What you are looking at

A square sheet of virtual ventricular muscle, 200 × 200 cells, integrated in your browser about thirty times a second. Black ink is depolarised tissue; rose ink is tissue that has fired and cannot yet fire again; bare paper is muscle ready to be excited. A wave can only travel into bare paper. That single rule is the whole of what follows.

Pace from the left edge and each beat sweeps across as a flat front trailing a rose tail — a rhythm. Now deliver one early beat at the ringed site. Too soon and the site is still rose: nothing happens at all. Too late and the tail is long gone, so the beat spreads as a clean expanding ring, reaches the walls, and dies — an excitable medium has no echo. In between there is a window, tens of milliseconds wide, in which the recovery front is still crossing the neighbourhood. The new wave cannot spread into the side that is still shut, so the ring never closes, and what should have been a circle is an arc with two free ends. A free end has nowhere to go but round.

That is the whole of it, and the window in the record is yours: each trial is plotted at the coupling interval you chose, with the state of the tissue it met. Nothing about the window is hard-coded — it is wherever this sheet, at this cycle length and this coupling, happens to put it. Move the site, change the pacing, and it moves.

History

George Ralph Mines cut a ring from a tortoise heart in 1913, sent a wave around it, and wrote down what has been the definition of an arrhythmia ever since: excitation chasing its own tail. He also identified the vulnerable period, and the risk of a shock delivered into it. He was found unconscious in his McGill laboratory later that year, aged 28, apparently mid-experiment; he died that evening. Arthur Winfree gave the geometry its name in the 1970s: his pinwheel experiment crossed a gradient of recovery with a stimulus, which is exactly what the premature beat below does. In 1992 Davidenko and Jalife photographed the rotor itself, in living muscle. The phase-singularity counter in the record is the method Gray, Pertsov and Jalife used in 1998 to argue that fibrillation is not chaos but a small number of these things, wandering.

Method

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Certificates of this run

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Owned approximations

This is a two-variable phenomenological model, not a cell. It has no ion channels, no calcium, no cell-to-cell heterogeneity, no fibre anisotropy — real myocardium conducts about three times faster along fibres than across them, which changes rotor shape. The sheet is two-dimensional and monodomain; that is why "defibrillate" here simply drives every cell to threshold at once. Real defibrillation works through virtual electrodes that only a bidomain description produces, and the honest version of that button would be a much larger program.

The pseudo-ECG is the standard large-volume-conductor integral, ∫∇u·∇(1/r), over an infinite homogeneous bath — no torso, no ribs, no lungs. Its shape is meaningful; its millivolts are not, which is why the gain is declared arbitrary and fixed on the first captured beat. Rhythm names in the record are a heuristic read of singularity count and interval scatter in a simulation, and nothing more than that.

Aliev & Panfilov, A simple two-variable model of cardiac excitation, Chaos, Solitons & Fractals 7 (1996) 293–301. Parameters are the commonly used set (k = 8, a = 0.15, ε₀ = 0.002, μ₂ = 0.3), with μ₁ on a slider. The model is dimensionless: the clock and the ruler on this page were set by the calibration above, not copied from a table.