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  • Book
  • Open Access
  • © 2023

Differential Equations for Studies in Computational Electrophysiology

  • This text provides easy access to a field of growing importance

  • It requires only knowledge of basic calculus and linear algebra

  • The text is open access, and the software for all examples of the text is freely available

Part of the book series: Simula SpringerBriefs on Computing (SBRIEFSC, volume 14)

Part of the book sub series: Reports on Computational Physiology (RCP)

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Softcover Book USD 49.99
Price excludes VAT (USA)
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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
  2. Tools for Differential Equations and Numerical Methods

    1. Front Matter

      Pages 1-1
    2. Getting Started

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 3-11Open Access
    3. A System of Ordinary Differential Equations

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 13-20Open Access
    4. The Diffusion Equation

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 21-32Open Access
    5. Implicit Numerical Methods

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 33-39Open Access
    6. Improved Accuracy

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 41-45Open Access
    7. A Simple Cable Equation

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 47-52Open Access
    8. Operator Splitting

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 53-62Open Access
  3. Models of Electrophysiology

    1. Front Matter

      Pages 63-63
    2. Membrane Models

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 65-78Open Access
    3. The Cable Equation

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 79-91Open Access
    4. Spatial Models of Cardiac Electrophysiology

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 93-105Open Access
    5. Re-Introducing the Cell: The Extracellular-Membrane-Intracellular (EMI) Model

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 107-117Open Access
    6. The Poisson-Nernst-Planck (PNP) Model

      • Karoline Horgmo Jæger, Aslak Tveito
      Pages 119-125Open Access
  4. Back Matter

    Pages 127-128

About this book

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.

Authors and Affiliations

  • Simula Research Laboratory, Oslo, Norway

    Karoline Horgmo Jæger, Aslak Tveito

Bibliographic Information

Buy it now

Buying options

Softcover Book USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access