Differential Equations for Studies in Computational Electrophysiology

• Main Author: Horgmo Jæger, Karoline (auth)
• Other Authors: Tveito, Aslak (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: Cham Springer Nature 2023
• Series: Simula SpringerBriefs on Computing; Reports on Computational Physiology
• Subjects: Mathematics; Computer science; Life sciences: general issues; Biophysics; Action potential; Cardiomyocytes; Differential equations; numerical methods; software; computational physiology; computational electrophysiology; Cable equation; bidomain; cell-based models
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.