The Stability of Spiral Waves

Introduction : An important role for the inwardly rectifying potassium current (I K1 ) has been postulated in controlling the stability and frequency of rotors responsible for ventricular tachycardia and fibrillation. We investigated the effects of Kir2.1 overexpression and Kir2.1AAA dominant-negative mutant suppression on the electrophysiology and inducibility, stability and frequency of spiral waves in an in vitro cardiac tissue model. Methods/Results : Neonatal rat ventricular myocytes (NRVMs) were transduced by lentiviral vectors encoding Kir2.1 or Kir2.1AAA. Immunostaining revealed Kir2.1 or mutant Kir2.1 protein overexpression and whole cell-clamp confirmed the predicted effects on I K1 , resting potential, and action potential duration (APD 80 ). Optical mapping was performed on confluent NRVM monolayers containing a 5 mm diameter central island of gene-modified NRVMs created by a stenciling technique. APs propagated with increased CV (25.1±2.7 cm/sec, n=7) and shortened APD 80 (73±11 msec, n=7) in islands of Kir2.1 overexpression, or decreased CV (13.1±1.1 cm/sec, n=7) and prolonged APD 80 (263±14 msec, n=7) in islands of Kir2.1AAA suppression, compared with normal CV and APD 80 of 19.2±0.4 cm/sec and 169±14 msec (n=7) in non-transduced islands. Reentry was initiated by rapid pacing. With Kir2.1 overexpression, reentrant waves anchored to the island and remained stable (89±15 minutes, n=3) with a frequency of 8±2 Hz. Superfusion with 0.5 mM BaCl 2 to block I K1 slowed reentry to 1 Hz and terminated it shortly after initiation. NRVM monolayers with islands of Kir2.1AAA suppression (n=3) displayed rapid spontaneous activity. Rapid pacing of these monolayers initiated an unstable figure-of-eight reentry (n=3) that degraded into single and multi-armed spiral waves, anchored to varying parts of the island with a maximum frequency of 2±1 Hz. Importantly, no reentry could be initiated in monolayers with non-transduced islands (n=3). Conclusion : Functional reentrant waves induced by rapid pacing are anchored to islands of localized Kir2.1 overexpression whereas they drop in frequency and meander in islands of dominant-negative suppression of Kir2.1, confirming the importance of I K1 for the stability of these waves in cardiac tissue.

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Cardiac electrical restitution properties and stability of reentrant spiral waves: a simulation study

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.1999.276.1.h269 ◽

1999 ◽

Vol 276 (1) ◽

pp. H269-H283 ◽

Cited By ~ 111

Author(s):

Zhilin Qu ◽

James N. Weiss ◽

Alan Garfinkel

Keyword(s):

Action Potential ◽

Antiarrhythmic Drugs ◽

Cardiac Tissue ◽

Potential Model ◽

Spiral Wave ◽

Spiral Waves ◽

Two Dimensional ◽

Recovery From Inactivation ◽

Main Determinants ◽

The Stability

Spiral wave breakup is a proposed mechanism underlying the transition from ventricular tachycardia to fibrillation. We examined the importance of the restitution of action potential duration (APD) and of conduction velocity (CV) to the stability of spiral wave reentry in a two-dimensional sheet of simulated cardiac tissue. The Luo-Rudy ventricular action potential model was modified to eliminate its restitution properties, which are caused by deactivation or recovery from inactivation of K+, Ca2+, and Na+ currents ( I K, I Ca, and I Na, respectively). In this model, we find that 1) restitution of I Ca and I Na are the main determinants of the steepness of APD restitution; 2) for promoting spiral breakup, the range of diastolic intervals over which the APD restitution slope is steep is more important than the maximum steepness; 3) CV restitution promotes spiral wave breakup independently of APD restitution; and 4) “defibrillation” of multiple spiral wave reentry is most effectively achieved by combining an antifibrillatory intervention based on altering restitution with an antitachycardia intervention. These findings suggest a novel paradigm for developing effective antiarrhythmic drugs.

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On the instability of viscous flow in a rapidly rotating pipe

Journal of Fluid Mechanics ◽

10.1017/s002211206900098x ◽

1969 ◽

Vol 35 (1) ◽

pp. 97-115 ◽

Cited By ~ 111

Author(s):

T. J. Pedley

Keyword(s):

Viscous Flow ◽

Bessel Functions ◽

Vortex Breakdown ◽

Reynolds Numbers ◽

Spiral Waves ◽

Wave Number ◽

Azimuthal Wave ◽

Inertial Instability ◽

Azimuthal Wave Number ◽

The Stability

The stability of almost fully developed viscous flow in a rotating pipe is considered. In cylindrical polar co-ordinates (r, ø, z) this flow has the velocity components\[ \{W_0o(1),\quad\Omega r[1+o(\epsilon)],\quad W_0[1-r^2/r^2_0+o(1)]\},_{+}^{+} \]where ε =Wo/2Ωr0and is bounded externally by the rigid cylinderr = r0, which rotates about its axis with angular velocity Ω. In the limit of small ε, the disturbance equations can be solved in terms of Bessel functions and it is shown that, in that limit, the flow is unstable for Reynolds numbersR=Wor0/vgreater thanRc[asymp ] 82[sdot ]9. The unstable disturbances take the form of growing spiral waves, which are stationary relative to the rotating cylinder and the critical disturbance atR = Rchas azimuthal wave-number 1 and axial wavelength 2πr0/ε. Furthermore, it is shown that the most rapidly growing disturbance forR > Rchas an azimuthal wave-number which increases withR. Some of the problems involved in testing the results by experiment are discussed and a possible application to the theory of vortex breakdown is mentioned. In an appendix this instability is shown to be an example of inertial instability.

