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Fractal Fract
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Fractals in the Neurosciences: From Self-Similar Structures to Scale-Free Dynamics
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Fractals in the Neurosciences: From Self-Similar Structures to Scale-Free Dynamics

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

Deadline for manuscript submissions: closed (7 May 2023) | Viewed by 12470

Special Issue Editors

Dr. Frigyes Samuel Racz

E-Mail Website
Guest Editor
Department of Neurology, Dell Medical School, The University of Texas at Austin, Austin, TX 78712, USA
Interests: fractal physiology; dynamic functional connectivity; brain–computer interfaces; neuromodulation; cognitive neuroscience; fractal connectivity; neuropsychiatric disorders
Dr. Peter Mukli

E-Mail Website
Guest Editor
Department of Biochemistry and Molecular Biology, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73104, USA
Interests: fractal time series analysis; brain networks; scale-free dynamics; physiological networks; aging; gait variability; neurovascular coupling; cerebrovascular function
Dr. Alexander J Bies

E-Mail Website
Guest Editor
Department of Psychology, Gonzaga University, Spokane, WA 99258, USA
Interests: cognitive neuroscience; neuroaesthetics; perception; fractals

Special Issue Information

Dear Colleagues,

Fractal phenomena are abundantly present in the nervous system, with anatomical structures and their dynamics emerging from the coordinated activity of neuronal and glial cells. Self-similar structures can be found not only at the macro-, meso- and microanatomical scales, but also at subcellular levels, such as in genetic patterns or molecular interaction networks. Moreover, neural activity was shown to express fractal dynamics when investigated with multiple techniques and modalities; examples include ion transfer kinetics, local field potentials or cerebral hemodynamics evoked by regional neural activity. It was demonstrated that time-varying functional connectivity patterns of the brain also exhibit (multi)fractality in their fluctuations. More recently it was revealed that the activity of distinct brain regions expressed coupling on multiple scales, leading to the emergence of the field of fractal connectivity. Finally, many researchers also hypothesized a self-organized critical state of brain function behind the emergence of scale-free dynamic patterns. Studies utilizing this non-exhaustive sample of fractal approaches not only provided a better understanding of the structural and functional organization of the brain, but also showed a potential utility in the diagnosis, monitoring or treatment of several pathological conditions, such as neuropsychiatric diseases or acute stroke.

The aim of this Special Issue is to provide a forum for the most recent advances in the fractal analysis of neural phenomena. The following topics for which manuscripts are welcomed include, but are not limited to:

  • Self-similar molecular networks in the brain;
  • Fractal analysis of neural and glial genetic sequences;
  • Fractal geometry of the brain;
  • Fractal and multifractal analysis of brain dynamics;
  • Fractal functional connectivity;
  • Criticality in the nervous system;
  • Applications of fractal methods in neuropathological conditions;
  • Novel methods in fractal analysis of neural data.

Reviews focusing on one or more of the aforementioned topics are also considered.

Dr. Frigyes Samuel Racz
Dr. Peter Mukli
Dr. Alexander J Bies
Guest Editors

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

  • bioinformatics
  • complex networks
  • criticality
  • fractals
  • fractal dynamics
  • long-range correlations
  • self-organization
  • self-similarity

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Published Papers (5 papers)

