Contents
Part I Introduction to Fractal Geometry and Its Applications to Neurosciences
1 The Fractal Geometry of the Brain: An Overview. Antonio Di Ieva
2 Box-Counting Fractal Analysis: A Primer for the Clinician. Audrey L. Karperien and Herbert F. Jelinek
3 Tenets and Methods of Fractal Analysis (1/ f Noise). Tatjana Stadnitski
4 Multifractal Analysis in Neuroimaging. Renaud Lopes
5 Fractal time series: Background, estimation methods and performances. Camillo Porcaro, Sadaf Moaveninejad, Valentina D’Onofrio, Antonio Di Ieva
Part II Fractals in Neuroanatomy and Basic Neurosciences
6 Fractals in Neuroanatomy and Basic Neurosciences: An Overview. Antonio Di Ieva
7 Morphology and Fractal-Based Classifications of Neurons and Microglia. Audrey L. Karperien and Herbert F. Jelinek
8 The Morphology of the Brain Neurons: Box-Counting Method in Quantitative Analysis of 2D Image. Nebojša Milošević
9 Neuronal Fractal Dynamics. Małgorzata Kołodziej and Przemysław Waliszewski
10 A Self-Similarity Logic Shape the Organization of the Nervous System? Diego Guidolin, Cinzia Tortorella, Raffaele De Caro, and Luigi F. Agnati
11 Fractality of Cranial Sutures. Takashi Miura
12 The Fractal Geometry of the Human Brain: An Evolutionary Perspective. Michel A. Hofman
Part III Fractals in Clinical Neurosciences
13 Fractal Analysis in Clinical Neurosciences: An Overview. Antonio Di Ieva
14 Fractal, pattern recognition, and AI: A personal journey in the Computational Neurosurgery. Antonio Di Ieva
15 Clinical sensitivity of fractal dynamics. Elzbieta Olejarczyk, Milena Cukic, Camillo Porcaro, Filippo Zappasodi, and Franca Tecchio
16 Tracking changes of brain morphology with fractal dimensionality. Leticia Díaz Beltrán, Christopher R. Madan, Carsten Finke, Stephan Krohn, Antonio Di Ieva, Francisco J. Esteban
17 Fractal Dimension Studies of the Brain Shape in Aging and Neurodegenerative Diseases. Jennilee M. Davidson, Luduan Zhang, Guang H. Yue, and Antonio Di Ieva
18 Fractal Analysis in Neurodegenerative Diseases. Daniel Pirici, Laurentiu Mogoanta, Daniela Adriana Ion, and Samir Kumar-Singh
19 Fractal Analysis of the Cerebrovascular System Physiopathology. Martin Soehle
20 Fractals and Chaos in the Hemodynamics of Intracranial Aneurysms. Gábor Závodszky, Dániel Gyürki, György Károlyi, István Szikora, and György Paál
21 Fractal-Based Analysis of Arteriovenous Malformations (AVMs). Antonio Di Ieva and Gernot Reishofer
22 Fractals in Neuroimaging. Salim Lahmiri, Mounir Boukadoum, and Antonio Di Ieva
23 Computational Fractal-Based Analysis of MR Susceptibility-Weighted Imaging (SWI) in Neuro-oncology and Neurotraumatology. Antonio Di Ieva
24 Texture Estimation for Abnormal Tissue Segmentation in Brain MRI. Syed M. S. Reza, Atiq Islam, and Khan M. Iftekharuddin
25 Multifractal analysis of brain tumor interface in glioblastoma. Jacksson S and Miguel Martín-Landrove
26 Fractal-Based analysis of histological features of Brain Tumors. Omar S. Al-Kadi and Antonio Di Ieva
27 Computational Fractal-Based Analysis of Brain Tumor Microvascular Networks. Antonio Di Ieva and Omar S. Al-Kadi
28 Fractal-based morphometrics of glioblastoma. Lee Curtin29 Percolation images: Fractal geometry features for brain tumor classification. Alessandra Lumini, Guilherme Freire Roberto, Leandro Alves Neves, Alessandro Santana Martins, Marcelo Zanchetta do Nascimento
30 On Multiscaling of Parkinsonian Rest Tremor Signals and Their Classification. Lorenzo Livi
31 Fractal phototherapy in maximixing retina and brain plasticity. Marina V Zueva, Natalia V Neroeva, Anastasia N Zhuravleva, Anna N Bogolepova, Vladislav V Kotelin, Denis V Fadeev, and Irina V Tsapenko
32 Fractal similarity of pain brain networks. Camille Fauchon, Hélène Bastuji, Roland Peyron, and Luis Garcia-Larrea
33 Fractal neurodynamics. Karolina Armonaite, Livio Conti, and Franca Tecchio
34 Fractal analysis of electrophysiological signals to detect and monitor depression: What we know so far? Milena Čukić, Elzbieta Olejarzcyk, and Maie Bachmann
