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Yves Coudière - One of the best experts on this subject based on the ideXlab platform.

  • Rush-Larsen time-stepping methods of high order for stiff problems in Cardiac Electrophysiology
    Electronic Transactions on Numerical Analysis, 2020
    Co-Authors: Yves Coudière, Charlie Douanla-lontsi, Charles Pierre
    Abstract:

    To address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly true in the context of Cardiac Electrophysiology, where reaction-diffusion equations are coupled with stiff ODE systems. Many research have been led in that way in the past 15 years concerning implicit-explicit methods and exponential integrators. In 2009, Perego and Veneziani proposed an innovative time-stepping method of order 2. In this paper we present the extension of this method to the orders 3 and 4 and introduce the Rush-Larsen schemes of order k (shortly denoted RL_k). The RL_k schemes are explicit multistep exponential integrators. They display a simple general formulation and an easy implementation. The RL_k schemes are shown to be stable under perturbation and convergent of order k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL_k method is numerically studied as applied to the membrane equation in Cardiac Electrophysiology. The RL k schemes are shown to be stable under perturbation and convergent oforder k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL k method is numerically studied as applied to the membrane equation in Cardiac Electrophysiology.

  • A domain decomposition strategy for a very high-order finite volumes scheme applied to Cardiac Electrophysiology
    Journal of Computational Science, 2019
    Co-Authors: Yves Coudière, Rodolphe Turpault
    Abstract:

    Abstract In this paper, a domain decomposition technique for a very high-order finite volumes scheme is proposed. The objective is to obtain an efficient way to perform numerical simulations in Cardiac Electrophysiology. The aim is to extend a very high-order numerical scheme previously designed, where large stencils are used for polynomial reconstructions. Therefore, a particular attention has to be paid to maintain the scalability in parallel. Here, we propose to constrain the stencils inside the subdomains or their first layer of neighbors. The method is shown to remain accurate and to scale perfectly up to the level where there are not enough cells in the subdomains. Hence, these high-order schemes are proved to be efficient tools to perform realistic simulations in Cardiac Electrophysiology.

  • Exponential Adams Bashforth integrators for stiff ODEs, application to Cardiac Electrophysiology
    arXiv: Numerical Analysis, 2018
    Co-Authors: Yves Coudière, Charlie Douanla Lontsi, Charles Pierre
    Abstract:

    Models in Cardiac Electrophysiology are coupled systems of reaction diffusion PDE and of ODE. The ODE system displays a very stiff behavior. It is non linear and its upgrade at each time step is a preponderant load in the computational cost. The issue is to develop high order explicit and stable methods to cope with this situation.In this article, is is analyzed the resort to exponential Adams Bashforth (EAB) integrators in Cardiac Electrophysiology. The method is presented in the framework of a general and varying stabilizer, that is well suited in this context. Stability under perturbation (or 0-stability) is proven. It provides a new approach for the convergence analysis of the method. The Dahlquist stability properties of the method is performed. It is presented in a new framework that incorporates the discrepancy between the stabilizer and the system Jacobian matrix. Provided this discrepancy is small enough, the method is shown to be A(alpha)-stable. This result is interesting for an explicit time-stepping method. Numerical experiments are presented for two classes of stiff models in Cardiac Electrophysiology. They include performances comparisons with several classical methods. The EAB method is observed to be as stable as implicit solvers and cheaper at equal level of accuracy.

  • Exponential Adams–Bashforth integrators for stiff ODEs, application to Cardiac Electrophysiology
    Mathematics and Computers in Simulation, 2018
    Co-Authors: Yves Coudière, Charlie Douanla-lontsi, Charles Pierre
    Abstract:

