Fractal Analysis in Biology and Medicine

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Life Science, Biophysics".

Deadline for manuscript submissions: 30 January 2026 | Viewed by 2055

Special Issue Editor


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Guest Editor
Institute of Histology and Embryology “Aleksandar Đ. Kostić”, Faculty of Medicine, University of Belgrade, 11000 Belgrade, Serbia
Interests: neuroscience; image analysis; morphometry; fractal theory; medical education

Special Issue Information

Dear Colleagues,

Ever since Benoit Mandelbrot coined the term fractal and paved the way for the development of fractal geometry and fractal analysis, researchers have found a way to utilize this non-linear analysis method in diverse areas of natural sciences.  During the previous two decades, there has been a tremendous increase in the number of published papers that relied on the use of fractal analysis to measure the complexity of a certain geometrical figure. The complexity is expressed as a fractal dimension, which depicts the space-filling properties of different irregularly shaped objects that can be found in various living and non-living objects. In the vast field of biomedical sciences these objects usually represent various forms of cells, their ultrastructural parts, such as the nucleus, chromatin, and organelles, or specific cell protrusions like dendrites, but also tissue elements or anatomical units of organs. Traditional quantitative, semiquantitative, and qualitative techniques of analysis of these structures provide results of limited value since these conventional methods are not able to detect subtle differences in histological images. However, fractal analysis has now proven to be a useful tool for the detection of those changes in biological objects obtained from both physiological and pathological conditions. In addition to objects obtained from histological images, fractal analysis is increasingly used in the analysis of various images obtained using different imaging methods and biological signals, such as the complexity-based analysis of brain and muscle electrical activity. Although fractal analysis has found its applicability in various fields of biomedical sciences, neuroscience research remains a major field of its utilization, due to its ability to quantify complex and branching structures, such as dendritic tree arborizations. Its simplicity, sensitivity, and cost-effectiveness allow researchers numerous possibilities to implement this non-linear method of analysis in their investigative work.

This Research Topic will welcome diverse types of articles including original research articles, review articles, technical note articles, and perspective articles related to the application of fractal analysis in different biomedical fields.

Topics of interest include diverse biomedical research areas as follows:

  • Fractals and fractal theory in biomedical sciences;
  • Fractal analysis of cell and tissue histological images;
  • Application of fractal analysis methods in neuroscience research;
  • Fractal dimension as a complexity discrimination method between physiological and pathological conditions;
  • Fractal analysis of various images and signals in medical diagnostics;
  • Multi-fractal analysis of biomedical images;
  • Utilization of related non-linear analysis methods in biomedical research.

Dr. Ivan Zaletel
Guest Editor

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Keywords

  • fractal analysis
  • fractal dimension
  • complexity
  • self-similarity
  • neuroscience
  • morphometry
  • cell and tissue analysis

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Published Papers (2 papers)

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Research

14 pages, 2847 KiB  
Article
Linear and Non-Linear Methods to Discriminate Cortical Parcels Based on Neurodynamics: Insights from sEEG Recordings
by Karolina Armonaite, Livio Conti, Luigi Laura, Michele Primavera and Franca Tecchio
Fractal Fract. 2025, 9(5), 278; https://doi.org/10.3390/fractalfract9050278 - 25 Apr 2025
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Abstract
Understanding human cortical neurodynamics is increasingly important, as highlighted by the European Innovation Council, which prioritises tools for measuring and stimulating brain activity. Unravelling how cytoarchitecture, morphology, and connectivity shape neurodynamics is essential for developing technologies that target specific brain regions. Given the [...] Read more.
Understanding human cortical neurodynamics is increasingly important, as highlighted by the European Innovation Council, which prioritises tools for measuring and stimulating brain activity. Unravelling how cytoarchitecture, morphology, and connectivity shape neurodynamics is essential for developing technologies that target specific brain regions. Given the dynamic and non-stationary nature of neural interactions, there is an urgent need for non-linear signal analysis methods, in addition to the linear ones, to track local neurodynamics and differentiate cortical parcels. Here, we explore linear and non-linear methods using data from a public stereotactic intracranial EEG (sEEG) dataset, focusing on the superior temporal gyrus (STG), postcentral gyrus (postCG), and precentral gyrus (preCG) in 55 subjects during resting-state wakefulness. For this study, we used a linear Power Spectral Density (PSD) estimate and three non-linear measures: the Higuchi fractal dimension (HFD), a one-dimensional convolutional neural network (1D-CNN), and a one-shot learning model. The PSD was able to distinguish the regions in α, β, and γ frequency bands. The HFD showed a tendency of a higher value in the preCG than in the postCG, and both were higher in the STG. The 1D-CNN showed promise in identifying cortical parcels, with an 85% accuracy for the training set, although performance in the test phase indicates that further refinement is needed to integrate dynamic neural electrical activity patterns into neural networks for suitable classification. Full article
(This article belongs to the Special Issue Fractal Analysis in Biology and Medicine)
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16 pages, 6041 KiB  
Article
Relating the Morphology of Bipolar Neurons to Fractal Dimension
by Bret Brouse, Jr., Conor Rowland and Richard P. Taylor
Fractal Fract. 2025, 9(1), 9; https://doi.org/10.3390/fractalfract9010009 - 28 Dec 2024
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Abstract
By analyzing reconstructed three-dimensional images of retinal bipolar neurons, we show that their dendritic arbors weave through space in a manner that generates fractal-like behavior quantified by an ‘effective’ fractal dimension. Examining this fractal weave along with traditional morphological parameters reveals a dependence [...] Read more.
By analyzing reconstructed three-dimensional images of retinal bipolar neurons, we show that their dendritic arbors weave through space in a manner that generates fractal-like behavior quantified by an ‘effective’ fractal dimension. Examining this fractal weave along with traditional morphological parameters reveals a dependence of arbor fractal dimension on the summation of the lengths of the arbor’s dendrites. We discuss the implications of this behavior for healthy neurons and also for the morphological deterioration of unhealthy neurons in response to diseases. Full article
(This article belongs to the Special Issue Fractal Analysis in Biology and Medicine)
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