Mathematical Modelling And Biomechanics Of The Brain

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Mathematical Modelling and Biomechanics of the Brain

Corina Drapaca,Siv Sivaloganathan
Mathematical Modelling and Biomechanics of the Brain Book PDF

Author : Corina Drapaca,Siv Sivaloganathan
Publisher : Springer Nature
Page : 155 pages
File Size : 44,9 Mb
Release : 2019-09-06
Category : Mathematics
ISBN : 9781493998104

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Mathematical Modelling and Biomechanics of the Brain by Corina Drapaca,Siv Sivaloganathan Pdf

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

Kent-André Mardal,Marie E. Rognes,Travis B. Thompson,Lars Magnus Valnes
Mathematical Modeling of the Human Brain Book PDF

Author : Kent-André Mardal,Marie E. Rognes,Travis B. Thompson,Lars Magnus Valnes
Publisher : Springer Nature
Page : 129 pages
File Size : 40,7 Mb
Release : 2022-02-25
Category : Mathematics
ISBN : 9783030951368

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Mathematical Modeling of the Human Brain by Kent-André Mardal,Marie E. Rognes,Travis B. Thompson,Lars Magnus Valnes Pdf

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.

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

Anonim
Mathematical Modelling in Motor Neuroscience State of the Art and Translation to the Clinic Gaze Orienting Mechanisms and Disease Book PDF

Author : Anonim
Publisher : Academic Press
Page : 426 pages
File Size : 48,9 Mb
Release : 2019-07-18
Category : Science
ISBN : 9780444642554

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

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

Biomechanics of the Brain

Karol Miller
Biomechanics of the Brain Book PDF

Author : Karol Miller
Publisher : Springer
Page : 353 pages
File Size : 40,9 Mb
Release : 2019-08-08
Category : Science
ISBN : 9783030049966

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Biomechanics of the Brain by Karol Miller Pdf

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.

Brain Dynamics

Hermann Haken
Brain Dynamics Book PDF

Author : Hermann Haken
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 51,8 Mb
Release : 2007-12-22
Category : Science
ISBN : 9783540752387

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Brain Dynamics by Hermann Haken Pdf

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.

Models of the Mind

Grace Lindsay
Models of the Mind Book PDF

Author : Grace Lindsay
Publisher : Bloomsbury Publishing
Page : 401 pages
File Size : 47,7 Mb
Release : 2021-03-04
Category : Science
ISBN : 9781472966452

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Models of the Mind by Grace Lindsay Pdf

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.

Natural Biodynamics

Vladimir G. Ivancevic,Tijana T. Ivancevic
Natural Biodynamics Book PDF

Author : Vladimir G. Ivancevic,Tijana T. Ivancevic
Publisher : World Scientific
Page : 1036 pages
File Size : 46,5 Mb
Release : 2005
Category : Science
ISBN : 9789812703163

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Natural Biodynamics by Vladimir G. Ivancevic,Tijana T. Ivancevic Pdf

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.

Neuroscience

Alwyn Scott
Neuroscience Book PDF

Author : Alwyn Scott
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 48,5 Mb
Release : 2007-12-14
Category : Science
ISBN : 9780387224633

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Neuroscience by Alwyn Scott Pdf

This book will be of interest to anyone who wishes to know what role mathematics can play in attempting to comprehend the dynamics of the human brain. It also aims to serve as a general introduction to neuromathematics. The book gives the reader a qualitative understanding and working knowledge of useful mathematical applications to the field of neuroscience. The book is readable by those who have little knowledge of mathematics for neuroscience but are committed to begin acquiring such knowledge.

Neuronal Mechanics and Transport

Daniel M. Suter,Kyle E. Miller
Neuronal Mechanics and Transport Book PDF

Author : Daniel M. Suter,Kyle E. Miller
Publisher : Frontiers Media SA
Page : 214 pages
File Size : 48,7 Mb
Release : 2016-05-26
Category : Electronic book
ISBN : 9782889198238

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Neuronal Mechanics and Transport by Daniel M. Suter,Kyle E. Miller Pdf

