3D polarization-interference holographic histology for wavelet-based differentiation of the polycrystalline component of biological tissues with different necrotic states. Forensic applications

Abstract

Significance: The interference-holographic method of phase scanning of fields of scattered laser radiation is proposed. The effectiveness of this method for the selection of variously dispersed components is demonstrated. This method made it possible to obtain polarization maps of biological tissues at a high level of depolarized background. The scale-selective analysis of such maps was used to determine necrotic changes in the optically anisotropic architectonics of biological tissues.

Objective: Development and experimental approbation of layered phase polarimetry of repeatedly scattered fields in diffuse layers of biological tissues. Application of scale-selective processing of the found coordinate distributions of polarization states in various phase sections of object fields. Determination of criteria (markers) for histological differential diagnosis of the causes of necrotic changes in optical anisotropy of biological tissues.

Approach: We used a synthesis of three instrumental and analytical methods. Polarization-interference registration of laser radiation scattered by a sample of biological tissue. Digital holographic reconstruction and layered phase scanning of distributions of complex amplitudes of the object field. Analytical determination of polarization maps of various phase cross-sections of repeatedly scattered radiation. Application of wavelet analysis of the distributions of polarization states in the phase plane of a single scattered component of an object field. Determination of criteria (markers) for differential diagnosis of necrotic changes in biological tissues with different morphological structure. Two cases are considered. The first case is the myocardium of those who died as a result of coronary heart disease and acute coronary insufficiency. The second case is lung tissue samples of deceased with bronchial asthma and fibrosis.

Results: A method of polarization-interference mapping of diffuse object fields of biological tissues has been developed and experimentally implemented. With the help of digital holographic reconstruction of the distributions of complex amplitudes, polarization maps in various phase sections of a diffuse object field are found. The wavelet analysis of azimuth and ellipticity distributions of polarization in the phase plane of a single scattered component of laser radiation is used. Scenarios for changing the amplitude of the wavelet coefficients for different scales of the scanning salt-like MHAT function are determined. Statistical moments of the first to fourth orders are determined for the distributions of the amplitudes of the wavelet coefficients of the azimuth maps and the ellipticity of polarization. As a result, diagnostic markers of necrotic changes in the myocardium and lung tissue were determined. The statistical criteria found are the basis for determining the accuracy of their differential diagnosis of various necrotic states of biological tissues.

Conclusions: Necrotic changes caused by "coronary artery disease-acute coronary insufficiency" and "asthma-pulmonary fibrosis" were demonstrated by the method of wavelet differentiation with polarization interference with excellent accuracy.

Keywords: biological tissue; holography; interference; lungs tissue; myocardium; optical anisotropy; polarization; statistical moments; wavelet analysis.

Fig. 1

Optical scheme for polarization-interference mapping of the Stokes vector parameters. (1) He–Ne laser; (2) collimator – “O”; (3), (11) beam splitters “BS”; (4), (5) mirrors – “M”; (6), (9), (13) polarizers “P”; (7), (10) quarter wave plates – “QP”; (8) object; (12) polarization objective – “O”; (14) digital camera – “CCD”; (15) personal computer – “PC.”

Fig. 2

Microscopic images (×40) of histological preparations of myocardium and lung tissue. (a) CHD; (b) ACI; (c) BA; (d) PF. Explanations in the text.

Fig. 3

(a), (b) Coordinate and (c), (d) probabilistic distributions of random values of the azimuth of polarization of object fields of myocardial samples of deceased as a result of (a), (c) ACI and (b), (d) CHD.

Fig. 4

Maps (left column) and multi-scale linear cross-sections (right column) of the polarization azimuth $\alpha ({\delta }_t^{\star }=\pi /8,m,n)$ wavelet coefficients $W_{a,b}$ of myocardium histological sections of those who died from CHD (top row bottom row) and ACI (bottom row). Two-dimensional array of values of the amplitudes of the wavelet coefficients (a), (c) and linear distributions of the amplitude of the wavelet coefficients for two scales of the MHAT function (b), (d).

Fig. 5

Scale dependences of (a) the mean $Z_1$ and (b) the variance $Z_2$ of the wavelet coefficients $W_{a,b}$ of the $\alpha ({\delta }_t^{\star }=\pi /8,m,n)$. Explanation in the text.

Fig. 6

(a), (c) Coordinate and (b), (d) probabilistic distributions of random values of the magnitude of the ellipticity of polarization of object fields of myocardial samples that died as a result of (a), (b) CHD and (3), (4) ACI.

Fig. 7

Maps (left column) and multi-scale linear cross-sections (right column) of the polarization ellipticity $\beta ({\delta }_t^{\star }=\pi /8,m,n)$ wavelet coefficients $W_{a,b}$ of myocardium histological sections of those who died from CHD (top row) and ACI (bottom row). Two-dimensional array of values of the amplitudes of the wavelet coefficients (a), (c) and linear distributions of the amplitude of the wavelet coefficients for two scales of the MHAT function (b), (d).

Fig. 8

Scale dependences of (a) the mean $Z_1$ and (b) the variance $Z_2$ of the wavelet coefficients $W_{a,b}$ of the $\beta ({\delta }_t^{\star }=\pi /8,m,n)$. Explanation in the text.

Fig. 9

(a), (c) Coordinate and (b), (d) probabilistic distributions of random values of the azimuth of polarization of object fields of lung tissue samples with (a), (b) BA and (c), (d) PF.

Fig. 10

Maps (left column) and multi-scale linear cross-sections (right column) of the polarization azimuth $\alpha ({\delta }_t^{\star }=\pi /8,m,n)$ wavelet coefficients $W_{a,b}$ of lung tissue histological sections those who died from BA (top row) and PF (bottom row). Explanation in the text.

Fig. 11

Scale dependences of (a) the mean $Z_1$ and (b) the variance $Z_2$ of the wavelet coefficients distributions for polarization azimuth maps $\alpha ({\delta }_t^{\star }=\pi /8,m,n)$. Two-dimensional array of values of the amplitudes of the wavelet coefficients (a), (c) and linear distributions of the amplitude of the wavelet coefficients for two scales of the MHAT function (b), (d).

Fig. 12

(a), (c) Coordinate and (b), (d) probabilistic distributions of random values of the magnitude of the ellipticity of polarization of object fields of lung tissue samples of deceased as a result of (a), (b) BA and (c), (d) PF.

Fig. 13

Maps $\beta ({\delta }_t^{\star }=\pi /8,m,n)$ (left column) and multi-scale linear cross-sections (right column) of the polarization ellipticity wavelet coefficients $W_{a,b}$ of lung tissue histological sections those who died from BA (top row) and PF (bottom row). Explanation in the text.

Fig. 14

Scale dependences of (a) the mean $Z_1$ and (b) the variance $Z_2$ of wavelet coefficients distributions for $\beta ({\delta }_t^{\star }=\pi /8,m,n)$. Explanation in the text.