. Appl. Opt. 55(12), B113–B119 (2016) 14. A. Dubolazov, N. Pashkovskaya, Y. Ushenko, Y. Marchuk, V. Ushenko, O. Novakovskaya, Birefringence images of polycrystalline films of human urine in early diagnostics of kidney pathology. Appl. Opt. 55(12), B85–B90 (2016) 15. M. Garazdyuk, V. Bachinskyi, O. Vanchulyak, A. Ushenko, O. Dubolazov, M. Gorsky, Polarization-phase images of liquor polycrystalline films in determining time of death. Appl. Opt. 55(12), B67–B71 (2016) 16. A. Ushenko, A. Dubolazov, V. Ushenko, Y. Ushenko, M. Sakhnovskiy, O. Olar, Methods and means of laser polarimetry microscopy of optically anisotropic biological layers. Proc. SPIE 9971, 99712B (2016) 17. O. Dubolazov, A. Ushenko, Y. Ushenko, M. Sakhnovskiy, P. Grygoryshyn, N. Pavlyukovich, O. Pavlyukovich, V. Bachynskiy, S. Pavlov, V. Mishalov, Z. Omiotek, O. Mamyrbaev, Laser Müller matrix diagnostics of changes in the optical anisotropy of biological tissues, in Information Technology in Medical Diagnostics II—Proceedings of the International Scientific Internet Conference on Computer Graphics and Image Processing and 48th International Scientific and Practical Conference on Application of Lasers in Medicine and Biology, 2018, pp. 195–203 (2019) 18. M. Borovkova, M. Peyvasteh, O. Dubolazov, Y. Ushenko, V. Ushenko, A. Bykov, S. Deby, J. Rehbinder, T. Novikova, I. Meglinski, Complementary analysis of Mueller-matrix images of optically anisotropic highly scattering biological tissues. J. Eur. Opt. Soc. 14(1), 20 (2018) 19. H. Zhengbing, M. Ivashchenko, L. Lyushenko, D. Klyushnyk, Artificial neural network training criterion formulation using error continuous domain. Int. J. Mod. Educ. Comp. Sci. (IJMECS) 13(3), 13–22 (2021).https://doi.org/10.5815/ijmecs.2021.03.02 20. H. Zhengbing, I. Tereikovskyi, D. Chernyshev, L. Tereikovska, O. Tereikovskyi, D. Wang, Procedure for processing biometric parameters based on wavelet transformations. Int. J. Modern Educ. Comp. Sci. (IJMECS) 13(2), 11–22 (2021).https://doi.org/10.5815/ijmecs.2021.02.02

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21. H. Zhengbing, R. Odarchenko, S. Gnatyuk, M. Zaliskyi, A. Chaplits, S. Bondar, V. Borovik, Statistical techniques for detecting cyberattacks on computer networks based on an analysis of abnormal traffic behaviour. Int. J. Comp. Netw. Inf. Secur. (IJCNIS) 12(6), 1–13 (2020).https:// doi.org/10.5815/ijcnis.2020.06.01 22. H. Zhengbing, S. Gnatyuk, T. Okhrimenko, S. Tynymbayev, M. Iavich, High-speed and secure PRNG for cryptographic applications. Int. J. Comp. Netw. Inf. Secur. (IJCNIS) 12(3), 1–10 (2020). https://doi.org/10.5815/ijcnis.2020.03.01 23. H. Zhengbing, I. Dychka, M. Onai, Y. Zhykin, Blind payment protocol for payment channel networks. Int. J. Comp. Netw. Inf. Secur. (IJCNIS) 11(6), 22–28 (2019).https://doi.org/10. 5815/ijcnis.2019.06.03 24. H. Zhengbing, Y.V. Bodyanskiy, N.Ye. Kulishova, O.K. Tyshchenko, A multidimensional extended neo-fuzzy neuron for facial expression recognition. Int. J. Intell. Syst. Appl. (IJISA) 9(9), 29–36 (2017). https://doi.org/10.5815/ijisa.2017.09.04 25. H. Zhengbing, I. Dychka, Y. Sulema, Y. Radchenko, Graphical data steganographic protection method based on bits correspondence scheme. Int. J. Intell. Syst. Appl. (IJISA) 9(8), 34–40 (2017).https://doi.org/10.5815/ijisa.2017.08.04 26. V.G. Kolobrodov, Q.A. Nguyen, G.S. Tymchik, The problems of designing coherent spectrum analyzers, in Proceedings of SPIE, 2013, vol. 9066, p. Article number 90660N, 11th International Conference on Correlation Optics18 September 2013 through 21 September 2013, Code 103970 27. V.A. Ostafiev, S.P. Sakhno, S.V. Ostafiev, G.S. Tymchik, Laser diffraction method of surface roughness measurement. J. Mater. Process. Technol. N63, 871–874 (1997) 28. I. Chyzh, V. Kolobrodov, A. Molodyk, V. Mykytenko, G. Tymchik, R. Romaniuk, P. Kisała, A. Kalizhanova, B. Yeraliyeva, Energy resolution of dual-channel opto-electronic surveillance system, in Proceedings Volume 11581, Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments 2020; 115810K, Wilga, Poland (2020). https:// doi.org/10.1117/12.2580338 29. V.H. Kolobrodov, V.I. Mykytenko, G.S. Tymchik, Polarization model of thermal contrast observation objects. Thermoelectricity 1, 36–49 (2020) 30. V.H. Kolobrodov, M.S. Kolobrodov, G.S. Tymchik, A.S. Vasyura, P. Komada, Z. Azeshova, The output signal of a digital optoelectronic processor, in Proc. SPIE 10808, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018, 108080W (1 October 2018) 31. G.S. Tymchik, V.I. Skytsyuk, T.R. Klotchko, H. Bezsmertna, W. Wójcik, S. Luganskaya, Z. Orazbekov, A. Iskakova, Diagnosis abnormalities of limb movement in disorders of the nervous system, in Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2017, 2017/8/7, pp. 104453S-104453S-11. https://doi.org/10.1117/12. 228100

Chapter 4

Study of Two-Dimensional Polarization Maps of the Skin for Differentiation of Lifetime and Post-mortal Nature and Temporal Dynamics of Abrasions

4.1 Study of Two-Dimensional Distributions of Azimuths of Polarization of Laser Images of the Skin with Lifetime and Post-mortal Abrasions The coordinate distributions of the azimuth a(x, y) and ellipticity b(x, y) [1–9] of laser radiation transformed by biomannequin skin samples were measured according to the scheme and methodology, which are given in Chap. 2, Sect. 2.3, Sub-Sect. 2.3.1. Series of Figs. 4.1 and 4.2 present the dependences a(x, y) and histograms of their values for the laser images of biomannequin skin tissue with lifetime (Fig. 4.1, observation time 1 year) and post-mortal (Fig. 4.2, observation time 1 year) changes. A comparative analysis of the obtained experimental data showed that, depending on the origin of abrasions, the distribution of azimuths of the polarization of the laser image of the studied histological sections of samples of abrasions of the skin are coordinate-inhomogeneous structures [10–14]. This may be due to the peculiarities of the coordinate distribution of collagen fibers of the skin architectonics and the degree of blood supply to the damaged dermal layer. In areas with a higher concentration of hemorrhages, a rapid change in the polarization azimuth is formed due to multiple light scattering by them of laser radiation. Therefore, in the polarization distribution of the dependence a(x, y), a small-scale structure of local quasistationary values ai (x, y) ≈ const is formed (see the upper parts of Figs. 4.1 and 4.2). The general level of the coordinate distribution of polarization azimuths for a laser image of skin tissue with lifetime damage (Fig. 4.1) is higher than the similar coordinate distribution of the plane of polarization of laser radiation transformed by skin tissue with post-mortal abrasions (Fig. 4.2). Conducting a qualitative analysis of histograms for lifetime and post-mortal abrasions, it is seen that the histograms of lifetime abrasion are characterized by a gradual © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Hu et al., Laser Polarimetry of Biological Tissues, SpringerBriefs in Applied Sciences and Technology, https://doi.org/10.1007/978-981-99-1734-1_4

43

44

4 Study of Two-Dimensional Polarization Maps of the Skin …

Fig. 4.1 Two-dimensional distribution of polarization azimuths and histograms of their values in a laser image of skin with lifetime abrasions (T = 1 h), (n = 20)

Fig. 4.2 Two-dimensional distribution of polarization azimuths and histograms of their values in the laser image of the skin with post-mortal abrasions (T = 1 h) (n = 12)

increase in azimuth to a level 125 of polarization, followed by a rapid drop to a level of 175, after which a gradual rise in azimuth is detected. As for the histogram post-mortal abrasion, the azimuth gradually decreases to the level 90 of polarization, followed by a gradual increase, that is, the histogram of the lifetime abrasion is irregularly-sinusoidal, and the histogram post-mortal abrasion is U-shaped. The histograms of the azimuths of the polarization a(x, y) of laser radiation scattered by skin tissues with both lifetime and post-mortal damage represent various types of distributions. Similar values of the histogram measured for the field of laser radiation scattered by skin tissue with post-mortem abrasions are mainly distributed in the areas of the two most probable values a(x, y). The discovered difference in the statistical structure of the polarization distributions of azimuths of laser radiation can be associated with a more intense blood supply to the dermal layer of lifetimely damaged skin. Therefore, the features of the orientational structure of optically anisotropic collagen fibers and the corresponding sections of the preferred values of polarization azimuths (Fig. 4.2) are somewhat averaged by multiple light scattering acts along the entire plane of the sample under study, and histograms are transformed a(x, y) to the side of equally probable statistical distributions.

