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Modeling Excitable Tissue : The EMI Framework.

Bibliographic Details
Main Author: Tveito, Aslak.
Other Authors: Mardal, Kent-Andre., Rognes, Marie E.
Format: eBook
Language:English
Published: Cham : Springer International Publishing AG, 2020.
Edition:1st ed.
Series:Simula SpringerBriefs on Computing Series
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • Intro
  • Preface
  • References
  • List of Contributors
  • Contents
  • Chapter 1 Derivation of a Cell-Based Mathematical Model of Excitable Cells
  • 1.1 Introduction
  • 1.2 Derivation of the EMI Model
  • 1.2.1 Fundamental Equations
  • 1.2.2 Model for the Intracellular and Extracellular Domains
  • 1.2.3 Model for the Membrane
  • 1.2.3.1 Ionic Current
  • 1.2.3.2 Capacitive Current
  • 1.2.3.3 Collecting the Ionic and Capacitive Currents
  • 1.2.4 Model for the Intercalated Disc
  • 1.2.5 Models of the Ionic Currents
  • 1.2.6 Summary of the Model Equations
  • 1.3 Conclusion
  • References
  • Chapter 2 A Cell-Based Model for Ionic Electrodiffusion in Excitable Tissue
  • 2.1 Introduction and Motivation
  • 2.2 Derivation of the Equations
  • 2.2.1 Equations in the Intracellular and Extracellular Volumes
  • 2.2.2 Membrane Currents
  • 2.2.2.1 Modelling Specific Ion Channels
  • 2.2.3 Summary of KNP-EMI Equations
  • 2.3 Numerical Solution of the KNP-EMI Equations
  • 2.4 Comparing KNP-EMI and EMI during Neuronal Hyperactivity
  • 2.4.1 Model Parameters and Membrane Mechanisms
  • 2.4.2 Results and Discussion
  • 2.5 Conclusions and Outlook
  • References
  • Chapter 3 Modeling Cardiac Mechanics on a Sub-Cellular Scale
  • 3.1 Introduction
  • 3.2 Models and Methods
  • 3.2.1 Fundamental Equations
  • 3.2.2 Specific Model Choices
  • 3.2.3 Numerical Methods
  • 3.3 Results
  • 3.4 Discussion
  • References
  • Chapter 4 Operator Splitting and Finite Difference Schemes for Solving the EMI Model
  • 4.1 Introduction
  • 4.2 The EMI Model
  • 4.2.1 Operator Splitting Applied to the EMI Model
  • 4.3 Simulating the Effect of a Region of Ischemic Cells
  • 4.4 A Scalable Implementation of the Splitting Scheme
  • 4.4.1 The Linear System for the Intracellular Potential
  • 4.4.2 The Linear System for the Extracellular Potential
  • 4.4.3 The Non-Linear ODE System for the Membrane Potential.
  • 4.4.4 The Implementation
  • 4.4.5 Parallelization
  • 4.4.6 Performance Results
  • 4.5 Software
  • 4.6 Conclusion
  • References
  • Chapter 5 Solving the EMI Equations using Finite Element Methods
  • 5.1 Introduction
  • 5.1.1 Preliminaries: Function Spaces and Norms
  • 5.2 Primal Formulations
  • 5.2.1 Single-Dimensional Primal Formulation
  • 5.2.2 Multi-Dimensional Primal Formulation
  • 5.3 Mixed Formulations
  • 5.3.1 Single-Dimensional Mixed Formulation
  • 5.3.2 Multi-Dimensional Mixed Formulation
  • 5.4 Finite Element Spaces and Methods
  • 5.5 Numerical Results
  • 5.5.1 Comparison of Convergence between Formulations
  • 5.5.2 Post-Processing the Transmembrane Potential
  • 5.6 Conclusions and Outlook
  • References
  • Chapter 6 Iterative Solvers for EMI Models
  • 6.1 Introduction
  • 6.2 Monolithic Solvers
  • 6.2.1 Single-Dimensional Primal Solvers
  • 6.2.2 Single-Dimensional Mixed Solvers
  • 6.2.3 Multi-Dimensional Solvers
  • 6.3 Domain Decomposition Solvers
  • 6.4 Solver Comparison
  • References
  • Chapter 7 Improving Neural Simulations with the EMI Model
  • 7.1 Introduction
  • 7.2 EMI Simulations of Neurons using the neuronmi Python Package
  • 7.3 Investigating the Ephaptic Effect between Neurons
  • 7.4 Investigating the Effect of Measuring Devices on Extracellular Potentials
  • 7.5 Reduced EMI Model
  • 7.6 Conclusions
  • References
  • Index.

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