Reduced‐order modeling for cardiac electrophysiology. Application to parameter identification

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.

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“…This task, which was mainly done manually in this work, should be addressed with an inverse problem strategy [7,16].…”

Section: Limitationsmentioning

confidence: 99%

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

Schenone

Collin

Gerbeau

2015

Numer Methods Biomed Eng

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“…We make use of the "Plateforme Fédérative pour la Recherche en Informatique et Mathématiques" (PLAFRIM 1 ), more details about the machine on which we run the simulations could be found in its web page 2 . We first fix the number of modes to 200.…”

Section: Scalability Of the Pod Methodsmentioning

confidence: 99%

“…To reduce its complexity, following [4,2], we choose to use the POD method (see [16,37]). This method is applied to data compression and model reduction of finite dimensional nonlinear systems, it's still known in other areas of science as the Karhunen-Loève (Karhunen, 1946;Loève, 1955).…”

Section: Reduced Order Methodsmentioning

confidence: 99%

“…Here we don't cite all the works that have been done in the literature, some other works could be found in the recent review of the bidomain model [15]. The computational cost of solving the bidomain problem becomes very important when we are interested in solving inverse problems [2]. Thus reducing the computational cost of the forward problem is a challenging issue.…”

Section: Introductionmentioning

confidence: 99%

“…It has also been used for the ionic model parameter estimation but more interestingly for infarction localisation based on simulated data [2]. The application of reduced order is appealing because it allows to dramatically decrease the computational cost of the forward problem and consequently in the inverse problem.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology

Corrado

Lassoued²,

Mahjoub³

et al. 2016

Mathematical Biosciences

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To cite this version:Cesare Corrado, Jamila Lassoued, Moncef Mahjoub, Nejib Zemzemi. Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology. Mathematical Biosciences, Elsevier, 2015Elsevier, , 10.1016Elsevier, /j.mbs.2015 AbstractIn this work we show the numerical stability of the Proper Orthogonal Decomposition (POD) reduced order method used in cardiac electrophysiology applications. The difficulty of proving the stability comes from the fact that we are interested in the bidomain model, which is a system of degenerate parabolic equations coupled to a system of ODEs representing the cell membrane electrical activity. The proof of the stability of this method is based an a priori estimate controlling the gap between the reduced order solution and the Galerkin finite element one. We present some numerical simulations confirming the theoretical results. We also combine the POD method with a time splitting scheme allowing a faster solution of the bidomain problem and show numerical results. Finally, we conduct numerical simulation in 2D illustrating the stability of the POD method in its sensitivity to the ionic model parameters. We also perform 3D simulation using a massively parallel code. We show the computational gain using the POD reduced order model. We also show that this method has a better scalability than the full finite element method.

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An atlas‐ and data‐driven approach to initializing reaction‐diffusion systems in computer cardiac electrophysiology

Hoogendoorn

Sebastián

Rodrı́guez

et al. 2016

Numer Methods Biomed Eng

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The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the initialization of reaction-diffusion systems for numerical simulations of cardiac EP from steady-state conditions. We exploit surface point correspondence to establish volumetric point correspondence. Upon introduction of a new 3D anatomy with surface point correspondence, a prediction of the cell model steady states is derived from the set of earlier biophysical simulations. We show that the prediction error is typically less than 10% for all model variables, with most variables showing even greater accuracy. When initializing simulations with the predicted model states, it is demonstrated that simulation times can be cut by at least two-thirds and potentially more, which saves hours or days of high-performance computing. Overall, these results increase the clinical applicability of detailed computational EP studies on personalized anatomies.

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Reduced‐order modeling for cardiac electrophysiology. Application to parameter identification

Cited by 47 publications

References 32 publications

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

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

Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology

An atlas‐ and data‐driven approach to initializing reaction‐diffusion systems in computer cardiac electrophysiology

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