4.1 Study of Two-Dimensional Distributions of Azimuths of Polarization … Table 4.1 Statistically averaged values of the average and dispersion of the distribution of azimuths of polarization of laser images of the skin (T = 1 h)

Statistical moments

Intact skin (n = 48)

Average, M 1

0.36 ± 0.05

45

Abrasions Lifetime (n = 20)

Post-mortal (n = 16)

0.58 ± 0.06

0.47 ± 0.04

P1

p < 0.001

p > 0.05

P2

p < 0.001

Dispersion, M 2 0.03 ± 0.004 0.11 ± 0.014 0.13 ± 0.012 P1

p < 0.001

P2

p < 0.001

p < 0.001

The discussion above indicates the prospects of using a statistical analysis of the azimuths of the polarization a(x, y) of laser radiation scattered by human skin tissue for differentiation the lifetime or post-mortal nature of injuries. Table 4.1 shows the results of a statistically reliable (within a group of 108 samples) study of the average (M1 ) and dispersion (M2 ) coordinate distributions of the following groups of histological sections: • intact skin; • skin with lifetime abrasion; • skin with post-mortal abrasion. The statistical moments of the first–second orders of magnitude were calculated using relation (2.5), (2.6) (see Chap. 2, Sect. 2.4) based on an analysis of 48,000 random values of the polarization azimuth determined within each pixel of a digital CCD camera (10) registering a laser image (Fig. 2.11, Chap. 2, Sect. 2.3). Analysis of the statistical structure of the coordinate distribution of the polarization azimuth values of histological sections of the dermis of the intact, lifetime, and postmortal abrasions of a human corpse showed that the indices for the comparison groups of the lifetime abrasion-control have a statistically significant difference. As for the indicator M 2 , namely the distributions of polarization azimuths, there is a statistically significant difference for both lifetime and post-mortal abrasion compared to the control. Lifetime and post-mortal abrasions themselves tend to statistically significant difference. Thus, the study of statistical moments (average and dispersion) of the distribution of polarization azimuths of laser images of damaged skin samples of biomannequin dermis can be used to differentiate the origin of abrasions—lifetime or post-mortal. On the other hand, the urgent task is to establish the temporal features of the change in the polarization structure of laser images of skin histological sections of these origin. These features of changes in the coordinate distributions of polarization states can be associated with temporary changes in the blood structure and rigor mortis of biological tissue. Such processes of cadaveric changes are manifested in an increase in optical anisotropy and an increase in the light scattering frequency, which lead to

46

4 Study of Two-Dimensional Polarization Maps of the Skin …

an increase in both the total rotation of the plane of polarization of the laser radiation and an expansion of the statistical range of variation of such angles or azimuths. Therefore, the next step in the study was to study the features of the topological (local spatial structure, coordinate distributions a(x, y)) structure of polarization images of two (in lifetime and post-mortal damaged) groups of histological sections of human body skin samples for a long time of observation after damage. The main object of such studies was the experimental tracking of a temporary change in the polarization structure of laser images of biomannequin skin by statistical analysis of the dependences of the statistical moments of the first and second orders of the coordinate distributions of polarization azimuth values. In the series of Figs. 4.3 and 4.4, it shows the dependences a(x, y) and histograms of their values determined 24 h after lifetime (Fig. 4.3) and post-mortal (Fig. 4.4) skin abrasions. Analysis of histograms of the distribution of polarization azimuths, depending on the duration of application of lifetime abrasion, shows a qualitative modification of the histogram with abrasions 24 h old compared with histograms with abrasions 1 h old.

Fig. 4.3 Two-dimensional distribution of polarization azimuths and histograms of their values in a laser image of skin with lifetime abrasions (T = 24 h), (n = 16)

Fig. 4.4 Two-dimensional distribution of polarization azimuths and histograms of their values in a laser image of skin with post-mortal abrasions (T = 24 h), (n = 16)

4.1 Study of Two-Dimensional Distributions of Azimuths of Polarization …

47

So, with the injury duration of 24 h, the histogram is characterized by a gradual decrease in azimuth to the level of polarization 80, followed by a rise in azimuth to the level of polarization 175. That is, a quality histogram resembles an irregular sinusoidal. As for the histogram for post-mortal abrasion, it is U-shaped, but somewhat narrow compared to a wide U-shaped one for the prescription of injury 1 h. A comparative analysis of the obtained experimental data on the structure of the distribution of polarization azimuths of laser images of histological sections of lifetime and post-mortal abrasion, recorded 24 h after application, was found: • The distributions of the azimuth of the polarization of laser radiation are largerscale coordinate-inhomogeneous structures compared with the distribution structures a(x, y) determined for different origin of histological skin Sects. 1 h after abrasion (Figs. 4.1 and 4.2). • The average statistical sizes of sites ai (x, y) ≈ const for polarization images of lifetime abrasion in the time interval from 1 to 24 h experience an increase in the range from 7–12 µm (Fig. 4.1) to 15–25 µm (Fig. 4.3). For laser images of histological sections of samples post-mortal abrasion, the change in the size of the polarization domains ai (x, y) ≈ const is much larger from 14–20 µm (Fig. 4.2) to 45–60 µm (Fig. 4.4). • The general level of values a(x, y) for laser images of skin tissues with both types of abrasion origin (Figs. 4.3 and 4.4), registered 24 h after their application, is higher than similar random values of the plane of polarization of laser radiation in the coordinate distributions of azimuths for skin tissues examined through an 1 h after abrasion (Figs. 4.1 and 4.2). A temporary change in the polarization structure of laser images of both types of abrasion origin is illustrated by the redistribution of extrema of the corresponding distribution histograms a(x, y). • For skin tissues with lifetime abrasions, there is a redistribution of random polarization azimuth values in the direction of both small and large values (Figs. 4.1 and 4.3). Such a transformation can be associated with the polymerization (accumulation) of blood and the formation of spatially oriented optically anisotropic fibrin fibrils, which, in combination with collagen bundles of the dermal layer, form not any statistically equally probable, but prevailing polarization azimuths corresponding to the “appearance” of new extrema of the corresponding histograms (Fig. 4.3). • For histological sections of skin samples with post-mortal abrasions, the temporary transformation of histograms of the distribution of polarization azimuth values of the corresponding laser images (Figs. 4.2 and 4.4) is not as expressive as in the case of lifetime abrasions. Therefore, the azimuth of the polarization of laser radiation is determined mainly as a result of the occurrence of phase shifts between the orthogonal components of its amplitude when interacting with optically anisotropic collagen fibers forming a dermal network layer. With an increase in time after abrasion, this mechanism remains dominant, which is manifested in a less dynamic change in the corresponding distribution histogram a(x, y) (Fig. 4.4), which is characterized by the redistribution of extrema from regions of

48

4 Study of Two-Dimensional Polarization Maps of the Skin …

Table 4.2 Statistically averaged values of the average and dispersion of the distribution of azimuths of polarization of laser images of the skin (T = 24 h)

Statistical moments

Intact skin (n = 48)

Abrasions Lifetime (n = 16)

Post-mortal (n = 16)

Average, M 1

0.29 ± 0.06

0.37 ± 0.046

0.23 ± 0.024

P1

p > 0.05

p > 0.05

P2

p < 0.05 0.21 ± 0.024

0.31 ± 0.025

P1

p < 0.001

p < 0.001

P2

p < 0.05

Dispersion, M2

0.05 ± 0.007

small and large values of polarization azimuth to the zone of its average values. Differences in the coordinate structure of polarized images of dermal tissue of intact skin, lifetime, and post-mortal abrasions objectively illustrate the significance of statistical moments of the first and second orders characterizing the distributions a(x, y), which were experimentally determined 24 h after applying abrasions (Table 4.2). Conducting a statistical analysis of the averaged dispersion of the distribution of polarization azimuths for 24 h, it is clear that in the comparison groups the lifetime abrasion-control and after the mortal abrasion-control for M1 , the difference is unreliable, while in the comparison group, the lifetime abrasion-post-mortal abrasion is reliable difference. For the second statistical moment (M2 ), a statistically significant difference exists in all three comparison groups. Thus, comparative statistical studies of the temporal evolution of the polarization distributions of turns of the amplitude plane of laser radiation transformed by histological sections of skin samples with lifetime and post-mortal abrasions revealed the sensitivity of statistical moments of the first and second orders characterizing the distribution of polarization azimuths a(x, y) to the time elapsed after traumatic injuries appearance. This fact is the basis for a more detailed, systematic study of the temporal dynamics of changes in the statistical structure of the polarization states of laser images of skin samples with different origin of abrasions.

4.2 Study of the Temporal Dynamics of Changes in the Average …

49

4.2 Study of the Temporal Dynamics of Changes in the Average and Dispersion of the Coordinate Distributions of the Azimuths of Polarization of Laser Images of Skin Abrasions In Figs. 4.5 and 4.6, it shows the results of temporary monitoring of changes in the average (M1 ) and dispersion (M2 ) coordinate distributions of polarization azimuths in laser images of histological sections of lifetime and post-mortal abrasions. Table 4.3 shows the results of time monitoring of changes of averaged value (M1 ) coordinate distributions of polarization azimuths in laser images of histological sections of lifetime and post-mortal abrasions, which show the presence of a statistically significant difference in time dynamics from 1 to 90 h. Table 4.4 shows the results of temporary monitoring of changes in the average (M1 ) and dispersion (M2 ) of coordinate distributions of polarization azimuths in laser images of histological sections of lifetime and post-mortal abrasions, which show that there is M2 a statistically significant difference between lifetime abrasions and post-mortal abrasions only in cases causing injury from 1 to 30 h. In subsequent time intervals, the difference is not significant. From an analysis of the temporal dependences of statistical moments of the first–second order of distribution of the values of the polarization azimuth of laser images of histological sections of the skin with lifetime and post-mortal abrasions,

Fig. 4.5 Temporal dependences of the change in the average coordinate distribution of the polarization azimuths of the laser image of the skin with lifetime (1) and post-mortal (2) abrasions

50

4 Study of Two-Dimensional Polarization Maps of the Skin …

Fig. 4.6 Temporal dependences of changes in the dispersion of the coordinate distribution of the polarization azimuths of the laser image of the skin with lifetime (1) and post-mortal (2) abrasions

it follows that the whole set of statistical moments of the first–second order experiences monotonous temporal changes in eigenvalues, reaching through certain time intervals of a stable level, the onset time of which is a criterion for establishing a time interval for applying abrasions. Thus, a statistical analysis of the transformation of the coordinate distributions of polarization azimuths turned out to be effective both in differentiating the origin of abrasion (lifetime or post-mortal) of the skin, as well as in determining the age of their application in the lifetime or post-mortal period. It should be noted that the change in the azimuth of the polarization of laser radiation converted by optical-anisotropic collagen fibrils mainly depends on their orientation in the plane of the histological section under study. Therefore, it is relevant to study another polarization parameter—polarization ellipticity, which is determined by the magnitude of birefringence or anisotropy of all structures (collagen network, fibrin filaments, uniform blood cells, blood plasma, etc.) of the dermal layer of human skin.

