arXiv subjects

Desmond Kabus

Publications and source records attributed to Desmond Kabus.

4 recordsLinked to original sources

arXiv2025

Microscopic Variability Alters Macroscopic Rotation Speed in Stochastic Spiral Waves

We present a general theory for noise-induced corrections to the angular velocity of spiral waves. Stochasticity produces two second-order effects: an instantaneous term from heterogeneity that always slows rotation, and an orbital-drift term from temporal fluctuations that can either accelerate or decelerate it. For our parameters, orbital drift is weaker, producing a net slowdown. Analytical predictions match Barkley-model simulations with temporal noise. Examination of additional noise types in silico confirms angular velocity slowing. This mechanism provides a robust route by which stochasticity reshapes spiral dynamics in excitable media, with direct implications for arrhythmias and neural wave propagation.

nlin.PS↗

arXiv2024

Strings, branes and twistons: topological analysis of phase defects in excitable media such as the heart

Several excitable systems, such as the heart, self-organize into complex spatio-temporal patterns that involve wave collisions, wave breaks, and rotating vortices, of which the dynamics are incompletely understood. Recently, conduction block lines in two-dimensional media were recognized as phase defects, on which quasi-particles can be defined. These particles also form bound states, one of which corresponds to the classical phase singularity. Here, we relate the quasi-particles to the structure of the dynamical attractor in state space and extend the framework to three spatial dimensions. We reveal that 3D excitable media are governed by phase defect surfaces, i.e. branes, and three flavors of topologically preserved curves, i.e. strings: heads, tails, and pivot curves. We identify previously coined twistons as points of co-dimension three at the crossing of a head curve and a pivot curve. Our framework predicts splitting and branching phase defect surfaces that can connect multiple classical filaments, thereby proposing a new mechanism for the origin, perpetuation, and control of complex excitation patterns, including cardiac fibrillation.

nlin.PS↗

arXiv2023

Analysis of complex excitation patterns using Feynman-like diagrams

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.

q-bio.OT↗

arXiv2023

Scroll Waves and Filaments in excitable Media of higher spatial Dimension

Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic or electrical scroll waves in the heart. Here we show that such phenomena can be extended to a space of four or more dimensions and propose that connections of excitable elements in a network setting can be regarded as additional spatial dimensions. Numerical simulations are performed in four dimensions using the FitzHugh-Nagumo model, showing that the vortices rotate around a two-dimensional surface which we define as the superfilament. Evolution equations are derived for general superfilaments of co-dimension two in an N -dimensional space and their equilibrium configurations are proven to be minimal surfaces. We suggest that biological excitable systems, such as the heart or brain which have non-local connections can be regarded, at least partially, as multidimensional excitable media and discuss further possible studies in this direction.

math.DS↗