Atrial Fibrillation Rotor 2D: Barkley Excitable-Medium Model

Stimulation Protocol

Rhythm state

quiescent

Tissue Properties

Conduction velocity (D) 1.00

Excitability threshold (b) 0.020

Fibrosis density 8%

Simulation speed 1.0×

Live Readouts

Model time

0.0

Active tissue

Probe cycle length

–

How it works

This 2D companion renders the reentrant-circuit phenomenon directly from above using the Barkley model (Barkley, 1990/1991) — a different two-variable excitable-medium formulation from the companion 3D simulator's Mitchell–Schaeffer ionic model, independently implemented here, that produces the same rotor physics:

du/dt = (1/ε)·u(1-u)(u − (v+b)/a) + D·∇²u
dv/dt = u − v

u is the fast excitation variable (what's drawn), v is the slow recovery variable that enforces a refractory period, a is fixed at 0.75, and ε = 0.02 sets the fast/slow timescale split that gives excitable-medium behaviour. D is the diffusive coupling that sets conduction velocity — verified numerically to scale the wavefront speed like √D, the standard reaction-diffusion result. b raises the excitation threshold, which lengthens the effective refractory tail the same way a longer Mitchell–Schaeffer τ_close does.

S1 fires a planar wave from the left edge, sweeping the sheet like a normal sinus beat.
S2 fires a second, spatially limited beat confined to tissue that has already recovered (v below threshold). If part of the S1 wake nearby is still refractory, the S2 front can only propagate into the recovered side — a unidirectional block — and curls around the refractory tail into a self-sustaining rotor, verified here to keep re-exciting the tissue long after a lone S1 beat would have died at the boundary.
Fibrosis marks random patches of tissue permanently inexcitable (u = v = 0, no diffusion contribution out), fragmenting a single rotor into multiple wavelets as fibrosis density rises — the multiple-wavelet mechanism linking diffuse fibrosis to fibrillation.

Colour runs resting (deep blue) → depolarized wavefront (red/white); a genuine rotor reads as a spiral arm that keeps rotating around a stationary core instead of a wave that sweeps through once and dies out.

Resting tissue Depolarized wavefront Fibrotic / inexcitable