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Titlebook: Differential Equations for Studies in Computational Electrophysiology; Karoline Horgmo Jæger,Aslak Tveito Book‘‘‘‘‘‘‘‘ 2023 The Editor(s)

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发表于 2025-3-21 19:47:01 | 显示全部楼层 |阅读模式
书目名称Differential Equations for Studies in Computational Electrophysiology
编辑Karoline Horgmo Jæger,Aslak Tveito
视频video
概述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 i
丛书名称Simula SpringerBriefs on Computing
图书封面Titlebook: Differential Equations for Studies in Computational Electrophysiology;  Karoline Horgmo Jæger,Aslak Tveito Book‘‘‘‘‘‘‘‘ 2023 The Editor(s)
描述.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..
出版日期Book‘‘‘‘‘‘‘‘ 2023
关键词Open Access; Action potential; Cardiomyocytes; Differential equations; numerical methods; software; comput
版次1
doihttps://doi.org/10.1007/978-3-031-30852-9
isbn_softcover978-3-031-30851-2
isbn_ebook978-3-031-30852-9Series ISSN 2512-1677 Series E-ISSN 2512-1685
issn_series 2512-1677
copyrightThe Editor(s) (if applicable) and The Author(s) 2023
The information of publication is updating

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发表于 2025-3-21 21:43:11 | 显示全部楼层
A System of Ordinary Differential Equationsependently, by Nagumo et. al. [2] in 1962. The model is a system of ordinary differential equations with two unknowns, and is commonly used as a simple model for the action potentials of excitable pacemaker cells.
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Operator Splittinglue the pieces together to yield a solution of the new problem. This approach is also very useful in software development; well-tested pieces of software can be glued together in order to obtain solutions to a wider class of problems. Operator splitting is a technique that illustrates this principle
发表于 2025-3-22 14:08:40 | 显示全部楼层
Membrane Modelswere simple, theoretical differential equations without units. From this point forwards, we will look at how to apply the methods introduced in the previous chapters to differential equations that are set up to model aspects of electrophysiology.
发表于 2025-3-22 19:13:23 | 显示全部楼层
The Cable Equatione will revisit the cable equation and go through a simple derivation of the model. In addition, we will consider the numerical solution of the cable equation for a neuronal axon with membrane dynamics modeled by the Hodgkin-Huxley model.
发表于 2025-3-22 22:30:52 | 显示全部楼层
Spatial Models of Cardiac Electrophysiologybsolutely essential in order to understand the electrophysiology of excitable cells. However, some essential properties can only be studied in spatially resolved models; i.e., in models representing spatial variation across a single cell or a collection of cells.
发表于 2025-3-23 01:35:31 | 显示全部楼层
Re-Introducing the Cell: The Extracellular-Membrane-Intracellular (EMI) Modeld and provides valuable insights into the conduction of electrical signals in cardiac tissue. However, the model has one glaring limitation: The cardiomyocyte is nowhere to be found in the model, since the extracellular space, the intracellular space and the cell membrane are all assumed to be every
发表于 2025-3-23 07:51:38 | 显示全部楼层
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