Fractal and Fractional Analysis in Biomedical Sciences and Engineering

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

Deadline for manuscript submissions: 31 May 2024 | Viewed by 5793

Special Issue Editor


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Guest Editor
Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, Zemun-Belgrade 11080, Serbia
Interests: applied physics; applied electromagnetics; biomedical engineering; biomedical signal processing; numerical methods

Special Issue Information

Dear Colleagues,

Over the past two decades, various signal and image analyses, as well as bioinformatics approaches have had a significant impact on research in the field of  life sciences. Problems arising in medical and biological research depend on a multitude of system parameters, sometimes in a non-linear way; as a result, these problems can be successfully addressed via the tools of a complex system analysis. Fractal and fractional analysis was originally rooted in theoretical developments, only to be recognized later as well suited for the analysis of problems occurring in nature. In particular, in the fields of medicine and biology, it was first noticed that heart rate signals and human walking signals exhibit fractal characteristics, and the anatomy of many organs and systems possesses a high degree of self-similarity and non-integer order features. Due to multiplicative processes in an organism, structures can be described in terms of scaled copies of self-similar entities, with a degree of randomness originating from underlying governing factors influencing growth, differentiation, and function. More recently, fractal-based methodologies were also applied to various classes of problems where an underlying fractal nature, although less evident, was expected, whereas new fractional-order integral and differential operators were developed under the rules of fractional calculus to facilitate the study and modeling of biomedical processes. Additionally, machine learning and artificial intelligence were employed, either separately or integrated with fractal and fractional frameworks, to study biomedical processes and the complex dynamics of biomedical systems. The developed fractal and fractional system and process models were further used as starting points for the optimization of tools and treatments in biomedical engineering.

This Special Issue aims to offer an overview of state-of-the-art developments in the field of fractal and fractional-based methodologies as applied to the analysis and modeling of biomedical entities and processes, as well as developments in biomedical engineering. We invite researchers from the health sector, industry, and academia to contribute to this Special Issue. Original research articles and  reviews are welcome. The vision of this Special Issue encompasses the most relevant developments in using novel approaches in life sciences, including conceptual and theoretical approaches, as well as numerical methods that can be applied in biomedicine, the fractal and fractional modeling of structure and processes, biomedical signal and image analyses, and experimental research illustrating the application of the above concepts to solve specific challenges. The topics of interest include, but are not limited to, the following:

  • Fractal and multifractal processes in living organisms/in vitro models;
  • Fractal and fractional approaches in disease development and treatment modeling;
  • Fractal operators and fractional dynamics as applied to life sciences;
  • Numerical schemes (fractional or integer-order) for computational biology;
  • Imaging technologies and medical image analysis and interpretation;
  • Machine learning and artificial intelligence applied to biomedical problems;
  • Fractional-order or integer-order neural networks and graph theory approaches;
  • Neuronal models and brain networks in health and disease;
  • Fractal modeling of protein structure and biochemical processes;
  • Fractal gene regulatory networks and gene expression, and DNA profiling;
  • Tissue electrical impedance models and measurements;
  • Fractional models of disease transmission and epidemic spread.

Dr. Andjelija Ž. Ilić
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal and multifractal analysis
  • fractal lacunarity analysis
  • fractional calculus
  • fractional differential equations
  • convergence and stability analysis
  • biological system complexity
  • non-linear biosystem dynamics
  • medical image and data analysis
  • neural networks and graphs
  • long-term correlation tracking

Published Papers (5 papers)

