Cardiac electrophysiology models

For more info about our services contact : help@bestpfe.com

Table of contents

Introduction
Thesis general context
Thesis outline
Published and pre-print articles
Introduction (Français)
Contexte général de la thèse
Plan de thèse
Articles publiés et pre-print
1 Cardiac electrophysiology: model, equations, inverse problems and approximations
1.1 Introduction
1.2 Heart physiology
1.3 Cardiac electrophysiology
1.4 Cardiac electrophysiology models
1.5 Inverse problems in cardiac electrophysiology
1.6 Reduced Order Methods: a brief overview
2 Numerical simulations of full electrocardiogram cycle
2.1 Introduction
2.2 Whole heart mesh
2.3 Modeling assumptions
2.4 Healthy and pathological numerical simulations
2.5 Electrodes vest
2.6 Chapter conclusions
2.A Mitchell and Schaeffer ionic model
2.B Minimal Ventricular ionic model
2.C Courtemanche, Ramirez and Nattel ionic model
3 Estimation of some FitzHugh-Nagumo model parameters
3.1 Introduction
3.2 State of the art and motivation
3.3 Regularity of the solution
3.4 Estimation of reaction parameter
3.5 Estimation of a parameter in the second equation
3.6 Chapter conclusions
4 Reduced-order modeling and parameters identification with POD
4.1 Introduction
4.2 Presentation of the model
4.3 Proper Orthogonal Decomposition method
4.4 Application of POD to forward problems
4.5 Application of POD to the parameters identification
4.6 Chapter conclusions
4.A Genetic algorithm
5 Long-time simulations and Restitution Curves with POD
5.1 Introduction
5.2 Presentation of the models
5.3 Restitution Curve definition
5.4 Parameters identification in 0D case
5.5 Parameters identification with an ECG-based RC
5.6 Chapter conclusions
6 Reduced Order Model with Approximated Lax Pairs
6.1 Introduction
6.2 The ALP method
6.3 ALP in cardiac electrophysiology
6.4 Numerical experiments
6.5 Chapter conclusions
7 Inverse problems with ALP reduced-order method
7.1 Introduction
7.2 An overview on data assimilation
7.3 Application to Micro-Electrode Arrays measures
7.4 Application to epicardium potential reconstruction
7.5 Chapter conclusions
8 ROM with ALP and Discrete Empirical Interpolation Method
8.1 Introduction
8.2 The ALP-DEIM method
8.3 ALP-DEIM in cardiac electrophysiology
8.4 Numerical experiments
8.5 Perspectives
8.6 Chapter conclusions
Conclusions
Conlcusions (Français)
A FELiScE
A.1 FELiScE general principles
A.2 Structure of the code
A.3 Electrophysiology equations implementation
A.4 Reduced-Order Models implementation
A.5 Author’s contributions
B High performance computing for the reduced basis method
Bibliography