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. 2023;15(3):35-40.
doi: 10.17691/stm2023.15.3.04. Epub 2023 May 28.

Practical Aspects of Using Multifractal Formalism to Assess the Morphology of Biological Tissues

A M Ignatova  1 , M A Zemlyanova  2 , O B Naimark  3 , N V Zaitseva  4
Affiliations

Practical Aspects of Using Multifractal Formalism to Assess the Morphology of Biological Tissues

A M Ignatova et al. Sovrem Tekhnologii Med. 2023.

Abstract

The aim of the study is to identify practical aspects of using multifractal formalism to assess the morphology of biological tissues.

Materials and methods: The objects of the study were histological images of lung tissues of Wistar rats without pathology and with detected pathological changes, obtained at 50×, 100×, 200× magnifications. Image processing was carried out using the ImageJ/Fiji universal software. The multifractal spectrum of the images, processed to obtain a linear contour, was calculated with the use of FracLac - a module for ImageJ. This module was used to determine the scaling exponent (the function of the Rényi exponent, τ(q)) and the singularity spectrum itself.

Results: The singularity spectra for tissues with no pathology have signs of multifractality. The image spectrum of tissue with pathology is shifted to the left relative to the spectrum characteristic of tissue without pathology. A decrease in the spectral height in the presence of pathology indicates a "simplification" of the alveolar pattern, which is presumably associated with the presence of widespread vasculitis, since it causes areas of hemorrhage to appear on the image; this leads to leveling the contour of the alveolar pattern, reducing the surface area of the alveoli and emerging areas inflamed by erythrocytes. At lower magnification, images with pathology lose signs of multifractality.

Conclusion: Correct results of assessing multifractal spectra of histological images can be achieved at 200× magnification and preprocessing to obtain linear contours. Significant differences between the morphological structure of lung tissues with and without pathology are observed when comparing the height, width, and position of the spectrum relative to the origin.

Keywords: alveolar pattern; fractal analysis; histology; image analysis; lung tissue.

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Conflict of interest statement

Conflicts of interest. There are no conflicts of interest.

Figures

Figure 1.
Figure 1.. Lung tissue of Wistar rats:
(a) without pathology; (b) with hyperplasia of the lymphoid tissue associated with the bronchial wall and widespread vasculitis; (c) with alveolar pulmonary edema; (d) with interstitial pneumonia; ×200
Figure 2.
Figure 2.. Lung tissue images of Wistar rats prepared for analysis:
(a) the result of binarization; (b) the result of edge detection; (c) the result of contour skeletonization
Figure 3.
Figure 3.. Image lacunarity functions
Figure 4.
Figure 4.. Image singularity spectra
D0 — monofractal dimension, Dq — informational dimension
Figure 5.
Figure 5.. Scaling exponents of images
See this image and copyright information in PMC

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