18 n = 16

24 n = 16

18 n = 16

24 n = 16

54 n=8

60 n=8

30 n = 16

36 n = 16

42 n = 16

48 n = 16

54 n = 20

60 n = 12

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.001

12 n = 16

48 n = 12

6° ± 0.45° 4° ± 0.35° 3° ± 0.25° 2° ± 0.15°

6 n = 16

42 n = 16

(Post-mortal) 23° ± 2.2° 19° ± 1.8° 17° ± 1.6° 14° ± 1.1° 12° ± 0.95° 9° ± 0.83° 7° ± 0.5°

1 n = 16

36 n = 12

70 n=8

80 n=8

90 n=8

70 n=8

80 n=8

90 n = 12

23° ± 2.1° 18° ± 1.9° 16° ± 1.7° 14° ± 0.9° 11° ± 0.7° 8° ± 0.6° 6° ± 0.4° 5° ± 0.5° 4° ± 0.4°

30 n = 16

P

Abrasions

Time (T)

43° ± 3.8° 38° ± 2.6° 34° ± 3.5° 30° ± 2.4° 27° ± 2.3°

12 n = 12

(Lifetime)

6 n = 16

1 n = 20

Abrasions

Time (T)

Table 4.3 Temporal dynamics of changes in the average (M1 ) distribution of polarization azimuths of laser images of histological sections of lifetime and post-mortal abrasions

4.2 Study of the Temporal Dynamics of Changes in the Average … 51

1 n = 16

P

18 n = 16

12 n = 16

18 n = 16

11 ± 1.05 13 ± 1.14

12 n = 12

30 n = 16

36 n = 12

24 n = 16

30 n = 16

36 n = 16

15 ± 1.25 17 ± 1.31 18 ± 1.9

24 n = 16

42 n = 16

21 ± 1.7

42 n = 16

48 n = 16

24 ± 1.9

48 n = 12

60 n=8

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.05

p < 0.05

p < 0.05

70 n=8

80 n=8

90 n=8

54 n = 20

60 n = 12 p < 0.05

p < 0.05

70 n=8

80 n=8

90 n = 12

25 ± 2.17 28 ± 2.16 29 ± 2.4 30 ± 2.5 31 ± 3.04

54 n=8

19.5 ± 1.8 21 ± 1.96 21.5 ± 2.1 23 ± 2.95 24 ± 1.83 25 ± 2.25 26 ± 2.45 27 ± 2.35 29 ± 2.65 31 ± 3.15

6 n = 16

p < 0.001 p < 0.001

(Post-mortal) 19 ± 1.2

Abrasions

10 ± 0.86

8 ± 0.7

(Lifetime)

Time (T)

6 n = 16

1 n = 20

Abrasions

Time (T)

Table 4.4 Temporal dynamics of changes in the dispersion (M2 ) distribution of polarization azimuths of laser images of histological sections of lifetime and post-mortal abrasions

52 4 Study of Two-Dimensional Polarization Maps of the Skin …

4.3 Study of Two-Dimensional Distributions of Ellipticity of Polarization …

53

4.3 Study of Two-Dimensional Distributions of Ellipticity of Polarization of Laser Images of Skin with Lifetime and Post-mortal Abrasions In the series of Figs. 4.7 and 4.8, it shows the coordinate dependences of ellipticity b(x, y) and histograms of their values for the laser image of histological sections of biomannequin skin tissue with lifetime (Fig. 4.7) and post-mortal (Fig. 4.8) abrasions after 1 h of observation. An analysis of the obtained polarization distributions found that in lifetime and post-mortal abrasions, the distribution of the ellipticity of the polarization of the laser image of the examined histological sections of the damaged skin samples is the domain, coordinately-heterogeneous structures. Local values of ellipticity in the corresponding image caused by both the coordinate distribution of the birefringence index of collagen fibers of the skin architectonics and the concentration of polymer as a result of blood coagulation, fibrin in the dermal layer of the skin. In areas with a higher concentration of hemorrhages, large values

Fig. 4.7 Two-dimensional distribution of polarization ellipticity and histograms of their values in a laser image of skin with lifetime abrasions (T = 1 h), (n = 20)

Fig. 4.8 Two-dimensional distribution of polarization ellipticity and histograms of their values in a laser image of skin with post-mortal abrasions (T = 1 h), (n = 16)

54

4 Study of Two-Dimensional Polarization Maps of the Skin …

of polarization ellipticity are formed (due to increased anisotropy). Therefore, in the polarization distribution of the dependence b(x, y), the scale structure of the local polarization domains bi (x, y) ≈ const is formed (see the upper parts of Figs. 4.7 and 4.8). The general level of ellipticity in the laser image of the skin with lifetime abrasions (Fig. 4.7) is higher than the similar coordinate distribution b(x, y) of the plane of laser radiation transformed by the skin tissue with post-mortal abrasions (Fig. 4.8). The histograms of the coordinate distributions of the ellipticities b(x, y) of the polarization of laser radiation scattered by skin tissues with both lifetime and postmortal abrasions are similar bells symmetrical with respect to the main extremum of the distributions. The main difference in the statistical structure of the polarization distributions of the ellipticity of laser radiation is the localization of the extremum of the histogram of the laser image of the skin with lifetime abrasions in the region of large values b(x, y)—51 and 62. The revealed difference can be associated with a large blood supply (and, accordingly, a greater degree of birefringence) of the dermal layer of lifetimely damaged skin. A qualitative analysis of the histograms of the two-dimensional distribution of polarization ellipticity indicates that the histograms of lifetime and post-mortal abrasions have the same peak-like character, but differ in azimuth, which significantly prevails in lifetime abrasions. Table 4.5 shows the results of studies of statistically averaged (within a group of 72 samples) values of the 1st (M1 ) and 2nd (M2 ) statistical moments of the coordinate distribution of the ellipticity of polarization images of histological sections of intact skin, lifetime and post-mortal abrasions. An analysis of the coordinate distributions of the polarization ellipticity values of laser images of histological sections of intact skin, lifetime, and post-mortal abrasions showed that the averaged polarization ellipticity distribution index M1 in the comparison group and lifetime abrasion-control have a statistically significant difference, and in the comparison group post-mortal abrasion-control, the difference is unreliable, which allows to differentiate between lifetime and post-mortal abrasion. Table 4.5 Statistically averaged values of the average and dispersion of the distribution of ellipticity of polarization of laser images of the skin (T = 1 h)

Statistical moments

Intact skin (n = 48)

Abrasions Lifetime (n = 20)

Post-mortal (n = 16)

25 ± 1.8

14 ± 1.4

P1

p < 0.001

p > 0.05

P2

p < 0.001

Average, M1

10 ± 1.1

6 ± 0.2

11 ± 1.2

P1

p > 0.05

p < 0.001

P2

p < 0.001

Dispersion, M2

5 ± 0.46

4.3 Study of Two-Dimensional Distributions of Ellipticity of Polarization …

55

As for the indicator M2 , the lifetime abrasion with the control practically does not differ, while after the mortal abrasion, it acquires a significant difference with the control. Thus, information on statistical moments (average and dispersion) of the distribution of ellipticity of polarization of laser images of damaged skin samples can be used to differentiate the origin of abrasions—lifetime or post-mortal. The next step in the study was to study the local or domain structure of the coordinate distributions of the ellipticity of laser images of histological sections of lifetime and post-mortal abrasions for a long time of observation after damage by analyzing the dependences of statistical moments of first–second orders of distributions of values b(x, y). In the series of Figs. 4.9 and 4.10, it shows the coordinate dependences of the polarization ellipticity and the histogram of the probable distribution of their random values, determined after 24 h in lifetime (Fig. 4.9) and post-mortal (Fig. 4.10) appearance of biomanekens abrasions.

Fig. 4.9 Two-dimensional distribution of ellipticity of polarization and histograms of their values in the laser image of skin with lifetime abrasions (T = 24 h), (n = 16)

Fig. 4.10 Two-dimensional distribution of polarization ellipticity and histograms of their values in the laser image of skin with post-mortal abrasions (T = 24 h), (n = 16)

56 Table 4.6 Statistically averaged values of the average and dispersion of the distribution of ellipticity of polarization of laser images of the skin (T = 24 h)

4 Study of Two-Dimensional Polarization Maps of the Skin … Statistical moments

Intact skin (n = 48)

Abrasions Lifetime (n = 20)

Post-mortal (n = 16)

Average, M1

5 ± 0.56

16 ± 1.7

7 ± 0.6

P1

p < 0.001

p > 0.05

P2

p < 0.001 9 ± 0.82

13 ± 1.14

P1

p > 0.05

p < 0.001

P2

p < 0.001

Dispersion, M2

7 ± 0.57

An analysis of the experimental data on the coordinate structure of the polarization ellipticity of laser images of histological sections of lifetime and post-mortal abrasions recorded 24 h after damage showed that qualitatively histograms acquire changes that are manifested by a narrowing of their spectrum. Differences in the coordinate structure of the ellipticity of polarized images of the derma of intact skin, lifetime, and post-mortal abrasions objectively illustrate the average and dispersion characterizing the distribution b(x, y), which are experimentally determined 24 h after the damage and are shown in Table 4.6. Analysis of the statistical moments of the first and second orders of the distribution of the ellipticity of polarization of the laser images of histological sections of the dermis of intact skin, lifetime, and post-mortal abrasions recorded 24 h after the lesion showed the presence of a statistical difference in the comparison group lifetime abrasion-control for M1 that allows you to use the indicator M1 to determine the lifetime injury. As for the indicator M2 , it is more characteristic for post-mortal abrasion. This fact is the basis for a more detailed, systematic study of the temporal dynamics of the statistical structure of the polarization states of laser images of skin samples with different origin of damage.

4.4 Investigation of the Temporal Dynamics of Changes in the Average and Dispersion of the Coordinate Distribution of the Ellipticity of Polarization of Laser Images of Skin Abrasions In Figs. 4.11 and 4.12, it shows the results of a study of the temporal evolution of changes in the average (M1 ) and dispersion (M2 ) coordinate distributions of the ellipticity of polarization in laser images of skin histological sections with lifetime and post-mortal abrasions. Table 4.7 shows the results of studies of the temporal evolution of the change in the average (M1 ) of the coordinate distribution of polarization ellipticity in laser

4.4 Investigation of the Temporal Dynamics of Changes in the Average …

57

Fig. 4.11 Temporal dependences of the average of two-dimensional distribution of the ellipticity of polarization of laser images of skin with lifetime (1) and post-mortal (2) abrasions

Fig. 4.12 Temporal dependences of the dispersion of two-dimensional distribution of the ellipticity of polarization of laser images of skin with lifetime (1) and post-mortal (2) abrasions

images of skin histological sections with lifetime and post-mortal abrasions with a change in the hourly interval of 6 h, which show that differentiation of lifetime or post-mortal origin of skin abrasions is possible in time from 1 to 60 h. Table 4.8 shows the results of studies of the temporal evolution of the dispersion (M2 ) of the coordinate distribution of polarization ellipticity in laser images of skin

1 n = 16

P

11 ± 0.8

6 n = 16

9 ± 0.6

12 n = 16

18 ± 1.5

12 n = 12

7 ± 0.7

18 n = 16

16 ± 1.4

18 n = 16

6 ± 0.5

24 n = 16

15 ± 1.3

24 n = 16

5 ± 0.3

30 n = 16

14 ± 1.1

30 n = 16

4 ± 0.5

36 n = 16

12 ± 0.9

36 n = 12

3 ± 0.25

42 n = 16

11 ± 0.7

42 n = 16

54 n=8

2 ± 0.15

48 n = 16

60 n = 12

5 ± 0.4

60 n=8

66 n = 12

3 ± 0.4

66 n=8

72 n=8

72 n=8

78 n=8

78 n=8

p < 0.001 p < 0.001 p > 0.05 p > 0.05 p > 0.05

54 n = 20

10 ± 0.8 8 ± 0.6

48 n = 12

p < 0.001 p < 0.001 p < 0.001 p < 0.001 p < 0.001 p < 0.001 p < 0.001 p < 0.001 p < 0.001

(Post-mortal) 14 ± 1.2

Abrasions

21 ± 1.6

25 ± 1.7

(Lifetime)

Time (T)

6 n = 16

1 n = 20

Abrasions

Time (T)

Table 4.7 Temporal dynamics of changes in the average (M1 ) of the distribution of ellipticity of polarization of laser images of histological sections of lifetime and post-mortal abrasions

58 4 Study of Two-Dimensional Polarization Maps of the Skin …

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps …

59

histological sections with lifetime and post-mortal abrasions with a change in the hourly interval of 6 h, which show that there is a statistically significant difference in two intervals: from 1 to 24 h and for an interval of 36 h. All other time ranges do not have a statistically significant difference. An analysis of the time dependences of the average and dispersion of the distribution of values of the ellipticity of polarization of laser images of skin histological sections with lifetime and post-mortal injuries implies that the whole set of statistical moments of the first–second orders experiences monotonous temporal changes in eigenvalues, reaching a stable level after certain time intervals, the onset time of which is a criterion for establishing the interval for determining the time of abrasion. Thus, the statistical analysis of the transformation of the coordinate distribution of the ellipticity of polarization also proved to be effective (although less sensitive than in the case of analysis of the distribution of polarization azimuths of laser images of lifetime and post-mortal abrasions—Tables 4.7 and 4.8, Figs. 4.11 and 4.12) as in differentiating the origin of the damage (lifetime or post-mortal) skin, as well as in determining the prescription of their application. On the other hand, for reliable, objective analysis and differentiation of twodimensional distributions of polarization parameters of a coordinate-inhomogeneous, domain structure of laser images of histological sections of damaged skin, their correlation analysis, and related spatial-frequency analysis may become promising.

