Reentrant arrhythmias can be simulated in electrophysiological models of electrical impulse propagation governed by a reaction-diffusion system. To facilitate the initiation of a large number of independent episodes of simulated arrhythmias with controllable level of complexity, a new approach is proposed for thin-walled geometries in which depolarization wave dynamics is essentially two-dimensional. Points representing phase singularities are first randomly distributed over the epicardial surface and are assigned a topological charge (direction of rotation). A qualitatively-correct phase map is then reconstructed on the whole surface by interpolation. The eikonal-diffusion equation is used to iteratively regularize the phase map based on a priori information on wavefront propagation. An initial condition for the reaction-diffusion model is created from the resulting phase map with multiple functional/anatomical reentries. Results in an atrial model demonstrate the ability to generate statistical realizations of the same dynamics and to vary the level of complexity measured by the number of phase singularities. A library of 100 simulations with an average number of phase singularities ranging from 1 to 10 is created. An extension to volumetric patient-specific atrial models including fiber orientation and a fast conducting system is presented to illustrate possible applications.
Phase singularity analysis provides a quantitative description of spiral wave patterns observed in chemical or biological excitable media. The configuration of phase singularities (locations and directions of rotation) is easily derived from phase maps in two-dimensional manifolds. The question arises whether one can construct a phase map with a given configuration of phase singularities. The existence of such a phase map is guaranteed provided that the phase singularity configuration satisfies a certain constraint associated with the topology of the supporting medium. This paper presents a constructive mathematical approach to numerically solve this problem in the plane and on the sphere as well as in more general geometries relevant to atrial anatomy including holes and a septal wall. This tool can notably be used to create initial conditions with a controllable spiral wave configuration for cardiac propagation models and thus help in the design of computer experiments in atrial electrophysiology.
Les régimes publics de protection sociale sont majoritairement contributifs (pour 57 % des prestations versées en 2014), ce qui signifie que le montant des prestations dépend des cotisations préalablement payées par l’assuré (retraite, assurance chômage). Toutefois, en raison de la complexité de la fiche de paye, il est difficile de penser que les salariés identifient effectivement les cotisations contributives prélevées sur leur salaire, alors même que ces cotisations accordent des droits individuels, et peuvent être vues comme un revenu différé ou une assurance obligatoire plutôt que comme un impôt. Une clarification de la fiche de paye pourrait mettre en avant la notion de « salaire complet » (salaire net et cotisations contributives, soit environ 150 % du salaire net), plus représentatif de la véritable rémunération du salarié.
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