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Mathematical Modelling and Biomechanics of the Brain

Mathematical Modelling and Biomechanics of the Brain
Author: Corina Drapaca
Publisher: Springer Nature
Total Pages: 155
Release: 2019-09-06
Genre: Mathematics
ISBN: 1493998102
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This monograph aims to provide a rigorous yet accessible presentation of some fundamental concepts used in modeling brain mechanics and give a glimpse of the insights and advances that have arisen as a result of the nascent interaction of the mathematical and neurosurgical sciences. It begins with some historical perspective and a brief synopsis of the biomedical/biological manifestations of the clinical conditions/diseases considered. Each chapter proceeds with a discussion of the various mathematical models of the problems considered, starting with the simplest models and proceeding to more complex models where necessary. A detailed list of relevant references is provided at the end of each chapter. With the beginning research student in mind, the chapters have been crafted to be as self-contained as possible while addressing different clinical conditions and diseases. The book is intended as a brief introduction to both theoreticians and experimentalists interested in brain mechanics, with directions and guidance for further reading, for those who wish to pursue particular topics in greater depth. It can also be used as a complementary textbook in a graduate level course for neuroscientists and neuroengineers.

Mathematical Modeling of the Human Brain

Mathematical Modeling of the Human Brain
Author: Kent-André Mardal
Publisher: Springer Nature
Total Pages: 129
Release: 2022-02-25
Genre: Mathematics
ISBN: 3030951367
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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.

Biomechanics of the Brain

Biomechanics of the Brain
Author: Karol Miller
Publisher: Springer
Total Pages: 353
Release: 2019-08-08
Genre: Science
ISBN: 3030049965
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This new edition presents an authoritative account of the current state of brain biomechanics research for engineers, scientists and medical professionals. Since the first edition in 2011, this topic has unquestionably entered into the mainstream of biomechanical research. The book brings together leading scientists in the diverse fields of anatomy, neuroimaging, image-guided neurosurgery, brain injury, solid and fluid mechanics, mathematical modelling and computer simulation to paint an inclusive picture of the rapidly evolving field. Covering topics from brain anatomy and imaging to sophisticated methods of modeling brain injury and neurosurgery (including the most recent applications of biomechanics to treat epilepsy), to the cutting edge methods in analyzing cerebrospinal fluid and blood flow, this book is the comprehensive reference in the field. Experienced researchers as well as students will find this book useful.

Models of the Mind

Models of the Mind
Author: Grace Lindsay
Publisher:
Total Pages: 400
Release: 2021
Genre: Brain
ISBN: 9781472966445
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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.

Mathematical Modelling in Motor Neuroscience: State of the Art and Translation to the Clinic, Gaze Orienting Mechanisms and Disease

Mathematical Modelling in Motor Neuroscience: State of the Art and Translation to the Clinic, Gaze Orienting Mechanisms and Disease
Author:
Publisher: Academic Press
Total Pages: 426
Release: 2019-07-18
Genre: Science
ISBN: 0444642552
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Mathematical Modelling in Motor Neuroscience: State of the Art and Translation to the Clinic, Gaze Orienting Mechanisms and Disease, Volume 249, the latest release in the Progress in Brain Research series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of topics, including Sequential Bayesian updating, Maps and Sensorimotor Transformations for Eye-Head Gaze Shifts: Role of the Midbrain Superior Colliculus, Modeling Gaze Position-Dependent Opsoclonus, Eye Position-Dependent Opsoclonus in Mild Traumatic Brain Injury, Saccades in Parkinson's disease -- hypometric, slow, and maladaptive, Brainstem Neural Circuits for Fixation and Generation of Saccadic Eye Movements, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Progress in Brain Research series Includes the latest information on mathematical modeling in motor neuroscience

Brain Dynamics

Brain Dynamics
Author: Hermann Haken
Publisher: Springer Science & Business Media
Total Pages: 331
Release: 2007-12-22
Genre: Science
ISBN: 3540752382
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This is an excellent introduction for graduate students and nonspecialists to the field of mathematical and computational neurosciences. The book approaches the subject via pulsed-coupled neural networks, which have at their core the lighthouse and integrate-and-fire models. These allow for highly flexible modeling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. The more advanced pulse-averaged equations are discussed.