Understanding the underlying mechanisms of how axons and dendrites develop is a fundamental problem in neuroscience and a main goal of research on nervous system development and regeneration. Previous studies have provided a tremendous amount of information on signaling and cytoskeletal proteins regulating axonal and dendritic growth and guidance. However, relatively little is known about the relative contribution and role of cytoskeletal dynamics, transport of organelles and cytoskeletal components, and force generation to axonal elongation. Advancing the knowledge of these biomechanical processes is critical to better understand the development of the nervous system, the pathological progression of neurodegenerative diseases, acute traumatic injury, and for designing novel approaches to promote neuronal regeneration following disease, stroke, or trauma. Mechanical properties and forces shape the development of the nervous system from the cellular up to the organ level. Recent advances in quantitative live cell imaging, biophysical, and nanotechnological methods such as traction force microscopy, optical tweezers, and atomic force microscopy have enabled researchers to gain better insights into how cytoskeletal dynamics and motor-driven transport, membrane-dynamics, adhesion, and substrate rigidity influence axonal elongation. Given the complexity and mechanical nature of this problem, mathematical modeling contributes significantly to our understanding of neuronal mechanics. Nonetheless, there has been limited direct interaction and discussions between experimentalists and theoreticians in this research area. The purpose of this Frontiers Research Topic is to highlight exciting, and important work that is currently developing in the fields of neuronal cell biology, neuronal mechanics, intracellular transport, and mathematical modeling in the form of primary research articles, reviews, perspectives, and commentaries.

Numerical Pde Analysis Of The Blood Brain Barrier: Method Of Lines In R

Schiesser William E
Numerical Pde Analysis Of The Blood Brain Barrier Method Of Lines In R Book PDF

Author : Schiesser William E
Publisher : World Scientific
Page : 264 pages
File Size : 46,7 Mb
Release : 2018-12-21
Category : Science
ISBN : 9789813275812

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Numerical Pde Analysis Of The Blood Brain Barrier: Method Of Lines In R by Schiesser William E Pdf

The remarkable functionality of the brain is made possible by the metabolism (chemical reaction) of oxygen (O₂) and nutrients in the brain. These metabolism components are supplied to the brain by an intricate blood circulatory system (vasculature). The blood brain barrier (BBB), which is the central topic of this book, determines the rate of transfer from the blood to the brain tissue.In particular, mathematical models are developed for mass transfer across the BBB based on partial differential equations (PDEs) applied to the blood capillaries, the endothelial membrane, and the brain tissue. The PDEs derived from mass balances and computer routines in R are presented for the numerical (computer-based) solution of the PDEs. The computed concentration profiles of the transferred components are functions of time and space within the BBB system, i.e., spatiotemporal solutions.The R routines and the associated numerical algorithms for computing the numerical solutions are discussed in detail. The discussion is introductory, without formal mathematics, e.g., theorems and proofs. The general methodology (algorithm) for numerical PDE solutions is the method of lines (MOL).The models are used to study the transfer of oxygen and nutrients, harmful substances that should not enter the brain such as chemicals and pathogens (viruses, bacteria), and therapeutic drugs. The intent of the book is to provide a quantitative approach to the study of BBB dynamics using a computer-based methodology programmed in R, a quality open-source scientific programming system that is easily downloaded from the Internet for execution on modest computers.

The Brain: Unraveling the Mystery of How It Works

Thomas L. Saaty
The Brain Unraveling the Mystery of How It Works Book PDF

Author : Thomas L. Saaty
Publisher : RWS Publications
Page : 481 pages
File Size : 46,9 Mb
Release : 2019-03-01
Category : Computers
ISBN : 9781888603347

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The Brain: Unraveling the Mystery of How It Works by Thomas L. Saaty Pdf

This work confirms what many contemporary thinkers have claimed: that all human actions, sensations, thoughts and even emotions are derived from the synthesis of neural firings in the brain. This book offers the mathematics to describe how this happens and the nature of their interaction, feedback and synthesis. As an acknowledgement of his expertise, in 2017, the last year of his life, the highly acclaimed Neural Networks journal published two of his papers on the subject and the European Journal of Pure and Applied Mathematics published the article “Origin of neural firing and synthesis in making comparisons” co-authored with Dr Luis Vargas. The purpose of this book is to construct a scientific framework of the process by which the brain responds to stimuli and integrates sensory data and, further, how it synthesizes perceptions, memories, inputs from the muscles and nervous systems of the body and ideas. Because the brain puts pieces of information together in stages.

