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Stabilization of collapsing scroll waves in systems with random heterogeneities.

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Filaments in reaction-diffusion systems can collapse or persist by pinning to non-reactive objects. Sphere size and arrangement influence filament dynamics, with implications for excitable tissues like cardiac muscle.

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Area of Science:

  • * Biophysics
  • * Computational Biology
  • * Nonlinear Dynamics

Background:

  • * Excitation waves in three-dimensional reaction-diffusion systems can exhibit complex dynamics.
  • * Phase singularities, termed filaments, can form and rotate around these waves.
  • * Closed filaments typically shrink and collapse over time.

Purpose of the Study:

  • * To investigate the effect of non-reactive objects on the dynamics of circular filaments in reaction-diffusion systems.
  • * To understand how the arrangement, size, and number of objects influence filament pinning and collapse.
  • * To provide insights into the behavior of scroll waves in excitable biological tissues.

Main Methods:

  • * Numerical simulations of three-dimensional reaction-diffusion systems.
  • * Modeling of circular filaments interacting with non-reactive spherical objects.
  • * Analysis of filament dynamics, including contraction, pinning, and detachment.

Main Results:

  • * Filaments interact with non-reactive spheres, leading to pinning or detachment.
  • * The likelihood of filament pinning generally increases with the number and size of spheres.
  • * Exceptions exist, where small spheres can support filaments, and large spheres may not prevent passage.
  • * Filament contraction rate is reduced when pinned to spheres.

Conclusions:

  • * Non-reactive objects significantly alter filament dynamics in reaction-diffusion systems.
  • * Filament pinning to objects can stabilize or indefinitely sustain filaments, preventing collapse.
  • * Findings offer valuable insights into the role of obstacles, like scar tissue, in cardiac arrhythmias.