Publications by authors named "Vladimir Zykov"

Arrhythmia of the heart is a dangerous and potentially fatal condition. The current widely used treatment is the implantable cardioverter defibrillator (ICD), but it is invasive and affects the patient's quality of life. The sonogenetic mechanism proposed here focuses ultrasound on a cardiac tissue, controls endogenous stretch-activated Piezo1 ion channels on the focal region's cardiomyocyte sarcolemma, and restores normal heart rhythm.

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Self-organizing spiral electrical waves are produced in the heart during fatal cardiac arrhythmias. Controlling these waves is therefore an essential step in managing the disease. Here we present an effective method for controlling cardiac spiral waves using optogenetics.

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Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks.

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Lake Uchum is a newly defined meromictic lake in Siberia with clear seasonal changes in its mixolimnion. This study characterized the temporal dynamics and vertical profile of bacterial communities in oxic and anoxic zones of the lake across all four seasons: October (autumn), March (winter), May (spring), and August (summer). Bacterial richness and diversity in the anoxic zone varied widely between time points.

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We report experimental and numerical results on pattern formation of self-organizing Dictyostelium discoideum cells in a microfluidic setup under a constant buffer flow. The external flow advects the signaling molecule cyclic adenosine monophosphate (cAMP) downstream, while the chemotactic cells attached to the solid substrate are not transported with the flow. At high flow velocities, elongated cAMP waves are formed that cover the whole length of the channel and propagate both parallel and perpendicular to the flow direction.

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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 travelling both up and downstream.

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Many theoretical and experimental studies indicate that a propagation block represents an important factor in spiral wave initiation in excitable media. The analytical and numerical results we obtained for a generic two-component reaction-diffusion system demonstrate quantitative conditions for the propagation block in a one-dimensional and a two-dimensional medium due to a sharp spatial increase of the medium's excitability or the coupling strength above a certain critical value. Here, we prove that this critical value strongly depends on the medium parameters and the geometry of the inhomogeneity.

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Self-sustained waves of electrophysiological activity can cause arrhythmia in the heart. These reentrant excitations have been associated with spiral waves circulating around either an anatomically defined weakly conducting region or a functionally determined core. Recently, an ablation procedure has been clinically introduced that stops atrial fibrillation of the heart by destroying the electrical activity at the spiral core.

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The dynamics of traveling waves in a nonlinear dissipative system are studied analytically and numerically. Spatiotemporal forcing and feedback forcing are applied to the traveling waves in a phase-separated system undergoing chemical reactions. The stability of the traveling waves and interesting, unexpected behavior, including the reversal of the propagation direction are analyzed in one dimension.

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Two types of patterns rigidly rotating within a disk of a weakly excitable medium are studied using the free-boundary approach. The patterns are spots moving along the boundary of the disk and spiral waves rotating around the disk center. The study reveals a selection mechanism that uniquely determines the shape and the angular velocity of these patterns as a function of the medium excitability and the disk radius.

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A wave front interaction model is developed to describe the relationship between excitability and the size and shape of stabilized wave segments in a broad class of weakly excitable media. These wave segments of finite size are unstable but can be stabilized by feedback to the medium excitability; they define a separatrix between spiral wave behavior and contracting wave segments. Unbounded wave segments (critical fingers) lie on the asymptote of this separatrix, defining the boundary between excitable and subexcitable media.

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It is found that the dynamics of spiral waves subjected to global feedback is extremely sensitive to the domain shape. Bifurcations in the velocity field which specifies the resonant drift of the spiral wave core induced by global feedback are analyzed. It is shown, for example, that smooth variation of the eccentricity of an elliptical domain induces a cascade of bifurcations that can dramatically change the spiral wave evolution.

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The dynamics of spiral waves on a circular domain is studied by numerical integration of an excitable reaction-diffusion system with a global feedback. A theory based on the Fourier expansion of the feedback signal is developed to explain the existence and the stability of resonance attractors of spiral waves on domains of different sizes. The theoretical analysis predicts the existence of a discrete set of stable attractors with radii depending on the time delay in the feedback loop.

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During an experimental study of the resonance attractor for spiral waves in the light-sensitive Belousov-Zhabotinsky reaction, strong deviations of the attractor trajectories from circular orbits are observed if the time delay in the feedback loop becomes relatively long. A theory is developed that reduces the spiral wave dynamics under a long-delayed control to a higher order iterative map. Then the observed deviations are explained to be a result of instabilities appearing due to the Neimark bifurcation of the map.

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The effect of an external rhythm on rotating spiral waves in excitable media is investigated. Parameters of the unperturbed medium were chosen, such that the organizing spiral tip describes meandering (hypocyclic) trajectories, which are the most general shape for the experimentally observed systems. Periodical modulation of excitability in a model of the Belousov-Zhabotinsky (BZ) reaction forces meandering spiral tips to describe trajectories that are not found at corresponding stationary conditions.

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