The Fractal Geometry of the Brain

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

Part I. Introduction to Fractal Geometry and its Applications to Neurosciences.- The Fractal Geometry of the Brain: An Overview.- 2. Box-Counting Fractal Analysis: A Primer for the Clinician.- Tenets and Methods of Fractal Analysis (1/f noise).- 4. Tenets, Methods and Applications of Multifractal Analysis in Neurosciences.- Part II. Fractals in Neuroanatomy and Basic Neurosciences.- Fractals in Neuroanatomy and Basic Neurosciences: An Overview.- Morphology and Fractal-Based Classifications of Neurons and Microglia.- The Morphology of the Brain Neurons: Box-counting Method in Quantitative Analysis of 2D Image.- Neuronal Fractal Dynamics.- Does a Self-Similarity Logic Shape the Organization of the Nervous System?.- Fractality of Cranial Sutures.- The Fractal Geometry of the Human Brain: An Evolutionary Perspective.- Part III. Fractals in Clinical Neurosciences.- Fractal Analysis in Clinical Neurosciences: An Overview.- Fractal Analysis in Neurological Diseases.- Fractal Dimension Studiesof the Brain Shape in Aging and Neurodegenerative Diseases.- Fractal Analysis in Neurodegenerative Diseases.- Fractal Analysis of the Cerebrovascular System Physiopathology.- Fractal and Chaos in the Hemodynamics of Intracranial Aneurysms.- Fractal-based Analysis of Arteriovenous Malformations (AVMs).- Fractals in Neuroimaging.- Computational Fractal-Based Analysis of MR Susceptibility Weighted Imaging (SWI) in Neuro-oncology and neurotraumatology.- Texture Estimation for Abnormal Tissue Segmentation in Brain MRI.- Tumor Growth in the Brain: Complexity and Fractality.- Histological Fractal-based Classification of Brain Tumors.- Computational Fractal-based Analysis of the Brain Tumors Microvascular Networks.- Fractal  analysis of  electroencephalographic time-series (EEG-signals).- On Multiscaling of Parkinsonian Rest Tremor Signals and Their Classification.- Fractals and Electromyograms.- Fractal analysis in Neuro-ophthalmology.- Fractals in Affective and Anxiety Disorders.-Fractal Fluency: An Intimate Relationship Between the Brain and Processing of Fractal Stimuli.- Part IV. Computational Fractal-Based Neurosciences.- Computational Fractal-based Neurosciences: An Overview.- ImageJ in Computational Fractal-based Neuroscience: Pattern Extraction and Translational Research.- Fractal Analysis in MATLAB: A Tutorial for Neuroscientists.- Methodology to Increase the Computational Speed to Obtain the Fractal Dimension Using GPU Programming.- Fractal Electronics as a Generic Interface to Neurons.- Fractal Geometry meets Computational Intelligence: Future Perspectives.