Adaptive-step methods for Markov-based membrane models

Gomes, Johnny Moreira; Oliveira, Rafael Sachetto; Lobosco, Marcelo; Santos, Rodrigo Weber dos

doi:10.1016/j.cnsns.2020.105249

Cited by 6 publications

(7 citation statements)

References 29 publications

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“…In [24] , novel adaptive time-step numerical methods are proposed to solve stiff excitable models that use Markov chain formulations to describe ion channel dynamics. This type of models is becoming increasingly used to simulate electrical abnormalities due to mutations in genes encoding ion channels or to predict the effects of drug-channel interactions.…”

Section: Cardiac Systemsmentioning

confidence: 99%

Excitable dynamics in neural and cardiac systems

Barrio

Coombes

Desroches

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

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The application of mathematics, physics and engineering to medical research is continuously growing; interactions among these disciplines have become increasingly important and have contributed to an improved understanding of clinical and biological phenomena, with implications for disease prevention, diagnosis and treatment. This special issue presents examples of this synergy, with a particular focus on the investigation of cardiac and neural excitability.This issue includes 24 original research papers and covers a broad range of topics related to the physiological and pathophysiological function of the brain and the heart. Studies span scales from isolated neurons and small networks of neurons to whole-organ dynamics for the brain and from cardiac subcellular domains and cardiomyocytes to onedimensional tissues for the heart.This preface is part of the Special Issue on "Excitable Dynamics in Neural and Cardiac Systems".

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Section: Cardiac Systemsmentioning

confidence: 99%

Excitable dynamics in neural and cardiac systems

Barrio

Coombes

Desroches

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

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“…According to these approaches, the classical reaction–diffusion split of the EP problem leads to a linear partial differential equation and a spatially decoupled system of ordinary differential equations (ODEs). Most of the published literature related to time adaptivity focuses on the reaction subproblem 15,21–26 . This strategy appears to be an efficient and yet simple way to speed up cardiac EP simulations 11,25 .…”

Section: Introductionmentioning

confidence: 99%

“…Most of the published literature related to time adaptivity focuses on the reaction subproblem. 15,[21][22][23][24][25][26] This strategy appears to be an efficient and yet simple way to speed up cardiac EP simulations. 11,25 Additional research has investigated schemes to adapt the time step in both the reaction and the diffusion subproblems.…”

mentioning

confidence: 99%

A simple and efficient adaptive time stepping technique for low‐order operator splitting schemes applied to cardiac electrophysiology

Ogiermann

Perotti

Balzani

2023

Numer Methods Biomed Eng

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We present a simple, yet efficient adaptive time stepping scheme for cardiac electrophysiology (EP) simulations based on standard operator splitting techniques. The general idea is to exploit the relation between the splitting error and the reaction's magnitude—found in a previous one‐dimensional analytical study by Spiteri and Ziaratgahi—to construct the new time step controller for three‐dimensional problems. Accordingly, we propose to control the time step length of the operator splitting scheme as a function of the reaction magnitude, in addition to the common approach of adapting the reaction time step. This conforms with observations in numerical experiments supporting the need for a significantly smaller time step length during depolarization than during repolarization. The proposed scheme is compared with classical proportional–integral–differential controllers using state‐of‐the‐art error estimators, which are also presented in details as they have not been previously applied in the context of cardiac EP with operator splitting techniques. Benchmarks show that choosing the time step as a sigmoidal function of the reaction magnitude is highly efficient and full cardiac cycles can be computed with precision even in a realistic biventricular setup. The proposed scheme outperforms common adaptive time stepping techniques, while depending on fewer tuning parameters.

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“…In this way, a larger time step can be used to solve the diffusion term independently of the reaction term, which may be solved adaptively using a small time step. 5,6 Commonly, the decoupled reaction-diffusion system is solved by employing a semi-implicit scheme. The stiff reaction term is integrated using an explicit time integration method (e.g., forward Euler, Rush-Larsen 7 ) whereas the diffusion term is solved using an implicit time integration method (e.g., backward Euler, Crank-Nicolson).…”

Section: Introductionmentioning

confidence: 99%

“…The operator splitting technique 4 can be used to decouple the stiff reaction term and the diffusion term. In this way, a larger time step can be used to solve the diffusion term independently of the reaction term, which may be solved adaptively using a small time step 5,6 …”

Section: Introductionmentioning

confidence: 99%

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

Mountris

Pueyo

2021

Numer Methods Biomed Eng

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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.

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Adaptive-step methods for Markov-based membrane models

Cited by 6 publications

References 29 publications

Excitable dynamics in neural and cardiac systems

Excitable dynamics in neural and cardiac systems

A simple and efficient adaptive time stepping technique for low‐order operator splitting schemes applied to cardiac electrophysiology

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

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