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Derivation of a cell-based mathematical model of excitable cells. (English) Zbl 1470.92108

Tveito, Aslak (ed.) et al., Modeling excitable tissue. The EMI framework. Cham: Springer. Simula SpringerBriefs Comput., Rep. Comput. Physiol. 7, 1-13 (2021).
Summary: Excitable cells are of vital importance in biology, and mathematical models have contributed significantly to understand their basic mechanisms. However, classical models of excitable cells are based on severe assumptions that may limit the accuracy of the simulation results. Here, we derive a more detailed approach to modeling that has recently been applied to study the electrical properties of both neurons and cardiomyocytes. The model is derived from first principles and opens up possibilities for studying detailed properties of excitable cells. We refer to the model as the EMI model because both the extracellular space (E), the cell membrane (M) and the intracellular space (I) are explicitly represented in the model, in contrast to classical spatial models of excitable cells. Later chapters of the present text will focus on numerical methods and software for solving the model. Also, in the next chapter, the model will be extended to account for ionic concentrations in the intracellular and extracellular spaces.
For the entire collection see [Zbl 1467.92008].

MSC:

92C37 Cell biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences

Software:

CellML
PDFBibTeX XMLCite
Full Text: DOI

References:

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