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Author : J. Cronin
Publisher : CRC Press
Page : 146 pages
File Size : 47,8 Mb
Release : 1981-01-01
Category : Science
ISBN : 0824711572
Author : V. Chudnovsky,Richard D. Jenks
Publisher : CRC Press
Page : 428 pages
File Size : 55,9 Mb
Release : 1990-05-25
Category : Computers
ISBN : 0824783417
Talks from the International Conference on Computers and Mathematics held July 29-Aug. 1, 1986, Stanford U. Some are focused on the past and future roles of computers as a research tool in such areas as number theory, analysis, special functions, combinatorics, algebraic geometry, topology, physics,
Author : H. Melvin Lieberstein
Publisher : Elsevier Publishing Company
Page : 406 pages
File Size : 51,7 Mb
Release : 1973
Category : Blood flow
ISBN : UOM:39015011455758
Author : Andrew J. Pullan,Leo K. Cheng,Martin L. Buist
Publisher : World Scientific
Page : 446 pages
File Size : 55,9 Mb
Release : 2005
Category : Medical
ISBN : 9789812563736
This book on modelling the electrical activity of the heart is an attempt to describe continuum based modelling of cardiac electrical activity from the cell level to the body surface (the forward problem), and back again (the inverse problem). Background anatomy and physiology is covered briefly to provide a suitable context for understanding the detailed modelling that is presented herein. The questions of what is mathematical modelling and why one would want to use mathematical modelling are addressed to give some perspective to the philosophy behind our approach. Our view of mathematical modelling is broad ? it is not simply about obtaining a solution to a set of mathematical equations, but includes some material on aspects such as experimental and clinical validation.
Author : James Sneyd,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 47,9 Mb
Release : 2024-05-23
Category : Medical
ISBN : 0821867644
In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach. The book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done,what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective. The book is suitable for mathematicians and biologists interested in mathematical methods in biology.
Author : Piero Colli Franzone,Luca Franco Pavarino,Simone Scacchi
Publisher : Springer
Page : 397 pages
File Size : 54,9 Mb
Release : 2014-10-30
Category : Mathematics
ISBN : 9783319048017
This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematical and numerical foundations of computational electrocardiology, illustrating the current research developments in this fast-growing field lying at the intersection of mathematical physiology, bioengineering and computational biomedicine. This book is addressed to graduate student and researchers in the field of applied mathematics, scientific computing, bioengineering, electrophysiology and cardiology.
Author : Jane Cronin
Publisher : Cambridge University Press
Page : 294 pages
File Size : 50,8 Mb
Release : 1987-08-28
Category : Mathematics
ISBN : 0521334829
This book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work.
Author : Karoline Horgmo Jæger,Aslak Tveito
Publisher : Springer Nature
Page : 134 pages
File Size : 43,7 Mb
Release : 2023-05-27
Category : Mathematics
ISBN : 9783031308529
This open access text aims at giving you the simplest possible introduction to differential equations that are used in models of electrophysiology. It covers models at several spatial and temporal scales with associated numerical methods. The text demonstrates that a very limited number of fundamental techniques can be used to define numerical methods for equations ranging from ridiculously simple to extremely complex systems of partial differential equations. Every method is implemented in Matlab and the codes are freely available online. By using these codes, the reader becomes familiar with classical models of electrophysiology, like the cable equation, the monodomain model, and the bidomain model. But modern models that have just started to gain attention in the field of computational electrophysiology are also presented. If you just want to read one book, it should probably not be this one, but if you want a simple introduction to a complex field, it is worth considering the present text.
Author : Shinji Doi,Junko Inoue,Zhenxing Pan,Kunichika Tsumoto
Publisher : Springer Science & Business Media
Page : 159 pages
File Size : 46,9 Mb
Release : 2010-03-10
Category : Technology & Engineering
ISBN : 9784431538622
Biological systems inherently possess much ambiguity or uncertainty. Computational electrophysiology is the one area, from among the vast and rapidly growing discipline of computational and systems biology, in which computational or mathematical models have succeeded. This textbook provides a practical and quick guide to both computational electrophysiology and numerical bifurcation analysis. Bifurcation analysis is a very powerful tool for the analysis of such highly nonlinear biological systems. Bifurcation theory provides a way to analyze the effect of a parameter change on a system and to detect a critical parameter value when the qualitative nature of the system changes. Included in this work are many examples of numerical computations of bifurcation analysis of various models as well as mathematical models with different abstraction levels from neuroscience and electrophysiology. This volume will benefit graduate and undergraduate students as well as researchers in diverse fields of science.
Author : Piero Colli Franzone,Luca F. Pavarino,Simone Scacchi
Publisher : Springer
Page : 397 pages
File Size : 45,7 Mb
Release : 2014-11-02
Category : Mathematics
ISBN : 3319048023
This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematical and numerical foundations of computational electrocardiology, illustrating the current research developments in this fast-growing field lying at the intersection of mathematical physiology, bioengineering and computational biomedicine. This book is addressed to graduate student and researchers in the field of applied mathematics, scientific computing, bioengineering, electrophysiology and cardiology.
Author : James Keener,James Sneyd
Publisher : Springer Science & Business Media
Page : 547 pages
File Size : 47,5 Mb
Release : 2010-06-04
Category : Mathematics
ISBN : 9780387758473
Divided into two volumes, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing. New chapters on Calcium Dynamics, Neuroendocrine Cells and Regulation of Cell Function have been included. Reviews from first edition: Keener and Sneyd's Mathematical Physiology is the first comprehensive text of its kind that deals exclusively with the interplay between mathematics and physiology. Writing a book like this is an audacious act! -Society of Mathematical Biology Keener and Sneyd's is unique in that it attempts to present one of the most important subfields of biology and medicine, physiology, in terms of mathematical "language", rather than organizing materials around mathematical methodology. -SIAM review
Author : Lynn Arthur Steen
Publisher : MAA
Page : 182 pages
File Size : 52,8 Mb
Release : 2005
Category : Mathematics
ISBN : 0883858185
"Math and bio 2010 grew out of 'Meeting the Challenges: Education across the Biological, Mathematical and Computer Sciences,' a joint project of the Mathematical Association of America (MAA), the National Science Foundation Division of Undergraduate Education (NSF DUE), the National Institute of General Medical Sciences (NIGMS), the American Association for the Advancement of Science (AAAS), and the American Society for Microbiology (ASM)."--Foreword, p. vi
Author : James Keener,James Sneyd
Publisher : Springer Science & Business Media
Page : 767 pages
File Size : 54,5 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387227061
Divided into two parts, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing.
Author : Murray S. Klamkin
Publisher : SIAM
Page : 352 pages
File Size : 54,5 Mb
Release : 1987-01-01
Category : Technology & Engineering
ISBN : 1611971764
Designed for classroom use, this book contains short, self-contained mathematical models of problems in the physical, mathematical, and biological sciences first published in the Classroom Notes section of the SIAM Review from 1975-1985. The problems provide an ideal way to make complex subject matter more accessible to the student through the use of concrete applications. Each section has extensive supplementary references provided by the editor from his years of experience with mathematical modelling.
Author : Daniele Boffi,Luca F. Pavarino,Gianluigi Rozza,Simone Scacchi,Christian Vergara
Publisher : Springer
Page : 243 pages
File Size : 53,5 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9783319966496
The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in the field of bioengineering, applied mathematics, computer, computational and data science, and medicine wishing to become involved in the highly fascinating task of modeling the cardiovascular system.