5,045 research outputs found
Oscillations and traveling waves of calcium: a simplified model
We construct a heuristic model of calcium oscillations in pancreatic acinar cells. The model is
based on the two-state model of Sneyd et al. (Sneyd, J., A. LeBeau and D. Yule, 2000, Traveling
waves of calcium in pancreatic acinar cells: model construction and bifurcation analysis, Physica D,
in press) and is similar in spirit to the FitzHugh reduction of the Hodgkin-Huxley equations. The
simpliÂŻed model successfully reproduces the oscillatory behavior and wave behaviour of the more
complex model. In particular, the simpliÂŻed model provides an example of a simple, physiologically
relevant model that has a T-point and an associated spiral branch of homoclinic orbits
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
On polymorphic logical gates in sub-excitable chemical medium
In a sub-excitable light-sensitive Belousov-Zhabotinsky chemical medium an
asymmetric disturbance causes the formation of localized traveling
wave-fragments. Under the right conditions these wave-fragment can conserve
their shape and velocity vectors for extended time periods. The size and life
span of a fragment depend on the illumination level of the medium. When two or
more wave-fragments collide they annihilate or merge into a new wave-fragment.
In computer simulations based on the Oregonator model we demonstrate that the
outcomes of inter-fragment collisions can be controlled by varying the
illumination level applied to the medium. We interpret these wave-fragments as
values of Boolean variables and design collision-based polymorphic logical
gates. The gate implements operation XNOR for low illumination, and it acts as
NOR gate for high illumination. As a NOR gate is a universal gate then we are
able to demonstrate that a simulated light sensitive BZ medium exhibits
computational universality
Chaos at the border of criticality
The present paper points out to a novel scenario for formation of chaotic
attractors in a class of models of excitable cell membranes near an
Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics
admits a simple and visual description in terms of the families of
one-dimensional first-return maps, which are constructed using the combination
of asymptotic and numerical techniques. The bifurcation structure of the
continuous system (specifically, the proximity to a degenerate AHB) endows the
Poincare map with distinct qualitative features such as unimodality and the
presence of the boundary layer, where the map is strongly expanding. This
structure of the map in turn explains the bifurcation scenarios in the
continuous system including chaotic mixed-mode oscillations near the border
between the regions of sub- and supercritical AHB. The proposed mechanism
yields the statistical properties of the mixed-mode oscillations in this
regime. The statistics predicted by the analysis of the Poincare map and those
observed in the numerical experiments of the continuous system show a very good
agreement.Comment: Chaos: An Interdisciplinary Journal of Nonlinear Science
(tentatively, Sept 2008
Spontaneous spiking in an autaptic Hodgkin-Huxley set up
The effect of intrinsic channel noise is investigated for the dynamic
response of a neuronal cell with a delayed feedback loop. The loop is based on
the so-called autapse phenomenon in which dendrites establish not only
connections to neighboring cells but as well to its own axon. The biophysical
modeling is achieved in terms of a stochastic Hodgkin-Huxley model containing
such a built in delayed feedback. The fluctuations stem from intrinsic channel
noise, being caused by the stochastic nature of the gating dynamics of ion
channels. The influence of the delayed stimulus is systematically analyzed with
respect to the coupling parameter and the delay time in terms of the interspike
interval histograms and the average interspike interval. The delayed feedback
manifests itself in the occurrence of bursting and a rich multimodal interspike
interval distribution, exhibiting a delay-induced reduction of the spontaneous
spiking activity at characteristic frequencies. Moreover, a specific
frequency-locking mechanism is detected for the mean interspike interval.Comment: 8 pages, 10 figure
Multiple firing coherence resonances in excitatory and inhibitory coupled neurons
The impact of inhibitory and excitatory synapses in delay-coupled
Hodgkin--Huxley neurons that are driven by noise is studied. If both synaptic
types are used for coupling, appropriately tuned delays in the inhibition
feedback induce multiple firing coherence resonances at sufficiently strong
coupling strengths, thus giving rise to tongues of coherency in the
corresponding delay-strength parameter plane. If only inhibitory synapses are
used, however, appropriately tuned delays also give rise to multiresonant
responses, yet the successive delays warranting an optimal coherence of
excitations obey different relations with regards to the inherent time scales
of neuronal dynamics. This leads to denser coherence resonance patterns in the
delay-strength parameter plane. The robustness of these findings to the
introduction of delay in the excitatory feedback, to noise, and to the number
of coupled neurons is determined. Mechanisms underlying our observations are
revealed, and it is suggested that the regularity of spiking across neuronal
networks can be optimized in an unexpectedly rich variety of ways, depending on
the type of coupling and the duration of delays.Comment: 7 two-column pages, 6 figures; accepted for publication in
Communications in Nonlinear Science and Numerical Simulatio
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