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Parasites and Pattern Formation

Zeitschrift für Naturforschung A ◽

10.1515/zna-1999-0209 ◽

1999 ◽

Vol 54 (2) ◽

pp. 146-152 ◽

Cited By ~ 3

Author(s):

J. Ackermann ◽

T. Kirner

Keyword(s):

Pattern Formation ◽

Flow Reactor ◽

Spiral Waves ◽

Cooperative Interaction ◽

Biological Information ◽

Parameter Region ◽

Parasitic Species ◽

Model Complex ◽

Complex Patterns ◽

The Stability

Abstract Biological information is coded in replicating molecules. To maintain a given amount of in-formation a cooperative interaction between these molecules is essential. The main problem for the stability of a system of prebiotic replicators are emerging parasites. Stabilization against such parasites is possible if space is introduced in the model. Complex patterns like spiral waves and self-replicating spot patterns have been shown to stabilize such systems. Stability of replicating systems, however, occurs only in parameter regions were such complex patterns occur. We show that parasites are able to push such systems into a parameter region were life is possible. To demonstrate this influence of parasites on such systems, we introduce a parasitic species in the Gray-Scott model. The growing concentration of parasites will kill the system, and the cooperative Gray-Scott system will be diluted out in a well mixed flow reactor. While considering space, in the model stabilizing pattern formation in a narrow parameter region is possible. We demonstrate that the concentration of the parasitic species is able to push the system into a region were stabilizing patterns emerge.

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Open discussion

Symposium - International Astronomical Union ◽

10.1017/s0074180900029533 ◽

1982 ◽

Vol 99 ◽

pp. 605-613

Author(s):

P. S. Conti

Keyword(s):

Buenos Aires ◽

Large Mass ◽

List Type ◽

Common Phenomenon ◽

Open Discussion ◽

The Stability ◽

Ring Nebulae

Conti: One of the main conclusions of the Wolf-Rayet symposium in Buenos Aires was that Wolf-Rayet stars are evolutionary products of massive objects. Some questions:–Do hot helium-rich stars, that are not Wolf-Rayet stars, exist?–What about the stability of helium rich stars of large mass? We know a helium rich star of ∼40 MO. Has the stability something to do with the wind?–Ring nebulae and bubbles : this seems to be a much more common phenomenon than we thought of some years age.–What is the origin of the subtypes? This is important to find a possible matching of scenarios to subtypes.

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Symmetric Multistep Methods Revisited: II. Numerical Experiments

International Astronomical Union Colloquium ◽

10.1017/s0252921100031602 ◽

1999 ◽

Vol 173 ◽

pp. 309-314 ◽

Cited By ~ 3

Author(s):

T. Fukushima

Keyword(s):

Multistep Methods ◽

Computational Time ◽

Integration Time ◽

Implicit Methods ◽

Symmetric Methods ◽

Celestial Bodies ◽

The Stability ◽

Predictor Corrector ◽

Symmetric Multistep Methods ◽

Integration Errors

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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Uniformity of Magnification from Different Electron Microscopes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100060179 ◽

1967 ◽

Vol 25 ◽

pp. 32-33

Author(s):

Godfrey C. Hoskins ◽

V. Williams ◽

V. Allison

Keyword(s):

Diffraction Grating ◽

The Other ◽

Carbon Replica ◽

Electron Microscopes ◽

The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

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Effect of Improved ThO2 Particle Dispersion in Nickel on High-Temperature Strength

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100069211 ◽

1970 ◽

Vol 28 ◽

pp. 444-445

Author(s):

E. R. Kimmel ◽

H. L. Anthony ◽

W. Scheithauer

Keyword(s):

High Temperature ◽

Metal Matrix ◽

Oxide Particle ◽

Oxide Phase ◽

Dislocation Motion ◽

Particle Dispersion ◽

High Temperature Strength ◽

Strengthening Effect ◽

Oxide Particles ◽

The Stability

The strengthening effect at high temperature produced by a dispersed oxide phase in a metal matrix is seemingly dependent on at least two major contributors: oxide particle size and spatial distribution, and stability of the worked microstructure. These two are strongly interrelated. The stability of the microstructure is produced by polygonization of the worked structure forming low angle cell boundaries which become anchored by the dispersed oxide particles. The effect of the particles on strength is therefore twofold, in that they stabilize the worked microstructure and also hinder dislocation motion during loading.

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