A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes

DOI10.1016/j.mbs.2005.07.007zbMath1093.65086OpenAlexW2076184368WikidataQ46685222 ScholiaQ46685222MaRDI QIDQ2494894

Andrew J. Pullan, Mark L. Trew, Bruce H. Smaill, David P. Bullivant, Peter J. Hunter

Publication date: 30 June 2006

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mbs.2005.07.007

zbMATH Keywords

numerical examplesfinite differenceMoore-Penrose inverseelliptic equationbidomain equationsparabolic reaction-diffusion equationcardiac electrical activityirregular computational meshes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Physiology (general) (92C30) Initial value problems for second-order parabolic equations (35K15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

Towards accurate numerical method for monodomain models using a realistic heart geometry, Stability analysis of the POD reduced order method for solving the bidomain model in cardiac electrophysiology, A meshfree method for simulating myocardial electrical activity, Generalized finite difference method for solving two-dimensional non-linear obstacle problems, Solving anisotropic elliptic and parabolic equations by a meshless method: simulation of the electrical conductivity of a tissue, C <scp>haste</scp>  : incorporating a novel multi-scale spatial and temporal algorithm into a large-scale open source library, Simulation of cardiac electrophysiology on next-generation high-performance computers

Uses Software

• CUBIT

Cites Work

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• Modeling impulse propagation and extracellular potential distributions in anisotropic cardiac tissue using a finite volume element discretization
• Modelling and visualising the heart
• Improvements of generalized finite difference method and comparison with other meshless method
• A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium
• Spreading of excitation in 3-D models of the anisotropic cardiac tissues. I: Validation of the eikonal model
• Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation
• Generalized finite difference method for 3-D viscous flow in stenotic tubes with large wall deformation and collapse