1,508 research outputs found
Nonlinear physics of electrical wave propagation in the heart: a review
The beating of the heart is a synchronized contraction of muscle cells
(myocytes) that are triggered by a periodic sequence of electrical waves (action
potentials) originating in the sino-atrial node and propagating over the atria and
the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF)
or ventricular tachycardia (VT) are caused by disruptions and instabilities of these
electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent
wave patterns (AF,VF). Numerous simulation and experimental studies during the
last 20 years have addressed these topics. In this review we focus on the nonlinear
dynamics of wave propagation in the heart with an emphasis on the theory of pulses,
spirals and scroll waves and their instabilities in excitable media and their application
to cardiac modeling. After an introduction into electrophysiological models for action
potential propagation, the modeling and analysis of spatiotemporal alternans, spiral
and scroll meandering, spiral breakup and scroll wave instabilities like negative line
tension and sproing are reviewed in depth and discussed with emphasis on their impact
in cardiac arrhythmias.Peer ReviewedPreprin
Migraine aura: retracting particle-like waves in weakly susceptible cortex
Cortical spreading depression (SD) has been suggested to underlie migraine aura. Despite a precise match in speed, the spatio-temporal patterns of SD and aura symptoms on the cortical surface ordinarily differ in aspects of size and shape. We show that this mismatch is reconciled by utilizing that both pattern types bifurcate from an instability point of generic reaction-diffusion models. To classify these spatio-temporal pattern we suggest a susceptibility scale having the value [sigma]=1 at the instability point. We predict that human cortex is only weakly susceptible to SD ([sigma]<1), and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. We discuss the increased dynamical repertoire of cortical tissue close to [sigma]=1, in particular, the resulting implications on migraine pharmacology that is hitherto tested in the regime ([sigma]>>1), and potentially silent aura occurring below a second bifurcation point at [sigma]=0 on the susceptible scale
Self-organizing propagation patterns from dynamic self-assembly in monolayers
Propagation of localized orientational waves, as imaged by Brewster angle microscopy, is induced by low intensity linearly polarized light inside axisymmetric smectic-C confined domains in a photosensitive molecular thin film at the air/water interface (Langmuir monolayer). Results from numerical simulations of a model that couples photoreorientational effects and long-range elastic forces are presented. Differences are stressed between our scenario and the paradigmatic wave phenomena in excitable chemical media
Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics
Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh-Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue
Three-Dimensional Autonomous Pacemaker in the Photosensitive Belousov-Zhabotinsky medium
In experiments with the photosensitive Belousov-Zhabotinsky reaction (PBZR)
we found a stable three-dimensional organizing center that periodically emits
trigger waves of chemical concentration. The experiments are performed in a
parameter regime with negative line tension using an open gel reactor to
maintain stationary non-equilibrium conditions. The observed periodic wave
source is formed by a scroll ring stabilized due to its interaction with a
no-flux boundary. Sufficiently far from the boundary, the scroll ring expands
and undergoes the negative line tension instability before it finally develops
into scroll wave turbulence. Our experimental results are reproduced by
numerical integration of the modified Oregonator model for the PBZR. Stationary
and breathing self-organized pacemakers have been found in these numerical
simulations. In the latter case, both the radius of the scroll ring and the
distance of its filament plane to the no-flux boundary after some transient
undergo undamped stable limit cycle oscillations. So far, in contrary to their
stationary counterpart, the numerically predicted breathing autonomous
pacemaker has not been observed in the chemical experiment
Effects of external global noise on the catalytic CO oxidation on Pt(110)
Oxidation reaction of CO on a single platinum crystal is a reaction-diffusion
system that may exhibit bistable, excitable, and oscillatory behavior. We
studied the effect of a stochastic signal artificially introduced into the
system through the partial pressure of CO. First, the external signal is
employed as a turbulence suppression tool, and second, it modifies the
boundaries in the bistable transition between the CO and oxygen covered phases.
Experiments using photoemission electron microscopy (PEEM) together with
numerical simulations performed with the Krischer-Eiswirth-Ertl (KEE) model are
presented.Comment: 15 pages, 7 figures, accepted in J. Chem. Phy
Convective Instability and Boundary Driven Oscillations in a Reaction-Diffusion-Advection Model
In a reaction-diffusion-advection system, with a convectively unstable
regime, a perturbation creates a wave train that is advected downstream and
eventually leaves the system. We show that the convective instability coexists
with a local absolute instability when a fixed boundary condition upstream is
imposed. This boundary induced instability acts as a continuous wave source,
creating a local periodic excitation near the boundary, which initiates waves
traveling both up and downstream. To confirm this, we performed analytical
analysis and numerical simulations of a modified Martiel-Goldbeter
reaction-diffusion model with the addition of an advection term. We provide a
quantitative description of the wave packet appearing in the convectively
unstable regime, which we found to be in excellent agreement with the numerical
simulations. We characterize this new instability and show that in the limit of
high advection speed, it is suppressed. This type of instability can be
expected for reaction-diffusion systems that present both a convective
instability and an excitable regime. In particular, it can be relevant to
understand the signaling mechanism of the social amoeba Dictyostelium
discoideum that may experience fluid flows in its natural habitat.Comment: 10 pages, 13 figures, published in Chaos: An Interdisciplinary
Journal of Nonlinear Scienc
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