Modeling Excitable Tissue : : The EMI Framework.

• Superior document: Simula SpringerBriefs on Computing Series ; v.7
• Author: Tveito, Aslak.
• TeilnehmendeR: Mardal, Kent-Andre.; Rognes, Marie E.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2020.; Ã2021.
• Year of Publication: 2020
• Edition: 1st ed.
• Language: English
• Series: Simula SpringerBriefs on Computing Series
• Physical Description: 1 online resource (116 pages)

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.