35 Point of Care Testing (POCT) in Psychopathology using Fractal Analysis and Hilbert Huang Transform of Electroencephalogram (EEG). Mohammed Khan, and Herbert Jelinek
36 Fractals in Affective and Anxiety Disorders. Sergio Iglesias-Parro, Maria Felipa Soriano, and Antonio José Ibáñez-Molina
37 EEG complexity analysis of brain states, tasks and ASD risk. Stephen S Wolfson, Ian Kirk, Karen Waldie, Chris King
38 Fractals in neuropsychology and cognitive neuroscience. Antonio Cerasa
Part IV Computational and Translational Fractal-Based Neurosciences
39 Computational and Translational Fractal-Based Neurosciences: An Overview. Antonio Di Ieva
40 ImageJ in Computational Fractal-Based Neuroscience: Pattern Extraction and Translational Research. Audrey L. Karperien and Herbert F. Jelinek
41 Fractal Analysis in MATLAB: A Tutorial for Neuroscientists. Juan Ruiz de Miras
42 Fractal Analysis in eye-tracking. Robert Newport, Sidong Liu, and Antonio Di Ieva
43 Fractal Electronics for Stimulating and Sensing Neural Networks: Enhanced Electrical, Optical, and Cell Interaction Properties. S. Moslehi, C. Rowland, J.H. Smith, W.J. Watterson, Willem Griffiths, R.D. Montgomery, S. Philliber, C.A. Marlow, Maria-Thereza Perez, R.P. Taylor
44 Fractal Resonance: Can Fractal Geometry be used to Optimize the Connectivity of Neurons to Artificial Implants? C. Rowland, S. Moslehi, J.H. Smith, B. Harland, J. Dalrymple-Alford, and R.P. Taylor
45 Fractal Fluency: Processing of Fractal Stimuli Across Sight, Sound, and Touch. Richard P. Taylor, Catherine Viengkham, Julian H. Smith, Conor Rowland, Saba Moslehi, Sabrina Stadlober, Anastasija Lesjak, Martin Lesjak, and Branka Spehar
46 Cognitive and neural representations of fractals in vision, music and action. Mauricio de Jesus Dias Martins
47 Fractals in the neurosciences: A translational geographical approach. Ion Andronache, Daniel Peptenatu, Helmut Ahammer, Marko Radulovic, Goran J. Djuričić, Herbert F. Jelinek, Carlo Russo, and Antonio Di Ieva
48 Fractal Geometry Meets Computational Intelligence: Future Perspectives. Lorenzo Livi, Alireza Sadeghian, and Antonio Di Ieva
Antonio Di Ieva, MD, PhD, FRACS, is Professor of Neurosurgery at Macquarie Medical School, Macquarie University, Sydney, Australia; Professor of Neurosurgery, Ministry of Education, University and Research, Italy; Associate Professor of Neuroanatomy, Medical University of Vienna, Austria; Fellow of the Australian Research Council (ARC) and of the Royal Australasian College of Surgeons (RACS); Consultant Neurosurgeon, Macquarie Neurosurgery, Sydney, Australia; Founder and Head of the Computational NeuroSurgery (CNS) Lab at Macquarie University, Sydney, Australia; Neuroscience & AI Program Leader, Centre for Applied Artificial Intelligence, Macquarie University, Sydney, Australia
The new edition of the highly popular, The Fractal Geometry of the Brain, reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. It brings an understanding of fractals to clinicians and researchers even if they do not have a mathematical background, and it serves as a valuable tool for teaching the translational applications of computational fractal-based models to both students and scholars. As a consequence of the novel research developed at Professor Di Ieva's laboratory and other centers around the world, the second edition will explore the use of computational fractal-based analysis in many clinical disciplines and different fields of research, including neurology and neurosurgery, neuroanatomy and psychology, magnetoencephalography (MEG), eye-tracking devices (for the fractal computational characterization of “scanpaths”), deep learning in image analysis, radiomics for the characterization of brain MRIs, characterization of neuropsychological and psychiatric diseases and traits, signal complexity analysis in time series, and functional MRI, amongst others.
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