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Research

15 pages, 4497 KiB  
Article
Association between Opioid Dependence and Scale Free Fractal Brain Activity: An EEG Study
by Parikshat Sirpal, William A. Sikora, Desiree R. Azizoddin, Hazem H. Refai and Yuan Yang
Fractal Fract. 2023, 7(9), 659; https://doi.org/10.3390/fractalfract7090659 - 31 Aug 2023
Cited by 1 | Viewed by 1802 | Correction
Abstract
Self-similarities at different time scales embedded within a self-organizing neural manifold are well recognized. In this study, we hypothesize that the Hurst fractal dimension (HFD) of the scalp electroencephalographic (EEG) signal reveals statistical differences between chronic pain and opioid use. We test this [...] Read more.
Self-similarities at different time scales embedded within a self-organizing neural manifold are well recognized. In this study, we hypothesize that the Hurst fractal dimension (HFD) of the scalp electroencephalographic (EEG) signal reveals statistical differences between chronic pain and opioid use. We test this hypothesis by using EEG resting state signals acquired from a total of 23 human subjects: 14 with chronic pain, 9 with chronic pain taking opioid medications, 5 with chronic pain and not taking opioid medications, and 9 healthy controls. Using the multifractal analysis algorithm, the HFD for full spectrum EEG and EEG frequency band time series was computed for all groups. Our results indicate the HFD varies spatially and temporally across all groups and is of lower magnitude in patients not taking opioids as compared to those taking opioids and healthy controls. A global decrease in HFD was observed with changes in gamma and beta power in the chronic pain group compared to controls and when paired to subject handedness and sex. Our results show the loss of complexity representative of brain wide dysfunction and reduced neural processing can be used as an EEG biomarker for chronic pain and subsequent opioid use. Full article
(This article belongs to the Special Issue Fractals in the Neurosciences: From Self-Similar Structures to Scale-Free Dynamics)
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15 pages, 6419 KiB  
Article
Post Mortem Image Analysis of Astrocytes of the Human Principal Olivary Nucleus Using Geometrical and Fractal Parameters
by Damjan Stojić and Dragana Radošević
Fractal Fract. 2023, 7(1), 6; https://doi.org/10.3390/fractalfract7010006 - 21 Dec 2022
Viewed by 2595
Abstract
Based on their morphology, the most abundant cells within the nervous tissue of the central nervous system, astrocytes, can be divided into two types, protoplasmic astrocytes and fibrous astrocytes. A further analysis of the brain tissue with the preserved astrocytes from the human [...] Read more.
Based on their morphology, the most abundant cells within the nervous tissue of the central nervous system, astrocytes, can be divided into two types, protoplasmic astrocytes and fibrous astrocytes. A further analysis of the brain tissue with the preserved astrocytes from the human principal olivary nucleus, based on their morphological differences with age, is successfully performed in this paper. Moreover, the images of 294 astrocytes, 148 fibrous and 146 protoplasmic, from the principal olivary nucleus were used. Applied for the first time in astrocytes image analysis, the principal component analysis was used to find the most informative parameters among geometrical and fractal in each of the four predefined groups, i.e., categories, of the morphological measurements of astrocytes in the images. The proposed subsets representing different morphological features can be used to distinguish astrocyte subtypes and predict their changes during normal aging. The values of the adequated parameters in different subsets were compared between the fibrous and protoplasmic astrocytes and correlated with age. Significant differences (p < 0.05) between the two subtypes were found in four Euclidean and four monofractal parameters. In addition, significant correlations were found between selected parameters and the age of subjects. In the upcoming iterations of this procedure, possible refinement and upgrades are expected. Full article
(This article belongs to the Special Issue Fractals in the Neurosciences: From Self-Similar Structures to Scale-Free Dynamics)
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13 pages, 1933 KiB  
Article
Scale-Free Functional Brain Networks Exhibit Increased Connectivity, Are More Integrated and Less Segregated in Patients with Parkinson’s Disease following Dopaminergic Treatment
by Orestis Stylianou, Zalan Kaposzta, Akos Czoch, Leon Stefanovski, Andriy Yabluchanskiy, Frigyes Samuel Racz, Petra Ritter, Andras Eke and Peter Mukli
Fractal Fract. 2022, 6(12), 737; https://doi.org/10.3390/fractalfract6120737 - 13 Dec 2022
Cited by 4 | Viewed by 2024
Abstract
Dopaminergic treatment (DT), the standard therapy for Parkinson’s disease (PD), alters the dynamics of functional brain networks at specific time scales. Here, we explore the scale-free functional connectivity (FC) in the PD population and how it is affected by DT. We analyzed the [...] Read more.
Dopaminergic treatment (DT), the standard therapy for Parkinson’s disease (PD), alters the dynamics of functional brain networks at specific time scales. Here, we explore the scale-free functional connectivity (FC) in the PD population and how it is affected by DT. We analyzed the electroencephalogram of: (i) 15 PD patients during DT (ON) and after DT washout (OFF) and (ii) 16 healthy control individuals (HC). We estimated FC using bivariate focus-based multifractal analysis, which evaluated the long-term memory (H(2)) and multifractal strength (ΔH15) of the connections. Subsequent analysis yielded network metrics (node degree, clustering coefficient and path length) based on FC estimated by H(2) or ΔH15. Cognitive performance was assessed by the Mini Mental State Examination (MMSE) and the North American Adult Reading Test (NAART). The node degrees of the ΔH15 networks were significantly higher in ON, compared to OFF and HC, while clustering coefficient and path length significantly decreased. No alterations were observed in the H(2) networks. Significant positive correlations were also found between the metrics of H(2) networks and NAART scores in the HC group. These results demonstrate that DT alters the multifractal coupled dynamics in the brain, warranting the investigation of scale-free FC in clinical and pharmacological studies. Full article