    Abstract Models in Cardiac Electrophysiology are coupled systems of reaction diffusion PDE and of ODE. The ODE system displays a very stiff behavior. It is nonlinear and its upgrade at each time step is a preponderant load in the computational cost. The issue is to develop high order explicit and stable methods to cope with this situation. In this article, is analyzed the resort to exponential Adams–Bashforth (EAB) integrators in Cardiac Electrophysiology. The method is presented in the framework of a general and varying stabilizer, that is well suited in this context. Stability under perturbation (or 0-stability) is proven. It provides a new approach for the convergence analysis of the method. The Dahlquist stability properties of the method is performed. It is presented in a new framework that incorporates the discrepancy between the stabilizer and the system Jacobian matrix. Provided this discrepancy is small enough, the method is shown to be A(alpha)-stable. This result is interesting for an explicit time-stepping method. Numerical experiments are presented for two classes of stiff models in Cardiac Electrophysiology. They include performance comparisons with several classical methods. The EAB method is observed to be as stable as implicit solvers and cheaper at equal level of accuracy.

  • Efficient high order schemes for stiff ODEs in Cardiac Electrophysiology
    arXiv: Numerical Analysis, 2017
    Co-Authors: Charlie Douanla Lontsi, Yves Coudière, Charles Pierre
    Abstract:

    In this work we analyze the resort to high order exponential solvers for stiff ODEs in the context of Cardiac Electrophysiology modeling. The exponential Adams-Bashforth and the Rush-Larsen schemes will be considered up to order 4. These methods are explicit multistep schemes.The accuracy and the cost of these methods are numerically analyzed in this paper and benchmarked with several classical explicit and implicit schemes at various orders. This analysis has been led considering data of high particular interest in Cardiac Electrophysiology : the activation time ($t\_a$ ), the recovery time ($t\_r $) and the action potential duration ($APD$). The Beeler Reuter ionic model, especially designed for Cardiac ventricular cells, has been used for this study. It is shown that, in spite of the stiffness of the considered model, exponential solvers allow computation at large time steps, as large as for implicit methods. Moreover, in terms of cost for a given accuracy, a significant gain is achieved with exponential solvers. We conclude that accurate computations at large time step are possible with explicit high order methods. This is a quite important feature when considering stiff non linear ODEs.

Charles Pierre - One of the best experts on this subject based on the ideXlab platform.

  • Rush-Larsen time-stepping methods of high order for stiff problems in Cardiac Electrophysiology
    Electronic Transactions on Numerical Analysis, 2020
    Co-Authors: Yves Coudière, Charlie Douanla-lontsi, Charles Pierre
    Abstract:

    To address the issues of stability and accuracy for reaction-diffusion equations, the development of high order and stable time-stepping methods is necessary. This is particularly true in the context of Cardiac Electrophysiology, where reaction-diffusion equations are coupled with stiff ODE systems. Many research have been led in that way in the past 15 years concerning implicit-explicit methods and exponential integrators. In 2009, Perego and Veneziani proposed an innovative time-stepping method of order 2. In this paper we present the extension of this method to the orders 3 and 4 and introduce the Rush-Larsen schemes of order k (shortly denoted RL_k). The RL_k schemes are explicit multistep exponential integrators. They display a simple general formulation and an easy implementation. The RL_k schemes are shown to be stable under perturbation and convergent of order k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL_k method is numerically studied as applied to the membrane equation in Cardiac Electrophysiology. The RL k schemes are shown to be stable under perturbation and convergent oforder k. Their Dahlquist stability analysis is performed. They have a very large stability domain provided that the stabilizer associated with the method captures well enough the stiff modes of the problem. The RL k method is numerically studied as applied to the membrane equation in Cardiac Electrophysiology.

  • Exponential Adams Bashforth integrators for stiff ODEs, application to Cardiac Electrophysiology
    arXiv: Numerical Analysis, 2018
    Co-Authors: Yves Coudière, Charlie Douanla Lontsi, Charles Pierre
    Abstract:

