A Coupled System of PDEs and ODEs Arising in Electrocardiograms Modeling

Boulakia, Muriel; Fernández, Miguel Ángel; Gerbeau, Jean-Frédéric; Zemzemi, Néjib

doi:10.1093/amrx/abn002

Cited by 41 publications

(58 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The FitzHugh like models have been studied in [17,10,11,16]. In these models, there are no obvious bounds on the gating variable.…”

Section: Phenomenological Models A) the Fitzhugh Like Models (8)mentioning

confidence: 99%

“…In particular, no proof of uniqueness of solutions exists in the literature because of the non-linearity in the coupling terms between w and V m . b) The Mitchell-Schaeffer model (9) The Mitchell-Schaeffer model has been studied in [10,32,16]. This model and its regularized version have a very specific structure.…”

Section: Phenomenological Models A) the Fitzhugh Like Models (8)mentioning

confidence: 99%

“…Several mathematical analyses concern only the macroscopic bidomain equations (see [11,10,8] for instance) and these analyses can be extended to the case of the microscopic bidomain equations with some slightly different assumptions on the non-linear terms I ion and g. These assumptions take into account the functional framework in which we have to work. Namely, we have to use the trace space H 1/2 (Γ m ) instead of the more standard functional space H 1 (Ω).…”

Section: Phenomenological Models A) the Fitzhugh Like Models (8)mentioning

confidence: 99%

“…In [6] and [50], it is proven using Γ-convergence. The existence and the uniqueness of a solution for the bidomain model at the macroscopic scale have been studied for different ionic models in the literature [17,57,64,8,10,11].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model

Collin

Imperiale

2018

Math. Models Methods Appl. Sci.

View full text Add to dashboard Cite

The aim of this paper is to provide a complete mathematical analysis of the periodic homogenization procedure that leads to the macroscopic bidomain model in cardiac electrophysiology. We consider space-dependent and tensorial electric conductivities as well as space-dependent physiological and phenomenological non-linear ionic models. We provide the nondimensionalization of the bidomain equations and derive uniform estimates of the solutions. The homogenization procedure is done using 2-scale convergence theory which enables us to study the behavior of the non-linear ionic models in the homogenization process.

show abstract

“…The FitzHugh like models have been studied in [17,10,11,16]. In these models, there are no obvious bounds on the gating variable.…”

Section: Phenomenological Models A) the Fitzhugh Like Models (8)mentioning

confidence: 99%

Section: Phenomenological Models A) the Fitzhugh Like Models (8)mentioning

confidence: 99%

Section: Phenomenological Models A) the Fitzhugh Like Models (8)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model

Collin

Imperiale

2018

Math. Models Methods Appl. Sci.

View full text Add to dashboard Cite

show abstract

“…The mathematical model used to generate the computational ECGs has been presented in other works ( [1,2]) but to keep this paper as self contained as possible, we briefly recall it in this section.…”

Section: Modelmentioning

confidence: 99%

From Intracardiac Electrograms to Electrocardiograms: Models and Metamodels

Ebrard

Fernández

Gerbeau

et al. 2009

Functional Imaging and Modeling of the Heart

View full text Add to dashboard Cite

Abstract. We consider the problem of building a standard electrocardiogram (ECG) from the electrical potential provided by a pacemaker in a few points of the heart (electrogram). We use a 3D mathematical model of the heart and the torso electrical activity, able to generate "computational ECG", and a "metamodel" based on a kernel ridge regression. The input of the metamodel is the electrogram, its output is the ECG. The 3D model is used to train and test the metamodel. We illustrate the performance of the proposed strategy on simulated bundle branch blocks of various severities and a few clinical data.

show abstract

PDE constrained optimization of electrical defibrillation in a 3D ventricular slice geometry

Chamakuri

Kunisch

Plank

2015

Numer Methods Biomed Eng

View full text Add to dashboard Cite

A computational study of an optimal control approach for cardiac defibrillation in a 3D geometry is presented. The cardiac bioelectric activity at the tissue and bath volumes is modeled by the bidomain model equations. The model includes intramural fiber rotation, axially symmetric around the fiber direction, and anisotropic conductivity coefficients, which are extracted from a histological image. The dynamics of the ionic currents are based on the regularized Mitchell-Schaeffer model. The controls enter in the form of electrodes, which are placed at the boundary of the bath volume with the goal of dampening undesired arrhythmias. The numerical optimization is based on Newton techniques. We demonstrated the parallel architecture environment for the computation of potentials on multidomains and for the higher order optimization techniques.

show abstract

A Coupled System of PDEs and ODEs Arising in Electrocardiograms Modeling

Cited by 41 publications

References 16 publications

Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model

Mathematical analysis and 2-scale convergence of a heterogeneous microscopic bidomain model

From Intracardiac Electrograms to Electrocardiograms: Models and Metamodels

PDE constrained optimization of electrical defibrillation in a 3D ventricular slice geometry

Contact Info

Product

Resources

About