Spiraling Tales

    At the end of 1989 I designed the experiment  ambitioned long before by Winfree to get spiral rotating
in thin "slices" of myocardial tissue. After trying up several different arrangement to use
Paul Kent's (graduate student of Physiology at SUNY) optical mapping setup (which was designed  for salamander olfactory bulb stuff!)
I got, with  Jorge Davidenko, the first successful (but still very "handmade") visualization of a spiral
using voltage sensitive dyes (and  DAM, to kill the muscle movements, Davidenko's idea).
Nature (the journal) and Science  rejected the manuscript, but eventually  appeared in PNAS (vol  87,  pages 8785-8789) in
november of 1990.
Already by the paper's debut I was very intrigued by the stability of our spirals, my numerical simulations said otherwise: spirals
must break up if tissue were healthy, oxygenated and with all calcium stuff untouched, or at least shall show bistability.
(e.g., for some initial conditions one should get spirals;  under other initial conditions break up and complex stuff).
By looking at  the Action Potential Duration  (APD) restitution function (the function relating how long the excited states last as a function of
how long the recent non-excited state was) I  was convinced that spirals were not supposed to last long in healthy
2d myocardial in vitro experiments. Still today (a decade latter) we do not know if  2d slices( of "real" tissue, not models, of course) can support
stable spirals AND complex patterns, as we discussed in a recent editorial

Below are the original 1989 simulations using a very simple model showing periodic or complex
patterns at two region of parameter space (more details in the NIH proposal I wrote in 1990, which
received a nice review , but I never got one cent out of it, but that is another story...)


(I) Snapshots (from A to I) showing the first few rotations from initial conditions up to the asymptotically
stable periodic solution. Slope of the  APD restitution < 1.

(II) Same initial condition as above in (I) but with parameters corresponding to
APD restitution with slope > 1 at short re-excitation intervals. Note the rupture of
the vortex core and the subsequent "centrifugal" growing disorder leading to
the aperiodic spatiotemporal dynamics.