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps of Skin Abrasions It is known that the best analytical tool for evaluating such domain structures is the determination of the autocorrelation function (see Chap. 2, Sect. 2.4, relation 2.7), which allows us to estimate the degree of similarity of the coordinate distributions of azimuths and the ellipticity of polarization of the laser image in its various coordinate regions [1–11]. Each extremum of such a spectrum corresponds to the number of polarization domains of a particular geometric size in the studied distribution of polarization parameters a(x, y) and b(x, y). Therefore, the calculation of such a spatial-frequency spectrum, where high frequencies ( d1 ) correspond to small-scale structures, and conversely, low frequencies characterize the presence of large-scale domains in various experimental distributions, makes it possible to very accurately estimate their coordinate changes under the influence of both traumatic and temporary factors. Using such a frequency analysis, a comparative study of the temporal changes in the amplitude and the corresponding number of extrema in the distribution of the calculated power spectra of two-dimensional distributions of polarized states a(x, y) and b(x, y) laser radiation scattered by the skin samples was carried out. Due to the fact that the values of the extrema of the power spectrum are very large and lie in a

P

18 n = 16

12 n = 16

36 n = 12

30 n = 16

36 n = 16

10 ± 1.1 11 ± 0.9

30 n = 16

48 n = 12

54 n=8

60 n=8

66 72 78 n= n= n= 8 8 8

42 n = 16

p > 0.05 p < 0.001 p > 0.05

48 n = 16

54 n = 20

60 n = 12

66 72 78 n= n= n= 12 8 8

13 ± 0.9 15 ± 1.1 17 ± 1.4 18 ± 1.6 20 ± 2.4

42 n = 16

13.5 ± 1.1 14 ± 1.3 15 ± 1.25 16 ± 1.45

24 n = 16

9.5 ± 0.8

24 n = 16

p < 0.001 p < 0.001 p < 0.001

13 ± 0.9

18 n = 16

7.5 ± 0.5 9 ± 0.74

12 n = 12

11.5 ± 0.95 12 ± 1.1

6 n = 16

p < 0.001 p < 0.001

(Post-mortal) 11 ± 1.2

1 n = 16

Time (T)

7 ± 0.6

6 ± 0.5

(Lifetime)

Abrasions

6 n = 16

1 n = 20

Abrasions

Time (T)

Table 4.8 Temporal dynamics of changes in the dispersion (M2 ) of the distribution of ellipticity of polarization of laser images of histological sections of lifetime and post-mortal abrasions

60 4 Study of Two-Dimensional Polarization Maps of the Skin …

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps …

61

very wide range, logarithmic representations of this distribution are traditionally used in the form of LogPSDa − log(x) or LogPSDb − log(y). Here, the parameters x, y have the meaning of spatial frequencies ( d1 ) in one or another coordinate direction [15–17]. So, the larger the geometric size of the plot of certain values of the polarization parameters in its coordinate distribution, the less the spatial frequency corresponds to it, and vice versa [18–29]. The extrema of the power spectra LogPSDa, b characterize the total number of structural sections in the corresponding distributions a, b(x, y). Thus, based on a comparative analysis of the time evolution of the dependences LogPSDa, b − log(x) calculated on the basis of experimental data for a group of human skin tissue samples, a targeted search for a particular diagnostic criterion can be carried out, on the basis of which can be realized additional possibilities of objective determination of the time of application of traumatic injuries. This section presents the results of an experimental measurement of the structure of autocorrelation functions and Log–log dependences of the spectra of coordinate distributions a(x, y) of laser images of a set of skin histological sections of the following origins: • lifetime abrasions and examined after 1 h (a(x, y)—Fig. 4.13) and 24 h (a(x, y)— Fig. 4.15) after damage; • post-mortal abrasions and examined after 1 h (a(x, y)—Fig. 4.14) and 24 h (a(x, y)—Fig. 4.16) after damage. For a comparative analysis of a series of autocorrelation functions of the distribution of the polarization parameters a(x, y) of laser images of damaged skin, we L of its half-width L, where X introduce an indicator of the relative value L = X is the full interval of the change in the coordinate (x) of the distribution of azimuth or ellipticity of polarization. Features of the distribution of the extrema of the Log–log dependences LogPSDa, b − log(x) of the power spectra of the coordinate polarization distributions will be characterized by the dispersion of their deviations from the average value.

Fig. 4.13 Two-dimensional autocorrelation functions of the power of the distribution of the azimuths of polarization of the laser image of the skin with lifetime abrasions (T = 1 h), (n = 20)

62

4 Study of Two-Dimensional Polarization Maps of the Skin …

Fig. 4.14 Two-dimensional autocorrelation functions of the power of the distribution of the azimuths of polarization of the laser image of the skin with post-mortal abrasions (T = 1 h), (n = 20)

Fig. 4.15 Two-dimensional autocorrelation functions of the power of the distribution of the polarization azimuths of the laser image of the skin with lifetime abrasions (T = 24 h), (n = 16)

Fig. 4.16 Two-dimensional autocorrelation functions of the power of the distribution of the polarization azimuths of the laser image of the skin with post-mortal abrasions (T = 24 h), (n = 16)

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps …

63

4.5.1 Correlation Analysis of Coordinate Distributions of the Azimuth of Polarization of the Laser Images of Skin Abrasions Let us analyze the correlation and spatial-frequency structure of the coordinate distributions of the polarization azimuths of laser images of skin histological sections with lifetime (Fig. 4.13) and post-mortal (Fig. 4.14) abrasions 1 h after their appearance. Each of the figures consists of two fragments, which are formed by the coordinate (topological) and analytical representations of the autocorrelation functions (ACF). From the obtained data on the features of the correlation structure of laser images of the skin with various origin of abrasions, studied 1 h after their application, we can draw the following conclusions: • the two-dimensional autocorrelation functions of the coordinate distributions of the azimuths of polarization of laser images of skin samples of both origins are azimuthally symmetric structures, which is associated with the central symmetry of the orientations of birefringent collagen fibers of the architectonic skin mesh; • for a polarized image of a skin sample with lifetime abrasions, ACF has a larger half-width L (~0.33) compared to the similar correlation parameter determined for the ACF of the laser image of skin tissue with post-mortal abrasions (~0.25). With an increase in time (24 h after abrasion), the correlation structure of the coordinate distributions of the azimuths of polarization of laser images of histological sections of lifetime tissue (Fig. 4.15) and post-mortal (Fig. 4.16) abrasions experiences the following changes: • the azimuthal symmetry of the two-dimensional topological distributions of ACF values is maintained, but the rate of decrease in their relative magnitude is slowed down in comparison with similar correlation dependences measured for laser images of the skin 1 h after abrasion (“lifetime”—Figs. 4.13 and 4.15 and “postmortal”—Figs. 4.14 and 4.16); • quantitative differences in the correlation functions characterize the changes in the corresponding values of the reduced half-width parameter (L), the value of which increases and amounts to 0.41 (Fig. 4.15) for samples with lifetime and 0.33 (Fig. 4.16) abrasions post-mortality, respectively. Table 4.9 shows the statistically averaged values and ranges of changes in the correlation parameter (L) of laser images of two groups of skin histological sections with lesions of both origins. From the data in Table 4.9 on the time dependences of the half-width of the autocorrelation functions of the distribution of the azimuths of polarization of laser images of lifetime and post-mortal abrasions, it follows that over time, the parameters of the reduced half-width significantly change both in lifetime and post-mortal abrasions.

64

4 Study of Two-Dimensional Polarization Maps of the Skin …

Table 4.9 Statistically averaged values of the reduced half-width (L) of the autocorrelation functions of the distribution of polarization azimuths in skin images Reduced half-width, L

Abrasions Lifetime (n = 36)

Post-mortal (n = 32)

1 h, L

0.32 ± 0.038

0.25 ± 0.029

24 h, L

0.41 ± 0.042

0.33 ± 0.041

P

p < 0.001

p < 0.001

The logical continuation of the study of the dependences of the correlation structure of the change in the polarization structure of laser images of lifetime and postmortal abrasions was the use of a spatial-frequency analysis of their coordinate distributions of the azimuths of polarization.

4.5.2 Spatial-Frequency Analysis of Coordinate Distributions of Azimuths of Polarization of Laser Images of Skin Abrasions The comparative analysis results: • type (fractal, stochastic, and statistical, see Chap. 2, Sect. 2) of the distribution of the azimuths of polarization; • dispersion of the distribution of extremes of the Log–log dependences of the power spectra of the coordinate distributions of the azimuths of polarization of laser images of skin samples with various injuries; • time dependencies of the 2nd statistical moment. A comparative analysis of the structure of the Log–log dependences of the power spectra of the coordinate distributions of the azimuths of polarization of laser images of skin samples with various abrasions revealed that for the observation time of 1 h after applying abrasions (Figs. 4.13 and 4.14), they have a stochastic form (see Chap. 2, Sect. 2.5) regardless of the origin of abrasions. With an increase in the observation time up to 24 h, the structure of the Log–log dependences of the power spectra of the coordinate distributions of the azimuths of polarization of laser images of skin samples from various abrasions (Figs. 4.15 and 4.16) is transformed into a statistical one (see Chap. 2, Sect. 2.5). Thus, it was experimentally established that the type of coordinate distribution of the azimuths of polarization of laser images of skin tissue cannot serve as an objective criterion for differentiating the origin of damage. A more effective solution to this problem was a statistical analysis of the distribution of the extrema of the Log–log dependences of the power spectra of the coordinate distributions of the azimuths of polarization of laser images of skin samples with various abrasions.

