The dynamics of three-dimensional scroll waves in excitable media

Keener, James P.

doi:10.1016/0167-2789(88)90080-2

Cited by 196 publications

(229 citation statements)

References 10 publications

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“…For more details, see Keener (1988). Later, in Biktashev et al (1994), it was shown that due to the symmetry of the scroll ring, the phase φ is the same everywhere on the ring and the torsion τ of the filament is zero.…”

Section: Perturbation Methodsmentioning

confidence: 98%

“…The filament dynamics was represented by coordinates along its length s and in normal p and binormal q directions yielding to V (s, p, q, t) = V 0 (r, θ + φ(s, t) − ωt) + V 1 + · · · (where r and θ are the polar coordinates in the plane p, q). Using the Frenet-Serret equations (Keener 1988) we can express the threedimensional Laplacian in terms of the coordinates s, p and q. We represent the three-dimensional space in the neighborhood of the filament using the coordinate representation X + pN + qB.…”

Section: Perturbation Methodsmentioning

confidence: 99%

“…Keener derived the equation of filament motion as a function of its curvature and twist (Keener 1988). In general, the equations resulting from the calculation show the evolution of the phase of rotation around the filament (φ), and the filament (X) evolution in the normal and binormal directions.…”

Section: Perturbation Methodsmentioning

confidence: 99%

“…As in the previous section, the theory predicts a linear dependence of the radius of the scroll ring on the curvature. The parameters D n = b 2 and D b = c 3 can be obtained by calculating the adjoint eigenfunctions of the linearization around a stable rotating scroll wave (Keener 1988). Note, however, that the finding of the adjoint solution is not trivial and they can be obtained mainly using numerical methods (Biktasheva et al 2010).…”

Section: Perturbation Methodsmentioning

confidence: 99%

“…It was also predicted that negative filament tension may result in turbulent behavior (Brazhnik et al 1987). Later, the dynamics of curved and twisted filaments was studied using a perturbation theory (Keener 1988). A further important advance was the numerical calculation of the linear stability spectrum of scroll waves and the characterization of the eigenmodes corresponding to the negative filament tension (Henry and Hakim 2000).…”

Section: Theory On Filament Dynamicsmentioning

confidence: 99%

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Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics

2012

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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.

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Section: Perturbation Methodsmentioning

confidence: 98%

Section: Perturbation Methodsmentioning

confidence: 99%

Section: Perturbation Methodsmentioning

confidence: 99%

Section: Perturbation Methodsmentioning

confidence: 99%

Section: Theory On Filament Dynamicsmentioning

confidence: 99%

See 3 more Smart Citations

Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics

2012

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Basic Mechanisms of Cardiac Arrhythmias

Jalife

Delmar

Anumonwo

et al. 2009

Basic Cardiac Electrophysiology for the Clinician

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Liquid Marble Photosensor

et al. 2019

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A liquid marble is a liquid droplet coated by a hydrophobic power. The liquid marble does not wet adjacent surfaces and therefore can be manipulated as a dry soft body. A Belousov-Zhabotinsky (BZ) reaction is an oscillatory chemical reaction exhibiting waves of oxidation. We demonstrate how to make a photo-sensor from BZ medium liquid marbles. We insert electrodes into a liquid marble, prepared from BZ solution and coated with polyethylene powder. The electrodes record a potential difference which oscillates due to oxidation wave-fronts crossing the electrodes. When the BZ marble is illuminated by a light source, the oxidation wave-fronts are hindered and, thus, the electrical potential recorded ceases to oscillate. We characterise several types of responses of BZ marble photosensors to various stimuli, and provide explanations of the recorded activity. BZ liquid marble photosensors may find applications in the fields of liquid electronics, soft robotics and unconventional computing.

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The dynamics of three-dimensional scroll waves in excitable media

Cited by 196 publications

References 10 publications

Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics

Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics

Basic Mechanisms of Cardiac Arrhythmias

Liquid Marble Photosensor

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