Yves Bourgault

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The bidomain model is a system of partial differential equations used to model the propagation of electrical potential waves in the myocardium. It is composed of coupled parabolic and elliptic partial differential equations, as well as at least one ordinary differential equation to model the ion activity through the cardiac cell membranes. The purpose of(More)
Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical(More)
A stabilized semidiscrete finite element discretization of the transient transport equation is studied in the framework of anisotropic meshes. A priori and a posteriori error estimates are derived, the involved constants being independent of the mesh aspect ratio, only space discretization being considered. Numerical results on nonadapted, anisotropic(More)
The bidomain model is the current most sophisticated model used in cardiac electrophysiology. The monodomain model is a simplification of the bidomain model that is less computationally intensive but only valid under equal conductivity ratio. We propose in this paper optimal monodomain approximations of the bidomain model. We first prove that the error(More)
Simulations of the mechanics of the left ventricle of the heart with fluid-structure interaction benefit greatly from the parallel processing power of a high performance computing cluster, such as HPCVL. The objective of this paper is to describe the computational requirements for our simulations. Results of parallelization studies show that, as expected,(More)
Nonlinear reaction-diffusion systems are widely employed to study the spatio-temporal chaotic behavior that occurs in excitable media such as cardiac tissue where sufficiently strong perturbations can excite nonlinear propagating waves which can form spiral waves in two dimensions or scroll waves in three dimensions. The numerical simulation of these waves(More)
This article proposes two avenues to help improve the realism of numerical computations for cardiac electrophysiology while maintaining manageable computational resources. We first propose an asymptotic analysis to adjust the parameters and use a simple two-variable ionic model to reproduce the main characteristics of the cardiac action potential (AP) in(More)
The simulation of cardiac electrophysiological waves are known to require extremely fine meshes, limiting the applicability of current numerical models to simplified geometries and ionic models. In this work, an accurate numerical method based on a time-dependent anisotropic remeshing strategy is presented for simulating three-dimensional cardiac(More)