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps … Table 4.10 Statistically averaged values of the dispersion of the distribution of extrema Log–log dependences of the power spectra of the distribution of azimuths of polarization of laser images of the skin

Dispersion

65

Abrasions Lifetime (n = 36)

Post-mortal (n = 32)

1 h, L

0.01 ± 0.0013

0.015 ± 0.0012

24 h, L

0.021 ± 0.0024

0.027 ± 0.0021

P

p < 0.001

p < 0.001

Table 4.10 shows the statistically averaged values and ranges of variation of the dispersion of the distribution of extrema Log–log dependences of the power spectra of the coordinate distributions of the azimuths of polarization of laser images of two groups of skin histological sections with abrasions of both origins. From the Table 4.10 data on the temporal dispersions of the distributions of the Log–log extrema of the dependences of the power spectra of the distributions of the azimuths of polarization of laser images of the skin, it follows that the considered parameters significantly change over time. Polarization images of skin tissue with lifetime abrasions are characterized by lower (by ¼—½) dispersion values than the corresponding correlation structures of laser images of samples post-mortal abrasions of biomanekens. This circumstance may serve as an additional criterion for differentiating the origin of skin abrasion. A sharp in comparison with the time dependences of the dispersion defined for the Log–log dependences of the power spectra of the distribution of the azimuths of polarization and the time range of the dispersion of the correlation structure of laser images of the skin can be used to extend the time interval for determining the prescription of the application of abrasions. To this end, a number of experimental studies have been carried out. For a group of skin histological sections of biomaneken after traumatic injuries, according to the experimental conditions described in the “materials and research methods” chapter, the distribution of azimuths of the polarization of laser radiation was determined for 96 h at specified intervals (12–24 h) (see Chap. 2, Sect. 2.3), and the Log–log dependence of the corresponding power spectrum was calculated. Based on the obtained set of experimental data, a series of dependencies LogPSDa − log(x) were found, the parameters of which served as the object of comparative analysis. An analysis of the experimental data obtained for constructing a series of dependencies LogPSDa − log(x) and their temporal evolution shows that a significant difference in this indicator between lifetime abrasions and post-mortal abrasions is in the range from 1 to 24 h. Over time, after the application of traumatic injuries, the second statistical moment experiences changes in a wide range of eigenvalues ranging from 7 to 8 times (Fig. 4.17). The processes of increasing the temporal dispersion values are related to the fact that the maximum contribution to the formation of the dispersion value of the distribution of the extrema of the power spectrum LogPSDa − log(x) is made by those maxima that relate to the high spatial-frequency region, which correspond

66

4 Study of Two-Dimensional Polarization Maps of the Skin …

Fig. 4.17 Temporal dependences of the dispersion of the extrema of the Log–log dependences of the power spectra of two-dimensional distributions of the azimuths of polarization of laser images of lifetime (1) and post-mortal (2) abrasions

to small-scale structures of the coordinate distribution of the azimuth of polarization of laser images of the skin. In both parts of the spectrum, the dependences increase monotonically, reaching a certain saturation, starting from a certain value of time T ∗ , which determines the limiting interval for determining the prescription of damage (Table 4.11). The time interval for determining the prescription of application of skin abrasions, determined by the method of statistical analysis of the distribution of the extrema of dependencies LogPSDa − log(x), is for the lifetime abrasion—from 1 to 24 h, the post-mortal abrasion—from 1 to 24 h.

4.5.3 Correlation Analysis of Coordinate Distributions of Ellipticity of Polarization of Laser Images of Skin Abrasions This section presents the results of an experimental measurement of the structure of autocorrelation functions and the Log–log dependences of the spectra of coordinate distributions of ellipticity b(x, y) of laser images of a set of skin histological sections of the following origins: • lifetime abrasion and examined after 1 h (b(x, y)—Fig. 4.18) and 24 h (b(x, y)— Fig. 4.20) after damage;

0.018 ± 0.0073

0.01 ± 0.0013

(Lifetime)

0.021 ± 0.012

0.015 ± 0.0012

p < 0.001

(Post-mortal)

P

p < 0.001

12 (n = 16)

1 (n = 16)

Abrasions

Time (T)

12 (n = 12)

1 (n = 20)

Abrasions

Time (T)

p < 0.001

0.027 ± 0.0025

24 (n = 16)

0.021 ± 0.0025

24 (n = 16)

p > 0.05

0.036 ± 0.0027

48 (n = 16)

0.034 ± 0.0026

48 n = 12

p > 0.05

0.083 ± 0.0059

72 (n = 8)

0.071 ± 0.0057

72 n=8

p > 0.05

0.091 ± 0.0075

96 (n = 12)

0.072 ± 0.0065

96 n = 12

Table 4.11 Temporal dependence of the dispersion of the extrema of the Log–log dependences of the power spectrum of the distribution of the polarization azimuths of the laser images of histological sections of lifetime and post-mortal abrasions

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps … 67

68

4 Study of Two-Dimensional Polarization Maps of the Skin …

Fig. 4.18 Two-dimensional autocorrelation functions of power of the distribution of the ellipticity of polarization of the laser image of the skin with lifetime abrasions (T = 1 h), (n = 20)

• the post-mortal abrasion was examined after 1 h (b(x, y)—Fig. 4.19) and 24 h (b(x, y)—Fig. 4.21) after damage. The correlation and spatial-frequency structures of the coordinate distributions of the ellipticity of polarization of laser images of skin histological sections with lifetime (Fig. 4.18) and post-mortal (Fig. 4.19) abrasions 1 h after their appearance are analyzed.

Fig. 4.19 Two-dimensional autocorrelation functions of the power of the distribution of the ellipticity of polarization of the laser image of the skin with post-mortal abrasions (T = 1 h), (n = 16)

Fig. 4.20 Two-dimensional autocorrelation functions of the power of the distribution of the ellipticity of polarization of the laser image of the skin with lifetime abrasions (T = 24 h), (n = 16)

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps …

69

Fig. 4.21 Two-dimensional autocorrelation functions of the power of distribution of the ellipticity of polarization of the laser image of the skin with post-mortal abrasions (T = 24 h), (n = 16)

From the data obtained on the features of two-dimensional autocorrelation functions (Figs. 4.16 and 4.18) of coordinate distributions of the ellipticity b(x, y) of polarization of laser images of skin samples, we can conclude that, as in the case of ACF (Figs. 4.13, 4.14, 4.15 and 4.16) of the distributions of azimuth of polarization a(x, y), they are azimuthally symmetric structures due to the central symmetry of the distribution of the values of the birefringence index of collagen fibers of the architectonic network. For the polarization image of skin samples with lifetime abrasions, ACF has a lower half-width L (~0.36) compared to the similar correlation parameter determined for the ACF laser image of skin tissue with post-mortal abrasions (~0.43). With an increase in time (24 h after abrasion), the autocorrelation structure of the coordinate distributions of the ellipticity of polarization of laser images of tissue histological sections of lifetime tissue (Fig. 4.20) and post-mortal (Fig. 4.21) abrasions will change—the ACF half-width will increase compared to similar correlation dependences measured for laser images of the skin 1 h after abrasions appearance (“lifetime”—Fig. 4.18 and “post-mortal”—Fig. 4.19). Quantitative differences in ACF characterize the corresponding value of the reduced half-width parameter (L), the value of which is 0.47 (Fig. 4.20) for samples with lifetime abrasions, and post-mortal abrasions are 0.59 (Fig. 4.21), respectively. Table 4.12 shows the statistically averaged values and ranges of changes in the correlation parameter (L) of the coordinate distributions of the ellipticity of polarization of laser images of two groups of histological skin sections with lifetime and post-mortal abrasions. Table 4.12 Statistically averaged values of the reduced half-width of the autocorrelation functions of the distribution of the ellipticity of polarization of skin images

Reduced half-width, L

Abrasions Lifetime (n = 36) Lifetime (n = 36)

1 h, L

0.36 ± 0.043

0.43 ± 0.049

24 h, L

0.47 ± 0.054

0.59 ± 0.064

P

p > 0.05

p < 0.001

70

4 Study of Two-Dimensional Polarization Maps of the Skin …

The analysis shows that over time, the half-width index of the ACF of the distributions of the ellipticity of polarization for lifetime abrasions does not statistically significantly change, and for post-mortal abrasions, it acquires significant changes. From the data on Table 4.12 on the time dependences of the half-width of the autocorrelation function of the distribution of the ellipticity of polarization of laser images of lifetime and post-mortal skin abrasions, it follows that the correlation parameter L increases with an increase in the observation time for lifetime abrasions by 1/4, and for post-mortal abrasions, by more than 1/3. Large values of the half-width of the correlation functions of polarization images of skin tissue with post-mortal abrasions can be associated with a temporary increase in the size (Figs. 4.7 and 4.9 and Figs. 4.8, 4.10) of elliptically polarized domains (bi (x, y) ≈ const) of the corresponding laser images of damaged skin samples. In order to obtain information about the possibility of determining the time of damage and the differentiation of their origin by continuing to study the dependences of the correlation structure of the change in structure of elliptically polarized laser images of lifetime and post-mortal abrasions, a spatial-frequency analysis of coordinate distributions of the ellipticity of polarization was applied.

4.5.4 Spatial-Frequency Analysis of Coordinate Distributions of Ellipticity of Polarization of Laser Images of Skin Abrasions As in the case of the study of polarization azimuths (This chapter, Sub-Sect. 4.5.2), an analysis of the Log–log dependences of the power spectra of the coordinate distributions of the ellipticity of polarization of laser images of skin samples with different origin of abrasions found that for all observation times after abrasion (Figs. 4.18, 4.19, 4.20 and 4.21), they have a stochastic appearance (see Chap. 2, Sect. 2.1) regardless of the origin of abrasions. Thus, it has been experimentally established that the self-similarity of the coordinate distribution of the ellipticity of polarization of laser images of skin tissue cannot serve as an objective criterion for differentiating the origin of abrasion. To solve this problem, we performed a statistical analysis of the distribution of the extrema of the Log–log dependences of the power spectra of the coordinate distributions of the ellipticity of polarization of laser images of skin samples with different origin of abrasions. From the data in Table 4.13, it follows that, regardless of the origin of abrasions, the statistical parameter of the distributions of the extrema of the Log–log dependences of the power spectra of the distributions of the ellipticity of polarization of laser images of the skin increases with increasing observation time and changes significantly with time. An additional criterion for differentiating the origin of abrasion can be data on smaller (by 1/5–1/3) dispersion values for the distribution of ellipticity of polarization

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps … Table 4.13 Statistically averaged values of the dispersion of the distribution of extrema of the Log–log dependences of the power spectra of the distribution of the ellipticity of polarization of laser images of the skin

Dispersion

71

Abrasions Lifetime (n = 36)

Lifetime (n = 36)

1 h, L

0.05 ± 0.0031

0.06 ± 0.0059

24 h, L

0.07 ± 0.0054

0.11 ± 0.012

P

p < 0.001

p < 0.001

images of skin tissue with lifetime abrasions than the similar correlation structures of laser images of samples post-mortal abrasions of biomanekens. In Table 4.14 and in Fig. 4.22, it shows the results of the time dynamics of changes in the dispersion of the extrema of dependencies LogPSDa − log(x). From the results of a statistical analysis of the time dependences of the dispersion of the extrema of the power spectrum of the distribution of the ellipticity of polarization of laser images of the skin, it follows that over time after applying abrasions, the second statistical moment experiences changes in a wide range of eigenvalues ranging from 4 to 6 times (Fig. 4.22). Statistical analysis shows that the possibility of diagnosing lifetime and post-mortal abrasions persists for the first 12 h after an injury. The increase in the dependences is due to the fact that the maximum contribution to the formation of the dispersion of the distribution of the extrema of the power spectrum is made by those maxima related to the region of high spatial frequencies that form small-scale polarization domains in the coordinate distributions of the ellipticity of laser abrasion images. The time dependences of the dispersion undergo monotonic growth, reaching a certain saturation, starting from a certain value of time T ∗ , which determines the limiting interval for determining the prescription of application of skin abrasions. The time interval for determining the prescription of application of skin abrasions, determined by the method of statistical analysis of the distribution of extrema of dependencies LogPSDb − log(x), is 24 h for “lifetime” ones; “post-mortals"—24 h. The results of an experimental study of the coordinate distributions of azimuths and ellipticity of polarization and temporal dynamics of the change in the structure of power spectra of the indicated two-dimensional distributions of the parameters of the polarization of laser radiation transformed by histological sections of the skin of biomanekens allow us to draw the following conclusions: 1. The justified processes of the formation of coordinate distributions of polarization parameters and changes in the spatial-frequency structure of the power spectra of the distributions of the azimuth and the ellipticity of polarization of laser images of lifetime and post-mortal skin lesions of biomanekens were analyzed, and the ways of their diagnostic use were established. 2. Coordinate distributions of azimuths and ellipticities of polarization of laser radiation scattered by abrasions of the skin tend over time after appearance the structure of their polarization domains to growth.

