3,201 research outputs found
Pulse propagation in discrete systems of coupled excitable cells
Propagation of pulses in myelinated fibers may be described by appropriate
solutions of spatially discrete FitzHugh-Nagumo systems. In these systems,
propagation failure may occur if either the coupling between nodes is not
strong enough or the recovery is too fast. We give an asymptotic construction
of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with
numerical simulations and discuss evolution of initial data into pulses and
pulse generation at a boundary. Formulas for the speed and length of pulses are
also obtained.Comment: 16 pages, 10 figures, to appear in SIAM J. Appl. Mat
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
Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
We study the problem of initiation of excitation waves in the FitzHugh-Nagumo
model. Our approach follows earlier works and is based on the idea of
approximating the boundary between basins of attraction of propagating waves
and of the resting state as the stable manifold of a critical solution. Here,
we obtain analytical expressions for the essential ingredients of the theory by
singular perturbation using two small parameters, the separation of time scales
of the activator and inhibitor, and the threshold in the activator's kinetics.
This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2
Equation-free modeling of evolving diseases: Coarse-grained computations with individual-based models
We demonstrate how direct simulation of stochastic, individual-based models
can be combined with continuum numerical analysis techniques to study the
dynamics of evolving diseases. % Sidestepping the necessity of obtaining
explicit population-level models, the approach analyzes the (unavailable in
closed form) `coarse' macroscopic equations, estimating the necessary
quantities through appropriately initialized, short `bursts' of
individual-based dynamic simulation. % We illustrate this approach by analyzing
a stochastic and discrete model for the evolution of disease agents caused by
point mutations within individual hosts. % Building up from classical SIR and
SIRS models, our example uses a one-dimensional lattice for variant space, and
assumes a finite number of individuals. % Macroscopic computational tasks
enabled through this approach include stationary state computation, coarse
projective integration, parametric continuation and stability analysis.Comment: 16 pages, 8 figure
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