A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology

Anaya, Verónica; Bendahmane, Mostafa; Mora, David; Sepúlveda, Mauricio

doi:10.1093/imanum/drz001

Cited by 20 publications

(8 citation statements)

References 59 publications

(50 reference statements)

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“…The FHN model incorporates only two variables of activation and recovery and maintains much simpler structure compared with detailed cellular models. It describes the macroscopic level pattern rather than ionic phenomena, which significantly reduces the computational complexity, thus is a popular choice for simulating the electrical activities in high dimensional cardiac tissue [18,19].…”

Section: Cardiac Tissue Modelmentioning

confidence: 99%

A Two-Stage Model Identification Method for Simulation of Electrical Wave Propagation in Heart Tissue

2020

IEEE Access

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Computer modeling and simulation is fast-moving towards clinical applications to advance cardiac diagnosis and aid treatment planning. As cardiac models become more popular and useful, the need to tailor these models for individual subjects has grown. Therefore, model identification becomes an important step of cardiac modeling. Cardiac model identification is a challenging task, particularly for simulation in high organizational scales such as tissue and organ scales, as the models are nonlinear and involve hidden ion channel gating variables. In this study, we proposed a two-stage model calibration algorithm to estimate the parameters of cardiac tissue model using membrane potential data. Specifically, an ensemble Kalman Filter (EnKF) is used in the first stage to track the membrane potentials and the hidden ion channel gating variables; the outputs from the EnKF are used as the initial values to calculate forward prediction in the second stage. The optimization algorithm minimizes the sum of squared errors in both stages through a coarse and a fine optimization. The proposed method is validated through multiple simulation designs, which shows good accuracy and efficiency. INDEX TERMS Cardiac model, ensemble Kalman Filter, model calibration, stochastic optimization.

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Section: Cardiac Tissue Modelmentioning

confidence: 99%

A Two-Stage Model Identification Method for Simulation of Electrical Wave Propagation in Heart Tissue

2020

IEEE Access

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“…The VEM also permits to easily implement highly regular conforming discrete spaces [18,22] which make the method very feasible to solve various fourth-order problems [8,35,14,34,36]. Regarding VEM for time dependent problems, we mention the following works [2,1,4,6,9,39,38,40].…”

Section: Introductionmentioning

confidence: 99%

Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation

Adak¹,

Mora²,

Natarajan³

2022

Preprint

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In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose C 1 conforming virtual element method (VEM) of arbitrary order, k ≥ 2, to approximate the model problem numerically. We employ VEM to discretize the space variable and fully implicit scheme for temporal variable. Well-posedness of the fully discrete scheme is proved under certain conditions on the physical parameters, and we derive optimal order of convergence in both space and time variable. Finally, numerical experiments are presented to illustrate the behaviour of the proposed numerical scheme.

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“…Several virtual element methods based on conforming and non-conforming schemes have been developed to solve a wide variety of problems in Solid and Fluid Mechanics, for example [4][5][6]9,11,12,14,19,25,27,30,42,46,47]. Moreover, the VEM for thin structures has been developed in [16,24,29,30,44,45], whereas VEM for nonlinear problems have been introduced in [3,15,26,35,36,50] In this paper, we analyze a conforming 1 Virtual Element Method to approximate the isolated solutions of the von Kármán equations. We consider a variational formulation in terms of the transverse displacement and the Airy stress function, which contains bilinear and trilinear forms.…”

Section: Introductionmentioning

confidence: 99%

A virtual element method for the von Kármán equations

2021

Self Cite

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In this article we propose and analyze a Virtual Element Method (VEM) to approximate the isolated solutions of the von Kármán equations, which describe the deformation of very thin elastic plates. We consider a variational formulation in terms of two variables: the transverse displacement of the plate and the Airy stress function. The VEM scheme is conforming in H2 for both variables and has the advantages of supporting general polygonal meshes and is simple in terms of coding aspects. We prove that the discrete problem is well posed for h small enough and optimal error estimates are obtained. Finally, numerical experiments are reported illustrating the behavior of the virtual scheme on different families of meshes.

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A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology

Cited by 20 publications

References 59 publications

A Two-Stage Model Identification Method for Simulation of Electrical Wave Propagation in Heart Tissue

A Two-Stage Model Identification Method for Simulation of Electrical Wave Propagation in Heart Tissue

Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation

A virtual element method for the von Kármán equations

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