Lifetime

48 (n = 16)

0.11 ± 0.022

p > 0.05

12 (n = 16)

0.07 ± 0.0024

p < 0.001

Abrasions

Lifetime

P

Time (T)

48 (n = 12)

0.08 ± 0.0043

12 (n = 12)

0.05 ± 0.0013

Abrasions

Time (T)

p > 0.05

0.14 ± 0.025

72 (n = 8)

0.11 ± 0.055

72 (n = 8)

p > 0.05

0.19 ± 0.0178

96 (n = 12)

0.14 ± 0.065

96 (n = 12)

p > 0.05

0.21 ± 0.0205

120 (n = 12)

0.15 ± 0.071

120 (n = 16)

p > 0.05

0.23 ± 0.0215

144 (n = 8)

0.15 ± 0.065

144 (n = 16)

Table 4.14 Temporal dependence of the dispersion of the extrema of the Log–log dependences of the power spectrum of the distribution of the ellipticity of polarization of laser images of histological sections of lifetime and post-mortal abrasions

72 4 Study of Two-Dimensional Polarization Maps of the Skin …

4.5 Correlation and Frequency-Spectral Analysis of Polarization Maps …

73

Fig. 4.22 Temporal dependences of the dispersion of the extrema of the Log–log dependences of the power spectra of two-dimensional distributions of the ellipticity of polarization of laser images of lifetime (1) and post-mortal (2) skin abrasions

3. The possibilities of diagnosing damage time by temporarily monitoring changes in the average M1 (1–90 h) and dispersion M2 (1–30 h) of the coordinate distributions of azimuths and ellipticity of polarization of laser images of histological sections of skin abrasion samples of biomanekens are determined. 4. Identified and analyzed trends in temporal changes in the set of extreme values of the Log–log dependences of two-dimensional distributions of azimuth and ellipticity of polarization of laser radiation converted by histological sections of skin abrasion. 5. By studying the dispersion of the distributions of the extrema of the power spectra of the parameters of the polarization of laser radiation, time intervals for determining the prescription of appearance of lifetime and post-mortal abrasions are established. 6. The shortest time of determination the time of abrasion appearance (up to 8 h) is given by studies of the temporary change in the dispersion of the extrema of the power spectrum of the distribution of the azimuths of polarization of laser radiation scattered by skin tissue. 7. The maximum period for determining the time of damage (up to 90 h) is given by studies of the temporal variation of the dispersion of the extrema of the power spectrum of distribution of ellipticity of polarization of the laser image.

74

4 Study of Two-Dimensional Polarization Maps of the Skin …

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Chapter 5

Study of the Evolution of Phase Images of the Skin for Differentiation of the Lifetime and Post-mortal Skin Abrasions and the Time of Their Appearance

5.1 Investigation of the Temporal Dynamics of Changes of Phase Shifts Between Orthogonal Components of the Amplitude of Laser Radiation Scattered by Skin Abrasions The coordinate distribution of the phase shifts φ(x, y) was measured according to the scheme and methodology described in Chap. 2, Sect. 2.4 [1–15]. Series of Figs. 5.1 and 5.2 illustrates the dependences φ(x, y) for laser images of skin tissue with lifetime (Fig. 5.1) and post-mortal (Fig. 5.2) abrasions. A comparative analysis of the obtained experimental data on the phase structure of laser images was found: • Regardless of the origin of the damage, the distribution of phase shift values between the orthogonal components of the laser radiation amplitude is coordinated nonuniform, which indicates the statistical nature of the formation of oedema of the skin tissue and its blood supply. • Areas with a higher concentration of haemorrhages correspond to areas with a greater degree of phase shifts of laser radiation, which are formed due to anisotropy of both collagen bundles and fibrin formed as a result of blood coagulation. • The general level of change in the values φ(x, y) for laser images of skin tissue with both lifetime (Fig. 5.1) and post-mortal (Fig. 5.2) abrasions has certain limitations, as indicated by the corresponding histograms. This circumstance may be associated with a certain thickness and concentration of haemorrhages in the thickness of the dermal layer. The differences in the structure of the phase distributions of laser images of the skin with different origins of abrasions are illustrated in Table 5.1. A statistical analysis indicates the presence of a statistically significant difference M 1 in the comparison groups in the absence of it in the case of comparison of lifetime © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Hu et al., Laser Polarimetry of Biological Tissues, SpringerBriefs in Applied Sciences and Technology, https://doi.org/10.1007/978-981-99-1734-1_5

77

78

5 Study of the Evolution of Phase Images of the Skin for Differentiation …

Fig. 5.1 Two-dimensional distribution of phase shifts between orthogonal components of the amplitude and histogram of their values in the laser image of the skin with lifetime abrasions (T = 1 h) (n = 20)

Fig. 5.2 Two-dimensional distribution of phase shifts between orthogonal components of the amplitude and histogram of their values in the laser image of the skin with post-mortal abrasions (T = 1 h) (n = 16)

5.1 Investigation of the Temporal Dynamics of Changes of Phase Shifts … Table 5.1 Statistically averaged values of the average and dispersion of the distribution of phase shifts between the orthogonal components of the amplitude of the laser images of the skin with lifetime and post-mortal abrasions (T = 1 h)

Statistical moments

Intact skin (n = 48)

Average, M1

0.21 ± 0.032

79

Abrasions Lifetime (n = 20)

Post-mortal (n = 16)

0.53 ± 0.026

0.46 ± 0.034

P1

p < 0.001

p < 0.001

P2

p > 0.05 0.09 ± 0.0011

0.13 ± 0.016

P1

p < 0.001

p < 0.001

P2

p < 0.001

Dispersion, M2

0.04 ± 0.007

and post-mortal abrasions. The indicator M2 determines a statistically significant difference in all comparison groups. Analysis of temporal changes in the structure of the coordinate distributions of phase shifts between the orthogonal components of the amplitude of laser radiation scattered by skin tissues showed that with an increase in the observation time after abrasions appearance, a dynamic increase in the values of phase shifts between orthogonal components of the amplitude along the entire plane of the studied histological sections of skin tissue is observed in Figs. 5.3 and 5.4.

Fig. 5.3 Two-dimensional distribution of phase shifts between orthogonal components of the amplitude and histogram of their values in the laser image of the skin with lifetime abrasions (T = 24 h), (n = 16)

80

5 Study of the Evolution of Phase Images of the Skin for Differentiation …

Fig. 5.4 Two-dimensional distribution of phase shifts between orthogonal components of the amplitude and histogram of their values in the laser image of the skin with post-mortal abrasions (T = 24 h), (n = 16)

This fact is indicated by the transformation of histograms of random values φ(x, y) occupying a significantly larger dynamic range compared with the similar dependences of the phase images of skin tissue recorded 1 h after abrasion. An increase in the phase-shifting ability of lifetime skin abrasion samples can be associated with the manifestation of two factors. The first is blood coagulation and the formation of optically anisotropic fibrin, and the substance of which introduces additional phase shifts between the orthogonal components of the amplitude of the laser wave. The second is oedema, which also leads to an increase in optical anisotropy due to the occurrence of mechanical stresses. Objectively, the differences between the statistical structure of the phase images of lifetime and post-mortal abrasions of the skin of biomanekens characterize the first and second statistical moments, and the value of which was determined within a statistically significant number of histological sections, given in Table 5.2. A comparative analysis of the average and dispersion of the coordinate distributions of phase shifts between the orthogonal components of the amplitude of the laser radiation scattered by histological sections of skin samples after 1 and 24 h of observation after abrasion revealed a statistical difference in the indicator M1 in the comparison groups in lifetime abrasions—control and post-mortal abrasions— control in the absence of a difference between lifetime and post-mortal abrasions. As for the indicator M2 , there is a significant difference in the comparison groups post-mortal abrasions—control and lifetime abrasions—control. Over a time period

5.1 Investigation of the Temporal Dynamics of Changes of Phase Shifts … Table 5.2 Statistically averaged values of the average and dispersion of the distribution of phase shifts between the orthogonal components of the amplitude of the laser images of the skin with lifetime and post-mortal abrasions (T = 24 h)

Statistical moments

Intact skin (n = 48)

81

Abrasions Lifetime (n = 16)

Post-mortal (n = 16)

Average, M 1 0.12 ± 0.019

0.34 ± 0.036

0.25 ± 0.054

P1

p < 0.001

p < 0.001

P2

p > 0.05 0.13 ± 0.017

0.26 ± 0.031

P1

p > 0.05

p < 0.001

P2

p < 0.001

Dispersion, M2

0.08 ± 0.009

of 1 to 24 h, the average coordinate distribution φ(x, y) for lifetime abrasions of a skin decreases by more than ½ and for post-mortal abrasions by ¾. The dispersion of the coordinate distributions of phase shifts in the corresponding laser images of lifetime and post-mortal abrasions increase by ½ and 2 times, respectively. The differences between the statistical moments of the first and second orders for abrasions of different origin reach 1/3 (M1 ) and almost 2 times (M2 ). A further temporary transformation of the phase structure of lifetime and postmortal abrasions is illustrated in Figs. 5.5 and 5.6 and Table 5.3, which presents data on the coordinate and statistical structure of the two-dimensional distribution of phase shifts between the orthogonal components of the amplitude of the laser radiation scattered by skin tissue 48 h after abrasion. Analysing the histograms, it can be seen that over time, additional extrema appear in the post-mortal abrasions compared with the similar distributions recorded for 1 h (Figs. 5.1 and 5.2) and 24 h (Figs. 5.3 and 5.4) after abrasions appearance. Thus, it can be stated that studies of the temporal evolution of changes in the statistical structure of the coordinate distributions of phase shifts φ(x, y) of scattered laser radiation are promising and effective for differentiating the origin of damage, as well as for determination the time of appearance of such damage. Table 5.3 shows the results of temporary monitoring of changes in statistical moments of the first-order phase distribution of laser images of skin tissue with various abrasions. Statistical analysis indicates the presence of statistical differences for changes in the average (M1 ) distribution of the degree of depolarization within 130 h after the injury. Table 5.4 shows the results of temporary monitoring of changes in statistical moments of the second-order phase distribution of laser images of skin tissue with abrasions of various origins. which showed the presence of a statistical difference between lifetime abrasions and post-mortal abrasions in the time interval from 1 to 100 h. Figures 5.7 and 5.8 show the results of temporary monitoring of changes in the statistical moments of the first and second orders of distribution of phases of laser images of skin tissue with different origin of abrasions.