    Models in Cardiac Electrophysiology are coupled systems of reaction diffusion PDE and of ODE. The ODE system displays a very stiff behavior. It is non linear and its upgrade at each time step is a preponderant load in the computational cost. The issue is to develop high order explicit and stable methods to cope with this situation.In this article, is is analyzed the resort to exponential Adams Bashforth (EAB) integrators in Cardiac Electrophysiology. The method is presented in the framework of a general and varying stabilizer, that is well suited in this context. Stability under perturbation (or 0-stability) is proven. It provides a new approach for the convergence analysis of the method. The Dahlquist stability properties of the method is performed. It is presented in a new framework that incorporates the discrepancy between the stabilizer and the system Jacobian matrix. Provided this discrepancy is small enough, the method is shown to be A(alpha)-stable. This result is interesting for an explicit time-stepping method. Numerical experiments are presented for two classes of stiff models in Cardiac Electrophysiology. They include performances comparisons with several classical methods. The EAB method is observed to be as stable as implicit solvers and cheaper at equal level of accuracy.

  • Exponential Adams–Bashforth integrators for stiff ODEs, application to Cardiac Electrophysiology
    Mathematics and Computers in Simulation, 2018
    Co-Authors: Yves Coudière, Charlie Douanla-lontsi, Charles Pierre
    Abstract:

    Abstract Models in Cardiac Electrophysiology are coupled systems of reaction diffusion PDE and of ODE. The ODE system displays a very stiff behavior. It is nonlinear and its upgrade at each time step is a preponderant load in the computational cost. The issue is to develop high order explicit and stable methods to cope with this situation. In this article, is analyzed the resort to exponential Adams–Bashforth (EAB) integrators in Cardiac Electrophysiology. The method is presented in the framework of a general and varying stabilizer, that is well suited in this context. Stability under perturbation (or 0-stability) is proven. It provides a new approach for the convergence analysis of the method. The Dahlquist stability properties of the method is performed. It is presented in a new framework that incorporates the discrepancy between the stabilizer and the system Jacobian matrix. Provided this discrepancy is small enough, the method is shown to be A(alpha)-stable. This result is interesting for an explicit time-stepping method. Numerical experiments are presented for two classes of stiff models in Cardiac Electrophysiology. They include performance comparisons with several classical methods. The EAB method is observed to be as stable as implicit solvers and cheaper at equal level of accuracy.

  • Efficient high order schemes for stiff ODEs in Cardiac Electrophysiology
    arXiv: Numerical Analysis, 2017
    Co-Authors: Charlie Douanla Lontsi, Yves Coudière, Charles Pierre
    Abstract:

    In this work we analyze the resort to high order exponential solvers for stiff ODEs in the context of Cardiac Electrophysiology modeling. The exponential Adams-Bashforth and the Rush-Larsen schemes will be considered up to order 4. These methods are explicit multistep schemes.The accuracy and the cost of these methods are numerically analyzed in this paper and benchmarked with several classical explicit and implicit schemes at various orders. This analysis has been led considering data of high particular interest in Cardiac Electrophysiology : the activation time ($t\_a$ ), the recovery time ($t\_r $) and the action potential duration ($APD$). The Beeler Reuter ionic model, especially designed for Cardiac ventricular cells, has been used for this study. It is shown that, in spite of the stiffness of the considered model, exponential solvers allow computation at large time steps, as large as for implicit methods. Moreover, in terms of cost for a given accuracy, a significant gain is achieved with exponential solvers. We conclude that accurate computations at large time step are possible with explicit high order methods. This is a quite important feature when considering stiff non linear ODEs.

Hervé Delingette - One of the best experts on this subject based on the ideXlab platform.

  • STACOM - Towards real-time computation of Cardiac Electrophysiology for training simulator
    Statistical Atlases and Computational Models of the Heart. Imaging and Modelling Challenges, 2013
    Co-Authors: Hugo Talbot, Christian Duriez, Hadrien Courtecuisse, Jatin Relan, Maxime Sermesant, Stéphane Cotin, Hervé Delingette
    Abstract:

    This work aims at developing a training simulator for interventional radiology and thermo-ablation of Cardiac arrhythmias. To achieve this, a real-time model of the Cardiac Electrophysiology is needed, which is very challenging due to the stiff equations involved. In this paper, we detail our contributions in order to obtain efficient Cardiac Electrophysiology simulations. First, an adaptive parametrisation of the Mitchell-Schaeffer model as well as numerical optimizations are proposed. An accurate computation of both conduction velocity and action potential is ensured, even with relatively coarse meshes. Second, a GPU implementation of the Electrophysiology was realised in order to decrease the computation time. We evaluate our results by comparison with an accurate reference simulation using model parameters, personalized on patient data. We demonstrate that a fast simulation (close to real-time) can be obtained while keeping a precise description of the phenomena.

