Degenerate Evolution Systems Modeling the Cardiac Electric Field at Micro- and Macroscopic Level

Franzone, Piero Colli; Savaré, Giuseppe

doi:10.1007/978-3-0348-8221-7_4

Cited by 113 publications

(134 citation statements)

References 28 publications

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“…Usually uniqueness is forced by requiring that u e has zero average on X. Let [9,29]. The Monodomain problem has been proposed as a simplification of the Bidomain one.…”

Section: The Bidomain Monodomain and Hybridomain Modelsmentioning

confidence: 99%

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An a posteriori error estimator for model adaptivity in electrocardiology

Mirabella

Nobile

Veneziani

2011

Computer Methods in Applied Mechanics and Engineering

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“…Usually uniqueness is forced by requiring that u e has zero average on X. Let [9,29]. The Monodomain problem has been proposed as a simplification of the Bidomain one.…”

Section: The Bidomain Monodomain and Hybridomain Modelsmentioning

confidence: 99%

“…For well-posedness analysis of this problem, we still refer to [9]. The Monodomain model is a single parabolic reaction-diffusion PDE for the transmembrane potential, replacing the two equations of the original model.…”

Section: The Bidomain Monodomain and Hybridomain Modelsmentioning

confidence: 99%

An a posteriori error estimator for model adaptivity in electrocardiology

Mirabella

Nobile

Veneziani

2011

Computer Methods in Applied Mechanics and Engineering

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“…Just to mention a few results, Colli Franzone and Savaré [16] present a weak formulation for the bidomain model and show that it has a structure suitable to apply the theory of evolution variational inequalities in Hilbert spaces. Bendahmane and Karlsen [6] prove existence and uniqueness for the bidomain equations using the Faedo-Galerkin method and compactness theory for the existence proof.…”

Section: Related Workmentioning

confidence: 99%

“…[16,23,32]) is the most widely used model to describe the electrical activity (the propagation of action potential) in a slice of the cardiac muscle. In this model, the myocardium is regarded as a two-phase medium consisting in two interpenetrating and superimposed (anisotropic) continuous media, the intracellular (i) and extracellular (e) tissues, which occupy the same three-dimensional area and are separated from each other (and connected at each point) by the cardiac cellular membrane.…”

Section: Scopementioning

confidence: 99%

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

Bendahmane

Bürger

Ruiz–Baier

2010

Mathematics and Computers in Simulation

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A finite volume method for solving the monodomain and bidomain models for the electrical activity of myocardial tissue is presented. These models consist of a parabolic PDE and a system of a parabolic and an elliptic PDE, respectively, for certain electric potentials, coupled to an ODE for the gating variable. The existence and uniqueness of the approximate solution is proved, and it is also shown that the scheme converges to the corresponding weak solutions for the monodomain model, and for the bidomain model when considering diagonal conductivity tensors. Numerical examples in two and three space dimensions are provided, indicating experimental rates of convergence slightly above first order for both models.

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“…Existence and regularity results for this degenerate system can be found in Colli Franzone and Savaré [2002]. The system uniquely determines v, while the potentials u i and u e are defined only up to a same additive time-dependent constant related to the reference potential, chosen to be the average extracellular potential in the cardiac volume by imposing H u e dx = 0.…”

Section: The Cardiac Bidomain and Monodomain Modelsmentioning

confidence: 99%

Parallel Solution of Cardiac Reaction-Diffusion Models

Pavarino

Franzone

Lecture Notes in Computational Science and Engineering

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Summary. We present and study a parallel iterative solver for reaction-diffusion systems in three dimensions arising in computational electrocardiology, such as the Bidomain and Monodomain models. The models include intramural fiber rotation and anisotropic conductivity coefficients that can be fully orthotropic or axially symmetric around the fiber direction. These cardiac models are coupled with a membrane model for the ionic currents, consisting of a system of ordinary differential equations. The solver employs structured isoparametric Q1 finite elements in space and a semi-implicit adaptive method in time. Parallelization and portability are based on the PETSc parallel library and large-scale computations with up to O(10 7 ) unknowns have been run on parallel computers. These simulation of the full Bidomain model (without operator or variable splitting) for a full cardiac cycle are, to our knowledge, among the most complete in the available literature.

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Degenerate Evolution Systems Modeling the Cardiac Electric Field at Micro- and Macroscopic Level

Cited by 113 publications

References 28 publications

An a posteriori error estimator for model adaptivity in electrocardiology

An a posteriori error estimator for model adaptivity in electrocardiology

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

Parallel Solution of Cardiac Reaction-Diffusion Models

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