82

5 Study of the Evolution of Phase Images of the Skin for Differentiation …

Fig. 5.5 Two-dimensional distribution of phase shifts between orthogonal components of the amplitude and histogram of their values in the laser image of the skin with lifetime abrasions (T = 48 h), (n = 12)

Fig. 5.6 Two-dimensional distribution of phase shifts between orthogonal components of the amplitude and histogram of their values in the laser image of the skin with post-mortal abrasions (T = 48 h), (n = 16)

5.1 Investigation of the Temporal Dynamics of Changes of Phase Shifts …

83

Table 5.3 Temporal dynamics of changes in the average (M1 ) distribution of the degree of depolarization of laser images of histological sections of lifetime and post-mortal abrasions Time (T) Abrasions 1 n = 20

10 n = 12

20 n = 16

30 n = 16

40 n = 16

50 n = 12

60 n=8

Lifetime

0.53 ± 0.041 0.51 ± 0.037 0.44 ± 0.041 0.34 ± 0.031 0.29 ± 0.021 0.2 ± 0.018

0.19 ± 0.015

P

p > 0.05

Abrasions 70 n=8

p > 0.05

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p < 0.001

80 n=8

90 n=8

100 n = 16

110 n=8

120 n = 16

130 n = 16

Lifetime

0.18 ± 0.013 0.15 ± 0.014 0.13 ± 0.011 0.11 ± 0.008 0.08 ± 0.009 0.06 ± 0.007 0.05 ± 0.004

P

p < 0.001

p < 0.001

p < 0.001

p < 0.001

Time (T) Abrasions

1 n = 16

10 n = 16

20 n = 16

30 n = 16

40 n = 16

50 n = 16

60 n = 12

Post-mortal

0.46 ± 0.047

0.39 ± 0.036

0.27 ± 0.021

0.23 ± 0.019

0.18 ± 0.013

0.13 ± 0.011

0.11 ± 0.009

P

p > 0.05

p > 0.05

p < 0.001

p < 0.001

p < 0.001

p < 0.001

p > 0.05

Abrasions

70 n=8

80 n=8

90 n = 12

100 n = 12

110 n=8

120 n = 12

130 n = 12

Post-mortal

0.09 ± 0.007

0.06 ± 0.005

0.04 ± 0.003

0.02 ± 0.002

P

p < 0.001

p < 0.001

p < 0.001

p < 0.001

Analysis of the set of curves shown in Figs. 5.7 and 5.8 shows that the values of the entire set of statistical moments characterizing the distribution of phase shifts in the laser image of skin tissue are extremely sensitive to changes in the observation time after applying abrasion over a long time interval from 1 to 130 h. The whole set of statistical moments M1 and M2 experiences monotonous temporal changes in eigenvalues, reaching a stable level through specific (individual for each moment) time intervals. Therefore, the ranges for determining the time of application of skin abrasions are within: • lifetime abrasions—from 1 to 100 h (average and dispersion of distributions φ(x.y)); • post-mortal abrasions—from 1 to 100 h (average and dispersion of distributions φ(x.y)). The main result of studies of the temporary transformation of coordinateinhomogeneous phase images of histological sections of damaged skin samples can be considered proven to be able to comprehensively differentiate the origin (lifetime or post-mortal) of abrasion and set the time for its appearance over a long period from 90 to 130 h. These intervals are almost twice as large as those determined by statistical analysis of the temporal evolution of the distribution of polarization parameters of laser images of damaged skin tissues. In addition in previous studies of temporary monitoring of changes in the coordinate distributions of azimuths and ellipticities of polarization of laser images of the

0.24 ± 0.018

p > 0.05

80 n=8

0.35 ± 0.024

0.23 ± 0.019

p < 0.001

70 n=8

0.33 ± 0.027

p < 0.001

Post-mortal

P

Abrasions

Post-mortal

P

p < 0.001

10 n = 16

1 n = 16

Abrasions

Time (T)

0.25 ± 0.019

p < 0.001

0.22 ± 0.017

p < 0.001

Lifetime

P

p > 0.05

80 n=8

p < 0.001

70 n=8

P

0.1 ± 0.08

0.07 ± 0.009

Lifetime

Abrasions

10 n = 12

1 n = 20

Abrasions

Time (T)

p < 0.001

0.37 ± 0.031

90 n = 12

p < 0.001

0.26 ± 0.021

20 n = 16

p < 0.001

0.26 ± 0.021

90 n=8

p < 0.001

0.11 ± 0.009

20 n = 16

p < 0.001

0.38 ± 0.034

100 n = 12

p < 0.001

0.27 ± 0.024

30 n = 16)

p < 0.001

0.29 ± 0.023

100 n = 16

p < 0.001

0.14 ± 0.011

30 n = 16

p > 0.05

110 n=8

p < 0.001

0.29 ± 0.027

40 n = 16

p > 0.05

0.30 ± 0.026

110 n=8

p < 0.001

0.16 ± 0.013

40 n = 16

p > 0.05

120 n = 12

p < 0.001

0.30 ± 0.028

50 n = 16

p > 0.05

0.31 ± 0.025

120 n = 16

p < 0.001

0.18 ± 0.015

50 n = 12

p < 0.001

0.31 ± 0.025

60 n = 12

p > 0.05

0.31 ± 0.029

130 n = 16

p < 0.001

0.19 ± 0.017

60 n=8

Table 5.4 Temporal dynamics of changes in dispersion (M2 ) of the distribution of the degree of depolarization of laser images of histological sections of lifetime and post-mortal abrasions of a person

84 5 Study of the Evolution of Phase Images of the Skin for Differentiation …

5.1 Investigation of the Temporal Dynamics of Changes of Phase Shifts …

85

Fig. 5.7 Temporal dependences of the average coordinate distribution of phase shifts of laser images of tissue with lifetime (1) and post-mortal (2) skin abrasions

Fig. 5.8 Temporal dependences of the dispersion coordinate distribution of phase shifts of laser images of tissue with lifetime (1) and post-mortal (2) skin abrasions

skin, efficiency was established in terms of extending the interval for determining the prescription of the appearance of damage and determining the dynamics of the dispersion of the distribution of extrema of the Log–log dependences of the power spectra of the corresponding polarization parameters. Based on this, the next step in the study was to establish the patterns of formation and subsequent temporary change in the correlation structure of phase images of histological sections of lifetime and post-mortal abrasion.

86

5 Study of the Evolution of Phase Images of the Skin for Differentiation …

5.2 Correlation and Spatial-Frequency Structure of Phase Images of Histological Sections of Abrasions of the Skin of Biomannequin In order to extend the time intervals for diagnosing the time of appearance traumatic skin lesions by searching for new additional parameters, a comparative study of the topological and statistical structure of the autocorrelation functions and power spectra of phase shift distributions between the orthogonal components of the amplitude of the scattered laser radiation at different observation times after abrasions appearance was conducted [16–22]. The series of Figs. 5.9 and 5.10 shows the results of a study of two-dimensional (upper fragment) and total ACF coordinate distributions of phase shifts between orthogonal components of the skin amplitude for 1 h after abrasion. From the obtained data on the structural features of the ACF of the phase distributions of laser images of skin with various abrasions studied 1 h after their application, it can be seen that in both cases they are azimuthally symmetric structures due to the central symmetry of the orientation of the birefringent collagen fibres of the architectonic network. The ACF of the phase image of skin samples with lifetime abrasions

Fig. 5.9 Two-dimensional autocorrelation functions of the power of the distribution of phase shifts between orthogonal components of the amplitude and histograms of their values in the laser image of the skin with lifetime abrasions (T = 1 h), (n = 20)

Fig. 5.10 Two-dimensional autocorrelation functions of the power of the distribution of phase shifts between orthogonal components of the amplitude and histograms of their values in the laser image of the skin with post-mortal abrasions (T = 1 h), (n = 16)

5.2 Correlation and Spatial-Frequency Structure of Phase Images …

87

has a larger half-width L (~0.18) compared to the similar correlation parameter determined for the two-dimensional correlation function of the phase image of skin tissue with post-mortal abrasions (~0.13). Figures 5.11 and 5.12 illustrate the structure of the two-dimensional and total ACF of the coordinate distributions of phase shifts between the orthogonal components of the amplitude of the dermis of the skin for 24 h after abrasion. With an increase in time (24 h after damage), the correlation structure of the coordinate distributions of phase shifts in laser images of tissue histological sections of lifetime (Fig. 5.11) and post-mortal (Fig. 5.12) abrasions is transformed as follows. The azimuthal symmetry of two-dimensional ACF is maintained with a simultaneous change in the correlation parameter of the reduced half-width L. . The value of which is 0.23 (Fig. 5.11) for samples with lifetime abrasions and is 0.19 (Fig. 5.12) for post-mortal abrasions, respectively. A further (48 h after damage) change in the correlation structure of phase images of histological sections of lifetime and post-mortal abrasions is illustrated by the data shown in Figs. 5.13 and 5.14. From the analysis of the ACF series determined for 48 h after appearance of skin lesions of biomanekens, there is a further tendency to increase the half-width of the corresponding autocorrelation distributions of phase images.