  • Towards Real-Time Computation of Cardiac Electrophysiology for Training Simulator
    2012
    Co-Authors: Hugo Talbot, Christian Duriez, Hadrien Courtecuisse, Jatin Relan, Maxime Sermesant, Stéphane Cotin, Hervé Delingette
    Abstract:

    This work aims at developing a training simulator for interventional radiology and thermo-ablation of Cardiac arrhythmias. To achieve this, a real-time model of the Cardiac Electrophysiology is needed, which is very challenging due to the stiff equations involved. In this paper, we detail our contributions in order to obtain efficient Cardiac Electrophysiology simulations. First, an adaptive parametrisation of the Mitchell-Schaeffer model as well as numerical optimizations are proposed. An accurate computation of both conduction velocity and action potential is ensured, even with relatively coarse meshes. Second, a GPU implementation of the Electrophysiology was realised in order to decrease the computation time. We evaluate our results by comparison with an accurate reference simulation using model parameters, personalized on patient data. We demonstrate that a fast simulation (close to real-time) can be obtained while keeping a precise description of the phenomena.

A. Natale - One of the best experts on this subject based on the ideXlab platform.

Hugo Talbot - One of the best experts on this subject based on the ideXlab platform.

  • STACOM - Towards real-time computation of Cardiac Electrophysiology for training simulator
    Statistical Atlases and Computational Models of the Heart. Imaging and Modelling Challenges, 2013
    Co-Authors: Hugo Talbot, Christian Duriez, Hadrien Courtecuisse, Jatin Relan, Maxime Sermesant, Stéphane Cotin, Hervé Delingette
    Abstract:

    This work aims at developing a training simulator for interventional radiology and thermo-ablation of Cardiac arrhythmias. To achieve this, a real-time model of the Cardiac Electrophysiology is needed, which is very challenging due to the stiff equations involved. In this paper, we detail our contributions in order to obtain efficient Cardiac Electrophysiology simulations. First, an adaptive parametrisation of the Mitchell-Schaeffer model as well as numerical optimizations are proposed. An accurate computation of both conduction velocity and action potential is ensured, even with relatively coarse meshes. Second, a GPU implementation of the Electrophysiology was realised in order to decrease the computation time. We evaluate our results by comparison with an accurate reference simulation using model parameters, personalized on patient data. We demonstrate that a fast simulation (close to real-time) can be obtained while keeping a precise description of the phenomena.

  • Towards Real-Time Computation of Cardiac Electrophysiology for Training Simulator
    2012
    Co-Authors: Hugo Talbot, Christian Duriez, Hadrien Courtecuisse, Jatin Relan, Maxime Sermesant, Stéphane Cotin, Hervé Delingette
    Abstract:

    This work aims at developing a training simulator for interventional radiology and thermo-ablation of Cardiac arrhythmias. To achieve this, a real-time model of the Cardiac Electrophysiology is needed, which is very challenging due to the stiff equations involved. In this paper, we detail our contributions in order to obtain efficient Cardiac Electrophysiology simulations. First, an adaptive parametrisation of the Mitchell-Schaeffer model as well as numerical optimizations are proposed. An accurate computation of both conduction velocity and action potential is ensured, even with relatively coarse meshes. Second, a GPU implementation of the Electrophysiology was realised in order to decrease the computation time. We evaluate our results by comparison with an accurate reference simulation using model parameters, personalized on patient data. We demonstrate that a fast simulation (close to real-time) can be obtained while keeping a precise description of the phenomena.