202 research outputs found
An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum
Motivated by recent experimental studies, we derive and analyze a
twodimensional model for the contraction patterns observed in protoplasmic
droplets of Physarum polycephalum. The model couples a model of an active
poroelastic two-phase medium with equations describing the spatiotemporal
dynamics of the intracellular free calcium concentration. The poroelastic
medium is assumed to consist of an active viscoelastic solid representing the
cytoskeleton and a viscous fluid describing the cytosol. The model equations
for the poroelastic medium are obtained from continuum force-balance equations
that include the relevant mechanical fields and an incompressibility relation
for the two-phase medium. The reaction-diffusion equations for the calcium
dynamics in the protoplasm of Physarum are extended by advective transport due
to the flow of the cytosol generated by mechanical stresses. Moreover, we
assume that the active tension in the solid cytoskeleton is regulated by the
calcium concentration in the fluid phase at the same location, which introduces
a chemomechanical feedback. A linear stability analysis of the homogeneous
state without deformation and cytosolic flows exhibits an oscillatory Turing
instability for a large enough mechanochemical coupling strength. Numerical
simulations of the model equations reproduce a large variety of wave patterns,
including traveling and standing waves, turbulent patterns, rotating spirals
and antiphase oscillations in line with experimental observations of
contraction patterns in the protoplasmic droplets.Comment: Additional supplemental material is supplie
Reentry produced by small-scale heterogeneities in a discrete model of cardiac tissue
Reentries are reexcitations of cardiac tissue after the passing of an excitation wave which can cause
dangerous arrhythmias like tachycardia or life-threatening heart failures like fibrillation. The heart is formed by a
network of cells connected by gap junctions. Under ischemic conditions some of the cells lose their connections,
because gap junctions are blocked and the excitability is decreased. We model a circular region of the tissue where
a fraction of connections among individual cells are removed and substituted by non-conducting material in a twodimensional
(2D) discrete model of a heterogeneous excitable medium with local kinetics based on electrophysiology.
Thus, two neighbouring cells are connected (disconnected) with a probability f (1 - f). Such a region is assumed to be
surrounded by homogeneous tissue. The circular heterogeneous area is shown to act as a source of new waves which
reenter into the tissue and reexcitate the whole domain. We employ the Fenton-Karma equations to model the action potential for the local kinetics of the discrete nodes to study the statistics of the reentries in two dimensional networks
with different topologies. We conclude that the probability of reentry is determined by the proximity of the fraction of
disrupted connections between neighboring nodes (Peer ReviewedPostprint (published version
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
GVO Spanien: Genboom mit Folgen
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Zwei grosse Kleine treten ab
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