Spiral waves in excitable media with negative restitution

Area of Science:

• Computational Physics
• Biophysics
• Mathematical Biology

Background:

• Spiral waves are crucial patterns in excitable media, relevant to phenomena like cardiac arrhythmias.
• Negative restitution, a property where repolarization time shortens with preceding longer action potentials, can influence wave dynamics.
• Understanding these dynamics is key to addressing cardiac instabilities.

Purpose of the Study:

• To numerically investigate the impact of negative restitution on spiral wave dynamics in excitable media.
• To explore the critical slope of the restitution curve that triggers significant changes in spiral wave behavior.
• To assess the potential link between observed instabilities and cardiac fibrillation.

Main Methods:

• Numerical simulations using two distinct models: a cellular automaton and a reaction-diffusion model.
• Systematic variation of the negative restitution parameter, specifically the slope of the restitution curve.
• Analysis of spiral wave behavior, including stability, breakup, and pattern formation.

Main Results:

• No significant effects on spiral wave dynamics were observed for restitution curve slopes less steep than -1.
• Slopes steeper than -1 led to significant changes: average restitution time shifted to approximately -1 slope, and spiral waves broke up.
• Turbulent patterns emerged in media with steeper negative restitution slopes.

Conclusions:

• Negative restitution with slopes steeper than -1 can destabilize spiral waves in excitable media.
• The observed spiral wave breakup and turbulence may offer insights into the mechanisms of cardiac fibrillation.
• Further research is warranted to fully elucidate the role of negative restitution in cardiac electrophysiology.