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.

Differential Equations for Studies in Computational Electrophysiology (Reports on Computational Physiology)

Computers & Technology

Tveito, Aslak

Horgmo Jæger, Karoline

Computer Science

Springer

Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.

Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models (Lecture Notes in Computational Science and Engineering, 111)

Lines, Glenn T.

Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs.  Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.

This book teaches basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Coverage details such topics as separation of variables, Fourier analysis, maximum principles, and energy estimates. The book introduces numerical methods in parallel to the classical theory and also includes many engaging exercises.

Introduction to Partial Differential Equations: A Computational Approach (Texts in Applied Mathematics, 29)

Winther, Ragnar

This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. It gives an introduction to the most important models, followed by a detailed description of numerical techniques. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers. The results presented in the book will be of particular interest to researchers in bioengineering and computational biology.

Computing the Electrical Activity in the Heart (Monographs in Computational Science and Engineering, 1)

Nielsen, Bjørn Frederik

Cai, Xing

Sundnes, Joakim

Lines, Glenn Terje

Mardal, Kent-André

In diesem Buch werden die Grundlagen partieller Differentialgleichungen sowie mit der Untersuchung numerischer Methoden für diese partiellen Differentialgleichungen in Zusammenhang stehende wichtige Überlegungen vorgestellt. Standardthemen wie Trennung der Variablen, Fourier Analysis, Maximumprinzipien und Energieabschätzungen werden behandelt. Numerische Verfahren werden parallel zur klassischen Theorie vorgestellt. Die Eigenschaften von Differentialgleichungen werden anhand numerischer Experimente veranschaulicht, und die Theorie der finiten Differentialapproximationen wird entwickelt. Numerische Verfahren werden eingeführt, um die Bedeutung des Rechnens bei partiellen Differentialgleichungen zu zeigen und die starke Interaktion zwischen mathematischer Theorie und der Entwicklung numerischer Verfahren zu illustrieren. Besonderer Wert wurde im gesamten Buch auf eine möglichst gleichgewichtige Darstellung der analytischen und der numerischen Verfahren gelegt.

Einführung in partielle Differentialgleichungen: Ein numerischer Zugang (Springer-Lehrbuch) (German Edition)

This is the softcover reprint of a popular book teaching the basic analytical and computational methods of partial differential equations. It includes coverage of standard topics such as separation of variables, Fourier analysis, and energy estimates.

This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. It gives an introduction to the most important models, followed by a detailed description of numerical techniques. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers. The results presented in the book will be of particular interest to researchers in bioengineering and computational biology.

Humor & Entertainment

Elements of Scientific Computing (Texts in Computational Science and Engineering, 7)

Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.

Langtangen, Hans Petter

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Books by Tveito, Aslak

See the best price to sell, buy, or rent books by Tveito, Aslak. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Differential Equations for Studies in Computational Electrophysiology (Reports on Computational Physiology)

Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models (Lecture Notes in Computational Science and Engineering, 111)

Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models (Lecture Notes in Computational Science and Engineering, 111)

Introduction to Partial Differential Equations: A Computational Approach (Texts in Applied Mathematics, 29)

Computing the Electrical Activity in the Heart (Monographs in Computational Science and Engineering, 1)

Einführung in partielle Differentialgleichungen: Ein numerischer Zugang (Springer-Lehrbuch) (German Edition)

Introduction to Partial Differential Equations: A Computational Approach (Texts in Applied Mathematics, 29)

Computing the Electrical Activity in the Heart (Monographs in Computational Science and Engineering, 1)

Elements of Scientific Computing (Texts in Computational Science and Engineering, 7)

Elements of Scientific Computing (Texts in Computational Science and Engineering, 7)