(This article belongs to the Special Issue Fractals in the Neurosciences: From Self-Similar Structures to Scale-Free Dynamics)
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11 pages, 1857 KiB  
Article
Tool Embodiment Is Reflected in Movement Multifractal Nonlinearity
by Yvan Pratviel, Veronique Deschodt-Arsac, Florian Larrue and Laurent M. Arsac
Fractal Fract. 2022, 6(5), 240; https://doi.org/10.3390/fractalfract6050240 - 26 Apr 2022
Cited by 2 | Viewed by 2840
Abstract
Recent advances in neuroscience have linked dynamical systems theory to cognition. The main contention is that extended cognition relies on a unitary brain-body-tool system showing the expected signatures of interaction-dominance reflected in a multifractal behavior. This might be particularly relevant when it comes [...] Read more.
Recent advances in neuroscience have linked dynamical systems theory to cognition. The main contention is that extended cognition relies on a unitary brain-body-tool system showing the expected signatures of interaction-dominance reflected in a multifractal behavior. This might be particularly relevant when it comes to understanding how the brain is able to embody a tool to perform a task. Here we applied the multifractal formalism to the dynamics of hand movement while one was performing a computer task (the herding task) using a mouse or its own hand as a tool to move an object on the screen. We applied a focus-based multifractal detrended fluctuation analysis to acceleration time series. Then, multifractal nonlinearity was assessed by comparing original series to a finite set of surrogates obtained after Iterated Amplitude Adjusted Fourier transformation, a method that removes nonlinear multiscale dependencies while preserving the linear structure of the time series. Both hand and mouse task execution demonstrated multifractal nonlinearity, a typical form of across-scales interactivity in cognitive control. In addition, a wider multifractal spectrum was observed in mouse condition, which might highlight a richer set of interactions when the cognitive system is extended to the embodied mouse. We conclude that the emergence of multifractal nonlinearity from a brain-body-tool system pleads for recent theories of radical tool embodiment. Multifractal nonlinearity may be a promising metric to appreciate how physical objects—but also virtual tools and potentially prosthetics—are efficiently embodied by the brain. Full article
(This article belongs to the Special Issue Fractals in the Neurosciences: From Self-Similar Structures to Scale-Free Dynamics)
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11 pages, 1572 KiB  
Article
Multifractality in the Movement System When Adapting to Arm Cranking in Wheelchair Athletes, Able-Bodied Athletes, and Untrained People
by Laurent M. Arsac and Thierry Weissland
Fractal Fract. 2022, 6(4), 176; https://doi.org/10.3390/fractalfract6040176 - 22 Mar 2022
Cited by 2 | Viewed by 2007
Abstract
Complexity science has helped neuroscientists shed new light on brain-body coordination during movement performance and motor learning in humans. A critical intuition based on monofractal approaches has been a fractal-like coordination in the movement system, more marked in motor-skilled people. Here we aimed [...] Read more.
Complexity science has helped neuroscientists shed new light on brain-body coordination during movement performance and motor learning in humans. A critical intuition based on monofractal approaches has been a fractal-like coordination in the movement system, more marked in motor-skilled people. Here we aimed to show that heterogeneity in scaling exponents of movements series, literally multifractality, may reflect a special kind of interactions spanning multiple temporal scales at once, which can be grasped by a focus-based multifractal detrended fluctuation analysis. We analyzed multifractality in the variability structure of a 10-min arm cranking movement series repeated as 3 sets a day for 3 days, comparatively with their linearized (phase-randomized) surrogate series in sedentary (SED) untrained people, wheelchair athletes (WATH), and able-bodied athletes (ATH). Arm cranking exercise was chosen to minimize external variations, which tend to interfere with internal origin of variability. Participants were asked to maintain a regular effort and torque output served as the performance variable. Our first hypothesis suggests greater multiscale interactions in trained (WATH, ATH) versus untrained (SED) people, reflected in a wider range of scaling exponents characterizing movement series, providing the system with significant robustness. As a second hypothesis, we addressed a possible advantage in WATH over ATH due to greater motor skills in upper-limbs. Multifractal metrics in original and surrogate series showed ubiquitous, but different, multifractal behaviors in expert (ATH and WATH indistinctively) versus novice (SED) people. Experts exhibited high multifractality during the first execution of the task; then multifractality dropped in following repetitions. We suggest an exacerbated robustness of the movement system coordination in experts when discovering the task. Once task novelty has worn off, poor external sources of variability and limited risks of task failure have been identified, which is reflected in the narrower range of scale interactions, possibly as an energy cost effective adaptation. Multifractal corollaries of movement adaptation may be helpful in sport training and motor rehabilitation programs. Full article
(This article belongs to the Special Issue Fractals in the Neurosciences: From Self-Similar Structures to Scale-Free Dynamics)
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