Detailed publication list of Hervé Henry (home)

Table of contents:

1. Scroll and spiral waves in excitable media (go there)
   
2. Cardiac modelling: mechanism toward spiral waves (go there)
   
3. Crack propagation (go there)

Scroll ans spiral wave dynamic, instabilities (top, home)

Linear Stability of Scroll Waves

A full linear stability of a straight scroll wave in an excitable medium is presented. The five eigenmode branches which correspond to deformation in the third dimension of the five main modes of two-dimensional (2D) spiral dynamics are found to play a dominant role. Modulations in the third dimension have stabilizing or destabilizing effects on the different modes depending on the parameter regimes. For untwisted scroll waves, our numerical results confirm the relation between the long-wavelength behavior of the translation branches and 2D spiral drift in an external field but show no similar direct relation for the meander branches. The influence of twist on the different branches is investigated. In particular, the sproing instability is seen to arise from the twist induced deformation of the translation branches above a threshold twist.

Scroll waves in isotropic excitable media : linear instabilities, bifurcations and restabilized states

Scroll waves are three-dimensional analogs of spiral waves. The linear stability spectrum of untwisted and twisted scroll waves is computed for a two-variable reaction-diffusion model of an excitable medium. Different bands of modes are seen to be unstable in different regions of parameter space. The corresponding bifurcations and bifurcated states are characterized by performing direct numerical simulations. In addition, computations of the adjoint linear stability operator eigenmodes are also performed and serve to obtain a number of matrix elements characterizing the long-wavelength deformations of scroll waves.

Spiral wave drift in an electric field and scroll wave instabilities

I present the numerical computation of speed and direction of the drift of a spiral wave in an excitable medium in the presence of an electric field. In contrast to earlier results, the drift speed presents a strong variation close to the parameter value where the drift speed component along the field changes direction. Using a simple phenomenological model and results from a numerical linear stability analysis of scroll waves, I show this behavior can be attributed to a resonance of the meander modes with the translation modes of the spiral wave. Extending this phenomenological model to scroll waves also clarifies the link between the drift and long wavelength instabilities of scroll waves.

Wave nucleation rate in excitable systems in the low noise limit

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially-extended non-potential pair of equations driven by thermal (i.e. white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other non-equilibrium pattern-forming processes.

Cardiac Electrophysiology / modelling  (top, home)

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome.

Dynamics of conduction blocks in a model of paced cardiac tissue

We study numerically the dynamics of conduction blocks using a detailed electrophysiological model. We find that this dynamics depends critically on the size of the paced region. Small pacing regions lead to stationary conduction blocks while larger pacing regions can lead to conduction blocks that travel periodically towards the pacing region. We show that this size-dependence dynamics can lead to a novel arrhythmogenic mechanism. Furthermore, we show that the essential phenomena can be captured in a much simpler coupled-map model.

1. One dimensionnal alternans and onset of conduction block.
2. After a while conduction block disapear.
3. The time at which conduction block  disappear depends on the size of the pacing region: top and bottom are paced with 10 and 11 grid points respectively and the same stimulation protocol. movie.
   
4. Onset of spiral waves.

Crack propagation (top, home)

Dynamic instabilities of fracture under biaxial strain using a phase field model

We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under bi-axial load. Our model again reproduces well observed supercritical Hopf bifurcation, and is therefore the first simulation which does so.