Neural and Brain Modeling

Neural and Brain Modeling
Author: Ronald MacGregor
Publisher: Elsevier
Total Pages: 656
Release: 2012-12-02
Genre: Science
ISBN: 0323143849
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Neural and Brain Modeling reviews models used to study neural interactions. The book also discusses 54 computer programs that simulate the dynamics of neurons and neuronal networks to illustrate between unit and systemic levels of nervous system functions. The models of neural and brain operations are composed of three sections: models of generic mechanisms; models of specific neuronal systems; and models of generic operations, networks, and systems. The text discusses the computational problems related to galvanizing a neuronal population though an activity in the multifiber input system. The investigator can use a computer technique to simulate multiple interacting neuronal populations. For example, he can investigate the case of a single local region that contains two populations of neurons: namely, a parent population of excitatory cells, and a second set of inhibitory neurons. Computer simulation models predict the various dynamic activity occurring in the complicated structure and physiology of neuronal systems. Computer models can be used in "top-down" brain/mind research where the systemic, global, and emergent properties of nervous systems are generated. The book is recommended for behavioral scientists, psychiatrists, psychologists, computer programmers, students, and professors in human behavior.

Dynamic Deformation and Mechanical Properties of Brain Tissue

Dynamic Deformation and Mechanical Properties of Brain Tissue
Author: Yuan Feng
Publisher:
Total Pages: 147
Release: 2012
Genre: Electronic dissertations
ISBN:
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Traumatic brain injury is an important medical problem affecting millions of people. Mathematical models of brain biomechanics are being developed to simulate the mechanics of brain injury and to design protective devices. However, because of a lack of quantitative data on brain-skull boundary conditions and deformations, the predictions of mathematical models remain uncertain. The objectives of this dissertation are to develop methods and obtain experimental data that will be used to parameterize and validate models of traumatic brain injury. To that end, this dissertation first addresses the brain-skull boundary conditions by measuring human brain motion using tagged magnetic resonance imaging. Magnetic resonance elastography was performed in the ferret brain to measure its mechanical properties in vivo. Brain tissue is not only heterogeneous, but may also be anisotropic. To characterize tissue anisotropy, an experimental procedure combining both shear testing and indentation was developed and applied to white matter and gray matter. These measurements of brain-skull interactions and mechanical properties of the brain will be valuable in the development and validation of finite element simulations of brain biomechanics.

Natural Biodynamics

Natural Biodynamics
Author: Vladimir G. Ivancevic
Publisher: World Scientific
Total Pages: 1036
Release: 2005
Genre: Science
ISBN: 9812703160
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This comprehensive volume is a graduate-level text in human biodynamics, written in the unified categorical language of modern differential geometry and topology. Combining mathematics, physics and robotics with human physiology, this is the first book that describes all levels of human biodynamics, from musculo-skeletal mechanics to the higher brain functions. The book develops and uses a variety of research methods, ranging from chaos theory and Haken's synergetics, through quantum mechanics, to nonlinear control and artificial intelligence, to provide the means to understand, predict and control the behavior of human-like systems in their full neuro-musculo-skeletal complexity. The applications of this unique scientific methodology range from prediction of human neuro-musculo-skeletal injuries to brain-like control of humanoid robots.

Computer Models in Biomechanics

Computer Models in Biomechanics
Author: Gerhard Holzapfel
Publisher: Springer Science & Business Media
Total Pages: 406
Release: 2012-10-17
Genre: Technology & Engineering
ISBN: 9400754639
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This book contains a collection of papers that were presented at the IUTAM Symposium on “Computer Models in Biomechanics: From Nano to Macro” held at Stanford University, California, USA, from August 29 to September 2, 2011. It contains state-of-the-art papers on: - Protein and Cell Mechanics: coarse-grained model for unfolded proteins, collagen-proteoglycan structural interactions in the cornea, simulations of cell behavior on substrates - Muscle Mechanics: modeling approaches for Ca2+–regulated smooth muscle contraction, smooth muscle modeling using continuum thermodynamical frameworks, cross-bridge model describing the mechanoenergetics of actomyosin interaction, multiscale skeletal muscle modeling - Cardiovascular Mechanics: multiscale modeling of arterial adaptations by incorporating molecular mechanisms, cardiovascular tissue damage, dissection properties of aortic aneurysms, intracranial aneurysms, electromechanics of the heart, hemodynamic alterations associated with arterial remodeling following aortic coarctation, patient-specific surgery planning for the Fontan procedure - Multiphasic Models: solutes in hydrated biological tissues, reformulation of mixture theory-based poroelasticity for interstitial tissue growth, tumor therapies of brain tissue, remodeling of microcirculation in liver lobes, reactions, mass transport and mechanics of tumor growth, water transport modeling in the brain, crack modeling of swelling porous media - Morphogenesis, Biological Tissues and Organs: mechanisms of brain morphogenesis, micromechanical modeling of anterior cruciate ligaments, mechanical characterization of the human liver, in vivo validation of predictive models for bone remodeling and mechanobiology, bridging scales in respiratory mechanics