MATHICSE Technical Report : Isogeometric approximation of cardiac electrophysiology models on surfaces: an accuracy study with application to the human left atrium
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This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error ...
We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...
In the present paper, an optimal control problem constrained by the tridomain equations in electrocardiology is investigated. The state equations consisting in a coupled reaction-diffusion system modelling the propagation of the intracellular and extracell ...
In this project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-UniformRational B-Splines) basis ...
We present a model for mechanical activation of the cardiac tissue depending on the evolution of the transmembrane electrical potential and certain gating/ionic variables that are available in most of electrophysiological descriptions of the cardiac membra ...
In this report, we first introduce operator splitting as a way to solve nonlinear reaction-diffusion PDEs. We then present a flux-limiting technique for anisotropic diffusion problems that allows to recover the discrete maximum principle. Finally, we imple ...
In everyday life of an engineer, CAD (Computer Aided Design) and FE (Finite Element) programs play an important role. The two different structures, CAD and FE programs, use different mathematical functions. In CAD programs, so called NURBS find their appli ...
In this project, we present some applications of Isogeometric Analysis in stationary fluid dynamics problems. Specially, we focus on the numerical solution of the Stokes and Navier-Stokes equations and the fulfillment of the inf-sup conditions, specificall ...
We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-spli ...
Presently, the cells' electrical activity is measured either by extracellular microelectrode array (MEA) or by microscopic fluorescence imaging methods. The MEA is a non-invasive in vitro technique which allows long-term recording at multicellular level wh ...