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Research

18 pages, 2141 KiB  
Article
Efficient Analysis of Large-Size Bio-Signals Based on Orthogonal Generalized Laguerre Moments of Fractional Orders and Schwarz–Rutishauser Algorithm
by Eman Abdullah Aldakheel, Doaa Sami Khafaga, Islam S. Fathi, Khalid M. Hosny and Gaber Hassan
Fractal Fract. 2023, 7(11), 826; https://doi.org/10.3390/fractalfract7110826 - 16 Nov 2023
Cited by 1 | Viewed by 985
Abstract
Orthogonal generalized Laguerre moments of fractional orders (FrGLMs) are signal and image descriptors. The utilization of the FrGLMs in the analysis of big-size signals encounters three challenges. First, calculating the high-order moments is a time-consuming process. Second, accumulating numerical errors leads to numerical [...] Read more.
Orthogonal generalized Laguerre moments of fractional orders (FrGLMs) are signal and image descriptors. The utilization of the FrGLMs in the analysis of big-size signals encounters three challenges. First, calculating the high-order moments is a time-consuming process. Second, accumulating numerical errors leads to numerical instability and degrades the reconstructed signals’ quality. Third, the QR decomposition technique is needed to preserve the orthogonality of the higher-order moments. In this paper, the authors derived a new recurrence formula for calculating the FrGLMs, significantly reducing the computational CPU times. We used the Schwarz–Rutishauser algorithm as an alternative to the QR decomposition technique. The proposed method for computing FrGLMs for big-size signals is accurate, simple, and fast. The proposed algorithm has been tested using the MIT-BIH arrhythmia benchmark dataset. The results show the proposed method’s superiority over existing methods in terms of processing time and reconstruction capability. Concerning the reconstructed capability, it has achieved superiority with average values of 25.3233 and 15.6507 with the two metrics PSNR and MSE, respectively. Concerning the elapsed reconstruction time, it also achieved high superiority with an efficiency gain of 0.8. The proposed method is suitable for utilization in the Internet of Healthcare Things. Full article
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18 pages, 1850 KiB  
Article
Analysis of the Corneal Geometry of the Human Eye with an Artificial Neural Network
by Waseem, Asad Ullah, Fuad A. Awwad and Emad A. A. Ismail
Fractal Fract. 2023, 7(10), 764; https://doi.org/10.3390/fractalfract7100764 - 17 Oct 2023
Viewed by 968
Abstract
In this paper, a hybrid cuckoo search technique is combined with a single-layer neural network (BHCS-ANN) to approximate the solution to a differential equation describing the curvature shape of the cornea of the human eye. The proposed problem is transformed into an optimization [...] Read more.
In this paper, a hybrid cuckoo search technique is combined with a single-layer neural network (BHCS-ANN) to approximate the solution to a differential equation describing the curvature shape of the cornea of the human eye. The proposed problem is transformed into an optimization problem such that the L2error remains minimal. A single hidden layer is chosen to reduce the sink of the local minimum values. The weights in the neural network are trained with a hybrid cuckoo search algorithm to refine them so that we obtain a better approximate solution for the given problem. To show the efficacy of our method, we considered six different corneal models. For validation, the solution with Adam’s method is taken as a reference solution. The results are presented in the form of figures and tables. The obtained results are compared with the fractional order Darwinian particle swarm optimization (FO-DPSO). We determined that results obtained with BHCS-ANN outperformed the ones acquired with other numerical routines. Our findings suggest that BHCS-ANN is a better methodology for solving real-world problems. Full article
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12 pages, 14149 KiB  
Article
Unsupervised Deep Learning Approach for Characterizing Fractality in Dried Drop Patterns of Differently Mixed Viscum album Preparations
by Carlos Acuña, Maria Olga Kokornaczyk, Stephan Baumgartner and Mario Castelán
Fractal Fract. 2023, 7(10), 733; https://doi.org/10.3390/fractalfract7100733 - 04 Oct 2023
Viewed by 1188
Abstract
This paper presents a novel unsupervised deep learning methodology for the analysis of self-assembled structures formed in evaporating droplets. The proposed approach focuses on clustering these structures based on their texture similarity to characterize three different mixing procedures (turbulent, laminar, and diffusion-based) applied [...] Read more.
