Analysis of complex excitation patterns using Feynman-like diagrams

Area of Science:

• Complex Systems Science
• Biophysics
• Non-linear Dynamics

Background:

• Excitable media, such as neural and cardiac tissues, exhibit complex self-organizing patterns.
• Wave breaks in these systems can lead to rotating patterns and turbulence, with mechanisms not fully understood.
• Classical phase singularity theory is challenged by observations of conduction block lines as phase discontinuities.

Purpose of the Study:

• To develop a theoretical framework for understanding complex dynamics in excitable systems.
• To identify fundamental building blocks governing pattern formation and transitions.
• To provide a unified language for analyzing excitation patterns.

Main Methods:

• Theoretical modeling using three quasiparticles: heads, tails, and pivots, termed 'cardions'.
• Computational simulations to observe cardion interactions and bound states.
• Experimental validation using optical voltage mapping on cultured human atrial myocytes (hiAMs).

Main Results:

• A theoretical framework based on cardions successfully captures rich dynamics in excitable systems.
• Cardions combine into at least four distinct bound states.
• Vortex pair creation and annihilation are explained as sequences of cardion dynamics, visualized using Feynman-diagram-like representations.

Conclusions:

• Cardions offer a new, unified language for analyzing dynamical transitions in excitation patterns.
• The framework provides mechanistic insights into complex pattern formation and behavior in excitable media.
• This approach enhances the theory and analysis of non-linear dynamics in biological and chemical systems.