A dual adaptive explicit time integration algorithm for efficiently solving the cardiac monodomain equation

The monodomain model is widely used in in‐silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so that they can be solved separately. Commonly, the diffusion t...

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Bibliographic Details
Published in:International journal for numerical methods in biomedical engineering Vol. 37; no. 7; pp. e3461 - n/a
Main Authors: Mountris, Konstantinos A., Pueyo, Esther
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.07.2021
Wiley Subscription Services, Inc
Subjects:
adaptive explicit integration
Algorithms
cardiac electrophysiology
Cardiology
Computer applications
Diffusion
Heart
Implicit methods
Integration
Methods
Myocardium
operator splitting
Propagation
Splitting
Time integration
cardiac electrophysiology
adaptive explicit integration
operator splitting
ISSN:2040-7939, 2040-7947, 2040-7947
Online Access:Get full text
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Summary:The monodomain model is widely used in in‐silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so that they can be solved separately. Commonly, the diffusion term is solved implicitly with a large time step while the reaction term is solved by using an explicit method with adaptive time stepping. In this work, we propose a fully explicit method for the solution of the decoupled monodomain model. In contrast to semi‐implicit methods, fully explicit methods present lower memory footprint and higher scalability. However, such methods are only conditionally stable. We overcome the conditional stability limitation by proposing a dual adaptive explicit method in which adaptive time integration is applied for the solution of both the reaction and diffusion terms. We perform a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions. Results show that the proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting‐based methods. We propose a fully explicit method for solving the monodomain model for in‐silico cardiology by applying adaptive time integration for both the reaction and diffusion terms. Benchmark simulations show the ability to preserve accuracy and improve computational efficiency compared to standard operator‐splitting.
Bibliography:Funding information
European Social Fund; Gobierno de Aragón, Grant/Award Numbers: LMP124‐18, T39_20R; H2020 European Research Council, Grant/Award Number: ERC‐StG‐638284; Ministerio de Ciencia e Innovación, Grant/Award Number: PID2019‐105674RB‐I00
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ISSN:2040-7939
2040-7947
2040-7947
DOI:10.1002/cnm.3461