This paper presents a novel unsupervised deep learning methodology for the analysis of self-assembled structures formed in evaporating droplets. The proposed approach focuses on clustering these structures based on their texture similarity to characterize three different mixing procedures (turbulent, laminar, and diffusion-based) applied to produce Viscum album Quercus 103 according to the European Pharmacopoeia guidelines for the production of homeopathic remedies. Texture clustering departs from obtaining a comprehensive texture representation of the full texture patch database using a convolutional neural network. This representation is then dimensionally reduced to facilitate clustering through advanced machine learning techniques. Following this methodology, 13 clusters were found and their degree of fractality determined by means of Local Connected Fractal Dimension histograms, which allowed for characterization of the different production modalities. As a consequence, each image was represented as a vector in R13, enabling classification of mixing procedures via support vectors. As a main result, our study highlights the clear differences between turbulent and laminar mixing procedures based on their fractal characteristics, while also revealing the nuanced nature of the diffusion process, which incorporates aspects from both mixing types. Furthermore, our unsupervised clustering approach offers a scalable and automated solution for analyzing the databases of evaporated droplets. Full article
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16 pages, 2068 KiB  
Article
Fractal Parameters as Independent Biomarkers in the Early Diagnosis of Pediatric Onset Inflammatory Bowel Disease
by Vedrana Makević, Ivan D. Milovanovich, Nevena Popovac, Radmila Janković, Jelena Trajković, Andrija Vuković, Bojana Milosević, Jovan Jevtić, Silvio R. de Luka and Andjelija Ž. Ilić
Fractal Fract. 2023, 7(8), 619; https://doi.org/10.3390/fractalfract7080619 - 11 Aug 2023
Cited by 1 | Viewed by 1021
Abstract
Inflammatory bowel disease (IBD), which encompasses two different phenotypes—Crohn’s disease (CD) and ulcerative colitis (UC)—consists of chronic, relapsing disorders of the gastrointestinal tract. In 20–30% of cases, the disease begins in the pediatric age. There have been just a few studies that used [...] Read more.
Inflammatory bowel disease (IBD), which encompasses two different phenotypes—Crohn’s disease (CD) and ulcerative colitis (UC)—consists of chronic, relapsing disorders of the gastrointestinal tract. In 20–30% of cases, the disease begins in the pediatric age. There have been just a few studies that used fractals for IBD investigation, but none of them analyzed intestinal cell chromatin. The main aim of this study was to assess whether it is possible to differentiate between the two phenotypes in pediatric patients, or either of the phenotypes versus control, using the fractal dimension and lacunarity of intestinal cell chromatin. We analyzed nuclei from at least seven different intestinal segments from each group. In the majority of colon segments, both the fractal dimension (FD) and the lacunarity significantly differed between the UC group and CD group, and the UC group and control group. In addition, the ileocecal valve and rectum were the only segments in which CD could be differentiated from the controls based on the FD. The potential of the fractal analysis of intestinal cell nuclei to serve as an observer-independent histological tool for ulcerative colitis diagnosis was identified for the first time in this study. Our results pave the way for the development of computer-aided diagnosis systems that will assist the physicians in their clinical practice. Full article
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18 pages, 546 KiB  
Article
Parameters Identification and Numerical Simulation for a Fractional Model of Honeybee Population Dynamics
by Slavi Georgiev and Lubin Vulkov
Fractal Fract. 2023, 7(4), 311; https://doi.org/10.3390/fractalfract7040311 - 04 Apr 2023
Cited by 4 | Viewed by 903
Abstract
In order to investigate the honeybee population dynamics, many differential equation models were proposed. Fractional derivatives incorporate the history of the honeybee population dynamics. We numerically study the inverse problem of parameter identification in models with Caputo and Caputo–Fabrizio differential operators. We use [...] Read more.
In order to investigate the honeybee population dynamics, many differential equation models were proposed. Fractional derivatives incorporate the history of the honeybee population dynamics. We numerically study the inverse problem of parameter identification in models with Caputo and Caputo–Fabrizio differential operators. We use a gradient method of minimizing a quadratic cost functional. We analyze and compare results for the integer (classic) and fractional models. The present work also contains discussion on the efficiency of the numerical methods used. Computational tests with realistic data were performed and are discussed. Full article
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