Rodolphe Turpault

Multifocal ectopic Purkinje-related premature contractions: a new SCN5A-related cardiac channelopathy.

OBJECTIVES The aim of this study was to describe a new familial cardiac phenotype and to elucidate the electrophysiological mechanism responsible for the disease. BACKGROUND Mutations in several genes encoding ion channels, especially SCN5A, have emerged as the basis for a variety of inherited cardiac arrhythmias. METHODS Three unrelated families comprising 21 individuals affected by multifocal ectopic Purkinje-related premature contractions (MEPPC) characterized by narrow junctional and rare sinus beats competing with numerous premature ventricular contractions with right and/or left bundle branch block patterns were identified. RESULTS Dilated cardiomyopathy was identified in 6 patients, atrial arrhythmias were detected in 9 patients, and sudden death was reported in 5 individuals. Invasive electrophysiological studies demonstrated that premature ventricular complexes originated from the Purkinje tissue. Hydroquinidine treatment dramatically decreased the number of premature ventricular complexes. It normalized the contractile function in 2 patients. All the affected subjects carried the c.665G>A transition in the SCN5A gene. Patch-clamp studies of resulting p.Arg222Gln (R222Q) Nav1.5 revealed a net gain of function of the sodium channel, leading, in silico, to incomplete repolarization in Purkinje cells responsible for premature ventricular action potentials. In vitro and in silico studies recapitulated the normalization of the ventricular action potentials in the presence of quinidine. CONCLUSIONS A new SCN5A-related cardiac syndrome, MEPPC, was identified. The SCN5A mutation leads to a gain of function of the sodium channel responsible for hyperexcitability of the fascicular-Purkinje system. The MEPPC syndrome is responsive to hydroquinidine.

Late-time/stiff-relaxation asymptotic-preserving approximations of hyperbolic equations

We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective system of equations describing the late-time/stiff relaxation singular limit. The structure of this new system is discussed and the role of a mathematical entropy is emphasized. Second, we propose a new finite volume discretization which, in late-time asymptotics, allows us to recover a discrete version of the same effective asymptotic system. This is achieved provided we suitably discretize the relaxation term in a way that depends on a matrix-valued free-parameter, chosen so that the desired asymptotic behavior is obtained. Our results are illustrated with several models of interest in continuum physics, and numerical experiments demonstrate the relevance of the proposed theory and numerical strategy.

A mathematical model of the Purkinje-muscle junctions.

This paper is devoted to the construction of a mathematical model of the His-Purkinje tree and the Purkinje-Muscle Junctions (PMJ). A simple numerical scheme is proposed in order to perform some simple numerical experiments.

Multigroup model for radiating flows during atmospheric hypersonic re-entry

The system that has to be solved to compute radiation hydrodynamics is quite difficult from a numerical point of view. For most applications, the simulations are done thanks to uncoupled or eventually loosely coupled codes. However, in some hypersonic regimes, the effects of radiative transfer can drastically modify the hydrodynamics flow. For such applications, it is important to have a model that fully couples hydrodynamics and radiation in order to have a good behaviour of the solution. However, coupling with the full radiative transfer equation is usually very expensive hence it is not reasonable for multidimensionnal unsteady computations. Our choice is to use a moment model for the radiation part, which is way cheaper. This model uses an entropic closure that allows to be consistant with the fundamental physical properties such as energy conservation, entropy dissipation and flux-limitation. We also developed it to be multigroup in order to correctly predict the solution of strongly frequency-dependent problems.

Asymptotic preserving scheme for the shallow water equations with source terms on unstructured meshes

The following work is devoted to the construction and validation of a numerical scheme for the 2D shallow water system on unstructured meshes, supplemented by topography and friction source terms. Approximate solutions of frictionless flows are obtained considering a suitable formulation of the conservation laws, involving the water free surface and some fractions of water, accounting for the topography variations. The discretization of the friction source terms relies on the use of a modified Riemann solver for the flux computation. The resulting scheme is then corrected in order to achieve an asymptotic regime preservation. A MUSCL reconstruction is also performed to increase the space order of accuracy. The overall numerical approach is shown to be consistent, well-balanced and to satisfy a domain invariant principle. These results are assessed through several benchmark tests, involving complex geometry and varying bathymetry. In the presence of dry areas, special interest is given to the wave front speed computation, highlighting the stability of the method, even when implementing the asymptotic preserving correction.

Space-time Generalized Riemann Problem Solvers of Order k for Linear Advection with Unrestricted Time Step

This work concerns high-order approximations of the linear advection equation in very long time. A GRP-type scheme of arbitrary high-order in space and time with no restriction on the time step is developed. In the usual GRP solvers, we consider a polynomial approximation of the solution in space in each cell at the initial time. Here, we add a second polynomial approximation of the solution in time in each interface. Thanks to this double approximation, the resulting scheme is compact. It is proved to be of order k+1 in space and time, where k is the degree of the polynomials. Thanks to the compactness of the scheme, a two-dimensional extension is detailed on unstructured meshes made of triangles. Several numerical test-cases and comparison with existing methods illustrate the excellent behaviour of the scheme.

An asymptotic-preserving scheme for systems of conservation laws with source terms on 2D unstructured meshes

A finite volumes numerical scheme is here proposed for hyperbolic systems of conservation laws with source terms which degenerate into parabolic systems in large times when the source terms become stiff. In this framework, it is crucial that the numerical schemes are asymptotic-preserving i.e. that they degenerate accordingly . Here, an asymptotic-preserving numerical scheme is designed for any system within the aforementioned class on 2D unstructured meshes. This scheme is proved to be consistent and stable under a suitable CFL condition. Moreover, we show that it is also possible to prove that it preserves the set of (physically) admissible states under a geometrical property on the mesh. Finally, numerical examples are given to illustrate its behavior.

Discrete-Velocity Models for Numerical Simulations in Transitional Regime for Rarefied Flows and Radiative Transfer

In this paper we propose a deterministic eulerian approach for kinetic relaxation models. This approach is based on adefinition of the discrete equilibrium using a discrete equivalent of the minimum entropy principle. This leads to discrete models which are entropic and conservative. Two applications to gas dynamics and to radiative transfer are presented. Numerical experiments illustrate the performance of numerical codes based on this approach.

An admissibility and asymptotic-preserving scheme for systems of conservation laws with source term on 2D unstructured meshes

The objective of this work is to design explicit finite volumes schemes for specific systems of conservations laws with stiff source terms, which degenerate into diffusion equations. We propose a general framework to design an asymptotic preserving scheme, that is stable and consistent under a classical hyperbolic CFL condition in both hyperbolic and diffusive regime, for any two-dimensional unstructured mesh. Moreover, the scheme developed also preserves the set of admissible states, which is mandatory to keep physical solutions in stiff configurations. This construction is achieved by using a non-linear scheme as a target scheme for the diffusive equation, which gives the form of the global scheme for the complete system of conservation laws. Numerical results are provided to validate the scheme in both regimes.

A mathematical model of the ventricular conduction system

Models in electrocardiology represent the heart muscle as a 3D continuous media, while the special conduction network (His bundle and Purkinje cells), is more accurately represented as a 1D media. We introduce the mathematical equations that are used to model this 1D media as a tree and how it couples to the 3D muscle domain. The coupling needs some scaling parameters that are clearly described. Simple numerical are presented to illustrate the model.