A finite volume scheme for cardiac propagation in media with isotropic conductivities

DOI10.1016/j.matcom.2009.12.010zbMath1192.92002OpenAlexW2135500037MaRDI QIDQ982906

Mostafa Bendahmane, Ricardo Ruiz-Baier, Raimund Bürger

Publication date: 28 July 2010

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10533/144261

zbMATH Keywords

reaction-diffusion systemfinite volume approximationconvergence to the weak solutionaxially symmetric bidomain model

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) PDEs of mixed type (35M10) Degenerate parabolic equations (35K65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Biophysics (92C05) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items

Uniform Null Controllability for a Degenerating Reaction-Diffusion System Approximating a Simplified Cardiac Model, A unified analysis for reaction-diffusion models with application to the spiral waves dynamics of the Barkley model, A positive cell vertex Godunov scheme for a Beeler–Reuter based model of cardiac electrical activity, An intergrid transfer operator using radial basis functions with application to cardiac electromechanics, Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology, A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology, Finite element and finite volume-element simulation of pseudo-ECGs and cardiac alternans, Stability of conductivities in an inverse problem in the reaction-diffusion system in electrocardiology

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A two-current model for the dynamics of cardiac membrane
• Adaptive mesh refinement for hyperbolic partial differential equations
• Reaction-diffusion systems for the macroscopic bidomain model of the cardiac electric field
• Stability and convergence of a finite volume method for two systems of reaction-diffusion equations in electro-cardiology
• Analysis of a class of degenerate reaction-diffusion systems and the bidomain model of cardiac tissue
• Mathematical physiology. II: Systems physiology
• Existence and uniqueness of the solution for the bidomain model used in cardiac electrophysiology
• Convergence of a finite volume scheme for the bidomain model of cardiac tissue
• A numerically efficient model for simulation of defibrillation in an active bidomain sheet of myocardium
• An operator splitting method for solving the bidomain equations coupled to a volume conductor model for the torso
• Convergence of discrete duality finite volume schemes for the cardiac bidomain model
• Simulating patterns of excitation, repolarization and action potential duration with cardiac bidomain and monodomain models
• Discrete Sobolev inequalities andL^perror estimates for finite volume solutions of convection diffusion equations
• A multiresolution space-time adaptive scheme for the bidomain model in electrocardiology
• Adaptivity in Space and Time for Reaction-Diffusion Systems in Electrocardiology
• DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS
• A PARALLEL SOLVER FOR REACTION–DIFFUSION SYSTEMS IN COMPUTATIONAL ELECTROCARDIOLOGY
• Computing the Electrical Activity in the Heart
• Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method