A ghost structure finite difference method for a fractional FitzHugh-Nagumo monodomain model on moving irregular domain

Wang, Y., Cai, L., Feng, X., and (2021) A ghost structure finite difference method for a fractional FitzHugh-Nagumo monodomain model on moving irregular domain. Journal of Computational Physics, 428, 110081.

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Abstract

In this paper, a ghost structure (GS) finite difference method is proposed to simulate the fractional FitzHugh-Nagumo (FHN) monodomain model on a moving irregular computational domain. In the GS formulation the moving irregular domain is converted into a fixed regular domain (called ghost structure), and the transmembrane potential is described in the Eulerian coordinates, while the membrane dynamics are described in the Lagrangian coordinates. The transformation between the Lagrangian variables and the Eulerian variables is achieved by an integral transformation which involves a delta function. The GS formulation allows to compute the transmembrane potential in a fixed regular domain using the finite difference method on a Cartesian grid, which has a huge advantage for approximating domain-dependent fractional derivatives. To overcome the difficulty caused by running time-consuming loops to compute the transformation between the Eulerian and Lagrangian variables, two fast algorithms are proposed to compute the transformation. Extensive numerical tests are provided to demonstrate the effectiveness and robustness of the proposed GS finite difference method for solving the fractional FHN monodomain model. We first numerically study the transmembrane potential propagation in both healthy hearts and hearts with arrhythmia by simulating the model in the transverse of a ventricle. We then study the transmembrane potential propagation during the pumping process, which requires to simulate the model in the moving longitudinal section of a ventricle. Our numerical results show that the change of spatial derivatives can affect the propagation velocity and the width of the transmembrane potential wave, and for a heart with arrhythmia, the transmembrane potential begins to enter cyclically the region where cardiomyocytes have been excited and then stimulates cardiomyocytes to contract again.

Item Type: Articles Published Yes Luo, Professor Xiaoyu and Gao, Dr Hao Luo, X.Formal analysis, Supervision, Writing – review and editingGao, H.Formal analysis, Supervision, Writing – review and editing Wang, Y., Cai, L., Feng, X., Luo, X., and Gao, H. College of Science and Engineering > School of Mathematics and Statistics > Mathematics Journal of Computational Physics Elsevier 0021-9991 1090-2716 17 December 2020 Copyright © 2020 Elsevier Inc. First published in Journal of Computational Physics 428: 110081 Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
172141EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - Mathematics
303232EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)Xiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S030875/1M&S - Mathematics