Gradient flows and variational principles for cardiac electrophysiology: toward efficient and robust numerical simulations of the electrical activity of the heart

DOI10.1016/j.cma.2014.02.002zbMath1296.76186OpenAlexW1991236422MaRDI QIDQ459139

Daniel E. Hurtado, Duvan Henao

Publication date: 8 October 2014

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2014.02.002

zbMATH Keywords

variational principlesgradient flowFitzhugh-Nagumocardiac electrophysiologysaddle-point variational problems

Mathematics Subject Classification ID

Physiology (general) (92C30) Biomechanical solid mechanics (74L15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Physiological flows (76Z05)

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Cites Work

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• Computational modeling of electrochemical coupling: a novel finite element approach towards ionic models for cardiac electrophysiology
• Reaction-diffusion systems for the macroscopic bidomain model of the cardiac electric field
• Stable three-dimensional action potential circulation in the FitzHugh- Nagumo model
• Non-periodic finite-element formulation of Kohn-Sham density functional theory
• Non-periodic finite-element formulation of orbital-free density functional theory
• Re-entry in an anatomical model of the heart
• Mathematical physiology
• Mathematical models and numerical methods for the forward problem in cardiac electrophysi\-ol\-o\-gy
• Error estimation and adaptive meshing in strongly nonlinear dynamic problems
• The variational formulation of viscoplastic constitutive updates
• Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation
• Finite element analysis of geometrically necessary dislocations in crystal plasticity
• EXISTENCE AND CONVERGENCE RESULTS FOR THE GALERKIN APPROXIMATION OF AN ELECTRONIC DENSITY FUNCTIONAL
• Poincare constants for finite element stars
• Computational modeling of cardiac electrophysiology: A novel finite element approach
• On the numerical implementation of variational arbitrary Lagrangian–Eulerian (VALE) formulations
• Neumann Eigenvalue Estimate on a Compact Riemannian Manifold
• Implicit Time Discretization and Global Existence for a Quasi-Linear Evolution Equation with Nonconvex Energy
• Convergence of the Galerkin approximation of a degenerate evolution problem in electrocardiology
• Multiscale Modeling for the Bioelectric Activity of the Heart