Analysis of complex excitation patterns using Feynman-like diagrams

Scientific Reports, vol. 14, pp. 28962

Abstract

Many extended chemical and biological systems self-organise into complex patterns that drive the medium behaviour in a non-linear fashion. An important class of such systems are excitable media, including neural and cardiac tissues. In extended excitable media, wave breaks can form rotating patterns and turbulence. However, the onset, sustaining and elimination of such complex patterns is currently incompletely understood. The classical theory of phase singularities in excitable media was recently challenged, as extended lines of conduction block were identified as phase discontinuities. Here, we provide a theoretical framework that captures the rich dynamics in excitable systems in terms of three quasiparticles: heads, tails, and pivots. We propose to call these quasiparticles 'cardions'. In simulations and experiments, we show that these basic building blocks combine into at least four different bound states. By representing their interactions similarly to Feynman diagrams in physics, the creation and annihilation of vortex pairs are shown to be sequences of dynamical creation, annihilation, and recombination of the identified quasiparticles. We draw such diagrams for numerical simulations, as well as optical voltage mapping experiments performed on cultured human atrial myocytes (hiAMs). Our results provide a new, unified language for a more detailed theory, analysis, and mechanistic insights of dynamical transitions in excitation patterns.

Authors 3

1. Louise Arno

   KU Leuven

   Affiliation as printed

   Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Etienne Sabbelaan 53, 8500, Kortrijk, Belgium

   iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Oude Markt 13, 3000, Leuven, Belgium

2. Desmond Kabus Aachen Laboratory of Experimental Cardiology

   KU Leuven · Leiden University Medical Center

   Affiliation as printed

   Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Etienne Sabbelaan 53, 8500, Kortrijk, Belgium

   Laboratory of Experimental Cardiology, Leiden University Medical Center (LUMC), Albinusdreef 2, 2333 ZA, Leiden, The Netherlands

   iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Oude Markt 13, 3000, Leuven, Belgium

3. Hans Dierckx

   KU Leuven

   Affiliation as printed

   Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Etienne Sabbelaan 53, 8500, Kortrijk, Belgium. dr.h.dierckx@gmail.com

   iSi Health, Institute of Physics-based Modeling for In Silico Health, KU Leuven, Oude Markt 13, 3000, Leuven, Belgium. dr.h.dierckx@gmail.com

   Department of Mathematics, KU Leuven Campus Kortrijk (KULAK), Etienne Sabbelaan 53, 8500, Kortrijk, Belgium