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Spiral wave dynamics in excitable media with spherical geometries
Katrin Rohlf1, Leon Glass, Raymond Kapral
1Department of Mathematics, Ryerson University, 350 Victoria Street, Toronto, Ontario M5B 2K3, Canada.
Chaos (Woodbury, N.Y.)
|October 4, 2006
Summary
This study explores spiral wave dynamics in spherical shells and spheres, revealing how medium excitability and geometry influence wave organization. Findings offer insights into wave patterns in systems like the heart and chemical reactions.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Computational Physics
Background:
- Spiral and scroll waves are complex spatiotemporal patterns observed in various excitable media.
- Understanding their organization is crucial for fields ranging from cardiac physiology to chemical kinetics.
- Previous studies often focused on planar geometries, limiting insights into curved surfaces.
Purpose of the Study:
- To investigate the spatial and temporal organization of spiral and scroll waves in spherical geometries (shells and solid spheres).
- To analyze the influence of medium excitability, domain topology, and size on wave dynamics and clustering.
- To compare wave behavior in spherical systems with that in planar two-dimensional media.
Main Methods:
- Computational simulations were employed to model the evolution of spiral and scroll waves.
- System parameters, including medium excitability and domain geometry, were systematically varied.
- Results from spherical simulations were contrasted with those from equivalent planar systems.
Main Results:
- The excitability of the medium significantly impacts the dynamics and clustering of spiral waves.
- Spherical topology and size impose specific restrictions on the spatial organization of single and multi-armed spiral waves.
- Distinct differences in wave dynamics were observed between spherical and planar geometries.
Conclusions:
- The geometry of the medium plays a critical role in dictating spiral and scroll wave organization.
- These findings enhance our understanding of wave propagation in curved biological and chemical systems.
- The study provides a foundation for further research into complex wave phenomena in non-planar domains.
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