Fig. 5.11 Two-dimensional autocorrelation functions of the distribution of phase shifts between orthogonal components of the amplitude and histograms of their values in the laser image of the skin with lifetime abrasions (T = 24 h), (n = 16)

Fig. 5.12 Two-dimensional autocorrelation functions of the distribution of phase shifts between orthogonal components of the amplitude and histograms of their values in the laser image of the skin with post-mortal abrasions (T = 24 h), (n = 16)

88

5 Study of the Evolution of Phase Images of the Skin for Differentiation …

Fig. 5.13 Two-dimensional autocorrelation functions of the power of the distribution of phase shifts between orthogonal components of the amplitude and histograms of their values in the laser image of the skin with lifetime abrasions (T = 48 h), (n = 12)

Fig. 5.14 Two-dimensional autocorrelation functions of the power of the distribution of phase shifts between orthogonal components of the amplitude and histograms of their values in the laser image of the skin with post-mortal (T = 48 h), (n = 12)

Table 5.5 shows the statistically averaged values and ranges of changes in the correlation parameter L of phase images of histological sections of skin abrasions of two origin. From the data in Table 5.5 on the time dependences of the half-width of the correlation parameter L of the phase images of lifetime and post-mortal abrasions, it follows that its value increases with an increase in the observation time for lifetime abrasions of the skin by 3/4 for post-mortal abrasions by twice. The results can be associated with the experimentally determined (Figs. 5.1, 5.2, 5.3, 5.4, 5.5 and 5.6) specific temporary increase in the size of the phase domains (φi (x.y) ≈ const) of the corresponding laser images of damaged skin samples and Table 5.5 Statistically averaged values of the reduced half-width L of the autocorrelation functions of phase distribution in laser images of abrasions

Reduced half-width L

Intact skin (n = 48)

Abrasions Lifetime (n = 48)

Post-mortal (n = 48)

1 h. L

0.09 ± 0.0097

0.18 ± 0.041

0.13 ± 0.062

24 h. L

0.11 ± 0.015

0.23 ± 0.029

0.19 ± 0.038

48 h. L

0.15 ± 0.019

0.31 ± 0.035

0.26 ± 0.028

5.3 Spatial-Frequency Analysis of a Temporary Change in the Coordinate …

89

is expressed in an increase in the half-width of the corresponding autocorrelation functions. The continuation of the study of the dependences of the correlation structure of the phase structure of laser images of lifetime and post-mortal abrasions was applied using spatial-frequency analysis which turned out to be effective in setting the range of installation the time of abrasion appearance and their coordinate distributions φ(x.y).

5.3 Spatial-Frequency Analysis of a Temporary Change in the Coordinate Phase Distributions of Laser Images of Skin Abrasions This section of the monograph contains the results of a comparative analysis of the type (fractal, stochastic, and statistical, see Chap. 2, Sect. 2.5) of the phase distribution and time dependences of the dispersion of the extrema distribution of the Log–log dependences of the power spectra of the coordinate distributions of phase shifts between the orthogonal polarization components of laser images of skin samples with different damages. A comparative analysis of the structure of the Log–log dependences of the power spectra of the coordinate phase distributions of laser images of skin samples with different origins of lesions found that for the entire observation time range (from 1 to 48 h) after damage (Figs. 5.9, 5.10, 5.11, 5.12, 5.13 and 5.14) they have a stochastic form (see Chap. 2, Sect. 2.5) regardless of the origin of abrasions. So, we can state that the type of coordinate phase distribution of laser images of skin tissue cannot serve as an objective criterion for differentiating the origin of abrasions. More effective for solving the problem regarding the lifetime or the post-mortal origin of damage is a statistical analysis of the distribution of the extrema of the Log–log dependences of the power spectra of the coordinate distributions of phase shifts between the orthogonal components of the polarization of the laser images of the samples of lifetime and post-mortal abrasions. Table 5.6 shows the statistically averaged (within two groups of histological skin sections with lesions of both origin) values and ranges of variation of the dispersion of the distribution of extremes of the Log–log dependences of the power spectra of the coordinate distributions of phase shifts in a series of corresponding laser images. The data given in Table 5.6 illustrate, irrespective of the origin of the damage, a 2.75-fold increase in the dispersion of the distribution of extremes of the Log–log dependences of the power spectra of the phase distributions of the laser images of lifetime abrasions; for post-mortal abrasions—2 times during the observation time from 1 to 48 h.

90

5 Study of the Evolution of Phase Images of the Skin for Differentiation …

Table 5.6 Statistically averaged values of the dispersion of the distributions of extrema of the Log–log dependences of power spectra of phase distributions of the skin laser images

Dispersion

Intact skin (n = 48)

Abrasions Lifetime (n = 48)

Post-mortal (n = 48)

1h

0.04 ± 0.006

0.08 ± 0.0091

0.14 ± 0.016

24 h

0.06 ± 0.007

0.14 ± 0.022

0.19 ± 0.021

48 h

0.08 ± 0.009

0.21 ± 0.027

0.27 ± 0.032

Phase images of skin tissue with lifetime abrasions are characterized by lower (by 1/3–3/4) dispersion values than the value of a similar statistical moment characterizing the correlation structures of the phase distribution of laser images of samples post-mortal abrasions of biomanekenes. This circumstance can serve as an additional criterion for differentiating the origin of damage to the human skin. Slower, in comparison with the time dependences of the dispersion determined for the Log–log dependences of the power spectra of the distribution of azimuths of polarization, an increase in the dispersion values of the phase distribution of laser images of skin tissues can be used to further extend the time interval for determination of prescription of damage. Table 5.7 shows the results of a study of the temporal dynamics of the dispersion of the extrema of the dependencies LogPSDφ − log(x). which were determined at certain time intervals after abrasions appearance according to the experimental procedure given in Chap. 2, Sect. 2.3, Sub-Sect. 2.3.1, relation (2.3). An analysis of the obtained experimental data revealed the following features of the time evolution of dependencies LogPSDφ − log(x): • Over time, after the application of traumatic injuries, the second statistical moment varies over a wide range of eigenvalues ranging from 2.5 to 3.5 times. • For abrasions of both origins, the temporal dependences of the dispersion experience a monotonic decrease, reaching a certain saturation starting with a certain value of time T* which determines the limiting interval for determining the prescription of damage. An experimental study of the temporal evolution of the structure of the Log– log dependences of the power spectra of two-dimensional phase shift distributions between the orthogonal components of the laser radiation amplitude of different spectral ranges scattered by histological sections of human skin allows us to draw the following conclusions: 1. The coordinate distributions of phase shifts between the orthogonal components of the amplitude of the laser radiation scattered by damaged skin tissues tend to change in the overall level of relative values over time after causing damage, which is manifested in the transformation of the corresponding histograms. Extremes are formed in the region of medium and large phase values. 2. Certain possibilities for diagnosing the time of damage by hourly monitoring changes in the average and dispersion of the coordinate distributions of phase shifts in the image of lifetime and post-mortal abrasions of biomanekens.

36 n = 12

52 n=8

76 n = 12

100 n = 16

112 n = 16

124 n = 16

148 n= 16

160 n= 16

1 n = 16

Time

12 n = 16

24 n = 16

M 2 (T) 0.13 ± 0.011 0.11 ± 0.013 0.09 ± 0.01 (post-mortal)

Abrasions 52 n = 16

76 n = 12

100 n = 12

0.07 ± 0.008 0.06 ± 0.005 0.04 ± 0.004 0.025 ± 0.001

36 n = 16

112 n = 12

124 n = 16

148 n= 16

160 n= 12

0.10 ± 0.008 0.09 ± 0.007 0.08 ± 0.009 0.07 ± 0.006 0.06 ± 0.005 0.05 ± 0.004 0.045 ± 0.003 0.004 ± 0.004 0.035 ± 0.003 0.02 ± 0.002

24 n = 16

M 2 (T) (lifetime)

12 n = 12

1 n = 20

Abrasions

Time

172 n= 16

172 n= 16

Table 5.7 Temporal dependence of the range of variation of the dispersion of the extrema of the power spectra of the phase shift distributions between the orthogonal components of the amplitude of the laser images of the skin

5.3 Spatial-Frequency Analysis of a Temporary Change in the Coordinate … 91

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5 Study of the Evolution of Phase Images of the Skin for Differentiation …

3. The tendencies of a temporary change in the set of extreme values of the set of Log–log dependences of two-dimensional phase shift distributions between the orthogonal components of the polarization of laser radiation transformed by histological sections of damaged skin have been identified and analysed. 4. By studying the dispersion of the distributions of the extrema of the power spectra of the phase parameters of the scattered laser radiation, time intervals for determination of the prescription of appearance of lifetime, and post-mortal abrasions of the skin are established. 5. The shortest time to determine the time of damage is given by studies of the temporal variation of the dispersion of the extrema of the power spectra of the distribution of the phases of the laser radiation scattered post-mortal abrasions. 6. The maximum time for determining the time of damage is given by studies of the temporal variation of the dispersion of the extrema of the power spectra of the phase distribution in the laser image of lifetime abrasion.

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Conclusions

The problem of determining the lifetime or the after-mortal nature of causing bodily damages, as well as the time of their prescription, refers to issues that most often have to be addressed in forensic practice and requires the development of objective evidence-based criteria using modern of physical research methods [1–24]. 1. The relationships between lifetime or post-mortal abrasions formation and statistical (average and dispersion) and spatial-frequency (dispersion of the extrema of Log–log dependences of power spectra) parameters characterizing the coordinate distribution of intensity, azimuths, ellipticity, and phase shifts between orthogonal components of laser wave in the images. Skin biomannequin are defined and theoretically justified. 2. Statistical criteria for the differentiation of lifetime or post-mortal origin of human skin lesions were revealed. 3. The effectiveness in determining the time intervals during the application of lifetime and post-mortal abrasions: for the dispersion of the distribution of intensity (Ω I ) from 1 to 8 h; and (ΩPSD ) for the dispersion of the distribution of the extrema of the Log–log dependences of the intensity power spectra no statistically significant difference. 4. When comparing the average data of the extremes of the power spectra of laser images of histological sections of lifetime abrasion with intact skin (control), the difference is statistically significant. The same difference appears when comparing the post-mortal abrasion with the control and the difference between the lifetime and the post-mortal abrasion is unreliable. 5. Statistically averaged values of the distributions of the extrema of the power spectra of the intensity of laser images of the skin when comparing the confidence indicator between intact skin with lifetime abrasions and post-mortal abrasions, the difference is not significant. The same difference exists when comparing damage to each other. The analysis of the second statistical moment indicates the presence of a difference between damage and control and the absence of a difference between the damage itself. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 Z. Hu et al., Laser Polarimetry of Biological Tissues, SpringerBriefs in Applied Sciences and Technology, https://doi.org/10.1007/978-981-99-1734-1

95

96

Conclusions

6. The temporal dynamics of changes in the average (M 1 ) distribution of polarization azimuths of laser images of histological sections of lifetime and post-mortal abrasions shows a statistically significant difference from 1 to 90 h, and the temporal dynamics of changes in the dispersion (M 2 ) of the distribution of the azimuths of polarization of laser images of histological sections of lifetime and post-mortal abrasions shows the presence of a statistically significant difference from 1 to 30 h. 7. The temporal dynamics of changes in the average (M 1 ) distribution of the ellipticity of laser images of histological sections of lifetime and post-mortal abrasions shows the possibility of differentiating lifetime or post-mortal origin of skin abrasions within 1 to 60 h. At the same time, it was found that the temporal dynamics of the dispersion (M 2 ) of the distribution of the ellipticity of laser images of histological sections of lifetime and post-mortal abrasions allows them to be differentiated in two intervals: from 1 to 24 h and for the interval of 36 h. 8. A statistical analysis of the temporal dynamics of changes in the average (M 1 ) and dispersion (M 2 ) distribution of the degree of depolarization of laser images of histological sections of lifetime and post-mortal abrasions of a person indicates the presence of a statistically significant difference for changes in average (M 1 ) from 1 to 130 h and for changes in dispersion (M 2 )—from 1 to 100 h.

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