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External Excitation of Neurons Using Electric and Magnetic Fields in One- and Two-dimensional Cultures

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On interplay between excitability and geometry.

Andrew Adamatzky¹

¹Unconventional Computing Laboratory, University of the West of England, Bristol BS16 1QY, UK.

|November 23, 2019

Summary

Decreasing excitability in a medium causes localized wave fragments to emerge and propagate ballistically. This study numerically investigates excitation wave-front behavior in constrained geometries and random graphs, revealing excitability

Keywords:

Excitable medium FitzHugh–Nagumo model Wave-fronts

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Area of Science:

Complex Systems
Biophysics
Mathematical Biology

Background:

Excitable media exhibit wave propagation, typically circular or spiral, from local excitations.
Reduced excitability can lead to localized wave fragments propagating ballistically, deviating from standard behavior.

Purpose of the Study:

To numerically investigate the behavior of excitation wave-fronts in geometrically constrained media.
To analyze how excitation wave-fronts explore random planar graphs under varying excitability.
To understand the role of excitability in controlling wave propagation dynamics in complex environments.

Main Methods:

Numerical simulations using the FitzHugh-Nagumo model.
Analysis of excitation wave-front propagation in geometrically constrained environments and random planar graphs.

Main Results:

Excitability level dictates the transition from continuous wave propagation to fragmented, ballistic wave-fronts.
Wave propagation is significantly influenced by geometric constraints, including angled branches and sudden expansions.
Excitation wave patterns in random planar graphs are determined by the medium's excitability.

Conclusions:

Excitability is a critical parameter controlling the nature and exploration patterns of excitation waves.
Geometric constraints and graph topology interact with excitability to produce diverse wave propagation dynamics.
The findings provide insights into wave dynamics in complex biological and physical systems.