title: Fractals in the Neurosciences, Part I: General Principles and Basic Neurosciences.
abstract: The natural complexity of the brain, its hierarchical structure, and the sophisticated topological architecture of the neurons organized in micronetworks and macronetworks are all factors contributing to the limits of the application of Euclidean geometry and linear dynamics to the neurosciences. The introduction of fractal geometry for the quantitative analysis and description of the geometric complexity of natural systems has been a major paradigm shift in the last decades. Nowadays, modern neurosciences admit the prevalence of fractal properties such as self-similarity in the brain at various levels of observation, from the microscale to the macroscale, in molecular, anatomic, functional, and pathological perspectives. Fractal geometry is a mathematical model that offers a universal language for the quantitative description of neurons and glial cells as well as the brain as a whole, with its complex three-dimensional structure, in all its physiopathological spectrums. For a holistic view of fractal geometry of the brain, we review here the basic concepts of fractal analysis and its main applications to the basic neurosciences.
authors.affiliation: Division of Neurosurgery, St. Michael's Hospital, University of Toronto, Toronto, Canada Centre for Anatomy and Cell Biology, Department of Systematic Anatomy, Medical University of Vienna, Vienna, Austria diieva@hotmail.com.
authors.forename: Antonio
authors.initials: A
authors.lastname: Di Ieva
authors.affiliation: Humanitas Clinical and Research Center, Rozzano, Milan, Italy.
authors.forename: Fabio
authors.initials: F
authors.lastname: Grizzi
authors.affiliation: Deparment of Biomedical Engineering, Khalifa University of Science, Technology and Research, Abu Dhabi, United Arab Emirates Australian School of Advanced Medicine, Macquarie University, Sydney, Australia.
authors.forename: Herbert
authors.initials: H
authors.lastname: Jelinek
authors.affiliation: HolGenTech Inc., Sunnyvale, CA, USA.
authors.forename: Andras J
authors.initials: AJ
authors.lastname: Pellionisz
authors.affiliation: Institute of Scientific Interdisciplinary Studies, Locarno, Switzerland.
authors.forename: Gabriele Angelo
authors.initials: GA
authors.lastname: Losa
keywords: brain; complexity; fractal analysis; fractal geometry; microglia; neuroanatomy; neuron; neurosciences