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.
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This open access text aims at giving you the simplest possible introduction to differential equations that are used in models of electrophysiology. By using these codes, the reader becomes familiar with classical models of electrophysiology, like the cable equation, the monodomain model, and the bidomain model.
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1. Getting Started.- 2. A System of Ordinary Differential Equations.- 3. The Diffusion Equation.- 4. Implicit Numerical Methods.- 5. Improved Accuracy.- 6. A Simple Cable Equation.- 7. Operator Splitting.- 8. Membrane Models.- 9. The Cable Equation.- 10. Spatial Models of Cardiac Electrophysiology.- 11. The Extracellular-Membrane-Intracellular (EMI) Model.- 12. The Poisson-Nernst-Planck (PNP) Model.- Index.
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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
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GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
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Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
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Produktdetaljer

ISBN
9783031308512
Publisert
2023-05-28
Utgiver
Vendor
Springer International Publishing AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Graduate, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet