Mathematical Modeling of Electrocardiograms: A Numerical Study

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

doi:10.1007/s10439-009-9873-0

Cited by 132 publications

(141 citation statements)

References 51 publications

Supporting

Mentioning

138

Contrasting

Unclassified

Order By: Relevance

“…The two problems are weakly coupled, following the procedure explained in [2]. Differences of potentials on standard points of Γ ext define the ECG (Figure 1, left).…”

Section: Resolution Of the Direct Problemmentioning

confidence: 99%

“…The present study follows another route: assuming that a source model is available in the heart, we endeavor to estimate some parameters of this model from the body surface potential. The source model considered in this study is the one proposed in [2]. The inverse procedure is based on a genetic algorithm which evaluates a reduced order approximation of the direct problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Parameter Identification in Cardiac Electrophysiology Using Proper Orthogonal Decomposition Method

Boulakia

Gerbeau

2011

Functional Imaging and Modeling of the Heart

View full text Add to dashboard Cite

Abstract. We consider the problem of estimating some parameters (like ionic models or parameters involved in the initial stimulation) of a model of electrocardiograms (ECG) from the data of the Einthoven leads. This problem can be viewed as a first attempt to identify or to locate a pathology. The direct model is based on the bidomain equations in the heart and a Poisson equation in the torso and. To keep the computational time reasonable, the evaluation of the direct problem is approximated with a reduced order model based on Proper Orthogonal Decomposition (POD). The optimization problem is solved using a genetic algorithm. Numerical tests show that, with noisy synthetic data, the proposed procedure allows to recover ionic parameters and initial activation regions with a fair accuracy.

show abstract

“…The two problems are weakly coupled, following the procedure explained in [2]. Differences of potentials on standard points of Γ ext define the ECG (Figure 1, left).…”

Section: Resolution Of the Direct Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parameter Identification in Cardiac Electrophysiology Using Proper Orthogonal Decomposition Method

Boulakia

Gerbeau

2011

Functional Imaging and Modeling of the Heart

View full text Add to dashboard Cite

show abstract

“…To define the transmission conditions at the heart-body interface ∂Ω H , we assume that the extracellular current does not flow through the pericardium (isolated heart σ e · ∇u e · n = 0 (9) and we consider the resistor-capacitor conditions [5]:…”

Section: Coupling With the Bodymentioning

confidence: 99%

“…The simulation of 12-lead ECG based on partial differential equations (PDE) -as opposed to cellular automata [64] -appeared during the last decade [5,41,50,51,60]. More recently, a focus on the T-wave was proposed [29,34].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

Schenone

Collin

Gerbeau

2015

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

This work is dedicated to the simulation of full cycles of the electrical activity of the heart and the corresponding body surface potential. The model is based on a realistic torso and heart anatomy, including ventricles and atria. One of the specificities of our approach is to model the atria as a surface, which is the kind of data typically provided by medical imaging for thin volumes. The bidomain equations are considered in their usual formulation in the ventricles, and in a surface formulation on the atria. Two ionic models are used: the Courtemanche-Ramirez-Nattel model on the atria, and the "Minimal model for human Ventricular action potentials" (MV) by Bueno-Orovio, Cherry and Fenton in the ventricles. The heart is weakly coupled to the torso by a Robin boundary condition based on a resistorcapacitor transmission condition. Various ECGs are simulated in healthy and pathological conditions (left and right bundle branch blocks, Bachmann's bundle block, Wolff-ParkinsonWhite syndrome). To assess the numerical ECGs, we use several qualitative and quantitative criteria found in the medical literature. Our simulator can also be used to generate the signals measured by a vest of electrodes. This capability is illustrated at the end of the article.

show abstract

“…Alternatively, most previous works have considered IMEX time discretizations and/or operator splitting schemes, where the reaction and diffusion terms are treated separately, see e.g. [4,6,8,14,20,22,28,35,38,45,47,[53][54][55]. The advantage of IMEX and operator splitting schemes is that they only require the solution of a linear system for the parabolic and elliptic PDEs at each time step.…”

Section: Introductionmentioning

confidence: 99%

A comparison of coupled and uncoupled solvers for the cardiac Bidomain model

2013

View full text Add to dashboard Cite

Abstract. The aim of this work is to compare a new uncoupled solver for the cardiac Bidomain model with a usual coupled solver. The Bidomain model describes the bioelectric activity of the cardiac tissue and consists of a system of a non-linear parabolic reaction-diffusion partial differential equation (PDE) and an elliptic linear PDE. This system models at macroscopic level the evolution of the transmembrane and extracellular electric potentials of the anisotropic cardiac tissue. The evolution equation is coupled through the non-linear reaction term with a stiff system of ordinary differential equations (ODEs), the so-called membrane model, describing the ionic currents through the cellular membrane. A novel uncoupled solver for the Bidomain system is here introduced, based on solving twice the parabolic PDE and once the elliptic PDE at each time step, and it is compared with a usual coupled solver. Three-dimensional numerical tests have been performed in order to show that the proposed uncoupled method has the same accuracy of the coupled strategy. Parallel numerical tests on structured meshes have also shown that the uncoupled technique is as scalable as the coupled one. Moreover, the conjugate gradient method preconditioned by Multilevel Hybrid Schwarz preconditioners converges faster for the linear systems deriving from the uncoupled method than from the coupled one. Finally, in all parallel numerical tests considered, the uncoupled technique proposed is always about two or three times faster than the coupled approach.Mathematics Subject Classification. 65N55, 65M55, 65F10, 92C30.

show abstract

Mathematical Modeling of Electrocardiograms: A Numerical Study

Cited by 132 publications

References 51 publications

Parameter Identification in Cardiac Electrophysiology Using Proper Orthogonal Decomposition Method

Parameter Identification in Cardiac Electrophysiology Using Proper Orthogonal Decomposition Method

Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions

A comparison of coupled and uncoupled solvers for the cardiac Bidomain model

Contact Info

Product

Resources

About