4 research outputs found
Spiral anchoring in anisotropic media with multiple inhomogeneities: a dynamical system approach
Various PDE models have been suggested in order to explain and predict the
dynamics of spiral waves in excitable media. In two landmark papers, Barkley
noticed that some of the behaviour could be explained by the inherent Euclidean
symmetry of these models. LeBlanc and Wulff then introduced forced Euclidean
symmetry-breaking (FESB) to the analysis, in the form of individual
translational symmetry-breaking (TSB) perturbations and rotational
symmetry-breaking (RSB) perturbations; in either case, it is shown that spiral
anchoring is a direct consequence of the FESB.
In this article, we provide a characterization of spiral anchoring when two
perturbations, a TSB term and a RSB term, are combined, where the TSB term is
centered at the origin and the RSB term preserves rotations by multiples of
, where is an integer. When
(such as in a modified bidomain model), it is shown that spirals
anchor at the origin, but when (such as in a planar
reaction-diffusion-advection system), spirals generically anchor away from the
origin.Comment: Revised versio
Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems
A comparative study of nonequilibrium dynamics in complex and real Ginzburg-Landau equations
Complex and real Ginzburg-Landau equations have been numerically studied by implementing Euler discretization technique. In addition to characterizing the differences and similarities of patterns involving these two continuum dynamical equations, in a wide range of appropriate parameter space, we have also made quantitative comparisons of growth dynamics in the two cases. In most part of the above-mentioned parameter space the complex Ginzburg-Landau equation exhibits frozen spiral dynamics. Results on the unlocking of this freezing are also presented
The Virtual Ventricular Wall: A Tool for Exploring Cardiac Propagation and Arrhythmogenesis
Methods for the experimental and clinical investigation of cardiac arrhythmias are limited to inferring propagation within the myocardium, from surface measurements, or from electrodes at a few sites within the cardiac wall. Biophysically and anatomically detailed computational models of cardiac tissues offer a powerful way for studying the electrical propagation processes and arrhythmias within the virtual heart. We use virtual tissues to study and visualise the effects of patho- and physiological conditions, and pharmacological interventions on transmural propagation in the virtual ventricular walls. Class III drug actions are quantitatively explained by changes induced in the transmural dispersion of action potential duration. We illustrate the automated construction of a virtual anisotropic ventricle from Diffusion Tensor MRI for individual hearts, and use it to explore mechanisms leading to ventricular fibrillation. The virtual ventricular wall provides an effective tool for exploring, evaluating and visualising processes during the initiation and maintenance of ventricular arrhythmias