Multiscale Biomechanical Modeling of the Brain

Mark F. Horstemeyer,Raj K. Prabhu
Multiscale Biomechanical Modeling of the Brain Book PDF

Author : Mark F. Horstemeyer,Raj K. Prabhu
Publisher : Elsevier
Page : 276 pages
File Size : 41,8 Mb
Release : 2021-11-02
Category : Technology & Engineering
ISBN : 9780128181447

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Multiscale Biomechanical Modeling of the Brain by Mark F. Horstemeyer,Raj K. Prabhu Pdf

Multiscale Biomechanical Modeling of the Brain discusses the constitutive modeling of the brain at various length scales (nanoscale, microscale, mesoscale, macroscale and structural scale). In each scale, the book describes the state-of-the- experimental and computational tools used to quantify critical deformational information at each length scale. Then, at the structural scale, several user-based constitutive material models are presented, along with real-world boundary value problems. Lastly, design and optimization concepts are presented for use in occupant-centric design frameworks. This book is useful for both academia and industry applications that cover basic science aspects or applied research in head and brain protection. The multiscale approach to this topic is unique, and not found in other books. It includes meticulously selected materials that aim to connect the mechanistic analysis of the brain tissue at size scales ranging from subcellular to organ levels. Presents concepts in a theoretical and thermodynamic framework for each length scale Teaches readers not only how to use an existing multiscale model for each brain but also how to develop a new multiscale model Takes an integrated experimental-computational approach and gives structured multiscale coverage of the problems

Mathematical Models and Computer Simulations for Biomedical Applications

Gabriella Bretti,Roberto Natalini,Pasquale Palumbo,Luigi Preziosi
Mathematical Models and Computer Simulations for Biomedical Applications Book PDF

Author : Gabriella Bretti,Roberto Natalini,Pasquale Palumbo,Luigi Preziosi
Publisher : Springer Nature
Page : 261 pages
File Size : 41,7 Mb
Release : 2023-09-17
Category : Mathematics
ISBN : 9783031357152

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Mathematical Models and Computer Simulations for Biomedical Applications by Gabriella Bretti,Roberto Natalini,Pasquale Palumbo,Luigi Preziosi Pdf

Mathematical modelling and computer simulations are playing a crucial role in the solution of the complex problems arising in the field of biomedical sciences and provide a support to clinical and experimental practices in an interdisciplinary framework. Indeed, the development of mathematical models and efficient numerical simulation tools is of key importance when dealing with such applications. Moreover, since the parameters in biomedical models have peculiar scientific interpretations and their values are often unknown, accurate estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In the light of the new challenges brought by the biomedical applications, computational mathematics paves the way for the validation of the mathematical models and the investigation of control problems. The volume hosts high-quality selected contributions containing original research results as well as comprehensive papers and survey articles including prospective discussion focusing on some topical biomedical problems. It is addressed, but not limited to: research institutes, academia, and pharmaceutical industries.

Modeling in the Neurosciences

G. N. Reeke,R.R. Poznanski,K. A. Lindsay,J.R. Rosenberg,O. Sporns
Modeling in the Neurosciences Book PDF

Author : G. N. Reeke,R.R. Poznanski,K. A. Lindsay,J.R. Rosenberg,O. Sporns
Publisher : CRC Press
Page : 736 pages
File Size : 41,9 Mb
Release : 2005-03-29
Category : Mathematics
ISBN : 9780203390979

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Modeling in the Neurosciences by G. N. Reeke,R.R. Poznanski,K. A. Lindsay,J.R. Rosenberg,O. Sporns Pdf

Computational models of neural networks have proven insufficient to accurately model brain function, mainly as a result of simplifications that ignore the physical reality of neuronal structure in favor of mathematically tractable algorithms and rules. Even the more biologically based "integrate and fire" and "compartmental" styles of modeling suff

Neural Tissue Biomechanics

Lynne E. Bilston
Neural Tissue Biomechanics Book PDF

Author : Lynne E. Bilston
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 52,8 Mb
Release : 2011-07-23
Category : Technology & Engineering
ISBN : 364213890X

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Neural Tissue Biomechanics by Lynne E. Bilston Pdf

Damage to the central nervous system resulting from pathological mechanical loading can occur as a result of trauma or disease. Such injuries lead to significant disability and mortality. The peripheral nervous system, while also subject to injury from trauma and disease, also transduces physiological loading to give rise to sensation, and mechanotransduction is also thought to play a role in neural development and growth. This book gives a complete and quantitative description of the fundamental mechanical properties of neural tissues, and their responses to both physiological and pathological loading. This book reviews the methods used to characterize the nonlinear viscoelastic properties of central and peripheral neural tissues, and the mathematical and sophisticated computational models used to describe this behaviour. Mechanisms and models of neural injury from both trauma and disease are reviewed from the molecular to macroscopic scale. The book provides a comprehensive picture of the mechanical and biological response of neural tissues to the full spectrum of mechanical loading to which they are exposed. This book provides a comprehensive reference for professionals involved in pre prevention of injury to the nervous system, whether this arises from trauma or disease.