Download or read book Mathematics of Cell Electrophysiology written by J. Cronin and published by CRC Press. This book was released on 1981-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Cardiac Electrophysiology written by Piero Colli Franzone and published by Springer. This book was released on 2014-10-30 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematically Modelling the Electrical Activity of the Heart written by Andrew J. Pullan and published by World Scientific. This book was released on 2005 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computational Electrophysiology written by Shinji Doi and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Equations for Studies in Computational Electrophysiology written by Karoline Horgmo Jæger and published by Springer Nature. This book was released on 2023-05-27 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Aspects of Hodgkin Huxley Neural Theory written by Jane Cronin and published by Cambridge University Press. This book was released on 1987-08-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Cardiac Electrophysiology written by Piero Colli Franzone and published by Springer. This book was released on 2014-11-02 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computers in Mathematics written by V. Chudnovsky and published by CRC Press. This book was released on 2020-12-17 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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,
Download or read book Mathematical Physiology Blood Flow and Electrically Active Cells written by H. Melvin Lieberstein and published by Elsevier Publishing Company. This book was released on 1973 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Mathematical Modeling in Physiology Cell Biology and Immunology written by James Sneyd and published by American Mathematical Soc.. This book was released on with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematically Modelling the Electrical Activity of the Heart written by Andrew Pullan and published by . This book was released on 2005 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical and Numerical Modeling of the Cardiovascular System and Applications written by Daniele Boffi and published by Springer. This book was released on 2018-11-03 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modeling Excitable Tissue written by Aslak Tveito and published by Springer Nature. This book was released on 2020-10-30 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access volume presents a novel computational framework for understanding how collections of excitable cells work. The key approach in the text is to model excitable tissue by representing the individual cells constituting the tissue. This is in stark contrast to the common approach where homogenization is used to develop models where the cells are not explicitly present. The approach allows for very detailed analysis of small collections of excitable cells, but computational challenges limit the applicability in the presence of large collections of cells.
Download or read book Introduction to Computational Cardiology written by Boris Ja. Kogan and published by Springer Science & Business Media. This book was released on 2009-12-09 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Computational Cardiology provides a comprehensive, in-depth treatment of the fundamental concepts and research challenges involved in the mathematical modeling and computer simulation of dynamical processes in the heart, under normal and pathological conditions. About this textbook: - Presents descriptions of models used in both biology and medicine for discovering the mechanisms of heart function and dysfunction on several physiological scales across different species. - Provides several examples throughout the textbook and exercises at the end which facilitate understanding of basic concepts and introduces, for implementation, treated problems to parallel supercomputers. Introduction to Computational Cardiology serves as a secondary textbook or reference book for advanced-level students in computer science, electrical engineering, biomedical engineering, and cardiac electrophysiology. It is also suitable for researchers employing mathematical modeling and computer simulations of biomedical problems.
Download or read book Some Mathematical Questions in Biology written by Hans G. Othmer and published by American Mathematical Soc.. This book was released on 1989-12-31 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 22nd annual Symposium on Some Mathematical Questions in Biology, held in May, 1988 in Las Vegas. The diversity of current research in the dynamics of excitable media is reflected in the six papers in this volume. The topics covered include a mathematical treatment of phase-locking, numerical results for models of synchronization in the mammalian sinoatrial node, simulations of a model of the hippocampus, and wave propagation in excitable media. Both experimental and theoretical aspects are treated. Aimed at mathematicians, physiologists, and cardiologists, the book requires only background in differential equations. Readers will gain a broad perspective on current research activity in the modeling, analysis, and simulation of systems with excitable media.
Download or read book Mathematical Analysis of Complex Cellular Activity written by Richard Bertram and published by Springer. This book was released on 2015-10-09 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells Review 2: Vivien Kirk, James Sneyd: Nonlinear Dynamics of Calcium
Download or read book Computational Cardiology written by Frank B. Sachse and published by Springer. This book was released on 2005-01-12 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to computer-based modeling in cardiology, by taking an educational point of view, and by summarizing knowledge from several, commonly considered delimited areas of cardiac research in a consistent way. First, the foundations and numerical techniques from mathematics are provided, with a particular focus on the finite element and finite differences methods. Then, the theory of electric fields and continuum mechanics is introduced with respect to numerical calculations in anisotropic biological media. In addition to the presentation of digital image processing techniques, the following chapters deal with particular aspects of cardiac modeling: cardiac anatomy, cardiac electro physiology, cardiac mechanics, modeling of cardiac electro mechanics. This book was written for researchers in modeling and cardiology, for clinical cardiologists, and for advanced students.
