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Modelling morphogenetic processes in excitable media using novel cellular automata.

M Markus1

  • 1Max-Planck-Institut für Ernährungsphysiologie, Dortmund, FRG.

Biomedica Biochimica Acta
|January 1, 1990
PubMed
Summary
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This study introduces novel cellular automata with randomly distributed elements, overcoming anisotropy issues in simulating excitable media. The model accurately replicates complex wave patterns observed in biological systems and chemical reactions.

Area of Science:

  • Computational Biology
  • Nonlinear Dynamics
  • Biophysics

Background:

  • Cellular automata offer an efficient alternative to partial differential equations for simulating excitable media.
  • Existing cellular automata models exhibit anisotropy, leading to wave shapes dependent on cell geometry.

Purpose of the Study:

  • To develop an anisotropic-free cellular automaton model for simulating excitable media.
  • To validate the model against experimental observations in various biological and chemical systems.

Main Methods:

  • A novel cellular automaton model based on a random distribution of excitable elements was developed.
  • The model was parameterized with a minimal set of three parameters.
  • An extension with two additional parameters was used to derive a dispersion relation.

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Main Results:

  • The model successfully generated target patterns, spirals, rotating waves around holes, and turbulence.
  • Simulated wave behaviors, including a linear eikonal equation, matched experimental data from the Belousov-Zhabotinskii reagent, heart muscle, cerebral cortex, and slime mold.
  • Three-dimensional scroll waves were simulated, consistent with experimental findings.
  • An extended model produced a dispersion relation comparable to experimental and partial differential equation analyses.

Conclusions:

  • The proposed random-distribution cellular automaton effectively simulates anisotropic-free wave propagation in excitable media.
  • This model provides a versatile and accurate tool for studying complex phenomena in biological and chemical systems.
  • The model's ability to reproduce diverse wave patterns highlights its potential for further research in nonlinear dynamics and computational biology.