This open access book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images. The book's presentation concludes with the reader solving a simplified PDE model of gadobutrol diffusion in the brain that incorporates diffusion tensor images, of various resolution, and complex, multi-domain, variable-resolution FEniCS meshes with detailed markings of anatomical brain regions. After completing this book, the reader will have a solid foundation for performing patient-specific finite element simulations of biomechanical models of the human brain.
The human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate – and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it. In Models of the Mind, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain's processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. Each chapter of Models of the Mind focuses on mathematical tools that have been applied in a particular area of neuroscience, progressing from the simplest building block of the brain – the individual neuron – through to circuits of interacting neurons, whole brain areas and even the behaviours that brains command. In addition, Grace examines the history of the field, starting with experiments done on frog legs in the late eighteenth century and building to the large models of artificial neural networks that form the basis of modern artificial intelligence. Throughout, she reveals the value of using the elegant language of mathematics to describe the machinery of neuroscience.
The book was written as an attempt to find the solution to one of the most complex and unsolved issues of the human anatomy: the understanding of the human brain and the principles according to which it operates. Currently, it is important to look at the challenge in an alternatively non-standard, yet still systemic way, paying less attention to details and outlining the ways out of this crisis of neuroscience. The purpose of this monograph is to describe the author's theory about the brain's architecture and operation to the medical and scientific community. Accompanied with extensive clinical, research and training experience, the author's theoretical concepts of the brain synthesized with scientific evidence brought about the conclusion that low efficiency in neurologic therapy and mental diseases; the inability to work out mathematical models and simulations that could compete with the human brain; an academic dead end in the development of artificial intelligence; as well as high energy consumption of the computing innovations were conditioned by the inaccurate methodology and outdated anatomical and physiological views of the neurologists and neuroscientists on information processing in the brain, registration of memories and basic functions of the key morphological structures of the brain. The morphological structure and physiological functions of all known anatomical formations of the brain were defined in the late nineteenth century. Since then, these functions have been accepted as dogmatic. The book shows that present day multi-level neuroresearch relies on the foundation of systemic, morphofunctional and neuroanatomic knowledge about the brain structure. It looks for correlations between genome and post-genome data of molecular research in the brain tissue, as well as with neuropsychological and cognitive data; that is, the book intends to integrate the non-integrable into unified information space. The systemic approach in neuroresearch has become outdated by now and interferes with scientific development. The information approach in the author's research of the genome, transcriptome, proteome in health and in disease permitted the analysis of the inductivity and magnetization of the nervous tissue. It also provided the explanation for targeted movement of the data in the module of the nervous tissue. The author came to the conclusion that gene, protein and neural networks "confused and chained" the pathways of scientific thought. Neural networks are only logistic constructions to provide data transfer in the brain between different modules of the nervous tissue. The author presumes that the funds invested in the development of brain simulations and artificial intelligence will hardly result in the expected advantages. If we are unable to step over the stereotypes of the systemic, morphofunctional research of the previous century, no progress shall come about. The author's theoretical survey resulted in the unique information-commutation theory of the brain and formulation of the key principles of brain operation. As a clinician and professor of neurology, the author underpins his theory with clinical examples. This book presents the framework of the ideas that require experimental research and proof.
This book introduces mathematicians to real applications from physiology. Using mathematics to analyze physiological systems, the authors focus on models reflecting current research in cardiovascular and pulmonary physiology. In particular, they present models describing blood flow in the heart and the cardiovascular system, as well as the transport of oxygen and carbon dioxide through the respiratory system and a model for baroreceptor regulation.
This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.
Deepen students' understanding of biological phenomenaSuitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeli
This updated second edition provides the state of the art perspective of the theory, practice and application of modern non-invasive imaging methods employed in exploring the structural and functional architecture of the normal and diseased human brain. Like the successful first edition, it is written by members of the Functional Imaging Laboratory - the Wellcome Trust funded London lab that has contributed much to the development of brain imaging methods and their application in the last decade. This book should excite and intrigue anyone interested in the new facts about the brain gained from neuroimaging and also those who wish to participate in this area of brain science.* Represents an almost entirely new book from 1st edition, covering the rapid advances in methods and in understanding of how human brains are organized* Reviews major advances in cognition, perception, emotion and action* Introduces novel experimental designs and analytical techniques made possible with fMRI, including event-related designs and non-linear analysis
Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.
Nearly 80 short papers originating from the 14th International Symposium on Intracranial Pressure and Brain Monitoring held in Tuebingen, Germany, in September 2010 present experimental as well as clinical research data related to the naming topics of the conference. The papers have undergone a peer-reviewing and are organized in the following sections: methods of brain monitoring and data analysis, methods of invasive and non-invasive ICP assessment, the role of autoregulation, the role of tissue oxygenation and near-infrared spectroscopy, hydrocephalus/IIH imaging and diagnosis, management and therapy of hydrocephalus, management and therapy of traumatic brain injury, management and therapy of subarachnoid and intracranial hemorrhage, experimental approaches to acute brain disease. The book gives a good overview on the latest research developments in the field of ICP and related brain monitoring and on management and therapy of relevant acute brain diseases.
Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory. - Fully revised material and corrected text - Additional chapters on extracellular potentials, motion detection and neurovascular coupling - Revised selection of exercises with solutions - More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts
