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Alternative stable scroll waves and conversion of autowave turbulence
A J Foulkes1, D Barkley, V N Biktashev
1Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, Liverpool L69 3BX, United Kingdom.
Chaos (Woodbury, N.Y.)
|January 5, 2011
Summary
This study reveals that alternative stable vortices in excitable media can transition between states, mimicking transitions from ventricular fibrillation (VF) to ventricular tachycardia (VT) through perturbations.
Area of Science:
- Computational biology
- Nonlinear dynamics
- Physiology
Background:
- Spiral and scroll waves (vortices) are fundamental phenomena in excitable media.
- The FitzHugh-Nagumo model is a widely used mathematical model for simulating excitable systems.
- Bistability between alternative stable vortices with distinct periods is observed.
Purpose of the Study:
- To investigate rotating spiral and scroll waves in the FitzHugh-Nagumo model.
- To analyze the filament tension of alternative stable vortices.
- To understand the dynamics and potential physiological relevance of these vortices.
Main Methods:
- Utilized the FitzHugh-Nagumo model for simulations.
- Employed response functions to predict filament tension.
- Performed direct numerical simulations to confirm predictions.
Main Results:
- Identified a parameter region with bistable vortices of distinct periods.
- Predicted and confirmed negative filament tension for slow-period scrolls and variable tension for fast-period scrolls.
- Demonstrated that slow-period scrolls resemble delayed after-depolarizations and can lead to turbulence (ventricular fibrillation).
- Showed that positive filament tension scrolls stabilize or collapse (monomorphic ventricular tachycardia).
Conclusions:
- Filament tension is a critical parameter determining vortex behavior.
- Perturbations can induce transitions between vortex states, mirroring clinical transitions between ventricular fibrillation and ventricular tachycardia.
- The study provides insights into the mechanisms underlying cardiac arrhythmias.
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