Ventricular Fibrillation: Spiral Wave Breakup (2D)

Tissue Electrophysiology

Excitability threshold (a) 0.150

Excitation time-scale (ε₀) 0.0020

Restitution slope (μ₁) 0.20

Diffusive coupling (D) 1.00

S1–S2 Reentry Protocol

Click the tissue once to fire S1, a planar wave from the left edge. Watch it sweep across, then click again to fire S2 in the bottom-left quadrant while the S1 wake is still refractory there — timed right, the wavefront breaks and curls into a reentrant rotor. After S1+S2, clicking delivers a small ectopic stimulus at the cursor.

Live Readouts

Protocol stateQuiescent

Time since S1—

Excited tissue0.0%

Wavefront count0

Probe cycle length—

How it works

Cardiac tissue is an excitable medium: a resting cell fires an action potential once a diffusing depolarization wave pushes it past threshold, then stays refractory before it can fire again. This panel integrates the Aliev–Panfilov model, a two-variable reaction-diffusion reduction of ventricular action-potential dynamics used throughout the cardiac-arrhythmia literature:

∂u/∂t = D∇²u − k·u·(u−a)·(u−1) − u·v
∂v/∂t = (ε₀ + μ₁·v /(μ₂+u))·(−v − k·u·(u−a−1))

u is the fast transmembrane-voltage-like variable (depolarization), v is the slow recovery/gate variable, and D∇²u is diffusive current spreading through the finite-difference tissue sheet — both fields are genuinely integrated on the grid every frame, not scripted.

S1–S2 cross-field protocol — the classic way to induce reentry experimentally and in silico: a planar S1 wave is fired, and a second S2 stimulus is delivered into a region still partially refractory from S1. If the timing lands in that vulnerable window, the S2 wavefront can only propagate in one direction (unidirectional block) and curls around the refractory tail into a spinning reentrant spiral (rotor) — the reaction-diffusion analogue of monomorphic ventricular tachycardia.
Restitution slope (μ₁) sets how strongly the recovery gate's time-constant depends on prior activity, which steepens the action-potential-duration (APD) restitution curve. By the Nolasco–Dahlen/Weiss restitution hypothesis, once that slope exceeds 1 the beat-to-beat APD begins to alternate (electrical alternans) and a single stable rotor becomes dynamically unstable, spontaneously fragmenting its arm into multiple independent daughter wavelets — the accepted reaction-diffusion mechanism for how organized reentrant tachycardia degenerates into the spatially chaotic activity of ventricular fibrillation.
Excitability (a) and excitation time-scale (ε₀) control the wavefront's curvature sensitivity and depolarization duration; lowering a or raising ε₀ narrows the excitable wake and further destabilizes the spiral core.
Diffusive coupling (D) sets conduction velocity between neighbouring cells; reducing it mirrors the effect of fibrotic or ischemic tissue with reduced gap-junction coupling, which is itself pro-fibrillatory.

Time and space here are the model's own dimensionless units (standard for Aliev–Panfilov studies), not calibrated milliseconds — the qualitative route from a clean S1–S2 reentry to fibrillatory breakup is what this simulation reproduces faithfully, not absolute cardiac timing.

Click the tissue to fire S1 — a planar activation front from the left edge.

Depolarized (u≈1) Refractory tail (high v) Resting (u≈0)