Nucleation and Collapse of Scroll Rings in Excitable Media

Bánsági, Tamás; Steinbock, Oliver

doi:10.1103/physrevlett.97.198301

Cited by 48 publications

(41 citation statements)

References 25 publications

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“…Notice that in 3D most global perturbations (e.g., heat and light) are affected by undesired gradients and/or temporal delays. It will hence be interesting to extend our studies to systems such as the three-dimensional BZ reaction or three-dimensional samples of cardiac tissue [3,35]. However, one can expect that the response of vortices (scroll waves) in these systems is more complicated as spiral rotation occurs around one-dimensional filaments rather than the pseudo-one dimensional core region of the vortex.…”

Section: Discussionmentioning

confidence: 99%

Spiral defect drift in the wave fields of multiple excitation patterns

Dutta

Steinbock

2011

Phys. Rev. E

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Spiral waves in excitable systems decay to drifting defects if forced by high-frequency wave trains. Using the Barkley model, we analyze the drift velocity in planar wave trains as a function of wave frequency. Within two antiparallel, planar wave trains of equal frequency a defect is pushed into the collision region where it stops. Within two circular wave fields, however, it continues its drift in a direction perpendicular to the axis connecting the pacemakers. Depending on the forcing frequency and the initial position, this motion occurs either away from or towards the pacemaker axis. Three circular wave fields can be used to position the defect at a unique point close to the center of the pacemaker triangle. The results are also observed in experiments with the Belousov-Zhabotinsky reaction.

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Section: Discussionmentioning

confidence: 99%

Spiral defect drift in the wave fields of multiple excitation patterns

Dutta

Steinbock

2011

Phys. Rev. E

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“…For beautiful experimental results based on computer tomography see [BS06]. For numerical simulations in an excitable media reaction-diffusion setting see [FM00], for example, and the references there.…”

Section: Discussionmentioning

confidence: 99%

Spiral wave dynamics: Reaction and diffusion versus kinematics

Fiedler

Georgi

Jangle

2007

Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology

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In nature, spatio-temporal patterns in excitable media occur in seemingly unlimited variety. As early as 1946 Wiener and Rosenblueth [WR46] introduced the concept of excitable media to explain the propagation of electrical excitation fronts in the heart. Waves of electrical activity in the heart muscle assist its rhythmic contractions. The presence of spiral waves can indicate dangerous fibrillation. This is one of the motivations why the dynamics and control of spiral waves are studied. Furthermore spiral waves are typical, almost ubiquitous, patterns in excitable media; see [ZE06] in this volume. Mathematically, self-organized spiral patterns are a striking phenomenon of reaction-diffusion systems, in its own right, motivated by a large variety of application areas.Slime mold aggregation is another example. As long as food in form of bacteria is present the slime mold cells live independently in the soil. As food becomes rare they form a multicellular "organism". This "organism" moves in order to find appropriate conditions for production and dispersal of spores. During the early phase of aggregation, chemotactic movement can proceed in form of spiral waves [FL98].Spiral waves also arise in the oxidation of carbon-monoxide on platinum surfaces [BM03]. In 1972 they have been dicovered by Winfree [Win72] in the photosensitive Belousov-Zhabotinsky (BZ) reaction, see for recent investigations for example [ZBB + 03, ZBB + 04, ZE04]. Both reactions are studied in the SFB 555. The classical BZ reaction is a catalytic oxidation of malonic acid, using bromate in an acidic environment. Experimentally it exhibits well reproducible drift, meander and "chaotic" motions of the spiral wave and its tip.In several experiments and numerical simulations, transitions from rigidly rotating spiral waves to other more complicated waves have been observed. The dynamics near rigidly rotating waves and their transition to meandering and drifting spirals has been studied extensively; see, for instance

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“…Both layers are chemically identical and con- Ultra-pure water with a resistivity of 18.2 MΩ cm is used to prepare all the solutions as well as the BZ gels. Notice that this BZ system has positive filament tension [26] and accordingly all free scroll rings shrink and vanish in finite time. The vortex pinning heterogeneity is a rigid, hexagonal mesh made of a black, non-reactive polymer of thickness 1.1 mm.…”

Section: Experimental Methodsmentioning

confidence: 99%

Pinning of scroll waves to flat and highly branched unexcitable heterogeneities

2017

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System heterogeneities such as organelles, cells, and anatomical features strongly affect nonlinear wave patterns in biological systems. These effects are more readily studied in otherwise homogeneous chemical reactions that allow the introduction of tailored structures. Following this approach, we investigate the dynamics of three-dimensional excitation vortices pinned to inert sheets with circular holes arranged on a hexagonal lattice. Experiments with the Belousov-Zhabotinsky reaction and numerical simulations of an excitable reaction-diffusion model reveal vortex pinning that circumvents the rapid collapse of free vortex rings. The pinned scroll waves are affected by the topological mismatch between their loop-like rotation backbone and the branched pinning structure. Depending on the initial condition, a multitude of stable vortex states exist all of which obey topological constraints suggesting spin-like states for the involved obstacle holes.

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Nucleation and Collapse of Scroll Rings in Excitable Media

Cited by 48 publications

References 25 publications

Spiral defect drift in the wave fields of multiple excitation patterns

Spiral defect drift in the wave fields of multiple excitation patterns

Spiral wave dynamics: Reaction and diffusion versus kinematics

Pinning of scroll waves to flat and highly branched unexcitable heterogeneities

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